The probability of selecting a black card or a jack is 15/26.
Given that, one card is selected from a deck of cards.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Total number of outcomes =52
The number of black cards in a deck =26
The number of jack cards in a deck =4
Probability of an event = 26/52 +4/52
= 30/52
= 15/26
Therefore, the probability of selecting a black card or a jack is 15/26.
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Final answer:
The probability of selecting a black card or a jack from a standard deck of 52 cards is 7/13.
Explanation:
To find the probability of selecting a black card or a jack from a standard deck of 52 cards, we need to consider the number of favorable outcomes and the total number of possible outcomes.
In a deck, there are 26 black cards (13 clubs and 13 spades) and a total of 4 jacks.
However, since two of the jacks are black, we must avoid counting them twice.
The probability becomes:
P(Black or Jack) = P(Black) + P(Jack) - P(Black and Jack)
P(Black) = 26/52, P(Jack) = 4/52, and P(Black and Jack) = 2/52
Thus, the probability is:
P(Black or Jack) = (26/52) + (4/52) - (2/52) = 28/52 = 7/13
Therefore, the probability of selecting a black card or a jack from a standard deck is 7/13.
Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussels sprouts. Of these students, \small \frac{2}{3} dislike lima beans; and of those who dislike lima beans, \small \frac{3}{5} also dislike brussels sprouts. How many of the students like brussels sprouts but dislike lima beans?
===============================================
How I got that answer:
Create a two-way table showing the breakdown of students who like or dislike either vegetable. This is shown in the attached image below. Anywhere there is a letter indicates we aren't able to determine that value. Luckily we dont need to know those values to answer the question.
----------
Let's say we had 3000 students. I picked some large number that is a multiple of 3. That way when we multiply by 2/3, we get a whole number.
Take 2/3 of 3000 and you should get 2000. So there are 2000 students who dislike lima beans. Write "2000" at the end of the "dislike lima beans" row which is where the total is. Above that we'll have 1000 people who like lima beans, but we dont need to use this value.
-----------
Of those 2000 students, 3/5 of them also dont like sprouts either. So (3/5)*2000 = 0.6*2000 = 1200 students do not like both veggies. Furthermore, 2000 - 1200 = 800 like sprouts but dont like lima beans.
Alternatively, 2/5 of the 2000 students like sprouts but dont like lima beans, so (2/5)*2000 = 0.4*2000 = 800.
A lazy high school senior types up application and envelopes to and different colleges, but puts the applications randomly into the envelopes. What is the expected number of applications that went to the right college?
To calculate the expected number of applications that went to the right college, we need to consider the probability of each application being placed correctly. Since the applications are placed randomly, each application has an equal chance of going to the right college. The expected number of applications that went to the right college is 1.
Explanation:To calculate the expected number of applications that went to the right college, we need to consider the probability of each application being placed correctly. Since the applications are placed randomly, each application has an equal chance of going to the right college. Let's say there are n applications and n colleges.
The probability of a specific application going to the right college is 1/n. Therefore, the expected number of applications that went to the right college can be calculated as:
Expected number = Total number of applications * Probability of an application going to the right college
Expected number = n * (1/n)
Expected number = 1
The expected number of applications that went to the right college is 1. This means that, on average, one application will go to the right college.
Yuan and his friends went to the movies. They ate 8 buckets of popcorn, 4 ice cream bars, and 6 boxes of chocolate. How many snacks did they eat in all?
Answer:
18 snacks
Step-by-step explanation:
Here we are considering that popcorn,icecreams,chocolate are snacks and each quantity represents each unit of snack.
Given that they ate 8 buckets of popcorn, 4 ice cream bars, and 6 boxes of chocolate
So the total number of snacks they ate are 8 + 4 + 6 = 18
For one month, Gilda's cell phone bill costs $40 plus an additional 8 cents per text message. Is she can only afford a total bill of $50 for a month, find the maximum number of text messages she can send in one month.
Answer:
Gilda can send 125 messages in one month.
Step-by-step explanation:
Given,
Total bill of 1 month = $50
Fixed charge of 1 month = $40
Charge of 1 message = 8 cents
∵100 cents = $1
∴8 cents = $0.08
Therefore Charge of 1 message = $0.08
We have to find out the number of messages that Gilda can send in 1 month.
