Mr. Brown's statistics class consists of 21 seniors. The class took two quizzes in one week, and 12 of the students in the class passed both quizzes. What is the probability that the same students who passed the first quiz also passed the second quiz given that 19 students passed the first quiz?

Answer:

x = 7 , x = 11

Step-by-step explanation:

x² - 18x + 81 = 4 ( subtract 81 from both sides )

x² - 18x = - 77

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 9)x + 81 = - 77 + 81

(x - 9)² = 4 ( take square root of both sides )

x - 9 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 9 to both sides )

x = 9 ± 2

then

x = 9 - 2 = 7

x = 9 + 2 = 11

Answer:

0

Step-by-step explanation:

(8x-1)/2=(8x+7)/5

We move all terms to the left:

(8x-1)/2-((8x+7)/5)=0

We calculate fractions

8x/()+(-((8x+7)*2)/()=0

We calculate terms in parentheses: +(-((8x+7)*2)/(), so:

-((8x+7)*2)/(

We multiply all the terms by the denominator

-((8x+7)*2)

We calculate terms in parentheses: -((8x+7)*2), so:

(8x+7)*2

We multiply parentheses

16x+14

Back to the equation:

-(16x+14)

We get rid of parentheses

-16x-14

Back to the equation:

+(-16x-14)

We get rid of parentheses

8x/()-16x-14=0

We multiply all the terms by the denominator

8x-16x*()-14*()=0

We add all the numbers together, and all the variables

8x-16x*()=0

Answer:

X= 19/24

Step-by-step explanation:

Cross multiply the two sides then we have something like this 5(8x-1)=2(8x+7)

Solve the equation 40x-5=16x+14

Group the like terms 40x-16x=5+14

Solve the second equation and it gives us X= 19/24

The required repeated addition is given as 2.02 + 2.02 + 2.02.

The repeated addition of a number is the multiplication of the number with the number of times the number is repeated.

here,
The question seems to be incorrect,
The complete solution is provided at the end of the solution,
2.02 × 3, is the given expression, which is a multiplicative expression as 3 times of 2.02.
So the repeated addition is given as,
2.02 × 3 = 2.02 + 2.02 + 2.02

Thus, the required repeated addition is given as 2.02 + 2.02 + 2.02.

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Complete question.

Write 2.02 × 3 in repeated addition.

[tex]8\sqrt{3}-3\sqrt{6}[/tex]

=============================================

Work Shown:

[tex]\text{x} = 10\sqrt{3}-\sqrt{12}-3\sqrt{6}\\\\\text{x} = 10\sqrt{3}-\sqrt{4*3}-3\sqrt{6}\\\\\text{x} = 10\sqrt{3}-\sqrt{4}*\sqrt{3}-3\sqrt{6}\\\\\text{x} = 10\sqrt{3}-2\sqrt{3}-3\sqrt{6}\\\\\text{x} = (10\sqrt{3}-2\sqrt{3})-3\sqrt{6}\\\\\text{x} = (10-2)\sqrt{3}-3\sqrt{6}\\\\\text{x} = 8\sqrt{3}-3\sqrt{6}\\\\[/tex]

-------------------------------

Therefore,

[tex]10\sqrt{3}-\sqrt{12}-3\sqrt{6}\\ \ \text{simplifies to} \\ 8\sqrt{3}-3\sqrt{6}\\\\[/tex]

In other words we can say

[tex]10\sqrt{3}-\sqrt{12}-3\sqrt{6}=8\sqrt{3}-3\sqrt{6}\\\\[/tex]

--------------------------------

Verification:

Use a calculator to compute the following.

[tex]10\sqrt{3}-\sqrt{12}-3\sqrt{6} \approx 6.507937\\\\8\sqrt{3}-3\sqrt{6} \approx 6.507937\\\\[/tex]

Since we get the same approximate decimal value, it helps us confirm the answer is correct.

The numeric value of the function f(x) at x = 1 is given as follows:

f(1) = 24.

The table is composed by a set of points in the following format:

(x, f(x)).

In which the input and output variables are given as follows:

From the points given in the table, the numeric values are listed as follows:

Any of these values can be used to evaluate the function at the input of x, hence at the input of x = 1, the numeric value is given as follows:

f(1) = 24.

The function is given by the image presented at the end of the answer.

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On solving the question, we can say that - herefore , the required inequality expression is 4.50x+1.75y ≤50

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

One cupcake costs $4.50,

So, “x” cupcakes cost = 4.50x.

One brownie cost $1.75,

so “y” brownies cost = 1.75y.

thus, the total 4.50x+1.75y  must be less or equal to $50.

Therefore , the required inequality expression is 4.50x+1.75y ≤50

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Answer: 12 feet and 1 inch

Step-by-step explanation:

3 feet 10 inches

4 feet 11 inches

3 feet 4 inches

3+4+3 = 10 feet

10+11+4 = 25 inches

1 foot = 12 inches

25 / 12 = 2 (rounded up) feet with 1 inch left

10 + 2 = 12 feet and 1 inch

Answer: The solution of the ordered pairs are (0,1) and (1,3).

Step-by-step explanation:

The required equation is y = 1.4x - 295 shows the amount that must be repaid, y, when x dollars are borrowed.

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

The table below shows the amount that must be repaid, y, when x dollars are borrowed.

Amount Borrowed     Amount Repaid

    $100                              $155

    $200                             $295

    $600                             $855

    $900                             $1275

y - 155 = [(1275 - 155)/(900-100)](x-100)

y - 155 = (1120/800)(x-100)

y - 155 = 1.4(x-100)

y = 1.4x - 140 + 155

y = 1.4x - 295

Thus, the required equation is y = 1.4x - 295.

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Answer: Y = 1.4x + 15

Step-by-step explanation:

Multiply amount borrowed by 1.4 and add 15 gives you the amount repaid.

The linear function equation represented by the graph will be f(x) = [tex]-\frac{x}{3} - 3[/tex].

Let y = f(x)

Given, when x = 0, y = -3

and when y = 0, x = -9

(x₁ , y₁) = (0, -3)

(x₂ , y₂) = (-9, 0)

Now linear equation

[tex]\frac{y - y_{1} }{x - x_{1} } = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

[tex]\frac{y - (-3) }{x - 0 } = \frac{0 - (-3) }{-9 - 0 }[/tex]

y+3 =  [tex]-\frac{x}{3}[/tex]

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

or f(x) = [tex]-\frac{x}{3} - 3[/tex]

Therefore, the linear function equation represented by the graph will be f(x) = [tex]-\frac{x}{3} - 3[/tex].

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Step-by-step explanation:

Let M be the number of multiple choice problems and S be the number of short answer problems.

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

M * 3 + S * 4 = 111

M + S = 32

The first equation represents the total number of points on the test, and the second equation represents the total number of problems on the test.

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 M:

M = (111 - S * 4) / 3

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

(111 - S * 4) / 3 + S = 32

Solving this equation for S gives us the number of short answer problems:

S = 12

To find the number of multiple choice problems, we can substitute this value for S into the expression for M that we derived earlier:

M = (111 - 12 * 4) / 3

Solving this equation gives us the number of multiple choice problems:

M = 8

Therefore, there are 8 multiple choice problems and 12 short answer problems on the test.

The money earned by Conor if he works 3.25 hours at $9 an hour is $29.25.

The fundamental concept of making the same number of additions repeatedly is represented by the action of multiplication. The results of multiplying two or more integers are known as the products, and the factors that are used in the multiplication are referred to as the factors.

Given:

The pay rate for the work, W = $9,

The time of work, t = 3.25 hours,

Calculate the money earned by Conor as shown below,

The money earned by Conor = The pay rate for the work × The time of work,

The money earned by Conor = 9 × 3.25

The money earned by Conor = 29.25

Thus, the money earned by Conor is $29.25.

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Answer:

hope this helps

Step-by-step explanation:

To determine its end behavior, look at the leading term of the polynomial function. Because the power of the leading term is the highest, that term will grow significantly faster than the other terms as x gets very large or very small, so its behavior will dominate the graph

thanks for the points heres the answer 2

                                                                 18

The comparison that exists between two-and-one-fourth to two-and-one-eighth would be = 2 × 1/4 is greater than 2 × 1/8.

A fraction is defined as the representation of part of a whole number which has a numerator located at the top and the denominator located below.

The given number and fraction for comparison is as follows:

2 × 1/4 = 1/2

2 × 1/8 = 1/4

Therefore when two-and-one-fourth to two-and-one-eighth are compared the former is. greater than the later.

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On solving the provided question, we can say that - the initial value in number line will jump to +12 value

A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.

here,

the initial value of the number line is = 15

and on adding 12

it will jump to = 15 + 12

= 27

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Yosemite Falls in California is made of three smaller falls. The upper fall drops 1450 feet. The time it takes for the droplet to reach the next fall is 9.52 seconds.

Given data:

h(t)=-16 t²+1450

Where:

t = time in seconds after the initial fall

So,

0=-16 t²+1450

16 t² =1450

t² = 90.625

t =√90.625

t = 9.52 seconds

Therefore we can conclude that the time is 9.52 seconds.

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6. a) In 10 squares there are 22 dots

6. b) There are 102 squares are in the diagram which has 104 dots.

6. c) t(n) = a + (n - 1) d

7. a) mean = 6; median = 5

7. b) new card number = 14

This can be solved using geometic series concept.

A geometric series is one where each pair of consecutive terms' ratios is a fixed function of the summation index. The ratio is a rational function of the summation index in a more comprehensive sense. creates what is known as a hyper geometric sequence. It is arithmetic if there is a common difference between the sequences. You can bet that anything is geometric if it has a common ratio. Similar to how the word arithmetic series denotes that each phrase is the arithmetic mean of its two neighbors, the name geometric series denotes that each term is the geometric mean of its two neighbors.

6. In the given figure we see that the dots are present here form a series.

In 1 square there are 4 dots.

In 2 squares there are 6 dots.

In 3 squares there are 8 dots.

So, they form a series.

a)

In 10 squares there are 22 dots

b)

There are 102 squares are in the diagram which has 104 dots.

c)

The formula of the series is:

t(n) = a + (n - 1) d

here a = 4 and d = 2

7.

a)

Jemina has 3 cards with the number of 5,2 and 11

Thus, mean = 5+2+11 /3 = 6

median = 5

b)

Next Jemina takes another card and the mean goes up by 2.

So, the number of new card:

2+5+x+11/4 = 8

or, 18 + x = 32

or, x = 14

So, new card number = 14

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Answer:

Step-by-step explanation:

6. a) In 10 squares there are 22 dots

6. b) There are 102 squares are in the diagram which has 104 dots.

6. c) t(n) = a + (n - 1) d

7. a) mean = 6; median = 5

7. b) new card number = 14

The correct representations of the inequality are  -6x + 15 < 10 - 5x and x <-5. Options C and D

Inequalities are described as mathematical relations that makes a non-equal comparison between two elements, variables, numbers or mathematical expressions.

They are often used to compare two numbers on the number line based their sizes.

From the information given, we have the inequality;

–3(2x – 5) < 5(2 – x)

expand the bracket

-6x + 15 < 10 - 5x

collect like terms

-6x + 5x < 10 - 15

add or subtract the like terms

-x < -5

Make 'x' the subject of formula

x < 5

Hence, the value is -6x + 15 < 10 - 5x

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The complete question:

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

The functions graphed on the axes is expressed below:

F(x) = 2 for all x =  (-∞, 3) to (3, ∞)

F(X) = 5 for x = [3]

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

Given, a function in the graph below that is a straight line of y equal to 2 on all values of x except the x = 3

Thus the inequality of the given graph is

F(x) = 2 for all x =  (-∞, 3) to (3, ∞)

F(X) = 5 for x = [3]

Therefore, the given graph is a straight line that shows a discontinuity at x =3.

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There 9% represent babies born with a birth defect, and 09-99(9%) to represents babies without birth defects.

The percentage is defined as a ratio expressed as a fraction of 100.

According to one study, 45 out of every 500 babies born in the world have a serious birth defect.

Use two-digit numbers 00-99; let 00- represent babies born with some kind of major birth defect.

p = x/n

p = 45/500

p = 0.9 = 9%

So, the simplest way to assign random numbers to conduct a simulation based on this statistic, it can use 00-99(9%) to represent babies born with a birth defect, and 09-99(9%) to represent babies without birth defects.

Hence, the correct answer would be an option (B).

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Answer: 14

Step-by-step explanation:

300 minus 80 = 220

220 is the budget for the shirts so we divide 220 by 15 to get 14

Hope this helps!

Answer:14 shirts

Step-by-step explanation:300- 80 = 220

220/ 15 = 14.6  round 14.6 to 14 (because you cant buy half a shirt)

you can get 14 shirts

Dimensions of the portrait are 12.25 cm to the nearest tenth of a centimeter.

What are Dimensions?

The dimension of a mathematical space is defined as the smallest number of coordinates required to specify each point within it.

To have the area of the mat equal to the area of the portrait, the portrait and the mat must have the same area. Since the mat is 7 cm wide, we can use that to find the dimensions of the portrait.

If the portrait is square, the side length will be the same as the width of the mat, plus the width of the portrait.

So, portrait width = 7 cm + portrait width

Solving for portrait width:

portrait width = 7 cm / 2 = 3.5 cm

So, the dimensions of the portrait are 3.5 cm x 3.5 = 12.25 cm

Therefore, dimensions of the portrait are 12.25 cm to the nearest tenth of a centimeter.

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Answer:

  see attached

Step-by-step explanation:

You want to match the given word problem with a suitable equation for solving it.

The variable x is assigned to the larger of two numbers that differ by 2. That makes the smaller one (x -2). The sum of their squares is ...

  x² + (x -2)² = 394

Simplifying, we get ...

  x² +x² -4x +4 = 394

  2x² -4x -390 = 0 . . . . . . . matches the first equation

The numerator of the fraction is 5 more than its denominator, x, so will be (x +5). Adding 3 to numerator and denominator, we get ...

  [tex]\dfrac{(x+5)+3}{(x)+3}=\dfrac{4}{3}\\\\3(x+8)=4(x+3)\\\\\boxed{3x+24=4x+12}\qquad\textsf{matches the third equation}[/tex]

The sum of x and its inverse is 4/3, so we have ...

  x + 1/x = 4/3

Multiplying by 3x gives ...

  3x² +3 = 4x

  3x² -4x +3 = 0 . . . . . . . . . matches the second equation

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The volume of the cone if, The slant height is 5 cm, and the radius of the cone is 3 cm, is 37.68 cm³.

A 3D object's volume is the amount of actual space it occupies. It is a 2D shape's 3D equivalent of area. It is quantified in cubic units like cm³. By multiplying its length, height, and width, you may determine this.

Given:

The slant height, s = 5 cm, and the radius of the cone is 3 cm,

Calculate the height of the cone as shown below,

slant height² = height² + radius²

5² = h² + 3²

h² = 25 - 9

h = 4

Calculate the volume of the cone as shown below,

The volume of the cone = π × 3² × 4 / 3

The volume of the cone = 3.14 × 9 × 1.33

The volume of the cone = 37.68

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To simplify the expression (9 - 1x + 2x) - (2x^2 - 3x + 5), you can follow these steps:

1. Combine like terms:

(9 + 2x) - (2x^2 - 3x + 5)

2. Simplify:

2x + 9 - (2x^2 - 3x + 5)

3. Combine like terms:

2x + 9 - 2x^2 + 3x - 5

4.Simplify:

-2x^2 + 5x + 4

Therefore, the simplified form of the expression is -2x^2 + 5x + 4.

Answer:

5

Step-by-step explanation:

Triangle ABC≅ Triangle DAB

use pytahgorean theorem:

ac^2=ab^2+bc^2

ac=[tex]\sqrt{ab^2+bc^2\\][/tex]

ac=[tex]\sqrt{4^2+3^2}[/tex]

ac=[tex]\sqrt{16+9}[/tex]

ac=[tex]\sqrt{25}[/tex]

ac=5

ac=bd=5 by congruency rules

As per the given function rule , y = -6x + 1 , the values will be 31, 7, 1, -5 -5 , 1, 1, -6X+1, -17.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).

The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.

As per the given function rule in the question i.e y = -6x + 1

X                         Y

-5                         31

-1                          7

0                           1

1                           -5

1                           -5

0                            1

0                            1

X                   -6X +1

3                         -17

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The exact solution to the system of equations shown on the graph is

(-1 1/5, 4 3/5)

The solution of a graph is where the two graphs intersects. This point is known as point of intersection and at this point we have the solution

The point of intersection of the two graphs as shown are read, Knowing that all interval marked represents one unit

x intersection: the point is more than -1 and not up to -1.5, which is a value at exactly half of the two intervals hence the possible option is -1 1/5

y intersection: the point is more than 4 and more than to 4.5, which is a value at exactly half of the two intervals hence the possible option is

4 3/5

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Using the concept of fraction, the percentage edited on the video is 62.5 percent.

Percentage is a standard mathematical concept used to express a portion of a whole number in terms of a hundred. It is denoted by the symbol “%” and is often expressed as a fraction or a decimal. For example, 25% can be expressed as 0.25 or 1/4.

In this problem, Thorton has done a 2.5 hours work. The percentage he has edited can be calculated using fraction or ratio as;

percentage edited = (2.5 / 4) × 100

Percentage = 0.625 × 100

Percentage = 62.5 %

From the above, Thorton has edited 62,5 percent of the video for his school project.

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