A committee of 4
is being formed randomly from the employees at a school: 4
administrators, 30
teachers, and 4
staff. What is the probability that all 4
members are teachers? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

The system of equations shown in this graph of a system of linear equations are:

In order to determine the required system of equations from this graph of a system of linear equations, we would find the slope of each line as follows:

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

For line 1, we have:

Points (x, y) = (0, 0) and (3, -2)

Slope = (-2 - 0)/(3 - 0)

Slope = -2/3.

Therefore, y = mx + c  ⇒ y = -2/3x + 0.

For line 2, we have:

Points (x, y) = (0, -5) and (4, -2)

Slope = (-2 - (-5))/(4 - 0)

Slope = (-2 + 5)/(4 - 0)

Slope = 3/4.

Therefore, y = mx + c  ⇒ y = 3/4x - 5.

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Answer:

O.B y = − 2/3x

      y = 3/4x − 5

Step-by-step explanation:

Answer:

1: [tex]y=-1x-3[/tex]

2: [tex]y=0.8x+4.2[/tex]

3: [tex]y=2x-3[/tex]

Step-by-step explanation:

Question 1: When lines are parallel, that means they're slope is the same and there y-intercept is different. So the first step is to calculate the slope of BC. If you look at BC you'll notice it goes down by 2 and goes forward by 2 so the slope is -2/2 or -1. This completes one part of the slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept. The y-intercept will be calculated using the point A. since the equation passes through point A

-1 = (-2)(-1) + b

-1 = 2 + b

-3 = b

y=-1x-3

Question 2: Same concept here, if you look at AC, you'll see it "rises" by 4 and "runs" by 5, thus the slope is 4/5. Since it passes through B we'll use that to find the y-intercept

5 = (4/5)(1) + b

5 = 4/5 + b

b = 4.2

Question 3: It "rises" by 6 and "runs" by 3, thus the slope is 6/3 which is 2.

Plug in known values

3=(3)(2) + b

3 = 6 + b

-3 = b

Answer:

27.03 or 27 3/100

Step-by-step explanation:

Plug in numbers

The solution to the fraction expression at x = 1¹/₁₀ is: 10.97

The fraction expression is given as:

3(5 - ¹/₆x) + ¹/₈(32 + 6x) + 7.3x - 5 * 0.05x

Breaking this down gives us:

15 - ¹/₂x + 4 + ³/₄x + 7.3x - 0.25x

= 19 - 7.3x

Now, we want to plug in 1¹/₁₀ for x.

1¹/₁₀ can be expressed as ¹¹/₁₀ and as such:

19 - 7.3(¹¹/₁₀) = 10.97

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Graph B is the graph that describes the function.

A quadratic graph is a graph of quadratic functions which have the power of the variable as 2. They are usually u-curved or inverted v-curved.

Analysis:

if we solve the quadratic function, y = [tex]x^{2}[/tex] -4x -12

when the curve touches the x-axis y = 0

[tex]x^{2}[/tex] -4x -12 = 0

[tex]x^{2}[/tex]  -6x +2x -12 = 0

x(x-6) +2(x-6)

(x+2)(x-6) = 0

x = -2 or 6

From the graph, The second graph(graph B) shows the points on the x-axis x = -2 and x = 6.

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Answer:

D. 1.37, -1.37

Step-by-step explanation:

9x² = 17

x² = (17 / 9)

x = ± √(17 / 9)

x = ± (√17) / 3

x = 1.37, - 1.37

1. The equation of the parallel line is y = -x - 1.

2. The equation of the perpendicular line is y = 3/2x - 4.

Lines that are parallel have the same slope while slope values for perpendicular lines are negative reciprocals.

1. The slope (m) of y = -x + 1 is -1. Substitute m = -1 and (x, y) = (4, -5) into y = mx + b:

-5 = -1(4) + b

-5 = -4 + b

-5 + 4 = b

b = -1

Substitute b = -1 and m = -1 into y = mx + b

y = -x - 1

2. The slope (m) of y = -2/3x + 5 is -2/3.

Negative reciprocal of -2/3 is 3/2.

Substitute m = 3/2 and (x, y) = (2, -1) into y = mx + b:

-1 = 3/2(2) + b

-1 = 3 + b

-1 - 3 = b

b = -4

Substitute b = -4 and m = 3/2 into y = mx + b

y = 3/2x - 4

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The Empirical Rule is also referred to as the 68-95-99.7 rule and it can be defined as a statistical rule which states that:

By applying the empirical rule to the data contained in the histogram, we can logically deduce the following points:

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You will need 292.5 mL of the 10% solution and 2925 mL of pure alcohol.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

You require 450 mL of a 65% alcohol solution.

On hand, you have a 10% alcohol mixture.

Then the amount of the 10% alcohol mixture and pure alcohol that you need to obtain the desired solution will be

Let x be the amount of the 10% of alcohol is needed.

Then the equation will be

⇒ 450 · 0.65

⇒ 292.5 mL pure alcohol

Then the alcohol mixture will be

0.1x = 292.5

    x = 2925 mL of alcohol mixture

You will need 292.5 mL of the 10% solution and 2925 mL of pure alcohol.

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The values of x in 2cos(2x) = 11cos(x) + 1 are x = 1.82 and x = 4.46

The equation is given as:

2cos(2x) = 11cos(x) + 1

Expand cos(2x)

2(cos²(x) - sin²(x)) = 11cos(x) + 1

sin²(x) = 1 - cos²(x)

So, we have:

2(cos²(x) - 1 + cos²(x)) = 11cos(x) + 1

Evaluate the like terms

2(2cos²(x) - 1) = 11cos(x) + 1

Expand

4cos²(x) - 2 = 11cos(x) + 1

Rewrite as:

4cos²(x) - 11cos(x)  - 2 - 1 = 0

4cos²(x) - 11cos(x)  - 3 = 0

Let cos(x) = y.

So, we have

4y² - 11y - 3 = 0

Expand

4y² + y - 12y - 3 = 0

Factorize

y(4y + 1) - 3(4y + 1) = 0

Factor out 4y + 1

(y - 3)(4y + 1) = 0

Solve for y

y = 3 or 4y = -1

This gives

y = 3 or y = -1/4

Recall that y = cos(x)

So, we have:

cos(x) = 3 or cos(x) = -1/4

The cosine of x is always between -1 and 1 (inclusive).

So, we have:

cos(x) = -1/4

Take the arc cos

[tex]x =\cos^{-1}(-1/4)[/tex]

Evaluate the arccos (in radians)

x = 1.82 and x = 4.46

Hence, the values of x in 2cos(2x) = 11cos(x) + 1 are x = 1.82 and x = 4.46

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Answer:

[tex]theta=47.33 degrees[/tex]

Step-by-step explanation:

sin theta=opposite/hyp

sin theta=500/680

theta in degrees=47.33

Answer:

The angle is 47.33°

Step-by-step explanation:

We have the hypotenuse as 680 ft and the opposite side as 500 ft, so we can use sin as a way to find the angle:

sin θ = opposite side / hypotenuse

sin θ = 500 ft / 680 ft

sin θ = 0.7353

θ = sin^-1 (0.7353) [this is called inverse of sine]

θ = 47.33°

Answer:

===========================

Let the numbers be:

Since both M and E include B, we can show the total as:

and

The total can be expressed as:

Substitute values and solve for B:

This is matching the answer choice B)

Maths be A and English be B

A intersection B be X

Option B

Sam run for total 6.08 miles.

Sam run 3 1/4 miles on Tuesday and then ran 2 5/6 miles on Wednesday.

Fraction is ratio of integers. example- 7/8.

Sam run [tex]3\frac{1}{4}[/tex] miles on Tuesday.
on [tex]2\frac{5}{6}[/tex] on Wednesday
Total run =Run on tuesday + Run on wednesday

Total run = [tex](3\frac{1}{4} )+(2\frac{5}{6} )[/tex]

= 13/4 + 17/6

Total run = 6.08

Thus Sam run for total 6.08 miles

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Answer:

v = 34 in

Step-by-step explanation:

triangle BIG is similar to triangle MOP

This means that the length of their corresponding sides

are proportional.

Then

[tex]\frac{v}{51} =\frac{60}{90}[/tex]

Then

90v = 51 × 60

then

90v = 3060

Then

v = 3060/90

Then

v = 34

Answer:

21 because -1/4a - 4 is 22

Answer:

[tex] \dfrac{2\sqrt{a}}{a} [/tex]

Step-by-step explanation:

[tex] 2a^{-\frac{1}{2}} = [/tex]

[tex]= 2 \times \dfrac{1}{\sqrt{a}}[/tex]

[tex]= 2 \times \dfrac{1}{\sqrt{a}} \times \dfrac{\sqrt{a}}{\sqrt{a}}[/tex]

[tex] = \dfrac{2\sqrt{a}}{a} [/tex]

5 hours of math tutoring must be mixed with 5 hours of arts tutoring to make $45 per hour.

Mr. Robert charges $50 per hour for math tutoring and charges $40 per hour for language arts tutoring.

Let, he mixed x hours of math tutoring to 5 hours of arts tutoring.

Then, Income from x hours of math tutoring = $50x

Income from 5 hours of arts tutoring = 5×$40 = $200

Total mixed income in (x+5) hours = $(50x+200)

According to the question, in mixed process he make $45 per hour. So, for (x+5)hours he earns $(x+5)45

So, The equation becomes,

50x+200 = (x+5)45

⇒ 50x+200 = 45x+225

⇒ 50x-45x = 225-200

⇒ 5x = 25

⇒ x = 25/5

⇒ x = 5

So, 5 hours of math tutoring must be mixed.

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Hello,

look at the picture

The value of her investment at the end of 3 years is £10955.08

The given parameters are

The value is then calculated as:

Value = P * P(1 + r)^t

So, we have:

Value = 5000 + 5000 * (1 + 6%)^3

Evaluate the expression

Value = 10955.08

Hence, the value of her investment at the end of 3 years is £10955.08

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This is the new coordinate for Z  (-1, 3)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The point Z is (-3, 4) is translated using the rule

x,y  → (x+2),(y-1)

Then simply plug-in the values of x and y which are x = -3 and y = 4

x,y → ((-3) +2), (4 -1)  which is (-1, 3)

Hence, this is the new coordinate for Z  (-1, 3)

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An equation represents a line that passes through (-2, 4) and has a slope of 2/5 is y-4 = 2/5(x+2)

The equation of a line in point-slope form is expressed as;

y-y1 = m(x - x1)

where

m is the slope

(x1, y1) is any pint on the line

Substitute the given parameter

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

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

Hence an equation represents a line that passes through (-2, 4) and has a slope of 2/5 is y-4 = 2/5(x+2)

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Answer: A. (2, 5), (3, 6), (6,9)

Step-by-step explanation:

Each value of x maps onto only one value of y.

The average speed for the entire journey will be 53.333 miles per hour.

The average speed is the ratio of the total distance traveled to the total time taken by the body. Its unit is m/sec.

The distance from the Springfield, MA, to Boston is, L

v₁ is the velocity during traveling from Boston to Springfield, MA

v₂ is the  velocity during traveling from Springfield, MA to Boston

t₁ is the time needed to travel from Boston to Springfield, MA

t₂ is the time needed to travel from Springfield, MA to Boston

t is the total time period of the journey

v is the average speed

From the formula of distance;

Distance = speed × time

The speed of train for the going from Springfield, MA, to Boston is 40 mph. The time period is calculated as;

L = v₁ × t₁

t₁ = L/v₁

t₁ = L/40

The speed of train for the going from Boston to Springfield, MA, is 80 mph. The time period is calculated as;

L = v₂ × t₂

t₂ = L/v₂

t₂ = L/80

The total time is taken;

t = t₁ + t₂

t =  (L/40)+( L/80)

t=3L/80

The ratio of total distance traveled to the total time spent by the body is known as average speed, calculated as;

Average speed = Total distance / Total time

v = 2L / (3L/80)

v= (2L × 80)/3L

v = 160 / 3

v = 53.333 miles per hour.

Hence the average speed for the entire journey will be 53.333 miles per hour.

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Answer:

Step-by-step explanation:

pounds to ounces: 16 ounces in a pound a trick to know is if you look at the pound symbol lb it looks like 16 in a way so 16*3= 48 48 is your answer

For the given systems A and B:

1) Replace the first equation of A by the sum between the two equations of A.

2) Yes, the systems are equivalent.

Here we have the two systems of equations:

A:

6x - 5y = 1

-2x + 2y = -1

B:

4x - 3y = 0

-2x + 2y = -1

The second equation is the same in both systems, so we only look at the first equations.

In A we have:

6x - 5y = 1

If we add the second equation of A, then we get:

(6x - 5y) + (-2x + 2y) = 1 + (-1)

4x - 3y = 0

This is the first equation of B.

Then we need to replace the first equation by the sum between the first and second equations.

2) Are the systems equivalent?

Yes, because we did not "modify" system A, we just rewrite it and we got system B, then both systems have the same solutions.

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Answer: A) , Yes

Step-by-step explanation:

The expected population of each country in 2025 are 22261221, 1465382683, 116537821 and 60347662

The expected population of each country is calculated as:

P(n) = a *(1 + r)^n

Where:

2025 is 25 years since 2000.

This means that:

n = 25

So, we have:

Australia

P(25)= 19169000 * (1 + 0.6%)^25

P(25)= 22261221

China

P(25)= 1261832000* (1 + 0.6%)^25

P(25)= 1465382683

Mexico

P(25)= 100350000 * (1 + 0.6%)^25

P(25)= 116537821

Zaire

P(25)= 51965000* (1 + 0.6%)^25

P(25)= 60347662

Hence, the expected population of each country in 2025 are 22261221, 1465382683, 116537821 and 60347662

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Decompose the terms in the sum as

[tex]4 + 15 + 26 + \cdots + 213 = 4 + (4 + 11) + (4 + 2\times11) + \cdots + (4 + 19\times11)[/tex]

so there are 20 terms in the sum. Then our sum simplifies to

[tex]4 + 15 + 26 + \cdots + 213 = 4\times20 + (0+1+2+\cdots+19)\times11[/tex]

Now, if

[tex]S = 1 + 2 + 3 + \cdots + 17 + 18 + 19[/tex]

we can reverse the order of terms to get the same sum,

[tex]S = 19 + 18 + 17 + \cdots + 3 + 2 + 1[/tex]

so that doubling up the sum gives

[tex]2S = (1 + 19) + (2 + 18) + \cdots + (18 + 2) + (19 + 1) = 19\times20 \implies S=19\times10=190[/tex]

So, our sum evaluates to

[tex]4 + 15 + 26 + \cdots + 213 = 4\times20 + 190\times11 = \boxed{2170}[/tex]

From the first two inference, it takes her phone 1 minute to charge 2% i.e 1 minute of charge = 2% of battery.

Therefore; charging from scratch,

1 min = 2%

x mins = 50%.

using cross multiplication,

x mins = (50% × 1 min) ÷ 2%.

x = 25 mins.

For 90%, applying the same formula,

y min = (90% × 1 min) ÷ 2%

y = 45 mins.

So from zero percent, it will take Dana's phone 25 minutes to charge to 50% and 45 minutes to charge to 90%.

Step-by-step explanation:

23 by 13 is the answer cause 23 i s23

The statements that are true of the given function f(x) = 1/2x + 3/2 are:

f(0) = 3/2

f(2) = 7/2

f(4) = 7/2

We have,

Let's evaluate the given function f(x) = 1/2x + 3/2 for the given values of x and check which statements are true:

f(-1/2) = 1/2 * (-1/2) + 3/2 = -1/4 + 3/2 = (6 - 1)/4 = 5/4 = 1.25

Statement: f(-1/2) ≠ 2 (False)

f(0) = 1/2 * 0 + 3/2 = 0 + 3/2 = 3/2

Statement: f(0) = 3/2 (True)

f(1) = 1/2 * 1 + 3/2 = 1/2 + 3/2 = 4/2 = 2

Statement: f(1) ≠ -1 (False)

f(2) = 1/2 * 2 + 3/2 = 1 + 3/2 = 2 + 3/2 = 4/2 + 3/2 = 7/2

Statement: f(2) = 7/2 (True)

f(4) = 1/2 * 4 + 3/2 = 2 + 3/2 = 4/2 + 3/2 = 7/2

Statement: f(4) = 7/2 (True)

Therefore,

The statements that are true of the given function f(x) = 1/2x + 3/2 are:

f(0) = 3/2

f(2) = 7/2

f(4) = 7/2

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Answer:

see below

Step-by-step explanation:

D miles / M miles per gallon  = gallons used

Using linear pairs,

[tex]115+5x=180\\\\5x=65\\\\x=\boxed{13}[/tex]

By the exterior angle theorem,

[tex]2y=45+5(13)\\\\2y=45+65\\\\2y=110\\\\y=\boxed{55}[/tex]