Find the volume of a cone with a height of 8 m and a base diameter of 12 mUse the value 3.14 for it, and do not do any rounding.Be sure to include the correct unit in your answer.

Wayne has a bag filled with coins.

Number of quarters = 7

Number of dimes = 8

Number of nickels = 3

Number of pennies = 9

So, the total number of coins is

Total = 7 + 8 + 3 + 9 = 27

What is the probability that Wayne chooses a quarter or nickel?

How many coins are either quarter or nickel?

quarter or nickel = 7 + 3 = 10

So, the probability is

Therefore, the probability that Wayne chooses a quarter or nickel is 10/27

Answer: the pre-tax subtotal is $330

Explanation:

Let x represent the pre tax total

If the tax rate in the area is 8.2%, it means that the amount of tax paid is

8.2/100 * x = 0.082x

pretax total + tax = after tax subtotal

Given that after tax subtotal is $357.06, then

x + 0.082x = 357.06

1.082x = 357.06

x = 357.06/1.082

x = 330

the pre-tax subtotal is $330

To find the number of missing pages:

rewriting the expression as homogeneous fractions:

simplifying it:

ANSWER

you have left 3/10 page.

The amount should be charged to each attendee to cover the cost of the event is (300 + 45x) / x

Given,

The cost of a convention center to host an event = $300 + $45 per person attending

Number of attendees = x

We have to find a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event.

Here,

Total cost for the event = Fixed cost + cost per person attending x number of person

Total cost = 300 + 45 × x

Total cost = 300 + 45x

Now,

The amount should be charged to each attendee to cover the cost of the event = (300 + 45x) / x

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The first step will be to review all of the types of graphs or charts mentioned in the options.

The following diagram shows an example of each type of graph:

In this case, we need a graph to show the number of people by age group that attended the movie.

In this case, the line graph, the area chart, and the scatter chart will not represent the information in the best way, but a column graph, a bar graph, or a pie chart will give a better idea of the number of people by age group that went to see the movie.

Answer:

-Column graphs

-Pie charts

-Bar graphs

The statement holds true for all true values of is cos²θ = 1 − sin²θ

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Answer:

a. Additive Identity

Explanation:

Given the equation:

When zero(0) is added to 'a', the result is still 'a'.

The number 0 is the additive identity of 'a'.

Answer : $7.5

1 pack of starbursts cost $1.50 at shoprite.

How much will 5 packs cost

Let the cost in dollars of 5 packs of starbursts be x

1 pack will cost $1.50

5 packs will cost $x

Mathematically,

1 pack ---------------- $1.50

5 packs -------------= $x

Cross multiply

1 * x = 5 x 1.50

x = $7.5

Hence, 5 packs of starbursts would cost $7.5

From the information given,

gus bought 2/3 pound of turkey. If tukey costs 9 dollars per pound, it means that the cost of 2/3 pound of turkey is

2/3 x 9 = 6

gus bought 1/4 pound of ham. If ham costs 7 dollars per pound, it means that the cost of 1/4 pound of ham is

1/4 x 7 = 7/4 = 1.75

Total amount spent = amount spent on turkey + amount spent on ham

Total amount = 6 + 1.75

Total amount = $7.75

First, in order to get to know if 256 it is a rational or irrational number we have to begin with the definition of what is rational and irrational number.

Rational numbers are all the number that can be represented as fractions, while the irrational numbers are all the numbers that can not be expressed as fractions.

In this case, then we can confirm that the number 256 can be considered as a rational number because it can be expressed as the quotient of the two integers: for example 256/1.

Given the following equation:

We will graph the given function using the points that will be written in ordered-pairs.

The given function is a quadratic function with a vertex = (0, 0)

We will graph the points using five points

The vertex and 4 points, 2 points before the vertex and 2 points after the vertex.

So, we will substitute x = -4, -2, 2, 4

So, the points are: (-4, 16), (-2, 4), (0, 0), (2, 4), (4, 16)

The graph using the points will be as follows:

A polygon is a closed shape with straigh sides, then

2. Is the figure a polygon? YES.

Since the figure is a polygon

1a. Is this polygon concave or convex? It is concave. A concave polygon will always have at least one reflex interior angle, tha is, it has on interior angle greater than 180 degrees.

1b. Is this polyogn regular, equiangular, equilateral or none of these? The marks on the picture mean that all the sides have the same length. This is the definition of equilateral. Then the answer is equilateral.

1c. What is the name of this polygon? We can see it has 4 equal sides and is concave, then his name is Concave Equilateral Quadrilateral.

Given: The line segment ST as shown in the image

To Determine: The bisector of ST and the value of ST

Solution

It can be observed from the first image, the bisector of ST is line MW

For the second image, the bisector of ST is line LM

For first exercise, the bisector is MW, ST = 38

For the second exercise, the bisector is LM, ST = 30r

The chance of the first student chosen not secretly being a robot is 2/6, but if the student is secretly a robot, then it doesn’t matter who the second student chosen is, because “neither” cannot be obtained.

So, 2/6th the time we care about the second student. There is in this case 1 non robot among the 5 remaining students, so the chance is 1/5 of picking that second non robot.

Hence;

2/6 x 1/5 = 2/30 = 1/15

By using the GCF and distributive property, the sum of 15+27 = 42

The expression is

15 + 27

GCF is the greatest common factor, the greatest common factor is the highest number that divides exactly into two or more numbers.

The distributive property states that multiplying the sum of two or more variables by a number will produce the same result as multiplying each variables individually by the number and then adding the products together.

The expression is

= 15 + 27

= 3(5 + 9)

= 3 × 14

= 42

Hence, by using the GCF and distributive property, the sum of 15 + 27 = 42

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What is the simplified form of the expression square root of -64

we have

Remember that

64=2^6

and

i^2=-1

substitute

Let n be the lesser number of the three. Therefore,

Solving for n,

Then, the three numbers are 72, 73, and 74. The answer is 74

Given:

m∠3 = 63°

Let's find the m∠5 and m∠8.

• m∠5:

Angle 5 and angle 3 are alternate interior angles.

Alternate interior angles are angles formed on the opposite sides of the transversal.

To find the measure of angle 5, apply the Alternate Interior Angles theorem which states that when two parallel lines are cut by a transversal, the alternate interior angles are congruent.

The measure of angle 5 will also be 63 degrees.

Thus, we have:

m∠3 = m∠5 = 63°

m∠5 = 63°

• m∠8:

Angle 8 and angle 5 are linear pair of angles.

Angles that form a linear pair are supplementary.

Supplementary angles are angles that sum up to 180 degrees.

Thus, we have:

m∠8 + m∠5 = 180

m∠8 + 63 = 180

Subtract 63 from both sides:

m∠8 + 63 - 63 = 180 - 63

m∠8 = 117°

Therefore, the measure of angle 8 is 117 degrees.

ANSWER:

• m,∠,5 = 63°

• m∠8 = 117°

We need to translate the vertex F of triangle BDF. When we translate it 2 units to the left and 4 units down, we obtain the point F'.

We know that triangle BDF has vertices B(4,3), D(6,3), and F(6,1).

The first coordinate of each point represents its x-coordinate (the distance from the y-axis). And the second coordinate of each point represents its y-coordinate (the distance from the x-axis).

So, this triangle is shown below:

Now, we need to translate the point F 2 units to the left, to obtain the redpoint below. And then translate it 4 units down, to obtain F' (the yellow point):

Therefore, the F' has coordinates:

F'(4,-3)

A geometric sequence is defined as:

Where r ≠ 0 is the common ratio and a ≠ 0 is the first term of the sequence.

From the statement, we know that r = 2/3 and the first term is a = 5.

Replacing these numbers in the expression of the 7th term, we get:

320/729

The equation that gives us the amount of gas left in her car, given the driven miles, is

Notice that when x=25, there will remain 14 gallons of gas in the tank.

The x-intercept is

(375,0). This is the maximum distance one can drive when the amount of gas in the tank reaches zero gallons.

On the other hand, the y-intercept is

(0,15). This is the number of gallons in the tank when we have driven 0 miles.

First, because of the roof having an inclination, we need to calculate the lenght of the surface we want to roof. The width will be the same.

Let's take a look at the situation:

Since we're on a right triangle, we can say that:

Solving for R,

Since we already know that the lenght of the gym's floor is 390',

We get that the lenght of the surface we want to roof is 421.38'

Now, let's take a look at the surface we want to roof:

Since the roof is a standard gable roof with 3’ of overhang on all sides, we add 6' to each dimension:427

Our total roofing area would be:

We then divide this total area by the area of one of our "squares":

We round to the nearest integer from above, since we can't buy a fraction of a square.

(this is called ceiling a number)

Therefore, we can conclude that Mark needs 1180 squares of roofing.

ANSWER:

The value of AB is 23

STEP-BY-STEP EXPLANATION:

We know that AB is part of AC, and that DB cuts into two equal parts (half) since it is a median, therefore the value of AB would be

In the given figure we can observe a triangle with vertices located at:

(-3,-2)

(-5,-4)

(1,-5).

We need to draw it after a 90° clockwise rotation.

We can apply the rule for 90° clockwise rotation, which is:

Each point of the given figure has to be changed from (x, y) to (y, -x) and then we need to graph the new coordinates.

By applying the rule to the given coordinates we obtain:

Now we have to draw the new coordinates:

Okay, here we have this:

Considering the provided figure, we are going to calculate the requested surface area, so we obtain the following:

So to calculate the surface area we will first calculate the area of the base, the area of the short side and the area of the longest side, then we have:

Base area=6 in * 14 in=84 in^2

Short side area=8 in * 6 in = 48 in^2

Longest side area=8 in * 14 in=112 in^2

Total surface area=Base area+ 2(Short side area) + 2(Longest side area)

Total surface area=84 in^2+ 2(48 in^2) + 2 (112 in^2)

Total surface area=84 in^2+ 96 in^2 + 224 in^2

Total surface area=404 in^2

Finally we obtain that the total surface area in square inches of the toy box is 404 in^2.

The representation of a quadratic eqauation in vertex form is

The given vertex is,

And the given point through which the graph passes is,

Substitute the values in the formula of quadratic equation.

Hence, the equation in vertex form will be,

We have to find the equation of the quadratic function.

We know the vertex, located in (4,6), and one point (-5,-2).

The x-coordinate of the vertex (4) is equal to -b/2a, being a the quadratic coefficient and b the linear coefficient.

Now, we have 2 points to define the 3 parameters, so one of the parameters is undefined.

We start with the vertex, that we know that is:

Then, we can write the equation as:

If we replace the point (-5,-2) in the equation, we get:

We replace the vertex coordinates and get:

Then, the linear coefficient b is:

And the constant term is:

The quadratic coefficient is a=-0.01

The linear coefficient is b=0.79

the constant term is c=4.42

1. The scholar made a mistake in the last step

where he said x=3.5

[tex]0.5x = 7 \\ \frac{0.5x}{0.5} = \frac{7}{0.5} \\ x = 14[/tex]

SCHOLA DIVIDED 7 BY 2 INSTEAD OF DIVIDING BY 0.5

2.TO CHECK IF 3 as a solution satisfies the equation I will first look in what the LHS is equal to by plugging in 3 in the place of n. SO THAT n=3 SATISFIES THE EQUATION LHS=RHS

[tex]lhs = - \frac{1}{2} (2(3) - 8) + 3 \\ lhs = - \frac{1}{2} (6 - 8) + 3 \\ lhs = - \frac{ 1}{2} ( - 2) + 3 \\ lhs = 1 + 3 \\ lhs = 4[/tex]

Now I will check what The RHS IS EQUAL TO BY ALSO PLUGGING IN 3 IN THE PLACE OF n

[tex]rhs = \frac{1}{4} (8(3) - 4) - 1 \\ rhs = \frac{1}{4} (24 - 4) -1 \\ rhs = \frac{1}{4} (20) - 1 \\ rhs = 5 - 41\\ rhs = 4[/tex]

FROM WHAT I FOUND LHS=RHS THIS MEANS THAT n=3 SATISFIES THE EQUATION BECAUSE IT IS BALANCED. WHAT IS ON THE LEFT HAND SIDE IS EQUAL WITH WHAT IS ON THE RIGHT HAND SIDE.

I HOPE THIS HELPS.

explanation

To determine how much Gretchen paid, we will have to list out the number of Video purchases made for drama, action, and comedy videos.

Let the Action videos be represented by A

Let the Comedy videos be represented by C

Let the Drama videos be represented by D

Also,

A has 3 purchases

C has 5 purchases

D has 2 purchases

Therefore, we will have the expression

If she paid $4 for each, then

The total videos purchased = 3+5+2=10

Thus, the total amount paid will be

Thus, Gretchen paid $40