A sailboat depreciates at 15% of its original value each year. If the sailboat was $9500 at its time of purchase, what is the value of the sailboat after 7 years?

Answers

Answer 1

Answer: The sailboat would be fully depreciated when the 7th year comes when it was depreciated 15% every year. This is because when you try to multiply 15% by 7 it would give you 105%, it already exceeds the 100% value of the sailboat.

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Please explain each step 5x-7=7x-17

Answers

Let's get the same terms on the same side.
I am going to remove 5x from both sides of the equation by subtracting 5x

5x - 5x -7 = 7x -5x - 17
-7 = 2x - 17 now lets remove the 17 from both sides
-7 + 17 = 2x (why do we add 17? Think of 2x -17 as 2x + -17. Tor remove a negative number we add it.
Now we finally have 10=2x and if we divide both sides by 2

10 = 2x
2 2 we get that x = 5
Let's check by substituting 5 in the original equation:
5(5) - 7 = 7(5) - 17
25 - 7 = 35 - 17
18 = 18

A cup of coffee at 181 degrees is poured into a mug and left in a room at 66 degrees. After 6 minutes, the coffee is 139 degrees. Assume that the differential equation describing Newton's Law of Cooling is (in this case) dT/dt=k(T-66).1) What is the temperature of the coffee after 16 minutes?
2) After how many minutes will the coffee be 100 degrees?

Answers

The temperature of the coffee after 16 minutes is 134 degrees and after 1.3 minutes the coffee be 100 degrees.

What is Differential equation?

A differential equation is an equation that contains one or more functions with its derivatives.

A cup of coffee at 181 degrees is poured into a mug and left in a room at 66 degrees.

After 6 minutes, the coffee is 139 degrees.

Assume that the differential equation describing Newton's Law of Cooling is (in this case) dT/dt=k(T-66).

T=∫k(t-66)dt

=k(t²/2-66)+c

When t=0 and T=181

181=k(0-66)+c

181=-66k+c

when t=6, T=139

139=k(6²/2-66)+c

139=-48k+c

-42=-18k

Divide both sides by 18

k=7/3

139=-48×7/3+c

c=139+112=251

T=7/3(t-66)+251

The temperature of the coffee after 16 minutes

T=7/3(16-66)+251

T=7/3(-50)+251

T=134 degrees

After how many minutes will the coffee be 100 degrees

100=7/3(t-66)+251

100=7/3t-7/3(66)+251

100=7/3t-154+251

100=7/3t+97

100-97=7/3t

3=7/3t

9/7=t

1.3=t

Hence, the temperature of the coffee after 16 minutes is 134 degrees and after 1.3 minutes the coffee be 100 degrees.

To learn more on Differentiation click:

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Answer:

Step-by-step explanation:

$(dT)/(dt) =k(t-66)\nT=\int\ {k(t-66)} \, dt=K((t^2)/(2) -66)+c\nwhen t=0,T=181\n181=K(0-66)+c\n181=-66k+c\nwhen t=6,T=139\n139=k((6^2)/(2) -66)+c\n139=-48k+c\n181-139=-66k+48k\n-42=-18k\n7=3k\nk=(7)/(3) \n139=-48*(7)/(3) +c\nc=139+112=251\nT=(7)/(3) (t-66)+251\nnow complete the question$

Simply this expression 4(-8x + 5) – (-33x – 26) = totally lost on this one can someone please help me :) and please explain how you figured this out

Answers

Simplifying 4(-8x + 5) + -1(-33x + -26) = 0 Reorder the terms: 4(5 + -8x) + -1(-33x + -26) = 0 (5 * 4 + -8x * 4) + -1(-33x + -26) = 0 (20 + -32x) + -1(-33x + -26) = 0 Reorder the terms: 20 + -32x + -1(-26 + -33x) = 0 20 + -32x + (-26 * -1 + -33x * -1) = 0 20 + -32x + (26 + 33x) = 0 Reorder the terms: 20 + 26 + -32x + 33x = 0 Combine like terms: 20 + 26 = 46 46 + -32x + 33x = 0 Combine like terms: -32x + 33x = 1x 46 + 1x = 0 Solving 46 + 1x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-46' to each side of the equation. 46 + -46 + 1x = 0 + -46 Combine like terms: 46 + -46 = 0 0 + 1x = 0 + -46 1x = 0 + -46 Combine like terms: 0 + -46 = -46 1x = -46 Divide each side by '1'. x = -46 Simplifying x = -46

Which value of a correlation coefficient represents the strongest relationship between the two variables in a given linear regression model? a) -0.94
b) 0
c) 0.5
d) 0.91

Answers

Answer: a) -0.94

Explanation:

The closer r gets to +1 or -1, the stronger the linear relationship will be.

If r is really close to +1, then we have a strong positive linear relationship. If r is close to -1, then we have a strong negative linear relationship.

Of the four choices given, we see that r = -0.94 is the closest to either endpoint mentioned. The next closest is r = 0.91

Put another way, we're looking for the r value that is furthest way from 0, but also that makes the inequality $-1 \le r \le 1$ true. Choice A fits that description best.

Final answer:

The value of -0.94 represents the strongest relationship between the two variables in a given linear regression model.

Explanation:

The value of a correlation coefficient ranges from -1 to 1. The closer the value is to -1 or 1, the stronger the relationship between the two variables in a linear regression model. Therefore, the value of "-0.94" represents the strongest relationship among the given options. A negative correlation coefficient indicates an inverse relationship, meaning that as one variable increases, the other variable decreases.