(a) cone, (b) sphere, (c) cylinder, (d) prism.

a) The expected annual rainfall accumulated in this lake is 30 million tons. b) The standard deviation of the annual amount of rainfall in this lake is 10 million tons. c) P(X < 4) = 0.3085. d) P(2 < X < 5) = 0.4293.

a) To find the expected annual rainfall accumulated in this lake, we first need to calculate the shape parameter (alpha) and the rate parameter (gamma). alpha = 3 and gamma = 5. Then, we find the expected value of the gamma distribution using the formula E(X) = alpha * gamma. This gives us E(X) = 3 * 5 = 15. Therefore, the expected annual rainfall accumulated in this lake is 30 million tons (2 * 15). b) To find the standard deviation of the annual amount of rainfall in this lake, we first need to calculate the variance of the gamma distribution using the formula variance = alpha/gamma^2. This gives us variance = 3/25 = 0.12. The standard deviation of the annual amount of rainfall in this lake is the square root of 0.12, which is 0.346. This is equivalent to 10 million tons (2 * 0.346). c) To find P(X < 4), we can use the R programming language. In R, we can use the pgamma() function to calculate the cumulative probability of a gamma distribution. We use the parameters alpha and gamma (3 and 5 respectively) and the value 4. This gives us P(X < 4) = 0.3085. d) To find P(2 < X < 5), we can use the R programming language. In R, we can use the pnorm() function to calculate the cumulative probability of a normal distribution. We use the parameters alpha and gamma (3 and 5 respectively) and the values 2 and 5. This gives us P(2 < X < 5) = 0.4293.

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Zachary' Diner old 28 milkshake with whipped cream on top and 72 milkshake without whipped cream,  percentage of the milkshake had whipped cream is 28%.

Zachary ordered 28 milkshake with whipped cream on top and 72 milkshake without whipped cream.

So total number of milkshake is 100

So percentage of milkshake had whipped cream will be,

28/100 x 100

=28%

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

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Answer:

In one hour, 75 calendars were printed, which is 30% of the total number of calendars (250). Therefore, the percent of the calendars printed in one hour is 30%.

Answer: 30

Step-by-step explanation: The answer would be 30 because if you took 75 and divided by 200 you would end up with a product of about 30! Hopefully this helped you!!

The smallest positive integer that is neither prime nor square and that has no prime factor less than 50 is 3137.

This can be determined by using the prime factorization method. Prime factorization is a process of breaking down a number into its prime factors. The prime factors of a number are the factors that are only divisible by one and itself. For 3137, the prime factors are 3, 7, 17 and 37 since these are the only prime numbers that can divide 3137 evenly. Since none of the prime factors are less than 50, 3137 is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50.

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The Typewriters should be guaranteed for 7.72 months, which would give a 5% chance of requiring a major repair before the end of the guarantee period.

Typewriter repair times have a normal distribution, with a mean of 11 months and a standard deviation of 2 months. To find the warranty period at which only her 5% of typewriters fail before the warranty expires, we need to find the corresponding z-score and solve it after the warranty period.

Using the standard normal distribution table, we find that the Z-score corresponding to a cumulative probability of 0.95 is approximately 1.64.

This means that 95% of typewriters will need major repairs after 11 + 1.64 * 2 = 14.28 months.

To ensure that only 5% of typewriters fail before the warranty expires, the warranty period should be set to 11 - 1.64 * 2 = 7.

72 months.

Finally, the typewriter still has about 7.72 months of warranty, and only 5% of cars fail before the warranty runs out.

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The faster train would be travelling at 120 mph.

Let's give the slower train's speed the designation of x mph. The speed of the speedier train would then be x + 10 mph.

The 4.5 hours it took the two trains to arrive at their meeting point and their varying speeds can be used to calculate the distance that each train covered. The relative speed is equal to the product of the velocities of the two trains,

Therefore (x) + (x + 10) = 2x + 10 mph.

Distance = rate x time gives the distance covered by each train.

The slower train's route can be expressed as follows:

x * 4.5 hours = 495 miles.

Additionally, the quicker train covered 495 miles in (x + 10) * 4.5 hours.

We can now use these two equations to solve for x:

x * 4.5 = 495

x = 110 mph

And, the faster train would be traveling at 110 + 10 = 120 mph.

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The conversion factor from Celsius to Fahrenheit is 37.78.

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On solving the provided question, we can say that in the triangle LM = 2*(IJ) x = |-6| = 6 and LM = 4x + 8 = 32 units

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

given,

LM = 4x + 8 and IJ = 5x +22

in the triangle LM = 2*(IJ)

4x + 8 = 2*(5x + 22)

4x + 8 = 10x + 44

6x + 36

x = |-6| = 6

LM = 4x + 8 = 32 units

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No, they don't have the same solution. Then the correct option is B.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

−12x + 9y = 7              ...1

9x − 12y = 6               ...2

From equations 1 and 2, then we have

−36x + 27y = 21              ...3

36x − 48y = 24               ...4

Add both equations, then we have

27y − 48y = 21 + 24

− 21y = 45

y = − 45/21

y = − 15/7

Then the value of the variable 'x' is given as,

9x − 12(−15/7) = 6

9x + 180/7 = 6

9x = −138/7

x = −46/21

No, they don't have the same solution. Then the correct option is B.

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The code that creates a function that will return the product of two integers is given below:

#include <iostream>

using namespace std;

/* Your code goes here */

int main() {

  int input1, input2;

  int result;

  cin >> input1;

 cin >> input2;

  result = ComputeVal(input1, input2);

  cout << result << endl;

  return 0;

}

In mathematics, whole numbers and negative numbers are grouped together as integers. Integers, like whole numbers, do not include the fractional portion.

Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions. On integers, we can carry out all mathematical operations, including addition, subtraction, multiplication, and division.

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(i) State whether the term is a variable name or a variable value.

(ii) State the level of measurement.

A. age

(i) Variable name.

(ii) Ratio.

Explanation: "Age" is the name of the variable and it is a numerical value representing the number of years a person has lived. It is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).

B. conservative

(i) Variable name.

(ii) Nominal.

Explanation: "Conservative" is the name of b and it refers to a political ideology. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., conservative, liberal, socialist) and have no meaningful mathematical operations.

C. strongly oppose

(i) Variable value.

(ii) Ordinal.

Explanation: "Strongly oppose" is a value of the variable, and it refers to a person's opinion or attitude towards a certain issue. It is measured on an ordinal scale, meaning it has a rank or order (e.g., strongly oppose, somewhat oppose, neutral, somewhat support, strongly support). However, the difference between two values is not necessarily equal (e.g., the difference between strongly oppose and neutral might be different from the difference between neutral and strongly support).

D. region

(i) Variable name.

(ii) Nominal.

Explanation: "Region" is the name of the variable and it refers to a geographical area, such as the Midwest or the South. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Midwest, South, West, Northeast) and have no meaningful mathematical operations.

E. 57 years

(i) Variable value.

(ii) Ratio.

Explanation: "57 years" is a value of the variable "Age" and it represents the number of years a person has lived. As mentioned above, "Age" is measured on a ratio scale, meaning it has a meaningful zero point (e.g., 0 years old) and the difference between two values is meaningful (e.g., the difference between 10 and 20 years is the same as the difference between 30 and 40 years).

F. strictly enforced

(i) Variable value.

(ii) Ordinal.

Explanation: "Strictly enforced" is a value of a variable, and it refers to the level of enforcement of a rule or law. It is measured on an ordinal scale, meaning it has a rank or order (e.g., not enforced, loosely enforced, strictly enforced). However, the difference between two values is not necessarily equal (e.g., the difference between not enforced and loosely enforced might be different from the difference between loosely enforced and strictly enforced).

G. Catholic

(i) Variable name.

(ii) Nominal.

Explanation: "Catholic" is the name of the variable and it refers to a religious affiliation. It is measured on a nominal scale, meaning it is a categorical variable with no inherent order. The categories can simply be labeled or named (e.g., Catholic, Protestant, Jewish, Muslim) and have no meaningful mathematical operations.

H. Gender

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Answer:

Congruence D transformation follows the rule (x,y)--> (-x,y)

The differential equations a) y' = cos(x), b) y' = sin(x), c) y' = 4-y, d) y' = x, e) y' = y, and f) y' = x-y all match the corresponding slope fields shown in figures A-F respectively.

a. y'=cos(x): This differential equation describes the slope field shown in figure A. To calculate the slope of a given point (x,y), we can use the formula y'=cos(x). For example, if x=π/2 and y=1, the slope of the line at that point is y'=cos(π/2)=-1.

b. y'=sin(x): This differential equation describes the slope field shown in figure B. To calculate the slope of a given point (x,y), we can use the formula y'=sin(x). For example, if x=0 and y=1, the slope of the line at that point is y'=sin(0)=0

c. y'=4-y: This differential equation describes the slope field shown in figure C. To calculate the slope of a given point (x,y), we can use the formula y'=4-y. For example, if x=0 and y=2, the slope of the line at that point is y'=4-2=2.

d. y'=x: This differential equation describes the slope field shown in figure D. To calculate the slope of a given point (x,y), we can use the formula y'=x. For example, if x=3 and y=2, the slope of the line at that point is y'=3.

e. y'=y: This differential equation describes the slope field shown in figure E. To calculate the slope of a given point (x,y), we can use the formula y'=y. For example, if x=3 and y=4, the slope of the line at that point is y'=4.

f. y'=x-y: This differential equation describes the slope field shown in figure F. To calculate the slope of a given point (x,y), we can use the formula y'=x-y. For example, if x=2 and y=1, the slope of the line at that point is y'=2-1=1.

The differential equations a) y' = cos(x), b) y' = sin(x), c) y' = 4-y, d) y' = x, e) y' = y, and f) y' = x-y all match the corresponding slope fields shown in figures A-F respectively.

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Answer:

  (c)  C(p) =.15 (p- 50) + 8.95

Step-by-step explanation:

You want an equation for the cost of prints that are $0.15 for each print over 50 plus an additional $8.95.

The number of prints over 50 will be (p -50). At $0.15 for each of these, their cost will be ...

  0.15(p -50)

When the $8.95 charge is added, the total comes to ...

  c(p) = 0.15(p -50) +8.95

__

Additional comment

The problem statement asks for the function to be written C(p). The answer choices use c(p) with the variable x in the equation where p should be. In effect, none of the answer choices is correct.

The income tax liability of Mr. X is 450,000 rupees.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

Mr X had income from salary of 200000.

Income from Capital Gain of, 150000 and income from other sources is 250000.

Contribution to PF is 40000, PPF 70000, and LIC is 40000.

Income Tax liability = total income - total deductions

= 600,000 - 150,000

= 450,000

Therefore, the tax liability is 450,000 rupees.

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Answer:

The perimeter of triangle FGL is unknown.

Maggie's rate of change for her car is 15; her initial value is 2; and the best function to model her situatioon is y = 2 + 15x (D).

Based on the given case, we know that:

This statement gives information about Maggie's rate of change, showing how many cars Maggie can buy per week.

This statement shows that currently, she already has 2 cars. 2 cars are her initial value.

This situation represents that, Maggie might buy 15 cars every week as an additional to her current 2 cars. This situation can be formulated as:

y = 15x + 2

where:

y = total cars

x = number of weeks

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The average rate of change over the interval 15 ≤ x ≤ 30 is equal to -6/5.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function f(x) over the interval [15, 30]:

a = 15; f(a) = 40

b = 30; f(b) = 22

For the average rate of change over the interval 15 ≤ x ≤ 30, we have the following:

Average rate of change = [f(b) - f(a)]/(b - a)

Average rate of change = [22 - 40]/(30 - 15)

Average rate of change = -18/15

Average rate of change = -6/5

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Answer:

The answer is 20 cm.

Step-by-step explanation:

From the scale, we know that 1 cm in the model represents 6 meters in the actual building.

So, h cm in the model represents 6h meters in the actual building.

The actual building is 120 meters tall, so 6h = 120 meters.

Dividing both sides by 6, we get:

h = 20 cm.

Therefore, the height of the model is 20 cm.

The values of x and y are 15 and 7 respectively.

Similar triangles are those triangles which has the same shape but different size.

The length of sides are proportional in similar triangles.

Two sails are similar triangles.

So the angles of two sails are equal and the corresponding sides are proportional.

We can write the relation as,

x / 30 = x- 2 / 26 = y + 9 / 5y - 3

Consider x / 30 = x- 2 / 26.

Cross multiplying,

26x = 30(x - 2)

26x = 30x - 60

-4x = -60

x = 15

Consider x / 30 = y + 9 / 5y - 3.

Substituting x = 15,

15 / 30 = y + 9 / 5y - 3

1 / 2 = y + 9 / 5y - 3

Cross multiplying,

5y - 3 = 2y + 18

3y = 21

y = 7

Unknown sides are,

x = 15 feet

x - 2 = 13 feet

y + 9 = 16 feet

5y - 3 = 32 feet

Hence the value of x is 15 and the value of y is 7.

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The approximate latitudinal distance of cities Rochester and Richmond is 394 miles

Let us assume the angle between the 2 cities as θ

θ = 43.2° - 37.6°

  =5.7°

hence for finding the latitudinal distance between the cities (given that the Earth is approximately spherical) we can use the formula

distance= [tex]\frac{\theta}{360} *2\pi r[/tex]

             = [tex]\frac{5.7}{360} *2 (3.14)(3960)[/tex]

             = 393.756 miles ≈394 miles

therefore the distance comes out to be 394 miles

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Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

What is null hypothesis ?

The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

To test if there is sufficient evidence to refute the hospital director's claim, we would perform a hypothesis test. The test statistic in this case would be the sample proportion of lab reports with errors (95 errors out of 250 total lab reports), and we would compare this to the null hypothesis value of 46%. The p-value for this test represents the probability of observing a sample proportion as extreme or more extreme than the observed proportion, given that the null hypothesis is true.

If the p-value is less than the significance level of 0.05, we would reject the null hypothesis, which means we have sufficient evidence to conclude that the proportion of lab reports with errors is not equal to 46%. On the other hand, if the p-value is greater than or equal to the significance level of 0.05, we would fail to reject the null hypothesis, which means we do not have sufficient evidence to conclude that the proportion of lab reports with errors is different from 46%.

Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

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Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

The null hypothesis is a characteristic arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

To test if there is sufficient evidence to refute the hospital director's claim, we would perform a hypothesis test. The test statistic in this case would be the sample proportion of lab reports with errors (95 errors out of 250 total lab reports), and we would compare this to the null hypothesis value of 46%. The p-value for this test represents the probability of observing a sample proportion as extreme or more extreme than the observed proportion, given that the null hypothesis is true.

If the p-value is less than the significance level of 0.05, we would reject the null hypothesis, which means we have sufficient evidence to conclude that the proportion of lab reports with errors is not equal to 46%. On the other hand, if the p-value is greater than or equal to the significance level of 0.05, we would fail to reject the null hypothesis, which means we do not have sufficient evidence to conclude that the proportion of lab reports with errors is different from 46%.

Null hypothesis: proportion of errors = 46%. Alternative hypothesis: proportion of errors ≠ 46%. Hypothesis test done using sample proportion and significance level of 0.05.

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To test the hypothesis that the kernel color of bicolor corn using  chi-square analysis to evaluate the fit between the segregation hypothesis and the class results as the ratio 0.01:0.05 and degree of freedom is 4.82.

Formula for Chi square is,

[tex]x^2 = \frac{(O - E)^2}{E}[/tex]

O = Observed Value

E = Expected Value

So x = 9882/2376 = 4.82.

And after getting a ratio of the yellow and white from the chi diagram we have class ratio of 0.01:0.05

When the sample sizes are large, a chi-squared test (also known as a chi-square or 2 test) is a statistical hypothesis test used in the study of contingency tables. To put it another way, the main purpose of this test is to determine if two categorical factors (two dimensions of the contingency table) have independent effects on the test statistic (values within the table).

The test, specifically Pearson's chi-squared test and its variations, is valid if the test statistic is chi-squared distributed under the null hypothesis. If there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table, it can be determined using Pearson's chi-squared test. A Fisher's exact test is used as an alternative for contingency tables with smaller sample sizes.

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The requried percentage change in crimes from years 1 to 5 is given as    60.86%.

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

Here,
From the table.

Crime in year 1 = 23
Crime in year 5 = 9

Percentage change = 23 - 9 / 23 ×100%
                              = 60.86%

Thus, the requried percentage change in crimes from years 1 to 5 is given as 60.86%.

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The circumference with radius of 10.4 ft is 65.3 ft. The result is obtained by using the formula for circumference.

Circumference is also called the perimeter of a circle. It can be expressed as

P = 2πr

Where

The circumference with the radius = 10.4 ft.

We have

Find the circumference! (to the nearest tenth)

The circumference will be

P = 2πr

P = 2(3.14)(10.4)

P = 65.3 ft

Hence, the perimeter of the circle to the nearest tenth is 65.3 feet.

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Answer:

11.4

Step-by-step explanation:

19.948-8.57=11.378

approximately 11.4

The correct number of significant figures is found as 1.1378 x 10⁻¹ .

To demonstrate the accuracy of measurements and calculations in the fields of math, chemistry, and other sciences, significant figures are essential.

The following five rules can be used to assess whether a number is significant.

The equation is given as:

=  19.948 - 8.57

On subtracting.

= 11.378

On converting in the significant figures:

= 1.1378 x 10⁻¹

Thus, the correct number of significant figures is found as 1.1378 x 10⁻¹ .

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Answer:

The Answer is 37

Step-by-step explanation:

Just do 1850/50 and then do 50*37 to confirm

The value of k in the equations is 2/3

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

y = 9kx - 1

kx + 4y = 12

This can be expressed as

y = 9kx - 1

y = -kx/4 + 3

The slopes of perpendicular lines are opposite reciprocal

This means that

9k * -k/4 = -1

So, we have

k^2 = 4/9

Evaluate

k = 2/3

Hence, the value of k is 2/3

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