Solve the formula 5x − 3y = 30 for y.

Mrs. Roger's class sold 21 soda bottles, and Mrs. Magoo's class sold 42 candy bars ,Mrs. Roger's class earned more money. Mrs. Roger's class earned $52.50, while Mrs. Magoo's class earned $50.40. Therefore, Mrs. Roger's class earned $2.10 more than Mrs. Magoo's class.

(a) Let x be the number of soda bottles sold by Mrs. Roger's class, and y be the number of candy bars sold by Mrs. Magoo's class. We can create a system of equations based on the information given:

Equation 1: 2.5x + 1.2y = 102.9 (the total amount earned by both classes)

Equation 2: x + y = 63 (the total number of items sold by both classes)

To solve for x and y, we can use substitution or elimination method. Using substitution, we can solve for x in Equation 2: x = 63 - y. Then we substitute this value of x in Equation 1:

2.5(63-y) + 1.2y = 102.9

Simplifying and solving for y, we get:

157.5 - 2.5y + 1.2y = 102.9

-1.3y = -54.6

y = 42

Substituting y=42 in Equation 2, we get:

x = 63 - y = 63 - 42 = 21

Therefore, Mrs. Roger's class sold 21 soda bottles, and Mrs. Magoo's class sold 42 candy bars.

(b) To find out which class earned more money, we can calculate the total earnings for each class:

Mrs. Roger's class: 2.5(21) = $52.50

Mrs. Magoo's class: 1.2(42) = $50.40

Mrs. Roger's class earned more money.

(c) Mrs. Roger's class earned $52.50, while Mrs. Magoo's class earned $50.40. Therefore, Mrs. Roger's class earned $2.10 more than Mrs. Magoo's class. This could be because the price per item for soda bottles was higher than for candy bars. Additionally, it's possible that the students in Mrs. Roger's class were more motivated to sell their items or had a larger network of potential buyers. The $2.10 difference may seem small, but it can add up over time and can make a difference in achieving the fundraising goals for the school.

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The solution is, the value of the variables are x = 40 and, y = 160.

Notice that "x" and "3x+20" are supplementary angles so their sum is 180°

(x) + (3x + 20) = 180

4x + 20 = 180

4x = 160

x = 40

To solve for "y", you have 2 options: either notice that "x" and "y-20" are supplementary angles so their sum is 180° or notice that "3x + 20" and "y - 20" are vertical angles so are equal to each other. I am going to solve using the first option because it is less work.

(x) + (y - 20) = 180°

40 + y - 20 = 180

y + 20 = 180

y = 160

Answer: x=40, y=160

The solution is, the value of the variables are x = 40 and, y = 160.

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complete question:

Find the value of each variable

Answer:

The trigonometric function that models the ocean tide for a period of 12 hours is f(x) = 6 sin (2πx/12).

Answer:

To break even the local arena must sell approximately 70,589 tickets. They would have a loss of $47625.

Step-by-step explanation:

The cost per night of the Icey blades contract can be expressed as a function of the gate receipts, with the flat cost added by 40% of all the gate receipts sold. This expression is shown below:

\(cost(x) = 60000 +0.4*x\)

Since each ticket costs $1.25, then the revenue of the arena can be shown as:

\(revenue(x) = 1.25*x\)

In order to break even the revenue must be equal to the cost, so:

\(revenue(x) = cost(x)\\1.25*x = 60000 + 0.4*x\\1.25*x - 0.4*x = 60000\\0.85*x = 60000\\x = \frac{60000}{0.85} = 70,588.24\)

To break even the local arena must sell approximately 70,589 tickets.

If the average attendance was 7500 per night, the profit would be:

\(profit = revenue(7500) - cost(7500)\\profit = 1.25*7500 - 60000 + 0.4*7500\\profit = 9375 - 60000 + 3000\\profit = -47625\)

They would have a loss of $47625

Answer:

m=4

Step-by-step explanation:

First get the equation in slope intercept form

y -4x =1

Add 4x to each side

y - 4x+4x = 4x+1

y = 4x+1

This is in the form

y = mx+b where m is the slope and b is the y intercept

The slope is 4

Parallel lines have the same slope

m =4

Answer:

50

Step-by-step explanation:

If YW bisects <XYZ then is twice as big as one of the bisected angles. So <XYZ = 50

Given are three vectors in set B.

To show that B is dependent

The determinant

Hence vectors are dependent

b) The given equation

Let us try parametrically

These 3 vectors are collinear and hence equation would be

c) Basis for B would be only 2 dimensional

i.e. any two vectors out of 3 form basis

The basis would be (1,0,1) and (0,1,2)

Answer:  you would need to cross the bridge 5 times

Step-by-step explanation:

costing a total of $42.50 for each option.

hope this helps

Answer: X = 6

Step-by-step explanation:

Answer: x = 6 beaues 3 + 5=  8 and 8-2 = 6 ezzz

Step-by-step explanation:

6 feet deep

height/length*width

11.94/2.6*1.4

Answer:

22:2

Step-by-step explanation:

First, you put the number of vanillas to the number of chocolates.

Answer:

x- intercept = - 8 , y- intercept = 4

Step-by-step explanation:

to find the x- intercept let y = 0 in the equation and solve for x

x - 2(0) = - 8

x - 0 = - 8

x = - 8 ← y- intercept

to find the y- intercept let x = 0 in the equation and solve for y

0 - 2y = - 8

- 2y = - 8 ( divide both sides by - 2 )

y = 4 ← y- intercept

Answer:4

Step-by-step explanation:

please brainliest

The quadratic function that represents the given graph is:

y = ¹/₂(x − 4)² - 1

The general form of a quadratic equation in Vertex Form is expressed as:

y = a(x − h)² + k,

where

(h, k) is the vertex.

From the given graph, we can see that the coordinates of the vertex is (4, -1). Thus, we have:

y = a(x − 4)² - 1

Looking at the four given options from Option A to Option D, we can deduce that only given option that gives us the coordinates of the quadratic curve vertex is option D.

Thus, we can conclude that the quadratic function that truly represents the given parabolic graph curve is:

y = ¹/₂(x − 4)² - 1

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Answer:

least to greatest: -16/32, -8/20, 3/5

Step-by-step explanation:

Hey there!

QUESTION #6.

3x = 27

DIVIDE 3 to BOTH SIDES

3x/3 =27/3

SIMPLIFY IT!
x = 27/3

x = 9

Therefore, the answer should be:

x = 9

QUESTION #7.

5x = 35

DIVIDE 5 to BOTH SIDES

5x/5 = 35/5

SIMPLIFY IT!
x = 35/5

x = 7

Therefore, the answer should be:

x = 7

QUESTION #9.
2x = 24

DIVIDE 2 to BOTH SIDES

2x/2 = 24/2

SIMPLIFY IT!

x = 24/2

x = 12

Therefore, the answer should be:

x = 12

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

K'(-2,-3), L'(-4,2), M(-3,0)

Step-by-step explanation:

If matrix transformation of ΔKLM, which has coordinates K(−2, 3),L(−4, −2), and M(−3, 0), for reflection across the x-axis. Then  the correct vertices of the image are K'(-2,-3), L'(-4,2) and M(-3,0).

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

Transformation of ΔKLM, which has coordinates K(−2, 3),L(−4, −2), and M(−3, 0),

As the triangle undergoes a reflection through x axis, the x coordinate will remain same but the y coordinate value will change with sign.

The vertices after transformation will be K'(-2,-3), L'(-4,2) and M(-3,0)

Hence the correct vertices of the image will be K'(-2,-3), L'(-4,2) and M(-3,0).

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Answer:

1.099 * 10^-8 ; 4.23 * 10^-5 ; 0.0036

Step-by-step explanation:

Given :

p = 0.6

Sample size, n = 20

P(x = 0)

Using binomial distribution formula :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

1 - p = 1 - 0.6 = 0.4

P(x = 0) = 20C0 * 0.6^0 * 0.4^20

P(x = 0) = 1 * 1 * 1.099511627776E−8

P(x = 0) = 1.099 * 10^-8

2) Exactly 3;

P(x = 3) = 20C3 * 0.6^3 * 0.4^17

P(x = 3) = 1140 * 0.216 * 0.00000017179869184

P(x = 3) = 0.0000423037098786816

P(x = 3) = 4.23 * 10^-5

3.) More than 17

P(x > 17) = P(x = 18) + P(x = 19) + P(x = 20)

Using calculator :

P(x > 17) = 0.0036

Step-by-step explanation:

\( \frac{3}{4} \div \frac{1}{2} \)

\( \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} \)

\( \frac{6}{4} = 1.5\)

Answer:

it shall be 6/4  

Step-by-step explanation:

HAve you heard of reciprocal? here's a example. (btw i recommond that you should search up what reciprocal means)

So bascilly you will turn the second number/ frcation around so for example :

3/5 divided by 4/5

      will turn into

reciprocal : 3/5 times 5/4

So to answer your question

3/4 divided by 1/2

will turn into

3/4 times 2/1

6/4  or 1 1/2 ( as a mixed number) or 3/2 ( as a reduced fraction)

hopefully this helps !

Answer:

Step-by-step explanation:

372 Millimeters

Answer:

2,300 millimeters

Step-by-step explanation:

when you convert 30 centimeters it’s 300 millimeters. When you convert 2 meters it’s 2,000 millimeters so…. That is the correct answer plus I just did the quiz and got it correct with that answer.

answer/explanation:

hope this helps

Answer:

\(P(7000<\bar X<7500)\)

And we can use the z score formula to solve this problem

\(z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\)

And replacing we got:

\( z = \frac{7000-7200}{\frac{1200}{\sqrt{30}}}= -0.913\)

\( z = \frac{7500-7200}{\frac{1200}{\sqrt{30}}}= 1.369\)

And we can find this probability with the normal standard distribution and with this difference:

\(P(-0.913<z<1.369)=P(z<1.369)-P(z<-0.913)= 0.9145 -0.1806= 0.7339\)

Step-by-step explanation:

Let X the random variable that represent the daily revenue of a population, and for this case we know the distribution for X is given by:

\(X \sim N(7200,1200)\)  

Where \(\mu=7200\) and \(\sigma=1200\)

We are interested on this probability

\(P(7000<\bar X<7500)\)

And we can use the z score formula to solve this problem

\(z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\)

And replacing we got:

\( z = \frac{7000-7200}{\frac{1200}{\sqrt{30}}}= -0.913\)

\( z = \frac{7500-7200}{\frac{1200}{\sqrt{30}}}= 1.369\)

And we can find this probability with the normal standard distribution and with this difference:

\(P(-0.913<z<1.369)=P(z<1.369)-P(z<-0.913)= 0.9145 -0.1806= 0.7339\)

 32

45

x6

Step-by-step explanation: 32

5

x6

9

=

32

45

x6

Answer: Its EB≅CB

Step-by-step explanation: I took the test

To determine the value of the exponential function:

we use the first values from the table and plug them in the expression for the function:

Therefore the base of the exponent function is 9

Step-by-step explanation:

Putting values

A = - 7(15 + 9)

A = - 7(24)

A = - 168

Answer:

17t+9

Step-by-step explanation: