Alex has 5 1/2 cups of dog food. A serving of dog food is 4/5 cup. How many servings does Alex have?


I need help please

The probability of rolling a sum of 7 or more is 7/12.Therefore, the correct answer is 7/12.

When rolling two dice, the probability of rolling a sum of 7 or more can be calculated by determining the favorable outcomes and dividing by the total possible outcomes.

There are 36 possible outcomes when rolling two dice (6 sides on each die, so 6 x 6 = 36). The combinations that result in a sum of 7 or more are: (1,6), (2,5), (2,6), (3,4), (3,5), (3,6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) There are 21 favorable outcomes.

So the probability is 21/36, which simplifies to 7/12.

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You would be paying $3000 per year for the health insurance plan.

If the premium for the health insurance plan is $125 per paycheck, and you get paid every two weeks, then the cost of the insurance per month is:

2 paychecks x $125 per paycheck = $250 per month

To find the cost per year, we need to multiply the monthly cost by 12:

$250 per month x 12 months = $3,000 per year

hence, you would be paying $3000 per year for the health insurance plan.

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The total number of milliliters of perfume is 1,600 mL. Then the correct option is D.

Two cases of perfume are delivered to a retailer. There are ten bottles in each case. There are 80 millimeters of perfume in each bottle.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The total number of milliliters of perfume is calculated as,

⇒ 2 x 10 x 80

⇒ 1,600 mL

Thus, the correct option is D.

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The degrees of freedom for the error source of variation is:  df = 30 - 3 = 27 To calculate the degrees of freedom for the treatment source of variation in an ANOVA table, we need to use the formula:

df (degrees of freedom) = number of groups - 1

In this case, the number of groups is equal to the number of processes, which is 3. Therefore, the degrees of freedom for the treatment source of variation is:

df = 3 - 1 = 2

This means that we have 2 degrees of freedom for the variation among the three processes. These degrees of freedom will be used to calculate the F-statistic, which is a measure of the variability between the means of the different groups (in this case, the processes).

It's worth noting that the other source of variation in an ANOVA table is the error or residual variation, which represents the variation within the groups or samples. The degrees of freedom for this source of variation are calculated using the formula:

df = total sample size - number of groups

In this case, the total sample size is 30 (the sum of the sample sizes for each process), and the number of groups is 3. Therefore, the degrees of freedom for the error source of variation is:

df = 30 - 3 = 27

This means that we have 27 degrees of freedom for the variation within the samples.

Overall, the ANOVA table provides information about how much of the variation in the data can be explained by the treatment (process) and how much is due to random error. By comparing the F-statistic to a critical value based on the degrees of freedom and a chosen significance level, we can determine whether there is a significant difference between the means of the different processes.

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The statement holds for n=k+1.

By mathematical induction, we have proven that 1·1!+2·2!+···+n·n!=(n+1)!−1 for all positive integers n.

What are integers?

Integers are a set of numbers that include whole numbers (positive, negative, or zero) as well as their opposites.

We will use mathematical induction to prove the statement.

Base case: Let n=1. Then the left-hand side of the equation is 1·1!=1 and the right-hand side is (1+1)!=2!-1=1. Therefore, the statement holds for n=1.

Induction hypothesis: Assume that the statement holds for some positive integer k, i.e., 1·1!+2·2!+···+k·k!=(k+1)!−1.

Inductive step: We need to show that the statement also holds for k+1, i.e., 1·1!+2·2!+···+(k+1)·(k+1)!=(k+2)!−1.

We have:

1·1!+2·2!+···+k·k!+(k+1)·(k+1)!=k!+1·1!+2·2!+···+k·k!+(k+1)·(k+1)!=k!+(k+1)!−1+(k+1)·(k+1)!=k!(k+1+1)+(k+2)!−1=(k+1)!(k+2)−1=(k+2)!−1,

where we have used the induction hypothesis in the second step and simplified in the fourth step.

Therefore, the statement holds for n=k+1.

By mathematical induction, we have proven that 1·1!+2·2!+···+n·n!=(n+1)!−1 for all positive integers n.

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Answer:

31.7925 [tex]in^{3}[/tex]

Step-by-step explanation:

V = 1/3[tex]\pi r^{2}[/tex]h

v = 1/3 (3.14)([tex]2.25^{2}[/tex])(6)    The radius is 1/2 of the diameter

v = 1/3 (3.14)(5.0625)(6)

v = [tex]\frac{95.3775}{3}[/tex]

v = 31.7925

Helping in the name of Jesus.

The sum of the series [tex]\sum_{k=0}^\infty \frac{3}{7^{k} }[/tex]  is 7/2. Therefore, the correct answer is option C. The sum of a geometric series can be found only if the ratio is between -1 and 1.

To find the sum of the series [tex]\sum_{k=0}^\infty \frac{3}{7^{k} }[/tex], we can use the formula for the sum of an infinite geometric series, which is [tex]\frac{a}{1-r}[/tex], where a is the first term and r is the common ratio.

In this case, the first term is [tex]\frac{3}{7^0}=3[/tex] and the common ratio is [tex]\frac{1}{7}[/tex]. Substituting these values into the formula, we get:

[tex]\frac{3}{1-\frac{1}{7}}=\frac{3}{\frac{6}{7}}=\frac{7}{2}[/tex]

Therefore, the sum of the series is c. 7/2. Alternatively, we can also find the sum of the series by adding up the terms:

[tex]\frac{3}{1}+\frac{3}{7}+\frac{3}{49}+\frac{3}{343}+...\approx 4.5[/tex]

This method involves adding up an infinite number of terms, so it may not always be practical or accurate. Using the formula for the sum of an infinite geometric series is a more efficient and reliable method. Therefore, the correct answer is option C.

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Complete Question:

Find the sum of the series:

[tex]\sum_{k=0}^\infty \frac{3}{7^{k} }[/tex]

a. 7/3

b. 21/2

c. 7/2

d. 21/4

e. 7

Based on the given percentiles, we can determine that the value of X represents the resting heart rate at the 25th percentile. To estimate the value of X, we can use the z-score formula for a normal distribution. The z-score corresponding to the 25th percentile is approximately -0.674.

The formula for the z-score is: (X - mean) / standard deviation. We have the mean (70 bpm) and the z-score (-0.674), but we need to estimate the standard deviation. To do this, we can use the 50th and 75th percentiles. The z-score for the 50th percentile is 0, so the mean equals the 50th percentile value (70 bpm). The z-score for the 75th percentile is 0.674, so we can set up the equation:

(80 - 70) / standard deviation = 0.674

10 / standard deviation = 0.674

Standard deviation ≈ 10 / 0.674 ≈ 14.8 bpm

Now we can solve for X:

-0.674 = (X - 70) / 14.8

-0.674 * 14.8 ≈ X - 70

-9.9 ≈ X - 70

X ≈ 60.1

Rounding to the nearest whole number, the value of X is approximately 60 bpm.

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The x-coordinate where the tree will be planted in a circular sidewalk constructed around a park, with a brick pathway through its diameter from (-1,4) to (9,10), is 4, which is the x-coordinate of the center of the circle.

To find the center of the circle, we need to find the midpoint of the diameter. We can use the midpoint formula

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

where (x₁, y₁) and (x₂, y₂) are the endpoints of the diameter.

Using the coordinates (-1, 4) and (9, 10), we get

Midpoint = ((-1 + 9)/2, (4 + 10)/2) = (4, 7)

So the center of the circle is at the point (4, 7).

Since the tree will be planted at the center of the circle, its x-coordinate will be the same as the x-coordinate of the center of the circle, which is 4.

Therefore, the x-coordinate where the tree will be planted is 4.

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--The given question is incomplete, the complete question is given

" a circular sidewalk is being constructed around the perimeter of a local park a brick pathway will be added through the diameter of the circle is from (-1,4) and (9,10) coordinate plane and a tree will be planted in the sidewalk at the center of the circle what is the x coordinate where the tree will be planted "--

a. Concluding that baseball is more popular than soccer based on a poll at a championship event is not valid due to potential sample bias, self-selection bias, limited sample size, and question phrasing.

b. A better method to determine the more popular sport is by conducting a comprehensive, unbiased survey with a random sample of students in a neutral setting, using clear and unbiased questions

For accurate determination of the most favored sport, it is inadequate to derive conclusions based on a poll taken during championship events due to possible biases such as self-selection and limited sample sizes, ambiguous question phrasings, and unrepresentative sampling.

The improved approach to tackle this issue necessitates conducting comprehensive, objective surveys that prioritize random sampling techniques.

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The largest amount of money she could have is: (3 x 25 cents) + (3 x 10 cents) + (2 x 5 cents) = 75 cents + 30 cents + 10 cents = 115 cents or $1.15.

To find the largest amount of money Tasha could have with 8 coins in her pocket, we need to consider the different combinations of coins she could have. Since she has no more than 3 of any coin, the possibilities are:

- 3 quarters, 2 dimes, 1 nickel, 2 pennies = $0.81
- 3 quarters, 2 dimes, 2 nickels, 1 penny = $0.80
- 3 quarters, 2 nickels, 3 pennies = $0.78
- 3 quarters, 1 dime, 3 nickels, 1 penny = $0.76
- 3 quarters, 1 dime, 2 nickels, 3 pennies = $0.74
- 3 quarters, 1 dime, 1 nickel, 4 pennies = $0.73
- 2 quarters, 3 dimes, 1 nickel, 2 pennies = $0.70
- 2 quarters, 3 dimes, 2 nickels, 1 penny = $0.69
- 2 quarters, 2 dimes, 3 nickels, 1 penny = $0.68
- 2 quarters, 2 dimes, 2 nickels, 2 pennies = $0.67

Therefore, the largest amount of money Tasha could have is $0.81 with 3 quarters, 2 dimes, 1 nickel, and 2 pennies.

To maximize the amount of money Tosha could have with 8 coins and no more than 3 of any coin, she should carry the coins with the highest denominations. In this case, she can have 3 quarters (25 cents each), 3 dimes (10 cents each), and 2 nickels (5 cents each). The largest amount of money she could have is:

(3 x 25 cents) + (3 x 10 cents) + (2 x 5 cents) = 75 cents + 30 cents + 10 cents = 115 cents or $1.15.

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The number of one-to-one functions from a set with five elements to sets with one, two, three, four, and five elements are 1, 20, 60, 120, and 1, respectively.To answer this question, we need to use the concept of one-to-one functions.

A one-to-one function is a function where each element in the domain corresponds to a unique element in the range. In other words, no two elements in the domain can have the same image in the range.

Let's consider each case separately.

1. Set with one element: In this case, there is only one possible function since there is only one element in the range that needs to be mapped to.

2. Set with two elements: There are a total of 20 possible one-to-one functions from a set with five elements to a set with two elements. To see why, we can think of it as choosing two distinct elements from the domain to map to the two elements in the range. There are 5 choices for the first element, and 4 choices for the second element (since we can't choose the same element twice). So the total number of possible functions is 5 x 4 = 20.

3. Set with three elements: There are a total of 60 possible one-to-one functions from a set with five elements to a set with three elements. To see why, we can think of it as choosing three distinct elements from the domain to map to the three elements in the range. There are 5 choices for the first element, 4 choices for the second element, and 3 choices for the third element. So the total number of possible functions is 5 x 4 x 3 = 60.

4. Set with four elements: There are a total of 120 possible one-to-one functions from a set with five elements to a set with four elements. To see why, we can think of it as choosing four distinct elements from the domain to map to the four elements in the range. There are 5 choices for the first element, 4 choices for the second element, 3 choices for the third element, and 2 choices for the fourth element. So the total number of possible functions is 5 x 4 x 3 x 2 = 120.

5. Set with five elements: In this case, there is only one possible function since there are five elements in both the domain and the range, and every element in the domain must be mapped to a unique element in the range.

In summary, the number of one-to-one functions from a set with five elements to sets with one, two, three, four, and five elements are 1, 20, 60, 120, and 1, respectively.

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The number of miles that Freya traveled in total is 320 miles.

Given that:

Bournemouth to Gloucester: v = 50 mph and t = 2.5 h

Gloucester to Anglesey: v = 65 mph and t = 3 h

We know that the speed formula

Speed = Distance/Time

The number of miles that Freya traveled in total is calculated as,

Distance = 50 x 2.5 + 65 x 3

Distance = 125 + 195

Distance = 320 miles

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The white cylindrical silo has a diameter of 30 feet, which means the radius is 15 feet. The height of the silo is 80 feet. The area of the red stripe on the cylindrical silo is approximately 565.5 square feet.

A red stripe with a horizontal width of 3 feet is painted on the silo, making two complete revolutions around it. This means the total length of the red stripe is 2 times the circumference of the base of the silo plus 2 times the circumference of the top of the silo. The circumference of the base of the silo is 2 times pi times the radius, which is 2 x 3.14 x 15 = 94.2 feet.
The circumference of the top of the silo is also 94.2 feet
So the total length of the red stripe is 2 x 94.2 + 2 x 94.2 = 376.8 feet.  The horizontal width of the red stripe is 3 feet, so the area of the red stripe is 376.8 x 3 = 1130.4 square feet.
To find the total surface area of the silo, we need to find the area of the two circular ends and the area of the curved surface. The area of each circular end is pi times the radius squared, which is 3.14 x 15 x 15 = 706.5 square feet.
The area of the curved surface is the product of the height, the circumference, and 2 (since there are two sides), which is 80 x 94.2 x 2 = 15,088 square feet.
So the total surface area of the silo is 2 x 706.5 + 15,088 = 15,501 square feet.
Therefore, the area of the red stripe as a percentage of the total surface area of the silo is (1130.4/15,501) x 100% = 7.29%.

A white cylindrical silo has a diameter of 30

feet and a height of 80

feet. A red stripe with a horizontal width of 3

feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet?

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To find the outward flux, we can use the divergence theorem, which states that the flux of a vector field through a closed surface S is equal to the volume integral of the divergence of the vector field over the region enclosed by S.

In this problem, the vector field is F = (tan y + (8y + 3z)i + 2z + 8 cos x) + (Vx^2 + y^2 + 22k). The surface S is the region bounded by the graphs of z = Vx^2 + y^2 and x^2 + y^2 +22 = 9.

To apply the divergence theorem, we first need to find the divergence of the vector field. Using the product and chain rules, we have:

div F = (∂/∂x)(tan y + (8y + 3z)) + (∂/∂y)(2z + Vx^2 + y^2 + 22) + (∂/∂z)(Vx^2 + y^2 + 22)

Simplifying each term, we get:

div F = 8 + 2Vx + 2y

Next, we need to find the volume enclosed by S. This can be done by integrating the equation of the sphere and the equation of the cylinder over their respective domains:

V = ∫∫∫ dV = ∫∫ dz dA = ∫∫ (9 - x^2 - y^2)^(1/2) dA

where the limits of integration are:

-3 ≤ x ≤ 3
-(9-x^2)^(1/2) ≤ y ≤ (9-x^2)^(1/2)

We can now apply the divergence theorem:

flux = ∫∫ F · dS = ∫∫∫ div F dV = ∫∫ dz dA div F

Using the limits of integration for V and A, we get:

flux = ∫∫ (9 - x^2 - y^2)^(1/2) dA (8 + 2Vx + 2y)

Using polar coordinates for A, we have:

flux = ∫0^2π ∫0^3 (9 - r^2)^(1/2) r dr dθ (8 + 2r cos θ + 2r sin θ)

Simplifying and evaluating the integral, we get:

flux = 216π

Therefore, the outward flux of the vector field F through the surface S is 216π.

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The probability of getting at least one 12 is 1 - 0.4989 = 0.5011.

When rolling a pair of dice, the probability of getting a 12 is 1/36, as there is only one combination (6,6) that results in a 12.

To determine the likelihood of a 12 appearing in 24 or 25 rolls, we can use the complement probability, which is the probability of a 12 NOT appearing in any of the rolls.

For 24 rolls, the probability of not getting a 12 in any roll is (35/36)^24 ≈ 0.5086. Therefore, the probability of getting at least one 12 is 1 - 0.5086 = 0.4914. Since it's slightly less than 50%, you should bet against a 12 appearing.

For 25 rolls, the probability of not getting a 12 in any roll is (35/36)^25 ≈ 0.4989. The probability of getting at least one 12 is 1 - 0.4989 = 0.5011. As it's slightly more than 50%, you should bet for a 12 appearing in one of the rolls.

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The solution to the initial value problem is:

u(x,t) = 6 sin(9πx/L) exp(-81kπ^2 t/L^2) + 3/2 sin(πx/L) exp(-kπ^2 t/L^2) - 1/2 sin(3πx/L) exp(-9kπ^2 t/L^2) + 2 cos(3πx/L) exp(-9kπ^2 t/L^2)

To solve the heat equation, we can use separation of variables method assuming that the solution can be written as a product of functions of x and t, i.e.,

u(x,t) = X(x)T(t)

Then, the heat equation becomes:

X(x)T'(t) = kX''(x)T(t)

Dividing both sides by kX(x)T(t) and rearranging, we get:

1/k * T'(t)/T(t) = X''(x)/X(x) = -λ

where λ is a constant.

We can then solve for X(x) and T(t) separately:

X''(x) + λX(x) = 0

The boundary conditions u(0,t) = u(L,t) = 0 give X(0) = X(L) = 0, which leads to the solution:

X(x) = B sin(nπx/L)

where n = 1,2,3,... and B is a constant.

Using the initial conditions, we can determine the coefficients B_n for each value of n:

u(x,0) = 6 sin(9πx/L) = B_9 sin(9πx/L)

So, B_9 = 6.

u(x,0) = 3 sin(πx/L) - sin(3πx/L) = B_1 sin(πx/L) - B_3 sin(3πx/L)

Solving for B_1 and B_3, we get:

B_1 = 3/2, B_3 = -1/2

u(x,0) = 2 cos(3πx/L) = B_3 cos(3πx/L)

So, B_3 = 2.

Now, we can solve for T(t) using T'(t)/T(t) = -kλ. This leads to the solution:

T(t) = C exp(-kλt)

where C is a constant.

Finally, we can write the solution to the heat equation as:

u(x,t) = ∑ B_n sin(nπx/L) exp(-k(nπ/L)^2 t)

Substituting the values of B_n for each initial condition, we get:

u(x,t) = 6 sin(9πx/L) exp(-81kπ^2 t/L^2) + 3/2 sin(πx/L) exp(-kπ^2 t/L^2) - 1/2 sin(3πx/L) exp(-9kπ^2 t/L^2) + 2 cos(3πx/L) exp(-9kπ^2 t/L^2)

Therefore, the solution to the initial value problem is:

u(x,t) = 6 sin(9πx/L) [tex]e^{-81kπ^2 t/L^2}[/tex] + 3/2 sin(πx/L)[tex]e^{-kπ^2 t/L^2}[/tex] - 1/2 sin(3πx/L) [tex]e^{-9kπ^2 t/L^2}[/tex] + 2 cos(3πx/L) [tex]e^{-9kπ^2 t/L^2}[/tex]

where k is the thermal diffusivity of the material.

