3. Solve the following questions.
(a) x +3 = 5
(b) 2x – 3 = 5

4. Solve the following questions.
(a) - 17 = -10

(b) x+7
___ =13
-2

​

Answer: B - $6,098.35

Step-by-step explanation:

This is a compound interest question. The compound interest formula is:

A = P ( 1 + r/n)^nt

A = Future amount of investment

P = Starting amount of investment

r = Rate of interest

n = Number of times interest compounds per year

t = Time (Years)

You must turn the percentage (1%) into a decimal by dividing by 100

1/100=.01

So, the equation for this question is:

A = 4,800(1+\(\frac{.01}{2}\))^(2)(24)

A = 4800(1.005)^48

A = 4800(1.2704891611)

A = 6,098.35

The Net Present Value (NPV) of the new refrigeration system is approximately $101,358.94.

To calculate the Net Present Value (NPV) of the new refrigeration system, we need to calculate the cash flows for each year and discount them to the present value. The NPV is the sum of the present values of the cash flows.

Here are the calculations for each year:

Year 0:

Initial investment: -$700,000

Working capital investment: -$70,000

Year 1:

Depreciation expense: $700,000 * 20% = $140,000

Taxable income: $250,000 - $140,000 = $110,000

Tax savings (35% of taxable income): $38,500

After-tax cash flow: $250,000 - $38,500 = $211,500

Years 2-5:

Depreciation expense: $700,000 * 20% = $140,000

Taxable income: $250,000 - $140,000 = $110,000

Tax savings (35% of taxable income): $38,500

After-tax cash flow: $250,000 - $38,500 = $211,500

Year 5:

Salvage value: $90,000

Taxable gain/loss: $90,000 - $140,000 = -$50,000

Tax savings (35% of taxable gain/loss): -$17,500

After-tax cash flow: $90,000 - (-$17,500) = $107,500

Now, let's calculate the present value of each cash flow using the discount rate of 10%:

Year 0:

Present value: -$700,000 - $70,000 = -$770,000

Year 1:

Present value: $211,500 / (1 + 10%)^1 = $192,272.73

Years 2-5:

Present value: $211,500 / (1 + 10%)^2 + $211,500 / (1 + 10%)^3 + $211,500 / (1 + 10%)^4 + $211,500 / (1 + 10%)^5

           = $174,790.08 + $158,900.07 + $144,454.61 + $131,322.37

           = $609,466.13

Year 5:

Present value: $107,500 / (1 + 10%)^5 = $69,620.08

Finally, let's calculate the NPV by summing up the present values of the cash flows:

NPV = Present value of Year 0 + Present value of Year 1 + Present value of Years 2-5 + Present value of Year 5

   = -$770,000 + $192,272.73 + $609,466.13 + $69,620.08

   = $101,358.94

Therefore, the new refrigeration system's Net Present Value (NPV) is roughly $101,358.94.

Learn more about Net Present Value on:

https://brainly.com/question/30404848

#SPJ11

Answer:K(24,-15) Because it's telling the first point of where it started and how it was rotated.

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\left(3+\frac{\frac{9}{2}}{\sqrt{5}}\right)\left(2-\sqrt{5}\right)n+\left(3-\frac{\frac{9}{2}}{\sqrt{5}}\right)\left(2+\sqrt{5}\right)\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\times \:a}\)

\(=\left(\frac{9}{2\sqrt{5}}+3\right)\left(2-\sqrt{5}\right)n+\left(-\frac{\frac{9}{2}}{\sqrt{5}}+3\right)\left(2+\sqrt{5}\right)\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\times \:a}\)

\(=\left(\frac{9}{2\sqrt{5}}+3\right)\left(2-\sqrt{5}\right)n+\left(-\frac{9}{2\sqrt{5}}+3\right)\left(2+\sqrt{5}\right)\)

\(=\frac{-12-9\sqrt{5}}{2\sqrt{5}}n+6n+\left(3-\frac{9}{2\sqrt{5}}\right)\left(2+\sqrt{5}\right)\)

\(=\frac{-12-9\sqrt{5}}{2\sqrt{5}}n+6n+\frac{12-9\sqrt{5}}{2\sqrt{5}}+6\)

\(=\frac{\sqrt{5}\left(\left(3\sqrt{5}-12\right)n+12-9\sqrt{5}\right)}{10}+6\)

a) The probability of missing for the first time on the sixth attempt is 0.07056.

b) The probability of making the first basket on the third shot is 0.063.

c) The probability of making the first basket on one of the first three shots is 0.973.

To find the probability in each scenario, we'll assume that each shot is independent, and the probability of making a foul shot is 70%.

a) Probability of missing for the first time on the sixth attempt:

To calculate this probability, we need to find the probability of making the first five shots and then missing the sixth shot. Since the probability of making a shot is 70%, the probability of missing a shot is 1 - 0.70 = 0.30. Therefore, the probability of missing the first time on the sixth attempt is:

P(missing on the 6th attempt) = (0.70)^5 * 0.30 = 0.07056.

b) Probability of making the first basket on the third shot:

Similarly, we need to find the probability of missing the first two shots (0.30 each) and making the third shot (0.70). The probability of making the first basket on the third shot is:

P(making on the 3rd shot) = (0.30)^2 * 0.70 = 0.063.

c) Probability of making the first basket on one of the first three shots:

In this case, we need to consider three possibilities: making the first shot, making the second shot, or making the third shot. The probability of making the first basket on one of the first three shots can be calculated as:

P(making on one of the first 3 shots) = P(making on the 1st shot) + P(making on the 2nd shot) + P(making on the 3rd shot)

= 0.70 + (0.30 * 0.70) + (0.30 * 0.30 * 0.70)

= 0.70 + 0.21 + 0.063

= 0.973.

Therefore, the probability of making the first basket on one of the first three shots is 0.973.

For more such questions on probability visit:

https://brainly.com/question/251701

#SPJ8

Answer:

The horizontal line on a graph.

Step-by-step explanation:

Answer:

The horizontal value in a pair of coordinates: how far along the point is.

The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5).

I hope this help you out

Answer:

7 is the answer

Step-by-step explanation:

22/2= 11-4= 7

Answer:

7

Step-by-step explanation:

let the number be n, then increased by 4 is n + 4

Doubling the result is 2(n + 4) , then

2(n + 4) = 22 ( divide both sides by 2 )

n + 4 = 11 ( subtract 4 from both sides )

n = 7

That is the number is 7

Answer:

the answer is 0 :)

Step-by-step explanation:

where the line starts is where the population started! hope this helped :)

Answer: 0

Step-by-step explanation:

The computation of the significance level shows that the p-value is less than 0.01 and the conclusion is that Americans use the internet more than 7 hours weekly.

It should be noted that the significance level simply means the probability that an event occured by chance.

From the complete question, it can be noted that at 0.01 significance level, the t statistic is 17.873 and the degree of freedom is 539.

The p-value for the right tailed test is 0. Therefore, since the p value is less than 0.01, we will reject the null hypothesis. The conclusion is that Americans use the internet more than 7 hours weekly.

Learn more about significance level on:

https://brainly.com/question/9163177

1/5

2/10

3/15

5/25

6/30

7/35

8/40

9/45

10/50

Answer:

1/5

Step-by-step explanation:

4/20=1/5

Answer:

16/32 simplified should be 1/2

Step-by-step explanation:

divide both by 16

16÷16 = 1

32÷16 = 2

Answer:

1/2 in fraction (or 0.5 in decimal)

Step-by-step explanation:

Q) Simplify 16/32 = ?

→ 16/32

→ (16 ÷ 16)/(32 ÷ 16)

→ 1/2 (or) 0.5

Hence, the final answer is 1/2.

Answer:

x=-5

Step-by-step explanation:

Answer:

Equation of the perpendicular line is x = -5

Step-by-step explanation:

The equation of the given line is y =-3

This means that the given line is parallel to the x axis. Imagine a horizontal line and for all values of x, the y value is constant -3. So the line perpendicular to this line would be one that is parallel to the Y axis. Imagine a vertical line. This line would have the same x value for all values of Y. Equation would be of the form

x = constant.

It is given that the line passes through (-5, -3), from which we get that constant value as -5.

Equation of the perpendicular line is x = -5

Answer:

A line segment is part of a line that has two endpoints and is finite in length. A ray is a line segment that extends indefinitely in one direction.

Step-by-step explanation:

hope it helps you and give me a brainliest

Answer:

A ray goes in one direction for forever, and also has an arrow.

A line segment is a segment, meaning that it has two end points and doesn't go on forever, it ends.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the third side be x

Triangle inequality theorem: sum of the length of any two sides must be greater than the third side length:

Combined together we have:

The third side must be between 10cm and 14 cm

AAA(Angle angle angle) Theorem can be used to prove given triangles as similar.

As we know we have to show all three angles equally.

so we have to show the similarities between T(DNM) and T(DFE) ....

(T Means Triangle.)

(A Means Angle)

As  D is a common vertex in both the triangles

by equations 1, 2, and 3 we can conclude that all three angles of T(DFE) =  T(DNM)

SO By the AAA rule, we can say that the two Triangles are similar.

Now we can say all the sides of T(DFE) will be in all propositions of T(DNM).

Like DN/DF=DM/DE=NM/FE

Learn More Similarities: https://brainly.com/question/14285697

Answer:

0, 5%, 1/5, 5

5% is equal to 5÷100=0,05

1/5 is equal to 1÷5=0,2

Answer:

a = 26

a ~ 21.8

Read explanation

Step-by-step explanation:

There are two possibilities;

\(a^{2}+c^{2}=b^{2}\)

Or

\(b^{2}+c^{2}=a^{2}\)

This is because one doesn't know the longest side, and hence there are two possibilities as to what the longest side is.

1. \(a^{2}+c^{2}=b^{2}\)

Substitute in the given values;

\(a^{2}+(10)^{2}=(24)^{2}\)

\(a^{2}+100=576\)

\(a^{2}=476\)

a=\(\sqrt{476}\)

a~21.8

2.\(b^{2}+c^{2}=a^{2}\)

Substitute in the given values;

\((24)^{2}+(10)^{2}=a^{2}\)

\(576+100=a^{2}\)

\(676=a^{2}\)

\(26=a\)

Answer:

Both answers are 47 degrees

Step-by-step explanation:

1. This is an isosceles triangle so the angle x is going to be the same as the opposite angle given which is 47. So x = 47 degrees

2. For this one, we are given the angle outside the same base angles so we take the 86 given from 180. 180-86=94. This 94 needs to be split between the two remaining angles so we divide it by 2. 94/2 = 47 degrees.

Answer:

1) C

Step-by-step explanation:

Step 1)

First we have to plot ↓

2x ≥ y + 2

And that looks like Image 1

Step 2)

Second we have to plot ↓

2x - 5y ≤ 10

and that looks like Image 2

(f - g)(x) = -x² - 3x + 6

(f × g)(x)= 12x - 8 - 3x³ + 2x²

(f / g)(x) = 12x - 8 - 3x³ + 2x²

The value of the function (f ° g)(-2) is -44

- f(x) = 4 - x²
- g(x) = 3x - 2

1. To find (f - g)(x), we need to subtract f(x) from g(x).

(f - g)(x) = f(x) - g(x)

= (4 - x²) - (3x - 2)

= 4 - x² - 3x + 2

= -x² - 3x + 6

2. To find (f × g)(x), we need to multiply f(x) and g(x).

(f × g)(x) = f(x) × g(x)

= (4 - x²) × (3x - 2)

= 12x - 8 - 3x³ + 2x²

3. To find (f / g)(x), we need to divide f(x) by g(x).

(f / g)(x) = f(x) / g(x)

= (4 - x²) / (3x - 2)

4. To find (f ° g)(x), we need to find f(g(x)).

f(g(x)) = f(3x - 2)

= 4 - (3x - 2)²

= -9x² + 12x - 2

5. To find (g o g)(x), we need to find g(g(x)).

g(g(x)) = g(3x - 2)

= 3(3x - 2) - 2

= 9x - 8

6. To evaluate (f × g)(2t³), we need to substitute 2t³ for x in (f × g)(x).

(f × g)(2t³) = 12(2t³) - 8 - 3(2t³)³ + 2(2t³)²

= 24t³ - 8 - 24t⁹ + 8t⁴

= -24t⁹ + 8t⁴ + 24t³ - 8

7. To evaluate (f ° g)(-2), we need to substitute -2 for x in (f ° g)(x).

(f ° g)(-2) = -9(-2)² + 12(-2) - 2

= -18 + (-24) - 2

= -44

Therefore, the value of (f ° g)(-2) is -44.

Learn more about function from the given link

https://brainly.com/question/11624077

#SPJ11

y = -1/3x + 1

y = -2x - 3

We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.

The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.

The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.

Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.

Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.

Answer:

Step-by-step explanation:

x = a - 2byx²

x - a = -2byx²

\(-2byx^{2}= x- a\\\\ y = \frac{x-a}{-2bx^{2}}\\\\ y =\frac{-(x-a)}{2bx^{2}}\\\\y=\frac{ -x + a}{2bx^{2}}\\\\y=\frac{ a -x }{2bx^{2}}\\\)

Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.

One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.

Learn more about chess: https://brainly.com/question/29897063

#SPJ11

Answer: 21.98

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

they gave us 53 and there is the 90 degree angle so you just add that and find the missing since itll equal 180

The correct alternative hypothesis for the Wilcoxon rank sum test is: ha: one distribution is shifted in a location higher or lower than the other. Option C is the answer.

This means that the test is designed to determine if there is a significant difference between the medians of two independent groups, rather than testing for a difference in means.

The null hypothesis for the test is that there is no significant difference between the two groups, while the alternative hypothesis states that there is a significant difference.

The Wilcoxon rank sum test is a nonparametric test and is used when the assumptions of the t-test are not met, such as non-normality or unequal variances.

Learn more about the alternative hypothesis at

https://brainly.com/question/27335001

#SPJ4