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mrs_skeptik [129]
3 years ago
14

A pizza shop sells three sizes of pizza, and they track how often each size gets ordered along with how much they profit from ea

ch size. Let X represent the shop's profit on a randomly selected pizza. Here's the probability distribution of X along with summary statistics:
Small Medium Large
X = profit ($) 4 8 12
P(X) 0.18 0.50 0.32
Mean: μX = $8.56
Standard deviation: σx =$2.77
The company is going to run a promotion where customers get $2 off any size pizza. Assume that the promotion will not change the probability that corresponds to each size. Let Y represent their profit on a randomly selected pizza with this promotion. What are the mean and standard deviation of Y?
Mathematics
1 answer:
777dan777 [17]3 years ago
3 0

Answer:

The mean and standard deviation of Y is $6.56 and $2.77 respectively.

Step-by-step explanation:

Consider the provided information.

Let Y represent their profit on a randomly selected pizza with this promotion.

The company is going to run a promotion where customers get $2 off any size pizza.

Therefore, Y=\text{Profit}-\$2

Y=X-\$2

So the mean will be reduced by 2.

\mu_Y=\mu_X-\$2

\mu_Y =\$ 8.56 - \$2

\mu_Y =\$6.56

If we add or subtract any constant number from a given distribution, then the mean is changed by the same number(i.e constant number) but the standard deviation will remain the same.

Therefore \sigma_Y=\sigma_X=2.77

Hence, the mean and standard deviation of Y is $6.56 and $2.77 respectively.

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2=16.5km
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3 years ago
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Which of these four sets of side lengths will form a right triangle? Set 1 4 cm, 5 cm, 6 cm Set 2 8 in., 12 in., 20 in. Set 3 10
Alenkasestr [34]

Answer:  The correct option is (D) SET 4.

Step-by-step explanation:  We are to select the correct set of side lengths that will form a right-angled triangle.

To form a right-angled triangle, we must have the following relation:

<em>Perpendicular² + Base² = Hypotenuse².</em>

<em>Hypotenuse is the length of the largest side; perpendicular and base are the two legs of the triangle.</em>

SET 1 :  14 cm, 5 cm, 6 cm.  

We have

5^2+6^2=25+36=61,\\\\14^2=196.

Therefore,

<em>Perpendicular² + Base² ≠ Hypotenuse².</em>

So, this set will not form a right-angled triangle.

SET 2 :  8 in., 12 in., 20 in.  

We have

8^2+12^2=64+144=208,\\\\20^2=400.

Therefore,

<em>Perpendicular² + Base² ≠ Hypotenuse².</em>

So, this set will not form a right-angled triangle.

SET 3 :  10 mm, 20 mm, 30 mm.  

We have

10^2+20^2=100+400=500,\\\\30^2=900.

Therefore,

<em>Perpendicular² + Base² ≠ Hypotenuse².</em>

So, this set will not form a right-angled triangle.

SET 4 :  12 ft, 16 ft, 20 ft.  

We have

12^2+16^2=144+256=400,\\\\20^2=400.

Therefore,

<em>Perpendicular² + Base² = Hypotenuse².</em>

So, this set will form a right-angled triangle.

Thus, the SET 4 will form a right-angles triangle.

Option (D) is correct.

5 0
3 years ago
Read 2 more answers
I need help.........
Otrada [13]
The first would be 4,000 and the second would be 400
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3 years ago
If the hypotenuse of a right triangle is 2 <img src="https://tex.z-dn.net/?f=%5Csqrt%7B3%7D" id="TexFormula1" title="\sqrt{3}" a
Svetradugi [14.3K]

Answer:

3

Step-by-step explanation:

a = the other leg:

a^{2} =(2\sqrt{3} )^{2} -(\sqrt{3}) ^{2} =(4)(3)-3=12-3

a^{2} =9

a=\sqrt{9}

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Hope this helps

5 0
1 year ago
After robbing a bank in dodge city, a robber gallops off at 14 mi/h. 20 minutes later, the marshall leaves to pursue the robber
Morgarella [4.7K]

For this case we have to write the equation of the position of each one.

We have then:

For the robber:

r = 14t

For the marshall :

r = 16 (t- (\frac{20}{60}))

r = 16 (t-\frac{1}{3})

By the time the marshall reaches the robber we have:

14t = 16 (t-\frac{1}{3})

From here, we clear the time.

We have then:

16t - 14t = \frac{16}{3}

2t = \frac{16}{3}

t =\frac{8}{3}

t = 2.7 h

Answer:

it takes the marshall to catch up to the robber about 2.7 hours.

4 0
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