A manufacturer knows that their items have a normally distributed length, with a mean of 15.8 inches, and standard deviation of 0.9 inches.
If 24 items are chosen at random, what is the probability that their mean length is less than 15.6 inches? (Give answer to 4 decimal places.)

Answer:

Please check answer for explanations

Step-by-step explanation:

Here, we want to shade the angle

From the measure given, we have the angle as located on the triangle EFD

So, we locate the triangle EFD

afterwards, we look at the angle given again and the letter in the middle

The letter in the middle is F from EFD

so this means that the particular angle we want to locate is on the angle F , which we can then proceed to shade

simply put, shade the measure of angle F in the triangle EFD

Answer:

200 adults

Step-by-step explanation:

1/8 of the passengers (children) is 40

Total passengers in the train is 8/8

Therefore to get the total number of passengers is given by

(8/8) × 40 × (8/1)

= 240 passengers

Adults in the train = Passengers - Children

= 240 - 40

= 200 adults

Multiply length added per day by number of days and add that to the starting length:

Equation: L = 4D + 56

replace d with number of days and solve:

L = 4(34) + 56

L = 136 + 56

L = 192 miles

Answer:

  A.  60 ft·lb

Step-by-step explanation:

You want the work done lifting a 15-lb flower pot to a height of 4 ft.

Work is the product of force and distance. When the pot is raised 4 ft, the work done is ...

  W = F·d

  W = (15 lb)(4 ft) = 60 ft·lb

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Value places in 123,456

1 = hundred thousands place

2 = ten thousands place

3 = thousands place

4 = hundreds place

5 = tens place

6 = ones place

If we use the table above for an example, we can see that "4" lies in the thousands place.

Best of Luck!

it should be flipped over the x-axis and translated to the right by 2

Answer:

Step-by-step explanation:

Could you show two points need to be calculated? A and D are the same in this case

Answer: The correlation coefficient (also known as Pearson's correlation coefficient or r) is a measure of the strength of the linear relationship between two variables. The value of the correlation coefficient ranges between -1 and 1, with a value of 1 indicating a perfect positive linear relationship, a value of -1 indicating a perfect negative linear relationship, and a value of 0 indicating no linear relationship.

In this case, the correlation coefficient that represents the strongest linear relationship is

0.9

The absolute value of the correlation coefficient measures the strength of the linear relationship, regardless of whether it is positive or negative. So, the absolute value of 0.9 and -0.3 are both 0.9. but as we are looking for the strongest linear relationship, the value of 0.9 is closer to 1 than -0.3 is and it indicates stronger positive relationship.

In summary, the closer the correlation coefficient is to 1 or -1, the stronger the linear relationship between the variables is. In this case, 0.9 has the strongest linear relationship of the given options.

Step-by-step explanation:

The Pythagorean Theorem is a mathematical theorem that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In other words, a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides. This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. The Pythagorean Theorem is one of the most well-known and widely used theorems in mathematics and has numerous applications in fields such as architecture, engineering, and physics.

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Answer: 3 x 3 I think

Step-by-step explanation:

Answer:

3x^2

Step-by-step explanation:

base times height

you do 3x times x to find area

x(3x)

3x^2

Answer: 1/11

Step-by-step explanation:

the probability that the next type of longboard sold will be a downhill long board  is 1/11. we need to first find the total number of longboards sold and the number of downhill longboards sold.

From the table, we can see that the total number of longboards sold is 6+9+5+2=22, and the number of downhill longboards sold is 2.

The probability of selling a downhill longboard next can be calculated as the number of downhill longboards sold divided by the total number of longboards sold:

P(downhill) = 2/22

This can be simplified to:

P(downhill) = 1/11

Therefore, thethe probability that the next type of longboard sold will be a downhill long board  is 1/11.

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There is sufficient evidence for significance level 10%  to conclude students with study skills course have higher exam scores using hypothesis test.

To conduct a hypothesis test,

set up the null and alternative hypotheses and perform the necessary calculations.

Null Hypothesis (H₀),

The study skills course did not have a significant effect on the mean final exam scores. µ = 77.6.

Alternative Hypothesis (Hₐ),

The study skills course had a significant effect on the mean final exam scores. µ > 77.6.

To test this hypothesis, use a one-sample t-test since we have a sample mean and population standard deviation.

Sample mean (X) = 79.5

Population mean (µ) = 77.6

Population standard deviation (σ) = 7.2

Sample size (n) = 36

Significance level (α) = 0.10 (10%)

First, let's calculate the test statistic (t-value),

t

= (X - µ) / (σ / √n)

= (79.5 - 77.6) / (7.2 / √36)

= 1.9 / (7.2 / 6)

= 1.9 / 1

= 1.9

Next, determine the critical t-value from the t-distribution calculator.

Since the alternative hypothesis is one-sided (µ > 77.6), interested in the upper tail of the distribution.

At a significance level of 0.10 with 35 degrees of freedom (n - 1 = 36 - 1 = 35), the critical t-value is approximately 1.310.

Since the calculated t-value (1.9) is greater than the critical t-value (1.310), we have evidence to reject the null hypothesis.

Therefore, using hypothesis test there is sufficient evidence at 10% significance level to conclude that students who took study skills course had higher exam scores.

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Step-by-step explanation:

the answer is in the image above

Answer:

The answer is below

Step-by-step explanation:

The model is a tile with length 1/4 in. and width 1/6 in while the actual tile has length 1/6 ft. and width 1/9 ft.

Firstly we have to convert the model length and width from inches to feet.

1 feet = 12 inches

model length =  1/4 in. = 1/4 in * (1/12) ft./in = 1/48 ft.

model width =  1/6 in. = 1/6 in * (1/12) ft./in = 1/72 ft.

Therefore:

Ratio of model length to actual length of tile = (1/48 ft.) / (1/6 ft.) = 1 / 8

Ratio of model length to actual length of tile = (1/72 ft.) / (1/9 ft.) = 1 / 8

Area of model tile = length * width = 1/48 ft. * 1/72 ft. = 1/3456 ft²

Area of actual tile = length * width = 1/6 ft. * 1/9 ft. = 1/54 ft²

Ratio of model area to actual area of tile = (1/3456 ft²) / (1/54 ft²) = 1 / 64

Answer:

m= (-4+2)/(4+3)

  =-2/7

Answer:

Step-by-step explanation:

The p-value can be found with the F-distribution table or statistical software. If the p-value is less than or equal to α, then answer is option (a),If the p-value is greater than α, then answer is option (b).

To determine the correct statistical decision based on the given F-statistic, F (3, 12) = 2.72, we need additional information such as the significance level (α) of the hypothesis test. The significance level is a predetermined threshold that is used to assess the statistical significance of the results.

The correct decision depends on whether the calculated p-value, which quantifies the strength of evidence against the null hypothesis, is less than or equal to the significance level (α).

To find the p-value, you would need the F-distribution table or statistical software.

Once you have the p-value, you can compare it to the significance level (α) to make a decision:

If the p-value is less than or equal to α, you would reject the null hypothesis, indicating a statistically significant mean difference.

If the p-value is greater than α, you would fail to reject the null hypothesis, suggesting that there is not a statistically significant mean difference.

Therefore, without the significance level or the p-value, it is not possible to determine the correct statistical decision.

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Answer:

5 x S = M (S=Students, M = money); 5 x 25 = 100

Answer: 1,468.5

Step-by-step explanation:

Hi, to answer this question we simply have to multiply the price of each share of stock ($19.58) by the number of shares of stock bought (75 ).

Mathematically speaking:

Price per share x number of shares = 19.58 x 75 = $1,468.5  

His purchase price was 1,468.5

Feel free to ask for more if needed or if you did not understand something.  

Answer:

89.97

Step-by-step explanation:

5.99+79.99 = 85.98 + 3.99  = 89.97

To determine whether the sequence \(\(a_n = \frac{1}{3n^4}\)\) is increasing, decreasing, or not monotonic, we can analyze the behavior of the terms as \(\(n\)\)increases.

Let's calculate the values of \(\(a_n\)\) for a few values of \(\(n\)\) to observe any patterns:

\(\(a_1 = \frac{1}{3(1)^4} = \frac{1}{3}\)\)

\(\(a_2 = \frac{1}{3(2)^4} = \frac{1}{48}\)\)

\(\(a_3 = \frac{1}{3(3)^4} = \frac{1}{243}\)\)

\(\(a_4 = \frac{1}{3(4)^4} = \frac{1}{768}\)\)

We can see that as \(\(n\)\) increases, the values of \(\(a_n\)\) are decreasing. This indicates that the sequence is decreasing.

To formally prove this, we can compare the terms \(\(a_n\)\) and \(\(a_{n+1}\)\) for any \(\(n\)\) :

\(\(a_n = \frac{1}{3n^4}\)\)

\(\(a_{n+1}\) = \(\frac{1}{3(n+1)^4}\)\)

To determine if \(\(a_n\)\) is less than \(\(a_{n+1}\)\) , we can simplify and compare the fractions:

\(\(\frac{1}{3n^4} < \frac{1}{3(n+1)^4}\)\)

Cross-multiplying and simplifying:

\(\(3(n+1)^4 < 3n^4\)\)

Expanding the binomial and further simplifying:

\(\(n^4 + 4n^3 + 6n^2 + 4n + 1 < n^4\)\)

Since the left side of the inequality is positive and the right side is \(\(n^4\)\) (which is positive for all \(\(n\))\) , we can see that the inequality is not true for any \(\(n\).\) Therefore, \(\(a_n\)\) is always less than \(\(a_{n+1}\)\) , indicating that the sequence is decreasing.

In conclusion, the sequence \(\(a_n = \frac{1}{3n^4}\)\)  is a decreasing sequence.

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Answer:

a. 8 y/s; divide 40(distance) by 5(time)

b. 1/8 2/16 3/24 4/32 5/40 6/48 7/56; multiply speed and time ex. 8×1=8; 8×2=16; 8×3=24 and so on

c. 80 yards; multiply time and distance 8×10

The differential equation to be solved is Nxy - 0.5ye-0.1x for osx54 with y(0) = 6.5 dx. This can be solved using Euler's method in MATLAB.

Follow the steps below.

Step 1: Create a function file - The differential equation needs to be defined in a function file first. Let's create a function file named "odefun.m".function dydx = odefun(x,y)

dydx = N*x*y - 0.5*y*exp(-0.1*x);

where N is a constant value that needs to be defined.

Step 2: Define the given values - Define the given values such as N, initial value y(0), and step size dx.

N = ...; %

Define N herey 0 = 6.5; %

Define initial value of y here. dx = ...; %

Define step size here

Step 3: Use Euler's method to solve the differential equation - Now, use Euler's method to solve the differential equation using a for loop. The MATLAB code is as follows: x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); %

Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end

Step 4: Plot the solution - Finally, plot the solution using the MATLAB command plot(x,y).

The complete MATLAB code is given below:

N = ...; %

Define N here y0 = 6.5; %

Define initial value of y here dx = ...; %

Define step size here x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); % Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end plot(x,y)

The plot of the solution will be displayed.

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Answer:i think the anwser is 6

Step-by-step explanation:

The area of the surface defined by z = xy and x2 + y2 ≤ 22 would be, Area = ∬ sqrt(1 + r^2) * r dr dθ, with limits 0 ≤ r ≤ sqrt(2) and 0 ≤ θ ≤ 2π.Evaluate the integral to get the area of the surface.

To find the area of the surface defined by z = xy and x^2 + y^2 ≤ 2, we need to use a double integral over the region bounded by the inequality x^2 + y^2 ≤ 2.

First, we should rewrite the inequality in polar coordinates: x^2 + y^2 ≤ 2 becomes r^2 ≤ 2, where r is the radial distance and θ is the angle. This means 0 ≤ r ≤ sqrt(2) and 0 ≤ θ ≤ 2π.

Next, we find the Jacobian for the polar coordinates, which is |J(r,θ)| = r.

Now, we need to compute the magnitude of the gradient of z = xy in terms of polar coordinates. The gradient of z is given by the partial derivatives:

∂z/∂x = y and ∂z/∂y = x

In polar coordinates, x = r*cos(θ) and y = r*sin(θ). So, we have:

∂z/∂r = cos(θ)*∂z/∂x + sin(θ)*∂z/∂y = r*cos^2(θ) + r*sin^2(θ) = r

Now, we use the double integral to find the surface area:

Area = ∬ sqrt(1 + (∂z/∂r)^2) * |J(r,θ)| dr dθ

Area = ∬ sqrt(1 + r^2) * r dr dθ, with limits 0 ≤ r ≤ sqrt(2) and 0 ≤ θ ≤ 2π.

Evaluate the integral to get the area of the surface.

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A study by a business professor at Arizona State University found that students who missed two classes had grades that were one full letter grade lower than those who attended all classes. This suggests that attending class is essential for academic success.

There are a few reasons why missing class can lead to lower grades. First, students who miss class may miss important information that is covered in lectures. Second, they may miss opportunities to ask questions and get help from the professor. Third, they may fall behind on assignments and readings.

To avoid falling behind, it is important to attend all classes. If you must miss class, be sure to get notes from a classmate and ask the professor for any missed assignments or readings. By attending class and staying on top of your work, you can improve your chances of academic success.

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Complete question:

A study by a business professor at Arizona State University showed that, on average, is students' grades wet down one full grade for every _ classes they missed.

a. one

b. two

c. three

d. four

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

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

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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Answer:

y=(x+1)^(2)-9

Step-by-step explanation:

Answer:

Y=(x+1)^2-9

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

To calculate x we must use the trig function of tangent:

as tangent is opposite divides by adjacent we can get this equation:

\(\tan 30 = \frac{9}{x}\) which is equal to:

\(x=\frac{9}{\tan 30}\) So x must equal to 15.588.. (just put the second bit in the calculator

As all the values provided are integers you round this to the nearest whole number:

16 (as the third digit, 5, rounds up)

so our answer is 16