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3 years ago

Which statements are true?

Mathematics

1 answer:

geniusboy [140]3 years ago

7 0

Answer:

Step-by-step explanation:

Consider the rule

−

or All Slow Turtles Crawl for this type of problem.

Both of these rules indicate in which quadrant the trigonometric function is positive. In all quadrants except the first, only 1 out of the three trigonometric functions are positive; the other two are negative.

Quadrant 1: All are positive

Quadrant 2: Sine is positive

Quadrant 3: Tangent is positive

Quadrant 4: Cosine is positive

The acronym and the expression mentioned above are meant to facilitate your ability to remember these. Beware, though that C-A-S-T starts in the 4th quadrant and then goes to the 1st, 2nd and finally the 3rd, while "All Slow Turtles Crawl# goes from 1st to 4th.

Now, back to the problem at hand.

If cosine is positive, then we are already limited to 2 quadrants: IV and I. However, in quadrant I, all the functions are positive, and the problem says that sin is negative in this case. This leaves us one option: quadrant IV.

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The number of students in a class is 60. The number of boys is seven-fifths the number of girls. Find the number of boys in the

Fynjy0 [20]

Step-by-step explanation:

Let the number of girls = x

Therefore, no. of boys = $\frac{7}{5} \times x$

$\because \: no \: of \: boys + no \: of \: girls \: = 60 \\ \\ \therefore \: \frac{7}{5} x + x = 60 \\ \\ \therefore \: \frac{7x + 5x}{5} = 60 \\ \\ \therefore \: \frac{12x}{5} = 60 \\ \\ \therefore \: x = 60 \times \frac{5}{12} \\ \\ \therefore \: x = 5 \times 5 \\ \\ \therefore \: x = 25 \\ \\ \therefore \: \frac{7}{5} x = \frac{7}{5} \times 25 = 7 \times 5 = 35 \\$

Thus, no of boys in the class is 35.

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3 years ago

A random sample of 180 microbiology students were asked how many science classes he or she was enrolled in August 1990. The resu

frutty [35]

Answer:

$z=\frac{1.83-1.94}{\sqrt{\frac{1.48^2}{180}+\frac{1.62^2}{180}}}}=-0.673$

$p_v =2*P(z$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and a would NOT be a significant difference in the two means

Step-by-step explanation:

Data given and notation

$\bar X_{1}=1.83$ represent the mean in 1990

$\bar X_{2}=1.94$ represent the mean for 2005

$s_{1}=1.48$ represent the sample deviation for 1990

$s_{2}=1.62$ represent the sample standard deviation for 2005

$n_{1}=180$ sample size for 1990

$n_{2}=180$ sample size for 2005

t would represent the statistic (variable of interest)

$\alpha=0.05$ significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different, the system of hypothesis would be:

Null hypothesis: $\mu_{1}=\mu_{2}$

Alternative hypothesis: $\mu_{1} \neq \mu_{2}$

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

$z=\frac{1.83-1.94}{\sqrt{\frac{1.48^2}{180}+\frac{1.62^2}{180}}}}=-0.673$

What is the p-value for this hypothesis test?

Since is a bilateral test the p value would be:

$p_v =2*P(z$

Based on the p-value, what is your conclusion?

8 0

4 years ago

Which statements are true?​

Which statements are true?