Find the slope of the line that passes through (10, 3) and (1, 10).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Compound interest is the adding of interest to the principal sum of a loan or deposit. The rate of percentage per annum compound interest is 4%.

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.

\(A = P(1+ \dfrac{r}{n})^{nt}\)

where A is the final amount

P is the principal amount

r is the rate of interest

n is the number of times interest is charged in a year

t is the number of years

Given the principal amount is 2,500, the time period for which the amount is compounded is 4%. Also, the final amount is 2704.

2,704 = 2,500(1+R)²

1.04 = 1 + R

R = 0.04 = 4%

Hence, the rate of percentage per annum compound interest is 4%.

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Answer:

A. 30°, 70° and 80°

B. 10cm

Step-by-step explanation:

A. the two triangle have same angles

so the angles of triangle 2 are 30°, 70° and 80°

B. the perimeter of triangle, is twice as long as the perimeter of

triangle 2

so the perimeter of triangle 2 is 20÷2 = 10 cm

Suppose after the shock, the economy temporarily stays at the short-run equilibrium, then the output gap Y2−Y1 is: B< (less than)As the output gap measures the difference between the actual output (Y2) and potential output (Y1), when the output gap is less than zero, that is, the actual output is below potential output.

The inflation gap π2−π1 is 0. C= (equal)When the inflation gap is zero, it means that the current inflation rate is equal to the expected inflation rate.12. Suppose there is no government intervention, the economy will adjust itself from short-run equilibrium to long-run equilibrium, at such long-run equilibrium, output gap Y3−Y1 is 0. C= (equal). As the long run equilibrium represents the potential output of the economy, when the actual output is equal to the potential output, the output gap is zero.13.

The inflation gap π3−π1 is 0. C= (equal) Again, when the inflation gap is zero, it means that the current inflation rate is equal to the expected inflation rate.14. (1 point) Suppose the Fed takes price stability as their primary mandates, then which of the following should be done to address the shock. B monetary tightening When the central bank takes price stability as its primary mandate, it aims to keep the inflation rate low and stable. In the case of a positive shock, which can lead to higher inflation rates, the central bank may implement a monetary tightening policy to control the inflation.

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(a) The probability that all seven plants emerged from treated seeds is: P(7 treated) = 8C7 / 16C7 = 1 / 128, (b) The probability that six or fewer emerged from treated seeds is: P(6 or fewer treated) = 8C6 + 8C5 + 8C4 + 8C3 + 8C2 + 8C1 = 17 / 64.

(c) The probability that at least one emerged from untreated seeds is:

P(at least 1 untreated) = 1 - P(all treated) - P(6 or fewer treated) = 46 / 64

(a) There are 8C7 = 1 ways to choose 7 treated seeds out of 8. There are 16C7 = 128 ways to choose 7 seeds out of 16. So, the probability that 7 of the 7 plants that sprouted were treated is 1/128.

(b) There are 8C6 = 28 ways to choose 6 treated seeds out of 8. There are 8C5 = 56 ways to choose 5 treated seeds out of 8. There are 8C4 = 70 ways to choose 4 treated seeds out of 8. There are 8C3 = 56 ways to choose 3 treated seeds out of 8.

There are 8C2 = 28 ways to choose 2 treated seeds out of 8. There are 8C1 = 8 ways to choose 1 treated seeds out of 8. So, the probability that 6 or fewer of the 7 plants that sprouted were treated is 17/64.

(c) The probability that all 7 plants that sprouted were treated is 1/128. The probability that 6 or fewer of the 7 plants that sprouted were treated is 17/64. So, the probability that at least one of the 7 plants that sprouted was untreated is 1 - (1/128 + 17/64) = 46/64.

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The end behavior of the given polynomial is that as x → -∞ or  x → ∞, then, f(x) → 5

We are given the polynomial;

f(x) = 5x/(x - 25)

Now, we want to find the limits as x → ±∞. Let us rearrange the given polynomial to get;

f(x) = 5/(1 - (25/x))

Thus, applying limits we have;'

lim x → ±∞ [5/(1 - (25/x))]

From algebraic limit laws we know that;

If f(x) = k, then;

lim x → +∞ [f(x)] = k

Also, lim x → -∞ [f(x)] = k

Thus, applying limits at infinity to our polynomial gives;

lim x → ±∞ [5/(1 - (25/x))] = 5/(1 - 0) = 5

This is because lim x → ∞ for 1/x is 0.

