A service club is organizing a concert to raise funds for a retirement home. The club determines that the revenue from the concert can
be represented by R(x) = 0.0027x3 - 125, where x is the number of tickets sold. The cost to put on the concert is represented by the
function C(X) = 21x + 11,305.
Which of the following functions describes the funds raised, F(x), as a function of the number of tickets sold?
FX) = 0.0027x3 - 21x - 11,430
FAX) = 0.0027x3 + 21x - 11,180
FX) = 0.0027x3 - 21x - 11,180
F(X) = 0.0027x3+
+ 21-11,430

Answer: 114

Step-by-step explanation: You have 43 new catfish then you catch 88 but 17 of them have already been marked so you do not want to count those in the estimated population again because they have already been counted so you take 88 minus 17 and you get 71 new fish. So then you add the first new sample of fish 43 and then you add the second new sample of fish 71 and then you get 114

Answer: Option D.

Step-by-step explanation:

Here we see the cross-section of a cone when it is cut by a plane that is parallel to the base of the cone.

As the plane is parallel to the base, we expect to see a figure that has the same shape as the base ( a circle) (you can think that over the plane we have a smaller cone, and the base of that cone also must be circular)

So the correct option is D.

Answer:

Area of the figure = 254.5 cm²

Step-by-step explanation:

Area of rectangle = Length × Width

Area of triangle = 1/2(base × Height)

Dividing the figure into parts for convenience

So,

Rectangle 1  (the uppermost):

4 × 6 = 24 cm²

Rectangle 2 (below rectangle 1):

15 × 8 = 120 cm²

Rectangle 3 (with rectangle 2):

11 × 4 = 44 cm²

Triangle 1 :

1/2(7 × 19) = 133/2 = 66.5 cm²

Now adding up all to get the area of the figure:

Area of the figure = 24 + 120 + 44 + 66.5

Area of the figure = 254.5 cm²

Answer:C

Step-by-step explanation:

the x value  5  corresponds to two difference y-values.

Answer:

Step-by-step explanation:

At 300 miles per week, Chris drives 300×52 = 15,600 miles per year. His gas cost can be figured as ...

  (5 years)×(miles per year)÷(miles/gallon)×($ per gallon) = $273,000/(miles per gallon)

__

a) old car cost = repair cost + gas cost + insurance cost

  = 5($1200) + $273,000/22 + 5($500) ≈ $20,909 . . . over 5 years

__

b) new car cost = purchase cost + gas cost + insurance cost

  = $20,000 + $273,000/50 +5($900) = $29,960 . . . over 5 years

Answer:

62.93%

Step-by-step explanation:

We have to solve it by a Poisson distribution, where:

p (x = n) = e ^ (- l) * l ^ (x) / x!

Where he would come being the number of birds that there would be in 40 minutes, we know that in 2 hours, that is 120 minutes there are 13, therefore in 40 there would be:

l = 13 * 40/120

l = 4,333

Now, we have p (x> 3) and that is equal to:

p (x> 3) = 1 - p (x <= 3)

So, we calculate the probability from 0 to 3:

 p (x = 0) = 2.72 ^ (- 4.33) * 4.33 ^ (0) / 0! = 0.01313

p (x = 1) = 2.72 ^ (- 4.33) * 4.33 ^ (1) / 1! = 0.0568

p (x = 2) = 2.72 ^ (- 4.33) * 4.33 ^ (2) / 2! = 0.12310

p (x = 3) = 2.72 ^ (- 4.33) * 4.33 ^ (3) / 3! = 0.17767

If we add each one:

0.01313 + 0.0568 + 0.12310 + 0.17767 = 0.3707

replacing:

p (x> 3) = 1 - 0.3707

p (x> 3) = 0.6293

Which means that the probability is 62.93%

Answer:

2/3 * 460 = 306 and 2/3

Multiply 460 by 2/3 by first multiplying 460 by 2, then divide that by 3:

460 x 2 = 920

920 /3 = 306 2/3

The answer is 306 2/3

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

[tex]\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min[/tex]

So it will take them approximately 51.43 minutes to complete the project together.

Hey there!

First, let's take all of the expenses and change the ones that aren't monthly into monthly.

Groceries: $800/month

Car insurance: $87.5/month

Gasoline: $100/month

Now, let's add together all of our expenses

1090+800+125+87.5+100+200+50=2452.5

Now, we subtract that from her salary.

2300-2452.5=-152.5

Therefore, Rebecca's net monthly cash flow is -$152.5. She should spend a bit less on groceries, not do so much miscellaneous, find a place that charges less rent, drive less, etc. so she isn't spending more than she earns.

I hope that this helps! Have a wonderful day!

Answer:

what she/he said

Step-by-step explanation:

Answer:

  cos(20°)

Step-by-step explanation:

The "cofunction" is the function having the same value for the complement of the angle that this function has for the angle.

The cofunction of sine is cosine. The complement of 70° is 90° -70° = 20°.

  sin(70°) = cos(20°)

Answer:

10,15.20.25

Step-by-step explanation:

+5 in each number

Answer:

The maximum life expectancy for humans is approximately 87 years.

Step-by-step explanation:

We have to calculate the point in which both linear functions (Life expectancy from birth and Life expectancy from age 65) intersect, as this is the point in which is estimated to be the maximum life expectancy for humans.

NOTE: to simplify we will consider t=0 to the year 1900, so year 2010 becames t=(2010-1900)=110.

The linear function for Life expectancy from birth can be calculated as:

[tex]t=0\rightarrow y=45\\\\t=110\rightarrow y=78.7\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{78.7-45}{110-0}=\dfrac{33.7}{110}=0.3064\\\\\\y=0.3064t+45[/tex]

The linear function for Life expectancy from age 65 can be calculated as:

[tex]t=0\rightarrow y=75\\\\t=110\rightarrow y=84.5\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{84.5-75}{110-0}=\dfrac{9.5}{110}=0.0864\\\\\\y=0.0864t+75[/tex]

Then, the time t where both functions intersect is:

[tex]0.3064t+45=0.0864t+75\\\\(0.3064-0.0864)t=75-45\\\\0.22t=30\\\\t=30/0.22\\\\t=136.36[/tex]

The time t=136.36 corresponds to the year 1900+136.36=2036.36.

Now, we can calculate with any of both functions the maximum life expectancy:

[tex]y=0.0864(136.36)+75\\\\y=11.78+75\\\\y=86.78\approx87[/tex]

The maximum life expectancy for humans is approximately 87 years.

Answer:

The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1000, \pi = \frac{710}{1000} = 0.71[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 - 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.6819[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 + 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.7381[/tex]

The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).

Answer:

Yes,these two functions are the inverse of each other.

Step-by-step explanation:

They way of finding if two functions ([tex]f(x)\,\,and\,\,g(x)[/tex] ) are the inverse of each other is by studying if their composition renders in fact the identity. That is, we see if:

[tex]f(x) \,o \,g(x)=f(g(x))=x[/tex]

in our case:

[tex]f(g(x))=\frac{1}{g(x)+4} -9\\f(g(x))=\frac{1}{(\frac{1}{x+9} -4)+4}-9\\f(g(x))=\frac{1}{\frac{1}{x+9} }-9\\f(g(x))={x+9} -9\\f(g(x))=x[/tex]

The composition does render the identity, therefore, these two functions are indeed the inverse of each other

Answer:

18

Step-by-step explanation:

The greatest common factor is 18. All of the common factors are: 1, 2, 3, 6, 9, 18.

Answer:

There is only one greatest common factor of 36 and 90 which is 18. There are also a number of common factors including 1, 2, 3, 6, 9, 18.

Step-by-step explanation:

Answer:

[tex] P(X \geq 1) =1-P(X<1) =1-P(X=0) [/tex]

And we can use the probability mass function and we got:

[tex]P(X=0)=(4C0)(0.72)^0 (1-0.72)^{4-0}=0.00615[/tex]

And replacing we got:

[tex] P(X \geq 1) = 1-0.00615 = 0.99385[/tex]

Step-by-step explanation:

Let X the random variable of interest "number of graduates who enroll in college", on this case we now that:  

[tex]X \sim Binom(n=4, p=0.72)[/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 \geq 1)[/tex]

And we can use the complement rule and we got:

[tex] P(X \geq 1) =1-P(X<1) =1-P(X=0) [/tex]

And we can use the probability mass function and we got:

[tex]P(X=0)=(4C0)(0.72)^0 (1-0.72)^{4-0}=0.00615[/tex]

And replacing we got:

[tex] P(X \geq 1) = 1-0.00615 = 0.99385[/tex]

Answer:1. uses a related sample - repeated measures

2. . does not use a related sample--a

Step-by-step explanation:

Question 1.

step1  A repeated measure design is a design which measures a given sample repeatedly over a given time using different conditions or related measures.

step 2:In the treatment for compulsive hoarding, Here, measures are taken two times ie before and after treatment on the same 50 hoarders which shows a repeated measure, also the design is a within related sample of the same 50 hoarders to give measurement at different conditions  of treatment for  high and low hoarding scores so the design describes  a related sample - repeated measures

Question 2:

step 1 ; An unrelated sample  occurs when Samples being measured do not depend on each other  

Step 2;  1st Sample for comparison by John are random lonely people  and Second Sample are random non lonely people. so the two samples are independent on each other and will give different  measurement based on quality of sleep.   So the design does not use a related sample

Answer:

july 11

Step-by-step explanation:

