Help me, please asap

The width of a rectangle is 15 ft. shorter than its length. Its perimeter is 262 ft. Let l equal the length of the rectangle.

masha68 [24]

Let the length be l.
For now, let's make the width be w.
Additionally, l = w + 15. Using this equation, width can also be written as l - 15.
The perimeter of a rectangle is length + length + width + width. This can also be written as l + l + (l-15) + (l-15) = l + l + l - 15 + l - 15 = 4l - 30.
Using this equation:
4l - 30 = 262
4l = 292
l = 73

4(w + 15) - 30 = 262
4w + 60 - 30 = 262
4w + 30 = 262
4w = 232
w = 58

7 0

3 years ago

What is the area of this figure drag and drop the appropriate number into the box

lyudmila [28]

Answer:

142ft squared

Step-by-step explanation:

It was actually very easy, the working may not be clear and hard to understand but it's on the attached image. Hope I helped! :)

4 0

3 years ago

0.5+a=3.2 <br><br>Answer please

Black_prince [1.1K]

0.5 + a = 3.2

3.2 - 0.5 = 2.7

7 0

3 years ago

Suppose twenty-two communities have an average of = 123.6 reported cases of larceny per year. assume that σ is known to be 36.8

Delvig [45]

We are given the following data:

Average = m = 123.6
Population standard deviation = σ= psd = 36.8
Sample Size = n = 22

We are to find the confidence intervals for 90%, 95% and 98% confidence level.

Since the population standard deviation is known, and sample size is not too small, we can use standard normal distribution to find the confidence intervals.

Part 1) 90% Confidence Interval
z value for 90% confidence interval = 1.645

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.645* \frac{36.8}{ \sqrt{22}}=110.69$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.645* \frac{36.8}{ \sqrt{22}}=136.51$

Thus the 90% confidence interval will be (110.69, 136.51)

Part 2) 95% Confidence Interval
z value for 95% confidence interval = 1.96

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-1.96* \frac{36.8}{ \sqrt{22}}=108.22$

Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+1.96* \frac{36.8}{ \sqrt{22}}=138.98$

Thus the 95% confidence interval will be (108.22, 138.98)

Part 3) 98% Confidence Interval
z value for 98% confidence interval = 2.327

Lower end of confidence interval = $m-z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Lower end of confidence interval= $123.6-2.327* \frac{36.8}{ \sqrt{22}}=105.34$
Upper end of confidence interval = $m+z *\frac{psd}{ \sqrt{n} }$
Using the values, we get:
Upper end of confidence interval= $123.6+2.327* \frac{36.8}{ \sqrt{22}}=141.86$

Thus the 98% confidence interval will be (105.34, 141.86)

Part 4) Comparison of Confidence Intervals
The 90% confidence interval is: (110.69, 136.51)
The 95% confidence interval is: (108.22, 138.98)
The 98% confidence interval is: (105.34, 141.86)

As the level of confidence is increasing, the width of confidence interval is also increasing. So we can conclude that increasing the confidence level increases the width of confidence intervals.

3 0

4 years ago

A boat leaves a dock and travels 9 miles due north and 12 miles due west. Find how far the boat is from the dock. Type the corre

adelina 88 [10]

Answer:

15 miles

Step-by-step explanation:

Let's say the dock is at the origin on a coordinate plane and each unit is 1 mile. If the boat travels 9 mile due north, that means that we move up from the origin (0, 0) 9 units to point A (0, 9). Now, this boat moves 12 miles due west, so we will go 12 units to the left of (0, 9) to point B (-12, 9). See the attached drawing (sorry for the crudeness).

Notice that this is a right triangle with legs of 9 and 12. That means the distance from the boat to the dock is just the hypotenuse, so use the Pythagorean Theorem: distance = $\sqrt{9^2+12^2} =\sqrt{81+144} =\sqrt{225} =15$

Thus, the answer is 15 miles.

Hope this helps!

3 0

3 years ago

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