A recipe for 12 servings of soup calls for 8 cups of chicken broth. How
many cups of broth are needed to make 30 servings of the soup?

Answer:

b

Step-by-step explanation:

Answer:

For this set of numbers, we have a range of 82, a mean of 145, a variance of 618.86 and a standard deviation of 24.88.

Step-by-step explanation:

1. Let's find the range for the set of numbers given:

Don't forget that range is a measure of dispersion and is the difference between the lowest and highest values in this set of numbers.

Range = 193 - 111

Range = 82

2. For calculating the standard deviation, we should calculate first the mean and the variance, this way:

Mean = Sum of all the terms / Number of the terms of the set

Mean = (111 + 122 + 134 + 146 + 150 + 159 + 193)/ 7

Mean = 1,015/7

Mean = 145

Now, we proceed to calculate the variance this way:

Variance= Sum of the squared distances of each term in the set from the mean/ Number of terms of the set or sample

Let's calculate the squared distances of each term in the set from the mean:

111 - 145 = - 34 ⇒ - 34² = 1,156

122 - 145 = - 23 ⇒ - 23² = 529

134 - 145 = - 11 ⇒ - 11² = 121

146 - 145 = 1 ⇒ 1² = 1

150 - 145 = 5 ⇒ 5² = 25

159 - 145 = 14 ⇒ 14² = 196

193 - 145 = 48 ⇒ 48² = 2,304

Now replacing with the real values:

Variance = (1,156 + 529 + 121  1+ 25 + 196 + 2,304)/7

Variance = 4,332/7

Variance = 618.86 (Rounding to two decimal places)

Finally, we can calculate easily the standard deviation:

Standard deviation = √Variance

Standard deviation = √ 618.86

Standard deviation = 24.88 (Rounding to two decimal places)

Answer:

Dimension of box:-

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

                 [tex]500=x^2y[/tex]

Therefore, [tex]y=\dfrac{500}{x^2}[/tex]

It is open box. The surface area of box, S .

[tex]S=x^2+4xy[/tex]

Put  [tex]y=\dfrac{500}{x^2}[/tex]

[tex]S(x)=x^2+\dfrac{2000}{x}[/tex]

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

[tex]S'(x)=2x-\dfrac{2000}{x^2}[/tex]

For critical point, S'(x)=0

[tex]2x-\dfrac{2000}{x^2}=0[/tex]

[tex]x^3=1000[/tex]

[tex]x=10[/tex]

Put x = 10 into [tex]y=\dfrac{500}{x^2}[/tex]

y = 5

Double derivative of S(x)

[tex]S''(x)=2+\dfrac{4000}{x^3}[/tex] at x = 10

[tex]S''(10) > 0[/tex]

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²

Answer: 1/3

Step-by-step explanation:

5/15 divided both by 5 is 1/3

Answer:

5/6

Step-by-step explanation:

Add the fractions by finding the common denominator.

1/2 + 1/3

3/6 + 2/6

5/6

Answer:

The prepaid phone plan will have a steeper line and lower y-intercept.

I hope this is right

Step-by-step explanation:

prepaid phone plan y = .20x

contracted phone plan y = .02x + 50

The prepaid and the contracted plans are illustrations of linear functions, where the prepaid phone plan has a steeper line and lower y-intercept.

We have:

Prepaid

[tex]Rate = 0.20[/tex]

[tex]Monthly = 0[/tex]

Contracted

[tex]Monthly = 50[/tex]

[tex]Rate = 0.02[/tex]

For both plans, the cost function (y) is:

[tex]y =Monthly + Rate \times x[/tex]

Where:

[tex]x \to[/tex] Number of minutes

[tex]Rate \to[/tex] Steepness

So, we have:

Prepaid

[tex]y =0 + 0.20 \times x[/tex]

[tex]y =0.20x[/tex]

The y intercept (i.e. when x = 0) is

[tex]y = 0.20 \times 0 = 0[/tex]

Contracted

[tex]y = 50 + 0.02 \times x[/tex]

[tex]y = 50 + 0.02x[/tex]

The y intercept is:

[tex]y = 50 + 0.02 \times 0 = 50[/tex]

By comparing the steepness and the y-intercepts,

Hence, (a) is correct

See attachment for the graphs of both plans

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Answer:

The correct answer is A. f(x)= 2(3^x)

Step-by-step explanation:

The exponential function y = 2(3)ˣ, has an initial value of 2

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplicative rate of change

Given the exponential function y = 2(3)ˣ, has an initial value of 2

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Answer:

8/27  is the solution and the alternative form is 0.296 or 2/3 to the power of 3

Answer:

Step-by-step explanation:

The answer is 16

Answer:

Step-by-step explanation:

[tex]-15=(3x-10)-5x\\\\-15=3x-10-5x\qquad\text{combine like terms}\\\\-15=(3x-5x)-10\\\\-15=-2x-10\qquad\text{add 10 to both sides}\\\\-15+10=-2x-10+10\\\\-5=-2x\qquad\text{divide both sides by (-2)}\\\\\dfrac{-5}{-5}=\dfrac{-2x}{-2}\\\\2.5=x\to x=2.5[/tex]

Answer:

exact form x=5/2 decimal form2.5 mixed number form 2 1/2

Step-by-step explanation:

Answer:

Infinitely many solutions

Step-by-step explanation:

-6(4x+3)=6(-4x-3)

-24x-18=-24x-18

infinitely many solutions

Answer:

Step-by-step explanation:

2 • (xy - 4cs)

Final answer:

The probability of rolling an even number on a 9-sided die is 4/9.

Explanation:

To find the probability of rolling an even number on a 9-sided die, we need to determine the number of favorable outcomes (even numbers) and divide it by the total number of possible outcomes.

In this case, there are 4 even numbers on the die: 2, 4, 6, and 8. The total number of possible outcomes is 9 (since there are 9 sides on the die).

Therefore, the probability of rolling an even number is 4/9.

Answer:

343

Step-by-step explanation:

-(-7^3)=-(-7*-7*-7)=-(-343)=343

Answer:

Step-by-step explanation:

-(-7 to the power 3)

=-(-7×-7×-7)= -(-343)

=343

Answer:

Train b is moving faster than a by 45 units an hour

Step-by-step explanation:

The solution to the system of equations is (3,1)

Step-by-step explanation:

The system of equations represented by graph are:

[tex]y=4-x\\y=x-2[/tex]

Solving the system of equations

Let:

[tex]y=4-x\,\,\,eq(1)\\y=x-2\,\,\,eq(2)[/tex]

Putting value of y from eq(2) into eq(1):

[tex]x-2=4-x\\Simplifying:\\x+x=4+2\\2x=6\\x=6/2\\x=3[/tex]

So, Value of x = 3

Putting value of x into eq(2)

[tex]y=x-2\\y=3-2\\y=1[/tex]

So, value of y= 1

So, The solution to the system of equations is (3,1)

Keywords: System of equations

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Answer:

33

Step-by-step explanation:

9+2=1/3x

11=1/3x

x=11/(1/3)=(11/1)(3/1)=33/1=33

Answer:

23,490

Step-by-step explanation:

10% = 0.1

234900 x 0.1 = 23490

Answer:

[tex]0.5a[/tex]

Step-by-step explanation:

We have been given a trigonometric function [tex]g(a)=7.6\text{ cos}(0.5a)[/tex]. We are asked to find the argument of the cosine function.

We know that a trigonometric equation is solved for an unknown angle and that unknown angle is known as the argument of the trigonometric function. For example: [tex]\text{cos}(\theta)=0[/tex]. In this equation [tex]\theta[/tex] is the argument of the equation.

Upon looking at our given function, we can see that [tex]0.5a[/tex] is the argument.

The coordinates of the image after dilation are

A (-12 , -12) , B (6 , -3) , C (3 , 3) ⇒ answer B

Step-by-step explanation:

A dilation is a transformation that produces an image that is the

same shape as the original, but in a different size

When you dilate a figure, with

Then the coordinates of each point of the figure is multiplied by k

to find the image of the figure after dilation

∵ ABC has coordinates of A (-8 , -8), B (4 , -2), and C (2 , 2)

∵ ABC is dilated by scale factor 1.5

∵ The center of dilation is the origin

- Multiply the coordinates of points A, B, and C by 1.5

∴ The image of point A = (-8 × 1.5 , -8 × 1.5) = (-12 , -12)

∴ The image of point B = (4 × 1.5 , -2 × 1.5) = (-6 , -3)

∴ The image of point C = (2 × 1.5 , 2 × 1.5) = (3 , 3)

The coordinates of the image after dilation are

A (-12 , -12) , B (6 , -3) , C (3 , 3)

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Answer:

[tex]1000-40x>400[/tex]

Step-by-step explanation:

Let's call B the balance of Jacob's checking account. Each week he withdraws $40 from his actual balance of $1000, so if x is the number of weeks, the account's balance is

B=1000-40x

The balance must be more than $400, which means

[tex]1000-40x>400[/tex]

That is the inequality to model the situation. If we wanted to know the limit for x, we can solve the inequality. Operating:

[tex]1000-400>40x[/tex]

600>40X

[tex]x<\frac{600}{40}[/tex]

Or x<15

Which means Jacob can withdraw $40 14 times at most to maintain the minimum balance requirement

Answer:

400

Step-by-step explanation:

0.30 * x = 240

x = 240/0.30 = 800

0.50 * 800 = 400

Answer:

The value of 50 % of number is 400  .

Step-by-step explanation:

Given as :

Let The number be x

According to statement

30 percent of a number is 240

I.e 30 % of x = 240

Or, [tex]\frac{30}{100}[/tex] × x = 240

Or, 0.3 × x = 240

So.  x = [tex]\frac{240}{0.3}[/tex]

∴     x = 800

SO, The number is 800 .

Now again 50 percent of that number = y

I.e y = 50 % of x

or, y =  50 % of 800

Or, y =  [tex]\frac{50}{100}[/tex] × 800

Or, y = 0.5 × 800

∴    y = 400

Hence The value of 50 % of number is 400  . Answer

Answer:

[tex]\displaystyle 6x + y = 4[/tex]

Step-by-step explanation:

In the Linear Standard Formula [Ax + By = C], C represents the y-intercept, and since the instructions say "parallel line", you keep your '6' the same, and just alter 5 to 4.

* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], which was why 6 remained the way it was.

I am joyous to assist you anytime.

Answer:

slope = - 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (6, - 3)

m = [tex]\frac{-3-5}{6+2}[/tex] = [tex]\frac{-8}{8}[/tex] = - 1

Answer:

the object would weigh 18.36

since it is 1.2 times as much you multiply the weight of the object on earth by 1.2 and that's the answer

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

125 - 75= 50

50 ÷ 125 = 0.4

0.4 = 40%

Answer:M=24

Step-by-step explanation:

There are 2 ways to do this

---------------------------------------------------

Method 1) Divide both sides by 25, then add 2 to both sides

25(M-2) = 650

M-2 = 650/25

M-2 = 26

M = 26+2

M = 28

---------------------------------------------------

Method 2) Distribute the 25 through to each term inside the parenthesis. Then isolate for M by adding 50 to both sides, and then dividing both sides by 2.

25(M-2) = 650

25M - 50 = 650

25M = 650+50

25M = 700

M = 700/25

M = 28

---------------------------------------------------

Answer:

y = c/z²  

Step-by-step explanation:

(1) y ∝ 1/x²or

   y = a/x² where a is a constant

   x ∝ z or x = bz, where b is a constant

Substitute x into (1)

y ∝ a/(bz)² = a/(b²z²) = (a/b²)/z²

a is a constant and b is a constant, so a/b² is a constant.

Let c = a/b². Then

y = c/z²

Answer:

=3

Step-by-step explanation:

Okay so you 1/2 divided by 1/6

Answer:

3

Step-by-step explanation:

1/2÷ 1/6

=  

1/2×6/1

=  

1 × 6

2 × 1

=  

6/2

=  

6 ÷ 2

2 ÷ 2

=  3

Just Divide 1/6 by 1/2