For the real-valued functions f(x) = 2x+10 and g(x) = x-1, find the composition f•g and specify its domain using interval notation.(f•g)(x)=Domain of f•g: (The 2x+10 is square rooted)

Answer:

1/3

Step-by-step explanation:

[tex]\frac{5}{6}*\frac{2}{5} = \frac{5*2}{6*5} =\frac{10}{30} = \frac{1}{3}[/tex]

5 and 5 cancel out, 2 becomes 1, and 6 simplifies to 3.

Given the word problem, we can deduce the following information:

1. Fernando picks a marble at random.

2. Without putting the first marble back, he picks a second marble at random.

To determine if the events are dependent or independent, we first note that dependent events influence the probability of other events, while independent events do not affect one another.

Since Fernando picks a marble without putting the first marble back, the probability of the second pick is affected.

Therefore, the answer is dependent.

Given the equation :

The first step is to add 5 to both sides

so,

When you have a function written in explicit form with two variables(let's call them 'x' and 'y'), it is written as a combination of 'x' and 'y' equal to some constant.

To "solve for x in terms of y", is the same as rewritting this function as an equality in the following form:

Let's try an example to show how this works.

Given the following function:

Now, solving for x in terms of y, is the same as rewriting x as a function of y.

In functions, for any value of x, there's a unique value for y.

On the table, in the x column, having 6 yielding two different values of y in rows 2 and 3 will mean that it's not a function because the y values must be unique.

Therefore, the answer is 6

Solution:

Given:

Since both events are independent, then;

Hence,

The number of students taking an online course and prefer basketball to football is;

Therefore, the number of students taking an online course and prefer basketball to football is 408

The given expression in the form of (a + ib) can be written as -

-2/3 + i(4/3).

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted [i], called the imaginary unit and satisfying the equation -

[tex]{\displaystyle i^{2}=-1}[/tex]

Every complex number can be expressed in the form a + bi, where [a] and [b] are real numbers

We have the following expression -

(4 - 2i)/3i

We have -

(4 - 2i)/3i

4/3i - 2i/3i

- 2/3 + i(4/3)

Therefore, the given expression in the form of (a + ib) can be written as -

-2/3 + i(4/3).

To solve more questions on Complex numbers visit the link below -

https://brainly.com/question/20566728

#SPJ1

Answer:

Step-by-step explanation:

Answer

Explanation

We want to convert 300 fluid ounces per minute into fluid ounces per second.

Note that

1 minute = 60 seconds

We then do the conversion thus

Initial investment = $100

The balance increases annually at a rate = 4%

The increased amount = 4% of $100

This gives

Hence the investment increase annually by $4 yearly

In the second year the investment will increase by 2 x $4 = $8

In the third year the investment will increase by 3 x $4 = $$12

This implies that

In n years

The investment will increase by n × $4 = $4n

The balance at n years is given as

Balance = Investment + year increment

This is as shown below

3⁴ is factor rainbows for the number 81.

What does a math factor mean?

81 is a perfect square number.

Hence, we can express it as 9 × 9 = 81.

9 can further be factored as 3 × 3 = 9.

Factor of 81 = 1,3,9,27,81

negative factor of 81 = -1,-3,-9,-27,-81

prime factors of 81 = 3 * 3 * 3 * 3  = 3⁴

Learn more about factors

brainly.com/question/24182713

#SPJ1

Given the functions

First, we get the composite function

To get f(√5x³), we will substitute x in f(x) with √5x³ as shown:

The square root and power 2 cancel each other

Answer:

Solution

Given that a square window has an area of x² + 12x + 36

The length of one side of the square = x+6

There are 11 apples on the basket, if 5 of them are green and the rest are red, to determine the number of red apples, you have to calculate the difference between the total and the number of green apples:

a) There are 6 red apples on the basket, the ratio of all apples to red apples can be expressed as follows:

First, write the total number of apple and then write the number of red apples, separate both values by a colon

b) To write the ratio of red apples to green apples you have to write the number of red apples on the basket and the number of green apples, both values separated by a colon:

STEP - BY - STEP EXPLANATION

What to find?

P(X < 2)

Given:

From the given table;

P(X=-2) = 0.1

P(X=-1)=0.1

P(X=0)=0.2

P(X=1)=0.2

Substitute the values into the formula above and simplify.

Hence, P(X < 2)=0.6

ANSWER

0.6

The equation given is a one variable equation, "p".

The question asks to find the value of "p", which is the pounds of peanuts.

So, we need to solve the euqation for "p".

First, we need to put all the terms that have "p" in one side. For this, we will have to use the distributive property in the parenthesys first:

Now, we can substract 4.05p in both sides to get the "p" term of the left to the right:

Now, we do the same for the 13.50, substract it in both sides:

Now, we can divide both sides by 0.45:

So, the answer is p = 2, thus, you need 2 pounds of peanuts for the trail mix.

Solve the following system of equations by using elimination:

Using Elimination method:

Substitute the value of y in equation (1):

Therefore the value of x = 28 and y = -10

Hence the correct answer is (x,y) = (28,-10)

INFORMATION:

We know that:

- Rhombus STAR has vertices S(-1,2), T(2,3), A(3,0), and R(0,-1)

And we must calculate the perimeter of the rhombus

STEP BY STEP EXPLANATION:

To calculate it, we must find first the measure of one of the sides.

We can find one of the sides calculating the distance between two consecutive vertices.

So, calculating the distance between vertices S and T

Finally, to find the perimeter, we need to use that the rhombus has 4 equal sides. So, we the perimeter would be

ANSWER:

D. 4√10

Here are the steps in multiplying binomials using the distributive property:

1. Multiply the first 2w and first 7 by the terms inside the second parenthesis/binomial. Add the products.

2. Simplify.

3. Combine similar terms like -14w and 14w and the result is 0.

Hence, the product of the two binomials is 4w² - 49.

Note that the area of a square is the square of its side.

If the area is 12 square inches, the side is approximately :

And the area will be :

The answers are :

3.46 inches

and

11.9716 square inches

From Phyllis's graph:

At the start of training, Phyllis runs more miles per week than Nigel because Phyllis runs 6 miles per week, while Nigel runs 4 miles per week

x = 1/5

The given equation is:

5x + 6 = 7

Step 1: Collect like terms

Note that 6 becomes -6 when it crosses to the right side of the equality sign

5x = 7 - 6

5x = 1

Step 2: Divide both sides by 5

5x / 5 = 1 / 5

x = 1 / 5

Sarah wants to buy a blouse that costs $28. Her mom said she can buy this when it goes on sale for 2/7 of the original price.

2/7 part of 28 is

So, the selling price will be $8.

Given:

The sequence is 8, 16, 32, 64.

The first term is 8.

The opposite of a number is the same distance from 0 on a number line as the original number, but on the other side of 0, then we have to invert the sign of the original number, if we have a positive one and we are told to find its opposite we just put it a negative sign, if the original number is negative then we rewrite it as a positive number.

In this case, we have 18/19, then the opposite number of it is -18/19

13/4 m or 3.25 meters

1) Given the width is 10/8 meter

The length is 3/8 meter

2) To wrap the rectangular desk let's use this formula, for the Perimeter (2p):

2p= 2(w+l) Plug into w and l the measures

2p = 2(3/8 +10/8) Proceed with the sum within the parentheses

2p = 2(13/8) Distribute the factor

2p =13/4

3) Hence, the perimeter is 13/4 or 3.25 meters

The solution for the given inequality is x≥3. Therefore, option C is the correct answer.

The given inequality is (7x-3)/9 ≥ 8-2x.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Inequality can be solved as follows:

(7x-3)/9 ≥ 8-2x

Multiply 9 on both the sides of an inequality, we get

7x-3 ≥ 9(8-2x)

⇒ 7x-3≥72-18x

Add 3 on both the sides of an inequality, we get

7x≥75-18x

Add 18x on both the sides of an inequality, we get

25x≥75

⇒ x≥3

The solution for the given inequality is x≥3. Therefore, option C is the correct answer.

To learn more about the inequalities visit:

https://brainly.com/question/20383699.

#SPJ1

The only incorrect choice in the options is B.

A number line with a closed circle on 9 and shading to the left

The given inequality is expressed as:

This means that x is includes 9 and all the numbers above 9.

From the number line drawn above. A number line with a close circle on 9 and shading to the right is drawn.

Given:

point (2,-3) and (-3,7)

First, solve for the slope of the line

Now that we have solved for the slope, substitute it to the slope-intercept form y = mx + b to find the y-intercept. Use the point (2,-3) but using (-3,7) works just as well.

The slope intercept form of the line is

Rearrange it to follow the standard form Ax + By = C, and we have