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prisoha [69]
2 years ago
9

Harmony earns a \$42{,}000$42,000dollar sign, 42, comma, 000 salary in the first year of her career. Each year, she gets a 4\%4%

4, percent raise.
Which expression gives the total amount Harmony has earned in her first nnn years of her career?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
42{,}000\left(\dfrac{1-0.04^n}{0.96}\right)42,000(
0.96
1−0.04
n

​
)42, comma, 000, left parenthesis, start fraction, 1, minus, 0, point, 04, start superscript, n, end superscript, divided by, 0, point, 96, end fraction, right parenthesis

(Choice B)
B
42{,}000\left(\dfrac{1-1.04^n}{-0.04}\right)42,000(
−0.04
1−1.04
n

​
)42, comma, 000, left parenthesis, start fraction, 1, minus, 1, point, 04, start superscript, n, end superscript, divided by, minus, 0, point, 04, end fraction, right parenthesis

(Choice C)
C
42{,}000\left(\dfrac{1-1.04^n}{0.96}\right)42,000(
0.96
1−1.04
n

​
)42, comma, 000, left parenthesis, start fraction, 1, minus, 1, point, 04, start superscript, n, end superscript, divided by, 0, point, 96, end fraction, right parenthesis

(Choice D)
D
42{,}000\left(\dfrac{1-0.96^n}{-0.04}\right)42,000(
−0.04
1−0.96
n

​
)
Mathematics
1 answer:
grandymaker [24]2 years ago
6 0

Answer:

A=42000(1.04)^n

Step-by-step explanation:

This is a compound interest formula expressed as:

A=P(1+i)^n

Where:

  • n is time in years
  • i is the rate of interest
  • A is the accumulated amount after n years
  • P is the initial amount.

#We substitute the given values to determine amount after n years as follows:

A=P(1+i)^n\\\\=42000(1+0.04)^n\\\\=42000(1.04)^n

Hence, the amount earned after n years is given by the expression A=42000(1.04)^n

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A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for t
hoa [83]

Answer:

Since p value <0.1 accept the claim that oven I repair costs are more

Step-by-step explanation:

The data given for two types of ovens are summarised below:

Group   Group One     Group Two  

Mean 85.7900 78.6700

SD 15.1300 17.8400

SEM 1.9533 2.3840

N 60       56      

Alpha = 10%

H_0: \mu_1 - \mu_2 =0\\H_a: \mu_1 - \mu_2> 0

(Right tailed test)

The mean of Group One minus Group Two equals 7.1200

df = 114

 standard error of difference = 3.065

 t = 2.3234

p value = 0.0219

If p value <0.10 reject null hypothesis

4) Since p value <0.1 accept the claim that oven I repair costs are more

 

3 0
2 years ago
f1(x) = ex, f2(x) = e−x, f3(x) = sinh(x) g(x) = c1f1(x) + c2f2(x) + c3f3(x) Solve for c1, c2, and c3 so that g(x) = 0 on the int
eimsori [14]

Answer:

(C1, C2, C3) = (K, K, -2K)

For K in the interval (-∞, ∞)

Step-by-step explanation:

Given

f1(x) = e^x

f2(x) = e^(-x)

f3(x) = sinh(x)

g(x) = 0

We want to solve for C1, C2 and C3, such that

C1f1(x) + C2f2(x) + C3f3(x) = g(x)

That is

C1e^x + C2e^(-x) + C3sinh(x) = 0

The hyperbolic sine of x, sinh(x), can be written in its exponential form as

sinh(x) = (1/2)(e^x + e^(-x))

So, we can rewrite

C1e^x + C2e^(-x) + C3sinh(x) = 0

as

C1e^x + C2e^(-x) + C3(1/2)(e^x + e^(-x)) = 0

So we have

(C1 + (1/2)C3)e^x + (C2 + (1/2)C3)e^(-x) = 0

We know that

e^x ≠ 0, and e^(-x) ≠ 0

So we must have

(C1 + (1/2)C3) = 0...........................(1)

and

(C2 + (1/2)C3) = 0..........................(2)

From (1)

2C1 + C3 = 0

=> C3 = -2C1.................................(3)

From (2)

2C2 + C3 = 0

=> C3 = -2C2................................(4)

Comparing (3) and (4)

2C1 = 2C2

=> C2 = C1

Let C1 = C2 = K

C3 = -2K

(C1, C2, C3) = (K, K, -2K)

For K in the interval (-∞, ∞)

3 0
2 years ago
A machine takes 5.4 hours to make 9 parts. At that rate how many parts can the machine make in 25.8 hours
Sliva [168]
\frac{5.4}{9} = \frac{25.8}{x}    Cross multiply.

5.4x=9*25.8

5.4x=232.2    Divide both sides by 5.4

x=43
4 0
2 years ago
Read 2 more answers
How would you choose to reduce the system shown to a 2 × 2? Explain why you would choose this approach. –3x + y – 2z = 10 (1) 5x
gladu [14]
-3x + y - 2z = 10      |* -1
3x  -  y  +2z = -10
5x  -2y -2z =  12 
---------------------------      I add these equations   term by term 
8x  - 3y  = 2 

-3x  + y - 2z =10                       ⇒  -3x  + y   - 2z =10
x     -y    +z = 23         | *2              2x   - 2y + 2z = 46
                                                   -----------------------------  I add these eq.
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8x  - 3y  = 2 
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this is the system after i reduce it ( it has only two variables x and y)




4 0
2 years ago
Read 2 more answers
Poiseuille's Law states that the volume, V, of blood flowing through an artery in a unit of time at a fixed pressure is directly
eimsori [14]

Answer:

11.58%

Step-by-step explanation:

The initial volume if blood flowing through the artery is given by

V=kr^4

To achieve a new volume of 155% (55% increase) of the initial volume, the new radius must be:

V'= 1.55V\\1.55V=k(r')^4\\1.55kr^4 = k(r')^4\\(\sqrt[4]{1.55}*r)^4=(r')^4 \\(1.1158*r)^4=(r')^4 \\r'=1.1158*r

Since the new radius is 1.1158 times larger than the initial radius, the percentage increased is:

I=(1.1158 - 1)*100\%\\I= 11.58\%

7 0
2 years ago
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