Solution,
Let the total number of messages that Gilda can send in 1 month be 'x'.
Total bill of the month is the sum of fixed charge and charge of 1 message multiplied with total number of messages.
So, framing the above sentence in equation form, we get;
Total bill of 1 month =Fixed charge of 1 month+Charge of 1 message× total number of messages
On substituting the given values, we get;
[tex]40+0.08x=50\\\\0.08x=50-40\\\\0.08x=10\\\\x=\frac{10}{0.08}=125[/tex]
Hence Gilda can send 125 messages in one month.
A rectangular prism has these dimensions. The area of the base of the prism is 360 square centimeters The height of the prism is 19 centimeters What is the volume, in cubic centimeters, of the rectangular prism?
The volume of rectangular prism is 6840 cubic centimeters.
Step-by-step explanation:
Given,
Area of base of rectangular prism= l*w = 360 cubic centimeters
Height of rectangular prism = h = 19 centimeters
Volume of rectangular prism = Length * Width * Height
Volume of rectangular prism = l*w*h
Volume of rectangular prism = [tex]360*19=6840\ cubic\ centimeters[/tex]
The volume of rectangular prism is 6840 cubic centimeters.
Keywords: prism, rectangle
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A student with two summer jobs earns $10 per hour at a café and $8 per hour at a market. The student would like to earn at least $800 per month.
A. Write and graph an inequality to represent the situation. Include clear labels on the graph.
B. The student works at the market for 60 hours per month and can work at most 90 hours per month. Can the student earn at least $800 each month? Explain how you can use your graph to determine this.
Help
Answer:
A.) View Image
B.) Not possible. If you look at the graph,the student must work at the cafe at least 80 hours and at the the market for at least 100 hours to earn the minimum $800 they wanted.
60 hours is below the minimum required time of both place. 90 hours can only satisfy the minimum work hour of one of the place, they need to satisfy the minimum of both places.
In other word, they must work at least 180 hours to earn the $800+ they wanted
Step-by-step explanation:
Set up your equation.
let c be hour worked at cafe and m be hours worked at market.
solve for any of the variable. I solved for c because it looked easier. solving for m will give you the same graph as well.
Graph your equation like usual. Since it's a ≥ sign then you must shade above the line. The shaded part represents the hours that the student can work at both place to earn at least $800
Office Furniture Makers, Inc. uses machines to produce high quality office chairs for other firms. The initial cost of one customized machine is $750,000. This machine costs $12,000 a year to operate. Each machine has a life of 3 years before it is replaced. What is the equivalent annual cost of this machine if the required return is 10 percent? (Round your answer to whole dollars.)
The equivalent annual cost of the machine, considering a 10% return, is approximately $309,535 per year.
Explanation:First, accumulate the total cost over the lifespan of the machine which is $750,000 (initial cost) + ($12,000 * 3 years) = $786,000. The equivalent annual cost can be calculated using the formula for the present value of an annuity: PV = PMT [(1 - (1 + r)^-n ) / r], where 'PMT' is the payment per period, 'r' is the rate of return, and 'n' is the number of periods. Rearrange to calculate PMT: PMT = PV * r / (1 - (1 + r)^-n). Substituting in given values gives us, PMT = $786,000 * 0.1 / [1 - (1 + 0.1)^-3] = $309,535/year.
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An egg farm packages 264 total cartons of eggs each month.The farm has three different sizes of cartons.The small carton holds 8 eggs,and 1/6 of the total cartons are small.TThe medium carton holds 12 eggs and 2/3 of the total Cardinals are medium to large carton holds 18 eggs and the rest of the total clients are large determine how many of each size of the curtain is needed each month then determine how many eggs are needed to fill the 264 cartons show your work or explain your answers
I don't know.. can you please explain it?
Kyle sold 28 boxes of fruit for a fundraiser.Omar sold 2 times as many boxes of fruit ad Kyle sold.What is the total number of boxes that Kyle and Omar sold?
Answer: 84
Step-by-step explanation:
K=28
O=2K=2*28=56
O+K=56+28=84
The total number of boxes that Kyle and Omar sold is 84.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variables called division.
Multiplication = to multiply any two or more numbers or variables called multiplication.
As per the given,
Kyle sold 28 boxes of fruit.
Omar sold 2 times,
28 x 2 = 56 boxes
Total boxes = 56 + 28 = 84 boxes
Hence "The total number of boxes that Kyle and Omar sold is 84".
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PLEASE HELP ME!!!! WILL GIVE BRAINLIEST!!!
If (x − 5) is a factor of the polynomial function f(x) = 3x^2 − 23x + 40, which of the following is another factor?
A. (3x − 8)
B. (3x + 8)
C. (8x − 3)
D. (8x + 3)
Answer:
option a is correct , watch explanation
Answer:
There are two factors of the function. You already said the first one, x-5. The second factor is Option A
Hope this helps, comment for any questions. If you like this answer please mark me the brainliest! Thanks!
A fly trapped inside a cubical box with side length 1 meter decides to relieve its boredom by visiting each corner of the box. It will begin and end in the same corner and visit each of the other corners exactly once. To get from a corner to any other corner, it will either fly or crawl in a straight line. What is the maximum possible length, in meters, of its path?
Answer:
(4 √ 3 + 4 √2 ) m
Step-by-step explanation:
The insect can travel from one corner directly to opposite corner in four different ways
each can be calculated using Pythagoras theorem
firstly for one face we need to calculate the diagonal
H² = 1² + 1² = 2
H = √2
then we calculate the diagonal opposite a corner
for example
A to H where A is at the bottom and H opposite A in another plane at the top in the cubical box
(Interior diagonal for A to H)² = √2² + 1² = 3
Interior diagonal from A to H = √ 3
there are four such corners, the fly will travel 4 √ 3 and it could also go 4 √2 diagonally to the the other corners
maximum possible length in meters = (4 √ 3 + 4 √2 ) m
In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt
Answer:
Total number of ways will be 20
Step-by-step explanation:
We have given three identical green shirts and three identical red shirts
So total number of shirts = 3+3 = 5
We have to distribute these shirts to 6 children so that each children got one shirt
Number of ways will be equal to [tex]=\frac{6!}{3!3!}=20[/tex] ( Here we divide by 3!3! because three green shirts and 3 red shirts are identical )
Twice The sum of a number and three times the second number is four. The difference of 10 times the second number And five times the first is 90 find the numbers
Answer: The first number is [tex]-10[/tex] and the second number is [tex]4[/tex]
Step-by-step explanation:
Let be "x" the first number and "y" the second number.
The word "Twice" indicates multiplication.
By definition, the sum is the result of an addition.
"is" indicates an equal sign.
Therefore, "Twice the sum of a number and three times the second number is four" can be expressed as:
[tex]2(x+3y)=4[/tex] [Equation 1]
A difference is the ressult of a subtraction, then " The difference of 10 times the second number and five times the first is 90" can be expressed as:
[tex]10y-5x=90[/tex] [Equation 2]
To find the numbers:
1. Solve for "x" from the Equation 1:
[tex]2(x+3y)=4\\\\2x+6y=4\\\\x=\frac{4-6y}{2}\\\\x=2-3y[/tex]
2. Substitute this equation into the Equation 2 and solve for "y":
[tex]10y-5(2-3y)=90\\\\10y-10+15y=90\\\\25y=100\\\\y=\frac{100}{25}\\\\y=4[/tex]
3. Substitute the value of "y" into the equation [tex]x=2-3y[/tex] and evaluate:
[tex]x=2-3(4)\\\\x=-10[/tex]
The values of m and n are whole numbers greater than 1. Which is true about the quotient m/n÷1/n? The expression will always equal n. The expression will always equal m. The expression will equal n only when m > n. The expression will equal m only when m > n.
Answer:
The value of the quotient is always equal to m
Step-by-step explanation:
The values of m and n are whole numbers greater than 1.
We are given a quotient that is [tex]\frac{\frac{m}{n} }{\frac{1}{n}}[/tex].
In this we have fractions in both numerator and denominator.
The given quotient will be the same if we multiply the numerator with the inverse of the denominator.
So we multiply the numerator [tex]\frac{m}{n}[/tex] with the inverse n.
So the quotient will become = [tex]\frac{m}{n} \times n[/tex] = m
Hence the value of the quotient is always equal to m.
