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11Alexandr11 [23.1K]

2 years ago

6

Terry invested money in a biotech stock whose growth is modeled by the function f(x) = 0.01(2)x, where x represents number of da

ys. Find the approximate average rate of change from day 2 to day 10.

2 answers:

Luden [163]2 years ago

8 0

Answer:

The average rate of change is 1.275

strojnjashka [21]2 years ago

3 0

Answer:

The average rate of change is 1.275

Step-by-step explanation:

The average rate of change of f(x) from x=a to x=b is given by:

$\frac{f(b)-f(a)}{b-a}$

The money Terry invested is modeled by the function $f(x)=0.01(2)^x$ where x represents number of days.

The average rate of change from day 2 to day 10 is given by:

$\frac{f(10)-f(2)}{10-2}$

$f(10)=0.01(2)^{10}=10.24$

$f(2)=0.01(2)^{2}=0.04$

The average rate of change becomes:

$\frac{10.24-0.04}{8}$

$=\frac{10.2}{8}=1.275$

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2 years ago

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An artist cuts 4 squares with sides of length x ft from the corners of a 12 ft-by-18 ft rectangular piece of sheet metal. She be

ehidna [41]

Answer:

$V = 216x - 60x^2 + 4x^3$

Step-by-step explanation:

The volume V of the fountain is equal to:

V = L*W*h

Where L is the lenght of the fountain, W is the width of the fountain and h is the high of the fountain

We already know that h is equal to x. On the other hand, if we cut a square with side of length x, L and W are calculated as:

L = 18 - 2x

W = 12 - 2x

So, replacing L, W and h on the equation of the volume, we get:

V = (18-2x)*(12-2x)*x

Finally, simplifying the function we get:

$V = ((18*12)+(18*(-2x))+(-2x*12)+((-2x)*(-2x)))*x$

$V = (216-36x-24x+4x^2)*x\\V = (216-60x+4x^2)*x\\V = 216x - 60x^2 + 4x^3$

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2 years ago

Lila wrote an equation of the cost for printing brochures, where x represents the number of brochures and y represents the total

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Answer:

The answer is C. Lila made an error in Step 3 when she did not use the x- and y-coordinates from the same ordered pair.

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Given the point (-3, 6) and a line y=2x-8, write an equation of a line through the point and parallel to the line.

ch4aika [34]

Answer: y = 2x

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y = 2x - 8

Comparing with the slope intercept form, slope = 2

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (- 3,-6) is 2

To determine the intercept, we would substitute m = 2, x = - 3 and

y = - 6 into y = mx + c. It becomes

- 6 = 2 × - 3 + c

- 6 = - 6 + c

c = - 6 + 6 = 0

The equation becomes

y = 2x

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2 years ago

Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by model

Ann [662]

Answer:

(1) The degrees of freedom for unequal variance test is (14, 11).

(2) The decision rule for the 0.01 significance level is;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.

(3) The value of the test statistic is 0.3796.

Step-by-step explanation:

We are given that you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne's attire with those of Calvin Klein.

The following is the amount ($000) earned per month by a sample of 15 Claiborne models;

$3.5, $5.1, $5.2, $3.6, $5.0, $3.4, $5.3, $6.5, $4.8, $6.3, $5.8, $4.5, $6.3, $4.9, $4.2 .

The following is the amount ($000) earned by a sample of 12 Klein models;

$4.1, $2.5, $1.2, $3.5, $5.1, $2.3, $6.1, $1.2, $1.5, $1.3, $1.8, $2.1.

(1) As we know that for the unequal variance test, we use F-test. The degrees of freedom for the F-test is given by;

$\text{F}_(_n__1-1, n_2-1_)$

Here, $n_1$ = sample of 15 Claiborne models

$n_2$ = sample of 12 Klein models

So, the degrees of freedom = ( $n_1-1, n_2-1$ ) = (15 - 1, 12 - 1) = (14, 11)

(2) The decision rule for 0.01 significance level is given by;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.

(3) The test statistics that will be used here is F-test which is given by;

T.S. = $\frac{s_1^{2} }{s_2^{2} } \times \frac{\sigma_2^{2} }{\sigma_1^{2} }$ ~ $\text{F}_(_n__1-1, n_2-1_)$

where, $s_1^{2}$ = sample variance of the Claiborne models data = $\frac{\sum (X_i-\bar X)^{2} }{n_1-1}$ = 1.007

$s_2^{2}$ = sample variance of the Klein models data = $\frac{\sum (X_i-\bar X)^{2} }{n_2-1}$ = 2.653

So, the test statistics = $\frac{1.007}{2.653 } \times 1$ ~ $\text{F}_(_1_4,_1_1_)$

= 0.3796

Hence, the value of the test statistic is 0.3796.

3 0

2 years ago