determine whether these two functions are inverses. ​

Answer:

40.5 ft

162 ft

16 in

7.2 in

13.9 ft

Step-by-step explanation:

1) V=√32d

d= ?

V=36 ⇒ 36²= 32d  ⇒ d= 1296/32=40.5 feet

2) S= 5.5√d

S= 70 mph, d=?

70²= 5.5²d ⇒ d= 4900/ 30.25≈ 162 feet

3) d= 0.25√h

d= 1 mile, h=?

1²= 0.25²h ⇒ h= 1/0.0625= 16 in

4) a= 4, b= 6, c=?

c²= a²+b² ⇒ c= √a²+b²= √4²+6² = √52≈ 7.2 in

5) c= 16 foot, b= 8 feet, a=?

c²= a²+b² ⇒ a= √c² - b²= √16²-8²= √256- 64= √192≈13.9 feet

Answer:

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

And if we use the probability mass function we got:

[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]  

[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]  

And replacing we got:

[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=4, p=0.6)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

We want to find the following probability:

[tex] P(X >1)[/tex]

And for this case we can use the complement rule and we got:

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

And if we use the probability mass function we got:

[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]  

[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]  

And replacing we got:

[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]

Answer:

The correct answer is:

r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75.

This is because Juan got a $0.50 raise which means that his new rate will be $0.50 more than his original rate (r).

Answer:

$9.75

Step-by-step explanation:

Answer:

a = 30

b = 6/7

Step-by-step explanation:

The number of yeast cells after t hours is modeled by the following equation:

[tex]f(t) = a(1 + be^{-0.7t})[/tex]

In which a is the initial number of cells.

At time t = 0 the population is 30 cells

This means that [tex]a = 30[/tex]

So

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

And increasing at a rate of 18 cells/hour.

This means that f'(0) = 18.

We use this to find b.

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

So

[tex]f(t) = 30 + 30be^{-0.7t}[/tex]

Then, it's derivative is:

[tex]f'(t) = -30*0.7be^{-0.7t}[/tex]

We have that:

f'(0) = 18

So

[tex]f'(0) = -30*0.7be^{-0.7*0} = -21b[/tex]

Then

[tex]-21b = 18[/tex]

[tex]21b = -18[/tex]

[tex]b = -\frac{18}{21}[/tex]

[tex]b = \frac{6}{7}[/tex]

The graph of the compound inequality can be seen at the end.

Here we have two inequalities that depend on p, these are:

4p + 1 > -15

6p + 3 < 45

First, we need to isolate p on both inequalities.

4p + 1 > -15

4p > -15 - 1

p > -16/4

p > - 4

6p + 3 < 45

6p < 45 - 3 = 42

p < 42/6 = 7

So we have the compound inequality:

p > -4

p < 7

or:

-4 < p < 7

Then this represents the set (-4, 7) where the values -4 and 7 are not included, so we should graph them with open circles.

The graph of the inequality is something like the one below.

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Answer:

(a)650 ways

(b)650 ways

(c)676 ways

Step-by-step explanation:

There are 26 red and 26 black cards.

If a card is dealt to each of 2 players, we want to find out how many different ways this can be done.

(a)Both cards are red

If both cards are red:

The first red card can be dealt in 26 ways.

The second red card can be dealt in 25 ways.

Therefore: Both Red cards can be dealt in: 26 X 25 = 650 ways

(b)Both cards are black

If both cards are black:

The first black card can be dealt in 26 ways.

The second black card can be dealt in 25 ways.

Therefore: Both black cards can be dealt in: 26 X 25 = 650 ways

(c)One card is black and the other is red.

The red card can be dealt in 26 ways.

The black card can be dealt in 26 ways.

Therefore: Both cards can be dealt in: 26 X 26 = 676 ways

Answer:

The 1st graph

Step-by-step explanation:

The quickest and easiest way is to just graph y < x² + 4x + 5. When you do so you should be able to see your answer.

Answer: the answer is c (the third answer ) ‼️

Step-by-step explanation:

The data in the given residual plot shows that model C has the best fit.

A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit.

Given:

The residual plot of the values in the graph,

The points in the first graph are very far from the x-axis and y-axis so, it is not the best fit,

The points in the second graph are very far from the x-axis and y-axis, and they are symmetric to the y-axis but not the best fit.

Most of the points are close to the x-axis, so it is the best fit,

Thus, the third graph is the best line of fit.

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Answer:

he domain of the composition is all real x values except for x = -1

In other words: [tex]\left \{ x \, |\, x \neq -1} \right \}[/tex]

Step-by-step explanation:

Let's find the composition [tex]f(g(x))[/tex] in order to answer about its domain (where on the Real number set the function is defined), give the two functions:

[tex]f(x)= \frac{1}{x+4}[/tex]    and    [tex]g(x)=\frac{8}{x-1}[/tex]  :

[tex]f(g(x))=\frac{1}{g(x)+4} \\f(g(x))=\frac{1}{\frac{8}{x-1} +4} \\f(g(x))=\frac{1}{\frac{8+4(x-1)}{x-1} }\\f(g(x))=\frac{x-1}{8+4x-4} \\f(g(x))=\frac{x-1}{4+4x} \\[/tex]

This rational function is defined for every real number except when the denominator adopts the value zero. Such happens when:

[tex]4+4x=0\\4x=-4\\x=-1[/tex]

So the domain of the composition is all real x values except for x = -1

Answer:

24

Step-by-step explanation:

Use the Pythagorean theorem.

Where the sum of the two legs squared is equal to the hypotenuse squared.

10² + x² = 26²

100 + x² = 676

x² = 576

x = √576

x = 24

The value of x is 24.

Answer:

The expected number of adult workers with a high school diploma is 4.

Step-by-step explanation:

This random variable X can be modeled with the binomial distribution, with parameters n=10 (the sample size) and p=0.4 (the probability that a adult worker have a high school diploma).

The expected value of X is then the mean of the binomial distribution with the parameters already mentioned.

This is calculated as:

[tex]E(X)=\mu_b=n\cdot p=10\cdot0.4=4[/tex]

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

The number with the smallest denominator is the larger number and [tex]\frac{1}{12}[/tex] is the number with the smallest denominator out of [tex]\frac{1}{12} , \frac{1}{32} , \frac{1}{48} , \frac{1}{18}[/tex].

Answer:

1/12

Step-by-step explanation:

Start with a number, for example 100.

Now divide 100 by several numbers which are greater and greater:

100/1 = 100

100/2 = 50

100/4 = 25

100/10 = 10

100/100 = 1

As you divide the same number, 100, by a greater number, the result becomes smaller.

As we divide 100 by 1, then by 2, then by 4, etc., we are always dividing 100 by a greater and greater number. The result is smaller and smaller, 100, 50, 25, etc. If you always divide the same number by other numbers, the larger the number you divide by, the smaller the result.

Numbers in order from greatest to smallest:

1/12, 1/18, 1/32, 1/48

Answer: The greatest number is 1/12

Answer:

B. Length A of Rasheeda’s garden is 27 ft.

C. Length B of the book’s garden is 12 ft.

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

Step-by-step explanation:

step 1

Find the dimension of the book's garden

we know that

Book scale: 1 inch = 2 feet

That means

1 inch in the drawing represent 2 feet in the actual

To find out the actual dimensions, multiply the dimension in the drawing by 2

so

Length A of the book’s garden

Width B of the book’s garden

step 2

Find the dimension of Rasheeda’s garden

we know that

Rasheeda's Scale: 2 inch = 3 feet

That means

2 inch inches the drawing represent 3 feet in the actual

To find out the actual dimensions, multiply the dimension in the drawing by 3 and divided by 2

so

Length A of Rasheeda's garden

Width B of Rasheeda's garden

Verify each statement

A. Length A of the book’s garden is 18 ft.

The statement is false

Because, Length A of the book’s garden is 36 ft (see the explanation)

B. Length A of Rasheeda’s garden is 27 ft.

The statement is true (see the explanation)

C. Length B of the book’s garden is 12 ft

The statement is true (see the explanation)

D. Length B of Rasheeda’s garden is 6 ft.

The statement is false

Because, Length B of Rasheeda’s garden is 9 ft. (see the explanation)

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

The statement is true

Because the difference between 36 ft and 27 ft is equal to 9 ft

F. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.

The statement is false

Because, Length B of the book’s garden is 3 ft greater than length B of Rasheeda’s garden.

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Answer:

B. Length A of Rasheeda’s garden is 27 ft.

C. Length B of the book’s garden is 12 ft.

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

(second, third, and fifth choices)

Explanation: I did the quiz and got it right.

Hope this Helps!

Answer:

Yes because yes.

Step-by-step explanation:

Y + e + s = Yes

Answer:

b. Skewed-left

Step-by-step explanation:

The histogram will be expressed with the x-axis representing the salaries, in growing amount to the right. The y-axis will represent the relative or absolute frequency.

We know that most of the players earn the minimum league wage. Then, we will have a high frequency in the low salaries classes, at the left of the histogram. A few players earn very high salaries, so we will have a right tail with high values for the salaries a little frequency.

There is no symmetry in this histogram and it is not uniform, as there is no representative mean salary.

As most of the data will be close to the left side, we can conclude that the histogram will be skewed-left.

The Histogram of salary data, with most having less salary is RIGHT Skewed

Given : Data of players' salary is concentrated towards towards most players having less ( minimum ) salary.

Right Skewness denotes a distribution where Tail is on the right side. This implies data is highly concentrated toward left side, ie lower independent variable (x - here 'salary') values.

Left Skewness denotes a distribution where Tail is on the left side. This implies data is highly concentrated towards right side, ie higher independent variable (x - here 'salary') values.

In this case : As more players have lower values of independent variable ie salary, so the data will be concentrated at left - having tail at right.

Hence, it will be Skewed Right

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Answer:

The large sample size 'n' =  199.6569≅ 200

Step-by-step explanation:

Step(i):-

Given Standard deviation of salary for all baseball players for 2015 is about $5,478,384.55

Standard deviation of  of salary for all baseball players for 2015

  (S.D ) σ =  $5,478,384.55

Given estimate of this average salary for all baseball players for 2015

                          =  $497,000

Given Margin of error of error is  =  $497,000

Level of significance ∝ = 80%

The critical value Z₀.₂₀ = 1.282  

Step(ii):-

Margin of error of error is  determined by

          [tex]M.E = \frac{Z_{0.20} S.D}{\sqrt{n} }[/tex]

         [tex]497,000 = \frac{1.282 X 5,478,384.55}{\sqrt{n} }[/tex]

Cross multiplication , we get

 [tex]\sqrt{n} = \frac{1.282 X 5,478,384.55}{497,000 }[/tex]

On calculation , we get

√n = 14.13

Squaring on both sides, we get

n = 199.6569

Conclusion:-

The large sample size 'n' =  199.6569≅ 200

Answer:

2 is the coefficient

Step-by-step explanation:

2 is the coefficient bc a coefficient is the number next to a variable (such as x)  and 2 is next to x and is the only one in the equation

Answer:

-2

Step-by-step explanation:

Answer:

15 is the answer to the question

Answer:

15, which for some reason does not seem to be an option.

Step-by-step explanation:

Product means to multiply to numbers, items etc.

5 times 3, as you should know, is 15.

Hope this helps.

Answer:

The explanation is:

All interior angles in an equilateral triangle are congruent, making them all 60° by the sum of angles in a triangle. Because alternate interior angles of parallel lines are congruent, x = 60°.

Answer:

Step-by-step explanation:

Step 1: Consider P(1) that is n = 1

[tex]1^2 = \frac{1(1+1)(2*1+1)}{6}=\frac{6}{6}=1 \checkmark[/tex]

Step 2: Suppose the equation is true up to n. That is

[tex]1^2 + 2^2+3^2+........+n^2 = \dfrac{n(n+1)(2n+1)}{6 }[/tex]

Step 3: Prove that the equation is true up to (n+1). That is

[tex]1^2 + 2^2+3^2+........+n^2 + (n+1)^2 = \dfrac{(n+1)(n+2)(2n+3)}{6 }[/tex]

The easiest way to prove it is to expend the right hand side and prove that the right hand side = the right hand side of step 2 + (n+1)^2

From step 2, add (n+1)^2 both sides. The left hand side will be the left hand side of step 3, now, the right hand side after adding.

[tex]\dfrac{n(n+1)(2n+1)}{6 }+(n+1)^2 = \dfrac{2n^3+3n^2+n}{6}+\dfrac{6n^2+12n+6}{6}[/tex]

[tex]=\dfrac{2n^3+9n^2+13n+6}{6}[/tex]

If you expend the right hand-side of the step 3, you will see they are same.

Proof done

Answer:

see below

Step-by-step explanation:

1^2+2^2+3^2+...+n^2=n(n+1)(2n+1)/6

Step1

Verify it for n=1

1^2= 1(1+1)(2*1+1)/6= 1*2*3/6= 6/6=1 - correct

Step2

Assume it is correct for n=k

1^2+2^2+3+2+...+k^2= k(k+1)(2k+1)/6

Step3

Prove it is correct for n= k+1

1^2+2^2+3^2+...+(k+1)^2= (k+1)(k+2)(2k+2+1)/6

prove the above for k+1

1^2+2^2+3^2+...+k^2+(k+1)^2= k(k+1)(2k+1)/6 + (k+1)^2=

= 1/6(k(k+1)(2k+1)+6(k+1)^2)= 1/6((k+1)(k(2k+1)+6(k+1))=

=1/6((k+1)(2k²+k+6k+6))= 1/6(k+1)(2k²+4k+3k+6))=

= 1/6(k+1)(2k(k+2)+3(k+2))=

=1/6(k+1)(k+2)(2k+3)

Proved for n= k+1 that:

the sum of squares of (k+1) terms equal to  (k+1)(k+2)(2k+3)/6

Answer:

  $106.67

Step-by-step explanation:

Using the example, for 3 hours work, Alex would be paid ...

  (2 hr)($30/hr) +(1 hr)($20/hr) = $60 +$20 = $80

At the same rate of pay, for 4 hours work, the pay would be ...

  pay/(4 hr) = $80/(3 hr)

  pay = $80(4/3) ≈ $106.67

Alex's pay for 4 hours of work is $106.67.

Answer:

csc 270° is the answer.

Answer:

-7/2

Step-by-step explanation:

To find the y coordinate of the midpoint and the y coordinates together and divide by 2

(2+-9)/2

-7/2

Answer:

2 goes in green box

Step-by-step explanation:

(9,2) (-7,-9)

(x1, y1) (x2,y2)

Midpoint is (x1+x2)/2 , (y1+y2)/2

(9-7)/2= 1

(2-9)/2 = -7/2

Answer:

Haha proofs are an interesting thing. Usually, nothing is to scale, which is why you can't measure anything. They are pretty annoying, but it helps to know why certain things are the way that they are and develop justification skills for higher level math.

Sorry to discourage you, but you're going to see "Justify" quite a lot in calculus and beyond which is basically a more informal version of a proof

you can never escape it tbh lol

We can't just measure the two figures to see if they are congruent as congruence is about shape and size.

It should be noted that congruence simply means that the shapes have identical length, angles, and size.

Therefore, we can't just measure the two figures to see if they are congruent as congruence is about shape and size.

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Answer:

they may like it

they may dislike it

Step-by-step explanation:

they amy think ots essentiall

they may think its unescary

Answer:

We conclude that older people are more likely to be victimized.

Step-by-step explanation:

We are given that a survey shows that 10% of the population is victimized by property crime each year.

A random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 12.35%

Let p = population proportion of people who are victimized.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]p \leq[/tex] 10%      {means that older people are less likely to be victimized or remains same}

Alternate Hypothesis, [tex]H_A[/tex] : p > 10%      {means that older people are more likely to be victimized}

The test statistics that would be used here One-sample z-test for proportions;

                             T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion of older people who are victimized = 12.35%

            n = sample of older citizens = 527

So, the test statistics  =  [tex]\frac{0.1235-0.10}{\sqrt{\frac{0.10(1-0.10)}{527} } }[/tex]  

                                       =  1.798

The value of z-test statistics is 1.798.

Since in the question, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for right-tailed test.

Since our test statistics is more than the critical value of z as 1.798 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that older people are more likely to be victimized.

Answer:

The probability that the student answers at least seventeen questions correctly is [tex]8.03\times 10^{-10}[/tex].

Step-by-step explanation:

Let the random variable X represent the number of correctly answered questions.

It is provided all the questions have five options with only one correct option.

Then the probability of selecting the correct option is,

[tex]P(X)=p=\frac{1}{5}=0.20[/tex]

There are n = 20 question in the exam.

It is also provided that a student taking the examination answers each of the questions with an independent random guess.

Then the random variable can be modeled by the Binomial distribution with parameters n = 20 and p = 0.20.

The probability mass function of X is:

[tex]P(X=x)={20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x};\ x =0,1,2,3...[/tex]

Compute the probability that the student answers at least seventeen questions correctly as follows:

[tex]P(X\geq 17)=P (X=17)+P (X=18)+P (X=19)+P (X=20)[/tex]

[tex]=\sum\limits^{20}_{x=17}{{20\choose x}\ 0.20^{x}\ (1-0.20)^{20-x}}\\\\=0.00000000077+0.000000000032+0.00000000000084+0.000000000000042\\\\=0.000000000802882\\\\=8.03\times10^{-10}[/tex]

Thus, the probability that the student answers at least seventeen questions correctly is [tex]8.03\times 10^{-10}[/tex].

Answer:

543

Step-by-step explanation:

let x= total salary

0.25x=135.75

x=543

Answer:

[tex]\$ \: 543.00[/tex]

Step-by-step explanation:

[tex]25\% \times x =135.75[/tex]

[tex]1/4 \times x =135.75[/tex]

[tex]0.25 \times x =135.75[/tex]

[tex]x=135.75 \times 4[/tex]

[tex]x=543[/tex]

Answer:

[tex]\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2[/tex]

And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:

[tex] \bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0[/tex]

And we can solve for [tex]\sum_{i=1}^n w_f *X_f [/tex] and solving we got:

[tex] 3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f [/tex]

And from the previous result we got:

[tex] 3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f[/tex]

And solving we got:

[tex] \sum_{i=1}^n w_f *X_f =120 -67.2= 52.8[/tex]

And then we can find the mean with this formula:

[tex] \bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3[/tex]

So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0

Step-by-step explanation:

For this case we know that the currently mean is 2.8 and is given by:

[tex] \bar X = \frac{\sum_{i=1}^n w_i *X_i }{24} = 2.8[/tex]

Where [tex] w_i[/tex] represent the number of credits and [tex]X_i[/tex] the grade for each subject. From this case we can find the following sum:

[tex]\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2[/tex]

And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:

[tex] \bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0[/tex]

And we can solve for [tex]\sum_{i=1}^n w_f *X_f [/tex] and solving we got:

[tex] 3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f [/tex]

And from the previous result we got:

[tex] 3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f[/tex]

And solving we got:

[tex] \sum_{i=1}^n w_f *X_f =120 -67.2= 52.8[/tex]

And then we can find the mean with this formula:

[tex] \bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3[/tex]

So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0