Answer:
The probability of getting a four of a kind is 29/23030 = 0.00126.
Step-by-step explanation:
The poker deck has 52 cards, divided in 4 suits, and each suit has 13 different denominations.
In this exercise you are given that the 2 cards you are dealt have different denominations, lets call them A and B, so in order to make a 4 of a kind, you need to get from the 5 remaining community cards, 3 cards that have the denomination of one of A or B.
You cant get a four of a kind with two different denominations at the same time, because you need to reserve the majority of the community cards for just one of them. So each four of a kind is a disjoint event from the others.
Recall that, apart from the obvius four of a kind that you can get with A and B, you can still get four of a kind with any other denomination, because 4 of the community cards can still have the same denomitation.
Lets first calculate the probability to get a four of a kind with A. With B it is the same computation and the result will, therefore, be the same.
First, note that the order in which the cards are given doesnt matter, so we can calculate the probability of getting triple A in the flop (in other words, the first 3 given cards), and then multiply by all possible permutations.
Since you start with one A in your hand, there are 3 in the deck of 50 cards (remove the two cards given to you). The probability of drawing the first A is 3/50. The probability to draw the second A once you drew the first one is 2/49 (because you removed another A from the deck). The probability for the third A to be drawn is 1/48. This gives us a probability of
3/50 * 2/49 * 1/48 = 1/19600
of drawing the 3 A in the first 3 given cards. The other 2 cards can be anything.
To draw 3 aces in 5 cards we need to multiply be the total amount of ways to put 3 cards in a set of 5. That number is equivalent to the number of ways to pick places for the three A ignoring the order for them. That is, [tex] {5 \choose 3} = 10 . [/tex] So, in total, the probability to get a four of the kind A is
10 * 1/19600 = 1/1960
Similarly, the probability to get a four of a kind with B is 1/1960.
To get a four of a kind with any other kind, we need first to specify the kind; we have 13-2 = 11 possibilities to choose (we substract the 2 kinds A and B). Then we need to specify how the cards of that kind will be placed among the community cards. We have as many possibilities as the total amount of ways to pick where the other card will be, that is, 5 possibilities. Hence, we have 55 possibilities to make a four of a kind with a kind different than A or B.
We need to calculate now what is the probability of getting 4 cards of a specific kind in a specific way, for example, the first four cards. That probability is
4/50 * 3/49 * 2/48 * 1/47 = 1/230300
because we start with 50 cards on the deck with 4 cards of them being of the kind we need, and we remove them one by one.
As a result, the probability of getting a four of a kind with a different kind than A and B is 55/230300 = 11/46060.
By summing disjoint cases, We conclude that that the probability to get a four of a kind is
11/46060 + 1/1960 + 1/1960 = 29/23030 = 0.00126
The solar eclipse travels 2300 miles in 1 hour. In the first 20 minutes it travels 766 2/3 miles. How long does it take for the solar eclipse to travel 1150 miles?
Answer:
Solar Eclipse will required 30 mins to travel Distance of 1150 miles.
Step-by-step explanation:
Given:
Total Distance = 2300 miles
Time required = 1 hr
we will convert hour in minutes.
1 hr = 60 mins
hence Time = 60 mins
We need to find the time required to travel 1150 miles.
We will first find the speed at which solar eclipse travels.
Speed can be calculated by dividing Distance with time.
Speed = [tex]\frac{Distance}{time}[/tex]
Substituting the values we get;
Speed = [tex]\frac{2300}{60}=38.33\ mi/hr[/tex]
Now to find Time required to travel 1150 miles we will divide 1150 miles with Speed.
Time required to travel 1150 miles = [tex]\frac{1150}{38.33}= 30\ mins[/tex]
Hence Solar Eclipse will required 30 mins to travel Distance of 1150 miles.
3(8-3t)=5(2+t)(if there is no solution,type in ''no solution'') t= Answer
Answer:
t = 1
Step-by-step explanation:
3 (8 - 3t) = 5 (2 + t)
24 - 9t = 10 + 5t
- 9t - 5t = 10 - 24
- 14t = - 14
- t = - 14/14
- t = - 1
t = 1
16. In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
Answer:
Step-by-step explanation:
Total number of students = 68
Let history = H
Maths = M
English = E
n(H) = 25
n(M) = 25
n(E) = 34
n(HnMnE) = 3
Total = n(H) + n(M) + n(E) - people in exactly two groups + 2(people in exactly 3 groups) + people in none of the groups
68 = 25 + 25 + 34 - people in exactly two groups - 6 +0
68 = 84 -6 - people in exactly two groups
68 = 78 - people in exactly two groups
People in exactly two groups = 78 - 68
= 10
OR
From the venn diagram, people in exactly two groups are represented by x, y and z
Total = 25 - x - y - 3 + 25 - x - z - 3 + 34 - y - z - 3 + x + y + z + 3
68 = 50 - x - 3 + 34 - y - z - 3
68 = 84 - 6 - x - y - z
68 = 78 - x - y - z
68 - 78 = - x - y - z
-10 = -(x + y + z)
x+y+z = -10/-1
x+y+z = 10
The number of students that registered for exactly two courses = 10
Answer:
[tex[ two groups=-68+25+25+34 -6=10[/tex]
Step-by-step explanation:
For this case we have a diagram of the situation on the figure attached.
And for this case we can us the following rule from probability:
[tex]P(AUBUC) = P(A)+P(B) +P(C) -P(A and B)- P(A andC)-P(B and C) +P(A and B and C)[/tex]
Or equivalently:
[tex] total= A+ B +C - two groups -2*[people in3 groups]+ nonegroups[/tex]
We know the total on this case total=68, the people for history is A=25, for math B=25 and for english C=34, and the people in all the groups 3, so we can replace:
[tex]68=25+25+34- two groups -2*3 +0[/tex]
And if we solve for the poeple in two groups we got:
[tex[ two groups=-68+25+25+34 -6=10[/tex]
Let w be the amount Juan earned walking dogs then (2w-6) is the amount Juan earned mowing lawns the total amount Juan earned is w +(2w-6) or w-6 Emma wrote the expression 2(3w-6) to represent the amount of the money that Juan spent is she correct explain
Answer:
The expression written by Emma to represent the amount of the money that Juan earned is WRONG.
Step-by-step explanation:
Here, the amount earned by Juan by walking dogs = w
The amount earned byJuan lowing lawns = (2w - 6)
Now, the total amount earned by Juan
= Amount earned from (Mowing Lawn + Walking dogs)
= w + (2 w - 6)
On further simplification, we get:
w + (2 w - 6) = w + 2w - 6 = 3w-6 = 3(w-2)
So, the total amount earned by Juan = 3(w-2)
Now, the expression written by Emma = 2(3w-6)
and 2(3w-6) ≠ 3(w-2)
Hence, the expression written by Emma to represent the amount of the money that Juan earned is WRONG.
solve 5(x-y)+2y=5 step by step
Answer:
y = -5/3 + 5/3x
Step-by-step explanation:
Solve for y. View image.
1. Quadrilateral ABCD has vertices A(-1, 1), B(2, 3), C(6, 0) and D(3, -2). Determine using coordinate geometry whether or not the diagonals* of ABCD a. Bisect each other. B. Are congruent. C. Are perpendicular.1. Quadrilateral ABCD has vertices A(-1, 1), B(2, 3), C(6, 0) and D(3, -2). Determine using coordinate geometry whether or not the diagonals* of ABCD a. Bisect each other. B. Are congruent. C. Are perpendicular.
Answer:
The Conclusion is
Diagonals AC and BD,
a. Bisect each other
b. Not Congruent
c. Not Perpendicular
Step-by-step explanation:
Given:
[]ABCD is Quadrilateral having Vertices as
A(-1, 1),
B(2, 3),
C(6, 0) and
D(3, -2).
So the Diagonal are AC and BD
To Check
The diagonals AC and BD
a. Bisect each other. B. Are congruent. C. Are perpendicular.
Solution:
For a. Bisect each other
We will use Mid Point Formula,
If The mid point of diagonals AC and BD are Same Then
Diagonal, Bisect each other,
For mid point of AC
[tex]Mid\ point(AC)=(\dfrac{x_{1}+x_{2} }{2},\dfrac{y_{1}+y_{2} }{2})[/tex]
Substituting the coordinates of A and C we get
[tex]Mid\ point(AC)=(\dfrac{-1+6}{2},\dfrac{1+0}{2})=(\dfrac{5}{2},\dfrac{1}{2})[/tex]
Similarly, For mid point of BD
Substituting the coordinates of B and D we get
[tex]Mid\ point(BD)=(\dfrac{2+3}{2},\dfrac{3-2}{2})=(\dfrac{5}{2},\dfrac{1}{2})[/tex]
Therefore The Mid point of diagonals AC and BD are Same
Hence Diagonals,
a. Bisect each other
B. Are congruent
For Diagonals to be Congruent We use Distance Formula
For Diagonal AC
[tex]l(AC) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
Substituting A and C we get
[tex]l(AC) = \sqrt{((6-(-1))^{2}+(0-1)^{2} )}=\sqrt{(49+1)}=\sqrt{50}[/tex]
Similarly ,For Diagonal BD
Substituting Band D we get
[tex]l(BD) = \sqrt{((3-2))^{2}+(-2-3)^{2} )}=\sqrt{(1+25)}=\sqrt{26}[/tex]
Therefore Diagonals Not Congruent
For C. Are perpendicular.
For Diagonals to be perpendicular we need to have the Product of slopes must be - 1
For Slope we have
[tex]Slope(AC)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Substituting A and C we get
[tex]Slope(AC)=\dfrac{0-1}{6--1}\\\\Slope(AC)=\dfrac{-1}{7}[/tex]
Similarly, for BD we have
[tex]Slope(BD)=\dfrac{-2-3}{3-2}\\\\Slope(BD)=\dfrac{-5}{1}[/tex]
The Product of slope is not -1
Hence Diagonals are Not Perpendicular.
Two buses use the stop at Meadowland Road and Mockingbird Lane. Bus 143 stops every 30 minutes on its express route to downtown. Bus 62 stops there every 8 minutes on its west side route. If they were both at the stop at 6:30 AM, when will they arrive together again?
Answer:
8:30 AM
Step-by-step explanation:
Given:
Bus 143 stops every 30 minutes on its express route to downtown
and Bus 62 stops there every 8 minutes on its west side route
both meet at the bus stop at 6.30 AM
to find when they would meet the second time we need to find LCM( 30,8)
= 120
Hence the two buses would meet after 120 minutes that is 2 hours.
Hence they would be meet at 6.30+2= 8.30 AM
Let d(t) be the total number of miles Joanna has cycled, and let t represent the number of hours after stopping for a break during her ride.
d(t)=12t+20
So,_______ d(4) = . This means that after _____________, Joanna __________.
At t = 4, the distance traveled is 68 miles. This means that after the break, Joanna traveled 48 miles.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The linear function is given below.
d(t) = 12t + 20
The distance traveled when t = 4 is calculated as,
d(4) = 12 x 4 + 20
d(4) = 48 + 20
d(4) = 68 miles
So, at t = 4, the distance traveled is 68 miles. This means that after the break, Joanna traveled 48 miles.
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How would you use a completely randomized experiment in each of the following settings? Is a placebo being used or not? Be specific and give details.
(a) A veterinarian wants to test a strain of antibiotic on calves to determine their resistance to common infection. In a pasture are 22 newborn calves. There is enough vaccine for 10 calves. However, blood tests to determine resistance to infection can be done on all calves.
A- Use random selection to pick 5 calves to inoculate.
B- No placebo is being used.
C- After inoculation, test 5 calves to see if there is a difference in resistance to infection between the two groups.
D- After inoculation, test 10 calves to see if there is a difference in resistance to infection between the two groups.Use random selection to pick 10 calves to inoculate.
E- A placebo is used for the remaining 12 calves.
F- After inoculation, test all calves to see if there is a difference in resistance to infection between the two groups.
(b) The Denver Police Department wants to improve its image with teenagers. A uniformed officer is sent to a school one day a week for 10 weeks. Each day the officer visits with students, eats lunch with students, attends pep rallies, and so on. There are 18 schools, but the police department can visit only half of these schools this semester. A survey regarding how teenagers view police is sent to all 18 schools at the end of the semester. (Select all that apply.)
A- After the police visits, survey all the schools to see if there is a difference in views between the two groups.
B- After the police visits, survey 9 of the schools to see if there is a difference in views between the two groups.
C- No placebo is being used.
D- A placebo is used for the remaining 9 schools.
E- Use random selection to pick nine schools to visit.
F- Use random selection to pick 18 schools to visit.
(c) A skin patch contains a new drug to help people quit smoking. A group of 75 cigarette smokers have volunteered as subjects to test the new skin patch. For one month, 40 of the volunteers receive skin patches with the new drug. The other volunteers receive skin patches with no drugs. At the end of the two months, each subject is surveyed regarding his or her current smoking habits.
A- Then record the smoking habits of the 35 volunteers to see if a difference exists between the two groups.
B- No placebo is being used.
C- Use random selection to pick 35 volunteers for the skin patch with the drug.
D- Then record the smoking habits of the 40 volunteers to see if a difference exists between the two groups.
E- Use random selection to pick 40 volunteers for the skin patch with the drug.
F- A placebo patch is used for the remaining 35 volunteers in the second group.
G- Then record the smoking habits of all volunteers to see if a difference exists between the two groups.
Answer:
(a)
Use random selection to pick 10 calves to inoculate.(you didn't mention this option in the question instead you mix it with other option)
(B).No placebo is being used.
(F).After inoculation, test all calves to see if there is a difference in resistance to infection between the two groups.
(b)
(C).No placebo is being used.
(E).Use random selection to pick nine schools to visit.
(A).After the police visits, survey all the schools to see if there is a difference in views between the two groups.
(c)
(F.)A placebo patch is used for the remaining 35 volunteers in the second group.
(E).Use random selection to pick 40 volunteers for the skin patch with the drug.
(G).Then record the smoking habits of all volunteers to see if a difference exists between the two groups.
Step-by-step explanation:
In question one the answer is mixed with other option so the correct answer statements are provided along with the option for all questions. Placebo is not used in question (a) scenario because it is mentioned in the statement that there is enough vaccine is present and sample of 10 calves is selected from 22 calves and we test all calves after the inoculation because it is mention that blood test should be done on all calves.
Placebo is not used in question (b) scenario because it is mentioned in the statement that the police department can visit half of 18 schools and random sample of 9 schools are selected and it is mentioned in the statement that survey is sent to all 18 school so after the police visit all schools are surveyed to see the difference in views
Placebo patch is used in question (c) because it is mentioned in the statement that 40 out of 75 received the new skin patch so, the remaining 35 received placebo patch and random sample of 40 volunteers are selected for new skin patch. It is mentioned in the statement that each subject is survey so in the end smoking habits of all volunteers are recorded.
In the given settings, a completely randomized experiment can be used to test the effects of different interventions. Placebo is not being used in these experiments.
Explanation:In a completely randomized experiment, the researcher randomly assigns subjects to different treatment groups to determine the effect of the treatment. In the given settings:
(a) A veterinarian wants to test a strain of antibiotic on calves. A completely randomized experiment can be conducted by randomly selecting 5 calves from the pasture to inoculate with the antibiotic while the remaining 17 serve as the control group with no placebo being used. After inoculation, the resistance to infection can be tested on both groups to compare the difference.
(b) The Denver Police Department wants to improve its image with teenagers. A completely randomized experiment can be conducted by randomly selecting half of the 18 schools to receive the visits from the police officer while the other half serve as the control group with no placebo being used. Then, a survey can be sent to all 18 schools at the end of the semester to compare the views between the two groups.
(c) A skin patch contains a new drug to help people quit smoking. A completely randomized experiment can be conducted by randomly selecting 40 volunteers to receive the skin patch with the drug while the remaining 35 volunteers receive the placebo patch with no drugs. The smoking habits of both groups can be surveyed at the end of the two months to see if a difference exists between the two groups.
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The half-life of a substance is how long it takes for half of the substance to decay or become harmless (for certain radioactive materials). The half-life of a substance is 37 years and there is an amount equal to 202 grams now. What is the expression for the amount A(t) that remains after t years, and what is the amount of the substance remaining (rounded to the nearest tenth) after 100 years?
Answer:
31.0 grams.
Step-by-step explanation:
According to the given information
Half-life of a substance = 37 years
Initial amount = 202 gram
The exponential function for half-life of a substance is
[tex]A(t)=A_0(0.5)^{\frac{t}{h}}[/tex]
where, A₀ is initial amount, t is time and h is half life.
Substitute A₀=202 and h=37 in the above function.
[tex]A(t)=202(0.5)^{\frac{t}{37}}[/tex]
We need to find the amount of the substance remaining after 100 years.
Substitute t=100 in the above function.
[tex]A(100)=202(0.5)^{\frac{100}{37}}[/tex]
[tex]A(100)=31.0282146[/tex]
Round the answer to the nearest tenth.
[tex]A(100)\approx 31.0[/tex]
Therefore, the amount of the substance remaining after 100 years is 31.0 grams.
Elenas anut bought her a 150$ saving bond when she was born. When elena is 18 years old, the bond will have earned a 106% in interest. How much will the bond be worth when elena is 18 years old
Answer:
The Amount after 18 years is $66,942,391.5
Step-by-step explanation:
Given as :
The principal invested in saving bond = p = $150
The Time period for the bond = t = 18 years
The rate of interest applied on bond = 106%
Let The Amount after 18 years = $A
Now, From compound interest
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, A = $150 × [tex](1+\dfrac{\textrm 106}{100})^{\textrm 18}[/tex]
Or, A = $150 × [tex](2.06)^{\textrm 18}[/tex]
Or, A = $150 × 446,282.61
∴ A = $66,942,391.5
So,The Amount after 18 years = A = $66,942,391.5
Hence,The Amount after 18 years is $66,942,391.5 Answer
Which of the following functions is graphed below?
The function graphed below is
y = x³ - 3, x ≤ 2
= x² + 6, x > 2 ⇒ C
Step-by-step explanation:
The graph has two parts:
The first part start at x > 2 and its a part of parabola (quadratic function)The second part End at x = 2 and its a part of a cubic function∴ The graph represents two functions:
→ Quadratic function y = ax² + bx + c with domain x > 2
→ Cubic function y = ax³ + bx² + cx + d with domain x ≤ 2
∵ The answers have two functions:
→ y = x³ - 3 ⇒ cubic function
→ y = x² + 6 ⇒ quadratic function
∵ The domain of the cubic function is x ≤ 2
∵ The domain of the quadratic function is x > 2
∴ The answer is
y = x³ - 3, x ≤ 2
x² + 6, x > 2
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Answer:
y={x^3-3, x ≤ 2
{x^2+6, x>2
Step-by-step explanation:
a pex :)
In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct ________ and ________. blind sampling; random group assignment blind group assignment; random sampling random sampling; random group assignment blind group assignment; blind sampling
In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling and random group assignment
Explanation:
The terms Random sampling and Random group assignment are greatly different in process of the sample selection. The study related to the determination of how sample participants can be drawn from the population refers to the process of Random sampling. The sample participants are subjected to a treatment by the usage of a random procedure comprises the Random group assignment.
When a researcher wants validate externally then random selection can be used. When a researcher wants to determine the effects of treatment within that group which is known as determination of internal validity then he can opt for Random group assignment.
Answer:
In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.
Explanation:
Random selection is a representation of the sample of people for your research from a community. Random assignment is the assigning of the sample that describes various groups or operations in the study.
Reasons:
Random sampling enables us to get a sample representative of the community.Random assignment enables us to make positive that the only distinction among the various treatment combinations is what needs to study.Random assignment is crucial for sound empirical design. With adequately large representations, random assignment performs it unlikely that there are methodical variations among the groups.Thus we can say in order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.
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https://brainly.com/question/9423006Find the radius of the circle with an area of 153.9 in? Use 3.14 for T.
A. 3.5 in.
B. 7 in.
D. 14 in.
C. 7.9 in.
Answer:
B. 7 in.
Step-by-step explanation:
Area = A =pi r^2
r^2 = A / pi
r = √(A / 3.14)
= √(153.9 / 3.14)
= 7 in.
In a certain large city, 45% of families earn less than $35,000 per year. Assuming the distribution is binomial and you can use the exact binomial calculation, what's the probability, accurate to the number of decimal places given, that a simple random sample of 30 families will have 10 or fewer families earning less than $35,000 per year? Use the exact binomial calculation.
Answer:
The probability is %13,5
Step-by-step explanation:
If it is a binomial distribution function than we can find a probability of earning less or more than 35000$ in this certain large city. Lets assume that p is probability of earning less than 35000$ and q is earning more than 35000$.:
p=0,45
q=0,55
So general formula of n families that earning less than 35000$ is:
[tex]P(X=n)=combination(30,n)*0,45^n*0,55^{30-n}[/tex]
Probability of 10 or less families out of 30 families that earning less than 35000$ is:
[tex]combination(30,10)*0.45^{10}*0.55^{20}+combination(30,9)*0.45^9*0.55^{21}+combination(30,8)*0.45^8*0.55^{22}+combination(30,7)*0.45^7*0.55^{23}+combination(30,6)*0.45^6*0.55^{24}+combination(30,5)*0.45^5*0.55^{25}+combination(30,4)*0.45^4*0.55^{26}+combination(30,3)*0.45^3*0.55^{27}+combination(30,2)*0.45^2*0.55^{28}+combination(30,1)*0.45^{1}*0.55^{29}+combination(30,0)*0.45^0*0.55^{30}=0,135[/tex]
The correct probability that a simple random sample of 30 families will have 10 or fewer families earning less than $35,000 per year, using the exact binomial calculation, is approximately 0.0674.
To solve this problem, we will use the binomial probability formula, which is given by:
[tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \][/tex]
Given that 45% of families earn less than $35,000 per year, we have p = 0.45.
The number of families in the sample is n = 30
We want to find the probability that 10 or fewer families earn less than $35,000 per year, so k will range from 0 to 10.
Then, we sum these probabilities to find the cumulative probability of 10 or fewer families earning less than $35,000 per year.
Using the binomial probability formula, we calculate:
[tex]\[ P(X \leq 10) = \sum_{k=0}^{10} \binom{30}{k} (0.45)^k (0.55)^{30-k} \][/tex]
This calculation can be done using statistical software or a calculator that supports binomial probability calculations.
After performing the exact binomial calculation, we find that the probability is approximately 0.0674.
This is the probability that, in a random sample of 30 families from this city, 10 or fewer families will earn less than $35,000 per year.
If 4 more than 4 times a certain number is the same as 4 more than the product of 3 and 4, what is that number?
A. 3
B. 4
C. 5
D. 8
E. 12
Answer: the number is 3
Step-by-step explanation:
Let the number be represented by x.
If 4 more than 4 times a certain number is the same as 4 more than the product of 3 and 4, it means that
4x + 4 = 4 + 3×4
4x + 4 = 4 + 12
4x + 4 = 16
Subtracting 4 from the left hand side and the right hand side of the equation, it becomes
4x + 4 - 4 = 16 - 4
4x = 12
Dividing the left hand side and the right hand side of the equation by 4, it becomes
x = 12/4 = 3
I need some help with these 2 questions.
Answer:
see attached
Step-by-step explanation:
For the figure A, the figure is symmetrical about a vertical line through its center. It has line symmetry.
__
For the figure O, it is symmetrical about both vertical and horizontal lines, as well as being symmetrical about its center point. It has line and point symmetry.
The length of a rectangle Is twice the width of the rectangle the length of a diagonal of the rectangle is 25cm work out the ares of the rectangle give your answer as an integer
Answer:Area is 50 cm^2
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The formula for determining the area of a rectangle is expressed as
Area = LW
The length of a rectangle Is twice the width of the rectangle. This means that
L = 2W
The length of a diagonal of the rectangle is 25cm. This is the hypotenuse of the right angle triangle that is formed. Applying Pythagoras theorem,
25^2 = L^2 + W^2 - - - - - - - 1
Substituting L = 2W into equation 1, it becomes
25^2 = (2W)^2 + W^2
25^2 = 4W^2 + W^2 = 5W^2
Taking square of both sides,
W = √25 = 5
L = 2W = 3×5 = 10
Area = LW = 10×5 = 50 cm^2
The length of a rectangle is twice the width. Using the Pythagorean Theorem, we can find the dimensions of the rectangle and calculate its area. Hence the final answer is 248 cm².
Explanation:To find the area of a rectangle, we need to know both the length and the width of the rectangle.
Let's assume the width of the rectangle is 'w'.
According to the question, the length of the rectangle is twice the width, so the length of the rectangle is '2w'.
We can use the Pythagorean Theorem to find the length of the diagonal:
Using the formula a^2 + b^2 = c^2, where 'a' and 'b' are the length and width of the rectangle, and 'c' is the length of the diagonal, we can set up the equation:
w^2 + (2w)^2 = 25^2.
Simplifying the equation, we get: 5w^2 = 625
Dividing both sides of the equation by 5, we get: w^2 = 125
Taking the square root of both sides, we get: w = 11.18
The area of the rectangle is length times width, so the area is: 2w * w = 2 * 11.18 * 11.18 = 248.27
Rounding to the nearest integer, the area of the rectangle is approximately 248 cm².
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Which of the following ordered pair could NOT be included in this set if it is a function? { (-4, 2), (3, 6), (4, 3), (x, y) }
A) (x, y) = (4, -3)
B) (x, y) = (3, 6)
C) (x, y) = (1, 2)
D) (x, y) = (-3, 6)
Answer:
Option A) (x, y) = (4, -3)
Step-by-step explanation:
we know that
A function is a relation from a set of inputs (independent variable) to a set of possible outputs (dependent variable) where each input is related to exactly one output
we know that
The set of the function is { (-4, 2), (3, 6), (4, 3), (x, y) }
The ordered pair (x, y) = (4, -3)
could not be included, because for the input value of x=4, the function would have two output values (y=-3,y=3) and remember that each input is related to exactly one output
Solve
3x + 4y = 8
-2X + 5y = 3
Answer: x = 28/33, y = 25/23
( 28/23, 25/23)
Step-by-step explanation:
3x + 4y = 8 ----------------------(1)
-2x + 5y = 3 ---------------------(2)
Using elimination method
Consider the coefficient of y in equation 1 and 2
Therefore multiply as follows
(1) x 5 -------- 15x + 20y = 40.
(2) x 4 -------- -8x + 20y = 12
Therefore carry out subtraction on the two equations
23x + 0y = 28
23x = 28
x = 28/23.
Now substitute for x in any of the equations above to get y
3(28/23) +4y = 8
84/23 +4y = 8
Multiply through by 23 to have s simple linear equation
84 + 92y = 184
Collect like terms
92y = 184 - 84
92y = 100
y = 100/92
Reduce to lowest term by dividing by 4
y = 25/33.
(28/23, 25/23)------ solution
Check
Substitute for x and y values in any equations above.
3(28/23) + 4(25/23)
84/23 + 100/23
Resolved into fraction with 23 as the common LCM
184/23
= 8
im taking my final right now and don't want to fail please help.
Answer:
3n+2
Step-by-step explanation:
they informed that it is a linear function. so, let the required linear function be ax+b.[where, a and b are some constants and x is a variable ( input values)]
when x=1, the output is 5so, if x=1, ax+b=5so, a+b=5
if x=2, ax+b=8so,2a+b=8
solving the above 2 equations,subtract the first equation from second:
2a+b-a-b=8-5
a=3.
by substituting the value of a in one of the above equations,
you will get b as 2
so, when the input is n, output will be : 3n+2
if f is a differentiable function and f(0)=-1 and f(4)-3 then which of the following must be true there exists a c in [0,4] where f(c)=0
Answer:
True, see proof below.
Step-by-step explanation:
Remember two theorems about continuity:
If f is differentiable at the point p, then f is continuous at p. This also applies to intervals instead of points.(Bolzano) If f is continuous in an interval [a,b] and there exists x,y∈[a,b] such that f(x)<0<f(y), then there exists some c∈[a,b] such that f(c)=0.If f is differentiable in [0,4], then f is continuous in [0,4] (by 1). Now, f(0)=-1<0 and f(4)=3>0. Thus, we have the inequality f(0)<0<f(4). By Bolzano's theorem, there exists some c∈[0,4] such that f(c)=0.
The question is about the intermediate value theorem in calculus, which states a function takes on every value between f(a) and f(b) in a closed interval [a, b]. Given the function's values at 0 and 4, it must cross the x-axis, or equal zero, somewhere in the interval [0, 4].
Explanation:This is a question about intermediate value theorem, a fundamental theorem in calculus. The intermediate value theorem states that if a function is continuous on a closed interval [a, b], then it takes on every value between f(a) and f(b) at some point within that interval. If we know that f(0) = -1 and f(4) = 3, this means the function f crosses the x-axis (or, in other words, f(c) = 0 for some c) somewhere in the interval [0, 4] because zero lies between -1 and 3 (the function's values at 0 and 4 respectively).
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Jakubowski Farms Gourmet Bread Base is the brand name for a mix designed for use in bread making machines. The mixes are sold in 2-pound canisters for $14.99 plus shipping. People learn about the product through word-of-mouth and bread machine demonstrations the company's founder gives to groups in Wisconsin, where she lives. The products are only available through the mail. This is a description of the company's?
Answer:
The description of the company's is marketing mix.
Step-by-step explanation:
Consider the provided information.
Jakubowski Farms Gourmet Bread Base is the brand name for a mix designed for use in bread making machines which is the product.
We have given that the price is $14.99 plus shipping.
The promotion is word of mouth and public demonstrations.
The place is mail.
The marketing mix is defined as the set of actions or tactics that a company uses to market its brand or product. The 4Ps constitute a standard marketing mix-price, product, promotion and venue.
These four elements are the marketing mix—product, price, promotion, and place.
Hence, the description of the company's is marketing mix.
The low temperature on Monday was 6 degrees warmer than Sunday's low of -9°F.The low temperature on Tuesday was 3 degrees warmer than Monday's low.What was the low temperature on Tuesday.
Answer: the low temperature on Tuesday is 0 degree Fahrenheit
Step-by-step explanation:
The low temperature on Monday was 6 degrees warmer than Sunday's low of -9°F. This means that the temperature on Monday would be
- 9 + 6 = - 3 degrees Fahrenheit
The low temperature on Tuesday was 3 degrees warmer than Monday's low temperature. This means that the low temperature on Tuesday would be
- 3 + 3 = 0 degree Fahrenheit
Final answer:
By sequentially adding the temperature differences to each day's low, we find that Sunday's low was -9°F, Monday's was -3°F, and Tuesday's was 0°F. So the low temperature on Tuesday was 0°F.
Explanation:
The student's question involves calculating temperature changes over consecutive days. Here's the step-by-step explanation:
The low temperature on Sunday was -9°F.
Monday's low was 6 degrees warmer than Sunday's, so we add 6 to -9°F, resulting in -3°F for Monday's low.
Tuesday's low was 3 degrees warmer than Monday's, so we add 3 to -3°F, which is 0°F.
Therefore, the low temperature on Tuesday was 0°F.
Plz help, 15 points!
What is the slope of a line that is perpendicular to a line whose equation is 5y=10+2x
-------
Would it be -5/2 as in only the 5 is negative or the whole fraction is negative?
Answer: The slope of the line would be -5/2, and the whole fraction would be negative.
Step-by-step explanation:
Technically just the 5 is negative because the new slope is going down 5, yet on paper its just safer to write the whole fraction as a negative.
70 sixth-graders had an average weight of 90 pounds. 30 seventh graders had an average weight of 100 pounds. What was the average weight of all these students?
We know that 70 sixth graders had an average weight of 90 pounds, and 30 seventh graders had an average weight of 100 pounds.
We know that the weight of all 70 sixth graders will be 70*90, since we're multiplying the total amount of students by the average.
Using this same logic tells us that the total weight for the 30 seventh graders is 30*100
The average weight for all 100 students will be the total weight of the sixth graders (which is 70*90) added with the total weight of the seventh graders (which is 30*100), then finally divided by the total amount of students in the sample space (which is 100).
[tex]\dfrac{70(90)+30(100)}{100}[/tex]
[tex]=\dfrac{6300+3000}{100}[/tex]
[tex]=\dfrac{9300}{100}[/tex]
[tex]=93[/tex]
The average of all 100 students is 93 pounds.
Let me know if you need any clarifications, thanks!
If you invest a one-time lump sum of $28,000 into a mutual fund that will average 12% compounded monthly, how much will you have in 35 years? Pick the closest value.
Answer:
$1,828,669
Step-by-step explanation:
For the original lump sum of $28,000 is our principal, P, the annual interest rate r, compounded monthly for n=12 months throughout a period of 35 years (t) will have a final Accrued Amount of investment A given by the formula:
A= (Principal + Interest) = P(1 + r/n)^nt =28000(1+0.12/12)^35*12
=28000(1.01)^420=
28000*65.3096= $1828669
Michael and Ashley each buy x pounds of turkey and y pounds of ham. Turkey cost $3 per pound at store A and $4.50 per pound at store B. Ham cost $4 per pound at store A and $6 per pound at store B. Micheal spends $18 at store A, and Ashley spends $27 at store b could Micheal and Ashley bought the same amount of turkey?Explain.
Yes. Micheal and Ashley bought same amount of turkey which is 6 pounds.
Step-by-step explanation:
The question requires to you to form simultaneous equations and solve them.
Take the number of pounds for turkey to be x and that for ham to be y
For store A where michael spent $18
turkey cost $3 per pound ---- 3x
ham cost $4 per pound------4x
The equation for cost will be ; 3x+4y =18
For store B where Ashley spent $27
turkey cost $4.5 per pound
ham cost $6 per pound
The equation for cost is : 4.5x +6y=27
The two equations are;
3x+4y=18
4.5x+6y=27
Solving the equations by graph you get ;
x=6 and y=4.5 for both linear graphs. This means both equations produce similar amounts of turkey and ham . Micheal and Ashley bought same amount of turkey which is 6 pounds.
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The table shows the amount of money in your savings account over a period of 6 weeks. You plan to keep saving at the same rate until you have $825 in the account. Which equation could you use to find the number of weeks,n, it would take to reach your goal?
A 55⋅n=825
B 55⋅n+100=825
C 100−n=825
D 100⋅n+55=825
Answer:
Choice B
Step-by-step explanation:
Looks like interest isn't being used, so that makes it simple.
Every week the same amount is added, that means we can use a linear equation, which is what it is asking us to pick between so it all works out, awesome.
Now, we need two things to make an equation. the slope and two points. Definitely have points so we need the slope.
The slope is found by taking any two points and finding the difference of their y values and dividing that by the distance of their x values. so find two points (x1, y1) and (x2, y2) and then use the formula(y2-y1)/(x2-x1) Also, we will say number of weeks is the x and the amount of money is y
No matter which point you use you will get the slope is 55
From there we find the function with the formula y - y1 = m(x - x1)
We know m and I reccomend using (0, 100) as our x1 y1 because 0 will usually make things easier.
y - y1 = m(x - x1)
y - 100 = 55(x-0)
y = 55x + 100
you could have used any point again, 0 just means it goes away if you add 0 or subtract 0. Of course your problem uses n so just replace x with n. and y is the value we want to end at, which is 825
825 = 55n + 100, or arranging it so it's the same as the option, 55*n + 100 = 825, so that's choice B
The equation that calculates the weeks it would take to reach the target is : 55n = 825.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the table shows the amount of money in your savings account over a period of 6 weeks and you plan to keep saving at the same rate until you have $825 in the account.
Assume that it would take [n] weeks to reach the target. The unit rate from the given table can be calculated as -
m = (155 - 100)/(1 - 0)
m = 55
So, we can write the equation as -
55n = 825
Therefore, the equation that calculates the weeks it would take to reach the target is : 55n = 825.
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Before being put out of service, the supersonic jet Concorde made a trip averaging 120 mi/h less than the speed of sound for 0.1 h and 410 mi/h more than the speed of sound for 3.0 h. If the trip covered 3,990 mi, what is the speed of sound?
Answer:
894.19 mi/hr
Step-by-step explanation:
Total distance of the trip = 3990 mi
Let the speed of the sound be 'x' miles per hour
Now,
Total distance = Speed × Time
Therefore,
According to the question
3,990 mi = [ ( x - 120 ) × 0.1 ] + [ ( x + 410 ) × 3.0 ]
or
3,990 mi = 0.1x - 12 + 3x + 1230
or
0.1x + 3x = 2772
or
3.1x = 2772
or
x = 894.19 mi/hr