Answer below! Thank you :) and try to explain how you got it!

Consider the given expression,

The product of fractions is obtained in the form of a fraction whose numberator is the product of numerators of fractions, and the denominator of the product is the product of denominators of the given fractions,

Thus, the product of the given fractions is 4/14 .

To find the sum of the ari

Given:

Radius, r = 6

Let's find the chance of hitting the shaded area by finding the ratio.

Since the radius of the cirlce is 6, the length of one side of the square is the diameter:

s = 6 x 2 = 12

To find the ratio divide the area of the circle by area of the square. The area of the circle is the shaded area while the area of the square is the total possible area.

Thus,we have:

Therefore, the chance of hitting the shaded region is 78.54%

ANSWER:

78.54%

Determine the square root of 58.

So answer is 7.6.

The domain is all the x values included in the function, while the range are all the y values included in the function.

Based on the graph:

Answer:

• Domain:

• Range:

Answer:

P(x) = 1.3x² + 0.1x + 2.8

Explanation:

We need to find an equation that satisfies the relationship shown in the table. So, let's replace x by 2 and then compare whether the value of p(x) is 8.2 or not

P(x) = 1.3x³ + 0.1x² + 2.8x

P(2) = 1.3(2)³ + 0.1(2)² + 2.8(2)

P(2) = 16.4

Since P(2) is 16.4 instead of 8.2, this is not a correct option

P(x) = 1.3x² + 0.2x - 2.8

P(2) = 1.3(2)² + 0.2(2) - 2.8

P(2) = 2.8

Since 2.8 and 8.2 are distinct, this is not the correct option

P(x) = 2.3x² + 0.2x + 1.8

P(x) = 2.3(2)² + 0.2(2) + 1.8

P(x) = 11.4

Since 11.4 and 8.2 are distinct, this is not the correct option

P(x) = 1.3x² + 0.1x + 2.8

P(2) = 1.3(2)² + 0.1(2) + 2.8

P(2) = 8.2

Therefore, this is the polynomial function for the data in the table.

So, the answer is P(x) = 1.3x² + 0.1x + 2.8

ANSWER

60 possible outcomes

EXPLANATION

If he spins the 3-section spinner, there are 3 possible outcomes: Walk, Run, Stop.

If he spins the 4-section spinner, there are 4 possible outcomes: red, green, blue, orange.

If he spins the 5-section spinner, there are 5 possible outcomes: Monday, Tuesday, Wednesday, Thursday, Friday.

If he has to spin the three spinners, the total possible outcomes is the product of the possible outcomes of each spinner: 3x4x5 = 60.

The unknown length of the side labeled n is 10.5 units

Given:

Two similar triangles with one unknown

To find:

the unknown length of the side labelled n

For two triangles to be similar, the ratio of their corresponding sides will equal

The unknown length of the side labeled n is 10.5 units

From the trignometric ratio of right angle triangle :

The ratio for the tangent of any angle of right angle triangle is the ratio of the side Opposite to that angle to the adjacent side of that angle :

In the given triangle :The side opposite to the angle A is BC and the adjacent side AC

So,

In the figure : we have AC = 76, BC = 31 and AB = 82.1

Substitute the value and simplify :

Thus, tan A = 0.41

Now, the side opposite to the angle B is AC and the adjacent side is BC

thus :

In the figure : we have AC = 76, BC = 31 and AB = 82.1

Substitute the value and simplify :

tan B = 2.451

Answer :

tanA = 0.41

tanB = 2.45

We will first write A equation

Let x be the number of minutes

y = 0.10x + 50

Comparing the above with y=mx + b where m is the rate of change

m = 0.10

Company B

y = 0.05x + 75

comparing with y =mx + b

rate of change (m) = 0.05

Hence, company A has a higher rate of change at $0.10

The size of the plywood sheet used is;

Here, we want to get the size of the part of the plywood sheet lost

From the question, we are told that 1/8 inches is lost

The size lost would be;

This is the size that was lost

To get the total part of the plywood used, we simply add the width of all the strips to the amount of the plywood lost

We have this as;

The Equation is 10 + x= 30 and 20 actors are from third grade.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

There are 30 actors in a school play.

There are 10 actors from second grade.

The rest are from third grade.

let the actors in third grade is x.

Equation is:

Actors from second grade + Actors from third grade = Total actors

10 + x= 30

Now, solving

Subtract 10 from both side

10 +x - 10 = 30 - 10

x = 20

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The complementary angles are angles in which the sum of them is equal to 90º

So: 90º-10º=80º

So, the complementary angle is 80º

The answer is C, 30 square feet

The general function for describing the displacement from the mean position in harmonic motion is:

Where:

• A is the amplitude,

• T is the period,

• φ is initial phase displacement.

From the statement, we know that:

• the amplitude is 4 cm,

• at time t = 0 its displacement d from the rest is 0 → d(t = 0) = 0,

• initially, it moves in a negative direction.

s

From the circle given, it can be observed that AC is the diameter of the circle and it divides the circle into two equal parts. The total angle in a semi-circle is 180°. It then follows that

Hence, arcAD = 90°, arc BD = 142°, and arc BAC = 232°

An algebraic expression we can use to compare the price of IBM shares as being $74.50 more than AT&T shares is x + 74.50, where x is the value of AT&T shares.

An algebraic expression consists of variables, terms, constants, and mathematical operations, including addition, subtraction, multiplication, division, and others.

The five algebraic expressions include monomial, polynomial, binomial, trinomial, multinomial.

We can also describe algebraic expressions as falling under the following categories:

An example of an algebraic expression is 2x + 3y.

Let the value of AT&T share = x

Let the value of IBM share = x + 74.50

Thus, we can, algebraically, conclude that AT&T's share price is x while the price of IBM's share is x + 74.50 on that particular day.

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Notice that 100=10*10, and 10=2*5. 2 and 5 are prime numbers; therefore,

The answer is 100=2^2*5^2

Radical

x = √10 • tan 45° = √10• 1 = √10

then

x= √10

y= √x^2 + 10 = √ 10 +10 = √20

Then answer is

x=√10

y= √20

Answer:

Explanation:

From the graph, we ca

We have to find the solutions to the equation:

The absolute value function is in fact a piecewise function, so it may have two solutions.

We consider for the first solution that the argument inside the absolute function is positive, that is x + 4 > 0. Then, we will have:

Now, we consider that the the argument is negative and is made positive by the absolute value function (it will shift the sign, which can be represented by a multiplication by -1). This means that x + 4 < 0, and the solution will be:

We can see it in a graph as:

Answer: the solutions are x = 4 and x = -12.

Answer:

(f - g)( x ) = -x + 7

Domain;

Explanation:

Given the below functions;

To find (f - g)( x ), all we need to do is subtract g(x) from f(x) as shown below;

The domain of the function will be all values from negative infinity to positive infinty, written as;

According to the information given in the exercise:

- Group A contains a total of 155 people.

- One-fifth of that people will be selected to win $20 fuel cards.

- The total number of people in Group B is 686.

Then, you can determine that the number of people that will be selected to win $20 fuel cards is:

Therefore, the number of nonwinners in Group A is:

You know that Group B will receive the same number of fuel cards. Therefore, its number of nonwinners is:

Knowing all this information, you can set up the following ratio of nonwinners in Group A to nonwinners in Group B after the selections are made:

Hence, the answer is:

4 hours ---> 6 kilowatts

1 hour -----> x kilowatts

answer:

1.5 kilowatts per hour

Answer:

-35

Step-by-step explanation:

[tex]\frac{7}{9}[/tex] = [tex]\frac{b}{b - 10}[/tex]  multiply both sides by 9(b -10)

[tex]\frac{9(b - 10)}{1}[/tex]  [tex](\frac{7}{9})[/tex] = [tex]\frac{9(b -10)}{1}[/tex] [tex](\frac{b}{b-10})[/tex]  On the right side of the equation, the 9's cancel out and on the right side of the equation the (b -10) cancels out to leave

7(b -10) = 9b  Distribute the 7

7b - 70 = 9b  Subtract 7b from both sides

-70 = 2b  Divide both sides by 2

-35 = b

• Given the description "Six increased by twice a number is no more than 20", you need to know the following:

- In this case, the word "increased" indicates an Addition.

- The word "twice" indicates a Multiplication by 2.

- "No more than" indicates that six increased by twice a number must be less than or equal to 20.

- The inequality symbol whose meaning is "Less than or equal to" is:

Knowing the information shown before, you can write the following expression to represent "Six increased by twice a number" (Let be "x" the unknown number):

Therefore, you can write the following inequality that models the description given in the exercise:

• Now you need to solve it:

1. Apply the Subtraction Property of Inequality by subtracting 6 from both sides of the inequality:

2. Apply the Division Property of Inequality by dividing both sides of the inequality by 2:

• In order to graph the solution on a Number Line, you can follow these steps:

- Since the inequality symbol indicates that "x" is less than 7, it indicates that 7 is included in the solution. Therefore, you must draw a closed circle over that value.

- Draw a line from the circle to the left.

Then, you get:

Hence, the answer is:

- Inequality:

- Solution:

- Number Line:

The formula to find the area of a rectangle is:

Since the rectangle area is 170cm², we can write the following equation.

On the other hand, we know that the width of the rectangle is 6 less than twice its length. Then, we can write another equation.

Now, we solve the found system of equations.

For this, we can use the substitution method.

Step 1: we replace the value of w from Equation 2 into Equation 1. Then, we solve for l.

We can use the quadratic formula to solve the above equation.

Then, we have:

There are two solutions for l.

Since the value of l can not be negative, the value of l is 10.84.

Step 2: We replace the value of l into any of the equations of the system to find the value of w. For example, in Equation 1.

Now, the long side, the wide side and the diagonal of the rectangle form a right triangle.

Then, we can use the Pythagorean theorem formula to find the length of the diagonal.

In this case, we have:

Therefore, the length of the diagonal of the given rectangle is 19.06 cm rounded to 2 decimal places.

Given:

The general equation is

m is a slope and c is the y-intercept.

From equation (1),

From equation (2)

From equation (1) and (2)

Substitute equation (2) in (1)

Substitute in (2)

The required Z-score with a value of 120 would be 1.33.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

The given graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

As per the given information, the solution would be as

ц = 100

σ = 15

X = 120 (consider the value)

⇒ z-score = (X - ц )/σ₁

Substitute the values,

⇒ z-score = (120 - 100)/15

⇒ z-score = (20)/15

⇒ z-score = 1.33

Thus, the required Z-score with a value of 120 would be 1.33.

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Question 14.

Given the function:

Let's find the inverse of the function.

To find the inverse, take the following steps.

Step 1.

Rewrite f(x) for y

Step 2.

Interchange the variables:

Step 3.

Solve for y

Add 4 to both sides:

Multply all terms by 3:

Divide all terms by -2:

Therefore, the inverse of the function is:

Let's graph both functions.

To graph each function let's use two points for each.

• Main function:

Find two point usnig the function.

When x = 3:

When x = 0:

For the main function, we have the points:

(3, -6) and (0, -4)

Inverse function:

When x = 2:

When x = -2:

For the inverse function, we have the points:

(2, -9) and (-2, -3)

To graph both functions, we have:

ANSWER: