What is the exact circumference of a circle with a radius of 15 cm?

you roll a 6-sided die with faces numbered 1 through 6, and toss a coin what is the probability of rolling a 2 or getting heads

KatRina [158]

Answer:

2/3

Step-by-step explanation:

You have 6 possible outcomes. Getting 1 outcome is 1/6. You have 2 possible outcomes. Getting 1 outcome is 1/2.

Add 1/2 and 1/6 to get 2/3

5 0

2 years ago

A) Between x 2 and x 3, which function has a greater average rate of change than f(x)=1/6^-x

Arturiano [62]

Answer:

4^x+1

Step-by-step explanation:

because i got it wrong

3 0

2 years ago

Many, many snails have a one-mile race, and the time it takes for them to finish is approximately normally distributed with mean

Mamont248 [21]

Answer:

a) The percentage of snails that take more than 60 hours to finish is 4.75%.

b) The relative frequency of snails that take less than 60 hours to finish is 95.25%.

c) The proportion of snails that take between 60 and 67 hours to finish is 4.52%.

d) 0% probability that a randomly-chosen snail will take more than 76 hours to finish

e) To be among the 10% fastest snails, a snail must finish in at most 42.32 hours.

f) The most typical 80% of snails take between 42.32 and 57.68 hours to finish.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 50, \sigma = 6$

a. The percentage of snails that take more than 60 hours to finish is

This is 1 subtracted by the pvalue of Z when X = 60.

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

$Z = \frac{60 - 50}{6}$

$Z = 1.67$

$Z = 1.67$ has a pvalue 0.9525

1 - 0.9525 = 0.0475

The percentage of snails that take more than 60 hours to finish is 4.75%.

b. The relative frequency of snails that take less than 60 hours to finish is

This is the pvalue of Z when X = 60.

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

$Z = \frac{60 - 50}{6}$

$Z = 1.67$

$Z = 1.67$ has a pvalue 0.9525

The relative frequency of snails that take less than 60 hours to finish is 95.25%.

c. The proportion of snails that take between 60 and 67 hours to finish is

This is the pvalue of Z when X = 67 subtracted by the pvalue of Z when X = 60.

X = 67

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

$Z = \frac{67 - 50}{6}$

$Z = 2.83$

$Z = 2.83$ has a pvalue 0.9977

X = 60

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

$Z = \frac{60 - 50}{6}$

$Z = 1.67$

$Z = 1.67$ has a pvalue 0.9525

0.9977 - 0.9525 = 0.0452

The proportion of snails that take between 60 and 67 hours to finish is 4.52%.

d. The probability that a randomly-chosen snail will take more than 76 hours to finish (to four decimal places)

This is 1 subtracted by the pvalue of Z when X = 76.

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

$Z = \frac{76 - 50}{6}$

$Z = 4.33$

$Z = 4.33$ has a pvalue of 1

1 - 1 = 0

0% probability that a randomly-chosen snail will take more than 76 hours to finish

e. To be among the 10% fastest snails, a snail must finish in at most hours.

At most the 10th percentile, which is the value of X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

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

$-1.28 = \frac{X - 50}{6}$

$X - 50 = -1.28*6$

$X = 42.32$

To be among the 10% fastest snails, a snail must finish in at most 42.32 hours.

f. The most typical 80% of snails take between and hours to finish.

From the 50 - 80/2 = 10th percentile to the 50 + 80/2 = 90th percentile.

10th percentile

value of X when Z has a pvalue of 0.1. So X when Z = -1.28.

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

$-1.28 = \frac{X - 50}{6}$

$X - 50 = -1.28*6$

$X = 42.32$

90th percentile.

value of X when Z has a pvalue of 0.9. So X when Z = 1.28

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

$1.28 = \frac{X - 50}{6}$

$X - 50 = 1.28*6$

$X = 57.68$

The most typical 80% of snails take between 42.32 and 57.68 hours to finish.

5 0

3 years ago

URGENT PLEASE HELP!!!! GIVING BRAINLIEST!! If you answer this correctly ill answer some of your questions you have posted! (39pt

Musya8 [376]

Answer:

ΔMNO= 90°, m = 7.316 cm, n = 16.69 cm

Step-by-step explanation:

The little square in the corner tells you that the angle is 90°

Calculating the length of m

We know that the Tangent of an angle is gotten by dividing the opposite side by the adjacent side, i.e,

Tan Ф = Opposite ÷ Adjacent

hence:

Tan 26° = m ÷ 15

0.4877 = m / 15

make m the subject and multiply both sides by 15

0.4877 × 15 = m / 15 × 15

7.3155 = m

∴ m = 7.316 cm

Calculating the length of n

For this we can use the Pythagoras theorem that states, a² + b² = c² where m = a, b = 15 cm and c = n. Hence:

7.316² + 15² = c ²

53.52 + 225 = c ²

278·52 = c ²

c = √278·52

c = 16.69

∴ n = 16.69 cm

We could also use the Cosine of ΔOMN to get length n i.e,

The Cosine of an angle is equal to the adjacent side divided by the hypotenuse.

Cosine Ф = Adjacent ÷ Hypotenuse

Cosine 26° = 15 cm ÷ n

0.8987 = 15 / n

Make 15 the subject and multiply both sides by n

0.8987 × n = 15 / n × n

0.8987 n = 15

Divide both sides by 0.8987

0.8987 n ÷ 0.8987 = 15 ÷ 0.8987

∴ n = 16.69 cm

Hope this helps!

8 0

2 years ago

An entry code into a building is a 5-digit number.

lakkis [162]

Answer:B

Step-by-step explanation:

5 0

3 years ago