WILL GIVE BRINLIEST!!!!!!!!!!!!!!!!!!!!! WHAT IS LONG DIVISION?

To evaluate iterated integral given, we need to integrate with respect to y and then x, z. Starting with innermost integral, we integrate with respect to y from 0 to [tex]xe^-z.[/tex] so we get after evaluating iterated integral.:[tex]∫_0^6 (-z(1 - e^(-ln(5))) + e^(-z)(ln(5) - 2)z - z) dz = -111.53[/tex]  

Moving on to the middle integral, we integrate the result of the first integral with respect to x from 0 to ln(5). The integral of[tex]1-e^-xe^-z[/tex] with respect to x is [tex]x + e^-xe^-z,[/tex]so we have:
[tex]∫_0^ln(5) (x + e^(-x)e^(-z)) dx = (1/2)ln^2(5) + e^-z(ln(5) - 1) - 1[/tex]

Finally, we integrate the result of the second integral with respect to z from 0 to 6. The integral of [tex](1/2)ln^2(5) + e^-z(ln(5) - 1) - 1[/tex] with respect to z is -[tex]z(1 - e^(-ln(5))) + e^-z(ln(5) - 1)z - z[/tex], so we have:
[tex]∫_0^6 (-z(1 - e^(-ln(5))) + e^(-z)(ln(5) - 2)z - z) dz = -111.53[/tex]

Therefore, the value of the iterated integral is approximately -111.53. This is the final result of the iterated integral. The integral represents a multivariate function being integrated over the given limits.

The key is to integrate one variable at a time while treating others as constants, and successively updating the result as you move from innermost to outermost integral.

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The missing values in the table (in order from left to right) are:

We know that h(x) is a linear function, then we can write:

h(x) = a*x + b

By looking at the table, we can see the pair (0, 4), this means that:

h(0) = -4

Then:

a*0 + b =- 4

b = -4

So our function is:

h(x) = a*x + -4

To find the value of a, we can use other point. The next one is (2, 10), replacing these values we get:

10 = a*2 + -4

10 + 4 = a*2

14 = a*2

14/2 = a

7= a

The linear function is h(x) = 7x - 4

Now we can find the missing values in the table, these are:

h(1) = 7*1 - 4 = 3

h(3) = 7*3 - 4 = 17

h(5) = 7*5 - 1 = 34

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in Dallas, Texas to be classified as extremely wet, the amount of precipitation that must fall is approximately 4.74 inches.

To find the amount of precipitation that must fall in April for it to be classified as extremely wet, we need to find the z-score that corresponds to the upper 5% of the normal distribution.

Using a standard normal distribution table, we can find that the z-score corresponding to the upper 5% is approximately 1.645.

Now we can use the formula z = (x - μ) / σ, where z is the z-score, x is the amount of precipitation, μ is the mean (3.2 inches), and σ is the standard deviation (0.9 inches).

Plugging in the values, we get:

1.645 = (x - 3.2) / 0.9

Solving for x, we get:

x = 3.2 + 1.645 * 0.9

x = 4.7425

Therefore, for April in Dallas, Texas to be classified as extremely wet, the amount of precipitation that must fall is approximately 4.74 inches.
To determine the amount of precipitation required for April to be classified as extremely wet in Dallas, Texas, we need to find the value at the 95th percentile of the normal distribution, since the upper 5% corresponds to extremely wet conditions. The average precipitation is 3.2 inches, and the standard deviation is 0.9 inches.

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Answer: Graph A shows the correct probability distribution.

Step-by-step explanation:

The probability of the spinner landing on "A" is 1/2. Similarly, the probability of the spinner landing on "B" is 3/8. Therefore, the probability of the spinner landing on "C" is 1-1/2-3/8=1/8. So:

probability of landing on "A" is 1/2 = 0.5,

probability of landing on "B" is 3/8 = 0.375, and

probability of landing on "C" is 1/8 = 0.125.

Thus the correct probability distribution should be answer choice [tex]\boxed{\text{A}}.[/tex]

To make the indicated trigonometric substitution in the given algebraic expression, x² − 25x, with x = 5 sec(t), substitute and simplify to get 100(sec²(t) - 5sec(t)).

To make the trigonometric substitution, follow these steps:

1. Replace x with 5 sec(t) in the expression: (5 sec(t))² − 25(5 sec(t)).
2. Simplify (5 sec(t))²: 25 sec²(t).
3. Simplify 25(5 sec(t)): 125 sec(t).
4. Combine terms: 25 sec²(t) - 125 sec(t).
5. Factor out a common factor, which is 25 sec(t): 25 sec(t)(sec(t) - 5).

So, the simplified expression after making the trigonometric substitution is 100(sec²(t) - 5sec(t)).

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To find the probability that it takes no longer than 0.2 seconds for the second count, we need to use the Poisson distribution formula:
P(X ≤ 1) = e^(-λ) * (λ^0/0!) + e^(-λ) * (λ^1/1!)
P(X ≤ 1) = e^(-20) * (20^0/0!) + e^(-20) * (20^1/1!)
P(X ≤ 1) = 0.000000026 + 0.000000520
P(X ≤ 1) = 0.000000546
Then, the probability that it takes no longer than 0.2 seconds for the second count is 0.000000546.

We can use the Poisson distribution to solve this problem. Given that the mean number of alpha particle emissions from carbon-14 counted by a Geiger counter is 20 per second, let's find the probability of observing two counts within 0.2 seconds.

First, we need to calculate the mean for a 0.2-second interval, which is: 0.2 * 20 = 4.

Using the Poisson distribution formula:

P(X=k) = (e^(-λ) * λ^k) / k!

where P(X=k) is the probability of observing k counts in the given interval, λ is the mean (in our case, 4), and e is the base of the natural logarithm (approximately 2.71828).

We want the probability of observing 0, 1, or 2 counts in the 0.2-second interval:

P(X=0) = (e^(-4) * 4^0) / 0! ≈ 0.0183
P(X=1) = (e^(-4) * 4^1) / 1! ≈ 0.0733
P(X=2) = (e^(-4) * 4^2) / 2! ≈ 0.1465

Now, the probability that it takes no longer than 0.2 seconds for the second count is the probability of observing 2 or more counts in that time. We'll calculate the complementary probability and subtract it from 1:

P(X≥2) = 1 - (P(X=0) + P(X=1)) ≈ 1 - (0.0183 + 0.0733) ≈ 0.9084

So, there's approximately a 90.84% probability that it takes no longer than 0.2 seconds for the second alpha particle emission count of carbon-14.

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Answer:

-1

Step-by-step explanation:

2x - 2y = -12

-2y = -2x - 12

y = x + 6

m = 1

The equation of a perpendicular line to y = x + 6 must have a slope that is the negative reciprocal of the original slope.

m perpendicular = - 1/1

Simplify the result

m perpendicular = -1

So, the answer is -1

Answer:

Step-by-step explanation:

The fixed point traces out the diameter of the larger circle in a Tusi couple.

A Tusi couple is a mathematical device used to convert linear motion into circular motion. It consists of two circles, one smaller and one larger, with the smaller circle rolling inside the larger circle. As the smaller circle rolls, a fixed point on its circumference traces out the diameter of the larger circle.

To understand this concept, imagine the smaller circle placed inside the larger circle, touching at a single point. As the smaller circle rolls around the interior of the larger circle, the fixed point moves along a straight path, which is the diameter of the larger circle.

The fixed point's movement is a result of the combination of the circular motion of the smaller circle and its linear motion due to rolling. This mechanism allows for the conversion of the smaller circle's linear motion into the fixed point's circular motion, illustrating the geometric principle behind the Tusi couple.

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The probability that a randomly selected child has an IQ above 109 is approximately 0.2266 or 22.66%. So, correct option is D.

To find the probability that a randomly selected child has an IQ above 109, we need to standardize the IQ value and then use the standard normal distribution table or calculator.

First, we calculate the z-score corresponding to an IQ of 109 using the formula:

z = (x - μ) / σ

where x is the IQ value, μ is the mean, and σ is the standard deviation.

Substituting the given values, we get:

z = (109 - 100) / 12 = 0.75

Next, we can look up the probability of a standard normal random variable being greater than 0.75 in the standard normal distribution table or use a calculator. The probability is approximately 0.2266.

This means that out of 100 randomly selected children, we can expect around 23 to have an IQ above 109.

So, correct option is D.

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Answer:

8100

Step-by-step explanation:

Step-by-step explanation:

To round 8099 to the nearest ten, we need to look at the digit in the tens place, which is 0. Since 0 is less than 5, we round down the ones place to 0 and keep the digit in the tens place as it is. Therefore, rounding 8099 to the nearest ten gives us 8100.

(A) The sum can be expressed as the definite integral ∫0^1 2e^√(x) dx

(B) The sum can be expressed as the definite integral ∫0^1 x^27 dx

(A) To express the sum as a definite integral, we first need to find an expression for the Riemann sum

Σ n i=1 2 e ^√ i/n. 1/n

= ∑ i=1^n f(xi) Δx

where f(xi) = 2 e^√(xi/n) / n and Δx = 1/n. Here xi = i and n is the number of subintervals.

Now we can express the limit as a definite integral

lim n→ [infinity] Σ n i=1 2 e ^√ i/n. 1/n

= lim n→ [infinity] ∑ i=1^n f(xi) Δx

= lim n→ [infinity] ∑ i=1^n 2 e^√(xi/n) / n^2

= ∫0^1 2e^√(x) dx

where we have used the fact that Δx = 1/n approaches zero as n approaches infinity, and that the limit of the Riemann sum as n approaches infinity is equal to the definite integral over the interval [0,1].

(B) We can similarly express the sum as a definite integral

lim n→ [infinity] Σn i=1 i ^27 /n^28

= lim n→ [infinity] ∑ i=1^n f(xi) Δx

where f(xi) = (xi / n) ^27 and Δx = 1/n.

Now we can express the limit as a definite integral

lim n→ [infinity] Σn i=1 i ^27 /n^28

= lim n→ [infinity] ∑ i=1^n (xi / n) ^27 / n

= ∫0^1 x^27 dx

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The divisor and the remainder in the polynomial division are as follows:

We first find the remainder as follows:

Remainder = (3x² - 2x + 7) - (3x² + 6x - 3)

Remainder = -8x + 10

The divisor can be found using the formula below:

Dividend = divisor * quotient + remainder

Divisor = (dividend - remainder) / quotient

Substituting the values:

Divisor = 2x³ + 7x² - 4x + 7 - (-8x + 10) / 2x + 3

Divisor = 2x³ + 7x² - 4x + 7 + 8x - 10} / (2x + 3)

Divisor = 2x³ + 7x² + 4x - 3 / (2x + 3)

Using long polynomial division:

Divisor =  x² - 2x + 6

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If a sample includes three individuals with scores of 4, 6, and 8, the estimated population variance is (4 + 0 + 4) / 2 - 4. So, correct option is 4.

The estimated population variance formula is the sum of squared deviations from the mean divided by the degrees of freedom. In this case, the degrees of freedom would be n-1, where n is the sample size.

Using the given sample of 4, 6, and 8, we can calculate the sample mean as (4+6+8)/3 = 6.

Then, we calculate the deviations from the mean for each score:

4 - 6 = -2

6 - 6 = 0

8 - 6 = 2

We square each deviation to get 4, 0, and 4. Then, we sum the squared deviations: 4 + 0 + 4 = 8.

Since there are three scores in the sample, the degrees of freedom is 3 - 1 = 2.

Finally, we divide the sum of squared deviations by the degrees of freedom to get the estimated population variance: 8/2 = 4.

Therefore, option 4) (4 + 0 + 4) / 2 = 4 is the correct answer.

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Answer:

Let's start by writing the variation equation for BMI:

BMI = k * (weight / height^2)

where k is the constant of variation.

We can use the given information to solve for k:

15.53 = k * (131 / 77^2)

k = 15.53 * 77^2 / 131

k ≈ 6.584

Now we can use this value of k to find the BMI for the second individual:

BMI = 6.584 * (136 / 76^2)

BMI ≈ 20.12

Therefore, the BMI for an individual who is 76 in. tall and 136 lb is approximately 20.12.

have a nicesu day po! or night! if this helps you; consider rating me an 5stars and give thanks for more po!

(a) The demand function (390 - r)/10.

(b) The revenue function (390r - r²)/10.

(c) The price S19.5.

(d) The store should charge S17 per barstool to maximize its profit.

(a) To find the demand function, we can use the given information that for each S3 increase in price, the number of barstools sold decreases by 10 per month. Let p be the price charged for a barstool and r be the number of barstools sold each month. Then we have:

r = 120 - 10[(p-60)/3]

Simplifying this equation, we get:

r = 390 - 10p

Solving for p, we get the demand function:

p = (390 - r)/10

(b) The revenue function is given by:

R = p*r

Substituting the demand function from part (a) into the revenue function, we get:

R = [(390 - r)/10] * r

Simplifying this expression, we get:

R = (390r - r²)/10

(c) To find the price that maximizes revenue, we can differentiate the revenue function with respect to r and set the result equal to zero. Then we can solve for r and use the demand function from part (a) to find the corresponding price. We have:

dR/dr = 390/10 - 2r/10

Setting this expression equal to zero and solving for r, we get:

r = 195

Using the demand function from part (a), we can find the price that maximizes revenue:

p = (390 - r)/10 = (390 - 195)/10 = S19.5

(d) To find the price that maximizes profit, we need to consider the store's cost per barstool. Let C be the cost per barstool and P be the price charged per barstool. Then the profit function is given by:

π = (P - C) * r

Substituting the demand function from part (a), we get:

π = (P - C) * (390 - 10P)

Expanding this expression, we get:

π = -10P² + 400P - 390C

To maximize profit, we need to differentiate this expression with respect to P and set the result equal to zero. Then we can solve for P and use the demand function from part (a) to find the corresponding price. We have:

dπ/dP = -20P + 400

Setting this expression equal to zero and solving for P, we get:

P = 20

Using the demand function from part (a), we can find the price that maximizes profit:

p = (390 - r)/10 = (390 - 10*20)/10 = S17

Therefore, the store should charge S17 per barstool to maximize its profit.

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The series Σ(cos(15)k) from k=1 to infinity is convergent.

Σ[tex](cos(15)k)[/tex] from k=1 to infinity

To determine if this series converges or diverges, we can use the Ratio Test. The Ratio Test states that if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. If it's greater than 1, it diverges. If it's equal to 1, the test is inconclusive.

Step 1: Find the ratio of consecutive terms, a(k+1)/a(k)

a(k+1) = cos(15)(k+1)
a(k) = cos(15)k

Ratio: |a(k+1)/a(k)| = |cos(15)(k+1) / cos(15)k|

Step 2: Simplify the ratio

|cos(15)(k+1) / cos(15)k| = |cos(15)|

Since the ratio doesn't depend on k, the limit will just be the absolute value of the ratio itself.

Step 3: Compare the limit to 1

|cos(15)| < 1, since 0 < cos(15) < 1

According to the Ratio Test, since the limit of the absolute value of the ratio of consecutive terms is less than 1, the series converges.

Your answer: The series Σ(cos(15)k) from k=1 to infinity is convergent.

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Answer:

A) (– 3,0) and (1,0)

Step-by-step explanation:

Plugging the given x-values into the equation gives us;

ƒ(x) = x² + 2x – 3

f(-3) = (-3)² + 2(-3) - 3 = 0

and

f(1) = (1)² +2(1) - 3 = 0

Answer:

x=50

Step-by-step explanation:

the opposite angle is always equal to the angle next to it

The expected frequency for each day of the week is 12, and we can use the test statistic to compare the observed frequencies with the expected frequencies.

The data provided is in the form of a frequency table, which tells us the number of managers who reported the highest number of employee absences on each day of the week. To test our hypothesis, we need to calculate the expected frequency for each day of the week under the assumption of equal frequencies.

If employee absences occur with equal frequencies during the week, we would expect each day to have an equal number of reported highest absences. Since we have five days in a work week, we would expect the expected frequency for each day to be 60/5 = 12.

We can then use the chi-squared goodness of fit test to compare the expected frequencies with the observed frequencies (the frequencies in the table).

If the test statistic is large enough, we reject the null hypothesis and conclude that employee absences do not occur with equal frequencies during the week.

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The equation of the parabola is given as follows:

y = -28/19600(x - 140)² + 28.

The distances from the center for a height of 13 meters are given as follows:

37.53 m and 242.47 m.

The equation of a parabola of vertex (h,k) is given by the equation presented as follows:

y = a(x - h)² + k.

In which a is the leading coefficient.

It has a span of 280 meters, hence the x-coordinate of the vertex is given as follows:

x = 280/2

x = 140 -> h = 140.

The maximum height is of 28 meters, hence the y-coordinate of the vertex is given as follows:

y = 28 -> k = 28.

Hence the equation is:

y = a(x - 140)² + 28.

When x = 0, y = 0, hence the leading coefficient a is obtained as follows:

19600a = -28

a = -28/19600

Hence:

y = -28/19600(x - 140)² + 28.

The distance from the center at which the height is 13 meters is obtained as follows:

13 = -28/19600(x - 140)² + 28.

28/19600(x - 140)² = 15

(x - 140)² = 15 x 19600/28

(x - 140)² = 10500.

Hence the distances are obtained as follows:

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Answer: 50%

Step-by-step explanation: First, the probability of getting an odd card is .50. If you keep the card, there are now five cards left. The probability to select a card that is less than 7 on the second draw would be 1.00.

To find the total probability, we must do .50 * 1.00 = .50

Therefore, the total probability is .50, or 50%

In light of this, the circle graph named "New York City Visitors' Transportation" is divided into five sections, each of which is labelled as follows: walk 40%, bicycle 8%, car service 15%, bus 10%, and subway 27%. As a result, choice c) is accurate.

Data can be represented in graphs in a number of different ways. There are several common graph types, including:

Bar chart

Scatter plot

Box plot.

Pie graph

We must ascertain the percentage of visitors who used each mode of transportation in order to represent the data in the table as a circle graph, also referred to as a pie chart.

To do this, divide the total number of visits by the sum of visitors and multiply the result by 100.

Total number of visitors: 120 + 24 + 45 + 30 + 81 = 300

The percentage of people who walk into a store is (120/300)/100, or 40%.

The percentage of tourists who rode bicycles was (24 x 300 x 100), or 8%.

The percentage of visitors who used the transportation service was 15% (45/300/100).

10% of visitors used a bus to get about (30 out of 300).

27% of the 300 visitors—or 81 out of the 300—took the subway.

This makes the circle graph headed "New York City visitor's transportation," which is divided into five sections and has the labels "walk 40%, bicycle 8%, car service 15%, bus 10%, and subway 27%," the most accurate representation of the data in the table.

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The complete question is:

A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.

Type of Transportation Number of Visitors

Walk 120

Bicycle 24

Car Service 45

Bus 30

Subway 81

Which of the following circle graphs correctly represents the data in the table?

circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent

circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent

circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent

circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent

mean(y) = E(y) = 4

variance(y) = Var(y) = 2.8

a. To find P(X1 = 2, X2 = 2, X3 = 5), we use the fact that the three random variables are independent. Thus, we have:

P(X1 = 2, X2 = 2, X3 = 5) = P(X1 = 2) × P(X2 = 2) × P(X3 = 5)

Using the binomial probability formula, we get:

P(X1 = 2) = (4 choose 2) (1/2)^2 (1/2)^2 = 6/16

P(X2 = 2) = (6 choose 2) (1/3)^2 (2/3)^4 = 225/1944

P(X3 = 5) = (12 choose 5) (1/6)^5 (5/6)^7 = 0.1205

Therefore,

P(X1 = 2, X2 = 2, X3 = 5) = (6/16) × (225/1944) × 0.1205 = 0.0019 (rounded to four decimal places).

b. To find E(X1,X2,X3), we use the fact that the expected value of the product of independent random variables is the product of their expected values. Thus, we have:

E(X1,X2,X3) = E(X1) × E(X2) × E(X3)

Using the binomial distribution properties, we get:

E(X1) = 4 × (1/2) = 2

E(X2) = 6 × (1/3) = 2

E(X3) = 12 × (1/6) = 2

Therefore,

E(X1,X2,X3) = 2 × 2 × 2 = 8.

c. To find the mean and variance of y = X1 + X2, we use the linearity of the expected value and the fact that the variance of the sum of independent random variables is the sum of their variances. Thus, we have:

E(y) = E(X1 + X2) = E(X1) + E(X2) = 2 + 2 = 4

Var(y) = Var(X1 + X2) = Var(X1) + Var(X2) = 4 × (1/2) × (1 - 1/2) + 6 × (1/3) × (2/3) = 2.8

Therefore,

mean(y) = E(y) = 4

variance(y) = Var(y) = 2.8

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Answer:

first student's boy probability=4/11

second student's girl probability=6/10 or 7/10

Answer: 7 + 4 = 11, 4/11 = 0.36, 7/11 = 0.64

prob. of student being a boy is 0.36

prob. of student being a girl is 0.64

Step-by-step explanation:

to find the probability, you first add the numbers together to find the sum and divide the number of people from each gender by the sum

The given function f(x) is not a valid probability density function (pdf) of a continuous random variable X as it does not satisfy the normalization property.

The given function f(x) is defined as:

f(x) =

0.4, if 3 < x < 5

0, otherwise

To be a valid probability density function (pdf) of a continuous random variable X, a function must satisfy the following properties:

Non-Negativity: f(x) ≥ 0 for all x.

Normalization: The area under the curve of f(x) over the entire range of x must be equal to 1.

Let's check if the given function f(x) satisfies these properties:

Non-Negativity: For x ≤ 3 or x ≥ 5, f(x) = 0, which satisfies the non-negativity property. For 3 < x < 5, f(x) = 0.4, which is also non-negative.

Normalization: We need to integrate f(x) over the entire range of x to check if the area under the curve is equal to 1.

[tex]\int\limits^{\infty} _{-\infty}[/tex]f(x)dx = [tex]\int\limits^3_{-\infty}[/tex]0dx + [tex]\int\limits^{5} _{3}[/tex]0.4dx + [tex]\int\limits^{\infty} _{5}[/tex]0dx= 0 + 0.4(5-3) + 0 = 0.8

As the area under the curve of f(x) is not equal to 1, the given function f(x) is not a valid probability density function (pdf) of a continuous random variable X.

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