a. Three fifths of the students in the class are boys. If there are 15 boys in
the class, how many students are there in all?

Answer:

49

Step-by-step explanation:

because it is the middle

Answer:

Step-by-step explanation:

m∠GEH = m∠FH - m∠FEG

m∠GEH = 180 - 64 = 116°

The clockwise measure of arc angle ZX will be twice the measure of angle XYZ

ZX = 2(76) = 152

Arc length XYZ = 360 - 152 = 208°

Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

<95141404393>

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

For more questions on trigonometric form

https://brainly.com/question/31744474

#SPJ8

The polynomial that represents the area of the shaded region is given as follows:

x² - 3x + 36.

The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:

A = lw.

For the entire region, the area is given as follows:

A = (x + 1)(x + 1)

A = x² + 2x + 1.

The area of the white region is given as follows:

Aw = 5(x - 7)

Aw = 5x - 35.

Then the area of the shaded region is given as follows:

As = A - Aw

A = x² + 2x + 1 - (5x - 35)

A = x² + 2x + 1 - 5x + 35

A = x² - 3x + 36.

More can be learned about area at https://brainly.com/question/15673093

#SPJ1

The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

For more such questions on square root

https://brainly.com/question/428672

#SPJ8

Answer:

Here's how to solve

Step-by-step explanation:

67-43.

7-3=4

6-4=2

so 24 and to check if it is correct substitute 24 in the equation

24+43= 67

24 is your answer

Answer:

\(67 - 43 \\ \\ = 24 \\ then \\ 24 + 43 \\ = 67 \\ now \\ \)

The two angles are related in that they are supplementary angles

Supplementary angles would add tuo to 180 degrees according to the angle Theorem.

Adding the two given angles :

These angles are supplementary

The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.

Hence, the angles are related as they are supplementary angles .

Learn more on angles : https://brainly.com/question/11955149

#SPJ1

Answer:

The problem describes rolling an unfair number cube which lands with 6, and asks for the number of outcomes where X=0, X=1, X=2, and X=3.

X can be 0, 1, 2, or 3 if X equals the number of times she rolls a 6 over the course of three tries.

We must count the instances where none of the three trials yields a six in order to determine the number of occurrences where X = 0. Since there is a 0.4 percent chance that the cube will fall on 6, there is a 0.6 percent chance that it won't. Therefore, there are 0.6 * 3 = 0.216, or 21.6%, of outcomes where X = 0.

To find the number of outcomes where X=1, we need to count the number of outcomes where exactly one of the three trials results in a 6. There are three ways to choose which trial will result in a 6, and each of the other two trials must not result in a 6. Therefore, the number of outcomes where X=1 is 3 × 0.4 × 0.6^2 = 0.432 or 43.2%.

We must count the outcomes where precisely two out of the three trials yield a six in order to determine the number of events where X=2. There are three options for selecting the two trials that will end in a 6, and the third trial cannot also end in a 6. The proportion of outcomes where X=2 is therefore 3 0.4 2 0.6 = 0.288 or 28.8%.

Finally, to find the number of outcomes where X=3, we need to count the number of outcomes where all three trials result in a 6. This occurs with probability 0.4^3 = 0.064 or 6.4%.

Therefore, the number of outcomes where X = 0 is 21.6%, X=1 is 43.2%, X=2 is 28.8%, and X=3 is 6.4%.

Answer:

long division

Step-by-step explanation:

17\5=3

put down 2 then i'll make u go from there

Using the least common factor, it is found that she will do all the three activities again on the same day again in 48 days.

To find how many days it takes so that she will do all the three activities again on the same days, we have to find the least common factor of 4, 6 and 16.

It is done factoring them using prime factors, then:

4 - 6 - 16|2

2 - 3 - 8|2

1 - 3 - 4|2

1 - 3 - 2|2

1 - 3 - 1|3

1 - 1 - 1

Hence:

lcm(4,6,8) = 2x2x2x2x3 = 48

She will do all the three activities again on the same day again in 48 days.

To learn more about the least common factor, you can take a look at https://brainly.com/question/25924269

Answer:

3/4 servings

Step-by-step explanation:

Each serving = 1/2

There are 3/8 cookies.

How many times 1/2 "fits" into 3/8 = how many servings.

3/8 / 1/2

= 3/8 * 2

= 3/4 servings

The total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.

To determine the number of possible outcomes, we need to consider the number of outcomes for each event and then multiply them together.

1. Picking a marble: Let's assume there are n marbles to choose from. If there are n marbles, then the number of outcomes for this event is n.

2. Rolling a die: A standard die has 6 sides numbered 1 to 6. Therefore, the number of outcomes for this event is 6.

3. Picking a card: A standard deck of cards has 52 cards. Hence, the number of outcomes for this event is 52.

To find the total number of possible outcomes, we multiply the number of outcomes for each event together:

Total number of outcomes = (number of outcomes for picking a marble) × (number of outcomes for rolling a die) × (number of outcomes for picking a card)

Total number of outcomes = n × 6 × 52

Therefore, the total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.

Learn more about probability at https://brainly.com/question/13604758

#SPJ1

Answer:

5 2/3

Step-by-step explanation:

just trust me

Answer:

option b 5.6 is the correct answer

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

Here, we have,

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

Learn more about box-and-whisker plots on:

brainly.com/question/27849170

#SPJ1

Answer:

Total payable brokerage = £2350

Step-by-step explanation:

Given that:

Fixed fee charged by broker = £150

Percent of fee charged = 5.50%

Amount invested by customer = £40,000

Fee charged = \(\frac{5.50}{100}*40000\)

Fee charged = 5.50 * 400 = £2200

Total brokerage payable = £150 + £2200 = £2350

Hence,

Total payable brokerage = £2350

Answer:

-8

Step-by-step explanation:

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

Read more on rotation here: brainly.com/question/28854313

#SPJ1

Answer:$11.90

Step-by-step explanation:

Divide 59.50 by 5

I assume the integral is supposed to be

\(\displaystyle \int_C z^2\,dx + x^2\,dy + y^2\,dz\)

Parameterize C by

\((x(t),y(t),z(t)) = (1-t)(1,0,0) + t(5,1,2) = (1+4t, t, 2t)\)

with 0 ≤ t ≤ 1, and dx = 4 dt, dy = dt, and dz = 2 dt. Then the line integral is

\(\displaystyle \int_C z^2\,dx + x^2\,dy + y^2\,dz = \int_0^1 (2t)^2(4\,dt) + (1+4t)^2\,dt + t^2(2\,dt)\)

\(\displaystyle \int_C z^2\,dx + x^2\,dy + y^2\,dz = \int_0^1(1+8t+34t^2)\,dt\)

\(\displaystyle \int_C z^2\,dx + x^2\,dy + y^2\,dz = 1+4+\frac{34}3 = \boxed{\frac{49}3}\)

Answer:

350000

P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6

Answer:
V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Step-by-step explanation:

Set up the variables: Let V represent the number of vans, S represent the number of small trucks, and L represent the number of large trucks.

Write the equations:

V + S + L = 310 (total number of vehicles)

V = 2S (twice as many vans as small trucks)

35,000V + 70,000S + 60,000L = 15,000,000 (total cost of the vehicles)

Substitute equation 2) into equation 1):

2S + S + L = 310

3S + L = 310

Simplify equation 3) by substituting V = 2S:

70,000S + 70,000S + 60,000L = 15,000,000

140,000S + 60,000L = 15,000,000

Set up a system of equations:

3S + L = 310

140,000S + 60,000L = 15,000,000

Eliminate L by multiplying equation 1) by 60,000:

60,000(3S + L) = 60,000(310)

180,000S + 60,000L = 18,600,000

Subtract equation 2) from the new equation:

(180,000S + 60,000L) - (140,000S + 60,000L) = 18,600,000 - 15,000,000

40,000S = 3,600,000

Solve for S:

S = 90

Substitute the value of S into equation 1) to solve for L:

3(90) + L = 310

270 + L = 310

L = 40

Substitute the values of S and L into equation 2) to solve for V:

V = 2S

V = 2(90)

V = 180

The final answer is:

V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Answer:

180 Vans 90 Small trucks and 40 Large trucks

Step-by-step explanation:

Work Shown:

g(x) = x^2 - 4

g(f(x)) = ( f(x) )^2 - 4

g(f(x)) = ( 2x-1 )^2 - 4

g(f(x)) = (2x-1)(2x-1) - 4

g(f(x)) = 4x^2-2x-2x+1 - 4

g(f(x)) = 4x^2 - 4x - 3

Answer:

False

Step-by-step explanation:

Negative and Negative  always equals positive

Negative and positive always equal negative

Answer: 32.20$ Train Fee

Step-by-step explanation:

15% of 28 is 4.20... 4.20 will be added to the current Train Fee

   28.00$

 +   4.20$

    32.20$

Final result: The Train Fee will be 32.20$