The state test scores for 12 randomly selected high school seniors are shown on the right. Complete parts​ (a) through​ (c) below. Assume the population is normally distributed. 1420 1227 989 691 726 833 722 747 547 630 1442 948
​(a) Find the sample mean. x overbarequals nothing ​(Round to one decimal place as​ needed.)​
(b) Find the sample standard deviation. sequals nothing ​(Round to one decimal place as​ needed.) ​
(c) Construct a 90​% confidence interval for the population mean mu. A 90​% confidence interval for the population mean is ​

Answer:

AAO 22.902 A 45 12.632 13,939 945 559,302 5A , 480 1.17 6.044 36,491 ... 12.1 F 13.2 12.1 F 13.2 12.1 E 13.2 12.1 F 12.9 12.5 8.6 8.3 F 10.0 9.7 8.6 B.3 E 11.6 ... 10.5 D 11.8 10.5 C 11.8 10.5 D 11.8 10.5 с 11.8 10.5 U 11.8 10.5 D 13.3 12.7 ... 10.1 12.1 11.4 8.8 A.3 13.3 12.9 13.3 12.5 13.3 12.5 13.3 12.5 11.0 10.4 13.3 ...

Answer:

70/5 = 14 which then means it 14/1

Answer:

x=7

Step-by-step explanation:

direct variation is in the form y=kx

65 = k 13

by dividing both sides be 13, we see that 5 = k

thus, we can then take the next situation 35 = 5x

dividing both sides by 5 brings us to 7 = x

The probability that the third hole drilled is the first to yield a productive well is 0.192.

Learn more about the oil prospector:

https://brainly.com/question/12905157

#SPJ11

Answer:

4 : 3 : 3

Step-by-step explanation:

2/5 of 150 = 300/5 or 60;  therefore, there are 60 blue marbles

3/10 of 150 = 450/10 or 45;  therefore, there are 45 clear marbles

150 - (60 + 45) = number of green marbles;  there are 45 green marbles

Blue : Clear : Green ratio is 60 : 45 : 45 or 4 : 3 : 3

The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ1

Answer:

Y=5

Step-by-step explanation:

Answer: 66 2/3% decrease because you got less this week and if you do what you got this week over what you got last week then you get the percent dicrease

Step-by-step explanation:

Answer:

x = -∛115

Step-by-step explanation:

x^3 - (-115) = 0

= x^3 + 115

Factoring

(a+b) • (a^2-ab+b^2) =

   a^3-a^2b+ab^2+ba^2-b^2a+b^3 =

   a^3+(a^2b-ba^2)+(ab^2-b^2a)+b^3=

   a^3+0+0+b^3=

   a^3+b^3

(115 isn't a cube.)

Polynomial roots

P: -1, -5, -23, -115, 1, 5, 23, 115

Q: 1

P/Q: -1, -5, -23, -115, 1, 5, 23, 115

Divisor(s): None

In these sets of data, there are no rational roots shown.

Step-by-step explanation(part 2):

x^3 + 115 = 0

x^3 = -115

x  =  ∛-115

Negative numbers will always have real cube roots.

∛ -115 = ∛ -1 × 115  = ∛ -1 × ∛ 115 = (-1) × ∛ 115

Therefore,

x = -∛115

The lateral area of the right octagonal prism is 672 square inches

The formula for lateral area of a right octagonal prism is expressed as;

Lateral area = 8ah

Where;

Substitute the values into the formula

Lateral area = 8 × 7 × 12

Multiply through

Lateral area = 672 square inches

Thus, the lateral area of the right octagonal prism is 672 square inches

Learn more about lateral area here:

https://brainly.com/question/17056543

#SPJ4

The profit is maximized at $16,400 when the ticket price is $12.

To find the ticket price that maximizes the profit, we used the fact that the maximum or minimum value of a quadratic function occurs at its vertex. For a quadratic function in the form of P(x) = ax^2 + bx + c, the x-coordinate of the vertex can be found using the formula x = -b / 2a.

