The student council is selling cupcakes at the school play.

A truck stops at a gas station where diesel fuel costs $3.99 per gallon. The truck needs 8.8 gallons of diesel for the driver to

Dmitry [639]

36.00 will be enough to pay for fuel because if you multiply the 8.8 gallons of diesel needed by the fuel cost per gallon you get 35.112

6 0

2 years ago

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A book shelf holds twenty books. Eleven are hard- covered, nine of the books are nonfiction, and four of the nonfiction books ar

ololo11 [35]

Answer:

1) Find the probability that a chosen book is nonfiction and hard-covered. P(N ∩ H) = 4/20

2) Find the probability that a chosen book is hard-covered. P(H) = 11/20

3) Calculate the conditional probability. = 4/11

---------------------------------------------------------------------------------------------

1.) 4/20

2.) 11/20

3.) 4/11

7 0

2 years ago

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While at a carnival, Andrew comes across a game that involves rolling a die. According to the game's rules, if the number rolled

Reptile [31]

Answer:

he can expect to lose 0.5$

Step-by-step explanation:

To solve this problem we must calculate the expected value of the game.

If x is a discrete random variable that represents the gain obtained when rolling a dice, then the expected value E is:

$E =\sum xP (x)$

When throwing a dice the possible values are:

x: 1→ -$9; 2→ $4; 3→ -$9; 4→ $8; 5→ -$9; 6→ $12

The probability of obtaining any of these numbers is:

$p=\frac{1}{6}$

The gain when obtaining an even number is twice the number.

The loss to get an odd number is $ 9

So the expected gain is:

$E=-9*\frac{1}{6}-9*\frac{1}{6}-9*\frac{1}{6} + 4*\frac{1}{6} + 8*\frac{1}{6} + 12*\frac{1}{6}\\\\E =-27*\frac{1}{6} + 24*\frac{1}{6}\\\\E=-3*\frac{1}{6}\\\\E=-$0.5$

4 0

2 years ago

Here is a circle touching a square. The area of the square is 36cm squared. Work out the area of the circle. Give your answer in

Lena [83]

Answer:

see below

Step-by-step explanation:

Because the area of the square is 36 its side is 6 meaning the circle has a diameter of 6. This means that its radius is 3 so its area is 3² * π = 9π.

8 0

2 years ago

Gibbs Baby Food Company wishes to compare the weight gain of infants using its brand versus its competitor’s. A sample of 40 bab

Leviafan [203]

Answer:

$z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936$

The p value can be founded with this formula:

$p_v =P(z$

Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor

Step-by-step explanation:

Information given

$\bar X_{1}=7.6$ represent the mean for Gibbs products

$\bar X_{2}=8.1$ represent the mean for the competitor

$\sigma_{1}=2.3$ represent the population standard deviation for Gibbs

$\sigma_{2}=2.9$ represent the sample standard deviation for the competitor

$n_{1}=40$ sample size for the group Gibbs

$n_{2}=55$ sample size for the group competitor

$\alpha=0.05$ Significance level provided

z would represent the statistic

Hypothesis to verify

We want to check if babies using the Gibbs brand gained less weight, the system of hypothesis would be:

Null hypothesis: $\mu_{1}-\mu_{2}=0$

Alternative hypothesis: $\mu_{1} - \mu_{2}< 0$

The statistic would be given by:

$z=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

Replacing the info given we got:

$z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936$

The p value can be founded with this formula:

$p_v =P(z$

Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor

5 0

2 years ago