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VikaD [51]
3 years ago
6

Mark would like to build a rectangle frame. The dimensions of the frame are unknown, but the perimeter of the frame must be 80 y

ards. The length of the frame is six less than the width. What is the length of the frame?
Mathematics
1 answer:
kotykmax [81]3 years ago
6 0

Answer:

The length of the frame is 17

Step-by-step explanation:

The computation of the length of the frame is shown below:

As we know that

The perimeter of a rectangle is

= 2 (length + width)

where,

let us assume the width be x

So, the length is x - 6

And, the perimeter is 80 yards

So, now put these values to the above formula

80 yards = 2 (x - 6+ x)

80 yards = 2 (2x - 6)

80 yards = 4x - 12

92 = 4x

x = 23

So, the length of the frame is

= 23 - 6

= 17

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A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data
Rasek [7]

Answer: a. 1.981 < μ < 2.18

              b. Yes.

Step-by-step explanation:

A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.

First, we calculate mean of the sample:

\overline{x}=\frac{\Sigma x}{n}

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\overline{x}= 2.08

Now, we estimate standard deviation:

s=\sqrt{\frac{\Sigma (x-\overline{x})^{2}}{n-1} }

s=\sqrt{\frac{(2.31-2.08)^{2}+...+(2.02-2.08)^{2}}{11} }

s = 0.1564

For t-score, we need to determine degree of freedom and \frac{\alpha}{2}:

df = 12 - 1

df = 11

\alpha = 1 - 0.95

α = 0.05

\frac{\alpha}{2}= 0.025

Then, t-score is

t_{11,0.025} = 2.201

The interval will be

\overline{x} ± t.\frac{s}{\sqrt{n} }

2.08 ± 2.201\frac{0.1564}{\sqrt{12} }

2.08 ± 0.099

The 95% two-sided CI on the mean is 1.981 < μ < 2.18.

B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.

8 0
3 years ago
A company makes steel rods shaped like cylinders. Each rod has a radius of 4 centimeters and a height of 20 centimeters. If the
Tamiku [17]
(One steel rod’s volume) = 3.14 x 4^2 x 20

= 1004.8cm^3

(Used steel) / (One steel rod’s volume) =

(Made steel rod’s number)

The answer is 28
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2 years ago
Can someone please help me
Daniel [21]

Answer:

(-7.5, 3.5)

Step-by-step explanation:

midpoint \:  = ( \frac{x1 + x2}{2} \:  , \:  \frac{y1 + y2}{2} )

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= ( \frac{ - 15}{2} , \frac{7}{2} )

= ( - 7.5,3.5)

8 0
3 years ago
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