Answer:

the amount of alcohol to be added is 128 grams

Step-by-step explanation:

Given that:

The initial mass of the hand sanitizer = 480 grams

The initial strength of the hand sanitizer = 24 %

The new strength of the hand sanitizer = 40%

The objective here is to determine the final amount of alcohol that is to be added to get the new strength of the alcohol

First; let's find the mass of alcohol in the initial hand sanitizer;

SO;

= 24  % of 480

[tex]=\dfrac{24}{100}*480[/tex]

= 115.2 grams

If y should represent the mass of the alcohol added to have 40%; we have

The new amount of the alcohol to be[tex](115.2 + y) \ grams[/tex]

The new amount of the hand sanitizer will be[tex](480 + y) grams[/tex]

∴

For the new strength of sanitizer:

40 % of (480 + y) = (115.2 + y)

[tex]0.4 *(480 + y) = (115.2 + y) \\ \\ 192 + 0.4 y = 115.2 + y \\ \\ y (1 - 0.4) = 192 - 115.2 \\ \\ y= \dfrac{76.8}{0.6} \\ \\ y = 128 \ grams[/tex]

Thus ; we can conclude that the amount of alcohol to be added is 128 grams

Answer:

  see the attachment

Step-by-step explanation:

A "line of best fit" generally has about as much data above the line as below it. If the data has any trend, it generally follows the trend.

The best choice here is B.

Answer:Answer:

 see the attachment

Step-by-step explanation:

A "line of best fit" generally has about as much data above the line as below it. If the data has any trend, it generally follows the trend.

The best choice here is B.

Step-by-step explanation:

Complete Question:

Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width

is 11 ft, how many square feet of carpet does he need to buy?

Answer:

231 ft²

Step-by-step explanation:

==>GIVEN:

Length of room (L) = 21 ft

Width of room (W) = 11 ft

==>REQUIRED:

Square feet of carpet to be bought = area of the rectangular room

==>SOLUTION:

The room to be covered with carpet is rectangular in shape. In order to ascertain the square feet of carpet to be bought, we need to calculate the area of the room by using the formula for area of rectangle.

Thus, area of rectangle (A) = Length (L) × Width (W)

A = 21 × 11

A = 231 ft²

Square feet of carpet to be bought = 231 ft²

Answer:

Translate point J 12 units down and 6 units right.

Answer:

The length of the second line is [tex]9\frac{1}{15}[/tex] inches

Step-by-step explanation:

Given

Length of first line = [tex]6\frac{4}{10}[/tex] inches

Length of second line = [tex]2\frac{2}{3}[/tex] inches longer

Required

Length of second line.

Let the length of the second line be represented by x.

From the question, x is [tex]2\frac{2}{3}[/tex] inches longer than the first line;

This implies that:

[tex]x = 2\frac{2}{3} + 6\frac{4}{10}[/tex]

Convert both fractions to improper fractions

[tex]x = \frac{8}{3} + \frac{64}{10}[/tex]

Take LCM

[tex]x = \frac{80 + 192}{30}[/tex]

[tex]x = \frac{272}{30}[/tex]

Convert to mixed fraction

[tex]x = 9\frac{2}{30}[/tex]

Reduce fraction to lowest term

[tex]x = 9\frac{1}{15}[/tex]

Hence, the length of the second line is [tex]9\frac{1}{15}[/tex] inches

Answer:

21.b

22.c

Step-by-step explanation:

idk how to explain it lol I did mental math

Answer:

So I have never stepped foot into this. But I have experience from this. So for the first one we can use the compound intrest formula - A = P(1+r/n)^nt so if we do that we get.

A = 3000(1+0.05/1)^1*4

So then we get A is equal to 3646.52

The next one we need to calculate

A = P (1 + rt)

So now we do A = 3000(1+0.05*1)

A = 3000*1.05 = 3150. We add them together and we get 6796.52.

So we subtract 6000 from that. He earned

796.52 dollars

Answer:

x = -1 and y = 1/2

Step-by-step explanation:

Let u = 1/x, and v = 1/y

Then the pair of equations

-3/x + 4/y = 11

1/x - 2/y = -5

Can be written as

-3u + 4v = 11 .................................(1)

u - 2v = -5......................................(2)

From (2)

u = 2v - 5 .......................................(3)

Substituting (3) into (1)

-3(2v - 5) + 4v = 11

-6v + 15 + 4v = 11

-6v + 4v = 11 - 15

-2v = -4

v = 4/2 = 2

Substituting this value of v in (3)

u = 2v - 5

u = 2(2) - 5

= 4 - 5

= -1

That is

u = -1, v = 2

Since u = 1/x, and v = 1/y, we have

1/x = -1

=> x = -1

And

1/y = 2

=> y = 1/2

Therefore

x = -1 and y = 1/2

Answer:

Below.

Step-by-step explanation:

Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.