Use the given values to complete each table.
PLEASE HELP.

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Explanation:

First we need the arithmetic mean

Add up the values to get 1+2+4+4+5+6+6 = 28

Divide this over the number of values (n = 7) to get 28/n = 28/7 = 4

The mean is 4.

Next, we subtract the mean from each data value and square the difference

Add up those results: 9+4+0+0+1+4+4 = 22

Lastly, we divide over the number of items (n = 7) to get the population variance: 22/n = 22/7 = 3.14 approximately

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Side note:

If you wanted the sample variance, then you divide over n-1 = 7-1 = 6

22/(n-1) = 22/6 = 3.67 is the approximate sample variance

Answer:

[tex]3e^{2} + 12e[/tex]

Step-by-step explanation:

[tex]3ee+3e4[/tex]

[tex]3ee+3 * 4e[/tex]

[tex]3e^{2} + 12e\\[/tex]

[tex]3 \: {e}^{2} + 12 \: e[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]3 \: e \: ( \: e + 4 \: ) \\ \\ = 3 \: e \times \: e + 3 \: e \times 4 \\ \\ = 3 \: {e}^{2} + 12 \: e[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique }}{\orange{♡}}}}}[/tex]

Answer:

41

Step-by-step explanation:

The angle were looking for is on the other side of the figure. It is also on the inside so we would divide 82 in half giving us 41.

The Fourier series expansion of f(x) is

[tex]\displaystyle\frac{a_0}2+\displaystyle\sum_{n=1}^\infty \left(a_n\cos\left(\frac{2\pi nx}P\right)+b_n\sin\left(\frac{2\pi nx}P\right)\right)[/tex]

where P = 4 is the period of f(x), and the coefficients are

[tex]a_0=\displaystyle\frac2P\int_{-2}^2f(x)\,\mathrm dx=2[/tex]

[tex]a_n=\displaystyle\frac2P\int_{-2}^2f(x)\cos\left(\frac{2\pi nx}P\right)\,\mathrm dx=\frac{2\sin(n\pi)}{n\pi}=0[/tex]

[tex]b_n=\displaystyle\frac2P\int_{-2}^2f(x)\sin\left(\frac{2\pi nx}P\right)\,\mathrm dx=\frac{2(\cos(n\pi)-1)}{n\pi}=\begin{cases}0&\text{for }n=2k\\-\frac4{(2k-1)\pi}&\text{for }n=2k-1\end{cases}[/tex]

(where k is a positive integer)

The series for f(x) reduces to

[tex]\displaystyle f(x)=1-\displaystyle\sum_{k=1}^\infty \frac4{(2k-1)\pi}\sin\left(\frac{\pi(2k-1)x}2\right)[/tex]

(I've attached a plot showing the original function in blue and the Fourier expansion with k = 10 terms)

He used 620 gallons of gas

Answer

Two fractions are equivalent fractions when they represent the same part of a whole. Since equivalent fractions do not always have the same numerator and denominator, one way to determine if two fractions are equivalent is to find a common denominator and rewrite each fraction with that denominator.

Answer:

Step-by-step explanation:

x = number of pounds

5x<30

x<30/5

so she can buy X<6 pounds

Answer:

2.89, rounded to the nearest hundredth

Step-by-step explanation:

Given that GPA is weighted by credits, we must first multiply each grade by its credit amount and sum those up to weigh the credits. Then, we divide by the total amount of credits to get the GPA per credit.

So, we start with math,

3.7 *5 + 1.8 *3 + 2.8 * 5 + 2.8 * 4 = 49.1 as the total GPA weighted per credit.

Then, to find the average per credit, we divide by the total amount of credits, which is 5 + 3 + 5 + 4 = 17.

Our answer is 49.1/17 = 2.89, rounded to the nearest hundredth

Answer:

D. {3, 5, 7}

Step-by-step explanation:

Sets of y-values or outputs of a relation of a function = the range

The outputs/y-values of the relation mapped above are what we have on our right hand, which area {3, 5, 7}

Therefore,

Range = {3, 5, 7}

Answer:2647.5

Step-by-step explanation:

Answer:-244

Step-by-step explanation:

I think you subtract -290 from -46.

Sorry If I am wrong.

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Explanation:

Imagine reflecting everything so that location A is above location B. Effectively all you're doing is erasing the negative signs.

That would place A at 290 feet and B would be at 46 feet. The difference in elevation is 290-46 = 244 feet

Instead of reflecting, you can turn the page upside down and just ignore the negative signs, and then subtract like normal.

This trick only works if both elevations A and B are below sea level.

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Or you could subtract like so:

|A-B| = |-290-(-46)| = |-290+46| = |-244| = 244

The absolute value is used to ensure the result is not negative. A negative difference makes no sense. In this case, "difference" and "distance" mean the same thing more or less.

Answer:

OK!!.

N=N(½)ⁿ

n= Time/half life

N=Remaining Mass

N°=Initial Mass or Mass before decay.

t= time taken to decay(Its in Months in this case)

t½= Half Life of the Material. This is the time taken to decay to half its initial value.

N°= 2000mg

a).Equation that Models this is

since n=t/t½

N=N°(½)ⁿ =

N=N°(½)^t/t¹'². This should be your answer.

b). We're asked to find the remaining mass of substance in 4years.

t= 4years

Our Half life is in Months... So we gotta convert or time t from year to Months too.

4yrs === 4x12 = 48Months.

N° was given as 2000mg

N=N°(½)^t/t½

N= 2000(½)^48/3

N=2000(½)^16

Using your calc to evaluate (½)^16... Then multiply by 2000

N=0.0305mg will remain after 4years.

Or After 16Half Lives since 1 half life is 3months

c). We're looking for t this time

N=N°(½)^t/t½

Since it asked for 750mg to remain ... 750 is now our N --- Remaining Mass

750 = 2000(½)t/3

To Isolate "t" and make it the subject

750/2000 = (½)^t/3

0.375 = (½)^t/3

Taking ln(natural log) of both sides

Ln(0.375) = Ln(0.5)^t/3

From the rule of logarithm...

You can bring the power (I.e t/3) to the front

You'll have

Ln(0.375) = t/3Ln(0.5)

Dividing both sides by Ln(0.5) to isolate t

Ln(0.375)/Ln(0.5) = t/3

t/3 = 1.415

t= 3x1.415

t=4.25months.

Have a great day.

Hope this helps... I'm open to questions if you have any too.

it think it is 10 or so but like just read or it and you will get it :)

Answer:

I don't know sorry for your right question ok

Answer:

25

Step-by-step explanation:

Since the x values are the same

the distaance is simply the difference in the y values

23 - (-2) = 25

Answer:

34/3, -2/3

Step-by-step explanation:

See image below:)

Step-by-step explanation:

2x + 3y = 34

3y = 34 - 2x

y = 3x - 2x/3

Answer:

8

Step-by-step explanation:

The absolute value (the lines both sides of x) simply mean the number in between is positive. Since 1 is already positive, just add it to 7!

Answer:

Just plus everything together

X-3+4X+4+2X+1

Step-by-step explanation:

Answer:

42n+108

Step-by-step explanation:

21(2n+8)

42n+108

Answer:

Type I error (alpha error)

Step-by-step explanation:

Given that a TYPE 1 ERROR is a type of research error often referred to as false positive or alpha error and happens when a researcher wrongly rejects a true null hypothesis. This action by the researcher verifies a statistically significant difference even though there is no difference.

Hence, considering the situation described in the question above, the correct answer to the question is "TYPE 1 ERROR"

Answer:

12.86 cm³ of water is saved

Step-by-step explanation:

✔️Since width of new ice ball must be the same as the length of original cube, therefore, diameter of the ice ball = 3 cm

Radius of ice ball = ½(3) = 1.5 cm

Volume of the new sphere ice ball = ⁴/3πr³

Substitute

Volume of new sphere ice ball = ⁴/3 × π × 1.5³ = 14.14 cm³

✔️To find out how much water would be saved using the new sphere ice ball, let's find the volume of the cube then find the difference of both.

Volume of original ice cube with length 3 cm:

Volume of cube = s³

s = 3 cm

Volume of cube = 3³ = 27 cm³

Volume of water saved = 27 cm³ - 14.14 cm³

= 12.86 cm³

Answer: Arithmetic Sequence

Step-by-step explanation: It has a common difference of +3 at a constant rate

Answer: A and C

Step-by-step explanation: To see if it can be the side lengths of a right triangle we have to use the Pythagoras Theorem which is [tex]a^2 +b^2 = c^2\\[/tex]

C is always the largest length. Now we can sub the numbers in

[tex]5^2+\sqrt{6} ^2=\sqrt{31} ^2[/tex]

The squares and the square roots cancel each other out so we end up with

25+6=31

this is true so those are possible sides for a right triangle

Now for b:

[tex]\sqrt{5}^2 + \sqrt{5}^2 =50^2[/tex]

Again the squares and square roots cancel each other out

5+5=2500

This isn't true so it isn't the possible sides for a right triangle

Finally option C:

[tex]9^2+12^2=15^2[/tex]

81+144=225

225=225

This is true so it can be the side lengths that form a right triangle

Answer:

We reject  H₀, and conclude thet the mean lifetime of the bulbs differ from 51 month

Step-by-step explanation:

Manufacturing process under control must produce items that follow a normal distribution.

Manufacturer information:

μ  =  51 months     mean lifetime

σ  =  7 months       standard deviation

Sample Information:

x  =  51 months

n  =  60

Confidence Interval  =  90 %

Then significance level  α  =  10 %  α  =  0.1    α/2  =  0,05

Since it is a manufacturing process the distribution is a normal distribution, and with   n = 60 we should use a Z test on two tails.

Then from z- table z(c) for  α = 0,05  is  z(c)  = 1.64

Hypothesis  Test:

Null Hypothesis                              H₀            x  =  μ

Alternative Hypothesis                  Hₐ            x ≠  μ

To calculate z statistics  z(s)

z(s)  =   (  x   -  μ )  / σ /√n

z(s)  =   (  53  -  51 ) / 7 /√60

z(s)  =  2 * 7.746 / 7

z(s)  = 2.213

Comparing  z(s)  and  z(c)

z(s)  >  z(c)   then  z(s)  is in the rejection region

We reject  H₀, and conclude thet the mean lifetime of the bulbs differ from 51 month

Answer:

Fail to reject the null hypothesis

[tex]CI = (-4.278, 0.478)[/tex]

Step-by-step explanation:

Given

[tex]n_1=n_2 = 18[/tex]

[tex]\bar x_1 = 12.7[/tex]    [tex]\bar x_2 = 14.6[/tex]

[tex]\sigma_1 = 3.2[/tex]    [tex]\sigma_2 = 3.8[/tex]

[tex]\alpha = 0.05[/tex]

Solving (a): Test the hypothesis

We have:

[tex]H_o : \mu_1 - \mu_2 = 0[/tex]

[tex]H_a : u1 - u2 \ne 0[/tex]

Calculate the pooled standard deviation

[tex]s_p = \sqrt\frac{(n_1-1)\sigma_1^2 + (n_2-1)\sigma_2^2}{n_1+n_2-2}}[/tex]

[tex]s_p = \sqrt\frac{(18-1)*3.2^2 + (18-1)*3.8^2}{18+18-2}}[/tex]

[tex]s_p = \sqrt\frac{419.56}{34}}[/tex]

[tex]s_p = \sqrt{12.34}[/tex]

[tex]s_p = 3.51[/tex]

Calculate test statistic

[tex]t = \frac{x_1 - x_2}{s_p*\sqrt{1/n_1 + 1/n_2}}[/tex]

[tex]t = \frac{12.7 - 14.6}{3.51 *\sqrt{1/18 + 1/18}}[/tex]

[tex]t = \frac{-1.9}{3.51 *\sqrt{1/9}}[/tex]

[tex]t = \frac{-1.9}{3.51 *1/3}[/tex]

[tex]t = \frac{-1.9}{1.17}[/tex]

[tex]t = -1.62[/tex]

From the t table, the p value is:

[tex]p = 0.114472[/tex]

[tex]p > \alpha[/tex]

i.e.

[tex]0.114472 > 0.05[/tex]

So, the conclusion is that: we fail to reject the null hypothesis.

Solving (b): Construct 95% degree freedom

[tex]\alpha = 0.05[/tex]

Calculate the degree of freedom

[tex]df = n_1 + n_2 - 2[/tex]

[tex]df = 18+18 - 2[/tex]

[tex]df = 34[/tex]

From the student t table, the t value is:

[tex]t = 2.032244[/tex]

The confidence interval is calculated as:

[tex]CI = (x_1 - x_2) \± s_p * t * \sqrt{1/n_1 + 1/n_2}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/18 + 1/18}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/9}[/tex]

[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * 1/3[/tex]

[tex]CI = -1.90 \± 2.378[/tex]

Split

[tex]CI = (-1.90 - 2.378, -1.90 + 2.378)[/tex]

[tex]CI = (-4.278, 0.478)[/tex]

Answer:

56 cm squared

Step-by-step explanation:

First things first: Cop one triangle off the rectangle, and attach it to the other one, so the shape looks like a L

Now I can actually solve this:

The left side is 8 cm (because y = 8 cm)

The top is 10 cm

The middle is 6 cm

The inside left is 3 cm

And the very bottom is 2 cm

First, we'll solve for the newly constructed rectangle: 3 x 2. That equals 6.

Next, solve for the longer rectangle: 10 x 5. That's 50.

Now, add the two areas, and we get 56. So the area of the whole thing is 56 cm squared.

(Please keep in mind that I could be wrong, so double check it for me, thanks!)

9514 1404 393

Explanation:

  -4h ≤ -14

in this context is a relation that would tell how many hours it would take for the temperature to be at or below -14 degrees.

Answer:

substitute that (6) in X so f(6) = 2(6) which is = 12

Answer:

500 men

740 total people in community

Step-by-step explanation:

25:12 ratio

When using a ratio both sides should go up the same amount of times to get the number you are trying to reach. Since the women's amount was 240 we need to find the times it took to get from 12 to 240. You take the 240 and divide by 12. We find that the 12 was multiplied 20 times to get to 240. So you turn to the men's side and find the amount using the 25. We use X to signify the amount we are trying to find and the amount of times that 25 goes into X will be 20 to keep the ratio of men to women as specified. When solving for X you multiply both sides of the equation by 25 to find the amount. X will equal 500 (=20*25).

Then 240 women plus 500 men equals to 740 people in the community.

Women

240/12 = 20

Men

X/25=20

X=20*25

X=500

240 women+500 men=740 people