There are 7 girls and 3 boys in a class. Two students are to be
randomly chosen for a special project. What is the probability of
selecting a boy and a girl?

The value of angle BCD is determined as 108⁰.

option B is the correct answer.

The value of angle BCD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

arc AB =  m∠ACB

m∠ACB =  72⁰

The value of angle BCD is calculated as follows;

angle BCD = 180 - 72⁰ (sum of angles in a circle)

angle BCD = 108⁰

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There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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Answer:

the third option : reflected over the x-axis and rotated 90° counterclockwise.

Step-by-step explanation:

a rotation by 180° would result in the same orientation as the original - just mirrored across the origin. but since the orientation changed, the answer options with 180° are out.

and if it was reflected over the y-axis, then the rotation would have to be clockwise.

Answer:

12 tractors

Step-by-step explanation:

30/100 multiplied by 40 is 0.3 multiplied by 40

This gives you 12.

\(\frac{30}{100} \\ = 0.3\\0.3*40 = 12\\\)

Answer:

The monthly interest payment is $0.425, or approximately 43 cents.

Step-by-step explanation:

To find the monthly interest payment, we can use the following formula:

Monthly interest payment = (Average daily balance) x (Monthly interest rate)

The average daily balance can be estimated by assuming that it is equal to the average monthly balance. So, in this case, the average daily balance is:

Average daily balance = (Average monthly balance) / Number of days in the month

Assuming that there are 30 days in the month, we have:

Average daily balance = $1275 / 30 = $42.50

The monthly interest rate is equal to 1/12 of the annual interest rate, which is 12%. So, the monthly interest rate is:

Monthly interest rate = (1/12) x 12% = 1%

Now, we can use these values to calculate the monthly interest payment:

Monthly interest payment = $42.50 x 1% = $0.425

Therefore, the monthly interest payment is $0.425, or approximately 43 cents.

The simplified fοrm οf the expressiοn is 1 - cοs2x.

Trigοnοmetry is the branch οf mathematics that studies the relatiοnship between the sides and angles οf a triangle, particularly a right-angled triangle. The relatiοnship is shοwn by the ratiο οf the sides, which are trigοnοmetric ratiοs. There are six ratiοs in trigοnοmetry: sine, cοsine, tangent, cοtangent, secant, and cοsecant.

We can simplify the expressiοn cοs2x−2cοs2x+1 as fοllοws:

cοs2x − 2cοs2x + 1

= (cοs2x - cοs2x) - 2cοs2x + 1 (using the identity cοs2x = cοs2x - cοs2x + 1)

= -cοs2x + 1

= 1 - cοs2x

Therefοre, the simplified fοrm οf the expressiοn is 1 - cοs2x.

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Answer:

C. 1/1,000

Step-by-step explanation:

yes or no ?

Answer: the answer is B

How: just trust me bro I got you

Answer:

\(2\frac{2}{3} cups\)

Step-by-step explanation:

3cups - 1/3cups = 2 + 2/3cups

Answer:

1 cup of milk

Step-by-step explanation:

3 cups * 1/3 milk =

3 cups * 1 cup / 3 cups =

3 cups / 3 cups = 1 cup of milk

The statement that must be true for the parallelogram is

Alternate internal angles are pairs of angles that lie on opposite sides of a transversal line intersecting two parallel lines. The angles are on the interior (between the two parallel lines) and are not adjacent to each other.

These angles are equal in measure (i.e., they are congruent), which means that if one angle has a certain degree of measure, the other angle will have the same degree of measure.

In the problem, the diagonal of the parallelogram is the transversal line and it is used to make the alternate internal angle theorem possible

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The surface area of the square Pyramid with a side length of 2 yards and a slant height of 2 yards is 12 square yards.

The surface area of a square pyramid, we need to calculate the area of each face and then sum them up.

A square pyramid has four triangular faces and one square base. The area of the base is equal to the side length squared, while the area of each triangular face can be found using the formula: (1/2) * base * height.

Given that the side length of the square pyramid is 2 yards and the slant height is also 2 yards, we can calculate the surface area as follows:

Area of the base = (side length)^2 = 2^2 = 4 square yards

Area of each triangular face = (1/2) * base * height = (1/2) * 2 * 2 = 2 square yards

Now, let's calculate the total surface area of the square pyramid:

Total surface area = Area of the base + 4 * Area of each triangular face

Total surface area = 4 + 4 * 2 = 4 + 8 = 12 square yards

Therefore, the surface area of the square pyramid with a side length of 2 yards and a slant height of 2 yards is 12 square yards.

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Answer:

pie times radius square is equal to 147

when pie is 3, radius square is 49

radius is equal to 7

actual pie r square is 22/7 times 7 times 7 is 154

Step-by-step explanation:

ans is 154

Answer:

Step-by-step explanation:

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Answer:

Below

Step-by-step explanation:

Rate of change (aka the slope) = 2/5

Y Intercept = 10

Answer:

22

Step-by-step explanation:

The sum of the angles in a triangle are 180

Let the third angle be x

82+76+x = 180

158 +x = 180

x = 180-158

x =22

Now keep the,

Third unknown angle as y.

The formula we use,

→ Sum of all angles of triangle = 180°

Let's solve for y,

→ y + 82 + 76 = 180°

→ y + 158 = 180°

→ y = 180 - 158

→ [y = 22°]

Thus, option (B) is the answer.

You graph >7 with an open dot to the right.

The inequalities ≤ and ≥ would have a closed dot on the number line.

a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".

s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".

t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".

Inequality signs are mathematical symbols used to indicate that one quantity is greater than, less than, or equal to another quantity. These inequality signs includes:

These symbols are used in mathematical expressions and equations to compare values and express relationships between them.

Therefore, with a good understanding of inequality signs we conclude that:

On a graph, > 7 is with an open dot to the right.

Only the inequalities ≤ and ≥ would have a closed dot on the number line.

a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".

s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".

t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".

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The sketch of the given parametric equations is as appended.

Given parametric equations,

x(t) = 1+2t

y(t) = \(t^{2}\)

y = \(\frac{(x-1)^{2}}{4}\)

For bounding range of -2 ≤ t ≤ 2, corresponding values of x are as follows,

x = 2t + 1

For t = -2, x = 2(-2) + 1 = -3

For t = 2, x = 2(2) + 1 = 5

Hence the graph has been drawn with bounding limits of -3 ≤ x ≤ 5

The outcome is a parabola with vertex at (1,0) and open upwards. The curve moves towards infinity in upwards direction if there are no bounds / range.

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Answer:

D. e - 35

Step-by-step explanation:

We have that:

George earned e extra points.

Kate earned k extra points.

Kate earned 35 fewer extra credit points than George.

This means that k is e subtracted by 35, that is:

k = e - 35

So the correct answer is:

D. e - 35

The monthly Payment for the loan is approximately $271.24.

To calculate the monthly payment for the loan, we can use the formula for calculating the monthly payment on an intermediate-term loan. The formula is:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Given:

Loan Amount = $50,000

Interest Rate = 6.5% per year

Number of Years = 5

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is:

Monthly Interest Rate = (6.5% / 100) / 12 = 0.00541667

Plugging in the values into the formula, we get:

Monthly Payment = ($50,000 * 0.00541667) / (1 - (1 + 0.00541667)^(-5 * 12))

              = $271.24

Therefore, the monthly payment for the loan is approximately $271.24.

The owners of the restaurant want to use the loan to renovate the kitchen and expand the dining room, which they expect will generate additional monthly revenue between $2,000 and $5,000.

If we assume a conservative estimate of $2,000 per month in additional revenue, the loan payment of $271.24 represents approximately 13.56% of the additional revenue. This means that the owners would still have a significant portion of the additional revenue available for other expenses or profit.

On the other hand, if we consider the higher estimate of $5,000 per month in additional revenue, the loan payment would represent only about 5.42% of the additional revenue, leaving a substantial amount of money for other purposes.

Considering these calculations, it appears that taking this loan is a smart business decision. The monthly payment is manageable and leaves a significant portion of the additional revenue for the restaurant's operation and potential profit. However, it is essential for the owners to ensure that the projected additional revenue is realistic and sustainable to cover the loan payment and other business expenses.

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Answer:

20 000 cm^2

Step-by-step explanation:

One meter = 100 cm

so  m X m = m^2   = 100 x 100 cm^2 =10 000 cm^2

  so each m^ = 10 000 cm^2

     2 m^2  = 20 000 cm^2

Answer:

20,000

10,000 per/meter

2m² = 20,000cm²

Answer:

a)9. b) 12

Step-by-step explanation:

a) | -6 -3 | .

-6-3 = -9

|-9| =9

b) | 0 - 12 |.

0-12=-12

|-12|=12

Answer:

An alternative definition for the acceleration ax that can be written in terms of \(v_x\) and \(\frac{dv_x}{dx}\) is \(a_x=v_x \frac{dv_x}{dx}\)

Step-by-step explanation:

We know that :

\(a_x=\frac{dv_x}{dt}\)

Now we are supposed to find an alternative definition for the acceleration ax that can be written in terms of \(v_x\) and \(\frac{dv_x}{dx}\)

So, We will use chain rule over here :

\(a_x=\frac{dv_x}{dt}\\a_x=\frac{dv_x}{dt} \times \frac{dx}{dx}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt} [\frac{dx}{dt}=v_x]\\a_x=\frac{dv_x}{dx} \times v_x\\a_x=v_x\frac{dv_x}{dx}\)

Hence an alternative definition for the acceleration ax that can be written in terms of \(v_x\) and \(\frac{dv_x}{dx}\) is \(a_x=v_x \frac{dv_x}{dx}\)

The alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx is \(a_x = v_x \frac{dv_x}{dx}\)

Here we used the chain rule:

It is the basic method for differentiating a composite function. Here the first factor on the right, Df(g(x)), represents that the derivative of f(x) is first found and then x, wherever it arises, is replaced by the function g(x).

So,

\(a_x = \frac{dv_x}{dt}\\\\ = \frac{dv_x}{dt} \times \frac{dx}{dx}\\\\= \frac{dv_x}{dx} \times \frac{dx}{dt}\\\\ = \frac{dv_x}{dx} \times \frac{dx}{dt} (\frac{dx}{dt} = v_x)\\\\ = \frac{dv_x}{dx} \times v_x\\\\= v_x\frac{dv_x}{dx}\)

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13. Lorelei counted the faces on some three-dimensional figures. She found two figures with exactly 5 faces each. Which of two figures have exactly 5 faces each?

A. rectangular prism and triangular prism

B. rectangular pyramid and triangular pyramid

C. rectangular prism and triangular pyramid

D. rectangular pyramid and triangular prism

\( \\ \)

\(__________\)

A. rectangular prism and triangular prism

B. rectangular pyramid and triangular pyramid

C. rectangular prism and triangular pyramid

D. rectangular pyramid and triangular prism

Therefore, the answer is D. Rectangular Pyramid and Triangular Prism.

Answer:

the answerv is D

Step-by-step explanation: