Write 20 as a product of prime factors.

Answer:

The hypotenuse formula is simply taking the Pythagorean theorem and solving for the hypotenuse, c.

Step-by-step explanation:

Solving for the hypotenuse, we simply take the square root of both sides of the equation a² + b² = c² and solve for c . When doing so, we get c = √(a² + b²)

The length of the hypotenuse is 17 cm and this can be determined by evaluating the length of one side of each square and then applying the Pythagorean Theorem.

Given :

The side length of the smaller square can be calculated as:

\(a^2 = 64\)

a = 8

The side length of the larger square can be calculated as:

\(b^2 = 225\)

b = 15

So, the length of the perpendicular is 8 and the length of the base is 15. Now, apply the Pythagorean theorem in order to determine the length of the hypotenuse.

\(\rm H^2=P^2+B^2\)

Now, substitute the values of known terms in the above expression.

\(\rm H^2=(8)^2+(15)^2\)

\(\rm H = \sqrt{64+225}\)

H = 17 cm

Therefore, the correct option is D) Find the length of one side of each square and then apply the Pythagorean Theorem.

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.Answer: Length of segment RP is greater than 3.

Given that RS = 4 and RQ = 16, we need to find the length of segment RP. Now, we have to consider a basic property of triangles that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. We apply the same rule in the triangle PRS, PQS and PQR.As per the above property, PR+RS>PS ⇒ PR+4>PS...

(1) PR+PQ>QR ⇒ PR+16>QR...

(2) PQ+QS>PS ⇒ PQ+8>PS..

(3)Adding equation 2 to equation 3, we get PR+PQ+16+8>PS+QR⇒PR+PQ+24>PS+QR....

(4)Adding equation 1 to equation 4, we get 2(PR+PQ+12)>30 ⇒ PR+PQ+12>15 ⇒ PR+PQ>3..

. (5)Now, we consider a triangle PQR. As per the above property, PR+QR>PQ ⇒ PR+QR>16⇒ PR>16-QR.....(6)Substituting equation (6) in equation (5), we get 16-QR+PQ>3 ⇒ PQ>QR-13We know that PQ=QS+PS And RS=4Therefore, QS+PS+4>QR-13 ⇒ QS+PS>QR-17.We also know that PQ+QS>PS ⇒ PQ>PS-QS. Substituting these values in QS+PS>QR-17, we get PQ+PS-QS>QR-17 ⇒ PQ+QS-17>QR-PS. Again, PQ+QS>16⇒ PQ>16-QSPutting this value in PQ+QS-17>QR-PS, we get 16-QS-17>QR-PS ⇒ QS+PS>3On simplifying we get PS>3-QSSince RS=4, we have PQ+PS>3 and RS=4Therefore, PQ+PS+4>7 ⇒ PQ+PS>3On solving the equations we get: PS>3-QSQR>16-QS PQ>16-PSFrom the above equations, we have PQ+PS>3Therefore, the length of segment RP is greater than 3. Hence, we can conclude that the length of segment RP is greater than 3

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Without more information about how the segments are related, it's not possible to calculate the length of RP just from the lengths of RS and RQ.

The detailed information provided does not seem to relate directly to your question about finding the length of segment RP given the lengths of segments RS and RQ. Without additional information on the relationship between these segments (e.g., if they form a triangle or a straight line), it's not possible to calculate the length of RP directly from the given information. However, if RQ and RS are related in a certain way, such as the sides of a right triangle, we'd require the Pythagorean theorem or other geometric principles to find the length of RP.

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a) The cost of the stereo system is $4,760.

b) The total amount of interest paid is $1,760.

To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.

To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.

In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.

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The ratio of the Volume of the sphere whose radius are in ratio 1:2 is 1:8.

A sphere is a three dimensional figure, it is made of set of points that are all equidistant from the center.

The ratio of radii of two spheres is 1:2

Volume of a sphere is given by

V = (4/3) πr³

The ratio of two sphere is given by

V₁ / V₂ = (r₁/r₂)³

V₁ / V₂ = (1/2)³

V₁ / V₂ = 1/8

Therefore, the ratio of the Volume of the sphere whose radius are in ratio 1:2 is 1:8.

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Answer:

-8

Step-by-step explanation:

\( \frac{8 - 2x}{12} = 2\)

\(8 - 2x = 24\)

\( - 2x = 16\)

\(x = - 8\)

8- 2x/12 = 2

Multiply both sides by 12:

8 - 2x = 24

Subtract 8 from both sides:

-2x = 16

Divide both sides by -2:

X = -8

The determinant of an image matrix can only be equal to 1 or -1.

If we have an image matrix with the property that images, its determinant can only be equal to 1 or -1.

To understand why, let's first define what we mean by an image matrix. An image matrix is a square matrix A of size n x n, where each entry a_ij is either 0 or 1. We say that A is an image matrix if for every row i and column j, the sum of the entries in that row and column is odd. In other words, the row and column sums of A are all odd.

Now, let's consider the determinant of an image matrix A. The determinant of a matrix is a scalar value that can be calculated from its entries. Without loss of generality, let's assume that the first row of A has an odd sum, since we can always permute the rows and columns of A to achieve this.

We can expand the determinant of A along the first row to obtain:

det(A) = a_11 det(A_11) - a_12 det(A_12) + a_13 det(A_13) - ... + (-1)^(n+1) a_1n det(A_1n)

where A_ij is the matrix obtained by deleting the ith row and jth column of A. Each of the determinants det(A_ij) can be computed recursively using the same formula. Since each entry of A is either 0 or 1, the determinant det(A_ij) is either 0, 1, or -1.

Now, consider the ith term in the expansion of det(A). This term is of the form a_i1 det(A_i1), where a_i1 is either 0 or 1. Since the sum of the entries in the first row of A is odd, we know that there are an odd number of entries in that row that are equal to 1. Let k be the number of such entries. Then, det(A_i1) is the determinant of a (n-1) x (n-1) matrix in which each row and column sum is even, since we have deleted one row and one column that contained a 1. Therefore, det(A_i1) is either 1 or -1, since the determinant of a matrix with even row and column sums is always a square.

If k is odd, then the term a_i1 det(A_i1) is equal to either 1 or -1, depending on the value of a_i1. If k is even, then the term a_i1 det(A_i1) is equal to 0. Therefore, we have:

det(A) = ± 1

since the sum of an odd number of odd terms is odd, and the sum of an even number of odd terms is even (i.e., equal to 0 or ±2). Thus, the determinant of an image matrix can only be equal to 1 or -1.

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The slope of the line passing through the points (-5, -4) and (-13, 2) is -3/4.

Slope is simply expressed as a change in y over the change in x.

It is expressed as

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Given the points:
(-5, -4) and (-13,2)​

Point (-5, -4):

x₁ = -5

y₁ = -4

Point (-13,2)​:

x₂ = -13

y₂ = 2

Plug the given x and y values into the slope formula and simplify.

\(m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{2 - (-4)}{-13 - (-5)}\\\\m = \frac{2 + 4}{-13 + 5}\\\\m = \frac{6}{-8}\\\\m = -\frac{3}{4}\)

Therefore, the slope of the line is -3/4.

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Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

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Answer:

What is the law of large numbers? 

In probability theory, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times. 

What does it tell us about samples as they get larger and approach infinity?

As sample sizes increase, the sampling distributions approach a normal distribution. With "infinite" numbers of successive random samples, the mean of the sampling distribution is equal to the population mean (µ).

Hope this helps :)

Pls brainliest...

Answer:

6. 33% increase

Step-by-step explanation:

Equation of increase/decrease: (Final value-initial value)÷(Initial Value)

6. (66-44)÷(66)=0.33

-Multiply by 100 to get 33% increase

7. (6.5-6)÷(6)=0.083

-Round and multiply by 100 to get 8.0% increase

8. (56-36)÷(56)=0.357

Round and multiply by 100 to get 36% decrease

9. (72-18)÷72=0.75

Multiply by 100 to get 75% decrease

Answer:

from 44 to 66 7 from 6 to 6.5

1415.9090909091%

667 - 44

44

x 100% = 1415.9090909091%

8.3333333333%

6.5 - 6

6

x 100% = 8.3333333333%

i dont know the other one sorry :(

Answer:

133

Step-by-step explanation:

All 3 angles of a triangle must equal 180, so let's make these equal to that

\((x + 13) + (10x + 13) + (2x - 2) = 180\)

Now let's combine the X's and the regular numbers together.

\(13x + 24 = 180\)

Next, subtract 24 to get all the numbers on the right side.

\(13x = 156\)

And lastly, we divide by 13 to get X alone

\(x = 12\)

Since Q is (10x + 13), we plug that 12 in

\(10(12) + 13 = 133\)

\(\text{Solve:}\\\\-(5-(a+1))=9-(5-(2a-3))\\\\-(5-a-1))=9-(5-2a+3))\\\\-(4-a)=9-(8-2a)\\\\-4+a=9-8+2a\\\\-4+a=1+2a\\\\\text{Subtract a from both sides}\\\\-4=1+a\\\\\text{Subtract 1 from both sides}\\\\\boxed{-5=a}\)

Answer:

The answer is A: a=-5

Step-by-step explanation:

took the test

Answer:

35 boys

25 girls

Step-by-step explanation:

you will the total number of volunteers and divide that by the total number of "parts" in the ratio (7+5=12)

60 / 12 = 5

you then will multiply your answer (in this case, 5) to each part of the ratio (7 to find the number of boys, & 5 to find the number of girls)

5x7=35 boys

5x5= 25 girls

HOPE THIS HELPS!!!

Solution:

Given:

Angle P is measured in degrees.

where x = 4

Substituting the value of x in the equation,

Therefore, the measure of angle P is 71 degrees.

Step-by-step explanation:

Our equation;

\(-5=\frac{y-7}{9}\)

Multiply each side by 9 to remove the fraction;

\(-45=y-7\)

Add 7 to each side;

\(\boxed{-38=y}\)

Answer:

x-10 +x = 8 + 2x - 18

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The function \(f(x) = \frac{5}{4} (\frac{4}{5}) ^{x}\) represents the stretch of an exponential decay function.

The process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula \(y = a(1-b)^{x}\)

where,

y is the final amount,

a is the original amount,

(1 -b) is the decay factor,

and x is the amount of time that has passed.

For a  exponential decay function (1-b) is always less than 1. If (1-b) < 1 it represents the exponential growth function.

And if a < 1, then it represents vertical compression and if a > 1, then it represents vertical stretch.

According to given question.

We have some functions in which we have to find the which one represents the decay function.

According to the function

\(f(x) = \frac{4}{5}(\frac{5}{4} )^{x} }\)

For the decay function, the decay factor will always less than 1. In the above function the decay factor \(\frac{5}{4}\) i.e. 1.25 is greater than 1.

Therefore, the above function doesn't represent decay function.

\(f(x) = \frac{4}{5}( \frac{4}{5} )^{x}\)

Here, a < 1 i.e.  \(\frac{4}{5}\) is less than 1 so the given function is not a stretch of an exponential decay function.

\(f(x) = \frac{5}{4} (\frac{4}{5}) ^{x}\)

Here, b < 1 so it represents the exponential decay function. Also a > 1.

Therefore, the given function is the stretch of an exponential decay function.

\(f(x) = \frac{5}{4} (\frac{5}{4}) ^{x}\)

Here, a > 1 but b > 1. Therefore, the above function doesn't represent the exponential decay function. It represents the exponential growth function.

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Answer:

x = 24 , y = 19

Step-by-step explanation:

(2x + 13) and 47 + 3x are same- side interior angles and sum to 180° , so

2x + 13 + 47 + 3x = 180 , that is

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

Then 3x = 3 × 24 = 72

5y - 23 and 3x are corresponding angles and are congruent , then

5y - 23 = 72 ( add 23 to both sides )

5y = 95 ( divide both sides by 5 )

y = 19

Answer:

See below.

Step-by-step explanation:

A and B are automatically out, since they are not mixed fractions.

56 and 24 GCF is 8.

56/8 = 7

24/8 = 3

7/3 = 2 1/3

The answer is C.

-hope it helps

Answer: 2 1/3

Step-by-step explanation: The answer would be 2 1/3 because since 56 and 24 are factors of 4 you divided both of them by 4 which would give you 14/6. They're not factors of 4 no more, so you divide them by 2 which makes it 7/3. They are both prime numbers and 3 is a factor of 3 but 7 isn't and what you do to the bottom number has to be done to the top. There are no remainders in fractions so you simplify it which would you give you 2 1/3. 3 can go into 7, 2 times because 3x2 equals 6. The whole number is 2 now and the denominator stays the same. 2 ?/3. 2x3=6+1=7 so the numerator is 1. 2 1/3

The value of each trigonometric identity is:

3/2

5/6

14/3

We have,

We will use the trigonometric formula and substitute the given values.

So,

Cosec θ

This can be written as,

= 1/ sin θ

= 1/(2/3)

= 3/2

And,

Sin θ

This can be written as,

= 1/ cosec θ

= 1/(6/5)

= 5/6

And,

Sec θ

This can be written as,

= 1/cosθ

= 1/(3/14)

= 14/3

Thus,

The value of each trigonometric identity is:

3/2

5/6

14/3

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Anthony's "hiring process" or "recruitment period" was 30 days.

The blank can be filled with "hiring process" or "recruitment period" to indicate the duration between placing the advertisement for a new assistant on November 1 and hiring Marquis on December 1. This period represents the time it took Anthony to evaluate applicants, conduct interviews, and make the decision to hire Marquis.

The hiring process typically involves several steps, such as advertising the job opening, reviewing applications, conducting interviews, and finalizing the selection. The duration of this process can vary depending on various factors, including the number of applicants, the complexity of the position, and the efficiency of the hiring process.

In this case, the hiring process took 30 days, indicating the length of time it took for Anthony to complete the necessary steps and choose Marquis as the new assistant. This duration provides insight into the timeframe Anthony needed to assess candidates and make a hiring decision.

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a) The probability that a single randomly selected value is less than 76.3 is 0

b) Probability that a sample of size n = 21 is randomly selected with a mean less than 76.3 is 0.

a) Probability that a single randomly selected value is less than 76.3

use the z-score formula to calculate the probability.

\(z=\frac{x-\mu}{\sigma}\)

Where, x = 76.3, μ = 86 and σ = 1.5Plugging in the given values,  

\(z=\frac{76.3-86}{1.5}=-6.46\)

Now use a Z table to find the probability. From the table, the probability as  

\(P(Z < -6.46) \approx 0\)

.b) Probability that a sample of size n = 21 is randomly selected with a mean less than 76.3

sample mean follows a normal distribution with mean (μ) = 86 and

Standard deviation(σ) = \(\frac{1.5}{\sqrt{n}}\)

where, n = sample size = 21

Standard deviation(σ) = \(\frac{1.5}{\sqrt{21}}\)

Plugging in the given values,

Standard deviation(σ) = 0.3267

Now use the z-score formula to calculate the probability.  

\(z=\frac{\bar{x}-\mu}{\sigma}\)

Where, \(\bar{x}\) = 76.3, μ = 86 and σ = 0.3267

Plugging in the given values,  

\(z=\frac{76.3-86}{0.3267}=-29.61\)

Now use a Z table to find the probability. From the table, we get the probability as  

\(P(Z < -29.61) \approx 0\)

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point slope form is

\(y-y_1 = m(x-x_1)\)

we can find m with

\(m = \frac{y_2-y_1}{x_2-x_1}\\ m = \frac{14-1}{-2-5} \\m = \frac{13}{-7} \\\)

\(y - 1 = \frac{-13}{7} (x-5)\\or\\y - 14= \frac{-13}{7} (x+2)\)

It is true that the existence of two local maxima does not guarantee the presence of a local minimum. It is possible for a function to have multiple local maxima and no local minimum.

For example, consider the function f(x,y) = x^4 - 4x^2 + y^2. This function has two local maxima at (2,0) and (-2,0), but no local minimum. Therefore, the statement "if f(x,y) has two local maximal, then f must have a local minimum" is false. The presence or absence of local maxima and minima depends on the behavior of the function in the immediate vicinity of a point, and cannot be determined solely based on the number of local maxima. It is possible for a function to have an infinite number of local maxima and minima, or none at all. Therefore, it is important to carefully analyze the behavior of a function in order to determine the presence or absence of local extrema.

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bottom was cut off a bit its 4=b

Answer:

2ft 8in

Step-by-step explanation:

Text if you want explanation. Welcome❤

Answer:

the first one

Step-by-step explanation:

hash xhskkabiwjajdhueiajehwouqhwjw

Therefore, the potential profit from the mortgage scenario would be 233.1 seats.

To calculate the potential profit for a mortgage and renting scenario, we need the number of seats available (259 seats) and the average occupancy rate (90%). The profit can be determined by multiplying the number of seats by the occupancy rate.

For the mortgage scenario, assuming you own the property and generate revenue through ticket sales, the potential profit can be calculated as follows:

Profit = Number of seats * Occupancy rate

Profit = 259 seats * 0.90 (90% occupancy rate)

Profit = 233.1 seats

Therefore, the potential profit from the mortgage scenario would be 233.1 seats.

For the renting scenario, assuming you are leasing the property and generating revenue through rent payments, the potential profit calculation would be different. In this case, the profit would be determined by the rent amount minus any associated expenses (e.g., property taxes, maintenance costs, etc.).

To calculate the potential profit from renting, more information is needed, such as the rental rate and expenses associated with the property. Without these specific details, it is not possible to provide an accurate calculation of the potential profit.

In summary, the potential profit for the mortgage scenario would be 233.1 seats, based on the given occupancy rate. However, without additional information regarding the rental scenario, a specific calculation for the potential profit from renting cannot be provided.

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Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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