What is the probability that a randomly selected person from the survey prefers bacon.

a) The integral of \(fe^(5x-10) dx: (1/5)e^(5x-10) + C\)

b) The integral of cos(0.6x-13) dx: (1/0.6)sin(0.6x-13) + C

c) The integral of\(f(3x + 9)^3 dx: (1/9)(3x + 9)^4 + C\)

Integration shortcuts can be used to quickly evaluate definite or indefinite integrals without showing the step-by-step work. These shortcuts are based on recognizing patterns and applying the corresponding rules of integration.

a) The integral of \(fe^(5x-10)\) dx can be evaluated by applying the power rule of integration. The integral is\((1/5)e^(5x-10)\) + C, where C represents the constant of integration.

b) The integral of cos(0.6x-13) dx can be evaluated by using the basic integral formula for cosine. The integral is (1/0.6)sin(0.6x-13) + C.

c) The integral of \(f(3x + 9)^3\) dx can be evaluated by using the power rule of integration and applying the appropriate constant factor. The integral is\((1/9)(3x + 9)^4\) + C.

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The discrete probability distribution is discussed above.

Given is discrete probability distribution.

        \(${\displaystyle P(X\in E)=\sum _{\omega \in A}p(\omega )\delta _{\omega }(E)} =\)        

       \(${\displaystyle P(X\in E)=\int _{E}f(x)\,dx=\sum _{\omega \in A}p(\omega )\int _{E}\delta (x-\omega )=\sum _{\omega \in A\cap E}p(\omega )}\)

Therefore, the discrete probability distribution is discussed above.

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The answer is c. Statistic because the value is a numerical measurement describing a characteristic of a sample.

A statistic is a value that summarizes a characteristic of a sample. In this case, the percentage of employees in the sample who own a television (45%) is a statistic because it summarizes a characteristic of the sample of employees that was selected. A parameter, on the other hand, is a value that summarizes a characteristic of a population. For example, if we were to consider the percentage of all employees in the company who own a television, then the mean or median percentage of television ownership would be a parameter because it would describe a characteristic of the entire population of employees. In summary, statistics are values that describe a characteristic of a sample, while parameters are values that describe a characteristic of a population.

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Answer:

49.46

Step-by-step explanation:

Recall SOH CAH TOA

Here we have the adjacent side and the hypotonouse which means we'll use CAH

which means that

(let x=angle)

cosx=13/20

x=cos⁻¹*13/20

x=49.46

The Power e is to which a number should be raised to get the specified number is called the logarithm of that specific number. For example, the logarithm to the base of 10 of 1000 is 3 because 10 raised to the power 3 is 1000.

The logarithmic function is the reverse of the Mathematical function of the exponential function. The logarithmic function is log ax = y is equal to x = ay.

There are mainly two types of logarithms normally used in Mathematics. They are one is common logarithms and second natural logarithms.

The log number ‘e’ is an irrational Mathematical constant and is mostly used as the base of natural logarithms. The number ‘e’ is the only unique number in mathematics whose value of natural logarithm is equal to unity.

The value of log ‘e’ was calculated in 1683 by Jacob Bernoulli.

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Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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The three angles in the triangle ABC are approximately 0.45 radians (A and C) and 1.37 radians (B).

To determine the three angles in the triangle ABC, we can use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of the angles opposite those sides. The law of cosines states that for a triangle with sides a, b, and c, and angles A, B, and C opposite those sides:

```

a^2 = b^2 + c^2 - 2bc cos(A)

b^2 = a^2 + c^2 - 2ac cos(B)

c^2 = a^2 + b^2 - 2ab cos(C)

```

We can use these equations to solve for the three angles in the triangle ABC.

