Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100100100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 20 \text{ cm}20 cm20, start text, space, c, m, end text. How far did Chubby run? Round your answer to the nearest \text{cm}cmstart text, c, m, end text.

Answer:

The graph which shows the line y-1=2(x+2) is shown in the attachment

Answer:

The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour

Step-by-step explanation:

Represent the bus average speed with x and the motorcycle average speed with y

Given

[tex]x = y + 2[/tex]

Distance covered by bus = 165 miles

Distance covered by motorcycle in same time = 155 miles

Required

Determine the speed of each

Average Speed is calculated as;

[tex]Average\ Speed = \frac{Distance}{Time}[/tex]

Since the two are measured with the same time, represent time with T

For the bus

[tex]Average\ Speed = \frac{Distance}{Time}[/tex] becomes

[tex]x = \frac{165}{T}[/tex]

Make T the subject of formula

[tex]T = \frac{165}{x}[/tex]

For the motorcycle

[tex]y = \frac{155}{T}[/tex]

Make T the subject of formula

[tex]T = \frac{155}{y}[/tex]

Since, T = T; we have that

[tex]\frac{165}{x} = \frac{155}{y}[/tex]

Cross Multiply

[tex]165y = 155x[/tex]

Substitute [tex]x = y + 2[/tex]

[tex]165y = 155(y+2)[/tex]

Open Bracket

[tex]165y = 155y - 310[/tex]

Collect Like Terms

[tex]165y - 155y = 310[/tex]

[tex]10y = 310[/tex]

Divide both sides by 10

[tex]y = 31[/tex]

Recall that [tex]x = y + 2[/tex]

[tex]x = 31 +2[/tex]

[tex]x = 33[/tex]

Hence;

The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour

Answer:

a.0.375

b.0.125

c.0.375

1.0.375

2.0.125

3.0.375

Step-by-step explanation:

a.

The total events in a sample space are n(S)=8

The events that contains exactly two boys

Boy Boy Girl,Boy Girl Boy,Girl Boy Boy.

Let A be the event that there are exactly two boys. Thus, n(A)=3.

So, probability of exactly 2 boys is P(A)=n(A)/n(S)=3/8=0.375.

b.

The event that contains exactly 0 girls.

Boy Boy Boy

Let B be the event that contains exactly 0 girls. Thus, n(B)=1.

So, probability of exactly 0 girls is

P(B)=n(B)/n(S)=1/8=0.125.

c.

The events that contains exactly 1 girl.

Boy Boy Girl,Boy Girl Boy,Girl Boy Boy

Let C be the event that contains exactly 1 girl. Thus, n(C)=3.

So, probability of exactly 1 girl is

P(C)=n(C)/n(S)=3/8=0.375.

Q1 is same as part a.

Q2 is same as part b.

Q3. is same as part c

Answer:

[tex]P(Dogs) = 0.2025[/tex]

Step-by-step explanation:

Given

[tex]Proportion, p = 45\%[/tex]

Required

Probability of two people having dog

First, we have to convert the given parameter to decimal

[tex]p = \frac{45}{100}[/tex]

[tex]p = 0.45[/tex]

Let P(Dogs) represent the required probability;

This is calculated as thus;

P(Dogs) = Probability of first person having a dog * Probability of second person having a dog

[tex]P(Dogs) = p * p[/tex]

[tex]P(Dogs) = 0.45 * 0.45[/tex]

[tex]P(Dogs) = 0.45^2[/tex]

[tex]P(Dogs) = 0.2025[/tex]

Hence, the probability of 2 people having a dog is [tex]P(Dogs) = 0.2025[/tex]

Answer:

3 and 2

Step-by-step explanation:

I can't see your orginal equation. But it's probably 3 cos x . Which the amplitude is 3 then. Vertical translation would be how I move this graph up or down compared to the y axis. So if I were to add a +2 to the end of 3cos(x) I will move the graph up 2 spaces. So my final equation is 3cos (x)+2.

Answer:

2x + 5y + 15

Step-by-step explanation:

add like terms

(x+x) + (y+y)+3y+15

2x+2y+3y+15

2x + 5y + 15

i hope this helps!

Answer:

5/14

Step-by-step explanation:

You multiply the recripricoal in division problems:

5/2  ÷ 7/1 =

5/2 × 1/7 =

5/14

Answer:

5 / 14

Step-by-step explanation:

will make it simple... the technique is to flip the either 5/2 or 7/1

then multiply.

5/2 x 1/7 = 5 / 14

Answer:

Step-by-step explanation:

answer is c just took test

Answer:

_

3.126

Step-by-step explanation:

Bar notation is a way in Mathematics to write decimal number that are repetiting or infinite.

Bar notation symbol is – is placed above the first decimal number that repeats itself. It is easier than writing the same repeating number and over again. It tells us that this particular number with the bar over it, is repeated continuously till infinity

From the above question, we were asked to write 3.126666666666... using Bar notation

_

3.126666666666... = 3.126

The bar is placed over the digit 6

Answer:

Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.

Step-by-step explanation:

Answer:

A. they are parallel because their slopes are equal.

Step-by-step explanation:

edge 2020

Answer:

its A in egde

Step-by-step explanation:

Answer:

The 95% CI is   [tex]2.108 < \mu < 2.892[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean [tex]\mu = 2.5[/tex]

    The standard deviation is  [tex]\sigma = 0.8[/tex]

Given that the confidence level is  95% then the level of confidence is mathematically evaluated as

          [tex]\alpha = 100 - 95[/tex]

   =>  [tex]\alpha = 5\%[/tex]

  =>    [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the values is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically evaluated as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

here we would assume that the sample size is  n =  16 since the person that posted the question did not include the sample size

  So    

               [tex]E = 1.96* \frac{0.8}{\sqrt{16} }[/tex]

               [tex]E = 0.392[/tex]

The  95% CI is mathematically represented as

              [tex]\= x -E < \mu < \= x +E[/tex]

substituting values

              [tex]2.5 - 0.392 < \mu < 2.5 + 0.392[/tex]

substituting values

              [tex]2.108 < \mu < 2.892[/tex]

Answer:

The sample required is  [tex]n = 135[/tex]

Step-by-step explanation:

From the question we are told that

     The  standard deviation is  [tex]\sigma = 9[/tex]

      The margin of error is [tex]E = 2[/tex]

Given that the confidence level is  99%  then the level of  significance is mathematically evaluated as

         [tex]\alpha = 100-99[/tex]

        [tex]\alpha = 1 \%[/tex]

        [tex]\alpha = 0.01[/tex]

Next we will obtain the critical value  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table(reference  math dot armstrong dot edu) , the value is  

             [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 2.58[/tex]

The  sample size is mathematically represented as

          [tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]

substituting values

           [tex]n = [ \frac{ 2.58 * 9 }{2} ]^2[/tex]

            [tex]n = 135[/tex]

Answer:

The previous palindrome date in all formats came 909 years ago on 11/11/1111. The next will come in 101 years on 12/12/2121 and after that there will not be another until 03/03/3030.

It depends how you format the date. If you do mm/dd/yyyy format

mm = month

dd = day

yyyy = year

then the last palindromic date was September 10th, 2019 since this would be written as 9/10/2019 in the mm/dd/yyyy format

Taking out the slash symbols, we have the number 9102019 which is the same when we reverse the digits.

The answer will be different if you have the date format as dd/mm/yyyy

Answer:

D: 450 miles

Step-by-step explanation:

So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):

[tex]0.4D=180[/tex]

This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:

[tex]0.4D=180\\D=450[/tex]

So the answer is D or 450 miles.

Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.

Answer and Step-by-step explanation: The null and alternative hypothesis for this test are:

[tex]H_{0}: s_{1}^{2} = s_{2}^{2}[/tex]

[tex]H_{a}: s_{1}^{2} > s_{2}^{2}[/tex]

To test it, use F-test statistics and compare variances of each treatment.

Calculate F-value:

[tex]F=\frac{s^{2}_{1}}{s^{2}_{2}}[/tex]

[tex]F=\frac{1.26^{2}}{0.93^{2}}[/tex]

[tex]F=\frac{1.5876}{0.8649}[/tex]

F = 1.8356

The critical value of F is given by a F-distribution table with:

degree of freedom (row): 20 - 1 = 19

degree of freedom (column): 20 - 1 = 19

And a significance level: α = 0.05

[tex]F_{critical}[/tex] = 2.2341

Comparing both values of F:

1.856 < 2.2341

i.e. F-value calculated is less than F-value of the table.

Therefore, failed to reject [tex]H_{0}[/tex], meaning there is no sufficient data to support the claim that sham treatment have pain reductions which vary more than for those using magnets treatment.

Answer:

Option (1)

Step-by-step explanation:

Given question is incomplete; find the picture of the graph in the attachment.

Parent function f(x) = [tex]\frac{1}{2^x}[/tex]

When function 'f' is translated by 4 units up which is evident form the graph, the translated function obtained is,

g(x) = f(x) + 4

g(x) = [tex]\frac{1}{2^x}+4[/tex]

Therefore, Option (1). [Translation of 4 units up] is defined by the graph attached.

Answer:

Option (1)

Step-by-step explanation:

Answer:

C. 1/4

Step-by-step explanation:

Parallel lines always have the same slope.

Answer:

  C.  1/4

Step-by-step explanation:

Parallel lines have the same slope. If line b is parallel to line a, and line a has slope 1/4, then line b has slope 1/4.

Answer:

w ≥ -18

Step-by-step explanation:

Answer:

w is greater than or equal to-18

Answer:

111 ft²

Step-by-step explanation:

wall: 10 x 12 = 120

window: 3 x 3 = 9

wall - window = area to wallpaper

120 - 9 = 111

111 ft²

Answer:

111 sq ft

Step-by-step explanation:

wall: 10 x 12 = 120

window: 3 x 3 = 9

wall - window = area to wallpaper

120 - 9 = 111

111 ft²

Answer:

$188.91

Step-by-step explanation:

$999*.09=$89.91

$89.91+$99=$188.91

Answer:

0.4

Step-by-step explanation:

we are required to find the probability that the ring is within 12 meters from nthe car.

we start by defining a random variable x to be the distance from the car. the car is the starting point.

x follows a normal distribution (0,30)

[tex]f(x)=\frac{1}{30}[/tex]

[tex]0<x<30[/tex]

probabilty of x ≤ 12

= [tex]\int\limits^a_ b{\frac{1}{30} } \, dx[/tex]

a = 12

b = 0

[tex]\frac{1}{30} *(12-0)[/tex]

[tex]\frac{12}{30} = 0.4[/tex]

therefore 0.4 is the probability that the ring is within 12 feet of your car.

