Use the information in the problem to write an equation. Then use the equation machine to help you solve it.

8 years ago Marcus was 12 years old. How old is he now?

Marcus is _______ years old.

The solution to the linear system is x₁ = 0, x₂ = -5/4, and x₃ = 3/2.

We start with the augmented matrix:

[1 2 3 | 2]

[-1 2 5 | 5]

[2 1 3 | 9]

First, we eliminate the variable x₁ from the second and third equations by adding the first equation to them:

[1 2 3 | 2]

[0 4 8 | 7]

[0 -3 -3 | 5]

Next, we eliminate the variable x₂ from the third equation by adding 3/4 times the second equation to it:

[1 2 3 | 2]

[0 4 8 | 7]

[0 0 3 | 18/4]

Now, we have the system in row echelon form. We can perform backward substitution to find the values of the variables. Starting from the last equation, we have:

3x₃ = 18/4 -> x₃ = 18/4 / 3 = 3/2

Substituting this value back into the second equation, we have:

4x₂ + 8(3/2) = 7 -> 4x₂ + 12 = 7 -> x₂ = -5/4

Finally, substituting the values of x₂ and x₃ into the first equation, we have:

x₁ + 2(-5/4) + 3(3/2) = 2 -> x₁ - 5/2 + 9/2 = 2 -> x₁ = 0

Therefore, the solution to the linear system is x₁ = 0, x₂ = -5/4, and x₃ = 3/2.

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Influencers can also provide valuable feedback and insights into the target audience, allowing PR practitioners to refine their messaging and strategy.Social media influencers and public relations practitioners both share the same common goal, which is to communicate a message to a specific audience.

In this way, social media influencers complement the works of public relations practitioners through their reach and ability to effectively promote a message to their followers.Social media influencers can help to boost the image of a company, brand, or product, as they have a large and dedicated following. They also have the ability to influence their followers’ opinions and behavior, making them an attractive target for public relations practitioners to work with to achieve their goals. Influencers can also provide valuable feedback and insights into the target audience, allowing PR practitioners to refine their messaging and strategy.

In addition, social media influencers often have a more personal and relatable connection with their followers, which can be a valuable asset for public relations practitioners. By partnering with influencers, PR practitioners can leverage their credibility and trust with their followers to enhance the message they are trying to communicate.To summarize, social media influencers and public relations practitioners work together to achieve a common goal. Influencers can provide a valuable platform to reach a large audience and offer insights into the target demographic, while PR practitioners can leverage influencers’ credibility and trust with their followers to enhance their messaging and achieve their communication objectives.

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Answer:

21/2

Step-by-step explanation:

\(\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}\)

\(10\frac{1}{2}=\frac{10\cdot 2+1}{2}=\frac{21}{2}\)

\(=\frac{21}{2}\)

Hence, Answer = 21/2

Decimal form = 10.5

[RevyBreeze]

Answer:

  7 m/s²

Step-by-step explanation:

Since force and acceleration are proportional, multiplying the force by a factor of 14/6 = 7/3 will multiply the acceleration by that same factor:

  acceleration = (3 m/s²)(7/3) = 7 m/s²

Answer:

8 + 6b - b + 4=

8 + 4 = 12

6b + b = 7b

7b + 12 is the final answer

Step-by-step explanation:

Hope this helps! :)

Answer: 12+5b

Step-by-step explanation:

8+6b-b+4

combine like terms

8+4=12

6b-b=5b

12+5b

1) Note that the measures of dispersion are given as follows;


Mean = 22

Median = 20
Range = 39

2) The standard deviation based on the completed table is  11.696. See table attached.

Mean:

To find  the mean, you add up all the ages  and divide by the total number of ages:

= (2 + 8 + 14 + 19 + 20 +  21 + 26 + 33 + 36 +  41) /10

thus

Mean = 22.0

Median:

To find the median, you need to find the middle number when the ages are arranged in order:

2, 8, 14, 19, 20,  21, 26, 33, 36, 41

The middle numbers  are  (20 + 21)/2 = 20.5

so the median age is 20.5

Range:

To find the range, you subtract the smallest age from the largest age:

41 - 2 = 39

Therefore:

Mean = 22

Median = 20.5
Range = 39


2)

To find the standard deviation of the elephant ages, we first need to calculate the variance:

Find the mean (X):

X = (2 +  8 + 14 + 19 +  20 + 21 + 26 + 33 + 36 + 41)/ 10

X = 22

Subtract the mean from each value and square the result:

(x - X)²:

(2 - 22)² = 400

(8 - 22)² = 196

(14 - 22)² = 64

(19 - 22)² = 9

(20 - 22)² = 4

(21 - 22)² = 1

(26 - 22)² = 16

(33 - 22)² = 121

(36 - 22)² = 196

(41 - 22)² = 361

Sum up all the squared differences:

400 + 196 + 64 + 9 + 4 + 1 + 16 + 121 + 196 + 361 = 1368

Divide the sum by the number of values (n):

1368 / 20 = 136.8

Take the square root of the variance to get the standard deviation:
√136.8 = 11.696

Thus, the standard deviation =  11.696

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64.77% of a given amount remains after 900 years.

To determine the percentage of radioactive radium remaining after 900 years, we'll use the half-life formula:

Final Amount = Initial Amount * \(1/2^{(time elapsed / half-life)}\)

In this case, the half-life is 1599 years and the time elapsed is 900 years. We want to find the percentage remaining, so let's assume the initial amount is 100%.

Final Amount = 100 * \((1/2)^{(900 / 1599)}\)

Now, we'll calculate the exponent:

Exponent = 900 / 1599 ≈ 0.5635

Then, we'll compute the final amount:

Final Amount ≈ 100 * \((1/2)^{0.5635}\) ≈ 100 * 0.6477 ≈ 64.77%

After 900 years, approximately 64.77% of the initial radioactive radium remains. This percentage was found using the half-life formula, which accounts for the exponential decay of radioactive substances over time.

The formula shows how the remaining amount of a substance decreases as time progresses based on its half-life, which is the time it takes for half of the substance to decay. In this scenario, radium's half-life of 1599 years and the 900-year time frame were used to determine that roughly 64.77% of the initial radium remains.

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Answer:

im still middle school i love to help people who r in higher classes so ill try

Step-by-step explanation:

maybe divide 73% by 0.4

The amounts in this problem are given as follows:

1.

2. Percent error of 25%.

3. Increase of 176.25%.

4. Increase of 140%.

5. Decrease of 30%. (percent of change = -30%).

Out of 16 ounces, the percent error is of 2.5%, hence the measure is of:

0.025 x 16 = 0.4 ounces.

Then the minimum acceptable rate is:

16 - 0.4 = 15.6 ounces.

The maximum acceptable rate is:

16 + 0.4 = 16.4 ounces.

The percent error is the difference between the actual and the estimate measure, divided by the actual measure, hence:

(20 - 16)/16 = 4/16 = 0.25 = 25%.

The percent of increase is given by the increase(final - initial) divided by the initial amount, hence:

(44.2 - 16)/16 = 1.7625 = 176.25% percent increase.

For the gallons, the increase is calculated as follows:

(24 - 10)/10 = 1.4 = 140% increase.

The percent of decrease is given by the decrease(final - initial) divided by the initial amount, hence, for the pounds:

(50 - 35)/50 = 0.3 = 30%.

Since it is a decrease, the percent of change is negative, hence -30%.

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The Vamers live on a corner lot. Often, children cut across their lot to save walking distance. the walking distance that is saved by cutting across their property instead of walking around the lot is 20 feet (to the nearest integer)

information given in the question

hypotenuse = 48 feet

opposite = x

adjacent = x + 6

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

48² = x² + (x+6)²

2304 = x² + x² + 12x + 36

equating to zero

0 = x² + x² + 12x + 36 - 2304

0 = 2x² + 12x - 2268

2x² + 12x - 2268 = 0

x = 30.808  OR   -36.808

taking the positive value, x = 30.808 feet

adjacent = x + 6 = 30.808 + 6 = 36.808

The total distance

= adjacent + opposite

= 20.808 + 36.808

= 67.616

walking distance saved

= total distance - hypotenuse

= 67.616 - 48

= 19.616

= 19.62 feet (to the nearest hundredth)

= 20 feet (to the nearest integer)

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Division is one of the four fundamental arithmetic operations. The number of days this cat food will last is 14 days.

Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that each cat eats 1/4 of a tin of cat food each day. Therefore, the amount of food that two cats will eat in a day is,

= 2 ×  1/4 of a tin of cat food each day

= 1/2 of a tin of cat food each day

Further, it is given that Sally buys 7 tins of cat food. Therefore, the number of days this cat food will last is,

= Total cat food / Cat food needed in a day

= 7tin of cat food / 1/2 of a tin of cat food each day

= 14 days

Hence, the number of days this cat food will last is 14 days.

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Answer: well she has 3 bro's plus her is 4 peeps and 2 braces 27.32x2=54.64  10x4=40 so theygot 40 dollars and 52.64-40=14.64

Step-by-step explanation:

Answer:

14.64

Step-by-step explanation:

54.64 - 40.00 = 14.64 beacuse 2 x 27.32 = 54.64 and the each have 10 bucks and there are 4 people so 40 bucks.

Based on the assumptions, Phone B has a much higher probability of having a battery life between 18 and 22 hours compared to Phone A.

Probability is the measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory is widely used in fields such as mathematics, statistics, physics, economics, engineering, and social sciences to model and analyze uncertain situations and make predictions.

To find the probability that the battery life is between 18 and 22 hours for each phone using the normalcdf function, we need to know the mean and standard deviation of the battery life distribution for each phone.

Let's assume that for Phone A, the mean battery life is 20 hours with a standard deviation of 1 hour, and for Phone B, the mean battery life is 21 hours with a standard deviation of 0.5 hours.

For Phone A, using the normalcdf function on a calculator, we get:

normalcdf(18, 22, 20, 1)

This gives a probability of approximately 0.6827, or 68.27%, that the battery life is between 18 and 22 hours for Phone A.

For Phone B, using the normalcdf function on a calculator, we get:

normalcdf(18, 22, 21, 0.5)

This gives a probability of approximately 0.9973, or 99.73%, that the battery life is between 18 and 22 hours for Phone B.

Therefore, based on these assumptions, Phone B has a much higher probability of having a battery life between 18 and 22 hours compared to Phone A.

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Given the matrix expression A = (a 0 3(a-b) b) = (1 0 3 1) (a 0 0 b) (1 0 -3 1), we want to compute the matrix power Ak using the factorization A = PDP^-1.

First, we need to find the matrices P and D. The matrix D is a diagonal matrix consisting of the eigenvalues of A, which are a, b+3a, and b-3a. The matrix P is the matrix whose columns are the eigenvectors of A, which can be found by solving the system (A - λI)x = 0 for each eigenvalue λ.

Solving for each eigenvalue, we get λ1 = a with eigenvector (0,1), λ2 = b+3a with eigenvector (-3,1), and λ3 = b-3a with eigenvector (1,1). Thus, we have:

D = (a 0 0

0 b+3a 0

0 0 b-3a)

P = (0 -3 1

1 1 1

0 0 1)

To compute Ak, we can use the formula A^k = PD^kP^-1. Since D is a diagonal matrix, we can easily compute D^k by raising each diagonal entry to the power of k. Thus, we get:

D^k = (a^k 0 0

0 (b+3a)^k 0

0 0 (b-3a)^k)

Multiplying out the matrices P and P^-1, we get:

P^-1 = (1/3 -1/3 0

-1/3 2/3 -1/3

0 -1/3 1/3)

P^-1AP = D

Multiplying both sides by P^-1, we get:

A = PDP^-1

Now, substituting D^k into the formula A^k = PD^kP^-1, we get:

A^k = P D^k P^-1

Substituting the matrices P, P^-1, and D^k, we get the expression for Ak as:

Ak = (1/3)((b+3a)^k - (b-3a)^k) (1 -3(b-3a)^k/(b+3a)^k - 3(b+3a)^k/(b-3a)^k 1) (a 0 0 b)

Therefore, we have the expression for Ak.

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Answer:

C

Step-by-step explanation:

Answer:

138

Step-by-step explanation:

52÷4+5^3

52÷4+125

13+125

138

Danika walks 50 blocks in one week.

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer. The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to make repetitive adding of the same number easier. It is used for combining groups of identical size.

As per the data given,

We have,

Danika lives at 5 blocks from her school.

As Danika walks 5 blocks to and from school, making her round trip

So, total distance covered by Danika will be: 5 blocks + 5 blocks = 10 blocks.

As Danika walks to and from school 5 days a week,

Hence, she walks 10 blocks * 5 days = 50 blocks in one week.

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Part A: Based on the scatter plot given, the correlation coefficient of r = 0.01 is most likely accurate because the data points are far away from each other.

Part B: A casual relationship would be: the number of strawberries picked and the amount of fertilizers used.

Correlation coefficient, r, is quantitative measure that measures the extent to which two variables are associated.

The closer the data points are on a scatter plot, the closer the value of r is to 1 or -1.

Part A:

The data points in the scatter plot are farther apart and the trend slopes upwards to the right, this means that the correlation coefficient, r, would be positive but very low.

Thus, based on the scatter plot given, the correlation coefficient of r = 0.01 is most likely accurate because the data points are far away from each other.

Part B:

A casual relationship would be: the number of strawberries picked and the amount of fertilizers used.

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Answer:

4:7, 16:28, 32:56, 64:112

Step-by-step explanation:

You can go down 1, and you can also keep doubling. I hope this helped, I hope you get it right! Have a Good Day!

Answer: Choice C

i/j = h/k

=============================================

Explanation:

The triangle proportionality theorem basically says that if we draw a parallel line somewhere inside the triangle like this, then we'll split the sides into smaller pieces that are proportional to one another (eg: the longer side is say 3 times longer than the shorter side for each piece of the original triangle).

One statement we can make is j/k = i/h. This then can be rearranged into i/j = h/k after doing a bit of algebra. Other equations are possible, so there are many combos we could try.

(3,0) is an x-intercept of the continuous function in the table.

If the graph of a function crosses the x-axis, then the function has an x-intercept. The x-intercept(s) of a function are called the zeros or the roots of the function.

If the graph of function crosses the y-axis, then the function has a y-intercept. A function can have at most one y-intercept.

Given that,

The table with x as the domain and f(x) as the range.

To find the x-intercepts, we need to find all the x-values that support the equation; f(x) = 0. An x-intercept is the first component of the ordered pair (k,0). Where k is any real number.

A y-intercept is the second component of the ordered pair (0,c), where c is any real number.

From the table provided, stated that:

So, the x-intercept becomes: (3,0).

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The complete question is as follows:

Which is an x-intercept of the continuous function in the table? (0,-6) (3,0) (-6, 0) (0, 3)

The minimum amount of fence needed to enclose the lots is 120ft.

Adding areas of both fields, the combined area comes about to be 600sq ft.

The dimensions of the new plot are x length and y breadth. According to the question, there is a fence in the middle with y breadth.

g(x, y, z) = xy - 600

g(x, y, z) = 2x + 3y

∇g = ∇ (xy - 600) = (y, x)

∇f = ∇(2x + 3y) = (2, 3)

Now from the Lagrange method,

∇f = λ∇g

2 = λy

3 = λx

Now to get the value of lambda,

(2/y) = (3/x) = λ

x = 1.5y

Solving now we get,

1.5y² = 600

y = 20

x = 1.5 × 20 = 30

Thus after getting (x,y) we can put the value in the function to get the answer as 120ft.

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Answer:

32 boxes of gummies

I think it is 2, 0, 4 but it would be very helpful if you put in an image of the graph.

Have a great day :D

y = -1/3x + 1

y = -2x - 3

We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.

The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.

The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.

Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.

Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.

The correct option is B) Categorical

The variable X in this case is categorical. Categorical variables represent distinct categories or groups and do not have a numerical value associated with them. In this example, X represents different types of animals (cat, dog, pig, bear, lion), which are categories or groups.

Therefore, the correct answer is B) Categorical.

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Answer:

You are Amazing and Beautiful. I hope you have the greatest day and be happy and safe always! I don't have much to say but I hope you have an amazing year ahead and be successful always :)

Answer:

I hope everyone is safe during this quarantine. It is times like these where we are better together. We (my family and I) are praying for all those who have been affected or knows someone who has beed affected. Hope everyone is safe and healthy. And thanks to you, I am able to say something nice to those who need to hear it!

Step-by-step explanation:

The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

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Answer:

one solution

Step-by-step explanation:

since the variables are only to a power of one, the options are no solutions, one solution, and infinitely many solutions.

using the distributive property, 10(x+4)= 10x + 40. simplify the equation 10x + 40 - 3 = 14x +1 to 10x + 37 = 14x + 1. move variables to one side and constants to another to get 4x = 36. divide to get x=6. so the answer is one solution

since we don't have something like 1=0 where two unequal constants are said to be equal, the answer isn't no solutions

since we dont have something like 1=1 where the two sides of the equation are equal no matter what x is, the answer isn't infinitely many solutions

Answer:

only one

x = 9

Step-by-step explanation:

how many solutions are in 10(x + 4) – 3 = 14x + 1

10(x + 4) – 3 = 14x + 1

10x + 40 - 3 = 14x + 1

-4x = 36

x = 9

only one

x = 9