A 27-inch by 72-inch piece of cardboard is used to make an open-top box by removing a square from each corner of the cardboard and folding up the flaps on each side. What size square should be cut from each corner to get a box with the maximum volume? Enter the area of the square and do not include any units in your answer.

Answer:

40

Step-by-step explanation:

Since your only buying stickers you divide 10 by 0.25 to see how many you can purchase.

Answer:

It means a sticker costs $0.25 and a charm costs $0.5

Therefore without buying any charm

You can use $10 to buy 10/0.25

40 stickers

Step-by-step explanation:

Answer:  The required probability is [tex]\dfrac{14}{15}.[/tex]

Step-by-step explanation:  Given that the probabilities that A, B and C can solve a particular problem are [tex]\dfrac{3}{5},~ \dfrac{2}{3},~\dfrac{1}{2}[/tex] respectively.

We are to determine the probability that at least one of the group solves the problem , if they all try.

Let E, F and G represents the probabilities that the problem is solved by A, B and C respectively.

Then, according to the given information, we have

[tex]P(E)=\dfrac{3}{5},~~~P(F)=\dfrac{2}{3},~~P(G)=\dfrac{1}{2}.[/tex]

So, the probabilities that the problem is not solved by A, not solved by B and not solved by C are given by

[tex]P\bar{(A)}=1-P(A)=1-\dfrac{3}{5}=\dfrac{2}{5},\\\\\\P\bar{(B)}=1-P(B)=1-\dfrac{2}{3}=\dfrac{1}{3},\\\\\\P\bar{(C)}=1-P(C)=1-\dfrac{1}{2}=\dfrac{1}{2}.[/tex]

Since A, B and C try to solve the problem independently, so the probability that the problem is not solved by all of them is

[tex]P(\bar{A}\cap \bar{B}\cap \bar{C})=P(\bar{A})\times P(\bar{B})\times P(\bar{C})=\dfrac{2}{5}\times\dfrac{1}{3}\times\dfrac{1}{2}=\dfrac{1}{15}.[/tex]

Therefore, the probability that at least one of the group solves the problem is

[tex]P(A\cup B\cup C)\\\\=1-P(\bar{A\cup B\cup C})\\\\=1-P(\bar{A}\cap \bar{B}\cap \bar{C})\\\\=1-\dfrac{1}{15}\\\\=\dfrac{14}{15}.[/tex]

Thus, the required probability is [tex]\dfrac{14}{15}.[/tex]

Final answer:

To find the probability that at least one of A, B, or C solves the problem, calculate 1 minus the probability that none solve it. The individual non-solving probabilities are multiplied together and subtracted from 1, resulting in a final answer of 14/15.

Explanation:

To determine the probability that at least one person out of A, B, and C solves a problem, we must first understand that the probability of at least one event occurring equals 1 minus the probability that none of the events occur (in this case, that none of the people solve the problem).

We have the individual probabilities as follows:

Probability A solves the problem: 3/5

Probability B solves the problem: 2/3

Probability C solves the problem: 1/2

The probabilities that A, B, or C do not solve the problem are then 1 - (3/5), 1 - (2/3), and 1 - (1/2), respectively. To find the probability that none of them solve the problem, we multiply these probabilities:

P(none solve) = (1 - 3/5) × (1 - 2/3) × (1 - 1/2)

Calculating this gives us P(none solve) = (2/5) × (1/3) × (1/2) = 2/30 = 1/15. Thus, the probability that at least one person solves the problem is:

P(at least one solves) = 1 - P(none solve) = 1 - 1/15 = 14/15.

Answer:

21

Step-by-step explanation:

Answer:

Step-by-step explanation:

We want to determine 95% confidence interval of the population proportion of republican voters who feel that the federal government has too much power.

43% of 300 randomly selected republican voters feel that the federal government has too much power. This means that

p = 43/100 = 0.43

q = 1 - p = 1 - 0.43 = 0.57

n = 300

mean, u = np = 300 × 0.43 = 129

Standard deviation, s = √npq = √129×0.57 = 8.575

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean +/- z ×standard deviation/√n

It becomes

129 +/- 1.96 × 8.575/√300

= 129 +/- 0.9704

= 129 +/- 0.9704

The lower end of the confidence interval is 129 - 0.9704 =128.0296

The upper end of the confidence interval is 129 + 0.9704 =129.9704

Therefore, with 95% confidence interval, the mean of the population proportion of republican voters who feel that the federal government has too much power is between 128.0296 and 129.9704

To find the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power, use the formula CI = p ± Z * √((p*(1-p))/n), where p is the sample proportion, Z is the Z-score for the desired confidence level, and n is the sample size. Given the sample proportion of 0.43, sample size of 300, and desired confidence level of 95%, the confidence interval is approximately 0.381 to 0.479.

To find the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power, we can use the formula:

CI = p ± Z * √((p*(1-p))/n)

Where:

Given that the sample proportion is 0.43, the sample size is 300, and the desired confidence level is 95%, we can calculate the 95% confidence interval:

CI = 0.43 ± 1.96 * √((0.43*(1-0.43))/300)

Simplifying the equation, we get:

CI = 0.43 ± 0.049

Therefore, the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power is approximately 0.381 to 0.479.

Final answer:

The distance from Seattle to the rugged wilderness, calculated using the average speeds and total travel time, is found to be 7424 miles.

Explanation:

Given that a private plane traveled to and from a rugged wilderness, with average speeds of 312 mph on the way to the wilderness and 364 mph on the return trip to Seattle, and the total flying time for round trip was 44 hours, we can calculate the distance by using the formula for average speed, which is average speed = total distance/total time.

Let's denote the distance between Seattle and the wilderness as x miles. The time taken to fly to the wilderness is then x/312 and the time taken to fly back is x/364.

The total flying time of 44 hours can be split into the sum of the time going to the wilderness and coming back, which gives us:
(x/312) + (x/364) = 44.

To solve for x, we need to find a common denominator and solve the equation.

Common denominator for 312 and 364 is 114,048.

Convert the equation: (364x + 312x) / 114048 = 44.

Multiply both sides by 114048: 676x = 5018112.

Divide both sides by 676: x = 7424.

Therefore, the distance from Seattle to the rugged wilderness is 7424 miles.

Answer:

Easy, it is C) $136,800

Step-by-step explanation:

All you need to do is multiply $3,800 by 12 to get the yearly rent. To get $45,600 per year. You now multiply $45,600 by 3 to get the total price of the 3 year lease. You now have a total cost of $136,800 over the 3 year time period of the lease.

The question is flawed due to its opinion-based and leading nature. It presupposes information, leads the participant, and doesn't provide a full range of response options.

This question, as posed by the 1995 Corporation for Public Broadcasting poll, is opinion-based and leading. There are several factors that make this question flawed. Firstly, it presupposes information by referencing a psychological study that potentially not all participants may be aware of, providing an initial bias. Secondly, it leads the participant in the direction of agreeing with the study, providing no neutral or mixed opinion option. Lastly, the question does not allow for participants to disagree somewhat, only strongly, which may influence the responses to be more in line with the premise of the study. In reliable polling, questions should offer sufficient options for the participant to choose from that captures the range of potential opinions and should avoid leading language or assumptions to obtain an accurate representation of the participants' views.

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Answer:

A. 0.0021

Step-by-step explanation:

Given that the heights of men are normally distributed with a mean of 66.9 inches and a standard deviation of 2.1inches.

Sample size = 36

Std dev of sample = [tex]\frac{2.1}{\sqrt{36} } =0.35[/tex]

The sample entries X the heights are normal with mean= 66.9 inches and std deviation = 0.35 inches

Or we have

Z = [tex]\frac{x-66.9}{0.35}[/tex]

Hence the probability that they have a mean height greater than 67.9 inches

=[tex]P(X>67.9)\\=P(Z>\frac{1}{0.35)} \\=0.00214[/tex]

So option A is right answer.

Final answer:

To find the probability that the mean height of 36 randomly selected men is greater than 67.9 inches, calculate the z-score and find the corresponding area under the standard normal distribution curve.

Explanation:

To find the probability that the mean height of 36 randomly selected men is greater than 67.9 inches, we need to calculate the z-score and find the corresponding area under the standard normal distribution curve.

The z-score is calculated using the formula:

z = (x - μ) / (σ / √n)

Where x is the value we want to find the probability for, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values into the formula, we have:

z = (67.9 - 66.9) / (2.1 / √36) = 1.71

Using a standard normal distribution table or a calculator, we can find that the area to the right of a z-score of 1.71 is approximately 0.0436.

Since we want the probability of having a mean height greater than 67.9 inches, we need to calculate the area to the right of the z-score. Therefore, the probability is approximately 1 - 0.0436 = 0.9564.

Step-by-step explanation:

24. A

B' ( t ) = 10 [ 20 CDS ( t/10) ] = 2 COS ( t/10 )

B' ( 7 ) = 1.5

After 7 days the number of beds in use is increasing at the rate of 1 1/2 beds per day.

24.B

2 COS ( t/10) =0

using calculator t = 15.7

B (12) = 20 Sin (1.2) + 50 = 68.6 = 69

B (15.7) = 20 Sin (1.57) + 50 = 70

B (20) = 20 SIn (20) + 50 = 68.25 = 68

Maximum number of beds in use occurs in afternoon of 15th day and is 70 beds.

I hope that helps and I hope  it's right  

Answer:

     A = 6.13e^(0.00884769t)

Step-by-step explanation:

The exponential growth model can be written two ways. Comparing them, we can find the value of k.

  A = 6.13×(7.00/6.13)^(t/(2015-2000)) = 6.13×e^(kt)

Dividing by 6.13 and taking natural logs, we get ...

  t/15×ln(7.00/6.13) = kt

  k = ln(7.00/6.13)/15 . . . . . divide by t

  k ≈ 0.00884769

Then the exponential growth function can be written as ...

  A = 6.13e^(0.00884769t)

Answer:

x ^5 + x ^4 + x ^3 + x ^2 + x + 1

Answer:

The answer to your question is below

Step-by-step explanation:

[tex]\frac{x^{6}- 1 }{x -1} = \frac{x^{6}+ 0x^{5} + 0x^{4} + 0x^{3} + 0x^{2} + 0x - 1 }{x - 1}[/tex]

Synthetic division

                             1    0   0   0   0   0   -1    1

                                   1    1    1    1    1     1                                                

                             1    1     1    1    1    1    0              

Quotioent =    x⁵ + x⁴ + x³ + x² + x

Remainder = 0

Answer:

Explanation:

The vertical height of the cliff, 30 m tall, and the horizontal distance from the kayak to the base of the mountain form a right triangle.

The angle of depression is 40º.

By the alternate interior angles theorem, that depression angle is congruent to the elevation angle from the kayak to the spot where Bob is standing on.

The tangent trigonometric ratio relates the height (30 m) with the distance from the kayak to the base of the mountain:

Answer:

Gina's pay rate next month will be =$9.9 per hour

Step-by-step explanation:

Gina was initial earnings was = $10 per hour

She received an increase by = 10%

Increase in amount received = [tex]10\%\ of\ \$10= 0.1\times\$10 =\$1 [/tex]

New earnings = [tex]\$10+\$1=\$11[/tex] per hour

Next month her pay rate will decrease by = 10%

Decrease in pay rate next month will be = [tex]10\%\ of\ \$11= 0.1\times\$11 =\$1.1 [/tex]

Thus, Gina's pay rate next month will be = [tex]\$11-\$1.1=\$9.9[/tex] per hour

Answer: it will take 8.25 seconds to reach maximum height

Step-by-step explanation:

Initial velocity, u of baseball = 132 feet per second. The height of the baseball, h in feet after t seconds is given by the function h = −16t^2 + 132t + 4

The given function is a quadratic equation. If values of height attained is plotted against time, the graph will take the shape of a parabola whose vertex corresponds to the maximum height attained by the baseball

Vertex of the parabola = -b/2a

a = - 16

b = 132

Vertex = - 132/-16× 2 = -132/32

Vertex = 4.125

The maximum height is 4.125 feets

To determine the time it will take to reach the maximum height of 4.125 feets, we will substitute h = 4.125 in the equation

4.125 = −16t^2 + 132t + 4

−16t^2 + 132t - 0.125 = 0

Applying the general formula for quadratic equations,

t = [- b ± √b^2 - (4ac)]/2a

a = -16

b = 132

c = -0.125

t = [- 132 ± √132^2 - 4(-16 × - 0.125)]/2× -16

t = [- 132 ± √17424 - 8)]/-32

t = [- 132 ± √17416]/-32

t = (-132 ± 132)/-32

t = (-132 + 132)/-32 or (-132 -132)/-32

t = 0 or -264/-32

t = 8.25 seconds

Final answer:

The baseball reaches its maximum height after 8.25 seconds.

Explanation:

To find the time when the baseball reaches its maximum height, we need to determine the time at which the vertical velocity becomes zero. The equation for the height of the ball as a function of time is given as h = -16t² + 132t + 4. To find the time at which the velocity becomes zero, we need to solve the equation v = -16t + 132 = 0. Solving for t, we get t = 8.25 seconds. Therefore, the baseball reaches its maximum height after 8.25 seconds.

Answer: 336.4447 feet

Step-by-step explanation: from the picture I attached to this answer, you will see how I represented the question in a diagram

Point A being the point of his friends car, point B being the point of the hot air balloon when he noticed the angle of depression to his friends car to be 37 degrees, point C being the point of the hot air balloon after passing his friends car and noticing the angle of depression to be 38 degrees

From my diagram, I labeled y as the distance between B and C and we are told he traveled when a speed of 6 feet per second with a constant altitude, and after 1 and a half minutes he reached point C, which is 90 seconds

To get value of y we multiply the speed and the time, 90 multiplied by 6 which will give 540 feet

From my diagram, I calculated the angle inside the triangle to be 105, we all know the sum of angles in a straight line to be 180, and also knowing alternate angles, we have 37 and 38 degree as the angle outside the triangle at that point, so adding both angle 37+38=75 and subtracting that from 180 we get 105

So the get the distance between him and his friends when the angle of depression is 38 degree, which is the distance between point A and C which I labeled x, we use the sin rule

Sin rule states that the ratio between the length of a side of a triangle and the sin of the angle opposite it is constant for all sides of the triangle,

The steps are also solved in the picture I sent

So we have the ratio of x and sin37 is also equal to the ratio of 540 and sin105

So x divided by sin37 equals 540 divided by sin105

Sin37 equals 0.6018, sin105 equals 0.9659

So making x the subject of formula

We get x will be equal to (540*0.6018)/0.9659 which will give you 336.4447 feet

Using trigonometry and applying the concept of tangent to the angles of depression, we can construct two right triangles to calculate the horizontal distances and then use the Pythagorean theorem to calculate the distance from the balloon to the friend's car.

The question involves a man in a hot-air balloon tracking his distance from a car in a parking lot using the angles of depression before and after flying over the car. To solve this question, we will apply trigonometry specifically, the concept of tangent which relates the angle of depression to the sides of a right triangle formed by the observer's altitude and the horizontal distance.

Firstly, let's find the horizontal distance the man travels in a minute and a half at 6 feet per second:

Distance = speed × time = 6 feet/second × 90 seconds = 540 feet

Now, we form two right triangles: one before he flies over the car and one after. Both have the same altitude (since he maintains a constant altitude).

For the first triangle, using the 37° angle of depression, we can denote:

For the second triangle, using the 38° angle of depression, we can denote:

Solving these two equations we find the horizontal distance (x) and then can find the direct line distance using Pythagoras' theorem.

To find the distance, we will use the tangent of 38° (the angle of depression after passing the car) since that relates the perpendicular distance from the balloon to the car (which we are interested in) to the horizontal distance. Let's denote the perpendicular distance as 'h' (altitude of the balloon).

Tan(38°) = h / (x - 540 feet)

After some algebraic manipulation and applying trigonometry, we can solve for 'h' and find the direct line distance from the balloon to the car.

Answer: number of people that had allergic reactions is 0.7%

Step-by-step explanation:

The total number of people that came to try the company's product is 3000

21 out of the 3,000 people had an allergic reaction. We want to determine how many percent of the total number of 3000 people that tried the product is 21 people that had reaction

Percentage of people that had allergic reactions = number of people that had allergic reactions / total number of people that tried the products × 100

Percentage of people that had an allergic reaction

= 21/3000× 100

= 0.007 × 100 = 0.7%

Answer: The weight of X is [tex]33\dfrac{1}{3}\%[/tex] of weight of mixture.

Step-by-step explanation:

Since we have given that

Percentage of seed mixture X for ryegrass = 40%

Percentage of seed mixture Y for ryegrass = 25%

If a mixture of X and Y contains 30 percent ryegrass,

Let total seed mixture be 100

So, for seed X = x

For seed Y = 100-x

So, According to question,

[tex]0.4x+0.25(100-x)=30\\\\0.4x+25-0.25x=30\\\\0.15x=30-25\\\\0.15x=5\\\\x=\dfrac{5}{0.15}\\\\x=\dfrac{100}{3}[/tex]

So, weight of mixture X is given by

[tex]\dfrac{\text{Weight of X}}{\text{Weight of mixture}}\times 100\\\\=\dfrac{\dfrac{100}{3}}{100}\times 100\\\\=\dfrac{100}{3}\%\\\\=33\dfrac{1}{3}\%[/tex]

Hence, the weight of X is [tex]33\dfrac{1}{3}\%[/tex] of weight of mixture.

Answer:

volume of cone = 12.56 cubic units

Step-by-step explanation:

Volume of cone = 1/3  π r² h

            r = 2

            h = 3

then

V= 1/3 3.14 * (2) ² 3

 = 12.56 cubic units

Answer:

12.56 cubic units

Step-by-step explanation:

Right on Edge 2022

Answer:

C. straight

Step-by-step explanation:

 A Linear Pair is two adjacent angles whose non-common sides form opposite rays.

If two angles form a linear pair, the angles are supplementary.

A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.

In the figure given in attachment, AB and BC are two non common sides of ∠ABD and ∠DBC.

∠1 and ∠2 form a linear pair.

The line through points A, B and C is a straight line.

∠1 and ∠2 are supplementary.

Thus two non-common sides of adjacent supplementary angles form a straight angle.

Answer:

C. [tex]y - 9 = \frac{4}{5}(x + 7)[/tex]

Step-by-step explanation:

The equation of a straight line through a point [tex](x_{1}, y_{1})[/tex] with slope m is given by

                  [tex]y - y_{1} = m(x - x_{1})\\y - 9 = \frac{4}{5}(x - (-7))\\y - 9 = \frac{4}{5} (x + 7)[/tex]

Therefore the answer is C. [tex]y - 9 = \frac{4}{5}(x + 7)[/tex]

Final answer:

To find the values of a, b, c, and d in the equation 4cos(x)cos(2x)cos(4x) = cos(ax)+cos(bx)+cos(cx)+cos(dx), we can compare the coefficients of the cosine terms on both sides of the equation. By expanding and comparing coefficients, we can determine that a = 12, b = 10, c = 6, and d = 8. Therefore, a + b + c + d = 36.

Explanation:

To find the values of a, b, c, and d, we need to equate the coefficients of cos(ax), cos(bx), cos(cx), and cos(dx) on both sides of the equation.

4cos(x)cos(2x)cos(4x) = cos(ax)+cos(bx)+cos(cx)+cos(dx)

By expanding the left side and comparing coefficients, we get:

From these equations, we can determine that a = 12, b = 10, c = 6, and d = 8.

Therefore, a + b + c + d = 12+10+6+8 = 36.

Answer: -1.17522136 hertz

there you go :) just to let you know I’m in 7th

Answer:

  3 gallons

Step-by-step explanation:

He will make 8×(6 cups) = 48 cups of soup. There are 16 cups in a gallon, so 3·16 = 48 cups in 3 gallons.

Ariq will make 3 gallons of soup this year.

Final answer:

We found there were 7 Blue Jays, 42 sparrows, and 4 Falcons.

Explanation:

The question involves solving a simple algebraic problem to determine the number of sparrows and Blue Jays when given the total number of birds and the number of Falcons.

To solve this, let's define the number of Blue Jays as x.

The number of sparrows is six times the number of Blue Jays, so we can express that as 6x.

We are told there are four Falcons.

The total number of birds spotted is 53.

We can set up the equation as:

x + 6x + 4 = 53

Solving this equation:

Since x represents the number of Blue Jays, there are 7 Blue Jays.

To find the number of sparrows, multiply 7 by 6, which gives us 42 sparrows.

We were also told there are four Falcons.

So the group saw 42 sparrows, 7 Blue Jays, and 4 Falcons.

Answer:

(d.) 45, 54

Step-by-step explanation:

Let the first digit = y

Let the second digit = z

y +z = 9 ------------------------------------------ (1)

y²- yz +z² = 21------------------------------------(2)

From equation (2),

z = 9-y-------------------------------------------------(3)

Substitute equation (3) into (2):

y²- y(9-y) +(9-y)² = 21

y²-9y+y²+y²-18y+81 = 21

3y²-27y+ 81 = 21

3y²-27y+ 81-21= 0

3y²-27y+ 60= 0

y²- 9y +20= 0

(y -5) (y-4) =0

y= 5 or y =4

z = 4 or 5 (substituting into (3))

So the numbers are  54  or 45.

12 CDs ............... 2 %

x CDs .............100 %

x = 12×100/2 = 1200/2 = 600 Cds/month

The required number of CD that was sold last month is 600 CD's.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the number of total CDs sold be x,

The music department of a department store sold 12 jazz CDs last month.
Jazz sales during that month made up 2% of the music department's total sales.

2% of x = 12
x = 12 / 2%
x = 12 / 0.02
x = 600

Thus, the required number of CD that was sold last month is 60 CD's.

Learn more about percentages here:

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Answer:

Null hypothesis:[tex]p=0.25[/tex]  

Alternative hypothesis:[tex]p \neq 0.25[/tex]

z=2.53

pv=0.0114

So based on the p value obtained and using the significance given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they use the Internet differs from 0.25 or 25% .  

Step-by-step explanation:

1) Data given and notation

n=3010 represent the random sample taken

X represent the people who says that said that they use the Internet.

[tex]\hat p=\frac{X}{106}=0.27[/tex] estimated proportion of people who says that said that they use the Internet.

[tex]p_o=0.25[/tex] is the value that we want to test

[tex]\alpha[/tex] represent the significance level  

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that 50% of people who says that  they would watch one of the television shows.:  

Null hypothesis:[tex]p=0.25[/tex]  

Alternative hypothesis:[tex]p \neq 0.25[/tex]  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.27 -0.25}{\sqrt{\frac{0.25(1-0.25)}{3010}}}=2.53[/tex]

4) Statistical decision  

P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

We have the significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z>2.53)=2*(0.0057)=0.0114[/tex]  

So based on the p value obtained and using the significance given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they use the Internet differs from 0.25 or 25% .  

Answer:

Step-by-step explanation:

Given

no of houses that can be served by water is directly Proportional to the square of diameter

[tex]N\propto d^2[/tex]

[tex]N=kd^2[/tex]

where k =constant

10 cm diameter can supply 40 houses

[tex]40=k(10)^2[/tex]-----------1

For d=30 cm Pipe

[tex]N_1=k(30)^2[/tex]-------------2

divide 1 & 2

[tex]\frac{N_1}{40}=(\frac{30}{10})^2[/tex]

[tex]N_1=40\times 9=360 [/tex]

(b)for N=1440 houses

[tex]1440=k(d_2)^2[/tex] ----------------3

[tex]\frac{1440}{40}=(\frac{d_2}{10})^2[/tex]

[tex]d_2=6\times 10[/tex]

[tex]d_2=60 cm[/tex]

A water pipe with a diameter of 30 cm can serve 360 houses. And to serve 1440 houses, a water pipe with a diameter of 60 cm is required.

The relationship between the number of houses that could be supplied by the water pipe and the diameter of the pipe can be described as a direct square relationship. This means if you square the diameter of the pipe, you'll get the number of houses that can be served. We know from the given info that a 10 cm diameter pipe can serve 40 houses. Therefore, the constant of variation (k) can be calculated as k=No. of houses/diameter². Hence, k=40/10²=0.4.

a.) A pipe with a 30 cm diameter can serve 0.4*(30)² = 360 houses.

b.) For a new subdivision of 1440 houses, we rearrange the formula to find the required diameter: Diameter= sqrt(No. of houses/k) = sqrt(1440/0.4) = 60 centimeters.

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I think the answer would be -$5.17 because you would have to find the unexpected value.

I think the answer to this picture is 0.122

Game:

1/36(94) + 35/36(-8) = 94/36 -280/36 = -186/36 = -5.17

4. Add the probabilities together for 5 and under:

0.122 + 0.061 + 0.022 + 0.006 + 0.001 = 0.212

Airline :

Given: P = 70, P = 97% = 0.97, q = 1-0.97 = 0.03

Probability of being greater than 68:

(70 * 0.97^69 * 0.03^1) + (1*0.97^70*1)

= 0.2567 + 0.1185

= 0.375