solve the compound inequality -5<4x+3<=8

The result follows from the fundamental theorem of calculus.

[tex]\displaystyle \int_a^b f(x) \, dx = F(b) - F(a) = 2022 - 10 = \boxed{2012}[/tex]

Answer:

Step-by-step explanation:

let a be first term and r be c.r.

a_{n}=ar^{n-1}

a_{4}=ar^{4-1}=ar^3=135

a_{6}=ar^{6-1}=ar^5=1215a_{4}=1215 \times 135

divide

r^2=1215

r=√1215=35

a_{n}=35 a_{n-1}

Answer: m x H = [ -9  36  - 9/2 ]

Step-by-step explanation:

The probability that a class attendee is a non-member of the gym and is attending a barre class or is a member of the gym and is attending a boot camp class is 0.009.

Probability refers to a possibility that deals with the occurrence of random events.

The marketing team has gathered data from a random month, in which there were 2039 class attendees.

The probability that a class attendee is a non-member of the gym and is attending a barre class

= 185/2039

= 0.09

The probability that a class attendee is a member of the gym and is attending a boot camp class

= 204/2039

= 0.10004

The probability for both the event would be

= 0.09 x 0.10004

= 0.009

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Answer:

Is the question even complete ?

Step-by-step explanation:

We know that cos2x=cos²x-sin²x

=cos²x-(1-cos²x)         [since, cos²x+sin²x=1]

=cos²x-1+cos²x

=2cos²x-1

So, cos2x=2cos²x-1

Hence, cos²x= (1+cos2x)/2

Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables occurring on both sides of an equation. Geometrically, these identities involve certain trigonometric functions (such as sine, cosine, tangent) of one or more angles.

Most common trigonometric identities are:

- cos²x + sin²x = 1

- sec²x - tan²x = 1

- cosec²x - cot²x = 1

- cos2x = cos²x - sin²x

Therefore we get that the statement cos² x = (1 - cos 2x)/2 is false.

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Answer:The value of m for the given equation is, 35

Step-by-step explanation:

Given an equation:  https://tex.z-dn.net/?f=x%5E%7B3m%7D%3D(x%5E%7B65%7D)*(x%5E%7B40%7D)

Use the above property on  RHS in equation [1];

Since the base are same i.e, x ; we can add the exponents.

or

Using:  , then a=b.

Therefore, 3m=105.

Divide 3 on both sides of an equation:

Simplify:

m=35

Therefore, the valur of m is, 35.

Step-by-step explanation:

The graph of the cube root parent function y = RootIndex 3 StartRoot x EndRoot is translated to form f(x) shown on the graph.

On a coordinate plane, a cube root function goes through (negative 7, 0), has an inflection point at (negative 6, 1), and goes through (2, 3).

Which equation represents f(x)?

f(x) = RootIndex 3 StartRoot x + 6 EndRoot + 1

f(x) = RootIndex 3 StartRoot x minus 6 EndRoot + 1

f(x) = RootIndex 3 StartRoot x + 6 EndRoot minus 1

f(x) = RootIndex 3 StartRoot x minus 6 EndRoot minus 1

Answer:

Step-by-step explanation:

The translation of the parent function is:

g(x) = ∛(x + 6) + 1

How do translations work?

There are two types of translations, these are:

Horizontal translation:

For a function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

If N is positive, the translation is to the left.

If N is negative, the translation is to the right.

Vertical translation:

For a function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

If N is positive the translation is upwards.

If N is negative the translation is downwards.

Here we start with the parent function:

f(x) = ∛x

And we apply two translations such that:

g(x) = ∛(x + a) + b

Such that:

g(-7) = 0

g(2) = 3

Then we have the system of equations:

∛(-7 + a) + b = 0

∛(2 + a) + b = 3

From the options, the only ones that make the first option true are:

g(x) = ∛(x + 6) + 1

Such that when evaluated in x = -7 we get:

g(-7) =  ∛(-7 + 6) + 1 =  ∛(-1) + 1 = 0

When evaluated in x = 2 it gives:

∛(2 + 6) + 1 =  ∛(8) + 1 = 2+ 1 = 3

So the only option that meets these conditions is:

g(x) = ∛(x + 6) + 1

Which is a translation to the left of 6 units and up 1 unit.

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Answer:

2 5/7 5/7 -1/7, -5/7, 1 2/7, -2 2/7, -1 5/7

Answer: 1, -2, 1

Step-by-step explanation:

[tex]f(g(x))=f(x-1)=(x-1)^{2}=x^{2}-2x+1[/tex]

Answer:

Mrs. Martin has 19 Students

Step-by-step explanation:

first step: 100-5=95

second step: 95/19=5

So, 95 divided by the possible number of students which is 19 it yields the answer of 5 which is the number of cookies each of her student recieved.

A function assigns the values. The function that has the greatest y-intercept is h(x).

A function assigns the value of each element of one set to the other specific element of another set.

There are three function, g(x){given in the graph below}, f(x)= -6x-3, and -3h(x) = 2 cos(x + π) − 1, the y-intercept of the function is the point at which the graph intersects the y-axis. Therefore, the y-intercept are,

g(x) = -3

f(x) = -3

h(x) = 1

Hence, the function that has the greatest y-intercept is h(x).

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(a) X ≈ N (0.10 , 0.02²)

(b) The probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11% is 31%.

(c) The 60th percentile is 11%.

A. X ~ N( , )  

B. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11%.

C. Find the 60th percentile for this distribution.

According to the question,

The random variable X is defined as the THC content for a bag of marijuana that is sold on the street.

(a)The random variable X is Normally distributed with mean, μ = 0.10 and standard deviation, σ = 0.02.

Therefore, X ≈ N (0.10 , 0.02²)

(b) The value of P (X > 0.11) as follows:

P (X > o.11_ = P(X -μ/a > [tex]\frac{0.11-0.10}{0.02} \\[/tex])

= P(Z > 0.50)

= 1 -P (Z <0.50)

= 1- 0.69146

= 0.30854 ≈ 0.31

Hence,

the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 11% is 31%.

(c)Let x represent the 60th percentile value.

Then, P (X < x) = 0.60.

⇒ P (Z < z) = 0.60

The value of z is,

z = 0.26.

Now put the value of x as follows:

z = x - μσ

0.26 = x - 0.100.02

x = 0.10+ ( 0.26 x 0.02)

x = 0.1052

x ≈ 0.11

Therefore,

The 60th percentile is 11%

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Answer:

9

Step-by-step explanation:

The opposite sides of a parallelogram are congruent.

Answer:

9

Step-by-step explanation:

Parallel sides are always equal. :)

Answer:

log x to the base 2 +log x to the base 4 =2

or log x/ log 2+ log x /lig 4 =2

or log x /log2 + log x /2.log 2 = 2

or log x/log 2(1+1/2)= 2

or log x/log 2 = 4/3

or 3.log x =4.log2

or logx^3=log 2^4

or x^3= 2^4

or x =(2)^4/3 or 2.(2)^1/3 ,Answer.

hope this helps

Step-by-step explanation:

Considering that the mean of the normal distribution is the same as the median, the median is of 88%.

It states that, for a normally distributed random variable:

For the normal distribution, the median is the same of the mean, that is, the median is of 88%.

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A percentage is a way to describe a part of a whole. Jim's Height is 47.37% of Jack's height.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Giraffe Jack is 19 feet tall, and Ostrich Jim is 9 feet tall.

A.) The percent of Jack's height is Jim's height,

Percentage = (Height of Jack/Height of Jim) × 100%

                   = 19/9 × 100%

                   = 211.11%

Hence, Jack's Height is 211.11% of Jim's height.

B.) The percent of Jim's height is Jack's height,

Percentage = (Height of Jim/Height of Jack) × 100%

                   = 9/19 × 100%

                   = 47.37%

Hence, Jim's Height is 47.37% of Jack's height.

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Answer:

211.11%

Step-by-step explanation:

32 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the pints of 60% pure fruit juice

0.60x + 0.35(40 - x) = 0.40(40)

x = 8

= 40 - 8 (pints of 35% juice)

= 32

Thus, 32 pints and 8 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.

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The point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.

Given that, Terry brings home $14 per hour he works. When he started this job, he had $40 in the bank.

We need to write and graph the equation that would represent how much money Terry has in the bank (y) after x hours of work.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, y=40+14x

Graph the line using the slope and y-intercept, or two points.

Slope: 14

y-intercept: (0, 40)

The coordinates to plot the graph are (0, 40), (1, 54), (2, 68) and (3, 82).

The graph for the given equation is given below.

Therefore, the point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.

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Step-by-step explanation/Answer:

PE(MD)(AS) (a good way to remember how to solve order of operations)

Start:

P: Parenthesis

E: Exponent

M: Multiplication & D: Division

A: Addition & S: Subtraction

:End

*Multiplication and Division are grouped together because they are on the same level, you decide which to do first depending on which comes first in the equation. The same applies for addition and subtraction.

So:

first thing we can look is the parenthesis, but before we can solve the whole thing we must notice the exponent only on the four. Since it is inside the parenthesis we must solve it first.

1. 4^2 = 16

now we will solve the addition inside the parenthesis

2. 16-13 = 3

now lets continue with pemdas, no more parenthesis so we tackle exponents

3. 5^2 = 25

Lets rewrite our equation with the changes we have made

8 × 3 ÷ 3 + 25 + 4 × 3

Now we solve multiplication and division

Equations is worked left to right, like english is read, so we will start on the left side and continue to the right, only solving multiplication and division.

4. 8 x 3 = 24

5. 24 ÷ 3 = 8

6. 4 x 3 = 12

new equation: 8 + 25 + 12

now we can use addition and subtraction (no subtraction luckily!)

7. 8 + 25 = 33

8. 33 + 12 = 45

The conclusion about the relationship is

The complete question is:

Consider the function f(x) = 3x and a translation of f(x) named g(x). Janeen created a table for select values of x. Her table is shown below. What can be concluded about the relationship between the two functions? Check all that apply.

The functions have the same base.

The functions have the same range.

The functions have the same exponent.

The functions have the same domain.

g(x) is a translation left 1 unit.

g(x) is a translation right 2 units.

g(x) is a translation up 2 units.

Given function is:

f(x) = [tex]3^{x}[/tex]

g(x) = [tex]3^{x+1}[/tex]

Firstly, the functions have the same base i.e., base 3.

second, the functions have the same range.

As the range of f are all the values that f can assume. i.e., positive numbers and the range of g are all the values that g can assume. i.e., positive numbers.

third, both functions have the same domain as x = {0,1,2,3}.

Fourth, g(x) = f(x+1). So, g(x) is a translation left 1 unit.

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The statement "Grouped data is a data that has not been organized into intervals" is false.

Data presented in class intervals, such as 0-20, 20-40, and so on, is referred to as "grouped data."

Ungrouped data is information presented as individual values or integers, such as 15, 63, 34, 20, 25, and so on.

Assume we have a set of data with values between 0 and 50, such as 2, 17, 0, 1, 8, 19, 43, 2, 1, 32, and so on. In this situation, we may divide the data into categories like 0-10, 10-20,...,40-50. The data in this case are simply grouped.

Hence, the statement "Grouped data is a data that has not been organized into intervals" is false.

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Answer:

D. The graph of g(x) is shifted 3 units right and 4 units down.

Step-by-step explanation:

The graph of g(x) is shifted 3 units right and 4 units down

Answer:

  B.) The only solution is (4, - 1/2)

Step-by-step explanation:

To solve this system of equations using the substitution method, we need to use one equation to find an expression for one of the terms or variables that can be substituted for that term or variable in the other equation.

__

Here, it is convenient to use the second equation to write an expression for x:

  x -2 = -4y

  x = 2 -4y . . . . add 2 to both sides

Using this expression for x, we can write the second equation as ...

  3x +2y = 11

  3(2 -4y) +2y = 11 . . . . . substitute for x

  6 -10y = 11 . . . . . . . . eliminate parenthses

This 2-step equation can be solved in the usual way:

  -10y = 5 . . . . . . . subtract the constant to isolate the variable term

  y = -5/10 = -1/2 . . . . . divide by the coefficient of the variable

  x = 2 -4(-1/2) = 2 +2 = 4 . . . . . find the corresponding x-value

The only solution is (x, y) = (4, -1/2).

The only solution is (x, y) = (4, -1/2). so, the correct option is B.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

we have the system of equations;

3x+2y=11

x−2=−4y

By the substitution method;

use the second equation to write an expression for x:

 x -2 = -4y

 x = 2 -4y

substitute

 3x +2y = 11

 3(2 -4y) +2y = 11

 6 -10y = 11

solve

 -10y = 5

 y = -5/10 = -1/2

 x = 2 -4(-1/2)

x = 2 +2 = 4

Thus, The only solution is (x, y) = (4, -1/2). so, the correct option is B.

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The number of the units were started into production in a period will be 25,375.

A industry's fully prepared kinds of goods, as well as the primary materials needed to make them, are considered to as inventory.

If there were zero units of beginning work in process inventory, 4,714 units of ending work in process inventory, and 20,661 completed and transferred out units.

Completed and transferred out = 20,661

Ending Inventory = 4,714

Units accounted for = 25,375

Beginning Inventory = 0

Units started into production = [Units accounted for – Beginning work in progress Inventory] = 25,375

Units accounted for = 25,375

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Answer:

Statement 1 is correct

Angles UST and QSR are complementary.

Step-by-step explanation:

Complementary angles are those angles whose addition gives result of 90°

Congruent angles are those angles which are equal to each other.we can say that there values are same.

Here angle RSU is complementary to angle UST.

Therefore there addition is equal to 90°

∠RSU + ∠UST =  90° - (i)

Here angle QSR is congruent to angle RSU.

It means ∠QSR =∠RSU -(ii)

From equation (i) and (ii)

∠QSR + ∠UST =  90°

So angles UST and QSR are complimentary angles.

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Answer: A. They are complementary.

Step-by-step explanation: RIGHT ON EDGE 2023