a stack of books is 61 inches high. how high is it in feet and inchess

Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

a) To find the type I error probability, we need to find the probability of rejecting the null hypothesis (H0) when it is actually true. In this case,

Since the foam height is approximately normally distributed with a standard deviation of 20 millimeters and we are taking a sample of size n = 10, the standard error of the mean is:

20 : [tex]\sqrt{10}[/tex] = 6.3 millimeters.

This means that the mean of the sampling distribution of the mean is approximately normally distributed with a mean of 175 millimeters and a standard deviation of 6.3 millimeters.

To find the probability of rejecting the null hypothesis when it is actually true, we can use a z-score.

In this case, the z-score for a value of 185 millimeters is:

(185-175)/6.3 = 1.6

We can use a z-table or a calculator to find the probability of getting a value greater than 1.6 standard deviations above the mean in a normal distribution. This probability is equal to 1 - the probability of getting a value less than or equal to 1.6 standard deviations above the mean, which is:

1 - 0.9495 = 0.0505.

Therefore, the type I error probability, or the probability of rejecting the null hypothesis when it is actually true, is 0.0505 if the critical region is x > 185.

b) To find the boundary point of the acceptance region if alpha = 0.05, we need to find the critical value that corresponds to a type I error probability of 0.05.

To find the critical value, we can use the z-score formula:

z = (x - mean) / standard deviation

We can rearrange this formula to solve for x:

x = z * standard deviation + mean

Since we want the probability of getting a sample mean greater than x to be 0.05, we can use a z-table or a calculator to find the z-score that corresponds to a probability of 0.05 in a normal distribution. This z-score is approximately 1.645.

Substituting this value into the formula above, we get:

x = 1.645 * 6.3 + 175 = 185.095

Therefore, the boundary point of the acceptance region if alpha = 0.05 is approximately 185.095 millimeters.

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$76.25 will be the total cost of four games including discount.

Percent, A relative value that specifies one hundredth of an arbitrary amount. A percentage (representing 1%) is 1 in 100. So 100% represents the whole and 200% represents double the amount.

For example, 1 percent of 1,000 chickens is 1/100 of 1,000 or 10 chickens. 20% of the crowd is 20/100 1,000 or 200.

For the given case:

Original cost of each game = $30.50

75% of $30.50

(75/100) × 30.50

= $22.875

The cost of second game = 30.50 - 22.875

= $7.625

Since, 4 games are bought at once; this means 2 set of games with one on original price and another on discount price each.

Total cost of four games:

2 games at original price = 2 × 30.5

= $61

2 games at discount price = 2 × 7.625

= $15.25

Total = $61 + $15.25

= $76.25

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To generate the most money, the stadiums might set the price at $11.50.A mathematical equation known as a demand function expresses consumer demand as a function of a product or service's pricing and .

The price that customers are prepared to pay and the amount that they're willing to purchase are generally correlated through a demand function. Since the profit function is the sum of these two amounts, this relationship can be converted into one.

m=5−836−30=−36=−1

This is the number of tickets sold that will maximize the revenue because the second derivative is, in fact, negative. Let's go back to the demand function to determine the appropriate ticket price.

R=−x+23\s−x+23=0x=23

R=−1\sp=−12(23)+23=11.5

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A height with a z-score of 1 is the lowest, a height with a percentile rank of 80 percent is in the middle, and a height at the third quartile Q₃ is the highest.

A bell-shaped distribution is also known as a normal distribution. It is a symmetrical distribution where the mean, median, and mode are all equal. The distribution has two tails that extend out from the mean in either direction. A height with a z-score of 1 is the lowest because a z-score of 1 is one standard deviation below the mean. A height with a percentile rank of 80 percent is in the middle because it is the 80th percentile, meaning that 80 percent of the data is lower than it. A height at the third quartile Q₃ is the highest because it is the 75th percentile, meaning that 75 percent of the data is lower than it. In ascending order, the heights arranged are III, II, and I.

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Large sample significance tests for a single proportion are based on the  statistic binomial. the correct option is A

Significance test can be defined as tests for statistical significance indicate whether observed differences between assessment results occur because of sampling error. Significance tests give a formal process for using sample data to evaluate the likelihood of some claim about a population value.

Therefore a Large sample significance tests for a single proportion are based on the  statistic binomial.

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Answer:

Step-by-step explanation:

You want to know the least-cost path of a pipeline from 3 km offshore to 4 km east of the closest point on shore. The cost of pipe in the water is $0.5M/km, and onshore is $0.3M/km.

The solution in the general case for this kind of question is that the sine of the angle between the route directly to shore and the least-cost route is the ratio of the onshore cost to the in-water cost.

  sin(α) = (0.3M/km)/(0.5M/km) = 3/5

The distance from the closest point onshore (E) to the least-cost onshore point is the product of the distance from shore and the tangent of this angle:

  distance downshore = (3 km)·tan(arccos(3/5)) = 2.25 km

Since the refinery is 4 km downshore, this point is 1.75 km from the refinery.

The pipe should follow a direct path underwater from the well to a point 1.75 km west of the refinery, then downshore the remaining 1.75 km to the refinery.

If x represents the distance from the refinery to the point where the pipeline comes ashore, the cost of the route in millions will be ...

  c = 0.5√(3² +(4-x)²) +0.3x

where the square root function is calculating the underwater length of the pipeline using the Pythagorean theorem.

This cost function will be minimized when its derivative with respect to x is zero.

  c' = 0.5(1/2)(2x -8)/√(x² -8x +25) +0.3 = 0

  0 = 0.5(x -4) +0.3√(x² -8x +25) . . . . . . numerator of the combined terms

  4 -x = 0.6√(x² -8x +25) . . . . multiply by 2, add 4-x

  16 -8x +x² = 0.36x² -2.88x +9 . . . . . . square both sides

  0.64x² -5.12x +7 = 0 . . . . . subtract the right side

  x = (5.12 -√(5.12² -4(0.64)(7)))/(2(0.64)) = 2.24/1.28 = 1.75

The route with lowest cost comes ashore 1.75 km from the refinery.

__

Additional comment

The cost of the pipeline will be ...

  c = 0.5√(9 +(4-1.75)²) +0.3(1.75) = 0.5√14.0625 +0.525

  c = 2.4 . . . . million dollars

The attached graph shows the cost function has a minimum of 2.4M at a distance of 1.75 km from the refinery. The cost is only 2.5M if the pipe runs directly from the well to the refinery (x=0).

x be the distance (in miles) between point p and where the boat lands on the lakeshore.x = (7 - 3)/(3/4) = 4.5 miles.The boat should be landed 4.5 miles down the shore from point p.

The woman needs to get to a town 7 miles down the shore from point P. She can row the boat 3 miles per hour, and walk 4 miles per hour. The boat needs to be landed 4.5 miles down the shore from point P so she can get to the town in the least time. To figure out this distance, we subtract the 3 miles between the island and point P from the 7 miles between the town and point P. This gives us 4 miles. We then divide 4 miles by the ratio of her rowing rate (3) to her walking rate (4) to get 4.5 miles. Therefore, the boat should be landed 4.5 miles down the shore from point P.

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The given matrix has no solution.

What is the system of equations?

system of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns. Even then a solution is not guaranteed.

According to the question, the matrix is:

[tex]\left[\begin{array}{ccc}1&-5&-4\\0&0&7\\ \end{array}\right][/tex]

The linear equation will be:

x - 5y = -4

and

0x + 0y = 7

i.e,

   0 = 7       (Not possible)

Hence, the above given matrix has no solution.

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The largest value of these integers is 68

We are given that the average of 5 positive integers is 60

Let the five numbers be [tex]x_{1}, x_{2}, x_{3}, x_{4}, x_{5}[/tex]

Therefore,

[tex]\frac{x_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5}}{5} = 60[/tex]

[tex]{x_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5}} = (60)(5)[/tex]

[tex]{x_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5}} = 300[/tex]

Now, let the first (smallest) number be [tex]x[/tex]

Therefore, the last (largest) number will be equal to [tex]x + 10[/tex]

To maximise a number in the sum equation, we'll have to minimise all the other numbers.

Therefore, let it be

[tex]x + x + x + x + (x + 10) = 300[/tex]

[tex]5x + 10 = 300[/tex]

[tex]5x = 290[/tex]

Therefore, [tex]x = 58[/tex]

Now, we took the largest number as [tex](x + 10)[/tex]

Therefore, the largest number is (58 + 10)

The correct answer is 68

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Answer: 2/9 = 0.22

Step-by-step explanation: This is rounded to the nearest hundredth which is in the 2nd place after the decimal point.

Answer:

yes it is function.........

DB will appear at outputs A, and B.

Step 1

D flip flop stands for a delay flip flop that produces output that is identical to input after a brief delay. The flip flop's input and next state are equal.

Z is an output, and x and x inputs.

x'y + xA = DA= A*

B* = x'B + xA

z=A (output is independent of input) (output is independent of input)

The next states are A(t+1) and B(t+1). We must provide the next state value to D of the D flip flop in order to obtain the next states A(t+1), and B(t+1) for A, B(present state). So the sequential circuit will be:

Step 2

To get the next state as A(t+1)= x’A + xA, B(t+1)= x’B + xA, we have to give them to DA, DB of D flip flop because for D flip flop whatever is given to DA, DB will appear at output A, B.

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The graph of each given piecewise function is shown below .

In the question,

a piece wise function is given ,

we have to sketch the graph of the piecewise function ,

the piecewise function f(x) is  = [tex]\left \{ {-2x-1 , {x\leq 2} \atop -x+4 , {x > 2}} \right.[/tex]

when x ≤ 2 ,

we put x =2 , we get , f(2) = -2*2-1  = -5 .

So , the point is (2,-5) .

when we put x = 0 , f(0) = -2*0 - 1 = -1

so , the second point is (0,-1) .

Now , for x>2  

we put x= 4 , we get f(4) = 0

the point will, be (4,0)

we put x = 6 , we get , f(6) = -2 .

the point will be = (6,-2) .

On plotting all the four points , we get the graph as sketched below .

Therefore , the given piecewise function's graph is shown below.

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Answer:

To find the cash flows for this project, we need to calculate the net income for each year and then subtract any investments in net working capital and capital expenditures.

In year 0, the firm will incur the following expenses:

- Research and development costs: $490,000

- Cost of the machine: $290,000

- Shipping and installation costs: $59,000

- Increase in net working capital: $145,000

Total expenses in year 0: $490,000 + $290,000 + $59,000 + $145,000 = $984,000

The net income in year 0 is equal to the revenue minus the costs: $690,000 - $340,000 = $350,000.

Therefore, the cash flow in year 0 is:

FCF0 = $350,000 - $984,000 = -$634,000

In years 1, 2, and 3, the firm will incur the following expenses:

- Cost of goods sold: $340,000

- Depreciation: (This can be calculated using the MACRS depreciation schedule. For the first year, the depreciation will be 14.29% of the cost of the machine, or 0.1429 * $290,000 = $41,461. The depreciation in subsequent years can be calculated using the same method.)

- Increase in net working capital: $145,000

Total expenses in each of years 1, 2, and 3: $340,000 + Depreciation + $145,000

The net income in each of these years is equal to the revenue minus the costs: $690,000 - (Total expenses)

The cash flow in each of these years is equal to the net income minus any investments in net working capital and capital expenditures: Net income - Increase in net working capital - Depreciation

Substituting the appropriate values, we get:

Year 1: FCF1 = $690,000 - ($340,000 + $41,461 + $145,000) = $163,539

Year 2: FCF2 = $690,000 - ($340,000 + Depreciation + $145,000)

Year 3: FCF3 = $690,000 - ($340,000 + Depreciation + $145,000)

Note that the depreciation in years 2 and 3 can be calculated using the same method as in year 1.

So, the cash flows for this project are:

Year 0 1 2 3

FCF -$634,000 $163,539

I hope this helps!

The simplified form of the given expression is [x² - 5x -24]/[x² + 8x -9].

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given expression is

(x-8)(x+3)/(x+9)(x-1)

Now applying the formula (x - a)(x + b) = x² -(a - b)x -ab in the numerator:

= [x² - (8 - 3)x -8×3]/(x+9)(x-1)

= [x² - 5x -24]/(x+9)(x-1)

Again applying the formula (x - a)(x + b) = x² -(a - b)x - ab in the denominator:

= [x² - 5x -24]/[x² - (1 - 9)x -9×1]

= [x² - 5x -24]/[x² + 8x -9]

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The value of s for the given right angle triangle by Pythagoras' theorem will be 17.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

As per the given triangle, ABD is a right-angle triangle thus to Pythagora's theorem,

s² = 15² + 8²

s = 17

Hence "According to Pythagoras' Theorem, the value of s for the given right angle triangle is 17.".

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After evaluating the given integral by changing to polar coordinates we get [tex]7 e^8-31[/tex]

As per the details shared in the above question it is given that,

[tex]$x^2+y^2=64$[/tex]

[tex](x, y)=r(\cos \theta, \sin \theta)[/tex]

[tex]d A=r d r d \theta.[/tex]

Further solving above we get,

[tex]r^2=64 \\\Rightarrow & r=8 . \\0 \leq r \leq 8 ; & 0 \leq \theta \leq \pi / 2[/tex]

The polar coordinate,

[tex]\iint_{R} y e^x d A=\int_0^{\frac{\pi}{2}} \int_0^8 r^2 \sin \theta e^{r \cos \theta} d r d \theta[/tex]

[tex]& =\int_0^8 \int_0^{\frac{\pi}{2}} r^2 \sin \theta e^{r \cos \theta} d \theta ; \\& =\int_0^8\left[-r e^{r \cos \theta}\right]_0^{\pi / 2} d r[/tex]

[tex]=\int_0^8 r\left[-e^{r \cos \left(\frac{\pi}{2}\right)}+e^\alpha\right] d r .[/tex]

[tex]=\int_0^8 r e^r d r-\left.\frac{r^2}{2}\right|_0 ^8[/tex]

Now substituting the value we get,

[tex]7 e^8-31[/tex]

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Note the correct question should be ,

Evaluate the given integral by changing to polar coordinates.

[tex]\iint_R y e^x d A[/tex] , where R is the region in the first quadrant enclosed by the circle  [tex]x^2+y^2=64[/tex].

Step-by-step explanation:

the mean score is the sum of all scores divided by the number of scores.

64 = (s1+s2+s3+...+s26+s27)/27

64×27 = (s1+s2+s3+...+s26+s27)

1728 = (s1+s2+s3+...+s26+s27)

now, one of the scores changes from 47 to 74. that means the sum of all scores is increased by 74-47 = 27.

so, we get

1728 + 27 = (s1+s2+s3+...+s26+s27+27)

1755 = (s1+s2+s3+...+s26+s27+ 27)

we still have 27 scores, so for the updated mean we have to divide both sides by 27 again :

1755/27 = (s1+s2+s3+...+s26+s27+27)/27

65 = (s1+s2+s3+...+s26+s27+27)/27

the correct mean is therefore 65%.

Answer:

Area = Length * Width

Area = 5 units * 3 units

Area = 15 units²

(see attachment picture for the graph)

Step-by-step explanation:

Answer: 15 sq units

Step-by-step explanation:

1. graph it out, this will help visually.

2. find the distance/difference between the y's of (3,1) and (3, -2) to find the width, or (-2, -2) and (-2, 1). it is 3.

3. find the distance between the x's of (3,1) and (-2,1), or (3, -2) and (-2, -2). the distance is 5.

4. multiply the lengths together to find the area. :)

Answer:

90%

Step-by-step explanation:

63 of 70 can be written as:

63/70

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

63/70 × 100/100 = (63 × 100/70) × 1/100 = 90/100

Therefore, the answer is 90%

If you are using a calculator, simply enter 63÷70×100 which will give you 90 as the answer.

Answer:

8<r

Step-by-step explanation:

5 > r – 3

+3      +3

add 3 to both sides

8>r

move variable to the left and flip the sign

8<r

Answer: 7

Step-by-step explanation: cause I took the quiz…

When "twice the sum of a number and 3 equals three times the difference of the number and 3," the value of expression is 6.

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign.

Here,

let x be the number,

2x+3=3x-3

x=6

The value of expression is 6 when "twice the sum of a number and 3 is equal to three times the difference of the number and 3."

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1)test the claim that women and men have the same mean diastolic blood pressure .Let p1 be the mean diastolic blood pressure for women and let u2 be the mean diastolic blood pressure for men

there for we test

H0: u1 = u2

H1 : u1 =!u2

2)t= overline X 1 - overline X 2 sqrt((S_{1} ^ 2)/n_{1} + (S_{2} ^ 2)/n_{2})

= (69.81 - 69.35)/(sqrt((10.46 ^ 2)/26 + (11.2l ^ 2)/26)

= 0.153

3) P-value.

t-statistic value = 0.153 , alpha=0.05 then

p-value for two tail test = 0.879 which is greater than n = 0.05(0.879 > 0.05) So we do not reject H0.

4)Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

we concluded that the null hypothesis not rejected, at 95 % confidence H0:u1= u2 accepted.

that is we accept the claim that women and men have the same mean diastolic blood pressure.at 0.05 significance level.

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Hazel's new balance in the account is $1197

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

Previous balance = $876.21.

$2.39 in interest,

$616.46 in deposits,

$298.06 in withdrawals

Her new balance can be calculated using

New balance = Previous balance + interest + deposits - withdrawals

Substitute the known values in the above equation, so, we have the following representation

New balance = 876.21 + 2.39 + 616.46 - 298.06

Evaluate

New balance = 1197

Hence, the new balance is $1197

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On solving the provided question we can say that he probability of getting the following result using the binomial probability formula and the normal curve approximation is P(4, 16, 1/2) = 0.0280.

Probability is the possibility or chance that something will happen. Probability = how many different paths there are to success/the total number of events that might occur. A coin flip, for instance, has a 50% chance of coming up heads since there is only one method to acquire a head and there are a total of two possible outcomes (a head or tail). P(heads) = 1/2 is the formula.

P(4,16,1/2) = C(16,4)(1/2) 4(1 - 1/2)16 - 4 = C(16,4)(1/2)16 = 0.02777;

by help of table - P(4, 16, 1/2) = 0.0280

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Answer:

C. C and E

Step-by-step explanation:

As per the graph, both points C and E are points that are located on both the red and purple graphs.

Answer:

C.  point C and point E

Step-by-step explanation:

The solutions to the given linear-quadratic system of equations are the points where the line and curve intersect.

From inspection of the given graph, the points of intersection are:

No such c exist from 1 and hence mean value theorem fails, an example is given below.

Consider f(x)=[x] on [-1,1]

Then, f is not differentiable on x=0

Note that,

f'(x)=1  for x>0 and f'(x)=-1 for x<0

The Mean Value Theorem states that if a feature f is non-stop at the closed interval [a,b] and differentiable at the open interval (a,b), then there exists a factor c withinside the interval (a,b) such that f'(c) is same to the feature's common price of extrade over [a,b].

According to near value theorem we need,

a c (-1,1).

f'(c)= f(1)-f(-1)/1-(-1)

=|1|-|-1|/2

=1-1/2=0

i.e., f'(c)=0

While, no such c exist from 1 and hence mean value theorem fails.

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