What letter comes next in this pattern A,F,L,S

A.  The payback period is 7.2 years. The net present value of the proposed investment is 3720.55.

B. No, the project does not meet the company's cash payback criteria.

C.  Yes, the project does meet the net present value criteria for acceptance.

A. The truck costs $55,440 and generates annual cost savings of $7,700. So the payback period is the cost of the truck divided the expected amount the truck will generate.

                $55,440 / $7,700 = 7.2 years

To solve for the net present value, we say

Net Present Value = ∑ [(Cash inflow in period t) / (1 + \(r^{t}\)] - Initial Investment.

NPV = (($7,700 / (1 + 0.08)¹) = 7 129.63

+ ($7,700 / (1 + 0.08)²) = 6601.51

+ .($7,700 / (1 + 0.08)³ = 6112.51

+ ($7,700 / (1 + 0.08)⁴) = 5659.73

+ ($7,700 / (1 + 0.08)⁵) = 5240.49

+ ($7,700 / (1 + 0.08)⁶) = 4 852.31

+ ($7,700 / (1 + 0.08)⁷) = 4492.88

+($7,700 / (1 + 0.08)⁸)  = 4160.07

+ ($27,600 / (1 + 0.08)⁸)) = 14911.42

- $55,440

We add all these values together and subtract by  $55,440

7 129.63 + 6601.51 + 6112.51 + 5659.73 + 5240.49 +4 852.31 + 4492.88 + 4160.07 + 14911.42 - $55,440

59160.55 - 55,440

NPV = 3720.55

B. The cash payback period of the project is 7.2 years. The company's cash payback criteria state that a project should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life, which would be 4 years which is 50% of 8 years. Since 7.2 years is greater than 4 years, the project does not meet the company's cash payback criteria.

C. The positive NPV of $3,720.55 shows that embarking on the prooject will be valuable to the company. This means the project meets the NPV criteria for acceptance.

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Answer:

- 72 - 48i

Step-by-step explanation:

note that i² = - 1

(6i)(- 2i)(- 6 - 4i)

= - 12i²(- 6 - 4i)

= - 12(- 1)(- 6 - 4i)

= 12(- 6 - 4i) ← distribute parenthesis by 12

= - 72 - 48i

Answer:

4 x 8.5 x 12.5 =425 (multiple hight x width x length)

The volume of the box is \(425in^{3}\)

Answer:

at most 17 pitches per inning

Step-by-step explanation:

It is given that a baseball pitcher makes 53 pitches in the first 4 innings of a game and plans to pitch in the next 3 innings.

We need to write and solve an inequality to find the possible average pitches per inning the pitcher made in the next 3 innings if the pitcher is assigned a maximum of 105 pitches.

From part (a) we know  3 p + 53 3p+53 represents the total number of pitches made if the pitcher makes an average of  p pitches per inning in the next 3 innings.

If the pitcher can make at most 105 pitches, then:

3 p + 53 ≤ 105 3p+53≤105 ​  

To solve the inequality, first subtract 53 on both sides of the inequality to isolate the variable term:

3 p + 53 − 53 ≤ 105 − 53 3 p ≤ 53      

3p+53≤105 \(p\leq 17\frac{1}{3}\)

at most 17 pitches per inning

​

(Hope this helps can I pls have brainlist (crown)☺️)

Answer:

To calculate the percentage profit on the sale of the painting, we need to first find the difference between the selling price and the cost price. In this case, the selling price is £300 and the cost price is £180, so the difference is £300 - £180 = £120.

We can then divide this difference by the cost price and multiply by 100% to express the profit as a percentage. In this case, the profit is £120 / £180 * 100% = 66.67%.

Since we need to express the profit as a whole number, we can round this value to the nearest whole number, which gives us a profit of 67%. Therefore, Tom made a profit of 67% on the sale of the painting.

Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

Answer: 50

Step-by-step explanation:

Answer: any negative value

Step-by-step explanation:

g(x)= ax², inc on x<0 & dec on x>0

Firstly we need to get the derivative of g(x)

g'(x)=2ax

for inc interval g'(x) should be +ve

x<0 (i.e. x= -ve), then a must be -ve

for dec interval g'(x) should be +ve

x>0 (i.e. x= +ve), then a must be -ve

so in both cases a must be a negative constant

Answer:

I think its 144!!!!!!!!!!!!!!!!!!

Answer:

Diagram 2  (Bottom diagram)

Step-by-step explanation:

The ratio is twice as many (2)

2:1

Answer:

Step-by-step explanation:

Experimental probability:

Probability of yellow:

Answer:

Explained below.

Step-by-step explanation:

The random variable X is defined as the number of missing pulses and follows a Poisson distribution with parameter (μ = 0.50).

The probability mass function of X is as follows:

\(P(X=x)=\frac{e^{-\mu}\ \mu^{x}}{x!};\ x=0,1,2,3...\)

(a)

Compute the probability that a disk has exactly one missing pulse as follows:

\(P(X=1)=\frac{e^{-0.50}\ 0.50^{1}}{1!}=0.3033\)

Thus, the probability that a disk has exactly one missing pulse is 0.3033.

(b)

Compute the probability that a disk has at least two missing pulses as follows:

\(P(X\geq 2)=1-P(X<2)\\\)

                \(=1-[P(X=0)+P(X=1)]\\=1-[\frac{e^{-0.50}\ 0.50^{0}}{0!}+\frac{e^{-0.50}\ 0.50^{1}}{1!}]\\=1-0.6065-0.3033\\=0.0902\)

Thus, the probability that a disk has at least two missing pulses is 0.0902.

(c)

It is provided that the two disks selected are independent of each other.

The probability that a disk has no missing pulses is:

\(P(X=0)=\frac{e^{-0.50}\ 0.50^{0}}{0!}=0.6065\)

Compute the probability that neither of the two disks contains a missing pulse as follows:

\(P(X_{1}=0,\ X_{2}=0)=P(X_{1}=0)\times P(X_{2}=0)\)

                               \(=0.6065\times 0.6065\\=0.367842\\\approx 0.3678\)

Thus, the probability that neither of the two disks contains a missing pulse is 0.3678.

solve  -6x2-3x+12 dived by 3x-3 using pemdas

Step-by-step explanation:

The question is how to divide this this is how to solve it

we know that

A function is a binary relation over two sets that associates every element of the first set, to exactly one element of the second set

so

For one value of x there is only one value of y

Verify each options

Option A

The option A is a function

Option B

Is not a function , because we have the points (2,1) and (2,7)

one value of x and there are two values of y

Option C

Is not a function , because we have

(2,1) and (2,5) -----> one value of x and to values of y

(4,1) and (4,7) --> one value of x and to values of y

Option D

Is not a function ------> one value of x and 4 values of y

therefore

the answer is the option A

Answer:

GPS is access

Step-by-step explanation:

Answer:

22° + m<C = 90°

Step-by-step explanation:

We are given that <A (which is equal to 22°) and <B are vertical angles, and that <B is complementary to <C.

We want to write an equation that will help us solve <C.

Recall that vertical angles are congruent by vertical angles theorem.

This means that <A ≅ <B; it also means that the measure of <B is also 22°.

Also recall that complementary angles add up to 90°.

This means that m<B + m<C = 90°.

Since we deduced that m<B is 22°, we can substitute that value into the equation.

Hence, an equation that can be used to solve for <C is:

22° + m<C = 90°

The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

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0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.

---------------

For each student, there are only two possible outcomes. Either they score an A, or they do not. The probability of a student scoring an A is independent of any other student, which means that the binomial probability distribution is used to solve this question.

Additionally, to find the proportion of students who scored an A, the normal distribution is used.

----------------

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which  is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of a success.

----------------

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

----------------

Proportion of students that scored an A:

Scores have a mean of 79 and a standard deviation of 11.3, which means that \(\mu = 79, \sigma = 11.3\)

Scores of 90 or higher are graded an A, which means that the proportion is 1 subtracted by the p-value of Z when X = 90, so:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{90 - 79}{11.3}\)

\(Z = 0.97\)

\(Z = 0.97\) has a p-value of 0.8340.

1 - 0.8340 = 0.166

The proportion of students that scored an A is 0.166.

----------------

Probability that 6 students or more will score an "A" on the final exam:

Binomial distribution.

22 students, which means that \(n = 22\)

The proportion of students that scored an A is 0.166, which means that \(p = 0.166\)

The probability is:

\(P(X \geq 6) = 1 - P(X < 6)\)

In which

\(P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)\)

Then

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{22,0}.(0.166)^{0}.(0.834)^{22} = 0.0184\)

\(P(X = 1) = C_{22,1}.(0.166)^{1}.(0.834)^{21} = 0.0807\)

\(P(X = 2) = C_{22,2}.(0.166)^{2}.(0.834)^{20} = 0.1687\)

\(P(X = 3) = C_{22,3}.(0.166)^{3}.(0.834)^{19} = 0.2239\)

\(P(X = 4) = C_{22,4}.(0.166)^{4}.(0.834)^{18} = 0.2117\)

\(P(X = 5) = C_{22,5}.(0.166)^{5}.(0.834)^{17} = 0.1517\)

Then

\(P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0184 + 0.0807 + 0.1687 + 0.2239 + 0.2117 + 0.1517 = 0.8551\)

\(P(X \geq 6) = 1 - P(X < 6) = 1 - 0.8551 = 0.1449\)

Thus

0.1449 = 14.49% probability that 6 students or more will score an "A" on the final exam.

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To determine how much effort the gas undergoes as it changes from its original condition to its final one, Nora and Bob utilize the area underneath the line separating the two states and the first rule of thermodynamics.

When a gas changes from its initial condition to its final state, Nora and Bob explain how to compute the work that is done. They talk about compressing gas, thus something is being done to the gas.

You suggest using the area under the line separating the final and initial states to calculate the work done as well as the application of the first equation of thermodynamics, q=w.

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Answer:

product A

75%

67%

Product B

Step-by-step explanation:

I just found the percentage by dividing the amount of people who found relief into the whole

Hopes this helps please mark brainliest

Answer:

A. I did this one before so yeah!

Let's assume x gallons of milk containing 8% butterfat and y gallons of milk containing 2% butterfat are used.

The total amount of milk is x + y gallons, and we want it to be equal to 258 gallons.

To determine the amount of butterfat in the mixture, we can multiply the volume of each type of milk by its respective butterfat percentage and sum them up.

For milk containing 8% butterfat, the amount of butterfat is 0.08x (8% is equivalent to 0.08 as a decimal).

For milk containing 2% butterfat, the amount of butterfat is 0.02y (2% is equivalent to 0.02 as a decimal).

Since we want the final mixture to contain 7% butterfat, we can set up the following equation:

0.08x + 0.02y = 0.07(258)

Simplifying the equation, we have:

0.08x + 0.02y = 18.06

To solve for x and y, we need another equation. Since the total amount of milk is x + y = 258, we can rearrange it to y = 258 - x.

Substituting this value into the equation above, we get:

0.08x + 0.02(258 - x) = 18.06

Solving this equation will give us the values of x and y, which represent the gallons of milk containing 8% butterfat and 2% butterfat, respectively, needed to obtain the desired 258 gallons.

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Answer:

B

Step-by-step explanation:

Since x is 3, you go 3 units right. Since y is -2, you go 2 units down.

The expression is simplified to 2

It is important to note that the table of exact values for trigonometric identity differ with the particular identity in study.

From the table of exact values, we have that;

sin 15 = 0. 25

sin 30 = 0. 5000

sin 45 = 0. 7071

sin 60 = 0. 8600

sin 75 = 0. 9659

sin 90 = 1

To determine the value of the expression, we have to substitute the value of sin 30 as 0. 5000

4 sin 30°

⇒ 4 × 0. 5000

multiply through

⇒ 2

The value determined is 2

Thus, the expression is simplified to 2

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The shear plane angle is approximately 84.3°, and the chip thickness is approximately 15.1 mm.

To determine the shear plane angle and chip thickness in the given scenario, we can use the following formulas:

Shear Plane Angle (α):

tan(α) = tan(β - φ)

where β is the inclination angle of the machined surface (rake angle) and φ is the friction angle.

Chip Thickness (t):

t = tc / cos(α)

where tc is the uncut chip thickness.

Given:

Uncut chip thickness (tc) = 1.5 mm

Chip length (lc) = 40 mm

Length of the specimen (L) = 100 mm

Rake angle (β) = 15°

First, we need to calculate the shear plane angle (α):

tan(α) = tan(β - φ)

Since the friction angle (φ) is not given, we will assume a typical value of 5°.

tan(α) = tan(15° - 5°)

tan(α) = tan(10°)

α ≈ 84.3° (rounded to two decimal places)

Next, we can calculate the chip thickness (t):

t = tc / cos(α)

t = 1.5 mm / cos(84.3°)

t ≈ 15.1 mm (rounded to two decimal places)

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Answer:

The answer is below

Step-by-step explanation:

The next step to solve the system, would be to divide the second row by 3 and we would be left with:  3 * R2

[1 -5 3 0 -2

0 1 -7/3 0 4/3

0 0 1 2 -2]

Then what we will do is multiply row 3 by 7/3 and then subtract it from row 2, that is, R2 - 7/3 * R3, and it would look like this:

[1 -5 3 0 -2

0 1 0 14/3 -10/3

0 0 1 2 -2]

And these would be the next two steps in the process of solving the system.

The Option B statement "the opposite angles are equal" accurately describes a rhombus, as each of the four angles of a rhombus are equal to each other. This means that the opposite sides of the rhombus have the same measure.

A rhombus is a four-sided shape with all sides equal in length. It is also known as a diamond shape. The most important thing to remember about a rhombus is that the opposite angles are equal.

This means that the two angles across from each other on the rhombus have the same measure. This is what is meant by the statement "the opposite angles are equal," and it accurately describes a rhombus.

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Answer:

3) 5

4) 8.2

5) 6.8

6)FG = 6.4

7) EF = 3.6

8)DF = 4.8

Step-by-step explanation:

From the attached triangle, using trigonometric ratio we can find ∠G as; tan^(-1) (6/8)

Thus, ∠G = 36.87°

Still using trigonometric ratios;

FG/8 = cos 36.87°

FG = 8 cos 36.87°

FG = 6.4

3) EF + FG = EG

Since EG is 10, mean of EF and FG = 10/2 = 5

4) mean of EG and FG = (10 + 6.4)/2 = 8.2

5) EF + FG = EG

Thus; EF = EG - FG

EF = 10 - 6.4

EF = 3.6

Mean of EG and EF = (10 + 3.6)/2 = 6.8

6) FG = 6.4

7) EF = 3.6

8) Using trigonometric ratio;

DF/8 = sin 36.87

DF = 8 × 0.6

DF = 4.8

Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.

Step-by-step explanation:

To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.

Answer:

the afternoon is the right one

Answer:

30

Step-by-step explanation:

Complementary angles add to 90

x+60 = 90

x+60-60 = 90-60

x = 30

Answer: A

Step-by-step explanation:

Complementary angles sum up to 90 degrees. Thus, we can write that:

90=angle1+angle2

90-angle1=angle2

90-60=angle2

angle2=30