A class votes for their class president. Candidate A receives 21 votes, which is 60% of the vote. What is the total number of students who voted?

Part A: The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: The point (8, 2) is not included in the solution area.

Part C: The point (3, 1) represents one feasible solution that meets the constraints of the problem.

Part A: The graph of the system of inequalities consists of two lines and a shaded region. The line x + 3y = 8 is a solid line because it includes the equality symbol, indicating that points on the line are included in the solution set. The line x + y = 2 is also a solid line. The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: To determine if the point (8, 2) is included in the solution area, we substitute the x and y values into the inequalities:

8 + 3(2) ≤ 8

8 + 6 ≤ 8

14 ≤ 8 (False)

Since the inequality is not satisfied, the point (8, 2) is not included in the solution area.

Part C: Let's choose a point in the solution set, such as (3, 1). This point satisfies both inequalities: x + 3y ≤ 8 and x + y ≥ 2. In the context of the real-world scenario, this means that Michelle can buy 3 servings of dry food (x = 3) and 1 serving of wet food (y = 1) with her $8 budget. This combination of dog food allows her to feed at least two dogs at the animal shelter while staying within her budget. The point (3, 1) represents one feasible solution that meets the constraints of the problem.

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The constant of proportionality in table four is -1/3

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

In each of the table, we can check if proportionality exists.

In the first table, there's no proportionality.

In the second table, there's no proportionality

In the third table, there's no proportionality

In the fourth table, proportionality exist here which we can find the constant of proportionality.

When x = 6, y = -2

y = ax

a = constant of proportionality

-2 = a(6)

a = -1/3

The constant of proportionality is -1/3

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Answer:

x =  65 degrees.

Step-by-step explanation:

sin 25 = cos (90-25)

sin 25 = cos 65

In the equation, the value of x is,

⇒ x = 65

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Equation is,

⇒ sin 25° = cos x°

Now, We can simplify as;

⇒ sin 25° = cos x°

⇒ sin 25° = sin (90 - x)°

By comparing, we get;

⇒ 25 = 90 - x

⇒ x = 90 - 25

⇒ x = 65

Thus, In the equation, the value of x is,

⇒ x = 65

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c) It would be larger, because higher confidence requires a larger margin of error.

When increasing the confidence level from 95% to 99%, the margin of error of the confidence interval tends to increase. This is because a higher confidence level means we want to be more certain or have a higher level of confidence in capturing the true population parameter.

To achieve a higher confidence level, we need to widen the interval to account for more potential variability in the population. As a result, the margin of error increases, reflecting the increased uncertainty and the need for a larger range of values to capture the true population parameter with higher confidence.

Therefore, the margin of error of a 99% confidence interval, based on the same sample, would be larger compared to the 95% interval.

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There are 90 4-digit palindromes

Palindromes are numbers whose reverse is the same as the original number

Since the digit is 4, then

So, the total number of digits is:

\(n =9 * 10 * 1 * 1\)

Evaluate the product

\(n =90\)

Hence, there are 90 4-digit palindromes.

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Answer:

a reflection in the y axis followed by a translation 1 unit down

Step-by-step explanation:

Reflection over the y-axis then a unit down

Based on the information in the graph, we can infer that the missing numbers are: 9, 4, 19, 30, 84, 16, 8, 22, and 40.

To complete the table correctly we must identify the columns or rows with more data. These will be the easiest to complete. First of all, we must fill in those that already have a number in the total box because we can add the available numbers and later subtract them from the total to identify the missing number.

We can also find the numbers in the total cells by adding all the numbers in a column or row to find this result. Finally, the boxes that are being completed serve as clues to complete the others.

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Answer:

The answer is m = x + 2kn

Step-by-step explanation:

Rewrite the equation as  − 2 k n  +  m  =  x . Add  2 k n  to both sides of the equation.

The parametric equations for the tangent line to the curve with the given parametric equations at the specified point is  \(e^{(-2t)\)cos(3t), y =  \(e^{(-2t)\)sin(3t), z = \(e^{(-2t)\)

To find the parametric equations of the tangent line to a curve with given parametric equations at a point, we need to follow the following steps:

Let's apply these steps to the given problem:

Find the derivatives dx/dt, dy/dt, and dz/dt of the given parametric equations:

\(dx/dt = -2e^{(-2t)}cos(3t) - 3e^{(-2t)}sin(3t)\)

\(dy/dt = -2e^{(-2t)}sin(3t) + 3e^{(-2t)}cos(3t)\)

dz/dt = -2e^(-2t)