First, we need to find the lengths of the sides of the triangle. We can use the distance formula to find the lengths of the sides AB, BC, and AC:

```

AB = sqrt((7-2)^2 + (7-2)^2) = sqrt(50)

BC = sqrt((4-2)^2 + (8-2)^2) = sqrt(52)

AC = sqrt((7-4)^2 + (7-8)^2) = sqrt(10)

```

Now we can use the law of cosines to solve for the angles:

```

cos(A) = (b^2 + c^2 - a^2) / 2bc

cos(B) = (a^2 + c^2 - b^2) / 2ac

cos(C) = (a^2 + b^2 - c^2) / 2ab

```

```

cos(A) = (50 + 10 - 52) / (2 * sqrt(50) * sqrt(10)) = 0.9

cos(B) = (50 + 52 - 10) / (2 * sqrt(50) * sqrt(52)) = 0.2

cos(C) = (10 + 52 - 50) / (2 * sqrt(10) * sqrt(52)) = 0.9

```

Now we can use the inverse cosine function to find the values of A, B, and C:

```

A = acos(0.9) ≈ 0.45 radians

B = acos(0.2) ≈ 1.37 radians

C = acos(0.9) ≈ 0.45 radians

```

Therefore, the three angles in the triangle ABC are approximately 0.45 radians (A and C) and 1.37 radians (B).

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Answer:

x = 1

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4x−

5

5

=3

4x+−1=3

4x−1=3

Step 2: Add 1 to both sides.

4x−1+1=3+1

4x=4

Step 3: Divide both sides by 4.

4x

4

=

4

4

x=1

The probability that they are all of different colors when a bag contains 9 marbles is 9/28.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

Total number of marbles=9

Number of red marbles=3

Number of blue marbles=3

Number of yellow marbles=3

Three marbles are  selected from the bag at random probability that they are all different color:

\(\frac{^3C_1*^3C_1*^3C_1}{^9C_3} = \frac{9}{28}\).

Therefore, the probability that they are all of different colors is 9/28.

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Complete question:

A bag contains 9 marbles, 3 of which are red, 3 of which are blue, and 3 of which are yellow. If three marbles are selected from the bag at random, what is probability that they are all of different colors?

The conclusion is that in a bowl containing 9 marbles, at least 3 of them are red, at least 3 are blue, or at least 5 are said to be green.

The use of Pigeonhole Principle to prove the statement will be done in this question.

The Pigeonhole Principle is one that states that if there are more pigeons than pigeonholes, then at least one pigeonhole needs to have  more than one pigeon.

So lets assume for contradiction that there are not at least 3 red marbles, 3 blue marbles, or 5 green marbles.

Case 1: There are fewer than 3 red marbles.

If less than 3 red marbles, then max 2 red marbles. 9 - 2 = 7 marbles left. 7 marbles: blue/green. With more than 3 marbles and assumed 2 red marbles, it violate the Pigeonhole Principle.

Case 2: There are fewer than 3 blue marbles.

If 3 blue marbles, then max 2 blue marbles. 9-2=7 marbles left, red or green. "More marbles than pigeonholes - against the Pigeonhole Principle."

Case 3: There are fewer than 5 green marbles.

5 green marbles, 4 green marbles. We have more marbles than pigeonholes,  so against the Pigeonhole Principle.

So, there is  contradiction in all 3 cases, our initial assumption that there are not at least 3 red marbles, 3 blue marbles, or 5 green marbles have to be  false.

So, we can say that in a bowl containing 9 marbles, at least 3 of them are red, at least 3 are blue, or at least 5 are green.

Another is:

Total number of marbles=9

Number of red marbles=3

Number of blue marbles=3

Number of yellow marbles=3

So, the probability that they are all of different colors is 9/28.

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The cost of 1 drink is $1.20.

How to solve word problems?

Let cost of 1 hamburger be x

cost of 1 drink be y

The equations will be

x + 2y = 6  →  (i)

2x + 2y = 9.60  → (ii)

To solve the equations multiple the equation (i) by 2

2x + 4y = 12

2x + 2y = 9.60

Subtracting the equation (i) and (ii)

2y= 2.4

y = 2.4/1.2

y = 1.2

Hence, the cost of drink is $1.2.

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Usando proporciones, hay que Luis enviará 160 dólares a su familia.

Una proporción es una fracción de la cantidad total, y puede ser encontrada por intermedio de una regla de tres.

En este problema, la regla de tres es dada por:

15 dólares - 8 envíados

300 dólares - n envíados

Aplicando multiplicación cruzada:

15n = 300 x 8

n = (300 x 8)/15

n = 160

Luis enviará 160 dólares a su familia.

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\(vertex \: from \: y \: = - 4(x - 2) {}^{2} + 3\)

The half-life of the substance is approximately 17.78 days.

The exponential decay model for the mass of the substance can be written as:

\(m(t) = m0 \times e^{(-rt)},\)

where m0 is the initial mass, r is the decay rate parameter (as a decimal), and t is time in days.

If we want to find the half-life of the substance, we need to find the value of t when the mass has decreased to half of its original value (m0/2). In other words, we need to solve the equation:

m(t) = m0/2

\(m0 \times e^{(-rt)} = m0/2\)

\(e^{(-rt) }= 1/2\)

Taking the natural logarithm of both sides, we get:

-ln(2) = -rt

t = (-ln(2)) / r

Substituting the value of r (0.039), we get:

t = (-ln(2)) / 0.039

t ≈ 17.78 days

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Answer:

The length of one of the legs is a 18

Step-by-step explanation:

Here, we want to find the length of one of the legs

Since it’s an isosceles triangle, the length of two sides are equal.

what this mean is that;

x + 10 = 4x - 14

4x -x = 14 + 10

3x = 24

x = 24/3

x = 8

The length of the leg will be x + 10 = 8 + 10 = 18

Answer:

A

Step-by-step explanation:

So the minute hand if it goes around the entire clock (circle)  we have

360 degrees (think degrees wise) and 60 minutes (think minute wise.)

If we divide 360 degrees into 60 parts for each minute we have 360/60 = 6

degrees for each minute that passed.

From 12:12 to 12:50 we have 50-12= 38 minutes

38 minutes * 6 degrees for each minute = 228 degrees

Answer:

11/8

Step-by-step explanation:

Simplify 11/4 = 2 3/4

half of 2 = 1

half of 3/4 = 3/8

1 3/8 changed to an inproper fraction = 11/8

Answer:

True

Step-by-step explanation:

All of them match up

Answer:

f(x)=2x-11

f(6)=2(6)-11

    =12-11

    =1

and the answer is c.

Explanation:

f(6) means you have to replace all x's in the function with 6.

For example, if the problem was asking you what is the value of f(10) you would have to replace all the x's in the respective function with 10 and so on.

Answer:

28.3 (explaination below)! :)

Step-by-step explanation:

Use the formula for cicrumfrence: C=2πr

Radius can be found by splitting the given number in half, (unless you were given the radius already, then you'd just multiply by 2).

Plug in our numbers. C= 2π4.5

Then, multiply.

You'd get 28.27433388230814.

Rounding to the first decimal place, you'd have a final answer of  28.3.

Hope this helps!

For the first scenario where there are no further restrictions, we have 26 capital letters and 10 digits to choose from for each of the 7 characters. Therefore, the total number of possible license plates is:

(26+10) x (25+9) x (24+8) x (23+7) x (22+6) x (21+5) x (20+4) = 18,994,040,000

For the second scenario where the first 3 characters are letters and the last 4 are numbers, we have 26 choices for the first character, 25 choices for the second character, and 24 choices for the third character. For the last 4 characters, we have 10 choices for the first and third characters (since they must be numbers) and 26 choices for the second and fourth characters (since they must be letters). Therefore, the total number of possible license plates is:

26 x 25 x 24 x 10 x 26 x 10 x 26 = 45,697,920,000

For the third scenario where letters and numbers alternate, we have 26 choices for the first letter and 10 choices for the first number. For the remaining 5 characters, we have 25 choices for the letters and 9 choices for the numbers (since we cannot repeat the previous character). Therefore, the total number of possible license plates is:

26 x 10 x 25 x 9 x 25 x 9 x 25 = 45,562,500,000

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(a) The cost of 1 kg of turnips is £71.95, and

(b) The cost of 1 kg of mushrooms is £89.50.

To solve this problem, let's assign variables to the unknowns.

Let the cost of 1 kg of mushrooms be 'm' and the cost of 1 kg of turnips be 't'.

According to the given information:

Equation 1: 2m + 2.5t = 8.55

Equation 2: 3m + 4t = 13.10

We can solve these equations simultaneously to find the values of 'm' and 't'.

To eliminate the decimals, let's multiply both sides of Equation 1 by 10 and Equation 2 by 20:

20m + 25t = 85.50

60m + 80t = 262.00

Now, let's multiply Equation 1 by 12 and subtract Equation 2 multiplied by 5:

240m + 300t - (60m + 80t) = 1026.00 - 1310.00

180m + 220t = -284.00

We have a new equation:

180m + 220t = -284.00 ---(3)

Next, let's multiply Equation 1 by 18 and subtract Equation 2 multiplied by 4:

36m + 45t - (60m + 80t) = 154.35 - 524.00

-24m - 35t = -369.65

We have another new equation:

-24m - 35t = -369.65 ---(4)

Now, we have a system of linear equations with two variables. Let's solve this system by eliminating one variable.

Multiply Equation 3 by 35 and Equation 4 by 220:

6300m + 7700t = -9940.00 ---(5)

-5280m - 7700t = -81323.00 ---(6)

Adding Equations 5 and 6, we eliminate 't':

1020m = -91263.00

m = -91263.00/1020

m = -89.50

Substituting the value of 'm' back into Equation 3:

180(-89.50) + 220t = -284.00

-16110 + 220t = -284.00

220t = -284.00 + 16110

220t = 15826.00

t = 15826.00/220

t = 71.95.

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The probability is 1/24.

There are 4 meals and 4 people, so there are 4! = 24 ways to serve the meals to the people.

However, only one of these ways is correct, so the probability that the waiter will serve the correct meal to the correct person is:

P(correct) = 1/24

This is because there is only one way to serve the meals that matches the correct combination of alphabets used in Sonia.

Therefore, the probability that the waiter will serve the correct meal to the correct person is 1/24.

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Answer:

qualitative and ordinal.

Step-by-step explanation:

They are both two types of qualitative data under Categorical data.

Nominal and ordinal are the levels of measurement for which data can be qualitative. Therefore, the correct option is option A, D.

A categorization that describes the type of information contained inside the importance attributed to variables is called level of measurement and scale of measure. The most well-known classification was created by psychiatrist Stanley Smith Stevens and included four levels or measurement scales: nominal, ordinal, interval, or ratio.

This system of defining several measurement levels originated within psychology and has drawn heavy criticism from academics in other fields. Additional classifications include those made by Chrisman, Mosteller, and Tukey. Nominal and ordinal are the levels of measurement for which data can be qualitative.

Therefore, the correct option is option A, D.

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Hiero earns $17.50 per hour and worked 41 hours this week. Under the Fair Labor Standards Act (FLSA), non-exempt employees are entitled to receive overtime pay at a rate of 1.5 times their regular pay for hours worked beyond 40 hours in a workweek.

To calculate Hiero's regular pay for the week, we multiply his hourly rate by the number of regular hours worked, which is 40 hours in this case. Therefore, Hiero's regular pay for the week is:

Regular pay = Hourly rate x Regular hours worked

Regular pay = $17.50 x 40

Regular pay = $700

Now, to determine whether Hiero is eligible for overtime pay, we subtract the number of regular hours worked from the total number of hours worked. In this case, the total number of hours worked is 41. Therefore, Hiero worked 1 hour of overtime, for which he is entitled to receive overtime pay.

To calculate Hiero's overtime pay, we multiply his hourly rate by 1.5 and then by the number of overtime hours worked, which is 1 hour in this case. Therefore, Hiero's overtime pay for the week is:

Overtime pay = Hourly rate x 1.5 x Overtime hours worked

Overtime pay = $17.50 x 1.5 x 1

Overtime pay = $26.25

Therefore, Hiero's total pay for the week, including regular pay and overtime pay, is:

Total pay = Regular pay + Overtime pay

Total pay = $700 + $26.25

Total pay = $726.25

Hiero's regular pay for the week is $700.

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If we test the null hypothesis at the 5% level of significance, then the decision is (c)reject null hypothesis and conclude the means are different .

In the question ,

it is given that ,

the results of a mathematics placement exam for two different campuses of college ,

we have to test the hypothesis that the mean score on campus 1 is higher than on campus 2 .

sample size (n₁) is = 330

the sample size (n₂) is = 310

the sample mean (μ₁) = 33

the sample mean (μ₂) = 31

the standard deviation , σ₁ = 8

the standard deviation , σ₂ = 7

the test statistic test z can be calculated using the formula ,

z = (μ₁ - μ₂)/√(σ₁²/n₁ + σ₂²/n₂)

Substituting the values of the sample size , sample mean and standard deviation ,

we get ,

z = (33 - 31)/√(8²/330 + 7²/310)

Simplifying further ,

we get ,

Z = 3.37

the test is for the null hypothesis at the 5% level of significance .

that means ,

Z₀.₉₅ = 1.645 ;

So , the p value = P(Z > 3.37)

= 1 - P(Z < 3.37)

= 1 - 0.9996

= 0.0004

since the p-value is (0.0004) < the level of significance (0.05) .

we can reject the null hypothesis .

There is significant evidence to conclude that the mean score on campus 1 is higher than campus 2 .

Therefore , the correct option is (c) .

The given question is incomplete the complete question is

The results of a mathematics placement exam at two different campuses of mercy college follow: ( the table is given below)

The college wants to test the hypothesis that the mean score on campus 1 is higher than on campus 2. if we test the null hypothesis at the 5% level of significance, what is the decision ?

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Answer:

875 ft^2

Step-by-step explanation:

If   5 goes to 25  then the scale factor is 5

  35 ft^2  x 5  x 5 = 875 ft^2

Answer:

875 ft²

Step-by-step explanation:

Finding area of similar rectangles:

Scale factor = EF : AB

                    = 25 : 5

                    = 5 : 1

\(\sf \dfrac{Area \ of \ bigger \ rectangle}{Area \ of \ smaller \ rectangle}= (Scale \ factor)^2\)

\(\dfrac{Area \ of \ bigger \ rectangle}{35} =\left(\dfrac{5}{1}\right)^2\)

\(\text{Area of bigger rectangle = $\dfrac{25}{1}*35$}\)

Area or rectangle EFGH = 875 ft²

The correct statement is option C - The probability that a newly built house doesn't comply with municipal regulations is 0.80.Binomial experiments are the kind of probability experiments that have the following properties:Fixed number of trialsTwo possible outcomes for each trial: success and failure.

Successive trials must be independent.The probability of a successful trial remains constant throughout the experiment.With regard to the given question:To begin with, it is known from the past experience of the inspector that 8 out of every 10 newly built houses comply with municipal regulations. This suggests that the probability of a new built house complying with municipal regulations is 0.8, and the probability of it not complying with the regulations is 0.2 (i.e., 1 - 0.8).Since each inspection constitutes a trial with independent results from each other, the given experiment is a binomial with 13 identical trials. As there are two possible outcomes, i.e., compliance and non-compliance, it is a binomial experiment with "success" referring to the houses that comply with municipal regulations and "failure" referring to those that don't.As we know that the probability that a newly built house complies with municipal regulations is 0.8, the probability that it doesn't comply is 0.2. So, option C is incorrect.The expected value of newly built houses that will comply with municipal regulations is 13 * 0.8 = 10.40. Therefore, option D is correct.Answer: The probability that a newly built house doesn't comply with municipal regulations is 0.80.

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Answer:

they require the use of fractions.

Step-by-step explanation:

sum means to add both numbers

difference means to subtract the small number from the big number

quotient means to divide

product means to multiply

24. 13-9= 4

not sure what you meant by q23 and q25.

19. the sum of twelve and sixteen divided by the sum of three and four = 4

20. the difference of twenty-two and six divided by the sum of five and three = 2

21. the sum of thirty-six and fourteen divided by the product of two and five = 4

22. the quotient of thirty-two and four divided by the sum of one and three = 2

23. the sum of six and fifteen divided by 24 = 21/24

24. the difference of thirteen and nine = 4

25. the difference of thirty-one and seventeen divided by the product of ten = 7/5 = 1.4

Answer:

d. 132

Step-by-step explanation: