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4 years ago

What are the x-intercept and the y-intercept of the graph of y=−3x−18 ? Enter your answers in the boxes.

Mathematics

2 answers:

NeX [460]4 years ago

5 0

Y-intercept:x=0
Y=-3(0)-18
Y=-18

X-intercept:y=0
0=-3x-18
3x÷3=-18÷3
x=-6

Svetlanka [38]4 years ago

3 0

X-intercept (where x=0) is at -18, the y-intercept (where y=0) is -6

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A boat traveling upstream goes 84 kilometers in 7 hours. If the return trip takes only 3 hours, what is the speed (in kilometers

Hunter-Best [27]

Speed = Distance ÷ time

Speed upstream = 84 ÷ 7 = 12 km/h

Speed downstream = 84 ÷ 3 = 28 km/h

Speed in still water = 1/2(28 + 12) = 20 km/h

Answer: 20 km/h

8 0

3 years ago

The probability of flu symptoms for a person not receiving any treatment is 0.038. In a clinical trial of a common drug used to

alexgriva [62]

Answer:

36.32% probability that at least 47 people experience flu symptoms. This is not an unlikely event, so this suggests that flu symptoms are not an adverse reaction to the drug.

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 1164, p = 0.038$

$\mu = E(X) = np = 1164*0.038 = 44.232$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = 6.5231$

Estimate the probability that at least 47 people experience flu symptoms.

Using continuity correction, this is $P(X \geq 47 - 0.5) = P(X \geq 46.5)$ , which is 1 subtracted by the pvalue of Z when X = 46.5.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{46.5 - 44.232}{6.5231}$

$Z = 0.35$

$Z = 0.35$ has a 0.6368

1 - 0.6368 = 0.3632

36.32% probability that at least 47 people experience flu symptoms. This is not an unlikely event, so this suggests that flu symptoms are not an adverse reaction to the drug.

6 0

3 years ago

Consider the function y = -2-3cos (x+pi). What effect does the -2 have on the basic graph

Elenna [48]

ANSWER

-2 shift the graph of the basic function down by 2 units.

EXPLANATION

The given cosine function is:

$y = - 2 - 3 \cos(x + \pi)$