consider any two numbers a, b with a < b. if x is the uniform distribution on the interval [a, b], what is the variance of x?

If a rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals, the dimensions are 90 feet and 120 feet

From the figure

4x + 3y = 720

3y = 720 - 4x

y = 240 - (4/3)x

The area = l × w

Where l is the length

w is the width

Substitute the values in the equation

A = 2x × y

= 2x (240 - (4/3)x)

Apply the distributive property

= 480x - (8/3)x^2

Differentiate the values

0 = (-16/3)x + 480

(16/3) x = 480

x = 480 / (16/3)

x = 90 feet

Then,

y = 240 - (4/3)(90)

= 120 feet

Hence, the dimensions are 90 feet and 120 feet

I have answered the question is general, as the given question is incomplete.

The complete question is

A rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?

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In the given question, the absolute percentage increase is 1050 and the relative percentage increase is 32.3076%.

When you want to analyze how a value has evolved over time, a percentage increase is helpful.

Although percentage increase and absolute increase are fairly comparable, the former is more helpful when contrasting different data sets.

For instance, a change from 1 to 51 and a change from 50 to 100 both have an absolute change of 50, but the first change grew significantly more due to the higher percentage growth of 5000% compared to the second change of 100%.

The most popular method of assessing growth is percentage increase because of this.

So, the absolute and relative percentage increase is:

The town's population grew from 3,250 in 2008 to 4,300 in 2010.

2008: P1 = 3250

2010: P2 = 4330

Absolute variation:

Absolute difference = P2 - P1

Absolute difference = 4330 - 3250

Absolute difference = 1050

Relative increase:

Relative percentage = P2 - P1/P1 * 100

Relative percentage = 1050/3250 * 100

Relative percentage = 32.3076

Therefore, in the given question, the absolute percentage increase is 1050 and the relative percentage increase is 32.3076%.

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Correct question:
The population of the town increased from 3,250 in 2008 to 4,300 in 2010. Find the absolute and relative(percent) increase.

Answer: 4.857 x 10^4

Step-by-step explanation:

Answer: 2.5

Step-by-step explanation: 40 divided by 4 = 10  1.4 x 10 = 2.5

Answer:

2.5

Step-by-step explanation:

1/4 is equal to 0.25, So if it's 0.25 for 4 servings, the ratio is 0.25:4. You can the divide 40 by 4 and get 10. You can now take that ten and multiply it by 0.25 to get 2.5 or 2 and 1/2

500 Different number of committees are possible.

Initially we have 7 men and 6 women.

We have to select 4 men and 3 women to form a committee

Number of men are possible 7C4 = 35

Number of women are possible 6C3 = 20

2 of the men are refusing to server together

so we have to subtract the possibilities when these 2 men are sitting together.

we are considering 2 men are already sitting together.

now, we have only need of 2 men  from remaining 5 men.

number of ways to select 2 men from 5 men is 5C2 = 10

We have to subtract 10 from number of men possible.

Number of men possible when 2 of the men refuse to serve together =

35 - 10 = 25.

Number of possible committees are 25*20 = 500.

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The distance of 40 lb will be 5ft, according to the question.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have the given information:

The fulcrum be located from the 40 lb.

The weight of bar is 9ft long.

Now, we will calculate the distance,

40x = 50(x-1)

40x = 50x - 50

40x - 50x = -50

-10x = -50

x = 5

Therefore, the required answer is 5ft.

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The predicted number of calories in a sandwich containing 32 grams of fat is 559.

In algebra, the slope-intercept form of a linear equation is a typical approach to express a line on a graph. A linear equation is written as y = mx + b in standard form.

The y-intercept, or place where the line crosses the y-axis, is represented by the letters b and m, respectively. The point where the lines contacts the y-axis is known as the y-intercept, and the slope is a measurement of how steep the line is. Because it explicitly displays the slope and y-intercept, this equation's form is known as the slope-intercept form.

y = mx + b

Where m is the slope, x is the value of the independent variable, and b is the y-intercept. In this case, the slope is 13 and the y-intercept is 143. So, the equation of the line of best fit is:

y = 13x + 143

To predict the number of calories in a sandwich containing 32 grams of fat, you can plug in 32 for x in the equation:

y = 13 * 32 + 143

y = 416 + 143

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Answer: A 121/324

Step-by-step explanation:

1.0489343455493443 is the result so it is irrational

Answer:

11 or 12  ....?

Step-by-step explanation:

This seems simple... so simple i feel like im overthinking it (x_x)

A Square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side²

The formula to find the side length.

s = √A

The length of the side is 11.8 feet.

A Square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side²

We have,

The total area of the square landing path:

A = 140 square feet.

The formula to use is given,

s = √A

Now,

s = √140

s = √4 x 35

s = 2√35

[ √35 = 5.92 ]

s = 2 x 5.92

s = 11.8 feet

Thus,

The length of the side is 11.8 feet.

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The number of each ingredient of water and grape juice you can use for 75 quarts of punch would be = 112.5 of sparkling water and 56.25 of grape juice.

Recipe is defined as the comprehensive list of items that includes various measurements which is used for making different food meals.

The quantity of sparkling water used for each punch quarts = 1½ = 1.5

1.5 = 1

X = 75

make X the subject of formula;

X = 75×1.5

X = 112.5

The quantity of grape juice used for each punch quarts= ¾ = 0.75

0.75 = 1

y = 75

make y the subject of formula;

y = 0.75×75

y = 56.25

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There is sufficient evidence to conclude that the population standard deviation is different from 0.1.

What is test statistic?

A test statistic is a figure obtained from a statistical analysis. It explains how far your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

Given,

            [tex]H_0:\sigma =0.1\\H_a:\sigma \neq 0.1[/tex]

Test statistic:

Chi square=(20-1)*0.25^2/0.1^2=118.75

df=20-1=19

p-value=CHIDIST(118.75,19)=0.0000

Reject the null hypothesis.

Hence, there is sufficient evidence to conclude that the population standard deviation is different from 0.1.

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Answer:

Step-by-step explanation:

01:06

Answer:

1:06

Step-by-step explanation:

11:06 + 2:00 = 13:06

13:06-12:00= 1:6

The correct is b i.e; the critical value times the standard error of the sampling distribution

Given options are :

a. The biggest sampling error that can be made while maintaining a certain level of confidence.

b. the critical value multiplied by the sampling distribution's standard error

c. the discrepancy between the parameter and the point estimate.

Margin of error

= C * SE

Where C is critical value of on

of is the Standard error

The multiple of Critical Value and Standard error is the margin of error

Correct Option is b i. e the critical value times the Standard error of Sampling distribution

Therefore, The margin of error is the product of Critical Value and Standard Error.

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The probability of getting heads at least twice is 0.5

Since we are given two-sided coin, where the probability of getting heads is equal to the probability of getting tails.NO of outcomes in this case is 2,The probability of getting a head = 1/2, similarly probability of getting a  tail is =1/2 .So when a coin is flipped three times, the sample space for the event will be (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT),  H stands for head and T stands for tails, here for tossing the coin the number of outcomes is 8  .So the probability of getting at least two heads is:  4/8= 1/2 =0.5

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The radius of the circle will be 4.6m.

What is area of a circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value. The area of the circle will be A = [tex]\pi r^{2}[/tex].

The area of the circle given is = 15 m²

Sector of a circle with a central angle of 5π/11 rad

The area will be (1/2) * r² * Ф

15 = (1/2) * r² * (5π/11)

⇒r² = 30 * (11/5π)

⇒r² = 21.00

⇒r=4.6m

Hence, the radius of the circle will be 4.6m.

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Answer:

D. 7.00 < 210.00; h < 30; 30 hours

Step-by-step explanation:

He needs to do 30 hours because:

7.00 < 210$; representing h < = 30; and then you would equal 30 hours

Definitely not A or B because that would represent a fraction which we don’t want

C, also would not work because it would be the opposite.

( I am not stealing points. )

Answer: 45.93 ft

Step-by-step explanation:

Answer: No its not normal

Step-by-step explanation: The question says 60 and 100 beats per minute is normal. Rushing looks at his watch and counts 8 beats in 10 seconds

We can solve by:

[tex]\frac{8}{10}[/tex] = [tex]\frac{x}{60}[/tex] then from that answer we can check if x, the heartbeats falls between 60 and 100.

So to get 60, we have to multiply 10 by 6. We are using proportionality, so we do the same to the numerator to get 8 x 6= 48

We get  [tex]\frac{8}{10}[/tex] = [tex]\frac{48}{60}[/tex]. 48 beats do not fall between 60 and 100, thus the answer is it is not normal.

Answer:

Step-by-step explanation:

You want the volume and surface area of a rectangular crate that is 15 in long, 4 in wide, and 10 in high.

The volume is given by the formula ...

  V = LWH

For the given crate, the volume is ...

  V = (15 in)(4 in)(10 in) = 600 in³

The area is given by the formula ...

  A = 2(LW +H(L +W))

For the given dimensions, the crate has an area of ...

  A = 2((15 in)(4 in) +(10 in)(15 in +4 in)) = 2(60 in² +(10 in)(19 in))

  = 2(60 in² +190 in²) = 500 in²

The crate's volume is 600 cubic inches; its area is 500 square inches.

Answer:

y>2

Step-by-step explanation:

subtract 8 on both sides

Answer:

y > 2

Step-by-step explanation:

y + 8 > 10

Subtract 8 from both sides.

y > 10 - 8

y > 2

A 5% chance exists of concluding there is a difference when there isn't at a significance level of 0.05. Lower levels of significance suggest that you need more proof before you can rule out the null hypothesis.

In statistics, the analysis of variance (ANOVA) method is used to compare the means of two groups.

In an experiment with a completely randomized design, samples are at random assigned to either a treatment group or a placebo group.

For instance, if 40 persons are chosen to evaluate the effects of an analgesic,

four groups—Groups A, B, C, and D—could be created. Different dosages of the medication can be administered to Groups A, B, and C, while Group D receives a placebo. Due to the random grouping of the participants

, this is an illustration of a randomized design.

We assume that the sample populations are normally distributed and have the same variances in order for an ANOVA test to display completely randomized design.

Hence, A 5% chance exists of concluding there is a difference when there isn't at a significance level of 0.05. Lower levels of significance suggest that you need more proof before you can rule out the null hypothesis.

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Answer: (A) There is 1 unit between 0 and 1.

(B) There are 1 units between 0 and 1

(C) There are 0 and -3 so the sum of these two values is 3 units.

Step-by-step explanation:

How to find a distance between two integers? Easy!

First find the absolute value! Its gonna help a lot!

The total area bounded by curve f(x)=x³+1 between (0,2) will be 6 units.

The summing of discrete data is indicated by the integration. To determine the given functions that will characterize the area, displacement, and volume that result from a combination of small data that cannot be measured separately and integrals are calculated. The concept of limit is employed broadly in calculus whenever algebra and geometry are applied.

Given Graph = x³+1

Area between interval x€[0,2]

To get the desired area we have to integrate between x€[0,2]

[tex]\int\limits^2_0 {(x^3 + 1)} \, dx[/tex]

∫x³dx + ∫1dx

[tex]\frac{x^4}{4}[/tex] + x + c

We can find the area by lower limit - upper limit

Putting x = 0

we get result as c

Putting x = 2

We get result as 6+c

So desired area will be ( 6+c ) - c = 6

Hence the total area bounded by curve between (0,2) will be 6 units.

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Answer:

you have to divide

Step-by-step explanation:

621/9=69 so there are 69 blouses on each of the 9 racks

The array that has been sorted using insertion sorting 1 2 3 4 5 6 7 8 9.

A straightforward sorting algorithm called insertion sort functions like how you might arrange playing cards in your hands.

Initial Pass: 2 9 8 7 6 5 1 4 3

The array's first two members are initially compared using an insertion sort.

Since 9 is bigger than 2, they are not arranged in ascending order, and 2 is not in the proper place. So, switch 9 and 2.

Therefore, 2 is currently kept in a sorted sub-array.

Second Pass: Continue with the next two elements and compare them.

2 8 9 7 6 5 1 4 3

Here, 9 is bigger than 8, therefore both items appear to be in ascending order; as a result, there won't be any switching. Along with 8, 9 is also kept in a sorted sub-array.

Third pass: Currently, the sorted sub-array has two entries, which are 2 and 8.

Moving on to the following two components, which are 9 & 7,

2 7 8 9 6 5 1 4 3

Continue sorting similarly; the results would be 1 2 3 4 5 6 7 8 9.

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Answer:

g(x) = x+3

Step-by-step explanation:

f(x) = x+1

g(x) = f(x+2)

so g(x) = (x+2)+1

g(x)=x+3

4 bracelets and 3 Necklaces are made by the Jeweler.

Two or more expressions with an Equal sign is called as Equation.

Let us represent Bracelet as B and Necklace as N

B+N=7..(1)

7B+18N=82..(2)

From equation 1,

B=7-N

Now plug in B value in equation 2

7(7-N)+18N=82

49-7N+18N=82

49+11N=82

Subtract 49 on both sides

11N=33

N=3

Now we have to find B

B+N=7

B+3=7

Subtract 3 on both sides

B=4

Hence, 4 bracelets and 3 Necklaces are made by the Jeweler.

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The number of positive and negative real roots of the function

x³ - x² - x - 5 are 1 and 2 respectively.

What is Descartes' Rule?

Descartes' rule of sign is used to determine the number of real zeros of a polynomial function. It tells us that the number of positive real zeros in a polynomial function f(x) is the same or less than by an even numbers as the number of changes in the sign of the coefficients.

Number of positive real roots of f(x) ≤ Number of sign changes f(x)

Number of negative roots of f(x) ≤ Number of sign changes of f(-x)

According to the given questions:

The given polynomial function f(x) = x³ - x² - x - 5

We can observe the number of sign changes in the coefficients

The sign changes only once

hence there is one positive real root

Now, f(-x) = -x³ + x² - x + 5

Clearly sign changes 2 times evenly

Therefore the function has 2 negative real roots

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Answer:

Step-by-step explanation: