In a class of 30 students, 13 have a brother and 8 have a sister. There are 3 students who have a brother and a sister. What is the probability that a student who has a sister also has a brother?

The function has an average rate of change f is 1/2 over the interval

The possible graph that completes the question is added as an attachment

The interval is given as

-3 ≤ x ≤ 9

This can be rewritten as

x = -3 to x = 9

This can also be represented as

(a, b) = [-3, 9]

From the attached graph, we have

f(-3) = -1.5

Also, we have

f(9) = 0.5

The estimate (to one decimal place) of the average rate of change f is calculated as

Rate = [f(b) - f(a)]/[b - a]

This gives

Rate = [f(9) - f(-3)]/[9 + 3]

So, we have

Rate = [0.5 + 1.5]/[9 + 3]

Evaluate

Rate = 2/12

Simplify

Rate  = 1/6

Hence, the average rate of change f is 1/6

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Answer:

-2

Step-by-step explanation:

f(x) = -2 (1/2)^x

you find the y-intercept where x = 0

= -2 (1/2)^0

= -2 *1

= -2

316 is value of   circle's arc BC .

What is an arc in maths?

Short arc BC is the difference between 360° and long arc BAC

 arc BC = 360 - arc BAC

             = 360 - 44

              = 316

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Answer: b = 3.5, h = 4

Step-by-step explanation: a = 1/2bh, area of a triangle formula

7 = 1/2((b)(2b-3)) state h in terms of b

7 = 1/2(2b^2-3b) simplify

7 = b^2 - 1.5b simplify

b = 3.5 final answer

Then, solve for h.

h = 7 - 3 substitute

h = 4 final answer

hope this helps!

Step-by-step explanation:

area of a triangle

base × height / 2

in our case

base × height / 2 = 7

base × height = 14

height = 2×base - 3

we can use the last identity in the area equation and get

base × (2×base - 3) = 14

2×base² - 3×base - 14 = 0

the solution to a quadratic equation like

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

base = (3 ± sqrt((-3)² - 4×2×-14))/(2×2) =

= (3 ± sqrt(9 + 112))/4 = (3 ± sqrt(121))/4 =

= (3 ± 11)/4

base1 = (3 + 11)/4 = 14/4 = 7/2 = 3.5 in

base2 = (3 - 11)/4 = -8/4 = -2

negative numbers for sizes of physical objects don't make sense, so, base = 3.5 in is our solution.

height = 2×base - 3 = 2×3.5 - 3 = 7 - 3 = 4 in

base length = 3.5 in

height = 4 in

The slope intercept form of equation that models $20 startup fee and $5 monthly fee is y = 5x +20 , y is total fee and x is number of months

The slope intercept form of an equation is y = mx + c

where y is y coordinate, x is x coordinate, m is the slope of the line and c is y intercept.

Let the total fee after x months be y

Then y is sum of startup fee and sum of all month's fee

For x months total monthly fees = 5(x)

Therefore the total fee after x months , y = 5x +20 which is same as slope intercept form y=mx+c

when x= 0 ⇒ y = 20 , startup fee

Thus, the equation in slope intercept form is  y = 5x +20 ,where y is total fee and x is number of months.

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Answer: x = 65

Step-by-step explanation:

1) First find the mini triangles, left and right angles

We will be calling the left one A and the right one B.

2) Next use triangle sum to find B.

62 + 50 + b = 180

b = 68

3) Use triangle sum again to find A.

53 + 80 + a = 180

a = 47

4) Use triangle sum to find the top mini angle.

47 + 68 + c = 180

c = 65

5) Since x is in the vertical angle of c, they are equal

c = x

65 = x

In accordance with analytic geometry, the equation that represents the line is y = - (1 / 4) · x - 6.

Herein we find the representation of a line set on a Cartesian plane. According to analytic geometry, line are represented by equations of the form y = m · x + b, where m, b are the slope and the y-intercept, respectively.

Both the values of the slope and the y-intercept can be found by knowing the location of two points lying on the line. If we know that (x₁, y₁) = (0, - 6) and (x₂, y₂) = (4, - 7), then we find the following system of linear equations:

b = - 6                                    (1)

4 · m + b = - 7                        (2)

By (1) in (2):

4 · m - 6 = - 7

4 · m = - 1

m = - 1 / 4

The equation that represents the line is y = - (1 / 4) · x - 6.

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Using addition of polynomials, the function modeling the number of people attending degree-granting institutions is:

P(t) = 48.7t² + 678.5t + 17667.4.

The number of males is given by:

M(t) = 19.7t² + 310.5t + 7539.6.

The number of females is given by:

F(t) = 28t² + 368t + 10127.8.

The total number is given by the addition of the number of males and of females, that is:

P(t) = M(t) + F(t).

Which is an addition of polynomials. To add the polynomials, we combine the like terms, that is, adding the terms that have the same variable and exponent. Hence:

P(t) = M(t) + F(t).

P(t) = 19.7t² + 310.5t + 7539.6 + 28t² + 368t + 10127.8.

P(t) = 48.7t² + 678.5t + 17667.4.

Which is the desired function.

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Using simple linear equations we calculate that the change left will be $6.24 .

The equals sign is used to indicate that two expressions on each side of the equal sign are equal in the many mathematical formulas that are utilized to form an equation.

Let the change received be x.

Therefore let us construct an equation for the situation

cost of game + tax + change = 20

or, 12.98 + 0.78 + x = 20

or, 13.76 + x = 20

or, x = 6.24

Therefore he will receive   6.24 after solving the equation.

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The acceleration is 4.24 m^2/s

They are accelerations and vector quantities. The direction of an object's acceleration is determined by the direction of the net force acting on it. Acceleration describes the rate at which a speed changes over time.

The velocity is changing over time. The velocity is actually changing at a constant rate of 10 m/s per second. If an object's velocity is changing, it is said to be accelerating; it has acceleration.

According to question,

Acceleration = final velocity- initial velocity/ time

Final velocity = 14.8 and initial velocity = 4.2

Hence, acceleration = 14.8-4.2/2.5

=10.6/2.5

=4.24.

The acceleration is 4.24 m^2/s.

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The roots are

The polynomial can be modellled as ;

Let us use f(2) to obtain a value for a

The polynomal f(x) is given as

Answer:

plane

Step-by-step explanation:

The plane is flat like a wall or the floor. It has infinite length and infinite width but has no thickness (as thick as a line--which has no thickness) basically a line is one-dimensional and a plane is two-dimensional.

See image.

Answer:

8

Step-by-step explanation:

8x3 = 24
8+ 16 = 24

La solucion del sistema de ecuaciones es x = 1, y = 4, o (1, 4) en notación standard.

Aqui tenemos el sistema de ecuaciones:

x + y = 5

2x + y = 4

Si tomamos la segunda ecuación, y a esta le restamos la primera, obtendremos:

(2x + y) - (x + y) = 5 - 4

(2x - x) + (y - y) = 1

x = 1

De esta forma encontramos el valor de x, para encontrar el valor de y, deberemos reemplazar x = 1 en una de las ecuaciones. Yo usare la primear.

x + y = 5

1 + y = 5

y = 5 - 1

y = 4

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Answer:

A. 6°C

B. -4°C

C. -0.7°C

D. -1°C

Answer:

A. 6°C < 7°C.

B. -4°C < -3°C.

C. -0.8°C < -0.7°C < -0.1°C

D. -1°C > -2°C

The percent discount the card gives can be:

4% or 96%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Royal card for discount.

Multiplying the total price to pay with 0.96 means two cases.

0.96 = 96/100 = 96%

Cases 1:

If the percent discount is 96% we will multiply the total prices to pay by 0.96 and subtract the value from the total price.

Example:

Total price to pay = 100

0.96 x 100 = 96

Total price to pay = 100 - 96 = 4

Cases 2:

If the percent discount is 4% we will multiply the total prices to pay by 0.96 after subtracting 4% from 100%.

Example:

Total price to pay = 100

Discount = 4%

100% - 4% = 96%

96% = 0.96

Total price to pay = 0.96 x 100 = 96

Thus,

The percent discount the card gives can be:

4% or 96%.

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Answer:

x = 60

Step-by-step explanation:

(2x + 15)° and 135° are corresponding angles and are congruent , then

2x + 15 = 135 ( subtract 15 from both sides )

2x = 120 ( divide both sides by 2 )

x = 60

Answer:

x = 60

Step-by-step explanation:

The two angles are corresponding. This means that both of the angles are congruent (same). So, you set both of them equal to each other. That means to do 2x + 15 = 135. You do basic algebra and then you get 60 for x. Hope this helps!

The variable y is shown with no exponent. Any term with no exponent is understood to have an exponent of 1, so y has an exponent of 1.

Answer: 1110

Step-by-step explanation:

Answer:

1,110

Step-by-step explanation:

1. Multiply to the powers(?)

10 x 10 x 10 = 1000

10 x 10 = 100

10 = 10

2. Add

1000 + 100 + 10 = 1110

The numbers given as 0.868668666866668666668... and 0.868668666866668666668... are  irrational numbers

From the question, the numbers are given as

0.868668666866668666668... and 0.868668666866668666668...

As a general rule.

Numbers that end in three dots are irrational numbers

The above is true because

When numbers cannot be represented as a fraction of integers, then such numbers are irrational numbers

Hence, the numbers are irrational numbers

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Both the given values 0.868668666866668666668.. and 0.868668666866668666668... are irrational numbers.

An irrational number is a type of real number which cannot be represented as a simple fraction or the values that have face value are irrational numbers. Example: √2, √3, and π are all irrational.

Here,
Both numbers are irrational numbers, because

Thus, Both the given values 0.868668666866668666668.. and 0.868668666866668666668... are irrational numbers.

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The solution for the given inequality is p < -2.2. The graph that represents the solution is attached below.

From the question, we are to determine the graph for the solution set for the given inequality

The given inequality is p - 3.6 < -5.8

First, we will solve the inequality

Solving the inequality

p - 3.6 < -5.8

Add 3.6 to both sides

p - 3.6 + 3.6 < -5.8 + 3.6

p < -2.2

The solution is p < -2.2

The graph of the inequality is shown below

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Answer: number line with an open circle on point negative 2.2 and arrow shaded to the left

Step-by-step explanation:

If this guy is correct

The correct option is D that is bill is equal to or greater than $30

3.25 + 5.5s < =30

The first step in building the inequality is modelling Benjamin's spendings.

He buys a chocolate milk that costs $3.25, plus S stacks of pancakes, each at $5.50. Thus, in total, his spendings are of:

3.25 + 5.25s

He wants the bill to be of at most $30, that is, his spending has to be at most $30, thus:

T < 30

3.25 + 5.5s < =30

Thus the correct inequality is option D which is 3.25 + 5.5s < =30

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The coordinates of the orthocenter of triangle DEF are given as follows:

(6.67,  -2).

The orthocenter of a triangle is the point of intersection of the three altitude lines of the triangle.

Hence, we need to find two of the lines, and them find the intersection point between them, as the third line will necessarily intersect these lines at this point.

The midpoint of segment DE is:

(6, 1).

Which is the mean of the coordinates.

Vertex F is at point (8, -8), hence the slope of the line with these two points is:

m = (-8 - 1)/(8 - 2) = -9/2 = -4.5.

Hence:

y = -4.5x + b.

When x = 6, y = 1, hence we can find b as follows:

1 = -4.5(6) + b

b = 28.

Hence one line is:

y = -4.5x + 28.

The midpoint of segment EF is:

(8, -1.5).

Which is the mean of the coordinates.

Vertex D is at point (4, -3), hence the slope of the line with these two points is:

m = (-1.5 - (-3))/(8 - 4) = 0.375.

Hence:

y = 0.375x + b.

When x = 8, y = -1.5, hence we can find b as follows:

-1.5 = 0.375(8) + b

b = -4.5.

Hence the two lines that we have to find the intersection point is:

Then the x-coordinate of the orthocenter of the triangle is:

-4.5x + 28 = 0.375x - 4.5

4.875x = 32.5

x = 32.5/4.875

x = 6.67.

The y-coordinate of the orthocenter of the triangle is:

y = 0.375(6.67) - 4.5 = -2.

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The number of ways in which they can line up to wait for the next available teller is 362880.

We want to know how many different ways there are to line up 9 people.

= 9×8×7×6×5×4×3×2×1

= 362880

Thus, the number of ways in which they can line up to wait for the next available teller is 362880.

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Answer:

The answer would be 7 times 12
Eric will spend $84
I calculated it by seeing how much each of the pizzas cost-$7 the I figure out how many pizzas he need-12 Now what we need to do is multiply 7 and 12 because if one pizza is $7 (Stated in the written problem) then I know that it would be 7+7+7+7+7+7+7+7+7+7+7+7 12 times, one time for each pizza needed. The simpler version would be 7 time 12 which then we would get a value of $84.

Step-by-step explanation:

Hope this helps!!

Answers to all the subparts using equations are:

So, the answers to all the subparts are as follows:

(A) Equation that can be formed is:

(B) Cost of 12 pizzas:

Let, x = 12.

(C) Total cost can be calculated easily by substituting the number of pizzas bought which is 12 in this case in the place of x.

Therefore, answers to all the subparts using equations are:

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Correct question:

Eric is buying food for an upcoming holiday party. He can get pizzas for $7 each using a coupon he found online, and he wants to figure out the cost of buying 12 pizzas so he can plan his budget. Please provide answers to each of the following questions:

(A) What is the direct variation equation that represents this situation? (worth 2

points)

(B) How much will Eric spend if he buys 12 pizzas? (worth 2 points)

(C) Explain how you calculated his total cost for pizzas. (worth 2 points)

The following steps would be:

• TP and TP (for both triangles) are congruent by the reflexive property.

• The triangles are congruent by the SAS theorem.

• Angle S and angle O are congruent.