Let f(x) 1 -x^2/3. Show that f(- 1) = f(1) but there is no number c in ( -1, 1) such that f'(c )= 0. Why does this not contradict Rolle's Theorem?

The mathemematical sum of the three numbers 1+1+1 would give 3

Addition of numbers can involve 2 or more values using the additive sign '+'. For any given sum of values, the result obtained would be greater than any of the individual value in the sum.

Here, 1 + 1 + 1 means that we are adding 1 in three places. The value obtained would be 3.

Therefore, the sum of the 1+1+1 is 3

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Answer:

[tex]\frac{4685}{288}[/tex]

Step-by-step explanation:

The explanation is attached below.

The required target debt/equity ratio is 0.5 or 1:2.

To calculate the target debt/equity ratio,

Use the following formula,

⇒ Target D/E Ratio = (Target Equity / Target Debt)

First, we need to calculate the weights of equity and debt in the firm's capital structure.

We can use the following formula,

Weight of Equity = Equity / (Equity + Debt)

Weight of Debt = Debt / (Equity + Debt)

Since the firm is unlevered,

its capital structure consists only of equity.

Therefore,

The weight of equity is 1 and the weight of debt is 0.

Now we can use the weighted average cost of capital (WACC) formula to find the firm's current cost of equity.

The WACC formula is as follows,

WACC = (Weight of Equity Cost of Equity)

                        + (Weight of Debt Cost of Debt x (1 - Tax Rate))

Substituting the given values, we get:

⇒ 10% = (1 Cost of Equity) + (0 9% x (1 - 34%))

Solving for Cost of Equity, we get:

Cost of Equity = 10% - (0 9% (1 - 34%))

Cost of Equity = 10%

Since the firm desires a cost of equity of 14%,

we can set up an equation to solve for the target debt/equity ratio:

⇒ 14% = (1 / (1 + Target D/E Ratio)) 10% + ((Target D/E Ratio) / (1 + Target D/E Ratio)) 9% x (1 - 34%)

Simplifying the equation, we get:

⇒ 14% = 10% / (1 + Target D/E Ratio) + 0.0594 x Target D/E Ratio

Multiplying both sides by (1 + Target D/E Ratio), we get:

⇒ 0.14 + 0.14 Target D/E Ratio = 0.1 + 0.0594 Target D/E Ratio

Subtracting 0.0594 x Target D/E Ratio from both sides, we get:

⇒ 0.08 x Target D/E Ratio = 0.04

Dividing both sides by 0.08, we get:

⇒ Target D/E Ratio = 0.5

Therefore, the firm's target debt/equity ratio is 0.5 or 1:2.

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8 people didn't use any of the gym pool or track facilities.

The number of people use any facilities need to subtract the total number of people who used at least one facility from the total number of people in the sport centre.

The total number of people who used at least one facility by adding the number of people who used each facility and subtracting the number of people who used two facilities and three facilities:

Total = Gym + Pool + Track - (Gym and Pool) - (Pool and Track) - (Gym and Track) + (Gym and Pool and Track)

Total = 77 + 62 + 65 - 27 - 23 - 31 + 4

Total = 127

The number of people who didn't use any facilities is:

135 - 127 = 8

8 people didn't use any of the gym, pool or track facilities.

The number of individuals who did not utilise any facilities must be subtracted from the total number of individuals who utilised at least one facility.

The total number of individuals who utilised at least one facility is calculated by adding the individuals who utilised each facility and deducting the individuals who utilised two and three facilities:

Total = Fitness Centre + Pool + Track - Fitness Centre and Pool - Fitness Centre and Track - Fitness Centre and Pool and Track

Total = 77 + 62 + 65 - 27 - 23 - 31 + 4

Total = 134-127

= 8

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The value of the unknown c in the algebraic fraction equation is equal to -24

To solve the simple algebraic fraction equation, we cross multiply to eliminate the fractions, then simplify by solving for the unknown

Given the algebraic equation:

-c/6 = 4

(-c/6) × 6 = 4 × 6

-c = 4 × 6

-c = 24

multiply both sides by -1

-1 × -c = -1 × 24

c = -24

Therefore, the value of the unknown c in the algebraic fraction equation is equal to -24

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The volume of the cylindrical shaped pool with water is V = 75.4 feet³

Given data ,

Let the diameter of the pool be d = 8 feet

So , radius r = 4 feet

And , the height of the cylindrical pool is h = 3 feet

Now , the water is half full

So , Volume of Cylindrical pool is V = ( 1/2 ) πr²h

V = ( 1/2 ) ( 3.14 ) ( 4 )² ( 3 )

On simplifying , we get

V = 75.4 feet³

Hence , the amount of water in pool is V = 75.4 feet³

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The measure of p in the diagram is,

m∠P = 45°

We have to given that;

PM is perpendicular to MO.

