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3 years ago

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A juggler is performing an act by juggling several balls. The juggler throws the balls up at an initial height of 3.9 feet with

a speed of 14.8 feet per second. If the juggler did not catch a ball, about how long will it take the ball to hit the floor?

1 answer:

drek231 [11]3 years ago

7 0

It will hit the floor when h=0

-16t^2+14.8t+3.9=0

using the quadratic formula...

t=(-14.8±√468.64)/-32, since t>0

t ≈ 1.139 seconds

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5. I need help with question in the attached picture!

igomit [66]

ANSWER

x=100,y=10

EXPLANATION

The given logarithmic equations are;

$log_{10}( {x}^{2} {y}^{3} ) = 7$

This implies that,

${x}^{2} {y}^{3} = {10}^{7} ...(1)$

and

$log_{10}( \frac{x}{y} ) = 1$

This implies that,

$\frac{x}{y} = {10}^{1}$

$x = 10y...(2)$

Put equation (2) into equation (1)

${(10y)}^{2} {y}^{3} = {10}^{7}$

$10 ^{2} y^{2} {y}^{3} = {10}^{7}$

${y}^{5} = {10}^{5}$

Hence y=10.

This implies

$x = 10(10) = 100$

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3 years ago

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.

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3 years ago

Come on y'all....plz

boyakko [2]

Answer:

In image

Step-by-step explanation:

You need to draw it yourself

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3 years ago

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What is the best approximation of the surface area of this right cone?

inn [45]

$\bf \textit{total surface area of a cone}\\\\
s=\pi r\sqrt{r^2+h^2}+\pi r^2\quad 
\begin{cases}
r=radius\\
h=height\\
-----\\
r=12\\
h=9
\end{cases}
\\\\\\
s=\pi (12)\sqrt{12^2+9^2}+\pi (12^2)\implies s=12\pi \sqrt{225}+144\pi 
\\\\\\
s=12\pi (15)+144\pi \implies s=180\pi +144\pi \implies s=324\pi$

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3 years ago

Help I guess? sorry I'm asking a lot of questions today

valina [46]

Answer:

63 houses have been sold this year.

Step-by-step explanation:

There are 81 houses in the community. If 7/9 are sold this year, then all you have to do is multiplication.

In this case, you would multiply 81 by 7/9 to get your answer.

81/1 x 7/9:

Cancel out the 9 and the 81. Then the denominator will be 1 x 1 and the numerator would be 7 x 9. It would be 63 (7x9=63) over 1 (1x1=1) which is just 63. Make sure to include units.

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3 years ago

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