40 points. I need help with this, so I can explain it to my son. Thank you in advance

Answer:9.5

Step-by-step explanation:

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 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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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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Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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Answer: To calculate the distance the beetle walks diagonally across the table, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the two sides of the right triangle formed by the table are 160 cm and 90 cm. Let's call the hypotenuse (the distance the beetle walks) "d."

So, applying the Pythagorean theorem, we have:

d^2 = 160^2 + 90^2

Simplifying:

d^2 = 25600 + 8100

d^2 = 33700

Taking the square root of both sides:

d ≈ √33700

d ≈ 183.54 cm

Therefore, the beetle walks approximately 183.54 cm diagonally across the kitchen table.

The interval containing the middle 95% of the data based on the simulation results is approximately (0.35, 0.65), and the observed proportion of 0.55 falls within this interval, indicating that it is within the margin of error of the simulation results.

To create an interval containing the middle 95% of the data based on the simulation results, we can calculate the lower and upper bounds of the interval.

Let's analyze the simulation results and find the appropriate values.

Out of 200 simulations, we observe that the proportion of students who preferred Candidate A ranges from a minimum of 0.35 (35%) to a maximum of 0.65 (65%).

Since the simulations assume a 50-50 split, we can consider these values as the lower and upper bounds for the middle 95% of the data.

To find the range of the middle 95% of the data, we calculate the difference between the upper and lower bounds.

Upper bound: 0.65

Lower bound: 0.35

Range: 0.65 - 0.35 = 0.30  

To find the interval containing the middle 95% of the data, we divide the range by 2 and add/subtract it from the midpoint.

The midpoint is the average of the upper and lower bounds.

Midpoint: (0.65 + 0.35) / 2 = 0.50

Range / 2: 0.30 / 2 = 0.15

Lower bound of the interval: 0.50 - 0.15 = 0.35

Upper bound of the interval: 0.50 + 0.15 = 0.65

Therefore, the interval containing the middle 95% of the data based on the simulation results is approximately (0.35, 0.65).

Now let's compare the observed proportion from the poll to this interval. The poll indicates that out of a random sample of 80 students, 44 students said they would vote for Candidate A.

To calculate the observed proportion, we divide the number of students who preferred Candidate A (44) by the sample size (80).

Observed proportion: 44/80 = 0.55

The observed proportion of 0.55 is within the margin of error of the simulation results.

It falls within the interval (0.35, 0.65), indicating that the observed proportion is consistent with the simulation and aligns with the assumption of a 50-50 split in the population.

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The graph of the system of inequalities:

y  ≤ (1/4)*x - 2

y  ≥ −(5/4)x +2

Is in the image at the end.

Here we have the system of inequalities:

y  ≤ (1/4)*x - 2

y  ≥ −(5/4)x +2

To graph this, we just need to graph both of the linear equations, and we need to shade the region below the first line (the one with positive slope) and the region above the second line, the one with negative slope.

Then the graph of the system of inequalities is the graph you can see in the image at the end of the answer.

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Answer:23/93.

Step-by-step explanation:

Area of the given heptagon = 364 square unit.

The given figure is regular heptagon,

length of each side = 10

Distance between Centre and edge = 10.4

Since we know that,

A seven-sided polygon with seven angles, seven vertices, and seven edges is known as a heptagon. They may have the same or different length dimensions. It is a closed figure, and a regular heptagon is one with all equal seven sides.

Now,

Perimeter of the given heptagon = 7x10

                                                       = 70

Area of heptagon = perimeter x 10.4/2

                              = 70 x 5.2

                              = 364

Hence,

Area = 364 square unit.

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Answer:

x = 6
JN = 10

Step-by-step explanation:

if the values of SN and SP are the same, so are the corresponding sides next to the right angles.
which means:
if SP = SN, then JK = LM.
Use the reverse version of the function for calculating LM (3x + 2).
-2 * 1/3
Now apply that function to 20.
(20-2)/3
= 18/3
= 6.
x = 6
Now JK is a chord.
and Radius SQ intersects JK at a perpendicular right angle (at point N).
So JN would be half the length of JK.
20/2 = 10.
JN = 10

The equation 6y + y = 5 can be written in a slope-intercept form as y = 5/7.

We have,

To write the equation 6y + y = 5 in slope-intercept form (y = mx + b), we need to simplify the equation and isolate the y variable on one side.

Starting with the equation 6y + y = 5:

Combining the like terms on the left side gives us:

7y = 5

To isolate the y variable, we divide both sides of the equation by 7:

y = 5/7

Now the equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, since the equation only contains the variable y and no x, the slope (m) is not present, and the y-intercept (b) is 5/7.

Therefore,

The equation 6y + y = 5 can be written in a slope-intercept form as y = 5/7.

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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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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:

C. 50 cm²

Step-by-step explanation:

The volume of a triangular pyramid is calculated using the following formula:

Volume = (1/3) * Area of the base * Height

For Question:

length: 5cm

Breadth:5cm

Height : 6 cm

Now,

Volume = ⅓* Area of the base * Height

Volume = ⅓*length*breadth*height

Volume= ⅓*5*5*6=50 cm³

(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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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

Answer:

402.12 or just 402

Answer:

f(x) has the most x intercepts

Area of a polygon formula: = 2(1+[tex]\sqrt{2}[/tex]) side²

To find one side: 96 ÷ 8 = 12

implement formula

≈695.29351

To solve the compound inequality 2y + 3 ≥ -9 or -3y < -15, we'll solve each inequality separately and then combine the solutions.

First, let's solve the first inequality: 2y + 3 ≥ -9.

Subtract 3 from both sides:

2y ≥ -12

Divide both sides by 2 (note that dividing by a positive number does not change the inequality direction):

y ≥ -6

Next, let's solve the second inequality: -3y < -15.

Divide both sides by -3 (remember to reverse the inequality direction when dividing by a negative number):

y > 5

Now, let's combine the solutions. We have y ≥ -6 or y > 5.

In interval notation, we can express the solution as (-∞, -6] ∪ (5, ∞). This means that the solution includes all real numbers less than or equal to -6, as well as all real numbers greater than 5.

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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No, this shape does not belong in a group of shapes that have more than one pair of perpendicular sides.

In order to determine if the shape belongs to a group of shapes with more than one pair of perpendicular sides, we need to examine the number of right angles in the shape.

A right angle is a 90-degree angle, and shapes with perpendicular sides have right angles at their intersections. By counting the number of right angles in the shape, we can determine if it has more than one pair of perpendicular sides.

If the shape has only one right angle, then it does not have more than one pair of perpendicular sides. But if it has two or more right angles, then it would belong to the group of shapes that have more than one pair of perpendicular sides.

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Answer:

The area of the rectangle is 168 ft².

Step-by-step explanation:

Formula: A = lw

where l and w are the length and width of the rectangle respectively.

We're given with the length and the width as

a = 12 ft

b = 14 ft

Let's solve for the area using the formula above.

A = lw

A =  12ft(14ft)

A = 168 ft²

The missing sides of the triangle are

x = 6.32

y = 7.48

z = 11.83

The missing side x is calculated using similar triangles rules as below

x / 10 = 4 / x

cross multiply gives

x² = 40

x = √40 = 6.32

Other sides will solved by Pythagoras theorem.

the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let y be the required distance

y² = 6.32² + 4²

y² = 55.94

y = √55.94

y = 7.48

z² = 6.32² + 10²

z² = 139.94

z = √139.94

z = 11.83

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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 domain for n in the given Geometric sequence is the set of positive integers: {1, 2, 3, 4, 5, ...}.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant value called the common ratio (r).

In the given geometric sequence, the first term (a1) is -9 and the common ratio (r) is 5. Therefore, the sequence can be written as:

-9, -9 * 5, -9 * 5^2, -9 * 5^3, ...

To determine the domain for n, we need to determine the values of n for which the sequence is defined. In a geometric sequence, the term number n represents the position of a term in the sequence.

In this case, the first term corresponds to n = 1, the second term corresponds to n = 2, and so on. The domain for n consists of all the positive integers starting from 1, as the sequence extends indefinitely.

Therefore, the domain for n in the given geometric sequence is the set of positive integers: {1, 2, 3, 4, 5, ...}.

the domain does not include zero or negative values, as these positions in the sequence do not exist. The sequence only starts from the first term (n = 1) and continues indefinitely in the positive integer domain.

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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).