4. The table shows a preference schedule with four candidates. Under the plurality method, which (1 point)
candidate wins the election?
number of votes 15 11 9 6 2
1st
2nd
3rd
OA
OB
OC
OD
ACDBC
B
B
CDD
D|A|A|A|A|

Step-by-step explanation: there are 3 y's so the answer is 3y

and there are 2 x's so therefore the answer is 2x

and then you just add them together to get 3y + 2x

Answer:

x ≈ 12.7

Step-by-step explanation:

since the triangle is isosceles then the 2 legs are congruent, both 9

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² = 9² + 9² = 81 + 81 = 162 ( take square root of both sides )

x = [tex]\sqrt{162}[/tex] ≈ 12.7 ( to the nearest tenth )

Answer:

Solution is in the attached photo.

Step-by-step explanation:

This question tests on the concept of triangles, as this is an isosceles triangle, the other 2 unknown angles are the same, as well as the sine rule.

(a) The inverse variation equation that relates to x and y is  y = -20/x.

(b) The value of y when x = 25 is -0.8 or -4/5

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

(a) To write the inverse variation equation that relates to x and y, we look for the constant k connecting x and y

From the questiuon,

To remove the proprotionality/Variation sign, we introduce a constant k

Given:

Substitute into equation 1 and solve for k

Hence, the equation is y = -20/x.

(b) To find the value of y when x = 25, we subtitute into the equation

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Answer: hello am I solving for x?

Step-by-step explanation:question

Answer:

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

Let E represent the number of Eagle fans and S represent the number of Spartan fans at the start of the game.

We can set up two equations using the given information:

Now we can solve the equations.

From equation (1), we can replace E in equation (2), the solve for S:

Now find the number of Eagle fans using equation (1):

The Probability that the average weight of our sample is greater than 15.8 oz, given a sample size of 40 bags of candy, is approximately 0.8438 or 84.38%.

The probability that the average weight of our sample is greater than 15.8 oz, we need to use the concept of the sampling distribution of the sample mean and the Central Limit Theorem.

Given:

Population mean (μ) = 16 oz.

Population standard deviation (σ) = 1.25 oz.

Sample size (n) = 40 bags of candy.

The Central Limit Theorem states that for a large enough sample size (typically considered n > 30), the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.

In this case, we can assume that the sampling distribution of the sample mean is approximately normally distributed.

To calculate the probability, we need to standardize the sample mean using the z-score formula:

z = (x - μ) / (σ / sqrt(n))

where x is the given value (15.8 oz), μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the values:

z = (15.8 - 16) / (1.25 / sqrt(40))

z = -0.2 / (1.25 / 6.3246)

z = -0.2 / 0.1988

z ≈ -1.006

Now, we need to find the probability that the standardized sample mean is greater than -1.006. Since we want the probability of the sample mean being greater than 15.8 oz, we need to find the area under the normal curve to the right of z = -1.006.

Using a standard normal distribution table or a calculator, we can find that the corresponding probability is approximately 0.8438.

Therefore, the probability that the average weight of our sample is greater than 15.8 oz, given a sample size of 40 bags of candy, is approximately 0.8438 or 84.38%.

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Answer:

$148

Step-by-step explanation:

Expected winnings = ($0.00 x 0.83) + ($100.00 x 0.08) + ($500.00 x 0.08) + ($10,000.00 x 0.01)

Expected winnings = $0.00 + $8.00 + $40.00 + $100.00

Expected winnings = $148.00

Answer:

Step-by-step explanation:

To express 6√3 + 6i in polar form, we first need to find the magnitude and argument of the complex number.

The magnitude (or modulus) of the complex number is given by the formula:

|z| = √(a^2 + b^2)

where a and b are the real and imaginary parts of the complex number, respectively.

In this case, a = 6√3 and b = 6, so:

|6√3 + 6i| = √((6√3)^2 + 6^2) = √(108 + 36) = √144 = 12

The argument (or angle) of the complex number is given by the formula:

arg(z) = tan^-1(b/a)

In this case, arg(z) = tan^-1(6/6√3) = tan^-1(1/√3) = π/6

Therefore, the polar form of 6√3 + 6i is:

12(cos(π/6) + i sin(π/6))

or

12e^(iπ/6)

Answer:

40

Step-by-step explanation:

For finding the surface area of this rectancular prism, or any, we find the area of each shape. Then, we add up all of the areas together to get the surface area. There are 2 squares with 2 as a side length for each side. To find the area of a square, we can multiply any 2 sides. That is because the sides of the square is equal to eachother, so 2•2=4. Being 2 squares, they are both have area of 4. Looking at the 4 rectangles, they have a length of 4 and a width of 2. We multiply the height and width of a rectangle to get the area. 4•2=8, the area of each rectangle is 8. Now, we add up all of our areas. Two squares, each are 4 for their area. Add them up, you get 8 for the 2 squares. Then, we have 4 rectangles each are 8 for their area. 4•8=32 since they all have the same area. 32+8=40! 40 is the surface area of this net. I hope this helps, and have good day

When we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16.

To evaluate f(x)=(1/4)^-x for specific values of x, we can substitute the given values into the function expression and simplify the calculations.

Evaluating f(-2):

Substitute x = -2 into the function f(x):

f(-2) = (1/4)^-(-2) = (1/4)^2 = 1/16

Evaluating f(1):

Substitute x = 1 into the function f(x):

f(1) = (1/4)^-1 = 4^1 = 4

Evaluating f(2):

Substitute x = 2 into the function f(x):

f(2) = (1/4)^-2 = (1/4)^2 = 1/16

Therefore, the evaluations of f(-2), f(1), and f(2) are:

f(-2) = 1/16

f(1) = 4

f(2) = 1/16

In conclusion, when we evaluate the function f(x)=(1/4)^-x for x = -2, 1, and 2, we find that f(-2) = 1/16, f(1) = 4, and f(2) = 1/16. These values represent the corresponding outputs of the function for the given inputs.

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The third side of the triangle 12.5

A triangle is a polygon with three edges and three vertices. The important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

we the measurements of given two sides of the triangle 16.5 and 29

In a triangle, the sum of any two sides should be greater than the third side and the difference between any two sides should be lesser than that of the third side.

The sum of two sides rule

[tex]x + 16.5 > 29\\ x > 29 - 16.5\\ x > 12.5\\[/tex]

The difference between the two sides rule

[tex]29 - 16.5 < x \\ 12.5 < x[/tex]

Therefore, the value of x is 12.5

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Answer:

To determine the length you're referring to, we need more information about the specific configuration or diagram you're referring to. Please provide additional details or clarify your question so that I can assist you more accurately.

Step-by-step explanation:

Summary statistics provide a single number to describe data, while tables and graphs visually represent data to facilitate analysis and answer questions.

We have,

Data can be described by a single number using summary statistics. Summary statistics provide a concise representation of the main characteristics of a dataset.

Commonly used summary statistics include measures such as the mean, median, mode, range, variance, and standard deviation.

These single numbers provide insights into different aspects of the data, such as the central tendency, variability, or distribution.

Tables and graphs are effective tools for representing data and answering questions because they provide a visual representation that helps to organize and understand the information.

Tables present data in a structured format, typically using rows and columns, which allows for easy comparison and analysis.

They can display raw data, summary statistics, or both.

Graphs, on the other hand, use visual elements to represent data in a more intuitive and visual manner.

Different types of graphs can be used depending on the nature of the data and the question at hand.

For example, bar graphs can be used to compare categories or discrete data, line graphs can show trends over time, and scatter plots can display the relationship between two variables.

Tables and graphs help to answer questions about data by providing a clear and organized presentation.

They allow us to observe patterns, trends, and relationships, making it easier to draw conclusions and make informed decisions.

Visually representing data, tables, and graphs enhances our ability to analyze and interpret complex information quickly and effectively.

Thus,

Summary statistics provide a single number to describe data, while tables and graphs visually represent data to facilitate analysis and answer questions.

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Answer: y=4x+7

Step-by-step explanation:

-8x+2y=14

Convert to y=kx+b

2y=8x+14

y=4x+7

The cost of each pound of grass seed is $6.

A graph of the solution for the cost of each pound of grass seed is shown below.

In order to determine the cost of each pound of grass seed, we would assign a variable to the cost of each pound of grass seed and then translate the word problem into an algebraic linear equation.

Let the variable x represent the cost of each pound of grass seed.

Since Lori bought 3.6 pounds of grass seed and she was charged $22.90, including a tax of $1.30, an algebraic linear equation that best represent this situation is given by;

3.6x + 1.30 = 22.90

3.6x = 22.90 - 1.30

3.6x = 21.60

x = 21.60/3.6

x = $6.

In conclusion, we would sue an online graphing calculator to plot the solution for the cost of each pound of grass seed as shown in the image attached below.

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Answer:

A = 30 cm

B = 14 cm

C = 15 cm

D = 41 cm

Step-by-step explanation:

You can find A by multiplying 10 times 6 (because the other side of the square is ten and the side of A already has that 4 there it would be 6) which would be 60, then since it is a right triangle, you can divide that by two and get 30.

You can find B by multiplying 4 by 7 (because the other part of that side of the square is 3 so that part would be 7) which would be 28, then since it is a right triangle, you can divide that by two and get 14.

You can find C by multiplying 10 times 3 and getting 30, then since it is a right triangle, you can divide that by two and get 15.

You can find D by multiplying 10 by 10 (because it is a square) then you'll get 100 from that. Then you can subtract the rest of the triangles from it which would be 100 minus 30 minus 14 minus 15 and you would get 41 which would be triangle D.

Hope this helps!! Let me know if you need more explanation

Answer:

Use systems of equations to solve.

Let x represent the cost per pound of the espresso coffee beans and

y represent the cost per pound of the vanilla coffee beans.

6x + 5y = 77.50

20x + 13y = 234.50, both of these are given.

Rewrite these equations so you can eliminate one of the variables;

60x + 50y = 775, Multiply both sides of the equation by 10

60x + 39y = 703.5, Multiply both sides of the equation by 3

Now Subtract equation 2 from equation 1,

11y = 71.5

y = 6.5

Solve for x,

6x + 5(6.50)= 77.50

x = 7.50

Therefore, the cost per pound of the espresso coffee beans is $7.50, and

the cost per pound of the vanilla coffee beans is $6.50.

The information which would be enough to prove the triangles to be congruent are either DE = RP or ∠F = ∠Q.

Given two triangles,

ΔDEF and ΔRPQ.

If ΔDEF is congruent to ΔRPQ, then the corresponding vertices of D, E and F are R, P and Q respectively.

Already we have from the figure,

∠D = ∠R

DF = RQ

Now, it is enough to prove either DE = RP or ∠F = ∠Q.

When DE = RP, by SAS congruence theorem, corresponding two sides and the included angle of each triangle are equal and thus triangles are congruent.

When ∠F = ∠Q, by ASA congruence theorem, corresponding two angles and the included side of each triangle are equal and thus triangles are congruent.

Hence the information required are either DE = RP or ∠F = ∠Q.

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5m is the height of a cone with a diameter of 12 m whose volume is 188 m³.

To find the height of a cone, we can use the formula for the volume of a cone and solve for the height.

The formula for the volume of a cone is:

V = (1/3)× π × r² × h

Given that the diameter of the cone is 12 m, the radius (r) is half of the diameter, which is 6 m.

We are also given that the volume of the cone is 188 m³.

Using the formula, we can rearrange it to solve for the height (h):

h = (3V) / (πr²)

Plugging in the values:

h = (3 × 188) / (3.14 × 6²)

h = 564 / (3.14 × 36)

h = 564 / 113.04

h =4.9916

h=5

Therefore, the height of a cone with a diameter of 12 m whose volume is 188 m³ is 5 m.

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The value of x from given parallel lines is 2.

In the given figure, three lines are parallel and two lines are passing through.

When three or more parallel lines are cut by two transversals, the line segments formed are proportional.

That is, 2x/x = (x+4)/(4x-5)

2/1 = (x+4)/(4x-5)

2(4x-5)=1(x+4)

8x-10=x+4

8x-x=4+10

7x=14

x=2

Therefore, the value of x from given parallel lines is 2.

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The rate of change of y with respect to x for the given linear relationship is 10.

To determine the rate of change of y with respect to x, we can calculate the slope of the linear relationship between x and y using the formula:

slope = (change in y) / (change in x)

Given the values in the table:

x: -8.5, -6.5, -2.5, -1

y: -92, -72, -32, -17

We can calculate the change in y and change in x between any two points.

For example, between the first two points (-8.5, -92) and (-6.5, -72), the change in y is:

change in y = -72 - (-92) = -72 + 92 = 20

And the change in x is

change in x = -6.5 - (-8.5) = -6.5 + 8.5 = 2

Using the formula for slope:

slope = (change in y) / (change in x) = 20 / 2 = 10.

Therefore, the rate of change of y with respect to x is 10.

This means that for every unit increase in x, y increases by 10 units.

We can perform the same calculations for the other points in the table and observe that the rate of change of y with respect to x remains constant at 10.

Hence, the rate of change of y with respect to x for the given linear relationship is 10.

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The mean monthly rainfall is 3.245 inches.

For a set of N numbers {x₁, x₂, ...}, the mean of these N numbers is:

M = {x₁ + x₂ + ...}/N

Here we want to find the mean of the rainfall in inches, then we just need to add the 12 values in the table and then divide by 12, we will get:

M = (2.22+1.51+1.86+2.06+3.48+4.57+ 3.27 + 5.40 + 5.45 + 4.34+2.64+ 2.14)/12

M = 3.245

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The probability of pulling out a red pair of socks and sport shorts is 12/35.

We have,

10 pairs of socks, 6 are red, and 7 shorts, 4 of which are sport shorts.

So, The probability of pulling out a red pair of socks is given by:

= (number of red socks) / (total number of socks)

= 6 / 10

= 3 / 5

and, the probability of pulling out sport shorts is given by:

= (number of sport shorts) / (total number of shorts)

= 4 / 7

To find the probability of both events happening together

= P(red socks) x P(sport shorts)

= (3 / 5) x (4 / 7)

= 12 / 35

Therefore, the probability of pulling out a red pair of socks and sport shorts is 12/35.

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Borrowing $50,000 for 30 years at 11% instead of 10% would result in an extra cost of approximately $44.63 per month.

To estimate the extra cost per month of borrowing $50,000 for 30 years at 11% instead of 10%, you can follow these steps:

Calculate the monthly payment for each interest rate:

The formula to calculate the monthly payment for a fixed-rate loan is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M is the monthly payment,

P is the principal amount (loan amount),

r is the monthly interest rate (annual interest rate divided by 12),

n is the total number of monthly payments (number of years multiplied by 12).

Let's calculate the monthly payment at 10% interest rate first:

P = $50,000

r = 10% / 100 / 12 = 0.0083333 (monthly interest rate)

n = 30 years * 12 = 360 (total number of monthly payments)

M1 = $50,000 * (0.0083333 * (1 + 0.0083333)^360) / ((1 + 0.0083333)^360 - 1)

Calculate the monthly payment at 11% interest rate using the same formula:

P = $50,000

r = 11% / 100 / 12 = 0.0091667 (monthly interest rate)

n = 30 years * 12 = 360 (total number of monthly payments)

M2 = $50,000 * (0.0091667 * (1 + 0.0091667)^360) / ((1 + 0.0091667)^360 - 1)

Calculate the difference in monthly payments:

Extra cost per month = M2 - M1

Now let's perform the calculations:

M1 ≈ $446.92 (monthly payment at 10% interest rate)

M2 ≈ $491.55 (monthly payment at 11% interest rate)

Extra cost per month = $491.55 - $446.92 ≈ $44.63

Therefore, borrowing $50,000 for 30 years at 11% instead of 10% would result in an extra cost of approximately $44.63 per month.

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The coordinates in the solution to the systems of inequalities graphically is (-5, 1)

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

y < 1/2x + 5

y ≤ -3x - 2

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (-5, 1)

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Answer:

(-5, -5)

Step-by-step explanation:

Given system of linear inequalities:

[tex]\begin{cases}y < \dfrac{1}{2}x+5\\\\y\leq-3x-2\end{case}[/tex]

When graphing inequalities:

To graph linear inequalities, treat them as equations (swap the inequality sign for an "equals" sign). Plug in two values of x to find two points on the line to help draw the lines.  

Substitute x = 0 and x = 6 into the equation of the inequality to find two points on the line.

[tex]\begin{aligned}x=0 \implies y&=\dfrac{1}{2}(0)+5\\y&=5\end{aligned}[/tex]               [tex]\begin{aligned}x=6 \implies y&=\dfrac{1}{2}(6)+5\\y&=8\end{aligned}[/tex]

Plots points (0, 5) and (6, 8).

As the inequality sign is <, draw a dashed line through the plotted points and shade below the line.

Substitute x = 0 and x = 2 into the equation of the inequality to find two points on the line.

[tex]\begin{aligned}x=0 \implies y&=-3(0)-2\\y&=-2\end{aligned}[/tex]               [tex]\begin{aligned}x=2 \implies y&=-3(2)-2\\y&=-8\end{aligned}[/tex]

Plots points (0, -2) and (2, -8).

As the inequality sign is ≤, draw a solid line through the plotted points and shade below the line.

The solution set is the set of points contained within the overlapping shaded region and on the solid line.

Therefore, a point in the solution set is (-5, -5).

Answer:

Sure, I'd be happy to help you solve these equations! Here are the solutions to the equations you provided:

1. -3x+7=-8x+47

  Add 8x to both sides: 5x + 7 = 47

  Subtract 7 from both sides: 5x = 40

  Divide both sides by 5: x = 8

2. -13x+8=-8x-7

  Add 13x to both sides: 5x + 8 = -7

  Subtract 8 from both sides: 5x = -15

  Divide both sides by 5: x = -3

3. 6x+7=3x+19

  Subtract 3x from both sides: 3x + 7 = 19

  Subtract 7 from both sides: 3x = 12

  Divide both sides by 3: x = 4

4. 12x-8=10x+6

  Subtract 10x from both sides: 2x - 8 = 6

  Add 8 to both sides: 2x = 14

  Divide both sides by 2: x = 7

5. -7x-4=-10x-10

  Add 10x to both sides: 3x - 4 = -10

  Add 4 to both sides: 3x = -6

  Divide both sides by 3: x = -2

6. 7x-9=3x-5

  Subtract 3x from both sides: 4x - 9 = -5

  Add 9 to both sides: 4x = 4

  Divide both sides by 4: x = 1

7. 3x-9=5x-3

  Subtract 3x from both sides: -6 = 2x - 3

  Add 3 to both sides: -3 = 2x

  Divide both sides by 2: x = -3/2 or -1.5

8. 7x-1=5x+5

  Subtract 5x from both sides: 2x - 1 = 5

  Add 1 to both sides: 2x = 6

  Divide both sides by 2: x = 3

9. -7x-2=-3x-14

  Add 3x to both sides: -4x - 2 = -14

  Add 2 to both sides: -4x = -12

  Divide both sides by -4: x = 3

10. -3x-7=-8x-57

   Add 8x to both sides: 5x - 7 = -57

   Add 7 to both sides: 5x = -50

   Divide both sides by 5: x = -10

I hope this helps! Let me know if you have any further questions.

Answer:

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

What percent of $8400 is $672?

Answer:

8%

Step-by-step explanation:

To find the percentage that was donated to hospitals, we can set up the following equation:

[tex]\sf \dfrac{total\: donation}{ total \:sales} * 100 = percentage \:donated[/tex]

In this case, the total donation was $672 and the total sales were $8,400.

Substituting these values into the equation, we get:

[tex]\sf \dfrac{672}{8400} * 100 = percentage \:donated[/tex]

Simplifying this expression:

(0.08) * 100 = percentage donated

8% = percentage donated

Therefore, the home decor store donated 8% of $8,400 to hospitals.

The equation of circle with a center at (9, 5) that passes through (13, 7) is (x - 9)² + (y - 5)² = 20.

we have Center at (9, 5) and passes thorough (13, 7).

To find the equation of a circle with center (h, k) and a point (x, y) on the circle, we can use the standard form equation of a circle:

(x-h)² + (y-k)² = r²

So,  (x - 9)² + (y - 5)² = r

Since the circle passes through (13, 7), then

(13 - 9)² + (7 - 5)² = r²

²4 + (2)² = r²

16 + 4 = r²

20 = r²

So, the equation of circle is

(x - 9)² + (y - 5)² = 20

Therefore, the equation of circle with a center at (9, 5) that passes through (13, 7) is (x - 9)² + (y - 5)² = 20.

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Answer:

Solution is in the attached photo.

Step-by-step explanation:

This question tests on the concept on deriving equations and substitution of values.