Use a table to show the sample space of two-digit numbers using the digits 9,4,5,8

Even though the first student scored 150, the expected average IQ score for the remaining four students is still 100.

Explain average

The average is a statistical measure that represents the central tendency of a set of values. It is calculated by adding up all the values and dividing them by the total number of values. The average provides a single value that represents the typical value in the set and is often used to compare different sets of data or to summarize large amounts of data.

According to the given information

Let X be the random variable representing the IQ score of an individual student. Then, the sample mean of the five students, denoted by Y, can be expressed as:

Y = (X1 + X2 + X3 + X4 + X5) / 5

Given that the first student scored 150, the expected value of the sample mean of the remaining four students, denoted by E(Y|X1=150), can be calculated as follows:

E(Y|X1=150) = E((X2 + X3 + X4 + X5) / 4 | X1 = 150)

Since X1 = 150 is an observed value, we can treat it as a constant and apply the linearity of expectation:

E((X2 + X3 + X4 + X5) / 4 | X1 = 150) = (E(X2 | X1 = 150) + E(X3 | X1 = 150) + E(X4 | X1 = 150) + E(X5 | X1 = 150)) / 4

Now, since the sample is random, the remaining four IQ scores are also independent and identically distributed as X, with the same mean of 100. Therefore, we have:

E(X2 | X1 = 150) = E(X3 | X1 = 150) = E(X4 | X1 = 150) = E(X5 | X1 = 150) = E(X)

Thus, we can simplify the expression as:

E(Y|X1=150) = (4E(X) / 4) = E(X) = 100

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Equations are used to solve different types of problems in mathematics and in the real world.The five types of equation are 2x = 8,2y/2 = 8/2, (1/2)x + 2 = 3,3(x+4)= 21,0.4x + 1.2 = 2.6.

What is Equations Portfolio?

Equations are an essential part of mathematics and have various applications in real-world problems. In this portfolio, we will cover different types of equations and solve them step by step. This portfolio will cover one-step equations, equations with fractions, equations with the distributive property, and equations with decimals.

One-step equations are equations that can be solved in one step. For example, if we have the equation 2x = 8, we can solve it by dividing both sides by 2. Let's solve two one-step equations,

3x = 15

Dividing both sides by 3

3x/3 = 15/3

x = 5

Again,

2y = 8

Dividing both sides by 2

2y/2 = 8/2

y = 4

Equations with fractions are equations that contain fractions. To solve these equations, we need to clear the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. Let's solve two equations with fractions:

(1/2)x + 2 = 3

Subtracting 2 from both sides

(1/2)x = 1

Multiplying both sides by 2 (LCM of 1/2)

(1/2)x × 2 = 1 × 2

x = 2

(2/3)y - 1 = 3

Adding 1 to both sides

(2/3)y = 4

Multiplying both sides by 3 (LCM of 2/3)

(2/3)y × 3 = 4 × 3

y = 6

Equations with distributive property are equations that involve distributing a number or a variable to the terms inside the parentheses. Let's solve an equation with the distributive property,

3(x + 4) = 21

Distributing 3 to (x + 4)

3x + 12 = 21

Subtracting 12 from both sides

3x = 9

Dividing both sides by 3

x = 3

Equations with decimals are equations that contain decimal numbers. To solve these equations, we need to clear the decimals by multiplying both sides of the equation by a power of 10. Let's solve an equation with decimals,

0.4x + 1.2 = 2.6

Subtracting 1.2 from both sides

0.4x = 1.4

Multiplying both sides by 10 (power of 10 for one decimal place)

0.4x × 10 = 1.4 × 10

4x = 14

Dividing both sides by 4

x = 3.5

Now let's solve a real-world problem using an equation,

Sarah has $500 in her bank account. She wants to buy a dress for $120 and save the rest of the money. How much money will Sarah save?

Let x be the amount of money Sarah saves.

Total money = $500

Money spent on the dress = $120

Money saved = Total money - Money spent on the dress

x = 500 - 120

x = 380

Therefore, Sarah will save $380.

In conclusion, equations are used to solve different types of problems in mathematics and in the real world.

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The five types of equation are  2x = 8,2y/2 = 8/2,(1/2)x + 2 = 3,3(x + 4) = 21,0.4x + 1.2 = 2.6.

Equations are an essential part of mathematics and have various applications in real-world problems. In this portfolio, we will cover different types of equations and solve them step by step. This portfolio will cover one-step equations, equations with fractions, equations with the distributive property, and equations with decimals.

One-step equations are equations that can be solved in one step. For example, if we have the equation 2x = 8, we can solve it by dividing both sides by 2. Let's solve two one-step equations,

3x = 15

Dividing both sides by 3

3x/3 = 15/3

x = 5

Again,

2y = 8

Dividing both sides by 2

2y/2 = 8/2

y = 4

Equations with fractions are equations that contain fractions. To solve these equations, we need to clear the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. Let's solve two equations with fractions:

(1/2)x + 2 = 3

Subtracting 2 from both sides

(1/2)x = 1

Multiplying both sides by 2 (LCM of 1/2)

(1/2)x × 2 = 1 × 2

x = 2

(2/3)y - 1 = 3

Adding 1 to both sides

(2/3)y = 4

Multiplying both sides by 3 (LCM of 2/3)

(2/3)y × 3 = 4 × 3

y = 6

Equations with distributive property are equations that involve distributing a number or a variable to the terms inside the parentheses. Let's solve an equation with the distributive property,

3(x + 4) = 21

Distributing 3 to (x + 4)

3x + 12 = 21

Subtracting 12 from both sides

3x = 9

Dividing both sides by 3

x = 3

Equations with decimals are equations that contain decimal numbers. To solve these equations, we need to clear the decimals by multiplying both sides of the equation by a power of 10. Let's solve an equation with decimals,

0.4x + 1.2 = 2.6

Subtracting 1.2 from both sides

0.4x = 1.4

Multiplying both sides by 10 (power of 10 for one decimal place)

0.4x × 10 = 1.4 × 10

4x = 14

Dividing both sides by 4

x = 3.5

Now let's solve a real-world problem using an equation,

Sarah has $500 in her bank account. She wants to buy a dress for $120 and save the rest of the money. How much money will Sarah save?

Let x be the amount of money Sarah saves.

Total money = $500

Money spent on the dress = $120

Money saved = Total money - Money spent on the dress

x = 500 - 120

x = 380

Therefore, Sarah will save $380.

In conclusion, equations are used to solve different types of problems in mathematics and in the real world.

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* Kendra and her family used:

** 4 liters of fuel on day 1

*** 3 liters of fuel on day 2

**** 2 liters of fuel on day 3

***** 4 liters of fuel on day 4

So in total they used:

4 + 3 + 2 + 4 = 13 liters of fuel

Therefore, the amount of fuel they used in all is:

13 liters

From the given information, you can deduce that triangle QTR is equilateral and equiangular (all angles are 60 degrees)

b, c, d, and f are true

The opposite angles of a parallelogram are congruent (b)

If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent (d)

Angle RQT is congruent to angle QRT, and angle QRT is congruent to angle S. By the transitive property, angle RQT is congruent to angle S (c)

Transitive property, like c (f)

a) Classroom:

Perimeter = 2(length + breadth) = 2(10m + 8m) = 36m

Area = length x breadth = 10m x 8m = 80m^2

Volume = length x breadth x height = 10m x 8m x 3m = 240m^3

b) Box:

Perimeter = 2(length + breadth) = 2(40cm + 25cm) = 130cm

Area = 2(length x breadth + length x height + breadth x height) = 2(40cm x 25cm + 40cm x 30cm + 25cm x 30cm) = 41500cm^2

Volume = length x breadth x height = 40cm x 25cm x 30cm = 30000cm^3

c) Cabinet:

Perimeter = 2(length + breadth) = 2(80cm + 70cm) = 300cm

Area = 2(length x breadth + length x height + breadth x height) = 2(80cm x 70cm + 80cm x 2m + 70cm x 2m) = 12640cm^2

Volume = length x breadth x height = 80cm x 70cm x 2m = 112000cm^3

Note: It's important to use consistent units in calculations. In this case, I converted the dimensions to a common unit (meters or centimeters) before performing the calculations.

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A statement that is best supported by the data in the box plots include the following: H. the interquartile range of the data for the community college is greater than the interquartile range of the data for the university.

In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.

Mathematically, interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) of university = Q₃ - Q₁

Interquartile range (IQR) of university = 15 - 9

Interquartile range (IQR) of university = 6.

For the community college, we have;

Interquartile range (IQR) = 15 - 6

Interquartile range (IQR) = 9.

Therefore, 9 is greater than 6.

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The Correct Answer Is:  High-strength sports.

explanation:

Because for wrestling you have to use, you're strength. (And I just did the exam and I got it wrong for choosing the wrong answer, so I believe it's my answer. !!so, it's not high-power sports)

I hope it helps you!

:)

Answer: This triangle is isoscele

Step-by-step explanation:

Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman.

Numbers are mathematical units of measurement and labelling. It is a sign or collection of symbols that are used to represent a quantity, usually a real or integer number.

Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman. The idea of combination can be used to arrive to this number.

Calculating the number of possible combinations of a given number of things is done mathematically using the concept of combination. C(n,r) = n! / (r! (n - r)!), where n is the total number of items and r is the number of things to be picked at a time, is the formula used to compute it. In this instance, r is the number of persons to be picked, which is 3, and n is the total number of people to be chosen from the group, which is 18, consisting of 10 males and 8 women.

As a result, there are a total of 10 ways for men and 8 ways for women to form a committee of two men and one woman C(18,3) = 18! / (3! (18 - 3)!) = 18! / (3! 15!) = 1320.

Thus, there are 1320 different methods to create a committee of two men and one woman out of a group of ten men and eight women.

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The area of the garden which is same as the shape of an octagon would be = 101.2in².

To calculate the area of an octagon the formula that can be used is given below;

Area of an octagon = (number of sides × length of one side × apothem)/2

For an octagon = 8 sides

apothem = 5.5in

Length of one side = 4.6in

Area = 8×4.6×5.5/2

= 202.4/2

= 101.2in²

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Becca made a mistake while constructing triangle DEF by using the angles 50°, 65°, and 65°. The mistake she made was violating the triangle inequality theorem.

According to the theorem, the sum of any two sides of a triangle must be greater than the third side. In other words, if we add the lengths of two sides of a triangle, it must be greater than the length of the third side.

Since Becca only used angles to construct the triangle, she did not consider the side lengths of the triangle. Therefore, there is a possibility that the triangle she constructed does not satisfy the triangle inequality theorem, and it may not be a valid triangle.

In order to ensure the triangle is valid, Becca needs to consider the side lengths while constructing the triangle. She could use trigonometric ratios or a ruler and protractor to measure the side lengths and angles accurately.

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Answer:

135.07 mm2

Step-by-step explanation:

height = 10.39 mm

area = 135.07 mm2

Answer:

The comparison that is not correct is:

C. -8 > -6

This is not correct because -8 is actually less than -6. Therefore, the correct comparison would be -8 < -6.

The other comparisons are correct:

A. 1 > -9 (true, because 1 is greater than -9)

B. 3 < 6 (true, because 3 is less than 6)

D. -3 < 4 (true, because -3 is less than 4)

Answer: the 3d shape would be a rectangle. the hight is 3. and the diameter is 10

Step-by-step explanation:

Translate the solid circle 2 units to the left and 2 units down and dilate the solid circle by a scale factor of 2. and the circles are similar

(a) To move the solid circle exactly onto the dashed circle, we need to perform the following transformations:

Therefore, the blank spaces should be filled as follows:

Translate the solid circle 2 units to the left and 2 units down.

Dilate the solid circle by a scale factor of 2.

(b) Yes, the original solid circle and the dashed circle are not similar, because they have different radii.

This is because all circles are similar

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The reasonableness of the estimate depends on the quality and reliability of the data sources and methodology used to arrive at the estimate.

In order to determine whether 12% is a reasonable estimate of the proportion of all Americans who eat chocolate

frequently, we would need to define what is meant by "frequently."

If we define "frequently" as "at least once a week," then 12% may or may not be a reasonable estimate, depending on

the data source and methodology used to arrive at that estimate.

For example, if the estimate is based on a small sample size or a non-representative sample of the population, then it

may not be a reliable estimate of the true proportion of Americans who eat chocolate frequently. Additionally, if the

estimate is several years old, it may not accurately reflect current trends and habits.

On the other hand, if the estimate is based on a large, nationally representative sample of the population, and is

relatively recent, then 12% could be a reasonable estimate of the proportion of Americans who eat chocolate

frequently.

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The value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

UF × FS = VF × FT

8(10x - 1) = 9 × 16

80x - 8 = 144

80x = 144 + 8 {collect like terms}

80x = 152

x = 152/80 {divide through by 80}

x = 1.9

FS = 10(1.9) - 1 = 18

Therefore, the value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

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Answer:

y int: (0, -23)

Step-by-step explanation:

first you find the slope by taking two points and substituting it in rise over run ([tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex])

I used 25-13/-72+54 which eventually simplified to -2/3

You then use point slope form and plug in one pair of points

I used (-36,1) since it seemed the easiest

y-1=[tex]\frac{-2}{3}[/tex](x+36)   point slope form: [tex]y-y_{1}=m(x-x_{1} )[/tex]

y-1= [tex]\frac{-2}{3} x-\frac{72}{3}[/tex]

y-1=[tex]\frac{-2}{3} x-24[/tex]

y=[tex]\frac{-2}{3} x-23[/tex]

the number without the variable is always y int regardless of the numbers in the equation

therefore, the y int is (0,-23)

Answer:

1

Step-by-step explanation:

First of all we use the "law of sines"

to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x

and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°

180°=70°+51°+ x

x = 180°-121°

=59°

Using law of sines:

(sides are represented by small letters/capital letters are the angles)

a/sinA= b/sinB= c/sinC

We have one given side which is "9"

so,

9/sin70= x/sin59

doing the criss-cross method,

9×sin59=sin70×x

9×sin59/sin70=x

x=8.2 (answer 1)

I hope this was helpful <3

Rounding to the nearest hundredth, the arc length of one slice is approximately 53.67 feet.

Arc length is the distance along the curved line or arc of a circle, measured in linear units such as centimeters, feet, or meters. It is calculated as the product of the radius of the circle and the angle subtended by the arc at the center of the circle, expressed in radians.

Here,

Since the circle is divided into eight equal slices, each slice is 360/8 = 45 degrees. The arc length of one slice can be calculated using the formula:

Arc length = (angle/360) x 2πr

where angle is the central angle in degrees, r is the radius of the circle, and π is the constant pi.

In this case, the diameter of the circle is 137 feet, so the radius is half of that, or 68.5 feet.

Substituting the given values into the formula, we get:

Arc length = (45/360) x 2 x 3.14 x 68.5

Arc length = 0.125 x 2 x 3.14 x 68.5

Arc length = 0.785 x 68.5

Arc length = 53.67 feet

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Note that both of these absolute value inequalities have the same solution set as 5 < x < 7.

Inequality refers to the state of being unequal, uneven, or unfair in terms of social, economic, political, or other factors. It can be the result of various factors such as discrimination, prejudice, systemic biases, and unequal distribution of resources, opportunities, and power. Inequality can manifest itself in many forms, including income and wealth disparities, unequal access to education, healthcare, and housing, unequal treatment under the law, and marginalization of certain groups based on their race, gender, sexual orientation, religion, or other characteristics. Addressing inequality is an important challenge in creating a more just and equitable society.

to write an absolute value inequality with a solution set of 5 < x < 7, we need to use the form |x - b| < c, where b is the center of the solution set and c is the distance from the center to the edge of the solution set.

In this case, the center of the solution set is (5 + 7)/2 = 6, and the distance from the center to the edge is (7 - 5)/2 = 1.

Therefore, we can write the absolute value inequality as:

[tex]| x - 6 | < 1[/tex]

Alternatively, we can use the form |x - b| > c and write the absolute value inequality as:

[tex]x < 5 or x > 7[/tex]

Note that both of these absolute value inequalities have the same solution set as 5 < x < 7.

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The range is the best measure of variability for this data, and it equals 8.

In statistics, the range is a measure of variability that describes the difference between the largest and smallest values in a dataset. It is the simplest measure of variability and is calculated by subtracting the smallest value in the dataset from the largest value.

The range is a measure of variability that tells us the spread of the data, i.e., how far apart the minimum and maximum values are. It is calculated by subtracting the smallest value in the dataset from the largest value.

In the given line plot, the horizontal axis represents the number of rose bouquets purchased per day, and the vertical axis represents the frequency (i.e., how many times that particular number of rose bouquets was purchased). Based on the plot, we can see that the lowest number of rose bouquets purchased in a day is 1, and the highest number is 9. Therefore, the range is 9 - 1 = 8.

In contrast, the IQR (interquartile range) is a measure of variability that gives us an idea of how spread out the middle 50% of the data is. It is calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3). Since we do not have the values for Q1 and Q3, we cannot calculate the IQR for this dataset.

Therefore, the range is the best measure of variability for this data, and it equals 8.

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Para entender mejor esta función, podemos expandirla y simplificarla:

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

f(x) = [tex]-x^2 + 4x + 12[/tex]

Esta es una función cuadrática, lo que significa que tiene la forma de una parábola. El término cuadrático ([tex]-x^2[/tex]) hace que la parábola tenga una concavidad hacia abajo, lo que significa que el valor máximo de la función se encuentra en el vértice de la parábola.

Podemos encontrar el valor del precio de venta que maximiza la ganancia utilizando la fórmula x = -b/(2a), donde "a" es el coeficiente del término cuadrático y "b" es el coeficiente del término lineal.

En este caso, a = -1 y b = 4, por lo que:

x = -4/(2-1)

x = -4/-2

x = 2

Por lo tanto, el precio de venta que maximiza la ganancia es de 2 por unidad. Si se venden las unidades a este precio, la ganancia total sería de:

f(2) = [tex]-2^2 + 4(2) + 12[/tex]

f(2) = -4 + 8 + 12

f(2) = 16 dólares

Es importante tener en cuenta que la función f(x) también puede ser utilizada para calcular la ganancia total para cualquier precio de venta "x". Por ejemplo, si se venden las unidades a 3 por unidad, la ganancia sería:

f(3) = [tex]-3^2 + 4(3) + 12[/tex]

f(3) = -9 + 12 + 12

f(3) = 15 dólares

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The two column proof is written as follows

Statement                                                           Reason

MA = XR                                           given (opposite sides of rectangle)

MK = AR                                           given (opposite sides of rectangle)

arc MA = arc RK                               Equal chords have equal arcs

arc MK = arc AK                               Equal chords have equal arcs

An arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.

If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.

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Answer:

Answer is 20

Step-by-step explanation:

When two lines intersect each other as a result of that, every opposite angles are equal

so,

6x+20 = 140

6x = 120

x = 120/6

x = 20

Answer:

x = 20

Step-by-step explanation:

Vertically opposite are equal

therefore

6x + 20 = 140

6x = 140-20

6x = 120

6x/6 = 120/6

x = 20

the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.

How to solve the question?

To determine whether a triangle can be formed using the given side lengths, we need to apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

Let's check each option:

A. XY = 11 mm, YZ = 12 mm, XZ = 18 mm

To form a triangle, we need to check whether the sum of any two sides is greater than the third side. Let's check:

XY + YZ = 11 mm + 12 mm = 23 mm > XZ = 18 mm

YZ + XZ = 12 mm + 18 mm = 30 mm > XY = 11 mm

XY + XZ = 11 mm + 18 mm = 29 mm > YZ = 12 mm

All the combinations are greater than the third side, so a triangle can be formed with these side lengths.

B. XY = 16 mm, YZ = 12 mm, XZ = 23 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 16 mm + 12 mm = 28 mm > XZ = 23 mm

YZ + XZ = 12 mm + 23 mm = 35 mm > XY = 16 mm

XY + XZ = 16 mm + 23 mm = 39 mm > YZ = 12 mm

Again, all the combinations are greater than the third side, so a triangle can be formed with these side lengths.

C. XY = 16 mm, YZ = 17 mm, XZ = 18 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 16 mm + 17 mm = 33 mm > XZ = 18 mm

YZ + XZ = 17 mm + 18 mm = 35 mm > XY = 16 mm

XY + XZ = 16 mm + 18 mm = 34 mm > YZ = 17 mm

All the combinations are greater than the third side, so a triangle can be formed with these side lengths.

D. XY = 11 mm, YZ = 12 mm, XZ = 28 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 11 mm + 12 mm = 23 mm < XZ = 28 mm

YZ + XZ = 12 mm + 28 mm = 40 mm > XY = 11 mm

XY + XZ = 11 mm + 28 mm = 39 mm > YZ = 12 mm

The first combination is less than the third side, so a triangle cannot be formed with these side lengths.

Therefore, the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.

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