Bill is making a movie and needs to cast some actors. There are 5 actors ( Anne, Lisa, Diana, Maggie, and Susan ) interested in playing the female lead role, and 2 actors ( Jacob and Mark ) interested in playing the male lead role. Anne and Mark are Bill's siblings. What is the probability Bill will cast a family member in the movie?

Domain of f(x) is {x | x ≠ 6} and Domain of g(x) is {x | x ≠ +7 and x ≠ +7}.

The domain of a function is the set of all input values that make the function possible.

Now, for f(x) = (x + 6)/(x² - 12x + 36)

To find the domain, we equate the denominator to zero to find the numbers that can't be a domain. Thus;

x² - 12x + 36 = 0

Solving this using quadratic formula gives; x = 6. Thus, domain of f(x) is;

Domain = {x | x ≠ 6}

Now, for g(x) = (x + 7)/(x² - 49)

To find the domain, we equate the denominator to zero to find the numbers that can't be a domain. Thus;

x² - 49 = 0

Solving this using quadratic formula gives; x = +7 or -7. Thus, domain of g(x) is; Domain = {x | x ≠ +7 and x ≠ +7}

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for an angle of 780°, we can say that is really a 360° + 360° + 60°, so two full revolutions plus an extra 60°. Check the picture below, with the coterminal in green.

The size of the unknown angle "x".

We'll have to check which one is appropriate from SOHCAHTOA.

In this question we'll have to use cos because hypotenuse and adjacent is given.

[tex]\large\boxed{cos(A)=\frac{adj}{hyp}}[/tex]

Substitute according to the formula.

[tex]cos \: x= \frac{7}{11}[/tex]

We'll have to use cos inverse.

[tex]x={cos}^{-1}(\frac{7}{11})[/tex]

[tex]x=50.47880364[/tex]

[tex]\large\boxed{x=50.5°}[/tex]

Therefore, the size of the unknown angle "x" is 50.5°

The required measure of the angle x is given as 50°.

Given that,
The diagram shows a right-angled triangle. 7cm and 11cm and x degrees.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Apply cosine equation,
cosx =  7 / 11
cosx = cos50
x = 50°

Thus, the required measure of the angle x is given as 50°.

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Answer:

The Area is 25

Step-by-step explanation:

You will need distance formula for this questions

for AD, (0,4) and (4,7)

The formula is here

[tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

which gives you

[tex]\sqrt{\left(4-0\right)^2+\left(7-4\right)^2} = 5[/tex]

for AB

(0,4),(3,0)

[tex]\sqrt{\left(3-0\right)^2+\left(0-4\right)^2}=5[/tex]

The answer will be 5*5, which is 25

Answer:

18 inches = 1.5 feet

8 inches = 2/3 foot

y = 1.5 + (2/3)x

Yes the ladder be safe at this height.

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

Given:

ladder = 15 ft long.

top of the ladder is 14.2 ft above the ground.

Using trigonometry,

sin x = 14.2/15

sin x = 0.947

x= 71.262°

As, 78 > 71.262°

Hence, it would be safe to use the ladder of 15 ft long.

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Answer:

width=5yd and length=10yd

Step-by-step explanation:

To solve this problem, you need to start by asking what you do and don't know (always where to start with word problems)

We know that Area (A) = Length (L) * Width (W)

You know Area (A) = 50 sq. yds.

You don't know anything about the width, so let's just say Width (W) = x

And you know that the length is 5 yds longer than the width, so L = W + 5yd and, since W = x, we can say L = x + 5yd

Now, we recall that A = L * W, and, since A = 50, we can say 50 sq yd = L * W.

Well, now just plug in. What does W equal and L equal?

From above we plug in and can say that 50 sq yd = x * (x + 5 yd).

Multiply it out and you get 50 = x^2 + 5x (removing units for a moment so they don't clutter the lines).

Now there are a number of ways to solve this. You can tell (because of the "x^2") that it is quadratic. So let's get it equal to zero:

0 = x^2 + 5x - 50

Now you can factor it, use your quadratic formula, or (if you hated yourself) do it as a completing the square problem. I'm going to factor.

I can see from going through a list in my head that the factors 10 and -5 multiply to -50 and add to 5, so I know that

0 = x^2 + 5x - 50 = (x + 10)(x - 5)

And so you know that x = -10 or 5.

Well, you know the parking lot cannot be -10 yd long. So we must say that W = x = 5, and, since L = W + 5, then L = 5+5 = 10. So your width is 5 yd and length is 10 yd.

Answer:

6

Step-by-step explanation:

hope it helps

The solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

The figure is not given;

However, the question can still be solved without it

The given parameters are:

a = 31, b = 23, and c = 20

Calculate angle A using the following law of cosine

a² = b² + c² - 2bc * cos(A)

So, we have:

31² = 23² + 20² - 2 * 23 * 20 * cos(A)

Evaluate

961 = 929 - 920 * cos(A)

Subtract 929 from both sides

32 =- 920 * cos(A)

Divide both sides by -920

cos(A) = -0.0348

Take the arc cos of both sides

A = 92.0

Calculate angle B using the following law of sine

a/sin(A) = b/sin(B)

So, we have:

31/sin(92) = 23/sin(B)

This gives

31.0189 = 23/sin(B)

Rewrite as:

sin(B) =23/31.0189

Evaluate

sin(B) =0.7415

Take arc sin of both sides

B = 47.9

Calculate angle C using:

C = 180 - 92.0 - 47.9

Evaluate

C = 40.1

Hence, the solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

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Answer:

2Tu = 90

Step-by-step explanation:

You can substitute the values T = 5 and u = 9 into the expression to get: 2 × 5 × 9 which is 90 (2 × 45 = 90)

Hope this helps!

The final result is 90 when T = 5 and u = 9.

Here, we have to evaluate 2Tu when T = 5 and u = 9, we substitute the values of T and u into the expression and perform the operations accordingly.

Given expression: 2Tu

T = 5

u = 9

Now, let's substitute the values:

2 * 5 * 9

Next, perform the multiplication:

2 * 5 = 10

10 * 9 = 90

So, when T = 5 and u = 9, the value of 2Tu is 90.

We get, to evaluate 2Tu, we first multiply T and u together, and then multiply the result by 2.

In this case, we have T = 5 and u = 9.

So, we perform the following steps:

Multiply T and u: 5 * 9 = 45

Multiply the result by 2: 2 * 45 = 90

Thus, the final result is 90 when T = 5 and u = 9.

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Answer:

  0.98 seconds

Step-by-step explanation:

We assume the height of the volleyball is described by the equation for ballistic motion. We want to find the time it takes for the height to become zero.

__

The general form of the equation of height for ballistic motion is ...

  [tex]h(t)=-16t^2+v_0t+h_0\qquad\text{$v_0$ and $h_0$ are the initial velocity and height}[/tex]

The coefficient 16 in the equation is an approximation of 1/2g, where g is the acceleration due to gravity in ft/s². This means the units of time and distance are expected to be seconds and feet.

For the problem at hand, the initial velocity and height are 10.5 ft/s and 5 ft. Then the height equation is ...

  h(t) = -16t² +10.5t +5

__

Marsha has until the ball hits the ground to react to the serve. To find out how long that is, we need to solve the height equation for t when h=0. This is most easily done using the quadratic formula with ...

The solution is ...

  [tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}= \dfrac{-10.5\pm\sqrt{10.5^2-4(-16)(5)}}{2(-16)}\\\\=\dfrac{10.5\pm\sqrt{430.25}}{32}=\dfrac{21\pm\sqrt{1721}}{64}[/tex]

The positive solution is ...

  t ≈ 0.976327 ≈ 0.98

Marsha has about 0.98 seconds to react before the volleyball hits the ground.

_____

Additional comment

After about 0.33 seconds, Marsha knows she doesn't need to react at all. The serve will not clear the net. Its maximum height is about 6' 8 5/8". A women's volleyball net is 7' 4 1/8" high. Jennifer's serve velocity must be at least 12.3 ft/s for the ball to go over the net. With that upward velocity, Marsha has about 1.06 seconds to react.

a) [tex](a+b)(x)=a(x)+b(x)=7x+10+12x-18=\boxed{19x-8}\\[/tex]

b) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]

c) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]

d) [tex]a(b(x))=a(12x-18)=7(12x-18)+10=84x-126+10=\boxed{84x-116}[/tex]

Finding the correlation coefficient, it is found that the regression line shows a:

negative trend line with a strong relationship.

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is of -0.85, which is negative and strong.

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Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85,

The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph, y.

Finding the correlation coefficient, it is found that the regression line shows a: negative trend line with a strong relationship.

It is an index that measures the correlation between two variables, assuming values between -1 and 1.

If it is positive, the relationship is positive, that is, they are directly proportional. If it is negative, they are inversely proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85, which is negative and strong.

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Answer:

The lines would be equal, meaning the slope of the red line is also -3.

Step-by-step explanation:

SIMPLE:
Parallel lines have the same slope.

[tex]\text{Let,}\\\\~~~~~~~~~y = e^{\ln 8}\\\\\implies \ln y = \ln \left( e^{\ln 8} \right)\\\\\implies \ln y = \ln 8( \ln e)\\\\\implies \ln y = \ln 8\\\\\implies y = 8\\\\\implies e^{\ln 8} = 8\\\\\text{Hence,}~~ e^{\ln 8 } = 8[/tex]

Answer:

8

Step-by-step explanation:

One of the properties of natural logs is that

[tex]e^{lnx} = x\\\\So,\\\\e^{ln8} = 8[/tex]

The perimeter of the composite figure shown in the figure is equal to 5 · [2 + √2 · (1 + √5)] units (approx. 32.882 units) and the total area is 33.5 square units.

In this case we have a composite figure formed by six triangles and two rectangles. The perimeter is the sum of the side lengths and the area is the sum of the areas of the triangles and rectangles. The perimeter of the entire figure is described below:

p = AB + BC + CD + DE + EF + FG + GA

p = 5√2 + √10 + √10 + 5 + √10 + 5 + 2√10

p = 10 + 5√2 + 5√10

p = 10 + 5 · (√2 + √10)

p = 10 + 5√2 · (1 + √5)

p = 5 · [2 + √2 · (1 + √5)]

And the area of the composite figure is determined by the following expression:

A = 0.5 · (3) · (1) + (3) · (4) + 0.5 · (3) · (1) + 0.5 · (3) · (1) + 0.5 · (3) · (1) + (3) · (2) + 0.5 · (7) · (1) + 0.5 · (6) · (2)

A = 2 · (3) · (1) + (3) · (4) + (3) · (2) + 0.5 · (7) · (1) + 0.5 · (6) · (2)

A = 33.5

The perimeter of the composite figure shown in the figure is equal to 5 · [2 + √2 · (1 + √5)] units (approx. 32.882 units) and the total area is 33.5 square units.

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Answer:

Step-by-step explanation:

3a 2b ×2a 6b = (3 × 2)×(a × b) × (2 × 6)×(a × b)   [commutative property]

                      = (6×ab) × (12×ab)  [associative property]

                      = (6×12) × (ab×ab)  [commutative + associative]

                      = (72) × (ab)²

                      = 72× (ab)²

                      = 72a²b²  [exponent property]

Answer:

Initial balance$1000

interest rate 8%

Term 20yrs

Step-by-step explanation:

The final balance is $4,926.8.The total compound interest is $3,926.8.

The value of r is 2 %.

Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time. Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time. Formula. S.I. = (P × T × R) ⁄ 100.

Given:

Principal(P)= $4540

Rate = ?

Time=10  years

CI=$1328.54

We have to find the value of r.

According to given question we have

By the use of compound interest we have

[tex]CI=p((1+\frac{r}{100} )^{10} -1)\\\\1328.54 =4540 ((1+\frac{r}{100} )^{10} -1)\\\\\0.292= ((1+\frac{r}{100} )^{10} -1)\\[/tex]

After simplifying we get,

r=2 %

Therefore, the value of r is 2 %.

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Answer:

  -448

Step-by-step explanation:

The sum of 28 terms of the arithmetic sequence with first term 92 and common difference -8 can be found using the formula for the sum of an arithmetic series.

  Sn = (2a1 +d(n -1))(n/2) . . . . sum of n terms with first term a1, difference d

__

Using the above formula with a1=92, d=-8, and n=28, the sum is ...

  S28 = (2·92 -8(28 -1))/(28/2) = (184 -216)(14) = -448

The sum of the first 28 terms of the sequence is -448.

Answer:

8= 24b

8/8=24b/8

b=3

Step-by-step explanation:

Based on my own learning

Answer:

x>3

Step-by-step explanation:

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

Answer:

[tex]4\frac{7}{8}[/tex]

Step-by-step explanation:

The three heaviest eggs are between [tex]1\frac{1}{2}[/tex] and [tex]1 \frac{3}{4}[/tex]

Hope this helps and please feel free to comment, ask questions, give feedback, and correct me if I am wrong!

Have a great day!

:)

Answer:

The area is: 28.26 units^2

The diameter is: 18.84 units

Step-by-step explanation:

Area A=pie(3.14)R^2

Diameter D=pie(3.14)R2

If 5x - 17 ≥ 0, then |5x - 17| = 5x - 17 and the equation reduces to

-8 - 2 (5x - 17) = -14

-8 - 10x + 34 = -14

-10x = -40

x = 4

If 5x - 17 < 0, then |5x - 17| = -(5x - 17) = -5x + 17 and we have

-8 - 2 (-5x + 17) = -14

-8 + 10x - 34 = -14

10x = 28

x = 2.8

The plane that would produce a triangle is A, a cut parallel to the vertical axis, directly through the vertical axis.

A square pyramid is a geometric shape having four triangles, five faces and a square.  

Since the sides are equal, cutting parallel to the vertical axis forms a triangle.

Therefore, a cut parallel to the vertical axis, directly through the vertical axis would produce a triangle.

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Answer:

120 ft²

Step-by-step explanation:

The formula to find the area of a triangle is :

Area = [tex]\frac{1}{2}[/tex] × base × height

Given that,

base ⇒ 30 ft

height ⇒ 8 ft

Let us solve it now.

Area =  [tex]\frac{1}{2}[/tex] × base × height

Area =  [tex]\frac{1}{2}[/tex] × 30 ft × 8 ft

Area =  [tex]\frac{1}{2}[/tex] × 240 ft²

Area =  120 ft²

In this question we are provided with the base and height of a triangle. We are asked to calculate the area of the triangle.

Base = 30 feet

Height = 8 feet

We know,

[tex] \large \star \: \small\boxed{ \rm{ Area_{(triangle)} = \dfrac{1}{2} × b × h}}[/tex]

Where,

Substituting the values we get

[tex] \small\sf{ Area_{(triangle)} = \dfrac{1}{ \cancel{2}} × 30 × \cancel{8} \: \: 4}[/tex]

[tex] \longmapsto \small\rm Area_{(triangle)} = 30 × 4[/tex]

[tex] \small \underline{ \boxed{\sf {Area_{(triangle)} =120 \: {feet}^{2} }}}[/tex]

Hence,the area of the triangle is 120 feet².

[tex]\underline{\rule{71mm}{3pt}}[/tex]