The rectangle is the image after a dilation with the center of dilation at the origin of rectangle ABCD. The pre-image of A' point A, has coordinates of (–4, 3.2). What is the scale factor of the dilation and what are the coordinates of point C?

When a smaller, upside-down cone is placed inside a larger cone, both cones being similar and the vertex of the smaller one being at the center of the base of the larger one, the smaller cone would occupy 1/8 or 12.5% of the volume of the larger cone.

The relationship between the volume of the larger cone and the smaller, upside-down cone placed inside it is represented through the formula for the volume of a cone, which is 1/3 * π * r² * h, where 'r' is the radius of the base and 'h' is the height. If you manage to place the smaller cone such that it has the largest possible volume (which will happen when the smaller cone is similar to the larger cone), the smaller cone will have a height and radius proportionately smaller than the larger one.

Thus, the volumes are proportional to the cube of their corresponding proportions, so the smaller cone will occupy 1/n³ of the volume of the larger cone, where 'n' is the proportion between their linear dimensions. In this particular set-up, the 'n' will equal 2 because when the vertex of the smaller cone is at the center of the base of the larger cone, the smaller cone's height is half that of the larger cone. Hence, the smaller cone will occupy 1/2³ = 1/8 or 12.5% of the volume of the larger cone.

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Final answer:

To find the number of possible outcomes when rolling three eight-sided dice, you multiply the number of outcomes of each die together, resulting in 512 total outcomes.

Explanation:

To determine how many outcomes are possible when rolling three eight-sided dice, we need to calculate the total number of combinations that can occur. Since each die has eight possible outcomes and the dice are rolled simultaneously, the number of outcomes for each die can be multiplied together to find the total number of outcomes for all three dice.

So, the calculation for the total number of outcomes is as follows:

8 (outcomes for die 1) × 8 (outcomes for die 2) × 8 (outcomes for die 3) = 512 total outcomes.

Therefore, there are 512 different possible outcomes when rolling three eight-sided dice.

Answer:

The measure of KL is 12 meters.

Step-by-step explanation:

It is given that  △XYZ∼△DEF.

The corresponding sides of two similar triangles are proportional.

[tex]\frac{YZ}{EF}=\frac{XZ}{DF}[/tex]

[tex]\frac{10}{8}=\frac{15}{DF}[/tex]

[tex]10\times DF=15\times 8[/tex]

Divide both sides by 10.

[tex]DF=\frac{120}{10}[/tex]

[tex]DF=12[/tex]

Therefore we can say that if △XYZ∼△DEF, then the measure of DF is 12 meters.

Answer:

NONE OF THE ABOVE!!

Step-by-step explanation:

A regular polygon is equilateral and equiangular, and also, can be inscribed into a circle. The polygon shown doesn't meet any of these conditions.

Answer:

7/40

Step-by-step explanation:

once again not bothered

The probability she takes out exactly $2.50 is 7/40.

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the given situation,

Number of coins in Kia bag = 10 coins

Number of $1 coins = 3

Number of 50 pence coins = 7

Kia takes at random 3 coins from the bag and the number of ways are

[tex]10C_{3} =\frac{(10)(9)(8)}{(1)(2)(3)}[/tex]

⇒ [tex]10C_{3} =\frac{720}{6}[/tex]

⇒ 120

Kia takes out exactly $2.50

So the combination could be two $1 coins and one 50 pence coins,

⇒ [tex](3C_{2}) (7C_{1} )[/tex]

⇒ [tex](\frac{(3)(2)}{(1)(2)} )(7)[/tex]

⇒ 21

Thus the probability she takes out exactly $2.50 is P(E) = [tex]\frac{21}{120}[/tex]

⇒ 7/40

Hence we can conclude that the probability she takes out exactly $2.50 is 7/40.

Learn more about probability here

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We calculate P to be approximately $7,759.58, which is the amount Ryan invested initially.

To determine the initial investment that Ryan made, which grew to $12,835.94 after 10 years with an annual interest rate of 4.31% compounded monthly, we will use the formula for compound interest:

[tex]A = P(1 + r/n)^{nt}[/tex]

Where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times that interest is compounded per year.

t is the time the money is invested for, in years.

We know that:

A = $12,835.94

r = 4.31/100 = 0.0431

n = 12

t = 10

We need to solve for P:

P = A /[tex](1 + r/n)^{nt}[/tex]

Substituting the known values, we get:

P =[tex]$12,835.94 / (1 + 0.0431/12)^{12*10}[/tex]

P = $12,835.94 / [tex](1 + 0.0035925)^{120}[/tex]

P = $12,835.94 / ([tex]1.0035925)^{120}[/tex]

Calculating the value inside the parenthesis first:

[tex](1.0035925)^{120}[/tex] = 1.654297553

Now, we divide the final amount by this compound factor:

P = $12,835.94 / 1.654297553

P ≈ $7,759.58

Therefore, Ryan's initial investment was approximately $7,759.58.

[tex]Use\ (a-b)(a+b)=a^2-b^2.\\\\(7q-5)(7q+5)=(7q)^2-5^2=\boxed{49q^2-25}[/tex]

Final answer:

The product of the binomials (7q - 5) and (7q + 5) is found using the difference of squares formula, resulting in 49q² - 25.

Explanation:

To find the product of the given expressions (7q - 5)(7q + 5), we can use the difference of squares formula, which states that (a - b)(a + b) = a² - b².

Here, a is 7q and b is 5.

Applying the formula, we get:

This is because the mixed term +7q(-5) and the term -7q(+5) cancel each other out, leaving us with just the square terms.

The correct answer is  [tex]D = 23[/tex]

To solve this problem , let's define the given information:

Let [tex]T[/tex] be the total number of kids at the summer camp:

[tex]T = 150[/tex]

Let [tex]A[/tex] be the number of kids who chose archery for their morning activity:

[tex]\frac{A}{T} = \frac{3}{5}[/tex]

Let [tex]D[/tex] be the number of kids from the archery group who also chose drama in the afternoons:

[tex]\frac{D}{A} = \frac{1}{4}[/tex]

We want to find the value of [tex]D[/tex], which represents the number of kids who chose both archery in the morning and drama in the afternoons.

We can set up the following equations:

[tex]\frac{A}{T} &= \frac{3}{5}[/tex]

[tex]A &= \frac{3}{5}T[/tex]

[tex]A &= \frac{3}{5}(150)[/tex]

[tex]A &= 90[/tex]

[tex]\frac{D}{A} &= \frac{1}{4}[/tex]

[tex]D &= \frac{1}{4}A[/tex]

[tex]D &= \frac{1}{4}(90)[/tex]

[tex]D &= 22.5[/tex]

Therefore, the number of kids who chose both archery in the morning and drama in the afternoons is [tex]22.5 or 23[/tex] (since we cannot have a fractional number of kids).

[tex]D = 23[/tex]

Factor out the common numbers/variables from the terms given

4 is a common number

4m + 4p

4(m + p) is your answer

hope this helps

Answer:

0

if you were confused to the one on top

Answer:

its C

Step-by-step explanation:

(x, y) → (x + 8, y – 3)

Final answer:

To find the circle's equation from its diameter's endpoints, calculate the circle's center using the midpoint formula, then determine the radius with the distance formula. Finally, use these values in the circle's standard equation.

Explanation:

To find the equation of the circle, we first need to determine its center and radius. The midpoint of the diameter will give us the center of the circle, and the distance from one of the endpoints to the midpoint will give us the radius.

Step 1: Find the Center of the Circle

The midpoint formula ((x1 + x2)/2, (y1 + y2)/2) gives us the center of the circle. Applying this to our points (7, -7) and (5, -3):

Center = ((7 + 5) / 2, (-7 - 3) / 2) = (6, -5)

Step 2: Calculate the Radius

We use the distance formula, √((x2 - x1)² + (y2 - y1)²), between one of the endpoints and the center:

Radius = √((7 - 6)² + (-7 + 5)²) = √(1 + 4) = √5

Step 3: Write the Equation

Using the standard equation, (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius:

Equation: (x - 6)² + (y + 5)² = 5

This equation gives the precise location and size of the circle based on its diameter's endpoints.

To choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet with 10 different kinds of ice cream and 6 kinds of toppings, you can use the concept of combinations. The total number of ways to choose is 1800.

To determine the number of ways to choose 3 kinds of ice cream and 2 kinds of toppings from the dessert buffet, we can use the concept of combinations. We have 10 different kinds of ice cream to choose from, and we want to choose 3 of them. The number of combinations can be calculated using the formula:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of objects (10 ice cream flavors) and r is the number of objects to be chosen (3 ice cream flavors), and ! denotes factorial.

In this case, the number of combinations of ice cream flavors is:

C(10, 3) = 10! / (3!(10-3)!) = 120

Similarly, we have 6 different kinds of toppings to choose from, and we want to choose 2 of them. The number of combinations of toppings is:

C(6, 2) = 6! / (2!(6-2)!) = 15

Therefore, the total number of ways to choose 3 kinds of ice cream and 2 kinds of toppings is the product of the number of combinations of ice cream flavors and toppings:

Total number of ways = 120 * 15 = 1800

Answer:

got it right and was option A     thx

Step-by-step explanation:

Final answer:

To find the center of a wooden wheel for a toy car, use a carpenter's square to draw two perpendicular diameters across the wheel; their intersection is the center where the axle hole should be drilled.

Explanation:

To find the center of a wooden wheel using a carpenter's square, which is used to draw right angles, follow these steps:

This method effectively divides the wooden wheel into four equal quadrants, and the intersection point of the diameters marks the center, where the axle hole should be drilled.

∠V is calculated to be 70°.

When two triangles are similar (QRS ~ TUV), their corresponding angles are equal. This means:

Given ∠R = 47° and ∠Q = 63°, we know that ∠T = 63° and ∠U = 47°.

Since the sum of the angles in any triangle is 180°:

∠Q + ∠R + ∠S = 180°

Substituting the known values:

63° + 47° + ∠S = 180°

Solving for ∠S:

∠S = 180° - 63° - 47° = 70°

Therefore, ∠V = 70° because ∠S corresponds to ∠V in the similar triangles.

Complete question: Triangle QRS is similar to triangle TUV. ∠R=47°, ∠Q=63°. What is the measure of angle V?

The number of distinct ways the letters in TALLAHASSEE can be arranged is calculated using permutations with repetitions. It involves taking the factorial of the total number of letters and dividing by the factorial of the number of times each letter repeats.

To determine the number of distinct ways the letters in TALLAHASSEE can be arranged, we must consider it as a permutation problem with repeating elements. We need to calculate the factorial of the total number of letters and then divide by the factorial of the number of times each individual letter repeats.

The word TALLAHASSEE contains 11 letters in total:

The permutation formula considering repetitions is:

Number of arrangements = Total letters factorial / (Product of each letter's factorial)

Therefore:

Number of arrangements = 11! / (2! * 2! * 2! * 2!)

This would give us the total number of distinct arrangements of the letters in TALLAHASSEE.