The manufacturerâs suggested retail price (MSRP) of a certain item is $60. Store A sells the item for 20 percent more than the MSRP. The regular price of the item at Store B is 30 percent more than the MSRP, but the item is currently on sale for 10 percent less than the regular price. If sales tax is 5 percent of the purchase price at both stores, what is the result when the total cost of the item at Store B is subtracted from the total cost of the item at Store A?A. $0B. $0.63C. $1.80D. $1.89E. $2.10
Answer:
C. $1.80
Step-by-step explanation:
Given:
MSRP of a certain item = $60
Percentage of Selling by store A = 20%
Percentage amount will be = [tex]\frac{20}{100}\times 60 = \$12[/tex]
Sales tax = 5% on purchase price
Amount of sales tax = [tex]\frac{5}{100}\times 60 = \$3[/tex]
Total Cost of item at Store A is MSRP of a certain item plus Percentage amount of selling the item plus Amount of Sales tax.
framing in equation form we get;
Total Cost of item at Store A = [tex]60+12+3 =\$75[/tex]
Also Given:
Percentage of Selling by store B = 30%
Percentage amount will be = [tex]\frac{30}{100}\times 60 = \$18[/tex]
Regular price of item at store B = [tex]60+18 = \$78[/tex]
Percentage of discount of item at store B = 10% on regular price
Amount of discounted item at store B = [tex]\frac{10}{100}\times78 = \$7.8[/tex]
Now regular price of item with discount at store B will be equal to Regular price of item at store B minus Amount of discounted item.
regular price of item with discount at store B = [tex]78-7.8 = \$70.2[/tex]
Sales tax = 5% on purchase price
Amount of sales tax = [tex]\frac{5}{100}\times 60 = \$3[/tex]
Total Cost of item at Store B is regular price of item with discount at store B plus Amount of Sales tax.
framing in equation form we get;
Total Cost of item at Store B = [tex]70.2+3 =\$73.2[/tex]
The result when total cost of the item at Store B is subtracted from the total cost of the item at Store A = $73.2 - $75 = $1.80.
Hence the result is $1.80.
-6y-3=3-6y(if there is no solution,type in ''no solution'')y= Answer
Answer:
No solution
Step-by-step explanation:
-6y - 3 = 3 - 6y , add 6y on both sides to cancel them out
-3 = 3 , you're left with -3=3, which is impossible because they're
different numbers, therefore not solution.
-3 ≠ 3
Find a formula C(x,y,z) that gives the cost of materials for a closed rectangular box, with dimensions in feet. Assume that the material for the top and bottom costs $3 per square foot and the material for the sides costs $5 per square foot. Show all work in steps clearly.
Answer:
C(x,y,z)=6*x*y+10*x*z+10*y*z
Step-by-step explanation:
Lets assume that x is width, y is length and z is height. To find the area of the top and bottom surfaces we need to simply multiply length and width.
x*y
There is a 2 surface exist (top and bottom) we need to multiply this value with 2 again.
2*x*y
and the cost is 3$ for per square foot and the cost for top and bottom is:
6*x*y$
Surface areas of side surfaces are multiply of width, height and length, height:
x*z+y*z
There are 4 side surfaces exist. Therefore the are need to be multiply with 2.
2*x*z+2*y*z
and the cost is 5$ for per square foot and the cost for side surfaces is:
10*x*z+10*y*z
Total equality for cost is C(x,y,z)=6*x*y+10*x*z+10*y*z
To calculate the cost of materials for a closed rectangular box, use the formulas C(x,y) = 2 * (3xy) for the top and bottom and C(z,y) = 2 * (5zy) for the sides. Then, find the total cost by adding the costs together.
Explanation:To calculate the cost of materials for a closed rectangular box, we need to consider the dimensions of the box. Let's assume the dimensions are given as x, y, and z in feet.
The cost for the top and bottom parts of the box can be calculated using the formula C(x,y) = 2 * (3xy), where 3 is the cost per square foot and xy is the area of the top and bottom.
The cost for the side parts of the box can be calculated using the formula C(z,y) = 2 * (5zy), where 5 is the cost per square foot and zy is the area of the sides.
Finally, the total cost of materials for the box can be found by adding the costs for the top and bottom parts to the cost of the side parts: C(x,y,z) = C(x,y) + C(z,y).
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State if the triangles in each pair of similar. If so, State how you know they are similar and complete the similarity statement.
Answer:
Step-by-step explanation:
They are not similar. If they were, ∠LMF and ∠GHF would both have the same angle measure and they do not.
