An object is moving at a speed of 850 miles per hour. Express this speed in meters per minute.

The probability of each event occurring is the same (1/10), so the total probability of getting two "1's" in three draws without replacement is 3 * (1/10) = 3/10 = 0.3.

The probability of getting two "1's" in three draws without replacement from a box containing 5 tickets can be calculated as follows:
First, calculate the probability of getting two "1's" and one other number in a specific order, such as 1-1-x, where x represents any of the other numbers. The probability of this occurring is (2/5) * (1/4) * (2/3) = 1/10.
However, there are three different orders in which you can draw two "1's" and one other number: 1-1-x, 1-x-1, and x-1-1. Since these events are mutually exclusive, you can add their probabilities together.
The probability of each event occurring is the same (1/10), so the total probability of getting two "1's" in three draws without replacement is 3 * (1/10) = 3/10 = 0.3.
Therefore, the correct answer is a. 0.3.

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Answer

D= t^2 + 5.6

Step-by-step explanation:

D= t + 5.3 x t + 0.3

D= t^2 + 5.6

In the given situation (D) randomized block design was used to experiment with incorporating randomization into this study.

An experimental design known as a randomized block design divides the experimental units into units known as blocks.

The experimental units inside each block are assigned the treatments at random.

We have a fully randomized block design when each block has at least one instance of each treatment.

By ensuring that a crucial predictor of the outcome is fairly distributed amongst research groups to require them to be balanced, something that a completely randomized design cannot guarantee, a randomized block design differs from a completely randomized design.

Therefore, in the given situation (D) randomized block design was used to experiment with incorporating randomization into this study.

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Complete question:

R.A. Fisher, a famous statistician, describes a well-known design in his book, Design of Experiments. Five varieties of wheat were compared to determine which gave the highest yield in bushels per acre. Eight farms were available for planting. Each farm was divided into five plots. For each farm, the five varieties were randomly assigned to the five plots with one variety per plot. The varieties were planted on their assigned plots and their yields were measured and compared.

How was randomization incorporated into this study?

A. All five varieties were randomly assigned to the five plots at each farm.

B. The five varieties were randomly assigned to the eight farms - three varieties were planted twice and two varieties only once.

C. It was not incorporated. The wheat seeds were not randomly selected from the population of wheat seeds.

D. Experiment - randomized block design

The equation of the complex number in polar form is:

z = 14(cos (-π/3) + i sin (-π/3))

To write the complex number −7 + 7√3i in polar form, we need to find its magnitude and angle.

The magnitude of a complex number z = a + bi is given by the formula:

|z| = √(a² + b²)

In our question, a = −7 and  b = 7√3

Thus,  the magnitude of the complex number is:

|z| = √((-7)² + (7√3)²)

|z| = √196

|z| = 14

The polar form of a complex number is shown below:

z = r(cos θ + i sinθ)

θ = tan⁻¹(b/a)

θ = tan⁻¹(7√3)/(-7)

θ = tan⁻¹(-√3)

θ = -π/3 radians

Thus, equation in polar form is:

z = 14(cos (-π/3) + i sin (-π/3))

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Using linear function concepts, it is found that the speed of the motorboat is of 22 miles per hour.

A linear function is modeled by:

y = mx + b

In which:

In this problem, each second, the position increased by 22, hence the slope is of 22. Since velocity is the distance divided by the time, which in this problem is the slope, the speed of the motorboat is of 22 miles per hour.

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Answer:

When cooper was 15 years old, he scored an 85 on an iq test. he took the test again when he was 35 years old and scored an 85 again. this indicates that the iq test is highly: __________

Reliable

Because his scores were so close together the test would be considered as Reliable.

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Cumulative Frequency is used to calculate a class's relative frequency.

The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its forerunners.. Since all frequencies have already been added to the prior total, the final value will always be equal to the sum of all observations.

What is Relative frequency?

The ratio of the total number of outcomes in an experiment, also known as the number of trials, to the number of times an event occurs is called relative frequency.

Each class's "relative frequency" refers to the percentage of the data that belongs to that class. For a set of data of size n, it can be calculated by: Class frequency equals relative frequency Sample size equals f n. The frequencies of that class and all prior classes are added together to form the "cumulative frequency."

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4x + 7 + 2x + 5 = 180

6x + 12 = 180

6x = 168

x = 28

Answer:

1/2

Step-by-step explanation:

Filling out the tree diagram,

On the first throw, there is a 4/4 = 100%* chance Jennifer hits or misses. Therefore, the chance she misses is equal to the difference between

(chance she hits or misses) - (chance she hits) = 4/4 - 1/4 = 3/4

For the second throw, the chance she hits is independent of whether she hits or misses on the first throw. This means that it does not matter whether she hits or misses on the first throw; her chance to hit the second throw will always be 1/3. Therefore, 1/3 can go into the hit category on each hit line on the second throw, and in the miss category, we can put

100% - 1/3 = 1 - 1/3 = 3/3 - 1/3 = 2/3

For Jennifer to hit the bullseye at least once, she must either:

- Hit and then hit

- Hit and then miss

- Miss and then hit

From this, we can determine that if Jennifer hits the first bullseye, she will have hit it at least once, no matter what. Therefore, Jennifer must either:

- Hit the first one

- Miss and then hit

In probability, OR /either means that we add the probabilties. The probability that she hits the first one is 1/4, and the probability that she misses and then hits is

(probability she misses the 1st one) * (probability she hits the second one). We know to multiply here because both scenarios must happen, and for AND probabilities, we multiply. We thus have

(3/4) * (1/3) = 3/12 = 1/4 as the probabilty that she misses then hits, and 1/4 as the probability that she hits the first one. We add these up to get 1/4 + 1/4 = 2/4 = 1/2 as our probability that she hits the bullseye at least once

* we know 4/4 = 100% because 100% = 1, and anything divided by itself is equal to 1.

We are given a path c, and a vector field f. The path c is defined by r(t) = (t³, t², -2t) for 0 ≤ t ≤ 1. The vector field f = (-4sin x, 5cos y, 10xz). We are required to evaluate the line integral ∫cf ⋅ dr using the given information.To evaluate the line integral, we use the following formula:∫cf ⋅ dr = ∫abf(r(t)) ⋅ r'(t) dt.

Here, we can see that r(t) is already in vector form, so we don't need to convert it. We just need to find r'(t).Differentiating r(t) with respect to t, we get:r'(t) = (3t², 2t, -2)Substituting the given values of f and r'(t), we get:∫cf ⋅ dr = ∫₀¹ (-4sin t³, 5cos t², -20t³) ⋅ (3t², 2t, -2) dt= ∫₀¹ (-12t⁴ sin t³ + 10t cos t² - 20t⁴) dt= (-3t⁴ cos t³ + 5t³ sin t² - 5t⁵) from 0 to 1= -3 cos 1 + 5 sin 1 - 5The final answer is -3 cos 1 + 5 sin 1 - 5.

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The system of inequalities to represent the situation is 2x + 5y ≤ 77, x + y ≥ 19

You are in charge of getting food for the class from the corner store.  You can buy chips for $2 or a hoagie for $5.

There are 19 students in the class, so you need to buy at least 19 items, and you have $77 total.

Hence, the system of inequality to represent this situation is as follows:

let

x = number of chips

y = number of hoagies

Therefore, the inequalities is as follows:

2x + 5y ≤ 77

x + y ≥ 19

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Taking the quotient between the total volume and the flow rate, we can see that the correct option is D.

We know that water flows at a rate of 1.5*10^4 gallons per second. We know that 6.525*10^6 gallons flowed while Jeremy was watching, then the time that he has been watching is the quotient between these values, we will get:

time = ( 6.525*10^6)/(1.510^4) seconds =  (652.5/1.5) second = 435 seconds

We know that 60 secons = 1 minute, then:

435/60  = 7 + 15/60

So he has been watching for 7 minutes and 15 seconds, the correct option is D.