Plug in the value of t that corresponds to the given point (1,0,1) to find the corresponding values of dx/dt, dy/dt, and dz/dt:

dx/dt(1) = -2e⁻² ¹ cos(3(1)) - 3e⁻²  ¹ sin(3(1)) = -5.348

dy/dt(1) = -2e⁻² ¹ sin(3(1)) + 3e⁻² ¹)cos(3(1)) = 2.317

dz/dt(1) = -2e⁻² ¹ = -1.471

Use the point (1,0,1) and the values of dx/dt, dy/dt, and dz/dt at that point to write the equation of the tangent line in parametric form. Let's call the parametric equation of the tangent line (x(t), y(t), z(t)):

x(t) = 1 - 5.348(t-1)

y(t) = 0 + 2.317(t-1)

z(t) = 1 - 1.471(t-1)

Therefore, the parametric equations of the tangent line to the curve x =  \(e^{(-2t)\)cos(3t), y =  \(e^{(-2t)\)sin(3t), z = \(e^{(-2t)\) at the point (1,0,1) are x(t) = 1 - 5.348(t-1), y(t) = 2.317(t-1), z(t) = 1 - 1.471(t-1).

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Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.

To find the number of cups of rice that remained in the box, we need to calculate three-fourths (3/4) of the total amount of rice in the box.

The total amount of rice in the box is given as five and two-thirds cups. To work with a fraction, we can convert the mixed number to an improper fraction:

5 and 2/3 = (5 * 3 + 2) / 3 = 17/3 cups

Now, we can find three-fourths (3/4) of 17/3:

(3/4) * (17/3) = (3 * 17) / (4 * 3) = 51/12 = 4 and 3/12 = 4 and 1/4 cups

Therefore, after using three-fourths of the rice in the box, 4 and 1/4 cups of rice remained.

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Answer:

y = 4x - 1

Step-by-step explanation:

equation of a line in slope-intercept form: y = mx + b

m is the slope and b is the y-intercept

y = 4x - 1

Answer:

-3=b

Step-by-step explanation:

Hey there!

In order to find the value for b, we must first combine all like terms

-11-6b+3=16+2b

-8-6b=16+2b

-24=8b

Now we simplified the equation to a point where we can find the value of b in one step

-24/8 = 8b/8

-3=b

Answer:

-3

Step-by-step explanation:

Bring to the right of = the Number with b and to the left the other.

Remember to change sign of Number when you switch

So

\( - 11 + 3 - 16 = 2b + 6b\)

Do addition

\( - 24 = 8b\)

Find b

\(b = - 24 \div 8\)

b= -3

The probability that Lila selects a black ribbon and Jessica selects a green ribbon is the fraction 51/380. Option D is correct.

The probability of an event without replacement implies that once an item is drawn, then we do not replace it back to the sample space before drawing another item.

total number of ribbon = 3 + 17

total number of ribbon = 20

probability Lila selects a black ribbon at random = 3/20

probability Jessica selects a green ribbon at random from the remaining ribbons = 17/19

probability that Lila selects a black ribbon and Jessica selects a green ribbon = 3/20 × 17/19

probability that Lila selects a black ribbon and Jessica selects a green ribbon = 51/380

Therefore, the probability that Lila selects a black ribbon and Jessica selects a green ribbon is the fraction 51/380.

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Answer:

130°

Step-by-step explanation:

50 + x = 180°

Answer:

Opposite 50 would be 50 because they are parallel X which is corresponding to each other and the other two angles will be even as well because they are also corresponding

In a circle theres 360 degrees and 50+50=100

360-100=260 divide by 2 is 130

divide by two because of the two other missing angles.

your answer is 130°

a. To test Ella's claim at the 0.10 level of significance, we can perform a one-sample t-test with the given sample mean, sample standard deviation, sample size, and assuming a normal population distribution.

b. The null hypothesis (H₀) is that the mean amount of wireless data used by teenagers in her area is equal to or greater than the reported average. The alternative hypothesis (H₁) is that the mean amount of wireless data used by teenagers in her area is less than the reported average.

a. To test Ella's claim at the 0.10 level of significance, we can perform a one-sample t-test.

b. The null hypothesis (H₀) would state that the mean amount of wireless data used by teenagers in her area is equal to or greater than the reported average. The alternative hypothesis (H₁) would state that the mean amount of wireless data used by teenagers in her area is less than the reported average.

In symbols:

H₀: μ ≥ reported average

H₁: μ < reported average

In this case, since Ella claims that the mean is less than the reported average, the alternative hypothesis is one-tailed and represents the direction Ella is trying to prove.

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Answer:

3

Step-by-step explanation:

The horizontal component of the force is 25.98 lb and the vertical component is 15 lb.

A vector quantity has both magnitude and direction. It is added using parallelogram law of addition.

