to pay for a concert ticket, Geoff needs to earn $135 in commissions. what must Geoff's sales total (s) for the week? Use the equation to solve
A. $13.50
B. $1350
C. $125
D. $145

Answer:

see below

Step-by-step explanation:

As you can see 5 - 3 = 2, 2 - 3 = -1 and -1 - 3 = -4 so the rule is subtract 3.

The series converges for all values of x, with a radius of convergence (R) equal to infinity.

To find the Taylor series expansion of the function f(x) = sin(x) centered at x₀ = 0, we can use the Maclaurin series representation of sin(x). The Maclaurin series for sin(x) is given by:

sin(x) = x - (x³ / 3!) + (x⁵ / 5!) - (x⁷ / 7!) + ...

To determine the Taylor series about x₀ = 0, we substitute x = (x - x₀) = x into the Maclaurin series:

sin(x) = x - (x³ / 3!) + (x⁵ / 5!) - (x⁷ / 7!) + ...

This yields the Taylor series expansion of sin(x) centered at x₀ = 0:

sin(x) = Σ (-1)ⁿ * (x²ⁿ⁺¹ / (2n+1)!)

The radius of convergence (R) of the series can be determined using the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms in a series is L, then the series converges if L < 1 and diverges if L > 1.

Let's apply the ratio test to the series:

|((-1)ⁿ⁺¹ * (x²⁽ⁿ⁺¹⁾⁺¹ / (2(n+1)+1)!)) / ((-1)ⁿ * (x²ⁿ⁺¹ / (2n+1)!))|

= |(-1) * (x²ⁿ⁺³ / (2n+3)!) * ((2n+1)! / (x²ⁿ⁺¹))|

= |(-1) * (x²ⁿ⁺³ / (2n+3)!) * ((2n+1)! / (x²ⁿ⁺¹))|

= |(-1) * x² / (2n+3)(2n+2)|

Taking the limit as n approaches infinity:

\(lim_{n- > oo}\) |(-1) * x² / (2n+3)(2n+2)| = |(-1) * x² / (2∞+3)(2∞+2)|

= |(-1) * x² / ∞²|

Since the limit of a constant divided by infinity is 0, we have:

\(lim_{n- > oo}\) |(-1) * x² / (2n+3)(2n+2)| = 0

Therefore, the series converges for all values of x. This means the radius of convergence (R) is infinite:

R = ∞

To summarize, the Taylor series expansion of sin(x) centered at x0 = 0 is given by:

sin(x) = Σ (-1)ⁿ * (x²ⁿ⁺¹ / (2n+1)!)

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In R3, the equation x²=202 represents a sphere.

In R3, the equation x²=202 represents a sphere.

What is R3? R3 refers to three-dimensional space, which is commonly referred to as Cartesian space or Euclidean space. It has three axes that are perpendicular to each other, resulting in the X, Y, and Z axes.

The number of dimensions in Cartesian space varies, with Rn representing space in n dimensions.

What is a sphere? A sphere is a three-dimensional geometric shape that is perfectly round and has a constant surface distance from its center to all points on its surface.

The surface area of a sphere is determined by squaring its radius and multiplying it by π(4πr²).

The volume of a sphere is calculated by cubing its radius and multiplying it by (4/3)π (4/3)πr³).

Therefore, in R3, the equation x²=202 represents a sphere.

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Answer:

10 pounds of barley

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

7*5=35

therefore, 2*5=10

Option B

Yes, because every value of x corresponds to exactly one y-value .

The solution is, Deryl should deposit $214.24 monthly.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

here, we have,

The amount required to support annual payments of $100,000 for 25 years can be computed using the amortization formula:

 A = Pr/(1 -(1+r)^-t) . . . .

where A is the annual payment,

P is the initial principal amount,

r is the annual interest rate

and t is the number of years.

Filling in the numbers, we can find P to be ...

 P = A(1 -(1 +r)^-t)/r = 100,000(1 -1.1268^-25)/.1268 ≈ 748,767.70

This we want to be the future value (S) of the series of 360 monthly payments (P) earning annual rate r. The sum of those payments is ...

 S = P((1+r/12)^360 -1)/(r/12)

Filling in the numbers and solving for P, we get ...

 748767.70 = P((1.01^360 -1)/0.01) = 3494.96413P

 P = 748767.70/3494.96413 ≈ 214.24

Deryl should deposit $214.24 monthly.

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The probability of selecting a green ball is \($\frac{10}{14}$\).

This can be calculated using the formula for probability,\($P(A) = \frac{n(A)}\)\({n(S)}$\), where n(A) is the number of favorable outcomes and n(S) is the total number of possible outcomes.

In this problem, there are three possible containers that can be selected. The first contains 8 red balls and 4 green balls, the second contains 2 red balls and 4 green balls, and the third contains 2 red balls and 4 green balls.

Therefore, the total number of possible outcomes is 14 (8 + 4 + 2 + 4 + 2 + 4).

The number of favorable outcomes is 10 (4 + 4 + 2).

Therefore, the probability of selecting a green ball is \($\frac{10}{14}$\)

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Answer: Simplify

Step-by-step explanation:

Answer:

1, 3, 7, 21

Step-by-step explanation:

1, 3, 7, 21

(The bolded is one factor and the other that is not bolded is another factor)

1 times 21 is 21

3 times 7 is 21

Answer:

18c-30d+36

Step-by-step explanation:

distribute

Answer:

18c-30d+36

Step-by-step explanation:

As the spacing between joists increases, the maximum span for any board size will B. decrease only. This is because the wider the spacing between joists, the more weight and pressure will be placed on the boards that are spanning the gap between them.

This means that the boards will need to be stronger in order to support the weight without bending or breaking.
If the boards are not strong enough, they may sag or bow under the weight, which can create safety hazards or damage to the structure. Therefore, it is important to use the appropriate board size and spacing between joists for any given application in order to ensure structural integrity and safety.
In summary, increasing the spacing between joists will result in a decrease in the maximum span for any board size, as the boards will need to be stronger in order to support the weight and pressure. It is important to choose the right board size and joist spacing to maintain the structural integrity and safety of the building or structure.

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Answer:

212.8

Step-by-step explanation:

add the decimals

For the given parabola y = ax² + k when passes through the points

(-1, 3) and (3, -13) , then the value of a = -2, and k =5.

As given in the question,

Given equation of the parabola is :

y = ax² + k

When parabola is passes through the points ( -1, 3) and ( 3, -13) we get,

For (x, y) = (-1, 3)

3 = a(-1)² +k

⇒ a + k = 3  __(1)

For (x, y) = ( 3, -13)

-13 = a(3)² +k

⇒9a + k = -13 __(2)

Subtract (2) from (1) to get the value of k we have,

a + k = 3

9a + k = -13

-8a  = 16

⇒ a = -2

k = 3 -a

⇒k = 5

Therefore, for the given parabola y = ax² + k when passes through the points (-1, 3) and (3, -13) , then the value of a = -2, and k =5.

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In a poll conducted by a certain research​ center, 1046 adults were called after their telephone numbers were randomly generated by a​ computer, and were able to correctly identify the random sampling.

Each sample has an equal chance of being chosen as part of the sampling technique known as random sampling. A randomly selected sample is intended to be a fair representation of the entire population.

In statistics, a simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. It is a procedure for randomly choosing a sample.

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Answer:

Step-by-step explanation:

n x 5

Answer:  E, A, D, C, B

Step-by-step explanation:

First, we need to get y alone. So we will add 7 to the side of the equation that has the 4y in it.

So the first one will be.

Add 7 to both sides of the equation.

Now the second one is

4y = 25 + 7  Because what you do to one side of the equation, you do to the other. So we add 7 to 25.

Then the 3rd one will be 4y = 32  because 25+7 is equal to 32. But we still have that 4y on the other side of the equation. So the next equation is 4y = 32.

The second to last step is Divide both sides by 4  because thats

how you isolate y. So once you divide both sides by 4. You will get 8. Leading you into the next and final step.

Y = 8

And thats how you do it!

Here is an equation that could represent Ted's total September costs:

C = 3600 + 1.50x, where C is the total September cost and x is the number of 16-ounce bags of coffee sold.

This equation takes into account the monthly fixed costs of $3600, as well as the cost of the coffee that Ted sells at $1.50 per 16-ounce bag. If you know the number of bags of coffee that Ted sold in September, you can use this equation to calculate his total September costs. In general, cost refers to the amount of money that is required in order to obtain something. For example, the cost of a product or service is the amount of money that you need to pay in order to purchase or receive it. The cost of something can also refer to the resources that are required to obtain or produce it, such as time, effort, or materials.

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Answer:

y=-1/2x+5

Step-by-step explanation:

5 is where the line crosses the y axis and the amount the slope goes down is -1/2

Answer:

The slope is 30, and the y-intercept is 75.

Step-by-step explanation:

Use two points from the table, and find the equation of a line given two points.

Point 1: (1, 105)

Point 2: (3, 165)

y = mx + b

slope = m = (y_1 - y_1)/(x_2 - x_1)

m = (165 - 105)/(3 - 1) = 60/2 = 30

y = 30x + b

Use point (1, 105) for x and y.

105 = 30(1) + b

105 = 30 + b

b = 75

y = 30x + 75

The slope is 30, and the y-intercept is 75.

Answer:

64.2

Step-by-step explanation:

Find the last side of the triangle using the Pythagorean theorem.

Solve the equation for c.

c=√1037

Find B.

The angle B can be found using the inverse sine function.

Substitute in the values of the opposite side to angle  

B and hypotenuse √1037 of the triangle.

B=arcsin(29/√1037)

B=64.23067237

The likelihood of finding that the sample mean is between 59,050 and 60,950 miles can be determined by calculating the probability using the normal distribution with a sample size of 90, a population mean of 60,000 miles, and a population standard deviation of 4,000 miles.

To find out the probability of getting a sample mean between 59,050 and 60,950, a simulator is used to determine the tread life of tires mounted on light-duty trucks that follows a normal probability distribution.

Here, the population mean is 60,000 miles and the standard deviation is 4,000 miles. The given sample size is 90.

We can use the formula for standardizing the score. The standardized score for the lower limit of 59,050 is -2.78, and that of the upper limit of 60,950 is 2.78. Now, we need to find the probability of getting the mean value between -2.78 and 2.78.

We can use the standard normal distribution table to find the value, which is 0.9950 for z = 2.78 and 0.0050 for z = -2.78. Hence, the required probability is 0.9900.

Therefore, the likelihood of finding that the sample mean is between 59,050 and 60,950, for a sample size of 90 tires, is 0.9900.

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Answer:

it's ¢.34

Step-by-step explanation:

a gallon has 16 cups

since there are two gallons that's 32

the price of the two gallons divided my 32 is how much each cup would be so 10.88/32 would be ¢.34

By hypothesis testing, The chef believes the complaint rate is less than 8%, when in fact it is not less than 8%. The chef continues to use the new recipe but experiences a large number of unsatisfied customers.

What does testing your hypotheses mean?

To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample.

               First, a hazy assumption about the parameter or distribution is made.

What is hypothesis testing, and how can it be used?

A statistician will test a hypothesis about a population parameter in a process known as hypothesis testing. The type of data used in the study and its purpose will determine the methodology the analyst uses.

                     The plausibility of a hypothesis is evaluated using sample data in a process known as hypothesis testing.

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However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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The x value of the solutions to the system is 4

From the question, we have the following parameters that can be used in our computation:

The graph

This point of intersection of the lines of the graph represent the solution to the system graphed

From the graph, we have the intersection point to be

(x, y) = (4, -2)

This means that

x = 4

Hence, the x value of the solutions to the system is 4

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Serena leans a 24-foot ladder against a 22.8-foot-tall building to climb on the roof is 71.8 degree.

Measurement of Angle:

The measurement of angles is done using basic geometric tools such as protractors and compasses. This tool helps to find precise measurements of angles. A protractor helps provide accurate measurements of angles, while compasses help construct angles. Angles are measured in three ways: degrees, radians, and revolutions.

According to the Question:

Suppose the measure of angle is θ, then we have

   Sinθ = 22.8/24

⇒ Sinθ = 0.95

Therefore,

θ = Sin⁻¹ (0.95)

  = 71.8 degree.

Therefore, Serena leans a 24-foot ladder against a 22.8-foot-tall building to climb on the roof is 71.8 degree.

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