Jennifer first spins a spinner and then flips a coin. Complete the following table representing the sample space for this compound event

On solving the provided question, we can say that - the area of the triangle is - A = 1/2 X 10X 20 = 100 mm sq.

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

here,

b = 10 mm

H = 20 mm

A = 1/2 X B X H

A = 1/2 X 10 X20

A = 100 mm sq.

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The required equation is

Percent Remaining = (100 grams) * (0.5)^(12 weeks / 6 weeks)

Generally, The equation that determines the percent of an initial amount of a radioisotope remaining after t weeks is:

Percent Remaining = (Initial Amount) * (0.5)^(t/Half-Life)

In this equation, "Initial Amount" is the amount of the radioisotope at the start of the time period being considered (for example, at the start of the autopsy).

"Half-Life" is the length of time it takes for half of the radioisotope to decay.

"t" is the length of time that has passed since the start of the time period being considered.

The term (0.5)^(t/Half-Life) represents the fraction of the initial amount of the radioisotope that remains after t weeks.  This term is called the decay constant.

It is raised to the power of t/Half-Life because the decay constant is the fraction of the radioisotope that remains after one half-life.

If t is equal to the half-life, then the decay constant is raised to the power of 1, which is equal to itself.

If t is twice the half-life, then the decay constant is raised to the power of 2, which means that only a quarter of the initial amount remains.

For the radioisotope Xenos-6, the half-life is 6 weeks. Using the equation above, we can determine the percent of the initial amount of Xenos-6 remaining after any number of weeks by plugging in the appropriate values.

For example, if we have an initial amount of 100 grams of Xenos-6 and we want to know the percent remaining after 12 weeks, we would plug in the values like this:

Percent Remaining = (100 grams) * (0.5)^(12 weeks / 6 weeks)

This would give us a result of 25%, which means that 25 grams of Xenos-6 would remain after 12 weeks.

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Answer:

Step-by-step explanation:

The number which is a perfect cube among the given options is 27, which is option (b).

Given are some numbers.

It is required to find the number which is the perfect cube.

Now first, understand what numbers can be classified under the group of perfect cubes.

Perfect cubes are numbers that are formed by multiplying any number by itself 3 times.

That is, a number x is a perfect cube if there exists another number y such that:

x = y × y × y

x = y³

Here, from the given options:

27 = 9 × 3

    = 3× 3 × 3

That is, 27 is a perfect cube.

Hence, the correct option is (b).

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The circumference (c) is the dependent variable.

The radius (r) is the independent variable.

An independent variable is a variable that does not depend on any other variable for its value

A dependent variable is a variable depend on any other variable for its value.

In the rule c = 6.3r, the circumference (c) of a circle depends on the  radius for its value while the radius (r) does not depend on the circumference for its value.

Thus, the circumference (c) is the dependent variable while the radius (r) is the independent variable

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14/45 part of the book report was lost when the power filled

A fraction represents a part of a whole.

Given that Beau typed 8/15 Open his book report on his computer then he printed out 2/9 of his book report on his computer printer set an there was a power outage

Beau discovered that he hadn’t shaved his book report for the power went off.

We have to find the fractional part of the book report was lost when the power filled

8/15-2/9

LCM of 15 and 9 is 45

24-10/45

14/45

Hence, 14/45 part of the book report was lost when the power filled

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The inequality could be solved in order to get first gift certificate by customer is 12p≥100-25,   So Option (F) is correct.

Inequalities is a mathematical term, Which we use for comparison of two unequal expressions, It simply means that both the expressions are not equal. we express inequalities by following symbols  ">", "<"," ≤", "≥".

Suppose total purchase is, p

Each purchase is worth 12 points,

when customer sign up automatically earns 25 points,

And, when total sum of points will be more than 100 customer  will receive a gift,  

So sum of points for total purchase and points earned for sign up should be more than 100,

12p+25≥100.

Hence, 12p≥100-25

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The shoe owner should go for weighted mean when placing an order for shoes.

The study of data gathering, analysis, interpretation, presentation, and organization is known as statistics. In other words, gathering and summarising data is a mathematical discipline. Additionally, statistics might be considered a subfield of applied mathematics. However, uncertainty and variation are two crucial and fundamental concepts in statistics. Only statistical analysis can determine the uncertainty and variation in many sectors.

Given  Mr. Gilpin owns a shoe store,

when placing an order he should go for the average of the shoes that most of people use,

the average is shown by the mean but for the specific size he has to go with weighted mean,

A weighted mean is an average that is created by allocating various weights to various individual data. The weighted mean is equivalent to the arithmetic mean if all of the weights are identical.

Hence Mr. Gilpin should go with the weighted mean.

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The graph of the solution to the inequality 5/8z > 5/6 is attached

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

5/8z > 5/6

Multiply both sides of the inequality by 1/5

So, we have the following representation

1/8z > 1/6

Multiply both sides of the inequality by 8

So, we have the following representation

z > 8/6

Evaluate the quotient

This gives

z > 1.33

The above inequality means that the inequality starts from 1.33 and faces the right side

See attachment for the graph

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A statement which correctly describes the comparison between the shapes of the box plots include the following: A. The Bulldogs' distribution is symmetric, but the Wolverines' distribution is negatively skewed.

In Mathematics, skewness can be defined as a measure of the asymmetry of a box plot (box-and-whisker plot) or histogram and as such, a box plot (box-and-whisker plot) or histogram has a normal distribution when it is symmetrical.

By critically observing the box plot (box-and-whisker plot) which represent basketball scores for the Bulldogs basketball team has a median of 80 (vertical line dividing the box into two equal halves), which simply means that both whiskers on either sides of the box plot (box-and-whisker plot) are relatively equal and symmetric.

On the other hand (conversely), the box plot (box-and-whisker plot) for the Wolverines basketball team shows that the median is more closer to the third quartile (upper quartile) and the whisker to the right of the box plot is longer, which ultimately implies that Wolverines' distribution is negatively skewed.

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Complete Question:

These box plots show the basketball scores for two teams.

Bulldogs

55 70 80 90 105

Wolverines

35 55 80 85 96

Basketball scores

Compare the shapes of the box plots.

A. The Bulldogs' distribution is symmetric, but the Wolverines' distribution is negatively skewed.

B. Both distributions are symmetric.

C. Both distributions are negatively skewed.

D. The Bulldogs' distribution is symmetric, but the Wolverines' distribution is positively skewed​

The value of the segment MN is 23

An area or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.

From the question,

LN = 54

LM = 31

The value of MN = must be determined.

LM + MN = LN

54 = 31 + MN

Substract 31 from both sides of the equation

54 - 31 = 31 + MN - 31

23 = MN

Hence, The value of  MN is 23.

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First, we can set up the ratio of carrots to potatoes as 3:4. Since there are 12 carrots, we can set up the following proportion:

3/4 = 12/x

To solve for the number of potatoes, we can cross-multiply to get:

4x = 12 * 4

x = 48/4

x = <<48/4=12>>12 potatoes.

Therefore, there are 12 potatoes in the sack.

Answer:

Here's a graph that represents the relationship between the number of carrots and the number of potatoes in the sack:

Carrots (x) Potatoes (y)

0 0

3 4

6 8

9 12

12 16

As you can see from the graph, if there are 12 carrots in the sack, then there are 16 potatoes in the sack.

You can also use this graph to find the number of potatoes if you know the number of carrots, or to find the number of carrots if you know the number of potatoes. Simply find the number of carrots or potatoes on the x-axis or y-axis, and then follow the line upward or downward until you reach the line that represents the relationship between carrots and potatoes. The number you reach on the other axis is the number of carrots or potatoes.

Step-by-step explanation:

Answer:

q = ± 5[tex]\sqrt{5}[/tex]

Step-by-step explanation:

f(q) = q² - 125

to find the roots , let f(q) = 0 , that is

q² - 125 = 0 ( add 125 to both sides )

q² = 125 ( take square root of both sides )

q = ± [tex]\sqrt{125}[/tex]  = ± [tex]\sqrt{25(5)}[/tex] = ± ([tex]\sqrt{25}[/tex] × [tex]\sqrt{5}[/tex] ) = ± 5[tex]\sqrt{5}[/tex]

Emma is planning to cut 5 pieces of yarn and she should make each piece 7 inches long.

The acts of simplifying something to make it simpler to perform or comprehend, or the item that is simplified: The group offers guidance on streamlining trade processes.

Given, Emma is using this bar model to plan to cut 35 inches of yarn into equal pieces. As we can see in the picture she is planning to cut 5 pieces

Size of each  yarn  = 35/5 = 7

Therefore, Emma intends to cut five pieces of yarn, each measuring seven inches.

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the answer is 2 .

2 is the coefficient of y= 2x²+x-1

The length of the shorter side of the parallelogram is 39.5 inches.

A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.

Given;

The perimeter of a parallelogram is equal to the perimeter of a triangle with side lengths of 56 inches, 56 inches, and 99 inches.

The perimeter of the triangle,

= 56 + 56 + 99

= 211 inches.

And the perimeter of the parallelogram = The perimeter of the triangle.

Let x be the shorter side of the parallelogram.

Then,

2 (x+66) = 211

2x + 132 = 211

2x = 211-132

x = 79/2

x = 39.5 inches.

Therefore, the shorter side is 39.5 inches.

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After figuring out the answer to the above question, we can state that: v = 60 X (4.5 / 7.5), v = 36, 36 Liters in the equation.

A mathematical equation is a formula that joins two statements with the equal sign, or =, to represent equality. A mathematical statement demonstrating the equivalence of two mathematical expressions is the definition of an equation in algebra. For instance, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. All mathematical formulas, including equations, contain an equal sign. Algebra is frequently utilized in equations. When calculating a number in mathematics without knowing its exact value, algebra is used.

[tex]12.5 X (60 - v) + 20v= 17.60\\7.5v = 17.70 - 12.5 X 60\\v= 60 X ( 4.5 / 7.5)\\v = 36\\36 Liters[/tex]

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Using the formula of probability without replacement, the probability of selecting 2 greens without replacement is 1/12

When things are taken out of a set or collection as they are chosen, the probability that a certain occurrence will take place is known as probability without replacement. In probability with replacement, the elements are altered after each choice is made, but the set is left alone.

We use the following formula to determine probability without replacement:

P(Event) = Number of positive results / Number of potential results

Where the total number of items in the set represents the number of outcomes that are feasible, and the number of positive outcomes is the number of items that meet the event requirements.

Total number of possible outcomes = 3 + 3 + 3 = 9

P(green) = (3 / 9) * (2 / 8)

P(green) = 1 / 12

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Complete Question:

A bag holds 3 red marbles and 3 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be green?

Correct option is B, Tossing their heads in sprightly dance, saw I ten thousand at a glance.

Nature is the most beautiful aspect of the entire planet, according to the poem I Wandered Lonely As A Cloud. Daffodils are used in the poem to symbolize the joy and splendor of nature. The poet claims that the times he spent admiring those daffodils were the happiest of his life. Between 1804 and 1807, Wordsworth penned "I Wandered Lonely As A Cloud." While out for a stroll in the English countryside, he and his sister came across a lovely belt of daffodils. In order to express the emotion that overcame him at that precise moment, Wordsworth wrote this poem.

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The volume of the composite figure with the indicated side length dimensions is obtained by finding the sum of the volume of the square pyramid and the cuboid to get the volume as about 1295.1 mm³.

A composite figure is a figure that consists of the sum of two or more regular figures.

The possible question is to calculate the volume of the shape;

The specified figure is a composite figure, consisting of a cuboid and a triangular prism

The volume of the figure = The volume of the cuboid + The volume of the prism as follows;

Volume of the cuboid = 13 mm × 13 mm × 5 mm = 845 mm³

The volume of the rectangular pyramid is found using the formula for the a pyramid as follows;

V = (1/3) × Base area × Height

The height of the pyramid is h = √(10.3² - (13/2)²) = √(63.84)

Therefore; V = (1/3) × 13 mm × 13 mm × √(63.84) mm ≈ 450.1 mm³

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We can notice that this is a quadrilateral with two pairs of equal sides, with that we will see that:

m∠D = 98°

In the image we can see a quadrilateral ABCD, on that image we can see that:

AB = CD

AD = BC

You can notice that because of the "arrows" on the sides.

From that, we can conclude that the measures of the angles meet the conditions:

m∠A = m∠C

m∠D = m∠B

On the image we also can see that:

m∠B = 98°

And the measure of angle B is equal to the measure of angle D, then we can conclude that the measure of angle D is also 98°, so:

m∠D = 98°

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Each expression should be matched to the correct location on the table as follows;

(2 · 3⁻²)³ (5·3²)²/(3⁻²)(5·2)² = 2.

(3³)(4⁰)²(3·2)⁻³(2²) = 1/2.

(3⁷· 4⁷)(2·5)⁻³(5)²/(12⁷)(5⁻¹)(2⁻⁴) = 2.

(2.3)⁻¹ (2⁰)/(2 . 3)⁻¹ = 1.

In order to match each exponential expression to the correct location on the table, we would have to simplify each exponential expression by using the properties of exponents as follows;

(2 · 3⁻²)³ (5·3²)²/(3⁻²)(5·2)² = (2³)(3⁻⁶)(5²)(3⁴)/(3⁻²) (10²)

(2³)(3⁻⁶)(5²)(3⁴)/(3⁻²) (10²) = (2.2².5²) (3⁻⁶.3⁴)/(3⁻²) (10²)

(2.2².5²) (3⁻⁶.3⁴)/(3⁻²) (10²) = (2)(10²)(3⁻²)/(3⁻²) (10²)

(2)(10²)(3⁻²)/(3⁻²) (10²) = 2

Exponential expression 2:

(3³)(4⁰)²(3·2)⁻³(2²) = (3^3)(1^2) (3^-3)(2^-3) (2^2)

(3^3)(1^2)(3^-3) (2^-3) (2^2) = (2^(-3 + 2))

(2^(-3 + 2)) = 2^-1

2^-1 = 1/2

Note: A number with an exponent of 0 is equal to 1.

Exponential expression 3:

(3⁷· 4⁷)(2·5)⁻³(5)²/(12⁷)(5⁻¹)(2⁻⁴) = (12⁷)(2⁻³)(5⁻³)(5²)/(12⁷)(5⁻¹)(2⁻⁴)

(12⁷)(2⁻³)(5⁻³)(5²)/(12⁷)(5⁻¹)(2⁻⁴) = (2⁻³)(5^(-3 + 2))/(5⁻¹)(2⁻⁴)

(2⁻³)(5^(-3 + 2))/(5⁻¹)(2⁻⁴) = (2⁻³)(5⁻¹)/(5⁻¹)(2⁻⁴)

(2⁻³)(5⁻¹)/(5⁻¹)(2⁻⁴) = 1/2⁻¹

1/2⁻¹ = 2

Exponential expression 4:

(2.3)⁻¹ (2⁰)/(2 . 3)⁻¹ = 2⁰

2⁰ = 1

Note: You should multiply numbers that have the same exponent and add exponents with the same base.

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The range of the given function f(x)= -3x+1 for domain {-2, -1, 0}

is { 1<= x <=7}.

What is range and domain of a function?

Domain

The set of all possible values which qualify as inputs to a function is known as the domain of the function, or it can also be defined as the entire set of values possible for independent variables. The domain can be found in – the denominator of the fraction is not equal to zero and the digit under the square root bracket is positive. (In the case of a function with fraction values).

Range

The set of all the outputs of a function is known as the range of the function or after substituting the domain, the entire set of all values possible as outcomes of the dependent variable.

Now

To find range for f(x)= -3x+1 for domain {-2, -1, 0}

we can just put values

f(-2)=7

f(-1)=4

f(0)=1

Hence, range is { 1<= x <=7}.

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An example to support Fabian statement is that 25% of 100 is more than 10% of 100.

An example to negate Fabian statement is that 25% of -100 is less than 10% of -100.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100

An example to support Fabian statement is that 25% of 100 is more than 10% of 100. In this case, 25 it more than 10.

An example to negate Fabian statement is that 25% of -100 is less than 10% of -100. In this case, -25 is less than -10.

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Step-by-step explanation:

Let X be the number of pounds of peanuts selling for 85 cents per pound and Y be the number of pounds of peanuts selling for 98 cents per pound.

We can set up the following system of equations to represent this situation:

X * 0.85 + Y * 0.98 = 0.90 * (X + Y)

X + Y = 40

The first equation represents the total cost of the blend, and the second equation represents the total number of pounds of peanuts.

To solve this system of equations, we can use a method such as graphing, substitution, or elimination.

Using the substitution method, we can solve for one variable in terms of the other and substitute it into the other equation. For example, we can solve the first equation for X:

X = (0.90 * (X + Y) - Y * 0.98) / 0.85

Then, we can substitute this expression for X into the second equation:

(0.90 * (X + Y) - Y * 0.98) / 0.85 + Y = 40

Solving this equation for Y gives us the number of pounds of peanuts selling for 98 cents per pound:

Y = (40 * 0.85 - 0.90 * X) / (0.10 - 0.98)

To find the value of X, we can substitute this expression for Y into the first equation and solve for X:

X * 0.85 + (40 * 0.85 - 0.90 * X) / (0.10 - 0.98) * 0.98 = 0.90 * (X + (40 * 0.85 - 0.90 * X) / (0.10 - 0.98))

Solving this equation for X gives us the number of pounds of peanuts selling for 85 cents per pound:

X = 18.75

Therefore, 18.75 pounds of peanuts selling for 85 cents per pound must be mixed with 40 pounds of peanuts selling for 98 cents per pound to produce a blend selling for 90 cents per pound.

Answer:

TSA of a cuboid = 136[tex]mm^{2}[/tex]

Step-by-step explanation:

Given,

l = 8mm

b = 3mm

h = 4mm

To Find: The TSA of a cuboid

TSA = 2(lb+bh+lh)

       = 2(8x3+3x4+8x4)

        = 2(24 + 12 + 32)

         = 136[tex]mm^{2}[/tex]

The inequality which correctly supports Fabian's claim as described above is; 0.25 × 100 > 0.1 × 80.

The inequality which shows that Fabian's claim as described above is incorrect is; 0.25 × 100 > 0.1 × 1000.

To start with, in a bid to write the given word phrase which happens to be Fabian's claim as an algebraic expression; we have that;

Let x be the first number and let y be the second number.

On this note, we have that;

( 25% × x ) > ( 10% × y )

0.25x > 0.1y

Consequently, the complete inequality which supports Fabian's claim is when x = 100 and y = 80 so that we have;

0.25 × 100 > 0.1 × 80; 25 > 8 which holds true.

Aslo, The inequality which shows that he is incorrect is; when x = 100 and y = 1000 so that we have;

0.25 × 100 > 0.1 × 1000; 25 > 100 which does not hold true.

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The equation of the tangent line to the graph of the given function at the point (2,-2) is y = x-4

The tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point.

Given that, a function f(x) = x³-3x²+x, We need to find the equation of the tangent line to the graph of the function at the point (2,-2)

The given function is f(x) = x³-3x²+x, we have x = 2,

Finding the slope of the line,

f'(x) = 3x²-6x+1

Slope = f(2)

f(2) = 12-12+1 = 1

Since, the tangent line passes through (2,-2) and have slope 1,

We know, the equation of the tangent line can be found using the formula  y-y₁ = m(x-x₁), where m is the slope and (x₁, y₁) is the coordinate points of the line.

y-(-2) = 1(x-2)

y+2 = x-2

y = x-4

Hence, the required equation is y = x-4

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Tom's pencil is 3x + 10cm longer  than Ellen's.

What is arithmetic operation?

The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators.

For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-" Multiplication (Identifying the result; "x" Finding the quotient in division (÷).

Given:

Ellen has a pencil 2x+15cm long.

Tom has a pencil 5x+25cm long.

We have to find how much longer is Tom's pencil than Ellen's.

This is calculated as:

Length of Tom's pencil - Length is Ellen's pencil

Length of Tom's pencil: 5x+25cm long.

Length of Ellen's pencil : 2x+15cm long.

= (5x + 25)cm - (2x + 15)cm

= 5x + 25 - 2x - 15

= 5x - 2x + 25 - 15

= 3x + 10 cm

Therefore, Tom's pencil is 3x + 10cm longer  than Ellen's.

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Answer:

I'm not really sure if this is the right answer because I'm in high school and your in collage so here's what I can do:

A graph of the system of inequalities is shown in the image and one possible solution is the ordered pair (-4, 24).

In order to solve these system of inequalities graphically, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Note: 1 quarter is equal to 0.25 dollar, 1 nickel is equal to 0.5 dollar, and 1 dime is equal to 0.1 dollar.

Since Arun has no less than 20 coins worth a maximum of $0.40 combined, an inequality to represent this is given by;

x + y ≥ 20

For a maximum of $0.40 combined, we have:

0.5x + 0.1y ≤ 0.40

From the graph (see attachment), a possible solution is given by the ordered pair (-4, 24).

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