eva is working two summer jobs, making $16 per hour tutoring and $8 per hour clearing tables. Last week eva worked 3 times as many hours clearing tables as she worked hours tutoring hours and earned a total of $80. Graphically solve a system of equations in order to determine

The location of point A''' after the three transformations would be (-4, 1).

To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.

When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).

When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).

When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).

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The zeros and the multiplicities are

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

f(x) = (x + 6)³(x - 11)²(x - 6)(x + 5)³

The power of each factor are the multiplicities

So, we have

Zero(s) of multiplicity one:

x - 6 = 0

Zero(s) of multiplicity two:

x - 11 = 0

Zero(s) of multiplicity three:

x + 6 = 0 and x + 5 = 0

When evaluated, we have

Zero(s) of multiplicity one:

x = 6

Zero(s) of multiplicity two:

x = 11

Zero(s) of multiplicity three:

x = -6 and x = -5

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Question Completion:

California (population about 40 million) has about twice as many people as New York State (population about 20 million). Without calculation, pick the correct option and explain your choice.

If the underlying population SDs are equal, a simple random sample of 1000 people in California is

(i) about half as accurate

(ii) about 1/V2 times as accurate

(iii) about as accurate

(iv) about V2 times as accurate

(v) about twice as accurate

as a simple random sample of 1000 people in New York State.

Answer:

If the underlying population SDs are equal, a simple random sample of 1000 people in California is

(i) about half as accurate

as a simple random sample of 1000 people in New York State.

Step-by-step explanation:

Since the population of California is about 40 million, which is twice as many people as in New York State (approximately 20 million), in taking a sample size, that of California supposed to be as twice as New York's.

Therefore, if the random sample of 1,000 people is taken from California, just as a random sample of 1,000 people is also taken from New York State, we can conclude that the accuracy of population standard deviation of California will be about half as accurate as the standard deviation of New York's population.

This is because accuracy is enhanced by a larger sample size.  This means that if the sample size of California is 2,000, the SD would have been equally as accurate as New York's.

Answer:

To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:

EAR = (1 + r/n)^n - 1

where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.

For daily compounding, n = 365 (since there are 365 days in a year), so we have:

EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%

To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:

EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%

Therefore, the effective annual rate for hourly compounding is approximately 7.27%.

Answer:

the value of the t test statistic is - 3.419

Step-by-step explanation:

Given that;

n₁ = 18, u₁ = 78.3, s₁ = 6.4

n₂ = 11, u₂ = 84.3, s₂ = 5.3

α = 0.1

Now The hypothesis are;

H₀ : u₁ = u₂

H₁ : u₁ < u₂

To compute the value of the t test statistic;

t = [(x₁ - x₂) / s × √(1/n₁ + 1/n₂)]

where

s = √ [ ((n₁-1) × s₁² + (n₂ - 1 ) × s₂²) / ( n₁ + n₂ - 2)]

s = √ [ ((18-1) × 6.4² + (11 - 1 ) × 5.3²) / ( 18 + 11 - 2)]

s = √ [ (7 × 40.96 + 10 × 28.09 ) / 27 ]

s = √ [ (286.72 + 280.9) / 27 ]

s = √(567.62/27)

s = √21.0229

s = 4.585

Now  t test statistics t = [(x₁ - x₂) / s × √(1/n₁ + 1/n₂)]

t = [(78.3 - 84.3) / 4.585 × √(1/18 + 1/11)]

t = -6 / (4.585 × 0.3827)

t = - 6 / 1.7546795

t = - 3.419

Therefore the value of the t test statistic is - 3.419

as as level of significance α  = 0.1

df = 18+11-2 = 27

∴ T(csal) = t(0.1, 27) = -1.313

That is

t(statistics) < t(cal)

{ - 3.419  < -1.313 }

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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The value of n in the given equation is 1.

Define Algebraic Expression

In mathematics, an expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)

Given equation,

-1/2 (2n + 4) + 6 = -9 + 4(2n + 1)

Now, solve for n

first, solve the brackets

-1/2 * 2n + (-1/2) * 4 + 6 = -9 + 4*2n + 4 * 1

-n - 2 + 6 = -9 + 8n + 4

Solve the constants on both the sides,

-n + 4 = 8n - 5

Now, take out n value one side and constant terms other side

-n - 8n = -5 - 4

-9n = -9

Cancel out -9 from both the sides,

n = 1

Hence, the value of n in the given equation is 1.

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Answer:

0

Step-by-step explanation:

Answer: There are no solutions.

Step-by-step explanation: 4(x−2)=4x+10

(4)(x)+(4)(−2)=4x+10

4x+−8=4x+10

4x−8=4x+10

4x−8−4x=4x+10−4x

−8+8=10+8

0=18

There are no solutions.

A. The grams of rice served for 64 portion is 8960 grams.

B. The expression for the total weight in grams of rice needed for p portions is  140p.

C. The portion when a total weight of 11340 grams was served is 81 portion

D. The expression  for the number of portions served if the total rice weighed t grams is t / 140

The school cafeteria serves portions of fried rice that are 140 grams each.

A.

64 portions of rice are served. The grams of rice served is as follows:

1 portion = 140 grams

64 portions = ?

cross multiply

grams of rice served = 64 × 140

grams of rice served = 8960 grams

B.

The expression for the total weight in grams of rice needed for p portions is as follows:

total weight = 140p

C.

The portion when a total weight of 11340 grams was served is as follows:

140 grams = 1 portion

11340 grams = ?

portion = 11340 / 140

portion = 81 portion

D.

The expression  for the number of portions served if the total rice weighed t grams is as follows:

portion = t / 140

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By similarity of triangle the height of a children will be 4ft.

Similar triangles are that kind of triangles that have the same shape, but different  sizes. examples of similar objects are All equilateral triangles, squares of any side lengths. In another words, if two triangles having their corresponding angles are congruent and corresponding sides are in equal proportion then two triangles are said to be similar. It is denoted  by ‘~’ symbol.

We can use the property of similar triangles to estimate the height of the child:

The ratio of the height of the adult to the length of their shadow is the same as the ratio of the height of the child to the length of their shadow:

height of adult / length of adult shadow = height of child / length of child shadow

Plugging in the values we know:

6 / 15 = height of child / 10

Solving for the height of the child:

height of child = (6 / 15) * 10 = 4 feet

Therefore, the estimated height of the child is 4 feet.

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Answer:

41428.57

Step-by-step explanation:

Average rate of change=(y2-y1)/(x2-x1)

(840,000-550000)/(11-4)

=41428.57

Answer:

2.5 times 4.5 times .5 = 5.625 ft squared

Step-by-step explanation:

Lets look at our Formula

.5 times base of triangle (b) times height of triangle (h)

Based on the photo, the height is 4.5 feet and the base is 2.5 feet.

4.5 times 2.5 times .5 (the 1/2 in the formula) = 5.625 ft squared.

Remember that it is 1/2 times the base and height, b/c triangle is half of square. Ft squared because ft times ft equals ft squared

Given the composite figure shown in the exercise, you can identify that it is formed by a rectangular prism and a triangular prism.

The surface area of a rectangular prism can be calculated by using this formula:

Where "l" is the length, "w" is the width and "h" is the height.

In this case, you can identify that:

Then, substituting values into the formula and evaluating, you get:

The surface area of a triangular prism can be found by using this formula:

Where "b" is the base of the base, "h" is the height of the base, "P" is the perimeter of the base, and "H" is the height of the triangular prism.

In this case:

Then, substituting values and evaluating, you get:

Therefore, the surface area of the composite figure can be found by adding the surface area of the rectangular prism and the surface area of the triangular prism:

Hence, the answer is:

The characteristic polynomial  x³ - 7x² + 16x - 12  The characteristic polynomial of a square matrix in linear algebra is a polynomial that is invariant under matrix similarity and has the eigenvalues as roots.

Its coefficients include the determinant and the trace of the matrix.

Characteristic polynomial of a 3×3 matrix A is given by ; x³ - trace(A)x² + (A​​​​​​11 + A​​​​​​22 + A​​​​​​33 )x - determinant(A)

Where A​​​​​​ii is the determinant of the matrix obtained by deleting i​​​​​​ th row and i th column.

Here trace(A) = sum of the diagonals = 12 - 7 + 2 = 7

A​​​​​​11 = -7 × 2 = -14

A​​​​​​22 = 2 × 12 = 24

A​​​​​​33 = ( 12×-7) - (-10×9) = 6

Determinant(A) = 12(-7×2 - 0) + 10(2×9 - 0) = 12

Substituting these values in above equation , we obtain;

x³ - 7x² + (-14 + 24 + 6)x - 12 = x³ - 7x² + 16x - 12.

Hence x³ - 7x² + 16x - 12 is the characteristic polynomial of A.

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Answer:

D. It is a two-dimensional object.

The statement D is true about the figure above. The figure is a circle, which is a two-dimensional object.

Statement A is not true. A point is a location in space, but a circle is a shape that takes up space and has a defined area.

Statement B is not true either. A circle has only one measurement, which is its radius or diameter. The radius is the distance from the center of the circle to any point on its circumference, while the diameter is the distance across the circle through its center.

Statement C is also not true. A circle cannot "grow" into a three-dimensional object because it is a two-dimensional object that exists in a flat plane. However, multiple circles can be stacked on top of each other to form a cylinder, which is a three-dimensional object.

The correct statement is that the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 16 over 40.

We know that there are 40 students at summer camp who are divided into two groups for either swimming or hiking. Each camper flips a coin, where heads represents swimming and tails represents hiking. The outcome frequency for swimming is 16 and for hiking is 24.
To compare the probabilities, we need to first understand the difference between theoretical probability and experimental probability. Theoretical probability is the expected probability of an event occurring based on mathematical calculations and assumptions, whereas experimental probability is the actual observed probability of an event occurring based on data from experiments or observations.
Option 1 states that the theoretical probability of swimming is one half, but the experimental probability is 24 over 40. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is equal to one half, and the experimental probability of swimming is also 40%, which is equal to 16 over 40. Therefore, this option is false.
Option 2 states that the theoretical probability of swimming is one half, but the experimental probability is 16 over 40. This statement is correct because the theoretical probability of swimming is 50%, which is equal to one half, and the experimental probability of swimming is also 40%, which is equal to 16 over 40. Therefore, this option is true.
Option 3 states that the theoretical probability of swimming is 16 over 24, but the experimental probability is one half. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is not equal to 16 over 24, and the experimental probability of swimming is also 40%, which is not equal to one half. Therefore, this option is false.
Option 4 states that the theoretical probability of swimming is 24 over 40, but the experimental probability is one half. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is not equal to 24 over 40, and the experimental probability of swimming is also 40%, which is not equal to one half. Therefore, this option is false.
In conclusion, the correct statement is that the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 16 over 40.

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Option D is the correct answer.

From the graph, we can conclude that,

1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.

2. The points on the lines of the shaded region are also included in the solution.

The only option that matches with the above conditions is option D. So, option D is the correct answer.

Let us verify it.

Now, let us consider a point that is inside the shaded region and also on any one line.

Let us take (0, 2).

Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.

Considering the inequalities,

y ≥ 3x - 2

x + 2y ≤ 4

Solving we get,

2 ≥ 3(0) - 2

2 ≥ -2

x + 2y ≤ 4

0 + 2(2) ≤ 4

4 ≤ 4

Here, both inequalities are correct.

So, option D is the correct answer.

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The complete question is =

Which system of linear inequalities is graphed?

A. y < 3x-2

x + 2y ≥ 4

B. y < 3x - 2

x + 2y > 4

C. y > 3x - 2

x + 2y < 4

D. y ≥ 3x - 2

x + 2y ≤ 4

The value of x for each item is given as follows:

28. x = 5.

29. x = 3.44.

For item 28, we apply the crossing chord theorem, which states that the products of the parts of the chords are equal, hence the value of x is obtained as follows:

16x = 10 x 8

16x = 80

x = 5.

For item 29, we apply the two secant theorem, hence the value of x is obtained as follows:

10(x + 10) = 12(12 + 25)

10x + 100 = 444

10x = 344

x = 3.44.

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Answer:

11 cups

Step-by-step explanation:

1.50x10=15 and that wouldn't be the answer because, he needs to cover all of his supplies.  1.50x11=16.5, and that is enough money to cover all of his supplies. So he would need 11 cups total.

Answer

25/1 and 43/125

Step-by-step explanation:

Answer: Number 2

Step-by-step explanation: yes

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

In order of blank boxes going from left to right then down will be 1, 9, 5, 75, 35.

The missing table is given below.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Shawn is collecting money from students at his school for a charity.

The table gives the ratios of the number of students who have donated and the amount of money he has collected from them.

Since 30 is 1/3 of 90, we know the ratio is 1:3.

In order of blank boxes going from left to right then down

1, 9, 5, 75, 35

The complete table is attached below.

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Answer:

45

Step-by-step explanation:

translation :

140% of x = $63

x = $63 ÷ 1.4

x = $45

FUN FACTS :

interesting: 100% means double that number or times 2

if a price is $20 & it increases 100% in price that means its $20 times 2 or $40

percent means per 100

cent means 100 in latin

that's why the decimal moves 2 spaces

for the 2 zeros in 100

chatgpt

Answer:

Step-by-step explanation: reduce mean divide so 400 divided by 4 =28

Airplane 1 had the fastest rate of descent during its landing.

To compare the rates of descent of the two airplanes, we need to convert both rates to a common unit of measurement. Let's convert both rates to feet per minute (ft/min) to make the comparison easier.

Airplane 1 had a rate of descent of -130 ft/s, which is equivalent to:

-130 ft/s × 60 s/min = -7800 ft/min

Airplane 2 had a rate of descent of -97/8 ft/s, which is equivalent to:

(-97/8) ft/s × 60 s/min = -729.375 ft/min

Comparing these two rates, we can see that Airplane 1 had the faster rate of descent during its landing:

-7800 ft/min (Airplane 1) > -729.375 ft/min (Airplane 2)

Therefore, Airplane 1 had the fastest rate of descent during its landing.

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Answer:

Step-by-step explanation: