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omeli [17]
3 years ago
6

Find the mean, median, mode, and range of this data: 49, 49, 54, 55, 52, 49, 55. If necessary, round to the nearest tenth. A. 51

.9, 52, 49, 6 B. 52.9, 52, 49, 104 C. 51.9, 53, 49, 6 D. 52, 52.9, 49, 104
Mathematics
1 answer:
DENIUS [597]3 years ago
3 0
The answer is A.

Hope I helped.
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A ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,corr
lina2011 [118]

Answer:

(a) the new angle the ladder makes with the ground is 32.7^o

(b) the ladder slipped back about 5 meters

Step-by-step explanation:

Notice that the ladder doesn't change its length in the process.

So let's start from the initial situation , finding the distance from the ground at which the ladder touches the wall when the angle with the ground is 70^o. Notice that this situation is represented by a right angle triangle with the right angle between the wall and the ground (see attached image), and that we can use the sine function to find the side opposite to the 70 degree angle:

sin(70^o)=\frac{opposite}{hypotenuse} \\sin(70^o)=\frac{h}{10}\\h=10\, sin(70^o) \approx 9.4 \,\,m

therefore 9.4 meters is approximately the height at which the ladder touches the wall initially.

Now, if the tip of the ladder goes down the wall 4 meters, it is now at 9.4 m - 4 m = 5.4 m from the ground. We can therefore use again the sine function to solve for the new angle:

sin(x)=\frac{opposite}{hypotenuse} \\sin(x)=\frac{5.4}{10} \\sin(x)=0.54\\x=arcsin(0.54)\\x= 32.7^o

To answer the second question we need to find the original distance from the wall that the bottom of the ladder was originally, and for that we can use the cosine function:

cos(70^o)=\frac{adjacent}{hypotenuse} \\cos(70^o)=\frac{x}{10}\\x=10\,cos(70^o)\\x\approx 3.4  \,\,m

Now fro the new position of the bottom of the ladder relative to the wall:

cos(32.7^o)=\frac{adjacent}{10} \\adjacent=10\,cos(32.7^o)\\adjacent\approx 8.4\,\,m

then the difference in between those two distances is what we need:

8.4 m - 3.4 m = 5 m

4 0
3 years ago
A cylinder has a base radius of 6 feet and a height of 12 feet.What is it's volume in cubic feet, to the nearest tenths place
Neporo4naja [7]

Answer:

volume = \pi {r}^{2} h \\ =  3.14 \times  {6}^{2}  \times 12 \\  = 1357.2 \:  {ft}^{3}

8 0
3 years ago
You are comparing two refrigerator models. Their annual electricity consumption is shown below. Assume that the cost of electric
Otrada [13]

Answer:

Savings = $13

Step-by-step explanation:

$0.12 = 1 kilowatt-hour

So,

For Top-Freezer Refridgerator:

$0.12 × 529 = 1 × 529 kilowatt-hour

$63.48 = 529 kilowatt-hour

For Side-by-Side Refridgerator:

$0.12 × 634 = 1 × 634 kilowatt-hour

$76.08 = 634 kilowatt-hour

Savings = Side-by-Side Refridgerator - Top-

Freezer Refridgerator

Savings = $( 76.08 -63.48 )

Savings = $12.6

Savings = $13

5 0
3 years ago
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Keith_Richards [23]

Answer:

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7 0
3 years ago
Someone help me and explain . this is confusing.
pentagon [3]

Answer:

on the image

Step-by-step explanation:

sorry for handwriting lol, hope this helps

7 0
3 years ago
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