Final answer:
Mathematics question on similar triangles; triangles are similar if they have congruent corresponding angles and proportional sides obtained through AA, SSS, or SAS criterion. A similarity statement describes the correspondence of the vertices.
Explanation:
The question provided falls within the subject of Mathematics, specifically within the study of geometry and the concept of similar triangles. To determine if two triangles are similar, we must check if they have the same shape, which implies that their corresponding angles are equal and their corresponding sides are in proportion. In other words, two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional. This can be verified by angle-angle similarity (AA), side-side-side similarity (SSS), or side-angle-side similarity (SAS). The similarity statement provides the order of correspondence of vertices between similar triangles.
When evaluating if triangles BAO and B1A1O are similar, we must compare their corresponding angles and sides. If the given information indicates that at least two angles of one triangle are congruent to two angles of another triangle (AA criterion), or that the sides are proportional (SSS or SAS criterion), then the triangles are similar. For instance, if ∠BAO ≅ ∠B1A1O and ∠BOA ≅ ∠B1O1A1, then by the AA criterion, the triangles are similar, and we could write the similarity statement as triangle BAO ∼ triangle B1A1O.
Find the difference.
(5x2 + 2x + 11) - (7 + 4x - 2x2)
A.
9 - 2x - 2x2
B.
3x2 - 2x + 4
C.
3x2 + 6x + 4
D.
7x2 - 2x + 4
[tex]\text{Solve:}\\\\(5x^2 + 2x + 11) - (7 + 4x - 2x^2)\\\\5x^2+2x+11-7-4x+2x^2\\\\7x^2+2x+11-7-4x\\\\7x^2-2x+11-7\\\\\boxed{7x^2-2x+4}[/tex]
Answer:
D. 7x2 - 2x + 4
Step-by-step explanation:
5x2 + 2x + 11 - 7 - 4x +2x2
7x2 + 2x + 11 - 7 - 4x
7x2 - 2x + 11 - 7
7x2 - 2x + 4
A number consists of two digits whose sum is 12. If 16 is added to the number, then one of the digits is four times the value of the other. What is the number?
Answer: The number is 12.
Step-by-step explanation:
Since we have given that
Sum of two digits = 12
Let the one's digit be 'x'
Let the ten's digit be '12-x'
So, Original number would be
[tex]x+10(12-x)\\\\=x+120-10x\\\\=-9x+120[/tex]
If 16 is added to the number, then one of the digit is four times the value of the other.
According to question, we get that
[tex]-9x+120+16\\\\=-9x+136[/tex]
so, the one's digit be 'x'.
Let the ten's digit be '4x'.
so, New number would be
[tex]10x+4x=14x[/tex]
According to question, it becomes,
[tex]14x=-9x+136\\\\14x+9x=136\\\\23x=136\\\\x=\dfrac{136}{23}=12[/tex]
So, the number would be
[tex]-9x+120=-9\times 12+120=-108+120=12[/tex]
Hence, the number is 12.
Answer:
66
Step-by-step explanation:
Brute force:
2 digit numbers that has sum of 12:
39, 48, 57, 66
Add 16 to the numbers:
55, 64, 73, 82
Find the number that shows a digit is 4 times the value of other:
82 (2x4 =8)
Ten spheres each with radius of 2 cm are fully immersed in a cylinder of water with radius 10 cm. find the rise in water level
Answer:
no. of spjeres=10
radius of those cylinders =2cm
radius of the cylinder in which water is poured=10
rise in water water level =10×2÷10 = 2cm
The rise in water level will be 2 centimeters when spheres are fully immersed in a cylinder.
What is the volume of a cylinder?The volume of a cylinder is defined as the space occupied by the cylinder and the volume of any three-dimensional shape is the space occupied by it.
Ten spheres, each with a radius of 2 cm, are fully immersed in a 10 cm cylinder of water.
As per the given question, we have
The number of spheres = 10
The radius of those cylinders = 2cm
The radius of the cylinder in which water is poured = 10
According to the condition, the required solution would be as:
The rise in water level = 10 × 2 ÷ 10
The rise in water level = 20/10
Apply the division operation, and we get
The rise in water level = 2 cm
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Lynn rents a luxury car at the Edmonton Internacional Airport. She wants a nice
vehicle for her 3 day trip. She figures she will put on about 400 km during the three
days.
a. What would be the cost of the Standard Daily Rate plus Mileage plan?
b. What would be the cost of the Unlimited Mileage plan?
c. Which is the better plan?
Answer:
Step-by-step explanation:
Looking at the table,
a) the standard daily rate for a luxury car is $70. Since Lynn wants to rent the luxury car for 3 days, it means that the standard rate for 3 days would be
3 × 70 = $210
She figures she will put on about 400 km during the three
days. The cost of renting the luxury car per kilometer(mileage) is 30 cents. Therefore, the cost for 400 kilometers would be
400 × 30 = 12000 cents.
Converting 12000 cents to dollars, it becomes
12000/100 = $120
Total cost of renting the luxury car would be
120 + 210 = $330
b) the daily cost of the unlimited mileage daily for the luxury car is $105
Total cost of renting the luxury car for 3 days would be
105 × 3 = $315
c) the standard daily rate is better because it is cheaper
Write down a 3-digit number where digits are in decreasing order. Reverse the digits and subtract it from the first number.
Step-by-step explanation:
987 → 789
987 - 789 = 198
876 → 678
876 - 678 = 198
765 → 567
765 - 567 = 198
654 → 456
654 - 456 = 198
543 → 345
543 - 345 = 198
432 → 234
432 - 234 = 198
321 → 123
321 - 123 = 198
Generally it is always like that:
3 ≤ x ≤ 9
100x + 10(x-1) + (x - 2) → 100(x - 2) + 10(x - 1) + x
(100x + 10(x - 1) + (x - 2)) - (100(x-2) + 10(x-1) + x)
= 100x + 10(x - 1) + (x - 2) - 100(x - 2) - 10(x - 1) - x cancel 10(x - 1)
= 100x + x - 2 - 100x + 200 - x cancel 100x and x
= 100 - 2
= 198
A standard deck of cards has 52 cards, 4 of each type (Ace, King, Queen, Jack, 10,...,2). From a well-shuffled deck, you are dealt a hand of 5 cards (without replacement).
(a) What is the probability that you are dealt at least one face card (that is a king, queen or jack)?
(b) What is the probability that you are dealt with both; at least one ace and at least one face card?
Answer:
a)%85,5
b)%92,2
Step-by-step explanation:
a) To determine the probability of getting a hand with at least one face, we need to calculate the probability of the hand without any face firstly.
[tex](36/52)*(35/51)*(34/50)*(33/49)*(32/48)=0,145[/tex]
Then, we need to deduct this value from the probability 1
[tex]1-0,145=0,855[/tex]
The probability of the hand with at least one face is %85,5.
b)To determine the probability of a hand with at least one ace and face we will track the same road again.
[tex](32/52)*(31/51)*(30/50)*(29/49)*(28/48)=0,0775[/tex]
Then, we need to deduct this value from the probability 1
[tex]1-0,0775=0,922[/tex]
The probability of the hand with at least one ace and one face is %92,2.
Yesterday Nadia consumed 250 grams of carbohydrate, 75 grams of protein, and 60 grams of fat. What percentage of Calories of her day's intake came from fat?
Final answer:
To calculate the percentage of calories from fat, multiply the grams of fat by the calories per gram of fat and divide by the total calories consumed.
Explanation:
To calculate the percentage of calories from fat in Nadia's daily intake, we need to know the total number of calories she consumed. Let's assume it was 2000 calories. First, we calculate the number of calories from fat by multiplying the grams of fat consumed (60g) by the number of calories per gram of fat (9 calories/g). This gives us 540 calories from fat. Then, we calculate the percentage by dividing the calories from fat (540 calories) by the total calories consumed (2000 calories) and multiplying by 100. So, the percentage of calories from fat in Nadia's day's intake is 27%.
can someone help me right now!!!
Which of the following is a solution to this inequality?
y less than two thirds times x plus 2
(0, 3)
(−3, 1)
(3, 5)
(1, 2)
Final answer:
To determine which of the given points satisfy the inequality y < (2/3)x + 2, substitute the x and y values of each point into the inequality and check if it is true. The only solution to the inequality is (0, 3).
Explanation:
To determine which of the given points satisfy the inequality y < (2/3)x + 2, we can substitute the x and y values of each point into the inequality and check if the inequality is true.
Taking the first point (0, 3), we substitute x=0 and y=3 into the inequality: 3 < (2/3)(0) + 2. Simplifying, we have 3 < 2, which is true. Therefore, (0, 3) is a solution to the inequality.
Next, let's check the other points: (-3, 1), (3, 5), and (1, 2).
By substituting the x and y values of each point into the inequality, we find that (-3, 1), (3, 5), and (1, 2) are not solutions to the inequality. Therefore, the only solution to the inequality is (0, 3).
Ron walks 0.5 mile on a track in 10 minutes. Stevie walks 0.25 mile on the track in 6 minutes find the unit rate for each walker in miles per hour. Who is faster?
Answer:
Ron's speed = 3 miles/hour
Stevie's speed = 2.5 miles/hour
On comparing we see Ron is walking faster than Stevie.
Step-by-step explanation:
Given:
Ron takes 10 minutes to walk on a track to cover a distance of 0.5 miles
Stevie takes 6 minutes to walk on a track to cover a distance of 0.25 miles
To find their unit rates in mile per hour and choose the faster one.
Solution:
Unit rate in miles per hour signifies their speeds. Thus, we will find out their speeds.
Ron:
Distance= 0.5 miles
Time = 10 minutes = [tex]10\ min\times \frac{1\ hr}{60\ min}=\frac{1}{6}[/tex] hours
Speed = [tex]\frac{Distance}{Time}=\frac{0.5}{\frac{1}{6}}=0.5\times6=3\ miles/hour[/tex]
Stevie
Distance = 0.25 miles
Time = 6 minutes = [tex]6\ min\times \frac{1\ hr}{60\ min}=\frac{1}{10}[/tex] hours
Speed = [tex]\frac{Distance}{Time}=\frac{0.25}{\frac{1}{10}}=0.25\times10=2.5\ miles/hour[/tex]
Thus, we have
Ron's speed = 3 miles/hour
Stevie's speed = 2.5 miles/hour
On comparing we see Ron is walking faster than Stevie.
Statistical hypothesis testing allows you to: a.Estimate the standard deviation of your sample distribution b.Use sample statistics to make decisions about population parameters c.Eliminate all potential errors in your research d.Use non-probability samples to make inferences about a population
Answer:
Option B) Use sample statistics to make decisions about population parameters
Step-by-step explanation:
Statistical hypothesis testing
Hypothesis testing is a statistical method that is used in making statistical decisions using a sample that is taken from the population. Statistical hypothesis testing is basically an assumption that we make about the population parameter. with the help of sample statistic.Calculations are performed on samples to gather more information about the population.This helps us to know that the particular sample belongs or does not belong to the population and estimate the parameters of the population with the help of this claim.Probability sampling involves random selection from the population and non-probability sampling relies on the selection based on judgement of the researcher.Thus, Option B) Use sample statistics to make decisions about population parameters is the correct answer.
A rectangular lot whose perimeter is 260 ftis fenced along three sides. An expensive fencing along the lot's length cost $ 18per foot. An inexpensive fencing along the two side widths costs only $ 3per foot. The total cost of the fencing along the three sides comes to $ 1800.What are the lot's dimensions?
Step-by-step explanation:
A rectangular lot whose perimeter is 260 ft is fenced along three sides. An expensive fencing along the lot's length cost $ 18per foot. An inexpensive fencing along the two side widths costs only $ 3per foot.
So we have
l + 2 w = 260 -------------------eqn 1
And total cost is 1800 $
That is
18 l + 2 x 3 w = 1800
3l + w = 300 -------------------eqn 2
eqn 2 x 2
6l + 2w = 600 -------------------eqn 3
eqn 3 - eqn 1
6l + 2w - l - 2w = 600 - 260
5l = 340
l = 68 ft
Substituting in eqn 1
68 + 2 w = 260
2w = 192
w = 96 ft
Lot's dimension is 68 ft x 96 ft
Calculate the simple interest paid on a loan of $544 at 3% for three months.
$48.96
$4.80
$4.90
$4.08
Answer:
Step-by-step explanation:
Answer: interest at the end of 3 months is $4.08
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 3 months = 3/12 = 0.25 years
P = $544
R = 3%
Therefore
I = (544 × 3 × 0.25)/100
I = 408/100
I = 4.08