Here is a sequence of numbers 64,49,36,25,16 find the next number in the sequence

a. The proportion of students who had a final grade score of 64 or below is 0.3085

To find the proportion of students who had a final grade score of 64 or below, we can use the standard normal distribution formula which is:

z = (x - µ) / σ where

z is the z-score,

x is the value of the variable,

µ is the mean, and

σ is the standard deviation.

We have x = 64, µ = 67, and σ = 6.

Plugging in these values, we have:

z = (64 - 67) / 6 = -0.5

Using a standard normal distribution table or calculator, we can find that the proportion of students who had a final grade score of 64 or below is 0.3085 (rounded to four decimal places).

b. To find the proportion of students who earned a final grade score between 58 and 75 is 0.8414 .

We can again use the standard normal distribution formula to find the z-scores for each value and then find the area between those z-scores using a standard normal distribution table or calculator. Let's first find the z-scores for 58 and 75:z₁ = (58 - 67) / 6 = -1.5z₂ = (75 - 67) / 6 = 1.33

Now, we need to find the area between these z-scores. Using a standard normal distribution table or calculator, we can find that the area to the left of z₁ is 0.0668 and the area to the left of z₂ is 0.9082. Therefore, the area between z₁ and z₂ is:0.9082 - 0.0668 = 0.8414 (rounded to four decimal places).

c. To find the final grade score required to earn an A last year was 72.28.

We need to find the z-score that corresponds to the top 19% of the distribution. Using a standard normal distribution table or calculator, we can find that the z-score that corresponds to the top 19% of the distribution is approximately 0.88. Now, we can use the z-score formula to find the final grade score:

x = µ + σz where

x is the final grade score,

µ is the mean,

σ is the standard deviation, and

z is the z-score.

We have µ = 67, σ = 6, and z = 0.88.

Plugging in these values, we have:

x = 67 + 6(0.88) = 72.28 (rounded to two decimal places). Therefore, the final grade score required to earn an A last year was 72.28 (rounded to two decimal places).

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The area of the irregular shape is 84 ft square.

The diagram is a trapezium. A trapezium is a quadrilateral. Therefore, the area of the trapezium can be found as follows:

area of the trapezium = 1 / 2 (a + b)h

where

Therefore,

a = 10 ft

b = 18 ft

c = 6 ft

area of the trapezium = 1 / 2 (10 + 18)6

area of the trapezium = 1 / 2 (28)6

area of the trapezium = 168 / 2

area of the trapezium = 84 ft²

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Answer:

The range of possible values of x are;

x > 6

Step-by-step explanation:

To form a triangle, the length of two sides must be greater than the third side

Thus;

6x + 3 + 4x-17 > x + 40

6x + 4x-14 > x + 40

10x-14 > x + 40

10x-x > 40 + 14

9x > 54

x > 54/9

x > 6

the Nash equilibrium is not necessarily the best or most desirable outcome for the players involved. It simply represents a stable state where no player has an incentive to unilaterally deviate from their chosen strategy.

To determine the Nash equilibria in a game, we need to analyze the strategies of each player and identify the combinations of strategies where no player has an incentive to unilaterally deviate.

Given the options:

1. (P1=Shot, P2=Shot)

2. (P1=No shot, P2=No shot)

3. (P1=Shot, P2=No shot)

4. (P1=No shot, P2=Shot)

Let's analyze each combination:

1. (P1=Shot, P2=Shot):

If both players choose to shoot, they both face the risk of being shot and getting injured. Neither player has an incentive to deviate from this strategy, as changing to "No shot" would expose them to the risk of being shot without being able to retaliate. Therefore, (P1=Shot, P2=Shot) is a Nash equilibrium.

2. (P1=No shot, P2=No shot):

If both players choose not to shoot, they avoid the risk of being injured. Again, neither player has an incentive to unilaterally deviate from this strategy, as changing to "Shot" would expose them to the risk of being injured without gaining any advantage. Therefore, (P1=No shot, P2=No shot) is a Nash equilibrium.

3. (P1=Shot, P2=No shot):

If Player 1 chooses to shoot while Player 2 chooses not to shoot, Player 1 has an advantage and can potentially eliminate Player 2 without being injured. In this scenario, Player 2 may have an incentive to deviate from "No shot" and switch to "Shot" to protect themselves. Therefore, (P1=Shot, P2=No shot) is not a Nash equilibrium.

4. (P1=No shot, P2=Shot):

Similarly, if Player 1 chooses not to shoot while Player 2 chooses to shoot, Player 2 has an advantage and can potentially eliminate Player 1 without being injured. In this scenario, Player 1 may have an incentive to deviate from "No shot" and switch to "Shot" to protect themselves. Therefore, (P1=No shot, P2=Shot) is not a Nash equilibrium.

Based on the analysis, the Nash equilibria in this game are:

- (P1=Shot, P2=Shot)

- (P1=No shot, P2=No shot)

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Answer:

Option B)  \(\frac{1}{6}\) Inches

Step-by-step explanation:

Maria's Centipede = \(1\frac{1}{12}\) inches = \(\frac{13}{12}\) inches

Jerome Centipede = \(\frac{11}{12}\)

To see how much longer Maria's centipede was than Jerome's, we'll subtract the two:

=> \(\frac{13}{12} -\frac{11}{12}\)

=> \(\frac{13-11}{12}\)

=> \(\frac{2}{12}\) inches

=> \(\frac{1}{6}\) Inches

The correct answer is $56,000.the total profit for Pinewood Furniture Company, considering only the production of 200 chairs and 400 tables

To determine the total profit for Pinewood Furniture Company, we need to calculate the profit generated from producing 200 chairs and 400 tables.

Each chair generates a profit of $80, and if 200 chairs are produced, the total profit from chairs would be:

200 chairs * $80/profit per chair = $16,000.

Similarly, each table generates a profit of $100, and if 400 tables are produced, the total profit from tables would be:

400 tables * $100/profit per table = $40,000.

Therefore, the total profit for Pinewood Furniture Company, considering only the production of 200 chairs and 400 tables, would be:

$16,000 (profit from chairs) + $40,000 (profit from tables) = $56,000.

Hence, the correct answer is $56,000.

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Answer:

0 is sin 90⁰ ...hmmm...kui

ANSWER

EXPLANATION

We want to factor the given expression using the greatest common factor.

To do this, we have to factor out common terms in the terms given in the expression. The two terms in the expression are divisible by 10.

Hence, we can factor the expression as follows:

The expression has been factored using GCF.

(a) The log returns of Apple Inc and Johnson & Johnson do not follow a normal distribution.

(b) The tails of the log returns of both stocks are compared with a t-distribution with 4 degrees of freedom.

(a) To determine if the log returns of Apple Inc and Johnson & Johnson follow a normal distribution, we can perform a normality test, such as the Shapiro-Wilk test, Anderson-Darling test, or Kolmogorov-Smirnov test, on the log return data. If the p-value from the test is less than the chosen significance level (e.g., 0.05), we reject the null hypothesis of normality.

(b) To compare the tails of the log returns with a t-distribution, we can fit a t-distribution with 4 degrees of freedom to the data and compare the probability density functions (PDFs) of the t-distribution and the empirical distribution of the log returns.

This can be visually assessed by plotting the PDFs or quantitatively analyzed using statistical measures such as the Kullback-Leibler divergence or the Kolmogorov-Smirnov test.

(c) To compare the distributions of the log returns during the 2008 financial crisis and two years after the crisis, we can create side-by-side boxplots, histograms, and QQ-plots. The boxplots will show the distribution's central tendency, spread, and skewness.

The histograms will provide a visual representation of the frequency distribution, and the QQ-plots will compare the quantiles of the log returns with the theoretical quantiles of a normal distribution.

(d) To determine the appropriate degree of freedom for modeling the log returns of Apple Inc two years after the financial crisis, we can fit various t-distributions with different degrees of freedom to the data and compare their goodness-of-fit using statistical measures like Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC).

The best fitting t-distribution will have the lowest AIC or BIC value. A QQ-plot and a histogram with the overlayed density of the best fitting t-distribution can be used to visually assess the goodness-of-fit.

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Answer:

- sin(x) is the ratio of the opposite leg to the hypotenuse in a right triangle, while cos(x) is the ratio of the adjacent leg to the hypotenuse in a right triangle.

-The graph of y = sin(x) at x = 0 starts at the origin, and then increases, while the graph of y = cos(x) starts at a max, and then decreases.

