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3 years ago

Question 3 options:

Mathematics

1 answer:

melomori [17]3 years ago

5 0

The height of an object can be represented as a function of time.

It takes the rocket 25 seconds to hit the ground

The height function is given as:

$\mathbf{h(t) = 400t - 16t^2}$

When the rocket hits the ground, we have:

h(t) = 0

So, the height function becomes

$\mathbf{ 400t - 16t^2 = 0}$

Rewrite as:

$\mathbf{ 16t^2 = 400t}$

Divide both sides by 16t

$\mathbf{ t = 25}$

Hence, it takes the rocket 25 seconds to hit the ground

Read more about height functions at:

brainly.com/question/22573423

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hoa [83]

Answer:

$A=22.5\ \text{feet}^2$

Step-by-step explanation:

We have,

Height of a cone is 12 feet

Volume of the cone is 90 feet

It is required to find the area of the base of the cone.

The base of a cone is circular in shape.

The formula used to find the volume of a cone is given by :

$V=\dfrac{1}{3}\pi r^2 h$

here, $\pi r^2=A$ (area of base of cone)

$V=\dfrac{1}{3}\times Ah\\\\A=\dfrac{3V}{h}\\\\A=\dfrac{3\times 90}{12}\\\\A=22.5\ \text{feet}^2$

So, the area of the base of the cone is $22.5\ \text{feet}^2$ .

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3 years ago

A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCI/L of radon. The resulting reading

valkas [14]

Answer:

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu \neq 100$

$t=\frac{98.375-100}{\frac{6.109}{\sqrt{12}}}=-0.921$

$p_v =2*P(t_{11}$

Step-by-step explanation:

1) Data given and notation

Data: 105.6, 90.9, 91.2, 96.9, 96.5, 91.3, 100.1, 105.0, 99.6, 107.7, 103.3, 92.4

We can calculate the sample mean and deviation for this data with the following formulas:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i- \bar X)^2}{n-1}}$

The results obtained are:

$\bar X=98.375$ represent the sample mean

$s=0.6.109$ represent the sample standard deviation

$n=12$ sample size

$\mu_o =100$ represent the value that we want to test

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

z would represent the statistic (variable of interest)

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

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 100pCL/L, the system of hypothesis are :

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu \neq 100$

Since we don't know the population deviation, 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".

3) Calculate the statistic

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

$t=\frac{98.375-100}{\frac{6.109}{\sqrt{12}}}=-0.921$

4) P-value

First we need to find the degrees of freedom for the statistic given by:

$df=n-1=12-1=11$

Since is a two sided test the p value would given by:

$p_v =2*P(t_{11}$

5) Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significant different from 100 at 5% of significance.

3 0

3 years ago

A pizza shop sells three sizes of pizza, and they track how often each size gets ordered along with how much they profit from ea

777dan777 [17]

Answer:

The mean and standard deviation of Y is $6.56 and $2.77 respectively.

Step-by-step explanation:

Consider the provided information.

Let Y represent their profit on a randomly selected pizza with this promotion.

The company is going to run a promotion where customers get $2 off any size pizza.

Therefore, $Y=\text{Profit}-\$2$

$Y=X-\$2$

So the mean will be reduced by 2.

$\mu_Y=\mu_X-\$2$

$\mu_Y =\$ 8.56 - \$2$

$\mu_Y =\$6.56$

If we add or subtract any constant number from a given distribution, then the mean is changed by the same number(i.e constant number) but the standard deviation will remain the same.

Therefore $\sigma_Y=\sigma_X=2.77$

Hence, the mean and standard deviation of Y is $6.56 and $2.77 respectively.

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3 years ago