Derrick adds equations A and B to solve this system of equations. What makes this approach a valid method in general for solving a system of equations?

A. As long as addition is used on both sides or subtraction is used on both sides, a true equation will remain true.


B. Adding a quantity like 5x+4y
to one side of an equation and another quantity like 24
to the other side maintains the equality if the two quantities are equal.


C. Because the y
-terms cancel:

(5x+4y)+(3x−4y)=5x+3x+4y−4y=8x

D. The method will give the correct solution, x=5
and y=−1/4
.

5(5)+4(−14)=24

3(5)−4(−14)=16

To determine how far a cheetah could run in 15 seconds at the given rate, we can use the formula:

distance = rate x time

Where the rate is the speed at which the cheetah is running and time is the duration of the run.

We are given that the cheetah runs 420 feet in 6 seconds. To find the rate at which the cheetah is running, we can divide the distance by the time:

Now we can use the rate and the given time of 15 seconds to find the distance the cheetah could run:

Therefore, the cheetah can run 1050 feet in 15 seconds.

To communicate information about the public in broadly understandable terms, researchers and pollsters often rely on aggregated statistical data. By compiling and analyzing large sets of information, they can identify patterns and trends that can be presented in a way that is easy for people to understand.

For example, they may use graphs, charts, or other visual aids to convey complex information in a clear and concise manner. This can be particularly important when trying to share findings with the general public or with policymakers who may not have a background in statistics or research methodology. By using aggregated statistical data, researchers and pollsters can help ensure that important information is communicated effectively and accurately.

This allows them to present complex information in a more accessible and easily digestible format for a wider audience.

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Each guy-wire is approximately 315.08 feet long.

We can use trigonometry to find the length of the guy-wires. Let's call the length of each guy-wire "x".

First, we can use the tangent function to find the height of the triangle formed by the first guy-wire and the antenna:

tan(0.33) = height/x

Rearranging, we get:

height = x * tan(0.33)

Similarly, we can use the tangent function to find the height of the triangle formed by the second guy-wire and the antenna:

tan(0.38) = height/x

Again, rearranging, we get:

height = x * tan(0.38)

Since both of these triangles share the same height, we can set the two expressions for height equal to each other:

x * tan(0.33) = x * tan(0.38)

Dividing both sides by x gives:

tan(0.33) = tan(0.38)

This equation is not true for all values of alpha and beta, but we are given that it holds for this particular case. Using this equation, we can solve for x:

x = 160 / tan(0.33)

x ≈ 315.08 feet

Therefore, each guy-wire is approximately 315.08 feet long.

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The decision and outcome that represents a Type I error in this scenario is if the prisoner is released and kills a family of five in cold blood within 48 hours. A Type I error occurs when the null hypothesis is rejected even though it is actually true. In this case, if the parole board releases the prisoner based on the hypothesis that they have been rehabilitated but in reality, they have not been rehabilitated, it would result in a Type I error. The prisoner's release would lead to a tragic outcome, which could have been avoided if the null hypothesis had not been rejected.

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The statement is true. This means that r'(t) is orthogonal (perpendicular) to r(t) for all t.

If |r(t)| = 1 for all t, then r(t) is a unit vector for all t. Differentiating both sides of this equation with respect to t, we get:

|r(t)|' = 0

Using the chain rule and the fact that the magnitude of a vector is the square root of the dot product of the vector with itself, we have:

|r(t)|' = (r(t) · √r(t))

= (2r(t) · r'(t)) / (2|r(t)|)

= r(t) · r'(t) / |r(t)|

= r(t) · r'(t)

Since |r(t)|' = 0, we have:

r(t) · r'(t) = 0

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The standard deviation of the data-set is given as follows:

s = 4.14.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The data-set in this problem is given as follows:

3, 4, 5, 7, 10, 12, 15.

Hence the mean is:

Mean = (3 + 4 + 5 + 7 + 10 + 12 + 15)/7

Mean = 8.

The sum of the differences squared for the data-set is given as follows:

SS = (3 - 8)² + (4 - 8)² + (5 - 8)² + (7 - 8)² + (10 - 8)² + (12 - 8)² + (15 - 8)²

SS = 120.

The standard deviation is given by the square root of the sum of the differences squared divided by the cardinality, hence:

s = sqrt(120/7)

s = 4.14.

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The Empirical Rule is a statistical principle that applies to normally distributed data. It states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.

In this case, the mean triglyceride level for the residents of the assisted living facility is 200, with a standard deviation of 50. If samples of 100 residents are taken, the sample mean triglyceride level will also be normally distributed, with a mean of 200 and a standard deviation of 5 (calculated as 50 divided by the square root of 100).

To find the range within which 95% of all the sample means will fall, we need to look at two standard deviations above and below the mean. Two standard deviations above the mean are 210 (calculated as 200 + 2*50), and two standard deviations below the mean are 190 (calculated as 200 - 2*50).

Therefore, we can conclude that 95% of all sample means will fall between 190 and 210. So the lower value is 190, and the upper value is 210.

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True. The cofactor expansion of the determinant of a matrix A along any row or column will yield the same result.

The cofactor expansion of the determinant of a matrix A along a row or a column is given by the formula:

```
det(A) = a1j * C1j + a2j * C2j + ... + anj * Cnj
```

where `aij` is the element in the ith row and jth column of A, and `Cij` is the (i,j)-cofactor of A.

The (i,j)-cofactor of A is defined as `(-1)^(i+j) * Mij`, where `Mij` is the determinant of the (n-1) by (n-1) matrix obtained by deleting the ith row and jth column of A.

To see why the cofactor expansion is independent of the row or column chosen, consider the formula for the determinant of a matrix obtained by transposing A:

```
det(A^T) = det([a11, a21, ..., an1],
               [a12, a22, ..., an2],
               ...,
               [a1n, a2n, ..., ann])
```

By the cofactor expansion along the first row of A^T, we have:

```
det(A^T) = a11 * C11' + a12 * C12' + ... + a1n * C1n'
```

where `Cij'` is the (i,j)-cofactor of A^T.

Now note that `Cij' = (-1)^(i+j) * Mji`, where `Mji` is the determinant of the (n-1) by (n-1) matrix obtained by deleting the jth row and ith column of A. But this is precisely the (j,i)-cofactor of A. Therefore, we have:

```
det(A^T) = a11 * C11 + a21 * C21 + ... + an1 * Cn1
```

which is the cofactor expansion of det A along the first column of A. Since the transpose of a matrix has the same determinant as the original matrix, we conclude that the cofactor expansion of det A along any row is equal to the cofactor expansion along any other row.

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The  upper triangular matrix R is invariant under multiplication by the transpose of Q. This relationship is sometimes referred to as the "QR factorization identity".

If A=QR, where Q is an n×n matrix with orthonormal columns and R is an n×n upper triangular matrix, then we can express A as:

A = QR = Q(QT)R

Since Q has orthonormal columns, its transpose QT is its inverse. Therefore:

Q(QT)R = I_n R = R

where I_n is the n×n identity matrix. So we can see that R is equal to Q(QT)R, which is the product of Q and the transpose of Q. This product is equal to the identity matrix times R, so we can say that:

R = QT R

In other words, the upper triangular matrix R is invariant under multiplication by the transpose of Q. This relationship is sometimes referred to as the "QR factorization identity".

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0.3673 is the value of the variable n.

The given expression is [tex]\frac{m(nx^2-y)}{z}=5n[/tex]

First, let's plug the given values into the equation:

[tex]\frac{6(n2^2-(-3))}{-5}=5n[/tex]

Simplifying:

[tex]\frac{6(n4+3)}{-5}=5n\\6(4n+3)=-25n\\24n+25n=18\\n=18/49[/tex]

n = 0.3673

Therefore, n is approximately equal to 0.3673.

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The probability of winning $3,899 is 0.0001, which is a very small probability, but still possible.

To write the probability distribution for a player's winnings in the Pick 4 game, we need to consider all the possible outcomes and their probabilities.

There are a total of 10,000 possible four-digit numbers that can be drawn in the game. Since the player has to match the numbers in the exact order, there is only one winning combination for each four-digit number. Therefore, the probability of winning is 1/10,000.

To calculate the player's winnings, we need to subtract the $1 cost of playing from the $3,900 prize. Thus, the player's net winnings can be calculated as follows:

Net Winnings = $3,900 - $1 = $3,899

The probability distribution for the player's winnings can be summarized in the following table:

| Winnings (x) | Probability (P) |
|--------------|-----------------|
| $0           | 0.9999          |
| $3,899       | 0.0001          |

Note that the table shows the possible winnings (x) in ascending order, as requested. The probability of winning $0 is 0.9999, which means that the player is most likely to lose their $1 bet.

