A college conducted a survey of randomly selected freshmen about their choice of major. The table shows the results of the survey. English 50. Science 35. Engineering 40. Business 45. Education 60. Undecided 50. Other 20. Which inference about all freshmen at this collage is best supported by this information?

This statement is False as the probability of intersection of two events is always less than the probability of union.

This assertion is untrue. Contrary to popular belief, the likelihood of two occurrences coming together is always higher than or on pair with the likelihood of them colliding.

The chance of two events A and B occurring together can be calculated using the following formula to see why:

According to this equation, the probability of A and B joining together is equal to the total of their individual probabilities less the likelihood of their colliding.

When we rewrite this calculation and focus only on the likelihood of the intersection, we obtain:

Now it is clear that the probability of the intersection is determined by subtracting the probability of their union from the sum of the probabilities of A and B.

P(A) and P(B) are both less than or equal to P(A B), since probabilities can never be negative. P(A + B) is therefore less than or equal to twice P(A + B) when they are added together. Thus, it follows:

This indicates that, contrary to what the original statement implied, the probability of the intersection is not greater than or equal to the probability of the union.

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The radius of the wheel 0.35m

The number of revolutions is 100

The distance is 220 meter

Distance in one revolution= 220/100

= 2.2 meter

The radius of the wheel can be calculated as follows

radius= 2.2/2(3.142)

= 2.2/6.29

= 0.35

Hence the radius of the wheel is 0.35 meter

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The error bound will be 0.877 with the sample mean being 13.30 with a sample standard deviation of 1.55.

To find the error bound, we need to calculate the margin of error, which is the maximum likely difference between the true population mean and the sample mean. We can find this using the formula:

Margin of error = z* (standard deviation / sqrt(sample size))

Where z* is the critical value of the standard normal distribution that corresponds to the desired confidence level.

Since the confidence level is 95%, we can use the z* value of 1.96, which represents the number of standard deviations from the mean that includes 95% of the population.

Plugging in the values we have:

Margin of error = 1.96 * (1.55 / sqrt(12))

Simplifying this, we get:

Margin of error = 1.96 * 0.448 = 0.877

Therefore, the error bound is 0.877. This means we can be 95% confident that the true population means for the amount of soda served in the 16 oz. serving size falls within the range of 13.30 ± 0.877, or between 12.423 and 14.177.

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The number of solutions of the system composed by the two equations of this problem is given by the number of points of intersection of the graphs of two equations.

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

Hence, in this problem, you must graph the two functions, using a graphing calculator, and then identify the number of times that the two equations intersect.

The problem is incomplete, hence the procedure to obtain the number of solutions to the system of equations is presented.

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Answer:

B

Step-by-step explanation:

have a nice day :)

Answer:

x > 4; r–1(x) = 4 + StartRoot StartFraction 11 Over x EndFraction EndRoot

Step-by-step explanation:

We are given that

\(r(x)=\frac{11}{(x-4)^2}\)

We have to find the domain of restriction on r(x) and corresponding inverse function.

Let

\(y=r(x)=\frac{11}{(x-4)^2}\)

\((x-4)^2=\frac{11}{y}\)

\(x-4=\sqrt{\frac{11}{y}}\)

\(x=\sqrt{\frac{11}{y}}+4\)

\(r^{-1}(y)=\sqrt{\frac{11}{y}}+4\)

Now, replace x by y and y by x then, we get

\(r^{-1}(x)=\sqrt{\frac{11}{x}}+4\)

The function is not defined at x=4

But,

The inverse function defines for all positive real values.

Therefore, domain of r(x)=x>4 and inverse function

\(r^{-1}(x)=\sqrt{\frac{11}{x}}+4\)

Option:

x > 4; r–1(x) = 4 + StartRoot StartFraction 11 Over x EndFraction EndRoot

Answer:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Step-by-step explanation:

b

Answer:

10 pounds

Step-by-step explanation:

given ratio weight:added weight=10:1

100:x=10:1

100/x=10/1

solving for x

100=10x

x=10

sample size of 6945 parents.

To determine the sample size, we can use the formula:

n = ((z*σ)/E)^2

where:

z = the z-score associated with the confidence level (98% confidence level corresponds to a z-score of 2.33)

σ = the population standard deviation (given as 35.8 dollars)

E = the margin of error (10 dollars)

Substituting the given values, we get:

n = ((2.33*35.8)/10)^2

n = (83.414)^2

n = 6944.4

Rounding up to the nearest A, we get a sample size of 6945 parents.

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The solution to the two equations will be (0,2).

A finite set of equations for which we searched for common solutions is referred to in mathematics as a system of equations, also known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized.

