If the standard deviation of a data set were originally 8 and if each value in the data set were multipled by 1. 75 what would be the standard deviation of the resulting data

Answer:

D. 75 m²

Step-by-step explanation:

l = 15m

b = 5m

area of rectangle = l × b = 15 × 5 = 75 m²

The minimal point does not have x = 0.

(a) Kuhn-Tucker conditions for the minimal value of fThe Kuhn-Tucker conditions are a set of necessary conditions for a point x* to be a minimum of a constrained optimization problem subject to inequality constraints. These conditions provide a way to find the optimal values of x1, x2, ..., xn that maximize or minimize a function f subject to a set of constraints. Let's first write down the Lagrangian: L(x, y, λ1, λ2, λ3) = f(x, y) - λ1(x+y-1) - λ2(xy-3) - λ3x - λ4y Where λ1, λ2, λ3, and λ4 are the Kuhn-Tucker multipliers associated with the constraints. Taking partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4 and setting them equal to 0, we get the following set of equations: 4x - 2y - λ1 - λ2y - λ3 = 0 2y - 2x - λ1 - λ2x - λ4 = 0 x + y - 1 ≤ 0 xy - 3 ≤ 0 λ1 ≥ 0 λ2 ≥ 0 λ3 ≥ 0 λ4 ≥ 0 λ1(x + y - 1) = 0 λ2(xy - 3) = 0 From the complementary slackness condition, λ1(x + y - 1) = 0 and λ2(xy - 3) = 0. This implies that either λ1 = 0 or x + y - 1 = 0, and either λ2 = 0 or xy - 3 = 0. If λ1 > 0 and λ2 > 0, then x + y - 1 = 0 and xy - 3 = 0. If λ1 > 0 and λ2 = 0, then x + y - 1 = 0. If λ1 = 0 and λ2 > 0, then xy - 3 = 0. We now consider each case separately. Case 1: λ1 > 0 and λ2 > 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have the following possibilities: x + y - 1 = 0, xy - 3 ≤ 0 (i.e., xy = 3), λ1 > 0, λ2 > 0 x + y - 1 ≤ 0, xy - 3 = 0 (i.e., x = 3/y), λ1 > 0, λ2 > 0 x + y - 1 = 0, xy - 3 = 0 (i.e., x = y = √3), λ1 > 0, λ2 > 0 We can exclude the second case because it violates the constraint x, y ≥ 0. The first and third cases satisfy all the Kuhn-Tucker conditions, and we can check that they correspond to local minima of f subject to the constraints. For the first case, we have x = y = √3/2 and f(x, y) = -1/2. For the third case, we have x = y = √3 and f(x, y) = -2. Case 2: λ1 > 0 and λ2 = 0From λ1(x + y - 1) = 0, we have x + y - 1 = 0 (because λ1 > 0). From the first Kuhn-Tucker condition, we have 4x - 2y - λ1 = λ1y. Since λ1 > 0, we can solve for y to get y = (4x - λ1)/(2 + λ1). Substituting this into the constraint x + y - 1 = 0, we get x + (4x - λ1)/(2 + λ1) - 1 = 0. Solving for x, we get x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4. We can check that this satisfies all the Kuhn-Tucker conditions for λ1 > 0, and we can also check that it corresponds to a local minimum of f subject to the constraints. For this value of x, we have y = (4x - λ1)/(2 + λ1), and we can compute f(x, y) = -3/4 + (5λ1^2 + 4λ1 + 1)/(2(2 + λ1)^2). Case 3: λ1 = 0 and λ2 > 0From λ2(xy - 3) = 0, we have xy - 3 = 0 (because λ2 > 0). Substituting this into the constraint x + y - 1 ≥ 0, we get x + (3/x) - 1 ≥ 0. This implies that x^2 + (3 - x) - x ≥ 0, or equivalently, x^2 - x + 3 ≥ 0. The discriminant of this quadratic is negative, so it has no real roots. Therefore, there are no feasible solutions in this case. Case 4: λ1 = 0 and λ2 = 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have x + y - 1 ≤ 0 and xy - 3 ≤ 0. This implies that x, y > 0, and we can use the first and second Kuhn-Tucker conditions to get 4x - 2y = 0 2y - 2x = 0 x + y - 1 = 0 xy - 3 = 0 Solving these equations, we get x = y = √3 and f(x, y) = -2. (b) Show that the minimal point does not have x=0.To show that the minimal point does not have x=0, we need to find the optimal value of x that minimizes f subject to the constraints and show that x > 0. From the Kuhn-Tucker conditions, we know that the optimal value of x satisfies one of the following conditions: x = y = √3/2 (λ1 > 0, λ2 > 0) x = √3 (λ1 > 0, λ2 > 0) x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4 (λ1 > 0, λ2 = 0) If x = y = √3/2, then x > 0. If x = √3, then x > 0. If x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4, then x > 0 because λ1 ≥ 0.

