The weight of an object on the moon is
5 of its weight on Earth. If a moon rock
weighs 202 lb on Earth, how much did
the moon rock weigh on the moon?
Give your answer as a simplified mixed number.
Enter the number that belongs in the green box.

Answer: Reject [tex]H_0[/tex] if the confidence interval does not contain the value of the hypothesized mean [tex]\mu_0[/tex].

Step-by-step explanation:

In the case of Confidence Intervals and Two-Tailed Hypothesis Tests,

Null hypothesis : [tex]H_0:\mu=\mu_0[/tex]  [There is no change in mean.]

Alternative hypothesis: [tex]H_a:\mu\neq\mu_0[/tex]  [There is some difference.]

Since confidence intervals contain the true population parameter ( mean).

So, Decision rule states that

Answer:

18 minutes

Step-by-step explanation:

1: Calculate how many minutes are in an hour

2: Take 3:16 and add until 3:34

The part of an hour  3/10

Elapsed time is the time taken by an event to occur between the start of the time and the end of the time. In simple words, we can say that the amount of time that has passed between the beginning and the end of an event is called the elapsed time. We can determine this time by subtracting the end time and the start time. The formula to calculate the elapsed time is simply to subtract the hours and minutes separately. It gives the duration of an event.

Elapsed time means the time that has elapsed between the start of the time and the end of the time.

For example, if a man starts traveling at 10:30 AM and ends the journey at 12:15 PM, the time elapsed is the duration of his journey, that is, the time between 12:15 PM and 10:30 AM. Elapsed time is an important concept as it helps us to learn to read the time on a clock and measure the time taken for an event to occur.

Formula:

Elapsed Time = End Time - Start Time

As, 3:16 p.m. shows 44  minutes before 4:00 p.m.

and, 3:34 p.m. shows 26 minutes before 3: 34 p.m.

As, there is difference of

=44-26

=18 minutes

Hence, the part of an hour = 18/60= 3/10

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Answer:

  It has the same domain as the function [tex]f(x)=-\sqrt{-x}[/tex].

Step-by-step explanation:

The function ...

  [tex]f(x)=\sqrt{-x}[/tex]

has a domain of all non-positive numbers and a range of all non-negative numbers. Anything with a -x under the radical will have the same domain. Any positive root will have the same range.

__

So, we can say it has the same domain as ...

  [tex]f(x)=-\sqrt{-x}[/tex]

Answer:

A on edge

Step-by-step explanation:

hehe

Answer:

XYZ = 21.8

Step-by-step explanation:

the missing angle is XYZ

using a calculator:

so XYZ = 21.8

Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

The Patel, Lopez, and Russo families all had parties recently. There were 152 adults at the Lopez party. The ratio of adults to children at the Russo party was 5 to 4. What was the ratio of adults to children at the Patel party?

(1) The Russo party had 31 more adults than children, and 47 more adults than did the Patel party.

(2) The Patel party had 40 more children, though 4 fewer people in total, than did the Lopez party, where the ratio of adults to children was 8 to 5.

Answer: Let the number of children in Russo party be x, The Russo party had 31 more adults than children, therefore the number of adults at the Russo party = x + 31. The ratio of adults to children at the Russo party was 5 to 4, we can find the number of children using:

[tex]\frac{5}{4}=\frac{x+31}{x}\\ 5x=4x+124\\x=124[/tex]

The number of children at the Russo party is 124 and the number of adult is 155 (124 + 31).

They  are 47 more adults at the Russo party than the Patel party, the number of adult at the Patel party = 155 - 47 = 108

the ratio of adults to children was 8 to 5 at the Lopez party, There were 152 adults at the party. Let x be the number of children at the Lopez party therefore:

[tex]\frac{8}{5}=\frac{152}{x}\\ 8x=760\\x=95[/tex]

The Patel party had 40 more children than the Lopez, the number of children at the Patel party = 135 (95 + 40).

The ratio of adults to children at the Patel party is [tex]\frac{108}{135} =\frac{4}{5}[/tex]

Hey there! I'm happy to help!

The distance around a circle is the circumference. To find it, you multiply the diameter of the circle by pi (we will use 3.14).

First, let's find the circumference of Nathan's circle. We see that the radius is 29. The diameter is twice the radius, so the diameter is 56. We multiply this by 3.14, giving us 175.84 m.

We see that Rachel is 2.5 m further from the center than Nathan's, so her radius is 31.5 m. We multiply by two to give us the diameter, giving us 63. We multiply this by 3.14, giving us 197.82.

Now, we subtract Nathan's lap distance from Rachel's to see how much longer her's is.

197.82-175.84=21.98

Therefore, the distance Rachel runs is 21.98 meters longer than the distance Nathan runs.

Have a wonderful day! :D

Answer:

A. 141.4 cm

Step-by-step explanation:

The piramide is 141.4cm

Answer: 4

Step-by-step explanation: use pick’s theorem to solve.

I+B/2-1.

We can substitute the variables with our information from the graph:

0+10/2-1=5-1=4 that’s the answe

Hope this helps

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

Explanation:

The boundary line is y = 2x-2. This line goes through (0,-2) and (2,2). Use the slope formula to find the slope to be m = 2, and use the y intercept b = -2 to help form the equation.

Since the boundary line is solid, we will have "or equal to" as part of the inequality sign. This indicates points on the boundary are part of the solution set. Furthermore, we will have a greater than sign because the shaded region is above the boundary. Therefore, we change the equal sign to a "greater than or equal to" sign, going from y = 2x-2 to [tex]y \ge 2x-2[/tex]

If we simply did [tex]y > 2x-2[/tex] without the "or equal to" portion, then the boundary line would be dotted or dashed to tell the reader "points on the boundary are not part of the solution set".

Answer:

Matched pairs design

Step-by-step explanation:

Looking at the options;

-It's not a completely randomized design because a randomized design will assign all individuals to a group which in this case it doesn't.

- It's not a randomized block design because randomized block design will group the subjects in question into 2 or more blocks which have a common characteristic and will then randomly assign subjects in each of the blocks.

-It's a matched pair because every individual/subject undergoes measurements both before and after being treated with the drugs.

Thus, the correct option is matched pairs design.

Answer:

Hey there!

Angle 6 and angle 7 are actually supplementary angles, which are angles that add to 180 degrees.

Complementary angles are angles that add to 90 degrees.

Hope this helps :)

Answer:

∠6 & ∠7 are not complementary angles

Step-by-step explanation:

∠6 & ∠7 are supplementary angles on a line

Answer:

[tex]x=y-22[/tex]

Step 1:

In order to solve this equation, we must subtract the y on both sides so the y could be cancelled out on the left and could move to the right side of the equation.

[tex]y=3x+22-2x\\=-y+3x+22-2x[/tex]

Step 2:

Then, we add 2x on the right side of the equation to cancel out the -2x and bring it to the left of the equation, where the y was before.

[tex]=-y+3x+22-2x\\2x=-y+3x+22[/tex]

Step 3:

Then, we do the same thing with 3x: subtract it from the right side and add it to the 2x, which becomes -x.  

[tex]2x=-y+3x+22\\2x-3x=-y+22\\-x=-y+22[/tex]

Step 4:

Finally, we divide all the numbers by -1 to get our final answer! Reminder: we are doing all this because we have to isolate the x, since we are solving for x.

[tex]-x=-y+22\\\frac{-x}{-1} =\frac{-y}{-1}+\frac{22}{-1} \\x=y-22[/tex]

Our answer is x = y - 22. Hope this helps!

Answer:

answer: x=y-22

Step-by-step explanation:

first subtract y from both sides. then, add -2x on both sides and subtract 3x from the right so the 2x will be -x. divide everything by a - and the answers x=y-22

Answer:

Hey there!

Angle QRS is 70, and since it is located on the circle, we have a useful formula. If 141x-1 is called y, then 70 is half of that.

Thus, we have 141x-1=140

141x=141

x=1

Hope this helps :)

146

Step-by-step explanation:

Given:

[tex]x - \dfrac{1}{x} = 12[/tex]

To Find:

[tex] \sf \: The \: value \: of \: {x}^{2} + \dfrac{1}{ {x}^{2} } [/tex]

How to find:

Just square both side, Solve as a equation and get the answer. Simple, Isn't it?

Solution:

See in attachment.

Answer:

146

Step-by-step explanation:

The answer of this question id 146 .

you can do this type of numericals by above process.

Answer:

the first one has one solution because eventually they will cross

Answer: 1 real and 2 complex.

Step-by-step explanation:

A cubic polynomial is written as:

a*x^3 + b*x^2 + c*x + d

And the zeros are such that:

a*x^3 + b*x^2 + c*x + d  = 0

As the degree of the polynomial is 3, then we have 3 solutions (where some of them may be equal)

Now, an easy way to see the real and complex zeros of a polynomial is:

If after a change in curvature, the line touches the x-axis : that is a real zero

if it does not, then there we have a complex zero.

Here we can see two lines that do not touch the x-axis and one line that does touch the x-axis.

Then we have 2 complex zeros and one real zero.

Answer: [tex]4\sqrt{3}[/tex] .

Step-by-step explanation:

Distance formula : Distance between points (a,b) and (c,d) is given by :-

[tex]D=\sqrt{(d-b)^2+(b-a)^2}[/tex]

Distance between points [tex](-4\sqrt{2},\sqrt{12}) \text{ and }(-\sqrt{32}, 2\sqrt{3})[/tex].

[tex]D=\sqrt{(2\sqrt{3}-(-\sqrt{12}))^2+(-\sqrt{32}-(-4\sqrt{2}))}\\\\=\sqrt{(2\sqrt{3}+\sqrt{2\times2\times3})^2+(-\sqrt{4\times4\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}-\sqrt{2^2\times3})^2+(-\sqrt{4^2\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}+2\sqrt{3})^2+(-4\sqrt{2}+4\sqrt{2})^2}\\\\=\sqrt{(4\sqrt{3})^2+0}\\\\=4\sqrt{3}\text{ units}[/tex]

Hence, the correct option is [tex]4\sqrt{3}[/tex] .

Answer: 6

Step-by-step explanation: 1. 5c-c= 4c. The equation would then be 4c+10=34.

2. From there, you subtract 10 from both sides of the equation. By doing this, you have the variable and the nonvariable on separate sides of the equation.

3. After doing that, you should have 4c=24. To get the variable by itself, divide both sides by 4. 4c/4 is c and 24/4 is 6.

The final answer is 6. Hope this helped you:)

Answer:

s= 14

Step-by-step explanation:

The missing side is s

sin 30° = 7/s        switch s and sin 30°

s = 7/sin 30°

sin 30° is 0.5

so :

Answer:

(3x + 20)° + 70° = 180°

Step-by-step explanation:

Answer:

       Age                               Frequency                   Cumulative Frequency

 Less than 30                             27                                       27

 Less than 40                             37                                27 + 37  =  64

 Less than 50                              1 1                                 64 + 11   =  75

 Less than 60                               3                                  75 + 2   =  77

 Less than 70                               5                                   77 + 5   =  82

 Less than 80                               1                                     82 + 1  =  83

 Less than 90                              2                                    83 +2  =  85

Step-by-step explanation:

Given:

The Frequency Distribution table of ages of best actresses when award was won

To find:

Construct the cumulative frequency distribution

Solution:

In order to construct cumulative frequency distribution for the given data, each frequency from above table is added to the sum of the previous frequencies. For example, frequency for Less than 40  is 37 and the previous frequency (less than 30) is 27 so in order to calculate cumulative frequency 27 i.e. previous frequency is added to 37 (frequency of less than 30). The complete table is given above.

Answer:

Explained below.

Step-by-step explanation:

The z-test statistic is given as follows:

[tex]Z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}[/tex]

Here,

[tex]\bar X=\text{Sample Mean}\\\\\mu=\text{Population Mean}\\\\\sigma=\text{Population standard deviation}\\\\n=\text{Sample size}[/tex]

The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or greater than what was the truly observed value of the test statistic.

(i)

The difference between the sample mean and the original population mean are directly proportional to the z-test statistic.

So, increasing the  difference between [tex]\bar X[/tex] and [tex]\mu[/tex] will lead to an increase in the z-score.

And as the Z-score increases the p-value of the test decreases.

Thus, the complete statement is:

"Increasing the difference between the sample mean and the original population mean will result in an increase in the absolute value of z, and a decrease in the probability of obtaining a sample with that mean."

(ii)

The population standard deviation is inversely proportional to the z-test statistic.

So, increasing the population standard deviation will lead to a decrease in the z-score.

And as the Z-score decreases the p-value of the test increases.

Thus, the complete statement is:

"Increasing the population standard deviation will result in a decrease in the absolute value of z, and an increase in the probability of obtaining a sample with that mean"

(iii)

The number of scores in the sample is directly proportional to the z-test statistic.

So, increasing the number of scores in the sample will lead to an increase in the z-score.

And as the Z-score increases the p-value of the test decreases.

Thus, the complete statement is:

"Increasing the number of scores in the sample will result in an increase in the absolute value of z, and an decrease in the probability of obtaining a sample with that mean."

Answer:

D

Step-by-step explanation:

To be a function each value of x must correspond to only one, unique value of y.

In the given ordered pairs

Each x- value corresponds to exactly one y- value

Answer:

33/2

Step-by-step explanation:

6 * 11/4 = 66/4 = 33/2

Answer:

Step-by-step explanation:

The unit of a volume: [tex]cm^3[/tex]

The unit of a density: [tex]\dfrac{g}{cm^3}[/tex]

The density is [tex]\dfrac{mass}{volume}[/tex]

Substitute:

[tex]\dfrac{8.05g}{cm^3}=\dfrac{750g}{V}[/tex]

cross multiply

[tex]8.05gV=750gcm^3[/tex]

divide both sides by 8.05g

[tex]V\approx93.17cm^3[/tex]

The formula of a volume of a square pyramid:

[tex]V=\dfrac{1}{3}a^2H[/tex]

a - length of  square base

H - height of a pyramid

We have:

[tex]V=93.17cm^3;\ H=13.5cm[/tex]

Substitute:

[tex]93.17=\dfrac{1}{3}a^2(13.5)[/tex]

multiply both sides by 3

[tex]279.51=13.5H[/tex]

[tex]297.51=13.5a^2[/tex]

divide both sides by 13.5

[tex]a^2\approx20.7\to a=\sqrt{20.7}\approx4.55(cm)[/tex]

Answer:

Step-by-step explanation:

volume of pyramid=1/3×base area×height

let the length of base=x

base area=x²

volume V=1/3×x²×13.5=4.5 x²

mass=volume×density

750=4.5 x²×8.05=36.225 x²

x²=750/36.225

x=√(750/36.225)≈4.55 cm

Answer:   simplified algebraic expression  : x

Step-by-step explanation:

The given phrase : 100 % of x

We can write 100 as 1 because 100% means complete or entire part.

Also, replace 'of' by '×' (Multiply sign).

So, the given phrase will become

1 × x   [Algebraic expression]

= x         [Simplified]

hence, the simplified algebraic expression is 'x'.

Answer:

x = 10

Step-by-step explanation:

A parallelogram's angles should all add up to 360 degrees. 130+130 is equal to 260 degrees. 360-260 is equal to 100. Because we need to find the individual angles of Angle A and Angle C, we will divide 100 by two. That leaves us with 50 degrees for Angle A and Angle C EACH. We know Angle C is equal to 5x. So, we would divide 50 by 5, which leaves us with 10 degrees. Therefore, x = 10.

Answer:

$104

Step-by-step explanation:

If the cost in the store is x we can write:

75%x = 78

0.75x = 78

x = 78 / 0.75 = 104

Answer:

$104 in the store

Step-by-step explanation:

To find the original cost before the discount, you divide the discounted price by the percentage, getting 104.

The division of 12e⁵ by 3e³ will be 4e².

In mathematics, the arithmetic operation has four main operators such as addition, subtraction, multiplication, and division.

The symbol of + represents the addition

The symbol of ÷  represents the division

The symbol of - represents subtraction

The symbol of × represents multiplication

Given the division,

12e⁵ by 3e³

⇒ 12e⁵ / 3e³

⇒ 12/3 × e⁵/e³

⇒ 4e²

Hence "The division of 12e⁵ by 3e³ will be 4e²".

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Step-by-step explanation:

this is substitution method

Answer:

2x + y = 21

+

x - y = 6

_________

3x = 27

x = 27 ÷ 3

x= 9

x - y = 6

9 - y = 6

9 - 6 = y

3 = y

Therefore, x= 9 and y = 3