Answer:

150<60+30n

Step-by-step explanation:

150 is the maximum amount that she can spend on gas. (which is the total)

she already spend $60

each fill up (n) costs 30

Answer:

the answer is B)

Step-by-step explanation:

Answer:

316.08 inches

Step-by-step explanation:

There are 3 feet in a yard, and there is 12 inches in 1 foot, so there are 36 inches in one yard. If there is 8 7/9 yards it is the same at 8.78 yards, and  8.78 x 36 = 316.08 inches. Therefore 8 7/9 yards = 316.08 inches.

Answer:

Step-by-step explanation:

We could start by listing multiples of 4 and looking for patterns. Do  

you know what a multiple of a number is?  It's that number multiplied  

by another number. So the first multiple of 4 is 4x1, the second  

multiple of 4 is 4x2=8, the third multiple of 4 is 4x3=12, etc.  

Let's make a table of multiples of 4 from 1 to 100, with columns A-E  

across the top and rows 1-5 down the left-hand side:

    A      B      C      D      E

1    4      8     12     16     20

2   24     28     32     36     40

3   44     48     52     56     60

4   64     68     72     76     80

5   84     88     92     96    100

Now let's look at these multiples, remembering that there will be nine  

more tables like this one from 101-1000.

Let's look for 6,7,8,9, and 0 in the columns first. Aha! We can erase  

all of columns B, D, and E because there's a 6 or an 8 or a 0 in each  

number in those columns.  Now we're left with just:

    A      C  

1    4     12  

2   24     32  

3   44     52  

4   64     72  

5   84     92  

Now let's look at the rows. Wow! We can eliminate rows 4 and 5 because  

they have 6, 7, 8, or 9, leaving:

    A      C  

1    4     12  

2   24     32  

3   44     52  

Just 6 numbers left!

So if from 1-100 there are 6 multiples of four that do not contain any  

of the digits 6, 7, 8, 9, or 0, how many multiples of four like this  

are there from 1-1000?

Answer:

the slope of the read line is also -2

Step-by-step explanation:

Answer:

The present value is  [tex]PV = \$ 396,987[/tex]

Step-by-step explanation:

From the question we are told that

   The  interest payment per year is  [tex]C = \$ 85[/tex]

    The principal payment is  [tex]P = \$ 1000[/tex]

     The  duration is  n =  8   years

      The  interest rate is  [tex]r = 10\% = 0.10[/tex]

The present value is  mathematically represented as

      [tex]PV = [ \frac{C}{r} * [1 - \frac{1 }{ (1 +r)^n} ] + \frac{P}{(1 + r)^n} ][/tex]

substituting values

      [tex]PV = [ \frac{85}{0.10} * [1 - \frac{1 }{ (1 +0.10)^8} ] + \frac{1000}{(1 + 0.10)^ 8} ][/tex]

      [tex]PV = \$ 396,987[/tex]

Answer:

A: 19

Step-by-step explanation:

For this, we can complete the square. We first look at the first 2 terms,

t^2 and -6t.

We know that [tex](t-3)^2[/tex] will include terms.

[tex](t-3)^2 = t^2 - 6t + 9[/tex]

But [tex](t-3)^2[/tex] will also add 9, so we can subtract 9. Putting this into the equation, we get:

[tex]m(t) = (t-3)^2 - 9 +28[/tex]

[tex]m(t) = (t-3)^2 +19[/tex]

Using the trivial inequality, which states that a square of a real number must be positive, we can say that in order to have the minimum number of members, we need to make (t-3) = 0. Luckily, 3 months is in our domain, which means that the minimum amount of members is 19.

Answer:

Step-by-step explanation:

Decay of carbon - 14 is exponential in nature . It decays as follows .

[tex]N=N_0e^{-\lambda t}[/tex]  λ is called decay constant .

λ = .693 / T where T is half life .

Half life of carbon-14 is 5700 years

λ = .693 / T

= .693 / 5700

= 12.158 x 10⁻⁵ year⁻¹

[tex]N=N_0e^{-\lambda t}[/tex]

N = .71 N₀

[tex].71 N_0 =N_0e^{-\lambda t}[/tex]

[tex].71 =e^{-\lambda t}[/tex]

Taking ln on both sides

ln .71 = - λ t

ln .71 = - 12.158 x 10⁻⁵  t

-0.3425 =  - 12.158 x 10⁻⁵  t

t = .3425 / 12.158 x 10⁻⁵

2817  years .

Answer: intersecting lines

Step-by-step explanation:

Answer:

The relationship of the lines would be Parallel.