use the appropriate normal distribution to approximate the resulting binomial distributions. a fair coin is tossed 130 times. what is the probability of obtaining between 55 and 69 tails, inclusive? a) 0.7523 b) 0.7134 c) 0.7221 d) 0.7179 e) 0.7494 f) none of the above.

Emma would need to invest about $320 to increase her value by $480 over the course of 8 years.

We may use the compound interest formula to determine how much Emma would need to invest:

[tex]\mathrm{A = P(1 + r/n)^{(nt)}}[/tex]

Where:

A is equal to the final sum, in this case $480.

P is the principal sum, which represents the initial investment that we're looking for.

r = the yearly interest rate (0.055 in decimal form, or 5.5%)

n = the number of times the interest is compounded annually (in this case, n = 1 because it is compounded annually).

t = the number of years, in this instance 8 years.

Let's substitute the known values into the formula and solve for P:

[tex]\mathrm{480 = P(1 + 0.055/1)^{(1\times8)}}[/tex]

Simplifying:

[tex]480 = \mathrm P(1.055)^8[/tex]

Dividing both sides by (1.055)⁸:

[tex]\mathrm {P = \frac{480 }{ (1.055)^8}}[/tex]

P ≈ $480 / 1.50

P ≈ $320

Hence the amount to be invested is $320.

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Answer:

28

Step-by-step explanation:

substitute the given values into the expression

x(2 - 4y² )

= - 2(2 - 4(- 2)² )

= - 2(2 - 4(4))

= - 2(2 - 16)

= - 2(- 14)

= 28

Correct option is " B " the is the test statistics is 1.341 when sample 1: n₁=16, x₁=44, and s₁=5 and sample 2:x₂ = 41, s₂ = 6, n₂ = 9.

Given that,

Assume you are conducting a two-sample test of averages and that the variances in the population are identical. The information below is ours:

Sample 1: n₁=16, x₁=44, and s₁=5.

Sample 2:x₂ = 41, s₂ = 6, n₂ = 9.

We have to find the test statistic.

We know that,

n₁ = 16

x₁ = 44

s₁ = 5

n₂ = 9

x₂ = 41

s₂ = 6

We have

t= (x₂ - x₁)/√(n₁-1)s₁²+(n₂-1)s₂²/n₁+n₂-2(1/n₁+1.n₂)

t = 1.341.

Therefore, Correct option is " B " the is the test statistics is 1.341 when sample 1: n₁=16, x₁=44, and s₁=5 and sample 2:x₂ = 41, s₂ = 6, n₂ = 9.

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The ratio of the area of a square inscribed in a semicircle to the area of a square inscribed in a circle is 2/5.

What is a semicircle?

A semicircle in mathematics is a one-dimensional locus of points that makes up one-half of a circle. A semicircle's entire arc always measures 180 degrees. There is only one symmetry line in it.

For instance, if the radius is known, we can use the formula, which states that the area of a semicircle is equal to half that of a circle. As a circle's area is r2, Therefore, a semicircle's area is equal to 1/2(r2), where r is its radius. 3.14, or 22/7, is the value of.

Solution Explained:

Let's assume and take

The dimensions of the little square ABCD = 2 x 2 =4

of the little triangle's hypotenuse Radius of the semi-circle for BCG

H=sqrt(5) = The semicircle's radius

IHJK = 2sqrt is the diagonal of the huge square (5)

One side of the large square is IHJK when sin(45) x 2sqrt(5) = sqrt(10).

Therefore, the area of ABCD/area of IHJK is equal to 4/sqrt(10)2 = 2/5.

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The students weren't assigned the treatments (new menu item) at random.

In an experiment, randomization refers to assigning volunteers randomly to the treatment. For example, we may define randomization as setting people to therapy at random.  

The results are fair because randomization eliminates bias. To make the results of the experiment precise, it ensures that the groups created for experimenting are as similar to one another as possible.

In the given example, the menu items are not randomly assigned. Because the students were given a choice to choose a menu item instead of selecting the new menu item randomly.  If randomly assigned all the new menu items will have an equal probability of being chosen.

Therefore, option b is the correct option.

The complete question is -

Thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. Each student was given a choice between the macaroni and cheese and the Cajun potato barrels. From the sample, 20 students selected macaroni and cheese and 16 students chose the Cajun potato barrels. Each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). Which of the following prevents this study from being a well-designed experiment?

a) There was no replication because students did not eat both menu items.

b) The treatments (new menu item) were not randomly assigned to the students.

c) An item that is currently on the menu should have been used as a control.

d) Students should not have been randomly selected.

e) There were no problems, and the study was a well-designed experiment.

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The dimensions of the rectangle that will maximize the area of the window are length, L = 3.41 feet and width, w = 3.41 feet

Given: Perimeter (P) = 19 feet

Perimeter of window = Perimeter of rectangle + Perimeter of semicircle

P = 2(2r + L) + πr

where r = radius of the semicircle and   L = length of the rectangle

width(w) of the rectangle = 2r

Note: the diameter of the semicircle is the width of the rectangle

19 =  2(2r + L) + πr

19 = 4r + 2L + πr

2L = 19-4r-πr

L = 19/2 -2r- πr/2

Find the area (A) of the window:

A = Area of Rectangle + Area of Semicircle

A = 2rL + 1/2πr²

Put L into A = 2rL + 1/2πr²:

A = 2r(19/2 -2r- πr/2) + 1/2πr²

A = 19r - 4r² - πr² + 1/2πr²

A = 19r - 4r² - 1/2πr²

To maximize the area, differentiate both sides and set A' = 0

A = 19r - 4r² - 1/2πr²

A'  = 19 - 8r - πr

0  = 19 - 8r - πr

8r + πr = 19

r(8 + π) = 19

r = 25/(8 + π)

width(w) = 2r

w = 2[19/(8 + π)]

w = 38/(8 + π)

w = 3.41 feet

put r = 19/(8 + π) into L = 25/2 -2r- πr/2:

L = 19/2 -2(19/(8 + π))- π(19/(8 + π))/2

L = 19/2 - 38/(8 + π) - 19π/2(8 + π)

L = [19(8 + π) - 19(2)- 19π] / [2(8 + π)]

L = 38/(8 + π)

L =  3.41 feet

Therefore, the dimensions of the rectangle are length of 3.41 feet and width of 3.41 feet

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The sum of their ages 5 years ago is x + y -10.

The process of subtracting one number from another is known as subtraction.

Given that, Jean is x years old and her younger brother is y years old.

Age of Jean 5 years ago is:

x - 5

The age of Johnathan 5 years ago is:

y - 5

The sum of their ages 5 years ago is:

x - 5 + y - 5

= x + y -10

Hence, the sum of their ages 5 years ago is x + y -10.

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a. The transformed equation is given as follows: h(x) = |x - 2| - 3.

b. The graph of the two functions is shown by the image presented at the end of the answer.

The translations are movements to the triangle in each of these directions:

The parent function in this problem is given as follows:

f(x) = |x|.

The first translation was a vertical translation three units down, hence we have that:

g(x) = f(x) - 3 = |x| - 3.

The second translation was a horizontal translation two units right, hence the have that the definition of the transformed equation h(x) is given as follows:

h(x) = g(x - 2) = |x - 2| - 3.

The graph of the functions is given by the image shown at the end of the answer, and the translations are verified on every point of the function, but especially the vertices.

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If a certain unit of a commodity is produced with a marginal cost of [tex]\frac{dc}{da} =9x^{2}+4x+15x^{1/4} +10[/tex], the cost of producing the first 126 units is 289.4

How to differentiate a function?

Differentiation is a way of showing rate of change of a function at a given time.

The given function  [tex]\frac{dc}{da} =9x^{2}+4x+15x^{1/4} +10[/tex],

Differentiate with respect to x

[tex]\frac{dc}{da} =18x+4+\frac{15}{4} x-^{3/4}[/tex]

input the value 100 for the value of x,

This implies that [tex]\frac{dc}{da} =18x+4+\frac{15}{4} x-^{3/4}[/tex]

[tex]\frac{dc}{da}[/tex]=1800+4+[tex]\frac{15}{4}[/tex] x[tex]\frac{1}{\sqrt[4]{100^{3} } }[/tex]

[tex]\frac{dc}{da}=1800+4+\frac{15}{4}x\frac{1}{3.16}[/tex]

Simplifying further

[tex]\frac{da}{da} =1804+4.75[/tex]

[tex]\frac{dc}{da} =1808.75\\[/tex]

To produce the first 16 units,

[tex]\frac{1808.75}{100} }[/tex] x [tex]\frac{16}{1}[/tex]

The cost of producing the first 16 units is 289.4

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Answer:i am pretty sure it is c

Step-by-step explanation:

this is because it says Which graph best shows how many days each project has lasted? and c is the only one that is talking about days

The measure of the radius of the sphere is given as follows:

r = 359 cm.

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

V = πr²h

Which is the base area given by πr² multiplied by the height h.

In the context of this problem, the parameters are given as follows:

The volume of the circumscribed cylinder is 2154.04π cm^3, hence the equation to solve for r is given as follows:

πr²h = 2154.04π

2πr³ = 2154.04π

2r³ = 2154.04

r = cube root of (2154.04/2)

r = 359.

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The critical value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% significance level is 0.84

Given that,

Of the 62 swim teachers who participated in the survey, 37 claimed that teaching the butterfly stroke is the most challenging. Find the criticial value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% level of significance.

This is right tailed test

Z [tex]\alpha[/tex]  = Z 0.01 = 0.84   ( Using z table )  

Therefore, the critical value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% significance level is 0.84

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Based on the slopes of both lines, the relationship between both lines is: D. a and b are perpendicular.

The relationship between two lines that are parallel is that they have the same slope, while the relationship between perpendicular lines is that their slopes are negative reciprocals of each other.

Find the slope of the line that passes through (-5, -2) and (-5, -5):

Slope (m) = change in y / change in x = (-5 -(-2)) / (-5 -(-5))

m = (-5 + 2) / (-5 + 5)

m = -3/0 [cannot divide, therefore, the slope is undefined).

The line is therefore a vertical line.

Find the slope of the line that passes through (0, 4) and (5, 4):

Slope (m) = change in y / change in x = (4 - 4) / (5 - 0)

m = 0/5

m = 0

This line is an horizontal line.

In conclusion, the relationship between a vertical and a horizontal line is that they are perpendicular to each other, therefore, the answer is: D. a and b are perpendicular.

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The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.

Traditional IT and project finance methods offer a key business risk and, if not modified, jeopardize the future of technology-based enterprises.

This excerpt from the whitepaper Changing the Finance Method by Keanen Wold, Levi Geinert, Shaun Norris, Charles Betz, Beth Dumke, Sam Guckenheimer, and Troy Magennis discusses that contradiction over how traditional financing methods handle ethical concerns and also what Agile and DevOps teams require to execute successfully.

Balancing the high-risk investment in innovation (research and development department) with regular business-as-usual responsibilities has always been difficult for organizations. Too much risk might, in the case of an unexpected failure, result in a business's dissolution; too little innovation could ultimately cause the company to be overtaken and lose market share to rivals and new upstarts.

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The gain Renata Corporation got from the sale of equipment is $16420

The tax depreciation method used in the United States is called MACRS, or Modified Accelerated Cost Recovery System. In other words, the method used to determine your business's tax deductions based on the depreciation of your tangible (depreciable) assets is known as MACRS depreciation.

Equipment Book value =

Purchase price - MACRS depreciation

= $328, 400 - $147,780

=$1,80,620

Gain = sale price - Book value

= $197, 040 - $180620

=$ 16420

Gain up to total depreciation is to be treated as ordinary income, that is up to $147, 780. since the gain is $16,420 within depreciation, it is treated as ordinary income.

Renata Corporation has a gain of $16,420 of which $16, 420 is treated as ordinary income due to the section 1245 recapture

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The measure of the angle RQP = 60 degrees and the value of x is 16 and the measure of the arc RMP is 240 degrees.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).

It is given that:

A circle:

The measure of the arc RMP = 360 - Arc RP

The measure of the arc RMP = 360 - 120 = 240 degrees

The measure of the angle RQP = 1/2[240 - 120]

The measure of the angle RQP = 60 degrees

In the second circle:

9(9 + x) = 15(15)

9 + x = 25

After solving we get:

x = 16

Thus, the measure of the angle RQP = 60 degrees and the value of x is 16 and the measure of the arc RMP is 240 degrees.

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Answer:

It should be 1/5

Since the fractional versions of the ratios are equal, the ratios are equivalent.

The number of files sorted in the first one and a half hours of sorting is 945.

Here, we are given that a group of clerks must sort 1775 files.

Each clerk sorts at a constant rate of 30 files per hour.

Let the number of clerks who start working initially be x.

Thus, they will sort 30x files in the first hour.

After the first hour, let the number of clerks who stop working be a

Thus, the number of files sorted in the second hour will be 30(x - a)

Similarly, the number of files sorted in the third hour will be 30(x - 2a)x

In the last 10 minutes, the number of files sorted will be 5(x - 3a)

Thus, we can form the following equation-

30x + 30(x - a) + 30(x - 2a) + 5(x - 3a) = 1775

30x + 30x - 30a + 30x - 60a + 5x - 15a = 1775

95x - 105a = 1775

19x - 21a = 355

x = (355 + 21a)/ 19

since x and a both have to be integers, (355 + 21a) must be divisible by 19.

This is the case when a = 3

⇒ x = (355 + 21*3)/ 19

x = 418/ 9

x = 22

Now, the number of files sorted in first one and a half hours will be-

30x + 15(x - a)

= 30*22 + 15(22 - 3)

= 660 + 15*19

= 660 + 285

= 945

Thus, the number of files sorted in the first one and a half hours of sorting is 945.

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Answer: 32 jackets

Step-by-step explanation:

add 1280 to 1176 then divide the sum by 75

Answer:

200

Step-by-step explanation:

To find that out, you divide 1,000 by 5.

1,000 ÷ 5 = 200

Could you please mark me as Brainliest? Thank you!

Answer: 200

Step-by-step explanation: 1000 divided by 5 = 200

Answer:

45, odd

Step-by-step explanation:

54-9=45

The equations out of the following that are true would be:

The remaining two I am not certain if they are true or not. The way they were laid out made little to no sense. If you could maybe evaluate further on the other options, perhaps I can double check them for you and see if there are any other remainder options that are true. However, I know for certain that A and B are true.

Answer:

32−4x=12,

25 over x end fraction plus 4 equals 9 ((25)/(x)+ 4 equals 9), and

x over 5 end fraction plus 5 equals 6 ((x)/(5) plus 5 equals 6)

Step-by-step explanation:

hope this help

The work that has been done on player 2 by player 1 is a negative work. Option A.

We define the work done as a situation in which the force that is applied moves a distance in the direction of the force. In this case we ought to know that a negative work is said to be done when the object is found to slow down at te application of the force. The meaning of this is that the force acts in such a way as to slow down motion which makes it a negative force.

For the fact that football player one pushes against football player two, causing player two to slow down from moving any farther down the field, a negative work is done.

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Answer: 4 hours

Step-by-step explanation:

322.58 - 200.14 = 122.44

122.44 divided by 30.61 = 4

The number form that includes only rational numbers are

(-2/3, 0, 0.321, √49, 101/3}

A rational number is one that has the form p/q, where p and q are both integers and q is not zero

Rational function means that the equation will be a fraction

examining the numbers

(-2/3, 0, 0.321, √49, 101/3}

-2/3 is already a fraction

0 = 0/1 hence can be written as a fraction

√49 = 7 = 7/1

101/3 already a fraction

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Each of the three angles of the triangles whose sum of angles is 180 degree measures 75°, 65°, and 40°

An easy geometric instrument like a protractor is used to measure angles. A protractor is employed more frequently than a compass. Angle measurement is important for determining the precise angle. In geometry, there are several sorts of angles that we face in our daily lives, and we may measure angles using these tools.

Basic geometric instruments like a protractor and a compass are used to measure angles. These instruments aid in determining an angle's precise measurement. A protractor aids in producing an accurate angle measurement, while a compass aids in creating the angle. Angles can be measured in three different ways: in degrees, radians, and revolutions.

Here, we have

Let the largest angle be x degrees, the median y, and the smallest z.

x = 2y - 55

z = y - 25

x + y + z = 180

Substituting for x in the last equation:

2y - 55 + y + z = 180

3y + z = 235  

From the second equation:

- y + z = -25     Subtract this from the last equation:

4y = 260

y = 65 degrees

z = 65 - 25 = 40 degrees.

and x = 180 - 65 - 40 = 75 degrees.

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The given series [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] is convergence and the sum of the series is 33/28.

In the given question we have to check whether the series converge or not. If the series does converge, then we have to find the sum.

The given series is [tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex].

Firstly we check the convergence of the given series.

When a series approaches a limit, it is considered to be convergent if both convergent and divergent behaviour occur. The deletion of a finite number of terms from the beginning of a series has no impact on convergence or divergence.

We can write the series as:

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex]

As |0.3|<1 and |0.2|<1

Then [tex]\sum_{n=1}^{\infty}(0.3)^{n-1}\text{ and }\sum_{n=1}^{\infty}(0.2)^n[/tex] is convergent.

So [tex]\sum_{n=1}^{\infty} (0.3)^{n-1}-\sum_{n=1}^{\infty}(0.2)^{n} \right[/tex] is also convergent.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\sum_{n=1}^{\infty} (0.3)^{n-1}-(0.2)\sum_{n=1}^{\infty}(0.2)^{n-1} \right[/tex]

Series [tex]\sum_{n=1}^{\infty}(x)^{n-1}[/tex] converges to 1/x-1 for |x|<1.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{1-0.3}-(0.2)\frac{1}{1-0.2}[/tex]

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ]=\frac{1}{0.7}-\frac{0.2}{0.8}[/tex]

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 10/7 - 1/4

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex] = 33/28

Hence, the sum of the given series is 33/28.

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The right question is:

Determine whether the series is convergent or divergent.

[tex]\sum_{n=1}^{\infty}\left [ (0.3)^{n-1}-(0.2)^{n} \right ][/tex]

If is is convergent, find the sum. (If the quantity diverges, enter diverges.)

Answer:

On the 4th day, the sum of penalties and charges will be the same in both the school library and the town library.

Step-by-step explanation:

School library

Penalty-25

Every day charge-5

City library

Penalty-5

Every day charge-10

Let the day when total fee at both libraries will be same be x

Total charge in school library-25+5x

Total charge in city library-5+10x
They both amount to be equal