The slope at [1,pi/2] from -8x^3/siny

The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.573.

Given that the time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds.

We know that the exponential probability distribution function is given by

f(x) = λ e^(-λx)

Where λ is the rate parameter of the distribution and is equal to 1/mean in this case. So, λ = 1/14.

Now, we need to find the probability that the arrival time between vehicles is 12 seconds or less. Mathematically, we can express this as:

P(X ≤ 12) = [tex]\int\limits^{12}_0[/tex] λ e^(-λx) dx

Integrating this expression, we get:

P(X ≤ 12) = [-e^(-λx)]_[0,12] = -e^(-λ12) + e^(-λ0)

Since e^(-λ×0) is equal to 1, we have:

P(X ≤ 12) = 1 - e^(-λ×12)

Substituting the value of λ, we get:

P(X ≤ 12) = 1 - e^(-12/14)

P(X ≤ 12) ≈ 0.573

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The given question is incomplete, the complete question is:

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 14 seconds . What is the probability that the arrival time between vehicles is 12 seconds or less?

Therefore, the can of beans that is the best deal is option b, which has the lowest price per unit volume.

Volume is a measure of the amount of space occupied by an object or a substance. It is often measured in cubic units such as cubic centimeters, cubic inches, or cubic meters. The formula for finding the volume of different objects may vary based on their shape and size, but it typically involves measuring the length, width, and height of the object and multiplying them together.

Here,

To determine which can of beans is the better deal, we need to compare their volumes and prices per unit volume.

The volume of the small can of beans is:

V₁ = πr₁²h₁

= π*(1)²*(3)

= 3π

The price per unit volume of the small can is:

P₁ = $1.49 / 3π

≈ $0.157 per cubic inch

For the other cans of beans, we can calculate their volumes and prices per unit volume:

a. V₂ = πr₂²h₂

= π*(3)²*(9)

= 81π

P₂ = $39.95 / 81π

≈ $0.155 per cubic inch

b. V₃ = πr₃²h₃

= π*(2)²*(3)

= 12π

P₃ = $5.96 / 12π

≈ $0.132 per cubic inch

c. V₄ = πr₄²h₄

= π*(3)²*(3)

=27π

P₄ = $13.41 / 27π

≈ $0.165 per cubic inch

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The true statements are:

A. The graph of function f(x) = -√(√(√x)) will look like the graph of f(x)=√x but will reflect it about the x-axis and shrink it vertically by a factor of 1/2.

D. f(x) = √x has the same domain but a different range as f(x) = -√x.

A graph is a visual representation of a mathematical relationship or data. It consists of points or vertices connected by edges or lines to show the relationship between them.

A function is a mathematical concept that relates an input value to an output value, such that for each input, there is exactly one output. It can be represented as a set of ordered pairs, a graph, or an equation.

According to the given information:

A. The statement A is true. The graph of function f(x) = -√(√(√x)) is a transformation of the function f(x) = √x. The negative sign outside the square roots will reflect the graph of f(x) = √x about the x-axis, and the multiple square roots will shrink the graph vertically by a factor of 1/2.

B. The statement B is false. The graph of function f(x) = -√(√x) is also a transformation of the function f(x) = √x, but it will only reflect the graph about the x-axis. It will not shrink the graph vertically.

C. The statement C is false. The graph of function |f(x)| = √(√(√x)) is not a transformation of f(x) = √x. The absolute value bars will make the graph symmetric about the y-axis, but it will not shrink it horizontally.

D. The statement is true. The graph of function f(x) = √x and f(x) = sqrt(x) are equivalent, and have the same domain (all non-negative real numbers) but different ranges. The range of f(x) = √x is [0, infinity) while the range of f(x) = sqrt(x) is (0, infinity).

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The probability of obtaining a grid that does not have a 2 × 2 red square is 127/128 and the value of (p + q + 1) / 310  is 0.82.

Total number of outcomes = [tex]2^9[/tex] = 512

We will subtract the outcomes of obtaining a grid that does not have a

2 × 2 red squares from the total outcomes.

Favorable outcomes = Total outcomes - outcomes having [tex]2[/tex] × [tex]2[/tex] red squares

                                   = [tex]2 ^3 - 4[/tex]

                                    = 508

So favorable outcomes are 508.

Probability calculates the chances of experiments occurring. It is obtained by the ratio between favorable outcomes and total outcomes. It is basically how likely something is to happen.

Probability = Favorable outcomes / Total no. of outcomes

                  = 508 / 512

                  = p/q

                 = 127/128

So, the probability of obtaining a grid that does not have a 2 × 2 red square is 127/128.

        Now, the value of (p + q + 1)/310

     =  (127 + 128 + 1)/310

   = 256/310

= 0.82

Therefore, the value of (p + q + 1) / 310 is 0.82.

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The complete question is -

"Each unit square of a 3 * 3 square grid is to be colored either blue or red for each square, either color is equally likely. The probability of obtaining a grid that does not have a 2 * 2 red square is CHCF(p,q) is 1). Find this probability and then find the value of  (p + q + 1) / 310 ?"

The speed of boat is 5/6 meter per second and height of boat is 50[tex]\sqrt{3}[/tex] meter.

An angle is a shape created by two rays or lines that meet at the same terminal. The Latin word "angulus" (which means "corner") is where the term "angle" first appeared. The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "" is used to denote angles. The Greek letter,,, etc. can be used to represent the angle between the two beams.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

After solving the figure:

The speed of boat is 5/6 meter per second and height of boat is 50[tex]\sqrt{3}[/tex] meter.

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The speed of the boat from point C to point B is approximately 10.82 meters per second.

What is speed ?

Speed is a measure of how fast an object is moving. It is the rate at which an object covers distance.

We can use trigonometry to solve for h and the speed of the boat. Let's start with h:

From the right triangle CLB, we have:

tan 30° = h / CB

where CB is the distance between points C and B, which is given as 50 meters. Solving for h, we get:

h = CB * tan 30° = 50 * tan 30° ≈ 28.87 meters

So the height of the lighthouse is approximately 28.87 meters.

Now let's find the speed of the boat. We know that the boat travels from point C to point B in 1 minute, which is equivalent to 60 seconds. Let's define the speed of the boat as v, in meters per second. Then we have:

v = CB / t

where t is the time it takes for the boat to travel from point C to point B. We can find t using the distance formula:

[tex]CB = \sqrt{(x_B - x_C)^2 + (y_B - y_C)^2[/tex]

where x and y are the coordinates of each point. From the diagram, we can see that:

[tex]x_C = 0[/tex]

[tex]y_C = 0[/tex]

[tex]x_B = BL * cos \theta[/tex]

[tex]y_B = BL * sin \theta[/tex]

where BL is the distance from point B to the foot of the lighthouse, which is equal to h / tan θ. Therefore:

CB [tex]= \sqrt{((BL * cos \theta)^2 + (BL * sin \theta)^2)[/tex]

     [tex]= \sqrt{(BL^2 * (cos^2 \theta + sin^2 \theta))[/tex]

     [tex]= BL = h / tan \theta[/tex]

Substituting the values we have found, we get:

v = CB / t = (h / tan θ) / 60 ≈ 10.82 meters per second

Therefore, the speed of the boat from point C to point B is approximately 10.82 meters per second.

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The variance of the number of green voters in the sample is 160.

What is variance?

In statistics, variance is a measure of the spread or variability of a set of data. It measures how much the values in a dataset differ from the mean or average value. Specifically, variance is the average of the squared differences from the mean.

We can use the binomial distribution to model the number of green voters in the sample, where the probability of success (voter being green) is p = 0.2 and the number of trials (voters in the sample) is n = 1000.

The expectation or mean of the number of green voters in the sample is given by the formula:

E(X) = np

where X is the random variable representing the number of green voters in the sample. Substituting the values, we get:

E(X) = 1000 * 0.2 = 200

So we expect to see about 200 green voters in the sample.

The variance of the number of green voters in the sample is given by the formula:

Var(X) = np(1 - p)

Substituting the values, we get:

Var(X) = 1000 * 0.2 * (1 - 0.2) = 160

So the variance of the number of green voters in the sample is 160.

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Check the picture below.

btw that picture above is misleading, whenever is 3 longer than 7?  and 2 longer than 7? =)

so let's just get the area of the trapezoidal face and multiply that by the depth of 7.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=2\\ b=4\\ h=3 \end{cases}\implies A=\cfrac{3(2+4)}{2}\implies A=9 \\\\[-0.35em] ~\dotfill\\\\ (9)(7)\implies \text{\LARGE 56}\qquad \impliedby volume[/tex]

A hexagonal pyramid has seven vertices.

A hexagonal pyramid contains 12 edges.

A hexagonal pyramid has seven faces.

A hexagonal pyramid is a type of pyramid that exists. A hexagonal pyramid has a hexagonal foundation and isosceles triangles as the faces that join the pyramid together at the top.

A hexagonal pyramid is a 3D pyramid with a hexagonal foundation and sides or faces in the shape of isosceles triangles that form the hexagonal pyramid at the apex or top of the pyramid. A hexagonal pyramid has six sides and six isosceles triangular lateral faces. Heptahedron is another name for a hexagonal pyramid. A hexagonal pyramid has seven faces, twelve edges, and seven vertices. For your convenience, an image of a hexagonal pyramid is provided below.

A hexagonal pyramid has seven vertices in toa

\x linking the triangle edges to the primary vertex and six base edges.

A hexagonal pyramid has seven faces, one for each side of the triangle, and one base.

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a). The difference between the two population means is estimated at a location to be 2.7.

b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.

c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).

d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.

Using the equation [tex]x_1-x_2[/tex], we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample

[tex]1(x_1=22.8)[/tex] and deducting it from the mean of Sample [tex]2(x_2=20.1)[/tex].

With the use of the equation [tex]df=n_1+n_2-2[/tex], it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because [tex]n_1[/tex] = 20 and [tex]n_2[/tex] = 30.

We must apply the formula to determine the margin of error at 95% confidence [tex]ME=t*\sqrt[s]{n}[/tex].

The sample standard deviation (s) is equal to the average of [tex]s_1[/tex] and [tex]s_2[/tex] (3.4), the t value with 95% confidence is 1.67, and n is equal to the

average of [tex]n_1[/tex] and [tex]n_2[/tex] (25). When these values are entered into the formula, we get [tex]ME=1.67*\sqrt[3.4]{25}=1.7[/tex].

Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means [tex]CI=x_1-x_2+/-ME[/tex].

The confidence interval's bottom limit in this instance is [tex]x_1-x_2-ME2.7-1.7=0.0[/tex] and the upper limit is [tex]x_1+x_2+ME=2.7+1.7=5.4[/tex].

As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.

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Answer: x= 7191.509 ft

Step-by-step explanation:

Sin9/1 = 1125/x

X/1 = 1125/sin9

Answer: 18 square feet im pretty sure

Step-by-step explanation:

Answer:  B)  216

Step-by-step explanation:

Answer: 6 units

Step-by-step explanation:

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

In this case, we know that the radius (r) of the cylinder is 5, and the volume (V) is 150π. Substituting these values into the formula, we get:

150π = π(5²)h

Simplifying the equation, we get:

150 = 25h

Dividing both sides by 25, we get:

h = 6

Therefore, the height of the cylinder is 6 units.