The sum of two vector quantities is always a vector quantity.

The sum of two vector quantities can vary from their scalar difference to their scalar addition.

Given that,

The force applied by the man is 30 lb.

The angle the force makes with ground is 30°.

For a vector A making angle x with the horizontal axis the horizontal and vertical component are given as,

The horizontal component is ACos(x)

And, the vertical component is ASin(x)

Thus, the horizontal and vertical component of the force are

Horizontal component = 30Cos(30°)

                                      = 30 × √3 / 2

                                      =  25.98

Vertical component = 30Sin(30°)

                                  = 30 × √3/2

                                  = 15

Hence, the horizontal and vertical components of the force are 25.98 lb and 15 lb respectively.

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When you observe the movement of the car in front of you on the freeway, you notice that the speedometer says v₀ and the car appears to be coming towards you at a speed of 41v₀.

Similarly, the car behind you is gaining on you at a speed of 41v₀. The speed that someone standing on the ground would say each car is moving would be v₀, as the cars seem to be at rest in relation to the ground.

When you want to swim straight across the river with a speed of t₀3L, you should swim perpendicular to the direction of the current.

The angle between the direction of your motion and the current direction will be 90 degrees

The width of the river is 31L, and you want to swim straight across it with a speed of t₀3L.

If we consider the time it takes to cross the river is t and the velocity of the current is vc, then:

31L = (t₀ − t)c31L = t₀(1 − t)t = 3t₀/2 - L/vc

We observe that it takes the fish 61t₀ to swim downstream and 31t0 to swim upstream.

Now we want to calculate the speed of the current of the river. If we let the speed of the fish be vf and the velocity of the current be vc, then

vf + vc = L/61t₀ and vf - vc = L/31t₀.

By adding these two equations, we get

vf = L(2/61t₀), and by subtracting the second equation from the first, we get

vc = L/61t₀ - L/31t₀ = L/183t₀

Therefore, we get that the speed of the current of the river is L/183t₀ for part (b). In part (c), we can determine that to swim straight across the river with a speed of t₀3L, we should swim perpendicular to the direction of the current, and in part (d), we can calculate the time it would take to cross the river with the given information.

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Answer:

If 6_3 means 6-3, do parentheses first and get:

22 + 3* 32=

Then exponents!

4+ 3*9=

4+27=

31

We have shown that for any given ε > 0, we can choose δ = 1/(-B) such that for all x satisfying 0 < |x - 2| < δ, it follows tha\(t |(x - 2)/(x^2 - 2x)| < ε.\)

What is Epsilon-delta?

Epsilon-delta is a concept used in calculus and mathematical analysis to define limits and continuity rigorously. It provides a precise way of expressing the idea of a function approaching a particular value as the input approaches a given point.

To prove the limit statement using formal definitions, we want to show that for any given ε > 0, there exists a δ > 0 such that for all x satisfying 0 < |x - 2| < δ, it follows that \(|(x - 2)/(x^2 - 2x)| < ε.\)

Given -B < 0, we need to find δ > 0 such that for all x, if 0 < |x - 2| < δ, then \(|(x - 2)/(x^2 - 2x)| < -B.\)

Let's begin the proof:

Proof:

Given ε > 0, we need to find δ > 0 such that for all x, if 0 < |x - 2| < δ, then \(|(x - 2)/(x^2 - 2x)| < ε.\)

We can start by manipulating the expression \(|(x - 2)/(x^2 - 2x)|\)to simplify it further:

\(|(x - 2)/(x^2 - 2x)| = |(x - 2)/x(x - 2)|\)

Now, notice that we can cancel out the (x - 2) term from the numerator and denominator since x ≠ 2 (otherwise the denominator would be zero).

\(|(x - 2)/(x^2 - 2x)| = 1/|x|\)

Now, we want to find δ > 0 such that for all x, if 0 < |x - 2| < δ, then 1/|x| < ε.

Since we are given -B < 0, we can choose δ = 1/(-B).

Now, let's consider any x such that 0 < |x - 2| < δ.

From the choice of δ, we have 0 < |x - 2| < 1/(-B), which implies |x| > 1/δ = -B.

Since |x| > -B, we have 1/|x| < 1/(-B) = δ.

Therefore, we have shown that for any given ε > 0, we can choose δ = 1/(-B) such that for all x satisfying 0 < |x - 2| < δ, it follows that \(|(x - 2)/(x^2 - 2x)| < ε.\)

Hence, the limit statement holds, and we have proven it using formal definitions.

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We have proved the trigonometric expression cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A) by using C/D formula.

We are given the expression:

cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A)

We need to prove the expression.