Thus, f(x) has horizontal asymptotes at y = 5

Thus, we conclude that the end behavior is that as x → -∞ or  x → ∞, then, f(x) → 5

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Answer:

15.................

Step-by-step explanation:

please Mark my answer in brainlist

Answer:

141,620,000

Step-by-step explanation:

I hope that's what you meant ^^

Answer:

141,620,000

Step-by-step explanation:

................

Answer:29 ft by 58 ft

Step-by-step explanation:

Answer: Let the number = x

5x+10 = 120

Or, 5x = 120 - 10

Or, 5x = 110

Or, x = 110/5

Or, x = 2

Step-by-step explanation:

Answer:

Area=78m^2

Step-by-step explanation:

4*12=48m^2 <-- The area of a rectangle LxW

12*5=60 60/2=30 <-- The area of a triangle (HxB)/2

30+48=78m^2 Add them together to get the total area

Answer:

Step-by-step explanation:

Given the coordinate points (6, -3) and (7, -10), we are to find the equation of a line passing through this two points;

The standard equation of a line is y = mx+c

m is the slope

c is the intercept

Get the slope;

m = Δy/Δx = y2-y1/x2-x1

m = -10-(-3)/7-6

m = -10+3/1

m = -7

Get the intercept;

Substitute the point (6, -3) and m = -7 into the expression y = mx+c

-3 = -7(6)+c

-3 = -42 + c

c = -3 + 42

c = 39

Get the required equation by substituting m = -7 and c= 39 into the equation y = mx+c

y = -7x + 39

Hence the required equation is y = -7x + 39

Answer:

25 kids

Step-by-step explanation:

Let k = total number of kids running

this equation can be derived from the question

56% x k = 14

0.56 x k = 14

divide both sides of the equation by 0.56

k = 14/0.56

k = 25

Answer:

25

Step-by-step explanation:

Applying the power of power rule, the completed equation is given as follows:

\(x^{10} = (x^5)^2\)

The power of a power rule is used when a single base is elevated to multiple exponents, and states that simplified expression is obtained keeping the base, while the exponents are multiplied.

Hence the missing exponent for this problem is obtained as follows:

2x = 10

x = 10/2

x = 5.

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Answer:

5. 11.25 mi/hr

6. 24 hours

Step-by-step explanation:

5. The return trip at 9 mph took 5 hours.  So the distance is 45 miles.

The total distance traveled is therefore 90 miles, and the total time is 3 + 5 = 8 hours.

The average speed is distance divided by time, or (90 mi) / (8 hr) = 11.25 mi/hr

6. If t is the time it takes driving there, then t−4 is the time it takes to drive back.

Distance = speed × time, so the forward trip is 25t miles, and the return trip is 30(t−4) miles.  These distance are equal, so:

25t = 30(t−4)

25t = 30t − 120

120 = 5t

t = 24

Answer:

Step-by-step explanation:

hello,

arithmetic sequence means that you go from one term to the next one by adding or subtracting a constant value

check the first sequence

-20

-25

-30

-35

-40

each time 5 is subtracted

-20 - 5 = -25

-25 - 5 = -30

-30 - 5 = -35

-35 - 5 = -40

so the correct answer is the first one.

hope this helps

The height of the pyramid is 16 feet.

What is Pythagoras Theorem?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can use the Pythagorean theorem to find the height of the pyramid.

The slant height of the pyramid is the hypotenuse of a right triangle whose legs are the height of the pyramid and half the length of the base of the pyramid. Since the base is a square, half the length of the base is 12 feet.

Using the Pythagorean theorem:

height² + 12² = 20²

height² = 20² - 12²

height² = 256

height = 16 feet

Therefore, the height of the pyramid is 16 feet.

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In a family with five girls and the probability of a boy being born is 1/2, the probability of the next child being a boy is still 1/2.

The previous births do not affect the probability of the next birth since each birth is an independent event.

The probability of an event occurring is determined by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event of interest is the birth of a boy.

Since each birth is an independent event, the probability of having a boy on any given birth is always 1/2, regardless of the previous children born.

In the given scenario, the family already has five girls. This information is not relevant to the probability of the next child being a boy. The gender of the previous children does not affect the probability of the next child being a boy or a girl.

Therefore, the probability of the next child being a boy remains 1/2, as it is for any independent birth event.

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Answer:

6 dollars

Step-by-step explanation:

its math

Answer:

B) 2.5

Step-by-step explanation:

To find the rate of change you need to find the slope.

Slope is Rise over Run (Rise/Run)

How many times do you need to rise to get to the same height of the point of 2? 5 times

Next how many times do you need to run to get to the same length of 2? 2

Rise=5 Run=2

5/2 or 2 1/2

And since 1/2 is the same as 0.5 we can replace the 1/2 as 0.5 and the answer will be 2.5

Hope this helps!

Answer:

y = (-5/2)x - 3

Step-by-step explanation:

To find an equation of a line that is perpendicular to the given line and passes through the point (0, -3), we need to use the fact that perpendicular lines have opposite reciprocal slopes.

The given line has a slope of 2/5, so the slope of the line perpendicular to it is:

-1 / (2/5) = -5/2

This means that the equation of the perpendicular line has the form:

y = (-5/2)x + b

where b is the y-intercept we want to find.

Since the line passes through the point (0, -3), we can substitute these values into the equation and solve for b:

-3 = (-5/2)(0) + b

b = -3

Therefore, the equation of the line perpendicular to y = 2/5x + 4 with a y-intercept of -3 is:

y = (-5/2)x - 3

The airplane flies at 324 mi/h with no wind. the rate of the wind is 36 mi/h.

Let x represent the rate when there is no wind.

And let y serve as a representation of the wind's speed.

Given:

With no wind

1152 miles is the distance (d).

Time (t) equals 4 hours.

without wind, rate = x-y

In a formula,

speed=rate=distance/time

Substituting these values, we get

x - y=1152/4

288m/h

x- y=288 .......... equation 1

Finding the rate with the wind:

distance = 1152 miles

time(t) = 3.2 hours

rate = x+y

Substituting these values, we get

rate=distance/time

x+y=1152/3.2

=360m/h

x+y=360 .......... equation 2

now we will solve the equations simultaneously,

x - y=288

x+y=360

We will add the relevant terms in both equations using the Elimination Method.

2x=648

Then divide both sides by 2,

x=648/2=324

x=324m/h

To find the rate of the wind:

We shall substitute 324 for x in equation 2.

324+y=260

y=360- 324

y=36m/h

Therefore, the rate of the airplane with no wind is 324m/h.

The rate of the wind is 36 m/h.

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Information is needed to evaluate the project's financial viability, considering factors such as the initial investment, expected cash flows, cost of capital, and project duration.

To calculate the year 1 operating cash flows (OCF), we need to subtract the year 1 costs from the year 1 revenues:

OCF = Year 1 Revenues - Year 1 Costs

OCF = $192,000 - $125,000

OCF = $67,000

To find the depreciation expense in year 3, we need to determine the depreciation method. The provided information is incomplete regarding the depreciation method, so we cannot calculate the depreciation expense in year 3 without knowing the specific method.

The change in Net Working Capital (NWC) in year 2 can be determined by multiplying the Net Working Capital percentage (given as a percentage of t+1 revenues) by the year 1 revenues and subtracting the result from the year 2 revenues:

Change in NWC = (Year 2 Revenues - Net Working Capital percentage * Year 1 Revenues) - Year 1 Revenues

Without the specific Net Working Capital percentage or Year 2 Revenues values, we cannot calculate the exact change in NWC in year 2.

The net cash flow from salvage (ATSV) is calculated by multiplying the Salvage Value percentage by the Initial Cost:

ATSV = Salvage Value percentage * Initial Cost

ATSV = 28% * $390,000

ATSV = $109,200

To calculate the project's NPV, we need the cash flows for each year, the cost of capital, and the project duration. Unfortunately, the information provided does not include the cash flows for each year, so we cannot calculate the project's NPV.

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The complete question is:

Below are your numerical inputs for the problem: 4 & Initial Cost (\$) & 390000 5 & Year 1 Revenues (\$) & 192000 6 & Year 1 Costs (\$) & 125000  7 & Inflation & 2.75% 8 & Project Duration (years) & 6 9 & Depreciation Method & 10 & Tax Rate & 11 & Net Working Capital (\% oft+1 Revenues) & MACRS 12 & Salvage Value (\$) & 28.00% 13 & Cost of Capital & 15.00% & 245000 How much are the year 1 operating cash flows (OCF)? How much is the depreciation expense in year 3 ? What is the change in Net Working Capital (NWC) in year 2? What is the net cash flow from salvage (aka, the after-tax salvage value, or ATSV)? What is the project's NPV? Would you recommend purchasing the ranch? Briefly explain.

Answer:

Step-by-step explanation:

1) Separate the equations that are in the "()" and solve.

2)solve the equations out of the "()".

~Don't forget to use the unit for the answer!

*unit is x*

Answer:

it should be number A hope that helps

The correct Option (B). Succession may be defined as the change in the ecological community of the species with respect to time. Two main types of succession are primary succession and secondary succession.

The living things that accumulate in the succession is from the simple organism to the complex organism. First lichens will evade in the land. After lichens grass then shrubs and finally the trees will cover the area and convert into the forest.

Primary succession occurs in basically dead areas—regions where the soil is incapable of supporting life due to causes such as lava flows, newly created sand dunes, or glacier-left boulders.

Pioneer microorganisms, plants (lichens and mosses), grassy stage, smaller shrubs, and trees are all stages of primary succession. When there is food available, animals begin to return. The climax community stage is reached when the ecosystem is fully functional.

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Full Question :

After a town is abandoned, the concrete parking lots remain empty and inactive for hundreds of years. What is the most likely order of ecological succession in that area?

A.grass → trees → lichens → moss

B.lichens → grass → shrubs → trees

C.lichens → grass → trees → shrubs

D.shrubs → grass → trees → lichens

a) Approximate Doubling Time Dappx = 70/r, where r is the annual interest rate in percentage terms.Assuming that r = 5%, 10%, 20%, 40%, and 60%Doubling time for 5% = 70/5 = 14 yearsDoubling time for 10% = 70/10 = 7 yearsDoubling time for 20% = 70/20 = 3.5 yearsDoubling time for 40% = 70/40 = 1.75 yearsDoubling time for 60% = 70/60 = 1.1667 yearsb) Exact Doubling Time Dexact = ln2/r where r is the annual interest rate in decimal terms.

Assuming that r = 5%, 10%, 20%, 40%, and 60%For 5%: ln2/0.05 ≈ 13.86 yearsFor 10%: ln2/0.1 ≈ 6.93 yearsFor 20%: ln2/0.2 ≈ 3.47 yearsFor 40%: ln2/0.4 ≈ 1.73 yearsFor 60%: ln2/0.6 ≈ 1.16 yearsc)

The percentage error is given by:(Dexact − Dappx)/Dexact × 100%For 5%: (13.86 - 14)/13.86 x 100% ≈ 1.18%For 10%: (6.93 - 7)/6.93 x 100%

≈ 1.15%For 20%: (3.47 - 3.5)/3.47 x 100%

≈ -0.86%For 40%: (1.73 - 1.75)/1.73 x 100%

≈ -1.15%For 60%: (1.16 - 1.1667)/1.16 x 100%

≈ -0.60%Note that the percentage error is small for lower values of interest rates but increases as the interest rate increases.

Also, the percentage error is negative for 20%, 40%, and 60%, which means that the approximate doubling time is actually larger than the exact doubling time.

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Answer:

56$

Step-by-step explanation:

40% of 20 = 8 - 20 = 12 times 3 = 36+20=56

Answer:

You are selecting marbles with replacement. The marble selections (trials) are independent and the marble selection follows the binomial distribution.

The probability of selecting a red marble the first time is 1313.

(This is because 4 out of 12 marbles are red and412412 reduces to 1313.

The probability of selecting a red marble the second time is 1313.

The marble selections are independent and you can multiply the two probabilities to get the following:

probability of getting 2 reds = (13)2(13)2

=19=19.

So the probability of getting two reds is 1919.

The critical value to be used in constructing the 99% confidence interval is 2.576.

Step 1: Finding the Critical Value

To determine the critical value for constructing a 99% confidence interval, we need to refer to the z-table or use a statistical calculator. The critical value corresponds to the desired level of confidence and takes into account the sample size.

Since the sample size is large (n = 77) and the population is assumed to be approximately normal, we can use the z-distribution to find the critical value. For a 99% confidence interval, the critical value is found by subtracting half of the desired confidence level from 1 and dividing the result by 2.

In this case, the calculation would be:

(1 - 0.99) / 2 = 0.005

The corresponding critical value is then determined by finding the z-score that has an area of 0.005 in the upper tail of the standard normal distribution. Consulting a z-table or using a statistical calculator, the critical value is approximately 2.576 (rounded to three decimal places).

Therefore, the critical value to be used in constructing the 99% confidence interval is 2.576.

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