Graph y=x^2-4 and 4-x^2 on the same coordinate plane. Write an equation for the part of the graph which is above the y-axis.

A person places, by using the continuous compound interest formula, the value of the investment account after 4 years can be calculated.

The continuous compound interest formula is given by the equation V = P * e^(rt), where V represents the value of the account, P is the principal initially invested, e is the base of the natural logarithm (approximately 2.71828), r is the interest rate, and t is the time in years. In this scenario, the initial principal P is $4080, the interest rate r is 5.7% (or 0.057 as a decimal), and the time t is 4 years.

Plugging these values into the formula, we have V = 4080 * e^(0.057*4). Using a calculator, we can evaluate this expression to find the value of V. After performing the calculation, the value of V is approximately $4946.68, rounded to the nearest cent. Therefore, after 4 years, the amount of money in the investment account will be approximately $4946.68.

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Answer:

THE ANSWER IS AS FOLLOWS

Step-by-step explanation:

The following statements are true based on the given information:

- The largest total number of electronic devices sold was on Wednesday.

- The smallest number of TVs sold was on Monday.

- The same number of phones was sold on each of Monday, Tuesday, and Wednesday. (Note: we cannot tell from the chart whether this number was zero or some other value.)

- On Tuesday, more tablets were sold than any other type of electronic device.

A graph is a way to represent a lot of data in such a visual format.

Hence, The correct statements are A, B, and D.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

The statement that is correct about the given table is,

A.) The largest total number of electronic devices sold was on Wednesday.

B.) The smallest number of TVs sold was on Monday.

D.) On Tuesday, more tablets were sold than any other type of electronic device

hence, the correct statements are A, B, and D.

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The amount of Jacob's purchase, including the sales tax, will be $83.16.

We need to add the cost of the coat and the hat, and then add the 8% sales tax on the total amount.

Cost of the coat: $62.75

Cost of the hat: $14.25

Total cost of the coat and hat: $62.75 + $14.25 = $77.00

To find the amount after adding the 8% sales tax, we calculate 8% of $77.00 and add it to the total:

Sales tax: 8% of $77.00 = 0.08 * $77.00 = $6.16

Total amount of Jacob's purchase: $77.00 + $6.16 = $83.16

Therefore, the amount of Jacob's purchase, including the sales tax, will be $83.16.

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Area enclosed by spiral and straight line segment.

The polar curve r = 8θ, 0 ≤ θ ≤ 5.2, is a spiral that starts at the origin and spirals outward as θ increases. To find the area enclosed by the closed curve obtained by joining the ends of this spiral with a straight line segment, we need to find the coordinates of the endpoints of the spiral and then calculate the area of the enclosed region.

The endpoints of the spiral occur at θ = 0 and θ = 5.2. At these values of θ, we have:

r(0) = 8(0) = 0

r(5.2) = 8(5.2) = 41.6

Therefore, the endpoints of the spiral are (0,0) and (41.6, 5.2).

To calculate the area enclosed by the curve, we can divide the region into two parts: a sector of a circle and a triangle.

The sector of a circle is defined by the angle θ = 5.2 and the radius r = 41.6. The area of this sector can be calculated as:

A_sector = (1/2) * r² * θ

= (1/2) * (41.6)² * 5.2

= 4455.68

The triangle is defined by the two endpoints of the spiral and the point where the spiral intersects the x-axis. The x-intercept of the spiral occurs when r = 0, which happens at θ = 0. The coordinates of this point are (0,0). The area of the triangle can be calculated as:

A_triangle = (1/2) * base * height

= (1/2) * 41.6 * 5.2

= 108.16

Therefore, the total area enclosed by the closed curve is:

A_total = A_sector + A_triangle

= 4455.68 + 108.16

= 4563.84

Hence, the area enclosed by the closed curve obtained by joining the ends of the spiral r = 8θ, 0 ≤ θ ≤ 5.2 by a straight line segment is approximately 4563.84 square units.

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The area enclosed by the curve r = 8θ from θ=0 to θ=5.2 and the straight line segment connecting the ends of this spiral is approximately 884.736 square units. We compute it using the formula for the area of a polar curve and calculus techniques.

The subject of this problem is mathematics, more specifically, calculus and polar coordinates. It is asking us to calculate the area enclosed by a closed curve, specifically a spiral defined by the polar equation r = 8θ where θ ranges from 0 to 5.2, and a straight line segment that connects the ends of the spiral.

To find the area of the region, we will use the formula for the area of a polar curve, A = 0.5∫[α,β]r(θ)^2 dθ, where α and β are the bounds of θ. Enumerating the steps:

Therefore, the approximate area enclosed by the closed curve and the straight line segment is 884.736 square units.

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The function that is undefined for x=0 is y=√x+2.

The functions y=³√x-2 and y=√x-2 are defined for all real numbers

since the only restriction would be taking the square root or cube root of a negative number, but in these functions, x-2 is always non-negative.

On the other hand, the function y=√x+2 is undefined for x=-2,

since the expression inside the square root would be negative.

Therefore, the function that is undefined for x=0 is y=√x+2.

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The population in this scenario is option D) The SAT scores from all recent applicants.

The admission committee at the university was interested in the average SAT score of the recent high school graduates who had applied to the university. Therefore, the population of interest is the SAT scores of all recent applicants. However, since the number of applicants was very large, the committee chose to sample 50 applicants randomly and evaluate the average of the 50 scores. This sample was used to estimate the population mean SAT score. It is important to note that the sample of 50 applicants is not the population in this scenario. Instead, it is a subset of the population that was selected to estimate the population mean. The statistician will use this sample mean to make inferences about the population mean SAT score.

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The answer is a general method for finding the basis of the kernel and the image of a linear transformation.

The method involves solving a system of equations and finding the span of the columns of the matrix. The answer is:

To find a basis of ker T, we need to solve the equation T(x) = 0 for x. This means finding the null space of the matrix that represents T with respect to some bases. To do this, we can use row reduction or Gaussian elimination to find the reduced row echelon form of the matrix and then write the general solution in terms of free variables. The vectors that correspond to the free variables form a basis of ker T.

To find a basis of im T, we need to find the span of the columns of the matrix that represents T with respect to some bases. This means finding the column space of the matrix.

To do this, we can use row reduction or Gaussian elimination to find the reduced row echelon form of the matrix and then identify the columns that contain leading ones. The vectors that correspond to those columns form a basis of im T.

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Therefore, the maximum distance between Emma and Lily over the time interval 0<= t <= 15 is 22.8 units.

To answer this question, we need to know the position functions of Emma and Lily over the time interval 0<= t <= 15. Let's assume that Emma's position function is given by x(t) = 2t^2 + 5t and Lily's position function is given by y(t) = 3t^2 - 6t + 8. To find the maximum distance between Emma and Lily, we need to find the maximum value of the distance function between them. The distance between Emma and Lily at time t is given by D(t) = sqrt((x(t) - y(t))^2). Simplifying this expression, we get D(t) = sqrt((2t^2 + 5t - 3t^2 + 6t - 8)^2) = sqrt((t^2 + 11t + 64)^2). To find the maximum value of D(t) over the interval 0<= t <= 15, we can take the derivative of D(t) and set it equal to 0. After some calculations, we find that the maximum value of D(t) occurs at t = 7.5 seconds, and the maximum distance between Emma and Lily is approximately 22.8 units. Therefore, the maximum distance between Emma and Lily over the time interval 0<= t <= 15 is 22.8 units.

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A) the probability that the month selected for the annual sale will be September or October is 1/6.

A) Since we are interested in the probability of selecting September or October, which are two out of the 12 months, the probability can be calculated as:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 2 months / 12 months

Probability = 1/6

Therefore, the probability that the month selected for the annual sale will be September or October is 1/6.

B) To calculate the probability, we need to sum the number of days in September and October and divide it by the total number of days in a year (365 or 366 in a leap year).

Probability = (30 + 31) days / 365 or 366 days

Probability ≈ 61/365 or 366

The exact probability will depend on whether it is a leap year or not.

Comparing the answers from part A and part B, we can see that the probability of selecting September or October using days is slightly different from the probability calculated assuming each month has an equal probability of being selected.

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The equations of the vertical asymptotes of the function f(x) = (4x+1)(5x-1)/(x^2-9) are x = -3 and x = 3, and the equation of the horizontal asymptote is y = 20.

To find the equations of the vertical and horizontal asymptotes of the function f(x) = (4x+1)(5x-1)/(x^2-9), we first need to identify any values of x that make the denominator of the fraction equal to zero. These values of x correspond to vertical asymptotes.

The denominator of the fraction is x^2 - 9, which equals zero when x = ±3. Therefore, the vertical asymptotes of the function occur at x = -3 and x = 3.

To find any horizontal asymptotes, we can examine the behavior of the function as x approaches infinity and negative infinity. We can do this by dividing the numerator and denominator of the fraction by the highest power of x in the denominator, which is x^2. This gives:

f(x) = (4x^2 + x - 5) (5x^2 - x - 1) / (x^2 - 9x^2/x^2)

Simplifying, we get:

f(x) = (4 + 1/x - 5/x^2) (5 - 1/x - 1/x^2) / (1 - 9/x^2)

As x approaches infinity, the terms involving 1/x and 1/x^2 become negligible compared to the other terms, so we can approximate the function as:

f(x) ≈ (4) (5) / (1) = 20

As x approaches negative infinity, the same terms involving 1/x and 1/x^2 become negligible, and the function can again be approximated as:

f(x) ≈ (4) (5) / (1) = 20

Therefore, the function has a horizontal asymptote at y = 20.

In summary, the equations of the vertical asymptotes of the function f(x) = (4x+1)(5x-1)/(x^2-9) are x = -3 and x = 3, and the equation of the horizontal asymptote is y = 20.

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We can either reject or fail to reject the null hypothesis and draw our conclusion.

Based on the newspaper article's statement, we can assume that the majority of Americans who do not attend college do so for reasons other than financial constraints. To test this claim, we can conduct a hypothesis test to determine if the data provide strong evidence to support this statement.

Let's set up the null and alternative hypotheses for this test. Our null hypothesis (H0) is that the proportion of Americans who do not attend college due to financial constraints is equal to or greater than 50%. Our alternative hypothesis (Ha) is that the proportion of Americans who do not attend college due to financial constraints is less than 50%.

Next, we need to collect data and calculate the point estimate for the proportion of Americans who do not attend college due to financial constraints. Once we have our point estimate, we can calculate the test statistic and p-value.

If the p-value is less than the significance level (typically 0.05), we can reject the null hypothesis and conclude that there is strong evidence to support the newspaper article's statement. However, if the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the statement.

Based on the results, we can either reject or fail to reject the null hypothesis and draw our conclusion.

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Answer: b

Step-by-step explanation: b

The equation given, r = 8 sec(θ), is an equation in polar coordinates. To convert it to a cartesian equation, we can use the following relationships:

x = r cos(θ)

y = r sin(θ)

Substituting r = 8 sec(θ) into these equations, we get:

x = 8 sec(θ) cos(θ)

y = 8 sec(θ) sin(θ)

Next, we can use the identity sec²(θ) = 1/cos²(θ) to write sec(θ) in terms of cos(θ):

sec(θ) = 1/cos(θ)

Substituting this into our equations for x and y, we get:

x = 8/cos(θ)

y = 8 tan(θ)

Finally, we can eliminate θ by squaring both sides of the equation sec²(θ) = 1/cos²(θ) and using the trigonometric identity 1 + tan²(θ) = sec²(θ). This gives us:

cos²(θ) = 1/(1 + tan²(θ))

Substituting this into our equations for x and y, we get:

x = 8 cos(θ) / sqrt(1 + tan²(θ))

y = 8 sin(θ) / sqrt(1 + tan²(θ))

Simplifying further, we can write:

x² / 64 - y² / 64 = 1

This is the cartesian equation for the curve defined by r = 8 sec(θ). It is the equation of a hyperbola centered at the origin, with vertices at (8, 0) and (-8, 0), and asymptotes given by the lines y = ±x/8.

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The probability of drawing a seven and then a four when randomly drawing two cards without replacement is 0.0045 or approximately 0.45%.

The probability of drawing a seven and then a four when randomly drawing two cards without replacement can be calculated using the following steps:

First, we need to determine the total number of possible outcomes when drawing two cards from a standard deck of 52 cards without replacement. This can be found using the combination formula:

C(52,2) = 52! / (2! * (52-2)!) = 1,326

Next, we need to determine the number of favorable outcomes where we draw a seven and then a four.

There are four sevens and four fours in a deck of 52 cards, so the probability of drawing a seven on the first draw is 4/52. Since we are not replacing the card, there are now 51 cards left in the deck, and three of them are fours. Therefore, the probability of drawing a four on the second draw is 3/51.

The probability of drawing a seven and then a four is the product of the probabilities of drawing a seven on the first draw and a four on the second draw:

P(seven and then four) = (4/52) * (3/51) = 0.0045 or approximately 0.45%.

Therefore, the probability of drawing a seven and then a four when without replacement is 0.0045 or approximately 0.45%.

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according to question So, y in terms of x is:

y = -3 / (124)(5x - 5x - 3)

Assuming the equation is 5x – 5x – 3 = (124)(5y), the left-hand side simplifies to:

0 - 3 = -3

Therefore, we have:

-3 = (124)(5y)

Solving for y, we get:

y = -3 / (124)(5)

y = -3 / 620

what is equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and logarithms. Equations can be linear or nonlinear, and they can have one or multiple variables. The solutions to an equation are the values of the variables that make the equation true.

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We used the formula for the expected value of a discrete random variable to compute E(X) for the random variable representing the product of two fair 10-sided dice. We found that the probability mass function of X is uniform over the set {1,2,...,100}, and used this fact to compute the expected value as the average value of the set, which turns out to be 50.5.

To find the expected value of the product of two 10-sided dice, we can use the formula for the expected value of a discrete random variable: E(X) = Σx P(X=x), where x ranges over all possible values of X and P(X=x) is the probability that X takes the value x.

Let's first consider the possible values of X. The minimum value is 1 (when both dice show 1), and the maximum value is 100 (when both dice show 10).

For any value x between 1 and 100, there is exactly one way to obtain that value as the product of two numbers between 1 and 10 inclusive. Therefore, the probability mass function of X is uniform over the set {1,2,...,100}.

Using the formula for the expected value, we have E(X) = Σx P(X=x) = (1/100)Σx=1 to 100 x = (1/100)(5050) = 50.5. Therefore, we expect the product of two fair 10-sided dice to be slightly greater than 50 on average.

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The angle the ramp makes with the ground is approximately 32.1 degrees.

To determine the angle that the ramp makes with the ground, we can use trigonometry.

We can consider the ramp as the hypotenuse of a right triangle, where the vertical height represents the distance from the top of the ramp to the ground (10.8 inches), and the horizontal length represents the length of the ramp (18.6 inches).

Calculate the tangent of the angle:

Tangent (θ) = Opposite / Adjacent

Tangent (θ) = 10.8 / 18.6

Find the inverse tangent to get the angle:

θ = arctan (10.8 / 18.6)

Using a scientific calculator or trigonometric table, we find that arctan (10.8 / 18.6) is approximately 0.5774 radians.

Convert radians to degrees:

To express the angle in degrees, we multiply the radians value by (180 / π):

θ (degrees) = 0.5774 * (180 / π)

Calculating this, we find that the angle is approximately 32.1 degrees. Therefore, the ramp makes an angle of approximately 32.1 degrees with the ground.

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The columns of A' are the coordinates of T(1, 0) and T(0, 1) relative to the basis B'

To find the matrix A' for T relative to the basis B', we need to apply T to each vector in the basis and express the result as a linear combination of the basis vectors.

Let's first apply T to the first basis vector (1, -2):

T(1, -2) = (1 - (-2), -2 - 3(1)) = (3, -5)

To express this vector as a linear combination of the basis vectors, we need to solve the equation:

(3, -5) = a(1, -2) + b(0, 3)

This gives us the system of equations:

3 = a

-5 = -2a + 3b

Solving for a and b, we get:

a = 3

b = -1

Therefore, (3, -5) = 3(1, -2) - (0, 3).

Next, we apply T to the second basis vector (0, 3):

T(0, 3) = (0 - 3, 3 - 3(0)) = (-3, 3)

To express this vector as a linear combination of the basis vectors, we need to solve the equation:

(-3, 3) = a(1, -2) + b(0, 3)

This gives us the system of equations:

-3 = a

3 = -2a + 3b

Solving for a and b, we get:

a = -3

b = 2

Therefore, (-3, 3) = -3(1, -2) + 2(0, 3).

Putting it all together, the matrix A' for T relative to the basis B' is:

A' = [[3, -3], [-1, 2]]

Note that the columns of A' are the coordinates of T(1, 0) and T(0, 1) relative to the basis B'

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The average value of y for the part of the curve [tex]y = 4x - x^3[/tex] in the first quadrant is 2.

To find the average value of y for the part of the curve [tex]y = 4x - x^3[/tex] in the first quadrant, we need to calculate the definite integral of y with respect to x over the interval where x ranges from 0 to the x-coordinate of the point where the curve intersects the x-axis.

The curve [tex]y = 4x - x^3[/tex] intersects the x-axis at two points, (0, 0) and (2, 0). Therefore, the interval of interest for calculating the average value of y in the first quadrant is from x = 0 to x = 2.

To find the average value of y, we can use the following formula:

Average value of y = (1 / (b - a)) * ∫[a, b] y dx

In this case, a = 0 and b = 2, and y = 4x - x^3.

Therefore, the average value of y in the first quadrant can be calculated as follows:

Average value of y = (1 / (2 - 0)) * ∫[tex][0, 2] (4x - x^3) dx[/tex]

Simplifying the integral:

Average value of

[tex]y = (1 / 2) * \int\limits[0, 2] (4x - x^3) dx[/tex]

[tex]= (1 / 2) * [2x^2 - (1/4)x^4]\ evaluated \ from \ 0 \ to \ 2\\= (1 / 2) * [(2(2)^2 - (1/4)(2)^4) - (2(0)^2 - (1/4)(0)^4)]\\= (1 / 2) * [(8 - 4) - (0 - 0)]= (1 / 2) * [4]= 2[/tex]

Therefore, the average value of y for the part of the curve [tex]y = 4x - x^3[/tex] in the first quadrant is 2.

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The trapezoid with bases of 16 feet and 10 feet and a height of 3 feet has an area of 39 ft².

The formula for the area of a trapezoid is:

A = (1/2) × (Base 1 + Base 2) × height

Substituting the given values, we get ;

A = (1/2) × (16 + 10) × 3

Use the arithmetic operation of addition;

A = (1/2) × 26 × 3

A =  39 ft²

Therefore, the area of the trapezoid is 39 ft²

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the value of the iterated integral is (π/8) (2 - e^(-16)).

We have the iterated integral:

∫[0,4] ∫[0,√(16-x^2)] e^(-x^2-y^2) dy dx

To convert this to polar coordinates, we need to express x and y in terms of r and θ.

We have:

x = r cos(θ)

y = r sin(θ)

We also need to express the differential element dA in terms of polar coordinates. We have:

dA = r dr dθ

Substituting these expressions into the given integral, we get:

∫[0,π/2] ∫[0,4] e^(-r^2) r dr dθ

The limits of integration for θ are 0 to π/2 because the region lies in the first and second quadrants.

We can evaluate this integral using the fact that the integral of e^(-r^2) is √π/2:

∫[0,π/2] ∫[0,4] e^(-r^2) r dr dθ

= ∫[0,π/2] [-1/2 e^(-r^2)] [0,4] dθ

= ∫[0,π/2] (1/2 - 1/2 e^(-16)) dθ

= π/4 - π/8 (1 - e^(-16))

= (π/8) (2 - e^(-16))

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There is not enough evidence to conclude that one of the miles has a hill.

It should be noted that to test the claim that it takes the same time to ride each of the miles, we can use a one-way ANOVA (analysis of variance) test.

First, we need to calculate the mean time for each mile:

Mile 1: (3*60 + 14 + 23 + 24 + 22 + 21)/5 = 3 minutes 24.8 seconds

Mile 2: (3*60 + 19 + 23 + 20 + 17 + 20)/5 = 3 minutes 19.8 seconds

Mile 3: (3*60 + 33 + 31 + 29 + 31 + 28)/5 = 3 minutes 30.4 seconds

The degrees of freedom for the between-groups and within-groups variations are dfB = 2 and dfW = 12, respectively.

Using a significance level of 0.05 and looking at an F-distribution table for dfB = 2 and dfW = 12, we find that the critical F-value is 3.89. Since the calculated F-statistic (1.93) is less than the critical F-value (3.89), we fail to reject the null hypothesis that the mean times for each mile are equal.

Therefore, there is not enough evidence to conclude that one of the miles has a hill.

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A certain statistics instructor participates in triathlons. The accompanying table lists times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3-mile loop. Use a 0.05 significance level to test the claim that it takes the same time to ride each of the miles. Does one of the miles appear to have a hill?

Mile 1 3:14 3:23 3:24 3:22 3:21

Mile 2 3:19 3:23 3:20 3:17 3:20

Mile 3 3:33 3:31 3:29 3:31 3:28

To simplify the given Boolean expression using DeMorgan's theorems, we start by applying the first theorem which states that the complement of a sum is equal to the product of complements.

Let's simplify step by step:

F(A,B,C) = ((A + B').CD)'

Applying the complement on the outermost expression:

F(A,B,C) = ((A + B').CD)'

Using DeMorgan's theorem on the inner expression (A + B'):

F(A,B,C) = (A'.(B'.CD))'

Now, applying the complement on the innermost expression (B'.CD):

F(A,B,C) = (A'.(B'.CD))'

Using DeMorgan's theorem again on (B'.CD):

F(A,B,C) = (A'.B + A'.C' + D')

Thus, the simplified Boolean expression using DeMorgan's theorems is F(A,B,C) = A'.B + A'.C' + D'. This expression is the minimum, simplest form of the given Boolean expression.

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The probability P(T < 1.35) for a t-distribution with 14 degrees of freedom is approximately 0.905.

To find this probability, you can follow these steps:

Step 1: Identify the given parameters. In this case, the t-distribution has 14 degrees of freedom (df = 14) and we want to find the probability for T < 1.35.

Step 2: Use a t-distribution table or calculator to find the corresponding probability. For this example, you can find a t-distribution table online or in a statistics textbook. Locate the row corresponding to 14 degrees of freedom and look for the column with a t-value closest to 1.35. The intersection of the row and column will provide the probability value.

Step 3: Alternatively, you can use a statistical software or online calculator that allows you to input the degrees of freedom and the t-value to compute the probability. Most calculators will provide a result for P(T < 1.35) directly.

By following these steps, you should find that the probability P(T < 1.35) for a t-distribution with 14 degrees of freedom is approximately 0.905.

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Theresa would need 16/5 cups or 3 1/5 cups of sugar to make 2 4/5 Batches of cookies.

To find the total amount of sugar required for 2 4/5 batches of cookies, we need to multiply the amount of sugar required for one batch by 2 4/5.

First, we need to convert the mixed number 1 1/3 into an improper fraction:

1 1/3 = 4/3

Now, we can multiply the amount of sugar required for one batch by 2 4/5:

2 4/5 × 4/3 cups = 12/5 × 4/3 cups = 48/15 cups

To simplify this fraction, we can divide both the numerator and denominator by 3:

48/15 cups = 16/5 cups

Therefore, Theresa would need 16/5 cups or 3 1/5 cups of sugar to make 2 4/5 batches of cookies.

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Answer:

[tex]\text{m}\angle L = 65\°[/tex]

[tex]\text{m}\angle M = 65\°[/tex]

[tex]\text{m}\angle N = 50\°[/tex]

Step-by-step explanation:

First, we can solve for the variable a by using two pieces of knowledge:

Using this knowledge, we can deduce that [tex]\text{m}\angle L = \text{m} \angle M = 2a + 40[/tex], and we can form the following equation to solve for a:

[tex]2(2a + 40) + 4a = 180[/tex]

↓ applying the distributive property ... [tex]a(b + c) = ab + ac[/tex]

[tex]4a + 80 + 4a = 180[/tex]

↓ combining like terms

[tex]8a + 80 = 180[/tex]

↓ subtracting 80 from both sides

[tex]8a = 100[/tex]

↓ dividing both sides by 8

[tex]\boxed{a = 12.5}[/tex]

Now that we know what a is, we can solve for the measure of each angle in the triangle.

[tex]\text{m}\angle L = 2a + 40[/tex]

[tex]\text{m}\angle L = 2(12.5) + 40[/tex]

[tex]\text{m}\angle L = 25 + 40[/tex]

[tex]\boxed{\text{m}\angle L = 65\°}[/tex]

____________________

[tex]\text{m}\angle M = \text{m}\angle L = 65\°[/tex]

[tex]\boxed{\text{m}\angle M = 65\°}[/tex]

____________________

[tex]\text{m}\angle N = 4a[/tex]

[tex]\text{m}\angle N = 4(12.5)[/tex]

[tex]\boxed{\text{m}\angle N = 50\°}[/tex]

Answer:

V = π(18^2)(9) = 9,160.88 ft^3

V = 3.14(18^2)(9) = 9,156.24 ft^3

The city's mean annual rainfall is 40.5 inches.To find the mean annual rainfall for the city, we can use the standard normal distribution and the given probability.

We know that the standard deviation (σ) of the city's yearly rainfall totals is 1.8 inches.

We are given the probability P(Z ≥ 1.5) = 0.668, where Z is a standard normal random variable.

Using the standard normal distribution table or calculator, we can find the corresponding Z-score for the given probability:

Z-score = 1.5

Now, we can use the Z-score formula to calculate the mean (μ) of the annual rainfall:

Z = (X - μ) / σ

Plugging in the values we have:

1.5 = (43.2 - μ) / 1.8

Solving for μ:

43.2 - μ = 1.5 * 1.8

43.2 - μ = 2.7

μ = 43.2 - 2.7

μ = 40.5

Therefore, the city's mean annual rainfall is 40.5 inches.

Learn more about Standard Normal Distribution here:

https://brainly.com/question/2527973

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