What are the exact values of a and b ?

CORRECT ANSWER

PROVIDE EXPLANATION

Mary paid $3.80 per pound and Mark paid $4.00 per pound.

19 ÷ 5 = 3.80

16 ÷ 4 = 4

Mary's unit rate is less than Mark's unit rate.

To compare the unit rate of Mary and Mark, we need to find how much each of them paid per pound of grapes.

Mary paid $19 for 5 pounds of grapes, so her unit rate can be calculated as:

The unit rate of Mary = Total cost of grapes / Total amount of grapes purchased

= $19 / 5 pounds

= $3.80 per pound

Mark paid $16 for 4 pounds of grapes, so his unit rate can be calculated as:

The unit rate of Mark = Total cost of grapes / Total amount of grapes purchased

= $16 / 4 pounds

= $4.00 per pound

Comparing the unit rate of Mary and Mark, we can see that Mary paid less per pound of grapes than Mark did.

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1) The equation of a line of best fit is; y = -1.15x + 102.8

2) The predicted monthly cost for an average temperature of 25°F is $74.05

The equation of a line of best fit is represented by the equation;

y = mx + c

where;

m is the slope

c is the y-intercept

1. To calculate the slope here, we will use the formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

Using two coordinate points on the scatter plot, (72, 20) and (20, 80), we have the slope as;

Slope (m) = (80 - 20)/(20 - 72)

Slope = 60/-52

Slope = -1.15.

Plug in -1.15 for m and (a, b) = (72, 20) into the formula; y = mx + c to get;

20 = -1.15(72) + c

c = 20 + 82.8

c = 102.8

The equation  will now be;

y = -1.15x + 102.8

2. Monthly heating cost, y, for a month with an average temperature of 25°F (x) will be calculated by plugging in 25 for x in the equation of line of best fit gotten earlier to get;

y = -1.15(25) + 102.8

y = 102.8 - 28.75

y = $74.05

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Answer:

35ft squared

Step-by-step explanation:

First lets try solving the rectangular middle part

Width is 3 ft

Height is 5ft + 4ft = 9ft

3*9ft= 27ft. This is area of middle rectangular section

For the triangle, we subtract 3 from the rectangle from 11ft and divide by 2 because the two triangle on the edges are the same.

11-3=8

8/2=4

Triangle area formula = Base*Height / 2

4*4/2

16/2

4ft squared

and the other triangles area is also 4ft squared because they are congruent. So you add all the sections of the area up

27ft+4ft+4ft=35ft squared

35ft squared is the answer.

Hope this helps :)

Answer:

Step-by-step explanation:

-1 +2=1

2+2=4

5+1=6

Answer:

Diameter = 33 feet

Step-by-step explanation:

Diameter = 2 x radius

Given that the volume = 18174 [tex]ft^{3}[/tex], then;

Volume of sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]

where r is the radius of the sphere.

Thus,

18174 = [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]r^{3}[/tex]

         = [tex]\frac{88}{21}[/tex] [tex]r^{3}[/tex]

18174 x 21 = 88 [tex]r^{3}[/tex]

381654 = 88 [tex]r^{3}[/tex]

[tex]r^{3}[/tex] = [tex]\frac{381654}{88}[/tex]

   = 4336.9773

r = [tex]\sqrt[3]{4336.9773}[/tex]

r = 16.3078

The diameter of the sphere = 2 x 16.3078

                                              = 32.6156

                                              = 33 feet

Answer:

a) 15m²

b) 750cm³

Step-by-step explanation:

(3+2)/2=5/2=2.5

2.5x6=15

a) 15m²

1/20=x/15

15=20x

x=15/20

x=3/4 = 0.75

1 liter is 1000cm³

1000x0.75

b) 750cm³

Answer:

  (b)  No solution

Step-by-step explanation:

You want the solution to 0.5(-2+ 4d) - 2d = -13.

Eliminating the parentheses using the distributive property, we have ...

  -1 +2d -2d = -13

Collecting terms gives ...

  -1 = -13 . . . . . false

No value of d will make this true. There is No Solution.

On solving the provided question, we can say that - the percentage value of 12 % of 90 = 10.8

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

12% of 90 = 12/100 X 90

= 0.12 X 90 = 10.8

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Answer:

B

[tex]circumference = \pi \: d \\ = 3.14 \times 20 \\ = 62.8 \: inches[/tex]

Answer:

Step-by-step explanation:

Y WILL BE 11 THATS ALL I KNOW

Answer:

(x+6)^2 + (y-4)^2=36

Step-by-step explanation:

E2020

Answer:

-5/4

Step-by-step explanation:

slope(m)= y2-y1/x2-x1

from the graph 5-0/-2-2

=5/-4

answer = -5/4

Answer:

7. x = 37.5

8. x = 8

Step-by-step explanation:

7. The sides of the triangles are proportional, therefore:

x/20 = (46 - 16)/16

x/20 = 30/16

Cross multiply

x*16 = 30*20

16x = 600

Divide both sides by 16

x = 600/16

x = 37.5

8. The sides of the triangles are proportional. Therefore,

(7x - 1)/22 = (3x + 1)/10

Cross multiply

10(7x - 1) = 22(3x + 1)

70x - 10 = 66x + 22

Collect like terms

70x - 66x = 10 + 22

4x = 32

4x/4 = 32/4

x = 8

Answer:

10/50 = 20/100

Step-by-step explanation:

Another way to represent this formula is:

[tex]\frac{is}{of} = \frac{percent}{100}[/tex]

Allow me to explain this to you.

What is 20% of 50?

"WHAT IS"

"20% (PERCENT)"

"OF 50"

[tex]\frac{x}{50} =\frac{20}{100}[/tex]

The variable, x, was used to replace the unknown value, which is 10.

Answer:

x = -8

Step-by-step explanation:

3x + 15 - 8 - 9x = 55

(3x+−9x)+(15+−8)=55(Combine Like Terms)

−6x+7=55

−6x=48

x=−8

Answer:$5.07

Step-by-step explanation:you are welcome

Brendon paid $5.075 in total.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

Given that, Brendon bought an iced tea that cost $4.06 plus 7% sale tax if Brandon left on 18% tip on the $4.06

The total he pay =

= 7% of 4.06 + 18% 0f 4.06 + 4.06

= 0.2842+0.7308+4.06

= 5.075

Hence, Brendon paid $5.075 in total.

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Answer:

9 over 12 and 20 over 12.......

Answer:

The decision rule for rejecting the null hypothesis is [tex]t < -1.721[/tex]

Step-by-step explanation:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is believed that the machine is underfilling the bags.

At the null hypothesis, we test if the mean weight of the bag is the desired value of 410, that is:

[tex]H_0: \mu = 410[/tex]

At the alternate hypothesis, we test if the bag is underfilled, that is, the mean weight is below the desired value, so:

[tex]H_0: \mu < 410[/tex]

Type of test:

As we test if the mean is less than a value, we have a left-tailed test.

We have the standard deviation for the sample, which means that the t-distribution is used.

We have 22 - 1 = 21 degrees of freedom, with a level of significance of 0.05.

Using a calculator, the critical value is [tex]t_c = -1.721[/tex]

Determine the decision rule for rejecting the null hypothesis.

We reject the null hypothesis if the test statistic is less than the critical value, so the decision rule for rejecting the null hypothesis is [tex]t < -1.721[/tex]

Answer:

no f-ing clue

Step-by-step explanation:

On solving the provided question, we can say that 50 will therefore be the missing number in the odd numbers 2 5 10 x 2637.

A number that is odd is one that can't be partitioned flawlessly into matches. One remains after dividing an odd number by two. The numbers 1, 3, 5, 7, 9, 11, 13, and 15 are consecutively odd. While odd numbers cannot be divided in half, even numbers can. 3, 5, 7, 9, 11, 13, and 15 are unusual cases. Even numbers include 2, 4, 6, 8, 10, 12, and 14.

According to the given question:

Following the numbers 3, 5, 7, 9, 11, and 13, which are all odd numbers, the provided series moves on to 13.

Therefore,

After 37, there will be a break before 50.

50 will therefore be the missing number.

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On solving the provided question, we can say that in this function f(x) = /16/1224 x^2 + 7x/5 + 1.5 = > f(2) = 2234.2454

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

in this function

f(x) = /16/1224 x^2 + 7x/5 + 1.5

f(2) = 2234.2454

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Answer: -2, -3, and -4.

Step-by-step explanation:

The range is all the Y Values the graph uses, and the Y values range from -0.5 to -5.5, making every number in between those included.

Answer:

40 Post-it notes

Step-by-step explanation:

10/2 = 5 on the side that measures 10"

16/2 = 8 on the side that measures 16"

5 x 8 = 40 post-it notes

Answer:

40

Step-by-step explanation

area of whiteboard is [tex]160 inches^{2}[/tex]

area of post it is [tex]4 inches ^{2}[/tex]

160/4 is 40 post it notes

Step-by-step explanation:

Hamiltonian function, also called Hamiltonian, mathematical definition introduced in 1835 by Sir William Rowan Hamilton

Answer:

1.) True

2.) True

3.) False

4.) True

Hope this helps!

Answer:

When the leading coefficient is positive, the graph opens up. It means the vertex is its minimum.

When the leading coefficient is negative, the its vertex is its maximum.

In algebra, the vertex form of a quadratic equation is a way of expressing the equation in the form:[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola defined by the equation. The value of 'a' determines whether the parabola opens up or down and the value of 'h' and 'k' determine the position of the vertex on the coordinate plane.

For example, the standard form of a quadratic equation is:

[tex]y = ax^2 + bx + c[/tex]

To convert this to vertex form, you would first complete the square to get all the terms of x on one side of the equation and a constant on the other side. Then, you would put the equation in the form shown above.

So, given the equation [tex]y = 3x^2 + 6x - 4[/tex], we can complete the square to get:

[tex]y = 3(x^2 + 2x) - 4[/tex]

then rearrange it to

[tex]y = 3(x^2 + 2x + 1) -7 = 3(x+1)^2-10[/tex] which is in vertex form with vertex (-1,-10)

The vertex form of a quadratic function provides a convenient way to quickly identify the vertex of the parabola without having to complete the square every time.

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The correct question is:

Explain vertex form.