2. Andrea and Casey work at a restaurant over the summer. Andrea gets paid $25 when they
work along with an average of $9 in tips every hour. Casey only gets $10 when they work,
but they make an average of $14 in tips every hour. Write a system of equations to determine
how many hours it takes for Andrea and Casey to make the same amount of money? How
much money is it?

The following statements are true about the function f(x) = -( x-4) ² -1

1. The y intercept is (0,-17)

2. The axis of symmetry x = 4

3. The x intercept is (3,0)

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

The equation f(x) = -(x-4)² -1 can be expanded as

f(x) = -x²+8x-16-1 = -x²+8x-17

therefore when x = 0

the y-intercept = -17

therefore the y intercept = (0,-17)

The x intercept of the function,

when y = f(x) and y = 0

-(x-4)² = 1

-(x-4) = 1

-x+4 = 1

-x = -3

x = 3

the x intercept of the function is (3,0)

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The weight of Franklin’s mountain bike in kilograms which  weighs 17,000 grams is equal to option A. 17 kilograms.

Weight of Franklin’s mountain bike  in grams is equal to 17,000 grams

Convert the grams into kilograms.

One kilograms is equal to one thousand grams

1 kilograms = 1000 grams

⇒ 1 grams = ( 1 / 1000 ) kilograms

⇒ 17,000 grams = ( 17,000 / 1000 ) kilograms

⇒ 17,000 grams = 17 kilograms

Therefore, after converting grams into kilograms the weight of Franklin’s mountain bike whose weight in grams is 17,000 grams  is equal to option A. 17 kilograms.

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The centroid of the given triangle is [tex]( 2\frac{2}{3} , -3\frac{1}{3} )[/tex], which is option B.

What is a centroid of a triangle?

A place where a triangle's medians coincide is the centroid of the triangle. The line segments that are drawn from a vertex to the midpoint of the vertex's opposite side are known as medians.

A triangle is divided into two smaller triangles with equal areas by each of its medians. The centroid of a triangle is where the medians of the triangle cross. Unlike other points of concurrency in a triangle, the centroid always lies inside one.

The formula of the centroid of a triangle when the coordinates of the vertices are known is:

Centroid = [tex](\frac{x_1 +x_2+x_3}{3} , \frac{y_1 +y_2+y_3}{3})[/tex]

From the graph, we can find the vertices of the triangle

A = (x₁, y₁) = (-3,-7)

B = (x₂,y₂) = (5,1)

C = (x₃,y₃) = (6,-4)

Centroid = [tex](\frac{x_1 +x_2+x_3}{3} , \frac{y_1 +y_2+y_3}{3}) = (\frac{-3+5+6}{3} ,\frac{-7+1-4}{3}) = (\frac{8}{3} ,\frac{-10}{3} ) = ( 2\frac{2}{3} , -3\frac{1}{3} )[/tex]

Therefore the centroid of the given triangle is [tex]( 2\frac{2}{3} , -3\frac{1}{3} )[/tex].

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The additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem is option C, MN/LK||MN.

The SAS (Side-Angle-Side) similarity theorem states that if two triangles have two pairs of corresponding sides that are in proportion, and the included angles are congruent, then the triangles are similar.

In this case, we know that ΔLKN and ΔKNM share the angle at vertex K, and we also know that LN/MN and LK/KN are in proportion.

However, we need to establish that MN/LK||MN, which means that MN is parallel to LK and forms a transversal with LN.

This information is necessary to establish that the included angles between the corresponding sides are congruent, which is required for the triangles to be similar.

Therefore, option C is the correct additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem.

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Answer:

b) 2/3

Step-by-step explanation:

For a 6-sided die

total number of numbers: 6

numbers less than 2: 1

prime numbers: 2, 3, 5

total number of desired outcomes: 1 + 3 = 4

p(less than 2 or prime) = 4/6 = 2/3

The next two days when Alicia would be allowed to eat junk foods are Thursday and Tuesday.

The first day after Saturday when Alicia would have junk food can be determined by counting the fifth day after Saturday.

Sunday - first day

Monday - second day

Tuesday - third day

Wednesday - fourth day

Thursday - fifth day

The next day after Thursday when Alicia would have junk food is the fifth day after Thursday.

Friday - first day

Saturday - second day

Sunday - third day

Monday - fourth day

Tuesday - fifth day

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The percentage of white marbles on the jar is obtained dividing the number of white marbles by the total number of marbles.

A percentage is calculated applying a proportion, dividing the number of total outcomes by the number of desired outcomes, and then multiplying by 100%.

The outcomes for this problem are given as follows:

The problem is incomplete, hence the standard procedure to obtain the percentage of white marbles was presented.

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Increase the accuracy of your measurements by using a more precise instrument or tool, such as a protractor or ruler.

The accuracy of the intersection of your three circles may not have been exact due to imprecise measurements taken. To improve the results, you could use a more precise instrument or tool, such as a protractor or ruler. With a protractor , you can measure the angle of the intersection of the circles more accurately. If a ruler is used, make sure that it is a straight edge, and measure the distance between the circles to ensure they intersect at the same point . Once the measurement is taken, draw the circles and their intersection accordingly. Doing this will help improve the accuracy of the intersection of the three circles and yield better results.

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Answer:

144 egg sandwiches

Step-by-step explanation:

[tex]25\% + 45\% = 70\%[/tex], and [tex]100\% - 70\% = 30\%.[/tex] Thus, [tex]30\%[/tex] of the [tex]480[/tex] sandwiches are egg sandwiches. Since "of" means multiply, we have [tex]30\% \cdot 480.[/tex] We know [tex]30\% = \frac{30}{100} = \frac{3}{10},[/tex] so we can rewrite it as [tex]\frac{3}{10} \cdot 480.[/tex] We cancel [tex]480[/tex] with [tex]10[/tex] which is [tex]480 \div 10 = 48.[/tex] We multiply [tex]48[/tex] by the numerator, [tex]3,[/tex] to get [tex]48 \cdot 3 = 144.[/tex] Thus, Lillian makes [tex]\boxed{144 \text{ egg sandwiches.}}[/tex]

The height of the plane is 1023 meters and the height of the tree is 307 feet.

Given the data in question 9, this forms a right-triangle.

To determine the height of the plane x, we use trigonometric ratio

Tangent = Opposite / Adjacent

tan( 12 ) = x / 4812m

x = tan( 12 ) × 4812m

x = 1023m

Therefore, the height of the plane is 1023 meters.

Option A) 1023 meters is the correct answer.

Given the data in question (10)

Solve for x using trigonometric ratio,

Tangent = Opposite / Adjacent

tan( 62 ) = x / 160ft

x = tan( 62 ) × 160ft

x = 301ft

Now, height of the tree will be;

Height = x + height of tool

Height = 301ft + 6ft

Height = 307 ft

Therefore, the height of the tree is 307 feet.

Option D) 307 feet is the correct answer.

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Answer: All she needs to sell is 53 tickets

Step-by-step explanation: You divide 160 by 3 which gives you 53.3333 so you take the decimal place and get rid of it and it gives you 53. So she needs to sell at least 53 tickets to reach her goal

Answer:

Step-by-step explanation:

Perpendicular line will have a slope that is the negative reciprocal so slope of 3 becomes - [tex]\frac{1}{3}[/tex].

then use point slope:

y - y = m(x - x)

Use the 2 points (8, -4)

y - -4 = -[tex]\frac{1}{3}[/tex] (x - 8)

y + 4 = -[tex]\frac{1}{3}[/tex] (x - 8)

y + 4 = -[tex]\frac{1}{3}[/tex]x + [tex]\frac{8}{3}[/tex]

y + 4 - 4 = -[tex]\frac{1}{3}[/tex]x  - [tex]\frac{4}{3}[/tex]

y = - [tex]\frac{1}{3}[/tex]x - [tex]\frac{4}{3}[/tex]

Parallelline will have the same slope m = 3.

use point slope again

y - -4 = 3(x -8)

y + 4 = 3x - 24

y + 4 -4 = 3x - 24 -4

y = 3x -28

As the angle increases from 0 to π/2, the value of sine increases, and the value of cosine decreases.

Trigonometry is a branch of mathematics that deals with the relationships between angles and sides of triangles.

Let us first understand the concept of sine and cosine. In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite to the angle and the length of the hypotenuse. Similarly, the cosine of an angle is defined as the ratio of the length of the adjacent side and the length of the hypotenuse.

As the angle θ increases from 0 to π/2, the length of the opposite side (the numerator in sine) of the triangle increases, and the length of the hypotenuse (the denominator in sine) remains the same. Therefore, the value of sine increases as θ increases.

On the other hand, as the angle θ increases from 0 to π/2, the length of the adjacent side (the numerator in cosine) decreases and the length of the hypotenuse (the denominator in cosine) remains the same. Therefore, the value of cosine decreases as θ increases.

This behavior is consistent with the fact that sine is an increasing function, while cosine is a decreasing function within this range of angles.

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Complete Question:

If 0< θ <π/2, as Theta increases, the value of

cos(θ) [Decreases/Increases/Remains The Same]

and the value of sin(θ) [Decreases/Increases Remains The Same]​

Hi there, here's your answer:

Given 2 angles:

(6d + 8)° and (8d + 4)°

Observe the figure carefully. You will notice that the two angles form a linear pair.

We know that in a linear pair, sum of the two angles = 180°.

Hence,

(8d + 4 + 6d + 8)° = 180°

(14d + 12)° = 180°

(14d)° = (180 - 12)°

= 14d = 168°

Or

d = 12

Thus, we find the value of d to be d = 12.

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The people having to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least 1/2 is 5.

X = No of people having same month birth day

We need, P(X 2) ≥ 1/2

= 1-P(X ≤1) ≥ 1/2

1-P(No one having same month birth day) ≥ 1/2

P(No one having same month birth day)≤ 1/2..........................(1)

Now, k = Minimum no of people required to satisfy (1)

P(No one having same month birth day) =

[tex]\frac{11*10*9......*(12-k+1)}{12*12*12......*12}[/tex]

for k= 4

P(No one having same month birth day) =

[tex]\frac{11.10.9}{12.12.12} = 0.572 \geq 0.5[/tex]

for k= 5

P(No one having same month birth day) =

[tex]\frac{11.10.9.8}{12.12.12.12} = 0.38 \leq 0.5[/tex]

Therefore , the people having to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least 1/2 is 5.

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The area of the side panel of the stairway is 360 square inches.

The side panel of the stairway is essentially a right triangle with the three steps forming the three horizontal segments (treads) and the three risers forming the three vertical segments (risers).

The height of the side panel would be the total height of the three risers, which is -

3 risers x 8 inches/riser = 24 inches

The length of the side panel would be the total length of the three treads, which is -

3 treads x 10 inches/tread = 30 inches

Now, we can calculate the area of the side panel using the formula for the area of a right triangle:

Area = (base x height)/2

we have the base as the length of the side panel (30 inches) and the height is the total height of the three risers (24 inches).

Substituting these values into the formula we get,

Area = (30 inches x 24 inches)/2

Area = 360 square inches

Therefore, the area of the side panel of the stairway is 360 square inches.

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When the smaller data point is included, the mean will drop when compared to the other values, but the median may increase or decrease depending on whether the collection of numbers is even or odd.

1. Calculate the original set of numbers' mean and median.

2. Include the lesser data point in the collection.

3. Determine the updated median and mean.

4. Evaluate the original mean and median in comparison to the new mean and median. Depending on whether the collection of numbers is even or odd, the median will decline while the mean will increase.

We must first determine the mean and median of the initial set of data in order to evaluate how the addition of a smaller data point will impact those values. Adding together all the values and dividing by the total number of values yields the mean. We place the middle value in the set of integers after sorting them from least to largest to determine the median. We include the new, smaller data point in the set after finding the mean and median. We next perform the same calculations as previously to determine the new mean and median. Finally, we contrast the updated mean and median with the baseline values. The median may stay the same or drop depending on whether the set of numbers is even or odd, while the mean often decreases as it is compared to other values. The mean and median of a set of numbers can therefore be significantly affected by the addition of a tiny data point.

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The complete question is

how do you know how adding a smaller data point will affect the mean or median if its smaller than them other value.

Answer:

$0.22.

Step-by-step explanation:

To find the cost per ounce of juice, divide the total cost of 32 ounces of juice by the number of ounces:

7.04 ÷ 32 ounces = 0.22 per ounce

So, the cost per ounce of juice is approximately $0.22.

Answer:

0.22

Step-by-step explanation:

On solving the provided question, we can say that equation, k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.

A mathematical equation is a formula that links two assertions and signifies equivalence with the equals sign (=). In algebra, a mathematical statement that proves the equality of two mathematical expressions is referred to as an equation. The equal sign, for instance, separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14. There is a mathematical formula that explains the link between the two phrases that appear on either side of a letter. Frequently, the symbol and the single variable are the same. like in 2x - 4 = 2, for example.

a. f(x) = 2x+4 represents the function where you multiply the input by 2, then add 4 to the result.

b. g(x) = 2(x+4) represents the function where you add 4 to the input, then multiply the result by 2.

c. h(x) = 4x+2 represents the function where you multiply the input by 4, then add 2 to the result.

d. k(x) = 4(x + 2) represents the function where you add 2 to the input, then multiply the result by 4.

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The two plants would have the same height in 7 weeks and the height would be 31 inches.

The form of the expression that represents the length of the plant on the window sill is:

initial length + (length of growth per week x number of weeks)

3 + (4 x w)

3 + 4w

The form of the expression that represents the length of the plant on the coffee table is:

initial length + (length of growth per week x number of weeks)

17 + (2 x w)

17 + 2w

When the two plants have the same height, the two expressions would be equal:

17 + 2w = 3 + 4w

17 - 3 = 4w - 2w

14 = 2w

w = 14/2

w = 7 weeks

Height of the plant = 3 + 4(7)

3 + 28 = 31 inches

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Multivariable calculus in college is generally more challenging than AP Calculus BC due to the additional complexity of working with functions of several variables.

Multivariable calculus in college typically goes beyond the content covered in AP Calculus BC in high school. While both cover calculus concepts, multivariable calculus adds the complexity of working with functions of several variables, including partial derivatives, multiple integrals, and vector calculus. As a result, the difficulty level of multivariable calculus in college can be significantly higher than AP Calculus BC. However, this can vary depending on the individual student and the rigor of their high school AP course.

AP Calculus AB and BC are two levels of Advanced Placement calculus courses typically offered in high school.

AP Calculus AB covers a wide range of calculus topics including limits, derivatives, integrals, applications of derivatives and integrals, and the Fundamental Theorem of Calculus. The focus is on single-variable calculus, meaning students work with functions of one variable.

AP Calculus BC, on the other hand, covers all the topics included in AB as well as additional concepts such as parametric, polar, and vector functions, series, and sequences. The course is designed to be more challenging and covers more advanced topics in calculus, including applications of calculus in physics and engineering.

Overall, AP Calculus BC is considered to be a more rigorous course than AP Calculus AB, but both courses prepare students for college-level calculus.

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The number of panels that Plant B produced is; 11000 panels

We are told that Plant A produced 4000 fewer panels than Plant B did.

Thus;

A = B - 4000    -----(1)

Four percent of the panels from Plant A and 2% of the panels from Plant B were defective. Thus;

0.04A + 0.02B = 500   ------(2)

Put eq 1 in eq 2 to get;

0.04(B - 4000) + 0.02B = 500

0.04B - 160 + 0.02B = 500

0.06B = 660

B = 660/0.06

B = 11000 panels

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The function that has a simplified base of (4∛4) is 4(∛16[tex])^({2x)[/tex].

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

From the general formula of an exponential function, we know that;

f(x) = a[tex](b)^x[/tex]

Now, we have;

f(x) = (4∛4[tex])^x[/tex]

4(∛16[tex])^({2x)[/tex], the base is (∛16)²

(∛16)²

= √(16^(⅔))

=256^(⅓)

= 4∛4

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Answer:

C.

Step-by-step explanation:

Took the test. :)

Answer:

solution: Mr. Schwartz will need to order more wheels after building 12 cars.

explanation:

Mr. Schwartz begins with total number of wheels = 85

he has to order more wheels once he left with less than 40 wheels

so min. no. of wheels he can use before ordering more wheels = 85-40 = 45

Mr. Schwartz uses 4 wheels to build 1 car

Mr. Schwartz uses 45 wheels to build 45÷4 = 11.25 cars

then, if he builds 12 cars then he needs 12×4 = 48 wheels

total supply of wheels he begins with = 85

wheels he used to build 12 cars = 48

so total number of wheels remaining are = 85-48 = 37

since 37 is less than 40 so after building 12 cars Mr. Schwartz need to order more wheels.

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The polynomial for the shaded area will be 3x² + 15x and x² + 6x + 8.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

19. The area is given as,

A = (x + 5)(3x)

A = 3x² + 15x

19. The area is given as,

A = (x + 4)(x + 2)

A = x² + 6x + 8

The polynomial for the shaded area will be 3x² + 15x and x² + 6x + 8.

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5050 flips expect to make before running out of coins .

Let's approach this problem using the concept of geometric distribution.

The probability of getting heads on any given coin flip is 1/2, assuming a fair coin.

So the probability of getting tails on a given flip is also 1/2.

The number of flips it takes to get the first head is a geometric distribution with a probability of success p = 1/2.

The expected number of flips until the first head appears is 1/p = 2 flips.

After the first head appears, there will be 99 coins left to flip.

The expected number of flips until the next head appears is still 2, since the probability of getting heads on any given flip is still 1/2.

So the expected number of flips until the second head appears (and the number of coins remaining drops to 98) is 2+1 = 3 flips.

Similarly, the expected number of flips until the third head appears (and the number of coins remaining drops to 97) is 2+1+1 = 4 flips.

We can generalize this pattern: after k heads have been obtained, the expected number of additional flips until the next head appears (and the number of coins remaining drops to 100-k) is k+1 flips.

Using this formula, we can calculate the expected number of flips to obtain all 100 heads:

E(number of flips) = (2 + 3 + 4 + ... + 101)

= (1 + 2 + 3 + ... + 100) + 100

= (100 x 101 / 2) + 100

= 5050

Therefore, we expect to make 5050 flips before running out of coins to flip and obtaining all 100 heads.

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The correct interpretation of the 90% confidence interval is given as follows:

There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).

It means that it is x% likely that the true population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.

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The equation of the circle graphed above is equal to (x - 1)² + (y - 6)² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

By critically observing the graph of this circle, we have the following parameters:

Radius, r = 3 units.

Center, (h, k) = (1, 6).

Substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 1)² + (y - 6)² = 3²

(x - 1)² + (y - 6)² = 9.

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£40 is shared as £5, £15 and £20. 88p is shared as 16p, 32p and 40p. 180° is shared as 40°, 40° and 100°

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

a) Share £40 in the ratio 1:3:4

For the first ratio = (1/8) * £40 = £5

For the second ratio = (3/8) * £40 = £15

For the third ratio = (4/8) * £40 = £20

b) Share 88p in the ratio 2:4:5

For the first ratio = (2/11) * 88p = 16p

For the second ratio = (4/11) * 88p = £32

For the third ratio = (5/11) * 88p = 40p

c) Share 180° in the ratio 2:2:5

For the first ratio = (2/9) * 180° = 40°

For the second ratio = (2/9) * 180° = 40°

For the third ratio = (5/9) * 180° = 100°

The ratios are shown above

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After '2' hours, both Car A and Car B will be '20' miles from McDonald Middle School

What is a graph?

A diagram or pictorial representation that organises the depiction of data or values is known as a graph.

The relationships between two or more items are frequently represented by the points on a graph.

Given that, both the cars are traveling at a constant speed and given a graph showing the distance from The school in Y-axis and Time in X-axis

To find the point where the cars meet, We should look at the point of intersection of both the lines of Car A and Car B

We can see the point of intersection to be (2 hours, 20 miles)

i.e., After 2 hours, Both the cars are 20 miles from the school

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