It is 12 miles from house to school
Solution:
Given that, Jeff wants to know how many miles it is from his house to school
On a map, the scale is 0.5 inches = 2 miles
His house island school are 3 inches apart on the map
So, from the given scale,
0.5 inches = 2 miles
Distance between school and house in map = 3 inches
Therefore,
0.5 inches = 2 miles
Muliply both sides by 6
[tex]0.5 \times 6\ inches = 6 \times 2\ miles\\\\3\ inches = 12\ miles[/tex]
Thus, it is 12 miles from house to school
A chemist has two brine solutions, one containing 4% salt and the other containing 30% salt. How many gallons of each solution should she mix to obtain 45 gallons of a solution that contains 18.4% salt?
Answer:
Number of gallons of 4% salt solution in the mixture = 20.08
Number of gallons of 30% salt solution in the mixture = 24.92
Step-by-step explanation:
Given:
There are two bottles of brine solution:
1 has 4% salt
2 has 30% salt
The chemist mixes some gallons of each bottle to get a 45 gallons solution containing 18.4% salt.
To find the gallons of each solution taken to make the mixture.
Solution:
Let the number of gallons of 4% salt solution mixed be = [tex]x[/tex]
So, number of gallons of 30% salt solution mixed will be = [tex]45-x[/tex]
Amount of salt in [tex]x[/tex] gallons of 4% salt solution will be :
⇒ Percentage concentration x Gallons of solution
⇒ [tex]0.04\times x[/tex]
⇒ [tex]0.04x[/tex]
Amount of salt in [tex](45-x)[/tex] gallons of 30%% salt solution will be :
⇒ Percentage concentration x Gallons of solution
⇒ [tex]0.3\times (45-x)[/tex]
Using distribution
⇒ [tex]13.5-0.3x[/tex]
Total amount of salt in 45 gallons of solution can be given as:
⇒ [tex]0.04x+13.5-0.3x[/tex]
Combining like terms
⇒ [tex]-0.26x+13.5[/tex]
Amount of salt in 45 gallons of 18.4% solution:
⇒ [tex]0.184\times 45[/tex]
⇒ [tex]8.28[/tex]
Thus, we have:
[tex]-0.26x+13.5=8.28[/tex]
Subtracting both sides by 13.5
[tex]-0.26x+13.5-13.5=8.28-13.5[/tex]
[tex]-0.26x=-5.22[/tex]
Dividing both sides by -0.26.
[tex]\frac{-0.26x}{-0.26}=\frac{-5.22}{-0.26}[/tex]
∴ [tex]x=20.08[/tex]
Number of gallons of 4% salt solution in the mixture = 20.08
Number of gallons of 30% salt solution in the mixture = [tex]45-20.08[/tex] = 24.92
A helicopter leaves bristol and flies due east for 10 miles.Then the helicopter flies 8miles north before landing. What is the direct distance of the helicopter from bristol?
Answer:
The distance of the helicopter from the bristol is approximately 12.81 miles
Step-by-step explanation:
Given:
Helicopter flies 10 miles east of bristol.
Then the helicopter flies 8 miles North before landing.
To find the direct distance between the helicopter and bristol.
Solution:
In order to find the distance of the helicopter from the bristol before landing, we will trace the path of the helicopter
The helicopter is first heading 10 miles east of bristol and then going 8 miles due north.
On tracing the path of the helicopter we find that the direct distance of the helicopter from the bristol is the hypotenuse of a right triangle formed by enclosing the path of the helicopter.
Applying Pythagorean theorem to find the hypotenuse of the triangle.
[tex]Hypotenuse^2=Short\ leg^2+Shortest\ leg^2[/tex]
[tex]Hypotenuse^2=10^2+8^2[/tex]
[tex]Hypotenuse^2=100+64\\Hypotenuse^2=164[/tex]
Taking square root both sides.
[tex]\sqrt{Hyptenuse^2}=\sqrt{164}\\Hypotenuse = 12.81\ miles[/tex]
Thus, the distance of the helicopter from the bristol is approximately 12.81 miles
Fastest answer gets brainlyest!
Which exponential expression represents the numerical expression
3 · 3 · 3 · 3 ?
(112)3
(12)3
(3)4
4
Answer:
(3)4
Step-by-step explanation:
3 x 3 x 3 x 3 can also be written as (3)4 or 3 to the 4th power
The Simmons family and the Wright family each used their sprinklers last summer. The water output rate for the Simmons family's sprinkler was 20l per hour. The water output rate for the Wright family's sprinkler was 35l per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output 1475l of . How long was each sprinkler used?
Answer:
y=25 and x=30.
Step-by-step explanation:
See picture
Answer:the number of hours that the Simmons family used their sprinklers last summer is 30
the number of hours that the Wright family used their sprinklers last summer is 25
Step-by-step explanation:
Let x represent the number of hours that the Simmons family used their sprinklers last summer.
Let y represent the number of hours that the Wright family used their sprinklers last summer.
The families used their sprinklers for a combined total of 55 hours, it means that
x + y = 55
The water output rate for the Simmons family's sprinkler was 20l per hour. The water output rate for the Wright family's sprinkler was 35l per hour. The total water output was 1475l. It means that
20x + 35y = 1475 - - - - - - - - - - 1
Substituting x = 55 - y into equation 1, it becomes
20(55 - y) + 35y = 1475
1100 - 20y + 35y = 1475
- 20y + 35y = 1475 - 1100
15y = 375
y = 375/15 = 25
x = 55 - y = 55 - 25
x = 30
If the parent function is y = 1/x, describe the change in the equation y = - 1/x-1 - 10
A. Reflected across the x-axis, moves 1 unit to the right, and 10 units up.
B. Moves 1 unit to the right and 10 units down.
C. Reflected across the x-axis, moves 1 unit to the right, and 10 units down.
D. Reflected across the x-axis, moves 1 unit to the left, and 10 units down.
Answer:
C
Step-by-step explanation:
Firstly, we have 1/x as the parent function. 1/x-1 describes the graph of 1/x to shift 1 unit right. -1/x-1, states that it is reflected across the x-axis. And -1/x-1 -10 states that it is shifted 10 units down.
If it takes 6 printing presses 4 hours to print 5000 newspapers, how long should it take 3 presses to print 3000 newspapers?
Answer:
4 hrs 48 min
Step-by-step explanation:
It takes 6 presses 4 * 3/5 = 12/5 hours to print 3000 newspapers.
It takes 3 presses 2 * 12/5 = 24/5 hours = 4h48min to print 3000 newpapers
A builder of tract homes reduced the price of a model by 15%. If the new price is $425,000, what was it's original price? How much can be saved by purchasing thr model?
Answer:
Step-by-step explanation:
Let x represent the original price of the model.
A builder of tract homes reduced the price of a model by 15%. This means that x was reduced by 15%. The amount by which x was reduced would be
15/100 × x = 0.15 × x = 0.15x
The new price would be
x - 0.15x = 0.85x
If the new price is $425,000, then it means that
0.85x = 425000
x = 425000/0.85
x = $500000
The amount that can be saved by purchasing the model at the new price would be
500000 - 425000 = $75000
Final answer:
The original price of the home was $500,000 before a 15% reduction. The new price is $425,000. Therefore, a buyer would save $75,000 by purchasing the home at the reduced price.
Explanation:
To find the original price of the home before the 15% reduction, we can use the formula for percentage decrease, which is:
Original Price = New Price / (1 - Rate of Decrease)
Here, the New Price is $425,000 and the Rate of Decrease is 15%, or 0.15 when converted to decimal form. Plugging the numbers into the formula gives us:
Original Price = $425,000 / (1 - 0.15) = $425,000 / 0.85
Original Price = $500,000
The amount that can be saved by purchasing the model at the reduced price is the difference between the original price and the new price:
Savings = Original Price - New Price
Savings = $500,000 - $425,000
Savings = $75,000
7.) Solve. Use the calculator set for degrees. Round answers to 4 decimal places.
Find sin 45° using 15° and 30°
a.) 0.9659
b.) 0.8660
c.) 0.4830
d.) 0.2241
e.) 0.7071
Answer:
The answer to your question is sin 45° = 0.6494
Step-by-step explanation:
Data
sin 45° = ?
Process
Formula
sin (15 + 30) = sin (15)cos(30) + cos(15)sin(30)
sin 15 = 0.2334
sin 30 = 0.4540
cos 15 = 0.9723
cos 30 = 0.8910
Substitution
sin(15 + 30) = (0.2334)(0.8910) + (0.9723)(0.4540)
= 0.2080 + 0.4414
= 0.6494
None of the options
The solution set of a linear system involving variablesx1; xnis a list of numbers(s1; sn) that makes each equation in the system a true statement when the valuess1; snare substituted forx1; xn respectively.A) True B) False
Answer:
A) True
Step-by-step explanation:
Solution: When values of the ordered pair (v1, v2, ... , vn) are substituted in every equation of the linear system with variables x1, x2, ... , xn and these values satisfy each and every equation then it's called a solution.
If t follows a t7 distribution, find t0 such that (a) p(|t | < t0) = .9 and (b) p(t > t0) = .05.
Answer:
a) [tex] P(-t_o < t_7 <t_o) =0.9[/tex]
Using the symmetrical property we can write this like this:
[tex] 1-2P(t_7<-t_o) =0.9[/tex]
We can solve for the probability like this:
[tex] 2P(t_7<-t_o) = 1-0.9=0.1[/tex]
[tex] P(t_7<-t_o) =0.05[/tex]
And we can find the value using the following excel code: "=T.INV(0.05,7)"
So on this case the answer would be [tex] t_o =\pm 1.895[/tex]
b) For this case we can use the complement rule and we got:
[tex] 1-P(t_7<t_o) = 0.05[/tex]
We can solve for the probability and we got:
[tex] P(t_7 <t_o) = 1-0.05=0.95[/tex]
And we can use the following excel code to find the value"=T.INV(0.95;7)"
And the answer would be [tex] t_o = 1.895[/tex]
Step-by-step explanation:
Previous concepts
The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."
Solution to the problem
For this case we know that [tex] t \sim t(df=7)[/tex]
And we want to find:
Part a
[tex] P(|t|<t_o)=0.9[/tex]
We can rewrite the expression using properties for the absolute value like this:
[tex] P(-t_o < t_7 <t_o) =0.9[/tex]
Using the symmetrical property we can write this like this:
[tex] 1-2P(t_7<-t_o) =0.9[/tex]
We can solve for the probability like this:
[tex] 2P(t_7<-t_o) = 1-0.9=0.1[/tex]
[tex] P(t_7<-t_o) =0.05[/tex]
And we can find the value using the following excel code: "=T.INV(0.05,7)"
So on this case the answer would be [tex] t_o =\pm 1.895[/tex]
Part b
[tex] P(t>t_o) =0.05[/tex]
For this case we can use the complement rule and we got:
[tex] 1-P(t_7<t_o) = 0.05[/tex]
We can solve for the probability and we got:
[tex] P(t_7 <t_o) = 1-0.05=0.95[/tex]
And we can use the following excel code to find the value"=T.INV(0.95;7)"
And the answer would be [tex] t_o = 1.895[/tex]
The t0 values in the queries are the t-values at which certain probabilistic conditions about the t7 distribution are met. These can be obtained from t-distribution tables or calculated with statistical software.
Explanation:The questions deal with the probabilities under a t-distribution with 7 degrees of freedom. The t-distribution is a type of probability distribution that is symmetric, bell-shaped and has heavier tails compared to the normal distribution. It's often used when the size of the sample is small and/or the population standard deviation is unknown.
