Suppose that demand, D, for a particular product is given by the function D = 100 - 2p, where p is the price in dollars of the product and D is the number of products that can be sold at that price. What does the slope of this function mean in the context of the problem?

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:

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:

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:

X=12

Step-by-step explanation:

Given that: X:24 = 6:X

Then:

[tex]\dfrac{X}{24}= \dfrac{6}{X}\\$Cross multiply\\X^2=24 \times 6\\X^2=144\\X=\pm\sqrt{144}\\X=\pm 12[/tex]

Since we require the positive value of X

X=12.

Answer:

Yes because yes.

Step-by-step explanation:

Y + e + s = Yes

Answer:

a) P(Y=10)=0.0013

b) P(Y≤5)=0.00000035

c) Mean = 17.5

S.D. = 2.29

Step-by-step explanation:

We can model this as a binomial random variable with n=25 and p=0.7.

The probability that k students from the sample are foreign students can be calculated as:

[tex]P(y=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(y=k) = \dbinom{25}{k} 0.7^{k} 0.3^{25-k}\\\\\\[/tex]

a) Then, for Y=10, the probability is:

[tex]P(y=10) = \dbinom{25}{10} p^{10}(1-p)^{15}=3268760*0.0282475249*0.0000000143\\\\\\P(y=10)=0.0013\\\\\\[/tex]

b) We have to calculate the probability P(Y≤5)

[tex]P(y\leq5)=P(Y=0)+P(Y=1)+...+P(Y=5)\\\\\\P(x=0) = \dbinom{25}{0} p^{0}(1-p)^{25}=1*1*0=0\\\\\\P(y=1) = \dbinom{25}{1} p^{1}(1-p)^{24}=25*0.7*0=0\\\\\\P(y=2) = \dbinom{25}{2} p^{2}(1-p)^{23}=300*0.49*0=0.0000000001\\\\\\P(y=3) = \dbinom{25}{3} p^{3}(1-p)^{22}=2300*0.343*0=0.0000000025\\\\\\P(y=4) = \dbinom{25}{4} p^{4}(1-p)^{21}=12650*0.2401*0=0.0000000318\\\\\\P(y=5) = \dbinom{25}{5} p^{5}(1-p)^{20}=53130*0.16807*0=0.0000003114\\\\\\\\[/tex]

[tex]P(y\leq5)=0+0+0.0000000001+0.0000000025+0.0000000318+0.00000031\\\\P(y\leq5)= 0.00000035[/tex]

c) The mean and standard deviation for this binomial distribution can be calculated as:

[tex]\mu=np=25\cdot 0.7=17.5\\\\\sigma=\sqrt{np(1-p)}=\sqrt{25\cdot0.7\cdot0.3}=\sqrt{5.25}=2.29[/tex]

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:

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:

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:

[tex]=\frac{-209}{29}y[/tex]

I hope this help you :)

Answer:

The relative change from Ohio to Indiana is 49.04

Step-by-step explanation:

Answer:

[tex]\frac{9}{2}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{6}[/tex]

Multiply and flip

[tex]\frac{3}{4}[/tex] x [tex]\frac{6}{1}[/tex]

= [tex]\frac{18}{4}[/tex]

= [tex]\frac{9}{2}[/tex]

The value of the division of the two numbers 3/4 and 1/6 results in an improper fraction of 9/2.

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.

In this case, we want to divide 3/4 by 1/6, so we multiply 3/4 by the reciprocal of 1/6.

The reciprocal of a fraction is obtained by flipping the fraction upside down. The reciprocal of 1/6 is 6/1 or simply 6.

Therefore, to solve 3/4 divided by 1/6, we can multiply 3/4 by 6:

(3/4) x 6

= (3 x 6) / 4

= 18/4

To simplify the result, we can divide the numerator and denominator by their greatest common divisor, which is 2:

18/4

= (18/2) / (4/2)

= 9/2

So, the division of 3/4 by 1/6 is equal to 9/2.

In mixed number form, 9/2 can be expressed as 4 1/2, meaning there are 4 whole units and 1/2 unit remaining.

Therefore, 3/4 divided by 1/6 is equal to 4 1/2.

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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:

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]

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:

Initial Value Problem: [tex]\frac{d^2 x}{dt^2} = -32, x(0) = 200, \frac{dx}{dt}(0) = 40[/tex]

[tex]x(t) = -16t^2 + 40t +200[/tex]

Step-by-step explanation:

The ball is thrown vertically downward, this means that acceleration due to gravity, [tex]g = \frac{dx^{2} }{dt^{2} } = - 32 ft/s^2[/tex]

The height of the ball at time, t = 0 at the top of the building will be: [tex]x(0) = 200 ft[/tex]

The velocity at which the ball is thrown from the top of the building, [tex]\frac{dx}{dt} (0)= 40 ft/s[/tex]

Therefore the initial value problem is written below:

[tex]\frac{d^2 x}{dt^2} = -32, x(0) = 200, \frac{dx}{dt}(0) = 40[/tex]

Let us solve for x(t)

[tex]\frac{d^2 x}{dt^2} = -32\\d(\frac{dx}{dt} )= -32 dt\\[/tex]

Integrate both sides

[tex]\frac{dx}{dt} = -32t + k_1\\\frac{dx}{dt} (0) = 40\\40 = -32(0) + k_1\\k_1 = 0\\\frac{dx}{dt} = -32t + 40[/tex]

Integrate both sides

[tex]x(t) = -16t^2 + 40t + k_2\\x(0) = 200\\200 = -16(0) + 40(0) + k_2\\k_2 = 200\\x(t) = -16t^2 + 40t +200[/tex]

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 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:

It will take to long to type it all but i think i figured it out. The children would have to take several trips. 2 kids would go, then one kid goes back to get the other kid, crosses again, then goes back, gets out, and two witches go (the parents of the kids on the other side), leaving one set of witch and child still needing to cross. One of the children on the other side brings the boat back and picks up the left over kid, now just one witch needing to cross, the two kids cross then the one kid with his mother on the other side takes the boat back again to get his mom.

And then when it gets to the other side the witch there eats it

Step-by-step explanation:

To safely cross the river, the witches and children can follow these steps:

Two witches (W1 and W2) cross the river, leaving one witch (W3) behind.

W1 returns alone to the starting side.

W1 and one child (C1) cross the river, leaving C1 on the other side.

W2 takes two children (C2 and C3) across the river, leaving them on the starting side.

W1 and W3 cross the river, leaving C2 and C3 behind.

W1 returns alone to the other side.

W1 and C1 cross the river, leaving W3 on the other side.

W2 and W3 cross the river.

W2 returns alone to the starting side.

W2 and C2 cross the river, leaving C3 behind.

W1 and C3 cross the river

To solve this puzzle, the witches and children can follow these steps to cross the river without any harm coming to the children:

Two witches cross the river: Two witches (W1 and W2) row the boat to the other side of the river, leaving one witch (W3) on the starting side.

One witch returns alone: W1 leaves the other witch (W2) on the other side and rows back alone to the starting side of the river.

One witch and one child cross the river: W1 takes one child (C1) with her and they both row across the river to the other side. W1 leaves C1 on the other side and rows back alone to the starting side.

Two children cross the river: W2, who has been waiting on the other side, takes two children (C2 and C3) and rows across the river to the starting side. W2 leaves C2 and C3 on the starting side and rows back alone to the other side.

Two witches cross the river: W1 returns to the other side and picks up the remaining witch (W3). They both row across the river to the starting side, leaving C2 and C3 on the other side.

One witch returns alone: W1 rows back alone to the other side.

One witch and one child cross the river: W1 takes C1 and rows across the river to the starting side, leaving W3 on the other side.

Two witches cross the river: W2 returns to the starting side and picks up W3. They both row across the river to the other side.

One witch returns alone: W2 rows back alone to the starting side.

One witch and one child cross the river: W2 takes C2 and rows across the river to the other side, leaving C3 on the starting side.

Two children cross the river: W1 returns to the starting side and picks up C3. They both row across the river to the other side.

Now, all three witches and all three children have safely crossed the river without any harm coming to the children.

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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:

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:

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: £192.50

Step-by-step explanation:

550 x 0.35 = 192.50

Answer:

[tex] z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22[/tex]

And we can find this probability using the normal standard distribution and we got:

[tex] P(z<-2.22) =0.0132[/tex]

Step-by-step explanation:

For this case we have the foolowing parameters given:

[tex] \mu = 520[/tex] represent the mean

[tex] \sigma =90[/tex] represent the standard deviation

[tex] n = 100[/tex] the sample size selected

And for this case since the sample size is large enough (n>30) we can apply the central limit theorem and the distribution for the sample mean would be given by:

[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}}) [/tex]

And we want to find this probability:

[tex] P(\bar X <500)[/tex]

We can use the z score formula given by:

[tex] z = \frac{500-520}{\frac{90}{\sqrt{100}}}= -2.22[/tex]

And we can find this probability using the normal standard distribution and we got:

[tex] P(z<-2.22) =0.0132[/tex]

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 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:

(-1,5)

Step-by-step explanation:

When a line segment is divided in the ratio m:n, we use the section formula to determine the point P which divides the line segment:

The coordinates of x and y are:

[tex](x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)[/tex]

Given:

[tex]A(x_1,y_1)=(-7, 4)\\B(x_2,y_2)=(8, 9)\\AP:PB=m:n=2:3[/tex]

The coordinates of P is:

[tex](x,y)=\left(\dfrac{2*8+3*-7}{2+3}, \dfrac{2*9+3*4}{2+3}\right)\\=\left(\dfrac{-5}{5}, \dfrac{25}{5}\right)\\\\=(-1,5)[/tex]

Answer:

they may like it

they may dislike it

Step-by-step explanation:

they amy think ots essentiall

they may think its unescary

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].