What is 974.362 rounded to the nearest ten

Andrew believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request.

Artist 52 [7]

Honor roll Not on honor roll Total
Received math class requested 315 64 379
Did not get math class requested 41 80 121
Total 356 144 500

Honor roll: request granted: 315/356 = 0.88 x 100% = 88%
Not Honor roll request granted: 64/144 = 0.44 x 100% = 44%

Honor roll students were given preference in granting request than those not in the honor roll.

5 0

2 years ago

In triangle $DEF,$ $\angle D = 30^\circ,$ $\angle F = 60^\circ,$ and $EF = 6.$ Find $DE + DF.$ [asy] unitsize(2 cm); pair D, E,

sergey [27]

Answer:

Step-by-step explanation:

The answer to this question is 12+6sqrt3.

This is because of the 30, 60, and 90 degree rule. The rule states that the hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.

Using the rule you now know that DF is 12. Then use the Pythagorean Theorem to find the length of DE. 12^2=144, and 6^2=36. 144-36=108.

The square root of 108 simplified=6sqrt3.

Then you add them together and get 12+6sqrt3.

5 0

2 years ago

A member of a student team playing an interactive marketing game received the fol- lowing computer output when studying the rela

nirvana33 [79]

Answer:

$p_v = 2*P(t_{n-2} > |t_{calc}|)= 0.91$

So on this case for the significance level assumed $\alpha=0.05$ we see that $p_v >\alpha$ so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.

So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.

Step-by-step explanation:

Let's suppose that we have the following linear model:

$y= \beta_o +\beta_1 X$

Where Y is the dependent variable and X the independent variable. $\beta_0$ represent the intercept and $\beta_1$ the slope.

In order to estimate the coefficients $\beta_0 ,\beta_1$ we can use least squares procedure.

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: $\beta_1 = 0$

Alternative hypothesis: $\beta_1 \neq 0$

Or in other words we want to check is our slope is significant (X have an effect in the Y variable )

In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal

The significance level assumed on this case is $\alpha=0.05$

The standard error for the slope is given by this formula:

$SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

Th degrees of freedom for a linear regression is given by $df=n-2$ since we need to estimate the value for the slope and the intercept.

In order to test the hypothesis the statistic is given by:

$t=\frac{\hat \beta_1}{SE_{\beta_1}}$

The p value on this case would be given by:

$p_v = 2*P(t_{n-2} > |t_{calc}|)= 0.91$

So on this case for the significance level assumed $\alpha=0.05$ we see that $p_v >\alpha$ so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.

So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.

3 0

2 years ago

1 point) As reported in "Runner's World" magazine, the times of the finishers in the New York City 10 km run are normally distri

BigorU [14]

Answer:

(a) E (X) = 61 and SD (X) = 9

(b) E (Z) = 0 and SD (Z) = 1

Step-by-step explanation:

The time of the finishers in the New York City 10 km run are normally distributed with a mean,μ = 61 minutes and a standard deviation, σ = 9 minutes.

(a)

The random variable X is defined as the finishing time for the finishers.

Then the expected value of X is:

E (X) = 61 minutes

The variance of the random variable X is:

V (X) = (9 minutes)²

Then the standard deviation of the random variable X is:

SD (X) = 9 minutes

(b)

The random variable Z is the standardized form of the random variable X.

It is defined as: $Z=\frac{X-\mu}{\sigma}$

Compute the expected value of Z as follows:

$E(Z)=E[\frac{X-\mu}{\sigma}]\\=\frac{E(X)-\mu}{\sigma}\\=\frac{61-61}{9}\\=0$

The mean of Z is 0.

Compute the variance of Z as follows:

$V(Z)=V[\frac{X-\mu}{\sigma}]\\=\frac{V(X)+V(\mu)}{\sigma^{2}}\\=\frac{V(X)}{\sigma^{2}}\\=\frac{9^{2}}{9^{2}}\\=1$

The variance of Z is 1.

So the standard deviation is 1.

8 0

2 years ago

The epicenter of an earthquake is the point on Earth’s surface directly above the earthquake’s origin. A seismograph can be used

DaniilM [7]

Answer:

I used desmos and plotted all three circles. The point that hey all intersected was (-1, 3).

Step-by-step explanation:

5 0

2 years ago