This pentagonal prism is cut by the plane shown. The plane is parallel to the base of the pentagonal prism. What is the shape of the cross-section?

given data:

Spongebob was trying to fill up Gary's bath with water. He noticed the tub filled up 1 gallon per minute.

to find what kind of data this is.

it is discrete because it is measurable. that is countiuse while countable.

Thus the answer is discrete.

SOLUTION

From the question, the original price of the jeans was $40, then the price was reduced to $35. Decrease in price becomes

Percent decrease becomes

hence the answer is 12.5%

Explanations:

Answer:

sixth power is the exponent of 1.

To obtain the result, multiply 1 by itself 6 times:

1x1x1x1x1x1=1

1^6 = 1

Given a polynomial of factors below,

To find the values of x at f(x) = 0, substitute for f(x) into the equation above,

C is the right option

In the diagram we are given that angle S = angle T

We are given that side SV = side TV

We know that vertical angles are equal so angle RVT = angle UVT

WE have 2 angles and the included side so we can use the ASA Congruence theorem which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

There is enough information to use the ASA Congruence Theorem.

Answer:

The probability that the sum of her two rolls has an odd number of factors will be;

Explanation:

We want to find the probability that the sum of her two rolls has an odd number of factors.

For the two rolls the total number of possible outcomes is;

Let us list out the possible outcomes of the two rolls;

From the listed possible outcomes, the number of oucomes with odd number of factors of the sum is;

Total number of possibles outcomes is;

The probability that the sum of her two rolls has an odd number of factors will be;

Let's call x to the original price.

Given that Mason used a 30% coupon, then he paid 0.3x dollars less.

After the discount, the cost of the computer was $728, then

x - 0.3x = 728

0.7x = 728

x = 728/0.7

x = 1040

The original price of the computer was $1040

Mason saves 30% of $1040, which is computed as follows:

Mason saves $312

M= 205 - 2d

1) We can write a mathematical sentence for that situation, considering Jack's initial amount of money: $205 and the fact that we don't know the number of days (d). But we do know that each day costs Jack $2, i.e. minus 2 dollars per day.

2) Therefore, we can write out the following:

Where M stands for Jack's money and "d" stands for the number of days.

3) Hence the answer is

M= 205 - 2d

The equation system is:

So we can made the equation equal so:

Now we can replace the value of x to find y in the first equation so:

so the solution is:

Answer:

Question 1

d) 180

Question 2:

b T <8, 14>

Explanation:

Here is a graph of the two points.

As can be seen, the two points are on the opposite sides of teacher other, meaning the point (-3,4) has to rotate 180 degrees to get to (3, -4) and vice versa.

Question 2

The coordinates of A and B are

A = (5, 6)

B = (-3, -8 )

If we want to go from B to A, we need to add 8 to the x-coordinate and 14 to the y-coordinate.

Therefore, the translation

ok

$256 --------------------------- 10%

x --------------------------100%

x = (100 x 256) / 10

x = 25600 / 10

x = $2560

I earned $2560 over the summer

we are given the following system of equations:

Equation (2) can be rewritten dividing by 5 on both sides as:

Solving the operations:

Since equation (2) is the same equation as equation(1), this means that the system has infinite solutions.

8 and 7 are like terms, because they share the same power of x:

Would lines 4x+3y=52 and 3x-4y=44 be perpendicular parallel or neither?

step 1

Find out the slopes of the given lines

4x+3y=52

isolate the variable y

3y=-4x+52

y=-(4/3)x+52/3 ------> m=-4/3

3x-4y=44

4y=3x-44

y=(3/4)x-44/4 ------> m=3/4

step 2

Compare their slopes

m=-4/3 and m=3/4

the slopes are opposite reciprocal

that means

Let's first list down the information given in the scenario:

a.) In 2 years ariel wants to buy a bicycle that costs 1,000.00

b.) She opens a savings account that earns 9% interest compounded quarterly

Question: How much will she have to deposit as principal to have enough money in 2 years to buy the bike?

To be able to determine the principal amount Ariel will need to deposit, let's use this formula for Compound Interest:

Where:

A = Is the final amount/ cost of the bicycle = 1,000

n = Number of times the interest is being compounded = 4

r = Interest rate = 9%

t = No. of periods elapsed/ No. years the principal money be deposited

P = Principal amount/ amount to be deposited

Let's now find the principal amount:

Therefore, Ariel must deposit a principal amount of 836.94 for her to be able to buy the bike in 2 years.

Answer:

Let the number of packages delivered by Ralph's Express be x.

The number of packages delivered by Speedee Delivery would then be 4x.

The number of packages delivered by Send Quick Package Service would be x-5.

Adding all of these together,

x + 4x + (x - 5) = 6x -5

6x - 5 = 55

6x = 60

x = 10

Hence,

Ralph's Express delivered 10 packages.

Speedee Delivery delivered 40 packages.

Send Quick Package Service delivered 5 packages. Hope this help's you

Step-by-step explanation:

If we want to solve this problem we first need to list a few properties of trigonometric functions:

We are told that cot(θ)=1/2. Using the first equation and this data we obtain the following:

We multiply both sides and we get an expression for the cosine of θ:

Now we are going to take the second property I wrote in the begining and replace the cosine of θ with this new expression that we found:

We must solve this equation for the sine of θ. We can multiply both sides by 4/5:

And we apply a square root to both sides:

We are told that θ is located in quadrant I which means that its sine is positive. Therefore we get:

Then the answer is 2/√5

You can identify that the following is a Decimal number:

In order to convert a Decimal number to an Equivalent fraction, you can follow the steps shown below:

1. You need to write the Decimal number 0.005 as the numerator of the fraction and the denominator must be 1:

2. Now you can multiply the numerator and the denominator by 1,000, in order to remove the decimal places of the numerator (notice that it has three decimal places):

3. Finally, you have to reduce the fraction. Notice that you can divide the numerator and the denominator by 5. Then, you get:

The answer is:

Simplify the equation x^2 - 8x + 16 = 0 to obtain the value of x.

Equation has one solution, x = 4.

Simplify the equation x ( x - 1 ) = 8 to obtain the value of x.

This is a quadratic equation which is not a perfect square so it has two solutions.

Simplify the equation x^2 = 16 to obtain the value of x.

Thes equation has two solution x = 4 and x = -4.

So equation x^2 - 8x + 16 = 0 has only one solution and remaining equation has two solutions.

From the given box plot, let's express the difference in the medians of the IQR of each data.

Given:

Median of class A = 56

Q1 of class A = 50

Q3 of class A = 58

Median of class B = 52

Q1 of class B = 48

Q3 of class B = 54

Thus, we have:

IQR for class A = Q3 - Q1 = 58 - 50 = 8

IQR for class B = Q3 - Q1 = 54 - 48 = 6

Diffrence in median = 56 - 52 = 4

Thus, to find the expression of the difference in medians as a multiple of IQR of each data, we have:

Let's solve for each difference.

Difference class A:

Difference class B:

ANSWER:

Given

When you power a number by a determined exponent "n" it means that you are multiplying said number n-times by itself. We know that if you multiply 1 by 1 the result is 1, no matter how many times you do it, then 1 multiplied 5 times by itself is also equal to 1:

Then, you can write the calculation as:

Solve the addition in the denominator's place and then solve the division

The result of the calculation is 4

The inverse operation for addition is subtraction.

Hence, the answer is Subtraction.

Evaluate the value of expression.

So answer is 14y.

Given that

The vertices of the polygon ABCD are A(1,1), B(2,3), C(3,2), and D(2,1). ANd it is reflected about the x-axis.

So we have to find the vertices of the polygon A'B'C'D'.

Explanation -

Since the reflection is about the x-axis, the x-axis will be unchanged and the y-axis will be changed.(sign will be changed)

And it will be changed by the factor +2 in upwards directions.

So if A, B, C, D are reflected across x-axis.

The new points will be A' = (1,-1)

B' = (2,-3)

C' = (3,-2)

D' = (2,-1)

Now we have to add 2 in the y axis as they move upwards.

Then, the required points will be

Answer:

A.

Step-by-step explanation:

A. People could be influenced into groupthink and reject antibiotics without knowing the facts.

Let's rewrite the expression as:

Which is the standard equation of a circle:

Where (h,k) is the coordinates of center of the circle and r is the radius

Therefore, the center is:

And the radius is:

The expression for number of employee after n year if population, P decreases at rate of r % is,

Substitute the values in the formula to determine the population after 16 years.