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andrey2020 [161]

2 years ago

4

The water temperature at the beach started at 82 degrees, and it is rising 0.6 degrees each hour. If the water temperature is no

w 85 degrees, write and solve an equation to find h, the number of hours that have passed.

1 answer:

Olenka [21]2 years ago

5 0

Answer:

5 hours

Step-by-step explanation:

The initial temperature is $82\degree C$

The rate at which it is rising is $0.6\degree C$ each hour.

For h hours, the temperature at the beach is modeled by:

$T=0.6h+82$

if the temperature is 85 degrees, then we substitute ans solve for h

$85=0.6h+82$

$\implies 85-82=0.6h$

$\implies \frac{3}{0.6}=h$

$h=5$

Therefore 5 hours have passed

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The Venn diagram shows the results of two events resulting from rolling a number cube.

tankabanditka [31]

Answer:

$P(A|B)=\frac{2}{3}$

$P(A)*P(B)=\frac{1}{3}$

$P(A) =\frac{2}{3}$

$P(B) =\frac{1}{2}$ .

Step-by-step explanation:

We use the Venn diagram to calculate the desired probabilities.

Note that there are 6 possible results in the sample space

S = {1, 2, 3, 4, 5, 6}

Then note that in the region representing the intercept of A and B there are two possible values.

So

$P (A\ and\ B) = \frac{2}{6} = \frac{1}{3}$

In the region that represents event A there are 4 possible outcomes {4, 5, 1, 2}

So

$P(A) = \frac{4}{6} = \frac{2}{3}$

In the region that represents event B there are 3 possible outcomes {1, 2, 6}

So

$P(B) = \frac{3}{6} = \frac{1}{2}$ .

Now

$P(A | B)=\frac{P(A \ and\ B)}{P(B)}\\\\P(A | B)=\frac{\frac{1}{3}}{\frac{1}{2}}\\\\P(A|B)=\frac{2}{3}$

$P(A)*P(B)=\frac{2}{3}*\frac{1}{2}=\frac{1}{3}$

6 0

2 years ago

The XO Group Inc. conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of

slavikrds [6]

Answer:

a) 0.0392

b) 0.4688

c) At least $39,070 to be among the 5% most expensive.

Step-by-step explanation:

Problems of normally distributed samples can be 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:

$\mu = 29858, \sigma = 5600$

a. What is the probability that a wedding costs less than $20,000 (to 4 decimals)?

This is the pvalue of Z when X = 20000. So

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

$Z = \frac{20000 - 29858}{5600}$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

So this probability is 0.0392.

b. What is the probability that a wedding costs between $20,000 and $30,000 (to 4 decimals)?

This is the pvalue of Z when X = 30000 subtracted by the pvalue of Z when X = 20000.

X = 30000

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

$Z = \frac{30000 - 29858}{5600}$

$Z = 0.02$

$Z = 0.02$ has a pvalue of 0.5080.

X = 20000

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

$Z = \frac{20000 - 29858}{5600}$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

So this probability is 0.5080 - 0.0392 = 0.4688

c. For a wedding to be among the 5% most expensive, how much would it have to cost (to the nearest whole number)?

This is the value of X when Z has a pvalue of 0.95. So this is X when Z = 1.645.

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

$1.645 = \frac{X - 29858}{5600}$

$X - 29858 = 5600*1.645$

$X = 39070$

The wedding would have to cost at least $39,070 to be among the 5% most expensive.

5 0

2 years ago

Company B Loses $1,575 for every employee who quit before 90days, What what is the total amount the company will lose if 2 emplo

Sergeu [11.5K]

Answer: The total amount is $4,725.

Step-by-step explanation:

1. Based on the information given in the problem, when an employee quit before 90 days, the company loses $1,575.

2. Then, the number of employees that quit before 90 days were:

$(2+1)=3$ employees

3. To calculate the total amount that the company will lose if these 3 employees quit before 90 days, you must multiply 3 employees by $1,575, as following:

$total=(3)(1,575dollars)\\total=4,725dollars$

4. The result is $4,725.

5 0

2 years ago

Cassandra calculated the total volume of the figure below. A rectangular prism has a length of 7 inches, width of 6 inches, and

RideAnS [48]

Answer:

1,2,4

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

A prisoner is trapped in a cell containing three doors. The first door leads to a tunnel that returns him to his cell after two

Greeley [361]

Answer:

The expected number of days until the prisoner reaches freedom is 2.8.

Step-by-step explanation:

Door 1: 0.3 probability of being selected. Leads to his cell after two days' travel.

Door 2: 0.5 probability of being selected. Leads to his cell after four days' travel.

Door 3: 0.2 probability of being selected. Leads to his cell after one day of travel.

What is the expected number of days until the prisoner reaches freedom?

We multiply the probability of each door being used by the time that it leads to the cell. So

E = 0.3*2 + 0.5*4 + 0.2*1 = 2.8

The expected number of days until the prisoner reaches freedom is 2.8.

4 0

2 years ago