What is the product of 0.6 and 7

The space program has 6 astronauts in outer space and 10 astronauts on Earth. What is the ratio of the number of astronauts in o

natulia [17]

6:16

explanation:
6+10=16
6 is the amount in outer space
ration is 6:16

4 0

2 years ago

An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out squares of equal size from the fou

Burka [1]

Answer:

Maximum volume of the box will be 7.41 cubic feet.

Step-by-step explanation:

Open box has been made from a metal sheet measuring 3 ft and 8 ft.

Let four square pieces were removed from the four corners with one side measurement x ft.

Volume of the open box = Length × width × height

Length of the box = (3 - 2x) ft

Width of the box = (8 - 2x) ft

Height of the box = x ft

Volume of the box = (3 - 2x)(8 - 2x)x

V = (24 - 6x - 16x + 4x²)x

V = 24x - 22x² + 4x³

Now we take the derivative of V with respect to x and equate the derivative to zero,

$\frac{d}{dx}(V)=\frac{d}{dx}(24x - 22x^{2}+4x^{3})$

V' = 24 - 44x + 12x²

V' = 0

12x² - 44x + 24 = 0

3x² - 11x + 6 = 0

3x² - 9x - 2x + 6 = 0

3x(x - 3) - 2(x - 3) = 0

(3x - 2)(x - 3) = 0

(3x - 2) = 0

and (x - 3) = 0

Therefore, x = 3, $\frac{2}{3}$

For x = 0.67

Length of the box = (3 - 2x) = 3 - 1.34

= 1.66 ft

Width of the box = (8 - 2x) = 8 - 1.34

= 6.66 ft

Volume of the box = 0.67 × 1.66 × 6.66

V = 7.41 cubic feet.

Similarly, for x = 3,

Length of the box = (3 - 2\times 3) = -3

which is negative but the length of the box can not be negative.

Therefore, maximum volume of the box will be 7.41 cubic feet.

6 0

3 years ago

Whats twenty times twenty

Mekhanik [1.2K]

400 is the answer to your question

4 0

3 years ago

Read 2 more answers

Congress regulates corporate fuel economy and sets an annual gas mileage for cars. A company with a large fleet of cars hopes to

attashe74 [19]

Answer:

a) Null hypothesis: $\mu \leq 30.2$

Alternative hypothesis: $\mu > 30.2$

b) $X \sim N(\mu=32.12, \sigma=4.83)$

And the distribution for the random sample is given by:

$\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)$

c) $t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81$

$p_v =P(t_{(49)}>2.81)=0.0035$

d) If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.

e) The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation

$\bar X=32.12$ represent the sample mean

$s=4.83$ represent the sample standard deviation

$n=50$ sample size

$\mu_o =30.2$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

a. Define the parameter and state the hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 30.2 mpg, the system of hypothesis would be:

Null hypothesis: $\mu \leq 30.2$

Alternative hypothesis: $\mu > 30.2$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

b. Define the sampling distribution (mean and standard deviation).

Let X the random variable who represent the variable of interest. And we know that the distribution for X is:

$X \sim N(\mu=32.12, \sigma=4.83)$

And the distribution for the random sample is given by:

$\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)$

c. Perform the test and calculate P-value

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=50-1=49$

Since is a one right tailed test the p value would be:

$p_v =P(t_{(49)}>2.81)=0.0035$

d. State your conclusion.

If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.

e. Explain what the p-value means in this context.

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

6 0

3 years ago

For the parallelogram ABCD the extensions of the angle bisectors AG and BH intersect at point P. Find the area of the parallelog

natita [175]

Answer:

The area of a parallelogram is 360 in.²

Step-by-step explanation:

Where DG = GH

GP = 12 in.

AB = 39 in.

∠DAB + ∠ABC = 180° (Adjacent angles of a parallelogram)

Whereby ∠DAB is bisected by AG and ∠ABC is bisected by BH