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3 years ago

Solve the following: S5 for 600 + 300 + 150 + .

1 answer:

8 0

600 + 300 + 150 + . . . is a geometric sequence with a = 600 and r = 1/2
Sn = a(1 - r^n)/(1 - r)
S5 = 600(1 - (1/2)^5)/(1 - 1/2) = 600(1 - 1/32)/(1/2) = 1,200(31/32) = 1,162.5

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2 years ago

What is 29/5as a mixed number

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5 4/5 is a mixed number of 29/5.

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3 years ago

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Describe the rotation of J

Serga [27]

Answer:

The coordinates of J' when rotating by 90° counterclockwise will be: J'(3, 1)

The coordinates of J' when rotating by 90° clockwise will be: J'(-3, -1)

Step-by-step explanation:

Square JKLM with vertices

J(1, -3)

K(5, 0)

L(8, -4)

M(4, -7)

We have to determine the answer for the image J' of the point (1, -3) when we rotate the point by 90° counterclockwise, we need to switch x and y, make y negative.

In other words, the rule to rotate a point by 90° counterclockwise.

P(x, y) → P'(-y, x)

As we are given that J(1, -3), so the coordinates of J' will be:

J(1, -3) → J'(3, 1)

Therefore, the coordinates of J' when rotating by 90° counterclockwise will be: J'(3, 1).

When the point is rotated by 90° clockwise, we need to switch x and y, make x negative.

In other words, the rule to rotate a point by 90° clockwise.

P(x, y) → P'(y, -x)

As we are given that J(1, -3), so the coordinates of J' will be:

J(1, -3) → J'(-3, -1)

Therefore, the coordinates of J' when rotating by 90° clockwise will be: J'(-3, -1)

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3 years ago

According to data from a medical association, the rate of change in the number of hospital outpatient visits, in millions, in

GaryK [48]

Answer:

a) $f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000$

b) f(t=2015) = 264,034,317.7

Step-by-step explanation:

The rate of change in the number of hospital outpatient visits, in millions, is given by:

$f'(t)=0.001155t(t-1980)^{0.5}$

a) To find the function f(t) you integrate f(t):

$\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt$

To solve the integral you use:

$\int udv=uv-\int vdu\\\\u=t\\\\du=dt\\\\dv=(t-1980)^{1/2}dt\\\\v=\frac{2}{3}(t-1980)^{3/2}$

Next, you replace in the integral:

$\int t(t-1980)^{1/2}=t(\frac{2}{3}(t-1980)^{3/2})- \frac{2}{3}\int(t-1980)^{3/2}dt\\\\= \frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}+C$

Then, the function f(t) is:

$f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'$

The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient visits.

Hence C' = 264,034,000

The function is:

$f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000$

b) For t = 2015 you have:

$f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7$

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3 years ago

If a = 4 and b = 7, what is the value of the following expression? 20 ÷ a + 7 • b A. 28 B. 84 C. 54 D. 33

expeople1 [14]

Answer:

Step-by-step explanation:

20 ÷ a + 7 • b

Let a = 4 and b = 7

20 ÷ 4 + 7 • 7

Multiply and divide first

5 + 49

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3 years ago

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