Find the slope of the line that passes through (10, 10) and (3, 2).

Answer:

If two lines are perpendicular and neither one is vertical, then one of the lines has a positive slope, and the other has a negative slope. Hope this helps.

Step-by-step explanation:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

test scores = 82, 89, and 91

average ≤ 93

inequality = ?

Step 02:

x = score on the next test

inequality:

(82 + 89 + 91 + x ) / 4 ≤ 93

Answer:

\(y = -\frac{1}{5}x + 5\)

Step-by-step explanation:

Given

\(5\ minutes = 4\ miles\)

\(15\ minutes = 2\ miles\)

Required

Determine the equation

y represents distance

x represents time

So, the given parameters can be modeled (x,y) as:

\((x_1,y_1) = (5,4)\)

\((x_2,y_2) = (15,2)\)

First, we need to determine the slope of the function.

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{2 - 4}{15 - 5}\)

\(m = \frac{-2}{10}\)

\(m = -\frac{1}{5}\)

The equation can be determined using:

\(y - y_1 = m(x - x_1)\)

Where

\(m = -\frac{1}{5}\)

\((x_1,y_1) = (5,4)\)

\(y - y_1 = m(x - x_1)\)

becomes

\(y - 4 = \frac{-1}{5}(x - 5)\)

Open bracket

\(y - 4 = -\frac{1}{5}x + 1\)

Solve for y

\(y = -\frac{1}{5}x + 1 + 4\)

\(y = -\frac{1}{5}x + 5\)

Answer:

2

Step-by-step explanation:

As per the interval, x = 1 and y = 5/2

Substitute x into the expression:

3 - 1 = 2

To determine the necessary sample size for a 95% confidence interval (CI) with a maximum width of 0.10, we need to use the formula:

n = [z*σ / E]^2

Where:
- n is the sample size
- z is the z-score associated with the desired confidence level (in this case, 1.96 for 95% CI)
- σ is the standard deviation of the population (unknown in this case)
- E is the maximum error margin, which is half of the maximum width of the CI (0.10/2 = 0.05)

Since we do not know the standard deviation of the population (p), we can use the worst-case scenario of p = 0.5, which results in the largest possible sample size. This is also known as the conservative or worst-case estimate.

Thus, plugging in the values:

n = [1.96*sqrt(0.5*0.5) / 0.05]^2
n = 384.16

Rounding up to the nearest integer, the necessary sample size is 385. Therefore, a sample size of at least 385 is required to achieve a 95% CI with a maximum width of 0.10, regardless of the value of p.
To determine the sample size necessary for a 95% confidence interval (CI) for the proportion p with a width of at most 0.10, you can use the formula for the margin of error (ME) in a proportion:

ME = z * sqrt((p * (1-p)) / n)

Here, z is the critical value corresponding to the desired level of confidence (95%), n is the sample size, and ME is the margin of error. Since the desired width of the CI is 0.10, the margin of error is 0.10/2 = 0.05, as the CI spans both above and below the point estimate.

For a 95% CI, the z-value is 1.96. Since we want the sample size irrespective of p, we need to find the maximum value for the expression (p * (1-p)). This occurs when p = 0.5. So, we can use the formula:

0.05 = 1.96 * sqrt((0.5 * (1-0.5)) / n)

Now, we need to solve for n:

(0.05 / 1.96)^2 = (0.5 * 0.5) / n
0.000645^2 = 0.25 / n
n = 0.25 / 0.000645
n ≈ 387.596

Since the sample size must be a whole number, we can round up to 388 to ensure the CI width is at most 0.10.

So, the necessary sample size is 388.

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Answer:

20.25-923

Step-by-step explanation:

20.25-923

912+11=923

Answer:

The type of number that represents -4/2 is:

Choice B) Integer

Choice C) Rational

Step-by-step explanation:

The number -4/2 is an integer because it represents a whole number (-2) and it is also a rational number because it can be expressed as a fraction of two integers.

-4/2 is an :

Solution:

Before we make any decisions about the type of number -4/2 is, let's simplify it first.

It's the same as -2. Now, let's familiarize ourselves with the sets of numbers out there. Where does -2 fit in?

______________

This set incorporates only positive numbers and zero. So -2 doesn't belong here.

This set incorporates whole numbers and negative numbers. So -2 belongs here.

This set has integers, fractions, and decimals. So -2 does belong here too.

This is a set for numbers that cannot be written in fraction form (a/b, where b ≠ 0). So -2 doesn't belong here.

-4/2 belongs in the integer and rationals set.

Answer:

24

Step-by-step explanation:

What you have here is a permutation, seeing as each element can only be used once.

We have 4 letters initially, so we can choose any 1 as our first letter. We have 4 choices for our first letter

However, once we choose our first letter, we can't use it anymore, so, for our second letter, we can only choose from the remaining 3 letters.

Furthermore, once we choose our second letter, we can only choose our 3rd letter from the remaining two letters we didn't choose yet.

Finally, our last letter will always be the one we didn't choose the last 3 times. So there is only one choice here.

Going off of this, we have four choices for the 1st letter, three choices for the 2nd letter, two choices for the 3rd letter, and one choice for the 4th letter

The way to calculate how many permutations we have without repetition is using factorials

N!

Where N is the number of elements you have.

In this case, it would be 4!

4! is 4 * 3 * 2 * 1

Which equals 24

If you notice, each number in 4! is the number of options we have for each choice. 4, then 3, and so on

With 95% confidence that the true population mean weight of the sardine cans is between 7.813 oz and 7.887 oz.

In this scenario, we have a cannery that claims their sardine cans have a net weight of 8 oz. We want to test this claim by taking a simple random sample of 30 cans and measuring their weights.

From our sample of 30 cans, we calculated a sample mean of 7.85 oz and a standard deviation of 0.1 oz. The sample mean is an estimate of the population mean, and the standard deviation tells us how much the weights in our sample vary from the mean.

To determine the cutoff values for the middle 95% of the mean weights in this distribution based on the sample data, we can use the t-distribution with n-1 degrees of freedom. The degrees of freedom in this case are 29, which is one less than the sample size.

Using a t-distribution table or calculator, we can find the t-value for a 95% confidence level with 29 degrees of freedom, which is approximately 2.045. We can use this t-value to calculate the margin of error for the sample mean as:

margin of error = t-value * (standard deviation / square root of sample size)

= 2.045 * (0.1 / √(30))

= 0.037

The margin of error tells us how much the sample mean is likely to vary from the true population mean. To find the cutoff values for the middle 95% of the mean weights, we add and subtract the margin of error from the sample mean as follows:

lower cutoff value = sample mean - margin of error

= 7.85 - 0.037

= 7.813

upper cutoff value = sample mean + margin of error

= 7.85 + 0.037

= 7.887

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The answer choices which are functions as required are;

The answer choices which are not functions are;

A function is a special kind of relation in which case no single input, x value is assigned more than 1 output value. On this note, it follows that the answer choices which are functions are those in which case, every input value only has one out put value assigned to it.

Ultimately, the relations which are functions are; {(-4, 4), (-3, 4), (-2, 4), (-1, 4)} and {(2,-6), (-2,-6), (3,5), (0,0)} .

Those which are not functions are; {(1,7), (0,4), (-3,5), (1,9)} and {(8,-12), (-8 , 14), (7, -15), (-8, 18)}.

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Answer:

y = 2/3x + 3 2/3

Step-by-step explanation:

slope intercept form: y = mx + b

isolate the y => y = 2/3(x - 2) + 5 => y = 2/3x - 4/3 + 5 => y = 2/3x + 3 2/3

Answer:

\(\frac{2c-2b}{cd-3t}\)

Step-by-step explanation:

In the experiment, the independent variable is the amount of sunlight received by the clover plants.

The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.

The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.

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Answer:

The answer is C.

Answer:b

Step-by-step explanation:

The Solution.

Writing the above equation in index form, we have

To evaluate the series Σ(n^2 - 4n + 5)/(n-1) from n=8 to ∞ using the Integral Test, we compare it with the integral of the corresponding function.

Step 1: Determine the corresponding function f(n):

f(n) = (n^2 - 4n + 5)/(n-1) Step 2: Check the conditions of the Integral Test:

(a) The function f(n) is positive and decreasing for n ≥ 8: To check positivity, observe that the numerator (n^2 - 4n + 5) is always positive (quadratic with positive leading coefficient). To check decreasing, take the derivative of f(n) with respect to n and show that it is negative:

f'(n) = (2n - 4)(n-1)/(n-1)^2

The factor (n-1)/(n-1)^2 is always positive, and (2n - 4) is negative for n ≥ 8, so f'(n) is negative for n ≥ 8.

(b) The integral ∫(8 to ∞) f(n) dn is finite or infinite: Let's evaluate the integral: ∫(8 to ∞) f(n) dn = ∫(8 to ∞) [(n^2 - 4n + 5)/(n-1)] dn

= ∫(8 to ∞) [n + 3 + 2/(n-1)] dn

= [(1/2)n^2 + 3n + 2ln|n-1|] evaluated from 8 to ∞

As n approaches infinity, the terms involving n^2 and n dominate, while the term involving ln|n-1| approaches infinity slowly. Therefore, the integral is infinite.

Step 3: Apply the Integral Test:

Since the integral ∫(8 to ∞) f(n) dn is infinite, by the Integral Test, the series Σ(n^2 - 4n + 5)/(n-1) from n=8 to ∞ is also divergent.

Therefore, the series does not converge.

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Answer: 0 = -4x + b

Step-by-step explanation: Write -4x as -4 over 1 (-4/1) and using rise over run you move down 4 and right 1. Then you move up 4 and left 1. Plot those two points where you stopped. That doesn't matter though in this case, you only need the equation.

Answer:

29 text messages

Step-by-step explanation:

1.45 divided by .05 to get 29 text messages

Answer:

29

Step-by-step explanation:

well if 0.05x2 is 0.10, 0.05x10 is p.50 then 0.05x20 is 1.00 0.45 is one 0.05 away from .50, it is 1.45

it is 29

Answer:

504

Step-by-step explanation:

140 divided by 5 is 28 so for every centimeter there is 28 kilometers so 18x28=504

Answer:

5000

Step-by-step explanation:

\( \frac{52}{100} = \frac{2600}{x} \\ x = 5000\)

The number of degrees of freedom we should use is 14 for makin95% confidence interval.

Degrees of freedom of an estimate is the number of independent pieces of information that went into calculating the estimate. It’s not quite the same as the number of items in the sample. In order to get the df for the estimate, you have to subtract 1 from the number of items.

Degree of freedom of sample size of n : n -1

When we don't have any idea about population standard deviation,

and also, the sample size is less than 30 .

We use t-distribution to calculated the statistics.

According to the question,

We are making a 95% confidence interval

The sample is 15 (<30) . So , we have to adjust and use a t-value instead of a Z score in order to account for the smaller sample size and using the sample SD.  

Note that the t-value depends on the degrees of freedom (df) as a reflection of sample size. When using the t-distribution to compute a confidence interval, df = n-1.

So , making 95% confidence interval for population mean from sample size 15 , we need degree of freedom of 14

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Answer:

S = 3

S = 5

S = 7

S = 9

Step-by-step explanation:

t = 3s + 2

when t = 11

11 = 3s + 2

11 – 2 = 3s

9 = 3s

s = 3

t = 3s + 2

when t = 17

17 = 3s + 2

17 – 2 = 3s

15 = 3s

s = 5

t = 3s + 2

when t = 23

23 = 3s + 2

23 – 2 = 3s

21 = 3s

s = 7

t = 3s + 2

when t = 29

29 = 3s + 2

29 – 2 = 3s

27 = 3s

s = 9

I HOPE ALL THIS HELPS

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The z score for the actor is -2.04, and the z score for the actress is 1.69. The actor had the more extreme age as their z score was further away from the mean compared to the actress.

z score for actor

z = (32 - 43.7) / 8.8 = -2.04

z score for actress

z = (53 - 34.5) / 11.2 = 1.69

Since the z score for the actor is more negative than the z score for the actress, the actor had the more extreme age.

The z score is a measure of how far a specific value is away from the mean, in terms of standard deviations. A negative z score indicates that the value is below the mean, while a positive z score indicates that the value is above the mean.

In this case, both the actor and the actress had ages that were below the mean for their respective genders. However, the actor's age was further below the mean than the actress's age. Therefore, the actor had the more extreme age.

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Answer:4x2−6x−4

Step-by-step explanation:

(4x+2)(x−2)

=(4x+2)(x+−2)

=(4x)(x)+(4x)(−2)+(2)(x)+(2)(−2)

=4x2−8x+2x−4

=4x2−6x−4

Answer:

(4x+2)(x-2)

= 4x(x-2) +2(x-2)

=4x^2-8x + 2x-4

=4x^2 - 6x -4

Answer:

Step-by-step explanation:

gnag  dsewhqjhnqrhjwqkhjqrkhwq

The inequality states that the value of z must be greater than or equal to 0 and less than or equal to h, which ensures that all points within the slab are included.

The slab bounded by the planes 0 and ​(planes​ included) is a region in three-dimensional space that is defined by two parallel planes, one located at z = 0 and the other at

z = h.

Any point inside this region has a z-coordinate that is greater than or equal to 0 and less than or equal to h. Therefore, we can describe this region using an inequality in terms of z, as shown above.The inequality 0 ≤ z ≤ h is a useful one because it ensures that all points within the slab are included.

If we were to use a strict inequality like 0 < z < h, we would exclude points on the boundary of the slab. On the other hand, if we were to use an inequality like z ≤ h or 0 ≤ z, we would include points outside the slab. Therefore, the inequality 0 ≤ z ≤ h is the most appropriate one for describing this region. Inequalities are mathematical expressions that relate two quantities using a less than, greater than, less than or equal to, or greater than or equal to sign. Inequalities can be used to describe a variety of geometric shapes and regions in space, such as slabs bounded by two parallel planes.

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