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timurjin [86]
2 years ago
11

Natasha is a bank teller. She received a 5% raise last year and a subsequent merit raise of 3% this year. What is the accumulati

ve or compound effect of these two raises as a percentage? Use the 1+ track of the last nine lines of Section 3.5 of the text and do not round.
(a) 8% (b) 15% (c) 8.15% (d) 0.15% (e) 2% (f) none of the above
Mathematics
1 answer:
Anvisha [2.4K]2 years ago
8 0

Answer:

The correct answer is C. 8.15%.

Step-by-step explanation:

Given that Natasha is a bank teller, and she received a 5% raise last year and a subsequent merit raise of 3% this year, to determine what is the accumulative or compound effect of these two raises as a percentage, the following calculation must be performed, assuming, as an example, that her starting salary was $ 2,000:

(2,000 x 1.05) x 1.03 = X

2,100 x 1.03 = X

2,163 = X

2,000 = 100

2,163 = X

2,163 x 100 / 2,000 = X

216,300 / 2,000 = X

108.15 = X

108.15 - 100 = 8.15

Thus, the compound effect of both salary increases is a salary increase of 8.15%.

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An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial co
Blizzard [7]

Answer:

(a) C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2

    p(x)=320-7.7p

    R(x)=(320-7.7p)p=320p-7.7p^2

(b) x=82 \text{planes}

(c) p=\$30.91 M\;\; \text{per plane}

(d) maximum profit =\$ 15.90M

Step-by-step explanation:

Given that,

The company estimates that the initial cost of designing the aeroplane and setting up the factories in which to build it will be 500 million dollars.

The additional cost of manufacturing each plane can be modelled by the function.

m(x)=20x-5x^{\frac{3}{4}}+0.01x^2

(a)  Find the cost, demand (or price), and revenue functions.

   C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2

   p(x)=320-7.7p

   R(x)=(320-7.7p)p=320p-7.7p^2

(b)  Find the production level that maximizes profit.

    f=R(x)-C(x)

 \Rightarrow f=320p-7.7p^2-(500+20x-5x^{\frac{3}{4}}+0.01x^2)

\Rightarrow df=320dp-15.4pdp-20dx+5(\frac{3}{4} )x^{\frac{-1}{4} }dx-0.02xdx

     x=320-7.7p

     p=\frac{320-x}{7.7}

    \frac{dp}{dx} = \frac{-1}{7.7}

\frac{df}{dx}=\frac{320}{-7.7} -\frac{15.4(320-x) }{7.7(\frac{-1}{7.7} )}-20+5\frac{3}{4} x^{\frac{-1}{4}} -0.02x=0

    \Rightarrow -41.5584+83.1169-0.2597x-20+3.75x^{\frac{-1}{4} }-0.02x=0

   \Rightarrow 21.5585+3.75x^{\frac{-1}{4} }-0.279x=0

   \Rightarrow x=82 \text{planes}

(c)  Find the associated selling price of the aircraft that maximizes profit.

  p=\frac{320-82}{7.7}

\Rightarrow p=\$30.91 M\;\; \text{per plane}

(d)  Find the maximum profit.

Manufacturing cost of one plane is:

m(1)=20-5+0.01

         =\$15.01 M

maximum profit =\$(30.91-15.01)M

                           =\$15.90M

3 0
2 years ago
Can someone plz help me with this one problem plzzzzz I’m marking brainliest!!!
Andre45 [30]
2=6
4=8
6=10
8=12
I added +4 for each
8 0
2 years ago
X + 2y = 7<br> 3x - 2y = -3
VladimirAG [237]
Use Subtraction

1. Subtract
x+2y=7
3x-2y=-3
-------------
4x+0y=4 SIMPLIFY 4x=4

2. DIVIDE

4x=4
x=1

Substitute that into either of the original equations to get x=1, y=3





4 0
3 years ago
Sameen bought 2 1/5 pounds of carrots for $6.60. At that rate, how much would 1 pound of carrots cost?
Vanyuwa [196]

Answer:

3$

Step-by-step explanation:

4 0
2 years ago
What is a relative frequency?
SVETLANKA909090 [29]

Answer:

"A relative frequency distribution is a table that shows the relative frequency for all categories as shown below. Notice that the sum of the relative frequencies is always equal to 1. The percentage of a category is found by multiplying the relative frequency of that category by 100."

Credits To: statistics-made-easy.com › what-is-relative-frequency

4 0
2 years ago
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