Crane Corporation is considering purchasing a new delivery truck. The new truck would cost $55,440. The new truck is expected to generate a cost savings of $7,700. At the end of 8 years, the company will sell the truck for an estimated $27,600.

Traditionally the company has used a rule of thumb that a proposal should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life. Larry Newton, a new manager, has suggested that the company should not rely solely on the payback approach, but should also employ the net present value method when evaluating new projects. The company's cost of capital is 8%.

a) Compute the cash payback period and net present value of the proposed investment.
b) Does the project meet the company's cash payback criteria?
c) Does it meet the net present value criteria for acceptance?

90-degree clockwise rotation transforms the coordinates the following way:

Now, after performing 90-degree clockwise rotation, we also move our point 3 units down, meaning, the final coordinates of the point are

Now we are told that the coordinates of the resultant point are

meaning

Solving for x gives

Hence, the coordinates of the original point are

which is choice D.

The value of f(g(1) from the table of functions is given as 1.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

when x = 1

g(x) = 3

or f(g(1) = f(3) = 1

The value of f(g(1) from the table of functions is given as 1.

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23 cuh thats the awnser and im smartest person on urt

Answer:

Answer B

Step-by-step explanation:

Answer:

C) 12, 20, 24

Step-by-step explanation:

A similar triangle with a scale factor of 4 means the other measurements can be divisible by 4 to get the original measurements of 3, 5, 6.

This also means that you can multiply each of the original values (3, 5, 6) by 4 to get you the other dimensions.

3 * 4 = 12

5 * 4 = 20

6 * 4 = 24

Answer:

Option A is the right answer mate...

The statement that accurately compares the cost of blueberries is; C: Blueberries are $0.80 per pound less expensive at the farmer’s market.

Given that at a grocery store, blueberries come packaged in 8-ounce containers for $2.80.  

Thus;

Cost of 1-ounce blueberries = 2.80/8 = $ 0.35  

Cost of 1 pound which is 16 ounces = $ 0.35 × 16 = $ 5.6  

It is also given that, at a farmer's market, blueberries cost $4.20 for 14 ounces

Thus;

Cost of 1-ounce blueberries = 4.20/14 = $ 0.3  

Cost of 1 pound which is 16 ounces = $ 0.3 × 16 = $ 4.8  

Thus, difference between both costs = $ 5.6 - $ 4.8 = $ 0.8

Therefore,

Blueberries are $0.80 per pound less expensive at the farmer’s market.

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The missing options are;

Blueberries are $0.23 per pound more expensive at the farmer’s market.

Blueberries are $0.50 per pound less expensive at the farmer’s market.

Blueberries are $0.80 per pound less expensive at the farmer’s market.

Blueberries are $1.40 per pound more expensive at the farmer’s market.

9514 1404 393

Answer:

Step-by-step explanation:

The parts are named as follows:

  minuend - subtrahend = difference

  4178       -    538         =  3640

_____

Additional comment

The numbers shown in the problem statement here do not form a correct subtraction problem. There is a typo somewhere.

Answer:

\(\approx 13^\circ\)

Step-by-step explanation:

Given two lines with the equations:

\(9x - y = 4\\ 8x + y = 6\)

First of all, let us learn the formula for finding the angle between the two lines with given equations:

\(tan\theta = \dfrac{m_1-m_2}{1+m_1m_2}\)

\(m_1, m_2\) are the slopes of the two lines respectively.

Let us convert the given equation to point intercept form.

Point intercept form of a line is given as:

\(y = mx+c\)

\(y = 9x-4\\y =-8x+6\)

Comparing with slope intercept form, we get:

\(m_1 = 9\\m_2 = -8\)

Using the above formula:

\(tan\theta =\dfrac{9 -(-8)}{1+9(-8)}\\\Rightarrow tan\theta = -\dfrac{17}{71}\\\Rightarrow \theta = -13.46^\circ\\\)

Therefore, the acute angle between the two lines is \(\approx 13^\circ\)

The acute angles between the equations is 13.46 degree.

To find the acute angles between the two equation, let's write out the individual slope of each equation.

Given Data

The given equations can be rearranged into equation of line.

\(9x-y=4\\ y=9x-4\\ slope=m_1=9\)

The second equation can also be rearranged as and solving for the slope

\(8x+y=6\\ y=6-8x\\ y=-8x+6\\ slope = m_2 = -8\)

Since we have the slopes of the two equation, we can now find the acute angle between them.

θ = \(tan^-^1[\frac{m_1-m_2}{1+m_1m_2}]\\ \)

substituting the values and solving for the angle

\(x = tan^-^1[\frac{9-(-8)}{1+(9*-8)}]\\ x = tan^-^1[17/-71]\\ x=-13.46 = 13.46^0\)

The acute angle between the equations is 13.46 degree

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Using a right-angled triangle the value of Cos C is  24/25 and Sin A is 20/29.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

A right triangle ABC has complementary angles A and C.

Using a right-angled triangle if Sin A = 24/25 then the other side =7

Therefore Cos C = 24/25

Similarly,

Using a right-angled triangle if Cos C = 20/29 then the other side =21

Therefore Sin A = 20/29

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Answer: 20%

Step-by-step explanation: Annual depreciation = $2,600 * 12 = $31,200

Annual depreciation rate = Annual depreciation /Depreciable costs

= $31,200 / ($188,000 - $32,000)

= 20%

a) The relations is classified as a linear relation.

b) The relation is classified as a quadratic relation.

For item a, we have that when x is increased by one, the first differences are always of -2, meaning that the output y decreases by 2.

Hence in item a we have a linear relation with an slope of -2.

For item b, the first differences are given as follows:

7, 5, 3, 1.

Then the second differences are given as follows:

-2, -2, -2.

As the second differences are constant, the relation is a quadratic relation.

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The solution of the inequality is 8 ≥  x  or x > 10. The graph of the solution is attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Solving for x:

11≥ 2x - 5 or 2x - 5 > 15

Collect like terms:

11 + 5 ≥ 2x  or 2x > 15 + 5

16 ≥ 2x  or 2x > 20

8 ≥  x  or x > 10

Note:  8 ≥  x can also be written as x ≤ 8

We can combine the two as follow:

Inequality notation: 8 ≥  x > 10

The graph of the solution is attached

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Answer:

C: 12+20-54

Step-by-step explanation:

4(3+5)-3.92= -22

12+20-54= -22

:))

This process required 3 to be subtracted 5 consecutive times, so again we see that 15 ÷ 3 = 5. The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient.

Division is a simple operation in which a number is divided. It's easiest to think of it as a number of objects being divided among a certain number of people.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

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Answer:

9.8333... or 59/6

Step-by-step explanation:

According to my calculator

Answer:

\(\dfrac{59}{6}\)

Step-by-step explanation:

Let x be the answer,

\(x = \dfrac{91 + 129 + 16}{24}\)

\(x = \dfrac{236}{24}\)

\(x = \dfrac{59}{6}\)

It is about 0.83 in decimal or 10 twelfths (10/12) in fraction form. I hope this helped! So sorry if it's wrong!!!

Answer: x=16

Step-by-step explanation:

log₇(3x²+x)-log₇x=2

Domian:

1)

3x²+x>0

x(3x+1)>0

-∞__+__-1/3__-__0__+__∞

x∈(-∞,-1/3)U(0,∞)

2)

x>0

Hence, x∈(0,∞)

Thus x∈(0,∞)

In this problem we use the following formula:

                       \(\boxed {log_ax-log_ay=log_a\frac{x}{y}}\)

\(\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\Hence,\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\ Divide\ both\ parts \ of\ the \ equation\ by\ 3:\\\\x=16\)

The extraneous solution to the logarithmic equation log7 (3x³ + x)-log7(x)=2 is x= 4.

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.

We have Logarithmic expression as

log7 (3x³ + x)-log7(x)=2

we know, \(log_ax - log_a y= log_a (x/y)\)

Using the above property as

log7 (3x³ + x)-log7(x)=2

\(log_7\) (3x³ + x) - \(log_7\) x =2

\(log_7\) x(3x² +1) / x = 2

\(log_7\) (3x²+1) = 2(1)

\(log_7\) (3x²+1) = 2(1)\(log_7 (7)\)

\(log_7\) (3x²+1) = \(log_7\)7²

Now, comparing we get

3x² +1 = 7²

3x² = 48

x² = 16

x = 4

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Answer:

x=3

Step-by-step explanation:

What u should always do is look at the letters of the triangles given:

It will tell u that:

\( \frac{tu}{dc} = \frac{uv}{cb} \)

Now we once again just sub in the values:

\( \frac{12}{9} = \frac{20}{4x + 3} \)

we can simplify the fraction on the right

\( \frac{4}{3} = \frac{20}{4x + 3} \)

And now we cross multiply

3×20=4(4x+3)

60=16x+12

60-12=16x

48=16x

Therefore :

x=3

Answer: c = about 7.21

Step-by-step explanation:

ok - pythagorean theorum

6^2+4^2=C^2

36 + 16 = c^2

52 = c^2

root both sides

c = about 7.21

The solution to the equation 6^2 + 4^2 = C^2 is approximately 7.21

The equation is given as:

6^2 + 4^2 = C^2

Evaluate the exponents of 6 and 4

36 + 16 = C^2

Evaluate the sum

52 = C^2

Take the square root of both sides

7.21 = C

Rewrite as:

C = 7.21 (approximated)

Hence, the solution to the equation is approximately 7.21

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Answer:

\(2z + 38\)

Step-by-step explanation:

\(1. \: 4 + 2z + 34 \\ 2. \: 2z + (4 + 34) \\ 3. \: 2z + 38\)

\(a*b\) must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.

Let n be an integer and a, b be relatively prime integers, each of which divides n. This means that a and b have no common factors other than 1. According to the Fundamental Theorem of Arithmetic, the prime factorization of n can be written as n = p1^k1 * p2^k2 * ... * pn^kn. Since a and b divide n, each of their prime factorizations must contain all of the prime factors of n, and the exponents must be less than or equal to the exponents of n. Therefore, a*b must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.

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The number 100 would land in column 2

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

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a) This refers to the mode = $575

b) This refers to the median = $581

c) This refers to the 86th Percentile = $612

d) This refers to the First Quartile = $552

e) The salary is that is 2 standard deviations below the mean = $529

f) About 36 percent of employee's salaries is above $592

g) $627 is 1.5 standard deviations above the mean

Given data

Mean = $585

Median = $581

Mode = $575

First Quartile = $552

Third Quartile = $605

Standard deviation = $28.

86th Percentile = $612

P64 = $592

a) What is the most common salary? $575

This refers to the mode = $575

b) What salary did half the employee's salaries surpass? $581

This refers to the median = $581

c) About what percent of employee's salaries is below $612?

This refers to the 86th Percentile = $612

d) What percent of the employee's salaries are above $552?

This refers to the First Quartile = $552

e) What salary is 2 standard deviations below the mean?

The mean is given as $585 and the standard deviation is $28

2 standard deviation below the mean is:

= 585 - 2 * 28

= 585 - 56

= $529

f) About what percent of employee's salaries is above $592?

P64 is given as $592 this refers to the percent of employee's salaries that falls under 64%. so the percent above is above 64 is given as:

= 100 - 64

= 36%

g) What salary is 1.5 standard deviations above the mean?

The mean is given as $585 and the standard deviation is $28

1.5 standard deviation below the mean is:

= 585 + 1.5 * 28

= 585 + 42

= $627

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The binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

To determine which binomial is a factor of the trinomial x² - 13x + 30, we need to factorize the trinomial completely.

In this case, we need to find two binomials in the form (x - a)(x - b) that satisfy the equation:

(x - a)(x - b) = x² - 13x + 30

So, (x - 3)(x - 10) = x² - 13x + 30.

Therefore, the binomials (x - 3) and (x - 10) are factors of the trinomial x² - 13x + 30.

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Answer:

B. The product of 5 and a number.

Product means multiplication is taking place. In this case, 5 is being multiplied with n.

Hope this helps!

The Surface area of Triangular Prism is 132 cm².

We have have the dimension of prism as

Sides = 3 cm, 4 cm, 5 cm

and, l = 10 cm

and, b= 4 cm

Now, Surface area of Triangular Prism as

= (sum of sides) l + bh

= (3 + 4 + 5)10 + 4 x 3

= 12 x 10 + 12

= 120 + 12

= 132 cm²

Thus, the Surface area of Triangular Prism is 132 cm².

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Answer:

See Explanation

Step-by-step explanation:

The question is incomplete. However, you can make use of the following tips to answer your question.

We have that:

\(x = 10.8\)

\(x + 29.2 = 40\)

because

\(10.8 + 29.2 = 40\)

Another possible expression is:

\(50.8 - x = 40\)

This is so, because:

\(50.8 - 10.8 = 40\)

Another one is:

\(2x + 18.4 = 40\)

This is so because:

\(2 * 10.8 + 18.4 = 40\)

So, all you need to do is to substitute 10.8 for x in the given expression,

If the solution equates to 40, then that's your answer

Answer:

33.20% probability that the sample mean would differ from the population mean by greater than 1 gallon

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.