Tuition for one year at the Community College of Camelot costs $6,000 per year. Avalon would like to attend this college and will save money each month for the next 2 years in order to reach her goal. Her parents will contribute 50% for his first year's tuition. If Avalon also receives a local scholarship for $600, how much money will she need to save each month for the next 2 years to have enough money for her first year of college?

The given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants.

Mutually exclusive and exhaustive variables: A variable is mutually exclusive and exhaustive if it includes all possible outcomes and each outcome can only be assigned to one variable category.a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday - Mutually exclusive and exhaustiveb. Days: Weekday and Weekend - Mutually exclusive and exhaustive c. Letters: Vowels and Consonants - Mutually exclusive and exhaustive. Letters: Alphabets and Consonants - Not mutually exclusive and exhaustiveThe given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants. Hence, the options a and c are correct.

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Answer:

50 mph

Step-by-step explanation:

We have the following point

(2,100)

We know that the equation has a y intercept of 0 which means our equation looks like this

y=mx

We know that when x=2 y=100 so

100=2m

m=50

50 mph

Answer:

It’s constant by 50 (1,50) (2,125) and so on

Step-by-step explanation:

25+25=50 75+50=125 and so on

Answer:

where is the list at?

Step-by-step explanation:

The area of the figure is 51.63 m²

A composite figure is figure that is made up of two or more different shapes.

The composite figure in the given image is made up of a rectangle, semicircle and a triangle. Therefore, the area of the composite figure will be the sum of the areas of the shape it is made of. Thus:

Area of figure = area if rectangle + area of semicircle + area of triangle

Area of figure = LW + 1/2πr² + 1/2bh

Area of figure = (6 × 5) + (1/2 × 3.14 × 3²) + (1/2 × 3 × 5)

Area of figure = 30 + 14.13 + 7.5

Area of figure = 51.63 m²

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Lorraine can fill 8 jars with the tomatoes from the 2.5-gallon pot.

First, we need to convert the volume of the pot from gallons to quarts, since the jars are measured in quarts:

2.5 gallons = 2.5 * 4 quarts = 10 quarts

Next, we can divide the total volume of the pot in quarts by the volume of each jar in quarts to find the number of jars Lorraine can fill:

10 quarts / 1.25 quarts per jar = 8 jars

So Lorraine can fill 8 jars with the tomatoes from the 2.5-gallon pot.

Mensuration is a branch of mathematics that deals with the measurement of various geometric figures and objects, such as lengths, areas, and volumes. It is concerned with finding the size, shape, and measurement of geometric objects, such as points, lines, circles, polyggon, and solids.

Mensuration is used in various areas of mathematics, science, and engineering to solve problems involving measurements, such as finding the area of a rectangle, the volume of a cylinder, the circumference of a circle, or the surface area of a sphere.

Mensuration provides a set of mathematical formulas and methods for measuring geometric objects, and it requires knowledge of basic concepts such as perimeter, area, volume, and surface area. These concepts are used to find the size of objects and to compare different objects to one another based on their measurements.

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as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

\(\stackrel{f(x)}{y}~~ = ~~2x^2+4x\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2y^2+4y} \\\\\\ x=2(y^2+2y)\implies \cfrac{x}{2}=y^2+2y\impliedby \begin{array}{llll} \textit{now let's complete the square}\\ \textit{to make it a perfect square trinomial}\\ \textit{by using our good friend, Mr "0"} \end{array} \\\\\\ \cfrac{x}{2}=y^2+2y(+1^2-1^2)\implies \cfrac{x}{2}=y^2+2y+1-1\implies \cfrac{x}{2}=(y^2+2y+1)-1\)

\(\cfrac{x}{2}+1=(y^2+2y+1^2)\implies \cfrac{x}{2}+1=(y+1)^2\implies \sqrt{\cfrac{x}{2}+1}=y+1 \\\\\\ \sqrt{\cfrac{x+2}{2}}=y+1\implies \sqrt{\cfrac{x+2}{2}}-1=y~~ = ~~f^{-1}(x)\)

A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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The minimum number of swaps required to flip the list is 2.

Array : Generally, in the field of applied sciences, knowledge structures called arrays and typically regarded as just arrays, each containing at least one array-index award or key. Arrays are stored so that formulas can use each component's index tuple to determine the placement of that component within the array.

Given an array with values 5, 10, 15, 20,25

swap reverses the array:

25, 10, 15, 20, 5

25, 20, 15, 10, 5

So, for reversing the number of swaps required list is 2 ..

This may be the smallest variation possible.

Hence, the minimum exchange required to achieve list reversal is two.

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The z-score when x=108 is 3.1034. The z-score tells you that x=108 is 3.1034 standard deviations to the left of the mean.

Z-score is used in statistics to compare a score to a normal distribution. The z-score is a measure of how far away from the mean a value is in standard deviation units.

To find the z-score when x = 108, we use the formula:

z = (x - μ) / σ

where x = 108, μ = 153, and σ = 14.5.

Substituting these values, we get:

z = (108 - 153) / 14.5 = -3.1034

So the z-score when x = 108 is -3.1034.

The z-score tells us how many standard deviations away from the mean a particular value is. In this case, since the z-score is negative, we know that x = 108 is to the left of the mean.

The absolute value of the z-score tells us how many standard deviations away from the mean the value is. In this case, the absolute value of the z-score is approximately 3.1034, which means that x = 108 is approximately 3.1034 standard deviations to the left of the mean.

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Answer:

b) 130

Step-by-step explanation:

The total of the internal angles of any simple hexagon (six sides)  is 720°.

720 = 150+95+105+145+95+x

720= 590 + x

720 - 590 = x

130 = x

Answer

47

Step-by-step explanation:

The larger of the two roots of the equation \(y = -2.2x^2 + 63.5x - 17\)would be 28.59.

Suppose that the given quadratic equation is

\(ax^2 + bx + c = 0\)

Then its roots are given as:

\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

The given quadratic equation is

\(y = -2.2x^2 + 63.5x - 17\)

now, the roots of the equation are

\(x = \dfrac{-63.5 \pm \sqrt{63.5^2 - 4(-2.2)(-17)}}{2(-2.2)}\\\\\\x = \dfrac{-63.5 \pm \sqrt{4032.25 - 149.6}}{(-4.4)}\\\\\\x = \dfrac{-63.5 \pm \sqrt{3882.65}}{(-4.4)}\\\\\\x = \dfrac{-63.5 \pm 62.31}{(-4.4)}\)

The two roots are 0.27 and 28.59.

Thus, the larger of the two roots of the equation \(y = -2.2x^2 + 63.5x - 17\)would be 28.59.

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The purpose of performing the overall F-test is to test whether at least one of the predictor variables is significant in a regression model.

This is option a.

The F-test is used to determine if the entire regression model is significant, rather than just one individual predictor variable. If the F-test is significant, it means that at least one of the predictor variables has a significant relationship with the dependent variable.

This can help us determine if the regression model is useful in predicting the dependent variable.

The F-test is an important step in regression analysis, as it can help us determine if our model is valid and useful for making predictions.

Hence Option A is correct.

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Answer:

y=mx+b, where m is slope, b is y-int and x and y are variables.

S = 40N + 1600

Graphing:

Plot your y-int at (0,1600). Plot your slope in. Draw a line thru the points.

Points: (1,1640), (2,1680) etc

Hope that helps. Brainliest is greatly appreciated!

96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25  is -1234

arithmetic sequence 1, -12, -25, .. .1,−12,−25

an arithmetic sequence can be written as

a , a + d , a + 2d , a + 3d , . . . . . a + (n-1)d

nth tern of an arithmetic sequence is

aₙ= a+ (n-1)d

a= first term of an arithmetic sequence

d = common difference of an arithmetic sequence

n = number of terms in an arithmetic sequence

So in the above arithmetic sequence

a= 1

d= -13

n= 96

a₉₆= 1+ (96-1)(-13)

    =  1- (95)13

    =  1- 1235

    = -1234

96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25  is -1234

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Answer:

100000 = 8 (4) ^t

Step-by-step explanation:

We are multiplying by 4 each time

y = a (4)^t

The initial amount is 8

y = 8 (4)^t

We want to get to 100000

100000 = 8 (4) ^t

Answer:

B

8 ⋅ 4^t  = 100,000

Step-by-step explanation:

Probability that computer chosen at random has defect is 0.0075.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.

It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 12.

Total number of computers=1200

Total number of damage computers=9

Probability that question chosen at random has defect = 9/1200=0.0075

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Answer:

33x - 14

Step-by-step explanation:

5x - 7 (2 - 4x)

5x - 14 + 28x

33x - 14

Answer:

it's 18x-10 and I'm also new and I searched it up in the internet

Step-by-step explanation:

ik online school is hard but they to download Every app thats for school so you can cheat

Answer:

15.6 ft²

Step-by-step explanation:

Given:

Radius (r) of circle = 5.7 ft

m<CBD = 55°

Required: Area of the shaded sector

SOLUTION:

Area of shaded sector = θ/360*πr²

Where,

θ = 55°

π = 3.14

r = 5.7 ft

Plug in your values

\( Area = \frac{55}{360}*3.14*5.7^2 \)

\( Area = \frac{55}{360}*3.14*32.49 \)

\( Area = 15.59 \)

Area of shaded sector to nearest tenth = 15.6 ft²

Answer:

unij.,hsakj hdku ugkzsssssssjbfskjgfbskufjbghjbgfhjbghbfkjhbfsdf  mdftedtmtedemedeedttfgtubjcufttttttttgxdcgfvcdhfvvvvvdyuyuyuyfyfyfftftftftftyytftfftftffttyfjvhghfhgfghfgfghfhgfghfhgfghfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfgfhf

Step-by-step explanation:

u suck balls

Given that MNPQ is a rectangle with verticles M(3, 4), N(1, -6), and P(6, -7), to find the coordinates of point Q, we can use the fact that opposite sides of a rectangle are parallel and have equal lengths.

First, let's find the vector MN and MP:

MN = N - M = (1 - 3, -6 - 4) = (-2, -10)
MP = P - M = (6 - 3, -7 - 4) = (3, -11)

Now, let's add the vector MN to point P:

Q = P + MN = (6 + (-2), -7 + (-10)) = (4, -17)

Therefore, the coordinates of point Q that make MNPQ a rectangle are Q(4, -17).


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The mass passes through the equilibrium position after approximately 0.45 seconds, and it attains its extreme displacement from the equilibrium position after around 1.15 seconds.

Given that an 80 lb weight stretches a spring 8 feet, we can determine the spring constant using Hooke's Law: F = kx, where F is the force, k is the spring constant, and x is the displacement from the equilibrium position. In this case, F = 80 lb and x = 8 ft, so k = F/x = 80 lb / 8 ft = 10 lb/ft.

To find the time when the mass passes through the equilibrium position, we can use the equation of motion for damped harmonic motion: m * d²x/dt² + bv = -kx, where m is the mass, b is the damping constant, and v is the velocity. We are given that the damping force is 10 times the instantaneous velocity, so b = 10 * v.

We can rearrange the equation of motion to solve for time when the mass passes through the equilibrium position (x = 0) by substituting the values: m * d²x/dt² + 10mv = -kx. Plugging in m = 80 lb / 32.2 ft/s² (to convert from lb to slugs), k = 10 lb/ft, and v = -18 ft/s (negative because it is downward), we get: 80/32.2 * d²x/dt² - 1800 = -10x. Simplifying, we have d²x/dt² + 22.43x = 0.

The general solution to this differential equation is of the form x = A * exp(rt), where A is the amplitude and r is a constant. In this case, the equation becomes d²x/dt² + 22.43x = 0. Solving the characteristic equation, we find that r = ±√22.43. The time when the mass passes through the equilibrium position is when x = 0, so plugging in x = 0 and solving for t, we get t = ln(A)/√22.43. Given that the mass is released from 4 feet above the equilibrium position, the amplitude A is 4 ft, and thus t = ln(4)/√22.43 ≈ 0.45 seconds.

To find the time when the mass attains its extreme displacement, we can use the fact that the maximum displacement occurs when the mass reaches its maximum potential energy, which happens when the velocity is zero. From the equation of motion, we can see that the velocity becomes zero when d²x/dt² = -10v/m. Substituting the values, we have d²x/dt² + 22.43x = -10(-18)/(80/32.2) = 7.238. Solving this differential equation with the initial condition that x = 4 ft and dx/dt = -18 ft/s at t = 0 (when the mass is released), we find that the time when the mass attains its extreme displacement is approximately 1.15 seconds.

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The degree measure of each of the angle in the triangle are m ∠V =88°, m ∠X = 46° and m ∠W = 46°.

Given that,

Triangle, ΔVWX is isosceles with base XW.

So, VX = VW

Angles opposite these sides are equal.

∠W = ∠X

Given,

m ∠X = (3x + 13)°

m ∠V = (5x + 33)°

m ∠W = 180° - ((3x + 13)° + (5x + 33)°)

          = 180 - (8x + 46)

          = 134 - 8x

Equating,

134 - 8x = 3x + 13

-11x = -121

x = 11

Measure of angles are,

m ∠X = (3x + 13)° = 46°

m ∠V = (5x + 33)° = 88°

m ∠W = (134 - 8x)° = 46°

Hence the angle measures are 88°, 46° and 46°.

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Answer:

y = ✔ 1x+ ✔ -3

Step-by-step explanation:

The equation of the line passing through the points (2, -1) and (10, 7) is y =  x - 3.

The point slope form of a line is given by -

y - y₁ = m(x - x₁)

Given is a line that passes through the points (2, -1) and (10, 7).

The point - slope form of a line is given by the general equation -

y - y₁ = m(x - x₁)

We will find the slope of the line as follows -

m = (7 + 1)/(10 - 2) = 8/8 = 1

The line passes through the point (2, -1), so we can write the equation of line as -

y - (- 1) = x - 2

y + 1 = x - 2

x - y = 3

y =  x - 3

Therefore, the equation of the line passing through the points (2, -1) and (10, 7) is y =  x - 3.

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Answer:

Step-by-step explanation:

\(y=-x^{2} +36\)

can be factored out as (-x-6)(x-6)

x-intercepts are: +6 and -6

represents the two ends of the rainbow

y-intercept: y=36

represents the highest point of the rainbow