Alleen can read 1. 5 pages for every page her friend can read. Alleen's mom was very excited and she said to Alleen: "So, if your friend reads 20 pages, you can read 25 in the same time period!" Is Alleen's mom correct?

The answer is 2, which represents the sum of the values of x for which f'(x) = 0.

To find the critical points of f(x), we need to find the derivative of f(x):

Setting f'(x) = 0 and solving for x, we get:

We can use the Rational Root Theorem to find possible rational roots of the equation. The possible rational roots are:

We can use synthetic division or long division to check which of these roots are actually roots of the equation. We find that the only real root is x = 5/4, and it has multiplicity 2.

The sum of the values of x for which f'(x) = 0 is simply the sum of the critical points of f(x). In this case, we only have one critical point: x = 5/4.

We first find the derivative of the given function and set it equal to zero to find the critical points. We use the Rational Root Theorem to find the possible rational roots of the equation, and then we use synthetic division or long division to check which of these roots are actually roots of the equation. In this case, we find that the only critical point of the function is x = 5/4 with multiplicity 2.

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Answer:

12(8) + (1/2)(13)(20) + (1/4)π(8^2)

= 96 + 130 + 4π = 226 + 16π ft^2

= about 276.27 ft^2

Answer:

To calculate the amount of money spent in interest alone over the course of a 30-year mortgage, we can use the formula:

Total Interest = (Monthly Payment x Number of Payments) - Principal

For a 3.5% 30-year mortgage with a principal of $180,000, the monthly payment can be calculated using the formula:

Monthly Payment = (Principal x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))

where Monthly Interest Rate = Annual Interest Rate / 12, and Number of Payments = 30 years x 12 months per year = 360.

Plugging in the values, we get:

Monthly Payment = (180,000 x 0.0035) / (1 - (1 + 0.0035)^(-360)) = $808.28

Using this monthly payment, we can calculate the total interest over the 30-year period:

Total Interest = ($808.28 x 360) - $180,000 = $101,020.80

Therefore, the correct answer is A. $110,880 (which is not one of the options given).

The fourth graph best represents a quadratic function with a range of all real numbers greater than or equal to 3

The graph that best represents a quadratic function with a range of all real numbers greater than or equal to 3 is a graph that opens upward and has a vertex at the point (h, k), where k is the minimum value of the function.

Since the range is all real numbers greater than or equal to 3, the minimum value occurs at or above 3.

Therefore, the vertex of the quadratic function lies on or above the horizontal line y = 3.

Hence, the fourth graph best represents a quadratic function with a range of all real numbers greater than or equal to 3

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In summary, we can say that there is a significant difference in the mean scores of the graduates in the two commercial institutes.

To determine if there is a significant difference between the mean scores of the graduates in the two commercial institutes, we can perform an independent samples t-test. Here's how to approach it:

Step 1: State the hypotheses:

Null hypothesis (H0): The mean scores of the graduates in the two commercial institutes are equal.

Alternative hypothesis (Ha): The mean scores of the graduates in the two commercial institutes are significantly different.

Step 2: Set the significance level:

The significance level (α) is given as 1%, which corresponds to a critical value of 0.01.

Step 3: Calculate the test statistic:

The test statistic for an independent samples t-test is calculated using the following formula:

t = (mean1 - mean2) / √[(S1^2 / n1) + (S2^2 / n2)]

Given:

Mean of the first group (mean1) = 65

Standard deviation of the first group (S1) = 15

Sample size of the first group (n1) = 35

Mean of the second group (mean2) = 70

Standard deviation of the second group (S2) = 10

Sample size of the second group (n2) = 35

Plugging in the values, we can calculate the test statistic:

t = (65 - 70) / √[(15^2 / 35) + (10^2 / 35)]

t = -5 / √[225/35 + 100/35]

t = -5 / √[325/35]

t ≈ -5 / 1.787

t ≈ -2.8 (rounded to one decimal place)

Step 4: Determine the critical value and compare:

Since the significance level (α) is 1%, the critical value for a two-tailed test is ±2.61 (obtained from a t-distribution table or a statistical software).

Since the calculated test statistic (-2.8) is greater than the critical value (-2.61) in absolute value, we reject the null hypothesis.

Step 5: Interpret the result:

Based on the test, we have sufficient evidence to conclude that there is a significant difference between the mean scores of the graduates in the two commercial institutes at the 1% level of significance.

In summary, we can say that there is a significant difference in the mean scores of the graduates in the two commercial institutes.

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the sum of the convergent series is 8.

To find the sum of the convergent series ∑(24/n(n+2)) where n starts at 1, we can re-write the given expression as a partial fraction decomposition:

24/n(n+2) = A/n + B/(n+2)

Solving for A and B, we find that A = 12 and B = -12. So the expression becomes:

12/n - 12/(n+2)

Now, we can compute the sum for the given series:

∑[12/n - 12/(n+2)] from n = 1 to infinity

As this is a telescoping series, most of the terms will cancel out. We are left with:

12/1 - 12/3 + 12/2 - 12/4 + ... + 12/∞ - 12/(∞+2)

The sum converges to:

12 - 12/3 = 12 * (1 - 1/3) = 12 * 2/3 = 8

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Answer:

20

Step-by-step explanation:

(x-3)+(8x+3)=180

9x=180

x=20

I think there might be a typo in the question - it looks like there's a missing second coordinate for vector v. Assuming that the second coordinate for v is also -7, here's the solution:

First, let's find the component form of 2u - 4v:

2u = 2(3,-7) = (6,-14)
4v = 4(-3,-7) = (-12,-28)

So 2u - 4v = (6,-14) - (-12,-28) = (6+12, -14+28) = (18,14)

Therefore, the component form of 2u - 4v is (18,14).

To find the magnitude of (18,14), we can use the Pythagorean theorem:

|(18,14)| = sqrt(18^2 + 14^2) = sqrt(360) ≈ 18.97

So the magnitude (length) of the vector 2u - 4v is approximately 18.97.
To find the component form of the vector 2u - 4v, we'll first perform scalar multiplication and then vector subtraction.

Scalar multiplication:
2u = 2(3, -7) = (6, -14)
4v = 4(-3, 1) = (-12, 4)

Vector subtraction:
2u - 4v = (6, -14) - (-12, 4) = (6 + 12, -14 - 4) = (18, -18)

So, the component form of the vector 2u - 4v is (18, -18).

To find the magnitude (length) of the vector, we'll use the formula: ||2u - 4v|| = √(x² + y²), where x and y are the components of the vector.

Magnitude = √((18)² + (-18)²) = √(324 + 324) = √(648) ≈ 25.46

The magnitude (length) of the vector 2u - 4v is approximately 25.46.

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The slope of the line  represents the rate of change in weight for every unit increase in length of the catfish.

The slope of the line of best fit in this scenario represents the rate of change or the relationship between the length and weight of the catfish. Specifically, the slope indicates the change in weight of the catfish for every unit increase in length.

If the slope is positive, it means that as the length of the catfish increases, its weight also tends to increase. If the slope is negative, it means that as the length of the catfish increases, its weight tends to decrease.

For example, if the slope of the line of best fit is 2, it means that for every one-inch increase in length, the weight of the catfish tends to increase by two pounds. Similarly, if the slope is -1, it means that for every one-inch increase in length, the weight of the catfish tends to decrease by one pound.

In summary, the slope of the line of best fit represents the relationship between the two variables being studied, in this case, the length and weight of the catfish.

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Answer:  B   28√15

Step-by-step explanation:

They want you to find the Area of the quadrilateral.  But if you can find the area of 1 trangle then you can double it because the 2 triangles are congruent.