We know that:

Cos C + Cos D = 2 cos ( C + D / 2) cos ( C - D / 2)

Using this identity, we get that:

= cos 5 A + cos A + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= 2 cos ( 5A + A / 2) cos ( 5A - A / 2) + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= 2 cos 3 A cos 2 A + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= cos 2 A ( 2 cos 3A + 1) = cos 2 A (1 + 2 cos 3 A)

= cos 2 A (1 + 2 cos 3 A) = cos 2 A (1 + 2 cos 3 A)

LHS = RHS

Hence proved.

Therefore, we have proved the trigonometric expression cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A) by using C/D formula.

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needless to say that the conversion from miles to kilometers uses a constant value, and therefore, they're directly proportional.

now, I could write the direct proportional relation blah blah but there's no need, we can simply squeeze it out of the table by simply checking how many kilometers there are in 1 mile.

well, we know that 11.0 miles give us 17.699 km, ok hmmm if we divide 17.699 ÷ 11 = 1.609.

if we do the same on table for 26 and 41.834, so 41.834 ÷ 26 = 1.609, and the next pair 54.706 ÷ 34 = 1.609, the value of 1.609 is consistent or constant, or namely that there are 1.609 kilometers in 1 mile.

The area of the walkway is 24π square meters.

To find the area of the walkway, we need to subtract the area of the inner circle from the area of the outer circle.

The inner circle has a radius of 5 meters, so its area can be calculated using the formula for the area of a circle: A_inner = π * \((r_inner)^{2}\).

A_inner = π * \(5^{2}\) = 25π square meters.

The outer circle has a radius equal to the sum of the inner radius and the width of the walkway. In this case, the outer radius is 5 + 2 = 7 meters.

The area of the outer circle can be calculated in the same way: A_outer = π * \((r_outer)^{2}\).

A_outer = π * \(7^{2}\) = 49π square meters.

Now, we can find the area of the walkway by subtracting the area of the inner circle from the area of the outer circle: A_walkway = A_outer - A_inner.

A_walkway = 49π - 25π = 24π square meters.

The area of the walkway is 24π square meters, where π (pi) is a mathematical constant approximately equal to 3.14159.

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To start, let's sketch the graph of the curve y = x from x = 0 to x = 20. This is simply a diagonal line that passes through the points (0,0) and (20,20), as shown below:

```
   |
20  |    *
   |   *  
   |  *  
   | *    
   |*    
0  --------------
  0   10   20
```

Now, we want to revolve this curve around the x-axis to create a solid shape. Specifically, we want to create a paraboloid, which is a three-dimensional shape that looks like an upside-down bowl.

To find the volume of this paraboloid, we need to use calculus. The basic idea is to slice the solid into very thin disks, and then add up the volumes of all the disks to get the total volume.

To do this, we'll use the formula for the volume of a cylinder, which is:

V = πr^2h

where r is the radius of the cylinder and h is its height. In our case, each disk is a cylinder with radius r and height h, where:

- r is equal to the y-value of the curve (i.e. r = y = x), since the disk extends from the x-axis to the curve.
- h is the thickness of the disk, which is a very small change in x. We can call this dx.

So, the volume of each disk is:

dV = πr^2dx
  = πx^2dx

To find the total volume of the paraboloid, we need to add up the volumes of all the disks. This is done using an integral:

V = ∫(from x=0 to x=20) dV
 = ∫(from x=0 to x=20) πx^2dx

Evaluating this integral gives us:

V = π/3 * 20^3
 = 8000π/3

So the exact volume of the paraboloid is 8000π/3.

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Answer:

right scalene triangle

The correct answer is c. both A and B are correct. When one increases the confidence level from 0.90 to 0.95, the margin of error will increase because a higher level of confidence requires a wider interval to capture the population parameter.

However, the resulting confidence interval will also capture the population parameter more often because the higher confidence level provides a greater level of certainty that the interval contains the true population parameter.

When one increases the confidence level (1-α), say from 0.90 to 0.95, both A and B are correct.

Explanation:
a. The margin of error will increase because increasing the confidence level means we are more certain that the population parameter lies within the confidence interval. To achieve this, the interval has to be wider, which results in a larger margin of error.

b. The resulting confidence interval will capture the population parameter more often because a higher confidence level indicates a higher probability that the interval contains the true population parameter. In this case, going from a 0.90 to 0.95 confidence level means that we would expect the interval to capture the true population parameter 95% of the time, as opposed to 90% of the time.

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Answer:

im not sure (dont take this down plz) but i think it is 2175 bc i dont belive there are not more then two or three ways to get that #

Answer:

Boom boom eat my but cheeks

Step-by-step explanation: