A self-serve frozen yogurt store sells servings up to 12 ounces. It charges $0.50 per ounce for a serving between 0 and 8 ounces, and $4 for any serving greater than 8 ounces and up to 12 ounces.


Build the function that models the relationship between the price p(w) and of the weight w of a serving of yogurt.

Answer: Option 2 is correct Y= -2x+1/2

Step-by-step explanation:

The solution is Option 2.

The equation of line in the slope intercept form is y = -2x + 1/2

where m is the slope m = -2 and the y intercept is 1/2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

The value of A is given by

y - 5/2 = -2 ( x + 1 )

Now , the slope intercept of the equation of line is given by

Equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

So , on simplifying the equation , we get

y - 5/2 = -2 ( x + 1 )

y - 5/2 = -2x - 2

Adding 5/2 on both sides of the equation , we get

y = -2x - 2 + 5/2

y = -2x + ( -4 + 5 ) / 2

y = -2x + 1/2

The slope of the equation A is m = -2

The y intercept of the equation A is 1/2

Hence , The equation of line in the slope intercept form is y = -2x + 1/2

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Answer:

it will be 100

Step-by-step explanation:

Answer:

Step-by-step explanation:

8➗2=4

since 1/2 is divinding

The solution of the equation x^ay! + 5xy + (4 + x)y = 0, where x > 0, can be represented as a power series of the form y = ΣCnx^n, where C0 = 1 and Cn = 0 for n = 1, 2, 3, ...

To find the solution of the equation x^ay! + 5xy + (4 + x)y = 0, we can represent the solution as a power series expansion of the form y = ΣCnx^n, where Cn is the coefficient of x^n and n ranges from 0 to infinity. Plugging the power series into the equation, we get:

x^a*(ΣCnx^nn!) + 5x*(ΣCnx^n) + (4 + x)(ΣCn*x^n) = 0

We can then collect the terms with the same powers of x:

ΣCnx^(n+a)n! + Σ5Cnx^(n+1) + Σ(4 + x)Cnx^n = 0

For the equation to hold true for all powers of x, each term with the same power of x must be zero. Therefore, we can determine the coefficients Cn for each power of x. For n = 0, the term ΣCnx^a0! simplifies to C0x^a0! = C0*x^a. Since the equation must hold for all x > 0, the coefficient C0 must be non-zero. Therefore, C0 = 1. For n = 1, the term Σ5Cnx^2 simplifies to 5C1x^2 = 0. Therefore, C1 = 0. Similarly, for n = 2, 3, 4, ... , the terms involving Cn will also be zero, as they are multiplied by powers of x. Hence, the solution of the equation x^ay! + 5xy + (4 + x)y = 0 can be represented as y = C0x^a = x^a, where a is a positive real number, and the coefficients Cn are zero for n = 1, 2, 3, ....

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Answer:

he must score 32 points in the next game in order to average 14 points per game.

Step-by-step explanation:

14 x 6 = 84

84-(13+10+14+9+6)=32

checking:

32 + 13 + 10 + 14 + 9 + 6 = 84

84 divided by 6 = 14

Step-by-step explanation:

b = 42

c = 138

plz mark my answer as brainlist plzzzz if you find it useful .

The volume of the cylinder is 10,099.09 inches³.

Here we have to find the volume of the cylinder.

Given data:

Circumference = 46 inches

height(h) = 5 foot = 12 × 5 = 60 inches

Circumference = 2πr

46 = 2 ×π × r

r = 23/π

The formula for the volume of the cylinder = πr²h

Volume = π( 23/π)² 60

               = 529× 60 / π

               = 10,099.09 inches³

Therefore the volume is 10,099.09 inches³.

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Answer:

Step-by-step explanation:

1. Solve one of the equations for one of the variables. For example, if the system is:

x + 2y = 7

3x - 4y = -2

2. You could solve the first equation for x by subtracting 2y from both sides:

x = 7 - 2y

3. Substitute the expression for the variable you solved for in step 1 into the other equation. For example, substituting x = 7 - 2y into the second equation gives:

3(7 - 2y) - 4y = -2

4. Simplify and solve for the remaining variable. Using the example from step 2, you would simplify the equation as follows:

21 - 6y - 4y = -2

21 - 10y = -2

-10y = -23

y = 23/10

5. Substitute the value of the variable you found in step 3 back into one of the original equations to solve for the other variable. Using the example from step 1, you would substitute y = 23/10 into x = 7 - 2y:

x = 7 - 2(23/10)

x = -9/5

6. Check your solution by substituting the values you found for x and y into both of the original equations. If the values satisfy both equations, then you have found the correct solution.

x + 2y = 7 becomes (-9/5) + 2(23/10) = 7, which is true

3x - 4y = -2 becomes 3(-9/5) - 4(23/10) = -2, which is also true

Therefore, the solution to the system of equations is x = -9/5 and y = 23/10.

Answer:

y = 3/2x + 3/2

Step-by-step explanation:

Slope is rise over run, or 3/2

The y intercept is at 3/2.

y = 3/2x + 3/2

The simplified form of each of the given expressions as required is as follows;

a. -2 + 5 = 3

b. (−4) • (6) = -24

c. 4 − (−3) = 4 + 3 = 7

d. 10 + (−2) − 7 = 10 - 2 - 7 = 1.

e. −5 − 3(2 − 6) = -5 -3(-4) = -5 + 12 = 7.

f. (3 − 3)(102 − 11) = (0) (91) = 0.

It follows from the task content that the given arithmetic operations are to be simplified.

The PEMDAS guidelines which prescribe the order of mathematical operations is used for the computation.

where;

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

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Rewrite the root expressions as fractional exponents:

\(\dfrac{\sqrt[3]{7}}{\sqrt[5]{7}} = \dfrac{7^{1/3}}{7^{1/5}}\)

Recall that \(\frac{a^m}{a^n} = a^{m-n}\), so that

\(\dfrac{7^{1/3}}{7^{1/5}} = 7^{1/3 - 1/5}\)

Simplify the exponent:

\(\dfrac13 - \dfrac15 = \dfrac5{15} - \dfrac3{15} = \dfrac{5-3}{15} = \dfrac2{15}\)

Then you end up with

\(\dfrac{\sqrt[3]{7}}{\sqrt[5]{7}} = 7^{2/15}\)

Answer:

from the picture the answer is D.

Step-by-step explanation:

\(2 \ti4mes \f7rac{?}{?} \)

to find x subtract 18x from 4x which will give you -14x=-36

divide both sides by -14

Answer:

x = 21

Step-by-step explanation:

9/3 = 3

7 x 3 = 21

Answer:

x = 21

9/3 = 3

(3)(7) = 21

And I got the answer from my brain

Step-by-step explanation:

The value of x is equal to 6.2.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data based on the information provided above, we have the following;

Total data, F(x) = x + x + 3 + x - 5 + 2x + 3

Total data, F(x) = 5x + 1

Now, we can calculate the value of x as follows;

8 = (5x + 1)/4

32 = 5x + 1

5x = 32 - 1

x = 31/5

x = 6.2

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X(s)/F(s) = 7 / (s^2 + 5s + 10) => x''(t) + 5x'(t) + 10x(t) = 7f''(t) + 35f'(t) + 70f(t) (3)X(s)/F(s) = 15 / (s + 10)(s + 11) => x''(t) + 21x'(t) + 110x(t) = 15f(t) - 150f'(t) + 1650f''(t) (4)

The given transfer functions are as follows:X(s)/F(s) = 7 / (s^2 + 5s + 10) (1)X(s)/F(s) = 15 / (s + 10)(s + 11) (2)Differential equation is required for each transfer function. The given functions represent the response of the system X(s) to the input F(s).The corresponding differential equation for the first transfer function is given by the inverse Laplace transform of (1),X(s)/F(s) = 7 / (s^2 + 5s + 10) => L^-1 [X(s)/F(s)] = L^-1 [7 / (s^2 + 5s + 10)]=> x''(t) + 5x'(t) + 10x(t) = 7f''(t) + 35f'(t) + 70f(t)The differential equation of the second transfer function is given by the inverse Laplace transform of (2),X(s)/F(s) = 15 / (s + 10)(s + 11) => L^-1 [X(s)/F(s)] = L^-1 [15 / (s + 10)(s + 11)]=> x''(t) + 21x'(t) + 110x(t) = 15f(t) - 150f'(t) + 1650f''(t)The final answers are:X(s)/F(s) = 7 / (s^2 + 5s + 10) => x''(t) + 5x'(t) + 10x(t) = 7f''(t) + 35f'(t) + 70f(t) (3)X(s)/F(s) = 15 / (s + 10)(s + 11) => x''(t) + 21x'(t) + 110x(t) = 15f(t) - 150f'(t) + 1650f''(t) (4)

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The formula in cell B3 is "=C3-0.2*EXP(C3)". It calculates the value by subtracting 0.2 times the exponential value of C3 from C3.

The formula "=C3-0.2*EXP(C3)" is present in cell B3. This formula calculates a value based on the value in cell C3. It starts by computing the exponential value of C3 using the "EXP" function, which raises the mathematical constant "e" to the power of C3. Then, it multiplies the exponential value by 0.2. This product is subtracted from the value in cell C3. Therefore, the resulting value in cell B3 is obtained by subtracting 0.2 times the exponential value of C3 from C3 itself.

The purpose of this formula could vary depending on the context of the spreadsheet. However, based on the given information, it seems to be calculating the difference between the value in cell C3 and a modified version of C3. The modification involves subtracting a fraction of the exponential value of C3 from C3. This could be used, for example, to analyze the impact of an exponential decay factor (0.2 in this case) on the original value in C3. The resulting value in cell B3 represents the difference between the original value and the modified value.

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Answer in the picture below!

Answer:

well i cant answr it if i oont have more inforomartion

Step-by-step explanation:

Answer:

Step-by-step explanation:

if we add 11,36,61,... to the bottom we get bottom as a multiple of numerator.

Answer:i think is the fourth one or the fifth one.

Step-by-step explanation:

Answer:

california

Step-by-step explanation:

Step-by-step explanation:

\(80 \div 100 \times 30 = \\ = 0.8 \times 30 = \\ = 24\)

Answer:

y=-6.

Step-by-step explanation:

1) the condition f(-1)=-6 and f(4)=-6 mean points A and B have coordinates (-1;-6) and (4;-6);

2) the points A and B has the same y-coordinate, it means, the required line is parallel to the x-axis and the required function is: y=-6.

P.S. the suggested way is not the only one.

The linear function f is f(x) = -6.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(-1) = -6

f(4) = -6

The linear function f can be in the form of f(x) = mx + c.

Now,

m = (-6 + 6) / (4 - 1)

m = 0/3

m = 0

Now,

f(-1) = -6

x = -1

f(x) = mx + c

f(-1) = 0 x -1 + c

-6 = 0 + c

c = -6

Now,

f(x) = -6

Thus,

The function f is a constant function.

f(x) = -6

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The surface area generated by revolving the curve y=f(x) on the interval [a,b] about the y-axis is given by the formula:

2π∫[a,b] f(x)√(1+(f'(x))^2) dx

To find the surface area generated by revolving the curve y=f(x) about the y-axis on the interval [a,b], we need to use the formula for the surface area of a surface of revolution.

This formula is derived by dividing the curve into small segments of length dx and approximating the surface area of each segment as a frustum of a cone. The formula for the surface area of a frustum of a cone is:

dA = 2πr √(dr^2 + dz^2)

where r is the radius of the circular cross-section of the frustum, and dz is the height of the frustum.

Using calculus, we can express r and dz in terms of x and dx. The radius of the circular cross-section of the frustum is equal to f(x), and the height of the frustum is equal to dx. Therefore, we have:

r = f(x)

dz = dx

Substituting these values into the formula for the surface area of a frustum of a cone, we get:

dA = 2πf(x) √(1 + (f'(x))^2) dx

To find the total surface area generated by revolving the curve y=f(x) on the interval [a,b] about the y-axis, we need to integrate dA from a to b:

A = ∫[a,b] dA

= ∫[a,b] 2πf(x) √(1 + (f'(x))^2) dx

This is the formula for the surface area generated by revolving the curve y=f(x) on the interval [a,b] about the y-axis.

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Answer:

only Rodger

Step-by-step explanation:

Roger:

38*6=228

80+(20*6)=200

He will save 28 dollars with the membership

Grace:

38*4=152

80+(20*4)=160

Grace will pay 8 dollars more with the membership

Answer:

\(x=\frac{1+\sqrt{31}}{2},\:x=\frac{1-\sqrt{31}}{2}\)

Step-by-step explanation:

\(-> 0=2x^2-2x-15\)

-zeros means the solution aka x intercept, meaning y=0

\(x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:2\left(-15\right)}}{2\cdot \:2}\)

=> according to quadratic formula

\(x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

where \(ax^2+bx+c=0\)

=> \(x_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{31}}{2\cdot \:2}\)

simplify

\(x_1=\frac{-\left(-2\right)+2\sqrt{31}}{2\cdot \:2},\:x_2=\frac{-\left(-2\right)-2\sqrt{31}}{2\cdot \:2}\)

\(x=\frac{1+\sqrt{31}}{2},\:x=\frac{1-\sqrt{31}}{2}\)

Cannot simplify farther

The inverse Laplace transform of s² + 2s + 10 / (3s + 2) using the First Translation Theorem is (1/3) * \(e^{-2/3t\) * δ(t) + (2/3) * \(e^{-2/3t}\) + (10/3) * \(e^{-2/3t}\).

To evaluate L⁻¹{s² + 2s + 10 / (3s + 2)}, we can use the First Translation Theorem along with the known Laplace transforms for certain functions.

First, let's rewrite the expression in terms of a shifted variable:

L⁻¹{s² + 2s + 10 / (3s + 2)} = L⁻¹{(s² + 2s + 10) / (3(s + 2/3))}

According to the First Translation Theorem, for a function f(t) with Laplace transform F(s), we have:

L⁻¹{F(s - a)} = e^(at) * L⁻¹{F(s)}.

Now, let's apply the First Translation Theorem to the terms in the expression:

L⁻¹{s² / (3(s + 2/3))} = \(e^{-2/3t}\) * L⁻¹{(s²) / (3s)} = \(e^{-2/3t}\) * (1/3) * L⁻¹{s} = \(e^{-2/3t}\) * (1/3) * δ(t).

Here, δ(t) represents the Dirac delta function.

L⁻¹{2s / (3(s + 2/3))} = \(e^{-2/3t}\) * L⁻¹{(2s) / (3s)} = \(e^{-2/3t}\) * (2/3) * L⁻¹{1} = \(e^{-2/3t}\) * (2/3) * 1 = (2/3) * \(e^{-2/3t}\).

L⁻¹{10 / (3(s + 2/3))} = \(e^{-2/3t}\) * L⁻¹{10 / (3s)} = \(e^{-2/3t}\) * (10/3) * L⁻¹{1} = \(e^{-2/3t}\) * (10/3) * 1 = (10/3) * \(e^{-2/3t}\).

Finally, combining the results:

L⁻¹{s² + 2s + 10 / (3s + 2)} = (1/3) * \(e^{-2/3t}\) * δ(t) + (2/3) * \(e^{-2/3t}\) + (10/3) * \(e^{-2/3t}\).

Therefore, using the First Translation Theorem, the inverse Laplace transform of s² + 2s + 10 / (3s + 2) is (1/3) * \(e^{-2/3t}\) * δ(t) + (2/3) * \(e^{-2/3t}\) + (10/3) * \(e^{-2/3t}\).

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The margin of error of the 99% confidence interval is given as follows:

0.0549 = 5.49%.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The parameters for this problem are given as follows:

\(n = 143, \pi = \frac{10}{143} = 0.0699\)

Hence the margin of error is of:

M = 2.575 x sqrt(0.0699 x 0.9301/143)

M = 0.0549 = 5.49%.

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ok

Budget =< lights + DJ + business fee

$500 =< $125 + $100x + $75

solve for x

500 =< 200 + 100x

500 - 200 =< 100x

300 =< 100x

x =< 300/100

x =< 3

The maximum number of hours is 3