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Readme [11.4K]
3 years ago
7

During the first year, ABC's stock price starts at $ \$100 $ and increases $ 100\% $. During the second year, its stock price go

es down $ 25\% $ from its price at the end of the first year. What is the price of the stock, in dollars, at the end of the second year?
Mathematics
2 answers:
Artemon [7]3 years ago
6 0

Answer:

Step-by-step explanation:

During the first year, ABC's stock price starts at $100 and increases by 100%. This means that the amount by which the stock increased would be

100/100 × 100 = $100

The new price of the stock would be 100 + 100 = $200

During the second year, its stock price goes down 25% from its price at the end of the first year. This means that the amount by which the stock reduced is

25/100 × 200 = 0.25 × 200 = $50

Therefore, the price of the stock, in dollars, at the end of the second year is

200 - 50 = $150

Reil [10]3 years ago
6 0

Answer:

150

Step-by-step explanation:

In the first year, the price doubles. This happens because 100% of 100 is 100, so 100+100 is 200, which is also 100 multiplied by 2. 25/100 which is 25%, multiplied by 200, is 50. So the answer is 200-50 which equals 150.

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defon
\begin{gathered} x^2+24=14x \\ x^2-14x+24=0 \end{gathered}

Therefore,

\begin{gathered} x^2-14x+24=0 \\ x^2-2x-12x+24=0 \\ x(x-2)-12(x-2)=0 \\ (x-2)(x-12)=0 \\ x=2 \\ or\text{ } \\ x=12 \end{gathered}

6 0
1 year ago
Which equation represents an exponential function that passes through the point (2, 80)?
Lena [83]

The function f(x) = 5(x)⁴, and f(x) = 5(4)ˣ represents the function that passes through the point (2, 80) option second and fourth are correct.

<h3>What is an exponential function?</h3>

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent \rm y = a^x

where a is a constant and a>1

We have; an exponential function that passes through the point (2, 80).

f(x) = 4(x)⁵

Plug (2, 80) in the abovew function:

f(2) = 4(2)⁵ = 128 (false)

f(x) = 5(x)⁴

Plug (2, 80) in the abovew function:

f(2) = 5(2)⁴ = 80 (true)

f(x) = 4(5)ˣ

f(2) = 4(5)² = 100 (false)

f(x) = 5(4)ˣ

f(2) = 5(4)² = 80 (true)

Thus, the function f(x) = 5(x)⁴, and f(x) = 5(4)ˣ represents the function that passes through the point (2, 80) option second and fourth are correct.

Learn more about the exponential function here:

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4 0
2 years ago
Flow meters are installed in urban sewer systems to measure the flows through the pipes. In dry weatherconditions (no rain) the
ziro4ka [17]

Answer:

a) \frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}

363.90 \leq \sigma^2 \leq 4430.80

Now we just take square root on both sides of the interval and we got:

19.08 \leq \sigma \leq 66.56

b) For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

Step-by-step explanation:

423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0

Part a

The confidence interval for the population variance is given by the following formula:

\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}

On this case we need to find the sample standard deviation with the following formula:

s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}&#10;And in order to find the sample mean we just need to use this formula:&#10;[tex]\bar x =\frac{\sum_{i=1}^n x_i}{n}

The sample deviation for this case is s=30.23

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=9-1=8

The Confidence interval is 0.98 or 98%, the value of \alpha=0.02 and \alpha/2 =0.01, and the critical values are:

\chi^2_{\alpha/2}=20.09

\chi^2_{1- \alpha/2}=1.65

And replacing into the formula for the interval we got:

\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}

363.90 \leq \sigma^2 \leq 4430.80

Now we just take square root on both sides of the interval and we got:

19.08 \leq \sigma \leq 66.56

Part b

For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

4 0
3 years ago
Jackson used the process of completing the square to solve the equation 2x2−12x=−6.
Nikolay [14]

Answer:

x=3-\sqrt{6},x=3+\sqrt{6}

Step-by-step explanation:

we are given equation as

2x^2-12x=-6

Since, we have to solve it by using complete square

so, firstly we will complete square

and then we can solve for x

step-1:

Factor 2 from both sides

2(x^2-6x)=-3\times 2

step-2:

Simplify it

x^2-6x=-3

step-3:

Add both sides 3^2

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now, we can complete square

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step-4:

Take sqrt both sides

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step-5:

Add both sides by 3

we get

x=3-\sqrt{6},x=3+\sqrt{6}


3 0
3 years ago
50 m decreased by 10%
Usimov [2.4K]

Answer:

45 meters

Step-by-step explanation:

because 10% of 50 is 5, you subtract 5 from 50;

50-5=45

6 0
3 years ago
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