Question 3 of 21
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 12x-8
y = 8x
O
A. (2, 16)
B. (5, 11)
O C. (4,12)
O
D. (3, 15)

Answer:

a

Step-by-step explanation:

in y intercept x = 0 so the choice a become the answer

Madison figures out the average and range of chloride readings from wells close to the ocean. Other than a query, she has carried out an operation. The answer id option (d).

The standard deviation is a measure of variance from the mean that takes spread, dispersion, and dispersion into account. The standard deviation displays a "typical" divergence from the mean. It is a well-liked measure of variability since it retains the primary units of measurement from the data set.  A minor variation occurs when the numbers are close to the mean, while a high variation occurs when they are far from the mean.

The standard deviation describes the degree to which the results deviate from the mean. The average deviation, which depends on all values, is the most often used metric for measuring dispersion. Consequently, the standard deviation's value can be altered even by a slight change in one value.

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a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

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In the context of the formula V x E = Motivation, the E represents Effort as a significant factor in determining an individual's motivation level.

In the formula, V x E = Motivation, the E stands for Effort.

Effort refers to the amount of energy and exertion put forth by an individual towards achieving a goal or desired outcome. It represents the level of dedication, commitment, and persistence in undertaking tasks or activities. Effort plays a crucial role in determining the level of motivation an individual possesses.

The formula V x E = Motivation suggests that motivation is a product of the value (V) an individual places on a specific goal or outcome and the effort (E) they are willing to invest in pursuing that goal. The more effort one puts in, the higher their motivation is likely to be.

Effort can encompass various components, such as physical exertion, mental focus, time commitment, and emotional investment. It involves pushing oneself beyond comfort zones, overcoming challenges, and maintaining a strong work ethic.

Therefore, in the context of the formula V x E = Motivation, the E represents Effort as a significant factor in determining an individual's motivation level.

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Based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.

Chebyshev's Theorem states that for any given number k greater than 1, at least (1 - 1/k²) of the data values in a dataset will fall within k standard deviations of the mean.

In this case, we have a sample size of 225 bags and a mean weight of 353 gm with a standard deviation of 6 gm.

To find a lower bound for the number of bags that weigh between 335 and 371 gm, we need to calculate the range within k standard deviations of the mean.

First, let's find the number of standard deviations for the given range:

Lower range: (335 - 353) / 6 = -3

Upper range: (371 - 353) / 6 = 3

Since we want to find the lower bound, we consider the lower range and use its absolute value: |-3| = 3.

Now, we can use Chebyshev's Theorem to find the lower bound:

(1 - 1/k²) ≤ (1 - 1/3²) = 1 - 1/9 = 8/9

This means that at least 8/9 of the bags will fall within 3 standard deviations of the mean.

To find the lower bound for the number of bags, we multiply this probability by the sample size:

Lower bound = (8/9) * 225 = 200

Therefore, based on Chebyshev's Theorem, we can conclude that the lower bound for the number of bags in a sample of 225 that weigh between 335 and 371 gm is 200 bags.

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The optimal solution for the given linear programming model is:

max z = 38

when x1 = 5, x2 = 10, x3 = 0

To solve the given linear programming model using the simplex algorithm, we start by converting the inequalities into equations and introducing slack variables. The initial tableau is constructed with the coefficients of the decision variables and the right-hand side constants.

Next, we apply the simplex algorithm to iteratively improve the solution. By performing pivot operations, we move towards the optimal solution. In each iteration, we select the pivot column based on the most negative coefficient in the objective row and the pivot row based on the minimum ratio test.

After several iterations, we reach the optimal tableau, where all the coefficients in the objective row are non-negative. The optimal solution is obtained by reading the values of the decision variables from the tableau.

In this case, the optimal solution is z = 38 when x1 = 5, x2 = 10, and x3 = 0. This means that to maximize the objective function, the decision variables x1 and x2 should be set to 5 and 10 respectively, while x3 is set to 0.

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Answer:

may be that is not V that mau be some numbers

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Answer:

f(4) =2*4-6 = 8-6 =2

Step-by-step explanation:

mark me as brainliest ❤️

Answer: 2

Step-by-step explanation: Substitute n for 4

f(n)=f(4)

2(4)-6=2

Answer:

9x -5

1/2(6x +22)

2(x-7)-9

x2 -11

Answer:

10

Step-by-step explanation:

Subtract -4 from 6

6 - -4

Subtracting a negative is like adding

6 +4

10

Answer:

-10

Step-by-step explanation:

If you subtract 6-(-4) it gives you -10

Hope this helps

Answer:

See below.

Step-by-step explanation:

So, Nikki earns $12 per hour.

And she also earns a 5% or 0.05 commission of her total sales each day.

On Saturday, she worked eight hours and she earned $139. In other words, she earned 8(12) or $96 from working her hours and another $43 (139-96) from her commission.

Thus:

\(139=96+0.05x\)

Where x represents Nikki's total sales on Saturday.

Further notes:

To solve, subtract 96 from both sides and divide by 0.05:

\(139=96+0.05x\\43=0.05x\\x=\$860\)

Thus, her total sales that day were $860.

Question:

52% of the total number of students in a school are boys. If there are 260 boys,​ how many students are there in total? how many of them are girls?

Answer and Step-by-step explanation:

The total amount of students is 500.

Yo get this by dividing 260 by 52%, or 0.52

Now, we know 260 is the amount of boys, so to find the amount of girls, we subtract 260 from 500.

500 - 260 = 240.

There are 240 students that are girls.

This also means that 48% of the total number of students in a school are girls.

#teamtrees #PAW (Plant And Water)

The annual simple interest rate for Lona's certificate of deposit is approximately 1.4% when rounded to the nearest tenth of a percent. Therefore, the annual simple interest rate for Lona's certificate of deposit is approximately 40.6%.

To find the annual simple interest rate, we can divide the total interest earned over the 36-month period by the principal amount and then multiply by 100 to convert it to a percentage.

Lona placed $6200 in the certificate of deposit, and she earns $70 each month for 36 months. To calculate the total interest earned, we can multiply the monthly interest of $70 by the number of months (36). This gives us a total interest of $2520.

Next, we divide the total interest earned ($2520) by the principal amount ($6200) and multiply by 100 to get the interest rate as a percentage.

($2520 / $6200) * 100 ≈ 40.6451613...

Rounding this value to the nearest tenth of a percent gives us approximately 40.6%. Therefore, the annual simple interest rate for Lona's certificate of deposit is approximately 40.6%.

If there are compounding periods or other terms associated with the certificate of deposit, the calculation of the interest rate may differ.

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The coordinates of point P' would be (-2, 0). To calculate this, we use the scaling and translation transformation equations.

The scaling transformation formula is (x, y) → (x', y') = (kx, ky), where k is the scale factor. In this case, k = 2/3. Therefore, the coordinates of point P' would be (2/3x, 2/3y).

The translation transformation formula is (x, y) → (x', y') = (x + h, y + k), where h is the horizontal shift and k is the vertical shift. In this case, h = -2 and k = 0. Therefore, the coordinates of point P' would be (2/3x-2, 0).

We know that the coordinates of point P is (0, 0). Therefore, the coordinates of point P' would be (2/3 x - 2, 0) = (-2, 0).

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Answer:127.5

Step-by-step explanation:

15% of 150 = 22.5

150-22.5=127.5

Answer:

Step-by-step explanation:

Your average waiting time will be approximately 1 minute.

As the first passenger, you will not have to wait for any other passengers to get in the taxi. However, the taxi will wait for 2 passengers to arrive or 3 minutes to pass since your boarding.

Since passengers arrive according to a Poisson process with an average of 60 passengers per hour, the arrival rate lambda can be calculated as:

lambda = average number of passengers per time unit = 60/60 = 1 passenger per minute

The time between two consecutive passenger arrivals follows an exponential distribution with parameter lambda. Thus, the probability of waiting less than t minutes for the second passenger to arrive can be calculated as:

P(wait < t) = 1 - e^(-lambda*t)

We need to find the average waiting time until the second passenger arrives. This can be calculated as the area under the probability distribution curve divided by the arrival rate lambda:

average waiting time = integral from 0 to infinity of t*(1 - e^(-lambda*t)) dt / lambda

Using integration by parts, we can solve this integral to get:

average waiting time = 1/lambda + (1 - e^(-lambda*t))/(lambda^2)

Plugging in the values, we get:

average waiting time = 1/1 + (1 - e^(-1*3))/(1^2) = 1 + (1 - 0.0498) = 1.9502 minutes

Therefore, as the first passenger, your average waiting time until the second passenger arrives is 1.9502 minutes.

To answer your question, let's consider the two possible scenarios:

1. Two passengers are collected: In this case, the first passenger (you) waits for the second passenger to arrive. Since the arrival rate is 60 passengers per hour, the average time between arrivals is 1 minute (60 minutes / 60 passengers).

2. Three minutes have expired: In this case, the taxi departs after 3 minutes even if only one passenger (you) is in the taxi.

On average, the waiting time for the first passenger (you) will be the minimum of these two scenarios. Thus, your average waiting time will be approximately 1 minute.

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The perimeter of the triangle will be 41ft

The perimeter of a triangle is the sum of all the sides of the triangle

From the given triangle, we need to get the third sidee firse as shown:

h² = 12² + 12²

h² = 144 + 144

h² = 288

h = 17ft

Perimeter = 12 + 12 + 17

Perimeter = 41ft

Hence the perimeter of the triangle will be 41ft

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Answer: 41 ft

Step-by-step explanation:

The only local minimum of the function is at x = 32/35.So, the x-coordinate of the local minimum is 32/35. Therefore, the answer is 32/35.

To find the x-coordinates of all local minima of the function g(x) = 7x5 – 8x4 + 2, we will take the first and second derivatives of the function and look for the values of x at which the second derivative is positive and the first derivative is zero. These x-values will be the local minima of the function. First derivative of g(x):g'(x) = 35x4 – 32x3At local minima, g'(x) = 0So, 35x4 – 32x3 = 0=> x3(35x – 32) = 0=> x = 0, 32/35 Second derivative of g(x):g''(x) = 140x3 – 96x2At x = 0,g''(0) = 0At x = 32/35,g''(32/35) > 0.

Therefore, the only local minimum of the function is at x = 32/35.So, the x-coordinate of the local minimum is 32/35. Therefore, the answer is 32/35.

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Answer:

9 cm

Step-by-step explanation:

As the circumference = 2*pi*r, as C = 18 pi cm = 2*pi*r, so r = 9 cm.

Answer:

no solution

Step-by-step explanation:

Given

2(n + 2) = 4n + 1 - 2n ← distribute parenthesis on left side

2n + 4 = 2n + 1 ( subtract 4 from both sides )

2n = 2n - 3 ( subtract 2n from both sides )

0 = - 3 ← not possible

This indicates the equation has no solution

The original equation 2(n + 2) = 4n + 1 - 2n has no solution for n.

To solve the equation 2(n + 2) = 4n + 1 - 2n, we can simplify and then solve for the variable n.

First, distribute 2 to the terms inside the parentheses:

2n + 4 = 4n + 1 - 2n

Next, combine like terms on the right side:

2n + 4 = 2n + 1

Now, subtract 2n from both sides to isolate the n term:

2n - 2n + 4 = 2n - 2n + 1

4 = 1

Since 4 is not equal to 1, there is no solution to this equation.

Therefore, the original equation 2(n + 2) = 4n + 1 - 2n has no solution for n.

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Answer:

I don omgbro why do I always have to wait

Step-by-step explanation:

What is (-3,9) ok so thanks for this app my crush says Ily to me cuz I gave her he right answer thanks alot brainly

We can distribute prizes in 17184279361888 ways when the prizes are identical such that either Alice or Bob or both receive a prize. We can distribute prizes in 345157879971232000 ways when the prizes are different.

Let us consider the two possible cases when the prizes are identical and different.

Case 1: Prizes are identical - In this case, we have ten prizes and 100 students. Since Alice and Bob are also among the students, we need to calculate the number of ways the prizes can be distributed such that either Alice or Bob or both receive a prize. We can use the complementary counting method to calculate this number of ways.

First, we find the total number of ways the prizes can be distributed without any restrictions. This is given by:

¹⁰⁰C₁₀ = 17310309456440 (the number of ways to choose 10 students from 100)

Now we find the number of ways the prizes can be distributed such that neither Alice nor Bob receives a prize. The number of ways the remaining 98 prizes can be distributed among the remaining 98 students is given by:

⁹⁸C₁₀ = 126410606437752 (the number of ways to choose 10 students from 98)

Hence, the number of ways the prizes can be distributed such that either Alice or Bob (or both) receive a prize is: 17310309456440 - 126410606437752 = 17184279361888

Case 2: Prizes are different - In this case, we also need to calculate the number of ways the prizes can be distributed such that either Alice or Bob or both receive a prize. However, since the prizes are different, the problem is slightly different.

Let us first calculate the total number of ways the prizes can be distributed without any restrictions.

This is given by: ¹⁰⁰P₁₀ = 9332621544394000000 (the number of ways to order 10 students from 100)

Now we need to subtract the number of ways the prizes can be distributed such that neither Alice nor Bob receives a prize. For Alice not to receive a prize, there are 9 prizes to choose from, and the remaining 98 students can be assigned the remaining 9 prizes in ⁹⁸P₉ ways.

Similarly, for Bob not to receive a prize, there are 9 prizes to choose from, and the remaining 98 students can be assigned the remaining 9 prizes in ⁹⁸P₉ ways. However, we have subtracted the number of ways Alice and Bob do not receive a prize twice, so we need to add this number back.

Hence, the number of ways the prizes can be distributed such that either Alice or Bob (or both) receive a prize is:

9332621544394000000 - 2(9 x ⁹⁸P₉ ) + 8 x ⁹⁷P₈ = 345157879971232000

We can distribute prizes in 17184279361888 ways when the prizes are identical such that either Alice or Bob or both receive a prize. We can distribute prizes in 345157879971232000 ways when the prizes are different such that either Alice or Bob or both receive a prize.

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Answer:

x

Step-by-step explanation:

The greatest common factor is x. This is the biggest term that each term can be divided by.

Answer:

Population density = 47 people per square miles

Step-by-step explanation:

From the picture attached,

Coordinates of vertex B → (3.87, 2.76)

Which represents length of vertex A from origin O (AD)= 2.76 units ≈ 276 miles

Length of vertex B from origin O (CD) = 3.87 units ≈ 3.87 miles

Area of rectangle ABCD = Length × Width

                                         = CD × AD

                                         = 387 × 276

                                         = 106812 square miles

Population of Colorado = 5029196 people

Population density of Colorado = \(\frac{\text{Total population}}{\text{Total area}}\)

                                                     = \(\frac{5029196}{106812}\)

                                                     = 47.08

                                                     ≈ 47 people per square miles

The population density at the end of 2010 in people per square mile is 47.

Length of vertex A from origin O (AD)= 2.76 units ≈ 276 miles

Length of vertex B from origin O (CD) = 3.87 units ≈ 3.87 miles

Now  

Area of rectangle ABCD = Length × Width

 = CD × AD

= 387 × 276

= 106812 square miles

And,

Population of Colorado = 5029196 people

So,  the population density is

\(= 5029196 \div 106812\)

= 47

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There are 27,720 different arrangements of red and yellow roses.

The total number of roses is 8 + 4 = 12. To find the number of different arrangements, we can use the formula for permutations, which is:

n! / (n - r)!

where n is the total number of objects and r is the number of objects we want to arrange.

In this case, we want to arrange all 12 roses, so n = 12. The number of red roses is 8, so r = 8. Therefore, the number of different arrangements of the roses is:

12! / (12 - 8)! = 12! / 4! = 27,720

So there are 27,720 different arrangements of the 8 red roses and 4 yellow roses.

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The pool holds about 245,000 gallons. Therefore, option (c) 244,596 gal is correct.

To find the number of gallons of water the pool holds, we need to convert the volume in cubic feet to gallons.

One cubic foot is equal to 7.4805194805 gallons, so to find the number of gallons in the pool, we can multiply the volume in cubic feet by the conversion factor:

1 cubic foot= 7.4805194805 gallons

gallons = 32,700 cubic feet * 7.4805194805 gallons/cubic foot

= 244,999.99968 gallons

Rounded to the nearest gallon, the pool holds about 245,000 gallons.

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One cubic foot is equal to 7.4805194805 gallons, so to find the number of gallons in the pool, we can multiply the volume in cubic feet by the conversion factor:

1 cubic foot= 7.4805194805 gallons

gallons = 32,700 cubic feet * 7.4805194805 gallons/cubic foot

= 244,999.99968 gallons

Rounded to the nearest gallon, the pool holds about 245,000 gallons.