Is 5 students for every teacher equal to 5 teachers for every student? Explain:

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Answer: Its D

Step-by-step explanation:

\(f(x) =x^5 -8x^3 +6x^2+7x-6\\\\= x^5 -2x^4+2x^4 -4x^3-4x^3+8x^2-2x^2+4x+3x -6\\\\=x^4(x-2) + 2x^3(x-2) -4x^2(x-2) -2x(x-2) +3(x-2)\\\\=(x-2)(x^4+2x^3-4x^2-2x+3)\\\\=(x-2)(x^4-x^3+3x^3-3x^2-x^2+x-3x+3)\\\\=(x-2)[x^3(x-1) +3x^2(x-1) -x(x-1) -3(x-1)]\\\\=(x-2)(x-1)(x^3 +3x^2 -x -3)\\\\=(x-2)(x-1)(x^3 -x^2 +4x^2-4x+3x-3)\\\\=(x-2)(x-1) [x^2(x-1)+4x(x-1) +3(x-1)]\\\\=(x-2)(x-1)(x-1) (x^2 +4x +3)\\\\=(x-2)(x-1)^2(x^2 +3x+x +3)\\\\=(x-2)(x-1)^2 [x(x+3) +(x+3)]\\\\=(x-2)(x-1)^2(x+1)(x+3)\)

Answer:

-6x^3 + 5x^2 + 13x - 20

Step-by-step explanation:

Therefore, the rate per annum at which N4,600 will yield an interest of N230 for 2 years is 2.5%.

Percent is a term used to describe a fraction or ratio that represents a portion of 100. It is often represented by the symbol % and is commonly used to express a portion or a rate of change. For example, if an item is discounted by 20%, it means the price has been reduced by 20% of the original price or 20/100 of the original price. Similarly, if someone earns a grade of 85% on a test, it means they answered correctly 85 out of 100 questions.

Here,

7. To find the time (in years) in which a loan of N3,900 at the rate of 5% yields N585.60 in simple interest, we can use the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Substituting the given values, we get:

585.60 = 3,900 * 0.05 * t

Solving for t, we get:

t = 3 years

Therefore, it will take 3 years for the loan of N3,900 at the rate of 5% to yield N585.60 in simple interest.

8. To find the time (in years) for a loan of N20,000 at the rate of 7% to accumulate N70,000 in simple interest, we can use the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Substituting the given values, we get:

70,000 = 20,000 * 0.07 * t

Solving for t, we get:

t = 50 years

Therefore, it will take 50 years for the loan of N20,000 at the rate of 7% to accumulate N70,000 in simple interest.

9. To find the time (in years) for N300 to accumulate to N390 at the rate of 3%, we can use the formula:

I = P * r *t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Substituting the given values, we get:

90 = 300 * 0.03 * t

Solving for t, we get:

t = 10 years

Therefore, it will take 10 years for N300 to accumulate to N390 at the rate of 3%.

10. To find the year in which N5,100 will yield an interest of N170 at the rate of 2.5% per annum, we can use the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Substituting the given values, we get:

170 = 5,100 * 0.025 * t

Solving for t, we get:

t = 2 years

Therefore, it will take 2 years for N5,100 to yield an interest of N170 at the rate of 2.5% per annum. If the interest is compounded, we would need to use the compound interest formula instead.

11. To find the rate per annum at which N4,600 will yield an interest of N230 for 2 years, we can use the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Substituting the given values, we get:

230 = 4,600 * r * 2

Solving for r, we get:

r = 0.025 or 2.5%

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a) The combined number of $3 carwashes for cars, c, and $5 carwashes for trucks or SUVs, t, needed can be represented by the equation y = c + t.

b) If only 5 cars are washed, the number of trucks or SUVs needed to be washed to raise the full $915 is 180.

An equation is a mathematical statement that shows that two mathematical expressions are equal or equivalent.

Equations use the equation symbol (=) to show the equality of expressions.

The total amount needed for the new equipment = $915

The charge for a car wash per car = $3

The charge for cash wash per truck or SUV = $5

Let the number of cars = c

Let the number of trucks or SUVs = t

c + t = y... Equation 1

3c + 5t = 915... Equation 2

If the number of cars, c = 5

From equation 2:

3c + 5t = 915

3(5) + 5t = 915

15 + 5t = 915

5t = 900

t = 180

Thus, from equation 2, we can determine that if cars are 5, the trucks or SUVs must be 180 to meet the target.

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As a result, $17.55 should be chosen as the selling price to sell 480,000 units for a profit of $1,500,000.

We must add the desired net profit of $1,500,000 to the total cost of producing the 480,000 units to determine the selling price.

You can determine the overall cost as follows:

Total cost equals fixed costs plus. (Variable costs per unit x Number of units)

Total expense equals $984,000 plus ($14.50 x 480,000)

Cost in total is $7,224,000.

To reach a net profit of $1,500,000, we must add the following sum to the whole expense:

Selling price is calculated as Total Cost + Desired Net Profit / Units Sold.

($7,224,000 + $1,500,000) / 480,000 = selling price

Price to Sell: $17.55

As a result, $17.55 should be chosen as the selling price to sell 480,000 units for a profit of $1,500,000.

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Answer:

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

To determine the selling price, we first need to calculate the total  variable cost:

Now calculate the required revenue:

Find the required selling price per unit:

Answer: A

2". 1. 0 a. Put a square box at the origin of the number line. b. Plot point C so it is located at 2 ... d. Plot a point at the midpoint of C and E. Label it H. Lesson 2. 1. Name the ... 2. Line & passes through point H and is parallel to the y-axis. Construct line l.



Step-by-step explanation:



Step-by-step explanation:

The graph of g(x) is obtained from the graph of f(x) by the following transformations:

- A horizontal stretch by a factor of 9. This is because the graph of g(x) is 9 times wider than the graph of f(x).

- A vertical translation down by 2 units. This is because the graph of g(x) is 2 units lower than the graph of f(x).

In other words, to obtain the graph of g(x) from the graph of f(x), we stretch the graph horizontally by a factor of 9 and then translate it down by 2 units.

Here is a more detailed explanation of the transformations:

- Horizontal stretch by a factor of 9: To stretch the graph horizontally by a factor of 9, we multiply all of the x-coordinates by 9. This means that every point on the graph of f(x) will be moved 9 units to the right on the graph of g(x).

- Vertical translation down by 2 units: To translate the graph down by 2 units, we subtract 2 from all of the y-coordinates. This means that every point on the graph of f(x) will be moved 2 units down on the graph of g(x).

The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.

The graph is given in the question.

As per the given line, we take two points (0, 4) and (5, 8)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 0, y₁ = 4

x₂ = 5, y₂ = 8

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 4 = (8 - 4)/(5-0 )[x -0]

⇒ y - 4 = (4/5)x

⇒ y = (4/5)x + 4

The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.

So, the equation of the line would be y = (4/5)x + 4.

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Answer:

78.4 square units

Step-by-step explanation:

First we will find the radius of the circle by using circumference formula of circle.

\(c = 2\pi \: r \\ 31.4 = 2 \times 3.14 \times r \\ \\ r = \frac{31.4}{2 \times 3.14} \\ \\ r = \frac{3140}{2 \times 314} \\ \\ r = \frac{10}{2} \\ \\ r = 5 \: units \\ \\ area \: of \: circle = \pi {r}^{2} \\ = 3.14 \times {5}^{2} \\ = 3.14 \times 25 \\ = 78.5 \: {units}^{2} \\ \)

Answer:

Step-by-step explanation: 5.) Circular shape.

     6.) Feet.

     7.) Circle.

     8.) The circumference is 9 and the radius is 18.

     9.)  By the way we would need to use The Circumference as 2 and the radius to be 9 to equal 18 for the radius circle.

9514 1404 393

Answer:

  1. DE=104°, FE=76°, DEF=180°, CFD=284°, DFE=256°

  6. x=6

  7. DE=167°, EF=13°, DFG=347°

Step-by-step explanation:

To solve these problems, you make use of the relationships between arcs and angles in a circle. Any resulting equations are solved in the usual way.

__

1. A central angle of 104° is shown. The two diameters divide the circle into 4 arcs. Two will have measures of 104°, the other two will be supplementary to those, so will have measures of 76°. The blanks can be filled by adding the arcs necessary to achieve the arc measure asked for.

__

6. Angles EFC and BFA are vertical angles, so have the same measure. Angle EFC is shown as being the sum of 90° and 27°. This means ...

  90+27 = 21x -9 . . . . . . two-step linear equation in x

__

7. The two marked arcs add to half a circle:

  (x -3)° +(12x -25)° = 180° . . . . . . . two-step linear equation in x

Once you have the value of x, you need to substitute it into the formulas for each of the arc measures, then make use of any necessary sum-of-arc relations to find the necessary arc lengths.

The average rate of change for the given function is 4.

The given function is \(f(x)=x^2\).

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another.

We know that for a given function f(x) the average rate of change on the interval a ≤ x ≤ b is given by: \(\frac{f(b)-f(a)}{b-a}\)

Now, with the interval 1 ≤ x ≤ 3, we get

\(f(3)=3^2=9\)

\(f(1)=1^2=1\)

Here, (9-1)/(3-1)

= 8/2

= 4

Therefore, the average rate of change for the given function is 4.

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Answer:

each week he works 57.76 hours

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

7+4×6=31

31+-19=50

the answer is 50

Answer:

Hi. I'm pretty sure you are supposed to use a compass (that's what I had to use for this math work). So basically what you have to do is for the dividing it in four one first divide it into two and divide those new parts in to four and then you have four equal parts, using a compass and/or straightedge works best. For dividing the segments into three parts measure it maybe with a ruler if you have one and mark the points where it can be equally divided.

Step-by-step explanation:

Hope you understand that :) I don't know how to show you on here sorry :(

GOOD LUCK!

My own multi-step combination problem is given below:

To solve this problem, Amanda  need to use the formula for combinations and it is:

nCr = n! / (r! x (n-r)!)

where:

n = total number of items to select from

r is the number of items to select.

First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:

5C3

=  5! / (3! x (5-3)!)

= 10

Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be

4C2

= 4! / (2! x  (4-2)!)

= 6

Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:

3C2

= 3! / (2! x  (3-2)!)

= 3

To have the total number of dinner menus, we have to multiply these three numbers together:

= 10 x 6 x 3

= 180

Therefore, one can say that Amanda have 180 different dinner menus that she can be create.

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After considering the given data we come to the conclusion that the length of AB is 12.124 units, under the condition that A (-3, 5) and B (4, -2) are the given coordinates.

The distance between two points in a plane can be found using the distance formula which is an application of the Pythagorean theorem. The formula is given by d=√ ( ((x₂ – x₁ )² + (y₂ – y₁ )²)

Here (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Applying the given coordinates of A (-3, 5) and B (4, -2), we can evaluate the distance between them as follows:

d = √( (4 - (-3))² + (-2 - 5)² )

 = √(7² + (-7)²)

 = √(98 + 49)

 = √147

 = 12.124

Therefore, the length of AB is approximately 12.124 units.

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Answer:

Step-by-step explanation:

Which number is the largest?

The first one is the largest as it has the greatest power

Answer:

The linear equation is:

y = 3*x

when x = 1

y = 3*1 = 3

when x = 2

y = 3*2 = 6

Then as x increases one unit, y increases 3 units.

Then the correct statement would be something like:

"For the linear function, y increases by a sum of 3 each time x increases 1"

The exponential function is:

y = 3^x

When x = 1

y = 3^1 = 3

When x = 2

y = 3^2 = 3*3

when x = 3

y = 3^3 = 3*3*3

So when x increases by 1, we multiply the previous value of y by 3.

Then the correct sentence is something like:

"For the exponential function, y increases by a factor of 3".

Answer: for the linear function y increases by a difference

for the exponential function y increases by a(n) ratio.

Step-by-step explanation:

The two solutions of the equation:

(6x - 12)/3 + 4 = 18/x

Are x = 3 and x = -3

Here we have the following equation:

(6x - 12)/3 + 4 = 18/x

Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.

Now, let's start by simplifying the left side:

(6x - 12)/3+  4 = 18/x

2x - 4 + 4 = 18/x

2x = 18/x

Now we can multiply both sides by x so we get:

2x^2 = 18

Now divide both sides by 2:

x^2 = 18/2

x^2 = 9

Finally, apply the square root in both sides:

√x^2 = ±√9

x = ±3

The two solutions are x = 3 and x = -3

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Answer:

z-y/x

Step-by-step explanation:

then z

then z-y

z-y/x

the value of k for the given right-angle triangles is 5.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, Two right-angle triangles one of them has a height of 7 cm and a weight of 1 cm. While others have a height and base of the same measurement k.

The Hypotaneuse of the triangles is equal and the same.

From the general formula of the Pythagorean theorem

Hypotaneuse²  = height + bsase²

in a triangle with a height of 7

Hypotaneuse² = 7² + 1²

Hypotaneuse² = 49 + 1

Hypotaneuse² = 50...(1)

In a triangle with a height of k

Hypotaneuse² = k² + k²

Hypotaneuse² = 2k²....(2)

Since Hypotaneuse is the same

From comparing both equations

50 = 2k²

k² = 25

k = 5

therefore, the value of k for the given right-angle triangles is 5.

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Answer:

Length of material needed = 35.8 feet

Step-by-step explanation:

Door of the wooden garage is in the shape of a rectangle with dimensions 16 ft × 8 ft.

Lincoln is going to place two boards in the shape of an X on the door.

From the picture attached,

Diagonals of the rectangular door will be equal in measure.

Therefore, length of the material = 2×(Diagonal of the rectangle)

By applying Pythagoras theorem in the rectangle,

(Diagonal)² = 16² + 8²

Diagonal = \(\sqrt{256+64}\) = 17.89

Therefore, length of material = 2 × 17.89

                                                = 35.77

                                                ≈ 35.8 feet

7. Radius of circle P = 2       Radius of circle Q = 1

Coordinates of the point of tangency (4,2)

The equation of the tangency line is x = 4

8. AB is not a tangent. BC² ≠ AB² + AC²

9. The three radii of the circle are; CB, CF and CD

A diameter of the circle is BD

A tangent of the circle is GE

A chord of the circle is BD

A secant of the circle is AD

A point of tangency is F

7. To find the radius, identify the diameter of the circle. For the diagram, it can be said that the diameter of the circle P is 4.

The radius then is 4/2 = 2.

The radius of circle q is 2/2 = 1

You could also use the formula

Distance = sqrt((x2 - x1)² + (y2 - y1)²)

8. √4² + √12² = √160

√13 = 169

Therefore AB is not tangent. It is less than BC

9. The line that cuts the circle into two halves is the diameter. The lines than further cuts the diameter into equal parts are the radii's

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Kim's test scores indicate that he scored as well as or better than 72% of the test takers, and 28% of the test takers scored better than him. His grade equivalent of 12.1 indicates that he would perform adequately in a twelfth grade science class.

His percentile of 88 indicates that he scored as well as or better than 88% of the test takers. His raw score of 72 does not directly indicate the percentage of questions answered correctly, but it can be assumed that he answered a majority of the questions correctly to achieve his score.

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3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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The volume of the isosceles trapezoidal prism is 1575 cubic meters.

To find the volume of the isosceles trapezoidal prism, we need to first calculate the area of the trapezoid base and then multiply it by the height of the prism.

The trapezoid base has two parallel sides, AB and DE, with lengths 10 m and 8 m respectively, and the distance between them, BC, is 25 m.

To calculate the area of the trapezoid base, we can use the formula:

Area = 0.5 \(\times\) (sum of parallel sides) \(\times\) height

In this case, the sum of the parallel sides is 10 m + 8 m = 18 m, and the height of the trapezoid is the distance BC, which is 25 m.

Plugging the values into the formula, we have:

Area = 0.5 \(\times\) (10 m + 8 m) \(\times\) 25 m

Area = 0.5 \(\times\) 18 m \(\times\) 25 m  

Area \(= 225 m^2\)

Now that we have the area of the trapezoid base, we can find the volume of the prism by multiplying it by the height of the prism, which is DP = 7 m.

Volume = Area of base \(\times\) Height

Volume \(= 225 m^2 \times 7 m\)

Volume \(= 1575 m^3\).

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