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3 years ago

Let g(x) = 4x - 20 and h(x) = -1/2x + k. For what value of k is the zero of h(x) equivalent to the zero of g(x)

Mathematics

1 answer:

uranmaximum [27]3 years ago

8 0

Answer:

Step-by-step explanation:

The zero of a function is also known as the x-intercept of a function. The x-intercept of a function exists where y = 0. So we will begin by setting each of those lines = 0:

4x - 20 = 0 and -1/2x + k = 0 and then solve each for x:

4x = 20 so

x = 5 and

-1/2x = -k and

1/2x = k so

x = 2k. Now we set the 2 x expressions equal to each other and solve for k:

5 = 2k so

k = 5/2

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2 years ago

The temperature was 75° Fahrenheit. The temperature dropped at a rate of 10° per hour.

Zigmanuir [339]

Answer:

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Step-by-step explanation:

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3 years ago

A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard devi

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Answer:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

Step-by-step explanation:

Data given and notation

$\bar X=3.4$ represent the sample mean

$\sigma=0.4$ represent the population deviation for the sample

$n=50$ sample size

$\mu_o =3.3$ represent the value that we want to test

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

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the mean is higher than 3.3, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.3$

Alternative hypothesis: $\mu > 3.3$

Compute the test statistic

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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".

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

$z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768$

P value

Since is a one right tailed test the p value would be:

$p_v =P(z>1.768)=0.039$

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