Given that there are two equations:-

g(x) = 3x + 2

f(x) = | x - 1 | + 1

The solution of the equations can be calculated as:-

- ( x - 1 ) + 1 = 3x + 2

-x + 1 + 1 = 3x + 2

4x = 2 - 2

x = 0

The value of the dependent variable is:-

y = 3x + 2

y = 0 + 2

y = 2

Hence, the solution of the system of equations will be ( 0, 2 ).

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5x+7y=25

5x-2y=-65

subtract both of the equations

5x-5x=0

7y--2y= 7y+2y=9y

25--65=25+65=90

0+9y=90

9y=90

divide both sides by 9 to get y by itself

9y/9=90/9

cross out 9 and 9 which becomes 1*1*y=y

90/9=10

y=10

find x by using the substitution method

5x+7y=25

5x+7(10)=25

5x+70=25

move +70 to the other side

sign changes from +70 to -70

5x+70-70=25-70

5x=-45

divide both sides by 5 to get x by itself

5x/5=-45/5

cross out 5 and 5 then becomes 1*1*x=x

-45/5=-9

x=-9

answer:

(-9,10)

Answer:

Step-by-step explanation:

x+3*2=12-2*2

x+6=12-4

x+6=8

  -6 -6

x=2

Answer:

5.44

Step-by-step explanation:

Answer:

answer is 63

Step-by-step explanation:

Given:

Function 1 is given in the graph.

Function 2 is,

To find:

The function has a larger maximum value.

Explanation:

From the graph,

We know that the maximum value of the function is the highest point of the function.

For the function 1, the maximum value is 1 at x = 4.

For the function 2,

Differentiating with respect to x, we get

Equate it with zero, and we get

Substituting x = 1 in function 2.

So, the maximum value is -14 at x = 1.

Then, comparing functions 1 and 2 we get,

Function 1 has the larger maximum value at (4, 1).

Final answer:

Function 1 has the larger maximum value at (4, 1).

Hey there!

Assuming:

(3^2 * 4^2)^5

If so,

(3^2 * 4^2)^5

= (3 * 3 * 4 * 4)^5

= (9 * 16)^5

= (144)^5

= 144^5

= 144 * 144 * 144 * 144 * 144

= 20,736 * 20,736 * 144

= 429,981,696 * 144

= 61,917,364,224

Therefore, your answer should be:

61,917,364,224

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

565.49 cm2

Step-by-step explanation:

The area of a circle is given by:

Area = pi * r^2

And the whole area represents a central angle of 2pi.

Then, to find the area of this sector, we just need to use a rule of three:

area of pi * r^2 -> central angle of 2pi

area of x -> central angle of 8pi/5

x * 2pi = pi * r^2 * 8pi/5

2x = r^2 * 8pi/5

x = r^2 * 4pi/5 = 15^2 * 4pi/5 = 565.49 cm2

Answer:180pi cm^2

Step-by-step explanation:

Cuz I got it right

A. can be used to test joint hypotheses.

In statistical analysis, F-statistics are used to compare the fit of two nested models, typically to test joint hypotheses. Maximum likelihood estimators are a popular method for estimating the parameters of a statistical model by maximizing the likelihood function. They are widely used in various fields due to their desirable properties, such as being consistent and asymptotically efficient.

When F-statistics are computed using maximum likelihood estimators, they can still be employed to test joint hypotheses. This involves comparing the difference in the log-likelihoods between two nested models, one being a restricted model and the other being an unrestricted model. The test statistic, in this case, follows an F distribution under the null hypothesis, which states that the restrictions imposed on the model are valid.

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The chi-square goodness-of-fit test can provide important information about whether the observed data significantly deviates from the expected distribution, which categories or bins contribute to the deviation, and the overall goodness-of-fit of the data to the expected distribution.

The chi-square goodness-of-fit test is a statistical test used to determine if a sample of data comes from a population with a specific distribution. Specifically, the test compares the observed frequencies of data in different categories or bins with the expected frequencies of data in those categories based on a hypothesized distribution.

It can determine whether the observed data significantly deviates from the expected distribution. If the test results in a p-value less than the chosen level of significance, it indicates that the observed data significantly deviates from the expected distribution, and the null hypothesis (that the data follows the expected distribution) can be rejected.

It can identify which categories or bins contribute the most to any significant deviation. The test statistic and associated p-value can help to identify which categories or bins show significant differences between the observed and expected frequencies.

It can provide information on the overall goodness-of-fit of the data to the expected distribution. The test statistic provides a measure of the overall goodness-of-fit, with higher values indicating greater deviation from the expected distribution.

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Answer:110x^2+7x-8

Step-by-step explanation:

7x- 8+2x5x11

7x-8+110x^2

reoder the terms

110x^2+7x-8

Note that the solution to y in the above-given matrix is 29/4 or 7.25

The matrix equation can be written in the form:

| 2  7 |   | x |   | 8 |

| 2  6 | * | y | = | 6 |

We can solve for y by first isolating the matrix with y on one side of the equation, and then applying matrix inverse to both sides. Here are the steps:

Step 1: Transpose the matrix on the left side

| x |   | 2  2 |^-1   | 8 |

| y | = | 7  6 |    * | 6 |

Step 2: Find the inverse of the matrix on the left side. The inverse of a 2x2 matrix [a, b; c, d] is given by 1/(ad - bc) * [d, -b; -c, a]. Applying this formula, we get:

| x |   | -3/4  1/4 |   | 8 |

| y | = |  7/4 -1/4 | * | 6 |

Step 3: Multiply the two matrices on the right side. We get:

| x |   | -3/4  1/4 |   | 8 |   |  1 |

| y | = |  7/4 -1/4 | * | 6 | = |  1 |

| x |   | -3/4*8 + 1/4*6 |   |  1 |

| y | = |  7/4*8 - 1/4*6 | = | 29/4 |

Therefore, the solution is y = 29/4.

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Answer:

ertyghujikol

Step-by-step explanation:

3456t7ujn

The area of the triangle is 31.54 square units

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

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

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

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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To calculate the probability that a randomly chosen applicant will score between 500 and 600 on the test, we need to use the standard normal distribution.

We'll convert the given scores into z-scores and then find the corresponding probabilities using a standard normal distribution table or a statistical calculator. First, let's calculate the z-score for the lower boundary of 500: z1 = (500 - 560) / 90 = -0.667

Next, let's calculate the z-score for the upper boundary of 600:
z2 = (600 - 560) / 90 = 0.444. Now, we can find the probability associated with each z-score. Using a standard normal distribution table or a calculator, we find that the probability corresponding to z1 is approximately 0.2525, and the probability corresponding to z2 is approximately 0.6700.

To find the probability between these two boundaries, we subtract the lower probability from the upper probability:
P(500 < X < 600) = P(z1 < Z < z2) = P(Z < z2) - P(Z < z1) = 0.6700 - 0.2525 = 0.4175 Therefore, the probability that a randomly chosen applicant will score between 500 and 600 on the test is approximately 0.4175, or 41.75%.

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Since y_1(0) = 1, it satisfies the initial condition. However, y_2(0) = 0 does not satisfy the initial condition, as it should be y(0) = 1. Therefore, only y_1(t) is a solution of the initial value problem.

To verify that both y_1(t) = 1 - t and y_2(t) = -t^2/4 are solutions of the initial value problem, we first need to understand what the problem is. An initial value problem is a differential equation that includes an initial condition. In this case, we can assume that the initial condition is y(0) = 1.
Now, let's substitute both y_1(t) and y_2(t) into the differential equation and see if they satisfy the initial condition. The differential equation is not provided, but assuming it is y'(t) = -t/2, we have:
y_1'(t) = -1
y_2'(t) = -t/2
Substituting y_1(t) and y_2(t) into the differential equation gives:
y_1'(t) = -1

= -t/2 (when t = 2)
y_2'(t) = -t/2

= -t/2 (for all t)
Thus, both y_1(t) and y_2(t) satisfy the differential equation. Now, let's check if they satisfy the initial condition.
y_1(0) = 1 - 0

= 1
y_2(0) = -0^2/4

= 0
In conclusion, y_1(t) = 1 - t is the only solution that satisfies the differential equation and initial condition, while y_2(t) = -t^2/4 is not a solution since it does not satisfy the initial condition.

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Answer: 2

Step-by-step explanation:

Answer:

y = 7.2

Step-by-step explanation:

y ÷ 6 = 1.2

y ÷ 6 × 6 = 1.2 × 6

y = 7.2

Hence, the cone is 8/3 cm tall as we can get the height using the following formula for a cone's volume.

A three-dimensional object's volume is a measurement of how much space it takes up. It is a real-world physical number that can be expressed in cubic measurements like cubic metres (m3), cubic centimetres (cm3), or cubic feet (ft3). Physics, chemistry, architecture, and mathematics all use the idea of volume extensively. Volume is frequently used to refer to the amount of space that an object or substance takes up, for instance the amount of a container, the volume of either a liquid, or the quantity of a gas. Depending on an object's shape, a different formula is required to determine its volume.

given

The formula V = (1/3)r2h, where V is the volume, r is the radius of the base, and h is the height, can be used to determine the volume of a cone.

Hence, by multiplying the circumference by two, we can determine the radius of the base:

12π / 2π = 6

Thus, the base's radius is 6 cm.

Also, we are informed that the cone's volume is 96. As a result, we can get the height using the following formula for a cone's volume:

V = (1/3)r2h

96 = (1/3)(6/2)h

96 = 36 h

96 / 36 = 8/3

Hence, the cone is 8/3 cm tall as we can get the height using the following formula for a cone's volume.

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Answer:

The second one.

Step-by-step explanation:

You are proving the om angle not pn.