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Answer:

see below

Step-by-step explanation:

1/2 + 4/6

Get a common denominator of 6

1/2 * 3/3 = 3/6

3/6 + 4/6 = 7/6

We change back to a mixed number

1  1/6

Answer:

7/6 or 1 1/6

Step-by-step explanation:

In this case, you're adding 1/2 plus 4/6.

One strategy you can use to solve this problem is by getting the common denominator.

1/2 is equal to 3/6.

Then you could add 3/6 to 4/6 and you'll get 7/6.

Now depending on the teacher they might want you to have an improper fraction or mixed number.

You can get this mixed number by dividing 7/6 which equals 1 1/6.

Hope this helped :)

Answer:

y=3x+3

Step-by-step explanation:

Answer:

No solutions (Maybe)

Step-by-step explanation:

If you input 0 into the equation you get -3=-4, which means it has no solutions.

There are infinitely many possible Jordan normal forms for a non-diagonalizable 5x5 complex matrix.

Given that A is a 5x5 complex matrix, the possible characteristic polynomial will have degree 5, and the minimal polynomial will divide the characteristic polynomial and have degree at most 5.

If A is not diagonalizable, then there will be at least one Jordan block in the Jordan normal form of A. The size of the largest Jordan block will be equal to the algebraic multiplicity of the corresponding eigenvalue. Since the characteristic polynomial has degree 5, there can be at most 5 Jordan blocks, and their sizes must sum to 5.

Therefore, the possible Jordan normal forms for A are:

A single 5x5 Jordan block

Two Jordan blocks, one of size 4 and one of size 1

Two Jordan blocks, one of size 3 and one of size 2

Three Jordan blocks, one of size 3 and two of size 1

Three Jordan blocks, one of size 2 and two of size 1

Four Jordan blocks, each of size 1

The minimal polynomial will be the product of linear factors corresponding to the distinct eigenvalues of A, and each factor will have multiplicity equal to the size of the largest Jordan block corresponding to that eigenvalue.

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The type of loan that Brady most likely getting  is option (a) conventional loan

Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.

ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.

VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.

Therefore, the correct option is (a) Conventional loan

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To serve 24 people with turkey, carter need to spend around 18 pounds for it  when he needs to pay three quarter for each.

Carter need to serve turkey for a total of 24 members. He wants to provide three quarter of a pound of turkey for each person.

Now, we need to calculate for total members attending the event.

Calculation for total amount of turkey = Total members * Amount for each person the to be  needed

Total amount of turkey = Members x Amount per person

Total amount of turkey = 24*(3/4)

Total amount of turkey= 6*3

Total amount of turkey=18

Therefore, 18 pounds of Total amount of turkey is needed to serve the total number of 24 people. In that way carter can have enough turkey to feed every one in the group who are attending the event.

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Answer:

Less

Step-by-step it is greater by 1.01

Answer:

Less than

Step-by-step explanation:

3 itself is already less than 4. How can 3.01 be greater than 4? When comparing positive numbers, compare from left to right. If the place of the first number is larger (for example comparing 10 with 100), than the one with the larger place is greater (tenth place will always be smaller than hundreds place).

If the first digit of both numbers are the same place (for example 10 and 20), than look at the value, which one is greater? Since 2 is greater than 1, we know 20 is bigger than 10. This holds true regardless of what follows the 2 or 1. For example, 20 is still bigger than 19.987

The only exception is when we are comparing 20 and 19.999 (where 9 is repeated). I will not be proving it here, but 0.999 (9 repeated) is said to be equal to one. Which means that 20 and 19.999 (9 repeated) are equal.

The polynomial of degree 9 centered at zero that best approximates f(x) = ln(x^3 + 5) is P_9(x). Note that due to the complexity of the derivatives, it's recommended to use computer software to compute the higher-order derivatives and the final polynomial form.

To find the polynomial of degree 9 (centered at zero) that best approximates f(x) = ln(x^3 + 5), you'll need to use Taylor series expansion.

Step 1: Find the derivative of f(x) up to the 9th order.
f(x) = ln(x^3 + 5)
f'(x) = (3x^2) / (x^3 + 5)
f''(x) = (6x(x^3 + 5) - 3x^2(3x^2)) / (x^3 + 5)^2
Repeat this process until you find the 9th derivative, f^9(x).

Step 2: Evaluate each derivative at the center, which is x = 0.
f(0) = ln(5)
f'(0) = 0
f''(0) = 0
Continue evaluating up to f^9(0).

Step 3: Construct the Taylor polynomial of degree 9 centered at zero.
P_9(x) = f(0) + (f'(0)/1!)*x + (f''(0)/2!)*x^2 + ... + (f^9(0)/9!)*x^9

Step 4: Substitute the values obtained in Step 2 into the Taylor polynomial.
P_9(x) = ln(5) + 0 + 0 + ... + (f^9(0)/9!)*x^9

The polynomial of degree 9 centered at zero that best approximates f(x) = ln(x^3 + 5) is P_9(x). Note that due to the complexity of the derivatives, it's recommended to use computer software to compute the higher-order derivatives and the final polynomial form.

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$0.80 because 4.80/6=0.8

Given,

F= Fixed Cost = $18,000

V= Variable Cost per unit = $0.90

P= Price per unit = $3.20

a) Q= Quantity = 12,000 cupcakes annually

Total Cost (TC) formula is:TC = F + V x Q = 18,000 + 0.90 × 12,000 = $29,400

Total Revenue (TR) formula is:TR = P × Q = 3.20 × 12,000 = $38,400

Profit formula is:Profit = TR − TC = 38,400 − 29,400 = $9,000.

b) The bakery will need to sell 6,924 cupcakes in order to break even.

The formula for the Break-even point (BEP) is BEP = F / (P - V) = 18,000 / (3.20 - 0.90) = 6,923.08 ≈ 6,924 cupcakes

5. The graphical representation of the Break-even volume for the Gobblecakes bakery is shown below:

8. Break-even volume as a percentage of maximum operating capacity will be = 58%

Break-even volume as a percentage = (Break-even volume / Maximum operating capacity) x 100%

                                                             = (6,923.08 / 12,000) x 100% = 57.69% ≈ 58%

11. The new Break-even point (BEP) will increase from 6,924 cupcakes to 8,750 cupcakes.

When the selling price for a cupcake changes from $3.20 to $2.75, the new Break-even point (BEP) will be:

BEP = F / (P - V) = 18,000 / (2.75 - 0.90) = 8,750 cupcakes

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The wheel will travel 131.8cm in 3 rotations.

The radius of the wheel, r = 7cm

Number of rotations, n= 3

distance covered in 1 rotation= circumference of circle=2πr

distance covered in 3 rotation= 2πr x 3

where π=3.14(fixed)

=2 x 3.14 x 7 x 3

Distance=131.88cm

Therefore, the distance covered in 3 rotations is 131.88cm

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Answer:

132cm

Step-by-step explanation:

use formula 22/7 *diameter which is 7*2 getting the answer as 44.For three rotations multiply the answer by three

9514 1404 393

Answer:

  (b)  3 cups

Step-by-step explanation:

One recipe uses 6 oz of orange juice. Multiplying the quantity by 4 means ...

  4 · 6 oz = 24 oz

of orange juice is needed. There are 8 oz in 1 cup, so this amount is ...

  (24 oz)/(8 oz/cup) = 3 cups

To make quadruple the recipe, 3 cups of orange juice are needed.

Answer:

-60

Step-by-step explanation:

-60 has the greatest absolute value.

|-60| = 60

Answer:

-60

Step-by-step explanation:
To sum it up shortly and easy absulate value is how much a number is far from zero, -60 is basically 60 numbers away from zero making it the greatest.

Therefore, the volume of the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is 96 cubic units.

To find the volume of the solid bounded by the coordinate planes (xy-plane, xz-plane, and yz-plane) and the plane 6x + 4y + z = 24, we need to determine the region in space enclosed by these boundaries.

First, let's consider the plane equation 6x + 4y + z = 24. To find the x-intercept, we set y = 0 and z = 0:

6x + 4(0) + 0 = 24

6x = 24

x = 4

So, the plane intersects the x-axis at (4, 0, 0).

Similarly, to find the y-intercept, we set x = 0 and z = 0:

6(0) + 4y + 0 = 24

4y = 24

y = 6

So, the plane intersects the y-axis at (0, 6, 0).

To find the z-intercept, we set x = 0 and y = 0:

6(0) + 4(0) + z = 24

z = 24

So, the plane intersects the z-axis at (0, 0, 24).

We can visualize that the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is a tetrahedron with vertices at (4, 0, 0), (0, 6, 0), (0, 0, 24), and the origin (0, 0, 0).

To find the volume of this tetrahedron, we can use the formula:

Volume = (1/3) * base area * height

The base of the tetrahedron is a right triangle with sides of length 4 and 6. The area of this triangle is (1/2) * base * height = (1/2) * 4 * 6 = 12.

The height of the tetrahedron is the z-coordinate of the vertex (0, 0, 24), which is 24.

Plugging these values into the volume formula:

Volume = (1/3) * 12 * 24

= 96 cubic units

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Answer:

  x = 3

Step-by-step explanation:

The two marked angles form a linear pair, so are supplementary. Their sum is 180°.

  (3x +136)° +(5x +20)° = 180°

  8x +156 = 180 . . . . . . . . . . . divide by °, collect terms

  8x = 24 . . . . . . . . . . . . . . subtract 156

  x = 3 . . . . . . . . . . . . . . divide by 8

_____

Additional comment

We suspect the intended answer for the second question is A 25° and 65°. These are possible measures for the acute angles in a right triangle, which must total 90°. No angle will be more than 90° (eliminates C and D), and the two smallest angles must total 90° (eliminates B).

If ū and ū have the same length, then the projection of u onto ū and the projection of ū onto ū will always have the same length. This is because the projection of a vector onto another vector is simply the vector that is parallel to the first vector and has the same length as the first vector.

If the two vectors have the same length, then the projection of one vector onto the other will also have the same length. If ū and ū do not have the same length, then it is possible for the projection of u onto ū and the projection of ū onto ū to have the same length.

This is because the projection of a vector onto another vector is not necessarily the same length as the first vector. If the two vectors are not parallel, then the projection of one vector onto the other will be shorter than the first vector. However, if the two vectors are perpendicular, then the projection of one vector onto the other will be the same length as the first vector.

The projection of a vector onto another vector is a vector that is parallel to the first vector and has the same length as the first vector. The projection of u onto ū can be calculated using the following formula:

proj_ū(u) = (u ⋅ ū) / ||ū||^2 * ū

where u ⋅ ū is the dot product of u and ū, and ||ū|| is the magnitude of ū. The projection of ū onto u can be calculated using the following formula:

proj_u(ū) = (ū ⋅ u) / ||u||^2 * u

where ū ⋅ u is the dot product of ū and u, and ||u|| is the magnitude of u. If ū and ū have the same length, then ||ū|| = ||u||. This means that the two formulas for the projection are the same, and the projection of u onto ū will have the same length as the projection of ū onto u.

If ū and ū do not have the same length, then ||ū|| ≠ ||u||. This means that the two formulas for the projection are not the same, and the projection of u onto ū may or may not have the same length as the projection of ū onto u. If the two vectors are not parallel, then the projection of one vector onto the other will be shorter than the first vector. However, if the two vectors are perpendicular, then the projection of one vector onto the other will be the same length as the first vector.

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385 sets of three teams { a , b , c } were there in which a beat b , b beat c , and c beat a.

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Given.

Assume that each team played 40 times, winning 20 games and losing 20 games. We can see that each side must have beaten each other once and won against each other once.

Combinations are:

As a result, if we choose any three teams, there will be just one set of games in which A defeats B, B defeats C, and C defeats A. As a result, we simply need to choose three teams from the available 21 options. (Remember that order is irrelevant to set notation.)

Thus

²¹C₃

= 21*20*19/3!

= 7*10*19

= 1330.

However, this is based on 40 games for each side. They actually only participated in 20 games, thus we divided this total by two (665) to arrive at the actual answer.

20 games were played by each side. There must be 21 teams because they cannot compete against one another.

Three-team groups can be chosen.

21!/3!18! = 1330 ways

During the round robin, each will have played the other.

For instance, AB, BC, and CA.

There are two typical results.

The other two players can be defeated by one person. Another winner and loser will result from those two players competing. A team will so win two games, lose two games, and win one game.

Alternatively, each side could have a win and a loss. The question is how many of those three-person groupings are there.

One team wins twice in the first scenario mentioned above. That means two of that team's victories. The games in the group have been chosen. This is achievable.

45 ways divided by 21 players from 10!/2!8! =

945 ways

Therefore, there must be 385 methods left over to represent the scenario in the question after deducting 945 from 1330.

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The correct answer is Option C. The requirement that is not needed for testing a claim about a mean with a known standard deviation is that the sample results (or more extreme results) can easily occur when the null hypothesis is true.

When testing a claim about a mean with a known standard deviation, there are certain requirements that need to be met.

Option A states that under a given assumption, there should be an exceptionally small probability of obtaining sample results as extreme as the ones observed. This is a requirement for testing the claim as it indicates the presence of a statistically significant difference.

Option B suggests that if the sample results (or more extreme results) cannot easily occur when the null hypothesis is true, it helps explain the discrepancy between the assumption and the observed data. This is also a requirement for testing the claim as it examines the plausibility of the null hypothesis.

Option D states that a conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test, which is a valid approach for testing the claim.

Option C, on the other hand, suggests that the sample results (or more extreme results) can easily occur when the null hypothesis is true. This is not a requirement for testing the claim about a mean with a known standard deviation. In fact, the opposite is true. When conducting hypothesis testing, we typically look for evidence that the sample results are unlikely to occur under the null hypothesis, indicating a significant difference or effect.

Therefore, Option C is the correct answer as it does not align with the requirements for testing a claim about a mean with a known standard deviation.

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Answer:

they are both variables so yes

The 99% confidence interval for the population mean time spent on the internet, in minutes, is given as follows:

(48.9, 59.5).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 50 - 1 = 49 df, is t = 2.68.

The parameter values are given as follows:

\(\overline{x} = 54.2, s = 14, n = 50\)

Then the lower bound of the interval is given as follows:

\(54.2 - 2.68\frac{14}{\sqrt{50}} = 48.9\)

The upper bound of the interval is given as follows:

\(54.2 + 2.68\frac{14}{\sqrt{50}} = 59.5\)

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GTT's expected market share is 45.45%, NCJ's expected market share is 31.82%, and Dash's expected market share is 22.73%. these percentages add up to 100%, as expected.

To find the long-run expected market share for each company, we need to use the concept of steady-state or equilibrium. In the long run, the market share of each company will remain constant if the number of customers gained is equal to the number of customers lost. This means that the rate of change of each company's market share will be zero.

Let's define the market share of each company at any point in time as follows:

GTT's market share = SGTT

NCJ's market share = SNCJ

Dash's market share = SDash

We can write the equations for the rate of change of each company's market share as follows:

dSGTT/dt = -0.2 SGTT + 0.05 SNCJ + 0.25 SDash

dSNCJ/dt = -0.05 SNCJ + 0.05 SGTT + 0.15 SDash

dSDash/dt = -0.15 SDash + 0.25 SGTT + 0.15 SNCJ

Note that the negative coefficients represent the percentage of customers lost by the company, and the positive coefficients represent the percentage of customers gained by the company.

To find the steady-state values of SGTT, SNCJ, and SDash, we need to set the rate of change of each company's market share to zero:

-0.2 SGTT + 0.05 SNCJ + 0.25 SDash = 0

-0.05 SNCJ + 0.05 SGTT + 0.15 SDash = 0

-0.15 SDash + 0.25 SGTT + 0.15 SNCJ = 0

We can solve these equations to get the steady-state values of SGTT, SNCJ, and SDash:

SGTT = 0.4545

SNCJ = 0.3182

SDash = 0.2273

Therefore, the expected long-run market share for each company is as follows:

GTT's expected market share: 45.45%

NCJ's expected market share: 31.82%

Dash's expected market share: 22.73%

Therefore, these percentages add up to 100%, as expected.

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The predicted effect on test scores when  income increases from $1,000 to $3,000 is ( a. 7.36.)

To find the predicted effect on test scores when income increases from $1,000 to $3,000, to substitute the values into the quadratic regression model and calculate the difference in test scores.

Given the quadratic regression model:

TestScore = 607.3 + 3.85Income - 0.0423Income^2

Let's calculate the test scores at income values of $1,000 and $3,000:

For income = $1,000 (1 in thousands):

TestScore1 = 607.3 + 3.85(1) - 0.0423(1)^2

= 607.3 + 3.85 - 0.0423

≈ 611.108

For income = $3,000 (3 in thousands):

TestScore2 = 607.3 + 3.85(3) - 0.0423(3)^2

= 607.3 + 11.55 - 0.3819

≈ 618.468

The predicted effect on test scores is the difference between TestScore2 and TestScore1:

Effect = TestScore2 - TestScore1

= 618.468 - 611.108

≈ 7.36

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Answer:

Ahmed is right in disagreeing with his friend

Step-by-step explanation:

We can easily determine that Ahmed's friend is wrong by looking at the fraction a/b which has to be less than 1 since the distance from A toschool  is less than the distance from A to B

Therefore b/a will be greater than 1 and hence b/a x length of BA will be greater than the distance from B to A which means the school cannot be located on the segment BA

An example will make this easier to understand
Let the segment AB be 12 units
Let a/b = 1/3
School is located 1/3 x AB length

b/a is reciprocal of 1/3 = 3
Friend suggests that school is b/a times distance BA
But b/a distance BA = 3BA which means the school is outside the segment BA

The correct answer is
The school is located (1 - a/b) the distance along BA

Answer:

B

Step-by-step explanation:

-2x<7-5

-2x<2 multiplied by -1 gives 2x>-2 and devided by 2 you have x>-1

Answer:

true

Step-by-step explanation:

hope this helps have an amazing day!

Answer:

T

Step-by-step explanation:

hope it help

The measure of the larger angle is obtained as follows:

70º

Two angles are defined as complementary is the sum of their measures is of 90º.

The variables that represent each angle in this problem are given as follows:

x and y.

They are complementary angles, hence:

x + y = 90.

The difference between four times the measure of the smaller angle and the measure of the larger angle is 10, hence:

4y - x = 10.

x = 4y - 10.

Hence the value of y is obtained as follows:

4y - 10 + y = 90

5y = 100

y = 100/5

y = 20º.

Hence the measure of the larger angle is given as follows:

x + 20 = 90

x = 70º.

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Answer:  -4.667/2.000 = -2.333

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :    y-(-7/3*x+5/2)=0

Simplify   \(\frac{5}{2}\)

Equation at the end of step : y -  ((0 -  (\(\frac{7}{3}\) • x)) +  \(\frac{5}{2}\))  = 0

The left denominator is : 3  The right denominator is : 2

Least Common Multiple:      6

 y - \(\frac{(15-14x)}{6}\)   = 0

y • 6 - \(\frac{(15-14x)}{6}\) \(\frac{6y + 14x - 15}{6}\)

\(\frac{ 6y + 14x - 15}{6}\)

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 2.500 and for x=2.000, the value of y is -2.167. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.167 - 2.500 = -4.667 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -4.667/2.000 = -2.333

 x-intercept = 15/14 = 1.07143

 y-intercept = 15/6 = 5/2 = 2.50000