Select the table that represents a linear function. (Graph them if necessary.)
OA. x 0 1 2 3
y 2 3 6 11
OB. x 0 1 2 3
y 1 3 9 27
OC. x 0123
y 0149
OD. x 012
3
y 39 15 21

The value of the function at x = 0 will be 1.

What is a function?

A statement, principle, or rule that creates a relationship between two variables is known as a function. Functions are abundant in mathematics and are required for the creation of complex relationships.

When the required parameters and natural laws are given values, the expression yields the calculation result that the mathematical model represents.

The table represents a function.

x     f(x)

-3     1

-1     8

0      1

3     0

6     13

9     -3

In the above table, we can see that at the value of x = 0 in the function the value of the whole function is 1.

Let's learn more about the function

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Given

Total investment of $3,300

5% profit and 2% profit totaling $126

The equations therefore will be

Use substitution method using the first equation

Now that we have solve for x, substitute it to the first equation to get the value of y

Therefore, the amount invested in mutual fund that earned 5% was $2000, and the amount invested that earned 2% was $1300.

Ok, so

We're going to simplify the following expression:

Remember that if we have two exponents elevating each other in the same base, they multiply.

So, this is equivalent to write:

Now, we can rewrite the last expression in this new one:

Answer:

Additive Identity

Step-by-step explanation:

Hello!

Adding 0 to any number will give you that number itself, as proven by adding 0 to 25, which gave us 25.

This is the identity property of addition, as the output would be identical to the sum of the non-zero terms.

We can also experiment with these:

For the vertical angles, the value of x is found as 5. The measure of the angle ∠QRT = 44° for the two intersecting lines.

For the given pair of angles in the question.

Two lines are intersecting to form two equations are vertical pairs.

∠QRT =  ∠VRS (vertical angles)

Put the values.

8x + 4 = 10x - 6

Simplifying.

2x = 10

x = 5

Put the values of 'x' in the angle.

∠QRT = 8x + 4

∠QRT = 8×5 + 4

∠QRT = 44

Thus, the measure of the angles ∠QRT is found as 44°.

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Evaluate the given expression at x=6. This is, replace every x in the equation for 6 and solve:

The balance after 6 months is 1197.04.

The sum of the interior angles of a triangle must add 180°.

C : 20 + 80 + 100 = 200 NO

D : 35+35+105 = 175 NO

A : 10+ 10+160 = 180 Yes

B : 15 +75 + 90 = 180 Yes

E :60+60+60 = 180 Yes

we calculate the area of one trangle and multiply by 2

we apply formula of the triangle area

where b is the base and h the height of the triangle

then replacing

area of one triangle is 15.6square centimeters

Area of both triangles

Area of the two triangle bases is 31.2 square centimeters

According to the solving the probability are as follows:

a) Event "A or B": {1, 2, 3, 4, 6}

(b) Event "A and B": {2, 4}

(c) The complement of the event A: {5, 6}

The term "sample space" refers to a collection of probable results from a random experiment. The letter "S" indicates that this is the sample space. Events are a subset of what might happen in an experiment. Depending on the experiment, the outcomes in a sample area could change. In discrete or finite sample spaces, there are only a finite number of possible outcomes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

the sample space is, 1, 2, 3, 4, 5, 6 i.e., U = {1, 2, 3, 4, 5, 6}

Event A: The number rolled is less than 5

i.e., A = {1, 2, 3, 4}

Event B: The number rolled is even

i.e., B = {2, 4, 6}

Event A Or B A∪B = {1, 2, 3, 4} ∪ {2, 4, 6}

= {1, 2, 3, 4, 6}

Event "A and B"A∩B = {1, 2, 3, 4} ∩ {2, 4, 6}

= {2, 4}

Compliment of the event A

Comp(A) = U/ A = {1, 2, 3, 4, 5, 6} / {1, 2, 3, 4}

= {5, 6}

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Answer:

2,300

Explanation:

This is given as:

Therefore, there are 2,300 ways that 3 persons can be selected from 25 people

The sum of all interior angles of a triangle is 180° thus the measure of one of the congruent angles is 42.25° so option (A) is correct.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.

Let's suppose the two congruent interior angles are x degrees.

It is known that the sum of all three angles inside a triangle will be 180°.

So,   m∠x+  m∠x +  95.5° = 180°

2m∠x = 180° - 95.5°

m∠x = 84.5/2 = 42.25°

Hence "The sum of all interior angles of a triangle is 180° thus the measure of one of the congruent angles is 42.25°".

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It takes the rocket to reach its maximum height h max = 17(ft).

So, h(t) = -16+ 32t+5:

Then, h max rocket = the maximum height of the toy rocket

Therefore, it takes the rocket to reach its maximum height h max = 17(ft)

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there is no solution (option C)

Given:

y > 3/2x - 2

y < 3/2x - 10

To find:

The solution to both graphs

To determine the solution of the graphs, we will consider their slopes

The slope of both inequalities is 3/2. If the slopes of two lines are the same, the lines are said to be parallel. This means both inequalities are parallel lines

For parallel lines, there is no solution because the lines do not intersect (meet).

Since both inequalities give parallel lines, there will be no solution (option C)

Answer:

[tex](f \circ g)(x) = 9x^2 + 5\\\\\\(g \circ f)(x) = 3x^2 + 15[/tex]

Step-by-step explanation:

We are given
[tex]f(x) = x^2+5\\\\g(x) = 3x\\\\(f\circ g)(x) = f(g(x))\\\\[/tex]

To find this, wherever you see an x in f(x) substitute the expression in g(x)

[tex](f\circ g)(x) = f(g(x))\\\\= f(3x)\\\\= (3x)^2 + 5\\\\=9x^2 + 5\\\\\\[/tex]

To find [tex](g \circ f)(x) = g(f(x))\\\\[/tex]

Wherever there is an x in the expression for g(x) substitute that x with the expression in f(x)

[tex](g \circ f)(x) = g(f(x))\\\\\\= g(x^2 + 5) = 3(x^2 + 5) \\\\= 3x^2 + 15[/tex]

Given the matrices A and B:

We know that:

Then, using the matrices A and B:

And the element C₄₁ (fourth row and first column) is:

Now, for the matrix (A + B) - A = B:

Notice that:

cannot be expressed as a product of factors, meaning that

is not a factor of the given polynomial.

Answer: Not a factor.

Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots e.t.c

Examples of radicals are

For exmaple,

Given the radical

To simplify into the simplest radical,

Factorize the perfect square

Then we take out the pairs

Simplify the result

Hence, the simplified radical of the example used is

The R= {y | y is an integer and -5 ≤ y ≤ -4} is null set because there is no integers between -5 and -4.

The set is

R= {y | y is an integer and -5 ≤ y ≤ -4}

An integer is a combination of number zero, all the positive numbers and negative numbers without any fraction.

Any set that does not contains any numbers or elements is called null set, which is also called empty set or void set. Null set can be denoted as {} or ∅.

The set is R= {y | y is an integer and -5 ≤ y ≤ -4}

There is no integers between -5 and -4, therefore it is a null set

Hence, The R= {y | y is an integer and -5 ≤ y ≤ -4} is null set because there is no integers between -5 and -4.

The complete question is :

Write the set in roaster form R= {y | y is an integer and -5 ≤ y ≤ -4}

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Answer:

-12≤x<1

Step-by-step explanation:minus both side by 4

The area of the regular polygon is a= 145.8 sq.cm

Perimeter of the polygon is p=108 cm.

Let apothem length be a

We know,

a=p x a/2

Putting the values,

145.8=108xa/2

a=2.7 cm

The length of the apothem is 2.7 cm

We want to solve

We can subtract 4/9 on both sides.

Now we have 3/9 on the right side, but we can simplify that fraction to 1/3

And now we have the result!

Therefore the final result is x = 1

Answer:

$ 0.75 for one pen

$1.05 per notebook

Step-by-step explanation:

John and Ariana bought school supplies. John spent $10.30 on 5 notebooks and 7 pens. Ariana spent $7.20 on 4 notebooks and 4 pens. What is the cost of 1 notebook and what is the cost of 1 pen?

John: 5n + 7p = 10.5

let's solve for n:

5n + 7p = 10.5

subtract 7p from both sides:

5n + 7p -7p = 10.5 - 7p

5n = 10.5 - 7p

divide both sides by 5:

5n/5 = (10.5 - 7p)/5

n = 2.1 - 7/5 p

Ariana: 4n + 4p = 7.20

Let's substitute in: n = 2.1 - 7/5 p

4n + 4p = 7.20

4(2.1 - 7/5p) + 4p = 7.20

multiply left side:

8.4 - 5.6p + 4p = 7.2

subtract 8.4 from both sides:

8.4 - 5.6p + 4p - 8.4 = 7.2 - 8.4

- 5.6p + 4p = -1.2

combine p terms on left side:

-1.6p = -1.2

divide both sides by -1.6:

-1.6p/(-1.6) = -1.2/(-1.6)

p = 0.75 cents for one pen

Now solve to find the price of a notebook:

4n + 4p = 7.20 when p = 0.75

4n + 4(0.75) = 7.20

4n + 3 = 7.20

subtract 3 from both sides:

4n + 3 - 3 = 7.20 - 3

4n = 4.2

divide both sides by 4:

4n/4 = 4.2/4

n = 1.05 per notebook

CHECK: when n = 1,05 and p = 0.75

John: 5n + 7p = 10.5

5(1.05) + 7(0.75) = 10.5

10.5 = 10.5

Ariana: 4n + 4p = 7.20

4n + 4p = 7.20

4(1.05) + 4(0.75) = 7.20

7.2 = 7.2

Answer assumes no additional sales tax.

The annual demand when the manager reviews the stock is 900 units.

Mean demand, d = 18 units per week

Standard deviation of weekly demand, σd = 6 units per week

Lead Time, LT = 1 week

Order Cost, S = $32 per order

Unit Cost, C = $90 per unit

Holding Cost, H = 10% of C = $9 per unit per year

Service level, SL = 98%

z score = NORMSINV(SL) = NORMSINV(98%) = 2.05

Operating weeks = 50 weeks per year

The annual Demand, D will be:

= 50*18

= 900 units

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5. Let the following inequality:

this is equivalent to:

this is equivalent to:

this is equivalent to:

solve for m:

that is :

6. Because of the graphic (real line), we can conclude that the correct interval would be:

Then we have to find the inequalities that have this solution interval.

a) Let the inequality

this is equivalent to:

this is equivalent to:

solve for x:

then. A) represent the graph.

b)Let the inequality

this is equivalent to:

this is equivalent to:

this is equivalent to:

solve for x:

then the solution interval would be:

then. B) represent the graph.

c) Let the inequality:

this is equivalent to:

this is equivalent to:

this is equivalent to:

solve for x:

that is:

then. C) represent the graph.

d) Let the inequality:

this is equivalent to:

this is equivalent to:

solve for x:

We can conclude that this interval does not represent the graph because:

Finally:

e) Let the inequality:

this is equivalent to:

this is equivalent to

that is:

that is:

THEN WE CAN CONCLUDE THAT THE CORRECT ANSWER ARE:

A), B), C) AND E)

EXPLANATION:

Given;

We are given a frequency table which displays a survey of numbers of customers that like hamburgers and burritos and those that do not like hamburgers and burritos.

Required;

We are required to analyze the table and use the values to answer the questions that follow.

Solution;

We shall begin by completing the table as follows;

Part A:

What percentage of the survey respondents do not like both burritos and hamburgers?

The percentage that do not like hamburgers is

The percentage that do not like burritos is

The percentage that does not like both burritos and hamburgers is;

Expressed as a percentage, this is

The marginal relative frequency of all customers that like hamburgers is the total of all hamburger lovers divided by the total of all respondents.

ANSWER:

Part (a) 26.34%

Part (b) 53.66%

Answer:

[tex]\frac{3}{13}[/tex]

Step-by-step explanation:

the fraction is formed by the number who prefer historical movies to the total preferring all movies.

total = 24 + 18 + 6 + 30 = 78

number preferring historical movies = 18

then fraction preferring historical movies is

[tex]\frac{18}{78}[/tex] ( divide numerator/ denominator by 6 )

= [tex]\frac{3}{13}[/tex] ← in simplest form

Answer:

From the Graph the total number of students who preferred historical movies =  18.

Similarly total number of  students = 24+18+6+30

                                                         = 78

Fraction of student who prefer Historical movies = 18/78

                                                                                = 3/13.

We want to find the percentage change;

We can do that using the formula;

Given:

Substituting the given values;

Given a right angle triangle:

The hypotenuse of the triangle = 17

The legs of the triangle are the sides 14 and x

We will find x using the Pythagorean theorem as follows:

Solve for x:

So, the answer is the first option

The mistake Ross has made was in line 2, and it is that we can only combine like terms, that is, terms that have the same variable at the same power. So

We cannot performe this operation.