0.

E

e

t

15. Luke needs a new fence around his garden,

but the gate across the narrow end of the

garden will not be replaced. Write and

evaluate a numerical expression to find

how many feet of fencing Luke needs.

14 ft

3 ft

12 ft

14 ft

Jessica has three dice with 10 sides, 13 sides and 5 sides respectively and she rolls all dice once and if Z is number of ones occur then

The expectation value i.e, E(Z) is 0.376 and variance V[Z] = 0.321..

Indicator method :

This is a powerful way to find expected counts. This follows from the observation that the number of "good" outcomes in a trial can be counted by first coding each "good" outcome as one, coding each other outcome as zero, and then adding 1 and 0.

let X₁ be the outcome of a 10 sided die

X₂ be the outcome of 13 sided die

X₃ be the outcome of 5 sided die

let l₁ ,I₂ ,I₃ be three indicator functions such that

I₁ =1 if X₁ = 1

=0 otherwise

I₂ = 1 if X₂ = 1

=0 otherwise

I₃ = 1 if X₃ = 1

=0 otherwise

so Z denotes the number of ones showing when the three dice are rolled once.

so Z=I₁ +I₂ +I₃

so E[Z]=E[I₁]+E[I₂]+E[I₃]

so E[I₁]=1×P[X₁=1] = 1/10

E[I₂]=1×P[X₂=1] = 1/13

E[I₃]=1×P[X₃=1] = 1/5

so, E[Z]=1/10+1/13+1/5=49/130 = 0.3769

the variance = V[Z] = V[I₁]+V[I₂]+V[I₃] since the outcomes of the 3 different die are independent to each other hence no covariance term.

V[I₁]= 1²P[X₁=1]- E²[I₁]=1/10 -(1/10)²= 0.09

V[I₂]= 1²P[X₂=1]- E²[I₂]=1/13-(1/13)²= 12/169 = 0.071

V[I₃]= 1²P[X₃=1]- E²[I₃]=1/5 -(1/5)²= 4/25 = 0.16

so V[Z]= 0.09 + 0.071 + 0.16 = 0.321

Hence, the expectation value i.e, E(Z) is 0.3769..

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Check the picture below.

Answer: 212.50

Step-by-step explanation: she has 60% or  127.5

Answer:

-1/2

Step-by-step explanation:

Slope= [tex]\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex].

(5-2)/(-8+2)

Simplify:

3/-6

-1/2

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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The correct option  b. trial-and-error, is employed in the approach to issue solving that entails testing each potential solution until one is successful.

Trial and error is attempting a way, seeing if it succeeds, and trying a different method if the first one doesn't.

Thus, trial-and-error, is employed in the approach to issue solving that entails testing each potential solution until one is successful.

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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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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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The angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.

what is the rate of change in calculus?

The rate of change defines the relationship between two changing variables. Consider a moving object that moves twice as much in the vertical direction (y) as it does in the horizontal direction (x). This can be expressed mathematically as y = 2x.

Let 'θ' represent the angle between the minute and hour hand.

Let θ1 be the angle between the minute hand and 12.

                     [tex]\frac{d\theta_2}{dt}=\frac{1}{60*12}\times2\pi\\\\\frac{d\theta_2}{dt}=\frac{\pi}{360}[/tex](Between hour hand and 12)

                     [tex]\theta=\pm(\theta_1-\theta_2)\\\\\frac{d\theta}{dt}=\pm(\frac{d\theta_1}{dt}-\frac{d\theta_2}{dt})\\\\\frac{d\theta}{dt}=\pm(\frac{\pi}{30}-\frac{\pi}{360})\\\\\frac{d\theta}{dt}=\pm5.5$ degree$[/tex]

Hence the angle between a clock's minute and hour hands changing at 10 o'clock in the morning is 5.5 degrees/minute.

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Answer:

1. EF ≈ 22.00

2. m∠E ≈ 36.20°

3. m∠F ≈ 53.81°

Step-by-step explanation:

1. Use the trigonometric function sine.

sin(60°) = EF / 25.4

EF = 25.4 sin(60°)

EF ≈ 22.00

2. Use the inverse of the trigonometric function sine (denoted arcsin).

sin(m∠E) = 15/25.4

m∠E = arcsin(15/25.4)

m∠E ≈ 36.20°

3. Use the inverse of the trigonometric function cosine (denoted arccos).

cos(m∠F) = 15/25.4

m∠F = arccos(15/25.4)

m∠F ≈ 53.81°

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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Answer:

24

Step-by-step explanation:

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. )

The equation of the line is [tex]y = -\frac{3}{4}x[/tex].

What is the equation of a line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

We have,

the line passes through the point (4,-3),

the points perpendicular to the line 4x - 3y = 3

The equation of a line in slope-intercept form is y = mx + c ( m is the slope and c is the y-intercept).

rearrange 4x - 3y = 3 into this form

subtract 4x from both sides

- 3y = - 4x + 3 ( divide all terms by - 3 )

[tex]y = \frac{4}{3}x - 1[/tex] ← in slope-intercept form

with slope m = 4/3,

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular} = \frac{1}{-m} = \frac{1}{-\frac{4}{3} } = \frac{3}{-4}[/tex]

[tex]y = -\frac{3}{4}x + c[/tex] ← is the partial equation

To find c substitute (4, -3) into the partial equation,

-3 = -3 + c

c = -3 + 3

c = 0,

[tex]y = -\frac{3}{4}x[/tex]

Hence, the equation of the line is [tex]y = -\frac{3}{4}x[/tex] .

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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

Answer: A 121/324

Step-by-step explanation:

1.0489343455493443 is the result so it is irrational

The efficiency of slotted aloha by letting n approach infinity is 1/e and the maximum value of probability is 1/n.

Given that:

No. of nodes = (n)

The efficiency of slotted aloha by letting n approach infinity is E (p)= np(1-p)^(n-1).

By derivation,

E' (p) =  n(1-p)^(n-1) - np(n-1)(1-p)^(n-2)

E' (p) =  n(1-p)^(n-2) x [(1- p) - p(n-1)]

E' (p) =  n(1-p)^(n-2) x [1-np]

Let E'(p) =0

i.e. Either,  n(1-p)^(n-2) = 0

=> p = 1 (minima)

Or [1-np] = 0

=> p = 1/n (maxima)

So, for the value of p* = 1/n, we can maximize this expression.

When  p = 1/n, the efficiency of slotted aloha is

E(p*) = n.1/n (1-1/n)^(n-1)

E(p*) = (1-1/n)^(n-1)

E(p*) = (1-1/n)^n/(1-1/n)

Since, [tex]\lim_{n \to \infty} (1-1/n) = 1\\[/tex]

[tex]\lim_{n \to \infty} (1-1/n)^n = 1/e[/tex]

So, when n approaches infinite,

Efficiency =>  [tex]\lim_{n \to \infty} E(p*) = 1/e[/tex]

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The graph which represents the equation f ( x ) = [ x + 1 ] is Option 4.

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = [ x + 1 ]

The function f ( x ) can be written as

y = [ x + 1 ] , where the equation f ( x ) = y

Substituting the value for x , we get

a)

when x = 0

The value of equation is

y = [ x + 1 ]

y = [ 0 + 1 ]

y = 1

So , the coordinates are ( 0 , 1 )

b)

when x = 1

The value of equation is

y = [ x + 1 ]

y = [ 1 + 1 ]

y = 2

So , the coordinates are ( 1 , 2 )

c)

when x = 2

The value of equation is

y = [ x + 1 ]

y = [ 2 + 1 ]

y = 3

So , the coordinates are ( 2 , 3 )

d)

when x = -1

The value of equation is

y = [ x + 1 ]

y = [ -1 + 1 ]

y = 0

So , the coordinates are ( -1 , 0 )

Hence ,

On plotting the points in the graph , we get the equation as y = x + 1

And the solution is Option D.

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Answer: 4.857 x 10^4

Step-by-step explanation:

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 percent of the probability that a female patient will have type-o blood is 46.7%

To know the percent of female patients who will be having type 0 blood, all you have to do is divide the number of female patients with O-blood type by the total number of patients with O-blood type. Then finally you will have to multiply the quotient by 100 to get the percent as follows:

number of females with o-blood type = 140 Females

total number of patients with o-blood type = 300 patients

Percentage of Females with o-blood type = (140/300) * 100 = 46.7%

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The number of movies on which Avery's songs were played is 2 times

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

Songs played in commercial = $40

Songs played in movie = $140

Total earnings = $480

Number of times played on commercial = 7

The above parameters when represented as an equation is

Total earnings = Songs played in commercial * Number of times played on commercial + Songs played in movie * Number of times played in a movie

Substitute the known values in the above equation, so, we have the following representation

40 * 7 + 140 * Number of times played in a movie = 480

Evaluate the products

280 + 140 * Number of times played in a movie = 480

So, we have

Number of times played in a movie = 200/140

Evaluate

Number of times played in a movie = 2

Hence, the number of times is 2 times

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Answer: 45.93 ft

Step-by-step explanation:

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: 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.

In Lorentz transformations we have velocity based factors that is not present in Galilean ones.

The relationship between two distinct coordinate frames that are moving relative to one another at a constant speed is known as a Lorentz transformation. Dutch physicist Hendrik Lorentz is credited with coining the name of the transformation. There are two frames of reference: Inertial Frames, which refer to motion that has a constant speed.

The relationship between two distinct coordinate frames that are moving relative to one another at a constant speed is known as a Lorentz transformation. Dutch scientist Hendrik Lorentz is credited with coining the term transformation. There are two frames of reference: Inertial Frames, which relate to motion that has a constant speed.

Any and all rulers and other self-contained length standards, such as those you might use to set up a measurement frame, can be contracted in length based on velocity. This results in the Lorentz factor at the place in the LT.

Any and all clocks and other physically independent systems, such as those used to record events in a measurement frame, are subject to velocity time dilation. As a result, the LF is temporarily in the LT.

The fact that applying Einstein synchronisation individually for each measurement frame turns out to be natural. Consequently, the position-dependent synchronisation offset between the clocks of one measurement frame and those of the other is represented by the enigmatic second term in the LT for the time.

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Answer:If Amy is not tardy, then she will not get a detention

Step-by-step explanation:

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:

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