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OLEGan [10]
2 years ago
14

In the children’s game Don’t Break the Ice, small plastic ice cubes are squeezed into a square frame. Each child takes a turn ta

pping out a cube of "ice" with a plastic hammer, hoping that the remaining cubes don’t collapse. For the game to work the cubes must be big enough so that they hold each other in place but not so big that they are too difficult to tap out. In an SRS of 43 "ice cubes" the average width was 29.5 millimeters with a standard deviation of 0.12mm. Construct a 95% confidence level for the true mean width. Group of answer choices
Mathematics
1 answer:
guajiro [1.7K]2 years ago
5 0

Answer:

(29.46 mm, 29.54 mm).

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 43 - 1 = 42

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 42 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.018

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 2.018\frac{0.12}{\sqrt{43}} = 0.04

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 29.5 mm - 0.04mm = 29.46 mm

The upper end of the interval is the sample mean added to M. So it is 29.5 mm + 0.04mm = 29.54 mm

The 95% confidence level for the true mean width is: (29.46 mm, 29.54 mm).

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What percent of 71 is 90?<br> of 71 is 90.
sashaice [31]

Answer: 126.76056338%

Step-by-step explanation: To answer the question what percent of 71 is 90, we translate the question into an equation.

We have <em>"what percent" </em>which we can represent by the variable X. Next we have <em>"of 71"</em> which means "times 71" and <em>"is 90" </em>means "equals 90."

Now to solve for <em>x</em>, since <em>x</em> is being multiplied by 71, we need to divide by 71 on both sides of the equation.

<em />

On the left side of the equation the 71's cancel and we have <em>x</em>.<em> </em>On the right side of the equation we have 90 divided by 71 which is 1.2676056338.

Now, remember that we want to write our answer as a percent. To write 1.2676056338 as a percent, we move the decimal point two places to the right and we get 126.76056338%.

3 0
3 years ago
Read 2 more answers
Solve the system by using a matrix equation
Sergeu [11.5K]

Answer:

Option A is correct (17,11).

Step-by-step explanation:

6x - 9y = 3

3x - 4y =7

it can be represented in matrix form as\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}3\\7\end{array}\right]

A= \left[\begin{array}{cc}6&-9\\3&4\end{array}\right]

X= \left[\begin{array}{c}x\\y\end{array}\right]

B= \left[\begin{array}{c}3\\7\end{array}\right]

i.e, AX=B

or X= A⁻¹ B

A⁻¹ = 1/|A| * Adj A

determinant of A = |A|= (6*-4) - (-9*3)

                                    = (-24)-(-27)

                                    = (-24) + 27 = 3

so, |A| = 3

Adj A=  \left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]

A⁻¹ =  \left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]/3

A⁻¹ =  \left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right]

X= A⁻¹ B

X=  \left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] *\left[\begin{array}{c}3\\7\end{array}\right]

X= \left[\begin{array}{c}(-4/3*3) + (3*7)\\(-1*3) + (2*7)\end{array}\right]

X= \left[\begin{array}{c}-4+21\\-3+14\end{array}\right]

X= \left[\begin{array}{c}17\\11\end{array}\right]

x= 17, y= 11

solution set= (17,11).

6 0
3 years ago
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PLEASE ANSWER ASAP
-Dominant- [34]

Answer:15/1


Step-by-step explanation: 300 Divided by 20 is 15 and i believe that is the answer im sorry if i am wrong


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3 years ago
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jeyben [28]

Answer:

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Step-by-step explanation:

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3 years ago
HELP PLSS WILL GIVE BRAINLIEST<br> Solve N = 3rt^4 - 5rz <br> (solve for z)
Whitepunk [10]

Answer:

Step-by-step explanation:

N = 3rt^4 - 5rz

now factor r out

N = r(3t^4-5z)

divide by r on both sides

N/r = (3t^4 - 5z)

subtract (3t^4)

N/r - 3t^4 = -5z

now divide by -5 to isolate the variable (z)

\frac{(n/r)-3t^4}{-5} = z

7 0
3 years ago
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