The average distance from earth to the sun is 92, 589, 230 miles. The distance from earth to the moon is 92,350,373 miles less than the distance from earth to the sun. Find the distance from earth to the moon and sun to moon.

Distance from earth to moon =238,857 miles ; Distance from sun to moon. = 92,350,373 miles
Distance from earth to moon=184,939,603 miles; Distance from sun to moon. = 277,528,833 miles
Distance from earth to moon=238,857 miles ; Distance from sun to moon. =92,828,087 miles

Answer:

t varies inversely to 30/r

Step-by-step explanation:

t varies inversely to r

(lol I can't seem to find the variation sign in the keyboard)

when you introduce the constant K the sign changes to =

t=k/r

if t=6, r=5

substitute the values

6=k/5

k= 6×5

k=30

we have found the constant so we add it to our initial equation

t inversely varies to 30/r

Answer:

Step-by-step explanation:

Hello,

Factor x^2 + 64.

[tex]\boxed{x^2+64=x^2+8^2=x^2-8^2i^2=(x-8i)(x+8i)}[/tex]

Factor 16x^2 + 49.

[tex]\boxed{16x^2+49=(4x)^2-(7i)^2=(4x-7i)(4x+7i)}[/tex]

Find the product of (x + 9i)^2.

[tex]\boxed{(x+9i)^2=x^2+18xi+(9i)^2=x^2+18xi-81=x^2-81+18xi}[/tex]

Find the product of (x − 2i)^2.

[tex]\boxed{(x-2i)^2=x^2-4xi-4=x^2-4-4xi}[/tex]

Find the product of (x + (3+5i))^2.

[tex]\boxed{(x + (3+5i))^2=x^2+(3+5i)^2+2x(3+5i)=x^2+9-25+30i+6x+10xi}\\\boxed{=x^2+6x-16+(30+10x)i}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

c

Step-by-step explanation:

outputs are on the right, which are the y-values.

Answer:

n=5*-45

n=225

:)

Step-by-step explanation:

Answer:

n = -225

Step-by-step explanation:

-45 = n/5

cross multiply

n = -45 x 5

n= -225

Answer:

Assume that Sk is valid for n=k and prove that Sn is valid for n= k+ 1

Step-by-step explanation:

This is Principle of Mathematical Induction ---PMI

Step 1: Verify that Sn is valid for n =1

Step 2:Assume that Sk is valid for n=k and prove that Sn is valid for n= k+ 1

Answer:

Step-by-step explanation:

The perimeter of the triangle △SMP is the sum of al the sides of the triangle.

Perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

Note that the triangle △LRN, △LSM, △MPN and △SRP are all scalene triangles showing that their sides are different.

Given LM=9, NR=16 and SR=8

NR = NP+PR

Since NP = PR

NR = NP+NP

NR =2NP

NP = NR/2 = 16/2

NP = 8

From △LSM,  NP = PR = MS = 8

Also since LM = MN, MN = 9

From △SRP, SR = RP = PS =  9

Also SR = MP = 8

From the equation above, perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

perimeter of △SMP = 8+8+9

perimeter of △SMP = 25

Answer:

x = 85 deg

Step-by-step explanation:

We can see that there are two straight lines that intersect and that the two angles given are opposite angles.

Because they are opposite angles, the two angles have the same value, i.e

(x + 5) = 90     (subtract 5 from each side)

x = 90 - 5

x = 85 deg

Answer:

t = 5,-1,3

Step-by-step explanation:

r=0.01t^3-0.07t^2+0.07t+0.15

For simplification let's multiply the equation by 100

100r = t³ - 7t² + 7t + 15

When r= 0

t³ - 7t² + 7t + 15= 0

Let's look for the value of t.

Let's try a possible division

(t³ - 7t² + 7t + 15)/(t-5) = t² -2t -3

So we've gotten one as t-5

Let's factorize t² -2t -3

= t² +t -3t -3

= t(t+1) -3(t+1)

= (t+1)(t-3)

So we have

(t-5)(t+1)(t-3)

What it means is that the possible values are when

t = 5,-1,3

These are also called the roots of the equation

Answer:I don’t know

Step-by-step explanation: fruit flys are weird

Answer:

Piecewise function;

y = 2x - 2 where x < 2

       4 where 2 ≤ x ≤ 5  

       y = x + 1 where x > 5

Step-by-step explanation:

Function graphed represents the piecewise function.

1). Equation of the line with y-intercept (-2) and slope 'm'.

 Since, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

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

                                        = 2

 Therefore, equation of this segment will be in the form of y = mx + b,

 ⇒ y = 2x - 2 where x < 2

2). Equation of a horizontal line,

 y = 4  where 2 ≤ x ≤ 5

3). Equation of the third line in the interval x > 5

 Let the equation of the line is,

 y = mx + b

 Where m = slope of the line

 b = y-intercept

 Here, slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

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

                           = 1

 Equation of this line will be,

 y = 1(x) + b

 y = x + b

 Since, this line passes through (5, 6),

 6 = 5 + b

 b = 6 - 5 = 1

 Therefore, equation of this line will be,

 y = x + 1 where x > 5

 Graphed piecewise function is,

 y = 2x - 2 where x < 2

       4 where 2 ≤ x ≤ 5  

       y = x + 1 where x > 5

Answer:

work is shown and pictured

Answer:

We Reject H₀ if t calculated > t tabulated

But in this case,

0.83 is not greater than 2.056

Therefore, we failed to reject H₀

There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.

Step-by-step explanation:

Refer to the attached data.

The Null and Alternate hypothesis is given by

Null hypotheses = H₀: μ₁ = μ₂

Alternate hypotheses = H₁: μ₁ ≠ μ₂

The test statistic is given by

[tex]$ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } } $[/tex]

Where [tex]\bar{x}_1[/tex] is the sample mean of people who do not exercise regularly.

Where [tex]\bar{x}_2[/tex] is the sample mean of people who do exercise regularly.

Where [tex]s_1[/tex] is the sample standard deviation of people who do not exercise regularly.

Where [tex]s_2[/tex] is the sample standard deviation of people who do exercise regularly.

Where [tex]n_1[/tex] is the sample size of people who do not exercise regularly.

Where [tex]n_2[/tex] is the sample size of people who do exercise regularly.

[tex]$ t = \frac{72.7 - 69.7}{\sqrt{\frac{10.9^2}{16} + \frac{8.2^2}{12} } } $[/tex]

[tex]t = 0.83[/tex]

The given level of significance is

1 - 0.95 = 0.05

The degree of freedom is

df = 16 + 12 - 2 = 26

From the t-table, df = 26 and significance level 0.05,

t = 2.056 (two-tailed)

Conclusion:

We Reject H₀ if t calculated > t tabulated

But in this case,

0.83 is not greater than 2.056

Therefore, We failed to reject H₀

There is no difference between the mean pulse rate of people who do not exercise and the mean pulse rate of people who do exercise.

Answer:

1.5 kg

Step-by-step explanation:

Assuming it scales linearly: the higher tin holds 9/6 as many biscuits, so:

9/6 · 1 kg = 1.5 kg

Answer:

The 25,000 registered voters

Step-by-step explanation:

Population includes the entirety of the set of data, it consists of all the elements of a data set. For example all the students in a school, all the citizens of a country etc.

While the sample is the elements of the population from which observations are drawn from.

Therefore, for the case above, the population is the entirety of the registered voters in the city, that is all the 25,000 registered voters.

Answer:

15

Step-by-step explanation:

Factors of 30:

1 , 2, 3, 5, 6, 10, 15, 30

Multiples of 3:

3, 6, 9, 12, 15, etc.

The first number (and only number) shared by both sets is 15, therefore 15 is your answer.

~

Answer:

Your answer would be 15

Step-by-step explanation:

It would be 15 because you can multiply it by 30, it goes into 3 evenly and 15 is an odd number

Answer:

Step-by-step explanation:

y = -3x - 2

5x + 2y = 15

5x + 2(-3x -2) = 15

5x -6x - 4 = 15

-x - 4 = 15

-x = 19

x = -19

y = -3(-19) - 2

y = 57 - 2

y = 55

(-19, 55)

solution is b

Answer:

c

Step-by-step explanation:

Answer:

N1,052,800.

Step-by-step explanation:

The starting salary of the officer = N57,000

Increase per annum =N2,800

The given pattern forms an arithmetic sequence since the annual salary increases by a fixed amount.

We are to determine the total amount of money that the officer will earn in 14 years.​

Sum of an arithmetic sequence, [tex]S_n=\frac{n}{2}[2a+(n-1)d]$ ,where: \left\{\begin{array}{lll}$First term, a=57,000\\$Common difference, d=2,800\\$Number of terms, n=14\end{array}\right[/tex]

[tex]S_{14}=\frac{14}{2}[2(57,000)+(14-1)(2,800)]\\=7[114,000+13*2800]\\=7[150,400]\\=1,052,800[/tex]

At the end of 14 years, the total amount earned by the officer will be N1,052,800.

Answer:

Right-angle triangle

Step-by-step explanation:

Answer:

D. 0.002

Step-by-step explanation:

Given;

total number of sample, N = 500 elements

50 elements are to be drawn from this sample.

The probability of the first selection, out of the 50 elements to be drawn will be = 1 / total number of sample

The probability of the first selection = 1 / 500

The probability of the first selection = 0.002

Therefore, on the first selection, the probability of an element being selected is 0.002

The correct option is "D. 0.002"

On the first selection, the probability of an element being selected is 0.002. Option D is correct.

Given information:

A population consists of 500 elements. so, the total number of samples will be [tex]N = 500[/tex] .

We want to draw a simple random sample of 50 elements.

The probability is defined as the preferred outcomes divided by the total number of samples.

So, the probability of first selection will be calculated as,

[tex]P=\dfrac{1}{500}\\P=0.002[/tex]

Therefore, on the first selection, the probability of an element being selected is 0.002.

For more details, refer to the link:

https://brainly.com/question/18722707

Answer:

y = 1/2x + 4

Step-by-step explanation:

Use the formula for the equation of a line.

y = mx + b

Where m is the slope, and b is the y-intercept.

The slope is given.

y = 1/2x + b

The points (x, y) are given.

(4, 6)

Put y as 6 and x as 4, solve for b.

6 = 1/2(4) + b

6 = 2 + b

6 - 2 = b

4 = b

The y-intercept is 4 or (0, 4).

The equation of the line is y = 1/2x + 4.

Answer:

(- 5, - 7 )

Step-by-step explanation:

Equate f(x) and g(x), that is

2x + 3 = - 4x - 27 ( add 4x to both sides )

6x + 3 = - 27 ( subtract 3 from both sides )

6x = - 30 ( divide both sides by 6 )

x = - 5

Substitute x = - 5 into either of the 2 functions for y- coordinate

Substituting into f(x)

f(- 5) = 2(- 5) + 3 = - 10 + 3 = - 7

Thus point of intersection = (- 5, - 7 )

Answer:

arccos (0.5) is [tex]\frac{\pi}{3}[/tex]

Step-by-step explanation:

With the arccos(0.5)  in this problem, you are asked which angle renders its cosine equal to 0.5 (or 1/2).

Recall that there are special angles in the unitary circle that render well know values like 1/2. There are two angle values between 0 and the full circle ([tex]2\pi[/tex] radians), that render cosine function equal 1/2, and they are: [tex]\frac{\pi}{3}[/tex], and [tex]-\frac{\pi}{3}[/tex].

The arccos uses just the first one as answer over the restricted domain between 0 and [tex]\pi[/tex], since otherwise it will not be considered a function.

So the answer is that the arccos (0.5) is [tex]\frac{\pi}{3}[/tex]

Answer:

A

90 degrees

anticlockwise.

Step-by-step explanation:

It looks much more complicated than it really is. I don't know how to explain this in any other form but to give the answers.

1 A

The center of rotation is where the 90 degree angle has its vertex. So that would be A.

1 B

Follow x. It rotates 90 degrees. So every point must rotate 90 degrees.

1 C

The direction is against the way the clock tells time, so the direction of rotation is anticlockwise.

Answer:

3/7

Step-by-step explanation:

total cards 3+4 = 7

Not green = 7-4 = 3 cards

P ( not green )= not green cards / total = 3/7

Answer:

3/7.

Step-by-step explanation:

There are seven cards in total, four of them being green.

The knowledge of the color of the other cards aren't really nessesary, so you can just subtract four from seven, which is three.

Hope this helped!

Explanation:

Given information:

From that we can see the data set is {4,5,5,6,6,6,6,7,7,7,7,8,8,8,9,9,10,10} which produces the dot plot you see in the image attachment below.

It's a bit tricky to see, but the graph is nearly symmetrical. If we were to remove the blue points in the dot plot I provided, then we'll get a perfectly symmetrical distribution. Symmetrical means one half is a mirror copy of the the other half. The center line of a symmetrical distribution is both the mean and median.

Answer:

The Answer On Edge Is A.), Have Fun Dreamers!

Step-by-step explanation:

Answer:  The ramp must be 32 feet long.  In inches, 384.

Step-by-step explanation:

For each 16 inches of run, there is one inch of rise. To get 24 inches of rise, multiply 16 by 24 to get 384 inches. To convert to a more useful measurement, convert to feet.  12 inches per foot.  384/12 = 32

Measurement is the process of assigning numbers to physical quantities and phenomena.

If a 1-inch rise for a 16-inch run makes it easier for the wheelchair rider, this can be expressed as:

1inch rise = 16-inch run

In order to determine how long must a ramp be to easily accommodate a 24-inch rise to the door, we can write:

24in rise = x

Divide both expressions:

[tex]\dfrac{1}{24}=\dfrac{16}{x}\\[/tex]

Cross multiply:

[tex]x=16 \times 24\\x=384inches[/tex]

Hence the ramp must be 384inches long in order to easily accommodate a 24-inch rise to the door.

Learn more here: https://brainly.com/question/14503610

Answer:

57,838.4 - 57,491.9 = 346.5 miles

346.5/17.5 = 19.8 miles per gallon.

Hope this helps :-)

Step-by-step explanation:

Answer:

1st 2nd 4th 5th

This is not the correct question, the correct question is;

Assume that the probability of the binomial random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. Find the probability that at least 35 households have a gas stove.

Answer: p ( x > 34.5 )  The area to the right of 34.5

Step-by-step explanation:

Given that, x = 35

when using normal approximation

Using continuity correction

so

p ( x ≥ 35 ) = p ( x > 34.5 )

More than means the area is towards the right.

Therefore, the area under the normal curve is,

p ( x > 34.5 ) The area to the right of 34.5

Answer: n = -2

Step-by-step explanation:

answer:

-2                                                    

step by step explanation: