Question 3 5 pts Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n=133, x=82; 90 percent 0.138

a) Mark earns $110 at the rock concert,  b) i) Mary's annual income is $66,000, c) Danny's regular salary is $400 and his overtime salary is $75. His total salary is $475.

a) Mark sells 200 programs, so he earns an additional $0.45 for each program. Therefore, his earnings from selling programs is 200 * $0.45 = $90. In addition, he earns a fixed amount of $20 for showing up. Therefore, his total earnings at the rock concert is $20 + $90 = $110.

b) i) Mary's annual income is her monthly salary multiplied by 12 since there are 12 months in a year. Therefore, her annual income is $5,500 * 12 = $66,000.

ii) Mary's gross earnings per pay period would depend on the pay frequency. If we assume a monthly pay frequency, her gross earnings per pay period would be equal to her monthly salary of $5,500.

iii) If Mary is paid semi-monthly, her earnings per pay period would be half of her monthly salary. Therefore, her earnings per pay period would be $5,500 / 2 = $2,750.

iv) If Mary is paid weekly, we need to divide her monthly salary by the number of weeks in a month. Assuming there are approximately 4.33 weeks in a month, her earnings per pay period would be $5,500 / 4.33 = $1,270.99 (rounded to the nearest cent).

c) To calculate Danny's regular salary and overtime, we need to consider his regular working hours and overtime hours.

Regular working hours: 8 hours on Monday + 8 hours on Tuesday + 8 hours on Wednesday + 8 hours on Thursday = 32 hours.

Overtime hours: 10 hours on Wednesday (2 hours overtime) + 10 hours on Friday (2 hours overtime) = 4 hours overtime.

Regular salary: Regular working hours * hourly rate = 32 hours * $12.50/hour = $400.

Overtime salary: Overtime hours * hourly rate * overtime multiplier = 4 hours * $12.50/hour * 1.5 = $75.

Therefore, Danny's regular salary is $400 and his overtime salary is $75. His total salary would be the sum of his regular salary and overtime salary, which is $400 + $75 = $475.

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The expression "3' - '2' + 'm' / 'n'" is invalid because it combines character literals and arithmetic operations. The expression "3' - '2' + 'm' / 'n'" is not valid in most programming languages.

It attempts to mix character literals ('3', '2', 'm', 'n') with arithmetic operations (-, +, /), which is not meaningful. In programming languages, characters are typically represented using character literals enclosed in single quotes.

While arithmetic operations are performed on numerical values. The expression should be revised to ensure that the operations are performed on numerical values rather than character literals.

For example, if 'n' and 'm' represent numerical values, the expression could be written as "3 - 2 + m / n" to perform arithmetic operations correctly.

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The equation \(x^{3} - 3\) has x values as 0, \(\sqrt{3}\) and -\(\sqrt{3}\).

We are given,

3 is subtracted from the cube of a number.

Let the number be x then we can write it as:

 \(x^{3}\) - 3

We are to solve for x.

We can write the equation as:

\(x^{3}\) - 3  = 0

x ( \(x^{2}\)- 3 ) = 0

x = 0 and ( \(x^{2}\) - 3 ) = 0

x = 0 and \(x^{2}\) = 3

x = 0 and x = ±\(\sqrt{3}\)

So we have,

x  = 0, \(\sqrt{3}\) and -\(\sqrt{3}\)

Thus we have x values as 0, \(\sqrt{3}\) and -\(\sqrt{3}\).

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The solution to the given expression is -15/4

Equations are expressions separated by an equal sign.

Given the expression 17 = -13 -8x

Add 13 to both sides

17 + 13 = -13 - 8x + 13

30  = -8x

Swap sides

-8x = 30

Divide both sides by -8

-8x/-8 = -30/8

x = -30/8

x = -15/4

Hence the solution to the given expression is -15/4

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Answer: \(\sqrt[3]{5x}\)

(a) The equation that models the position of the object at time t is given by: x(t) = A * cos(2πft), where x(t) represents the position of the object at time t, A is the amplitude, f is the frequency, and cos represents the cosine function. (b) To determine the position at t = 1.25 sec, we need additional information such as the amplitude of the oscillation or any other specific values. Without this information, it is not possible to provide a numerical answer. (c) The frequency of the oscillation can be calculated using the formula: f = 1/T, where T is the time period. Given that the time for one complete oscillation is 6 sec, the frequency can be determined as f = 1/6 Hz.

(a) To model the position of the object at time t, we can use the equation of simple harmonic motion:

x(t) = A * cos(ωt + φ)

where:

- x(t) represents the position of the object at time t.

- A is the amplitude, which is the maximum displacement from the equilibrium position.

- ω is the angular frequency, which determines the rate of oscillation.

- φ is the phase constant, which determines the initial position of the object.

Given that the object is pulled down a distance of 5 units from its equilibrium position, we know that the amplitude A = 5.

To find the angular frequency ω, we can use the formula: ω = 2π / T, where T is the time period for one complete oscillation. In this case, T = 6 seconds. Therefore, ω = 2π / 6 = π/3.

The equation that models the position of the object at time t is:

x(t) = 5 * cos((π/3)t + φ)

(b) To determine the position at t = 1.25 seconds, we substitute t = 1.25 into the equation:

x(1.25) = 5 * cos((π/3)(1.25) + φ)

(c) To find the frequency, we can use the formula: f = 1 / T, where T is the time period for one complete oscillation. In this case, T = 6 seconds. Therefore, the frequency f = 1 / 6.

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The given system of differential equations is:

x'(t) = -95x + 53y - 2xy

y'(t) = -185x - 203y - xy

To solve this system, we can use various methods such as substitution or matrix methods. Let's solve it using the matrix method.

We can rewrite the system of differential equations in matrix form as:

X' = AX

where X = [x y]', X' = [x'(t) y'(t)]', and A is the coefficient matrix:

A = [[-95 53], [-185 -203]]

To find the solutions, we need to find the eigenvalues and eigenvectors of matrix A. The eigenvalues are the roots of the characteristic equation det(A - λI) = 0, where I is the identity matrix. Solving this equation gives us the eigenvalues λ1 = -100 and λ2 = -198.

Next, we find the eigenvectors associated with each eigenvalue. For λ1 = -100, the corresponding eigenvector is [2 1]'. For λ2 = -198, the corresponding eigenvector is [-1 1]'.

Therefore, the general solution of the system of differential equations is:

X(t) = c1e^(-100t)[2 1]' + c2e^(-198t)[-1 1]'

where c1 and c2 are constants determined by initial conditions.

In summary, the solution to the system of differential equations is given by X(t) = c1e^(-100t)[2 1]' + c2e^(-198t)[-1 1]', where c1 and c2 are constants determined by the initial conditions.

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135 /43 = 3.14

60 * 3.14 = 188.4 minutes

Answer:

y ≤ 1/3x - 4

Step-by-step explanation:

it could not be options 3 or 4 because the y-intercept is -4, not +4

I picked a point in the shaded area to see which inequality, the first or the second, would make it true; the point I used was (3, -4)

1st option:  y ≥ 1/3x - 4        Is this true? -4 ≥ 1/3(3)  No, -4 is not GE 1

2nd option: y ≤ 1/3x - 4        Is this true? -4 ≤ 1/3(3)  Yes, -4 is LE 1  

Answer:

28

Step-by-step explanation:

3x² - 2x + 7

→ Substitute x = 3

3 × 3² - 2 × 3 + 7 ⇔ 3 × 9 - 6 + 7 ⇔ 27 - 6 + 7 ⇔ 21 + 7 ⇔ 28

Answer: Option (1)

Step-by-step explanation:

\(\angle DMA\) is another name for angle 3, but not \(\angle DME\).

Impulse, change in momentum, final speed, and momentum are all related concepts in the context of Newton's laws of motion. Let's go through each option and explain their relationships:

(a) Impulse delivered: Impulse is defined as the change in momentum of an object and is equal to the force applied to the object multiplied by the time interval over which the force acts.

Mathematically, impulse (J) can be expressed as J = F  Δt, where F represents the net force applied and Δt represents the time interval. In this case, you mentioned that the net force acting on the crates is shown in the diagram. The impulse delivered to each crate would depend on the magnitude and direction of the net force acting on it.

(b) Change in momentum: Change in momentum (Δp) refers to the difference between the final momentum and initial momentum of an object. Mathematically, it can be expressed as Δp = p_final - p_initial. If the crates start from rest, the initial momentum would be zero, and the change in momentum would be equal to the final momentum. The change in momentum of each crate would be determined by the impulse delivered to it.

(c) Final speed: The final speed of an object is the magnitude of its velocity at the end of a given time interval.

It can be calculated by dividing the final momentum of the object by its mass. If the mass of the crates is provided, the final speed can be determined using the final momentum obtained in part (b).

(d) Momentum in 3 s: Momentum (p) is the product of an object's mass and velocity. In this case, the momentum in 3 seconds would be the product of the mass of the crate and its final speed obtained in part (c).

To rank these quantities from greatest to least for each crate, you would need to consider the specific values of the net force, mass, and any other relevant information provided in the diagram or problem statement.

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The combined area of the four removed triangles is 48 sq.units. Answer: 48

We need to find out the combined area of the four removed triangles, in square units. Given: AB = 12 units.

Let's consider the given square, and let's draw an altitude BD and also draw perpendiculars to BD from the three vertices A, C and D.

Let AB = x cm. Area of square = x² sq.cm.

Now, we are cutting a triangle with base x and height x, which is a right-angled triangle. Hence, area of each removed triangle = (1/2) * x * x = (x²/2) sq.cm.

Now, BD = x/√2. Area of rectangle = AB * BD = 12 * 12/√2 = 72√2 sq.cm.

Now, area of 4 triangles = (x²/2) + (x²/2) + (x²/2) + (x²/2) = 2x² sq.cm.

We know that, Area of rectangle = Area of 4 triangles + Area of square => 72√2 = 2x² + x² => 72√2 = 3x² => x² = 24√2 cm² => x = √(24 * 2) cm = √(48) cm = 4√3 * √2 cm.

Area of 4 triangles = 2x² sq.cm = 2 * 24 cm² = 48 sq.cm.

Hence, the combined area of the four removed triangles is 48 sq.units. Answer: 48.

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These numbers represent the distribution of preferences among the surveyed respondents for different types of food.

The given survey results provide the count or frequency of respondents who identified each type of food as their favorite. Here's an explanation of the results:

Italian food: 10 respondents

This means that out of the total number of respondents surveyed, 10 individuals specified Italian food as their favorite.

Mexican food: 20 respondents

Similarly, 20 respondents, out of the total surveyed, mentioned Mexican food as their favorite.

Chinese food: 30 respondents

For Chinese food, 30 respondents favored it as their preferred cuisine among those surveyed.

Anything else: 40 respondents

The category "Anything else" indicates that 40 respondents had a favorite food other than Italian, Mexican, or Chinese cuisine.

Overall, these numbers represent the distribution of preferences among the surveyed respondents for different types of food.

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Answer:

$22,000

Step-by-step explanation:

Subtract the development cost from the amount it would make.

And boy, that's one expensive mousetrap.

The solution is: the solution for the system of linear equations 3x+2y=-6 and y=1/2x+4 is , x = -3.5 and, y = 2.25.

Here we have,

to determine the solution to the system:

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

3x + 2y = -6 ....1

and,  y=1/2x+4

=> 2y = x + 8

=> x - 2y = -8.....2

Add the equations

So, we have

4x = -14

Divide both sides by 4

x  = - 7/ 2

Substitute x  = - 7/ 2  in x - 2y = -8

we get,

-7/2 - 2y = -8

Evaluate

y = 2.25

Hence, the solution for the system of linear equations 3x+2y=-6 and y=1/2x+4 is , x = -3.5 and, y = 2.25

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Answer: 15.876kg

Step-by-step explanation:

This will increase the probability of rejecting a false null hypothesis and accepting a true alternative hypothesis.The political advisor should ensure proper sampling, increase the alpha level, and have a larger sample size to reduce the risk of making a Type II error. A type II error is when a null hypothesis is accepted when it is false.

Suppose a political advisor is interested in the proportion of the vote an opponent will receive. If he samples voters randomly and tests hypotheses regarding p, the population proportion, he should do the following to reduce his risk of making a Type II error:To reduce the risk of making a Type II error, a political advisor interested in the proportion of the vote an opponent will receive, if he samples voters randomly and tests hypotheses regarding p, the population proportion should ensure that he has a larger sample size for testing. A larger sample size can help in making his results statistically significant and that the results are a true representation of the population.Proper sampling can also help to reduce the risk of a Type II error. Random sampling of the voters ensures that there is no bias in the selection process, which can skew the results. A random sample of voters is a fair representation of the population, and results obtained from a random sample are more likely to be accurate. This reduces the likelihood of a Type II error.The advisor should also increase the alpha level to reduce the risk of a Type II error. By increasing the alpha level, he is lowering the rejection region, which will reduce the likelihood of a Type II error. This will increase the probability of rejecting a false null hypothesis and accepting a true alternative hypothesis.The political advisor should ensure proper sampling, increase the alpha level, and have a larger sample size to reduce the risk of making a Type II error. A type II error is when a null hypothesis is accepted when it is false.

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Answer:

70

Step-by-step explanation:

77÷7=11 I know Trust me

Answer:

b,e

Step-by-step explanation:

40*50=2000 sqft vegetables

40*30/2=600 sqft flowers

The parametric equations for the line through the point p = (-4, 4, 3) that is perpendicular to the plane 2x + y + 0z = 1 are:

The equation of the plane is given by 2x + y = 1Therefore, the normal vector of the plane is N = [2,1,0]A line that is perpendicular to the plane must be parallel to the normal vector, so its direction vector is d = [2,1,0].To find the parametric equations of the line, we need a point on the line. We are given the point p = (-4,4,3), so we can use that.

The parametric equations are:x = -4 + 2t, y = 4 + t, z = 3The point (x,y,z) will lie on the line if there exists some value of t that makes the equations true.At what point q does this line intersect the yz-plane?The yz-plane is given by the equation x = 0, so we substitute this into the parametric equations for x, y, and z to get:0 = -4 + 2tSolving for t, we get t = 2. Substituting this into the equations for y and z, we get:y = 4 + 2 = 6, z = 3So the point of intersection q is (0,6,3).

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Answer:

It's A

Step-by-step explanation:

B is out, because each step increases the value linearly by 1

C is out, because each step increases the value linearly by 9

D is out, because each step increases the value linearly by 6

A increases fivefold per step

I plotted the given ordered pairs as points on a plot and figured out the exact function for you, just so that you can look at it

we have that

$6.60 -----> represents 100%

Find out the difference

($15.70-$6.60)=$9.10

Applying proportion

Find out how much percentage represents the difference

100/6.60=x/9.10

solve for x

x=(100/6.60)*9.10

x=137.88%

Divide by 15

137.88%/15=9.19% each year

we have the exponential growth equation of the form

y=a(b)^x

where

a=6.60

b=1+0.0919=1.0919

x ----> number of years

y ----> hourly wage

so

For y=2(6.60)=$13.20

substitute in the equation

13.20=6.60(1.0919)^x

solve for x

(13.20/6.60)=(1.0919)^x

2=(1.0919)^x

apply log both sides

log(2)=x*log(1.0919)

x=7.9 years

x=8 years

Answer:

100 miles

Step-by-step explanation:

y=.55m+50 equation 1

y=.50m+55 equation 2

.55m+50=.50m+55 substitute value of y in equation 1 into equation 2

.05m=5

m=100

check answer by substituting 100 into both equations.

Y=.55(100)+50

y=55+50

y=105

y=.50m+55

y=.50(100)+55

y=50+55

y=105

By looking at the graph, we can see that:

For a function:

y = f(x)

We define the domain as the set of the possible inputs x, and the range as the set of the possible outputs y.

Here, to find the domain, we need to see the range of "horizontal values" that the graph takes. We can see that it goes from -7 to 6, then the domain is:

-7 ≤ x ≤ 6

The range goes from -4 to 5, so the range is: -4 ≤ y ≤ 5.

Then the correct option is the first one.

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Answer: The first 3 options

Step-by-step explanation:

You have to make sure that the given variable would be able to equal -5. The  \(\geq\) sign in the second and third answer show that the variable could be equivalent to -5.

Answer:

g > -7, f ≤ -5 and g ≥ -5

Step-by-step explanation:

the < and > symbols mean less than and greater than respectively, but not including. Therefore -5 cannot be a valid solution if the range is (for example) g > -5. However, ≤ and ≥ mean less/greater than or equal to, so -5 would be a valid solution for g ≥ -5 (for example).