What is the prime factorization of 20?
2 x 10 22 x 5 5 x 8 22 x 4

Answer:

The ramp must cover a horizontal distance of approximately 19.081 feet.

Step-by-step explanation:

Given the vertical distance (\(y\)), measured in feet, and the angle of the wheelchair ramp (\(\theta\)), measured in sexagesimal degrees. The horizontal distance needed for the ramp (\(x\)), measured in feet, is estimated by the following trigonometrical expression:

\(x = \frac{y}{\tan \theta}\) (1)

If we know that \(y = 1\,ft\) and \(\theta = 3^{\circ}\), then the horizontal distance covered by this ramp is:

\(x = \frac{1\,ft}{\tan 3^{\circ}}\)

\(x \approx 19.081\,ft\)

The ramp must cover a horizontal distance of approximately 19.081 feet.

Answer: 1. Not a right triangle 2. Right Triangle 3. Right triangle 4. Right triangle 5. Not a right triangle

Step-by-step explanation:

the right triangle has to have a pattern to go by, so only evens or only odd sides.

Answer:

1/12

Step-by-step explanation:

The probability that on any particular morning during the month at least one of the cars starts is 13/15, and for part (b) is 2/15.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

Mr. and Mrs. Spark have had poblems starting their two cars during the cold winter months.

P(first car starts) = 20/30 = 2/3

P(second car starts) = 18/30 = 3/5

P(both start)=2/5

a) at least one of the cars starts:

P(at least one starts)=1-P(none starts)

=1-(1/3)(2/5)=1-2/15=13/15

b) he cannot start either of his two cars:

P(neither starts)= (1/3)(2/5) = 2/15

Thus, the probability that on any particular morning during the month at least one of the cars starts is 13/15, and for part (b) is 2/15.

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The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\)

Option D is the correct answer.

We have,

In this equation, the variable x represents the number of times the square is cut in half, and y represents the surface area of the square.

As x increases, the exponent of 1/2 decreases, causing the value of y to decrease.

This exponential decay accurately represents the idea that the surface area becomes less and less but never reaches zero units²

Thus,

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\).

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The correct equation that would help model the surface area of a square piece of paper as it is repeatedly cut in half is:  \(\(y=36(\frac{1}{2})^x\)\)

As the square is cut in half, the side length of the square is divided by 2, resulting in the area being divided by \(\(2^2 = 4\)\).

Therefore, the equation \(y=36(\frac{1}{2})^x\)\)accurately represents the decreasing surface area of the square as it is repeatedly cut in half.

and, \(\(y=x^2+4x-16\)\)is a quadratic equation that does not represent the decreasing nature of the surface area.

and, \(\(y=-25x^2\)\) is a quadratic equation with a negative coefficient.

and, \(\(y=9(2)^x\)\)represents exponential growth rather than the decreasing nature of the surface area when the square is cut in half.

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According to the division property of equality, if both sides of an equation are divided by a common real integer that is not zero, the quotients remain equal.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

The four key terminology used in the division process are dividend, divisor, quotient and remainder. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

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b.) Given:

To determine whether the pair of the equations parallel perpendicular or neither:

Let us write it in slope intercept form,

The slopes are,

Since,

Hence, the lines are neither parallel nor perpendicular.

So, the answer is neither.

A. The area decreases by a factor of about 0.6565 after 10 years. B. The area decreases by a factor of about 0.0197 each month.

A. To find the factor by which the area decreases after 10 years, we need to compare the initial area (at t=0) to the area after 10 years (at t=10). We can use the formula for A(t) to calculate these values:

A(0) = 11 square kilometers (initial area)

A(10) = 11 ×(0.98)¹⁰ ≈ 7.22 square kilometers (area after 10 years)

The factor by which the area decreases after 10 years is the ratio of A(10) to A(0):

A(10) / A(0) ≈ 7.22 / 11 ≈ 0.6565

So the area decreases by a factor of about 0.6565 after 10 years.

B. To find the factor by which the area decreases each month, we need to first find the annual rate of decrease, and then convert it to a monthly rate. We know that the area decreases by 2 percent each year, so the annual rate of decrease is 0.02. To find the monthly rate of decrease, we can use the formula:

r = (1 + i)^(1/n) - 1

where:

r is the monthly rate of decrease

i is the annual rate of decrease (0.02 in this case)

n is the number of months in a year (12)

Plugging in the values, we get:

r = (1 + 0.02)^(1/12) - 1 ≈ 0.00165

So the area decreases by a factor of approximately:

(1 - r)¹² ≈ (1 - 0.00165)¹² ≈ 0.0197 each month. Therefore, the area decreases by a factor of about 0.0197 each month.

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Answer:

12

Step-by-step explanation:

its just how it is

First, let us calculate the forecast for week 7. The naïve method (most recent value) is used to make the forecast. The most recent value is 15, so the forecast for the next week, which is week 7, is 15.

Using the naïve method as the forecast for the next week, the following measures of forecast accuracy are calculated.The given data is as follows:

Week 1 2 3 4 5 6Value 19 13 16 10 18 15.

Now we will calculate the Mean absolute error:

Mae = (19-13)+(13-16)+(16-10)+(10-18)+(18-15) / 5=6+3+6+8+3 / 5=6.4.

Therefore, the Mean absolute error is 6.4.

Mean squared error can be calculated as follows:

Mse = [(19-13)²+(13-16)²+(16-10)²+(10-18)²+(18-15)²] / 5=196 / 5=39.2.

Therefore, the Mean squared error is 39.2.

Now let us calculate Mean absolute percentage error:

Map = [ (6/19) + (3/13) + (6/16) + (8/10) + (3/18) ] / 5= 0.962.

Therefore, the Mean absolute percentage error is 0.96.

The forecast for week 7 is 15. Mean absolute error is 6.4. Mean squared error is 39.2. Mean absolute percentage error is 0.96.

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Answer:

B. 16

Step-by-step explanation:

A. 4

B. 16

C. 36

D.64

Answer:

A. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.

Step-by-step explanation:

The required list that consists of the factor of 24 is 1, 2, 3, 4, 6, 8, 12, 24 Option C is correct.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

Here,
Given number is 24,
The factor of 24 is given as that number that can divides by 24 and able to give a whole number,
24 = 1, 2, 3, 4, 6, 8, 12, 24.

Thus, the required list that consists of the factor of 24 is 1, 2, 3, 4, 6, 8, 12, 24 Option C is correct.

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The set A ∩ B = {3}

The intersection of sets, denoted as A ∩ B, refers to the set that contains elements that are common to both sets A and B. In this case, set A consists of the elements {1, 2, 3, 6}, and set B consists of the elements {3, 4, 5}.

The intersection of A and B, written as A ∩ B, represents the set of elements that appear in both sets simultaneously.

To find the intersection of sets A and B, we examine each element of set A and check if it is also present in set B. In this case, the element 3 is the only element that exists in both sets.

Therefore, the intersection of sets A and B is {3}.

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Answer: See explanation

Step-by-step explanation:

Amount earned by movie = $3,000,000.

Percentage that went to movie = 60%

Percentage that went to theater = 40%

Revenue gotten by movie studio = 60% × $3,000,000

= 0.6 × $3,000,000

= $1,800,000

Revenue gotten by theaters = 40% × $3,000,000

= 0.4 × $3,000,000

= $1,200,000

The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.

The mean absolute deviation (MAD) measures the average distance between each data point and the mean of the dataset. To find the MAD, you need to follow these steps:

1. Calculate the mean of the dataset by adding up all the numbers and dividing the sum by the total number of data points. In this case, the dataset consists of the following numbers: 3, 6, 3.8, 3.2, and 3.4. Adding them up gives us a sum of 19.4. Dividing this sum by 5 (since there are 5 data points) gives us a mean of 3.88.

2. Find the absolute deviation for each data point by subtracting the mean from each data point and taking the absolute value. For example, for the first data point, 3, the absolute deviation would be |3 - 3.88| = 0.88. Repeat this step for all the data points.

3. Calculate the mean of the absolute deviations by adding up all the absolute deviations and dividing the sum by the total number of data points. In this case, the absolute deviations are: 0.88, 2.12, 0.72, 0.68, and 0.58. Adding them up gives us a sum of 4.98. Dividing this sum by 5 gives us a mean of 0.996.

So, the mean absolute deviation for the given dataset is approximately 0.996.


The mean absolute deviation helps us understand how much each data point varies from the mean of the dataset. By calculating the absolute deviation for each data point and finding the average, we can determine the typical amount of variation in the dataset.


The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.

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Usando proporciones, hay que el auto puede viajar 30 km.

Una proporción es una fracción de la cantidad total, y puede ser encontrada por intermedio de una regla de tres.

En este problema, la regla de tres es dada por:

12 litros - 90 km

4 litros - x km

Aplicando multiplicación cruzada:

\(12x = 360\)

\(x = 30\)

El auto puede viajar 30 km.

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Answer:

\(a_{n}\) = 2n - 3

Step-by-step explanation:

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

given a₁ = - 1 and a₅ = 7 , then

a₁ + 4d = 7 , that is

- 1 + 4d = 7 ( add 1 to both sides )

4d = 8 ( divide both sides by 4 )

d = 2

then

\(a_{n}\) = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

\(a_{n}\) = 2n - 3

Answer:

both angles = 46

Step-by-step explanation:

when two parallel lines are cut by a transversal all the obtuse angles are equal and all the acute angles are equal and the sum of one obtuse angle and one acute angle = 180

angle 5 is an obtuse angle and equals 134

all the acute angles equals 180-134=46

angles 2 and 4 are acute and equals 46

variety of statistics for 1057 inernet users are  = (0.9180, 0.8998)  solve by given question .

population proportion is the share of a population that belongs to a particular category. Confidence intervals are used to estimate population proportions.

Let p be the population proportion of respondents who say the Internet has been a good thing for them personally.

=p +- z*\(\sqrt{p*(1-p)/n}\)

where z* = Critical value p = Sample proportion,n = sample size.

As per given , we have

n= 1057 By z-table , Critical value for 95% confidence interval : z*= 1.96

Then, the 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. will be :

=p +- z*\(\sqrt{p*(1-p)/n}\)

=0.9+-1.96\(\sqrt{.9*(1-.9)/1057}\)

=0.9180, .8998

Hence, the required 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally = (=0.918, .881)

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Answer:0.5

Step-by-step explanation:

60➗12

Probability of an event is the measure of its chance of occurrence. The experimental probability of Janice rolling the number four is 0.2

Experimental probability calculates the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event

\(P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}\)

where, \(P_e(E)\) is denoting experimental probability of occurrence of E.

For this case, we're specified that:

The event in consideration is "Rolling the number 4"

The times she rolled the number 4 is: 12

She got four 12 times in 60 rolls of the considered cube.

Thus, we have:

Thus, we get:

\(P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}} = \dfrac{12}{60} = \dfrac{1}{5} = 0.2\)

Thus, the experimental probability of Janice rolling the number four is 0.2

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Answer:

Read below for each answer! (^-^)

Step-by-step explanation:

1: You got the first one right. The explanation does explain why but think about 0 as the surface of the water to better understand.

2: -3; it is between 2 and 4 with only one line through it meaning that it is -3.

3: 7. That's the greatest number both can divide into it.

4: The last one. Any positive number is greater than a negative one and peanut butter's freezing point is positive while the other one's is not.

5: You got it right again! -(-1) has two negatives. Two negatives (mostly) make a positive. So positive 1! Now describe that on a number line.

Hope this helps!

The probability of a student doing well on an exam given that they spend time reading is approximately 0.983 or 98.3%.

To calculate the probability of a student doing well on an exam given that the student spends time reading, we need to use conditional probability.

Let's denote:

P(R) as the probability of a student spending time reading (P(R) = 0.59),

P(E) as the probability of a student doing well on an exam (P(E)),

P(E|R) as the probability of a student doing well on an exam given that they spend time reading (P(E|R) = 0.58).

The formula for conditional probability is:

P(E|R) = P(E and R) / P(R).

Given that P(E and R) = 0.58 (the probability of a student doing well on an exam and spending time reading) and P(R) = 0.59 (the probability of a student spending time reading), we can substitute these values into the formula:

P(E|R) = 0.58 / 0.59 = 0.983.

Therefore, the probability of a student doing well on an exam given that the student spends time reading is approximately 0.983 or 98.3%.

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(a) A/x + Bx + \(C/(1 + x) + Dx^2 + Ex/(1 - x) + Fx^2\)

(b)A/x + \(B/x^2 + C/x^3\) + D/(x - 2) + \(E/(x^2\)+ 2x + 4) + F/(x + 2) + \(G/(x^2\) - 2x + 4)

(a) To perform partial fraction decomposition on the function:

\((x^4 (x^3 + x)) / (x^2 - x^4)\)

we first factor the denominator:

\(x^2 - x^4 = x^2(1 - x^2) = x^2(1 + x)(1 - x)\)

The partial fraction decomposition of the function is:

\((x^4 (x^3 + x)) / (x^2 - x^4) = A/x + Bx + C/(1 + x) + Dx^2 + Ex/(1 - x) + Fx^2\)

where A, B, C, D, E, and F are constants to be determined.

(b) To perform partial fraction decomposition on the function:

\(4 / (x^6 - 8x^3)\)

we first factor the denominator:

\(x^6 - 8x^3 = x^3(x^3 - 8) = x^3(x - 2)(x^2 + 2x + 4)(x + 2)(x^2 - 2x + 4)\)

The partial fraction decomposition of the function is:

\(4 / (x^6 - 8x^3)\) = \(A/x + B/x^2 + C/x^3\) + D/(x - 2) + \(E/(x^2 + 2x + 4) + F/(x + 2)\) + \(G/(x^2 - 2x + 4)\)

where A, B, C, D, E, F, and G are constants to be determined.

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Answer:

the answer is A.-3 and 3-3

Step-by-step explanation:

Circumference = πD

= 16π

= 50.265482457437

Area =

π( D )2

2

= 64π

= 201.06192982975

The Circumference of the circle is 50.24 meters and The area of the circle is 200.96 meters.

What is the Circumference of a Circle?

A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length. A circle is a closed, rounded shape whose border points are all equally spaced out from the center. The diameter and area of a circle are two crucial measurements of a circle.

What is the Area of a Circle?
The space a circle takes up on a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r×r×pi, where r is the circle's radius, is the formula for calculating a circle's surface area.

So, here in the question, It is given that:

The diameter of the circle (d) = 16 meters

and we know that the Radius of a circle is half of the diameter.

That is,

\(d = 2r\)

⇒\(r = \frac{16}{2}\)

⇒\(r = 8 m\)

So,

Circumference of the circle = 2πr

⇒Circumference = 2×3.14×8

⇒Circumference = 50.24 meters.

And, Area of the circle = π×r×r

⇒Area = 3.14×8×8

⇒Area = 200.96

Hence,

Circumference of the circle = 50.24 meters;

Area of the circle = 200.96 meters;

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Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

If A is a symmetric matrix, then A³ is also a symmetric matrix.

To prove this, we can use the definition of a symmetric matrix, which is a matrix that is equal to its transpose. In other words, if A is a symmetric matrix, then A = A^T.

Now, let's look at A³:

A³ = A * A * A

We can replace each A with A^T, since they are equal:

A³ = A^T * A^T * A^T

Now, we can use the property that the transpose of a product of matrices is equal to the product of their transposes in reverse order:

A³ = (A^T * A^T * A^T)^T

A³ = (A^T)^T * (A^T)^T * (A^T)^T

Since the transpose of a transpose is the original matrix, we can simplify:

A³ = A * A * A

Therefore, A³ is also a symmetric matrix.

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There are 450 triangles, we can pick that do not form an equilateral triangles when 15 dots are evenly spaced on the circumference of a circle.

Let's calculate the total no. of possible triangles, it depends on the combination. To make a triangle, we have to choose 3 dots out of 15.

Here, we will use the combination rule to find out the possible triangles,Thus, the total number of possible triangles = 15C3                                                                      = (15.14.13) / (1.2.3) = 455

Note that an equilateral triangle would be formed by connecting 3 equally spaced dots.

For an equilateral triangle, out of 15 dots, there would be 15 - 3 = 12 dots that will not be connected.

And 12/3 = 4 dots would be between any two connecting dots.

Taking 1st connecting dot, the second connecting dot would be

1 + 4 + 1 = 6th

Similarly, the third connecting dot would be 6 + 4 + 1 = 11th

So, the following connecting dots will form equilateral triangles: (1, 6, 11); (2, 7, 12); (3, 8, 13); (4, 9, 14); (5, 10, 15);

After applying the combination rule we found the total number of the possible triangle and there are 5 equilateral triangles:

So, there are 455 - 5 = 450 triangles that are not equilateral triangles.

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