We know the 2 triangles are congruent from the theorem  (see diagram

We also know that  QR=TR=SR  They are all radius

Let's solve for triangle PRS

PR = hypotenuse = 10+7 =17

SR=7  radius

Use pythagorean to find PS

c²=a²+b²

17²=7²+b²

289 = 49 + b²

b²=289 -49

b² = 240

b=√240

b=[tex]\sqrt{16*15}[/tex]

b= 4√15  This is PS

Area of triangle = 1/2 bh       b=PS   h=7

Area of triangle = 1/2 (4√15)(7)

Area of triangle = (2√15)(7)

Area of triangle = 14√15

Area of quadrilateral = 2 (14√15)        > 2 triangles make the quadrilateral

Area of quadrilateral =  28√15

The correct equation to predict the number of years it would take for the painting to have a value of $10,000 is 15,000(0.85)[tex]^{(t)}[/tex] = 10,000. The correct answer is option (c).

The initial value of the painting is $15,000, and its value is predicted to decay by 15% each year. This means that its value after t years can be represented by the equation:

V(t) = 15,000(0.85)[tex]^{(t)}[/tex]

We want to find the number of years it would take for the value to reach $10,000, so we set V(t) equal to 10,000 and solve for t:

10,000 = 15,000(0.85)[tex]^{(t)}[/tex]

Dividing both sides by 15,000 gives:

0.6667 = 0.85[tex]^{(t)}[/tex]

Taking the natural logarithm of both sides gives:

ln(0.6667) = t ln(0.85)

Solving for t gives:

t = ln(0.6667) / ln(0.85) = 2.294

So it would take approximately 2.294 years for the painting to have a value of $10,000. The right option is (c).

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Step-by-step explanation:

180° + 42° + x = 360°

222° + x = 360°

x = 138°

Answer:

138

Step-by-step explanation:

Since a circle is 360 degrees and it is split in half, each half would equal 180 degrees so you would subtract 42 from 180

the car is approximately 6.6 years old. The closest option provided is 6 years, so the answer is (C) 6 years.

Given:

y = A(1 – r)t

The value of a car is half what it originally cost, which means:

y = 1/2 A

The rate of depreciation is 10%, which means:

r = 0.1

Substituting these values in the equation, we get:

1/2 A = A(1 – 0.1)t

Simplifying, we get:

1/2 = 0.9t

Solving for t, we get:

t = ln(1/2) / ln(0.9) ≈ 6.6 years

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Note that Dawson's annual premium will be $2,462.40.

Dawson's annual premium will be $2,462.40.

This can be derived by going across from "Male 40-44" over to "20-year coverage" which is $13.68. Since $13.68 is per $1000 of coverage, you would multiply it by 180 to get $2,462.40.

An insurance premium is the amount of money paid by a person, firm, or enterprise to obtain an insurance coverage. The amount of the insurance premium is governed by a variety of factors and varies from one payee to the next.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

[tex]8 \frac{1}{3} \pi[/tex]

Step-by-step explanation:

volume of a sphere = 4/3 pi r²

r = 2.5

4/3× pi× 2.5² = 25/3pi

25/3 as a mixed number is 8 and 1/3

therefore rhe answer is 8 and 1/3 pi

The expression that represents the change in Emilio's savings each week is $7.50.

Emilio saving 25% of the money he earns babysitting, which means that he saves a quarter of his earnings. This can be expressed mathematically as:

savings = 0.25 x earnings

where "savings" is the amount Emilio saves and "earnings" is the amount he earns each week.

Substituting the given value of Emilio's average weekly earnings of $30, we get:

savings = 0.25 x $30

savings = $7.50

Therefore, Emilio saves $7.50 each week.

Since the question asks for the change in Emilio's savings each week, the expression that represents this is simply:

$7.50

This means that Emilio's savings increase by $7.50 each week.

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The student should receive $5.69 in change.

The price of the shirt after the coupon is applied is 0.75 times the regular price, so:

Price of the shirt = 0.75x

If x = $18, then the price of the shirt is:

Price of the shirt = 0.75($18) = $13.50

The clerk adds 6% sales tax to the price of the shirt:

Sales tax = 6% of $13.50 = 0.06($13.50) = $0.81

So the total cost of the shirt is:

Total cost = $13.50 + $0.81 = $14.31

If the student pays with a $20 bill, the change the student should receive is:

Change = $20 - $14.31 = $5.69

Therefore, the student should receive $5.69 in change.

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This prompt is about probability. The answers are given as follows;

Identifying the   probability of an event is crucial to making predictions based on its likelihood. T his involves calculating the probability either through historical data or experimentation.

Once determined, utilizing this value enables one to make future predictions regarding the occurrence of such events; for instance, 80% probability of precipitation tomorrow implies an 80% chance of rain.

Calculating probabilities has proven essential to sports betting because it helps bookmakers given some degree of foresight on which teams are going to win specific games or tournaments. Operating under the premise that there will always be two probable outcomes (either one side wins while another loses), these bookmakers could assign numerical values on what percentage they deem worthy enough for each team's chances.

Subsequently, using precise mathematical formulas and equations, bettors assess wagering-related uncertainties based on these predetermined likelihoods before deciding whether or not they should place money bets.

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The instantaneous rate of change in revenue at x=14 is $860 per camera.

The average change in revenue is $85 per camera [(ΔR/Δx) = 255/3].

a. The average change in revenue if production is changed from x=14 to x=17 is equal to the average rate of change of the revenue function over this interval:

Δx = 17 - 14 = 3

ΔR = R(17) - R(14) = (100017 - 517^2) - (100014 - 514^2) = $255

Therefore, the average change in revenue is $85 per camera [(ΔR/Δx) = 255/3].

b. The instantaneous rate of change in revenue at x=14 is equal to the derivative of the revenue function evaluated at x=14:

R(x) = 1000x - 5x^2

R'(x) = 1000 - 10x

R'(14) = 1000 - 10(14) = $860

Therefore, the instantaneous rate of change in revenue at x=14 is $860 per camera.

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Answer:

im pretty sure its A = 10

Laplace transform of f(t) = -1, 0 3 { F(x)

The Laplace transform of f(t) = S(t - 5), 0, 5 - F(3) is F(s) = (1/s) [tex]e^{(-5s)[/tex] - (1/3) [tex]e^{(-15)[/tex].

The Laplace transform of a function f(t) is given by:
F(s) = ∫[0,∞) e^(-st) f(t) dt
where s is a complex variable.
Using this formula, we can find the Laplace transform of f(t) as follows:
F(s) = ∫[0,∞) e^(-st) f(t) dt
    = ∫[0,∞) e^(-st) (-1) dt + ∫[0,∞) e^(-st) (0) dt + ∫[0,∞) e^(-st) (3) dt
    = -1/s + 0 + 3/s
    = (2/s) - (1/s)
Therefore, the Laplace transform of f(t) = -1, 0, 3 is F(s) = (2/s) - (1/s).
Now, let's move on to the second part of the question.

We need to find the Laplace transform of f(t) = S(t - 5), 0, 5 - F(3).
Here, S(t - 5) is the Heaviside step function, which is defined as:
S(t - 5) = 0, for t < 5
        = 1, for t ≥ 5
Using the Laplace transform formula, we can write:
F(s) = ∫[0,∞) e^(-st) S(t - 5) dt
Since S(t - 5) is equal to 0 for t < 5, we can split the integral into two parts:
F(s) = ∫[0,5) [tex]e^(-st)[/tex]S(t - 5) dt + ∫[5,∞) [tex]e^(-st)[/tex] S(t - 5) dt
The first integral is equal to 0, since S(t - 5) is 0 for t < 5.
For the second integral, we can use the fact that S(t - 5) = 1 for t ≥ 5. So, we get:
F(s) = ∫[5,∞) e^(-st) dt
    = [-1/s e^(-st)]_[5,∞)
    = (1/s) [tex]e^(-5s)[/tex]
Finally, we need to find F(3). Substituting s = 3 in the Laplace transform, we get:
[tex]F(3) = (1/3) e^(-15)[/tex]
Therefore, the Laplace transform of f(t) = S(t - 5), 0, 5 - F(3) is F(s) = (1/s) [tex]e^(-5s) - (1/3) e^(-15).[/tex]

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Answer:

[tex]y=log_{9} (x)[/tex]   (the middle choice)

Step-by-step explanation:

Key Concepts

Concept 1. Exponential vs logarithm

Concept 2. Logarithm rules

Concept 1. Exponential vs logarithm

The first two choices are logarithmic functions whereas the last function is an exponential function.  The graph cannot be that of an exponential function because exponential functions cannot cross the x-axis (an asymptote) unless a shift transformation is applied (which would look like adding or subtracting a constant number at the end of the equation.

A second way to verify is to simply input 2 into the function.  The number 2 raised to the 9 power is 2*2*2*2*2*2*2*2*2=512, but the graph clearly does not have a height of 512 when the input is 2.  Therefore, the correct answer cannot be the last choice.

Concept 2. Logarithm rules

One important rule for logarithms is that a number input into logarithm that matches the base of the logarithm will yield 1 as a result.  In other words:

For all real numbers b, such that b is positive and not equal to 1, [tex]log_{b}(b)=1[/tex]

Observe that for the first option, this means that [tex]log_{\frac{1}{9}}(\frac{1}{9})=1[/tex].  However, for an input of 1/9, the output is still below the x-axis -- a negative output -- clearly not 1.

Observe that for the second option, this means that [tex]log_{9}(9)=1[/tex], and that for an input of 9, the output on the graph is at a height of 1.

Therefore, the correct function for this question must be the middle option.

There are 720 different arrangements of the six children possible when Ben can't sit next to Dan.

There are 720 different arrangements of the six children possible.

The key to solving this problem is to recognize the fact that there are six children and six chairs, so each child has one and only one chair. This means that for each position in the row, one child must be placed in the chair.

To solve this problem we can use the permutation formula for "n objects taken r at a time without repetition," which is: n!/(n-r)!

In this case, n is 6 (the number of children) and r is 6 (the number of chairs). So, 6!/(6-6)! = 6!/(0!) = 6!/1 = 6! = 720.

Therefore, there are 720 different arrangements of the six children possible when Ben can't sit next to Dan.

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Step-by-step explanation:

Mean is less than 8

(1 + 1 + 6*8 + 10 ) / 9 = mean = 6.7

Answer:

A: The mean in less than 8

Step-by-step explanation:

Mean: Average

How to find the mean?

1. Add ALL the numbers given

     1: has 2 dots     8: has 6 dots     10: has 1 dot

so  2+6+1= 9

2. divide the result of point 1. by the amount of numbers given.

     9/3= 3

3.

  Numbers:

    1-2-3-4-5-6-7-8-9   3 is before 8 so it means it's less than 8.

Answer:80%

Step-by-step explanation:

Answer:

18 cent

Step-by-step explanation:

The intersection of a plane and a cylinder can result in the following polygons when the plane is either parallel or perpendicular to the base:

Oa Rectangle

Oc Square

Od Triangle

The angle and position of the plane relative to the cylinder intersect determines a myriad of shapes not limited to just one. Herein are the descriptions for a few that may arise:

Rectangle: If a plane intersects the cylinder but remains parallel to its base, the resulting outline shall be rectangular. This is due to the aforementioned plane cutting through the lateral surface of the circumference, forming two equal lines--thereby shaping a closed loop in an angular fashion.

Square: The intersection of a plane perpendicularly bisecting the base of a cylindrical object will conjure up a square shape congruent to the cylinders. In other words, a perfectly squared compartment matching with the pre-existing edges of the bottom curve of the cylinder.

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Answer: 8x +29

Step-by-step explanation:

5+8(3+x)

5+8(x+3)

__________

5 + 8(x+3)

5+ 8x +25

_________

5+8x+ 24

29+8x

____

8x+29