Mathemat

Use the Fundamental Counting Principle to find the total number of outcomes for each situation. a) Choosing a bagel with one typ

Sedbober [7]

There are 1/7 choices

8 0

3 years ago

An open box is made from a square piece of cardboard 30 inches on a side by cutting identical squares and turning up the sides.

pychu [463]

Step-by-step explanation:

A)

The length of the box is 30 − 2x inches.

The width of the box is 30 − 2x inches.

The height of the box is x inches.

So the volume is:

V = x (30 − 2x)²

B)

V(3) = 3 (30 − 6)² = 1728

V(4) = 4 (30 − 8)² = 1936

V(5) = 5 (30 − 10)² = 2000

V(6) = 6 (30 − 12)² = 1944

V(7) = 7 (30 − 14)² = 1792

As x increases, the volume of the box increases to a maximum and then decreases.

C)

The ends of the domain occur when V = 0.

0 = x (30 − 2x)²

x = 0 or 15

So the domain is (0, 15).

3 0

3 years ago

I really need the answers for these I don't understand this

Yuri [45]

I tryed my best to figure out what all of the numbers were. if i got any wrong then please tell me and i will put the right answer in the comments.

1) 3/5= 5/x (cross multiply)
3x=5(5)
3x=25
x= 25/3 -or- 8.33

2) 2/4=x/12 (cross multiply)
 2(12)=4x
 24=4x
 6=x
3) 10/x=5/9 (cross multiply)
10(9)=5x
90=5x
18=x
4) 5/5=x/18 (cross multiply)
5(18)=18x
90=18x
5=x

8 0

3 years ago

A math professor notices that scores from a recent exam are normally distributed with a mean of 61 and a standard deviation of 8

Alexeev081 [22]

Answer:

a) 25% of the students exam scores fall below 55.6.

b) The minimum score for an A is 84.68.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 61 and a standard deviation of 8.

This means that $\mu = 61, \sigma = 8$

(a) What score do 25% of the students exam scores fall below?

Below the 25th percentile, which is X when Z has a p-value of 0.25, that is, X when Z = -0.675.

$Z = \frac{X - \mu}{\sigma}$

$-0.675 = \frac{X - 61}{8}$

$X - 61 = -0.675*8$

$X = 55.6$

25% of the students exam scores fall below 55.6.

(b) Suppose the professor decides to grade on a curve. If the professor wants 0.15% of the students to get an A, what is the minimum score for an A?

This is the 100 - 0.15 = 99.85th percentile, which is X when Z has a p-value of 0.9985. So X when Z = 2.96.

$Z = \frac{X - \mu}{\sigma}$

$2.96 = \frac{X - 61}{8}$