ten more than the quotient of c and three

There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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Answer:

x^2

Step-by-step explanation:

Any even number raised to two is even.

Eg: 4^2 = 16

12^2 = 144

Etc...

And

Any odd number raised to two is odd.

Eg: 5^2 = 25

13^2 = 169

Etc...

And also x^2 is greater than 2x & x+3 & x+2

The simplified form of the given complex fraction is (2x+1)/(x+2).

The given complex fraction is \(\frac{\frac{2}{x+2} }{\frac{1}{x} } +\frac{1}{x+2}\).

Here, the given fraction can be solved as follows

2/(x+2) ×x/1 + 1/(x+2)

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

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

Therefore, the simplified form of the given complex fraction is (2x+1)/(x+2).

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The slope of a line is y=mx+c, where m is the slope. The lines is perpendicular to y = 1/4x -3 is Y=-4x+6.

The slope of a line is y=mx+c, where m is the slope.

The given line is y = 1/4x -3.

slope m1=1/4.

slope of second line=-(1/m)

=-(1/1/4)

=-4

point slope intercept form is y-y1=m(x-x1)

Equation of the perpendicular line passing through point (0,6) is

y-6=-4(x)

y=-4x+6

Therefore the line perpendicular to y = 1/4x -3 is Y=-4x+6.

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Answer:

Step-by-step explanation:

Answer

This statement is not correct.

Explanation

Not every straight line is a graph of a function.

Although, nearly all linear equations are functions because they pass the vertical line test. That is, most linear equations are set up that you can obtain a value for y, given a value for x.

Examples of linear equations that are functions include

y = 10

y = x

y = 2x

y = 7x + 14

y = − 2x − 7

The exceptions are relations that fail the vertical line test. The ones that don't give a y-value for every x.

Examples of linear equations that are not functions include

x = some constant

That is,

x = 7

x = -100 etc.

Hope this Helps!!!

The number of freshmen that are students is 738

Let y represent the number of students that are freshmen

The freshmen class is made up of 480 female students

This number represents 65% of the freshmen class

Therefore the total number of students that are freshmen can be calculated as follows

y × 65/100= 480

65y/100= 480

Cross multiply both sides

65y= 480 × 100

65y= 48000

y= 48000/65

y= 738.4

≅ 738

Hence 738 students are freshmen

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Answer:

$14.00

Step-by-step explanation:

So, the 20 peaches all weigh 4 oz, and there are 16 oz in 1 pound. 16 oz divided by 4 is also equal to 4 oz, so we need to divide $2.80 by 4, which would be $0.70. That means that a 4 oz peach would be $0.70, so we multiply that by 20, which gives us $14.00, so Stacey will need $14.00 to buy 20 peaches that each weigh 4 oz.

Answer:15x3 /=divide 5 = 9

Step-by-step explanation:

because if you do 15x3 it is 45 then you divide it by 5 and get 9 as your answer!

The probability of selecting two red marbles and one blue marble is \(\frac{4}{15}\)

To calculate the probability, we first determine the total number of possible outcomes. Since three marbles are being selected simultaneously, there are C(6, 3) = 20 different ways to choose three marbles from the six available.

Next, we consider the number of favorable outcomes, which in this case is selecting two red marbles and one blue marble. We can choose two red marbles from the four available in C(4, 2) = 6 ways, and we have only one blue marble to select. Therefore, there are 6 × 1 = 6 favorable outcomes.

Finally, we calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. Thus, the probability of selecting two red marbles and one blue marble is 6÷20, which simplifies to 3÷10 or approximately 0.4.

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Answer:

-3x(7x+8)

Step-by-step explanation:

-3x^2-18x^2-24x

-3x(x+6x+8)

-3x(7x+8)

The area of the given polygon is 30 square units.

The area of a triangle can be calculated using the formula 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)] where (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the coordinates of its vertices. This formula is also useful in finding the area of any polygon with given coordinates.

The area of the given polygon can be calculated by the expression of the area of triangle as 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)].

The given polygon can be divided into two ΔABC and  ΔACD,

Then, the area is given as follows,

Area of ΔABC +  Area of ΔACD

= 1/2|[-3(4 - 1) + -3(1 - 1) + 7(1  - 4)]| + 1/2|[-3(1 - 4) + 7(4 - 1) + 7(1 - 1)]|

= 1/2 × 30 + 1/2 × 30

= 30

Hence, the area of the given polygon is 30 square units.

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The value of x if the volume and 6 by the area of one face are equal is 6

The side length of the cube is given as

Side length = x

From the question, we have the statement to be

The volume of the cube and 6 times the area of one of its faces have the same value.

The volume of a cube with side length x is

V = x³

The surface area multiplied by 6 is

A = 6x²

When both have the same values, we have

x³ = 6x²

Divide both sides by x²

x = 6

Hence, the value of x is 6

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Josue used 150 square centimeters of wrapping paper to cover the cube-shaped gift box

To determine the amount of wrapping paper used by Josue for the cube-shaped gift box, we need to calculate the surface area of the cube.

The net of the gift box consists of six squares, each representing a face of the cube. The dimensions provided in the figure show that each side of the squares is 5 cm.

Since a cube has six faces, we need to calculate the total surface area by multiplying the area of one square face by six.

The formula to find the area of a square is side length squared, so we can calculate the area of one square face as 5 cm * 5 cm = 25 cm².

Now, to find the total surface area, we multiply the area of one face by six: 25 cm² * 6 = 150 cm².

Therefore, Josue used 150 square centimeters of wrapping paper to cover the cube-shaped gift box.

It's worth noting that this calculation assumes that there is no overlap or excess wrapping paper used while wrapping the gift box. Additionally, we have assumed that the dimensions provided are accurate and refer to the side length of the squares in the net.

Overall, the amount of wrapping paper used can vary based on the wrapping technique employed and any additional decorations or folds added to the gift box.

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Answer:

area of the figure= 58.3ft²

Step-by-step explanation:

area of the figure= area of trapezoid+ area of a rectangle

area of the figure= [½(a+b)*height]+ (length*breadth)

area of the figure= [½(3+14)*3]+ (11*3)

area of the figure=25.3+ 33

area of the figure= 58.3ft².

The first five terms of the sequence b_n = (-1)^n(4n-4) starting with n = 1 are: -4, 8, -12, 16, -20.

The sequence bn = (-1)^n(4n - 4) is an alternating sequence, where each term alternates in sign between positive and negative. The first term is 0, and every other term after that is also 0. This is because when n is odd, (-1)^n is equal to -1, and when n is even, (-1)^n is equal to 1. Therefore, the expression simplifies to 0.

For the even terms (n = 2, 4, 6, ...), the expression simplifies to 8n - 8. These terms are positive and increase by 8 as n increases.

For the odd terms (n = 3, 5, 7, ...), the expression simplifies to -8n + 8. These terms are negative and decrease by 8 as n increases.

Therefore, the first five terms of the sequence are 0, 8, -8, 0, 16, and the sequence continues alternating between 0 and positive/negative multiples of 8 as n increases.

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Answer:

3.1354776 m2

Step-by-step explanation:

Answer: 33.75

Step-by-step explanation:

5 times 3 is 15 and 15 times 2 1/4 is 33.75

Answer:

(2x+1)(2x+1)

Step-by-step explanation:

Factor=4x^2+4x+1

4x^2+4x+1 =(2x+1)(2x+1)

Answer:

  x = 28 649/700

Step-by-step explanation:

Add 780/28.

  1.07 +780/28 = x

  x = 28 649/700 = 28.92_714285(repeating)

_____

If one were concerned with significant digits, one could argue that the value should be rounded to 28.93, the precision of 1.07.

Answer:

  10.)  -46 -38i

  11.)  12 +8i

Step-by-step explanation:

You want the products (2+6i)(-8+5i) and 4i(2-3i) expressed in standard form.

An expression containing i can be expanded or simplified by treating i the same as any other variable. All instances of i² can be replaced by -1.

  (2 +6i)(-8 +5i) = (2)(-8) +2(5i) +(6i)(-8) +(6i)(5i)

  = -16 +10i -48i +30i² . . . . . . i² = -1

  = -46 -38i

  4i(2 -3i) = (4i)(2) +(4i)(-3i) = 8i -12i²

  = 12 +8i . . . . . . . i² = -1

Simplify the expression.

15x − 3y − 8

Mia and Vincent together can finish the work in 8.88 hours.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given,  Mia can choreograph the dance for the show in 20 hours.

So, the efficiency of Ma is (1/20).

Vincent can choreograph the dance by himself in 16 hours.

So, the efficiency of Vincent is (1/16).

Therefore, Together their efficiency is (1/20 + 1/16).

= (4 + 5)/80.

= 9/80.

Hence together they can do the work in 80/9 Or 8.88 hours.

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The solution to the equation 0.2(10 - 5c) = 5c - 16 is c = 3.

To solve the equation 0.2(10 - 5c) = 5c - 16, we will first distribute the 0.2 on the left side of the equation:

0.2 * 10 - 0.2 * 5c = 5c - 16

Simplifying further:

2 - 1c = 5c - 16

Next, we will group the variables on one side and the constants on the other side by adding c to both sides:

2 - 1c + c = 5c + c - 16

Simplifying:

2 = 6c - 16

To isolate the variable term, we will add 16 to both sides:

2 + 16 = 6c - 16 + 16

Simplifying:

18 = 6c

Finally, we will divide both sides by 6 to solve for c:

18/6 = 6c/6

Simplifying:

3 = c

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Answer:

y = -5/3x + 4

Step-by-step explanation:

slope = -5/3

-1 = -5/3(3) + b

-1 = -5 + b

4 = b

y = -5/3x + 4

Answer:

\(y=-\frac{5}{3}x+4\)

Step-by-step explanation:

To write down a line that is perpendicular to one line, make sure that their slopes give a product of -1:

\(\frac{3}{5}*m_2 =-1\\m_2=-\frac{5}{3}\)

Write down an equation in the point-slope form and replace everything in and simplify:

\(y_2-y_1=m(x_2-x_1)\\y-(-1)=-\frac{5}{3} (x-3)\\y+1=-\frac{5}{3}x+5\\y=-\frac{5}{3}x+4\\\)

The first four non-zero terms are \(4, 4t, -32/3 t^3\), and 0 (the coefficient of \(t^4\)). So the answer is: \(4, 4t, -32/3 t^3, 0\)

The Taylor series for a function f(t) about t = 0 is given by:

\(f(t) = f(0) + f'(0)t + (f''(0)/2!) t^2 + (f'''(0)/3!) t^3 + ...\)

To find the first four non-zero terms of the Taylor series for f(t) = 4 +

sin(4t), we need to find its first four derivatives evaluated at t = 0.

f(0) = 4 + sin(40) = 4

f'(t) = 4cos(4t)

f'(0) = 4cos(40) = 4

f''(t) = -16sin(4t)

f''(0) = -16sin(40) = 0

f'''(t) = -64cos(4t)

f'''(0) = -64cos(40) = -64

f''''(t) = 256sin(4t)

f''''(0) = 256sin(4 × 0) = 0

Substituting these values into the formula for the Taylor series, we get:

\(f(t) = 4 + 4t - (64/3!) t^3 + ...\)

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The magnitude of u × v is 0, if u and v are orthogonal

Orthogonal;

By virtue of being perpendicular to one another, orthogonal objects are connected in Euclidean geometry. Lines or line segments are said to be connected orthogonally if they are perpendicular at the point of intersection. Similar to this, if two vectors create a 90-degree angle, they are said to be orthogonal.

What use does orthogonal serve?

The orthogonal matrix's determinant has a value of 1. Its nature is symmetrical. The transpose and inverse of an orthogonal matrix are equivalent. The orthogonal matrix's eigenvalues are also equal to 1, and its eigenvectors are both orthogonal and real.

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Given margin of error increases as the margin of error increases.

To obtain a 3 percent margin of error at a 90% level of confidence, a sample size of about 750 is required. The sample size would be about 1,000 for a 95% level of confidence. Calculating the margin of error for various confidence levels is straightforward.

The ideal sample size for a population of 5,000 people has a 95% degree of confidence and a 5% margin of error, and it is 357. You may calculate this using our online calculator. This number can be used as a sample as well. It displays how many.

∴ For fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error increases as the margin of error increases.

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The value of 8h at $9/h will be $72. It should be noted that h means hours.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, the value of 8h at $9/h will be calculated by multiplying the value of the amount per hour by the total number of hours that are given. This will be Illustrated as:

= Number of hours × Amount per hour

= 8 × $9

= $72

In this case, it is important to note that h represents hours. Therefore, the amount for 8 hours is $72.

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Complete question

What is the value of 8h at $9/h. What are the units?