(a) In the first case, p(|t | < t0) = .9 means we are looking for the value of t (t0) for which 90% of the distribution lies within -t0 and t0. This induces that each tail beyond these points contains 5% of the distribution as the total probability is 1. This t0 value can be found in standard t-distribution tables or calculated using software like R, Python, or a scientific calculator capable of t-distribution calculations.
(b) For the p(t > t0) = .05 condition, you are looking for the t0 such that 5% of the t-distribution is to the right of this value. This t0 can be referred as the 95th percentile (or the 0.95 quantile) of the t-distribution. This because 95% of the distribution lies to the left of this point. This value can again be found in the t-distribution tables or calculated using relevant software.
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Ms.Shrewsberry gave out a quiz to all 132 of her students. Of all of the students that took the quiz 3/11 of received an A as a grade. How many students got an A?
Answer:
36 students got an'A' grade in the quiz.
Step-by-step explanation:
Given:
Total number of students taking the quiz = 132
Fraction of students getting an 'A' grade = [tex]\frac{3}{11}[/tex]
To find the number of students getting an 'A' grade.
Solution:
In order to find the number of students who got an 'A' grade in the quiz, we will find the fractional part who got an 'A' of the total students taking the quiz.
The fraction of students getting an 'A' is = [tex]\frac{3}{11}[/tex]
Thus, total number of student getting an 'A' is :
⇒ [tex]\frac{3}{11}[/tex] of [tex]132[/tex]
⇒ [tex]\frac{3}{11}\times 132[/tex]
⇒ [tex]\frac{396}{11}[/tex]
⇒ 36 (Answer)
A car and truck are 540 miles apart. The two vehicles start driving toward Each other at the same time. The car drives at a speed of 65 miles per hour, and the truck travels at a speed of 55 miles per hour. At which point will they both meet.
Answer:they would meet after 4.5 hours
Step-by-step explanation:
At the point where they will both meet, they would have covered a total distance of 540 miles.
Let t represent the time it will take the car and the truck to meet.
Distance = speed × time
The car drives at a speed of 65 miles per hour. Distance covered by the car in t hours would be
65 × t = 65t
The truck travels at a speed of 55 miles per hour.
Distance covered by the truck in t hours would be
55 × t = 55t
Therefore,. 65t + 55t = 540
120t = 540
t = 540/120 = 4.5 hours
Can someone help explain this, please?
OP=
4
6
8
Answer:
6
Step-by-step explanation:
jus did it
bob buys 100 candy bars at the store bob eats 47 of the candy bars
what does bob have left now
Answer:
Bob now has 53 candy bars.
Step-by-step explanation:
: )
Answer:
53 bars
Step-by-step explanation:
100-47=53
A financial analyst reports that for people who work in the finance industry, the probability that a randomly selected person will have a tattoo is 0.20.
Answer: Is there a question missing?
Step-by-step explanation:
Probability is the numerical measurement of the likeliness of an even to/not to occur. The probability of an event to/not to occur is always less or equal to 1 (It is never above 1).
It is possible to find the probability of success or the probability of failure of an event. Success is whatever is favourable to you, and Failure is the unfavourable occurence(s).
For example:
A coin has two sides, a head, and a tail. If you toss it once, you'll either get a head or a tail, both sides have equal likeliness of occurring. It is also important to know that the addition of the probability of success and the probability of failure of an even is exactly 1.
Probability of Success(p) + Probability of Failure (q) = 1
Simply,
p + q = 1
Which means if we are given the probability of the likeliness of an event, we can easily find the probability of its failure by subtracting it from 1.
Suppose we want to know the probability of having a head when the coin is tossed once, because we can only have one of the two sides at a time, we say the probability of having a head is 1 out of 2 possible outcomes. That is,
Probability of having a head = 1/2 or 0.5, which is less than 1.
Also, the probability of having a tail is 0.5. Suppose we didn't know, we can just say
p + q = 1
0.5 + q = 1
q = 1 - 0.5
= 0.5
In your statement above, the probability that a randomly selected person will have a tattoo is 0.2 tells us that 20%, or 1 out every 5 persons in the industry have a tattoo (0.2 is 20% of 1).
4x + y = 3 -2x + 3y = -19 what's the solution plz help
The solution to given system of equations is x = 2 and y = -5
Solution:
Given the system of equations are:
4x + y = 3 ---------- eqn 1
-2x + 3y = -19 ---------- eqn 2
We have to find the solution to above system of equations
We can solve the system by substitution method
From eqn 1,
4x + y = 3
Isolate y to one side
y = 3 - 4x ----------- eqn 3
Substitute eqn 3 in eqn 2
-2x + 3(3 - 4x) = -19
-2x + 9 - 12x = -19
Combine the like terms
-14x = -19 - 9
-14x = -28
Divide both sides of equation by -14
x = 2Substitute x = 2 in eqn 3
y = 3 - 4(2)
y = 3 - 8
y = -5Thus the solution is x = 2 and y = -5
The fish store is filling their 5 1/2 gallon tanks for a speacial fish display.They have filled 4 1/2 tanks so far.How many gallons of water have they used?
Answer:
2 1/4 gallons
Step-by-step explanation:
We assume your problem is intended to say there are five tanks, each having a volume of 1/2 gallon, and that 4.5 of these have been filled so far.
The volume of water used is ...
(4.5 tanks)(0.5 gal/tank) = 2.25 gal
2.25 gallons of water have been used.
If 8 identical blackboards are to be divided among 4 schools,how many divisions are possible? How many, if each school mustreceive at least 1 blackboard?
Response:
if8 boards are to be distributed then the number of ways can be8C4=70
and if every school must get atlest one board then it is possiblein 70-14 ways = 56 ways..
let abcd be the schools
a b c d
0 0 0 8 4C1= 4 (three schools dont get even1 board)
0 0 1 7 4C2= 6 (two schools dont get even 1board)
0 1 1 6 4C3 =4
hence 6+4+4=14.
Answer:
There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.
Step-by-step explanation:
Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.
The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is [tex] {11 \choose 3} = 165 . [/tex] As a result, we have 165 ways to distribute the blackboards.
If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is [tex] {7 \choose 3} = 35 [/tex]. Thus, there are only 35 ways to distribute the blackboards in this case.
If 8 identical blackboards are to be divided among 4 schools, there are 70 possible divisions. If each school must receive at least 1 blackboard, there are 56 possible divisions.
Explanation:If 8 identical blackboards are to be divided among 4 schools, the number of ways this can be done is 8C4, which is equal to 70.
If each school must receive at least 1 blackboard, then we need to subtract the cases where one or more schools do not receive a blackboard.
To calculate this, we can subtract the number of ways that three schools do not receive a blackboard (4C1 = 4), the number of ways that two schools do not receive a blackboard (4C2 = 6), and the number of ways that only one school does not receive a blackboard (4C3 = 4).
So, the number of divisions where each school receives at least 1 blackboard is 70 - 4 - 6 - 4 = 56 ways.
I don't kind fast food sells large burgers for five dollars each and french fries for three dollars each that day they sold six more french fries and burgers and their sales total of $98 how many French fries did they sell?
Answer:
They sold 16 French fries.
Step-by-step explanation:
Let x represent the number of large burgers that they sold on that day.
