If x = (1,2,3), y = (1,3,6,9,12)

If a point is reflected over the x-axis, the x-coordinate will not change. True False

leva [86]

The answer is true because only the y coordinate will change.

7 0

3 years ago

The population of coyotes in the northwestern portion of Alabama is given by the formula p (t )equals (t squared plus 100 )ln (t

elena-14-01-66 [18.8K]

Answer:

The rate of change of the Coyote population in 2002 is 32

Step-by-step explanation:

Given the formula for the population of a Coyotes in the Northwestern portion of Alabama, we are to calculate rate of change of the Coyote population in the year 2002 where t = 2

The formula is given as;

P(t) = (t^2 + 100) ln (t + 2)

The rate of change refers to the first integral of the formula;

Thus we need to calculate this by the use of product formula;

The first differential of t^2 + 100 is 2t

while that of ln(t + 2) is 1/(t + 2)

P’(t) = 2t(ln (t+2)) + (t^2 + 100) (1/t+2)

Now, we substitute 2 for the value of t here.

P’(2) = 2(2)( ln (2 + 2) + (2^2 + 100)(1/(2+2))

P’(2) = 4 ln 4 + 104(1/4)

P’(2) = 4ln 4 + 26

P’(2) = 5.55 + 26 = 31.55 which is approximately 32

8 0

3 years ago

An actor invests some money at 7%, and $24000 more than four times the amount at 8%. The total annual interest earned from the i

natita [175]

Answer:

$70,000 at 7%
$304,000 at 8%

Step-by-step explanation:

Given:

Total interest earned on two investments is $29,220.

An amount is invested at 7%.

$24,000 more than 4 times that amount is invested at 8%.

Find:

The amount invested at each rate.

Solution:

Our strategy will be to define a variable representing the amount invested at 7%, use that variable to write an expression for the amount invested at 8%, then write an equation for the total return on the investments.

Let x represent the amount invested at 7%. Then (24,000+4x) will be the amount invested at 8%. The total interest earned will be ...

interest on 7% account + interest on 8% account = total interest

0.07x + 0.08(24000+4x) = 29220

0.39x + 1920 = 29220 . . . . . . . . . . . simplify

0.39x = 27300 . . . . . . . . . . . . . . . . . .subtract 1920

x = 27300/0.39 = 70000 . . . . . . . . . divide by the coefficient of x

24,000 +4x = 24,000 +280,000 = 304,000 . . . . amount invested at 8%

He invested $70,000 at 7% and $304,000 at 8%.

Check

The answer must satisfy ...

7% interest + 8% interest = 29,220

0.07×70,000 +0.08×304,000 = 4,900 +24,320 = 29,220 . . . . as required

_____

Comment on 6-step method

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Identify the given information (Given)
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Explain why the answer makes sense (Check)

6 0

3 years ago

Rachel has a box in the shape of a prism with a square base. The capacity of the box is 150 cubic inches. The height of the box

hjlf

V = s²h

150 = s²h 
150 = s²(3/2)s 
(2/3)150 = s³ 
100 = s³ 
s = ∛100 (approx 4.642 in)

6 0

3 years ago

Shirley has a credit card that uses the previous balance method. The opening

vesna_86 [32]

Answer:

= $44.19

Step-by-step explanation:

APR = 19%

Billing cycle = 30 days

Balance = $2830

Let's first find the daily rate,

Daily rate = $\frac{0.19}{365} = 0.000521$

The daily rate = 0.000521

To calculate the amount Shirley was charged interest for the billing cycle, we use:

Daily rate * billing cycle * balance

Where,

Daily rate

= $\frac{0.19}{365}$

Billing cycle = 30 days

Balance = $2830

Therefore, expression to be used =

$(\frac{0.19}{365} * 30) * 2830 \\= $44.19$

8 0

3 years ago

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