Evaluate - 2/3 x for x = 3/4

Write an exponential equation in the form y = abx whose graph passes through points (−3, 24) and (−2, 12). y = 3x y = 3(0.5)x y

Bingel [31]

Answer:

Option B.

Step-by-step explanation:

The given exponential equation is

$y=ab^x$ ...(1)

It is given that the graph of above equation passes through points (−3, 24) and (−2, 12).

The graph passes through the point (-3,24), so substitute x=-3 and y=24 in equation (1).

$24=ab^{-3}$ ...(2)

The graph passes through the point (-2,12), so substitute x=-2 and y=12 in equation (1).

$12=ab^{-2}$ ...(3)

Divide equation (3) by equation (2).

$\dfrac{12}{24}=\dfrac{ab^{-2}}{ab^{-3}}$

$0.5=b$

Substitute b=0.5 in equation (2).

$24=a(0.5)^{-3}$

$24=\dfrac{a}{(0.5)^{3}}$

$24=\dfrac{a}{0.125}$

$24\times 0.125=a$

$3=a$

Substitute a=3 and b=0.5 in equation (1).

$y=3(0.5)^x$

Therefore, the correct option is B.

8 0

3 years ago

A medical researcher wishes to investigate the relationship between hours exercised and weight lost. The researcher randomly sam

nataly862011 [7]

Answer:

The researcher will conclude that there is a correlation between the number of hours worked out and the amount of pounds lost by people on the exercise program

Step-by-step explanation:

Here, we want to state what the conclusion of the researcher should be:

From the last part of the question, we can see that the test statistic is greater than the critical value

So what do we do in a case like this?

We can see that the researcher is trying to see if there is a correlation between hours worked out and the number of pounds lost over a specific period of time.

Now, let us form the null hypothesis;

The null hypothesis here H0 is that we do not have a correlation between number of hours spent working out and the amount of pounds lost

The alternative hypothesis here H1 is that there is a correlation between the number of hours spent working out and the amount of pounds lost

Since we have the value of the test statistic greater than the critical value, we reject the null hypothesis and accept the alternative hypothesis

So therefore, the researcher will conclude that there is a correlation between the number of hours worked out and the amount of pounds lost by people on the exercise program

3 0

3 years ago

What size pizza should she order to get 37.68in of crust?

Alex17521 [72]

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