A company produces a computer part and claims that 98% of the parts produced work properly. A purchaser of these parts is skeptical and decides to select a random sample of 250 parts and test cach one to see what proportion of the parts work properly. Based on the sample, is the sampling distribution of p
^
​
approximately normal? Why? a. Yes, because 250 is a large sample so the sampling distribution of β is approximately normal. b. Yes, because the value of np is 245 , which is greater than 10, so the sampling distribution of p
^
​
is approximately normal. c. No, because the value of n(1−p) is 5 , which is not greater than 10 , so the sampliog distribution of p is not approximately normal. d. No, because the value of p is assumed to be 98%, the distribution of the parts produced will be skewed to the left, so the sampling distribution of p
^
​
is not approximately notimal.

If Idil drove 12 miles in 1/5an hour on average, then she drove at an average speed of 60 miles per hour.

To calculate the average speed of Idil's car in miles per hour, we need to divide the distance she drove (12 miles) by the time it took her to drive that distance (1/5 hour):

Average speed = distance ÷ time

Average speed = 12 miles ÷ (1/5) hour

To divide by a fraction, we can multiply by its reciprocal, so:

Average speed = 12 miles × 5/1 hour

Average speed = 60 miles per hour

Therefore, Idil drove at an average speed of 60 miles per hour.

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Therefore, the solutions to the initial value problems by using the Laplace transform are:

\((a) y(t) = e^(-3t) cos(3t) + (1/2)sin(2t)\)

\((b) y(t) = 10sin(5t) - 20cos(5t)\)

To solve the initial value problem using Laplace transform, we'll apply the Laplace transform to both sides of the given differential equation and use the initial conditions to find the solution.

(a) Applying the Laplace transform to the differential equation and using the initial conditions, we have:

\(s²Y(s) - sy(0) - y'(0) + 9Y(s) = 1/(s² + 4)\)

Applying the initial conditions y(0) = 1 and y'(0) = 3, we can simplify the equation:

\(s²Y(s) - s(1) - 3 + 9Y(s) = 1/(s² + 4)(s² + 9)Y(s) - s - 3 = 1/(s² + 4)Y(s) = (s + 3 + 1/(s² + 4))/(s² + 9)\)

Using partial fraction decomposition, we can write:

\(Y(s) = (s + 3)/(s² + 9) + 1/(s² + 4)\)

Taking the inverse Laplace transform, we get:

\(y(t) = e^(-3t) cos(3t) + (1/2)sin(2t)\)

(b) Following the same steps as in part (a), we can find the Laplace transform of the differential equation:

\(s²Y(s) - sy(0) - y'(0) + 25Y(s) = 10(1/(s² + 25) - 2s/(s² + 25))\)

Simplifying using the initial conditions y(0) = 0 and y'(0) = 0:

\(s²Y(s) + 25Y(s) = 10(1/(s² + 25) - 2s/(s² + 25))(s² + 25)Y(s) = 10(1 - 2s/(s² + 25))Y(s) = 10(1 - 2s/(s² + 25))/(s² + 25)\)

Using partial fraction decomposition, we can write:

\(Y(s) = 10/(s² + 25) - 20s/(s² + 25)\)

Taking the inverse Laplace transform, we get:

\(y(t) = 10sin(5t) - 20cos(5t)\)

Therefore, the solutions to the initial value problems are:

\((a) y(t) = e^(-3t) cos(3t) + (1/2)sin(2t)\)

\((b) y(t) = 10sin(5t) - 20cos(5t)\)

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Answer:

Step-by-step explanation:

Add 4% food tax:

Total amount of purchase is:

Subtract $30 paid in cash:

Answer:

$5.25

Step-by-step explanation:

Cost of gasoline

⇒ 9.25 × $3.15 = $29.1375

Cost of gum

$1.10 plus 4% food tax:

⇒ $1.10 × 1.04 = $1.144

Total cost of purchases

Gasoline + gum + Windshield wiper fluid

⇒ $29.1375 + $1.144 + $4.97 = $35.2515 = $35.25 (nearest cent)

If $30.00 was paid by cash and the rest was paid for by debit card:

Debit card charge = $35.25 - $30.00 = $5.25

Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

Answer:

it wont let me write the graph

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Well 15/4 is 3.75 so to get the whole number you need to round up

.75 rounds up to .8 now round 3.8 well 3.8 rounded up is 4 there's your answer! :)

Answer:

B. Selling treasury securities

Step-by-step explanation:

I'm taking the quiz

The Federal Reserve can reduce the amount of money available in the economy is buying treasury securities.

Therefore, the correct answer exists as option B. Selling treasury securities.

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Answer:

Y would = 34

Step-by-step explanation:

that's what i got on edge and it was right

A sample that does not represent the entire group of interest is called a biased sample.

A biased sample is a sample that doesn't reflect the real-world population it is supposed to represent. It happens when the sample is chosen in such a way that some members of the population are less likely to be included than others.

Therefore, a biased sample may not be an accurate representation of the entire population.

For example, if a researcher wants to know how many people in a given area have access to the internet and chooses a sample of people from a high-income neighborhood, the results may be biased because people from low-income areas may have lower rates of internet access.

A biased sample can lead to inaccurate conclusions, and therefore, it's important to ensure that the sample is representative of the population. A random sample, on the other hand, ensures that all members of the population have an equal chance of being included in the sample.

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The estimated monthly payment for Brian's home loan would $1413.52.

To calculate the best estimate of the monthly payment for Brian's home loan, we can use the formula for calculating a fixed-rate mortgage payment.

The formula for the monthly payment of a fixed-rate mortgage is:

M = P * (r * (1+r)^n) / ((1+r)^n - 1),

where M is the monthly payment, P is the principal amount (loan amount minus down payment), r is the monthly interest rate, and n is the number of monthly payments.

In this case, Brian's principal amount is $220,000 - $22,000 = $198,000 (loan amount minus down payment). The monthly interest rate is 3.5% / 12 = 0.0029 (converted from annual interest rate to monthly rate), and the number of monthly payments is 180.

Plugging in these values into the formula, we get:

M = $198,000 * (0.0029 * (1+0.0029)^180) / ((1+0.0029)^180 - 1).

M = $198,000 * (0.0029 * (1+0.0029)^180) / ((1+0.0029)^180 - 1)

M = $1413.52

Evaluating this expression gives us the best estimate of the monthly payment. However, the calculation involves complex mathematical operations, and it is recommended to use a financial calculator or spreadsheet software to obtain an accurate estimate.

Note: It's important to consult with a financial advisor or a mortgage professional to get precise and personalized information about mortgage terms, interest rates, and monthly payments based on individual circumstances and loan options available.

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The given graph is of the equation y = x - 2

Select x-values and enter them into the equation to graph a function. You will obtain a y-value once those values have been entered into the equation. The coordinates of a single point are made up of the x and y values.

Step 1 is to determine the variables.

Step 2: Establish the range of the variable

Determine the graph's scale in step three.

Step 4 is to give each axis a number, a label, and a title.

5. Select the data points and plot them on the graph.

6. Create the graph.

After understanding the "how" of drawing a graph you will surely understand how to decide which equation's graph it is.

The given graph is of the equation

y = x - 2

because as in the graph

the slope cuts the points x = 4 and y = 2

and when we substitute this value in the above mentioned equation we get

2 = 4 - 2

which satisfies the condition .

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Answer:

400

Step-by-step explanation:

480-80=400

Answer

x=6

Step-by-step explanation:

80*x=480

80*6=480

Answer:

Compass, and straightedge/ruler.

Step-by-step explanation:

The two basic tools for doing geometric constructions are:

Compass: A compass is a drawing tool that consists of two arms, one with a sharp point and the other with a pencil or pen. It is used to draw circles, arcs, and to mark off distances.

Straightedge or Ruler: A straightedge is a tool with a straight, unmarked edge. It is used to draw straight lines, measure lengths, and create parallel or perpendicular lines.

These two tools, the compass and straightedge (or ruler), are fundamental for performing geometric constructions, where precise shapes and figures are created using only these tools and basic geometric principles.

Happy Juneteenth!

Answer:

A

Step-by-step explanation:

(1.7x10²³) and (3.4x10²³) cancel into 0.5.

0.5(8x10^-14) = 4x10^-14

Answer:

13.6x/3.4 x 10^14 This is a fraction by the way hope this helps

Step-by-step explanation:

13.6

x

3.4

⋅

10

14

A negative correlation coefficient indicates an inverse or indirect relationship between two variables. As one variable increases, the other tends to decrease or become smaller.

A correlation coefficient measures the strength and direction of the relationship between two variables. It can range from -1 to +1. A negative correlation coefficient indicates an inverse relationship between the variables.

In an inverse relationship, as one variable increases, the other variable tends to decrease or become smaller. Conversely, as one variable decreases, the other variable tends to increase or become larger. This means that the variables move in opposite directions.

For example, if we observe a negative correlation between the amount of studying done for an exam and the number of mistakes made, it means that as studying increases, the number of mistakes decreases, and vice versa.

On the other hand, a positive correlation coefficient indicates a direct relationship, where both variables tend to move in the same direction. In a positive correlation, as one variable increases, the other variable also increases, or as one variable decreases, the other variable decreases.

In conclusion, a negative correlation coefficient signifies an inverse relationship between two variables, where an increase in one variable is associated with a decrease in the other variable, and vice versa.

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Every coordinate point of the original triangle has its scale factor doubled by one-half if the scale factor is one. multiply by half after dilation with a scale factor of two.

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Every coordinate point of the original triangle has its scale factor doubled by one-half if the scale factor is one. multiply by half after dilation with a scale factor of two.

We locate the dilation's center point and measure the distances between it and other points on the preimage and the image in order to get the scale factor for the dilation. As correctly stated by Math Bits Notebook, the scale factor is determined by the ratio of these distances.

Keep in mind that each coordinate must be multiplied by the scale factor in order to enlarge an object in the coordinate plane. The mapping will be (x, y) (1.5 x, 1.5 y) with this dilation. The original is represented by the blue quadrilateral in the graph above, while the dilatation is shown by the red picture. Connect the image's vertices to the center of dilation by drawing straight lines.

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Answer:

2:3

Step-by-step explanation:

20-8=12( no of boys)

8 (no of girls )

girls: boys

8:12

2:3 is the ratio

Answer:

\(x + 2 = - 3x\)

\( - 4x = 2\)

\(x = - \frac{1}{2} \)

\( - 3( - \frac{1}{2} ) = \frac{3}{2} = 1 \frac{1}{2} \)

So the lines intersect at (-1/2, 1 1/2), or

(-.5, 1.5).

Answer: When you plug in an x-value into a function's derivative, the y-values you get back FROM THE DERIVATIVE tell you the slope of a tangent line to the original function at that value of x.

Step-by-step explanation:

Answer:

D 10x=150

Step-by-step explanation:

They are the same degree so they must equal eachother

Answer:

10x=150(Vertically Opposite Angle)

Answer: pretty sure it’s $56.25

Step-by-step explanation:

4200-1500= 2700 divided by 48 months (4 years).

Answer: Quinn is a contestant on a quiz show. Quinn's score changes by -15 points for 4 questions in a row. ) What is the total change in Quinn's score?

hope this help :}

The interval of convergence, I, is therefore $(-\infty, -4] \cup [4, \infty)$.

The radius of convergence, R, of the series $\sum\limits_{n=0}^{\infty} \sqrt{\frac{n}{6^n}}(x+4)^n$ is 0. The interval of convergence, I, is therefore $(-\infty, -4] \cup [4, \infty)$.

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Answer:

The formula for applying the Trapezoidal Rule to approximate the total fuel consumption during the hour is as follows:

Approximate integral ≈ (h/2) * [f(x₀) + 2f(x₁) + 2f(x₂) + 2f(x₃) + ... + 2f(xₙ₋₁) + f(xₙ)],

where:

- h represents the width of each interval (in this case, the time interval is 5 minutes, so h = 5 minutes = 1/12 hour).

- f(x₀), f(x₁), f(x₂), ..., f(xₙ) are the recorded fuel consumption values at each interval.

Let's calculate the approximate total fuel consumption using the Trapezoidal Rule:

h = 1/12

Approximate integral ≈ (1/12) * [2.5 + 2(2.4) + 2(2.3) + 2(2.4) + 2(2.4) + 2(2.5) + 2(2.6) + 2(2.5) + 2(2.4) + 2(2.3) + 2(2.4) + 2(2.4) + 2.3]

Simplifying the calculation:

Approximate integral ≈ (1/12) * [2.5 + 4.8 + 4.6 + 4.8 + 4.8 + 5.0 + 5.2 + 5.0 + 4.8 + 4.6 + 4.8 + 4.8 + 2.3]

Approximate integral ≈ (1/12) * [57.3]

Approximate integral ≈ 4.775

Therefore, the approximate total fuel consumption during the hour, using the Trapezoidal Rule, is 4.775 gallons.

Step-by-step explanation:

The Trapezoidal Rule is used to approximate the total fuel consumption during an hour-long trip based on recorded fuel consumption values at regular intervals.

To apply the Trapezoidal Rule, we divide the time interval (in this case, an hour) into subintervals of equal width. The fuel consumption values at the beginning and end of each subinterval are used to form trapezoids.

By dividing the area under the curve into trapezoids and calculating their areas, an estimation of the total fuel consumption can be obtained.

The area of each trapezoid is calculated by taking the average of the two fuel consumption values and multiplying it by the width of the subinterval. Summing up the areas of all the trapezoids gives an approximation of the total fuel consumption during the hour.

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A system of two linear equations in two variables that has infinite solutions will produce one line superimposed on the other line. This implies that both lines coincide. The correct option is d.

Linear equations are algebraic equations that can be used to represent straight lines on a graph. Linear equations are equations with two variables that can be represented on a graph as a straight line.

The general form of the linear equation is y = mx + b.

This form of the equation is used to represent the line on the graph.

A system of two linear equations in two variables represents two lines on the same graph. These lines are created by using two linear equations that are plotted on the same graph. Each line on the graph represents an equation in the system. The point where the two lines intersect represents the solution to the system of linear equations.

If the two equations in a system of linear equations in two variables represent the same line, then the system of equations will have infinite solutions. This is because both equations represent the same line, and there are an infinite number of points on that line that can be considered as solutions. This is the only case where a system of linear equations in two variables will have infinite solutions.

If we have a system of two linear equations in two variables that has infinite solutions, we would see one line superimposed on the other line. This implies that both lines coincide.  The correct option is d.

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To calculate the electric flux through each side of the box, we need to use Gauss's Law, which states that the electric flux through a closed surface is proportional to the total charge enclosed by that surface.

Given the magnitudes of the electric field on each side of the box, we can calculate the electric flux through each side using the formula:

Electric Flux = Electric Field * Area * Cos(θ)

where:

Electric Field is the magnitude of the electric field on a particular side of the box

Area is the area of that side of the box

θ is the angle between the electric field vector and the surface normal (which is 0 degrees for a perpendicular field)

Given the dimensions of the box, we can calculate the areas of each side:

Area of the right side = w * h

Area of the top and bottom sides = L * w

Area of the front and back sides = L * h

Area of the left side = w * h

Now, we can calculate the electric flux through each side:

Electric Flux through the right side = E₁ * Area of the right side * Cos(0°)

Electric Flux through the top side = E₂ * Area of the top side * Cos(0°)

Electric Flux through the bottom side = E₂ * Area of the bottom side * Cos(0°)

Electric Flux through the front side = E₂ * Area of the front side * Cos(0°)

Electric Flux through the back side = E₂ * Area of the back side * Cos(0°)

Electric Flux through the left side = E₃ * Area of the left side * Cos(0°)

To calculate the total charge enclosed by the Gaussian box, we use the formula:

Total Charge Enclosed = Electric Flux through the right side + Electric Flux through the left side

Now, let's calculate the values:

Area of the right side = w * h = 56.1 cm * 13.6 cm = 763.96 cm²

Electric Flux through the right side = 1156 N/C * 763.96 cm² * Cos(0°)

Area of the top and bottom sides = L * w = 89.5 cm * 56.1 cm = 5023.95 cm²

Electric Flux through the top side = 2842 N/C * 5023.95 cm² * Cos(0°)

Electric Flux through the bottom side = 2842 N/C * 5023.95 cm² * Cos(0°)

Area of the front and back sides = L * h = 89.5 cm * 13.6 cm = 1216.2 cm²

Electric Flux through the front side = 2842 N/C * 1216.2 cm² * Cos(0°)

Electric Flux through the back side = 2842 N/C * 1216.2 cm² * Cos(0°)

Area of the left side = w * h = 56.1 cm * 13.6 cm = 763.96 cm²

Electric Flux through the left side = 4484 N/C * 763.96 cm² * Cos(0°)

Total Charge Enclosed = Electric Flux through the right side + Electric Flux through the left side

Now, you can plug in the values and calculate the electric flux and total charge enclosed using the given magnitudes of the electric fields.

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Answer:

There was more variation in her time spent running outside.

Step-by-step explanation:

This is because the range for running outside is larger.

To find range you subtract the largest number in the data by the smallest.

RANGE FOR INSIDE: 150 - 25 = 125

RANGE FOR OUTSIDE: 200 - 50 = 150

Since the range is larger for the time outside spent running, there is more variation.

The fraction of report he finished is 3/8

A fraction represents part of a whole. When something is broken up into a number of parts, the fraction shows how many of those parts you have.

Given that, Frank wrote 1/4 of his book report before dinner. He wrote, 1/8 of the report after dinner.

The part of report he completed is the sum of both fractions, given,

1/8+1/4

Take LCM 8

(2+1)/8

= 3/8

Hence, The fraction of report he finished is 3/8

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