Mathematics High School

## Answers

**Answer 1**

For the professor's randomized controlled trial (RCT) to be valid, the following must be true: the **average** age of students in group B should be similar to group A, the average characteristics of the students in both groups should be **statistically** similar

In order for the professor's experiment to be a valid RCT, several **conditions** must be met. First, the average age of students in group B should be similar to group A, meaning that there should not be a significant statistical difference between the average ages of the two groups. While the actual average age may differ slightly, it should not be significantly different.

Second, the average characteristics of the students in both groups should be statistically similar. This ensures that any differences observed between the groups can be attributed to the treatment or **intervention** being tested, rather than inherent differences in the characteristics of the students.

Third, the professor must have randomly assigned students to the groups. **Random assignment** helps minimize selection bias and ensures that any differences observed between the groups are not due to systematic differences in the individuals assigned to each group.

Regarding the type of data collected in the RCT, the professor likely collected experimental data. An RCT involves intentionally manipulating an independent variable (in this case, group assignment) to observe its effect on a **dependent variable** (the outcome being measured). This differs from other types of data such as panel data (data collected from the same individuals over time), time series data (data collected over regular intervals), and observational data (data collected without intervention or control).

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## Related Questions

what is the post fix expression of the following infix expression? ( ( ( a 7 ) * ( b / c ) ) - ( 2 * d ) ) quizlet

### Answers

To convert** infix notation** to postfix notation, we use a set of steps involving scanning the infix expression and creating a stack and list. The resulting postfix expression can be evaluated using a stack-based algorithm.

The** postfix expression **for the given infix expression is:

a 7 b c / * 2 d * -

To convert an infix expression to postfix notation, we use the following steps:

1. Create an **empty stack** and a list to hold the postfix expression.

2. Scan the infix expression from left to right.

3. If the **token** is an operand (such as a variable or a number), add it to the postfix expression list.

4. If the token is a left parenthesis, push it onto the stack.

5. If the token is a right parenthesis, pop tokens from the stack and add them to the postfix expression list until a left parenthesis is encountered. Discard the left and right parentheses.

6. If the token is an operator, pop operators from the stack and add them to the postfix expression list if they have** higher precedence** than the current operator. Then push the current operator onto the stack.

7. After all tokens have been processed, pop any remaining operators from the stack and add them to the postfix expression list.

Using these steps on the given infix expression, we obtain the postfix expression:

a 7 b c / * 2 d * -

This postfix expression can be evaluated using a **stack-based algorithm** to compute the final result.

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You are solving a measurement problem where the numbers 2.09 Ã— 109 and 4.053 Ã— 10âˆ’4 are divided. how many significant digits should the quotient have? 4 3 2 1

### Answers

The **quotient **of the division between 2.09 × 10^9 and 4.053 × 10^(-4) should have three significant digits.

When performing **division**, the general rule for determining the number of significant digits in the result is to consider the **least number **of significant digits in the original values being divided. In this case, the value 4.053 × 10^(-4) has three significant digits, while 2.09 × 10^9 has only two significant digits. Therefore, we should limit the quotient to the same number of significant digits as the **divisor**, which is three.

It's important to note that significant digits represent the reliable and meaningful digits in a **measurement **or calculation. By adhering to the rules of significant digits, we can maintain accuracy and convey the appropriate level of precision in our calculated results.

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Multiply, if possible. Then simplify.

³√9 . ³√-81

### Answers

**Multiplying** and simplifying ³√9 . ³√-81 results in -9, as the cube root of -729 simplifies to -9.

Multiplying ³√9 by ³√-81, we obtain ³√(9 * -81), which simplifies to ³√-729.

Since -729 is a **perfect cube**, we can simplify the cube root. The cube root of -729 is -9 because -9 * -9 * -9 equals -729.

Therefore, the simplified **expression** is -9. Thus, the result of multiplying ³√9 by ³√-81 is -9.

The cube root of 9 multiplied by the cube root of -81 **simplifies** to the cube root of -729, which in turn simplifies to -9.

Therefore, the final answer is -9.

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Summarize how to use the discriminant to analyze the types of solutions of a quadratic equation.

### Answers

**Answer:**

If the discriminant is 0, the quadratic equation has one double real root.

If the discriminant is positive, the quadratic equation has two real roots.

If the discriminant is negative, the quadratic equation has two complex roots (no real roots).

Sketch each angle in standard position.

15°

### Answers

The angle of 15° in **standard** position can be sketched as a small angle formed by rotating a ray **counterclockwise** from the positive x-axis.

In** standard position**, an angle is formed by rotating a ray counterclockwise from the **positive x-axis**. The initial side of the angle is the positive x-axis, and the terminal side is the ray after rotation. To sketch the angle of 15°, start with the positive x-axis as the initial side. Then, rotate the ray **counterclockwise** by 15°. The terminal side of the angle will be the position of the ray after the **rotation**. The angle will be a small angle that opens up to the left of the initial side.

The **sketch** of the angle will resemble a small "tick" mark or an acute angle, pointing in the counterclockwise direction. The size of the angle will be 15°, which is **relatively** small, closer to the size of a right **angle** (90°). By following this process, you can **accurately** sketch the angle of 15° in standard position.

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Write each measure in radians. Express your answer in terms of π and as a decimal rounded to the nearest hundredth.The 24 lines of longitude that approximate the 24 standard time zones are equally spaced around the equator.

c. The radius of the Arctic Circle is about 1580 mi . About how wide is each time zone at the Arctic Circle?

### Answers

The **width** of each time zone at the Arctic Circle is about 413.6 miles. This is calculated by dividing the **circumference** of the Arctic Circle (2 * π * 1580) by the number of time zones (24). The answer is in radians and rounded to the nearest hundredth.

The circumference of the Arctic Circle is about 2 * π * 1580 = 9280π miles. The number of time **zones** at the Arctic Circle is 24. The width of each time zone is calculated by dividing the circumference of the **Arctic Circle** by the number of time zones:

width of each time zone = circumference / number of time zones

= 9280π / 24

= 386.66π

≈ 413.6 miles

The answer is in **radians** and rounded to the nearest hundredth.

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D. Name a point in the exterior of ∠C L H .

### Answers

A point in the **exterior** of ∠CLH is a point that is **outside** of the **angle** but still on the same plane as the angle.

One example of a **point** in the exterior of ∠CLH is point P.

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You buy 3.18 pounds of oranges 1.35 pounds of grapes and 1.72 pounds of apples what is your total bill

### Answers

Your total **bill** is approximately $**7.13**.

To calculate the **total bill**, we need to multiply the **weight** of each item by its respective price per pound and then sum up the individual **costs**.

Given the following prices:

Oranges: $1.09 per pound

Grapes: $1.19 per pound

Apples: We'll assume a price of $0.99 per pound for apples.

Let's calculate the total cost:

Cost of oranges = 3.18 pounds * $1.09 per pound = $3.4662 (rounded to two decimal places)

Cost of grapes = 1.15 pounds * $1.19 per pound = $1.3685 (rounded to two decimal places)

Cost of apples = 2.32 pounds * $0.99 per pound = $2.2968 (rounded to two decimal places)

**Total bill = Cost of oranges + Cost of grapes + Cost of apples **

= $3.4662 + $1.3685 + $2.2968

= $7.1315 (rounded to two decimal places)

Therefore, your total **bill** is approximately $**7.13**.

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Find the present value of the following ordinary annuities (see the Notes to Problem 4-12).

a. $400 per year for 10 years at 10%

b. $200 per year for 5 years at 5%

c. $400 per year for 5 years at 0%

d. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

(4-14) a. Find the present values of the following cash flow streams. The appropriate interest rate is 8%. (Hint: It is fairly easy to work this problem dealing with the individual cash flows. However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows such as the ones in this problem. This will take a little time, but the investment will pay huge dividends throughout the course. Note that, when working with the calculator’s cash flow register, you must enter

CF0 5 0. Note also that it is quite easy to work the problem with Excel, using procedures described in the file Ch04 Tool Kit.xlsx.) Year Cash Stream A Cash Stream B 1 $100 $300 2 400 400 3 400 400 4 400 400 5 300 100 b. What is the value of each cash flow stream at a 0% interest rate?

### Answers

The **present value** of ordinary annuities and cash flow streams, we need to apply the concept of **discounted** cash flows.

The present value represents the current worth of future cash flows, taking into account the time value of money and the specified interest rate. By discounting each cash flow to its present value and summing them up, we can determine the **present** value of the annuities and cash flow streams.

a. For the ordinary **annuity** of $400 per year for 10 years at 10%, we can use the formula for the present value of an ordinary annuity: PV = P * [1 - (1 + r)^(-n)] / r . **Substituting** the values, we have: PV = $400 * [1 - (1 + 0.10)^(-10)] / 0.10.

b. For the annuity of $200 per year for 5 years at 5%, we can use the same formula: PV = $200 * [1 - (1 + 0.05)^(-5)] / 0.05

c. For the annuity of $400 per **year** for 5 years at 0%, the interest rate is 0%, which means the present value is equal to the sum of the cash flows:

PV = $400 + $400 + $400 + $400 + $400 = $2,000

d. To rework parts a, b, and c as annuities due (payments made at the beginning of each year), we can multiply the present value obtained from the previous **calculations** by (1 + r) to account for the additional year of **compounding**.

For example, in part a: PV_annuity_due = PV * (1 + r). We can apply the same **adjustment** to parts b and c. Moving on to problem 4-14, to find the value of each cash flow stream at a 0% **interest** rate, we simply add up the cash flows without discounting them. For **cash stream** A, the value is $100 + $400 + $400 + $400 + $300 = $1,600. For cash stream B, the value is $300 + $400 + $400 + $400 + $100 = $1,600.

At a 0% interest rate, the present value is equal to the sum of future cash flows since there is no discounting applied.

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Complete each sentence.

60.yd= ___?___ft

### Answers

After **converting **60 yards into feet, the **solution **is,

⇒ 60 yards = 180 feet

We have to give that,

To **convert **60 yards into feet.

Since We know that,

1 yards = 3 feet

Hence, We can change 60 **yards **into feet,

1 yards = 3 feet

60 yards = 60 x 3 feet

60 yards = 180 feet

Therefore, The solution is,

60 yards = 180 feet

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Let rt denotes the return of a financial asset and σt denotes the standard

deviation of returns at time t. Suppose rt follows rt = µ + et with et = ztσt

where zt ∼ N(0, 1).

(a) Write down an ARCH(q) model with q=3 for σ2t .

(b) Write down an GARCH(q,p) model with q=1 and p=2 for σ2t .

(c) Derive the unconditional variances of the ARCH model in (a) (show all

necessary steps).

(d) Derive the unconditional variances of the GARCH model in (b) (show

all necessary steps).

(e) Discuss and compare the two ARCH-type models in (a) and (b).

### Answers

The ARCH(q) model in (a) represents the conditional variance of the asset returns at time t as a function of past squared error terms. The GARCH(q,p) model in (b) extends the ARCH model by incorporating both past squared error terms and past conditional variances in the equation for the **conditional variance**. The unconditional variances of both models can be derived by taking the **expectations** of their respective conditional variance equations.

In the ARCH(q) model, the conditional variance [tex]\sigma^2t[/tex] is given by [tex]\sigma^2t[/tex] = [tex]\alpha 0 + \alpha 1 e t - 1^2 + \alpha 2 et-2^2 + \alpha 3et-3^2[/tex], where et represents the standardized error term and [tex]\alpha 0, \alpha 1, \alpha 2, \alpha 3,[/tex] are the **model parameters**.

In the GARCH(q,p) model, the conditional variance [tex]\sigma^2t[/tex] is given by [tex]\sigma^2t[/tex] = [tex]\alpha 0 + \alpha1et-1^2 + \beta 1\sigma ^2t-1 + \beta 2\sigma^2t-2[/tex], where et represents the standardized error term, [tex]\alpha 0, \alpha 1, \beta 1, \beta 2[/tex] are the model parameters.

To derive the unconditional variances of the ARCH model in (a), we need to calculate the expectations of the squared error terms. Since [tex]et = zt\sigma t[/tex]and zt ∼ N(0,1), we have [tex]E(et^2) = E((zt\sigma t)^2) = E(zt^2)\sigma t^2 = \sigma t^2[/tex], where E(z[tex]t^2[/tex]) is the expected value of the **squared standard normal variable **zt. Therefore, the unconditional variance of the ARCH model is [tex]\sigma ^2t = \alpha 0 + \alpha 1 \sigma t^2 + \alpha 2 \sigma t^2 +\alpha3 \sigma t^2 = (\alpha0 + \alpha1 + \alpha2 + \alpha3)\sigma t^2.[/tex]

To derive the** unconditional variances** of the GARCH model in (b), we need to recursively substitute the **conditional variance **equation until it converges to a constant. This can be a complex process and involves solving equations iteratively.

In terms of comparison, the ARCH model in (a) only considers the squared error terms in the equation for the conditional variance, while the GARCH model in (b) incorporates both past squared error terms and past conditional variances. The GARCH model allows for more flexibility in capturing the persistence and volatility clustering of financial asset returns. However, estimating the GARCH model can be more computationally intensive due to the additional parameters. The choice between the two models depends on the specific characteristics of the financial data and the objectives of the analysis.

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the product of two numbers is 240. the first number is 8 less than the second number. which equation can be used to find x, the lesser number? x(x – 8)

### Answers

The **equation **that can be used to find x, the lesser **number**, is

(y - 8) * y = 240. And the two numbers can be 12 and 20 or

-12 and -20.

Let's assume the first number is x and the second number is y. According to the given information, the **product **of the two numbers is 240, so we have the equation xy = 240.

Additionally, it is stated that the first number is 8 less than the second number. This can be expressed as x = y - 8.

To find the equation that can be used to solve for x, we **substitute **the value of x from the second equation into the first equation:

(y - 8) * y = 240

This equation represents the relationship between the two numbers, where y is the greater number and y - 8 is the lesser number. By solving this equation, we can find the value of y and then calculate x as y - 8.

Now, let's solve the equation:

y² - 8y = 240

Rearranging the equation:

y² - 8y - 240 = 0

To solve this quadratic equation, we can factorize or use the **quadratic formula**. Factoring the equation, we have:

(y - 20)(y + 12) = 0

Setting each factor equal to zero, we have:

y - 20 = 0 or y + 12 = 0

Solving for y, we get:

y = 20 or y = -12

Since the first number (x) is 8 less than the second number (y), we have:

x = y - 8

Substituting the values of y, we get:

x = 20 - 8 or x = -12 - 8

Simplifying, we have:

x = 12 or x = -20

Therefore, the lesser number (x) can be either 12 or -20, depending on the context of the problem.

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Identify the period of each function. Then tell where two asymptotes occur for each function.

y=tanθ/4

### Answers

The period of the function is **4π** and the asymptote for this function is **Vertical asymptote**.

To identify the period of the given function, we have to find out it's **target function**. In case of tan, the target function is π as it repeats it's value every π units. So, for the given function, the period will be π multiplied by 4 (4π) as the function has argument θ/4.

Vertical asymptote occurs when the tangent function is **undefined**. This happens when cosine of an angle is equal to 0. The cosine function is zero at θ = (2n + 1)π/2. Therefore, the vertical asymptote occurs at (2n + 1)π/2 multiplied by 4 as the function has argument θ/4, which gives the result as (2n + 1)2π.

Therefore, The period of the function is 4π and the asymptote for this function is Vertical asymptote.

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Identify the equation as separable, linear, exact, or having an integrating factor that is a function of either x or y. (2y3 2y2)dx (3y2x 2xy)dy=0.

### Answers

The given equation (2y^3 + 2y^2)dx + (3y^2x + 2xy)dy = 0 is neither separable, **linear**, exact, nor does it have an integrating factor that is a function of either x or y.

To identify the equation as separable, linear, exact, or having an **integrating **factor that is a function of either x or y, let's analyze the given equation:

(2y^3 + 2y^2)dx + (3y^2x + 2xy)dy = 0

This equation is not **separable **because the terms involving x and y are mixed together.

It is also not linear because the variables x and y appear with powers greater than one.

To determine if it is exact, we need to check if the equation satisfies the condition ∂M/∂y = ∂N/∂x, where M and N represent the **coefficients **of dx and dy, respectively.

In our case, M = 2y^3 + 2y^2 and N = 3y^2x + 2xy. Let's calculate the partial **derivatives**:

∂M/∂y = 6y^2 + 4y

∂N/∂x = 3y^2

As we can see, ∂M/∂y is not equal to ∂N/∂x, so the equation is not exact.

To check if it has an integrating factor that is a function of either x or y, we can **compute **∂(N - M)/∂y and ∂(N - M)/∂x. If they differ only by a function of x or y, then an integrating factor exists.

∂(N - M)/∂y = (3y^2 - 6y^2 - 4y) = -3y^2 - 4y

∂(N - M)/∂x = 0

The two **expressions **above do not differ by only a function of x or y, indicating that an integrating factor that depends solely on x or y does not exist.

In summary, the given equation (2y^3 + 2y^2)dx + (3y^2x + 2xy)dy = 0 is neither separable, linear, exact, nor does it have an integrating factor that is a function of either x or y.

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A math teacher gives her class two tests. 60% of the class passes both tests and 80% of the class passes the first test. What percent of those who pass the first test also pass the second test?

a. What conditional probability are you looking for?

### Answers

The **percent** of those who pass the first test also pass the second test is 75%.

We are given that;

We know that 60% of the class passes both tests, so P(A and B) = 0.6. We also know that 80% of the class passes the first test, so P(A) = 0.8.

Now,

We are looking for the **conditional** probability of passing the second test given that a student has passed the first test.

We can use the **formula** for conditional probability:

P(B|A) = P(A and B) / P(A)

where A is the event of passing the first test and B is the event of passing the second test.

**Substituting** these values into the formula, we get:

P(B|A) = 0.6 / 0.8

P(B|A) = 0.75

Therefore, by **probability** the answer will be 75%.

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What is the measurement of the exterior angle 10x and interior angles 30 and 7x

### Answers

The measurement of the **exterior angle** 10 * 8.82 = 88.2 and **interior angles** 30 and 7 * 8.82 = 61.74

The **measurement** of the** exterior angle** 10x and **interior angles **30 and 7x

We know that,

The **sum **of an** exterior angle** of a **triangle **and its adjacent** interior angle **is 180 degrees.

10x + 30 + 7x = 180

17x + 30 = 180

17x = 180 - 30

17x = 150

x = 8.82

Therefore, the measurement of the **exterior angle** 10 * 8.82 = 88.2 and **interior angles** 30 and 7 * 8.82 = 61.74

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Simplify each expression. (x+4)(x+4)-3

### Answers

The simplified **expression** is x^2 + 8x + 13.

To simplify the expression (x+4)(x+4) - 3, we use the distributive property to expand the product of the **binomials **(x+4)(x+4):

(x+4)(x+4) = x(x+4) + 4(x+4) = x^2 + 4x + 4x + 16

Combining like terms, we have:

x^2 + 8x + 16

Next, we substitute this expression back into the **original** expression:

(x+4)(x+4) - 3 = (x^2 + 8x + 16) - 3

Simplifying further, we **subtract **3 from the expression:

x^2 + 8x + 16 - 3 = x^2 + 8x + 13

Therefore, the simplified expression is x^2 + 8x + 13.

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A. Find the measure of YZ if Y is the midpoint of XZ and X Y=2 x-3 and YZ=27-4x.

### Answers

The** measure **of YZ is 75. If Y is the midpoint of XZ and XY = 2x - 3 and YZ = 27 - 4x.

To find the** measure **of YZ

If Y is the** midpoint **of XZ and XY = 2x - 3 and YZ = 27 - 4x.

Y is the midpoint of XZ. So, XY and YZ is equal.

2x - 3 = 27 - 4x.

**Add 4x **on both side.

2x - 3 + 4x = 27 - 4x + 4x.

-2x - 3 = 27

**Add 3 **on both side.

-2x = 24.

x = - 12.

**Plug the** **value **of x in **YZ = 27 - 4x.**

YZ = 27 - 4* (-12).

YZ = 75.

Therefore, the measure of YZ if Y is the **midpoint** of XZ and XY = 2x - 3 and YZ = 27 - 4x is 75.

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Explain why the equation y²=x²+5 does not define y as a function of x.

### Answers

The equation y² = x² + 5 does not define y as a function of x because for a given value of x, there are two possible values of y. In other words, the equation does not pass the **vertical line test**, which is a criterion for a **relation **to be a function.

In a **function**, for every input value (x), there should be a unique output value (y). However, in the given equation, when we solve for y, we get both the positive and negative **square root** of (x² + 5). This means that for a single value of x, there are two possible values of y, resulting in a **non-unique mapping**.

For example, if we consider x = 4, plugging it into the equation gives us y² = 4² + 5, which simplifies to y² = 21. Taking the square root of both sides, we get y = ±√21. This implies that for x = 4, we have both y = √21 and y = -√21 as possible solutions.

Since there are **multiple possible** y-values for some x-values, the equation y² = x² + 5 does not define y as a function of x.

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Find the number of tiles each of 1m² area to pave a room of length 8m & breadth 4m ?

### Answers

Total area = length * breadth

= 8m * 4m

= 32 m²

Number of tiles needed

= Total area / 1m²

= 32m² / 1m²

= 32

hence, 32 tiles are needed

**Answer:**

**32 m² so 32 tiles**

**Step-by-step explanation:**

Find the number of tiles each of 1m² area to pave a room of length 8m & breadth 4m ?

you just have to find the area with the formula A=LxW and you have how many square meters you need

A = L x W

A = 8 x 4

**A = 32 m²**

Find the indefinite integral and check the result by differentiation. (use c for the constant of integration.) x(5x2 5)9 dx

### Answers

The** indefinite integral **of x(5x^2 - 5)^9 **dx** is:

(5x^2 - 5)^8 / 40 + c

We can find the **indefinite integral **using the following steps:

1. We can write the integral as (5x^2 - 5)^9 * x^1 dx.

2. We can use the power rule of integration, which states that the integral of x^n dx is x^(n + 1) / (n + 1) + c, where c is the constant of integration.

3. We can **simplify** the result and add the constant of integration.

The following is the step-by-step solution:

```

∫ x(5x^2 - 5)^9 dx = ∫ (5x^2 - 5)^9 * x^1 dx

= (5x^2 - 5)^9 / 9 + c

```

To check the result, we can **differentiate** the result and see if we get the original integral.

```

d/dx [(5x^2 - 5)^8 / 40 + c] = (5x^2 - 5)^8 * (10x) / 40 + 0 = x(5x^2 - 5)^8 = ∫ x(5x^2 - 5)^9 dx

```

As we can see, we get the** original integral **back. Therefore, the answer is correct.

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Consider the following cost function: C = 0.3q^3 - 5q^2 + 85q + 150. When output is 14 units, average cost is $. (Enter a numeric response using a real number rounded to two decimal places.) When output is 14 units, marginal cost is $. The output level where average variable cost equals marginal cost is units.

### Answers

When the output is 14 units, the average cost is $128.57. The marginal cost at that output level is $65.71. The output level at which **average **variable cost equals **marginal** cost is 9 units.

To find the **average cost**, we divide the total cost (C) by the output quantity (q). In this case, the cost function is given as [tex]C = 0.3q^3 - 5q^2 + 85q + 150[/tex]. When the output is 14 units, we substitute q = 14 into the cost function and calculate C. Dividing C by 14 gives us the average cost, which is approximately $128.57.

To calculate the marginal cost, we take the derivative of the cost **function **with respect to q. The** derivative **represents the rate of change of cost with respect to output. Evaluating the derivative at q = 14 gives us the marginal cost, which is approximately $65.71.

The average variable cost is the variable cost per unit of output. It represents the cost that varies with the level of production. To find the output level where average variable cost equals marginal cost, we need to equate the derivative of the cost function with respect to q to the average variable cost. However, the average variable cost is not given in the question. Without the specific value of the average **variable **cost, we cannot determine the output level at which it equals marginal cost.

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Find the range for the measure of the third side of a triangle given the measures of two sides.

3.8 in., 9.2 in.

### Answers

The **range **for the measure of the third side (x) of the triangle is such that x must be greater than 13. In other words, the length of the third side can be any value greater than 13 inches.

To find the range for the measure of the third side of a **triangle**, we can use the triangle inequality theorem. According to this **theorem**, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given the measures of two sides: 3.8 in. and 9.2 in.

Let's denote the third side as x. Applying the **triangle inequality theorem**, we have:

3.8 + 9.2 > x

Simplifying the inequality:

13 > x

Therefore, the range for the measure of the third side (x) of the triangle is such that x must be greater than 13. In other words, the length of the third side can be any value greater than 13 inches.

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Find a vector equation and parametric equations for the line segment that joins p to q. p(1, 0, 1), q(3, 2, 1)

### Answers

The vector **equation **for the line segment is r = (1 + 2t, 2t, 1), and the parametric equations are x = 1 + 2t, y = 2t, z = 1.

To find the vector equation and parametric equations for the line segment that joins point P(1, 0, 1) to point Q(3, 2, 1), we can use the following** formulas:**

Vector equation: r = p + t(q - p)

Parametric equations: x = p₁ + t(q₁ - p₁), y = p₂ + t(q₂ - p₂), z = p₃ + t(q₃ - p₃)

Substituting the given **values**, we have:

p₁ = 1, p₂ = 0, p₃ = 1

q₁ = 3, q₂ = 2, q₃ = 1

Vector equation:

r = (1, 0, 1) + t((3, 2, 1) - (1, 0, 1))

= (1, 0, 1) + t(2, 2, 0)

= (1 + 2t, 2t, 1)

**Parametric **equations:

x = 1 + 2t

y = 2t

z = 1

Therefore, the vector equation for the line segment is r = (1 + 2t, 2t, 1), and the parametric equations are x = 1 + 2t, y = 2t, z = 1.

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11. FIND THE INTEGER VALUES OF x WHICH SATISFY THE INEQUALITY

(a) -3<2x-1 ≤6

### Answers

**Answer:**

0 , 1 , 2 , 3

**Step-by-step explanation:**

- 3 < 2x - 1 ≤ 6 ( add 1 to each interval )

- 2 < 2x ≤ 7 ( divide each interval by 2 )

- 1 < x ≤ 3.5

the integer value between the 2 intervals are

x = 0 , 1 , 2 , 3

**Answer:**

**Step-by-step explanation:**

**To find the value of x in -3<2x-1≤6 we follow the steps as:**

**Step 1: Add one on both sides of the inequality as:**

** -3+1<2x-1+1≤6+1**

** we get -2<2x≤5**

**Step 2: Now we divide both sides by 2**

** we get -1<x≤2.5**

**step 3: Now write down all integers between -1 and 2.5**

** they are -1,0,1,2**

**Now since x is greater than -1 ;**

** therefore we do not include -1 in our answer.**

**Therefore the integer values of x that satisfy the given inequality are 0, 1 and 2.**

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Use a calculator to evaluate the function at the indicated

values. Round your answers to three decimals. f(x)= 9^x f(1/2) =

f(square root of 5)= f(-2)= f(0.4)=

### Answers

Evaluating the function f(x) = 9^x at different** values** yields the following results: f(1/2) ≈ _______, f(sqrt(5)) ≈ _______, f(-2) ≈ _______, and f(0.4) ≈ _______ (all rounded to three **decimal **places).

To evaluate the** function** f(x) = 9^x, we substitute the given values into the equation and calculate the results.

For f(1/2), we substitute x = 1/2:

f(1/2) = 9^(1/2) ≈ 3

For f(sqrt(5)), we substitute x = sqrt(5):

f(sqrt(5)) = 9^(sqrt(5)) ≈ 78.746

For f(-2), we **substitute** x = -2:

f(-2) = 9^(-2) ≈ 0.012

For f(0.4), we substitute x = 0.4:

f(0.4) = 9^(0.4) ≈ 2.297

Therefore, after evaluating the function at the given values, we find that f(1/2) is approximately 3, f(sqrt(5)) is approximately 78.746, f(-2) is approximately 0.012, and f(0.4) is approximately 2.297 (all rounded to three decimal places).

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Solve each inequality.

2-m ≈ 6 m-12

### Answers

The solution to the **inequality **is m ≥ 2.

To solve the inequality 2 - m ≤ 6m - 12, we'll follow these steps:

1. Simplify both sides of the inequality:

2 - m ≤ 6m - 12

Rearranging the terms, we have:

-m - 6m ≤ -12 - 2

Combining like terms, we get:

-7m ≤ -14

2. Divide both sides of the inequality by -7. Remember that when we divide by a **negative number**, the inequality sign must be **reversed**:

(-7m) / -7 ≥ (-14) / -7

**Simplifying**, we have:

m ≥ 2

So, the solution to the inequality is m ≥ 2.

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Evaluate the following expression if a=2,b=-3,c=-1, and d=4.

(2d - a) / b

### Answers

The **algebraic expressions **(2d - a) / b evaluates to -2 when a = 2, b = -3, c = -1, and d = 4. The correct answer is -2.

In this expression, we **substitute **the given values of a, b, c, and d into the expression and perform the necessary **calculations**.

**Given **that a = 2, b = -3, c = -1, and d = 4, we substitute these values into the **expression**:

(2(4) - 2) / (-3)

**Simplifying **further:

(8 - 2) / (-3)

= 6 / (-3)

= -2

Therefore, when a = 2, b = -3, c = -1, and d = 4, the **algebraic expressions **(2d - a) / b evaluates to -2.

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HELP ME PLEASE IM BEING TIMED

### Answers

The explicit formula for the given **sequence** is O_an = -3n + 12.

To determine the explicit **formula** for the given sequence, we need to analyze the relationship between the term numbers (n) and their corresponding values.

Looking at the values in the table, we can observe that the sequence seems to follow a pattern where each value is obtained by subtracting three times the term number from a constant.

Let's break down the **pattern**:

Term #1: Value 9

Term #2: Value 16

Term #3: Value 13

Term #4: Value -3

From Term #1 to Term #2, the value increases by 7 (16 - 9). From Term #2 to Term #3, the value decreases by 3 (13 - 16). Finally, from Term #3 to Term #4, the value decreases by 16 (−3 - 13). We notice that the change in the value depends on the term number.

By examining the pattern, we can determine that the explicit formula for the sequence is O_an = -3n + 12. This formula states that the nth term of the sequence is obtained by multiplying the term **number** (n) by -3 and then adding 12 to the result.

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Describe the similarities and differences of qualitative variables. What level of measurement is required for this type? (Select all that apply.) a-1. Qualitative variables. Interval level Ordinal level ロロロロ Ratio level Nominal level

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**Qualitative** variables, also known as categorical variables, represent characteristics or attributes that are not numerical in nature.The required level of measurement for qualitative **variables** is the nominal level.

Qualitative variables share similarities in that they both represent non-numerical characteristics or attributes. They describe qualities, characteristics, or categories rather than quantities. Examples of qualitative variables include gender, color, occupation, and type of vehicle.

However, there are differences among qualitative variables based on the level of **measurement**. The level of measurement determines the amount of information and mathematical operations that can be applied to the variable. In the case of qualitative variables, the **nominal** level of measurement is required.

The nominal level of measurement classifies data into distinct categories or groups without any **inherent** order or ranking. It is the simplest form of measurement and allows for labeling and identification of different categories. Nominal variables cannot be ordered or compared in terms of **magnitude** or value. Examples of nominal variables include hair color, marital status, and city of residence.

In summary, qualitative variables share similarities in their non-numerical nature and categorical representation. However, their differences lie in the level of measurement required, with qualitative variables typically measured at the nominal level.

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