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Using the data given, the 95% confidence interval of the true mean is (205.20 ; 230.20)

Given the data :

The confidence interval is defined as :

Since, sample size ls less than 30 we use a t-distribution table :

[tex] C.I = \bar{x} ± t_{α/2, n-1} \frac{s}{\sqrt{n}}[/tex]

Using a calculator :

Lower boundary = [tex] 217.7 - 2.26(\frac{17.49}{\sqrt{10}}) = 205.20[/tex]

Lower boundary = [tex] 217.7 + 2.26(\frac{17.49}{\sqrt{10}}) = 230.20[/tex]

Therefore, the confidence interval is (205.20 ; 230.20)

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The confidence interval is simply a range that contains the true mean of the population

The 95% confidence interval is [tex]\mathbf{(205,19, 230.20)}[/tex]

The given parameter is:

[tex]\mathbf{n = 10}[/tex]

Start by calculating the degree of freedom

[tex]\mathbf{df = n - 1}[/tex]

[tex]\mathbf{df = 10 - 1}[/tex]

[tex]\mathbf{df = 9}[/tex]

Next, calculate the mean

[tex]\mathbf{\bar x = \frac{\sum x}{n}}[/tex]

[tex]\mathbf{\bar x = \frac{225 + 240 + 215 + 206 + 211 + 210 + 193 +250 + 225 + 202}{10}}[/tex]

[tex]\mathbf{\bar x = \frac{2177}{10}}[/tex]

[tex]\mathbf{\bar x = 217.7}[/tex]

Calculate the standard deviation

[tex]\mathbf{\sigma = \sqrt{\frac{\sum (x - \bar x)^2}{n-1}}}[/tex]

[tex]\mathbf{\sigma = \sqrt{\frac{(225 -217.7)^2+ (240 -217.7)^2+..........+ (202 -217.7)^2}{10-1}}}[/tex]

[tex]\mathbf{\sigma = \sqrt{\frac{2752.1}{9}}}[/tex]

[tex]\mathbf{\sigma = 17.49}[/tex]

Calculate the standard error

[tex]\mathbf{SE = \frac{\sigma}{\sqrt n}}[/tex]

[tex]\mathbf{SE = \frac{17.49}{\sqrt {10}}}[/tex]

[tex]\mathbf{SE = 5.53}[/tex]

At 95%, df = 9. the t-value is:

[tex]\mathbf{t= 2.262}[/tex]

So, the confidence interval is:

[tex]\mathbf{CI = \bar x \pm t \times SE}[/tex]

So, we have:

[tex]\mathbf{CI = 217.7 \pm 2.262 \times 5.53}[/tex]

Split

[tex]\mathbf{CI = (217.7 - 2.262 \times 5.53, 217.7+ 2.262 \times 5.53)}[/tex]

[tex]\mathbf{CI = (205,19, 230.20)}[/tex]

Hence, the 95% confidence interval is [tex]\mathbf{(205,19, 230.20)}[/tex]

Read more about confidence intervals at:

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Answer:

3/16

Total no.of beads = 16

No.of blue beads = 3

Probability of picking a blue bead = 3/16

Step-by-step explanation:

Hope this helps

can i get braineist pls

Answer:

x=0

Step-by-step explanation:

0=6x-2x

0=4x

4x=0

and the answer is x=0

Answer:

put it in desmos and turn it into table

Answer:

reciprocal of 4= 1/4

reciprocal of 1/3=3

reciprocal of -1/7 = -7

reciprocal of -4/5=-5/4

Step-by-step explanation:

it's explained

Answer:

X=18

Step-by-step explanation:

To isolate X you need to get rid of the -15 to do that you can add 15 on both sides of the equation resulting in 3x=54 now you need to divide both sides by 3 to get x on its own which is X=18.

Answer:

2, √72, 8.7, √83, 9.25

Step-by-step explanation:

First, you need to find the integers of each number that is not already a integer.

Square root of 72: 8.48528137424

9.25

Square root of 83: 9.11043357914

2

8.7

Now, list the numbers by their whole number (in the ones place). If they have the same whole number, look at their tenths place and see which one is greater.

Overall, the answer would be 2, √72, 8.7, √83, 9.25.

Answer:

89.99

Step-by-step explanation:

u add i48934yr84 r84

Roberta paid the amount of $47.19 for the curtains before the sales tax.

The percentage is defined as a ratio expressed as a fraction of 100.

We have been given that equation editor A set of curtains normally sells for $58.99. Roberta used a coupon good for 20% off the regular price.

To determine the amount for the curtains before the sales tax

According to the given conditions, the solution would be as:

⇒ 58.99 × (1 - 20%)

⇒ 58.99 × (1 - 0.20)

Calculate the sum or difference and we get

⇒ 58.99 × 0.80

Apply the multiplication operation to get

⇒ 47.192

Round the number nearest to the hundredth,

⇒ 47.19

Therefore, Roberta paid the amount of $47.19 for the curtains before the sales tax.

Learn more about the percentages here:

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#SPJ5

Answer: c I believe

Step-by-step explanation:

Answer:

y = 5x -3

Step-by-step explanation:

Slope intercept form is y = mx + b

m = slope

b = the y intercept

The problem gives you a slope of 5, and it gives you the y interecept of -3.

Plug those into slope intercept form:

y = 5x -3

Answer:

see explanation

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

(a)

3 × a × 2 × b

= 3 × 2 × a × b

= 6ab

(b)

[tex]c^{5}[/tex] × c

= [tex]c^{(5+1)}[/tex]

= [tex]c^{6}[/tex]

(c)

2[tex]y^{4}[/tex] × 5y³

= 2 × 5 × [tex]y^{4}[/tex] × y³

= 10 × [tex]y^{(4+3)}[/tex]

=10[tex]y^{7}[/tex]

(d)

3gh² × 4g³h³

= 3 × 4 × g × g³ × h² × h³

= 12 × [tex]g^{(1+3)}[/tex] × [tex]h^{(2+3)}[/tex]

= 12[tex]g^{4}[/tex][tex]h^{5}[/tex]

Answer: a

Step-by-step explanation:

Answer:

b. 10a³ - 11a - 3

Step-by-step explanation:

1. Expand 3(a³ - 2a - 5)

= 3a³ - 6a - 15

2. Add 7a³ - 5a + 12 and 3a³ - 6a - 15

7a³ + 3a³ = 10a³

-5a + -6a = -11a

12 + -15 = -3

3. Answer: b. 10a³ - 11a - 3

Answer:

we need more information to solve your problem.

Step-by-step explanation:

Answer:

ok here ya go

Step-by-step explanation:

A way that I would teach someone something that I learned in math this year to someone else is simple. I would start by writing everything out so that they have a visual of what I am teaching them. I would also use a visual of a real world situation so that it relates to something they would understand. Teaching someone younger than you means they probably will not understand as easy as you understood it so, I would be very slow and make sure if they are confused to help them. I would also make sure not to be too bossy, understanding that they may not understand and that is ok.

x = frac{−1}{2}y + frac{45}{2}

Answer:

y- intercept = [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x + [tex]\frac{4}{5}[/tex] ← is in slope- intercept form

with y- intercept c = [tex]\frac{4}{5}[/tex]

Answer:

a. 53.68

b. 53.53

Step-by-step explanation:

a. Step 1: Approximate the value for [tex]\sqrt{62}[/tex]:

Since [tex]\sqrt{62}[/tex] is close to [tex]\sqrt{64}[/tex] (which is 8), this value can be approximated as a number that is less than but very close to 8. I chose 7.9.

The expression becomes 6(7.9)+2π

Step 2: Approximate the value for 2π

Since π is approximately 3.14, 2π is approximately 6.28.

The expression becomes 6(7.9)+6.28

Step 3: Use order of operations

6(7.9)+6.28=47.4+6.28=53.68

b. Step 4: If allowed, use a calculator to check how close your approximation is to the actual value

[tex]6\sqrt{62} +2\pi =53.5272[/tex]

The approximation 53.68 is decently close to the actual value, so no minor math errors were made.

Answer:

54     and 53.53  see below

Step-by-step explanation:

Estimate the square root first.  7x7 = 49  and 8x8=64 so you can use 8 for your estimate.  You can also estimate Pi as 3.

Now you have:

(6 x 8) + 2(3)   which is 48 + 6 = 54

Using your calculator you get

47.244 + 6.283 = 53.53  rounded to the nearest hundredth

Answer:

9/2 simplified

and 4 1/2 as a mixed number

Answer:

Fraction: 9/2

Mixed: 4 1/2

Step-by-step explanation:

We do this by first finding the greatest common factor of 90 and 20, which is 10.

Then, we divide both 90 and 20 by the greatest common factor to get the following simplified fraction:

9/2

Therefore, this equation is true:

90/20 = 9/2

If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction.

9/2 = 4 1/2

Answer:

443.2 grams

Step-by-step explanation:

Each can contains 55.4 grams of protein, and there are 8 cans, so the answer would be 55.4*8 = 443.2 grams.

Answer:

Perimeter = 36m

Step-by-step explanation:

Area = l x w

65m = 13m x w

5m = w

Perimeter = 2(l + w)

Perimeter = 2(13m + 5m)

Perimeter = 36m

Answer:

36m

Step-by-step explanation:

The equation for the area of a rectangle is A = w*l, where w = width and l = length

Since we already have the area and the width, we can plug those values into the equation to find the width (w)

A = w*l

65 = w*13

we can divide both sides by 13 to isolate the w variable, and we get that

w = 5

The equation for the perimeter of a rectangle is

P = 2(l +w)

P = 2(13 +5)

P =36

The perimeter is 36m

1-100%. You'll never know until you try it yourself.

Answer:

the answer is c :)

Step-by-step explanation:

Answer:

I think this is it 61.33

Have a blessed day <333

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope formula:

Substitute the values to get:

_________

[tex] \: [/tex]

(X1, X2) = (-68, 47)

(Y2, Y1) = (-66, 33)

Soo :

m = [tex]\frac{Y2 - Y1}{X2 - X1}[/tex]

m = [tex]\frac{33 - 47}{68 - 66}[/tex]

m = [tex]\frac{-14}{2}[/tex]

m = [tex]\boxed{\bold{-7}}[/tex]

Done.

Answer:

Slope = -3

Step-by-step explanation:

From (-1,0) to (0,-3), the line has a change of -3/1 (change in y/change in x) or -3

Answer:

the ball would be at the 31 yard line, because you are moving 6 yards closer to midfield which would be 50, and the end zone if he ran all the way there would be 69 more yards

Answer:

6

Step-by-step explanation:

Answer:

1.) Carries energy

Step-by-step explanation:

A good summary of an ATP molecule is a molecule that transfers energy between cells... meaning it carries energy from cell to cell. Furthermore, energy cannot be destroyed, and cannot be absorbed, only changed and transformed. This leaves us with two options, (1. Carries energy, and 4. None of the above). Since we already have a basic understanding of what an ATP molecule does, we can confidently determine that the correct answer is that an ATP molecule can best be described as carrying energy.