As Jupiter and Earth travel along their respective orbits, what happens to the one-way communication time of radio waves carrying information between the two planets?

Complete question is;

A researcher wishes to determine if aerobic exercise improves mental performance immediately following the exercise. He plans to have high school students participate in 30 minutes of aerobic exercise and then take a standard test of their reasoning skills. Suppose the scores of high school students on this test of reasoning skills immediately after 30 minutes of aerobic exercise follow a Normal distribution with mean μ and standard deviation σ = 4. Suppose also that, in the general population of all high school students, scores on the test of reasoning skills follow a Normal distribution with mean 25 and standard deviation σ = 4. The researcher, therefore, decides to test the following hypotheses.

H0 : μ = 25, Ha : μ > 25

To do so, the researcher has 10,000 high school students do 30 minutes of aerobic exercise and then, immediately following the exercise, take the test. The mean score for these students is = 25.2 and the P-value is less than 0.0001.

It is appropriate to conclude which of the following?

Select one:

A. The researcher has conclusively proved that, for high school students, 30 minutes of aerobic exercise substantially improves mental performance.

B. The researcher has strong evidence that, for high school students, 30 minutes of aerobic exercise substantially improves mental performance.

C. The researcher has moderate evidence that, for high school students, 30 minutes of aerobic exercise substantially improves mental performance.

D. None of the above

Answer:

D. None of the above

Step-by-step explanation:

We see that the researcher wants to test the hypotheses;

Null hypothesis; H0 : μ = 25,

Alternative hypothesis; Ha : μ > 25

Population mean = 25 and standard deviation σ = 4

After testing a sample of 1000 students, he discovered that;

Sample size; n = 1000

Sample mean; x¯ = 25.2

After calculations, he got P-value as less than 0.0001.

Now, he can't make any conclusion or evidence for this research because there is no population mean for the aerobic exercise and also no significance value in the entire question to compare the p-value with.

Thus, none of the options are correct.

Answer:

The average airspeed of the two planes is \(406.25\; \rm mph\).

Step-by-step explanation:

Let \(x\) denotes the average airspeed (in miles-per-hour) of the two planes. Let \(y\) denote the average speed of wind (also in miles-per-hour) along that route.

John is travelling against the head wind. Therefore, his ground speed would be the difference between his airspeed and the speed of the wind. That is:

\(\begin{aligned} & v(\text{John, ground speed})\\ =& v(\text{John, airspeed}) - v(\text{wind speed}) \\=& x - y\end{aligned}\).

On the other hand, Debby is travelling in the tail wind. Assume that Debby and John are taking the same route but in the opposite directions. The ground speed of Debby would be the sum of her airspeed and the speed of the wind:

\(\begin{aligned} & v(\text{Debby, ground speed})\\ =& v(\text{Debby, airspeed}) + v(\text{wind speed}) \\=& x + y\end{aligned}\).

Keep in mind that:

\(\text{Distance Traveled} = \text{Average Speed} \times \text{Time}\).

This equation can help relate time and ground speed to distance.

John traveled \(2100\) miles in \(5.6\) hours at a ground speed of \((x - y) \; \rm mph\). Therefore:

\(5.6\; (x - y) = 2100\).

Similarly, Debby traveled \(2100\) miles in \(4.8\) hours at a ground speed of \((x + y)\; \rm mph\). Therefore:

\(4.8\; (x + y) = 2100\).

Combine these two equations to obtain:

\(\left\lbrace\begin{aligned}& 5.6\; (x - y) = 2100 \\ & 4.8\; (x + y) = 2100\end{aligned}\right.\).

Solve this system of equations for \(x\) and \(y\):

\(\left\lbrace\begin{aligned}&x = 406.25 \\ &y = 31.25\end{aligned}\right.\).

In other words:

Answer:

-25 + 75 = 50

Step-by-step explanation:

Since we don't know the value of the bar, we will call it x.

-25 + x = 50

Add 25 to both sides to find the value of x.

x = 75

You can also double check this answer by doing simple math.

-25 + 75 = 50

Answer:

x=8, 3

Step-by-step explanation:

24 has 8 factors: 1,2,3,4,6,8,12,24

8 and 3 make 11

If you factor it out, the equation is (x-8)(x-3)=0

to get 0, only one of the expressions has to equal 0

so x can have 2 different values

Answer:

$471.43 per night

Step-by-step explanation:

$3,300 divided by 7= 471.428571429

Rounded up with eight and its 471.43

Answer:

Its C

Step-by-step explanation:

Answer:

c..........................

========================================================

Explanation:

What you type into that calculator (or any calculator really) is this

(124/360)*2*pi*9

This is because we use this generalized formula

L = (x/360)*2*pi*r

where,

So after typing in that expression, you should get roughly 19.47787445 as shown in the screenshot below.

This then rounds to 19.48

Note: I used the calculator's stored version of pi. If you used something like pi = 3.14, then the answer would be slightly different.

Answer:

b = -5

Step-by-step explanation:

Let's figure this equation, step by step.

-3b + 8 = 38 + 3b

Step 1: Subtract 3b from both sides. This cancels out the addition by 3b.

-3b + 8 - 3b = 38

Step 2: Combine -3b and -3b to get -6b.

-6b + 8 = 38

Step 3: Subtract 8 from both sides. This cancels out the addition by 8.

-6b = 38 - 8

Step 4: Subtract 8 from 38 to get 30.

-6b = 30

Step 5: Divide both sides by -6. This undoes the multiplication by -6.

b = 30/-6

Step 6: Divide 30 by -6 to get -5.

b = -5

Let's check our work by substituting -5 for b in the equation above.

-3(-5) + 8 = 38 + 3(-5)

15 + 8 = 38 + (-15)

23 = 23

Both sides are the same, so b = -5.

Answer:

3/8

Step-by-step explanation:

since there are 8 balls in total and 3 of them are green, you write the ratio as 3:8. This is the same as 3/8

Answer:

$18,750

Step-by-step explanation:

Take the earnings per week times the number of weeks

50 * 375

18,750

Answer:

$18,750

Step-by-step explanation:

If we want to find the nurse's aide's earnings for the year, we have to multiply her weekly salary by the number of weeks she worked.

weekly salary * number of weeks

She earns $375 per week and she worked for 50 weeks.

$375*50 weeks

375*50

Multiply the 2 numbers

18,750

Her total earnings for the year are $18,750

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Step-by-step explanation:

the answer would be 4 glasses of water

Answer:$920

Step-by-step explanation:

Step-by-step explanation:

The interest earned is $920.

Based on the general form of a wave function, the times the frequencies of the sound waves be the same in the interval [0°, 360°) is x = 180°, 210°, 270°, 330°.

Frequency is the number of vibrations of a wave per second.

The period of a wave is the time taken for one complete vibration.

Frequency and Period are inversely related.

Using the general form of a wave function:

where;

From the two wave functions:

y = 2sin2x

b = 2

period = 2π/2

period = π = 180°

Frequency =

y = −sin x

b = 1

Period = 2π/1

Period = 2π = 360°

Therefore, the times the frequencies of the sound waves be the same in the interval [0°, 360°) is x = 180°, 210°, 270°, 330°.

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Answer:

x = 0°, 180°, 210°, 330°

If you were to graph the two functions those would be the intersection points (after converting from radians to degrees)

The area of the square is given as 100 square unit

You should be aware that the square has all its sides equal

The perpendicular from opposite vertices represent distance

The given vertices are

(2,2) and (10,8)

Using the formula for distance between two points

d=√(10-2)²+(8-2)²

d=√8²+6²

d = √64+36

d=√100

This implies that d=10

The area of a square is given as s²

Area = 10²

Atrea = 100 square units

In conclusion, the area of the square is 100 square units

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Translated question:

The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square

This question is incomplete, the complete question is;

Trevor is interested in purchasing the local hardware/electronic goods store in a small town in South Ohio. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 60% of the business days it is open. Estimate the probability that the store will gross over $850 at least 6 out of 10 business day

Answer:

P( at least 6 out of 10 business days ) = 0.6312

Step-by-step explanation:

Given the data in the question;

p = 60% = 0.6

q = 1 - p = 1 - 0.6 = 0.4

Using Binomial distribution;

P( X = r ) = \(^nC_r p^rq^{n-r\)

where \(^nC_r = n!/(r!(n-r))\)

we substitute

P( at leas 6 ) = P(6) + P(7) + P(8) + P(9) + P(10)

= [¹⁰C₆ × 0.6⁶ × 0.4⁴] + [¹⁰C₇ × 0.6⁷ × 0.4³] + [¹⁰C₈ × 0.6⁸ × 0.4²] + [¹⁰C₉ × 0.6⁹ × 0.4¹] + [¹⁰C₁₀ × 0.6¹⁰ × 0.4⁰]

= [0.250] + [0.214] + [0.1209] + [ 0.0403] + [ 0.00604 ]

= 0.6312

Therefore, P( at least 6 out of 10 business days ) = 0.6312

Answer:

y + 4 = -(x - 8)

Step-by-step explanation:

The point-slope form equation is y - y1 = m(x - x1)

Since we're given m and since they use the 4 from (8, -4) as y - (-4) = y+4, we simply need to plug in 8 into the RHS of the equation and you can check the math.

If you substitute 8 and -4 for y and x, you have:

-4 + 4 = -1(8 - 8)

0 = -1 * 0

0 = 0

You'd get -2 on both sides if you used -6 and 10, but having an equal equation means our math is true/accurate.

Answer:

w(3-3+3)

Step-by-step explanation:

distibutitve property

Step-by-step explanation:

\( {a}^{2} + {b}^{2} = {c}^{2} \\ {9}^{2} + {40}^{2} = {41}^{2} \\ 81 + 1600 = 1681 \\ 1681 = 1681\)

Answer:

1711

Step-by-step explanation:

\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)

Make sure to follow order of operations!

The development made to the Judaism is mentioned below;

Action as Leader;

Abraham;

Abraham's care for others is one of his leadership strengths. Abraham expressed his sorrow for Sodom and Gomorrah when the Lord informed him that they would be destroyed. He "stick his neck out for his people," as one who cares for others. He pleaded with God on their behalf.

Moses;

Early on, Moses realized he didn't have to handle everything by himself. He eventually succeeded as a leader by using delegation.

David;

As a man of God, David had learned to wait on the Lord, but he also had to learn how to be patient with those around him.

Solomon;

His name in Hebrew means peace and he used his wisdom to bring about peace in the world through deeds rather than conquest.

Contribution to Judaism

Abraham;

Before Abraham, people believed in multiple gods; Abraham was the first to preach that there is only one God. Ironically, Terach, Abraham's father, had made a fortune by selling idols of several deities.

Moses;

The Jews were delivered from slavery in Egypt by Moses, who also guided them to the Holy Land that God had promised.

David;

Many of the Old Testament Psalms are attributed to him; they were probably penned on his renowned lyre, upon which he was reputed to be a master.

Solomon;

As the Israelite monarch who constructed the first Temple in Jerusalem, Solomon is well-known. He was also the second and final king of a united Israel, which was at the height of its power during his rule (after his father, David).

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The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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Caludia needs to pay 2917.6128 as a payment of compound interest capital+interest.

What is compound interest?

compound interest is interest on principal + interest and this denotes to the addition of interest to the principal amount of a loan or deposit.

Capital(p) = $6400

Rate of interest(r) = 11%

Years(n) = 3

The general formula of compound interest is \(A= p(1+\frac{r}{100}})^n\).

Now

\(A= 6400(1+\frac{11}{100}})^3\\A=6400 \times \frac{111}{100} \times \frac{111}{100} \times \frac{111}{100}\\A= 8752.8384\)

The entire amount (Capital+interest) is equal to $8752.8384.

If we take 1 year as a period then Claudia needs to pay \(\frac{8752.8384}{3}\\=2917.6128\)

Therefore, Claudia needs to pay 2917.6128 as a payment of compound interest capital+interest.

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Answer:

c

Step-by-step explanation:

Answer:

P=19.2 ft

Step-by-step explanation:

ACCORDING TO THE THEOREM,

BC=2(DE)

So BC =2(3.2)

BC=6.4 ft

Now

AB=2(EF)

AB=2(4)

AB=8 ft

Now

AC = 2(DF)

AC= 2(2.4)

AC=4.8 ft

Now we're gonna find the perimeter which is sum of all sides

Perimeter=4.8+8+6.4

P= 19.2 ft

In the linear graph, the value of x such that f(x) = -3 is -2.

A linear graph is a straight line or straight graph which is drawn on a plane connecting the points on x and y coordinates.

Therefore, a linear graph is represented in the form of a straight line.

It shows the relationship between variables x and y.

x is the horizontal variables while y is the vertical variables.

Therefore, the graph of the given function is f(x).

Let's use the graph to find x such that f(x) = - 3

f(x)  is the y coordinates of the linear graph.

Let's find x when f(x) = -3

Therefore,

x = - 2

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The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Check the picture below.