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andrezito [222]
2 years ago
15

Jared bought a Suzuki 1000 for $12,698. If it depreciates at a rate of 11% per year, how much will it be worth in 3 years

Mathematics
1 answer:
Serga [27]2 years ago
7 0
Original price = P = $12,698
Depreciation rate = r = 11% = 0.11
Time in years = t = 3
New price = A

The formula used will be:

A=P(1-r)^{t}

Using the values, we get:

A=12698(1-0.11)^{3}=8951.70

Thus, the worth of Suzuki after 3 years will be $8951.70
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The equation tan^2 x+1=sec^2 x is an identity true or false
Solnce55 [7]

Answer:

tan²x + 1 = sec²x is identity

Step-by-step explanation:

* Lets explain how to find this identity

∵ sin²x + cos²x = 1 ⇒ identity

- Divide both sides by cos²x

∵ sin x ÷ cos x = tan x

∴ sin²x ÷ cos²x = tan²x

- Lets find the second term

∵ cos²x ÷ cos²x = 1

- Remember that the inverse of cos x is sec x

∵ sec x = 1/cos x

∴ sec²x = 1/cos²x

- Lets write the equation

∴ tan²x + 1 = 1/cos²x

∵ 1/cos²x = sec²x

∴ than²x + 1 = sec²x

- So we use the first identity sin²x + cos²x = 1 to prove that

 tan²x + 1 = sec²x

∴ tan²x + 1 = sec²x is identity

8 0
3 years ago
Problem Situation: Ben buys a table for $240. He also buys 6 chairs that all cost the same amount. His total cost is $720. What
butalik [34]

Answer:

80 Dollars per chair

Step-by-step explanation:

Step One:

Subtract 720 by (-) 240

this should give you, 480

Step Two:

Divide 480 by 6

Which gives you your answer 80

5 0
2 years ago
The national mean annual salary for a school administrator is $90,00 a year (The Cincinnati Enquirer, April 7, 2012). A school o
timurjin [86]

Answer:

a) Null hypothesis:\mu = 90000  

Alternative hypothesis:\mu \neq 90000  

b) p_v =2*P(t_{(24)}  

c) If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

Step-by-step explanation:

1) Data given and notation  

77600 ,76000 ,90700 ,97200 ,90700 ,101800 ,78700 ,81300 ,84200 ,97600 ,

77500 ,75700 ,89400 ,84300 ,78700 ,84600 ,87700 ,103400 ,83800 ,101300

94700 ,69200 ,95400 ,61500 ,68800

We can calculate the sample mean and deviation with the following formulas:

\bar X =\frac{\sum_{i=1}^n X_i}{n}

s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

The values obtained are:

\bar X=85272 represent the mean annual salary for the sample  

s=11039.23 represent the sample standard deviation for the sample  

n=25 sample size  

\mu_o =90000 represent the value that we want to test

\alpha=0.05 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

Part a: State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean salary differs from 90000, the system of hypothesis would be:  

Null hypothesis:\mu = 90000  

Alternative hypothesis:\mu \neq 90000  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Part b: Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{85272-90000}{\frac{11039.23}{\sqrt{25}}}=-2.141    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=25-1=24  

Since is a two sided test the p value would be:  

p_v =2*P(t_{(24)}  

Part c: Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean for the salary differs from 9000 at 5% of significance.

6 0
3 years ago
9x + 8y3 – 7 = 3y3 -3<br> 9x+ 5y = 0
Vikki [24]

Answer:

102 actually just add it up

Step-by-step explanation:

add it up

5 0
3 years ago
Find the equation of the line through (-9,6) that is perpendicular to the line through (7,8),
Setler [38]

Step-by-step explanation:

I assume as "equation" we mean the slope-intercept form :

y = ax + b

"a" is the slope of the line (y coordinate change / x coordinate change when going from one point to another on the line). b is the y-intercept (the y value when x = 0).

we get the slope by finding the perpendicular slope of the first line.

the slope of the first line when going from (-3, -9) to (7, 8) :

x changes by + 10 (from -3 to +7).

y changes by + 17 (from -9 to +8).

so, that slope is 17/10.

the perpendicular slope is turning the original slope upside-down and flips the sign :

-10/17

so, a = -10/17

now, as we have only the slope and a point of the new line, we can use the point-slope form to stay and then transfer into the slope-intercept form.

y - y1 = a(x - x1)

where "a" is again the slope, and (x1, y1) is a point on the line

y - -6 = -10/17 × (x - -9)

y + 6 = -10/17 × (x + 9) = -10/17 × x - 90/17

y = -10/17 × x - 90/17 - 6 =

= -10/17 × x - 90/17 - 102/17 =

= -10/17 × x - 192/17

so, the equation is (in a maybe nicer way)

y = -1/17 × (10x + 192)

7 0
1 year ago
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