Here's a 3rd: sin(x) is the cofunction of cos(x), which means that sin(x) = cos(90-x). This also shows that they are different.

To solve this problem, we can use the binomial probability formula:

P(X = k) = (nCk) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes

n is the number of trials

p is the probability of success in a single trial

(nCk) represents the number of combinations of n items taken k at a time

k is the number of successes

Given that 45% of policies are terminated before their maturity date, the probability of success (p) is 0.45. The number of trials (n) is 10.

(a) To find the probability that eight policies are terminated before maturity:

P(X = 8) = (10C8) * 0.45^8 * (1 - 0.45)^(10 - 8)

(b) To find the probability that at least eight policies are terminated before maturity, we sum the probabilities from 8 to 10:

P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10)

(c) To find the probability that at most eight policies are not terminated before maturity, we sum the probabilities from 0 to 8:

P(X <= 8) = P(X = 0) + P(X = 1) + ... + P(X = 8)

These calculations can be done using a calculator or statistical software.

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The length of segment CB in trapezoid CBAD is 11.

In a trapezoid, the midsegment is the line segment that joins the midpoints of the two non-parallel sides. In this case, KJ is the midsegment of trapezoid CBAD, which means that it is parallel to both CB and AD, and its length is equal to the average of the lengths of CB and AD.

We are given that;

CB=4x-13

KJ=6x-18

DA=25

we can use the formula for the midsegment of a trapezoid to set up an equation and solve for x:

KJ = (CB + AD) / 2

6x - 18 = (4x - 13 + 25) / 2

6x - 18 = (4x + 12) / 2

6x - 18 = 2x + 6

4x = 24

x = 6

Now that we have found the value of x, we can substitute it back into the expression for CB to find its length:

CB = 4x - 13 = 4(6) - 13 = 11

Therefore, the answer of the given trapezoid will be 11.

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Answer:

where is the full question?

Step-by-step explanation:

Answer:

Part A: 60

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.

12, 24, 36, 48, 60.

---------------------------------

Part B: 9

81 / 72 = 9

----------------------------------

Part C: 9 (8 + 9)

GCF of 72 and 81 is 9...

Divide 72 by 9 and get 8.

Divide 81 by 9 and get 9.

To check multiply 9 with 8, and multiply 9 by 9.

----------------------------------

Easy! :D (if you don't mind, may I get brainliest please?)

Answer:

-2x^2-8x+12

Step-by-step explanation:

f(x)= 3x^2-2x+4

g(x)= 5x^2 +6x -8

(f-g)(x) =  3x^2-2x+4-(5x^2 +6x -8)

Distribute the minus sign

(f-g)(x) =  3x^2-2x+4-5x^2 -6x +8

Combine like terms

-2x^2-8x+12

Answer:

a = 0

Step-by-step explanation:

a + 5 = −5a + 5

subtract the 5a and bring it to the left and take the 5 on the left and bring it to the right then solve.

6a = 0

divide and you get

a = 0

Answer:

2.0, 2.4. 2.8

Step-by-step explanation:

The square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500 square mils.

To find the square mil area for a 2 inch wide by 1/4 inch thick copper busbar, we need to multiply the width and thickness of the busbar in mils.

1 inch = 1000 mils

So, the width of the busbar in mils = 2 inches x 1000 mils/inch = 2000 mils

And, the thickness of the busbar in mils = 1/4 inch x 1000 mils/inch = 250 mils

Therefore, the square mil area of the copper busbar = width x thickness = 2000 mils x 250 mils = 500,000 square mils.

Hence, the square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500,000 square mils.

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The child advocate collects data by randomly selecting 4 out of the 25 state orphanages. In each of the four selected orphanages, the child advocate surveys every child.

This approach allows the child advocate to obtain information from a representative sample of children in state orphanages. By surveying every child in the selected orphanages, the child advocate ensures that no child is excluded from the data collection process. This method provides a comprehensive understanding of the experiences, needs, and concerns of the children in the four chosen orphanages.

By collecting data in this manner, the child advocate can gather valuable insights that can inform policies and interventions to improve the well-being and support for children in state orphanages.

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w - z expressed in rectangular form is (1 - √3, -√3 + i).

Given: The complex numbers w = 2(cos(210°) + isin(210°)) and z = 2(cos(330°) + isin(330°))

To find: The expression of w - z in rectangular form using (x,y)

Solution: We know that rectangular form of complex number is given by:

z = x + iy

where x and y are the real and imaginary parts respectively.

So, w = 2(cos(210°) + isin(210°)) can be written as:

w = 2(cos(-150°) + isin(-150°))

Comparing with the rectangular form, we get:

x = 2cos(-150°) = 2 * (1/2) = 1 and

y = 2sin(-150°) = 2 * (-√3/2) = -√3

So, w = 1 - √3i

Similarly, z = 2(cos(330°) + isin(330°)) can be written as:

z = 2(cos(-30°) + isin(-30°))

Comparing with the rectangular form, we get:

x = 2cos(-30°) = 2 * (√3/2) = √3 and y = 2sin(-30°) = 2 * (-1/2) = -1

So, z = √3 - i

Now, w - z = (1 - √3i) - (√3 - i)

We get, w - z = 1 - √3i - √3 + i

Moving the real part to the front and the imaginary part to the end, we get: w - z = (1 - √3) + (-√3 + i)

Therefore, w - z expressed in rectangular form is (1 - √3, -√3 + i).

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Answer:

the answer is the 2nd option

Step-by-step explanation:

n=5/6

Answer:

n = 5/6

Step-by-step explanation:

Hey There!

our goal is to get the variable on one side (n) and the constant on the other

To do this we divide each side by 4/5

2/3 divided by 4/5 = 5/6

Therefore n = 5/6

Hope this helps :) and if you have any more questions just let me know

Answer:

56

Step-by-step explanation:

length times width

The equation would not have real roots.

We know that we can be able to use the discriminant to be able to know the kind of roots that the quadratic equation that we are dealing with would have. Thus the discriminant has the major role of showing us the kind of roots that we have.

Using;

√b^2 - 4ac

√(-2)^2 - 4(-3) (-6)

√-68

Thus the equation would not have a real root. This is clear from the solution that we have in trying to obtain the roots of the equation as shown.

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An equation of the line shown above in slope-intercept form is y = x/8 + 5/2.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided in the graph above, we have the following data points on its line:

At data point (60, 10), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 10 = (20 - 10)/(140 - 60)(x - 60)

y - 10 = 1/8(x - 60)

y = x/8 - 7.5 + 10

y = x/8 + 5/2

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Pack 216 cube-shaped boxes of edge 3 cm in a larger box with a volume of 5832 cubic cm.

The volume of each cube-shaped box is given by the formula:

\(V = edge^3\)

Substituting the value of edge as 3 cm, we get:

\(V = 3^3 = 27\) cubic cm

To find the number of boxes that can be packed in a larger box with a volume of 5832 cubic cm, we need to divide the volume of the larger box by the volume of each smaller box:

Number of boxes = Volume of larger box / Volume of each smaller box

Number of boxes = 5832 cubic cm / 27 cubic cm

Number of boxes = 216

Therefore, we can pack 216 cube-shaped boxes of edge 3 cm in a larger box with a volume of 5832 cubic cm.

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The surface area of the triangular base prism is 216 ft squared.

The prism above is a triangular base prism. The surface area of the triangular prism can be found as follows:

Therefore,

surface area of the prism = (a + b + c)l + bh

where

Therefore,

surface area of the prism = (10 + 6 + 8)7 + 6(8)

surface area of the prism = (24)7 + 48

surface area of the prism = 168 + 48

surface area of the prism =216 ft²

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L " (x - 1) dx integrals gives the volume of the solid generated by revolving R about the y-axis

The integration or antiderivative processes can be used to determine the curve's area under it. For this, we require the curve's equation (y = f(x)), the curve's axis boundary, and the curve's border limitations.

Let R be the area in the first quadrant enclosed by the hyperbolas xy = 1 and xy = 3, the lines y = x and y = 3x, and the lines xy = 1. The third quadrant is also constrained by those four curves, which we are ignoring. xy dA. = 1 v .

Let R be the region in the first quadrant bounded by the graph of y = Vx - 1. the x-axis, and the vertical line * = 10.

= L " (x - 1) dx integrals gives the volume of the solid generated by revolving R about the y-axis

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