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The ordinary number form of the mentioned scientific notation form of the number is 0.00604.

Scientific notation of representation of a number refers to converting a number to its readable form. It is applicable on both small and large numbers, where value of zeroes are represented in exponential form for easy interpretation.

The exponent of -3 is interpreted as three zeroes in the denominator. The division with zero will further shorten the number by adding zeroes to left hand side of the digit after decimal. Hence, the ordinary form of the number will be 0.00604.

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The bottom of the ladder is sliding along the ground away from the wall at a rate of 25/12 ft/s when it is 12 feet away from the base of the wall.

Let's denote the height of the ladder on the wall as y, and the distance of the ladder's bottom from the wall as x. We know that y and x are related by the Pythagorean theorem: [tex]x^2 + y^2 = 13^2.[/tex]

We are given that dy/dt = -5 ft/s (the negative sign indicates that the ladder is slipping down the wall) and we want to find dx/dt when x = 12 ft.

To solve for dx/dt, we need to relate x and y, and then differentiate with respect to time:

[tex]x^2 + y^2 = 13^2[/tex]

Differentiating both sides with respect to time t:

2x(dx/dt) + 2y(dy/dt) = 0

When x = 12 ft, we can solve for y using the Pythagorean theorem: y = sqrt[tex](13^2 - 12^2)[/tex] = 5 ft.

Substituting x = 12 ft and dy/dt = -5 ft/s into the above equation, we get:

2(12)(dx/dt) + 2(5)(-5) = 0

Simplifying and solving for dx/dt, we get:

dx/dt = 25/12 ft/s

Therefore, the bottom of the ladder is sliding along the ground away from the wall at a rate of 25/12 ft/s when it is 12 feet away from the base of the wall.

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Probability is the likelihood or chance of an event occurring.

In the given grid, there are 4 black points out of a total of 9 points.

Therefore, the probability of selecting a black point randomly is:

P(black) = Number of black points / Total number of points

= 4 / 9

= 0.444 or 44.4% (rounded to one decimal place)

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The probability of selecting a user who chooses cinnamon and is under 13 years old is: 0.18 or 18% (rounded to two decimal places).

In the problem, we are given the number of users who choose bacon and are under 13 years old, which is 8. We are also given the number of users who choose plain and are under 13 years old, which is 5. Therefore, the total number of users under 13 years old is 8 + 5 = 13.

Next, we are asked to find the probability of selecting a user who chooses cinnamon and is under 13 years old. We know that the number of users who choose cinnamon and are under 13 years old is 3. Therefore, out of the total 13 users under 13 years old, the probability of selecting a user who chooses cinnamon and is under 13 years old is:

The total number of users under 13 years old is 8 (choose bacon) + 5 (choose plain) = 13.

The number of users who choose cinnamon and are under 13 years old is 3.

Therefore, the probability of selecting a user who chooses cinnamon and is under 13 years old is:

3 / 13 ≈ 0.23 or 23% (rounded to two decimal places)

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Answer: To show that the number 52.470817081708 is rational, we need to express it as a ratio of two integers.

Let x = 52.470817081708. We can write x as a sum of its integer part and fractional part:

x = 52 + 0.470817081708

To convert the fractional part to a fraction, we can multiply both numerator and denominator by a power of 10 that will eliminate the decimal point. In this case, we can multiply by 10^12:

0.470817081708 = 470817081708 / 10^12

Therefore, we can write:

x = 52 + 470817081708 / 10^12

We can simplify the fraction by dividing both numerator and denominator by their greatest common divisor:

x = 52 + 163717 / 3125000

So we have expressed x as a ratio of two integers, 163717 and 3125000. Therefore, 52.470817081708 is a rational number.

The number 52.470817081708 is rational because it can be expressed as a ratio of two integers: 52470817081708

To show that 52.470817081708 is rational, we need to write it as a ratio of two integers.

First, we can see that the number has a repeating pattern of digits after the decimal point, which tells us that it can be expressed as a fraction. To do this, we'll count the number of decimal places in the repeating pattern, which is 12 in this case.

Next, we'll use the following formula to convert the repeating decimal to a fraction:

x = a + b/(10^n - 1)

Where:

- x is the repeating decimal
- a is the non-repeating part of the decimal (in this case, it's just the whole number 52)
- b is the repeating part of the decimal (in this case, it's the digits 470817081708)
- n is the number of digits in the repeating pattern (in this case, it's 12)

So plugging in our values, we get:

52.470817081708 = 52 + 470817081708/(10^12 - 1)

Simplifying the denominator, we get:

52.470817081708 = 52 + 470817081708/999999999999

To write this as a ratio of two integers, we'll simplify the fraction:

52.470817081708 = 52 + 235408540854/499999999999

So the number 52.470817081708 can be written as the fraction 52 + 235408540854/499999999999, which is a ratio of two integers. Therefore, we have shown that 52.470817081708 is rational.

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The correct prime numbers x that make this inequality true is,

⇒ x = 7, 11, 13, 17, 19

We have to given that;

The expression is,

''5 is less than x and x is less than or equal to 19.''

Now, We can formulate;

⇒ 5 < x ≤ 19

Hence, Possible prime numbers that make this inequality true are,

⇒ x = 7, 11, 13, 17, 19

Thus, The correct prime numbers x that make this inequality true is,

⇒ x = 7, 11, 13, 17, 19

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The equation of the graph is y = -| x | + 1

Given data ,

The graph of y = -|x| + 1 is a V-shaped graph with the vertex at the origin (0, 1), and it opens downwards along the y-axis. The negative sign in front of the absolute value function reflects the graph of y = |x| across the x-axis, flipping it upside down.

When x is greater than or equal to 0, the expression |x| becomes x, and the graph of y = -|x| + 1 will be y = -x + 1 for x ≥ 0.

When x is less than 0, the expression |x| becomes -x, and the graph of y = -|x| + 1 will be y = x + 1 for x < 0.

Thus, the graph of y = -|x| + 1 consists of two linear segments with slopes of -1, intersecting at the point (0, 1), and extends indefinitely in both directions along the x-axis.

Hence , the equation of graph is y = -| x | + 1

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y=-|x|+1

Step-by-step explanation:

I checked RSM, its correct

Answer:

x = 1.08 and x = -2.08

Step-by-step explanation:

We can solve this equation using the quadratic formula.

[tex]ax^2+bx+c=0[/tex]

Thus, in the equation given, 4 is our a value, 4 is (also) our b value and -9 is our c value.

The formula for the positive solution of the quadratic formula is

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]

The formula for the negative solution of the quadratic formula is

[tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

Positive solution:

[tex]x=\frac{-4+\sqrt{4^2-4(4)(-9)} }{2(4)}\\ \\x=\frac{-4+\sqrt{160} }{8}\\ \\x=1.08113883\\\\x=1.08[/tex]

Negative solution:

[tex]x=\frac{-4-\sqrt{4^2-4(4)(-9)} }{2(4)}\\ \\x=\frac{-4-\sqrt{160} }{8}\\ \\x=-2.08113883\\\\x=-2.08[/tex]

In descriptive statistics, the interquartile range tells you the spread of the middle half of your distribution. Quartiles segment any distribution that's ordered from low to high into four equal parts. The interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.

Answer:

the answer is true. may I get brainliest

TRUE. The critical value of a hypothesis test is based on the researcher's selected level of significance.

The critical value of a hypothesis test is based on the researcher's selected level of significance. The level of significance represents the probability of rejecting a true null hypothesis, and it determines the critical value, which is the point beyond which we reject the null hypothesis. Therefore, the higher the level of significance, the lower the critical value, and the easier it is to reject the null hypothesis.
True, the critical value of a hypothesis test is based on the researcher's selected level of significance. The level of significance determines the threshold for rejecting or failing to reject the null hypothesis, and the critical value is a point on the test statistic's distribution that corresponds to this threshold.

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Answer:

The answer for

<H=41°

<F=49°

Step-by-step explanation:

sum of angles in a triangle equals 180°

90+2x+35+3x+20=180

C.L.T.

2x+3x+90+20+35=180

5x+145=180

5x=180-145

5x=35

divide both sides by 5

5x/5=35/5

x=7

so<H=3(7)+20=21+20=41°

<F=2(7)+35=14+35=49°

The APR (annual percentage rate) for a $2,000 loan paid off in 12 equal monthly payments with a stated annual interest rate of 8% is 14.452%.

The annual percentage rate (APR) can be determined using an online finance calculator as follows:

The APR is the total cost of borrowing money, reflecting not only the interest rate but also other loan fees.

N (# of periods) = 12 months

PV (Present Value) = $2,000

PMT (Periodic Payment) = $-180

FV (Future Value) = $-0

Results:

I/Y = 14.452% if interest compounds 12 times per year (APR)

I/Y = 15.449% if interest compounds once per year (APY)

I/period = 1.204% interest per period

Sum of all periodic payments = $-2,160.00 ($180 x 12)

Total Interest = $160.00 ($2,000 x 8%)

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Answer:

In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM.

The object will be at the height of 78.4 meters after 2 seconds after substituting to the equation.

Given that,

An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform.

The equation for the object's height s at time t seconds after launch is,

s(t) = -4.9t² + 19.6t + 58.8

where s is in meters.

We have to find the height of the object after 2 seconds.

When t = 2,

s = (-4.9 × 4) + (19.6 × 2) + 58.8

s = -19.6 + 39.2 + 58.8

s = 78.4 meters

Hence the height of the object after 2 seconds is 78.4 meters.

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There are several subtypes of qualitative data techniques, including interview, focus groups, observations, case studies and document analysis.

Interviews: These are one-on-one conversations between the researcher and participant(s), where the researcher asks open-ended questions to gather information.

Focus Groups: These are group discussions where a researcher moderates the conversation and asks participants to share their experiences and opinions on a particular topic.

Observations: These involve the researcher directly observing and documenting behaviors, actions, and interactions of individuals or groups in a natural setting.

Case Studies: These involve in-depth exploration and analysis of a single individual or group, often used in fields such as psychology and social work.

Document Analysis: This involves reviewing and analyzing written or recorded materials such as texts, videos, or audio recordings to gain insight into a particular topic or phenomenon.

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We are given two sets of paired observations, which we will use to calculate the sample mean difference and the standard error of the mean difference:

Sample mean difference = x1 -x2 = (214+186+182+200+210+204+187+210+190+182+215+198)/12 - (188+210+199+209+207+195+203+191+190+211+199+181)/12 = 4.75

Sample standard deviation of the differences = s = √[(Σd²)/(n-1)] where d = (x1 - x2) - (x1 - x2), and n is the number of pairs.

d1 = (214 - 188) - 4.75 = 21.25

d2 = (186 - 210) - 4.75 = -28.75

d3 = (182 - 199) - 4.75 = -22.75

d4 = (200 - 209) - 4.75 = -9.75

d5 = (210 - 207) - 4.75 = -1.75

d6 = (204 - 195) - 4.75 = 3.25

d7 = (187 - 203) - 4.75 = -20.75

d8 = (210 - 191) - 4.75 = 13.25

d9 = (190 - 190) - 4.75 = -4.75

d10 = (182 - 211) - 4.75 = -28.75

d11 = (215 - 199) - 4.75 = 10.25

d12 = (198 - 181) - 4.75 = 12.25

Σd² = 1734.875

s = √(1734.875/11) = 5.076

Standard error of the mean difference = s/√n = 5.076/√12 = 1.469

Using a t-distribution with 11 degrees of freedom and a 99% confidence level (α = 0.01), we find the t-value to be 3.106. Therefore, the 99% confidence interval for the true mean difference between the cholesterol levels for people who take the new drug is:

(4.75 - 3.106(1.469), 4.75 + 3.106(1.469))

= (0.885, 8.615)

So we are 99% confident that the true mean difference between the cholesterol levels for people who take the new drug lies between 0.885 and 8.615 mg/dL.

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a) Only the first statement is true. As the sample size N becomes large, the sample mean of IID random samples from a population becomes more precise and approaches the true population mean.

However, there is no direct relationship between the sample size and the distribution of the sample mean.
The second statement is only true if the population is normally distributed. If the population is not normal, the distribution of the sample mean may not be normal, and the central limit theorem may not apply. Therefore, option c) is not the correct answer. Option d) is also not correct as the first statement is true.

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The oatmeal bar has a volume of 16 cubic inches.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

V = base area × height

Where w is the width, h is height and l is length

To find the volume of the rectangular prism oatmeal bar, we need to multiply the base area by the height.

So, the volume of the oatmeal bar can be calculated as:

Volume = Base Area × Height

Volume = 4 in² × 4 in

Volume = 16 in³

Therefore, the volume of 16 cubic inches.

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