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This scale drawing shows a reduction in a figure.

What is the value of x?

Enter your answer as a decimal in the box.

X =

The pair of figures are similar because:

• Both figures are parallelograms

• All sides are congruent.

• Scale factor 1: 2.5

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The pair of figures are similar because:

• Both figures are parallelograms

• All sides are congruent

• Angles W and Y are congruent with angles P and R

• Angles X and Z are congruent with angles S and Q

• Scale factor 1 : 2.5

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The new height above sea level would be Option (C) 3980m.

New sea-level = Previously given sea level + 20m

Given,

Height above sea previously = 4000m

Increase in sea level = 20m

Now, since there has been a rise in sea level due to global warming the distance between the previous 4000m mark and the sea level would decrease. This shall now be less than 4000m. The distance/height would reduce by 20m. It can also be observed that the distances below the sea level would increase due to a rise in the sea level mark.

∴ New height above sea level = 4000m - 20m

                                                 = 3980m.

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Answer: What is the probability that the ethical hacker will guess the pin code correctly on the first try?

Since the pin code consists of 10 possible digits (0 through 9), the probability of guessing the correct pin code on the first try is 1 in 10. This is because there is only one correct pin code out of the 10 possible options.

Therefore, the probability is 1/10 or 0.1 (or 10%).

Calculating the probability for each of the four situations:

(a) All four digits are unique (e.g., 1234):

In this case, there are 10 options for the first digit, 9 options for the second digit (since it can't be the same as the first), 8 options for the third digit, and 7 options for the fourth digit. The total number of possible combinations is given by:

10 × 9 × 8 × 7 = 5040

So, there are 5040 possible four-digit combinations when all digits are unique.

The probability of guessing the correct pin code on the first try in this situation is 1 in 5040, or 1/5040.

(b) Exactly one of the digits appears twice (e.g., 2334, 8185):

In this case, we have two scenarios to consider:

Scenario 1: The repeated digit is the first digit:

The first digit can be chosen in 10 ways, the second digit (repeated) can be chosen in 9 ways, and the remaining two distinct digits can be chosen in 8 and 7 ways, respectively. So, the total number of possible combinations is:

10 × 9 × 8 × 7 = 5040

Scenario 2: The repeated digit is not the first digit:

The first digit can be chosen in 9 ways (excluding the repeated digit), the repeated digit can be chosen in 10 ways, and the remaining two distinct digits can be chosen in 8 and 7 ways, respectively. So, the total number of possible combinations is:

9 × 10 × 8 × 7 = 5040

Combining both scenarios, we get a total of 2 × 5040 = 10080 possible combinations when exactly one of the digits appears twice.

The probability of guessing the correct pin code on the first try in this situation is 1 in 10080, or 1/10080.

(c) Two digits each appear twice (e.g., 1212, 8855):

In this case, there are two scenarios to consider:

Scenario 1: The two pairs of digits are different:

The first pair of digits can be chosen in 10 ways, the second pair of digits can be chosen in 9 ways, and the order of the pairs can be switched. So, the total number of possible combinations is:

10 × 9 × 2 = 180

Scenario 2: The two pairs of digits are the same:

The pair of digits can be chosen in 10 ways, and the order of the digits can be switched. So, the total number of possible combinations is:

10 × 1 = 10

Combining both scenarios, we get a total of 180 + 10 = 190 possible combinations when two digits each appear twice.

The probability of guessing the correct pin code on the first try in this situation is 1 in 190, or 1/190.

(d) One digit appears three times (e.g., 2226, 8188):

In this case, there are two scenarios to consider:

Scenario 1: The repeated digit is the first digit:

The first digit can be chosen in 10 ways, and the remaining two distinct digits can be chosen in 9 and 8 ways, respectively. So, the total number of possible combinations is:

10 × 9 × 8 = 720

Scenario 2: The repeated digit is not the first digit:

The first digit can be chosen in 9 ways (excluding the repeated digit), and the repeated digit can be chosen in 10 ways. The remaining distinct digit can be chosen in 8 ways. So, the total number of possible combinations is:

9 × 10 × 8 = 720

Combining both scenarios, we get a total of 2 × 720 = 1440 possible combinations when one digit appears three times.

The probability of guessing the correct pin code on the first try in this situation is 1 in 1440, or 1/1440.

To summarize, the probabilities for each of the four situations are:

(a) All four digits are unique: 1/5040

(b) Exactly one of the digits appears twice: 1/10080

(c) Two digits each appear twice: 1/190

(d) One digit appears three times: 1/1440

Based on the information given about the geometry, the value of CF will b A. 6cm.

Since OE and OF are both 4 cm, then OEF is an equilateral triangle. This means that EOF is 60 degrees.

Since AB is 12 cm, then AB is twice the length of OE. This means that ABE is a 30-60-90 triangle.

In a 30-60-90 triangle, the hypotenuse is twice the length of the side opposite the 30 degree angle. This means that CF is 6 cm.

In conclusion, the correct option is A.

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According to the synthetic division below, the true statements are as follows:

B. The number 4 is a root of F(x) = 3x2-13x+4.

D. (3x2 - 13x+4) - (x - 4) = (3x - 1)

F. (x-4) is a factor of 3x2.13x+ 4.​

Synthetic divisions are the manual ways of bypassing long divisions while performing the Euclidean dividion of polynomials. For the given expressions, we can determine the true statements in this way:

1. F(x) = 3x² - 13x +4.

(x-4) (3x-1)

So, x = 4 or 1/3

4 is an actual root of the function.

2. (3x² - 13x + 4) ÷ (x - 4) = (3x - 1)

3. 3x² - 13x + 4 = (x-4) (3x-1)

So, since all these expressions are true, they meet the requirements for the synthetic division.

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Complete Question:

According to the synthetic division below, which of the following statements are true? Check all that apply. 4 4)3 -13 12 3 0 O A. The number -4 is a root of F(x) = 3x2.13x + 4. B. The number 4 is a root of F(x) = 3x2-13x+4. O C. (3x2 - 13x + 4) - (x + 4) = (3x - 1) D. (3x2 - 13x+4) - (x - 4) = (3x - 1) O E. (x + 4) is a factor of 3x2 - 13x + 4. IF (x-4) is a factor of 3x2.13x+ 4.​

The surface area of a square pyramid attached is

40 square units

The surface area of a square pyramid is solved using the formula

= a² + 2 * a * l

where

a = side of the square

l = slant height

In the problem

a = 4

l = 3

plugging in the values

surface area of a square pyramid = 4² + 2 * 4 * 3

surface area of a square pyramid = 16 + 24

surface area of a square pyramid = 40 square units

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To find the other two numbers in the set, we need to determine the missing numbers that satisfy the given conditions.

The mode of a set of numbers is the value(s) that appear(s) most frequently. In this case, the mode is given as 19, which means that 19 appears more times than any other number in the set.

The mean of a set of numbers is calculated by summing all the numbers and dividing by the total count. In this case, the mean is given as 20.

Given that the seven numbers provided are 16, 17, 19, 19, 21, 21, and 25, we can calculate the sum of these numbers:

16 + 17 + 19 + 19 + 21 + 21 + 25 = 138

To find the sum of all nine numbers in the set, we can use the mean formula:

Mean = (Sum of all numbers) / (Total count)

20 = (138 + x + y) / 9

Simplifying the equation, we have:

180 = 138 + x + y

x + y = 42

Now, since the mode is 19, we know that either x or y (or both) must be 19. Since the mode appears twice, we can assign 19 to both x and y:

x = 19

y = 19

Therefore, the other two numbers in the set are both 19.

a) We can factor out a common factor of two from the denominator and a half from the numerator: (6p - 7q)/(12p - 14q) = (3p - 7q/2)/(6p - 7q)

b) The numerator and denominator can be factored to provide a common factor of2x²: (6x⁵ - 8x²)/(2x) = 2x³ - 4

c) A common factor of 5 may be extracted from the numerator: (10a + 15b)/5 = 2a + 3b

d) By grouping factors, we may factor the numerator: p² - 6q + 8/3p - 6 = [(p² - 6q) + 8]/[3(p - 2)] = (p - 2)(p - 4)/(p - 2) = p - 4 (where p ≠ 2)

Factorising is the process of employing brackets to represent an expression as the product of its components. We do this by eliminating any elements that are shared by all of the expression's terms. Maths. Algebra. We must eliminate any factors that are shared by each word in an expression before we can factorize it. Expanding brackets is the process's reverse.

Finding an expression's highest common factor (HCF), or the largest number or letter that each term can be split by, is necessary to ensure that it has been properly factorized. Otherwise, there will still be common factors inside the bracket, preventing the expression from being properly factorized.

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Explanation:

The horizontal component is found using cos fxn

80 x cos 20 =  75.2 pounds

The volume of the given figure is 750 in.

Given

Base =30in

Height = 8in

Side = 15

Side = 17

Required to calculate the volume of the given figure

Volume = Base x Height + 2 side x side (there are two rectangle)

             = 30 x 8 + 2 x 15 x 17

              = 750

The region that a 2D shape covers in an area versus the space a 3D shape occupies is the main distinction between area and volume. Geometry is filled with a wide variety of shapes and sizes.

A mass is a solid body or an assortment of distinguishable visual components that together make a solid form, such as lines, colors, textures, etc. Length, width, and depth make up the three dimensions of volume.

Thus, the volume of the given figure is 750.

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Using the compound interest formula,  the interest after one month is $1300

The compound interest formula is given by A = P(1 + r)ⁿ where

Now, since y borrow $25,000 at an interest rate of 5.2% compounded monthly and your monthly payment is $231.49. To find  the interest accrued in the first month, we proceed as follows.

So, in the compound interest formula, we have that

So, to find the amount after one month, we substitute the values of the variables into the equation. So, we have that

A = P(1 + r)ⁿ

A = 25000(1 + 0.052)¹

A = 25000(1.052)

A = 26300

So, the interest after one month is I = A - P

= $26300 - $25,000

= $ 1300

So, the interest is $1300

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Answer:

Answers following the rounding instructions:  see below for details

BC = 5.1

m∠B = 23°

m∠V = 116°

Step-by-step explanation:

Givens:

AC = 3

AB = 7

m∠A = 41°

Unknowns:

BC = ?

m∠B = ?

m∠C = ?

Find side BC using the law of cosines:  c² = a² + b² - 2ab cos(C)

a² = 3² + 7² - 2(3)(7)(cos41)

a = √9 + 49 - 42(cos41)

a = 5.128 ≈ 5.13

side BC = 5.13

Use the law of sines to find m∠B:  sin(A) / a = sin(B) / b = sin(C) / c

m∠B = sin⁻¹[sin41/5.13 x 3] = sin⁻¹(0.3837) = 22.56 ≈ 22.6°

Sum of interior angles of a triangle is 180, so now you can find m∠C:

m∠C = 180 - 22.6 - 41 = 116.44 ≈ 116.4°

Rounding side BC to nearest tenth: BC = 5.1

Rounding angles to nearest whole degree:

m∠B = 23°

m∠V = 116°

Answer:

x=12.124

simplified would be x=12

Step-by-step explanation:

Answer:

52750

Step-by-step explanation:

Step 1:  Identify the digit in the tens place:

Step 2:  Examine the digit to the right of the tens place:

Step 3:  Determine the rounding:

Since the digit to the right of the tens place is 4 (which is less than 5), we keep the tens place digit as is.

Original number: 52754.1683

Rounding to the nearest ten: 52750

Thus, rounding 52754.1683 to the nearest ten gives us 52750.

Step-by-step explanation:

B^2+8b+7 is a quadratic expression. It can be factored as (b+7)(b+1).

To factor a quadratic expression, you can use the following steps:

1. Find two numbers that add up to the coefficient of the middle term (8) and multiply to the constant term (7).

2. Write the quadratic expression as a product of two binomials, with the two numbers you found in step 1 as the coefficients of the terms in each binomial.

In this case, the two numbers that add up to 8 and multiply to 7 are 7 and 1. So, we can factor B^2+8b+7 as follows:

(b+7)(b+1)

This means that B^2+8b+7 is equal to the product of (b+7) and (b+1).

Here is a step-by-step explanation of how to factor B^2+8b+7:

1. The coefficient of the middle term is 8.

2. The constant term is 7.

3. The two numbers that add up to 8 and multiply to 7 are 7 and 1.

4. Therefore, B^2+8b+7 can be factored as (b+7)(b+1).

Answer:

I am confident the answer is H.

The two other positive angles of rotation that take A to B are 19π/6 and 31π/6.

The unit circle is rotationally symmetric, meaning that any angle of rotation on the unit circle will take a point to another point on the unit circle with the same distance from the origin. This means that if we rotate point A by 7π/6 radians, we can also rotate it by 19π/6 or 31π/6 radians and end up at the same point B.

The point A has polar coordinates (1, 0). This means that it is located at a distance of 1 unit from the origin and has an angle of 0 radians with the positive x-axis.

The point B has polar coordinates (√3/2, 1/2). This means that it is located at a distance of √3/2 units from the origin and has an angle of 7π/6 radians with the positive x-axis.

If we rotate point A by 19π/6 radians, we get a point with polar coordinates (√3/2, -1/2). This point is located at the same distance from the origin as point B and has the same angle with the positive x-axis.

Therefore, the two other positive angles of rotation that take A to B are 19π/6 and 31π/6.

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The best representation of the number of tiles that will be needed to cover the Floor is 80 tiles.

The number of tiles needed to cover the floor, we can calculate the total area of the floor and divide it by the area of each tile.

The area of the floor is given by the product of its length and width: 15 feet * 12 feet = 180 square feet.

The area of each tile is given by the product of its length and width: 1.5 feet * 1.5 feet = 2.25 square feet.

To find the number of tiles needed, we divide the total area of the floor by the area of each tile:

Number of tiles = (Total area of the floor) / (Area of each tile) = 180 square feet / 2.25 square feet = 80 tiles.

therefore, the best representation of the number of tiles that will be needed to cover the floor is 80 tiles.

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Answer:

domain= [-5,5]

range= [-3,3]

Step-by-step explanation:

the domain is with the x axis you have to look for the farthest x axis which would be - 5 in this case and the closest axis which is 5 so the x can be anywhere between - 5 and 5

then for the range is with the y axis you would look for the farthest y axis which is - 3 and the closes which is 3 so the y can be anywhere in between - 3 and 3

The quadratic equation in standard form that corresponds to the graph shown above is f(x) = x² + 2x - 8

In Mathematics and Geometry, the standard form of a quadratic function can be modeled and represented by using the following mathematical expression;

y = ax² + bx + c

Where:

In this scenario and exercise, we would write a quadratic function that represent f(x) in standard form and with a leading coefficient of 1 by using the roots (-4, 0) and (2, 0) as follows;

f(x) = (x + 4)(x - 2)

f(x) = x² - 2x + 4x - 8

f(x) = x² + 2x - 8

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Answer:

the volume of the square pyramid is 2430 cubic cm

Answer:

1296 cm³

Step-by-step explanation:

V = a² x [√s²- (a/2)²] / 3

a = 18 cm

s = 15 cm

V = 18² x [√15²-(18/2)²] / 3 = 18² x [√225-81] / 3

V = 324 x (√144/3) = 1296 cm³

The angles of the triangle are ordered as follows:

<B, <C and <A.

We consider a triangle with side lengths and angles related as follows:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

By the law of sines, we have that the greater angle measures are opposite to the greater side lengths.

Hence the angle measures for this problem are ordered as follows:

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The angles of triangle ABC is arranged below

angle b - smallest

angle c

angle a - largest

To determine the angles of triangle ABC in order from smallest to largest, we can use use the knowledge that the side with higest length will face the largest angle.

Let the angles be

angle c is opposite AB = 12

angle b is opposite AC = 11

angle a is opposite BC = 19

Using the knowledge as introduced we have that

angle a > angle c > angle b

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Check the picture below.

The required acceleration is 0.0666 [tex]m^{2}[/tex]/s.

Given that the velocity of the object is 2m/s and time is 30s.

Acceleration is the rate of change of velocity with respect to time.

To find the acceleration by using the  formula.

acceleration (a) = velocity (v) / time (t).

By using data and formula gives,

acceleration (a) = velocity (v) / time (t).

acceleration (a) = 2 / 30

acceleration (a) = 0.0666 [tex]m^{2}[/tex]/s.

Hence, the required acceleration is 0.0666 [tex]m^{2}[/tex]/s.

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(a) The area of the office is 53.55 meters square.

(b) The area of the Carpet would be 52.6656 meters square.

(c) The area of the surrounding is 0.8844 meters square.

Area of the office floor= Length × Breadth

                                     = 8.5 meters × 6.3 meters

                                     = 53.55 meters square

Area of the Carpet = Length × Breadth

                               = (8.5-0.06) meters × (6.3-0.06) meters

Since, 60 cm = 0.06 meters

Because 1 meter = 100 cm

                                = 52.6656 meters square

Area of surrounding = Area of Office floor - Area of Carpet

                                  = 53.55 meters square - 52.6656 meters square

                                  = 0.8844 meters square

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The room’s area, in square inches is,

⇒ A = 144LW square inches.

We have to given that,

A rectangular room is tiled with tiles 12 inches long and 12 inches wide.

And, The room is L tiles long and W tiles wide.

Hence, Lenght of L tiles,

= 12L

And, Length of W tiles,

= 12W

Since, We know that,

Area of rectangle is,

⇒ A = Length x width

Substitute given values, we get;

⇒ A = 12L x 12W

⇒ A = 144LW square inches.

Therefore, The room’s area, in square inches is,

⇒ A = 144LW square inches.

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The outcomes that are in the sample space are red, blue, green, red, blue, and blue.

From the question, we have the following parameters that can be used in our computation:

Spinner = 6 sections

This means that

The spinner has 6 sections and as such, the sample size of the spinner is 6

The sample space are the colors in the spinner

So, we have

Space = red, blue, green, red, blue, and blue.

Hence, the outcomes that are in the sample space are red, blue, green, red, blue, and blue.

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All the values of expressions are,

24. Sin x = 1/√17

25 cos x = 4/√17

26 tan x = 1/4

27. Sin y = 4/√17

28. Cos y = 1/√17

29. Tan y = 4

We have to given that,

A right triangle is shown in figure.

Now, We can simplify all the values,

24. Sin x = Opposite / Hypotenuse

sin x = 2 / 2√17

sin x = 1/√17

25) cos x = Base / Hypotenuse

cos x = 8 / 2√17

cos x = 4/√17

26) tan x = Opposite / Base

tan x = 2 / 8

tan x = 1/4

27. Sin y = Opposite / Hypotenuse

sin y = 8 / 2√17

sin y = 4/√17

28. Cos y = Base / Hypotenuse

cos y = 2 / 2√17

cos y = 1/√17

29. Tan y = Opposite / Base

tan y = 8 / 2

tan y = 4

Thus, All the values of expressions are,

24. Sin x = 1/√17

25. cos x = 4/√17

26. tan x = 1/4

27. Sin y = 4/√17

28. Cos y = 1/√17

29. Tan y = 4

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