Felicia earns $800 a month. The table shows her monthly budget.

Monthly Budget
Expense Amount of Money
College savings $200
Car payment $275
Cell phone $125
Clothes $50
Food $100
Other $50

Which statement is supported by the information in the table?
F.Felicia spends 10% of her monthly budget on clothes and food.
G.Felicia spends 25% of her monthly budget on her car payment.
H.Felicia spends 20% of her monthly budget on college savings.
J.Felicia spends 50% of her monthly budget on her car payment and cell phone.

I'm not really good at math and I'm doing a test online right now and I am very confused.

The required expression for part A ⇒ 2x(3x-8)

The required expression for part B ⇒2x(3x-8)

Part A:

The area of the rectangular space is given by the expression 6x²-16x, which is equal to the length times the width. We are given that the width of the rectangular space is 2x.

Therefore, we can write:

length x width = area

length x (2x) = 6x²-16x

length = (6x²-16x) / (2x)

Simplify the expression for length by factoring out 2x from the numerator:

length = 2x(3x-8)

So the expression for the length of the rectangular space is 2x(3x-8).

Part B:

To prove that our expression for the length is correct, we can multiply it by the width and show that we get the original expression for the area:

length x width = 2x(3x-8) x (2x)

                        = 4x²(3x-8)

                        = 12x³ - 32x²

Now we can compare this result with the original expression for the area, which is 6x²-16x.

We can simplify the original expression by factoring out 2x:

6x²-16x = 2x(3x-8)

We can see that the expression we obtained by multiplying the length and the width is equivalent to the original expression for the area, so our expression for the length is correct.

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The lengths of the sides of triangle PQR are:

PQ = QR = 9

RP = √90

To find the lengths of the sides of triangle PQR, we can use the distance formula. The distance between two points in 3D space (x₁, y₁, z₁) and (x₂, y₂, z₂) is given by:

d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Let's calculate the distances between the given points:

Distance PQ:

P(1, -3, -4) and Q(7, 0, 2)

d₁ = √[(7 - 1)² + (0 - (-3))² + (2 - (-4))²]

= √[6² + 3² + 6²]

= √[36 + 9 + 36]

= √81

= 9

Distance QR:

Q(7, 0, 2) and R(10, -6, -4)

d₂ = √[(10 - 7)² + (-6 - 0)² + (-4 - 2)²]

= √[3² + (-6)² + (-6)²]

= √[9 + 36 + 36]

= √[81]

= 9

Distance RP:

R(10, -6, -4) and P(1, -3, -4)

d₃ = √[(1 - 10)² + (-3 - (-6))² + (-4 - (-4))²]

= √[(-9)² + (3)² + (0)²]

= √[81 + 9 + 0]

= √90

Therefore, the lengths of the sides of triangle PQR are:

PQ = QR = 9

RP = √90

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The angle subtended at the center of the arc is 102⁰

Recall that to find the length of an arc on a circle, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.  If the central angle is measured in degrees, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.

Lenght of arc = A/360 *2пr

A = angle at center = ?

п = 22/7 r = radius = 840 feet

⇒1500 = A/360  2 *22/7 * 840

1500 = 36960A/2520

3780000= 36960A

making A the subject we have

3780000/36960 = A

A = 102.27

A= 102⁰

The angle is 102⁰

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The most likely mean for the sample distribution is option c. negatively skewed.

Based on the given information, we know that the mean (M) is less than both the median and the mode. This suggests that the distribution is skewed to the left (negatively skewed), with a long tail on the left side of the distribution.

The mean of a sample distribution is the average value of all the observations or measurements in the sample. It is calculated by adding up all the values in the sample and dividing the sum by the total number of observations in the sample.

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2y = 2y. As the two partial derivatives are equal, the curl of the vector field F is zero. Therefore, F is a conservative vector field.

Based on the given vector field F(x, y) = (y^2 - 2x)i + 2xyj, we can determine whether or not F is a conservative vector field by checking if it satisfies the conditions for being conservative.

A vector field is conservative if its curl is zero, meaning that the partial derivative of the second component (2xy) with respect to x is equal to the partial derivative of the first component (y^2 - 2x) with respect to y. Mathematically, this can be represented as:

∂(2xy)/∂x = ∂(y^2 - 2x)/∂y

Taking the partial derivatives, we get:

2y = 2y

As the two partial derivatives are equal, the curl of the vector field F is zero. Therefore, F is a conservative vector field. In a conservative vector field, the work done by the force is path-independent, and the potential energy can be defined as a function of position.

This means that the work done in moving an object from one point to another within the field only depends on the initial and final positions, and not on the specific path taken.

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Answer:

Diagram B

Step-by-step explanation:

This is because the line only goes through two points and many are dispered from the line, however diagram A and C have points fairly close to them

Visually inspecting the three scatterplots, the line of best fit does not accurately fit the points on the second graph. Hence, line of best fit should not have been drawn for the second graph as the relationship isn't linear.

The line of best fit minimizes the sum of the square of the mean distance between each point. Hence, the distance between the line and the best fit line should be as small as possible.

However, the second graph isn't linear, hence , a linear line cannot model the relationship.

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The correct answer is A. Standard deviation measures the dispersion or variability around the expected value or mean of a data set. It is a commonly used statistical measure to quantify the spread of data points.

Standard deviation is calculated by taking the square root of the variance. The variance is the average of the squared differences between each data point and the mean. By squaring the differences, negative values are eliminated, ensuring that the measure of dispersion is always positive.

A higher standard deviation indicates greater variability or dispersion of data points from the mean, while a lower standard deviation suggests that the data points are closer to the mean.

On the other hand, the mean (option B) is a measure of central tendency that represents the average value of a data set. It does not directly measure the dispersion or variability around the mean.

The coefficient of variation (option C) is a relative measure of dispersion that is calculated by dividing the standard deviation by the mean. It is useful for comparing the relative variability between different data sets with different scales or units.

The chi-square test (option D) is a statistical test used to determine if there is a significant association between categorical variables. It is not a measure of dispersion around the expected value.

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The projab = |b|cosθ = √34 × 23/(5 × √34) = 23/5 = 4.6 (rounded to one decimal place)Thus, the scalar projection of b onto a when b = h5, 3i, a = h4, 3i is 4.6.

Scalar projection of b onto a The scalar projection of a vector b onto another vector a is the magnitude of the component of b that is parallel to a. It is represented as follows:projab

= |b|cosθwhere, θ is the angle between the vectors a and b.|b| is the magnitude of the vector b.Now, given b

= h5, 3i, a

= h4, 3iWe know that,projab

= |b|cosθAlso,cosθ

= a.b/|a||b|Here, a.b represents the dot product of vectors a and b.|a| and |b| represent the magnitudes of vectors a and b respectively.|a|

= √(4² + 3²)

= √(16 + 9)

= √25

= 5|b|

= √(5² + 3²)

= √(25 + 9)

= √34 Thus,cosθ

= (h4, 3i).(h5, 3i)/(5 × √34)

= (4 × 5) + (3 × 3)/(5 × √34)

= 23/(5 × √34) .The projab

= |b|cosθ

= √34 × 23/(5 × √34)

= 23/5

= 4.6 (rounded to one decimal place)Thus, the scalar projection of b onto a when b

= h5, 3i, a

= h4, 3i is 4.6.

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Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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Answer:

See below!

Step-by-step explanation:

1) 720cm - m

2) 983 mm - m

3) 130.5kL - L

4) 0.03 g - mg

5) 997 g - kg

6) 9.1 l - ml

7)3.75 c - ml

8) 41.8 in - cm

9) 156.25 lb - kg

10) 9.5 gal - l

11) 680.4 g - lb

12) 4.725 m - ft

Hope this helps, have a lovely day! :)

6. False. The present value (PV) is the initial investment or the amount invested in the stock, which is $7,500, not the amount received today ($8,050).

7. $1,200 represents the variable PMT (Payment). It represents the total dividends received over the four-year period.

8. The future value (FV) amount is $8,050, which is the amount received from selling the stock today.

9. It is not necessary to clear the TVM (Time Value of Money) registers when the calculations are completed, and you don't need to perform any further calculations.

10. True. When the "periods per year" register is set to 1, the periodic rate (interest rate) should be entered directly into the i-register as a decimal value, such as 0.05 for 5%.

Therefore, the PV is not $8,050 but $7,500, representing the initial investment. The variable $1,200 represents the PMT (payment) or the total dividends received. The FV amount is $8,050, the selling price of the stock. Clearing the TVM registers is not necessary after completing calculations, and when "periods per year" is set to 1, the periodic rate is entered directly into the i-register.

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Answer:

Step-by-step explanation:

Slope-intercept equation of a line is,

y = mx + b

Here, m = Slope of the line

b = y-intercept

If m = -6 and b = 3,

Equation of the line will be,

y = -6x + 3

Input - output values got the graph of this line,

x          -1            0           1           2          

y           9           3          -3         -9

Now by plotting these points we can draw the line on graph.

Answer:

Step-by-step explanation:

Pi*r^2 = Area

20.5^2 * Pi = 1320.25

An equation to find out miles each lap around the pond is approximately 1.2 miles.

The distance of each lap around the pond is represented by 'x' miles.

Given:

In the morning, Madjeen jogs 3.5 laps around the pond.

In the evening, Madjeen jogs 1 lap around the pond.

Madjeen jogs a total of 5.4 miles.

The equation to represent the total distance:

Total distance = Distance of morning laps + Distance of evening laps

5.4 miles = 3.5 laps × x miles/lap + 1 lap × x miles/lap

Simplifying the equation:

5.4 = 3.5x + x

Combining like terms:

5.4 = 4.5x

Dividing both sides by 4.5:

x = 5.4 / 4.5

x = 1.2

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Using the given natural abundances of titanium-46, titanium-47, and titanium-48, we find that the average atomic mass of titanium on this planet is approximately 46.4 amu.

To calculate the average atomic mass of titanium on another planet, we need to consider the natural abundances of its isotopes. The average atomic mass is calculated by multiplying the mass of each isotope by its relative abundance and summing up these values.

Let's assume that the three isotopes of titanium on this planet are denoted as titanium-46, titanium-47, and titanium-48. The natural abundances of these isotopes are given as follows:

Isotope Natural Abundance

Titanium-46 70%

Titanium-47 20%

Titanium-48 10%

To calculate the average atomic mass, we multiply the mass of each isotope by its relative abundance and sum up these values. The atomic masses of titanium-46, titanium-47, and titanium-48 are approximately 46.0 amu, 47.0 amu, and 48.0 amu, respectively.

Average Atomic Mass of Titanium:

(46.0amu×70%)+(47.0amu×20%)+(48.0amu×10%)

=(32.2amu)+(9.4amu)+(4.8amu)

=46.4amu

Therefore, the average atomic mass of titanium on this planet is approximately 46.4 atomic mass units (amu).

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Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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Answer:

it would be 0.48

Step-by-step explanation:

yeah you divide

\({ \large{ \sf{ \dfrac{12}{25} = 0.48 }}}\)

Answer:

from 2 to 1 , there is a 50 percent change (decrease)

Answer:

my cat is very very fat ( true fact )

The actual odds against winning a bet that the outcome is an odd number on a modified roulette wheel with 44 slots are 23:21.

First, we need to determine the total number of possible outcomes. There are 44 slots on the wheel, so the total number of possible outcomes is 44.

Next, we need to determine the number of favorable outcomes. There are 21 odd numbers on the wheel (1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41), so the number of favorable outcomes is 21.

Finally, we need to calculate the odds against winning. The odds against winning are the ratio of the number of unfavorable outcomes to the number of favorable outcomes. There are 23 unfavorable outcomes (0, 00, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42), so the odds against winning are 23:21.

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Answer:

= -11/4

Step-by-step explanation:

To find the slope given two points

m = ( y2-y1)/(x2-x1)

   = (6 - -5)/(-2 -2)

   = (6+5)/(-2-2)

    = 11/-4

    = -11/4

Answer:

-2.75 (-2 3/4)

Step-by-step explanation:

you can do rise of a run whenever you have two points so you have 6-(-5)/-2-2 and solve so -11/4 and that equals -2.75.

The linear equation is equal to

y = -3x + 8

m = slope

x = input variable

c = 8

The given equation is linear function or linear equation

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

Definition of variables to suit the problem to be solved

y = output variable

m = slope

x = input variable

c = y intercept

In comparison, to the linear equation given as equal to

y = -3x + 8

m = -3

x = input variable

c = 8

putting the input variables gives out put accordingly

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Step-by-step explanation:

as you wrote correctly, proportional relationships are in the form

y = mx

that means the line has to go through the origin (0, 0). otherwise it is in the form

y = mx + b

which is still linear but not proportional.

1a.

the rate of change is between 2 points A and B

(Yb - Ya)/(b - a)

in our case e.g. (4, 5.52) and (8, 11.04)

(11.04 - 5.52)/(8 - 4) = 5.52 / 4 = 1.38

when we use other points we get the same result. we see e.g. that when we double x (pounds), then also y (cost) is doubled.

the rate of change is 1.38.

this is also called the slope of the line.

b.

as mentioned in a., when we multiply x by a factor, then y is multiplied by the same factor. it also means that the function contains (0, 0) : for 0 pounds we pay $0.

c.

y = 1.38x

2a.

the slope is (as it is the same as the rate of change) the ratio of (y coordinate change / x coordinate change) when going from one point on the line to another.

we try to find points with integer coordinates to do that.

I see e.g. (3, 4) and (6, 8).

x changes by +3 (from 3 to 6).

y changes by +4 (from 4 to 8).

so, the slope is +4/+3 = 4/3.

b.

the simplest indicator is that the line goes through the origin (0, 0), which it does.

c.

y = (4/3)x

Answer:

$6,480

Step-by-step explanation:

\(180(12)(3)=6,480\)

Hope this helps

Answer:

#540

Step-by-step explanation:

Alan saved $180 in each month

and we have 12 months in a year so we say

$180=12

x=36

here we cross multiply then we have 180 * 36 which is equal to $6480 after that we divide it by 12 and that's $540

Note: I got 36 months because 12 months in a year so multiply by three years that's 36 months

Answer:

The answer is 18

Step-by-step explanation:

Answer:

I am pretty sure it's 2.5 because my little sister got the question and I helped her with it!

Step-by-step explanation:

proof it's 2.5 !

divide y by x and you get 2.5

The length of the kite's line can be determined using the concept of similar triangles. By setting up a proportion between the length of the kite's line and its shadow, we can solve for the unknown length.

Let's denote the length of the kite's line as "x." We can form a proportion between the lengths of the kite's line and its shadow:

(line length)/(shadow length) = (height)/(shadow height)

Plugging in the given values, we have:

x/6 = 9/9

Simplifying the equation, we find:

x = 6

Therefore, the length of the kite's line is 6 feet.

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The student population of Memphis will be approx 1,011.45 in 6 years. Hence, 6 years is the required answer.

To model future population growth, we can use an exponential decay model since the population decreases at a rate of 12% each year. The general form of an exponential decay model is given by:

P(x) = P₀ * (1 - r)^x

Where P(x) represents the population after x years, P₀ is the initial population, r is the decay rate (expressed as a decimal), and x is the number of years.

In this case, the initial population (P₀) is 1800 and the decay rate (r) is 0.12 (12% expressed as a decimal). Plugging in these values into the exponential decay model, we have:

P(x) = 1800 * (1 - 0.12)^x

To find the population after 6 years (P(6)), we substitute x = 6 into the equation:

P(6) = 1800 * (1 - 0.12)^6

Simplifying the equation, we get:

P(6) ≈ 1800 * (0.88)^6 ≈ 1,011.45

Therefore, the student population of Memphis will be approximately 1,011.45 in 6 years based on the given exponential decay model.

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Answer:

The y-intercept in this situation shows the initial height of the elevator.

Step-by-step explanation:

No time has passed meaning that the elevator has not moved yet.

The required answers are is Linear regression will assume an ordering of the coded outcomes.

Linear regression assumes that the response variable is continuous and can take any value between negative infinity and positive infinity. It also assumes that there is a linear relationship between the response variable and the predictor variables. When the response variable is qualitative/categorical, it means that the categories are distinct and not ordered. Using linear regression would assume an ordering of the categories, which is not valid.

a) Linear regression will overfit the data

Linear regression is designed to minimize the sum of the squared errors between the predicted values and the actual values. When the response variable is qualitative/categorical, the model will try to fit a line through the categories, which will result in overfitting. This means that the model will perform well on the training data but will not generalize well to new data.

b) Linear regression will produce probabilities less than zero or bigger than one

Linear regression assumes that the response variable can take any value between negative infinity and positive infinity. This means that the predicted values can be less than zero or bigger than one, which is not valid when the response variable is a probability or a proportion.

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Answer:

y=|x-2|

Step-by-step explanation:

Answer:

I am pretty sure the answer is y=(x+2)

Step-by-step explanation:

The line is going upward so the answer has to have a + in it.  The y-intercept is 2.

Hope this helps! :)

Answer:

8 lol

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

15 +8=23