Find the domain and range of the function graphed below, in interval notation.

Answer:

11/6

Step-by-step explanation:

Answer:

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose a large shipment of televisions contained 9% defectives

This means that [tex]p = 0.09[/tex]

Sample of size 393

This means that [tex]n = 393[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]

What is the probability that the sample proportion will differ from the population proportion by less than 3%?

Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.

X = 0.12

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]

[tex]Z = 2.08[/tex]

[tex]Z = 2.08[/tex] has a p-value of 0.9812

X = 0.06

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]

[tex]Z = -2.08[/tex]

[tex]Z = -2.08[/tex] has a p-value of 0.0188

0.9812 - 0.0188 = 0.9624

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

Both E and F are sets.

E = {w | w ≤ 2}

means that E is the set of all numbers w satisfying the condition that w ≤ 2. In other words, E contains all real numbers less than and including 2.

Similarly,

F = {w | w > 9}

is the set of all real numbers strictly greater than 9.

The intersection of E and F, denoted E ∩ F, is the set that contains the overlap of the two sets, or all the numbers that are common to both sets. In this case, E ∩ F is the empty set; this is because all numbers small than 2 cannot be larger than 9, so E ∩ F = ∅.

The union of E and F, written as E ∪ F, is the set containing all elements from both sets. In interval notation, E = (-∞, 2] and F = (9, ∞), so E ∪ F = (-∞, 2] ∪ (9, ∞).

Answer:

the degree is the value of the biggest exponent = 5 (fifth degree)

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Since the highest power of x is 5, the degree of the polynomial x

3

−9x+3x

5

is 5.

Answer:

Look into the picture

Step-by-step explanation:

Let me know if there's something wrong to my answer

Answer:

(1,7), (2,2), (3,5) (4,8)

(2,6), (6,5), (3,2) (5,3)

(4,3), (3,3), (2,3) (1,3)

Step-by-step explanation:

those represent functions b/c the domain of the relation is not written twice

Hope that'll help!

Option C

SOLUTION:

We need to find the value of B - CF

First find the value CF:

[tex]CF=\left[\begin{array}{ccc}12&0&1.5\\1&-6&7\\\end{array}\right] \left[\begin{array}{ccc}-2&0\\0&8\\2&1\end{array}\right][/tex]

[tex]CF=\left[\begin{array}{ccc}12(-2)+0 *0+1.5*2&12*0+0.8+1.5*1\\1*(-2)+(-6)*0+7.2&1*0+(-6)*8+7.1\\\end{array}\right][/tex]

[tex]CF=\left[\begin{array}{ccc}-21&1.5\\12&-41\\\end{array}\right][/tex]

Now find value of B - CF:

[tex]B-CF=\left[\begin{array}{ccc}2&8\\6&3\\\end{array}\right] -\left[\begin{array}{ccc}-21&1.5\\12&-41\\\end{array}\right][/tex]

[tex]B-CF=\left[\begin{array}{ccc}23&6.5\\-6&44\\\end{array}\right][/tex]

∴ the value of B - CF is [tex]\left[\begin{array}{ccc}23&6.5\\-6&44\\\end{array}\right][/tex]

I hope this helps....

Answer:

Step 1

Because the number in front of the bracket is 1 and it is also affected by the negative sign(-),5 is supposed to be negative not positive because (negative by positive is negative)

And since the first step has an error in it,the remaining steps would also be wrong.

Answer:

0.8743 = 87.43% probability that more than one accident occurs per year

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Buchtal, a manufacturer of ceramic tiles, reports on average 3.1 job-related accidents per year.

This means that [tex]\mu = 3.1[/tex]

What is the probability that more than one accident occurs per year?

This is:

[tex]P(X > 1) = 1 - P(X \leq 1)[/tex]

In which

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

Then

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3.6}*(3.6)^{0}}{(0)!} = 0.0273[/tex]

[tex]P(X = 1) = \frac{e^{-3.6}*(3.6)^{1}}{(1)!} = 0.0984[/tex]

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0273 + 0.0984 = 0.1257[/tex]

[tex]P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1257 = 0.8743[/tex]

0.8743 = 87.43% probability that more than one accident occurs per year

Answer:

Yes

Step-by-step explanation:

If you replace each x with -3 and each y with 2 you get:

1) 2<-4*(-3)

2<12

True

2) -3+8*2>7

13>7

True

Therefore the point is part of the solution set

Answer:

9 4/24 or 9 1/6

9514 1404 393

Answer:

  (t, u, w) = (1, -2, -2)

Step-by-step explanation:

A graphing calculator makes short work of this, giving the solution as ...

  (t, u, w) = (1, -2, -2)

__

There are many ways to solve this "by hand." Here's one of them.

Add the first and third equations. Their sum is ...

  -3t +4w = -11 . . . . . [eq4]

Add this to twice the second equation. That sum is ...

  (-3t +4w) +2(-4t -2w) = (-11) +2(0)

  -11t = -11

  t = 1

Substituting this into the second equation gives ...

  -4(1) -2w = 0

  w +2 = 0 . . . . divide by -2

  w = -2 . . . . add -2

Substituting for t in the third equation lets us find u.

  2(1) -2u = 6

  -1 +u = -3 . . . . . divide by -2

  u = -2 . . . . add 1

The solution is (t, u, w) = (1, -2, -2).

The angle C of the triangle ABC is ( π - 3a ).

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

The angle will be calculated as follows:-

We know that the sum of the angles of the triangle is 180 degrees or π in radians.

∠A + ∠B + ∠C = π

a + 2a + ∠C = π

∠C = π - a - 2a

∠C = π - 3a

Therefore angle C of the triangle ABC is ( π - 3a ).

To know more about an angle follow

https://brainly.com/question/25770607

#SPJ2

Answer:

If you are working with equilateral triangles, divide 180 by three to find the value of X. All of the angles of an equilateral triangle are equal. Solve for X in interesting lines by finding the value of one adjacent angle and subtracting it from 180 degrees.

Step-by-step explanation:

Answer:

option one is the correct answer

Answer:

1/625

Step-by-step explanation:

Answer:

(-7, -1) =(x1,y1)

(8, 5)=(x2,y2)

now

[tex]slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]

[tex]or = \frac{5 - ( - 1)}{8 - ( - 7)} [/tex]

[tex]or = \frac{5 + 1} {8 + 7} [/tex]

[tex]or = \frac{6}{15} [/tex]

[tex]or = \frac{2}{5} [/tex]

Step-by-step explanation:

hope it is helpful to you ☺️

the median of restaurant b's cleanliness ratings is 2.

the median of restaurant b's food quality ratings is 4.

the median of restaurant b's service ratings is 3.

:))

Answer:

x=-6, y=0

Step-by-step explanation:

it's impossible to fully solve an equation where 2 variables are unknown. So we have to make it equal to 1 set. to do this, we have to think logically.

if y=x+6, then that means wherever it says y, we can put x+6. because x+6=x+6, right? so we plug x+6 into the second equation and get.

x+6=0.5x+3

to solve for x we subtract 6 from one side and 0.5 from the other and get

0.5x=-3

then we multiply both sides by 2 to make be a whole number

x=-6

now we just plug this into either equation. because the first one is easier, we can just set it up as

y=(-6)+6

which means y=0

Answer:

You're correct

Step-by-step explanation:

Answer:

By using a pair of compasses and a ruler you can draw all angles

Answer:

3396.65

Step-by-step explanation:

Let's start by cacluating the amount the bank is loaning us

800000*.8=640000

Let's now calculate the effective rate: .049/12= .004083333333

let x= payment

[tex]640000=x\frac{1-(1+.004083333333)^{-30*12}}{.004083333333}\\x=3396.651012[/tex]

Lauren will get 2/25 because the coin only lands on heads or tail

Answer:

The probability that the proportion of airborne viruses in a sample of 662 viruses would be greater than 6%=0.00427

Step-by-step explanation:

We are given that

[tex]\mu_{\hat{p}}=p=4%=0.04[/tex]

n=662

We have to find the probability that the proportion of airborne viruses in a sample of 662 viruses would be greater than 6%.

q=1-p=1-0.04=0.96

[tex]\sigma_{\hat{p}}=\sqrt{p(1-p)/n}[/tex]

[tex]\sigma_{\hat{p}}=\sqrt{\frac{0.04(1-0.04)}{662}}[/tex]

[tex]\sigma_{\hat{p}}=0.0076[/tex]

Now,

[tex]P(\hat{p}>0.06)=1-P(\hat{p}<0.06)[/tex]

[tex]=1-P(\frac{\hat{p}-\mu_{\hat{p}}}{\sigma_{\hat{p}}}<\frac{0.06-0.04}{0.0076})[/tex]

[tex]=1-P(Z<2.63)[/tex]

[tex]=1-0.99573[/tex]

[tex]P(\hat{p}>0.06)=0.00427[/tex]

Hence, the probability that the proportion of airborne viruses in a sample of 662 viruses would be greater than 6%=0.00427

Answer

all y values change sign that is reflection over x axis SKETCH IT !!!!

More

Answer:

y = -2(x + 3)² + 2

y = 2{ -(x + 3)²+ 1}

y = 2{ -(x² + 6x + 9) + 1}

y = 2{ -x² - 6x - 9 + 1}

y = 2{ -x² - 6x - 8 }

y = -2 { x² + 6x + 8}

OR

y = -2{(x + 4)(x + 2)}

Answer:

[-3, -1]

Step-by-step explanation:

The minimum y value is -3.

The maximum y value is -1.

-3 and -1 are included, so we use square brackets.

Answer: [-3, -1]

Given:

The graph that represents the enrollment for college R between 1950 and 2000.

To find:

The average rate of increase in enrollment per decade between 1950 and 2000?

Solution:

The average rate of change of function f(x) over the interval [a,b] is:

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

So, the average rate of increase in enrollment per year between 1950 and 2000 is:

[tex]m=\dfrac{f(2000)-f(1950)}{2000-1950}[/tex]

[tex]m=\dfrac{7-4}{50}[/tex]

[tex]m=\dfrac{3}{50}[/tex]

[tex]m=0.06[/tex]

It is given average rate of increase in enrollment per year between 1950 and 2000 is 0.06.

We need to find the average rate of increase in enrollment per decade between 1950 and 2000, So, multiply the average rate of increase in enrollment per year by 10.

[tex]0.06\times 10=0.6[/tex]

Therefore, the average rate of increase in enrollment per decade between 1950 and 2000 is 0.6.

Answer:

4.286

Step-by-step explanation:

you really need help with this ? you cannot just use your calculator ? that would have been faster than putting that question in here ...

remember, similar to the number positions in front of the decimal point, it is equally important to add the same positions after the decimal point.

we have 10th, 100th, 1000th, 10000th, 100000th, ... no end possible.

so we have

2.826 miles

and need to add 1.46 miles

2.826

1.46

----------

4.286

and the line of thinking goes from right to left

nothing plus 6 is 6

6 plus 2 is 8

4 plus 8 is 12, so we write 2 and carry over the 1

1 plus 2 plus 1 carry over is 4

if it helps, you can always add zeroes at the end of any digits after the decimal point, as you can also add zeroes in front to the digits before the decimal point to make both numbers have the same length and their decimal points are perfectly aligned.

our addition could have also looked like

2.826

1.460

with the same result

overall, if this is truly helping you, an example of using both leading and tailing zeroes could be

4278.9472081

0021.6380000

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

4300.5852081

Answer:

0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean diameter of 144 millimeters, and a variance of 49.

This means that [tex]\mu = 144, \sigma = \sqrt{49} = 7[/tex]

Sample of 46:

This means that [tex]n = 46, s = \frac{7}{\sqrt{46}}[/tex]

Wat is the probability that the sample mean would differ from the population mean by more than 2 millimeters?

Above 144 + 2 = 146 or below 144 - 2 = 142. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them and multiply by two.

Probability the sample mean is below 142:

p-value of Z when X = 142, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{142 - 144}{\frac{7}{\sqrt{46}}}[/tex]

[tex]Z = -1.94[/tex]

[tex]Z = -1.94[/tex] has a p-value of 0.0262

2*0.0262 = 0.0524

0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.

Answer:

pretty sure it could

Step-by-step explanation:

Answer:

What it's asking is for 2 angles at different angles of attack, are parallel

Step-by-step explanation:

for example, // these two slashes are parallel because they wont ever touch, it wants you to find if the angles are parallel or not.