A bag contains 2 gold marbles, 7 silver marbles, and 21 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?

Interest earned by Mary is $ 3,745.92 which is more than the interest than Josh earned that is $ 3,600.

For Mary:

Principal = $ 30,000

Interest rate = 4 %

Compounded annually

t = 3 years

Amount = $ 30,000 ( 1 + 4 / 100 )³

A = 30,000 ( 1.04)³

A = 30,000 ( 1.124864 )

A = $ 33,745.92

Interest = A - P = 33,745.92 - 30,000 = $ 3745.92

For Josh:

Principal = $ 30,000

Simple interest

t = 3 years

Interest = 30,000 × 3 × 4 / 100

Interest = $ 3600

Therefore, interest earned by Mary is $ 3,745.92 which is more than the interest than Josh earned that is $ 3,600.

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Answer:

[tex]\frac{\pi r^2}{2}[/tex]

Step-by-step explanation:

The area of a semicircle is half the area of a circle

The area of a circle is [tex]\pi r^2[/tex], where r is the radius of the circle, and [tex]\pi[/tex] is a mathematical constant, approximately 3.14. The area of the semicircle is half the area of the circle, or [tex]\frac{\pi r^2}{2}[/tex].

The solution of the system of equations are x = 7 and y = 77

Given data

y = 9x + 14

y = 6x + 35

solving using substitution method to solve the simultaneous equation we have

y = 9x + 14  equation 1

y = 6x + 35  equation 2

equating the both equations will give

9x + 14  = 6x + 35

9x - 6x = 35 - 14

3x = 21

x = 7

plugging x = 7 into equation 1

y = 9x + 14

y = 9 * 7 + 14

y = 63 + 14

y = 77

The solution of the system of equations are x = 7 and y = 77

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Answer:

Step-by-step explanation:

meow meow its 99

Using it's concept, the mean test score is of 4.9.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

From the frequency table, the sum of the 30 observations is given by:

0 x 3 + 1 x 2 + 2 x 6 + 3 x 1 + 4 x 1 + 5 x 3 + 6 x 2 + 7 x 4 + 8 x 4 + 9 x 2 + 10 x 2 = 146.

Hence the mean test score is given as follows:

M = 146/30 = 4.9.

The mean test score is of 4.9.

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Answer: 1. -4<n<4

2. n<-3 or n>19

3. n<=-36 or n>=44

Step-by-step explanation:

n=number

units from a number is measured using absolute value sign

1. 4 units from 0: |n-0|<4 ==> |n|<4

n<4, n>-4 ==> -4<n<4

2. 11 units from 8: |n-8|>11

n-8>11

n-8+8>11+8

n>19

n-8<-11

n-8+8<-11+8

n<-3

n<-3 or n>19

3. half a number is at 2 units from 20:  |n/2-2|>=20

n/2-2>=20

n/2>=22

n>=44

n/2-2<=-20

n/2<=-18

n<=-36

n<=-36 or n>=44

Answer:8977/1000

Step-by-step explanation:

The value of 8.977 as a ratio of two integers would be equal to 8977/1000  

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We need to Write 8.977 as a ratio of two integers.

We know that negative divided by a negative is positive, then;

8.977 can be written as;

8977/1000

Therefore, The value of 8.977 as a ratio of two integers can be written as

8977/1000

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Answer:

Hope this helps

Step-by-step explanation:

full explanation in the given picture

Answer: the fourth choice, or y=-3x+18

Step-by-step explanation:

using the point-slope form, we can plug in the values:

y-0= -3(x-6)

distributing the right side we get

y-0=-3x+18

putting it into y=mx+b form we get y=-3x+18

The solution to the linear equation is v = -36

Here we have a simple linear equation:

v/3 + 3 = v/4

To solve this, we need to isolate the variable v.

First, let's move all the terms with "v" to the left and the terms without to the right side, so we get:

v/3 - v/4 = -3

Now we can solve this:

4v/12 - 3v/12 = -3

v/12 = -3

v = -3*12

v = -36

The solution to the linear equation is v = -36

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The surface area of square pyramid is 64 ft²

What is square pyramid?
In terms of geometry, a square pyramid is a pyramid with a square base and four lateral faces. A pyramid is a type of polyhedron with three or more triangular faces that meet above its base (the apex). A square pyramid is a pentahedron, a three-dimensional shape with a total of five faces. The Great Pyramid of Giza is a well-known example of a real-life pyramid. When we learn about pyramids, we must also learn other concepts that are related to them, such as the volume and area of the pyramid. In this article, we will learn what a square pyramid is, its types, characteristics, surface area formulas, and volume formulas with numerous examples and solutions.

For a square pyramid, the surface area is given by the following equation:

SA = a^2 + 4(a)(h)
where a is the side length of the base and h is the slant height.
In this case, a = 4 and h = 3. Therefore,
SA = 4^2 + 4(4)(3)
SA = 16 + 48
SA = 64 ft^2

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We use Integers in everyday life when we solve real-world problems.

Let’s understand a real-life problem using integers.

Christian borrowed $1000 to buy a computer. After some time, she has paid back $250. How much does Christian still owe?

First, we will write a simple equation to represent the problem.

Let the amount that Christian still owes = 'x'

1000 = 250 + x

Now, we will rearrange the equation to isolate .

Then, solve for x.

The answer is 750.

Christian still owes = $750.

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The equation that represent the same salary is 55,000x+2,500x=64,000+1500x

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Given:

Katherine has a new job and earns salary of $55,000.  Katherine will receive a salary increase of $2,500 per year .

max has a new job and earns a salary of $64,000. Max will receive a salary increase of $1,500 per year.

So, in the case they would have the same salary for some x years the expression can be

Katherine salary along with increment= 55000+ 2500x

Max salary along with increment= 64000+ 1500x

Hence, equation ca be used to find x, the number of years it will take Katherine to earn the same salary as Max is 55,000x+2,500x=64,000+1500x.

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Answer:

132 feet per second

Step-by-step explanation:

The solution of the given equation is y = (6x - 11)/4.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given that equation as

⇒ 6x - 4y = 11

We have to determine the solution for y.

⇒ 6x - 4y = 11

Rearrange the terms of the above equation and solve for y,

⇒ 4y = 6x - 11

Divided by 4 on both the side of the equation, we get

⇒ y = (6x - 11)/4

Hence, the solution of the given equation is y = (6x - 11)/4.

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The rule for the cost function c(x) that gives the total daily cost of producing x bags of pretzels will be 1200 + 0.4x

b. The revenue function will be 1.80x.

c. The profit function p(x) is 1.4x - 1200.

It should be noted that fixed cost = 1200

Also, it costs 40 cents to produce each bag of pretzels. Therefore, the cost function will be:

= 1200 + 0.4(x)

= 1200 + 0.4x

The revenue function will be:

= Price × Quantity

= 1.80 × x

= 1.8x

c. The profit function p(x) will be:

= Revenue - Cost

= 1.8x - 1200 + 0.4x

= 1.4x - 1200

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The graph is made and attached.

Given, the equation is x ₋ √x₊3 = 0

substitute values for x from the interval ₋1 to 5 and then graph the points.

for x = ₋1:

₋1 ₋ √₋1 ₊ 3 = 0

₋1 ₋ 1.42 = 0

₋2.42

for x = 0

0 ₋ √0₊3 = 0

₋1.74

for x=1

1 ₋ √1₊3 = 0

1 ₋ √4 = 0

1 ₋ 2 = 0

₋1

for x = 2

2 ₋ √2₊3 = 0

2 ₋ √5 = 0

2 ₋ 2.24 = 0

0.24

for x = 3

3 ₋ √3₊3 = 0

0.55

for x = 4

4 ₋ √4₊3 = 0

4 ₋ √7 = 0

1.25

for x = 5

5 ₋ √5₊3 = 0

2.17

hence we have the points (₋1,₋2.42) (0,₋1.74)(1,₋1)(2,0.24)(3,0.55)(4,1.25) and(5,2.17)

plot the above points on the graph.

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Answer: D

Step-by-step explanation: It said the grandparents were less than 89 years old, if it said that the grandparents that were 89 and younger had remembered that's when you would use a solid circle because the 89 would be included. But since 89 isn't included then it's an open circle.

Answer:

12.87

Step-by-step explanation:

Since we know that line CD is a perpendicular bisector, triangle ACD is a right triangle, and thus we can apply the Pythagorean theorem to determine the length of side CD. Since the Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the adjacent sides, we can plug in the values of side AD and AC.

As side CD is the bisector of side AB, sides AD and DB are both half the length of side AB, so:
AD = 11/2
AD = 5.5

We now know two values of our equation, and thus we can solve for the missing third value.

5.5^2 + b^2 = 14^2
14^2 - 5.5^2 = b^2
196 - 30.25 = b^2
165.75 = b^2
[tex]\sqrt{165.75} = b[/tex]
b = 12.87

Answer:

Step-by-step explanation:

x + 139 + 37 + 53 = 360

              x + 229 = 360

                       x = 360-229

                       x = 131 degrees

Step-by-step explanation:

3xy² - x²

x = 2, y = 3

well, we simply replace every variable in the expression by the actual value and calculate.

3×2×3² - 2² = 6×9 - 4 = 54 - 4 = 50

Answer:3 11/14

Step-by-step explanation:im right

Answer:

6.505

Step-by-step explanation:

[tex]\frac{7}8}[/tex]  Put in your calculator 7 ÷ 8 and you will get .875  

So, 10 [tex]\frac{7}{8}[/tex] is 10.875  now subtract this from 4.37.  You can line up the decimals and then subtract or just have the calculator do this for you, if you are allowed.

10.875 - 4.37 = 6.505

The area is 108yd2(square yards).

In the given triangle a base

24yd and the corresponding height of 6 yds are given, so to calculate the area we can use:

A=12×b×h

If we substitute the given numbers we get:

A=[tex]\frac{1}{2}[/tex]×24×18

=12×9

=108

The units of base and height are the same (yards), so the calculated area is in yd2

The area is the quantity that expresses the extent of a region on the plane or on a curved surface. the world of a plane region or plane area refers to the area of a shape or planar lamina, while area refers to the area of an open surface or the boundary of a three-dimensional object. The area is often understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the quantity of paint necessary to cover the surface with a single coat. it's the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).

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Answer:

Step-by-step explanation:

Work done is transfer of energy...... but without complicating things a little further let's just consider the amount of work done while cleaning the backyard is the same regardless of who the doer is/ how many in number are the doers. So

So power is the time rate change of work done:

[tex]P=w/t\\[/tex]

let's say power of LeeAnn =L, Mandy=M

[tex]L=w/30 minutes\\M=w/25 minutes\\[/tex]

And if they worked together their power will add up to L+M

[tex]L+M=w/T\\[/tex], while T is the amount of time needed when they clean together.

[tex]L+M=w/T\\w/30min + w/25min =w/T\\1/30min+1/25min=1/T, w\neq 0\\1+(6/5)=30/T\\11/5=30/T\\11T=150\\T=150/11 min\\T=13.6 min[/tex]

The product of matrices A and B​ is  the elements 0 and 6 in the first row and -10 and -8 in the second row.

Given that the matrix A = 2 - 143 and B = -11-2-4.

Assume that the order of the matrix of A and B is 2x2.

The elements of matrix A are as below:a₁₁ = 2, a₁₂ = -1, a₂₁ = 4, a₂₂ = 3

The elements of matrix B are as below:b₁₁ = -1, b₁₂ = 1, b₂₁ = -2, b₂₂ = -4

We need to find the product of matrices A and B.

Let C denote the product of matrices A and B.

Then the order of the matrix C is 2x2 and its elements are calculated as follows : c₁₁ = a₁₁·b₁₁ + a₁₂·b₂₁ ⇒ c₁₁ = 2(-1) + (-1)(-2)⇒ c₁₁ = -2 + 2⇒ c₁₁ = 0 c₁₂ = a₁₁·b₁₂ + a₁₂·b₂₂⇒ c₁₂ = 2.1 + (-1)(-4)⇒ c₁₂ = 2 + 4⇒ c₁₂ = 6c₂₁ = a₂₁b₁₁ + a₂₂b₂₁⇒ c₂₁ = 4(-1) + 3(-2)⇒ c₂₁ = -4 -6⇒ c₂₁ = -10c₂₂ = a₂₁b₁₂ + a₂₂b₂₂⇒ c₂₂ = 4(1) + 3(-4)⇒ c₂₂ = 4 - 12⇒ c₂₂ = -8

Therefore the required matrix has the elements 0 and 6 in the first row and -10 and -8 in the second row.

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The matrix format was not clear from the question.So, assumptions were made to answer this question.

Answer:

1/8

Step-by-step explanation:

The simplification of the expression 20(6) - 7 using the laws of equation gives 113

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

20(6) - 7

Firstly, solve the equation inside the bracket to get:

120 - 7

Taking the difference of the two terms gives:

113

The simplification of the expression 20(6) - 7 using the laws of equation gives 113

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