Both Andrew and Karleigh recorded the distance they ran in x minutes on treadmills.
Andrew
Karleigh
Time in Distance
Minutes
in Miles
18
24
1.5
2
OA) (4,0)
Time in Distance
in Miles
Minutes
30
40
3
Andrew and Karleigh each run for 1 hour. Which statement explains who ran a
greater distance?
C)
Andrew ran a greater distance.
his table increased at a rate of
10
mile per minute.
4
B) Andrew ran a greater distance. The slope of the line described by the data in
his table increased at a rate of mile per minute compared to Karleigh's
12
The slope of the line described by the data in
mile per minute compared to Karleigh's
D) Karleigh ran a greater distance. The slope of the line described by the data in
her table increased at a rate of mile per minute compared to Andrew's
mile per minute

Answer:

60 divided 25

Step-by-step explanation:

The coach brought a mean (average) of 5 footballs.

The sum of all values divided by the total number of values yields the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this central tendency measurement.

We must tally up all of the footballs the coach brought and divide that amount by the number of times he brought them in order to determine the mean (average) number of footballs:

Total number of footballs = 5 + 4 + 4 + 6 + 4 + 7 + 5 + 7 + 2 + 6

Total number of footballs = 50

Number of times the coach brought footballs = 10

Mean number of footballs = Total number of footballs / Number of times the coach brought footballs

Mean number of footballs = 50 / 10

Mean number of footballs = 5

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The probability that the proportion of overweight or obese children in the sample will be greater than 0.57 is less than 50%.

The first paragraph summarizes the answer, stating that the probability is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

In the second paragraph, we can explain the reasoning behind this conclusion. The Central Limit Theorem states that for a large sample size, the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. In this case, the sample was taken in a way that meets the conditions for using the Central Limit Theorem.

Since the population proportion of overweight or obese children is 0.60, any sample proportion below this value is more likely to occur. Therefore, the probability of obtaining a sample proportion greater than 0.57 would be less than 50%. This is because the resulting z-score, which measures how many standard deviations the sample proportion is away from the population proportion, would be negative.

To summarize, the probability of the proportion of overweight or obese children in the sample being greater than 0.57 is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

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The length of the other diagonal of the rhombus is 24 units.

A rhombus is a parallelogram with four equal sides. Since the sides of the rhombus are 12 units long, all the sides are equal in length. One of the angles of the rhombus measures 60 degrees.

In a rhombus, the diagonals bisect each other at right angles, dividing the rhombus into four congruent right-angled triangles. The angle between the two diagonals is 60 degrees, which means that each right-angled triangle in the rhombus has a 30-degree angle.

To find the length of the other diagonal, we can use trigonometry. In a right-angled triangle with a 30-degree angle, the ratio of the length of the side opposite the angle to the length of the hypotenuse is 1/2. In this case, the side opposite the 30-degree angle is half the length of the diagonal we are trying to find.

Let's denote the length of the other diagonal as "d". Using trigonometry, we can set up the following equation:

sin(30 degrees) = (d/2) / 12

Simplifying the equation, we have:

1/2 = (d/2) / 12

Cross-multiplying, we get:

d/2 = 12 * 1/2

d/2 = 6

Multiplying both sides by 2, we find:

d = 12

Therefore, the length of the other diagonal of the rhombus is 24 units.

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The LU factorization of matrix A is A = LU, where L = [[1, 0, 0], [-2, 1, 0], [1.5, -3, 1]] and U = [[4, -8, 10], [0, 24, -27], [0, 0, -12.5]].

Let's go step by step to find the LU factorization of matrix A.

Matrix A:

A =

[4, -8, 10]

[-8, 8, -7]

[6, -7, 3]

Step 1:

Initialize the L matrix as an identity matrix of the same size as A.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 2:

Perform Gaussian elimination to obtain U.

- Multiply the first row of A by (1/4) and replace the first row of A with the result.

A =

[1, -2, 2.5]

[-8, 8, -7]

[6, -7, 3]

- Subtract 8 times the first row of A from the second row of A and replace the second row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[6, -7, 3]

- Subtract 6 times the first row of A from the third row of A and replace the third row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Step 3:

Update the L matrix based on the operations performed during Gaussian elimination.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 4:

The resulting matrix A is the upper triangular matrix U.

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Therefore, the LU factorization of matrix A is:

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

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Value of p is 0.5.

Given

Mean of a binomial distribution np = 12

Sample n = 60

The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure.

To calculate the mean of a binomial distribution B(n, p) we need to multiply the number of trials n by the probability of successes p,

mean = n × p .

Value of p:

np = 12

(60) p = 12

p = 12/60

p = 1/2

p = 0.5

Value of p is 0.5.

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The polynomial with zeros 2, -3, and 5 and degree 3 is P(x) = x^3 - 4x^2 - 11x + 30.

To form a polynomial with given zeros and degree, you can use the following steps:

Start with the given zeros: Let's say you have the zeros a, b, c, ..., up to the degree of the polynomial.

Use the zero-factor property: The zero-factor property states that if a polynomial has a zero at a certain value, then the corresponding factor of the polynomial is (x - zero).

Write down the factors: Write down the factors based on the zeros you have. For example, if you have zeros a, b, and c, the corresponding factors would be (x - a), (x - b), and (x - c).

Multiply the factors: Multiply all the factors together to obtain the polynomial expression.

Simplify the polynomial: Simplify the polynomial by expanding and combining like terms.

Here's an example to illustrate the process:

Let's say you want to form a polynomial with the zeros 2, -3, and 5, and the degree is 3.

The corresponding factors would be (x - 2), (x + 3), and (x - 5).

Multiplying these factors together, we get:

P(x) = (x - 2)(x + 3)(x - 5)

Expanding and simplifying:

P(x) = (x^2 + 3x - 2x - 6)(x - 5)

= (x^2 + x - 6)(x - 5)

= x^3 - 5x^2 + x^2 - 5x - 6x + 30

= x^3 - 4x^2 - 11x + 30

So, the polynomial with zeros 2, -3, and 5 and degree 3 is P(x) = x^3 - 4x^2 - 11x + 30.

By following these steps, you can form a polynomial with given zeros and degree.

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Answer:

When both equations have the same slope, but not the same y-intercept, they'll be parallel to each other and no intersections means no solutions. When both equations have different slopes than regardless of the y-intercept they'll intersect for certain, therefore it has exactly one solution.

Step-by-step explanation:

Got this from google hope it helps

Answer:

- \(\frac{11}{3}\)

Step-by-step explanation:

Using the rules of exponents

\(\frac{1}{a^{m} }\) ⇔ \(a^{-m}\)

\((a^{m}) ^{n}\) = \(a^{mn}\)

Consider the right side

\((\frac{1}{27}) ^{a+3}\)

= \((\frac{1}{3^3}) ^{a+3}\)

= \((3^{-3}) ^{a+3}\)

= \(3^{(-3a-9)}\)

Now we have

9 = \(3^{(-3a-9)}\) , that is

3² = \(3^{(-3a-9)}\)

Since the bases on both sides are equal, equate the exponents

- 3a - 9 = 2 ( add 9 to both sides )

- 3a = 11 ( divide both sides by - 3 )

a = - \(\frac{11}{3}\)

Answer:

Your answer is - 11/3

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

10

Answer:

It will be 3 because its take away hope this helped

Using the triangle inequality theorem, the largest possible whole-number length for the third side is 4.

The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides.

So, for a triangle with sides of length 1, 4, and x (where x is the length of the third side), we have:

1 + 4 > x

4 + x > 1

1 + x > 4

Simplifying these inequalities, we get:

5 > x

x > 3

x > -3 (this inequality is always true)

The largest possible whole-number length for the third side is 4, since it is the largest integer that satisfies the above inequalities.

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Answer:

\(2a+15abc+4\)

Step-by-step explanation:

\((2a-16abc-45)+(2a+7abc+11)\)

\(\implies 2a-16abc-45+2a+7abc+11\)

collect and combine like terms:

\(\implies 4a-9abc-34\)

\((6a+6abc-30)-(4a-9abc-34)\)

Apply the distributive law \(-\left(a-b\right)=-a+b\):

\(\implies 6a+6abc-30-4a+9abc+34\)

collect and combine like terms:

\(\implies 2a+15abc+4\)

This formula is the same as the formula we obtained for the definite integral of a linear function.

If f is a linear function with slope m and y-intercept b, then its equation can be written as:

f(x) = mx + b

To evaluate the integral of f(x) from a to b, we can use the formula for the definite integral of a linear function:

∫[a, b] f(x) dx = [(mx + b) * x]_a^b = (mb + bm) / 2 = mb + (b-a) * m / 2

Therefore, the integral of the linear function f(x) from a to b is:

∫[a, b] f(x) dx = mb + (b-a) * m / 2

Note that if we integrate a linear function over its entire domain, we get the area of the trapezoid formed by the function's graph, the x-axis, and the vertical lines at x = a and x = b. The formula for the area of a trapezoid is:

A = (b-a) * (f(a) + f(b)) / 2 = (b-a) * (ma + b + mb + b) / 2 = (b-a) * (ma + mb + 2b) / 2 = mb + (b-a) * m / 2

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The first five terms of the sequence are: 1, 5/8, 25/64, 125/512, 625/4096.

The sequence converges and the limit is 8/3.

To find the first five terms of the sequence with [(1−3/8)][∞]=1, we can start by simplifying the expression in the brackets:

(1−3/8) = 5/8

So, the sequence becomes:

(5/8)ⁿ, where n starts at 0 and goes to infinity.

The first five terms of the sequence are:

(5/8)⁰ = 1
(5/8)¹ = 5/8
(5/8)² = 25/64
(5/8)³ = 125/512
(5/8)⁴ = 625/4096

To determine whether the sequence converges, we need to check if it approaches a finite value or not. In this case, we can see that the terms of the sequence are getting smaller and smaller as n increases, so the sequence does converge.

To find its limit, we can use the formula for the limit of a geometric sequence:

limit = a/(1-r)

where a is the first term of the sequence and r is the common ratio.

In this case, a = 1 and r = 5/8, so:

limit = 1/(1-5/8) = 8/3

Therefore, the limit of the sequence is 8/3.

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The resize function should be called once if the initial size of the vector is greater than the number of items to be inserted, and additional space is needed for a few more elements.

It depends on the initial size of the vector and the number of items to be inserted. If the vector's initial size is less than or equal to the number of items to be inserted, then the resize function need not be called at all. If the initial size is greater than the number of items to be inserted, then the resize function can be called once to allocate space for a few more elements.

In general, the resize function should be called as few times as possible to minimize the number of memory allocations and improve performance. Ideally, the initial size of the vector should be chosen to be large enough to accommodate the expected number of elements to be inserted, but not so large as to waste memory.

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Answer:

$852

Step-by-step explanation:

From the given question, the following are given:

Present value, PV = $675

Rate, r = 6% = 0.06

Number of years, n = 2 years

Number of times per year, m = 2

The balance in his account is the future value (FV), so that;

Future value = PV\((1+r)^{nm}\)

                     = 675\((1+0.06)^{(2*2)}\)

                     = 675 x 1.26248

                     = 852.174

Future value = $852

Thus, the balance in Alex's account would be $852.

Answer:

The answer is B

Step-by-step explanation:Because as u see it says run

Answer:

9

Step-by-step explanation:

The formula for (a + b)^2 expands out to: a^2 + 2ab + b^2. In the case of this problem, a equals x and b equals 3. We can substitute to get:

(a + b)^2 = a^2 + 2ab + b^2

(x + 3)^2 = x^2 + 2(x)(3) + (3)^2

(x + 3)^2 = x^2 + 6x + 9

So, the missing term is 9.

Another way to do this is to multiply (x + 3)(x + 3) since it's the same thing:

(x + 3)(x + 3)

x^2 + 3x + 3x +9

x^2 + 6x + 9

By solving this way, you get the same answer.

Answer:

It would be 9.

Step-by-step explanation:

To do this, lets expand the equation (x+3)^2 by turning it into:

(x+3)(x+3)

Now, lets try something called the FOIL method. This is where all of the terms of the equation are multiplied in the order:

1) First

2) Outer

3) Inner

4) Last

So in (x+3)(x+3), each of the first parts of each parentheses box are x's, and x times itself equals x^2 so:

x^2 + ? + ? so far.

Next, with the Outer & Inner parts, they would be x * 3 and 3 * x. With this, you would get 3x and 3x. These can be added to get 6x, the middle part of the equation.

x^2 + 6x + ? so far.

Lastly, for the answer. Time to do the last part of each parentheses box, you would get 3 * 3, which gives you 9.

x^2 + 6x + 9.

The distribution of Y = -log(U) is exponential with a parameter 1.

Given that U is uniformly distributed on the interval (0, 1). We need to find the distribution of Y=−log(U).

Here, Y is a transformed variable of U.

Now we know the transformation of U into Y, we need to find the inverse transformation of Y into U.

To find the inverse transformation, we need to express U in terms of Y.

\(U = g(Y) = e^(-Y)\)

Let F_Y(y) be the cumulative distribution function (CDF) of Y.

Then, \(F_Y(y) = P(Y ≤ y)\)

For any y < 0,

we have

\(F_Y(y) = P(Y ≤ y)\)

= P(-log(U) ≤ y)

= P(log(U) ≥ -y)

For y ≤ 0,

P(log(U) ≥ -y) = 1

This is because log(U) is a decreasing function of U.

So, if -y ≤ 0, then U takes all the values between 0 and 1, hence the probability is 1.

For y > 0,

\(P(log(U) ≥ -y) = P(U ≤ e^(-y))\)

\(= F_U(e^(-y))\)

Hence,

\(F_Y(y) = F_U(e^(-y))\)

for y > 0

Hence, the cumulative distribution function (CDF) of Y is given by:

F_Y(y) = [0, for y < 0; 1, for y ≥ 0; \(1 - e^(-y)\), for y > 0]

Now, we can find the probability density function (PDF) of Y by differentiating the CDF of Y for y > 0:

\(f_Y(y) = F_Y'(y) = e^(-y)\) for y > 0.

Hence, the PDF of Y is given by:

f_Y(y) = [0, for y < 0;\(e^(-y)\), for y > 0]

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The advantages of the superposition theorem compared to other circuit theorems are its simplicity and modularity in circuit analysis, as well as its applicability to linear circuits.

Superposition theorem is a powerful tool in circuit analysis that allows us to simplify complex circuits and analyze them in a more systematic manner. When compared to other circuit theorems, such as Ohm's Law or Kirchhoff's laws, the superposition theorem offers several advantages. Here are two key advantages of the superposition theorem:

Simplicity and Modularity: One major advantage of the superposition theorem is its simplicity and modular approach to circuit analysis. The theorem states that in a linear circuit with multiple independent sources, the response (current or voltage) across any component can be determined by considering each source individually while the other sources are turned off. This approach allows us to break down complex circuits into simpler sub-circuits and analyze them independently. By solving these individual sub-circuits and then superposing the results, we can determine the overall response of the circuit. This modular nature of the superposition theorem simplifies the analysis process, making it easier to understand and apply.

Applicability to Linear Circuits: Another advantage of the superposition theorem is its applicability to linear circuits. The theorem holds true for circuits that follow the principles of linearity, which means that the circuit components (resistors, capacitors, inductors, etc.) behave proportionally to the applied voltage or current. Linearity is a fundamental characteristic of many practical circuits, making the superposition theorem widely applicable in real-world scenarios. This advantage distinguishes the superposition theorem from other circuit theorems that may have limitations or restrictions on their application, depending on the circuit's characteristics.

It's important to note that the superposition theorem has its limitations as well. It assumes linearity and works only with independent sources, neglecting any nonlinear or dependent sources present in the circuit. Additionally, the superposition theorem can become time-consuming when dealing with a large number of sources. Despite these limitations, the advantages of simplicity and applicability to linear circuits make the superposition theorem a valuable tool in circuit analysis.

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A hurricane is a big rotating storm system that develops over warm ocean waters and usually travels westward toward the American mainland.

An Atlantic Ocean hurricane or a northern Pacific Ocean hurricane is a tropical storm. In most years, hurricanes develop between June 1 and November 30. The Taino Indian word "hurakan," which means "god of wind," is where the word "hurricane" originates.

A hurricane is a big rotating storm system that develops over warm ocean waters and usually travels westward toward the American mainland. Depending on the maximum sustained wind speeds, hurricanes are either classed as tropical storms or hurricanes. Hurricanes have winds of 74 mph or more, whereas tropical storms have winds of 39 to 73 mph.

The hurricane's eye, which is a calm, clear region encircled by powerful winds, is the most hazardous component of the storm. The hurricane's eye, which can be up to 30 miles across, frequently experiences the storm's greatest rains and highest winds.

A hurricane's landfall can result in flooding from storm surges, strong winds, and heavy rains. The increase in sea level that happens as a cyclone nears land is known as a storm surge. Along with coastal locations, this increase in water level has the potential to inflict significant harm and flooding.

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Answer:

I think it is associative! Not sure though bc of the q!

Step-by-step explanation:

Answer: The mood of the third-person account is less emotional and more matter-of-fact. The mood of Claudette's account is less emotional and more matter-of-fact.

Step-by-step explanation:

Answer:

18x

Step-by-step explanation:

Collect like terms.

2((5x+4x)+(4-4))

Simplify (5x+4x)+(4−4) to 9x.

2×9x

Simplify.

18x

Given:

The expression is:

\(b^2+20b\)

To find:

The a monomial so that the trinomial may be represented by a square of a binomial.

Solution:

If an expression is \(x^2+bx\), then be need to add square of half of coefficient of x, i.e., \(\left(\dfrac{b}{2}\right)^2\) in the given expression to make in perfect square.

We have,

\(b^2+20b\)

Here, coefficient of b is 20,so wee need to add square of half of coefficient of b, i.e., \(\left(\dfrac{20}{2}\right)^2\).

\(\left(\dfrac{20}{2}\right)^2=10^2\)

\(\left(\dfrac{20}{2}\right)^2=100\)

Therefore, we need to add 100 to make \(b^2+20b\) a perfect square binomial.

Step-by-step explanation:

The equation of the line perpendicular to the line y = -3x + 6 and passing through the point (-2,8) is y = (1/3)x + (10/3).