Suppose that the function f is defined as follows.

There are exactly 250 blocks with exactly one face painted red.

What is cube ?

A cube is a three-dimensional solid shape with six square faces of equal size that meet at 90-degree angles. It is a special case of a rectangular prism, where all of the edges have the same length.

When the 10 x 10 x 10 cube is painted red on all faces, it means that all of the 1000 unit cubes inside the large cube are red.

When the cube is cut into ten 10 x 10 x 1 slices, each slice will contain 100 unit cubes. When each slice is cut into twenty-five 2 x 2 x 1 blocks, each block will contain 4 unit cubes.

Therefore, each 2 x 2 x 1 block will come from 4 unit cubes, and each unit cube will contribute to 4 different blocks.

To count the number of blocks with exactly one face painted red, we can focus on the blocks that have a red face on the bottom (or top) and three unpainted faces on the other sides. Each such block will correspond to one of the 100 unit cubes in a slice, and there are 10 slices, so there are 1000 such blocks in total.

However, each of these blocks has four unit cubes, so we need to divide by 4 to get the number of blocks. Therefore, the answer is:

1000 ÷ 4 = 250

Therefore, there are exactly 250 blocks with exactly one face painted red.

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The poster has an area equal to 192.423 square inches.

In this problem we must determine the area of a heart shaped poster, that is, the combination of the areas of a square and two semicircles, whose resulting formula is introduced below:

A = D² + (π / 4) · D²

Where:

If we know that π = 3.14 and D = 7 in, then the area of the poster is:

A = 7² + (π / 4) · 7²

A = (5π / 4) · 7²

A = 192.423 in²

The area of the poster is equal to 192.423 square inches.

The image is missing and the statement is not well explained. A correct statement is shown below:

Sarah uses a square with side length of 7 inches and two semicircles with diameter of 7 inches to design a heart shaped poster. Find the area of the heart. Then, find the approximate area by using 3.14.

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Answer:

8602

Step-by-step explanation:

To complete the steps to find 253 X 34, you can follow these steps:

Break down 34 into 30 + 4

Multiply 253 by 30 and 4 separately

Add the two products together

So, 253 X 34 = 253(30+4) = (253 X 30) + (253 X 4) = 7590 + 1012 = 8602

If (-8,3) lies on the circle and its Center is (-4,3) then, the radius of the circle is 4.

We know that the center of the circle is (-4, 3). Let's call the radius of the circle "r".

The distance between the center of the circle and the point (-8, 3) on the circle is equal to the radius "r".

Using the distance formula, we can find the distance between these two points;

d =√[(x2 - x1)² + (y2 - y1)²]

d = √[(-8 - (-4))² + (3 - 3)²]

d = √[(-8 + 4)² + 0²]

d = √[4²]

d = 4

Since the distance between the center of the circle and the point on the circle is equal to the radius, we have;

r = d = 4

Therefore, the radius of the circle is 4.

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Answer:

Step-by-step explanation:

The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."

When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.

Therefore, option 1 is the correct definitation of perpendicular lines.

Answer: 1. Two lines that intersect in a way that forms right angles.

Step-by-step explanation:

Hope this helped! :)

Answer: C

Step-by-step explanation:

We need to turn 50% into a fraction first to make it easier,

50% is equal to 1/2 because 50/100 is simplified to 1/2.

Now let's multiply!

24 x 1/2 = 24/2 = 12/1 = 12

Answer:

430

Step-by-step explanation:

Let's call the price of the television set before taxes "x".

The total cost including tax is $451.50, which is equal to x plus 5% of x (the tax). In other words:

x + 0.05x = $451.50

Simplifying the left side by factoring out x, we get:

1.05x = $451.50

Dividing both sides by 1.05, we get:

x = $430

Therefore, the price of the television set before taxes was $430.

The graphed line of the equation is attached 2x + 3y = -6

A linear equation is an expression that consists of a single power of the variable(s) in which it contains. This formulation can be impeccably illustrated in the following way:

ax + b = 0

The given equation 2x + 3y = -6 can be rearranged to get

y = -2/3x - 2

The x variables is plugged in to solve for y and used for the table of values for the graph

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Answer:

137 yd2

Step-by-step explanation:

The loan have a higher monthly payment Because the lease is riskier to the financing company.

To Determine the costs of buying versus leasing a motor vehicle, we need to consider the total costs associated with each option. For buying, the total cost is the sum of the down payment, loan payments, and the estimated value at the end of the loan, minus the resale value of the car.

On the other hand, for leasing, the total cost can be calculated as the sum of the security deposit, lease payments, and end-of-lease charges. We also need to consider the opportunity cost of investing the down payment and the security deposit.

We know that Melisha can pay for her vehicle with a 4-year loan or with a lease with the same down payment and same interest rate.

Therefore, the loan have a higher monthly payment Because the lease is riskier to the financing company.

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The height of the pyramid formed by the patio heater is 89.07 inches

An equation is an expression that shows how numbers and variables using mathematical operators.

