13. A local radio station is having a contest in which every 12th caller
receives a CD and every 10th caller wins free concert tickets. What
number caller would you need to be to win both prizes?

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$8500\\ r=rate\to 14\%\to \frac{14}{100}\dotfill &0.14\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1 \end{cases}[/tex]

[tex]A=8500\left(1+\frac{0.14}{1}\right)^{1\cdot 1}\implies A=8500(1.14)\implies \boxed{A=9690} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~~~~~~ \textit{Compound Interest Earned Amount}[/tex]

[tex]A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$8500\\ r=rate\to 14\%\to \frac{14}{100}\dotfill &0.14\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=8500\left(1+\frac{0.14}{1}\right)^{1\cdot 2}\implies A=8500(1.14)^2\implies \boxed{A=11046.6}[/tex]

Answer:

2

Step-by-step explanation:

You should substitute x = -1 to the f(x) and you will find:

[tex]f(-1)=\left(\frac{1}{2}\right)^{-1}=\frac{1}{2^{-1}}=2[/tex]

So, the answer for the ? is 2.

Using the exponential distribution, it is found that there is a 0.2231 = 22.31% probability after a call is received, it takes more than 3 minutes for the next call to occur.

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

In this problem, the mean is of two minutes, hence the decay parameter is given by:

[tex]\mu = \frac{1}{2} = 0.5[/tex]

The probability that it takes more than 3 minutes for the next call to occur is given by:

[tex]P(X > 3) = e^{-0.5 \times 3} = 0.2231[/tex]

0.2231 = 22.31% probability after a call is received, it takes more than 3 minutes for the next call to occur.

More can be learned about the exponential distribution at https://brainly.com/question/18596455

Answer:

y= -2

Step-by-step explanation:

y2-y1      6-y =  8

x2-x1       2-4= -2

To solve for y : Your answer has to be 8 then you divide 8/-2 = -4

6-y=8

subtract 6 from both sides   = -y =2

multiply each side by(-1)

to remove the - from Y         (-1)y =(-1)2

                                                   y =-2

Answer:

Step-by-step explanation:

A

exactly 4

There are 12 adults.

4 like oatmeal cookies the best.

P(exactly 4) = 4/12 = 1/3 = 0.3333...

B)

At least 4

4 5 6 7 8 9 10 11 12

So there are 9 choices (4 .. 12) of those who could like oatmeal cookies the best.

P(9) = 9/12 = 0.75

C)

1 2 3

There are at most 3 people who could like oatmeal cookies the best.

P(<4) = 3/12 = 0.25

Less than 4 who would choose oatmeal cookies = 1/4

Answer:

Step-by-step explanation

There are many ways to prove this identity. But, I will use the simplest one. If you have a right triangle, the length of the horizontal side is x, the length of the vertical side is y, and the hypotenuse is r. So, the relation between x and r can be written in cosine form:

[tex]\cos\theta=\frac{x}{r}[/tex]

The relation between y and r can be written in sine form:

[tex]\sin\theta=\frac{y}{r}[/tex]

Pythagoras told you that for the right triangle [tex]x^{2}+y^{2}=r^{2}[/tex] should be satisfied. Substitute x and y from the cosine and sine form:

[tex](r\cos\theta)^{2}+(r\sin\theta)^{2}=r^{2}[/tex]

[tex]r^{2}\cos^{2}\theta+r^{2}\sin^{2}\theta =r^{2}[/tex]

the square of r will cancel out, and you can get your identity:

[tex]\cos^{2}\theta+\sin^{2}\theta=1[/tex]

Answer:

[tex]x=\begin{bmatrix}-2\\-1\\\end{bmatrix}[/tex]

Step-by-step explanation:

(x+2) (x+1)=0

Isolate the X

=> [tex]\left(x+2\right)\left(x+1\right)=0[/tex]

Divide both sides by the coefficient:

=>[tex]x=\begin{bmatrix}-2\\-1\\\end{bmatrix}[/tex]

Answer:

22,080 tacos

Step-by-step explanation:

13,180 - 7,480 = 5700

5700 - 2500 = 3200

13,180 + 5700 + 3200 = 22,080

Answer:

Since in finding perimeter you add the lengths divide the number and substitute it into the formula for area

Answer:

the completed square is x=1, -3

Answer:

he makes $112.50

Step-by-step explanation:

first you have to find out how much he makes before tax is taken out. all you do is multiply 12.50 by 30, which gives you $375.00. then, you can either put in the calculator 30%375 or 0.3×375(both are the same thing) and you should get $112.50

Answer:

740,000

Step-by-step explanation:

The ten-thousands digit is the 4.

Change all digits to the right of the 4 to 0.

742,617 becomes 740,000.

Since the first digit to the right of the 4 is 2, and not a digit from 5 through 9, we keep the 4 and do not change it to 5.

Answer: 740,000

Answer:

the answer is 740000

Step-by-step explanation:

because I have big brain

Answer:

10.8 miles

Step-by-step explanation:

I hope this helps!

Answer:

Step-by-step explanation:

Let the time use by other one technician be x

if the other technician takes 6 minutes less than the first technician, then the time taken by the other technician will (x - 6)

The total amount of time t it would take to run the tests if the technicians work together will be expressed by taking the sum of the time taken by the two technician as shown.

First technician = x

Second technician = x-6

Sum of the time taken

t = x+ (x-6)

Hence option C is correct

Answer:

f(x)=11x-22

f(3)=11(3)-22

11(3)-22

33-22=11

Answer: I think its 39

Step-by-step explanation: I did the math

Jan's starting number was 10.

A number is an arithmetic value used for representing the quantity and used in making calculations.

Given that Jan doubled her starting number, added 5, subtract 7, divided by 3, then squared the result.

Let her original number be x

Therefore, {(2x +5 - 7)/3}² = 36

{(2x -2)/3}² = 36

(2x -2)/3 = 6

2x - 2 = 18

2x = 20

x = 10

Hence, Jan's starting number was 10.

For more reference on Numbers, click;

https://brainly.com/question/17429689

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Answer:

(3, -9)

Step-by-step explanation:

5x + y = 7

-x - 2y = - 15

What we can do is multiply the second equation by 5, as we try to combine both equations to get rid of x.

5x + y = 6

-5x - 10y = 75

-9y = 81

y = -9

Now we plug y back in.

5x - 9 = 6

5x = 15

x = 3

Answer:

biased

Step-by-step explanation:

even with the computer randomly picking people, they are still all on the mailing list.

Error

[tex]\\ \rm\Rrightarrow \dfrac{Difference}{Original}\times 100[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{4.25}{80}\times 100[/tex]

[tex]\\ \rm\Rrightarrow 0.0535(100)[/tex]

[tex]\\ \rm\Rrightarrow 5.35\%[/tex]

[tex] \boxed{ \pmb{\% \: error = \frac{ |approx - actual| }{actual} \times 100 }}[/tex]

[tex] \sf\% \: error = \frac{ |80 - 75.75| }{75.75} \times 100[/tex]

[tex] \sf\% \: error = \frac{ |4.25| }{ \frac{303}{4} } \times 100[/tex]

[tex] \sf\% \: error = \frac{ 4.25 }{ \frac{303}{4} } \times 100[/tex]

[tex] \sf\% \: error = \frac{ \frac{17}{ \cancel4} }{ \frac{303}{ \cancel4} } \times 100[/tex]

[tex] \sf\% \: error = \frac{ 17 }{ 303 } \times 100[/tex]

[tex] \sf\% \: error = \frac{ 1700 }{ 303 } [/tex]

[tex] \sf\% \: error = 5.6\%[/tex]

Answer:

Dimensions and angles.

Step-by-step explanation:

A 3d shape has length, width, and height. A 2d regualr shape has equal sides... what makes it irregular is the different angles.

I hope this helps you :)

Answer:

[tex]x = \sqrt{ {7}^{2} + {7}^{2} } \\ x= \sqrt{49 + 49} \\ x = \sqrt{98} \\ x= \sqrt{49 \times 2} \\ \boxed{x= 7 \sqrt{2} }[/tex]

What is the value of x in the triangle?

A. 7

B. 14

✓C. 7√2

D. 7√2/2

Answer:

Hi in my opinion maybe the answer is - 1

Answer:

(0, - 1)

Step-by-step explanation:

The y-intercept is the value of y when the x is equal to 0.

Answer:

1/4

Step-by-step explanation:

Answer:

Nope

Step-by-step explanation:

Nope

Answer:- 617/100+i root 2

Step-by-step explanation: simplify

Answer:

G. Water skiing > Cycling

Step-by-step explanation:

You burn more calories in water skiing

Answer:

Elga is 30 and Alvin is 15

Step-by-step explanation:

45-15=30

30-15=15

30+15=45

Answer:

[tex]\huge\boxed{\text{Alvin = 15, Elga = 30}}[/tex]

Step-by-step explanation:

In order to find Alvin and Elgas age, we can use a system of equations.

Let us assume that [tex]a[/tex] represents Alvin's age and [tex]e[/tex] represents Elgas age.

We can create two equations:

[tex]a = e-15[/tex]

[tex]a+e=45[/tex]

We can now use substitution to find each value. Let's substitute [tex]a = e-15[/tex] into [tex]a+e=45[/tex] as a.

[tex](e - 15) + e = 45[/tex]

We can now simplify this equation and solve for e.

[tex]2e-15 = 45\\2e = 60\\e = 30[/tex]

So we know that Elga is 30 years old. To find Alvin's age, we can substitute the value of e (30) back into one of the equations. Let's do it for [tex]a+e=45[/tex].

[tex]a + 30 = 45\\a = 45-30\\a=15[/tex]

So Elga is 30 years old and Alvin is 15 years old.

Hope this helped!

According to the histogram, it is found that about 10% of the students took less than 40 minutes to complete the exam.

An histogram is a graph that shows the number of times each element of x was observed.

In this problem, out of a total of 29 students, the histogram states that:

...

10% of 29 is given by:

0.1 x 29 = 2.9.

About 10% of 29 is of 3, hence, since 1 + 2 = 3, about 10% of the students took less than 40 minutes to complete the exam.

More can be learned about histograms at https://brainly.com/question/25836450