Please help! Which inequalities represents the domain & range of this problem

The r chart is used to monitor the dispersion of the process.

The r chart is a statistical tool used in quality control to monitor the dispersion or variability of a process. It is specifically used to track the range (the difference between the highest and lowest values) within subgroups of data. By plotting the ranges on the r chart over time, it becomes easier to identify any patterns or shifts in process variability. This helps in assessing the stability and consistency of the process, allowing for timely adjustments or interventions if needed.

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Answer:

4ny²+4n²-4n-8+y⁴-2y²

The equation models "Value of the house = 200,000 * (1 + 0.07t)" is properly representing the condition given.

Let's call the number of years passed "t".

The value of the house after t years is given by the equation:

Value of the house = 200,000 * (1 + 0.07t)

This equation models the situation where the value of the house increases by 7% each year, starting from 200,000.

A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.

Ax+By=C is the typical form for linear equations in two variables. 2x+3y=5, for example, is a simple linear equation. It is rather simple to get both intercepts when an equation is stated in this way (x and y).

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Answer:

1/2

Step-by-step explanation:

6 - 4(0) = 6 (incorrect answer)

6 - 4(1/2) = 4 (correct answer)

6 - 4(2) = -2 (incorrect answer)

6 - 4(4) = -10 (incorrect answer)

I hope this helps :)

Answer:

35

Step-by-step explanation:

Roses are red vilots are blue am not that pretty but Dam look at u

Answer:

35 cm²

Step-by-step explanation:

5 cm * 7 cm = 35 cm²

We will prove the statement  \(n^n / 3^n < n!\)for n ≥ 6 by induction. The base case is n = 6, and we will assume the inequality holds for some k ≥ 6. Using the induction hypothesis, we will show that it also holds for k + 1. Thus, proving the statement for n ≥ 6.

Base case: For n = 6, we have 6⁶ / 3⁶ = 46656 / 729 ≈ 64. As 6! = 720, we can see that the statement holds for n = 6.

Inductive step: Assume that the inequality holds for some k ≥ 6, i.e.,

\(k^k / 3^k < k!.\) We need to show that it holds for k + 1 as well.

Starting with the left side of the inequality:

\((k + 1)^{k + 1} / 3^{k + 1} = (k + 1) * (k + 1)^k / 3 * 3^k\)

\(= (k + 1) * (k^k / 3^k) * (k + 1) / 3\)

Since k ≥ 6, we know that (k + 1) / 3 < 1. Therefore, we can write:

\((k + 1) * (k^k / 3^k) * (k + 1) / 3 < (k + 1) * (k^k / 3^k) * 1\)

\(= (k + 1) * (k^k / 3^k)\)

< (k + 1) * k!

= (k + 1)!

Thus, we have shown that if the inequality holds for k, then it also holds for k + 1. By the principle of mathematical induction, the statement

\(n^n / 3^n < n!\) is proven for all n ≥ 6.

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Answer:

611,3300

Step-by-step explanation:

Its called g oogle.

Answer:

b

Step-by-step explanation:

I think

Answer:

i am pretty sure that the answer is A :)

The vocabulary terms have been matched to the correct definitions as follows;

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Answer:

(0,4)

Step-by-step explanation:

Here, we want to find the y-intercept of the quadratic function

g(x) = 5x^2 + 9x + 4

Mathematically, we know that the y-intercept is the position on the graph where we have x = 0

so, to find the y-intercept value, we have to find g(0)

simply put, we have to substitute the value of 0 for x

Mathematically, we have this as;

g(0) = 5(0)^2 + 9(0) + 4

g(0) = 0 + 0 + 4

g(0) = 4

thus, we have the y-intercept point as (0,4)

Work Shown:

c = number of calories in 236.5 grams of cereal

(110 calories)/(177.4 grams) = (c calories)/(236.5 grams)

110/177.4 = c/236.5

110*236.5 = 177.4*c

177.4c = 26015

c = 26015/177.4

c = 146.646 approximately

c = 146.6

There are roughly 146.6 calories in 236.5 grams of cereal.

In 236.5 grams of this cereal, there are 146.63 calories.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, There are 110 calories per 177.4 grams of cereal.

∴ In one gram of cereal of calories are (110/177.4) = 0.62 calories.

