Step by step explanation need it

Answer:

Step-by-step ex0.72

Answer:

A) Vertical test

B) y=x

C) x

D) domain

If the graph of an inverse passes the Vertical Line Test, you know that the inverse is a function.

Inverse functions are functions which can be reversed in to another function.

Then the function is said to be the inverse of the second function.

The test which is used to know whether an inverse is a function or not is Vertical line Test.

So, if the graph of an inverse passes the Vertical Line Test, you know that the inverse is a function.

Composition of a function and it's inverse is always x.

Let y = f(x) be a function. Then x = f⁻¹ (y)

(f⁻¹of)(x) = f⁻¹ (f(x)) = f⁻¹ (y) = x

The graph of an inverse is the reflection of the graph of the function over the line y = x.

The range values of the inverse function are the domain values of the original function.

Hence the blank terms are found.

Learn more about Inverse of Functions here :

https://brainly.com/question/30350743

#SPJ7

Answer:

b. 300x1 + 125x2 < = 4,000

Step-by-step explanation:

Maximum of 4,000 hours

This means that the the total amount of labor has to be of at most 4,000, that is:

[tex]T \leq 4000[/tex]

300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor

The total amount of labor is:

[tex]T = 300x1 + 125x2[/tex]

Uniting the two equations:

[tex]T \leq 4000[/tex]

[tex]300x1 + 125x2 \leq 4000[/tex]

And thus the correct answer is given by option b.

Answer:

16 x -3 and 16-3

Step-by-step explanation:

If you multiply 16 and -3 you get -48 and if you subtract 3 from 16 you get 13 (hope this helped) :)

Answer:

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

Step-by-step explanation:

Suppose that, in the past, 40% of all adults favored capital punishment. Test if the proportion has increased:

At the null hypothesis, we test if the proportion is still of 40%, that is:

[tex]H_0: p = 0.4[/tex]

At the alternative hypothesis, we test if the proportion has increased, that is, is greater than 40%, so:

[tex]H_1: p > 0.4[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that [tex]\mu = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]

Random sample of 15 adults, 8 favor capital punishment.

This means that [tex]n = 15, X = \frac{8}{15} = 0.5333[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.5333 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{15}}}[/tex]

[tex]z = 1.05[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion of 0.5333 or more, which is 1 subtracted by the p-value of z = 1.05.

Looking at the z-table, z = 1.05 has a p-value of 0.8531.

1 - 0.8531 = 0.1469.

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

Answer: Passes out in slow

Step-by-step explanation:

Step 1 be Einstein

k = -3

Step-by-step explanation:

Let's rewrite the equations in their slope-intercept forms:

[tex]y = \frac{1}{3}x + 2\:\:\:\:\:\:\:(1)[/tex]

[tex]y = kx + 12\:\:\:\:\:(2)[/tex]

In order for Eqn(2) to be perpendicular to Eqn(1), the slope of Eqn(2) must be the negative reciprocal of that of Eqn(1). Therefore, [tex]k = -3[/tex].

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Answer:

Step-by-step explanation:

16x-8y = 16 ⇒ 8x - 4y = 8, which is identical to the second equation.

The equations are equivalent, so there are an infinite number of solutions.

Answer:

top right

Step-by-step explanation:

roots of an equation = x-intercepts

Answer:

top right is the answer from my calculatins

There's nothing preventing us from computing one integral at a time:

[tex]\displaystyle \int_0^{2-x} xyz \,\mathrm dz = \frac12xyz^2\bigg|_{z=0}^{z=2-x} \\\\ = \frac12xy(2-x)^2[/tex]

[tex]\displaystyle \int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy = \frac12\int_0^{1-x}xy(2-x)^2\,\mathrm dy \\\\ = \frac14xy^2(2-x)^2\bigg|_{y=0}^{y=1-x} \\\\= \frac14x(1-x)^2(2-x)^2[/tex]

[tex]\displaystyle\int_0^1\int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy\,\mathrm dx = \frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx[/tex]

Expand the integrand completely:

[tex]x(1-x)^2(2-x)^2 = x^5-6x^4+13x^3-12x^2+4x[/tex]

Then

[tex]\displaystyle\frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx = \left(\frac16x^6-\frac65x^5+\frac{13}4x^4-4x^3+2x^2\right)\bigg|_{x=0}^{x=1} \\\\ = \boxed{\frac{13}{240}}[/tex]

Answer: Hello your question has some missing data attached below is the missing data

How well does the number of beers a student drinks predict his or her blood alcohol content (BAC)? Sixteen student volunteers at Ohio State University drank a randomly assigned number of 12-ounce cans of beer. Thirty minutes later, a police officer measured their BAC. Here are the data. The students were equally divided between men and women and differed in weight and usual drinking habits. Because of this variation, many students don’t believe that number of drinks predicts BAC well.

answer:

prediction  interval : (0.040 , 0.114)

Step-by-step explanation:

Given data:

Confidence level = 90%

Legal limit ( BAC ) = 0.08

solution

sample size = 16

Degree of freedom ( df ) = 14

critical t value =  1.761

X =  4.81

Σ(x-x)² (Sx) =  72.44

also standard error of estimates = 0.0204

Y=  -0.01270  +  0.01796 * 5 = 0.077

given that ; the predicted value of Y at x = 5

Considering individual response Y

standard error = 0.0211

margin of error = 1.761 * 0.021 = 0.0371

Hence the limits of the prediction interval is :

Lower limit  = 0.077 - 0.037 = 0.040.

Upper limit = 0.077 + 0.037 = 0.114

Finally

90% prediction interval  =  (0.040 , 0.114)

Answer:

A) 8/ 3(x-5)

Step-by-step explanation:

1) 2x+14/x^2-25 • 8x+40/6x+42=2(x+7)/ (x-5)(x+5) * 8(x+5)/ 6(x+7)

2)

after expressing every part of every fraction as product you should reduce the fraction. You can get rid of common divisor (x+5) in the denominator of the first fraction and the numerator of the second one and the common divisor (x+7) for the numerator of the first fraction and denominatorof the second one.

Then you'll get 2*8/ 6(x+5)   reduce it again, 2 and 6 have the common divisor 2

Then 8/3(x-5) is the correct answer

9514 1404 393

Answer:

  (a)  {(5, 2), (-4, 2), (3, 6), (0, 4), (-1, 2)}

Step-by-step explanation:

The only relation with no repeated x-values is the first one. The first relation is a function.

Answer:

mean: 84

median: 85

mode: 85

explainations for d and e below.

Step-by-step explanation:

mean:

(85+80+96+72+78+85+92)/7 = 544/7 = 84

median:

sort them in order from least to greatest first

72, 78, 80, 85, 85, 92, 96

find the middle number in that order, that's your median. in this case, it's 85.

mode:

number that appears the most in the order; the frequency. in this case as well, it's also 85.

answer for d:

the reason why the mean is lower than the median is because of the fact we were figuring out the average and had to divide, unlike the median where it's just the middle of the order we have.

answer for e:

(85+80+96+72+78+85+92+100)/8 = 644/8 = 80.5%

p.s: please subscribe to #gauthmath# sub reddit if you can for more help.

Answer:

right scalene

Step-by-step explanation:

Since all three sides have different lengths , this is a scalene triangle

(isosceles means two sides have the same lengths and equilateral means all three sides have the same length)

We have a right angle indicated by the box in the corner

Answer:

Megan’s at 2.5 inches per week

Answer:

115.625

PRT/100

Answer:

[tex]\displaystyle \frac{1}{9}[/tex]

Step-by-step explanation:

Hi there!

This question is asking us what the value of y is when x is -2, hence the point (-2,y).

[tex]y=3^x[/tex]

To find y, replace x in the equation with -2 and evaluate:

[tex]y=3^-^2[/tex]

When [tex]a^-^n[/tex] where n>0, [tex]a^-^n=\displaystyle \frac{1}{a^n}[/tex]:

[tex]y=\displaystyle \frac{1}{3^2} \\\\y=\displaystyle \frac{1}{9}[/tex]

I hope this helps!

Answer:     The answer is -2

Step-by-step explanation:

that is where the line starts

hope this helped

Answer:

x > -2

Step-by-step explanation:

The domain is the values that the input can take

x goes from -2( not including -2) to infinity

x > -2

Answer:

B) Its final coordinates are (8,-6)

Step-by-step explanation:

1. Translated 1 unit up and 4 units left

(-2,7) becomes (-6, 8)

2. Reflected about the x-axis

(-6,8) becomes (-6, -8)

3. Rotated 90° anticlockwise about the origin

(-6, -8) becomes (8, -6) because when rotating 90 degrees anticlockwise about the origin, point A (x,y) becomes point A' (-y,x). In other words, switch the x and y and make y negative.

Answer:

A. Men had less distress from nausea on average than women but we can not determine if this is a significant difference.

Step-by-step explanation:

Working based on the information given, the mean values of each group with with men having an average score of 1.02 and women have an average of 1.79 this reveals that distressing nausea on average is higher in women than in men . However, to test if there is a significant difference would be challenging as the information given isn't enough to make proceed with the test as the standard deviations of the two groups aren't given and no accompanying sample data is given.

Answer:

The answer is [tex]x=-16[/tex] ±[tex]2\sqrt{3}[/tex] in exact form or [tex]x=-12.535898[/tex], [tex]x=-19.464102[/tex] in decimal form.

Step-by-step explanation:

To solve this problem, start by moving all terms to the left side of the equation and simplify. Simplify the equation by subtracting 12 from both sides of the equation and squaring [tex]x+16[/tex], which will look like [tex]x^{2} +32x+256-12=0[/tex]. Next, simplify the equation again, which will look like [tex]x^{2} +32x+244=0[/tex].

Then, use the quadratic formula to find the solutions. The quadratic formula looks like[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex].

For this problem, the quadratic variables are as follows:

[tex]a=1[/tex]

[tex]b=32[/tex]

[tex]c=244[/tex]

The next step is to substitute the values [tex]a=1[/tex], [tex]b=32[/tex], and [tex]c=244[/tex] into the quadratic formula and solve. The quadratic formula will look like [tex]\frac{-32(+-)\sqrt{32^2-4(1*244)} }{2*1}[/tex]. To simplify the equation, start by simplifying the numerator, which will look like [tex]x=\frac{-32(+-)4\sqrt{3} }{2*1}[/tex]. Then, multiply 2 by 1 and simplify the equation, which will look like [tex]x=-16(+-)2\sqrt{3}[/tex]. The final answer is [tex]x=-16[/tex] ±[tex]2\sqrt{3}[/tex] in exact form. In decimal form, the final answer is [tex]x=-12.535898[/tex], [tex]x=-19.464102[/tex].  

Answer:  [tex]M = \pm\sqrt{\frac{3K}{4(5+7NK)}}\\\\[/tex]

======================================

Work Shown:

[tex]\frac{5}{K} = \frac{3}{4M^2} - 7N\\\\\frac{5}{K}+7N = \frac{3}{4M^2}\\\\\frac{5}{K}+7N*\frac{K}{K} = \frac{3}{4M^2}\\\\\frac{5}{K}+\frac{7NK}{K} = \frac{3}{4M^2}\\\\\frac{5+7NK}{K} = \frac{3}{4M^2}\\\\4M^2*(5+7NK) = K*3\\\\M^2 = \frac{3K}{4(5+7NK)}\\\\M = \pm\sqrt{\frac{3K}{4(5+7NK)}}\\\\[/tex]

Other forms are possible, but those forms would be equivalent to what is shown above.

Answer:

(11.242 ; 12.958)

Step-by-step explanation:

The confidence interval is obtained using the relation :

C. I = xbar ± Zcritical * s/√n

Given that ::

xbar = 12.1 ;

Standard deviation, s = 16.6

n = 1012

C. I = 12.1 ± 1.645 * (16.6/√1012)

C.I = 12.1 ± 0.8583881

C. I = 11.242 ; 12.958

Answer:

x = 20

y = 10

it's a 30-60-90 triangle

Answer:

-1.683

Step-by-step explanation:

Given :

Group 1 :

x1 = 667 ; n1 = 10 ; s1 = 20

Group 2 :

x2 = 679 ; n2 = 14 ; s2 = 15

The test statistic assuming equal variance :

x1 - x2 / √[Sp² * (1/n1 + 1/n2)]

sp² = [(n1 - 1)*s1² + (n2 - 1)*s2²] ÷ (n1 + n2 - 2)

Sp² = [(10 - 1)*20² + (14 - 1)*15²] = 296.59

Test statistic =

(667 - 679)/ √[296.59 * (1/10 + 1/14)]

-12 / 7.1304978

Test statistic = - 1.682

let the line between 2 tria be y

sin 60/8√2 = sin 90/y

y=13.06

sin 45/13.06 = sin 90/x

x=18.46

Answer:

First, find the hypotenuse of the right triangle with the 60° & 30°.

[tex]sin(60) = \frac{8\sqrt{2}}{h} \\\\sin(60)h=8\sqrt{2}\\\\\frac{\sqrt{3}}{2} h=8\sqrt{2}\\\\h=\frac{8\sqrt{2}}{\frac{\sqrt{3}}{2}}=8\sqrt{2}*\frac{2}{\sqrt{3}} =\frac{16\sqrt{2} }{\sqrt{3}} =\frac{16\sqrt{2}(\sqrt{3}) }{\sqrt{3}(\sqrt{3})} =\frac{16\sqrt{6} }{3}[/tex]

Use that side length to find x.

[tex]sin(45)=\frac{\frac{16\sqrt{6}}{3}}{x}\\\\sin(45)x=\frac{16\sqrt{6}}{3} \\\\\frac{\sqrt{2}}{2}x=\frac{16\sqrt{6}}{3} \\\\x=\frac{\frac{16\sqrt{6}}{3}}{\frac{\sqrt{2}}{2}}=\frac{16\sqrt{6}}{3}*\frac{2}{\sqrt{2}}=\frac{16\sqrt{2}\sqrt{3}(2)}{3\sqrt{2} }=\frac{32\sqrt{3} }{3}[/tex]

Answer:

b or a

Step-by-step explanation: