What is the difference between a relation
and a function? Is every relation a function? Is every
function a relation? Explain.
​

Answer:

4 quarts

Step-by-step explanation:

Answer:

Part 1) The system is solved using elimination

The cost  per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]

Part 2) The system is solved using substitution

The cost  per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]

Part 3) The system is solved by graphing

The graph in the attached figure

Step-by-step explanation:

Part 1) Solve the system by elimination

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

[tex]6x+4y=13.10[/tex] -----> equation A

[tex]4x+6y=13.10+0.60[/tex]

[tex]4x+6y=13.70[/tex]  -----> equation B

Solve the system by elimination

Multiply the equation A by -6 both sides

[tex]-36x-24y=-78.6[/tex] -------> equation C

Multiply the equation B by 4 both sides

[tex]16x+24y=54.8[/tex] -------> equation D

Adds equation C and equation D

[tex]-36x-24y=-78.6\\16x+24y=54.8\\----------\\-36x+16x=-78.6+54.5\\-20x=-23.8\\x=1.19[/tex]

Substitute the value of x in the equation A

[tex]6(1.19)+4y=13.10[/tex]

[tex]4y=5.96[/tex]

[tex]y=1.49[/tex]

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

Part 2) Solve the system by substitution

Let

x----> the cost per can of grape juice

y----> the cost per can of apple juice

we know that

[tex]6x+4y=13.10[/tex]    

[tex]4y=-6x+13.10[/tex]

[tex]y=-1.5x+3.275[/tex] -----> equation A

[tex]4x+6y=13.10+0.60[/tex]

[tex]4x+6y=13.70[/tex]  

[tex]6y=-4x+13.70[/tex]

[tex]y=-(4/6)x+13.70/6[/tex]

[tex]y=--0.67x+2.28[/tex] -----> equation B

Substitute equation B in equation A and solve for x

[tex]-0.67x+2.28=-1.5x+3.275[/tex]

[tex]1.5x-0.67x=3.275-2.28[/tex]

[tex]0.83x=0.995[/tex]

[tex]x=1.19[/tex]

Find the value of y

Substitute the value of x in the equation A

[tex]y=-1.5(1.19)+3.275=1.49[/tex]

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

Part 3) Solve the system by graphing

we have

[tex]y=-1.5x+3.275[/tex] -----> equation A

[tex]y=-(4/6)x+13.70/6[/tex] -----> equation B

Remember that

The solution of the system of equations is equal to the intersection point both lines

The solution is the point [tex](1.19,1.49)[/tex]

see the attached figure

therefore

The cost  per can of grape juice is [tex]\$1.19[/tex]

The cost per can of apple juice is [tex]\$1.49[/tex]

Answer:

Polygon Y's area is one ninth (1/9) of Polygon X's area

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

In this problem

Let

z-----> the scale factor

a-----> Polygon Y's area

b----> Polygon X's area

[tex]z^{2}=\frac{a}{b}[/tex]

we have

[tex]z=\frac{1}{3}[/tex]

substitute

[tex](\frac{1}{3})^{2}=\frac{a}{b}[/tex]

[tex]\frac{1}{9}=\frac{a}{b}[/tex]

[tex]a=\frac{1}{9}b[/tex]

therefore

Polygon Y's area is one ninth (1/9) of Polygon X's area

Answer:

1/9

Step-by-step explanation:

Step 1: Find the total area. Since it is a square all the sides are 12 ft so multiply 12 by 12

12 x 12 = 144

^^^This is the total area including the area around the pool. We just need the are of the pool

Step 2: Outside of the pool there are four little 2 ft by 2 ft squares that aren't part of pool, and therefore won't need to be covered. The area of these 2 ft by 2 ft square is 4ft (2 times 2 is 4). Since there are 4 of these squares we multiply 4 by 4 to get 16. This means that 16 ft of the 144 ft we found previously are not part of the pool and we must subtract 16 from 144 to get the total pool area

144 - 16 = 128

This means that the area of the pool is 128 ft

Hope this helped and made sense! Let me know!

Answer:

128

Step-by-step explanation:

Answer:

Step-by-step explanation:

Bill and Ted are going to order t-shirts for there school clubs. The t-shirts will have the club logo printed on the front. Bill and Ted ask two local t-shirt companies to give them a price. * Patty's Printing charges $21.50 for each t-shirt. * Sandra's shirts has a one-time set up fee for $63 and then charges $18 for each t-sh

Patty's Printing= 21.5x

Sandra's Shirts = 63+ 18x

x=30

Patty's Printing: 21.50 (30) = 645

Sandra's Shirts = 63+ 18 (30) = 603

Sandra's Shirts

Answer:

C, A, C

Hope This Helps!

12,450 so yeah your welcome have a fantasist day

Answer:

1) The system of linear equations is equal to

b+t=15  and 2b+3t=38

2) The number of bicycles ordered​ was 7 and the number of tricycles ordered​ was 8

Step-by-step explanation:

Let

b----> the number of bicycles ordered​

t----> the number of tricycles ordered​

we know that

b+t=15 -----> equation A

2b+3t=38 ---> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (7,8)

see the attached figure

therefore

The number of bicycles ordered​ was 7

The number of tricycles ordered​ was 8

The number of bicycles ordered​ was 7 and the number of tricycles ordered​ was 8.

Systems of equations are sets of equations where the solution is the intersecting point(s) between the equations.

Let, the number of tricycles and b represent the number of bicycles ordered​.

A recreation center ordered a total of 15 tricycles and bicycles from a sporting goods store.

[tex]\rm b+t=15[/tex]

The number of wheels for all the tricycles and bicycles totaled 38.

[tex]\rm 2b+3t=38[/tex]

From equation 1

[tex]\rm b+t=15\\\\b=15-t[/tex]

Substitute the value of b in equation 2

[tex]\rm 2b+3t=38\\\\ 2(15-t)+3t=38\\\\30-2t+3t=38\\\\t=38-30\\\\t=8[/tex]

Substitute the value of t in equation 1

[tex]\rm b+t=15\\\\b=15-t\\\\ b = 15-8\\\\b=7[/tex]

Hence, the number of bicycles ordered​ was 7 and the number of tricycles ordered​ was 8.

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Answer:

B. The temperatures were more consistent in Cape Town

Step-by-step explanation:

A low standard deviation indicates less variation away from the mean.

Since Cape Town has a lower standard deviation than Three Rivers, it is more consistent

Answer:

Option A. 6.247°

Step-by-step explanation:

we know that

1°=60'

1'=60"

we have

6° 14' 48"

Convert to decimal form

Convert seconds to minutes

48"=48/60=0.8'

so

6° 14' 48"=6° + 14' +0.8'=6° 14.8'

Convert minutes to degrees

14.8'=14.8/60=0.247°

so

6° 14.8' =6° + 0.247°=6.247°

Answer:

6.247

Step-by-step explanation:

Answer:

V = 3533

Step-by-step explanation:

Volume of a cylinder is given by

V = pi r^2 h

Using 3.14 for pi

V = (3.14) (7.5)^2 * 20

V = 3532.5

To the nearest whole number

V = 3533

Answer:

Step-by-step explanation:

[tex]x^2-4x-5=x^2+x-5x-5=x(x+1)-5(x+1)=(x+1)(x-5)[/tex]

Answer:

Volume  = 40in^3

Step-by-step explanation:

The volume of a box is:

Volume = width x lenght x height

Where:

width: 4in

Length: 5in

Height = 2in

Then: Volume = width x lenght x height = 4in x 5in x 2in = 40in^3

ANSWER

The volume is 40 cubic inches.

EXPLANATION

The dimensions of the box are ,

width, w=4 inches

height, h=2 inches

and

length, l=5 inches

The box is a rectangular prism.

The formula for finding the volume of a rectangular prism is

[tex]V=l \times b \times h[/tex]

We substitute the values to get,

[tex]V=4\times 5 \times 2 = 40 {in}^{3} [/tex]

Basically you do

2 x 3.14 x 8 squared

= 401.92

Then you do

401.92 + 14 x 8

=513.93

Hope this helps :)

Answer:

The correct answer is option option B 606.32 yd²

Step-by-step explanation:

Points to remember

Surface area of cone = πrl + πr²

Where r is the base radius and l is the lateral edge

To find lateral edge

l =  √(r²+ h²) =  √8² + 14²  = 16.12

To find the surface area of given cone

Here r = 8 yd and l = 16.12 yd

Surface area =  πrl + π r² = π * 8 * 16.12  + π8²

  = 606.32 yd²

For this case we must find the inverse of the following function:

[tex]f (x) = \sqrt [3] {x + 12}[/tex]

For this, we follow the steps below:

Replace f (x) with y:

[tex]y = \sqrt [3] {x + 12}[/tex]

We exchange the variables:

[tex]x = \sqrt [3] {y + 12}[/tex]

We solve the equation for "and":

[tex]\sqrt [3] {y + 12} = x[/tex]

We raise both sides of the equation to the cube to eliminate the root:

[tex](\sqrt [3] {y + 12}) = x ^ 3\\y + 12 = x ^ 3[/tex]

We subtract 12 on both sides of the equation:

[tex]y = x ^ 3-12[/tex]

Thus, the inverse function is:

[tex]f ^ {- 1} = x ^ 3-12[/tex]

Answer:

Option B

Option: B is the correct answer.

       B.    [tex]f^{-1}(x)=x^3-12[/tex]

The inverse function f(x) is calculated in the following steps.

The function f(x) is given by:

[tex]f(x)=\sqrt[3]{x+12}[/tex]

Now, we keep:

[tex]f(x)=y\\\\i.e.\\\\y=\sqrt[3]{x+12}[/tex]

Now, we interchange x and y

[tex]x=\sqrt[3]{y+12}[/tex]

Now, on taking cube on both side of the equation we have:

[tex]y+12=x^3\\\\i.e.\\\\y=x^3-12[/tex]

i.e.

[tex]f^{-1}(x)=x^3-12[/tex]

Answer:

36

Step-by-step explanation:

Answer:36

Step-by-step explanation:

here is your answer young man/lady

The mode is 12, the median is 18.5, the mean is 23.6667, and the range is 26.

The mode is 12 because it appears twice in the list. The median is 18.5 because it is the middle value when the numbers are arranged in ascending order. The mean is 23.6667 which is the sum of all the numbers divided by the total count. The range is 26 which is obtained by subtracting the smallest value (12) from the largest value (38).

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There are 3,024 different ways the coach can choose players for first base, second base, third base, and shortstop from a team of 9 players.

Since the positions are distinct (first base, second base, third base, and shortstop), and each position can only be filled by one player, we can use the permutation formula to calculate the number of arrangements.

The coach has 9 players to choose from for the first position.

After selecting one player for first base, there remain 8 players for the second position, 7 players for the third position, and 6 players for shortstop.

The total number of different ways the coach can choose players for the four positions is obtained by multiplying these numbers:

9 x 8 x 7 x 6 = 3,024

Hence, there are 3,024 different ways.

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Answer:

the inequality would be: 89+41+17.50x Is less than 200

Step-by-step explanation:

add all of the numbers together and the x with the 17.50. Add a less than inequality sign, then 200, which represents how much it would be for repairs

Answer:

[tex]130+17.50x \leq 200[/tex]

Step-by-step explanation:

The appliance repair company will repair his microwave for a service call fee of $89, a parts fee of $41, and a charge of $17.50 for every 15 minutes of labor.

If Josh spends $200 or more on repairs, he will replace the microwave.

Let x represents the number of 15-minute intervals of labor.

So, as per the scenario, the inequality becomes:

[tex]89+41+17.50x \leq 200[/tex]

=> [tex]130+17.50x \leq 200[/tex]

Solving for x

[tex]17.50x \leq 200-130[/tex]

[tex]17.50x \leq 70[/tex]

[tex]x \leq 4[/tex]

Hence, up to 4, 15 minutes interval that is one hour. the repair cost will be up to $200.

But after this it will cost more. Hence, Josh can opt for replacing after 4, 15 minutes intervals.

Ik for s fact the awnser not a

Answer:

B) [tex]-5x + 2y + 1 > 0[/tex]

Step-by-step explanation:

Given point is (-2,-1)

to find out which inequality satisfies this point we plug in x and y value of the given point in each inequality

A) [tex]5x - 2y + 1 > 0[/tex]

x=-2 and y=-1

[tex]5(-2) - 2(-1) + 1 > 0[/tex]

[tex]-10+2+1>0[/tex]

[tex]-7>0[/tex] is False

B) -5x + 2y + 1 > 0

[tex]-5(-2) +2(-1) + 1 > 0[/tex]

[tex]10-2+1>0[/tex]

[tex]9>0[/tex] is True

C) -2x + 5y - 1 > 0

[tex]-2(-2) +5(-1) -1 > 0[/tex]

[tex]4-5-1>0[/tex]

[tex]-2>0[/tex] is False

D) 2x + 5y - 1 > 0

[tex]2(-2) +5(-1) - 1 > 0[/tex]

[tex]-4-5-1>0[/tex]

[tex]-10>0[/tex] is False

Answer:

The correct answer is option B).  108°

Step-by-step explanation:

Points to remember

Sum of angles of hexagon is 720°

From the figure we can see a hexagon.

To find the m<B

m<B = 720 - ( m<A + m< C + m<D + m<E + m<F)

  = 720 - ( 170 + 133 + 102 + 117 + 90)

  = 720 - 612

  = 108°

Therefore m<B = 108° Option B is the correct answer

Answer:

B. 108 degrees

Step-by-step explanation:

Answer:

y=1

Step-by-step explanation:

5y(2x-1)=y(x+2)+20, x=3

5y(2(3)-1)=y(3+2)+20

5y(6-1)=y(5)+20

5y(5)=5y+20

25y=5y+20

25y-5y=20

20y=20

y=20/20

y=1

5y(2x-1)=y(x+2)+20, x=3​

Step 1: Substitute x with 3

5y(2(3) - 1) = y(3 + 2) + 20

Step 2: Combine like terms in the parentheses

5y(6 - 1) = y(3 + 2) + 20

5y(5) = y(3 + 2) + 20

5y(5) = y(5) + 20

Step 2: Distribute the number outside the parentheses to the numbers inside the parentheses

25y  = 5y + 20

Step 3: Combine like terms by subtracting 5y to both sides

25y-5y  = (5y-5y) + 20

20y = 20

Step 4: Divide 20 to both sides to isolate y

[tex]\frac{20y}{20} = \frac{20}{20}[/tex]

y = 1

Check:

5(1) (2(3) - 1) = 1(3+2) + 20

5(6-1) = 1(5) + 20

5(5) = 5 + 20

25 = 25

Hope this helped!

Answer:

3

Step-by-step explanation:

The mean absolute deviation of the data set is approximately 3.09.

The mean absolute deviation (MAD) is a measure of variability that indicates the average distance between observations in a data set and their mean.

To calculate the MAD, you first need to find the mean of the data set. In this case, the mean is 31.375.

Then, you calculate the absolute deviation of each data point from the mean. For example, the absolute deviation of the first data point (21) is 10.375 (|21 - 31.375|).

Once you have calculated the absolute deviation of each data point, you find the average of those absolute deviations. This is the mean absolute deviation.

In the example data set, the mean absolute deviation is approximately 3.

Find the mean of the data set: (21 + 22 + 24 + 26 + 27 + 28 + 20 + 30) / 8 = 31.375

Calculate the absolute deviation of each data point from the mean. For example, the absolute deviation of the first data point (21) is 10.375 (|21 - 31.375|).

Add up the absolute deviations of all the data points. In this case, the sum of the absolute deviations is 24.75.

Divide the sum of the absolute deviations by the number of data points to find the mean absolute deviation. In this case, the mean absolute deviation is 24.75 / 8 = 3.09375.

Therefore, the mean absolute deviation of the data set is approximately 3.09.

The complete question is:What is the mean absolute deviation of the data set?

(21, 22, 24, 26, 27, 28, 20, 303

2

3

6

22

Answer:

f(2) = 0

Step-by-step explanation:

Function f(t) is defined in three different ways depending on the value of t.

For t = 8, function f(t) is -64/t.

For t = 10, function f(t) is 14 - t.

We are not asked about f(8) or f(10). We are asked about f(2). The third definition of function f(t) is for all values of t that are not 8 or 10. 2 is not 8 or 10, so use the third definition of function f(t) and plug in 2 for t.

f(t) = t^2 - 3t + 2 for t not equal to 8 or 10.

f(2) = 2^2 - 3(2) + 2

f(2) = 4 - 6 + 2

f(2) = 0

For this case, when making the division of polynomials, we must build a quotient that when multiplied by the divisor of the same as the terms of the dividend, the sign is changed and they are eliminated until reaching the remainder of the division.

It must be fulfilled that:

[tex]Dividend = Quotient * Divider + Remainder[/tex]

When observing the attached figure, the quotient is:

[tex]x ^ 2-2x-3[/tex]

Answer:

[tex]x ^ 2-2x-3[/tex]

See attached image

ANSWER

Yes

EXPLANATION

The given relation is

2x-5y=-15

We solve for y to obtain:

-5y=-2x-15

Divide through by -5.

[tex]y = \frac{2}{5}x + 3[/tex]

This is linear relation.

There is a positive linear relationship between the two variables x and y.

Also we can see that the highest degree of the variables is unity.

Hence it represents a linear relationship between x and y.

Answer:

[tex]\frac{24}{5}[/tex]

Step-by-step explanation:

To evaluate division of fractions, that is

[tex]\frac{9}{-5}[/tex] ÷ [tex]\frac{-3}{8}[/tex]

Leave the first fraction, change division to multiplication and turn the second fraction upside down

[tex]\frac{9}{-5}[/tex] × [tex]\frac{8}{-3}[/tex] ( cancel the 9 and 3) giving

[tex]\frac{3}{-5}[/tex] × [tex]\frac{8}{-1}[/tex]

= [tex]\frac{3(8)}{-5(-1)}[/tex] = [tex]\frac{24}{5}[/tex]

To simplify a complex fraction, multiply both the numerator and the denominator by the same factor to eliminate fraction in the denominator, cancel common factors and follow rules of algebra to maintain equality.

To evaluate and simplify a complex fraction, we can use a strategy that involves multiplying the numerator and denominator by the same factor. For example, if our complex fraction had a denominator of 1/2, we could multiply both the numerator and the denominator by 2 to eliminate the fraction in the denominator. This approach ensures the units or variables cancel out where appropriate, leaving us with a simpler expression. When working with fractions, common factors can be identified and cancelled to simplify the fraction further. Always remember that fractions represent division, so when simplifying, divide the digit term of the numerator by that of the denominator and subtract the exponentials accordingly. This process is governed by the rules of algebra, maintaining the equality of the expression.

Answer:

Step-by-step explanation:

To find the arithmetical mean, add all the numbers togther and divide by the number of numbers.

The sum of all the numbers is ... 59.

There are 7 numbers.

59/7 which is about 8.43 is the arithmetic mean.

Arithmetic mean is 8.42 (Approximately)

Given that;

Values = 8,10,10,10,6,7,8

Find:

Arithmetic mean

Computation:

Arithmetic mean = Sum of all number / Number of term

Arithmetic mean = [8 + 10 + 10 + 10 + 6 + 7 + 8] / 7

Arithmetic mean = 59 / 7

Arithmetic mean = 8.42 (Approximately)

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Answer:

1. rectangular prism

2. cylinder

3. cone

4. triangular pyramid

5. sphere

Step-by-step explanation:

The probability that they are both white if the first sock is kept and second is drawn will be 8.33%.

Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.

A drawer contains 4 black socks, 3 white socks, and 2 red socks.

One sock is drawn from the drawer and kept.

The second sock is drawn from the drawer.

The total number of the event will be

Total event = 9

Then the probability that they are both white will be

P = (3/9) (2/8)

P = (1/3)(1/4)

P = 1/12

P = 0.0833

P = 8.33%

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The probability of drawing two white socks from the drawer is 2/27.

To find the probability that both socks drawn are white, we need to find the probability of drawing a white sock on the first draw and then drawing another white sock on the second draw.

There are a total of 9 socks in the drawer (4 black, 3 white, and 2 red).

The probability of drawing a white sock on the first draw is 3/9 (3 white socks out of 9 total socks).

After replacing the first sock, the total number of socks remains the same, but the number of white socks decreases to 2. So the probability of drawing a white sock on the second draw is 2/9.

Now, to find the probability of both events happening, we multiply the probabilities together: P(First white sock) * P(Second white sock) = (3/9) * (2/9) = 6/81 = 2/27.

Therefore, the probability that both socks drawn are white is 2/27.