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The particular solution to the given differential equation dy/dx = xy + 3x, with the initial condition y(0) = 4, is y(x) = 4e^(x^2/2) - 3x - 1.

To find the particular solution, we can use the method of integrating factors. The given equation is a first-order linear ordinary differential equation. Rearranging the equation, we have dy/dx - xy = 3x. Comparing this to the standard form dy/dx + P(x)y = Q(x), we have P(x) = -x and Q(x) = 3x.

1. To find the integrating factor, we multiply both sides of the equation by the integrating factor, which is defined as exp(integral(P(x) dx)). In this case, the integrating factor is exp(-x^2/2). Multiplying both sides of the equation by the integrating factor, we get exp(-x^2/2) dy/dx - xexp(-x^2/2) y = 3xexp(-x^2/2).

2. Now, we can recognize the left-hand side of the equation as the derivative of (y exp(-x^2/2)) with respect to x. Applying this derivative, we have d/dx (y exp(-x^2/2)) = 3xexp(-x^2/2). Integrating both sides with respect to x, we obtain y exp(-x^2/2) = ∫(3xexp(-x^2/2) dx).

3. Solving the integral on the right-hand side, we get ∫(3xexp(-x^2/2) dx) = -3exp(-x^2/2) + C, where C is the constant of integration. Multiplying both sides by exp(x^2/2), we have y = -3 + C_exp(x^2/2).

4. Using the initial condition y(0) = 4, we substitute x = 0 and y = 4 into the equation. This gives 4 = -3 + C_exp(0) = -3 + C. Solving for C, we find C = 4 + 3 = 7.

5. Substituting C = 7 into the equation y = -3 + C_exp(x^2/2), we obtain y = -3 + 7_exp(x^2/2) = 4_exp(x^2/2) - 3. Therefore, the particular solution to the given differential equation with the initial condition y(0) = 4 is y(x) = 4_exp(x^2/2) - 3x - 1.

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We need a minimum sample size of 336 to estimate the population proportion of U.S. adults who eat fast food four to six times per week with a 90% confidence level.

A) When there is no preliminary estimate available, we can use the worst-case scenario, which is p = 0.5 (since this gives the maximum possible variability). The margin of error is given as 3% or 0.03. The formula to calculate the minimum sample size needed is:

n = [Z² x p x (1 - p)] / E²

where Z is the z-value for the desired confidence level, p is the population proportion, and E is the margin of error.

At 90% confidence, the z-value is 1.645. Plugging in the values, we get:

n = [(1.645)² x 0.5 x (1 - 0.5)] / (0.03)²

n ≈ 1217.75

We need a minimum sample size of 1218 to estimate the population proportion of U.S. adults who eat fast food four to six times per week with a 90% confidence level and an accuracy of 3%.

B) If a proper study found that 11% of U.S. adults eat fast food four to six times per week, we can use this as a preliminary estimate and calculate the minimum sample size needed with the formula:

n = [Z² x p x (1 - p)] / E²

where p is the preliminary estimate of the population proportion (0.11), and the other variables are the same as before.

At 90% confidence, the z-value is 1.645. Plugging in the values, we get:

n = [(1.645)² x 0.11 x (1 - 0.11)] / (0.03)²

n ≈ 335.77

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The definition of slope-intercept form y=mx+b is given below.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

In geometry, there are two types of lines: straight and curved. Vertical and horizontal straight lines are further divided into categories. Parallel, intersecting, and perpendicular lines are further types of lines.

In the given question:-

The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope may be determined using a variety of approaches.

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Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

The term that describes measures that would be taken to decrease the size of a professional sports is contraction.

Contraction is the act of decreasing or drawing collectively to make smaller; the alternative of expansion. In this case, the proprietors need to lessen the wide variety of groups with the aid of using removing franchises which are dropping the maximum money. Players who're on Minor League or break up contracts aren't completely assured their salaries. A participant on a break up or Minor League settlement will earn the prorated part of his Major League earnings for time spent at the Major League roster.

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By using the formula for area of triangle using coordinates, the following results are obtained

13) Area of triangle = \(\frac{15}{2} \ sq. units\)

14) Area of triangle = \(\frac{49}{2} \ sq. units\)

What is area of triangle?

Area of a triangle is the total space taken by the triangle. If the coordinates of triangle are \((x_1, y_1), (x_2, _2) \ and \ (x_3, y_3)\), then area of triangle is calculated by the formula

Area of triangle = \(\frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|\)

13) The given coordinates are E (3, 1), F(3, -2) and G(-2, 2)

Area of triangle =

\(\frac{1}{2}|3(-2-2) + 3(2-1) + (-2)(1 -(-2))|\\\\\frac{1}{2}|3(-4) + 3(1) -2(3)|\\\\\frac{1}{2}|-12 + 3 - 6|\\\\\frac{1}{2}|-15|\\\\\frac{15}{2} \ sq. units\)

14) The given coordinates are E (-3, 4), F(4, 4) and G(3, -3)

Area of triangle =

\(\frac{1}{2}|(-3)(4-(-3)) + 4(-3-4) + 3(4-4)|\\\\\frac{1}{2}|(-3)(7)+4(-7)+3(0)]\\\\\frac{1}{2}|-21-28+0|\\\\\frac{1}{2}|-49|\\\\\frac{49}{2} \ sq. units\)

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Given: Radius of the wheel = 30 inches, Revolutions per minute = 401 rpmThe linear speed of the car in miles per hour can be calculated as follows:

Step 1: Convert the radius from inches to miles by multiplying it by 1/63360 (1 mile = 63360 inches).30 inches × 1/63360 miles/inch = 0.0004734848 milesStep 2: Calculate the distance traveled in one minute by the wheel using the circumference formula.Circumference = 2πr = 2 × π × 30 inches = 188.496 inchesDistance traveled in one minute = 188.496 inches/rev × 401 rev/min = 75507.696 inches/minStep 3: Convert the distance traveled in one minute from inches to miles by multiplying by 1/63360.75507.696 inches/min × 1/63360 miles/inch = 1.18786732 miles/minStep

4: Convert the distance traveled in one minute to miles per hour by multiplying by 60 (there are 60 minutes in one hour).1.18786732 miles/min × 60 min/hour = 71.2720392 miles/hour Therefore, the linear speed of the car is 71.3 miles per hour (rounded to the nearest tenth).Answer: 71.3

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The radius of the wheel on a car is 30 inches. If the wheel is revolving at 401 revolutions per minute, The linear speed of the car is approximately 19.2 miles per hour.

To find the linear speed of the car in miles per hour, we need to calculate the distance traveled in one minute and then convert it to miles per hour. Here's how we can do it step by step:

Calculate the circumference of the wheel:

The circumference of a circle is given by the formula

C = 2πr

where r is the radius of the wheel.

In this case, the radius is 30 inches, so the circumference is

C = 2π(30)

   = 60π inches.

Calculate the distance traveled in one revolution:

Since the circumference represents the distance traveled in one revolution, the distance traveled in inches per revolution is 60π inches.

Calculate the distance traveled in one minute:

Multiply the distance traveled in one revolution by the number of revolutions per minute.

In this case, it is 60π inches/rev * 401 rev/min = 24060π inches/min.

Convert the distance to miles per hour:

There are 12 inches in a foot, 5280 feet in a mile, and 60 minutes in an hour.

Divide the distance traveled in inches per minute by (12 * 5280) to convert it to miles per hour.

The final calculation is (24060π inches/min) / (12 * 5280) = (401π/66) miles/hour.

Approximating π to 3.14, the linear speed of the car is approximately (401 * 3.14 / 66) miles per hour, which is approximately 19.2 miles per hour.

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The confidence interval with the smaller margin of error will be the one with the smaller sample proportion difference.

(a) To calculate the point estimate of the proportion of respondents who think the country is headed in the right direction, divide the number of "yes" responses by the total number of respondents (2,500).
Point estimate = (number of "yes" responses) / 2,500
(b) To find the margin of error at 95% confidence, use the formula:
Margin of error = Z * √(p(1-p) / n)
Here, Z = 1.96 (from the standard normal distribution for 95% confidence), p is the point estimate calculated in part (a), and n = 2,500.
(c) To find the 95% confidence interval for the proportion of respondents who think the country is headed in the right direction, use the formula:
Confidence interval = point estimate ± margin of error
(d) To find the 95% confidence interval for the proportion of respondents who do not think the country is headed in the right direction, first calculate the point estimate for "no" responses:
Point estimate (no) = (number of "no" responses) / 2,500
Then calculate the margin of error and confidence interval as in parts (b) and (c).
(e) To determine which confidence interval has a smaller margin of error, compare the margin of error calculated in parts (b) and (d).

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Answer:

$183.3

Step-by-step explanation:

Ruth uses healthy credit to finance $2,200 for a hearing aid how much would she have to pay each month to pay back the loan in exactly 1 year

Ruth took a loan of $2,200

1 year = 12 months

Hence, the amount she would be paying monthly is calculated as:

$2,200/12 months

= $2,200/12

= $183.33333333

Approximately = $183.3

Therefore, Ruth would be paying $183.3 monthly.

Answer:

1=2 5=6 6=7 8=9 is the answer

Answer:

1089

Step-by-step explanation:

The original number is A0CD, We have that DC0A = 9 x A0CD.

If A =1, then D = 9 and we have:

9C01 = 9 x 10C9

In order for this expression to be true, the following must also be true:

(C x 9) + 8 must be divisible by 10, which means that C x 9 must end in a 2.

The only multiple of 9 (from 9 to 81) that ends in a 2 is 72.

72 = 9 x 8.

Therefore, C must be 8 and the original number is 1089. Multiply it by 9 to check the answer:

1089 x 9 = 9,081

Therefore, 1089 is correct.

We can prove that S(n+1,k)=S(n,k−1)+kS(n,k).

To prove that S(n+1,k)=S(n,k−1)+kS(n,k), we will use combinatorial argument.

Consider the set {1,2,...,n+1}. We want to partition this set into k unlabelled nonempty parts. There are two cases to consider:

Case 1: The element n+1 belongs to a part of size 1.

In this case, we have n elements to partition into k-1 parts. The number of ways to do this is S(n,k-1) since we are partitioning n elements into k-1 parts.

Case 2: The element n+1 belongs to a part of size m>1.

In this case, we have n elements to partition into k parts, with one part having size m-1. There are k ways to choose the part of size m-1, and m-1 ways to choose the element of that part that will be n+1. The remaining n-m+1 elements are partitioned into k-1 parts. The number of ways to do this is k(m-1)S(n-m+1,k-1).

Therefore, the total number of partitions of {1,2,...,n+1} into k unlabelled nonempty parts is S(n,k-1)+kS(n,k), which proves the desired formula S(n+1,k)=S(n,k−1)+kS(n,k).

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Answer:

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The coordinates of E, the midpoint of segment AB is (a/2, b/2, 0)

From the question, we have the following parameters that can be used in our computation:

B(0, b, 0)

C(0, 0, c)

A(a,0,0)

The coordinates of E, the midpoint of segment AB. is calculated as

E = 1/2(A + B)

using the above as a guide, we have the following:

E = 1/2 * (a + 0, 0 + b, 0 + 0)

When evaluated, we have

E = (a/2, b/2, 0)

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Answer:

b is less than or equal to -6

Step-by-step explanation:

1.  Multiply both sides by -1

2. Simplify

3. Divide both sides by 13