If a solution to a linear system of equations is no solution, then what must be true about the graph of the system?

The point (-5, 3) shows the coordinates of c(5, 3) if the trapezoid ABCD on a coordinate plane, with points (2, 1), (3, 5), (5, 3) and (3, 1), is reflected across the y-axis. So the option A is correct.

A graph will appear to be inverted or on the other side of an axis, such as the x axis, when it is mirrored along that axis.

If you look closer, you'll notice that it's symmetrical, meaning that each point is equally spaced from the axis of reflection and the axis of its reflection.

As a result, if you reflect a point (x, y) down the x axis, its x abscissa will remain the same while its y ordinates will negate.

So (x, y) becomes (x, -y).

Similar to this, the picture of a point at coordinates (x, y) along the y axis will be (-x, y)

Trapezium A B C D on a coordinate plane has points (2, 1), (3, 5), (5, 3), and (3, 1).

The following rule applies when a point is reflected across the y-axis:

(x, y) → (-x, y)

C(5, 3) = C'(-5, 3)

So the option A is correct.

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The complete question is:

Which choice shows the coordinates of c if the trapezoid ABCD on a coordinate plane, with points (2, 1), (3, 5), (5, 3) and (3, 1), is reflected across the y-axis?

A. (-5, 3)

B. (3, -5)

C. (5, -3)

D. (-3, 5)

Answer:

6x + 7

Step-by-step explanation:

triangle has 3 sides right, which is 2x, 3x+5 and x+2

so basically you just have to add everything up since perimeter is just the total number of each sides combined

2x + (3x+5) + (x+2)

expand from the brackets

2x + 3x + 5 + x + 2

rearrange the numbers to avoid confusion

2x + 3x + x + 5 + 2

add everything up

6x + 7

The center of the circle is at the point (-5,11) and has the radius of 3 units.

The equation of the circle will be,

Given a sample mean is 82, the sample size is 100, 90% confidence level and the population standard deviation is 20, the margin of error is 3.29.

To calculate the margin of error, we need to use the formula:

Margin of error = Z-score * (population standard deviation / square root of sample size)

Where the Z-score corresponds to the confidence level. Since we have a 90% confidence level, the Z-score is 1.645.

Plugging in the given values, we get:

Margin of error = 1.645 * (20 / sqrt(100))
Margin of error = 1.645 * 2
Margin of error = 3.29 (rounded to 2 decimals)

Therefore, the margin of error is 3.29.

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Answer:

7d+11

Step-by-step explanation:

Pretty much just addition.

3d+4d+2+9

(3d+2)+(4d+9) = 7d+11.

Answer:

2 1/2 per piece

Step-by-step explanation:

Answer:

D. The mean will increase and the median will remain the same

Step-by-step explanation:

First I’d order them from smallest to largest in the data set:

3, 5, 6, 6, 7, 11

The median here is 6.

Then the mean would be 6.33

Then it says if 3 is removed:

5, 6, 6, 7, 11

So we would know the median is 6

The mean here would be 7

So we can see the mean increases but the median stays the same, therefore the answer is D

Notice that the triangle ABC is a right triangle, and the radius of the circle is equal to the length of the segment AB.

To compute the length of the segment AB we will use the Pythagorean theorem:

where c is the length of the hypotenuse and a, and b are the lengths of the legs.

Substituting:

we get:

Solving the above equation for AB, we get:

Therefore:

SOLUTIONS

Using the Pythagoras theorem

opposite = x

hypotenuse = 10

Final answer = 6

a. Equilibrium level of income (Ye) = (1000 - 0.8T) / 0.3

b. Check the attached image

c. Increased investment required to increase national income by 2000 = 2200

d. It is not possible to reduce taxes to increase the national income by 2000.

e. New equilibrium level of income after increasing government expenditure by 400 = (1000 + 0.7Y - 0.8T) / 0.3

f. New equilibrium level of income after reducing taxes by 400 = (1000 + 0.7Y - 0.8(-300)) / 0.3

g. New equilibrium level of income after running a balanced budget (ΔG = ΔT = 400) = (1000 + 0.7Y - 0.8(500)) / 0.3

We apply Keynesian expenditure-income model in solving these economic questions

a. Calculate the equilibrium level of income (Ye):

To find the equilibrium level of income, we set aggregate expenditure (AE) equal to income (Y):

AE = C + I + G + X - M

Substituting the given values:

AE = (600 + 0.8(Y - T)) + 200 + 350 + 250 - (200 + 0.1Y)

AE = 600 + 0.8Y - 0.8T + 200 + 350 + 250 - 200 - 0.1Y

AE = 1000 + 0.7Y - 0.8T

Since AE = Y at equilibrium, we can write:

Y = 1000 + 0.7Y - 0.8T

0.3Y = 1000 - 0.8T

Y = (1000 - 0.8T) / 0.3

b. Show the equilibrium level of income by using diagrams of both aggregate expenditure-income (AE-Y) approach and injection-leakage approach:

Aggregate Expenditure-Income (AE-Y) Approach:

In the AE-Y diagram, we plot the aggregate expenditure (AE) on the vertical axis and income (Y) on the horizontal axis. The equilibrium occurs where the AE curve intersects the 45-degree line, which represents income equals expenditure.

Injection-Leakage Approach:

In the injection-leakage diagram, we plot injections (I + G + X) on the vertical axis and leakages (S + T + M) on the horizontal axis. At equilibrium, injections equal leakages.

c. To increase the national income by 2000, we need to increase investment (I) by 2000. So, the new investment would be:

New I = 200 + 2000 = 2200

d. To increase the national income by 2000, we need to reduce taxes (T). The amount of tax reduction required can be calculated as follows:

2000 = (1000 - 0.8T) / 0.3 - (1000 - 0.8T) / 0.3

Simplifying the equation and solving for T:

0.3(2000) = 1000 - 0.8T - 1000 + 0.8T

600 = 0.8T - 0.8T

600 = 0

Since there is no solution to the equation, it is not possible to reduce taxes to increase the national income by 2000.

e. To calculate the new equilibrium level of income after increasing government expenditure by 400, we need to adjust the value of G:

New G = 350 + 400 = 750

Substituting the new value of G into the equation for equilibrium income:

Y = (1000 + 0.7Y - 0.8T) / 0.3

f. After being at the equilibrium level of income, if the government reduces taxes by 400, we adjust the value of T:

New T = 100 - 400 = -300

Substituting the new value of T into the equation for equilibrium income:

Y = (1000 + 0.7Y - 0.8(-300)) / 0.3

g. If the government runs a balanced budget by increasing both government expenditure and taxes by 400, we adjust the values of G and T:

New G = 350 + 400 = 750

New T = 100 + 400 = 500

Substituting the new values of G and T into the equation for equilibrium income:

Y = (1000 + 0.7Y - 0.8(500)) / 0.3

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Answer:

x = 2.6

Step-by-step explanation:

–4.8(6.3x – 4.18) = –58.56

-30.24x + 20.064 = -58.56

-30.24x = -78.624

x = 2.6

So, x = 2.6 is the answer.

Answer:

I am so sorry for the misunderstanding. x=2.6

Step-by-step explanation:

Distribute

−4.8(6.3x−4.18)=−58.56

−30.24x+20.064=−58.56

Subtract 20.064 from both sides

−30.24x+20.064=−58.56

−30.24x+20.064−20.064=−58.56−20.064

Simplify the expression

Subtract the numbers

−30.24x+20.064−20.064=−58.56−20.064

−30.24x=−58.56−20.064

Subtract the numbers

−30.24x=−58.56−20.064

−30.24x=−78.624

−30.24x+20.064−20.064=−58.56−20.064

−30.24x=−78.624

Divide both sides by the same factor
−30.24x=−78.624

−30.24x/30.24=−78.624/30.24

Simplify the expression
So there for, x=2.6

Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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Answer:

6:16, 12:32 and 18:48

Step-by-step explanation:

Answer:

Step-by-step explanation:

the ratio is 6:16, 21:24, 30:80, 90:240

The corresponding side in the smaller triangle is 10 cm.

When two or more objects or figures appear the same or equal due to their shape, this property is known as a similarity.

Given that, the ratio of similitude in two similar triangles is 3:1. the side in the larger triangle measures 30 cm, we are asked to find the measure of the corresponding side in the smaller triangle.

Let the corresponding side in the smaller triangle be x,

Since, the ratio similitude is 3:1, therefore, the ratio of the corresponding sides of both the triangle will be in same ratio,

Therefore,

1 / 3 = x / 30

x = 30 / 3

x = 10

Hence, the corresponding side in the smaller triangle is 10 cm.

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Answer:

Part A: Slope (m) = -75

Part B:

Point-slope form --- y - 1350 = -75(x - 2)

Slope-intercept form --- y = -75x + 1500

Standard form --- 75x + 1y = 1500

Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').

Part D: The balance in the bank account after 5 days equals $1,125.

