It was claimed that when tossing a fair coin 4 times it is quite likely to not obtain 2 heads and 2 tails. However, when tossing a fair coin 4,000 times one should expect to obtain number of tails in the range between 1940 and 2060. Let us compare the situation for 2 versus 2,000 coins. Let X be the number of heads when tossing a fair coin 2 times and let Y be the number of heads when tossing a fair coin 2,000 times.
1. P(940 ≤ Y ≤ 1,060) is equal to:______.2. E(X) is equal to:______.3. The standard deviation of X is equal to:______.4. E(Y) is equal to:_______.

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images below to see the step by step explanation to the question above.

Answer:

Reflection over x, Stretch by 1/2, translate up 3 units

Step-by-step explanation:

:)

The graph of the function h(x) has undergone three transformations to produce the function f(x) = -1/2h(x) + 3: a reflection in the x-axis, a vertical scaling by 1/2, and a vertical shift upward by 3 units.

The function f(x) = -1/2h(x) + 3 has gone through three transformations to become the graph of h(x), which are determined by applying different values of x and the corresponding values of y. Firstly, the graph h(x) is reflected in the x-axis due to the negative sign in front of the h(x), which reverses the direction of the graph. Secondly, the graph is scaled vertically by a factor of 1/2 due to the multiplication of h(x) by 1/2, which compresses the graph towards the x-axis. Lastly, the graph is translated vertically upwards by 3 units as a result of the +3 in the equation, shifting the entire graph upwards.

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Answer:(6,-2)

Step-by-step explanation:

The center swimmer need to be located at the point (6, -2).

Standard form of a circle is given by the equation,

(x - h)² + (y - k)² = r²

where, (h, k) is the center of the circle and r is the radius of the circle.

Given are three points on a circle.

(13, -2), (-1, -2) and (6, -9).

Substituting each of the point in the standard form,

(13 - h)² + (-2 - k)² = r²

(-1 - h)² + (-2 - k)² = r²

(6 - h)² + (-9 - k)² = r²

Since the radius are equal,

(13 - h)² + (-2 - k)² = (-1 - h)² + (-2 - k)² = (6 - h)² + (-9 - k)²

Solving the first two equations, we get,

(13 - h)² = (-1 - h)²

28h = 168

h = 6

From the last two equations,

(-1 - h)² + (-2 - k)² = (6 - h)² + (-9 - k)²

49 + (-2 - k)² = (-9 - k)²

k = -2

Hence the center of the circle is (h, k) = (6, -2).

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Answer:

The amount of white fabric to coloured fabric as a ratio is 20:11

Step-by-step explanation:

We are given that For each 11 mm of colored fabric Nick uses to make his curtains, he also uses 2 cm of white fabric.

Length of colored fabric = 11 mm

Length of White fabric = 2 cm

1 cm = 10 mm

2 cm = 20 mm

So, length of white fabric = 20 mm

So, Ratio of the amount of white fabric to coloured fabric = [tex]\frac{20}{11}[/tex]

Hence the amount of white fabric to coloured fabric as a ratio is 20:11

Answer:

Pr(neither of two groups) = 0.0225

Step-by-step explanation:

Given:

15% of the students have never taken a statistics class = Pr(none)

Pr(none) = 0.15

40% have taken only one semester of statistics =Pr(one semester)

Pr(one semester) = 0.40

the rest have taken two or more semesters of statistics = Pr(two or more semester)

Pr(two or more semester) = 1 - [Pr(one semester) + Pr(none) ]

Pr(two or more semester) = 1-(0.40+0.15) = 1 - 0.55

Pr(two or more semester) = 0.45

Where Pr = probability

Let probability that neither of your two group mates has studied statistics = Pr(neither of two groups)

=Pr(none in group 1) ×Pr(none in group 2)

= 0.15 × 0.15

Pr(neither of two groups) = 0.0225

Answer:

A

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Look at the graph. You want to see how much distance he is at 9 minutes. Go all the way to 9 minutes, then go up. What coordinate does it fall in? (9,80). He travelled 80 meters in 9 minutes. (D)

Answer:

it would move upwards.

Step-by-step explanation:

there is no such thing as a negative exponent because, if you were suppose to graph that you have the parabola go up and down, and that is not how it works.

Answer: She can travel 450 miles with 18 gallons.

Step-by-step explanation:

[tex]\frac{4.8}{120}[/tex] =  [tex]\frac{18}{x}[/tex]   solve by cross product

4.8x = 2160

x= 450

Kelsey's car gets 25 miles per gallon, and with an 18-gallon tank, she can travel a total of 450 miles on a full tank.

To calculate how far Kelsey can travel on a full tank of fuel, first we need to determine her car's fuel efficiency and then apply it to the full tank capacity. We are given that her car can travel 120 miles on 4.8 gallons of gas. This gives us a fuel efficiency rate we can use to find out the total distance she can travel on 18 gallons.

Therefore, Kelsey can travel 450 miles on a full tank of fuel.

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Answer:

When x=0 y=6

When x=3 y=0

Step-by-step explanation:

-6x-3y ≤-18

Let x = 0

-6x-3y =-18

-3y =-18

Divide each side by -3

-3y/-3 = -18/-3

y = 6

Let y = 0

-6x-3y =-18

-6x =-18

Divide each side by -6

-6x/-6 = -18/-6

x = 3

Answer: 0.267

Step-by-step explanation:

The relative frequency is the number of times that we obtained a given outcome divided by the total numer of trials.

In this case we have 75 trials.

in 20 trials the outcome was a 3.

Then the relative frequency of the event "spin a 3" is:

p = 20/75 = 0.266... = 0.267

Answer:

look under the 3 and you get

Answer:

  313

Step-by-step explanation:

We observe that the numbers of cubicles on the open floors have not changed, so we can match the numbers to find the missing one.

The closed floor has 313 cubicles.

To find the number of cubicles on the closed floor, one must subtract the total number of cubicles available when one floor is closed from the original total of all floors. The closed floor has 313 cubicles.

The question asked is about determining the number of cubicles on a floor that is closed for repairs in a 4-story office building. Initially, the building has cubicles for 348 + 313 + 306 + 308 workers. When one floor is closed, it has cubicles for 348 + 306 + 308 workers. To find the number of cubicles on the closed floor, we subtract the total number of cubicles available while the floor is closed from the original total when all floors were open.

The calculation would be as follows:

Step-by-step calculation:

Therefore, there are 313 cubicles on the floor that is closed.

Answer:

[tex]0.428 - 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.3995[/tex]

[tex]0.428 + 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.4564[/tex]

We are confident that the true proportion of people satisfied with the quality of education the students receive is between (0.3995, 0.4564), since the lower value for this confidence level is higher than 0.38 we have enough evidence to conclude that the parents' attitudes toward the quality of education have changed.

Step-by-step explanation:

For this case we are interesting in the parameter of the true proportion of people satisfied with the quality of education the students receive

The confidence level is given 95%, the significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical values are:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The estimated proportion of people satisfied with the quality of education the students receive is given by:

[tex]\hat p =\frac{499}{1165}= 0.428[/tex]

The confidence interval for the proportion if interest is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

And replacing the info given we got:

[tex]0.428 - 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.3995[/tex]

[tex]0.428 + 1.96\sqrt{\frac{0.428(1-0.428)}{1165}}=0.4564[/tex]

We are confident that the true proportion of people satisfied with the quality of education the students receive is between (0.3995, 0.4564), since the lower value for this confidence level is higher than 0.38 we have enough evidence to conclude that the parents' attitudes toward the quality of education have changed.

Answer:26.6 miles

Step-by-step explanation:

Given

Charlie distance to his destination  is a linear function of total driving time

suppose distance d is related to time t as

[tex]d=mt+c\quad \ldots(i)[/tex]

at [tex]d=49\ miles[/tex] after [tex]t=15\ min[/tex]

Substitute in (i)

[tex]49=m(15)+c\quad \ldots(ii)[/tex]

at [tex]d=32.2\ miles[/tex] after [tex]t=39\ min[/tex]

[tex]32.2=m(39)+c\quad \ldots(iii)[/tex]

Solving (ii) and (iii) we get

[tex]m=-0.7[/tex]

substitute in eq (ii) we get

[tex]c=59.5[/tex]

so after [tex]t=47\ min[/tex]  

[tex]d=(-0.7)47+59.5[/tex]

[tex]d=59.5-32.9=26.6\ miles[/tex]

So 26.6 miles is left to travel after 47 minutes

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Took the assignment

Loan length affects total interest by spreading payments; interest rate directly impacts borrowing cost. Relative effect depends on borrower's goals.

The cost of interest for a loan is influenced by both the loan length (term) and the interest rate, but the degree of impact each has depends on several factors, including the specific terms of the loan and the borrower's financial situation. Let's break down their effects:

1. Loan Length (Term):

  - Longer loan terms typically result in lower monthly payments since they spread the principal amount over more payments.

  - However, longer terms also mean more time for interest to accrue, resulting in higher overall interest costs over the life of the loan.

  - For example, if Claudia takes out a loan with a longer term, she may pay less each month but end up paying more in total interest over the entire term compared to a shorter-term loan with the same interest rate.

2. Interest Rate:

  - The interest rate directly impacts the cost of borrowing. Higher interest rates mean higher monthly payments and more interest paid over the life of the loan.

  - Lower interest rates, on the other hand, result in lower monthly payments and less interest paid overall.

  - Even a small difference in interest rates can significantly affect the total interest paid over the life of the loan, especially for large loan amounts or longer terms.

Now, to determine which factor has a greater effect on the cost of interest for Claudia's loan, we need to consider her specific situation:

- If Claudia prioritizes minimizing her monthly payments, she might opt for a longer loan term despite potentially paying more interest in the long run.

- If Claudia is focused on minimizing the total interest paid over the life of the loan, she might prioritize securing a lower interest rate, even if it means higher monthly payments.

Ultimately, the relative importance of loan length and interest rate in determining the cost of interest depends on Claudia's financial goals, her ability to make monthly payments, and her overall financial situation. It's essential for her to carefully consider both factors and choose the loan terms that best align with her needs and financial objectives.

Answer:

6.28 gallons

Step-by-step explanation:

first we need to find the area of a half sphere, and then find how much paint will be needed for that area.

The area of a sphere:

[tex]a=4 \pi r^2[/tex]

thus, the area of half a sphere is:

[tex]a=2 \pi r^2[/tex]

we know that the radius is:

[tex]r=20ft[/tex]

we substitute this to find the area of the half sphere (the area they need to paint):

[tex]a=2\pi (20ft)^2\\a=2(3.1416) (400ft^2)\\a=2,513.27ft^2[/tex]

now the question is how many gallons of paint are needed to paint 2,513.27 square feet.

We are told that 1 gallon covers 400 square feet

thus, we must divide 2,513.27 by 400:

[tex]\frac{2,513.27ft^2}{400ft^2} =6.28[/tex]

6.28 gallons of paint are needed.

Answer:

  -4, 2

Step-by-step explanation:

The equation can be factored as ...

  (x +4)(x -2) = 0

This has solutions that make the factors zero:

  x = -4, x = 2

The solution set is {-4, 2}.

Answer:

Step-by-step explanation:

The shape of the cottage is cube

The edge of the cube is of length is 26ft

L_1 = 26ft.

The roof is in form of a square with with length 17ft.

L_2 = 17ft.

The roof is made up of 4 congruent isosceles triangles. Since the roof extends 2 ft over the edge of the cottage on each side, then the base of each triangle is 26 + 2 = 28 ft.

L_2 = 28 ft

Then, area of the roof is

A = 28²

A = 784 ft²

The triangular pyramid.

The triangular has four sides

Then,

Each of the area can be calculated using

A = ½ × b × h

Then, the four area of the triangular pyramid

A_total = 4 × ½ × b × h

A_total = 2 × b × h

The base of the triangle is 28ft.

The calculate the height of the triangle

Let's calculate the area of one of the triangles and then just multiply by 4. See attachment. Drop a perpendicular from the vertex of a triangle to its base. We now have the triangle broken up into two right triangles. The hypotenuse is 17 ft and one of the legs of the right triangle is 28 / 2 = 14 ft. Then the height is using Pythagoras theorem

a² = b² + c²

17² = 14² + h²

17² - 14² = h²

h² = 93

h = √93

Then, the area of the triangular pyramid is

A = 2 × b × h

A = 2 × 28 × √93

A = 540.04 ft²

Then, the area of the pyramid is approximately 540 ft², since the base of the pyramid cannot be seen.

But if we include the base, then, the total surface area is

A_t = A_triangular + A_base

A_t = 540 + 784

A_t = 1324 ft²

Answer:

D = 141

Step-by-step explanation:

The given quadratic equation is

[tex]5x^2+9x=3\\\\5x^2+9x-3=0[/tex].

It is required to find the value of the discriminant. The value of discriminant  of any quadratic equation is given by :

[tex]D=b^2-4ac[/tex]

Here, a = 5, b = 9 and c = -3

On plugging all the values, we get :

[tex]D=(9)^2-4\times 5\times (-3)\\\\D=141[/tex]

So, the value of discriminant for y is 141.

Answer:

We conclude that the proportion of adults who totally abstain from alcohol​ has changed.

Step-by-step explanation:

We are given that in 1943​, an organization surveyed 1100 adults and​ asked, "Are you a total abstainer​ from, or do you on occasion​ consume, alcoholic​ beverages?"

Of the 1100 adults​ surveyed, 429 indicated that they were total abstainers. In a recent​ survey, the same question was asked of 1100 adults and 352 in

Let p = proportion of adults who totally abstain from alcohol.

where, p = [tex]\frac{429}{1100}[/tex] = 0.39

So, Null Hypothesis, [tex]H_0[/tex] : p = 39%      {means that the proportion of adults who totally abstain from alcohol​ has not changed}

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 39%      {means that the proportion of adults who totally abstain from alcohol​ has changed}

The test statistics that would be used here One-sample z proportion statistics;

                    T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of adults who totally abstain from alcohol = [tex]\frac{352}{1100}[/tex] = 0.32

           n = sample of adults surveyed = 1100

So, test statistics  =  [tex]\frac{0.32-0.39}{\sqrt{\frac{0.32(1-0.32)}{1100} } }[/tex]  

                              =  -4.976

The value of z test statistics is -4.976.

Now, at 0.10 significance level the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Since our test statistics doesn't lie within the range of  critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the proportion of adults who totally abstain from alcohol​ has changed.

The student's question involves a statistical hypothesis test to compare the mean response times between drug-injected and control rats. The calculation of beta, representing the risk of Type II error, requires more information not provided in the question.

The given scenario involves setting up a hypothesis test to determine if the mean response time for drug-injected rats is significantly different from the control group (rats not injected with the drug) with a known mean response time of 1.2 seconds. The null hypothesis would state that the mean response time for drug-injected rats (μ) is equal to 1.2 seconds (H0: μ = 1.2), while the alternative hypothesis would state that the mean response time is greater than 1.2 seconds (Ha: μ > 1.2).

Given that the sample mean response time for drug-injected rats is 1.05 seconds, which is actually lower than the control mean, this initially suggests that the drug does not increase the response time but rather decreases it or has no effect. However, as the question indicates a confusion with the typo in sample mean, we will proceed with testing the hypothesis based on the provided assumption that the drug-injected rats have a mean response time of 1.1 seconds.

To calculate the value of beta (the probability of a Type II error, which occurs when the null hypothesis is not rejected even though it is false), we would need to define the rejection regions for our test. The rejection region is typically defined based on the significance level (alpha) and the distribution of the test statistic under the null hypothesis. Without specifics such as the sample size, standard deviation, and significance level for defining the rejection regions, we cannot calculate beta directly.

The volume of a spherical boulder with a diameter of 18 ft can be calculated using the formula V = 4/3πr³, with 'r' being the radius of the sphere. By substituting the radius of 9 ft (half of 18 ft), we find that the volume is approximately 3053.62 cubic feet.

To find the volume of a sphere, we use the formula: V = 4/3πr³, where 'r' is the radius of the sphere. The radius can be found from the diameter by dividing it by 2; therefore, for this boulder, the radius will be 18 ft/2 = 9 ft. Substituting 'r' into the volume equation: V = 4/3 * 3.14 * (9ft)³ = 3053.62 cubic feet. Therefore, the spherical boulder has a volume of approximately 3053.62 cubic feet.

To find the volume of a spherical boulder, we can use the formula for the volume of a sphere, which is V = (4/3)πr³. Given that the diameter of the boulder is 18 ft, we can find the radius by dividing the diameter by 2, which gives us a radius of 9 ft. Plugging this value into the formula, we get V = (4/3)π(9 ft)³. Using the value of π as 3.14, we can calculate the volume:

V = (4/3)(3.14)(9 ft)³ = (4/3)(3.14)(729 ft³) = 3053.96 ft³

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Answer:  y=-2x-8

Step-by-step explanation:

Parallel lines need to have the same slopes but different y-intercept.

y=-2x -9 is parallel to y=-2x - 8

Answer:

We need a sample size of at least 97.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.

We need a sample size of at least n.

n is found when [tex]M = 2, \sigma = 10[/tex].

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]2 = 1.96*\frac{10}{\sqrt{n}}[/tex]

[tex]2\sqrt{n} = 1.96*10[/tex]

[tex]\sqrt{n} = \frac{1.96*10}{2}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96*10}{2})^{2}[/tex]

[tex]n = 96.04[/tex]

Rouding up

We need a sample size of at least 97.

Answer:

9.

Step-by-step explanation:

[tex]f(x) = -(x - 3)^2 + 9[/tex] is a parabola in its vertex form. For clarity, let [tex]f(x) = a (x - h)^2 + k[/tex] represent this function.

Note that [tex]a[/tex], the leading coefficient, is negative. Therefore, this parabola opens downwards. The vertex of the parabola would be [tex](h,\, k)[/tex], which in this question is the point [tex](3,\, 9)[/tex]. Since the parabola opens downwards, that vertex would be a local maximum (a crest) on its graph.

Before concluding that the maximum area of this rectangle is [tex]9[/tex], make sure that [tex](3,\, 9)[/tex] is indeed on the graph of [tex]y = f(x)[/tex].

The length of a rectangle should be positive. Since [tex]x[/tex] represents the length of this rectangle, [tex]x > 0[/tex]. Also, since the perimeter should be less than [tex]12[/tex], the length of one side should be less than [tex]12 / 2 = 6[/tex]. Therefore, the domain of [tex]f[/tex] should be the open interval [tex](0,\, 6)[/tex]. (Endpoints not included.)

Indeed, [tex]x = 3[/tex] is in that interval. [tex](3,\, 9)[/tex] would be on the graph [tex]y = f(x)[/tex]. Therefore, [tex]9[/tex] is indeed the maximum area of this rectangle.

Side note: if the domain is a closed interval (i.e., endpoints included,) then consider checking the endpoints, as well.

Answer:

Step-by-step explanation:

9

Answer:

y-8+8

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

7 boys

Step-by-step explanation:

252525=3*5²*7*13*37

353535=3*5*7²*13*37

(252525; 353535)= 3 * 5 * 7 * 13 * 37 = 50505

The greatest number of teams possible=50505

252525=5*50505

353535=7*50505

So, are 50505 teams, each containing 5 girls and 7 boys.

7 boys

The circle graph and parabola graph do not represent the function because they both fail the vertical line test option (A) and (C) are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

Since a circle fails the vertical line test, it cannot be a function. In other words, we can create a vertical line that crosses a circle's graph more than once.

Not every parabola is a function. Only parabolas with upward or downward openings are regarded as functions.

Thus, the circle graph and parabola graph do not represent the function because they both fail the vertical line test option (A) and (C) are correct.

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The only graph that represents a function is the: Third Graph

What graph depicts a function?

To check whether the graph represents a function or not, we perform vertical line test.

Vertical Line test:

The Vertical Line Test is a method used to determine whether a given graph represents a function or not. To apply the test, draw a vertical line through the graph and observe the points of intersection. If the vertical line intersects the graph at exactly one point for each value of x, then the graph represents a function. If the vertical line intersects the graph more than once for any value of x, then the graph does not represent a function

Looking into the graphs, the vertical line intersects the graph C at only one point.

Hence, graph C represents a function.