So, In 236.5 grams of this cereal, there are (236.5×0.62) = 146.63 calories.

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Answer:

the answer is 32 S=32

Step-by-step explanation:

you have to find s right so you do 162-130 =32 or 130+32=162...

Answer:

x = 12, y = 8

Step-by-step explanation:

They're congruent, just sub numbers

The all zeros of the function and the polynomial as a product of linear factors has been obtained.

What is polynomial function?

In the polynomial function f(x), we find the zeros to be x = 2, x = -1, and x = 3.The zeros of a function refer to the values of the independent variable for which the function equals zero.

To find the zeros of a polynomial function and express it as a product of linear factors, follow these steps:

1. Write the polynomial function in its factored form.

2. Set each factor equal to zero and solve for the variable.

3. The solutions obtained in step 2 represent the zeros of the function.

For example, let's consider a polynomial function.

f(x) = x^3 - 2x^2 - 5x + 6.

To find the zeros, we can factor the polynomial as,

(x - 2)(x + 1)(x - 3)

Setting each factor equal to zero, we find the zeros to be,

x = 2, x = -1, and x = 3.

Therefore, the polynomial function f(x) can be expressed as a product of linear factors: f(x) = (x - 2)(x + 1)(x - 3).

This factorization represents a unique representation of the polynomial and ensures that it can be reconstructed accurately.

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Answer:

when you 4, your sister is 2 years old

now that you 100, your sister should be 50 years old

half equal x/2 x indicates 100

(a) The Rank sum for the Drug Group is 21.50. (b) The Rank sum for the Placebo Group is 6.50. (c) The total of the Drug and Placebo rank sums is N(N+1)/2, where N is the total number of patients.

(d) No, the expected value for the Rank sums of the two groups would not be the same if the null hypothesis were true and the drug worked no better than the placebo, as they have different sample sizes.

(e) The chart can be filled out as follows:

  Observed Rank Sum: Drug Group - 21.50, Placebo Group - 6.50

  Expected Rank Sum: Both groups - N(N+1)/2

  Observed - Expected: Drug Group - (Observed Rank Sum - Expected Rank Sum), Placebo Group - (Observed Rank Sum - Expected Rank Sum)

  Total - 28

(f) Due to small sample sizes, we can use the exact probability distribution of the rank sum distribution under the null hypothesis.

(g) Assuming the sample sizes are ≥7 and the Normal Approximation can be used, the absolute value of Z can be computed using the formula: |Z| = (Observed Rank Sum - Expected Rank Sum) / SER, where SER = sqrt((n1 * n2 * (N + 1)) / 12), and N is the total number of patients in both groups. The p-value can be found using the Z-table or a calculator.

In this scenario, the explanation provided is straightforward and concise. It covers the calculation of rank sums, the difference in expected values for the two groups, the filling out of the chart, the appropriate test statistic for small sample sizes, and the computation of Z and the p-value using the Normal Approximation. The response meets the required word count and provides a clear understanding of the steps involved in the analysis of the data from the Alzheimer drug study.

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Answer:

--------------------

Both angles PQS and PRS intercept same arc PS, hence they have same measure:

Substitute values and solve for x:

Plug in the value of x into either angle measure:

The intercepted arc is twice the inscribed angle measure:

The required value of the integral is - (20/9) π.

Given integral is ∫0π​5sin2(t)cos4(t)dt.

Integral is evaluated by using integration by parts method.

We know that, integration by parts formula is given by:

∫u dv = uv - ∫v du

where u and v are functions of x.

du and dv are the derivatives of u and v respectively and dx is the variable of integration.

Let's solve the given integral.5 ∫ 0π sin2(t) cos4(t) dt

Here, u = sin2(t) and dv = cos4(t)

dtdu = 2 sin(t) cos(t) dt and v = (sin2(t)) (cos2(t))dt5 ∫ 0π sin2(t) cos4(t) dt

                                                = 5 [sin2(t) (1/3 cos3(t)) | 0π - ∫ 0π (1/3 cos3(t)) (2 sin(t) cos(t)) dt]

                                                = 5 [sin2(t) (1/3 cos3(t)) | 0π - (2/3) ∫ 0π (sin(t))2 (cos(t))2 dt]

                                                = 5 [(1/3) sin2(t) cos3(t) | 0π - (2/3) ∫ 0π (1 - cos2(t)) (1 - sin2(t)) dt]

                                                = 5 [(1/3) sin2(t) cos3(t) | 0π - (2/3) ∫ 0π (1 - cos2(t) - sin2(t) + sin2(t) cos2(t)) dt]

                                                = 5 [(1/3) sin2(t) cos3(t) | 0π - (2/3) ∫ 0π (1 - cos2(t) - sin2(t) + sin2(t)) dt]

                                                = 5 [(1/3) sin2(t) cos3(t) | 0π - (2/3) ∫ 0π (1 - cos2(t) - sin2(t) + 1 - cos2(t)) dt]

                                                = 5 [(1/3) sin2(t) cos3(t) | 0π - (2/3) ∫ 0π (2 - cos2(t) - sin2(t)) dt]

                                                = 5 [(1/3) sin2(t) cos3(t) | 0π - (2/3) (2t - (1/2) sin(2t)) | 0π]

                                                = 5 [(1/3) sin2(t) cos3(t) | 0π - 4/3 π]

                                                = - (20/9) π.

So, the required value of the integral is - (20/9) π.

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The volume V of the solid is \(\left(0,\:\sqrt{\frac{65}{16}}\right)V+C\)

To find the volume of the solid obtained by rotating the region bounded by the curves y = 15x^2 and y = 65 - x^2 about the x-axis, we can use the method of cylindrical shells.

First, let's find the points of intersection between the two curves. Setting them equal to each other, we have:

15x^2 = 65 - x^2

Combining like terms, we get:

16x^2 = 65

Simplifying further, we find:

x^2 = 65/16

Taking the square root of both sides, we get:

x = ±√(65/16)

Since we are rotating about the x-axis, we only need to consider the positive square root, which is approximately 1.539.

Next, we need to find the height of each cylindrical shell. The height can be calculated as the difference between the two curves at a given x-value. So, the height h is:

h = (65 - x^2) - 15x^2
  = 65 - 16x^2

Now, we can set up the integral to find the volume V:

V = ∫[a,b] 2πrh dx

where a is 0 (the starting point) and b is the positive square root of 65/16 (the ending point).

V = ∫[0,√(65/16)] 2π(65 - 16x^2) dx

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The scale factor of the dilation of the triangles is 2

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

The similar triangles

The scale factor of the dilation is the division of the corresponding sides

So, we have

Scale factor = 6/3

When evaluated, we have

scale factor = 2

Hence the scale factor is 2

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The answer to the problem is 1843.

To solve the equation ? − 1529 = 314,

Let the unknown be x

we need to isolate the variable on one side of the equation.

Adding 1529 to both sides, we get:

x − 1529 + 1529 = 314 + 1529

Simplifying, we get:

x = 1843

Therefore, the answer is x = 1843.

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sin(t) = -sqrt(61) / 30, cos(t) = sqrt(61) / 15, and tan(t) = -5/3.

To find sin(t), cos(t), and tan(t) we need to use the coordinates of the terminal point p(x,y) determined by the real number t.
Given that the terminal point is (1/5, -2/6), we can find the values of sin(t), cos(t), and tan(t) using the following formulas:
sin(t) = y / r
cos(t) = x / r
tan(t) = y / x
where r is the distance from the origin to the point p(x,y), which can be calculated using the Pythagorean theorem:
r = sqrt(x^2 + y^2)
Plugging in the values for the coordinates of p(x,y), we get:
r = sqrt((1/5)^2 + (-2/6)^2) = sqrt(1/25 + 4/36) = sqrt(36/900 + 25/900) = sqrt(61/900)
sin(t) = (-2/6) / (sqrt(61/900)) = -sqrt(61) / 30
cos(t) = (1/5) / (sqrt(61/900)) = sqrt(61) / 15
tan(t) = (-2/6) / (1/5) = -5/3
Therefore, sin(t) = -sqrt(61) / 30, cos(t) = sqrt(61) / 15, and tan(t) = -5/3.

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Answer: 2-

Step-by-step explanation:

the 80% confidence interval for the difference p₁ - p₂ is (0.018, 0.316).

To construct the 80% confidence interval for the difference p1 - p2 between two proportions, we can use the formula:

CI = (p₁ - p₂) ± z * sqrt((p₁ * (1 - p₁) / n₁) + (p₂ * (1 - p₂) / n₂))

where p1 and p2 are the sample proportions, n1 and n₂ are the respective sample sizes, and z is the z-score corresponding to the desired confidence level.

Given:

x₁ = 40 (number of successes in sample 1)

n₁ = 80 (sample size of sample 1)

x₂ = 20 (number of successes in sample 2)

n₂ = 60 (sample size of sample 2)

To calculate the sample proportions, we divide the number of successes by the sample size for each sample:

p₁ = x₁ / n₁ = 40 / 80 = 0.5

p₂ = x₂ / n = 20 / 60 = 0.333

Next, we need to find the z-score corresponding to the 80% confidence level. The confidence level is the complement of the significance level, which is 1 - alpha. In this case, alpha is (1 - 0.8) / 2 = 0.1 / 2 = 0.05 (splitting equally in the two tails). The z-score for a 95% confidence level (which is the same as 1 - alpha) is approximately 1.96.

Plugging in the values into the formula:

CI = (0.5 - 0.333) ± 1.96 * sqrt((0.5 * (1 - 0.5) / 80) + (0.333 * (1 - 0.333) / 60))

Calculating the expression inside the square root:

sqrt((0.5 * 0.5 / 80) + (0.333 * 0.667 / 60)) = sqrt(0.002083 + 0.003703) = sqrt(0.005786) ≈ 0.076

Plugging the values back into the confidence interval formula:

CI = (0.5 - 0.333) ± 1.96 * 0.076

Calculating the confidence interval:

CI = 0.167 ± 1.96 * 0.076

CI = 0.167 ± 0.149

Rounding to three decimal places:

CI = (0.018, 0.316)

Therefore, the 80% confidence interval for the difference p₁ - p₂ is (0.018, 0.316).

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Answer:

yeah

Step-by-step explanation:

They do not intersect???

There are 15 different positive divisors (greater than 1) for the number m³pt. Here m, p, and t are distinct prime numbers. This is obtained by the prime factorization method.

The following are the steps to find the number of positive factors of a number:

Step 1: Find the L.C.M of the number by using the prime factorization method. For example: consider the number 24. Then, its prime factorization is as follows:

24 = 2 × 2 × 2 × 3

Step 2: Same bases should be added in powers. So, the factors we can write as

24 = 2³ × 3¹

Step 3: To find the number of positive factors of the number, the exponents of the prime factors is multiplied by adding 1.

I,e., N = (3 + 1)(1 + 1) = 4 × 2 = 8.

So, there are 8 factors for the number 32. They are 1, 2, 3, 4, 6, 8, 12, and 24.

It is given that, m, p, and t are distinct positive prime numbers.

Then, the number of positive divisors greater than 1 for the number m³pt are

m³× p × t

Since m, p, and t are prime factors, we can multiply their power by adding 1 to them. I.e.,

N = (3 + 1) (1 + 1) (1 + 1) = 4 × 2 × 2 = 16

So, there are a total of 16 factors for the given number (including 1). So, the number of factors greater than 1 is 16 - 1 = 15.

Therefore, there are 15 different positive divisors greater than 1 for the number having prime factors as m³pt.

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The measure of central location is found by arranging the data from smallest to largest and selecting the middle value is "Median".

The median is the midpoint value in an ascending-ordered dataset (from the smallest value to the largest value). If a dataset has an odd range of values, the median is the mean of a two middle values.

Some characteristics of median are-

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Answer:

Imposible!

Step-by-step explanation:

When it comes to passing a multiple choice math test without studying, it is important to understand that studying and preparation are key factors in achieving success. However, if you find yourself in a situation where you haven't had the opportunity to study, there are still some strategies you can employ to increase your chances of passing the test. Familiarize yourself with the format of multiple choice questions, read the questions carefully, eliminate obviously incorrect options, use the process of elimination, make educated guesses, and manage your time effectively. While these strategies may improve your chances of passing the test, it is important to note that studying and preparation are essential for long-term success in mathematics.

When it comes to passing a multiple choice math test without studying, it is important to understand that studying and preparation are key factors in achieving success. However, if you find yourself in a situation where you haven't had the opportunity to study, there are still some strategies you can employ to increase your chances of passing the test.

While these strategies may improve your chances of passing the test, it is important to note that studying and preparation are essential for long-term success in mathematics.

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