What is the length of EF in the right triangle below?
D
26
10
E
F

to keep it simple 0.014

to keep it long but sort of simple

0.0138888888888889

Answer:

0.0138, 8 is repeating

Step-by-step explanation:

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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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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The exponential function that best models the value of the stock after n weeks is given as follows:

v(n) = 1600(1 + r)^n.

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

The initial investment was of 1600, hence the parameter a is given as follows:

a = 1600.

The rate of change is obtained multiplying two consecutive values on the table, and will have the following format:

b = 1 + r.

In which r is the growth rate.

The problem is incomplete, hence the general procedure to obtain the function is presented.

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Answer:

72 inches

Step-by-step explanation:

Answer:

C. The cost of a box of cereal

Step-by-step explanation:

In the question, we are given the number of 3 boxes of cereal, 2 loaves of bread, and that the total cost is $15. We can see these numbers in the equation, and putting it into context, we see that the 15 is on the right side of the equation, which indicates cash. Therefore, the 3 and 2 are accounted for, but their prices are unknown. X is a placeholder for the unidentified cost of a box of cereal, and we know that it's the boxes of cereal and not the loaves of bread because there are 3 and not 2.

Answer:

200 lbs.

Step-by-step explanation:

Divide mass value by 16 to convert oz to lbs.

3,200/16=200

Answer:

y=2(x-2.5)

Step-by-step explanation:

Answer:

y = 2x - 5

Step-by-step explanation:

Let us consider the points (- 2, - 9) & (0, - 5)

Equation of line in two point form is given as:

[y-(-9)]/[-9-(-5)] = [x - (-2)]/[-2 - 0]

(y + 9)/(-9 +5) = (x + 2)/ (-2)

(y + 9)/(-4) = (x + 2)/(-2)

(y + 9)/(2) = (x + 2)/(1)

(y + 9) = 2(x + 2)

y + 9 = 2x + 4

y = 2x + 4 - 9

y = 2x - 5

This is the required function.

Answer:

A. 1mm = 5mi

Step-by-step explanation:

20 mi divided by 4 mm would simplify down to 5 mi per 1mm. If there is 4 mm then there is 5mi*4mm which equals out to 4 mm = 20 mi.

A scale of the map is the relationship between the distance on the map to the actual distance. The scale of the map is 1 mm: 5 miles (ml). Thus the option A is the correct option.

To find out the scale of the map, we have to know about scaling of map.

The scaling of map is the ratio or relationship between the distance of the map to the original distance.

Given information-

The distance of the two houses on the ground is 20 miles.

The distance of the two houses on the map is 4 mm.

Suppose the scale of the map is \(s\).

As the 20 miles distance on the ground is same as the 4 mm distance on the map.

Thus the scale of the map can be given as,

\(s=\dfrac{4\rm mm}{20\rm miles} \\s=\dfrac{1\rm mm}{5\rm miles}\)

Hence the scale of the map is 1 mm: 5 miles (ml). Thus the option A is the correct option.

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Answer:It will be -14 degrees, because in the negative side, droping or subtracting, would instead be adding. -9 - 5 = -14.

                                                                    9 + 5 = 14

Step-by-step explanation:

The question is incomplete. Here is the complete question.

In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each particpant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree", and these are assigned the numbers 1 or -1, respectively. pArticipnat's responses to the survey are encoded as a vector in R4, where coordinates coreespond to their answers to each question. Here are the questions:

Question #1: I prefer outdoor activities, rather than indoor activities.

Question #2: I prefer going out to eat in restaurants, rahter than cooking at home.

Question #3: I prefer texting, rather than talking on the phone.

Question #4: I prefer living in a small town, rather than in a big city.

Here are the results for the questionaire, with a group of 5 participants:

                        Question1     Question2   Question3       Question4

participant A           1                      1                   -1                      -1

participant B           -1                     1                    1                       1

participant C           -1                    -1                    1                       1

participant D           1                     -1                   -1                      -1

participant E            1                    -1                    1                       1

Two participants are considered to be "compatible" with each other if the angle between their compatibility vectors is 60° or less. Participants are considered to be "incompatible" if the angle between their compatibility vectors is 120° or larger. For angles between 60° or 120°, pairs of participants are warned that they "may or may not be compatible".

(a) Which pairs of paricipants are compatible?

(b) Which pairs of participants are incompatible?

(c) How would this method of testing compatibility change if the questionnaire also allowed the answer "Neutral", which would correspond to the number zero in a participant's vector? Would this be better than only

allowing  "Agree" or "Disagree"? Could anything go wrong if we allowed "Neutral" as an answer?

Answer: (a) Participants A and D; B and C; C and E.

(b) Participants A and B; A and C; A and E; B and D; C and D;

Step-by-step explanation: Vectors in R4 are vectors in a 4 dimensional space and are determined by 4 numbers.

Vectors form angles between themselves and can be found by the following formula:

cos α = \(\frac{A.B}{||A||.||B||}\)

which means that the cosine of the angle between two vectors is equal the dot product of these vectors divided by the product of their magnitude.

For the compatibility test, find the angle between vectors:

1) The vectors magnitude:

Magnitude of a vector is given by:

||x|| = \(\sqrt{x_{i}^{2} + x_{j}^{2}}\)

Since all the vectors have value 1, they have the same magnitude:

||A|| = \(\sqrt{1^{2} + 1^{2} + (-1)^{2} + (-1)^{2}}\) = 2

||A|| = ||B|| = ||C|| = ||D|| = ||E|| = 2

2) The dot product of vectors:

A·B = 1(-1) + 1(1) + (-1)1 + (-1)1 = -2

cos \(\alpha_{1}\) = \(\frac{-2}{4}\) = \(\frac{-1}{2}\)

The angle that has cosine equal -1/2 is 120°, so incompatible

A·C = 1(-1) + 1(-1) + (-1)1 + (-1)1 = -4

cos \(\alpha _{2}\) = -1

Angle = 180° --------> incompatible

A·D = 1(1) + 1(-1) + (-1)(-1) + (-1)(-1) = 2

cos \(\alpha _{3}\) = 1/2

Angle = 60° ---------> COMPATIBLE

A·E = 1.1 + 1(-1) + (-1)1 + (-1)1 = -2

cos \(\alpha_{4}\) = -1/2

Angle = 120° --------> incompatible

B·C = (-1)(-1) + 1(-1) + 1.1 + 1.1 = 2

cos \(\alpha _{5}\) = 1/2

Angle = 60° -------------> COMPATIBLE

B·D = (-1)1 + 1(-1) + 1(-1) + 1(-1) = -4

cos\(\alpha_{6}\) = -1

Angle = 180° -----------> incompatible

B·E = (-1)1 + 1(-1) + 1.1 + 1.1 = 0

cos\(\alpha _{7}\) = 0

Angle = 90° -------------> may or may not

C·D = (-1)1 + (-1)(-1) + 1(-1) + 1(-1) = -2

cos\(\alpha_{8} =\) -1/2

Angle = 120° ---------------> Incompatible

C·E = (-1)1 + (-1)(-1) + 1.1 + 1.1 = 2

cos \(\alpha_{9}\) = 1/2

Angle = 60° ---------------> COMPATIBLE

D·E = 1.1 + (-1)(-1) + (-1)1 + (-1)1 = 0

cos \(\alpha_{10}\) = 0

Angle = 90° -----------------> may or may not

(c) Adding zero (0) as a component of the vectors would have to change the method of compatibility because, to determine the angle, it is necessary to calculate the magnitude of a vector and if it is a zero vector, the magnitude is zero and there is no division by zero. So, unless the service change the method, adding zero is not a good option.

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

To determine the possible degree(s) of a function from the graph alone, you need to examine the behavior of the graph at the extremes (far left and far right) and consider the number of turning points or changes in direction. Here's a step-by-step approach:

Look at the far left side of the graph: Determine the behavior of the graph as it approaches negative infinity. Does the graph approach a specific value, such as a horizontal line (asymptote) or the x-axis? If the graph approaches a horizontal line, it suggests a polynomial function of even degree. If the graph approaches the x-axis, it indicates a polynomial function of odd degree or possibly a function with a root of multiplicity greater than one.

Look at the far right side of the graph: Determine the behavior of the graph as it approaches positive infinity. Similar to step 1, observe if the graph approaches a specific value or a horizontal line. The behavior at the far right side should be consistent with the behavior at the far left side. This can help you identify if the function is even or odd degree.

Examine the number of turning points or changes in direction: Count the number of times the graph changes direction. These points are where the slope of the graph changes from positive to negative or vice versa. The number of turning points can provide an indication of the degree of the polynomial. For example, if there are two turning points, it suggests a polynomial function of degree 3.

Remember that this method provides potential degrees, but it may not definitively determine the exact degree of the function. Additional information or analysis might be required for a more accurate determination.

Answer:D

Step-by-step explanation:

It is a monomial and the others and not

Answer:

Area = 200 + 50 + x

Step-by-step explanation:

Given

Length = 20

Width = 30

Side Walk = x

Required

Determine the area.

To do this we need to get the new worth and length by adding the length of the sidewalk.

This gives:

Length = 20 + x.

Width = 30 + x

So, area becomes.

Area = (20 + x)(30 + x)

Area = 600 + 20x + 30x + x²

Area = 200 + 50 + x²

Answer:

The correct option is A

Step-by-step explanation:

From the question we are told that

   The average  number of meetings  hours per week is \(\mu= 18 \ hours\)

    The standard deviation is  \(\sigma = 5.2 \ hours\)

     The sample size is  n=  35

     The sample average per week is  \(p = 16.8 \ hours\)

From each solution statement we can deduce that the confidence level is  

    \(t = 95\)%

Thus the significance level is  \(\alpha = 0.05\)= 5%

The z value for the significance level is gotten as 1.96 from the z-table

    The confidence level interval for the sample mean is mathematically evaluated as

            \(\= x = \mu \pm (1.96 * \frac{\sigma }{\sqrt{n} } )\)

 Sustituting values

           \(\= x = 18 \pm (1.96 * \frac{5.2 }{\sqrt{35} } )\)

             \(\= x = 18 \pm1.7\)

=>               \(18 - 1.7 < \= x < 18 +1.7\)

                  \(16.3 < \= x < 19.7\)

Answer:

39

Step-by-step explanation:

Answer: 39?

Step-by-step explanation: is it integers?

Answer:

20

Step-by-step explanation:

side BC = side AB

so their base angles that is ∠A = ∠C = (3x+20)°

now, total measure of the angles of a triangle is 180° & ∠B = x°

Now,

m∠A + m∠B + m∠C = 180

⇒ 3x + 20 + x + 3x + 20 = 180

⇒ 7x + 40 = 180

⇒ 7x = 140

⇒x = 20

\(x^5 \cdot (x^{-2})^{-6}\\\\=x^5 \cdot x^{(-2)(-6)}\\\\=x^{5} \cdot x^{12}\\\\=x^{5+12}\\\\=x^{17}\)

Answer:

There are a total of 5/35 ways that you and your friend are both chosen

Step-by-step explanation:

ap3x

1 ounce ----- 0.0625 pound

Answer:

This is a fraction equal to

36 mile ÷ 3 1

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 3

36 mile ÷ 3

3 1 ÷ 3

=  

12 mile

1 1

=  

12 mile

1

= 12 mile per 1

Answer:

8

Step-by-step explanation:

Because you can count the squares on the side or you can just do the square root of 64.

The slope of the image of the original line y = 2x - 4 after the transformation (x,y) (-x, -y) is -2.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of the original line y = 2x - 4 is 2.

To find the slope of the image after the transformation, we can apply the transformation rule to two points on the original line, and then find the slope of the line passing through the images of those two points.

Let's choose two points on the original line:

Point 1: (0, -4)

Point 2: (1, -2)

Now we apply the transformation rule to each of these points:

Point 1 image: (-0, -(-4)) = (0, 4)

Point 2 image: (-1, -(-2)) = (1, 2)

The images of these two points lie on the line y = -2x + 4. The slope of this line is -2.

Therefore, the slope of the image of the original line y = 2x - 4 after the transformation (x,y) (-x, -y) is -2.

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Answer:

Step-by-step explanation:

1) The newly opened Mario's Trattoria is expected to produce a continuous income stream at the rate of

R(t) = 130,000 to generate income at the rate of

R(t) = 200,000 Camille purchased a 14-year franchise for a computer outlet store that is expected to generate income at the rate of

R(t) = 400,000

Given statement solution is :- The correct answer is: The frequency is 3 more than expected.

To determine the expected frequency of landing on an even number when rolling a fair six-sided number cube, we need to calculate the probability of landing on an even number and multiply it by the total number of rolls.

The number cube has six possible outcomes: 1, 2, 3, 4, 5, and 6. Of these, three are even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2 or 0.5.

The expected frequency can be found by multiplying the probability by the total number of rolls:

Expected frequency = Probability of landing on an even number × Total number of rolls

Expected frequency = 0.5 × 30 = 15

Now, we can compare the expected frequency (15) to the actual frequency (18) given in the problem statement.

The actual frequency is 18, and it is 3 more than the expected frequency (18 - 15 = 3).

Therefore, the correct answer is: The frequency is 3 more than expected.

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Answer: 48 more monthly payments

Step-by-step explanation:

Answer: 400

Step-by-step explanation:

Answer:

41.305x6= 247.83

Step-by-step explanation: