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V125BC [204]
3 years ago
6

According to the manufacturer of the candy Skittles, 20% of the candy produced are red. If we take a random sample of 100 bags o

f Skittles, what is the probability that the proportion in our sample of red candies will be less than 20%
Mathematics
1 answer:
igomit [66]3 years ago
5 0

Answer:

Probability that the proportion in our sample of red candies will be less than 20% is 0.5 .

Step-by-step explanation:

We are given that 20% of the candy produced are red. A random sample of 100 bags of Skittles is taken.

The distribution we can use here is;

               \frac{\hat p - p}{\sqrt{\frac{\hat p (1- \hat p)}{n} } } ~ N(0,1)

where, p = 0.20 and n = 100

Let \hat p = proportion of red candies in our sample

So, P(\hat p < 0.20) = P(\frac{\hat p - p}{\sqrt{\frac{\hat p (1- \hat p)}{n} } } < \frac{0.20 - 0.20}{\sqrt{\frac{0.2 (1- 0.2)}{100} } } ) = P(Z < 0) = 0.5

Therefore, probability that the proportion in our sample of red candies will be less than 20% is 0.5 .

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lutik1710 [3]

Answer:

White Gold.

Step-by-step explanation:

This type of gold contains only 75% pure gold, not 100%.

4 0
3 years ago
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Solve x + 3y = 9<br> 3x – 3y = -13 (1 point)
Mariana [72]

Answer:

The values of x and y to the given equations are x=-1 and y=\frac{10}{3}

The solution is (-1,\frac{10}{3})

Step-by-step explanation:

Given equations are x+3y=9\hfill (1)

and 3x-3y=-13\hfill (2)

to solve the given equations by elimination method :

Adding the given two equations (1) and (2) we get

x+3y=9

3x-3y=-13

_______________

4x=-4

x=-\frac{4}{4}

Therefore x=-1

Now substitute the value x=-1 in equation(1) we get

(-1)+3y=9

3y=9+1

y=\frac{10}{3}

Therefore the values of x and y to the given equations are x=-1 and y=\frac{10}{3}

The solution is (-1,\frac{10}{3})

8 0
3 years ago
The third angle in an isosceles triangle is 32 more than 2 times as large as each of the two base angles. Find the measure of ea
DIA [1.3K]

Answer: the third angle is 106 degrees.

The base angles are 37 degrees each.

Step-by-step explanation:

In an isosceles triangle, the base angles are equal.

Let x represent the measure of each of the base angles.

The third angle in an isosceles triangle is 32 more than 2 times as large as each of the two base angles. It means that the measure of the third angle would be

(2x + 32) degrees

The sum of the angles inna triangle is 180 degrees. It means that

x + x + 2x + 32 = 180

4x = 180 - 32

4x = 148

x = 37

The third angle is

2x = 32 = (2 × 37) + 32

= 74 + 32 = 106

5 0
3 years ago
What was Mike's average rate of descent over his last three hours?
Romashka [77]

Answer:

<em>The average rate of descent over the last 3 hours is 1000 ft/h. </em>

Step-by-step explanation:

<u>Rate of Change</u>

It's usually referred to as to the variation that one magnitude has in reference to another. The reference magnitude can be time t. The rate of change is calculated as the slope of the curve that represents the function.

The image shows the variation of Mike's height above sea level in feet with time in hours. We need to calculate the rate of change in the last three hours (from 7 to 10).

The rate of change can be calculated with the slope of the line, which formula is:

\displaystyle m=\frac{h_2-h_1}{t_2-t_1}

Let's pick two points (7,4000) (10,1000):

\displaystyle m=\frac{1000-4000}{10-7}=\frac{-3000}{3}=-1000

m=-1000\ ft/h

Note the rate of change is negative, which means the height is decreasing.

The average rate of descent over the last 3 hours is 1000 ft/h.

8 0
3 years ago
A building casts a shadow that is 18 ft long. A woman standing near the building is 5.75 ft tall and 4 feet long. What is the he
Lynna [10]

Answer:

25 feet 6 inches

Step-by-step explanation:

Assuming that the woman is standing up straight, you have a situation where you have two similar right triangles. The legs of the smaller triangle are the woman's height and the length of her shadow, and the legs of the larger triangle are the building's height and the length of its shadow. We know that the sides of similar triangles are proportional, so we can write:

5ft8in =2ft=x%2Aft%2F18ft

Now you need to cross-multiply and solve for x, but multiplying feet times feet and inches is a messy calculation. Changing 5 ft 8 inches to 5 and 2/3 feet is messy also. My recommendation is to convert everything to inches, and then convert back to feet and inches when you are done.

5 ft 8 inches = (5 *12) + 8 = 68 inches

4 ft = 4 * 12 = 48 inches, and

18 ft = 18 * 12 = 216 inches.

Now the proportion looks like:

68%2F48=x%2F216, so

48x=14688 after cross-multiplying, and

x=306 after dividing by 48. So the building is 306 inches tall. But we want to know the height of the building in feet and inches. To convert back to feet and inches from inches, just do integer division by 12 where your answer is expressed as a quotient and a remainder. The quotient is the number of feet, and the remainder is the number of inches.

306 = 25 remainder 6, so the answer is 25 feet 6 inches.

Note that this answer makes sense. 5'8" is nearly 6'. 6' is one and a half times 4 feet, so the woman is a little less than one and a half times taller than her shadow is long. One and a half times the building's 18 ft shadow is 27 feet, and that is a little bit more than the 25'6' answer that we

5 0
3 years ago
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