What does A(2,5) become after rotated 360 degrees?

Use the exponential function y=500(.9)^x to find the value of the video game console after 4 years.

zysi [14]

Answer:

328.05 dollars

7 years

Step-by-step explanation:

1.

y=500(.9)^4 =328.05

What is being asked in the problem and what does that mean?

We are asked to the price of the video game after 4 years.

What do I know and what does it mean? What plan am I going to try?

We know the initial price is $500, the value depreciates 10% each year because we have .9 or 90% of the price going into the next year.

- value of the video game after first year 90% of 500 so is 450

- value of the video game after second year 90% of 450 so is 405

-value of the video game after third year 90% of 405 so is 364.5

-value of the video game after fourth year 90% of 364.5 so is 328.05

The plan is to substitute x with 4 and calculate y, y=500(.9)^4

What is your answer and what does it mean?

The answer is $328.05, and it means that the video game that was initially worth $500 it lost its' value by 10 % each of the four years.

2.

y= 500(.9)^x

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x =8, y= 500(0.9)^8 = 215.234 ≈215.23, this is less than $250

x = 7, y= 500(0.9)^7 = 239.148 ≈239.15, this is less than $250

x =6, y= 500(0.9)^6 = 265.721 ≈ 265.72, this is more than $250

What is being asked in the problem and what does that mean?

We are asked to find the value of x that represents the years such that the value of the console is still under $250.

What do I know and what does it mean? What plan am I going to try?

We know the value of y has to be less that $250, we know the inequality

[500(.9)^x ] < 250, the plan is to try different values for x until we have the maximum value of x that gives us less than 250.

8 0

3 years ago

What is the measure of angle A?

I am Lyosha [343]

First you have to find the angle B (check attachment)

$B = 180^{\circ} - 137^{\circ} = 43^{\circ}\\$

Then you can find the last angle inside the triangle, which I'll call C

$C = 180^{\circ} - 102^{\circ} - 43^{\circ} = 35^{\circ}$

Now you can find angle A

$A = 180^{\circ} - C = 180^{\circ} - 35^{\circ} = 145^{\circ}$

3 0

3 years ago

Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable

notsponge [240]

Complete Question

ymposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 129 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use = 0.01.

a. What is the value of the sample test statistic? (Round your answer to two decimal places.)

b. Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer:

a) $Z=2.45$

b) $P Value=0.0073$

Step-by-step explanation:

From the question we are told that:

Probability of Wishart and Leach $P=21.4=>0.214$

Population Size $N=498$

Sample size $n=12$

Therefore

$P'=\frac{129}{498}$

$P'=0.2590$

Generally the Null and Alternative Hypothesis is mathematically given by

$H_0:P=0.214$

$H_a:=P>0.214$

Test Statistics

$Z=\frac{P'-P}{\sqrt{\frac{P(1-P)}{n}}}$

$Z=\frac{0.2590-0.214}{\sqrt{\frac{0.214(1-0.214)}{498}}}$

$Z=2.45$

Therefore P Value is given as

$P Value =P(Z\geq 2.45)$

$P Value =1-P(Z\leq 2.45)$

$P Value =1-0.99268525$

$P Value=0.0073$

7 0

3 years ago

plz i need help with this its due tmrw!! (also my other most recent question is #6 of this and it would be nice for answers for

kipiarov [429]

7. You have $367.50 after two years.

Start by converting 2.5% into a decimal (divide by 100) and multiplying by 350 to find the rate of interest per year.

350(0.025) = 8.75

Since it's for two years, multiply by two.

8.75 x 2 = 17.5.

Add it on to he original, and we have

350 + 17.5 = 367. 5, or $367.50 when converted back to money.

8. The annual interest rate is 2.4%

find the interest rate per year:

120/2.5 = 48 dollars per year. this is the interest amount, we want to find the interest rate. To do this, find what % of 2000 that 48 is equal to.

Set up a system of equations and cross multiply.

$\frac{48}{2000} = \frac{x}{100}$

2000x = 48(100) > 2000x = 4800

2000/2000x = 4800/2000 > x = 2.4

So, the interest rate is 2.4%.

9. the interest paid is $300 after six months, and $600 after a year.

Find the interest rate, similar to problem 7.

3000 x 0.2 = 600. This means the interest paid is $600 a year. In six months, the total will be half, or $300.

10. four years.

Find interest rate.

200(0.035) = $7/year

Remember that value. Subtract needed from current.

228 - 200 = $28.

So, we have an interest rate of $7 a year and we need $28. Normally, we'd solve using an expression, but in this case we can use simple multiplication. Knowing that 7 x 4 = 28, We can decide that it will take four years.

5 0

3 years ago

Simplify and show step by step 30 POINTS!

PIT_PIT [208]

Step-by-step explanation:

the explanation is in the diagram above

4 0

3 years ago