Let y represent the number of French fries that they sold on that day.
fast food sells large burgers for five dollars each and french fries for three dollars each that day and their total sales was $98.It means that
5x + 3y = 98 - - - - - - - - - - - - - -1
they sold six more french fries than burgers. It means that
y = x + 6
Substituting y = x+ 6 into equation 1, it becomes
5x + 3(x + 6) = 98
5x + 3x + 18 = 98
8x = 98 - 18 = 80
x = 80/8 = 10
y = x + 6 = 10 + 6
y = 16
What are like terms? Provide an example with your description. Choose the correct answer below. A. Like terms are terms that have the same coefficient. For example, 3x and 3 are like terms since the coefficient of both is 3. B. Like terms are terms that contain the same common factor. For example, in the expression 6xplus+9plus+5x2, the terms 6x and 9 are like terms since they both share the common factor of 3. C. Like terms are terms that have the same variable factors as well as the same number of factors of each type. For example, 3x and 5x are like terms. D. Like terms are terms that appear in the same expression. For example, in the expression 3xplus+5, 3x and 5 are like terms.
Answer:
Option C.
Step-by-step explanation:
We need to find the correct definition of like terms.
Like terms :Two or more terms are called like terms if they have the same variables and same powers.
For example : 4xy and 9xy are like terms.
Option A is incorrect because 3x and 3 are not like terms.
Option B is incorrect because 6x and 9 are not like terms.
Option C is correct because like terms are terms that have the same variable factors as well as the same number of factors of each type. For example, 3x and 5x are like terms.
Option D is incorrect because 3x and 5 are not like terms.
Therefore, the correct option is C.
Mark retired from competitive athletics last year. In his career as a sprinter he had competed in the 100-meters event a total of 328 times. His average time for these 328 races was 10.23 seconds. The value 10.23 in this sentence is a?
Answer:
time
Step-by-step explanation:
8.) Simplify.
cot^2 0 - cot ^2 0 cos ^2 0
A.) tan^2 0
B.) -1
C.) 3
D.) sin ^2 0
E.) cos^2 0
Answer:
The answer to your question is letter E. cos²α
Step-by-step explanation:
cot²Ф - cot²Фcos²Ф
Remember that cot = [tex]\frac{cos \alpha}{sin \alpha }[/tex] ; substitute in the previous equation
[tex]\frac{cos^{2}\alpha }{sin^{2} \alpha} - \frac{cos^{2}\alpha }{sin^{2}\alpha } cos^{2}\alpha[/tex]
[tex]\frac{cos^{2}\alpha - cos^{4}\alpha }{sin^{2}\alpha }[/tex] Factor cos²α
[tex]\frac{cos^{2}\alpha(1 - cos^{2}\alpha }{sin^{2}\alpha }[/tex]
Remember that sin²α = 1 - cos²α
[tex]\frac{cos^{2}\alpha sin^{2}\alpha}{sin^{2} \alpha}[/tex]
Simplify
cos²α
When sugar is dissolved in water, the amount A that re- mains undissolved after t minutes satisfies the differential equation dA=dt D!kA (k>0). If 25% of the sugar dis- solves after 1 min, how long does it take for half of the sugar to dissolve?
Answer:
Sugar will dissolve to half of it's amount in 2.41 minutes.
Step-by-step explanation:
The given question is incomplete; here is the complete question.
When the sugar is dissolved in water, the amount A that remains undissolved after t minutes satisfies the differential equation
[tex]\frac{dA}{dt}=-kA, (k>0)[/tex]
If 25% of the sugar dissolves after 1 min, how long does it take for half of the sugar to dissolve.
The given differential equation is [tex]\frac{dA}{dt}=-kA[/tex]
In other form, dA = -kA.dt
We further integrate the equation,
[tex]\int\limits {dA}\,=\int{-kA}\, dt[/tex]
[tex]\int\limits{\frac{dA}{A} }\,=-k\int\, dt[/tex]
lnA = -kt + c
Or [tex]A=e^{c-kt}[/tex]
A = [tex]e^{c}.e^{-kt}[/tex] -----(1)
Here [tex]e^{c}[/tex] is a constant.
For t = 0,
[tex]A=e^{c}[/tex]
Let [tex]e^{c}=A_{0}[/tex]
Therefore, equation (1) will become
A = [tex]A_{0}e^{-kt}[/tex]
If sugar dissolves 25% in 1 minutes then undissolved sugar will be
100 - 25 = 75%
Now from the equation
[tex]0.75A_{0}=A_{0}e^{-k\times 1}[/tex]
[tex]e^{-k}=0.75[/tex]
By taking natural log on both the sides
[tex]ln(e^{-k})=ln(0.75)[/tex]
k = 0.2877
Now we have to calculate the time to dissolve half of the sugar, that means half the sugar will be undissolved.
Form the equation,
[tex]0.5A_{0}=A_{0}e^{-0.2877t}[/tex]
[tex]0.5=e^{-0.2877t}[/tex]
ln(0.5) = [tex]ln(e^{-0.2877t})[/tex]
0.6931 = 0.2877t
t = 2.41 minutes
The question deals with logarithmic differential equations. After finding the value of the decay constant (k), it's used to find the time it takes for half of the sugar to dissolve.
Explanation:The subject you're asking about is logarithmic differential equations. Let's start by writing the differential equation in its general form: dA/dt = -kA. This equation describes an exponentially decaying process, where the amount of undissolved sugar decreases proportionally to the amount of sugar left at any point in time (A).
From the problem, it's known that after 1 min 75% of the sugar remains, which means A = 0.75 and t = 1. We substitute these values into the equation to find the value of k.
Then we can use this information to calculate the time it takes for half of the sugar to dissolve. At this point A will be 0.5. We substitute A = 0.5 and the value of k from earlier into the equation and solve for t.
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Determine whether the study depicts and observational study or an experiment. A study is conducted to determine if there is a relationship between heart arrhythmias and caffeine consumption. A sample of 100 people with heart arrhythmia are asked about their caffeine consumption. Does the description correspond to an observational study or an experiment?
Answer:
The study is an observational study because the study examines individuals in the sample, but does not try to influence the response variable.
Step-by-step explanation:
Final answer:
The described study, which involves asking a sample of people with heart arrhythmias about their caffeine consumption to explore a relationship between the two, is an observational study. In this type of study, there is no manipulation of variables or conditions, just observations and recordings of naturally occurring phenomena.
Explanation:
The study described is investigating if there is a relationship between heart arrhythmias and caffeine consumption by asking a sample of people with heart arrhythmia about their caffeine intake. This corresponds to an observational study, not an experiment. In an observational study, researchers collect data on existing behaviors and outcomes without manipulating any variables or conditions. Participants are observed in their natural settings, and their experiences or characteristics are recorded to find correlations or associations between factors.
By contrast, an experiment involves the researcher actively manipulating one or more independent variables to investigate the effects on a dependent variable, often involving random assignment to different conditions, such as treatment versus control groups.
In the context provided, because there is no manipulation of participants' caffeine consumption and no assignment to different conditions, but rather a collection of data through questionnaires, this study is classified as an observational study.
A 150 pound person uses 6.6 calories per minute when walking at a speed of 4 mph. How long must the person walk at this speed to use at least 240 calories
Answer:
The person must walk 36.36 minutes to use at least 240 calories.
Step-by-step explanation:
Given:
A 150 pound person uses 6.6 calories per minute when walking at a speed of 4 mph.
Now, to find the time the person walk at this speed to use at least 240 calories.
As, given calories used per minute = 6.6.
So, to solve we use unitary method:
If 6.6 calories used in = 1 minute.
So, 1 calorie used in = [tex]\frac{1}{6.6}[/tex]
Thus, 240 calorie used in = [tex]\frac{1}{6.6} \times 240[/tex]
= [tex]\frac{1}{6.6} \times 240[/tex]
= [tex]\frac{240}{6.6}[/tex]
= [tex]36.36\ minutes.[/tex]
Therefore, the person must walk 36.36 minutes to use at least 240 calories.
The scatter plot below shows the number of prom tickets sold over a period of 7 days. The line of best fit drawn on the plot shown is used to predict the number of tickets sold on a certain day. Use the two points shown on the line of best fit to calculate its slope to the nearest tenth.
Answer:
The slope is [tex]4.2\ \frac{tickets}{day}[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
Let
x ----> the number of days
y ---> the number of tickets sold
we have the points
(1,30) and (7,55)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the given values in the formula
[tex]m=\frac{55-30}{7-1}[/tex]
[tex]m=\frac{25}{6}[/tex]
[tex]m=4.2\ \frac{tickets}{day}[/tex]
The length of a football field is x. The width of the field is 70 yards less than the length. Write an expression that represents the perimeter of the field without parentheses.
Answer: the expression representing the perimeter of the field is 4x + 280
Step-by-step explanation:
The perimeter of a figure is the distance around it.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
The length of a football field is x. The width of the field is 70 yards less than the length. This means that the width of the football field is x - 70 yards.
an expression that represents the perimeter of the field without parentheses would be
Perimeter = 2(x + x- 70) = 2(2x + 70)
= 4x + 280
Rahm took out a 25-year loan for $155,000 at an APR of 4.8%, compounded monthly, and he is making monthly payments of $888.15. What will his balance be with 17 years left on the loan?
Answer:
$198779.46
Step-by-step explanation:
We must determine the amount owed for the first 7 years. The monthly compound interest formula is:
[tex]A=P(1+r/12)^1^2^t-Xnt[/tex]
[tex]A=155000(1+0.048/12)^84-888.15[/tex]
[tex]A=216752.23-74604.6[/tex]
[tex]A=142147.63[/tex]
The balance will be $85690.81 after 7 years of paying
He will still have to pay:
[tex]A=142147.63(1+0.048/12)^8^4=198779.46[/tex]
He will have to pay $198779.46 for the last 17 years
Answer:
$123,692.61
Step-by-step explanation:
A ball is throw into the air from the top of a building. The height h(t) of the ball above the ground t seconds after it is thrown can be modeled by h (t) =-16t +64t+80 how many seconds after being thrown will the ball hit the ground
Answer: The ball will hit the ground 5 seconds after being thrown.
Step-by-step explanation:
The correct function is: [tex]h (t) =-16t^2 +64t+80[/tex]
You can rewrite the Quadratic function given in the exercise with making [tex]h(t)=0[/tex]. Then this is:
[tex]0=-16t^2 +64t+80[/tex]
Now you can simplify the equation dividing both sides by -16. So you get:
[tex]\frac{0}{-16}=\frac{-16t^2 +64t+80}{-16}\\\\0=t^2-4t-5[/tex]
To find the solution of the Quadratic equation, you can facfor it. In order to do this, it is necessary to find two numbers whose sum is -4 and whose product is -5. These number would be -5 and 1.
Therefore, you get this result:
[tex]0=(t-5)(t+1)\\\\t_1=5\\t_2=-1[/tex]
Since the time cannot be negative, you can conclude that the ball will hit the ground 5 seconds after being thrown.
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the following statements is true about the boldface numbers?
a) 72% is a sample; 56% is a population.b) 72% and 56% are both statistics.c) 72% is a statistic and 56% is a parameter.d) 72% is a parameter and 56% is a statistic.e) 72% and 56% are both parameters.
Answer:
c) 72% is a statistic and 56% is a parameter.
Step-by-step explanation:
Previous concepts
A statistic or sample statistic "is any quantity computed from values in a sample", for example the sample mean, sample proportion and standard deviation
A parameter is "any numerical quantity that characterizes a given population or some aspect of it".
Solution to the problem
For this case we know that they select a sample of 663 registered voters and the sample proportion from these registered voters is:
[tex] \hat p = 0.72[/tex] representing the sample proportion of people who voted in the election
They info that they have is that the true proportion before is [tex] p =0.52[/tex] and that represent a value related to the population.
So on this case the 0.72 represent a statistic since represent the sample and the 0.52 is a value who represent the population for this case is a parameter.
So the correct option is:
c) 72% is a statistic and 56% is a parameter.