At the movies, John was sent to the lobby to buy refreshments for his friends. Some wanted popcorn which sold for 50 cents a bag and others wanted caramel corn which was 75 cents a bag. If John bought 9 bags and spent $5.00, how many of each kind of bag did he buy?

The area of the triangle is 60 in²

An isosceles triangle is a triangle with two equal sides. The area of an isosceles triangle is given by:

A = 1/2[√(a² − b² ⁄4) × b],

Where a is the measure of equal sides and b is the base of triangle

From the given info, a = KL = LM = 13 in and b = KM = 10 in

A = 1/2[√(13² − 10² ⁄4) × 10]

A = 1/2[√(169 − 100 ⁄4) × 10]

A = 1/2[√(169 − 25) × 10]

A = 1/2[√(144) × 10]

A = 1/2[12 × 10]

A =  1/2[120]

A = 60 in²

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(a) P(N=0) = 0.00974

(b) P(N=n) = 1/3[10Cn(0.3)ⁿ(0.7)¹⁰⁻ⁿ + 10Cn(0.5)ⁿ(0.5)¹⁰⁻ⁿ + 10Cn(0.7)ⁿ(0.3)¹⁰⁻ⁿ]

(c) N does not have a binomial distribution.

(d) yes, it is a fair game.

(a) P(N=0) = 1/3P(N=0 | p = 0.3) + 1/3P(N=0 | p = 0.5) + 1/3P(N=0 | p = 0.7)

or P(N=0) = 1/3{(0.3)¹⁰ + (0.5)¹⁰ + (0.7)¹⁰)

or P(N=0) = 0.00974

(b) P(N=n) = 1/3[10Cn(0.3)ⁿ(0.7)¹⁰⁻ⁿ + 10Cn(0.5)ⁿ(0.5)¹⁰⁻ⁿ + 10Cn(0.7)ⁿ(0.3)¹⁰⁻ⁿ]

since, n=0, 1, 10

(c) N does not have binomial distribution but subparts in it have binomial distribution.

(d) yes, it is a fair game because only the first and third coins are biased and their biasness is tied (p = 0.3 and 0.7). Hence it is a fair game in the long run.

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For the sample (a) Mean is 30.8, the median is 31 and the standard deviation is 3.96, (b) the coefficient of skewness using Pearson's method is -0.151, and (c) the coefficient of skewness using the software method is 0.075.

Given values,

36, 26, 33, 28, 31

no. of values, n = 5

(a)

Mean, μ = Σx/n

= (36+26+33+28+31)/5 = 30.8

Now, Median, M = (n+1)/2th value

M = (5+1)/2 th = 3rd value

M = 31

Standard deviation(s) = [tex]\sqrt{ }[/tex]Σ(x-μ)²/n-1

= [tex]\sqrt{ \frac{(36-30.8)^{2}+(26-30.8)^2+(33-30.8)^2+(28-30.8)^2+(31-308)^2 }{4} }[/tex]

s = 3.96

(b) the coefficient of skewness using Pearson’s method

= 3(μ-M)/s = 3(30.8-31)/3.96 = -0.151

(c) the coefficient of skewness using the software method

= 1/s³(n-1)Σ(x-μ)³ = [tex]\frac{(36-30.8)^{3}+(26-30.8)^3+(33-30.8)^3+(28-30.8)^3+(31-30.8)^3 }{4(3.96)^3}[/tex]

= 0.075

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Answer:

The volume is 1449 ft^3

Step-by-step explanation:

Split each section, the living room and hallway, into two different rectangular prisms to solve for.

The larger rectangle will have a length of 15ft, a width of 12ft, and a height of 7ft as shown in the diagram. Multiply length, width, and height to find the volume of 1,260ft.

15*12*7=1,260

The smaller rectangle will have a length of 9ft. That's found by subtracting 15 from 24. The width will be 3ft. That's found from subtracting 9 from 12. The height is still 7. Multiple each together to find the second rectangle's volume of 189ft.

24-15=9

12-9=3

9*3*7=189

Add both volumes together and you have the volume of the whole space.

1,260+189=1449ft^3

The algebraic expression that represents the given sentence is:

8 (x + 5).

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. The values a expressed in an unknown number using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression.

In mathematics, a number that is obtained by multiplying two or more distinct variables together is referred to as the product.

Let us suppose the "a number", as x.

The sum of a number and 5 is represented as follows:

(x + 5)

The product of 8 and sum of a number and 5 is represented as follows:

8 (x + 5)

Hence, the algebraic expression that represents the given sentence is:

8 (x + 5)

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Answer:c

Step-by-step explanation:

Variables in mathematics are used to represent values or quantities that can change or vary.

The values are:

a) g(3b) = 9b² - 3b

b) f(2) + 1 = 9

What is a function?

A function is a mathematical relationship between a set of inputs (also known as domain) and a set of possible outputs (also known as a range). The inputs are usually represented by variables, such as 'x' in the examples you provided.

The given functions are

f(x) = 3x +2 and g(x) = x² - x,

a) g(3b) = (3b)² - (3b) = 9b² - 3b

b) f(2) = 3(2) + 2 = 6 + 2 = 8

so f(2) + 1 = 8 + 1 = 9

Hence, the values are:

a) g(3b) = 9b² - 3b

b) f(2) + 1 = 9

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The standard deviation of the weight of 4 men would be: 5 lbs.

The standard deviation of a sample of size 4 is the square root of the variance divided by the sample size. In this case, the standard deviation of the weight of 4 men would be:

√(100 / 4) = √(25) = 5 lbs

Please note that the standard deviation of a population is denoted by the Greek letter sigma (σ) and the standard deviation of a sample is denoted by the letter s.

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To represent the ratio of trains to airplanes, you can write it as:

4 : 8

This ratio shows that for every 4 model trains, there are 8 model airplanes. You could also simplify the ratio to 1:2 which means that for every 1 model train, there are 2 model airplanes.

Alternatively, you could express the ratio as a fraction:

4/8 = 1/2

This fraction shows that 1/2 of the models are model trains.

The solution is, 1/2 is a ratio to represent the ratio of trains to airplanes.

Here, we have,

To represent the ratio of trains to airplanes, you can write it as:

4 : 8

This ratio shows that for every 4 model trains, there are 8 model airplanes. You could also simplify the ratio to 1:2 which means that for every 1 model train, there are 2 model airplanes.

Alternatively, you could express the ratio as a fraction:

4/8 = 1/2

This fraction shows that 1/2 of the models are model trains.

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Using linear equation, Isaac saved $33.3 and June ran 20.25 miles in 3 days.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Let Eve saved = $x

then Isaac saved= 5x+x=$6x

where x=$5.55

Hence,

           Isaac saved=$33.3

Let June ran y mile in one day

so, In three days she ran = 3y mile where y=6.75 miles

Hence,

           June ran 20.25 miles in 3 days.

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Answer: The answer is 6.51

Answer:

6.51

Step-by-step explanation:

10.5%  to change to a decimal divide by 100%

.105 x 62 = 6.51

Answer:

see below

Step-by-step explanation:

total sum of all angles is 360

becuase they are all parallel, so the sum of A & D multiply by 2 = 360

so a+d = 180

5x+18 +3x+10 = 180

8x+28 =180

8x=152

x=19

A = 5*19+18 =113

D=3*19+10 =67

The interest will she earn in 1year is $45 if Rachel has $900 in a savings account. The interest rate is 5% per year and is not compounded.

What is Simple Interest ?

Simple Interest can be defined as the ratio of product of principal amount, time, rate and hundred.

Given ,

Rachel has $900 in a savings account. The interest rate is 5% per year and is not compounded.

we have to find interest will she earn in 1year

so we know that,

I  = PTR

I = 900*(0.05)*1

I = $45

So, The interest could be $45.

Therefore, The interest will she earn in 1year is $45 if Rachel has $900 in a savings account. The interest rate is 5% per year and is not compounded.

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The mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

The mean of a geometric distribution is given by:

Mean = 1/p

Here, p is the probability of success on a single trial.

In this case, p = 0.80

So, the mean of the geometric distribution = 1/0.80 = 1.25

The variance of a geometric distribution is given by:

Variance =[tex](1-p) / p^2[/tex]

By substituting the value of p = 0.80, we get:

Variance = [tex](1-0.80) / 0.80^2 = 0.20 / 0.64 = 0.3125[/tex]

So the variance of the geometric distribution = 0.3125

Therefore, the mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

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The table of values represented from 60 = 12m is

m      5

f(m)   60

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

60 = 12m

To determine the table of values, we start by solving for m in the equation 60 = 12m

So, we have

12m = 60

Divide both sides by 12

m = 5

So, the equation can be expressed as

f(m) = 12m

This implies that the table of values is

m      5

f(m)   60

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The cumulative distribution function of a continuous random variable is the probability that the random variable X is greater than or equal to x, where x is a specific value of the continuous random variable X. [FALSE ]

The cumulative distribution function of a continuous random variable is the probability that the random variable X is less than or equal to x, where x is a specific value of the continuous random variable X.

The cumulative distribution function is a function that is usually derived from a continuous random variable. We actually calculate the area underneath a probability density function between two points.

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The names possible to describe the shape Mr Meyer drew are square and rhombus.

A square is a quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles).

A rhombus is a quadrilateral whose four sides are all the same length.

We know a square has 4 sides that are equal and 4 right angles.

And Its properties are acquired by the shape Rhombus with equal sides, and opposite sides that are parallel to each other and angles are of right angle (90 degrees).

And many Quadrilaterals have a right angle but not 4 equal sides.

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The square feet of outdoor carpet needed for the hole is 42.

A composite figure is a given figure which is made up of more than one figure. Thus the total area of the figure is then the required area of the composite figure.

In the given diagram, the hole can be divided into a trapezium, rectangle and a triangle. So that;

i. Area of a trapezium = 1/2 (a + b)h

                                = 1/2 (3 + 6)4

                                = 9*2

                                = 18

Area of the trapezoidal part is 18 square feet.

ii. Area of a rectangle = length x width

                                    = 7*3

                                    = 21

Area of the rectangular part is 21 square feet.

iii. Area of a triangle = 1/2* base * height

                                  = 1/2 * 2* 3

                                  = 3

Area of the triangular part is 3 square feet.

Total area = 18 + 21 + 3

                 = 42 square feet

The area of outdoor carpet needed for the hole is 42 square feet.

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the customer saved 45% on the price of the radio compared to the original price.

25%

The original price of the radio = 100%

The 20% discount = 100%-20% = 80%

The 25% discount = 80%-25% = 55%

Overall percentage reduction = 100%-55% = 45%.

The original price of the radio was 100%. On the final day, the ale was discounted by 25%, which reduced the price to 80%. This was then further discounted by 20%, bringing the price to 55%. Therefore, the overall percentage reduction on the price of the radio was 45%. This means that the customer saved 45% on the price of the radio compared to the original price.

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Answer:

Step-by-step explanation:

Hello! Here are the steps to solve 4x - 8 = 3x + 13

4x - 8 = 3x + 13
    + 8         + 8
____________

4x       = 3x + 21
-3x        -3x
____________
x = 21

There is one solution because there is only one possibility for x.  Let's check the answer.

4(21) - 8 = 3(21) + 13
84 - 8 = 63 + 13
76 = 76

x = 21, x does equal 21 and the answer that there is only one solution is correct.

No solutions would mean that after you solved the equation, you would get something like 9 = 7, 2 = 5, etc. which is not true.  No solutions would mean that you would receive a false equation.

Infinite solutions would mean that after you solved an equation, such as 2x = 2y, you would get x = y.  There are infinite solutions for this because you can substitute infinite numbers in for x and y.  1 = 1, 2 = 2, 3 = 3, 4 = 4, 5 = 5, etc.

Answer:

X and y are the variables in the expression

Step-by-step explanation:

Variables are letters that represent an unknown value

For example, x + 4 = 7

In this equation, x is the variable because it is letter representing the unknown value

⇒ In 7x+ 4y+1 , x and y are the variables in the expression

The value of x when Sum of LHS = RHS is 4.

The letter "x" may be used in algebra to represent an unknown value. It might be called a "variable" or "unknown." If we make an effort, we can determine the value of x in the equation x + 2 = 7! The letter "x" is not required for a variable; it can also be "y," "w," or any other letter, name, or symbol.

The algebraic statement should typically take one of the following shapes: addition, subtraction, multiplication, and division. To find the value of x, first bring the variable to the left side, then shift every other value to the right side.

x + 5 + x+ 5+ x+ 5 = 27

3x + 15 = 27

3x = 27 - 15

x = 12/3

x = 4

Thus, The value of x when Sum of LHS = RHS is 4.

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Correct question:

Given both sides are equivalent expression and LHS sum = RHS. Find The value of x?

Answer:

Step-by-step explanation:

23 barrels an 3 budgets

As per the given length and width, the perimeter of rectangle is 16x² + 22x + 39

In math the term perimeter of rectangle is defined as the length of the outline of a shape.

In order to find the perimeter of a rectangle or square you have to add the lengths of all the four sides, then the formula is written as,

=> P = 2(l + w)

here l refers length and w refers the width of the rectangle.

Here we have given that the length of the rectangle in terms of x is 8x² +4x +7 and its width is 7x + 8.

Then the perimeter is calculated as,

=> P = 2(8x² +4x + 7 + 7x + 8)

When we simplify the expression, then we get,

=> P = 2(8x² + 11x +15)

When we multiply 2 with the expression, then we get,

=> P = 16x² + 22x + 39

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Answer :

a=93

b=19

Step-by-step explanation:

For (a)

Triangle total angles = 180

So we have

40+57+x = 180

x= 180 - 97

x= 83

Now,

x+ a =180( straight Angel)

83+a = 180

a = 93

Or,

You can use exterior angle theorem:

The exterior angle of a triangle is equal to the sum of the two opposite interior angles

a = 40+57

= 93

For (b)

Using the exterior angle theorem

b+38 =57

b = 57 - 38

= 19

Answer:

The correct answer is a= 97°

b=19°

Answer:

Step-by-step explanation:

The length of the rectangular backyard is represented by the polynomial 3x + 4 and the width is represented by the polynomial x - 1. To find the area, we can multiply the length and the width, which will give us the polynomial expression for the area.

So the polynomial that represents the area of the rectangular backyard is:

(3x + 4) * (x - 1) = 3x^2 + x - 4

If x = 6, then we can substitute this value into the polynomial expression for the area and find the area of the backyard:

3x^2 + x - 4 = 3(6)^2 + (6) - 4 = 108 square feet

So the area of the rectangular backyard when x = 6 is 108 square feet.

That the nimber value i

The probability that a randomly selected female senior will have a lower score than a male senior with a score of 1512 is approximately 0.788, or 78.8%.

What is the probability?

Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1. An event with a probability of 0 cannot occur, while an event with a probability of 1 is certain to occur.

To find the probability that a randomly selected female senior will have a lower score than a male senior, we need to use the standard normal distribution table, which gives the probability that a randomly selected value from a normal distribution with a mean of 0 and a standard deviation of 1 will be less than a certain value.

We can use the z-score formula to standardize the female senior's SAT score, which is given by:

z = (x - mean) / standard deviation

Where x is the female senior's SAT score, mean is the mean of the distribution of SAT scores for college bound female seniors, and standard deviation is the standard deviation of the distribution of SAT scores for college bound female seniors.

So the z-score for a female senior with a score of 1512 (the same as the mean of the male seniors) is:

z = (1512 - 1486) / 311 = 0.8

Looking at the standard normal distribution table, we can see that the probability that a value from a standard normal distribution is less than 0.8 is approximately 0.788.

Hence, the probability that a randomly selected female senior will have a lower score than a male senior with a score of 1512 is approximately 0.788, or 78.8%

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The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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