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3 years ago

5

The table represents some measurements that Johnny recorded in his math class. What values COULD x and y represent, respectively

?
A)radius and area of a circle
B)side length and area of a square
C)side length and volume of a cube
D)side length and volume of a cone

1 answer:

Law Incorporation [45]3 years ago

4 0

Based on the given data set:

x 1 2 3 4 5
y 1 8 27 64 125

the relationship between the two variables is notably:

y = x^3

this formula represents the volume of a cube:

V = s^3

Therefore, the answer is C) Side length and volume of a cube.

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There are 6 swimmers in a race. In how many ways can they finish in first and second place?

hodyreva [135]

Answer:

step 1. 6x2=12 first place way

step 2. 12×2=24

step 3. 24+6=30 second place way

6 0

2 years ago

An article describes an experiment to determine the effectiveness of mushroom compost in removing petroleum contaminants from so

alexgriva [62]

Solution :

Let $p_1$ and $p_2$ represents the proportions of the seeds which germinate among the seeds planted in the soil containing $3\%$ and $5\%$ mushroom compost by weight respectively.

To test the null hypothesis $H_0: p_1=p_2$ against the alternate hypothesis $H_1:p_1 \neq p_2$ .

Let $\hat p_1, \hat p_2$ denotes the respective sample proportions and the $n_1, n_2$ represents the sample size respectively.

$$\hat p_1 = \frac{74}{155} = 0.477419$

$n_1=155$

$$p_2=\frac{86}{155}=0.554839$

$n_2=155$

The test statistic can be written as :

$$z=\frac{(\hat p_1 - \hat p_2)}{\sqrt{\frac{\hat p_1 \times (1-\hat p_1)}{n_1}} + \frac{\hat p_2 \times (1-\hat p_2)}{n_2}}}$

which under $H_0$ follows the standard normal distribution.

We reject $H_0$ at $0.05$ level of significance, if the P-value or if $|z_{obs}|>Z_{0.025}$

Now, the value of the test statistics = -1.368928

The critical value = $\pm 1.959964$

P-value = $P(|z|> z_{obs})= 2 \times P(z< -1.367928)$

$=2 \times 0.085667$

= 0.171335

Since the p-value > 0.05 and $|z_{obs}| \ngtr z_{critical} = 1.959964$ , so we fail to reject $H_0$ at $0.05$ level of significance.

Hence we conclude that the two population proportion are not significantly different.

Conclusion :

There is not sufficient evidence to conclude that the $\text{proportion}$ of the seeds that $\text{germinate differs}$ with the percent of the $\text{mushroom compost}$ in the soil.

8 0

3 years ago

In the 2000 Sydney Olympics, a special program initiated by IOC president Juan Antonio Samaranch allowed developing countries to

jok3333 [9.3K]

Answer:

The means for times for the first round of the 100 meter men’s swim is 52.64789 seconds

The satandar deviation for times for the first round of the 100 meter men’s swim is 7.60182 seconds

Step-by-step explanation:

The sample mean for a set of n data is given by:

$\bar X = \frac{1}{n}\sum{x_i}$

In other words, the sample mean of the times for 71 times of the first round measured in seconds is:

$\bar X = \frac{1}{71}\sum{x_i} = 52.64789$ seconds

The sample standard deviation for a set of n data is given by:

$S = \sqrt{\frac{1}{n-1}\sum{(x_i - \bar x)^2}}$

In other words, the sample standard deviation of the times for 71 times of the first round measured in seconds is:

$S = \sqrt{\frac{1}{n-1}\sum{(x_i - \bar x)^2}} = 7.60182$ seconds

8 0

3 years ago

The ceiling of Katie’s living room is a square that is 12 ft long on each side. To decorate for a party, she plans to hang crepe

stellarik [79]

The equation is 12(10)=120ft

7 0

3 years ago

Find the distance between the points (7, -2) and (2, -10).

katrin2010 [14]

Answer:

$\sqrt{89}$

Step-by-step explanation:

d = $\sqrt{(x_{1}-x_{2} )^{2} +(y_{1} -y_{2} )^{2} }$

d = $\sqrt{(7-2)^{2} +(-2+10)^{2} }$

d = $\sqrt{5^{2} +(-8)^{2} }$

d = $\sqrt{25+64}$

d = $\sqrt{89}$

3 0

2 years ago