There are 120 children at a school assembly. 15 are 3rd graders; 45 are 4th graders; and 60 are 5th graders. Each student has entered their name in a drawing for a prize.
What is the probability that the winner will be a 3rd grade student?

Answer:

\( \frac{9x { }^{2 } - 63x}{ 3x} \\ = \frac{3x(3x - 21)}{3x} \\ = 3x - 21 \)

hope it helps:)

Answer:3x-21

Step-by-step explanation:

\(\frac{9x^{2} - 63x }{3x}\) ⇒ \(\frac{3x * (3x - 21) }{3x}\) ⇒ cancel out 3x ⇒ 3x - 21

Answer:

AA i think

Step-by-step explanation:

H, (7, 27)

Take a pair and plug in the x and y, so instead of y=4x-1 you would plug 27 and 7 in for x and y, giving you, 27=4(7)-1. Then you solve and see if it's true. 7 x 4 =28, 28-1 = 27, and 27=27 so that's true.

Then you plug those same numbers in for y=3x+6, so 27=3(7)+6. 7 x 3 = 21, 21 + 6 = 27, so that is also true.

I don't know if this is the way your teacher wants you to do it, but this is how I did it.

Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

Answer:

-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

800-8p<750

Answer:

Step-by-step explanation:

cos A = \(\frac{\sqrt{8} }{3}\)

Answer:

144 sq cm

Step-by-step explanation:

The base is a triangle. Area of a triangle is:

A = 1/2 b • h

A = 1/2(4)•3

A = 6

There are 2 of these bases.

Area of 2 bases= 12.

There are three rectangular sides. Area of a rectangle is:

A = l × w (or b•h)

A = 5 × 11 = 55

A = 3 × 11 = 33

A = 4 × 11 = 44

Add up three rectangular faces and two bases for Total Surface Area:

12 + 55 + 33 + 44

= 144 sq cm

Answer:

144 cm ²

Step-by-step explanation:

The surface area of a right triangular prism is made up of 2 congruent triangles (these are called the "bases") and 3 rectangles.

Surface area of a right triangular prism formula

Surface area = (S₁ + S₂ + S₃)L + bh

where:

⇒ Surface area = (3 + 4 + 5)11 + 4 × 3

                          = (12)11 + 12

                          = 132 + 12

                          = 144 cm²

Answer:

-3,1

Step-by-step explanation:

When you are doing Systems Of Equations using a graph, the point where the lines intersect is your answer

The system of equations as an augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

From the question, we have the following parameters that can be used in our computation:

x                  = 100

   -5m  - 7c  = 350

   -5m  - 9c  = 200

The above means that the variables in the system of equations are

x, m and c

So, we have the following representation

x    m     c        

1    0      0        100

0   -5    -7        350

0   -5    -9        200

When represented as an augmented matrix, we have

\(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

Hence, the augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

Read more about matrix at

https://brainly.com/question/11989522

#SPJ1

Answer: option D

Step-by-step explanation:

Given equation:

P = 6 w + 8 [eq1]

l=2w+4 [where l is length]

using eq1 we have:

6w=P-8

w=(P-8)/6

hence  option D

learn more about perimeter here:

https://brainly.com/question/28499208

#SPJ9

The solution of the expression is x=0 and it is the only solution that is an integer.

An expression in mathematics is a combination of numbers, variables, and mathematical operations that evaluates to a numerical value or an algebraic expression.

To do this, we need to pick a range of x values and substitute them into each equation to find the corresponding y values.

Next, we need to find the points of intersection between the two curves. These are the x values where the two curves cross each other and have the same y value. To find these points, we will set the two equations equal to each other and solve for x:

=> x=5x−x³

Expanding this equation, we get

=> 4x³+x=0.

Factoring this equation, we get

=> x(4x²+1)=0.

This gives us two solutions, x=0 and x=±i√(1/4), where i is the imaginary unit. Since x can only take on real values, x=0 is the only solution that is an integer.

Complete Question:

Use the open space to show all of your work. This includes: sketching the curves, finding and labeling the points of intersection, setting up the appropriate definite integral(s), and evaluating them. Place your numerical answer for the area of the region in the box. Leave your answer in exact form.

y = x,

y = 5x−x³

To know more about expression here.

https://brainly.com/question/14083225

#SPJ4

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

The transformation of f(x) to p(x) is that (a) the graph is reflected and shifted down

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

In the function equations, we can see that

f(x) = x²

p(x) = -f(x) - 3

So, we have

Vertical Difference = 0 - 3

Evaluate

Vertical Difference = - 3

This means that the transformation of f(x) to p(x) is that f(x) is reflected and shifted down 3 units to p(x).

Read more about transformation at

brainly.com/question/27224272

#SPJ1

Answer:

Area = 7822.61542 km²

Step-by-step explanation:

Área of a circle is:

area = π (d/2)²

π = 3.1416

d = diameter

In this case:

area = 3.1416 * (99.8/2)²

area = 3.1416 * 49.9²

area = 3.1416 * 2490.01

area = 7822.61542km²

Answer: 42

Step-by-step explanation:

Example:

Solve x + 7 < 15

Solution:

x + 7 < 15

x + 7 – 7 < 15 – 7

x < 8

Inequalities Of The Form “x – a < b” or “x – a > b”

The solution of the inequality 1 1/8 + b ≥ 7/16 will be;

⇒ - 11/16 ≤ b

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 1 1/8 + b ≥ 7/16

Now,

Solve the inequality as;

The inequality is,

⇒ 1 1/8 + b ≥ 7/16

Solve for b as;

⇒ 9/8 + b ≥ 7/16

Subtract 9/8 as,

⇒ 9/8 + b - 9/8  ≥ 7/16 - 9/8

⇒ b ≥ (7 - 18) / 16

⇒ b ≥ - 11/16

⇒ - 11/16 ≤ b

Thus, The solution of the inequality 1 1/8 + b ≥ 7/16 will be;

⇒ - 11/16 ≤ b

Learn more about the inequality visit:

https://brainly.com/question/24372553

#SPJ2

Using linear function concepts, it is found that the meaning of the slope is given by:

(B) the weekly change in the number of tickets sold.

A linear function is modeled by:

\(y = mx + b\)

In which:

From this, we have that the slope represents a rate of change, hence, option B is correct.

More can be learned about linear function concepts at https://brainly.com/question/24808124

The probability of observing no positive reading if all suspects are telling the truth is d. 0.59. Probability theory is a branch of mathematics that is used to model and analyze random events.

Probability can be used to predict the likelihood of different outcomes in a wide range of situations, from games of chance to scientific experiments to everyday events. Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

To solve this problem, we need to calculate the probability of observing no positive readings given that all suspects are telling the truth, which is equal to the probability that all 5 suspects receive a negative reading on the lie detector test. Since the lie detector will show a positive reading 10% of the time when a person is telling the truth, the probability that a suspect will receive a negative reading when telling the truth is 1 - 10% = 90%. Therefore, the probability that all 5 suspects will receive a negative reading when telling the truth is:

(90%)^5 = (0.9)^5 = 0.59049.

The correct answer is therefore (d) 0.59.

Learn more about probability, here https://brainly.com/question/30034780

#SPJ4

The inverse function:  \(f^{-1} (x) =\) \((\frac{x -5}{5} )^{2} -13\)

The inverse is defined on the domain x < 5 and x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5.

A function is a relationship that exists between two sets of numbers, with each input from the first set, known as the domain, corresponding to only one output from the second set, known as the range.

Given function is;   \(f(x) = 5\sqrt{(x + 13)} + 5\)

To find the inverse of the given function, we first replace f(x) with y:

⇒  \(y = 5\sqrt{(x + 13)} + 5\)

Subtract 5 from both sides:

⇒ \(y -5 = 5\sqrt{(x + 13)}\)

⇒ \(\frac{(y -5)}{5} = \sqrt{(x + 13)}\)

⇒ \((\frac{y -5}{5} )^{2} = x + 13\)

⇒ \((\frac{y -5}{5} )^{2} -13 = x\)

Now we have x in terms of y, so we can replace x with f⁻¹(x) and y with x to get the inverse function:

f⁻¹(x) = \((\frac{x -5}{5} )^{2} -13\)

The domain of the inverse function is x ≥ 5, because this is the range of the original function, and we were given that the inverse is defined on the domain x < 5. However, we must also exclude the value x = 5, because the denominator of the fraction \((\frac{x -5}{5} )^{2}\) becomes zero at this value. Therefore, the domain of f⁻¹(x) is x > 5.

We were given that x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5. Therefore, the domain of the inverse function becomes the range of the original function, and the range of the inverse function becomes the domain of the original function.

To know more about domain, visit:

https://brainly.com/question/26098895

#SPJ1

Answer: 0.0135

0.0009563758

0.00835

The length of the third side is 12 units

From the question, we have the following parameters that can be used in our computation:

A right triangle

This means that we can calculate the third length using the Pythagoras theorem

using the above as a guide, we have the following:

x = √(15² - 9²)

Evaluate the exression

x = 12

Hence, the third length is 12 units

Read more about right triangle at

https://brainly.com/question/2437195

#SPJ1

Answer:

I believe the correct answer would be X = \(\frac{1}{4} z\)

Step-by-step explanation:

You would set the denominator equal to 0

Then move the variable to the right

Lastly, divide both sides, which gives you your answer of X = \(\frac{1}{4} z\)

Hope this helped.

Answer:

(12(3)-3(1/3))/(4(3)-5)=5

Step-by-step explanation:

12 x 3= 36     3 x 1/3=1  

4 x 3=12

(36-1)/(12-5)

35/7

5

THE ANSWER IS 5

Answer:

9) 73

10) he set off at 1:55 pm

easy-Peasy

Answer:

17,420

Step-by-step explanation:

It the same on the other side so you would have to multiply 134 and 130 together which u get 17,420 and when u plug it in and divide it u get 130 degrees

Answer:

The right triangular pyramid volume is given by the formula V = 1 3 × B × h , where B is the area of the triangular base and h is the height (the distance from the apex to the base).

Step-by-step explanation:

Answer:

192 cubic feet

Step-by-step explanation:

The volume V of a triangular pyramid is given by the formula:

V = (1/3) * base area * height

where base area is the area of the triangular base.

In this case, the triangular base has a length of 8 ft and a width of 8 ft, so it is a square with area:

base area = length * width = 8 ft * 8 ft = 64 sq ft

Substituting the given values into the formula, we get:

V = (1/3) * 64 sq ft * 9 ft

V = 192 cubic feet.

Therefore, the volume of the triangular pyramid is 192 cubic feet.