Determine if events A and B are mutually exclusive.

P(A) = 3/10 P(B) = 9/20 P(A or B) = 3/4

a) mutually exclusive
b) not mutually exclusive

The child's percentile rank is 84.13%.

To determine the percentile rank of a score, you need to know the mean and standard deviation of the test, as well as the score in question. In this case, the mean is 120 and the standard deviation is 8.

To convert the child's score of 128 to a percentile rank, you would first convert it to a z-score using the formula (score - mean) / standard deviation = z-score.

In this case:

(128 - 120) / 8 = 1

This z-score of 1 represents the number of standard deviations above the mean the child's score is. To convert this z-score to a percentile rank, you can use a table of the standard normal distribution, which shows the proportion of values that are less than or equal to a given z-score.

A z-score of 1 corresponds to a percentile rank of 84.13%

So, the fifth grader who scored 128 on a standardized achievement test has a percentile rank of 84.13%. This means that 84.13% of students scored lower than the child on this test.

learn more about percentile: https://brainly.com/question/28839672

#SPJ1

Answer:

8/12=0.667

5/8=0.625

6/10=0.6

2/3=0.667

Step-by-step explanation:

6/10 would be your answer being that it is the smallest of them all

The exponential function f(x) = 2(4)ˣ doesn't belong to the other three.

What is an exponential function?

A mathematical function is an exponential function. The word, unless expressly stated differently, refers typically to the positive-valued function of a real variable. However, it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

Here, we have

Given:

y = 3ˣ,

f(x) = 2(4)ˣ

f(x) = (-3)ˣ

y = 5(3)ˣ

We have to determine which equation does not belong with the other three.

We concluded that

All equations are multiples of 3 but f(x) = 2(4)ˣ  is not a multiple of 3.

Hence, the exponential function f(x) = 2(4)ˣ doesn't belong to the other three.

To learn more about the exponential function from the given link

https://brainly.com/question/2456547

#SPJ1

Answer:

  $442.42

Step-by-step explanation:

You want the remaining available credit on a credit line of $500 when charges of $25.25 and $32.33 have been made.

The remaining credit is the original credit amount less the amount of credit used:

  $500 -25.25 -32.33 = $442.42

Cameron has credit of $442.42 available.

The value of the distance across the sea is 302 feet

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Two triangles are said to be similar if the ratio of their corresponding sides are in the same proportion.

Triangle PRE and triangle POC are similar triangles based on the angle - angle similarity. Hence:

PR / PO = RE/OC

substituting:

x/ (x + 135) = 185 / 335

335x = 185x + 45225

150x = 45225

x = 302 feet

The value of PR is 302 feet

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

When looking for the range of a graph, y-values are looked for.

What is the range?

A function's range can be used to describe one of two related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is exactly one y in Y such that f connects x to y for every x in X.

Here,

We have to determine when looking for the range of a graph, which values are looking for.

The domain is all x-values or inputs of a function and the range is all y-values or outputs of a function. When looking at a graph, the domain is all the values of the graph from left to right. The range is all the values of the graph from down to up.

Hence, when looking for the range of a graph, y-values are looked for.

To learn more about the range from the given link

https://brainly.com/question/2264373

#SPJ1

The number of minutes it will take Adam to solve 20 math problems is 70 minutes.

Number of math problems Adam solve in 42 minutes = 12

Number of minutes it will take Adam to solve 20 math problem = x

Number of math problem : Time taken

12 : 42 = 20 : x

12/42 = 20/x

12 × x = 20 × 42

12x = 840

divide both sides by 12

x = 840/12

x = 70 minutes

Hence, it will take Adam 70 minutes to solve 20 math problems.

Read more on ratio:

https://brainly.com/question/2328454

#SPJ1

The number is x = 0 or 18.The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.

Let x be the number.  Translation of the given information into algebra gives

√(2x) = x/3

Solve for x.  Note x ≥ 0.

2x = x2/9

If x ≠ 0,

2 = x/9 ⇒ x = 18

Solutions are x = 0 or 18.

The complete question is,

The square root of twice a number is equal to one-third of that number. Find the number.

To learn more about algebra refer to:

https://brainly.com/question/22399890

#SPJ1

The length of the given side must be less than 44189 feet as the sum of the length of the other two sides is always greater than the third side.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

Given here: Length of the triangle c=1949 ft. a=8 miles

Thus a in feet = 8×5280

                       =42240 ft

Thus the length of the third side must be less than the sum of the other two sides a and c

or b<42240+1949

    b<44189

Hence, The length of the given side must be less than 44189 feet as the sum of the length of the other two sides is always greater than the third side.

Learn more about triangles here:

https://brainly.com/question/11806229

#SPJ1

Please provide with the diagram for more exact value for b.

Answer:

Let x be the first number that the teacher wrote on the board and y be the second number. From the problem, we know that:

x + y = 58 (from Eric's calculation)

x - y = 28 (from Olivia's calculation)

To find the value of x, we can add the equations together:

x + y = 58

x - y = 28

2x = 86

x = 43

So the first number that the teacher wrote on the board is 43.

The statement " The sum of a negative and a positive number is a negative number " is false sometimes.

What is an integer?

A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8

The statement " The sum of a negative and a positive number is a negative number " is false sometimes.

When positive number is bigger than the smaller one, sum can be positive

Example:  

-4+3 = -1  ( statement is true, 3 is smaller )

but,

-4 + 6 = 2 ( statement is false, 6 is bigger)

To learn more about the Integer from the given link

https://brainly.com/question/17695139

#SPJ1

(i) 1050 as the product of its prime factors is 1050 = 2 x 3 x 5² x 7.

(ii) The two numbers having a highest common factor of 21 and

lowest common multiple of 1050 are (760,1160).

What is a prime factor?

A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth. Now, we may also apply the so-called prime factorization, which actually involves using factor trees, for numbers.

To get the prime factors of 1050, start dividing the number by its primes -

1050 ÷ 525 = 2

525 ÷ 175 = 3

175 ÷ 35 = 5

35 ÷ 7 = 5

7 ÷ 1 = 7

So here the prime factorisation of 1050 -

= 2 x 3 x 5 x 5 x 7

= 2 x 3 x 5² x 7

Therefore, the prime factors are 2, 3, 5, and 7.

Now, it is given that HCF of numbers = 21

LCM of numbers = 1050

Calculate the two numbers by using the following procedure -

Let the two numbers be 40x and 40y respectively.

Product of numbers = LCM × HCF

Now, the equation will be -

40x × 40y = 1050 × 21

40(x × y) = (1050 × 21)

xy = 22050/40

xy = 551.25 ≈ 551

So, the co-primes with product 551 are (1,551) and (19,29).

So, the prime numbers are (40×1,40×551) and (40×19,40×29).

Therefore, the most suitable pair is (40×19,40×29) = (760,1160).

To learn more about prime factor from the given link

https://brainly.com/question/18187355

#SPJ1

Answer: X= 72°

Here if we see the figure is not labelled so I am assuming it to A,B,C AS MAIN TRIANGLE and BD bisector of angle ABC.

We have to find out that angle DBC.

ANGLE CAB = ANGLE DBA

Hence Angle CDB = ANGLE CAB + ANGLE DBA

27° + 27° = CDB = 54° = ACB ( if sides are equal then opposite angles are also equal.)

so required angle x = 180° - 54° - 54° ( sum of angle of triangle equals 180)

so x= 72°

The function of the absolute value is always positive the correct answer would be option (B).

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

What is absolute value?

Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.  

For example, |5| is 5 because it is 5 units away from 0.  Also, |-5| is also 5 because -5 is 5 units from 0.

We have to determine the statement best describes the function.

We have been given that the graph represents the absolute value parent function.

Since the parent function's graph with an absolute value that is always positive.

Therefore, the graph of the absolute value parent function would be always positive.

Hence, the correct answer would be option (B)

The answer to the phrase 3+52 expanded is 28.When an expression is expanded, it is reduced to its most basic form.

We must multiply out the brackets in order to extend and simplify an expression. The resulting phrase is then made simpler by grouping like terms together.

It is possible to get rid of brackets by expanding them, often known as multiplying out.

Factorization is being done in reverse.Increasing each term inside a bracket by the expression outside the bracket is referred to as expanding it.

3+5^2

= 3 + 5²

= 3 + (5 × 5)

= 3 + 25

= 28

In response to the expression's expansion, 3+52 is 28.

To learn more about  expression refer

https://brainly.com/question/26430239

#SPJ1

Option C) The Polynomial is (4x +1)(2x² - 2)

The expansion will be 4x*2x² - 4x*2 + 2x² - 2

If no variable is included in parentheses and all terms that are similar have been merged, a polynomial is expanded. Multiply the components of a polynomial (typically by applying the distributive property), or carry out the corresponding operations, to extend it.

A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables. x² + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

When a polynomial with coefficients in a specific field or in integers is factored, its coefficients are expressed as the product of irreducible factors with coefficients in the same field.

The Polynomial is (4x +1)(2x² - 2)

The expansion will be 4x*2x² - 4x*2 + 2x² - 2

To learn more about Polynomials refer to :

https://brainly.com/question/27987739

#SPJ1

a. The equation for the State's GDP growth is g = 243(3.10)^t.

b. The equation is in the exponential family.

c. Oregon's GDP in 8 years from now will be $2072525 billion.

What is exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The Gross Domestic Product, GDP, of Oregon is 243 billion dollars with a growth rate of 3.10%

Let t = time in years

Let g = State's GDP amount

Start with $243 billion and each year add 3.10% growth is seen in the GDP.

1st year: Growth = 243 × (3.10) = $753.3 dollars

This is added to the previous amount -

= 243 + 243 × (3.10)

= 243 (1+3.10)

= 243 (4.10)

= $996.3 billion

2nd year: Previous amount + Growth in the previous amount

= 996.3 (1+4.10)

= 996.3 (5.10)

= $5081.13 billion

So, the exponential formula becomes -

g = 243(3.10)^t

Now, to find the value of GDP growth after 8 years, substitute t = 8.

g = 243(3.10)^t

g = 243(3.10)^8

g = 243(8528.91)

g = $2072525.13 ≈ 2072525 billion

Therefore, the GDP growth after 8 years is $2072525 billion.

To learn more about exponential function from the given link

brainly.com/question/11464095

#SPJ1

The expression having value 12 and contain four numbers and two different arithmetic operations is   2*2+4+4=12.

What are  arithmetic operations and its types?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.

The four basic arithmetic operations in Maths, for all real numbers, are:

Addition (Finding the Sum; ‘+’)

Subtraction (Finding the difference;  ‘-’)

Multiplication (Finding the product; ‘×’ )

Division (Finding the quotient; ‘÷’)

Now

as we solve given expression by applying arithmetic operations

=2*2+4+4

=4+8

=12

To know more about arithmetic operations visit the link

https://brainly.com/question/25834626?referrer=searchResults

#SPJ1

The number of free throws that Gabriel attempted if he missed 36, can be found to be 1, 800 free throws.

If Gabriel misses 2% of the free throws he attempts in a season, the forumula to find the percentage of free throws missed is:

Free throws missed / Total free throws attempted = 2%

We can then make the free throws missed the subject of the formula:

36 / Total free throws attempted = 0.02

Total free throws attempted = 36 / 0.02

Total free throws attempted = 1, 800

Find out more on free throws at https://brainly.com/question/29088761

#SPJ1

The answer for an outcome of P(No heads) is 12.5% . Option A is the answer.

There is only one outcome of the 3 coin tosses that results in no heads, and that is TTT.

The probability of getting TTT is 1/8, so P(No heads) = 1/8 = 12.5%.

Probability is a mathematical concept that quantifies the likelihood of an event occurring, expressed as a number between 0 and 1. A probability of 0 indicates that an event will never occur, while a probability of 1 indicates that an event is certain to occur. A probability between 0 and 1 represents the degree of uncertainty about the occurrence of an event, with larger values indicating a higher likelihood of the event taking place.

Learn more on calculating probability here https://brainly.com/question/24756209

#SPJ1

The percentage of business-hour usage that the Plan will be cheaper will be 22.6%.

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.

In this case, Plan X costs 6.5 cents per minute for calls between 8 A.M. and 6 P.M. weekdays and 4.5 cents per minute at other times. Plan Y costs 5.3 cents per minute any time.

The percentage of business-hour usage that the Plan will be cheaper will be:

= (6.5 - 5.3) / 5.3 × 100

= 1.2 / 5.3 × 100

= 22.6%

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

A constant term that makes the equation have infinite solutions include the following: C. 20

In Mathematics, an equation is said to have an infinitely many solutions when the left hand side and right hand side of the equation or inequality are the same and equal.

This ultimately implies that, an equation or an inequality would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and y-intercept for the two lines are the same.

By applying the rule for an infinitely many solutions, we have:

5x + 20 = 5x + 20

5x - 5x = 20 - 20

Read more on infinitely many solutions here: brainly.com/question/14626049

#SPJ1

Therefore , the solution of the given problem of arithmetic mean comes out to be a2=5 ,a3 = 17  and a4 = 29.

The sum of all values in a list multiplied by the total no. all items in the list yields the arithmetic average, often known as the group's means. The growth in arithmetic follows a similar pattern. The following equation + 7 + 9 equals 21, but 21 multiplied by 3 (there's several currently three numbers) equals 7, proving that the mean of the numbers 5, 7, while 9 is 4, and the median of the real numbers 5, 8, and 9 is 3.

Here,

Given :  a1 = -7

and common difference d = 12

Thus,

For a2 = a + d = -7 + 12 = 5

a3 = a+2d = -7 + 24 = 17

and a4 = a + 3d = -7 + 36 = 29.

Therefore , the solution of the given problem of arithmetic mean comes out to be a2=5 ,a3 = 17  and a4 = 29.

To know more about arithmetic mean  , visit

brainly.com/question/13000783

#SPJ1

The time on the first watch reads 2:31, followed by 3:13, 3:55, and 4:37 on the following watches.

The time on the first watch reads 2:31, followed by 3:13, 3:55, and 4:37 on the following watches.

Adding 42 minutes to the prior watch, which is currently showing the time 4:37, results in the final time reading of 5:19.

When x minutes have passed, let the clock hands align.

Clock hands align at 21.81 minutes after four.

Option B, 21.81 minutes, is the proper response, therefore.

They need to be 30 minutes apart for them to be moving in the opposing directions.

Minute hand will need to add 50 minute gaps as a result.

It takes 60 minutes to fill 55 minute gaps.

In light of this, 54 6/11 minutes after four is the right response.

To learn more about  time refer

https://brainly.com/question/9405574

#SPJ1

The linear equation of the line is slope =-1/5 and point is 10,2

The slope is given as:

m = -1/5

The point is given as:

10,2

A linear equation in slope intercept form is represented as:

y = m + p

So, we have:

y is intercept

mx is slope

p is point

y = -1/5x - 10

Add 10 to both sides

y + 10 = -1/5x

Express -1/5x as -1/5(x)

y + 10 = -1/5(x)

Subtract 0 from x

y + 10 = -1/5(x - 0)

Hence, the linear equation of the line is y = -1/5x - 10 and y + 10 = -1/5(x - 0)

To learn more about linear equation refers to;

https://brainly.com/question/17019628

#SPJ1

12 pairs could he predict will contain at least one six using empirical probability formula.

The empirical probability formula generates a ratio between the total number of times the desired occurrence was attempted to and the number of times it actually occurred. As an illustration, consider the case where I rolled the dice three times and each time I got 12, giving the result a statistical probability of 12/12 or 100%.

Probability is a form of ratio where we measure the likelihood of a given occurrence in comparison to all other possible outcomes.

Explanation:

12/10 * 10 = 6/5 * 10

               = 12.

To learn more about probability refer to:

https://brainly.com/question/24756209

#SPJ1

Answer:

what do u have to do like what the question

Answer: 20 people

Step-by-step explanation:

If each car has 2 benches and 2 people fit on each bench, you have to multiply 2 x 2 which equals 4. Then you have to multiply the number of how many people fit on each car by the number of cars. ( 4 x 5 = 20 ) Hence the answer is 20 people.

Answer:

20 people

Step-by-step explanation:

2 benches × 5 cars = 10 benches

10 benches with 2 people on each of them (10×2)

=20