In this case, we were given the function \(P(x) = -100x^2 + 2400x - 8000,\)where x represents the price per ticket. The coefficient of \(x^2\) is negative, which tells us that the graph of this function is a downward-facing parabola. The vertex of this parabola represents the maximum value of the function.

Using the formula x = -b / 2a, we found the x-coordinate of the vertex to be x = -2400 / 2(-100) = 12. This means that a ticket price of $12 will maximize the profit.

To verify that this is indeed the maximum profit, we substituted x = 12 into the profit function P(x):

\(P(12) = -100(12)^2 + 2400(12) - 8000 = 16,400\)

We can see that the profit is maximized at $16,400 when the ticket price is $12.

In summary, to find the ticket price that maximizes the profit, we used the formula x = -b / 2a to find the x-coordinate of the vertex of the quadratic function representing the profit from selling tickets to a musical. The maximum profit occurs at the ticket price that corresponds to the x-coordinate of the vertex.

To learn more about profit refer here:

https://brainly.com/question/15036999

#SPJ11

To determine the function f(r) such that f(r)r is solenoidal, we need to first understand what it means for a vector field to be solenoidal.

A vector field is said to be solenoidal if its divergence is zero everywhere. Mathematically, if the vector field F is given by F = (F1, F2, F3), then it is solenoidal if ∇ • F = 0, where ∇ is the divergence operator.

Now, let's consider the vector field G = f(r)r, where r is the position vector in three-dimensional space, and f(r) is a scalar function. We can express G in terms of its components as follows:

G = (f(r)x, f(r)y, f(r)z)

where x, y, and z are the components of the position vector r. To determine f(r) such that G is solenoidal, we need to find the divergence of G using the expression for the divergence of a product of a scalar and a vector:

∇ • G = ∇ • (f(r)r) = (∇f(r)) • r + f(r)∇ • r

Now, since r = xi + yj + zk, we have:

∇ • r = ∂x/∂x + ∂y/∂y + ∂z/∂z = 3

Substituting this into the expression for ∇ • G, we get:

∇ • G = (∇f(r)) • r + 3f(r)

For G to be solenoidal, we need ∇ • G to be zero everywhere. This implies that (∇f(r)) • r + 3f(r) = 0. Since r is a vector, we can write this as:

∇f(r) + 3f(r)*(r/r²) = 0

where r/r² is the unit vector in the direction of r.

Multiplying both sides by r, we get:

r • ∇f(r) + 3f(r) = 0

This is a first-order partial differential equation known as the radial form of Laplace's equation. The general solution to this equation is:

f(r) = A/r³ + B

where A and B are constants.

Therefore, the function f(r) such that f(r)r is solenoidal is given by:

f(r) = A/r³ + B

where A and B are constants.

Learn more about vector fields here brainly.com/question/29815461

#SPJ4

Answer: Option a.

Step-by-step explanation:

The data is:

The cost of mailing a letter is $0.37 for the first ounce.

$0.23 for each additional ounce or portion.

Then if we define the variable n, as the number of additional ounces, we can write this as:

F(n) = $0.37 + n*$0.27

This seems to be a linear relationship, but n only can take whole numbers, this means that if n is equal to 0.37, we should round it up (because we already have more than only one ounce).

Then we round up all the non-integers to the next integer.

for example, we round 1.45 to 2 and 1.876 to 2.

This means that F (1.45) = F(1.876) = F(2) = $0.37 + 2*$0.27

This is called a greastet integer function. then the correct option is a.

Answer:

Its B. Step Function, I just turned it in.

Step-by-step explanation:

Edge. 2020-21

The normal approximation to the p-value for fisher's exact test against the alternative that the Stanford team is better than the berkeley team is:0.0015

z = 0.94444 - 0.5 / √0.7222(1-0.7222)(1/18 + 1/18)

= 0.4444/√0.0223

=  2.9768

The p value is 0.0015

Hence the The normal approximation to the p-value for fisher's exact test against the alternative that the stanford team is better than the berkeley team is: 0.0015

Complete question

The University of California, Berkeley (Cal) and Stanford University are athletic archrivals in the Pacific 10 conference. Stanford fans claim Stanford's basketball team is better than Cal's team; Cal fans challenge this assertion.

In 2004, Stanford University's basketball team went nearly undefeated within the Pac 10. Stanford's record, and those of Cal and the other eight teams in the conference, are listed in In all, there were 89 games played among the Pac 10 teams in the season.

Stanford won 17 of the 18 games it played; Cal won 9 of 18. We would like to use these data to test the Stanford fans' claim that Stanford's team is better than Cal's. That is, we would like to determine whether the difference between the two teams' performance reasonably could be attributed to chance, if the Stanford and Cal teams in fact have equal skill.

To test the hypothesis, we shall make a number of simplifying assumptions. First of all, we shall ignore the fact that some of the games were played between Stanford and Cal: we shall pretend that all the games were played against other teams in the conference. One strong version of the hypothesis that the two teams have equal skill is that the outcomes of the games would have been the same had the two teams swapped schedules. That is, suppose that when Washington played Stanford on a particular day, Stanford won. Under this strong hypothesis, had Washington played Cal that day instead of Stanford, Cal would have won.

A weaker version of the hypothesis is that the outcome of Stanford's games is determined by independent draws from a 0-1 box that has a fraction pC of tickets labeled "1" (Stanford wins the game if the ticket drawn is labeled "1"), that the outcome of Berkeley's games is determined similarly, by independent draws from a 0-1 box with a fraction pS of tickets labeled "1," and that pS = pC. This model has some shortcomings. (For instance, when Berkeley and Stanford play each other, the independence assumption breaks down, and the fraction of tickets labeled "1" would need to be 50%. Also, it seems unreasonable to think that the chance of winning does not depend on the opponent. We could refine the model, but that would require knowing more details about who played whom, and the outcome.)

Nonetheless, this model does shed some light on how surprising the records would be if the teams were, in some sense, equally skilled. This box model version allows us to use Fisher's Exact test for independent samples, considering "treatment" to be playing against Stanford, and "control" to be playing against Cal, and conditioning on the total number of wins by both teams (26).

QUESTIONS:

5) The normal approximation to the P-value for Fisher's exact test against the alternative that the Stanford team is better than the Berkeley team is:

Read more on p value here:

https://brainly.com/question/4621112

#SPJ4

Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

To know more about Net present value   visit

https://brainly.com/question/32720837

#SPJ11

The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point

f(x) = 5x⁶ - 3x⁵

differentiation w.r.t x

=> f'(x) = 30x⁵ - 15x⁴

Putting f'(x) = 0

30x⁵ - 15x⁴ = 0

=> x⁴(30x - 15) =0

=> 30x - 15 = 0

=> x = 15/30

=> x = 0.5 , 0

Critical number is 0.5 , 0

(B) To find where f(x) is increasing

for x > 0.5 ,

(30x-15) > 0 => x⁴(30x - 15) > 0

Therefore , f(x) is increasing at ( 0.5 , ∞ )

(C)To find where f(x) is decreasing

for x < 0.5 ,

(30x-15) < 0 => x⁴(30x - 15) < 0

Therefore , f(x) is decreasing at ( -∞ , 0.5)

(D) Differentiation f'(x) again w.r.t to x

f'(x) = 30x⁵ - 15x⁴

f"(X) = 150x⁴ - 60x³

Substituting critical values of x

=> 150(0.5)⁴ - 60(0.5)³

=>9.375 - 7.5

=> -1.875 < 0 , Hence , x = 0.5 is point of maxima

(E) no point of minima

Similarly , we can solve other parts

To know more about Function here

https://brainly.com/question/28303908

#SPJ4

Step 1: The proposed probe for flaw detection in type 316L austenitic stainless steel plates is an eddy current probe with a suitable height, diameter, and frequency.

Step 2: Eddy current testing is an effective non-destructive testing method for detecting flaws in conductive materials. In this case, the eddy current probe should have a suitable height, diameter, and frequency to ensure accurate flaw detection.

The height of the probe should be adjusted to maintain a constant lift-off of 0.2 mm, which is the distance between the probe and the surface of the material being tested. This ensures consistent measurement conditions and reduces the influence of lift-off variations on the test results.

The diameter of the probe should be selected based on the size of the flaws and the desired spatial resolution. It should be small enough to accurately detect the flaws but large enough to cover the entire flaw area during scanning.

The frequency of the eddy current probe determines the depth of penetration into the material. Higher frequencies provide shallower penetration but higher resolution, while lower frequencies provide deeper penetration but lower resolution. The frequency should be chosen based on the expected depth of the flaws and the desired level of sensitivity.

Overall, the eddy current probe with suitable height, diameter, and frequency can effectively detect the artificial flaws in type 316L austenitic stainless steel plates fabricated using a powderbed-based laser metal additive manufacturing machine.

Learn more about eddy current probe
brainly.com/question/31499836

#SPJ11

Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

Answer:

volume = 14,137

Step-by-step explanation:

radius is the diameter divided by 2

30÷2=15

radius = 15 then square

15^2 = 225

formula of volume of a cone is 1/3*pi*raduis^2*the height

1/3(3.14)(225)(60)= 14,137

The volume of a cone with a diameter of 30 feet and a height of 60 feet is 14130.

The volume of the cone is given by;

\(\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\Where;\ r = radius \ and \ h = height\)

The volume of a cone with a diameter of 30 feet and a height of 60 feet.

The radius of the cone is;

\(\rm Radius =\dfrac{Diameter}{2}\\\\Radius=\dfrac{30}{2}\\\\Radius=15\)

Substitute all the values in the formula

\(\rm Volume \ of \ cone=\dfrac{1}{3}\pi r^2h\\\\ Volume \ of \ cone=\dfrac{1}{3}\times 3.14 \times 15^2 \times 60\\\\Volume \ of \ cone=14130\)

Hence, the volume of a cone with a diameter of 30 feet and height of 60 feet is 14130.

Learn more about the volume of cone here;

https://brainly.com/question/3013784

#SPJ2

If the null space of a 7 × 9 matrix is 3-dimensional, we can determine the rank of matrix A, the dimension of the row space of A, and the dimension of the column space of A.

The rank of a matrix is equal to the number of linearly independent columns or rows in the matrix. Since the null space is 3-dimensional, the rank of A would be 9 - 3 = 6.

The dimension of the row space, also known as the row rank, is equal to the dimension of the column space, or the column rank. Therefore, the dimension of the row space and the dimension of the column space of A would also be 6.

The rank of matrix A would be 6, and both the dimension of the row space and the dimension of the column space of A would also be 6.

Learn more about matrix here: brainly.com/question/28180105

#SPJ11

Answer:

2

Step-by-step explanation:

3(6+x) = 24

18 + 3x = 24

3x = 24 - 18

3x = 6

x = 6/3

= 2

If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.

When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.

This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.

The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.

In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.

It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.

Learn more about confidence interval at https://brainly.com/question/15576092

#SPJ11

Answer:

4 1/5

Step-by-step explanation:

1. \(\frac{7}{9} * 5\frac{2}{5} = \frac{7}{9} * \frac{27}{5}\)

2. \(\frac{7}{9} * \frac{27}{5} = \frac{7}{1} * \frac{3}{5}\)

3. \(7 * \frac{3}{5} = \frac{21}{5}\)

4. \(\frac{21}{5} = 4\frac{1}{5}\)

Answer:

4. Buffalo

Step-by-step explanation:

because it's negatives (with temperature) the bigger the number, the colder it is.

Answer:

Spanish - detected

English

la camiseta azul

ANSWER= the blue t-shirt

Answer:

A-the blue t-shirt

Step-by-step explanation:

Answer:

c = -22, 22

Step-by-step explanation:

\( {(x - 11)}^{2} = {x}^{2} - 22x + 121\)

\( {(x + 11)}^{2} = {x}^{2} + 22x + 121\)