1. The function below satisfies Rolle's Theorem on the specified interval. Find the value c in the interval (−4,−3)(-4,-3) such that f′(c)=0f'(c) = 0.
f(x)=x+12/x ; [−4,−3]

The difference between the circumference of the circle and the perimeter of the triangle is 28.2 units. (Option B)

To find the length of each side of triangle, the distance is calculated between the vertices using the formula:

d = √((x2 – x1)^2 + (y2 – y1)^2)

Hence,

AB =√((-4 – 0)^2 + (9 – 0)^2) = 9.85 units

AC = √((9 – 0)^2 + (4 – 0)^2) = 9.85 units

BC = √((9 – (-4))^2 + (4 –9)^2) = 13.93 units

Hence, the perimeter of the triangle = 9.85 + 9.85 + 13.93 = 33.6 units

As AB and AC is the radius of the circle, the circumference of the circle is:

C = 2πr = 2π(9.85) = 61.8 units.

Hence, the difference between the circumference of the circle and the perimeter of the triangle = 61.8 – 33.6 = 28.2 units.

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The final Factorisation of the expression of 5x³ + 40y⁶ is 5 ((x + 2y²) (x² - 2xy² + 4y⁴)).

When an algebraic equation is expressed as the sum of its factors, it has been factorized. There might be these variables, elements, or algebraic expressions.

A number is broken down for the factor into components that may be multiplied to produce the original number.

According to the question,

We have to factorize the expression

5x³ + 40y⁶

Taking a Common factor 5 out ,

5 (x³ + 8y⁶)

When the expression between the parenthesis is factored, we get:

5 ((x + 2y²) (x² - 2xy² + 4y⁴))

Right now, we cannot add another element.

Hence , The factored expression is given by: 5 ((x + 2y²) (x² - 2xy² + 4y⁴))

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The circumference of this circle is 2π

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

The arc is the circumference.

C = 2πr

C = 2x πx 6

C = 12π

A circle is 360 degrees.  The  arc is covering 60 degrees

60/360 = 1/6

The arc is 1/6 of the circle, so it will be 1/6 of the circumference

1/6 C = 1/6 (12π)

arc = 2π

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Answer:

1. 50 x 2 = 100

2. 60 x 3 = 180

3. 75 x 8 + 3 = 603

603 + 180 + 100 = 883

Step-by-step explanation:

Just multiply and add.

The expression that is equivalent to 6⁻¹⁰/(6⁴)(6⁰) is (d) 1/6¹⁴

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

6⁻¹⁰/(6⁴)(6⁰)

Express 6⁰ as 1

So, we have the following representation

6⁻¹⁰/(6⁴)(6⁰) = 6⁻¹⁰/(6⁴) * 1

Evaluate the products

6⁻¹⁰/(6⁴)(6⁰) = 6⁻¹⁰/(6⁴)

Apply the law of indices

So, we have

6⁻¹⁰/(6⁴)(6⁰) = 1/6¹⁰⁺⁴

Evaluate the differences

6⁻¹⁰/(6⁴)(6⁰) = 1/6¹⁴

Hence, the expression is (d) 1/6¹⁴

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The set of all  T's fixed points is {(x,0): x € R} of the linear transformation of vector(v).

linear transformation:

It is a function from one vector space to another that respects the structure of each vector space, which is also known as a linear operator or map

Two important examples of linear transformations are zero and identity transformation. The zero transformation defined by T(→x)=→(0) for all →x is an example of a linear transformation.

Similarly, the identity transformation defined by T(→x)=→(x) is also linear.

Note that the representation matrix for the reflection in the y-axis:

                              [tex]\left[\begin{array}{ccc}1&0\\0&-1\\\end{array}\right][/tex]

Here the condition

T(x,y)=

         [tex]\left[\begin{array}{ccc}1&0\\0&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}x\\-y\\\end{array}\right] =\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]

can only happen when y=0 and x is arbitrary.

Thus the fixed points for all T are points with y=0 or all points on the x-axis

Thus, The set of all T's fixed points is {(x,0): x€R}

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The 13th term of the given Arithmetic sequence is 38.

A list of integers with a distinct pattern is known as an arithmetic sequence. It is an arithmetic sequence if you can subtract any number in the sequence from the one before it and get a value that is either constant or always the same.  Here the constant value is called a common difference.

The formula for the nth term of the Arithmetic sequence is given by

Here we have

Arithmetic sequence: 2, 5, 8, 11,....  

Where first term a = 2

And common difference d = term2 - term 1 = 5 - 2 = 3

As we know nth term of AP = a + (n-1)d

=> 13th term of AP = a + (13-1)d = a + 12d

From the give data, a = 2 and d = 3

=>  13th term =  a + 12d  

= 2 + 12(3)

= 2 + 36

= 38

Therefore,

The 13th term of the given Arithmetic sequence is 38

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Answer:

1

Step-by-step explanation:

subtract the two numbers

Answer: 19

Step-by-step explanation: Imagine a number line -9 is on the left side and 10 is on the other. Now you have to clculate how many jumps or spaces it takes to reach 10. Which is 19, or 9 + 10.

I hope this helps.

The dimension of rectangle window to admit the most light is x = 16 / ( 8 - √3) and y = 24 - 8√3 /  8 - √3

According to the question,

The perimeter of the window is 16 feet

Also, Window is surmounted by an equilateral triangle

Let x and y be the dimensions of rectangular part of window and x be side of equilateral part. If A be the total area of window, then

A = x.y + (√3/4)x² -------------(1)

Also, x + 2y + 2x = 16

=> 3x + 2y= 16

=> y = 16-3x / 2

Replacing the value of y in equation (1)

=> A = x.(16-3x / 2) + (√3/4)x²

=> A = 8x - 3x²/2 +  (√3/4)x²

Differentiating A w.r.t x

=> A' = 8 - 3x +  (√3/2)x

For critical value , we put A'=0

=> 8 - 3x +  (√3/2)x = 0

=> x = 16 / ( 8 - √3)

Again, Differentiating A' w.r.t x ,

=> A'' = -3 + √3/2

which is Less than 0 ,

Therefore , A is maximum if x = 16 / ( 8 - √3) and y = 24 - 8√3 /  8 - √3

Hence, For admitting the most light the area should be largest , dimensions of rectangle are x = 16 / ( 8 - √3) and y = 24 - 8√3 /  8 - √3

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1. There are two performance obligations in a contract to buy a pair of SunBoots from Clarks Inc: Delivery of Sunboots and Discount Coupon.

2. The journal entry to record the revenue for the sale of 1,000 pairs of SunBoots when Clarks cannot estimate the standalone selling price of a pair of SunBoots sold without a coupon is as follows:

Debit Cash $70,000

Credit Sales Revenue $65,800

Credit Deferred Revenue from Discount Coupon $4,200

(To record the sale of 1,000 pairs of SunBoots, including the discount coupon.)

Performance obligations refer to distinct goods and services agreed to be provided in a contract between the two parties.

Performance obligations arise because each separate goods or services benefit the customer distinctly from others.

In accounting for the revenue or costs, efforts should be geared toward recognizing the activity as soon as they bestow or transfer economic benefits to the buyer.

Selling price per pair = $70

Discount coupon = 30%

Estimated percentage of customers who will utilize the coupon = 20%

The number of SunBoots sold = 1,000

Cash $70,000 Sales Revenue $65,800 Deferred Revenue from Discount Coupon $4,200 ($70,000 x 30% x 20%)

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The moment generating function of a Bern(p) random variable x is given by: M(t) = pe^(pt) + (1 - p).The moment generating function of a Bin(n, p) random variable y is given by:M(t) = (pe^(pt))^n + (1 - p)^n

To find the moment generating function of a Bern(p) random variable x, we first need to calculate the probability mass function of x.

p(x) = p^x (1-p)^(1-x).

The moment generating function of x is then given by the formula:

M(t) = pe^(pt) + (1-p).

To use the moment generating function of x to find the moment generating function of a Bin(n, p) random variable y, we first need to calculate the probability mass function of y.

p(y) = (n choose y)p^y(1-p)^(n-y).

The moment generating function of y is then given by the formula:

M(t) = (pe^(pt))^n + (1-p)^n.

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The Venn Diagram is shown at the end of the answer.

From the diagram, the percentages are given as follows:

The Venn Diagram is filled starting at the intervals involving most variables, that is, the intersections.

2% of people answered all three, hence space V on the diagram has a value of 2%, which is the intersection of the three sets.

3% of people answered light rail and bus, hence space IV has a value of 1%, as light rail and bus also involve light rail, bus and carpool.

6% of people answered light rail and carpool, hence space II has a percentage of 4%, following the same logic above.

2% of people answered carpool and bus, hence space V has a percentage of 0%.

11% of people answered carpool, hence space III has a percentage of 5%, as this percentage is a combination of:

From the total bus and light rail percentages, the percentages are given as follows:

The percentage of people that use at least one of these mediums is given as follows:

9 + 7 + 5 + 1 + 2 + 4 = 28%.

The percentage of people who use none of these mediums is given as follows:

100 - 28 = 72%.

Then the missing percentages at the end of the problem, along with their spaces, are given as follows:

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Answer:

Step-by-step explanation:The Sales Price is $425Explanation:First, we need to find the original price or: 15% of what is $75"Percent" or "%" means "out of 100" or "per 100", Therefore 15% can be written as 15100.When dealing with percents the word "of" means "times" or "to multiply".Finally, lets call the number we are looking for, or "what", n.Putting this altogether we can write this equation and solve for n while keeping the equation balanced:15100×n=$7510015⋅15100×n=10015⋅$7510015⋅15100×n=$750015n=$500Now that we know the original price we can subtract the discount or mark down from it.So, the Sales Price =$500−$75=$425

//The end result is that samplereadings is now [85, 43, -1].

Samplereadings is a website that offers free reading material for students. The website provides a variety of texts, including classic literature, non-fiction, and current topics. Users can read the texts online, or download a PDF version. Samplereadings also offers a range of additional resources, such as discussion questions, vocab lists, and comprehension quizzes to help students better understand and engage with the material.

samplereadings.unshift(samplereadings.pop()); //pop() removes the last element of the array and returns it, then unshift() adds the element to the beginning of the array.

samplereadings[samplereadings.length - 1] = -1; //sets the last element of the array to -1.

//The end result is that samplereadings is now [85, 43, -1].

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The true statement regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable is 0 < F(x) < 1. and F(x) = 1 for at least one value of x,  F(x) = 1 for all values of x > a, where a is a constant.

What is meant by probability density function?

In math, probability density function refers most commonly associated with absolutely continuous univariate distributions.

Here we need to find the true statement regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable.

In order to find the correct statement, we must know the definition of the cumulative density function also.

The cumulative density function means the probability function that X will take a value less than or equal to x.

Based on the both definition option (A), (B) and (C) are true.

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High off the ground the top of the ramp’s incline is 108.19 inch

Trigonometric ratios are what?

Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.

Given that :

hypotenuse = 153 inch

and angle is pi/4

Let h be the height

so sin pi/4 = h/153

h = 153 . sqrt 2/2

h = 108.19

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Fail to reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.

The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. Age Group Youths Young Adults Adults Seniors

Sample Size 102 258 319 31

x :2.00 3.10 3.06 2.81

s :1.59 1.66 1.69 1.87

for this test

P-value > 0.100

0.050 < P-value < 0.100

0.010 < P-value < 0.050

0.001 < P-value < 0.010

P-value < 0.001

Hence , Fail to reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.

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Answer: The final price of the living room set is $1,880 (Option A)

Step-by-step explanation: Market price of living room set = $2400

                                        Trade Discount offered= 30%

Therefore we deduct Trade Discount from the Market Price to arrive at the final price.

= 2400 - (2400*30%)

=2400-720

=1680

Freight charges incurred to bring an asset to use are added to the final price of the asset.

Therefore the Final Price = 1680+200

                                            =$1,880

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The polynomial f(x) of degree 3 is

f(x) = x³ + x² - 20x

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The zeroes of the polynomial are 0, -5, and 4.

This can be written as,

x = 0, x

x = -5, (x + 5)

x = 4, (x - 4)

x(x + 5)(x - 4)

(x² + 5x)(x - 4)

x³ - 4x² + 5x² - 20x

x³ + x² - 20x

Thus,

The polynomial is f(x) = x³ + x² - 20x

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Answer:

x = 25

Step-by-step explanation:

the angle in a semicircle is 90°

given the legs of the triangle are congruent then the triangle is isosceles with the 2 base angles congruent.

the sum of the 3 angles in the triangle = 180°

base angle = (180 - 90)° ÷ 2 = 90° ÷ 2 = 45° , then

2x - 5 = 45 ( add 5 to both sides )

2x = 50 ( divide both sides by 2 )

x = 25

The estimated regression equation for these data is Ŷ = 23.194 + 0.318x for every i=1,...,6.

What is meant by regression equation?

In math, the linear regression analysis output delivers some important information, which helps the researcher to predict the estimation, accuracy, and efficiency of the model.

Here we have the data on price and the overall score for stereo headphones that were tested by consumer reports were as follows.

And we need to find the estimated regression equation for these data.

Here let us consider x be the price in dollars of the stereo headphones of brand ii (the independent variable). and let y be the overall score of the stereo headphones of brand ii (the dependent variable).

Here first, we will compute the value of SSE.

The formula is given by

= > SSE = 1∑n​ (yi ​− y​)²

Therefore, we will show the table of values of xi​, Ŷ​, Ŷ​​, (yi​−Ŷ​​) and (yi​−Ŷ​)².

Now, we have to calculate the value of yi​^​, plug in the value of xi​ in the equation 

=> Ŷ = 23.194 + 0.318x for every i=1,...,6.

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Answer:

$14000

Step-by-step explanation:

= (3500 x 0.8 x 5) / 100

= $14000

I hope my answer helps you.

Comparison analysis is defined as describing the data in the sample with the use of percentages or averages. Hence, option A is the most suitable answer to this question.

Comparative analysis talks about the comparison of two or more data sets, or other objects. Comparing data becomes very easy when the data is consolidated with the help of average or mean, percentages, and rounding up of the decimals.

Comparison is a very important method to check the difference in the parameters of the two data sets. Not just comparing, summarization of this data is vital for understanding what that data actually means. Hence, we can say that comparison analysis is defined as describing the data in the sample with the use of percentages or averages.

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The complete question is -

Fill in the blanks -

________ analysis is defined as describing the data in the sample with the use of percentages or averages.

A) Comparison

B) Generalization

C) Relationship

D) Summarization

E) Confidence

The conclusion is that there is insufficient proof that the new training method increases training time at the 0.02 level of significance.

Hypothesis test: Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H₀

The average amount of time required to obtain an advanced driving license using conventional techniques is μ=90 hours.

According to the researcher, the new method can result in a longer training period.

A researcher tests the hypothesis with 190 pupils.

At the significance threshold of α=0.02, the researcher fails to reject the null hypothesis.

To put to the test

H₀:The average amount of time required for the new method to obtain an advanced driving license is 90 hours, or μ=90

Hₐ: The new method often requires more than 90 hours, or μ>90, to obtain an advanced driving license.

Failure to reject the null hypothesis indicates that there was insufficient data in our sample to draw a conclusion on the existence of the effect. The absence of data, however, does not demonstrate that the effect is unreal.

The new method takes fewer than 90 hours on average to get an advanced driving license as a result.

Therefore, the researcher's assumption that the new method would increase training time was unfounded.

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Answer:

A = 267 calories; B = 257 calories

Step-by-step explanation:

We can set up a system of equations to find how many calories each candy bar provides.

The information gives us:

A + 2B = 781 and 2A + B = 791.

Substitution will be easier, and we can isolate A from the first equation and then plug it in for A in the second equation:

[tex]A+2B=781\\2A+B=791\\\\A=781-2B\\\\2(781-2B)+B=791\\1562-4B+B=791\\1562-3B=791\\-3B=-771\\B=257[/tex]

Now we can plug in B into the first equation to find A:

[tex]A+2(257)=781\\A+514=781\\A=267[/tex]

If two cities on map are [tex]5\frac{3}{4}[/tex] inches apart, then the actual distance between the cities is 345 miles .

In the question ,

it is given that ,

the scale on the map is 1/2 inches is = 30 miles .

So , 1 inches on the map is = 60 miles.

So , the scale factor is 1 inch = 60 miles .

also given that the distance between the two cities on the map is = [tex]5\frac{3}{4}[/tex] inches ,

means , 23/4 inches .

So , the actual distance is = 23/4 × 60

Simplifying further ,

we get ,

= 345 miles .

Therefore , the actual distance is 345 miles , the correct option is (d) .

The given question is incomplete , the complete question is

The scale on a map reads 1/2 inch = 30 miles. If two cities on the map are [tex]5\frac{3}{4}[/tex] inches apart, find the actual distance between the cities.

A. 300 miles

B. 315 miles

C. 327 miles

D. 345 miles

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The answers are Triangle = 10, circle = 5, Two halves of Square = 2 and Fourth answer: 20

Logical or deductive reasoning involves using a given set of facts or data to deduce other facts by reasoning logically. It involves drawing specific conclusions based on premises.

Figuring out the triangle first is easiest because since 3 triangles make 30, then each triangle must be 10.

Now, we have our second equation become 10 + C + C = 20, and we get C=5 after solving for the value of the circle.

Our third equation will be 5 + S + S = 13, which becomes 5+2S=13, 2S=8, and then S=4, so the value of a square is 4

Our fourth equation will be 10 + 5*(1/2)(4) = ?, and we see that half of 4 is 2, so we have 10 + 5(2) = 10 + 10 = 20 as our answer.

Hence, The answers are Triangle = 10, circle = 5, Two halves of Square = 2 and Fourth answer: 20

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Answer:

A) [tex]g(x) = (x - 2 )^{2}[/tex]

Explanation:

Since the equation g(x) is similar to f(x), but translated horizontally, then we can conclude that there is a change in the x value.

Since, the equation g(x) is slide to the right by 2 factor, then there will be a change in x value by -2 factor.

For equation B, the graph will move to the left of f(x) by two factor.

For equation C, the graph will move up of f(x) by two factor.

For equation D, the graph will move down of f(x) by two factor.

Hypotheses: H0: μ1 = μ2 and H1: μ1 ≠ μ2.This hypothesis test is a two-tailed test.

Calculate the pooled standard deviation of the two samples.

Let x1 and x2 be the sample means of the National League and American League, respectively. Let s1 and s2 be the sample standard deviations of the National League and American League, respectively. Let n1 and n2 be the sample sizes of the National League and American League, respectively.

Pooled standard deviation = √[( (n1 - 1)s1^2 + (n2 - 1)s2^2 ) / (n1 + n2 - 2)]

s1 = 6.9282

s2 = 6.3246

n1 = 2

n2 = 2

Pooled standard deviation = √[( (2 - 1)6.9282^2 + (2 - 1)6.3246^2 ) / (2 + 2 - 2)]

Pooled standard deviation = 6.6759

Calculate the degrees of freedom (df).

Degrees of freedom (df) = n1 + n2 - 2

df = 2 + 2 - 2

df = 2

Calculate the t-statistic.

Let μ1 and μ2 be the population means of the National League and American League, respectively.

t-statistic = (x1 - x2 - (μ1 - μ2)) / √(s^2 / n1 + s^2 / n2)

x1 = 18

x2 = 19

μ1 = μ2

s2 = 6.6759

n1 = 2

n2 = 2

t-statistic = (18 - 19 - (μ1 - μ2)) / √(6.6759^2 / 2 + 6.6759^2 / 2)

t-statistic = (-1) / (4.4518)

t-statistic = -0.2244

At a significance level of 0.10,

The critical value for a two.

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