Now, If m ∠P = m∠2

then it's an isosceles triangle.

And, m ∠M = 90°, therefore it's an isosceles right triangle.

We know that,

the sum of measures of angles in a triangle is equal 180°.

Therefore we have the equation:

m∠P + m∠2  + m∠M = 180°

Substitute m∠M = 90° and m∠P = m∠2 = x:

x + x + 90° = 180°    

substract 90° from both sides

2x = 90°      

divide both sides by 2

x = 45°

m∠P = 45°

Thus, The measure of p in the diagram is,

m∠P = 45°

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Both containers hold the same amount of water.

Given are two solid figures, we need to compare which of them holds more water,

The container one has a base dimension of 3 ft × 180 in with height 90 in. and the second container has base dimension of 3 ft × 180 in with height 90 in.

To compare which container holds more water, we can calculate the volume of each container.

For consistency, let's convert all measurements to a single unit.

1 foot is equal to 12 inches, so the base dimensions of both containers can be expressed as

3 ft × (180 in + 3 ft × 12 in/ft) = 3 ft × 216 in

= 648 in × 648 in.

The volume of a container is calculated by multiplying the base area by the height.

Therefore, the volume of each container can be determined as follows:

Container 1:

Volume = Base area × Height

Volume = (648 in × 648 in) × 90 in

Container 2:

Volume = Base area × Height

Volume = (648 in × 648 in) × 90 in

Since the base dimensions and the height are identical for both containers, their volumes will also be the same.

Therefore, both containers hold the same amount of water.

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The experimental probability that more than 10 spins are needed to land on each letter at least once is 75%

Experimental probability is a type of probability that is based on actual observations or experiments.

In experimental probability, the probability of an event occurring is calculated by conducting experiments and observing the outcomes. The probability of the event is then calculated by dividing the number of times the event occurred by the total number of trials or experiments.

In this case, experimental probability = number of times the event occurred / total number of trials

Experimental probability = 0.1 + 0.35 + 0.3 / 1

= 0.75 / 1

= 75%

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The surface area of the rectangular prism is 396 square inches

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

7 in by 12 in by 6 in

The surface area of the rectangular prism is calculated as

Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)

Evaluate

Area = 396

Hence, the area is 396 square inches

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Answer:The employer pays .90 * 12240 = $ 11016. The emplyee pays .10 *12240 = $ 1224 = annual contribution. Contribution rate = (100% - 90%) = 10%.

Step-by-step explanation:

Answer:

a) $1,224

b) $51

Step-by-step explanation:

a) To calculate Darrell's annual contribution, we need to determine the portion he pays out of the total premium.

Given that the employer pays 90% of the cost, Darrell is responsible for the remaining 10%.

Annual contribution = Total premium × 10%

= $12,240 × 0.10

= $1,224

Therefore, Darrell's annual contribution is $1,224.

b) To find Darrell's semimonthly deduction, we divide his annual contribution by the number of semimonthly periods in a year.

Number of semimonthly periods in a year = 12 (months) × 2 (semimonthly periods per month) = 24

Semimonthly deduction = Annual contribution / Number of semimonthly periods

= $1,224 / 24

= $51

Therefore, Darrell's semimonthly deduction is $51.

Hope this helps!

The volume for each cone in this problem is given as follows:

11) V = 94 in³.

12) V = 367 ft³.

13) V = 1005 in³.

The volume of a cone of radius r and height h is given by the equation presented as follows:

V = πr²h/3.

For item 11, the dimensions are r = 3 in and h = 10 in, hence the volume is given as follows:

V = π x 3² x 10/3

V = 94 in³.

For item 12, the dimensions are r = 5 ft and h = 14 ft, hence the volume is given as follows:

V = π x 5² x 14/3

V = 367 ft³.

For item 13, the dimensions are r = 8 in(half the diameter) and h = 15 in, hence the volume is given as follows:

V = π x 8² x 15/3

V = 1005 in³.

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The mode of the data represented in this line plot will be 8.

Simply counting how several times each number looks in the data set can help you identify the mode, which is the integer that repeats the most frequently in the collected data. The figure with the largest total is the mode.

The value that appears the most frequently in data collection is its mode. By examining the line plot, we can observe that the number 8 and the six Xs above it are the most commonly occurring values. Consequently, 8 represents the data set's mode.

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The solution of expression after subtraction is,

⇒ 8249 L 860 ml

We have to given that;

Subtract measurements 450l 890ml from 8700l 750ml​

Now, WE can simplify as,

⇒ L      ml

8700    750

- 450     890

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

8249     860

Therefore, After subtraction we get;

⇒ 8249 L 860 ml

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Answer:

∆ABC ~ ∆QPR by SSS since 6/8 = 9/12.

Answer:

V = 381.7 or 121π

Step-by-step explanation:

V=4/3πr³

Radius is half the diameter so, 9/2 = 4.5

r=4.5

V = 4/3π(4.5)³

V=4/3π(91.125)

V = 381.7 or 121π

Answer:

B, C, E

Step-by-step explanation:

For a rectangle,

area = length × width

Let length = y.

Then the width is y - 5.

A = LW

750 = y(y - 5)

y(y - 5) = 750

y² - 5y - 750 = 0

All equations that can be put in the form above are correct.

A) y(y + 5) = 750

y² + 5y - 750 = 0

No

B) y² – 5y = 750

y² - 5y - 750 = 0

Yes

C) 750 – y(y – 5) = 0

750 - y² + 5y = 0

y²- 5y - 750 = 0

Yes

D) y(y – 5) + 750 = 0

y² - 5y + 750 = 0

No

E) (y + 25)(y – 30) = 0

y² + 25y - 30y - 750 = 0

y² - 5y - 750 = 0

Yes

Thomas Sowell's speech "Morality vs. Sanctimoniousness" addresses the distinction between genuine moral actions and the outward appearance of moral superiority.

The keynote of his speech is to prioritize practical and fruitful measures over merely appearing sensible or righteous. According to Sowell, it is crucial to solve prevalent social problems with pragmatic, yet effective solutions instead of adopting self-righteous attitudes that lack meaningful outcomes.

Essentially, he opines that authentic ethical principles should be anchored in consideration for others' welfare and empirical evidence rather than being fueled by personal moral validation or pretentiousness.

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Answer:

The answer is 5

Step-by-step explanation:

c²=3²+4²

c²=9+16

c²=25

[tex] \sqrt{ {c}^{2} } = \sqrt{25} [/tex]

c=5

The value of c is :

↬ c = 5, c = -5

Solution:

First off, we should square the numbers:

[tex]\sf{3^2+4^2=c^2}[/tex]

[tex]\sf{9+16=c^2}[/tex]

[tex]\sf{25=c^2}[/tex]

Now I square-root each side :

[tex]\sf{5=c}[/tex]

[tex]\sf{-5=c}[/tex]

This means that :

[tex]\sf{c=5,\:c=-5}[/tex]

How did this happen? We should know that once we take the square root of a number, we end up with two solutions that are opposites of each other. This phenomenon is explained below.

When we square 5, we get 25. When we square -5, we also get 25.

So then, when taking the square root of 25, we get both 5 and -5. And now, we know why.

Answer: To show that log5 7 = 1/(2n-1)(2mn-m-2), we'll start by using logarithmic properties and the given information.

First, let's express log9 75 in terms of the base 5 logarithm, using the change of base formula:

log9 75 = log5 75 / log5 9

Next, let's simplify the expression inside the logarithm by breaking down 75 and 9 into their prime factors:

log5 (3^2 * 5^2) / log5 (3^2)

Now, using logarithmic properties, we can split the logarithm of a product into the sum of logarithms:

log5 (3^2) + log5 (5^2) - log5 (3^2)

Simplifying further, we have:

2 log5 3 + 2 log5 5 - 2 log5 3

The 2 log5 3 and -2 log5 3 terms cancel each other out, leaving:

2 log5 5

Now, let's substitute the value of m from the given information (log5 21 = m) into the expression:

2 log5 5 = 2 (log5 (5^2)) = 2(2 log5 5) = 4 log5 5 = 4m

Now, let's substitute the value of n from the given information (log9 75 = n) into the expression:

4m = 4(log5 5) = 4(1/2 log5 (5^2)) = 4(1/2 log5 25) = 4(1/2 log5 (5^2 * 5^2))

Using logarithmic properties, we can split the logarithm of a product into the sum of logarithms:

4(1/2 (log5 5^2 + log5 5^2)) = 4(1/2 (2 log5 5 + 2 log5 5)) = 4(1/2 (4 log5 5))

Simplifying further, we have:

4(1/2) (4 log5 5) = 4(2 log5 5) = 8 log5 5 = 8n

Finally, substituting the values of m and n into the expression:

log5 7 = 1/(2n-1)(2mn-m-2) = 1/(2(8) - 1)(2(4m) - m - 2) = 1/(16 - 1)(8m - m - 2) = 1/15(7m - 2)

Therefore, we have shown that log5 7 = 1/(2n-1)(2mn-m-2) = 1/15(7m - 2), using the given values of log5 21 = m and log9 75 = n.

Answer:

? = 7

Step-by-step explanation:

The equation of the line parallel to another line will have the same slope. The given line y = 7x + 2 has a slope of 7.

To find the equation of the line that passes through the point (3, -1) and is parallel to the given line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

So, the equation of the line parallel to y = 7x + 2 and passing through the point (3, -1) is:

y - (-1) = 7(x - 3)

Simplifying this, we get:

y = 7x - 21 - 1

y = 7x - 22

So, the equation of the line is y = 7x - 22.

Given the form of the equation y + 1 = ?(x -3). We then know the answer is y + 1 = 7 (x - 3)

The line's equation is :

Solution:

If two lines are parallel then their slopes are equal.

The slope of [tex]\sf{y=7x+2}[/tex] is 7, so the slope of the line parallel to it is 7.

Now, we should plug the slope and the point into the point slope equation. See, we're even given a hint :

Remember : y - y₁ = m(x - x₁).

This hint tells us the point slope equation.

So I plugin :

[tex]\bf{y-(-1)=7(x-3)}[/tex]

Simplify.

[tex]\bf{y+1=7(x-3)}[/tex]

This is it, we don't have to simplify all the way to slope intercept.

Answer:

I estimate it is around 340 because 34 times 10 is 340 the product of 34 times 12 is 408

Step-by-step explanation:

The midpoint of this line segment (-3, -5) and (4, 5) is (0.5, 0).

In order to determine the midpoint of a line segment with two (2) end points, we would add each point together and then divide by two (2):

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

By substituting the given end points into the formula for the midpoint of a line segment, we have the following;

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(-3 + 4)/2, (-5 + 5)/2]

Midpoint = [(1)/2, 0/2]

Midpoint = (0.5, 0).

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Answer:

Polygon D is similar to polygon ABCD.

The correct statement regarding the measure of variability used to represent the data is given as follows:

The IQR of 10 is the most accurate to use, as the data is skewed.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

It is the measure of variability to be used when a data-set contains outliers, or is skewed, as is the case for this problem.

The charity received 18 donations, hence the quartiles are given as follows:

Hence the IQR is given as follows:

IQR = 22.5 - 12.5

IQR = 10.

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The equation for g (x) is,

⇒ g(x) = x² -3

Since, The function is,

⇒ f (x) = x²

when x = 0, f(x) = 0

hence it has vertex at (0,0)

Since, g(x) is shifter version of f(x) and has vertex at (-1, 4),

Then, g(x) must be shifted along y axis.

So, We get;

g(x)= x²+c

when x = - 1, g(x)= 4

4 = (-1)² + c

4 = 1 + c

c = 3

Thus, The equation for g (x) is,

g(x) = x² -3

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The pairs of alternate exterior angles in the given figure is Option D) ∠1 and ∠7; ∠2 and ∠8

Alternate exterior angles are a pair of angles formed by a transversal line intersecting two parallel lines and located on opposite sides of the transversal and on the exterior of the parallel lines. In other words, if two parallel lines are intersected by a third line (the transversal), then the pairs of angles on opposite sides of the transversal and outside the parallel lines are alternate exterior angles. These angles are congruent to each other.

In the given figure two parallel lines, which are crossed by a transversal line which forms angles.

Now according to the given figure

so, answer is Option D) ∠1 and ∠7; ∠2 and ∠8

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The correct statement regarding the transformation is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the dilation are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.

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