A project should take no more than 60 hours. If John can spare 7.5 hours per day to work on the project, what is the maximum number of days it will take him to finish

Work Shown:

4/3 = 72/x

4x = 3*72

4x = 216

x = 216/4

x = 54

Explanation:

Each fraction in the first step is of the form A/B, where A is the amount of punch and B is the amount of cranberry juice. Both measured in cups. In the 2nd step, I cross multiplied. Afterward, divide both sides by 4 to isolate x.

Li earns more than 78percentage of recent college graduates, and is in the 78th percentile of salaries earned.

1. Calculate the total number of recent college graduates surveyed: Multiply the total number of responses to the survey by 100 to get the total number of graduates surveyed.

2. Calculate the number of recent college graduates who earn less than or equal to Li's salary: Multiply the percentile (78%) by the total number of graduates surveyed to get the number of graduates who earn less than or equal to Li's salary.

3. Calculate the percentage of recent college graduates who earn less than or equal to Li's salary: Divide the number of graduates who earn less than or equal to Li's salary by the total number of graduates surveyed to get the percentage of graduates who earn less than or equal to Li's salary. The result will be 78%.

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Out of the given functions, a ,b, c, d , the function with complex roots are b and d.

What are complex roots?

Complex roots, also known as non-real roots, are roots of an equation that are not real numbers but instead are complex numbers. Complex roots are usually represented in the form of a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

The functions which have complex roots are b and d.

hence, out of the given functions, a ,b, c, d , the function with complex roots are b and d.

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The sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.

What is the eigenvalue?

Eigenvalues are the special set of scalar values that are associated with the set of linear equations most probably in the matrix equations. The eigenvectors are also termed characteristic roots.

To find the eigenvalues of matrix A, we can solve the characteristic equation |A - λI| = 0, where λ is a scalar and I is the identity matrix.

|A - λI| = 3- λ 1 4 0 2- λ 6 0 0 5- λ

= (3-λ)(5-λ) - 24 = λ^2 - 8λ - 15

Setting λ^2 - 8λ - 15 = 0, we can find the eigenvalues of the matrix by solving the quadratic equation.

λ^2 - 8λ - 15 = 0

λ = (8 ± √(8^2 + 4*15))/2

λ = (8 ± √(64 + 60))/2

λ = (8 ± √124)/2

So the eigenvalues of matrix A are λ_1 = (8 + √124)/2 and λ_2 = (8 - √124)/2

The sum of eigenvalues is λ_1 + λ_2 = (8 + √124)/2 + (8 - √124)/2 = 8

The product of eigenvalues is λ_1 * λ_2 = (8 + √124)/2 * (8 - √124)/2 = -15

Hence, the sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.

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The output is determined by the pattern of the input.

Pattern is a repeated design or motif used to create a visually pleasing effect. Patterns are often seen in nature, architecture, clothing, and artwork. Patterns can be used to create shapes, textures, and decorations. They can add interest and depth to a design. Patterns can be made up of geometric shapes, lines, curves, and combinations of those elements. They can be created with a variety of materials and techniques, including weaving, printing, embroidery, and painting. Patterns can be used to create continuity, emphasize a focal point, or provide a sense of balance. Patterns can be used to draw the eye to a particular area, or to create a sense of order and organization.

In this example, each output number is the sum of the two numbers before it. Therefore, the output is 6 (1 + 2), 12 (2 + 4), 18 (4 + 5), 24 (5 + 6), and 30 (6 + 8).

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149.0848502 decibels are emitted from a jet plane with a sound intensity of 8.1*10²

Decibels are units for expressing the ratio between two physical quantities, usually amounts of acoustic or electric power, or for measuring the relative loudness of sounds.

Number of watts per square meter

d = 10*log(I/IO)

IO = 10⁻¹²

Therefore: d = 10 * log(I/10⁻¹²

jet plane has a sound intensity of 8.1*10² watts per square meter.

Therefore: d = 10*log((8.1*10²) / 10⁻¹²)

10²/10⁻¹² = 10²⁽⁻¹²⁾ = 10⁽²⁺¹²⁾ = 10¹⁴

Therefore: d = 10 * log(8.1 * 10¹⁴)

log(8.1 * 10¹⁴) = 14.90848502

10 * that = 149.0848502 decibels

That's the value of d.

In conclusion, 149.0848502 decibels are emitted from a jet plane with a sound intensity

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Graph A.

Proportional relationships have to go through the origin, (0,0).

Answer:

x = 56

First number = 56

Second number = 280

Third number = 156

Total 331

Step-by-step explanation:

The solution of the compound inequality 3x + 5 > -1  or  -2x-7 > 5 is x > -2 or x < -6.

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.  

A compound inequality is an inequality that combines two simple inequalities.

Therefore,

3x + 5 > -1  or  -2x-7 > 5

Let's solve the inequality individually

3x + 5 > -1

3x > -1 - 5

3x > -6

x > -6 / 3

x > -2

Therefore,

-2x - 7 > 5

-2x > 5 + 7

-2x > 12

x > 12 / -2

x < -6

Hence,

x > -2 or x < -6

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a) To find the real and imaginary parts of a complex number, we can use the equation z = x + iy, where x is the real part and y is the imaginary part.

To sketch a stem plot, we need to plot the real part on the x-axis, and the imaginary part on the y-axis. For example, for the complex number z = 4 + 3i, the real part is x = 4 and the imaginary part is y = 3. Therefore, the stem plot would be (4, 3).

b) To find the magnitude and phase of a complex number, we can use the equation z = |z|e^(iθ), where |z| is the magnitude and θ is the phase. To sketch a stem plot, we need to plot the magnitude on the x-axis, and the phase on the y-axis. For example, for the complex number z = 4 + 3i, the magnitude is |z| = 5 and the phase is θ = arctan(3/4). Therefore, the stem plot would be (5, arctan(3/4)).

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1/6

The probability of an event is the number of ways the event can happen divided by the number of possible outcomes. In this case, the possible outcomes are the numbers on the die, which are 1, 2, 3, 4, 5, and 6.

The event of rolling a number greater than 5 or less than 3 can happen in two ways: rolling a 6 or rolling a 1 or 2. So the probability of this event is:

P(greater than 5 or less than 3) = (number of ways the event can happen) / (number of possible outcomes) = 2/6 = 1/3

So the answer is option D. 1/6

The domain of a function is the set of possible values that can be plugged into it.

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

The collection of all possible inputs and outputs constitutes a function's domain and range, respectively. Important features of a function are the domain and range. The domain accepts all potential input values from the set of real numbers, and the range accepts all function output values.

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No, it is not true that GCD(A, B, C).

What is the greatest common divisor?

The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF). For instance, since both 15 and 10 can be divided by 5, 5 is the biggest common factor between both.

Here, we have

Given: Aisha's number and Benoit's number have a common divisor greater than 1. Aisha's number and Carleen's number also have a common divisor greater than 1. Benoit's number and Carleen's number also have a common divisor greater than 1.

We have to determine if is it necessarily true that the greatest common divisor of all three numbers is greater than 1.

Here, we solve this with an example.

A = 6 = 2*3,

B = 14 = 2*7,

C = 21 = 3*7

There is no GCD greater than 1 that divides all of A, B and C.

Hence, No, it is not true that GCD(A, B, C).

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1. The coupon will save: $6.

2. The sales tax is of: $1.44.

3. The total price paid for the meal is of: $25.44.

The total cost is obtained applying the proportions in the context of this problem.

The initial fee for the meal is of:

$30.

With the coupon of 20% off, the amount paid is of:

0.8 x 30 = $24.

Meaning that the amount saved is of:

30 - 24 = $6.

After the sales tax, the total price is of:

1.06 x 24 = $25.44.

Meaning that the tax is of $1.44.

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c. +.80 is correct.

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The solution is a simple process of subtracting the largest coin value from the total amount, adding any coins that fit, and repeating the process until the total amount is reached. This algorithm guarantees that the minimum number of coins needed to arrive at the total will be displayed.

1. Start by subtracting the largest coin value from the total amount.

2. If the difference is greater than 0, add the coin to the total and repeat the process.

3. If the difference is 0, move onto the next smallest coin value.

4. Repeat the process until the total amount is reached.

5. Once the total amount is reached, the minimum amount of coins needed to arrive at the total will be displayed.

The solution is a simple process of subtracting the largest coin value from the total amount, adding any coins that fit, and repeating the process until the total amount is reached. This algorithm guarantees that the minimum number of coins needed to arrive at the total will be displayed.

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The general solution of the first-order linear differential equation y' - (ln x)y = [tex]3 x^x[/tex] is [tex]y=3x^{x} + cx^{x} e^{-x}[/tex]

As per the give,n data the given differential equation is:

y' - (ln x) y = 3 [tex]x^x[/tex]

Here have to determine the general solution of the first-order linear differential equation.

The differential equation is linear if the dependent variable y and its derivative only occur in the first degree.

Then, [tex]$\frac{d y}{d x}-(\ln x) y=3 x^x$[/tex]

This is of the form [tex]$\frac{d y}{d x}[/tex] + P(x)y = Q(x) which is the linear equation.

In order to solve this kind of differential equation, we have to multiply it by an integrating factor.

Here, P = - ln (x), Q(x) = 3 [tex]x^x[/tex]

I F = [tex]e^{\int P d x}[/tex]

I F = [tex]e^{-\int \ln (x)}[/tex]

I F = [tex]e^{-(x \ln x-x)}[/tex]

I F = [tex]e^{x-x \ln x}[/tex]

I F = [tex]\frac{e^x}{e^{x \ln x}}[/tex]

I F = [tex]\frac{e^x}{x^x}[/tex]

Hence, the general solution is

[tex]& y(I F)=\int Q(x)(I F) d x+c \\[/tex]

[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=\int 3 x^x\left(\frac{e^x}{x^x}\right) d x+c \\[/tex]

[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=\int 3 e^x d x+c \\[/tex]

[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=3 e^x+c \\[/tex]

[tex]& \Rightarrow y=3 x^x+c x^x e^{-x}[/tex]

Hence, the general solution is [tex]y=3x^{x} + cx^{x} e^{-x}[/tex]

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The probability that the student is female or earned grade C is 0.6

You should recall that probability is the chance of occurrence of an event E

P(E) = (Number of required outcome)/(number of possible outcomes)

The given parameters are

We'll use this table (below) to answer the questions

                         A B C Total

Male           16 17 11 44

Female           14 6 3 23

Total          30 23 14 67

Pr(E) = 23/67 + 14/67

Simplifying the fractions to have

37/67 = 0.55

Therefore this is approximately rounded to 1 decimal place as  0.6

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The operating activities section of the statement of cash flows for the company using the indirect method showed a net cash used by operating activities of $(4,400).

Net Loss $(16,000)

Adjustments to Reconcile Net Loss to Net Cash Used by Operating Activities:

Depreciation Expense 14,600

Decrease in Accounts Receivable 24,000

Increase in Salaries Payable (18,000)

Decrease in Interest Payable (8,000)

Net Cash Used by Operating Activities $(4,400)

The operating activities section of the statement of cash flows for the company using the indirect method showed a net cash used by operating activities of $(4,400). This was calculated by adjusting the net loss of $(16,000) with depreciation expense, decrease in accounts receivable, increase in salaries payable, and decrease in interest payable.

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I'm willing to pay up to $1 to play the game. If I get lucky and the coin lands on heads multiple times, I could potentially win more than $1.

The game is quite simple. I start with $1 and then flip a fair coin. If I get heads, I double my winnings and flip the coin again. I will keep flipping the coin until I get tails, at which point the game is over and I collect the money I have won. Depending on how lucky I get, I could potentially win more than $1. Therefore, I am willing to pay up to $1 to play the game. The expected value of this game is $1.50. This is because, on average, I will get heads 50% of the time and tails 50% of the time. So, if I get heads every time, I will double my winnings each time and end up with $2. If I get tails every time, I will end up with $1. Therefore, the expected value is the average of these two outcomes, which is $1.50. There is also some risk involved in this game. If I get unlucky and get tails on my first flip, then I will only get my money back and not make any profit. Therefore, I have to be willing to take on some risk if I want to try and make a profit. It is important to note that this game does not guarantee a profit. The expected value may be $1.50, but I could end up making less or more than that depending on how lucky I get. Therefore, I have to be willing to accept some uncertainty if I want to play this game.

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Let's call the grandmother's current age G and the grandson's current age S.

From the first piece of information given, we know that:

G = S + 48

From the second piece of information given, we know that:

G - 14 = 13S

We can use the first equation to substitute for G in the second equation:

(S + 48) - 14 = 13S

S + 34 = 13S

34 = 12S

S = 34/12

S = 2.8 years

So the grandson is 2.8 years old.

Now we can use this information to find the grandmother's age:

G = S + 48

G = 2.8 + 48

G = 50.8 years

So, the grandmother is 50.8 years old and the grandson is 2.8 years old.

(s+12)^3

I am wasting space here as you can tell but no fr the answer is (s+12)^3

Yes, this is reasonable. The circumcenter of a triangle is found by taking the average of the x-coordinates of the three points and the average of the y-coordinates of the three points, so for this triangle, the circumcenter would be at (5.67, 2.67).

The circumcenter of the triangular plot of land with vertices at (1, 5), (7, 5), and (8, 0) is at (5.67, 2.67), which is reasonable.

1. Calculate the average of the x-coordinates of the three vertices: (1 + 7 + 8) / 3 = 16 / 3 = 5.67

2. Calculate the average of the y-coordinates of the three vertices: (5 + 5 + 0) / 3 = 10 / 3 = 2.67

3. Therefore, the circumcenter of the triangle is (5.67, 2.67).

The circumcenter of the triangular plot of land with vertices at (1, 5), (7, 5), and (8, 0) is at (5.67, 2.67), which is reasonable.

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The elements of each set are given as follows:

a) A and C: {1, 3, 7}.

b) B U C = {1, 2, 3, 4, 6, 7, 8, 10}

c) C U C' = U.

The intersection operation between two sets is composed by the elements that belong to both sets, hence:

A and C: {1, 3, 7}.

(as the elements 1, 3 and 7 belong to both of the sets).

The union operation between two sets is composed by the elements that belong to at least one of the sets, hence:

B U C = {1, 2, 3, 4, 6, 7, 8, 10}

The union between a set and it's complement is always the universal set, hence:

C U C' = U.

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An equation to represent this proportional relationship is y = 65x.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (3, 195) and (6, 390) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 195 = (390 - 195)/(6 - 3)(x - 3)

y - 195 = 195/3(x - 3)

y - 195 = 65(x - 3)

y = 65x - 195 + 195

y = 65x

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The table indicates that purchase price is a function of demand, as each demand is mapped to a single purchase price.

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

The input and output variables for this problem are given as follows:

In the table, there are no repeated demand values, meaning that the purchase price is a function of the demand, as there are no inputs mapped to multiple outputs.

The table is given by the image presented at the end of the answer.

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I'm pretty sure the answer is D.mean absolute deviation.

I hope it'll help you.

The expression are matched to the simplest form as shown below

simplest form   Equation

12 - 1/2r              (13 - 3/2 r) - (1 - r)

r - 13/6                (7r - 3/2) - (2/3 + 6r)

13r + 20              (6r + 7) + (13 + 7r)

-12 + r                 (-8 - r) + (2r - 4)

The simplest form is solved by evaluating each of the equation in the problem

Evaluating the expressions

(6r + 7) + (13 + 7r)

collecting like terms

6r + 7r + 13 + 7

13r + 20

(13 - 3/2 r) - (1 - r)

opening the parenthesis (the negative sign before the second parenthesis changes the sign in the second parenthesis)

13 - 3/2 r - 1 + r

collecting like terms

13 - 1 - 3/2 r + r

12 - 1/2 r

(-8 - r) + (2r - 4)

collecting like terms

-8 - 4 - r + 2r

-12 + r

(7r - 3/2) - (2/3 + 6r)

opening the parenthesis (the negative sign before the second parenthesis changes the sign in the second parenthesis)

7r - 3/2 - 2/3 - 6r

collecting like terms

7r - 6r - 3/2 - 2/3

r - 13/6

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A parallelogram can only be a rectangle if the following conditions are satisfied: B) The diagonals must be congruent, and A) the diagonals must be congruent and perpendicular.

Therefore,

One feature of a parallelogram is that its diagonals are divided in half. A rectangle also has congruent diagonals.

In addition to being congruent, the diagonals in a square are perpendicular to one another.

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Answer:

  332 cm²

Step-by-step explanation:

You want to know the surface area of a tin can that is 7 cm in diameter and 11.6 cm high.

The area of a cylinder is given by the formula ...

  SA = πd(d/2 +h) . . . . . where d is the diameter and h is the height

Using the given values, d=7 and h=11.6, we find the area to be ...

  SA = (3.14)(7 cm)(3.5 +11.6 cm) ≈ 332 cm²

About 332 square centimeters of tin are required to make the can.