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3 years ago

13

Larry buys a tent that is on sale for 25% off the original price. The original price is $80 more than the sale price. What is th

e original price of the tent

1 answer:

myrzilka [38]3 years ago

3 0

Answer:

The original price of the tent = $320

Step-by-step explanation:

Let the original price be =$ $x$

Discount offered = $25$ % of the orignal price = $\frac{25}{100}\times x=0.25\times x =\$ 0.25x$

Original price is $80 more than sale price

Discount = Original price - Sale price = $80

So, we have

$0.25x=80$

We need to solve for $x$ to find original price

Dividing both sides by $0.25$

$\frac{0.25}{0.25}x=\frac{80}{0.25}\\x=\$320$

∴ The original price of the tent = $320

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2 years ago

If C(m) = 0.50m + 30 represents the cost of renting a car, how many miles were driven if the cost is $130?

Dimas [21]

Your answer is 200 miles

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3 years ago

Please help me with this math problem.

ladessa [460]

Answer:

-6v < -3; v> -0.5

Step-by-step explanation:

We have to find a number let say x

Given that:

-6v < x ........... eq1

v> - 0.5 ........... eq2

By taking equation 1

-6v < x

Dividing both sides by -6

(inequality will be inverted because of negative sign)

-6/-6 v > x/-6

v > x/-6 .........eq3

Now comparing eq2 and eq3 we get:

x/-6 = -0.5

Multiplying both sides by -6

x = -0.5 * -6

x = -3

So it will give:

-6v < -3; v> -0.5

I hope it will help you!

4 0

3 years ago

A random sample of 50 recent college graduates results in a mean time to graduate of 4.58 years, with a standard deviation of 1.

Anna007 [38]

Answer:

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

Yes, this confidence interval contradict the belief that it takes 4 years to complete a bachelor’s degree.

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population mean <em>μ, </em>when the population standard deviation is not known is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

The information provided is:

$\bar x=4.58\\s=1.10\\\alpha =0.10$

Compute the critical value of <em>t</em> for 90% confidence interval and (n - 1) degrees of freedom as follows:

$t_{\alpha/2, (n-1)}=t_{0.10/2, (50-1)}=t_{0.05, 49}=1.671$

*Use a <em>t</em>-table for the probability.

Compute the 90% confidence interval for population mean <em>μ</em> as follows:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

$=4.58\pm 1.671\times \frac{1.10}{\sqrt{50}}\\=4.58\pm 0.26\\=(4.32, 4.84)$

Thus, the 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

If a hypothesis test is conducted to determine whether it takes 4 years to complete a bachelor’s degree or not, the hypothesis will be:

<em>Hₐ</em>:<em> </em>The mean time it takes to complete a bachelor’s degree is 4 years, i.e. <em>μ </em>= 4.

<em>Hₐ</em>:<em> </em>The mean time it takes to complete a bachelor’s degree is different from 4 years, i.e. <em>μ </em>≠ 4.

The decision rule based on a confidence interval will be:

Reject the null hypothesis if the null value is not included in the interval.

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32 years, 4.84 years).

The null value, i.e. <em>μ </em>= 4 is not included in the interval.

The null hypothesis will be rejected at 10% level of significance.

Thus, it can be concluded that that time it takes to complete a bachelor’s degree is different from 4 years.

4 0

3 years ago

The 65 students in a classical music lecture class were polled, with the following results: 37 like Wolfgang Amadeus Mozart 36 l

Anna35 [415]

Answer:

a) 25

b) 30

c) 10

d) Not Mozart, 6

e) 2

Step-by-step explanation:

We use a Venn Diagram to solve this question.

I am going to say that:

A are the students who like Mozart.

B are the students who like Beethoven

C are the students who like Haydn.

We have that:

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

In which a are those who only like Mozart, $(A \cap B)$ are those who like Mozart and Beethoven, $(A \cap C)$ are those who like Mozart and Haydn and $(A \cap B \cap C)$ are those who like all three of them.

By the same logic, we have that:

$B = b + (A \cap B) + (B \cap C) + (A \cap B \cap C)$

$C = c + (B \cap C) + (A \cap C) + (A \cap B \cap C)$

We start finding these values from the intersection:

8 like all three composers

This means that $A \cap B \cap C = 8$

14 like Beethoven and Haydn

This means that:

$(B \cap C) + (A \cap B \cap C) = 14$

So

$B \cap C = 6$

21 like Mozart and Haydn

This means that:

$(A \cap C) + (A \cap B \cap C) = 21$

Then

$A \cap C = 13$

14 like Mozart and Beethoven

This means that:

$(A \cap B) + (A \cap B \cap C) = 14$

$A \cap B = 6$

31 like Franz Joseph Haydn

This means that C = 31. So

$C = c + (B \cap C) + (A \cap C) + (A \cap B \cap C)$

$31 = c + 6 + 13 + 8$

$c = 4$

36 like Ludwig van Beethoven

This means that $B = 36$

So

$B = b + (A \cap B) + (B \cap C) + (A \cap B \cap C)$

$36 = b + 6 + 6 + 8$

$b = 16$

37 like Wolfgang Amadeus Mozart

This means that A = 37. Then

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

$37 = a + 6 + 13 + 8$

$a = 10$

a. exactly two of these composers?

$(A \cap B) + (A \cap C) + (B \cap C) = 6 + 13 + 6 = 25$

b. exactly one of these composers?

$a + b + c = 10 + 16 + 4 = 30$

c. like only Mozart?

$a = 10$

d. like Beethoven and Haydn, but not Beethoven?

I will use not Mozart.

So $B \cap C = 6$

Not Mozart, 6.

e. like none of these composers?

At least 1:

$(A \cup B \cup C) = a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 10 + 16 + 4 + 6 + 13 + 6 + 8 = 63$

The total is 65

So 65 - 63 = 2 like none of these composers

4 0

2 years ago