PLEASE HELP 34 pointsssss

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{f(x)}{y}\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\sqrt{4y+5}}\implies x^2=4y+5\implies x^2-5=4y \\\\\\ \cfrac{x^2-5}{4}=y\implies \cfrac{1}{4}(x^2-5)=\stackrel{f^{-1}(x)}{y}\qquad x\geqslant 0[/tex]

now, I don't see any good reason why x ⩾ 0 or x ⩽ 0 , since any negative or positive values are perfectly valid.

Answer:

[tex]\textsf{C)} \quad f^{-1}(x)=\dfrac{1}{4}(x^2-5), \;\; x \geq 0[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\sqrt{4x+5}[/tex]

The domain of the given function is restricted to x ≥ -⁵/₄.

Therefore, the range of the given function is restricted to f(x) ≥ 0.

The inverse of a function is its reflection in the line y = x.

To find the inverse of a function, swap x and y:

[tex]\implies x=\sqrt{4y+5}[/tex]

Rearrange the equation to make y the subject:

[tex]\implies x^2=4y+5[/tex]

[tex]\implies 4y=x^2-5[/tex]

[tex]\implies y=\dfrac{1}{4}(x^2-5)[/tex]

Replace y with f⁻¹(x):

[tex]\implies f^{-1}(x)=\dfrac{1}{4}(x^2-5)[/tex]

The domain of the inverse of a function is the range of the original function.  

Therefore, the domain of the inverse function is x ≥ 0.

Therefore, the inverse of the given function is:

[tex]f^{-1}(x)=\dfrac{1}{4}(x^2-5), \;\; x \geq 0[/tex]

x + z can't be result in a value that's rational.

x + z is never rational.

Given,

In the question:

Let x be a rational number not equal to zero and let z be an irrational number.

To determine whether the operation results in a value that is always rational, never rational, or sometimes rational.

Now, According to the question;

Assume, x + z results in a value that is rational

m = x + z

z = m - x  (m, x is rational)

∴ m - x is a rational.

but z is an irrational number.

So, x + z can't be result in a value that's rational.

x + z is never rational.

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THe given series is GP series

common ratio n =5

The series is given 4,20,100...

then common ratio is 20/4=5

and another is 100/20=5

so common ratio is same

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The  slope-intercept form  is  y = -1/3x +7 .

What is an explanation of the slope-intercept form?

The standard form equation can be found by using the given point values in the given equation to find the new constant.

 x +3y = (6) +3(5) = 21

Solving for y puts this equation into slope-intercept form.

 3y = -x +21 . . . . . . . subtract x

 y = -1/3x +7 . . . . . . divide by 3.

This is slope-intercept form.

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The value of the expression (x-4) minus -8x² - 8 is [tex]8x^{2}[/tex]+x+4.

According to the question,

We have the following information:

x - 4 minus -8x² - 8

Now, we will convert this into an expression only using mathematical signs. So, we have the following expression:

(x-4)-(-8x² - 8)

Now, we know that the multiplication of two negative integers gives us the positive results and the multiplication of one positive and one negative integer give us the negative results.

So, we have the following expression after multiplying -1 into the bracket :

x-4+8[tex]x^{2}[/tex]+8

[tex]8x^{2}[/tex]+x+4

Hence, the value of the expression (x-4) minus -8x² - 8 is [tex]8x^{2}[/tex]+x+4.

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The percentage of students that graduated from college that also attended a high school is given as 0.7792 or 77.92 percent.

We have the Prob(attended public school | graduated)

The probability that a person attended public school and graduated as

Prob (P and G) = 0.80 x 0.75

= 0.6

The probability that a person graduated is given as

0.8*0.75 + (1 - 0.8 * 0.85)

= 0.6 + 0.17

= 0.77

Prob(P and G ) /Prob(G)

= 0.6 / 0.77

= 0.7792

The percentage is given as 77.92%

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The percentage of women that have heights between 64 and 66 inches is 42.06%

The third quartile is 65.1875 inches

Part a

Given: mean=63.5 inches

std. deviation=2.5 inches

To find percentage: we calculate probability and convert to percentage

P(64<X<66) would mean

Z statistic=64-63.5/2.5=0.2

                 =66-63.5/2.5=1

From Z table, we find corresponding probability values.

Therefore, P(64<X<66)=P(0.2<Z<1)=0.84134-0.42074

                                                                     =0.4206

Thus percentage=0.4206*100

                           =42.06%

Part b

Finding the third quartile, Q3

Q3=mean+(0.675)*std. dev

Q3=63.5+(0.675*2.5)

=65.1875 inches

Hence, the third quartile is 65.1875 inches  

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y = 0 is the horizontal asymptote for the given equation f(x)

To find : Horizontal Asymptote of function f(x)

Horizontal  Asymptote

A horizontal line that a function's graph appears to coincide with but does not actually do so is said to be its horizontal asymptote. The end behavior of the function is determined using the horizontal asymptote.

Given that,

A function is provided as

f(x) = 3/5x

x serving as the denominator

By setting the denominator equal to 0, we can easily determine the vertical asymptote i.e,

Make x=0,

Specifically, the vertical asymptote is at y=0 or x=0

Identifying the horizontal asymptote

Write x in terms of y, then look for any instances where y differs.

We are able to write the given function

x=3/5

Here, y=0 renders x undefinable.

Thus y=0 is the horizontal asymptote.

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Answer:

B

Step-by-step explanation:

Got it right.

The correct statement is 'Sally rode 39 miles in 3 hours. To compute Sally's unit rate, divide both the numerator and denominator by 3'

In this question, we have been given a statement 'Sally rode 39 miles in 3 hours. To compute Sally's unit rate, divide both the numerator and denominator by ____'

We need to complete given statement.

We know that, the denominator in unit rate is always 1.

So, to find unit rate we need to divide the denominator with the numerator in such way that the denominator becomes 1.

Sally's unit rate is 39/3 miles per hour

numerator = 39 and denominator = 3

We need to make denominator 1 so divide numerator as well as denominator by 3.

So, the unit rate would be, 13/1 = 13 miles per hour

Therefore, the correct statement is 'Sally rode 39 miles in 3 hours. To compute Sally's unit rate, divide both the numerator and denominator by 3'

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The cost of 15 cans will be AED 48.

According to the question,

We have the following information:

Cost of 10 cans = AED 32

Now, in order to find the cost of 15 cans, first we will find the cost of 1 can by dividing the total cost of 10 cans by the number of cans.

So, we have the following expression:

Cost of 1 can = 32/10

Cost of 1 can = AED 3.2

Now, we will find the cost of 15 cans using multiplication:

Cost of 15 cans = 15*3.2

Cost of 15 cans = AED 48

Hence, the cost of 15 cans will be AED 48.

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Answer:the answer is 3:2

Step-by-step explanation:

it is ratio of flour to sugar so the answer is 3:2

Answer:

Step-by-step explanation:

A recipe calls for 3 ounces of flour for every 2 ounces of sugar.Find the constant of proportionality

we have a ratio of 3 : 2

the constant of proportionality is:

3 : 2 = 1.5

Answer:

8√15

Step-by-step explanation:

4√6 × √10 = 4√(6 × 10) = 4√60 = 8√15

Answer:

slope: (11-1)/(-4+14)

m: 10/10

M: 1

11 = -4 + b

b = 15

y = x + 15

Answer:

first graph the y-intercept start at 0 and go up 2 plot that. Then, go up 7 from 2 and to the right 1

Step-by-step explanation:

x intercept is 9/4 and y intercept is -51/4 for equation 9x+4y=51.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given equation is nine times of x plus four y equal to fifty one

9x+4y=51

We have to convert this equation to slope intercept form

4y=51-9x

4y=9x-51

Divide both sides by 4

y=9/4x-51/4

x intercept is 9/4 and y intercept is -51/4

Hence x intercept is 9/4 and y intercept is -51/4 for equation 9x+4y=51.

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Answer:

Whichever ratio has more water will be less concentrated (less "grapefruity"), and whichever ratio has more of the concentrate will be more concentrated (more"grapefruity").

Answer:

Either this is not a right triangle or one of the side has the wrong measurement.

Step-by-step explanation:

This is either not a right triangle or one of the measurements is off

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]  

[tex]5^{2}[/tex] + [tex]12^{2}[/tex] = [tex]14^{2}[/tex]

25 + 144 = 196  

169 ≠196

The reason for 1/2 and not 5/10 is it is a norm in math to  reduce fractions to the least terms

This is a term used to refer to fractions that are equal even though they have different values in both he numerator and the denominator

Fractions are class of numbers that are of two parts the upper part is the numerator while the lower part is called the denominator.

In the given problem, 1/2

5/10 is an equivalent form of 1/2, this means that they are equal.

5/10 is shown to be equal to 1/2 by dividing by 5, this reduces the fraction to the least term which is 1/2. Using calculator can still show it that both numbers equal 0.5

In mathematics, it is preferred to reduce fractions to it's least form except it was stated.

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exact form

x=71/8

Decimal Form:

x=8.875

Mixed Number Form:

x=  8    7/8

Answer:

Step-by-step explanation:

8 7/8

Answer:

(5,0) (0,1)

Step-by-step explanation:

Answer:

The question is possibly mistyped.  The response below explains why, but also answers the questions based on a imagined relationship, instead of the one given.

Step-by-step explanation:

The equation 30 + 1.25x = 15 + 25X cannot be interpreted in the manner the questions are written.  It is really only an expression, since there is no y in the equation, only x.  We can, however, solve for x:

30+1.25x = 15 + 25x

30 - 15 = 25x - 1.25x

15 = 13.75x

x = (15/13.75)

x = 1.0909

There is no other information to discern what x represents.  It could be light years to a particular comet, grams of a reagent, hours until the meat is cooked, or anything the imagination allows.

If, however, the equation were something like:

  y = 1.25x + 15

we could answer the questions, as follows;

A pet sitter charges a flat fee of $15

sitter charges a flat fee of $15 plus $1.25/hr

The rest of the questions are not coherent.

==========

"two pet sitters the same?

plus $1.25 per hour to keep a dog during the day. A second pet

per hour. After (select)

Is the charge for the"

Type I error would be that we conclude to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually equal to 65%.

Type II error would be that we fail to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually different from 65%.

We are given that the percentage of households with more than 1 pet is 65%.

Let p = population % of households with more than 1 pet

So, Null Hypothesis,  : p = 65%     {means that the percentage of households with more than 1 pet is equal to 65 %}

Alternate Hypothesis,  : p  65%      {means that the percentage of households with more than 1 pet is different from 65 %}

Type I error states that the null hypothesis is rejected given the fact that null hypothesis was true. Or in other words, it is the probability of rejecting a true hypothesis.

So, in our case, type I error would be that we conculde to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually equal to 65%.

Type II error states that the null hypothesis is accepted given the fact that null hypothesis was false. Or in other words, it is the probability of accepting a false hypothesis.

So, in our case, type II error would be that we fail to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually different from 65%.

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Two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs

The two-sample t-test defined as the method used to test whether the unknown population means of two groups are equal. The two sample t-test is also called independent samples t-test. Because the two samples of the data are statistically independent.

A paired t-test is used to find the difference between two variables usually separated by time for the same subject. By using the paired t-test  we can find the mean difference between pairs of measurements is zero or not. So  paired t-test is used, when data is in the form of matched pairs

Hence, two sample t-test is used when the two samples of the data are statistically independent and the paired t-test is used, when data is in the form of matched pairs

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The equation which is not equivalent to 5x - 3 = 2x + 15 is 7x - 3 = 15

Given equation is 5x - 3 = 2x + 15.

5x - 3 = 2x + 15

5x - 3 - 5x = 2x + 15 - 5x                      ..........(Subtract 5x from both sides)

-3 = -3x + 15

this equation is an equivalent equation to  5x - 3 = 2x + 15.

Consider given equation,

5x - 3 = 2x + 15

5x - 3 + 3 = 2x + 15 + 3                      ............(Add 3 on both sides)

5x = 2x + 18

this equation is an equivalent equation to  5x - 3 = 2x + 15.

Therefore, the equation which is not equivalent to 5x - 3 = 2x + 15 is 7x - 3 = 15

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Answer:

(1,8.5)

Step-by-step explanation:

x=(-1+3)÷2

=1

y=(9+8)÷2

=8.6

(1 , 8.5)

Answer:

f(-3) = |(-3)-2| = |-5| = 5

The domain should be non-negative since time cannot be negative.

If the number of hours worked is [tex]h[/tex], the domain in inequality notation is [tex]h \geq 0[/tex].

Jahiem made about 3/2 cups of trail mix.

A ratio indicates the number of times one number contains another.

Given that, Jaheim made a bag of trail mix with 1/2 cup of almonds, 6/7 cup of apple slices, and 1/8 cup of pumpkin seeds.

The total amount of trail mix is:

1/2 cup of almonds + 6/7 cup of apple slices + 1/8 cup of pumpkin seeds

= 1/2 + 6/7 + 1/8

= (28 + 48 + 7)/56

= 83/56

≈ 3/2

Hence, Jahiem made about 3/2 cup of trail mix.

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