Answer:

To the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

A = the final amount (in this case, $82,000)

P = the principal (the initial investment, in this case, $64,000)

r = the interest rate (what we're trying to find)

n = the number of times the interest is compounded per year (in this case, 4, since it's compounded quarterly)

t = the number of years (in this case, 5)

Plugging in the values we know and solving for r, we get:

$82,000 = $64,000(1 + r/4)^(4*5)

$82,000/$64,000 = (1 + r/4)^20

1.28125 = (1 + r/4)^20

Taking the 20th root of both sides, we get:

(1.28125)^(1/20) = 1 + r/4

0.0167 = r/4

r = 0.0668 (rounded to four decimal places)

Therefore, to the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.

Sev needs to run 9 miles as per the below calculations to complete his target.

The target that Sev needs to achieve is 18 miles in a week. A week has 7 days. Sev is already done running for 5 days.
Day 1: 1.4 miles

Day 2: 1.4 miles

Day 3: 1.4 miles

Day 4: 2.4 miles

Day 5: 2.4 miles

Thus, Sev has run for 1.4*3 = 4.2 miles in the first 3 days.

Sev has run for 2.4*2 = 4.8 miles in the last 2 days.

So far, she has run 4.2 + 4.8 = 9 miles. Since her goal is to run 18 miles, she needs to run an additional: 18 - 9 = 9 miles to meet her goal.

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Answer:

17

Step-by-step explanation:

The midpoint theorem states that “The line segment in a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

therefore 2(x+5) = 3x-7

distribute

2x+10 = 3x-7

subtract 2x from both sides

2x+10 -2x = 3x-7 -2x

x-7 = 10

add 7 to both sides

x- 7 +7 = 10 + 7

x = 17

Answer:

Step-by-step explanation:

I think you are in 11th grade

we can use the theorem midpoint theorem.

as the mid-point theorem,

2(x+5)=3x-7

2x+10=3x-7

x=17

I really love your profile picture, is it real?

Answer:

∠A=∠P, AC = PR

Step-by-step explanation:

Because triangles ABC and PQR are congruent their corresponding angles and sides are congruent.

So

∠A=∠P

∠B=∠Q

∠C=∠R

Also

Side AB = Side PQ

Side BC = Side QR

Side AC = Side PR

The exact amount of copper foil covering the steeple is 720√3 square meters.

The lateral area of the prism is given as 2400 m². We know that the lateral area of a prism is given by the formula:

Lateral area = perimeter of base x height of the prism

Let's denote the side length of the hexagonal base by s. The perimeter of the base is then 6s, and the height of the prism is 100 m. Using the given lateral area, we can solve for s:

2400 = 6s x 100

s = 4 x √15

The base area of the steeple is the same as the base area of the prism, which is given by:

Base area = (3 x √3 x s²) / 2

The steeple is composed of equilateral triangles, so each face of the steeple is an equilateral triangle with side lengths. The area of an equilateral triangle is given by the formula:

Area = (√3 * s²) / 4

The total surface area of the steeple is the sum of the areas of its faces. There are six faces, so the total surface area is:

Total surface area = 6 x Area

Total surface area = 6 x (√3 x s²) / 4

Total surface area = (3 x √3 x s²) / 2

Substituting the value of s we found earlier, we get:

Total surface area = (3 x √3 x (4 x √15)²) / 2

Total surface area = 720 x √3

Therefore, the exact amount of copper foil covering the steeple is 720√3 square meters.

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Answer:

396 pi mm²

Step-by-step explanation:

The surface area of a cylinder:

The total surface area (A) of a cylinder is calculated by adding the areas of the two bases and the lateral surface area.

A = 2πr^2 + 2πrh

Given:

The surface area of the first cylinder (A1) = 594π mm^2

Height of the first cylinder (h1) = 24 mm

Height of the second cylinder (h2) = 16 mm

We can use the property of similarity and set up the proportion:

A1 / A2 = (h1 / h2)^2

Plugging in the given values, we get:

594π / A2 = (24 / 16)^2

Simplifying, we get:

594π / A2 = 3/2)^2

594π / A2 = 9/4

Cross-multiplying, we get:

A2 = (594π * 4) / 9

A2 = 264π mm^2

So, the correct surface area of the second cylinder is 264π mm^2.

When working with mu, sample size requirement is an important consideration. Mu, also known as the population mean, represents the average value of a variable across the entire population.

In order to estimate mu with a reasonable degree of accuracy, it is necessary to take a representative sample from the population.

The sample size required to accurately estimate mu will depend on a variety of factors, including the variability of the population, the desired level of precision, and the level of confidence required.
One of the most important factors influencing sample size requirements is the variability of the population.

The population is highly variable, larger sample sizes are required to obtain accurate estimates of mu.

This is because a larger sample size reduces the impact of random sampling error, allowing the true population to mean to be estimated with greater accuracy.

Similarly, when a high level of precision is required, larger sample sizes are necessary to ensure that the estimate of mu is sufficiently precise.
Another important consideration when determining sample size requirements is the desired level of confidence.

In order to estimate mu with a certain level of confidence, it is necessary to choose a sample size that provides the required level of precision.

If a researcher wants to estimate mu with 95% confidence, they may choose a sample size that provides an estimate with a margin of error of 5%.
When working with mu, sample size requirement is a critical factor in obtaining accurate estimates of the population mean.

The sample size required will depend on the variability of the population, the desired level of precision, and the level of confidence required.

By carefully considering these factors, researchers can select an appropriate sample size to ensure that their estimates of mu are reliable and meaningful.

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The time required to ring up the customer with 11 items is; 20 seconds

A linear equation is defined as an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

We are given the linear equation:

t = p + 9

Where;

p is the variable that represents the number of items being purchased

t reprensts the time required to ring up the customer.

Thus:

When p = 11 items, we have:

t = 11 + 9

t = 20 seconds

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The cost to charge an electric car's home battery charger is $3.355 (to the nearest penny).

The cost to charge an electric car's home battery charger can be calculated using the following equation:

Cost = (kW x hours x rate)

Where kW stands for kilowatts, hrs stands for hours and rate stands for the rate per kilowatt-hour.

In this case, we have: kW = 6.1, hrs = 11 and rate = $0.05

Therefore, Cost = (6.1 x 11 x 0.05) = $3.355

Therefore, it will cost $3.35(to the nearest penny) to charge the car's battery.

To calculate this cost, we first multiply the kW (6.1) by the hours (11) to get the total kWh used (67.1). We then multiply this number by the rate ($0.05) to get the total cost of charging the battery ($3.355). This cost is to the nearest penny as we rounded up to the nearest cent when multiplying the kWh by the rate.

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Complete Question:

An  electric car's home battery charger uses 6.1 kilowatts for 11 hours. If electricity costs $0.05 per kilowatt-hour, how much (in dollars, to the nearest penny) does it cost to charge the car's battery? Use  exact numbers; do not estimate.

The total revenue between the two companies is $3,200

To find the Nash Equilibrium, we need to look for a situation where neither firm has an incentive to change their strategy. This occurs when both firms are charging a price of $8 per month and each has 200 customers, resulting in total revenue of $3,200.

At this price and quantity, neither firm can increase their revenue by changing their strategy. If Netflix were to increase its price above $8, some of its customers would switch to Flixbuster, and Netflix's revenue would decrease. Similarly, if Flixbuster were to decrease its price below $8, it would gain customers from Netflix, but its revenue would still decrease.

Therefore, the Nash Equilibrium in this scenario is a price of $8 and 200 customers for each firm, resulting in total revenue of $3,200 between the two companies.

In mathematical terms, the Nash Equilibrium is a solution to the following system of equations:

Qn = 300 - P

Qf = 300 - P

TRn = P(Qn)

TRf = P(Qf)

where Qn and Qf are the quantities demanded by Netflix and Flixbuster, respectively, P is the price, and TRn and TRf are the total revenues earned by Netflix and Flixbuster, respectively. Solving this system of equations, we get P = 8 and Qn = Qf = 200, which results in total revenue of $3,200.

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Complete Question:

The following table shows a small community's demand for monthly subscriptions to a streaming movie service. Assume that only two firms (Nextflix and Flixbuster) sell in this market, that each firm offers the same quality of service and movie selection, and that each firm's marginal cost is constant and equal to 0 (zero) due to excess capacity.

Price/Month    Number of Total (P) Customers (Q)        Revenue/Month(TR)

$10                                                     0                                                         $0

9                                                      100                                                     900

8                                                      200                                                1,600

7                                                      300                                               2,100

If the two companies are behaving in each best interest, and the market is able to reach a Nash Equilibrium. What is the total revenue between the two companies?

Answer:

4

Step-by-step explanation:

4-0=4

Answer:

4 left

Step-by-step explanation:

then you have 4 apples

Sam will have to borrow $7840.

If Sam puts 20% down on a car that costs $9800, the down payment would be 20% of $9800 which is $1960.

The amount he will have to borrow is the difference between the cost of the car and the down payment. So, $9800 - $1960 = $7840.

This calculation can be done by first finding the percentage of the total cost that is required as a down payment and then subtracting that amount from the total cost to find the remaining amount that needs to be borrowed.

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There are 36 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

To find the number of ways the letters d, i, g, i, t can be arranged so that the two i's are not next to each other, follow these steps:
Consider the four non-i letters: d, g, t.

There are 3! (3 factorial) ways to arrange these letters, which is equal to 3 x 2 x 1 = 6 ways.

Since we want to prevent the two i's from being next to each other, we can think of placing them in the "gaps" between the non-i letters.

There are 4 possible gaps for the i's to be placed: (i) d (i) g (i) t (i).
Since there are two i's, we need to choose 2 of the 4 gaps to place them in.

This can be done in 4C2 ways (combination), which is equal to 4! / (2! x (4-2)!) = 6 ways.
Multiply the number of ways to arrange the non-i letters (step 1) with the number of ways to place the i's (step 3): 6 x 6 = 36.

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There are 72 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

To arrange the letters d, g, i, t, and i so that the two i's are not next to each other, follow these steps:

Step 1: Treat the two i's as one entity for now (denoted as [i]). So, we have 4 entities: d, g, t, and [i].
Step 2: Arrange these 4 entities (d, g, t, and [i]) in any order. There are 4! (4 factorial) ways to do this, which is 4 x 3 x 2 x 1 = 24 ways.
Step 3: Now, we need to separate the two i's. There are 3 spaces between the other letters (d, g, and t) where we can place the second i.
For example: if the arrangement is d-[i]-g-t, the second i can be placed in any of the three spaces indicated by the dashes.
Step 4: For each of the 24 arrangements from Step 2, there are 3 possible ways to place the second i. So, the total number of arrangements is 24 x 3 = 72 ways.

Thus, there are 72 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

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To find the area under the standard normal curve, we need to use a standard normal distribution table or a calculator with a normal probability distribution function.

(a) To find the area between z = -1.20 and z = 1.20, we can use the symmetry property of the normal distribution curve and find the area to the right of z = -1.20 and double it:

P(-1.20 < z < 1.20) = 2 * P(z < 1.20) - 1 = 2 * 0.8849 - 1 = 0.7698

Therefore, the area under the standard normal curve between z = -1.20 and z = 1.20 is approximately 0.7698.

(b) area between z = 1.23 and z = 1.87

P(1.23 < z < 1.87) = P(z < 1.87) - P(z < 1.23) = 0.9693 - 0.8907 = 0.0786

Therefore, the area under the standard normal curve between z = 1.23 and z = 1.87 is approximately 0.0786.

(c) area between z = -2.35 and z = -0.5

P(-2.35 < z < -0.5) = P(z < -0.5) - P(z < -2.35) = 0.3085 - 0.0094 = 0.2991

Therefore, the area under the standard normal curve between z = -2.35 and z = -0.5 is approximately 0.2991.

(d) To find the area to the right of z = 2.16

P(z > 2.16) = 1 - P(z < 2.16) = 1 - 0.9842 = 0.0158

Therefore, the area under the standard normal curve to the right of z = 2.16 is approximately 0.0158.

(e) To find the area between z = -0.8 and z = 1.53

P(-0.8 < z < 1.53) = P(z < 1.53) - P(z < -0.8) = 0.9370 - 0.2119 = 0.7251

Therefore, the area under the standard normal curve between z = -0.8 and z = 1.53 is approximately 0.7251.

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The value of x is given as follows:

x = 5.

The midsegment of a triangle is the line segment that connects the midpoint of two sides of the triangle. The Triangle Midsegment Theorem states that the midsegment of a triangle is parallel to the third side of the triangle, and its length is equal to half the length of the third side.

Thus the equation relating the lengths in this problem is given as follows:

3x + 11 = 2(x + 8)

3x + 11 = 2x + 16

x = 5.

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The probability that the arrival time between vehicles is 12 seconds or less is approximately 0.6321.

Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1.

The exponential probability distribution with a mean of 12 seconds is given by

f(x) = (1/12) × e^(-x/12)

where x represents the time between arrivals of vehicles.

To find the probability that the arrival time between vehicles is 12 seconds or less, we need to integrate the probability density function from 0 to 12

P(X ≤ 12) = [tex]\int\limits^{12}_0[/tex] f(x)dx

=  [tex]\int\limits^{12}_0[/tex]  (1/12) × e^(-x/12) dx

= [(-e^(-x/12))]_[0,12]

= (-e^(-12/12)) - (-e^(0/12))

= 1 - e^(-1)

≈ 0.6321

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The given question is incomplete, the complete question is:

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. What is the probability that the arrival time between vehicles is 12 seconds or less?

Answer:

1. Mean : 85.6

2. Median : 90

3. Mode : 95

4. Range : 35

Step-by-step explanation:

1. For Mean, you add up all the terms and divide the resulting sum by the number of terms. In this case there were 9 terms that added up to 770, and when you divided that result by 9, the answer was 85.555 repeating. Since the question asks to round to the nearest tenth 85.6 represents the correct mean or average of the class.

2. To find the median, line up all the numbers in order from least to greatest. Like so :

60,75,75,90,90,95,95,95,95

In order to find the median, find the middle term. Since there are 9 terms, the middle term will be the fifth one. In this case, the answer was 90.

3. Mode represents the number that appears the most in a data set. Look at the 9 terms and find the one that appears the most. In this case it is 90.

4. Lastly, to find the range, subtract the lowest value in the data set from the highest one. 95 is the highest and 60 is the lowest. Do [tex]95-60[/tex] and you will get an answer of 35.

Hope this helps!

Answer:

Mean: 85.6

Median: 90

Mode: 95

Range: 35

Step-by-step explanation:

Mean: Add up all the value and divide by the number of values you have.

75 + 95 + 90 + 95 + 60 + 95 + 75 + 95 + 90 = 770

770 / 9 = 85.6

Median: Rearrange in increasing order + look at middle number

60, 75, 75, 90, 90, 95, 95, 95, 95

Mode: Number that shows up the most.

95 shows up 4 times.

Range: Maximum - Minimum.

95 - 60 = 35.

The piecewise function when represented on the graph based on each domain is added as an attachment

Given that

So, we have the following piecewlse function that represents the scenario

f(x) = 12 when 0 < x ≤ 2

     = 19 when 2 < x < 6

     = 25 when 6 ≤ x ≤ 14

Next, we plot the function on the graph based on each domain

See attachment for the graph

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