Pythagoras theorem shows the relationship between the sides of a right angled triangle.

To find the height (h) of the pyramid. A right angled is form with base (b) = side of square / 2 = 22.8 / 2 = 11.4 in

Slant height (S) = 89.8 in

Using Pythagoras:

S² = h² + b²

89.8² = h² + 11.4²

h = 89.07 inches

The height of the pyramid is 89.07 inches

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Answer: Directly proportional.

Step-by-step explanation:

      y = -x is directly proportional for a few reasons.

➜ The graph of this equation is a straight line, so all the ratios of points are equal.

➜ The constant of proportionality (k) is equal to -1.

➜ This line intersects the graph at the origin (0, 0).

➜ See the graph below.

The rocket must travel at a rate of 2,200,000 feet per minute to reach escape velocity.

2.2×10^6 feet per minute is in its scientific notation.

In scientific notation, a number is written as the product of a coefficient and a power of 10.

So, 2.2×10^6 is already in scientific notation, where the coefficient is 2.2 and the power of 10 is 6.

If you want to convert it to standard notation, you can multiply the coefficient by the power of 10:

2.2×10^6 = 2.2 x 1,000,000 = 2,200,000

Therefore, the rocket must travel at a rate of 2,200,000 feet per minute to reach escape velocity.

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The value of angle JKN is 73°.

Given that the m ∠JKM = 106 degrees, m ∠LKM = 66, and KN bisects LKM.

So we need to find the value of ∠JKN,

So, using the angles addition postulate,

∠LKM = ∠LKN + ∠MKN

Therefore,

∠LKN = 66/2 [definition of bisector]

∠LKN = 33°

Again, using the angles addition postulate,

∠JKM = ∠JKL + ∠LKM

∠JKL = 106 - 66

∠JKL = 40°

Therefore,

∠JKN = ∠JKL + ∠LKN

∠JKN = 40 + 33

∠JKN = 73°

Hence, the value of angle JKN is 73°.

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Answer:

In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg.

[tex]n = \frac{2}{ \sqrt{3} } = \frac{2 \sqrt{3} }{3} [/tex]

[tex]m = \frac{4 \sqrt{3} }{3} [/tex]

To find the mean time it takes for Diane and her friends to complete the obstacle course, we added up the time taken by each person and divided by the total number of people. The mean time is 13.0 minutes.

Add up the time taken by each person

Diane: 12

Friend 1: 14

Friend 2: 10

Friend 3: 16

Total time = 12 + 14 + 10 + 16 = 52 minutes

Count the total number of people:

Diane and three friends, so the total number of people = 4

Divide the total time by the total number of people to find the mean time

Mean time = Total time / Total number of people

Mean time = 52 / 4

Mean time = 13.0 minutes

Therefore, the mean time it takes for Diane and her three friends to complete the obstacle course is 13.0 minutes.

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--The given question is incomplete, the complete question is given

" Diane is a camp counselor she designs a new obstacle course in testicles with three friends. The plot data shows the time it takes them to complete the obstacle course. What is the mean of time

the plot data for the time taken by each person in minutes is as follows

Diane: 12

Friend 1: 14

Friend 2: 10

Friend 3: 16 "--

Answer:

f(-1) = 16

Step-by-step explanation:

"output" and the f(x) setup just means to plug in -1 in place of x and calculate.

For the function f(x) = 12(3/4)ˣ you have to already know that once you put that -1 in place of x that the -1 power only goes to the 3/4, not the 12 and also what to do with a negative exponent.

Exponent rules are just shortcuts. The shortcut to know here is that the -1 exponent will flip the 3/4 over and make it 4/3 (there are math reasons for this, it's not random. But that's how it works)

So now you have

f(-1) = 12(3/4)⁻¹ which becomes

f(-1) = 12(4/3)

Now you need to know how to multiply with fractions. Here you have a whole, big number times a fraction, which is:

"big num×top all over bottom"

So multiply the 12 times the 4 and put it over the 3

f(-1) = 48/3 = 16

(or you can "cancel" the 12 with the 3 and get 4×4, which is 16, so it comes out the same)

[SKIP TO HERE IF YOU DON'T CARE WHY]

f(x) = 12(3/4)ˣ

f(-1) = 12(3/4)⁻¹

f(-1) = 12(4/3)

f(-1) = 16

Answer:

It's not clear what figure is being referred to. The provided numbers could be dimensions of a shape, but without additional information or context, it's impossible to determine the area of the figure. Can you please provide more details or a diagram?

Step-by-step explanation:

Her next step in obtaining the area of the triangle is replacing the numeric values of h and y into the area formula.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:

A = 0.5bh.

The dimensions for this problem are given as follows:

Hence the formula is:

A = 0.5yh.

Hence the actual values of y and h must be inserted into the formula to obtain the area of the triangle.

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The probability P (X≤2). from the probability distribution is 1/3

A continuous random variable is a type of random variable that can take on any value within a specific range, often an infinite range.

It has a probability distribution function that describes the probability of the variable taking on certain values within that range.

This means that

P (X≤2) =  the f(x) value

From the graph, we have

P (X≤2) = 1/3

Hence, teh value is 1/3

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Answer:

Rounding to the nearest hundredth, the surface area of the regular hexagonal pyramid is approximately 663.2 square centimeters.

Step by Step Explanation:

The surface area of a regular hexagonal pyramid can be calculated using the formula:

Surface area = (1/2) x Perimeter of base x Slant height + Base area

To find the perimeter of the hexagonal base, we can use the formula:

Perimeter of hexagon = 6 x Length of one side

Since the base edge length is 8 centimeters, the length of one side of the hexagon is also 8 centimeters. Therefore, the perimeter of the hexagonal base is:

Perimeter of base = 6 x Length of one side = 6 x 8 = 48 centimeters

To find the base area of the pyramid, we can use the formula:

Base area = (3/2) x (Square root of 3) x (Length of one side)^2

Substituting the values, we get:

Base area = (3/2) x (Square root of 3) x (8)^2 = 96(sqrt(3)) square centimeters

Now we can substitute the values into the surface area formula:

Surface area = (1/2) x Perimeter of base x Slant height + Base area

Surface area = (1/2) x 48 x 15 + 96(sqrt(3))

Surface area = 360 + 96(sqrt(3)) square centimeters

Bob needs to make at least 9 two-point baskets in the second half to break the school record of scoring 30 points in his basketball game.

To break the school record of scoring 30 points, Bob needs to score more than 30 points in his basketball game. Since he scored 13 points in the first half, he needs to score at least 17 points in the second half to break the record.

Let's assume that Bob makes x two-point baskets in the second half. Since each two-point basket contributes 2 points to his score, his total score from two-point baskets would be 2x.

Therefore, to break the school record, we need to solve the following inequality:

2x + 13 > 30

Subtracting 13 from both sides, we get:

2x > 17

Dividing both sides by 2, we get:

x > 8.5

Since Bob cannot make a fractional number of baskets, he needs to make at least 9 two-point baskets in the second half to break the school record.

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The volume of the triangular prism is 36 in³.

A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides.

To calculate the volume of the triangular prism, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

it is a zero dimensional point

Step-by-step explanation:

points are an exact location represented by a dot.

points do not have dimension (length, width, or height)

Answer:

Step-by-step explanation:

(a) Lett be the time (in days) since the start of the experiment, and let

y be the amount of the substance at time t.

Write a formula relating y to t.

Use exact expressions to fill in the missing parts of the formula.

Do not use approximations.

y = ei

Answer: (a) The formula relating the amount of substance, y, to time, t, is given by:

y = y₀ * e^(-λ*t)

where y₀ is the initial amount of the substance, λ is the decay constant, and e is the mathematical constant approximately equal to 2.71828.

The half-life, T½, is related to the decay constant as:

T½ = ln(2)/λ

We are given that the half-life of the substance is 16 days, so we can solve for λ:

λ = ln(2)/T½ = ln(2)/16

Substituting this value of λ in the formula for y, we get:

y = 65.7 * e^(-ln(2)*t/16)

(b) To find the amount of substance present after 13 days, we substitute t = 13 in the formula for y:

y = 65.7 * e^(-ln(2)*13/16) ≈ 42.1

Rounding to the nearest tenth, we get y ≈ 42.1 g. Therefore, approximately 42.1 g of the substance will be present after 13 days.

Step-by-step explanation:

A graph of the reflection of line segment AB is shown on the coordinate plane below.

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.

Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is represented by the following transformation rule:

(x, y)                                    →              (y, x)

Ordered pair A = (4, -1)    →        Ordered pair A' = (-1, 4).

Ordered pair B = (4, 5)    →        Ordered pair B' = (5, 4).

In this exercise, we would use an online graphing calculator to plot the image of line segment AB after a reflection about the line y = x.

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The solution to the equation x + 2(7 - x) = 12 is x = 2.

Given the equation in the question:

x + 2(7 - x ) = 12

To solve the  equation, you need to use algebraic techniques to isolate the variable x on one side of the equation.

x + 2(7 - x) = 12

Apply distributive property

x + 2×7 + 2×-x = 12

x + 14 - 2x = 12

Combine like terms by subtracting 14 from both sides:

x - 2x = 12 - 14

-x = -2

Solve for x by dividing both sides by -1:

-x/-1 = -2/-1

x = 2

Therefore, the value of x is 2.

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The horizontal asymptote is y = 3/2, and the slant asymptote is y = x/2.

We need to compare the degrees of the numerator and denominator.

The degree of the numerator is 2, and the degree of the denominator is also 2. Therefore, the horizontal asymptote is given by the ratio of the leading coefficients, which is 3/2. The horizontal asymptote is y = 3/2

Furthermore, f(x) = 3/2 + x/(2x² - 1)

This expression shows that the function has a slant asymptote given by the line: y = x/2

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