Evaluate the integral ∫∫∫Dxyz dV, where D is the region bounded below by xy-plane and above by the hemisphere z=√9−x2−y2.

As per the margin of error, the value of n is 1068

Margin of error

In statistics, margin of error refers the statistic expressing the amount of random sampling error in the results of a survey.

Given

Kim wants to determine a 99 percent confidence interval for the true proportion pp of high school students in the area who attend their home basketball games. Out of n randomly selected students she finds that that exactly half attend their home basketball games.

Here we need to find  how large would n have to be to get a margin of error less than 0.01 for p.

Let us assume the worst case of the point estimate of 99% and n refers size of sample

Here the margin of error is calculated as,

=> Margin of error = z1 - α * standard error of worst case point estimate

=>  z x 99% x √(0.5(1-0.5)/n)

=> 1.96 * 0.5/√n

Now, we have to equate to given margin of error of 0.03, then

=> 0.03 = 1.96*0.5/√n

Then we have to solve for n

=> n = (1.96*0.5/0.03)²

=> n = 32.67²

=>  n = 1067.11

When we round off it, then  we get,

=> n = 1068

To know more about Margin of error here.

https://brainly.com/question/10501147

#SPJ4

The confidence interval limits include 0, which suggests that the two population means might be equal. There does not appear to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

The correct option is (a)

"Information available from the question:"

This is incomplete question:

Complete question is this:

A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows.

Women             Men

x1 = 11.7hrs x2 = 14.2hrs

s1 = 3.9hrs s2 = 5.2hrs

n1 = 14         n2 = 17

The following 99% confidence interval was obtained for μ1 − μ2, the difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men:

-7.43hrs < μ1 − mμ2 < 2.43hrs

What does the confidence interval suggest about the population means?

a. The confidence interval limits include 0 which suggests that the two population means might be equal. There does not appear to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

b. The confidence interval includes only negative values which suggest that the mean amount of time spent watching television for women is smaller than the mean amount of time spent watching television for men.

c. The confidence interval limits include 0 which suggests that the two population means are unlikely to be equal. There appears to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

d. The confidence interval includes only positive values which suggest that the mean amount of time spent watching television for women is larger than the mean amount of time spent watching television for men.

Now, According to the question:

The given confidence interval is:

-7.43hrs < μ1 − mμ2 < 2.43hrs

The interval includes 0 and the populations sampled are small (< 30). Therefore, Option (a) is correct.

Hence, The confidence interval limits include 0, which suggests that the two population means might be equal. There does not appear to be a significant difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men.

Learn more about Confidence Interval at:

https://brainly.com/question/24131141

#SPJ4

Distance that plane has flown is 2812.5 feet.

What do you mean by trignometry?

Trigonometry  “triangle” is a branch of mathematics that studies the relationship between the side lengths and angles of triangles.

Trigonometric ratios of triangles are also called trigonometric functions. Sine, cosine, and tangent are three important trigonometric functions, abbreviated sin, cos, and tan. Let's see how these ratios or functions are evaluated in the case of right triangles.

It is given that a plane rises from take-off and flies at an angle of 9° with the horizontal runway. It has gained 450 feet

Let the distance be x

According to the question:

sin 9 = 450/x

0.16 = 450/x

x = 450/0.16

x = 2812.5

Therefore, distance that plane has flown is 2812.5 feet.

To learn more about the trignometry from the given link.

https://brainly.com/question/24349828

#SPJ1

Answer:

a+k =7

Step-by-step explanation:

In the given system of equations, ax + 3y = 10 and kx - 3y = 6, we are told that the solution to the system is (2,1). This means that when we plug the values x = 2 and y = 1 into the equations, we get two true statements.

To find the value of a + k, we can start by plugging the values x = 2 and y = 1 into the first equation to get:

a(2) + 3(1) = 10

Next, we can solve for a by dividing both sides of the equation by 2:

a + 3/2 = 5

a = 5 - 3/2 = 5/2

Next, we can plug the values x = 2 and y = 1 into the second equation to get:

k(2) - 3(1) = 6

Next, we can solve for k by dividing both sides of the equation by 2:

k - 3/2 = 3

k = 3 + 3/2 = 9/2

Finally, we can add the values of a and k to find the value of a + k:

a + k = (5/2) + (9/2) = 14/2 = 7

Therefore, the value of a + k is 7.

The polygon shown in the figure is trapezoid and the value if x is  .

What is trapezoid?

A trapezoid may be a polygonal shape that has just one try of parallel sides. These parallel sides also are referred to as parallel bases of trapezoid. the opposite 2 sides of trapezoids area unit non-parallel and referred to as legs of trapezoids

Main body:

by using the property of trapezoid ,

1/2(sum of both bases) = mid-line passing through trapezoid

according to question:

x = 1/2(x-8+2x-12)

x = 1/2(3x -20)

2x = 3x - 20

x = 20

Hence value of x is 20.

to know more about polygons , visit:

https://brainly.com/question/26583264

#SPJ1

The conclusion the residuals have an increasing variance as the dependent variable increases is correct.

What is scatter chart?

Charts that depict the relationship between two variables are known as scatter charts, also known as scatter plots. They are a very effective type of chart because they enable viewers to see relationships or trends right away that are difficult to see in almost any other form.

In order to observe and visually display the relationship between variables, a scatter plot is a common type of chart. Other names for it include scatter gram, scatter graph, and scatter chart.

The conclusion can be drawn from the scatter chart is,

The residuals have an increasing variance as the dependent variable increases.

There is a violation of the homoskedasticity (homogeneity of variance for residuals) assumption.

The given plot is used to check the assumption for homoskedasticity (homogeneity of variances) of data points.

Hence if the homoskedasticity assumption hold, the spread of data points should be along the line and the line should be approximately horizontal.

From the given plot we can see that spread is centered at the middle not equally distributed along the line which is a violation of the homoskedasticity assumption

Hence, the conclusion the residuals have an increasing variance as the dependent variable increases is correct.

To know more about scatter chart, click on the link

https://brainly.com/question/6592115

#SPJ4

The scatter chart is attached below.

The diameter of the top of the trash ball is 5 inch.

The diameter is the distance along the circle's center that must travel in order to touch two points on its periphery.

solution:

Given that the diameter of top of the trash can is 20 inch.

And the diameter of trash ball is 1/4th of the diameter of trash can.

The diameter of trash ball = 1/4 ( the diameter of trash can )

The diameter of trash ball = 1/4 (20 inch)

The diameter of trash ball = 20/4

The diameter of trash ball = 5 inch.

Therefore, the diameter of the top of the trash ball is 5 inch.

To learn more about the diameter from the given link

https://brainly.com/question/23220731

#SPJ1

Answer:

y=2x-14

Step-by-step explanation:

Perpendicular lines have slopes that are opposite reciprocals:

Example: 4 and -1/4 are opposite reciprocals

y = -x/2+2  ==> slope for this equation is -1/2

Now take opposite reciprocal of -1/2

1/(-1/2) * (-1) =

1 * (-2/1) * (-1) =

1 * (-2) * (-1) =

1 * 2 = 2

y=mx+b  

-4 = 2(5) + b  ==> plug in y=-4, x=5, and m=2 from (5, -4) and a slope of 2

-4 = 10 + b  ==> solve for b

-4 - 10 = 10 - 10 + b  ==> subtract 10 on both sides to isolate b

b = -14

y=2x+(-14)  ==> plugin -14 for b in y=mx+b

y=2x-14

Answer:

20

Step-by-step explanation:

Since all sides are equal, it's an equilateral triangle.

Each medium interior angle of an equilateral triangle is 60.

So,

3x = 60

x = 60/3

x = 20

The solution sets for the given quadratic equation 4x²-9x-9=0 are -3/4, 3

Any equation in algebra that can be rearranged in standard form as follows is known as a quadratic equation (from Latin quadratus, which means "square").

[tex]{\displaystyle ax^{2}+bx+c=0\,,}[/tex]

While a, b, and c are known values, x is an unknown value, and vice versa. The assumption is that a > 0; equations with a = 0 are thought to be degenerate because they become linear or even simpler. The terms "quadratic coefficient," "linear coefficient," and "constant or free term" can be used to distinguish the three values that make up the equation's coefficients, respectively.

Given,

4x²-9x-9=0

4x²-12x+3x-9=0

4x(x-3)+3(x-3)=0

(4x+3)(x-3)=0

4x+3=0, x-3=0

4x-3=0

4x=3

x= -3/4

x-3=0

x=3

Therefore, the solution sets for 4x²-9x-9=0 are -3/4, 3

Hence, the solution sets for the given quadratic equation 4x²-9x-9=0 are -3/4, 3

To know more about quadratic equation, visit:

https://brainly.com/question/1863222

#SPJ1

Using the t-distribution, it is found that the null hypothesis is rejected for a, b, c

Item a:

We have a right-tailed test, as it is being tested if the mean is more than a value.

The p-value is found using a t-distribution calculator, with 11 - 1 = 10 df and t = 1.91, hence it is of 0.0426.

The p-value is of 0.0426, which is less than 0.05, thus the null hypothesis is rejected.

Item b:

We have a left-tailed test, as it is being tested if the mean is less than a value.

The p-value is found using a t-distribution calculator, with 17 - 1 = 16 df and t = -3.45, hence it is of 0.0016.

The p-value is of 0.0016, which is less than 0.05, thus the null hypothesis is rejected.

Item c:

We have a two-tailed test, as it is being tested if the mean is different than a value.

The p-value is found using a t-distribution calculator, with 7 - 1 = 6 df and t = 0.83, hence it is of 0.4383.

The p-value is of 0.4383, which is more than 0.05, thus the null hypothesis is not rejected.

Item d:

We have a right-tailed test, as it is being tested if the mean is more than a value.

The p-value is found using a t-distribution calculator, with 28 - 1 = 27 df and t = 1.91, hence it is of 0.0195.

The p-value is of 0.0195, which is less than 0.05, thus the null hypothesis is rejected.

Therefore, in an independent random sample is selected from an approximately normal population with an unknown standard deviation. Using the t-distribution, it is found that the null hypothesis is rejected for a, b, c

To learn more about hypothesis test refer here brainly.com/question/16194574

#SPJ4

The logarithm of base 7 of t, as a logarithm of base 2 is given as follows:

log2(t)/log2(7).

A logarithm is defined as follows:

log_a(b).

In which:

To change the logarithm to a new base c, the logarithm is written by the fraction presented as follows:

log_c(b)/log_c(a).

In this problem, the logarithm is defined as follows:

log_7 t.

The new base is given as follows:

2.

(as stated in the problem, since we want the logarithm as a logarithm of base 2).

Hence, applying the change of base, the logarithm of base 2 will be given as follows:

log2(t)/log2(7).

As the term log2 represents the logarithm of base 2 of the term.

More can be learned about the change of base of a logarithm at https://brainly.com/question/12561540

#SPJ1

The probability that such cuts would be supported by at least 155 persons in a survey of 250 people is 0.62.

Probability is a branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or a statement being true. The probability of an occurrence is represented by a number between 0 and 1, where 0 signifies the event's impossibility and 1 denotes its certainty.

Assume 60% of the public favors huge government budget cutbacks.

We must determine the likelihood that, in a poll of 250 persons, at most 155 respondents approve such reduction.

As a result, the chance is 155/250 = 0.62.

Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

To know more about probability,

brainly.com/question/24756209

#SPJ1

The method for finding the instantaneous rate of change of the depth of the water; in feet per hour; at 6 AM is B. D' ( 6 ) = 0 .

Given :

The function D ( t ) = 10 + 4.9 cos ( pi/6 * t )

D is defined above models the depth, in feet, of the water t hours after 12 am. Which of he following shows the method for finding the instantaneous rate of change of the depth of the water, in feet per hour, at 6 am .

Differentiate :

D'( t )  = -4.9 sin ( πt / 6 ) ( π / 6 )

D'( 6 ) = -4.9 sin ( π ) ( π / 6 )

we know that

sin ( π ) = 0

so D'( 6 ) = 0

Learn more about the function here :

https://brainly.com/question/5975436

#SPJ4

Answer:

853.15766421

Step-by-step explanation:

The square root of 727878 would be 853.15766421.

Answer:

= 853.157664

Step-by-step explanation:

√727878 = 853.157664

...

..

.

The exponent in the term 5x⁶ is of the expression 6

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

Expression: 5x6+3yr-7yz2+2y/z

Rewrite the expression properly

So, we have the following representation

5x⁶ + 3yr - 7yz² + 2y/z

From the above expression, the spotlight is on the first term

i.e. 5x⁶

Considering an expression represented as axⁿ

Where x is a variable, the exponent is n

Using the above as a guide, we have the exponent of 5x⁶ to be 6

Hence, the exponent is 6

Read more about expressions at

https://brainly.com/question/15775046

#SPJ1

Answer:

14π in.

Step-by-step explanation:

First, we use the area to find the radius.

A = πr²

πr² = 49π in.²

r² = 49 in.²

r = √(49 in.²)

r = 7 in.

Now, we use the radius to fins the circumference.

C = 2πr

C = 2 × π × 7 in.

C = 14π in.

In the given Fibonacci sequence , 8th number is 13 mad 11th number is 55 .

What is a Fibonacci Sequence?

The Fibonacci Sequence is the series of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The next number is found by adding up the two numbers before it:

In a Fibonacci sequence, the number is equal to the sum of the two preceding numbers.

so the seventh number is 3+5 = 8

8th number is 5+ 8 = 13

11th number is 21+34 = 55

now the sequence becomes 0,1,1,2,3,5,8,13,21,34,55

Hence , the 8th number is 13 mad 11th number is 55.

Learn more about Fibonacci Sequence at :

https://brainly.com/question/16934596

#SPJ1

The area of the triangle with the vertices (0, 5), (2, -2), and (5, 1) by using the calculus is  21 square unit.

We need to find the equation among all possible pairs and then integrate the equations from one co-ordinate to another co-ordinate

Equation of line passing through (0,5) and (2,-2) is

y-5 = [(-2-5)/(2-0)](x-0)

=>y-5 = (-7) /2x

=>y= (-7/2x)+5 -------(eq1)

Equation of line passing through (0,5) and (5,1) is

y-5 = [(1-5) / (5-0)](x-0)

=>y-5 = (-4/5)x

=>y = (-4/5)x+5-------(eq2)

Equation of line passing from (2,-2) and (5,1) is

y-(-2) = [[1 - (-2)] / (5-2)] / (x-2)

=>y+2=(3/3)(x-2)

=>y=x-4--------(eq3)

Now, we use definite integration to find the area between the different equation of line.

So, area enclosed between the equations is given by the

area =[tex]\int\limits^5_2[/tex][(-4/5)x+5 - (-7/2)x + 5)dx  + [tex]\int\limits^5_1[/tex][(-4/5)x+5 -(x-4)]dx

=>area=[tex]\int\limits^5_2[/tex](7/2-4/5)x dx + [tex]\int\limits^5_1[/tex]((-9/5)x+9)dx

Using properties of integration,[tex]\int\limits x\, dx=x^{2}/2[/tex]

=>area=[tex]\int\limits^5_2[/tex](27/10)x dx + [tex]\int\limits^5_1[/tex](-9/5)x+9)dx

=>area=([27/10)×[5² - 2²])/2 + [ (-9/5)×(5²-1²) ]/2 +9×(5-1)

=>area=(27/20)×(25-4) + (-9/5)×24+9×4

=>area = (27×21)/20 + (-216)/5+ 36

=>area=(567/20) - (216/5) + 36

=>area= [(567-261×4)+(36×20)]/20

=>area=[(567-864)+720]/20

=>area=423/20

=>area=21 square unit.

Hence, area of triangle is 21 square unit.

To know more about area of triangle, visit here:

https://brainly.com/question/19305981

#SPJ4

The distance from the point to the parametric line is given as follows:

5 units.

The first step is obtaining the vector from the line L(0, 5 + 3t, 2 + t) to the point P(5,5,2), as follows:

P - L = (5, -3t, -t).

The direction vector of the line is given as follows:

(0, 3, 1).

The dot product of the vector with the direction of the line is of zero, hence:

(5, -3t, -t)(0, 3, 1) = 0

-9t - t = 0

-10t = 0

t = 0.

Thus the point on the line which we will use to obtain the distance is of:

(0, 5 + 3(0), 2 + 0) = (0,5,2).

The the distance is obtained applying the formula for the distance between two points as follows:

Distance = square root [(5 - 0)² + (5 - 5)² + (2-2)²] = 5 units.

More can be learned about the distance between point and line at https://brainly.com/question/17143316

#SPJ1

Answer:

---------------------------------

Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).

We can set inequality as:

The two consecutive positive integers as detailed in the question are;

15 and 16

Let the two consecutive integers be;

x and (x + 1).

We are told that the product of two consecutive positive integers is greater than their sum by 209.

Thus, the expression for this is;

x(x + 1) - 209 = x + x + 1

x² - x - 210 = 0

Using quadratic equation formula, we get;

x = -(-1) ± √((-1)² - 4(1 * -210))]/2(1)

x = (3 ± √(9 + 840)]/2

x = 15

Thus, the second number is; x + 1 = 15 + 1 = 16

Read more about Quadratic equations at; https://brainly.com/question/1214333

#SPJ1

The required value of PE is given as 22. The correct option is (B).

The PE ratio can be calculated by taking the ratio of the price of stock to the earning of the company per share.

The given question can be solved as,

The earning per share is $1.80.

And, the closing price i s $40.

Thus, the PE ratio can be calculated as follows,

PE = 40/1.80

     = 22.2

Which is equivalent to 22, rounding to the nearest whole number.

Hence, the PE ratio is given as 22.

To know more about PE ratio click on,

https://brainly.com/question/13633343

#SPJ1

To prove that the triangles are congruent by ASA, the statement and reason could be used as part of the proof is option (A) ∠FGH ≅ ∠KGJ because vertical angles are congruent.

Here we have two triangle FHG and KJG,

The sides HF and the side JK are parallel

The length of the side of the HG and the length of the side JG are equal

HG ≅ JG

According to the ASA property of congruent, if the two angle and one side of the triangle are equal to the two angle and one side of the other triangle, then the both triangles are congruent

Here we have to prove that angle FHG and angle KJG are vertical angles

Here the vertical angles are congruent

Therefore, the statement that can be the part of proof is option (a) angle FGH ≅ angle KGJ because vertical angles are congruent.

I have solved the question in general, as the given question is incomplete

The complete question is:

Given: HF || JK; HG ≅ JG

Prove: FHG ≅ KJG

To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

a) FGH ≅ KGJ because vertical angles are congruent.

b) JKG ≅ HFG because vertical angles are congruent.

c) FHG ≅ JKG because right angles are congruent.

d) HFG ≅ KJG because alternate interior angles are congruent.

Learn more about vertical angle here

brainly.com/question/24460838

#SPJ4

The equation of the circle is [tex](x+3)^2 + (y-5)^2 = 5^2[/tex]

What does the equation for a circle look like in cartesian form?

Cartesian coordinate system with the origin indicated in red and a circle with a radius of two. A circle has the equation (x a)^2 + (y b)^2 = r^2, where a and b are the center's coordinates (a, b) and r is the radius.

The equation of a circle has the following conventional Cartesian form:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex] ---------- 1

where (h, k) is the circle's center, (x, y) is any point on the circle, and r is its radius

Substitute the center (-3,5) into equation [1]:

[tex](x+3)^2 + (y-5)^2 = r^2[/tex] --------------------- 2

Substitute the point (1,8) into equation [2] and solve for r:

[tex](1+3)^2 + (8-5)^2 = r^2\\(4)^2 + (3)^2 = r^2\\16 + 9 = r^2\\25 = r^2\\r = 5[/tex]

Substitute 5 for r into equation [2]

[tex](x+3)^2 + (y-5)^2 = 5^2[/tex]

Hence the equation of the circle is [tex](x+3)^2 + (y-5)^2 = 5^2[/tex]

Learn more about equation for a circle

https://brainly.com/question/1471134

#SPJ1

Unit Fill Rate: The percentage of a customer's purchase that was shipped on time. This statistic calculates the quantity and time elapsed after the order was dispatched, rather than when the client made the purchase.

On-time delivery is a key performance indicator (KPI) used by ecommerce and other delivery organizations to evaluate their ability to complete a client purchase by the specified delivery date.

The metric used to quantify supply chain efficiency is on-time delivery, or OTD. This KPI indicates whether or not an organization is meeting its goals in terms of promised delivery times, and it is critical for measuring carrier performance as well as maintaining customer satisfaction.

Learn more about to measures the percentage visit here;

https://brainly.com/question/14126037

#SPJ4

The value of standard deviation is 88,389.

The Normal distribution id the contionuouse distribution with unimodal and symmetric shaped, it is widely used to approximated discrete distribution and sample mean and a total sum of the random variable, the approximation depends on the concept og the Central limit theorem.

The Central limit theorem states that the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough.

We have given that,

average = 2.500,000

standard deviation σ = 625,000

sample n = 50.

Therefore S = σ / √n

                    = 625000 / √50

                    = 625000 / 7.071

                 S = 88,389

Hence the standard deviation will be 88,389.

To know more about deviation here

https://brainly.com/question/16966492

#SPJ4

At 85% confidence interval, the margin of error is 1.44 when the distribution of this population is approximately normal and has a standard deviation of $9,166.

The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error. In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.

Given,

Starting salaries of 150 college graduates who have taken a statistics course have a mean of $42,991. Suppose the distribution of this population is approximately normal and has a standard deviation of $9,166.

Margin of error:

At 85% confidence level

α = 1 - 85%  

α = 1 - 0.85 = 0.15

Zα/2 = 0.075

α/2 = Z0.075

Zα/2 = 1.44

At 85% confidence interval, the margin of error is 1.44 when the distribution of this population is approximately normal and has a standard deviation of $9,166.

To learn more about margin of error, visit:

https://brainly.com/question/10501147

#SPJ1

Community colleges in the United States play an important role in higher education. In United States, everyone monitors they community colleges are primarily her two-year institutions of higher education that focus on teaching and learning and workforce preparation.

Community colleges are open access institutions that offer economically affordable entry into higher education. About half of first-time college-going students enroll in community colleges, which serve as her transition route to four-year colleges (Beach, 2011). However, despite the important role and primary focus of community colleges, students may view community college instruction as inferior and undesirable to her four-year college (Dougherty, Lahr, & Morest, 2017; Twombly, 2001; Twombly & Townsend, 2008). This general dissatisfied view of community college instruction has much to do with the historical legacy of community colleges, where most two-year schools are either officially called "junior colleges" or "junior colleges." is called Community colleges have reason to brag about progress. It tends to have a higher proportion of female and minority teachers compared to traditional her four-year colleges (Antonio, 2002; Marcotte, Bailey, Borkowski, & Kientz, 2005; Turner, 2001). While the high recruitment rate of minority teachers is laudable, most higher education institutions are still predominantly white and male dominated (with the exception of those serving minorities). Overall, despite the high proportion of women and minority teachers, empirical studies show that such teachers experience high levels of stress and frustration with the way students are treated in the classroom. (Allen et al., 2002; Pittman, 2010). For many teachers and teachers of color, the classroom environment serves as a reminder of the unfortunate social ills that plague our society (Harlow, 2003; Seo & Hinton, 2009).

Learn more about monitor:

https://brainly.com/question/3799624

#SPJ4