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a. The probability that X is greater than 500 is approximately 0.368.

b. The conditional probability that X is greater than 1000 is approximately 0.368.

a. To compute Pr[X > 500), we use the cumulative distribution function (CDF) of the exponential distribution, which is:

F(x) = 1 - e^(-x/B)

Plugging in B = 500 and x = 500, we get:

Pr[X > 500) = 1 - F(500) = 1 - (1 - e^(-500/500)) = e^(-1) ≈ 0.368

Therefore, the probability that X is greater than 500 is approximately 0.368.

b. To compute Pr[X > 1000 | X > 500), we use the definition of conditional probability:

Pr[X > 1000 | X > 500) = Pr[(X > 1000) ∩ (X > 500)] / Pr[X > 500)

Since X is a continuous random variable, we can rewrite the probability of the intersection using the minimum of X:

Pr[(X > 1000) ∩ (X > 500)] = Pr[X > max(1000, 500)] = Pr[X > 1000]

Plugging in B = 500 into the CDF, we have:

Pr[X > 1000] = 1 - F(1000) = 1 - (1 - e^(-1000/500)) = e^(-2) ≈ 0.135

We already know from part a that Pr[X > 500) = e^(-1) ≈ 0.368.

Putting it all together, we have:

Pr[X > 1000 | X > 500) = Pr[X > 1000] / Pr[X > 500) = (e^(-2)) / (e^(-1)) = e^(-1) ≈ 0.368

This result shows that the conditional probability that X is greater than 1000, given that it is already greater than 500, is the same as the probability that X is greater than 500 on its own. In other words, knowledge of the fact that X is already greater than 500 does not change our prediction about whether it will be greater than 1000 or not.

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Answer:

125 questions

Answer:

125 questions

Step-by-step explanation:

Alexa landed about 1.163 kilometers away from the skydiving center.

To find the distance from the skydiving center where Alexa landed, we need to use trigonometry. Since Alexa fell in a straight line perpendicular to the ground, we can create a right triangle with the distance she traveled (3.4 km) as the hypotenuse and the distance she landed from the center as one of the legs.

Let's call the distance Alexa landed "x". Then, using the trigonometric function "sine" (which is opposite over hypotenuse in a right triangle), we can set up the equation:

sin(20°) = x/3.4

To solve for x, we can first multiply both sides by 3.4 to isolate x:

x = 3.4 * sin(20°)

Using a calculator, we can evaluate sin(20°) to be approximately 0.342. Plugging this value into the equation, we get:

x = 3.4 * 0.342

x = 1.163 km (rounded to three decimal places)

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Complete question is:

Alexa's friends got her a skydiving lesson for her birthday. her helicopter took off from the skydiving center, ascending in an angle of 20°, and traveled a distance of 3.4 kilometers before she fell in a straight line perpendicular to the ground. How far from the skydiving center did Alexa land?

The ratio that is equivalent to 4:6 is 40:60

A ratio is a mathematical expression of comparing two similar or different quantities by division.

For examples if the ratio of cow to sheep In a farm is 3: 4, this means that for 3 cows in the farm there will be 4 sheeps

Equivalent ratios are the ratios that are the same when we compare them. Examples of equivalent ratios are 4:5 and 8 :10.

The equivalent of 4:6 can also be 2:3 but in the options we don't have that, another equivalent can be obtained by multiplying 10 to both sides

=4×10: 6× 10

= 40:60

therefore the equivalent of the ratio 4:6 is 40:60

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The exact length of the parametric curve is approximately 9.023 units.

To find the length of the parametric curve given by[tex]X = t - 3t^3[/tex] and [tex]Y = 3t^2[/tex], where 0 < t < 2, we can use the formula for the arc length of a parametric curve:

[tex]L = \int_a^b \sqrt(dx/dt)^2 + (dy/dt)^2 dt[/tex]

where a and b are the limits of the parameter t.

In this case, we have:

[tex]dx/dt = 1 - 9t^2[/tex]

dy/dt = 6t

Therefore,

[tex](\sqrt(dx/dt)^2 + (dy/dt)^2) = \sqrt((1 - 9t^2)^2 + 36t^2)[/tex]

The limits of integration are 0 and 2, since 0 < t < 2.

So, the length of the curve is:

[tex]L = \int_0^2 \sqrt((1 - 9t^2)^2 + 36t^2) dt[/tex]

This integral is difficult to solve analytically, but we can use numerical methods to approximate its value.

Using a numerical integration method such as Simpson's rule with a large number of subintervals, we find that the length of the curve is approximately 9.023 units.

Therefore, the exact length of the parametric curve is approximately 9.023 units.

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Answer:

4

Step-by-step explanation:

a/2 = 36/18

Reduce the right fraction.

a/2 = 2/1

Multiply both sides by 2.

a = 4

Answer: 4

We would expect about 316 visitors to purchase exactly one costume next week, rounded to the nearest whole number

To estimate the number of visitors who will purchase exactly one costume in a given week, we need to assume that the probability of a visitor purchasing exactly one costume remains constant over time.

This means that if we randomly select a visitor from the 400 expected visitors next week, the probability of that visitor purchasing exactly one costume is the same as the probability of a visitor purchasing exactly one costume on the day we have data for.

We can use the proportion of visitors who purchased exactly one costume on the day we have data for as an estimate of the probability of a visitor purchasing exactly one costume next week. Specifically, the proportion of visitors who purchased exactly one costume on that day was 108/137, or about 0.79.

This means that we can estimate the number of visitors who will purchase exactly one costume next week by multiplying the total number of visitors expected (400) by the probability of a visitor purchasing exactly one costume (0.79):

400 x 0.79 = 316

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The equation of the linear relationship in slope-intercept form is expressed as: y = 3x - 4.

To find the equation, pick two points on the line and find the slope (m), then find the y-intercept (b) of the line.

Using, (0, -4) and (1, -1):

Slope (m) = (-1 -(-4)) / (1 - 0)

m = 3/1

m = 3

The y-intercept (b) is -4.

Substitute m = 3 and b = -4 into y = mx + b:]

y = 3x - 4

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It will be impossible to know if the photographer has enough space left on her memory card without knowing the capacity of the card and the size of the planned photos for session D.

Main answer:

It is impossible to determine if the photographer has enough space left on her memory card without knowing the capacity of the card and the size of the planned photos for session D.

We must know capacity of the card and the size of the planned photos for session D. If combined size of the planned photos for session B and C is less than remaining space on the card after accounting for the 3.4 megabytes needed for session D, then, the photographer would have enough space.

But if combined size of the planned photos for session B and C is greater than the remaining space on the card after accounting for the 3.4 megabytes needed for session D, then, the photographer would not have enough space.

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we can expect to receive approximately 3 phone calls during the 1.5-hour movie, on average.

The probability of your phone ringing during a 1.5-hour movie can be calculated using the Poisson distribution formula:

P(X = k) = (e^-λ * λ^k) / k!

Where X is the number of phone calls, λ is the average rate of calls per unit time (in this case, 2 calls per hour), and k is the number of calls during the 1.5-hour period.

So, for k = 0 (no calls), the probability is: P(X = 0) = (e^-2 * 2^0) / 0! = e^-2 ≈ 0.1353

Therefore, the probability that your phone rings at least once during the movie is: P(X ≥ 1) = 1 - P(X = 0) = 1 - e^-2 ≈ 0.8647

To calculate the expected number of calls during the movie, we use the formula: E(X) = λ * t

Where t is the duration of the period (1.5 hours in this case). So, the expected number of calls during the movie is: E(X) = 2 * 1.5 = 3

Therefore, we can expect to receive approximately 3 phone calls during the 1.5-hour movie, on average.

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Answer:24

Step-by-step explanation:

If you do 72 divided by 3 you get 24