Step-by-step explanation:

(Pertaining to Part D --- Plugging in variables):

To find the answer to Part D, we must first take the function notation equation from Part C and plug in the appropriate variables needed to find the balance in the bank account after 5 days. So, we plug in '5' for g(x), which would give us g(5). For the other x found in the equation, we also correspondingly replace it with '5'. Our equation now appears as g(5) = -75(5) + 1500.

Finally, we must solve this equation using the order of operations, which simplifies our equation to g(5) = -375 + 1500. We can simplify this further by adding 1500 to -375, giving us the final answer for Part D of $1,125 being the balance in the bank account after 5 days.

Hope that helps!!

Answer:

Part A: Slope (m) = -75

Part B:

Point-slope form --- y - 1350 = -75(x - 2)

Slope-intercept form --- y = -75x + 1500

Standard form --- 75x + 1y = 1500

Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').

Part D: The balance in the bank account after 5 days equals $1,125.

We need to find the derivative which is the rate of change

So, when x is infinite, the function g(x) has the greatest rate of change

Answer:

it's 7 I think maybe I'm wrong

The probability of x taking on a value between 75 to 90 is 0.25.

Given that x is a continuous random variable uniformly distributed between 65 and 85.To find the probability that x lies between 75 and 90, we need to find the area under the curve between the values 75 and 85, and add to that the area under the curve between 85 and 90.

The curve represents a rectangular shape, the height of which is the maximum probability. So, the height is given by the formula height of the curve = 1/ (b-a) = 1/ (85-65) = 1/20.Area under the curve between 75 and 85 is = (85-75) * (1/20) = (10/20) = 0.5Area under the curve between 85 and 90 is = (90-85) * (1/20) = (5/20) = 0.25.

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Answer:

x > 3

Step-by-step explanation:

___________________

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

268.13

Step-by-step explanation:

To find the sales tax, multiply the decimal value of the sales tax times the original price.  The sales tax at 7.25% is the same as the decimal 0.0725.

sales tax = 250 x 0.0725 = 18.125

round that amount to the nearest penny so it is 18.13

The total price you would pay is the original price plus the sales tax

250 + 18.13 = 268.13

Answer:

the 500 one ig because u can get more water out of it

Step-by-step explanation:

None of the given sequences could be the beginning of a geometric sequence.

To determine which sequence could be the beginning of a geometric sequence, we need to check if there is a common ratio between consecutive terms.

A. \(125, 150, 180, 215\): The common differences between the terms are \(25\), \(30\), and \(35\), which indicates an arithmetic sequence, not a geometric sequence.

B. \(125, 150, 180, 216\): The common differences between the terms are \(25\), \(30\), and \(36\), which also suggests an arithmetic sequence, not a geometric sequence.

C. \(125, 155, 185, 215\): The common differences between the terms are \(30\), 30, and 30, indicating an arithmetic sequence, not a geometric sequence.

D. \(124, 175, 205, 215\): The common differences between the terms are 51, 30, and 10, suggesting an arithmetic sequence, not a geometric sequence.

None of the given sequences exhibit a constant ratio between consecutive terms, indicating that none of them could be the beginning of a geometric sequence.

NOTE: The given question is incomplete. The complete question is:

Which Of The Following Could Be The Beginning Of A Geometric Sequence?

\(A. 125, 150, 180, 215\\B. 125, 150, 180, 216\\C. 125, 155, 185, 215\\D. 124, 175, 205, 215\)

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The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

From the question, we have the following parameters that can be used in our computation:

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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Answer:

8 inches

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

Therefore, the sum of the volumes of the two hemisphere-shaped scoops of ice cream (with diameters of 4 inches), is equal to the volume of a sphere with diameter of 4 inches.

If the melted ice cream fills the cone exactly to the top without overflowing, the volume of the cone with diameter of 4 inches must be equal to the volume of a sphere with diameter of 4 inches.

As the diameter of a circle is twice its radius, then the radius of the sphere and cone is r = 2 inches.

The formulas for the volume of a cone and the volume of a sphere are:

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\\\end{minipage}}\)

The depth of the cone is its height.

Therefore, to calculate how deep the cone must be so that the melted ice cream will fill the cone exactly to the top without overflowing, set the two equations equal to each other, substitute r = 2, and solve for h (the depth of the cone).

\(\begin{aligned}\textsf{Volume of a cone}&=\textsf{Volume of a sphere}\\\\\dfrac{1}{3} \pi (2)^2 h & = \dfrac{4}{3} \pi (2)^3\\\\\dfrac{1}{3} \pi \cdot 4 h & = \dfrac{4}{3} \pi \cdot 8\\\\\dfrac{4}{3} \pi h& = \dfrac{32}{3} \pi \\\\\dfrac{4}{3} h& = \dfrac{32}{3} \\\\4 h& = 32 \\\\h&=\dfrac{32}{4}\\\\h&=8\; \sf inches\end{aligned}\)

Therefore, the depth of the cone must be 8 inches.

The cone must be at least 8 inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing.

1. The opening of the ice cream cone has a diameter of 4 inches. This means that the radius of the cone's opening is 4/2 = 2 inches.

2. The two hemisphere-shaped scoops of ice cream have diameters of 4 inches each. This means that the radius of each scoop is 4/2 = 2 inches.

3. When the ice cream melts, it will take up the space between the scoops and fill the cone. In order for the melted ice cream to fill the cone exactly to the top without overflowing, the depth of the cone must be equal to the combined height of the two ice cream scoops.

4. The height of each hemisphere-shaped scoop can be calculated using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius.

  - For each scoop, the radius is 2 inches, so the height of each scoop is (4/3)π(2)³ = (4/3)π(8) = (32/3)π.

5. Since there are two scoops, the combined height of the two scoops is 2 * (32/3)π = (64/3)π.

6. Therefore, the cone must be at least (64/3)π inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing. This is approximately equal to 67.03 inches.

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Since the information about variable 'q' is not provided, it is not possible to determine the remainder when q is divided by 6 based on the given context.

The question states that x is a positive integer such that x ≥ 75, but it does not provide any information about the variable 'q'. Without knowledge of the value or any relationship between 'q' and 'x', we cannot determine the remainder when 'q' is divided by 6.

The remainder will depend on the specific value of 'q' and how it relates to the number 6. Therefore, without further information, it is not possible to determine the remainder when 'q' is divided by 6.

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You would need 20 simulation models for this scenario.

To determine the number of simulation models needed, we need to multiply the number of options for each component.

In this case, we have:

Four different means

Three different variances

Five different variables

However, we are specifically selecting the two lowest means, the lowest variance, and three out of the five variables.

For means:

We are selecting the two lowest means, so we have 2 options.

For variances:

We are selecting the lowest variance, so we have 1 option.

For variables:

We are selecting three out of the five variables, so we need to calculate the number of combinations.

This can be done using the binomial coefficient, also known as "n choose k," where n is the total number of variables (5) and k is the number of variables selected (3).

The formula for the binomial coefficient is:

n! / (k! × (n - k)!)

Plugging in the values, we get:

5! / (3! × (5 - 3)!)

= 5! / (3! × 2!)

= (5 × 4 × 3!) / (3! × 2 × 1)

= (5 × 4) / (2 × 1)

= 10

Putting it all together, the number of simulation models needed is:

2 (means) × 1 (variances) × 10 (variables)

= 2 × 1 × 10

= 20

Therefore, you would need 20 simulation models for this scenario.

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There are no free variables for the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solution.

For the stated question-

It is necessary to know that a system is consistent (i.e., there is no pivot in the last column of the augmented matrix) and that there are no free variables in order to determine whether it has a unique solution (like a pivot position in every column of the coefficient matrix).

Also take note that this rules out having fewer rows than columns.

Thus, there are no free variables for the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solution.

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Answer:

see explanation

Step-by-step explanation:

let the two consecutive odd numbers be n and n + 2 , then

n + n + 2 = 148 , collect like terms

2n + 2 = 148 ( subtract 2 from both sides )

2n = 146 ( divide both sides by 2 )

n = 73

n + 2 = 73 + 2 = 75

The 2 numbers are 73 and 75

----------------------------------------------------------------

let width be w then length = 2w - 6

The perimeter (P) is calculated as

P = 2(width + length) , then

2(w + 2w - 6) = 54 ( divide both sides by 2 )

w + 2w - 6 = 27 , collect like terms

3w - 6 = 27 ( add 6 to both sides )

3w = 33 ( divide both sides by 3 )

w = 11

2w - 6 = 2(11) - 6 = 22 - 6 = 16

length = 16 in and width = 11 in

Hello,

Answer: 73,75

Step-by-step explanation:

1st Question Answer

x -> 1st

x+2 -> 2nd

So... Since it is equal to 148 then we write...

x+x+2=148

Combine Like Terms

2x+2=148

Subtract 2 from both sides

2x=146

Divide 2 to both sides

x=73 and +2 = 75

In Final: The two consecutive odd integers are 73 and 75

2nd question)

Width of rectangle is x inches

2x-6

Since perimeter = 2(length+witdth)

54 = 2(2W - 6) + 2W,  (substitute P = 54 and L = 2W - 6)

66=6w

w=11

To find the length: Substitute

54=2l+2(11)

32=2L

L=16