Working her way through school, Kathy works two part-time jobs for a total of 28 hours a week. Job A pays $6.10 per hour, and Job B pays $6.80 per hour. How many hours did she work at each job the week that she made $184.10? (Round to two decimal places if necessary.)​

The tables which shows a proportional relationship between x and y are table 3 and table 4.

Using ratio to find the proportional relationship

Table 1

x : y = 8 : 8

= 1 : 1

x : y = 12 : 10

= 6 : 5

Not proportional

Table 2:

x : y = 2 : 3

x : y = 3 : 8

Not proportional

Table 3:

x : y = 5 : 3

x : y = 10 : 6

= 5 : 3

Proportional

Table 4:

x : y = 4 : 1

x : y = 16 : 4

= 4 : 1

Proportional

Ultimately, table 3 and table 4 shoes a proportional relationship between x and y.

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The length in each circle is:

(a) CD = 19.5 units

(b) UZ = 12.8 units

(a) The Intersecting Secant-Tangent Theorem states that "if two secant lines intersect outside a circle, and a tangent line is drawn from the point of intersection to the circle, then the product of the lengths of the two secant segments is equal to the square of the length of the tangent segment".

Using the theorem, we have:

EC * ED = EG²

6.5 * ED = 13²

6.5ED = 169

ED = 169/6.5

ED = 26 units

ED = EC + CD

26 = 6.5 + CD

CD = 26 - 6.5

CD = 19.5 units

(b) The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

UZ * UW = UX * UY

UZ * 40 = 8 * 64

40UZ = 512

UZ = 512/40

UZ = 12.8 units

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Answer:

(- 3, 1.5)

--------------------------

Given system:

The first expression is ready to be substituted as no further operation is required to simplify it.

Find x:

Answer:0,2,4,6,8

Step-by-step explanation: the pounds and price rise at equal amount

Answer:

Statement is incorrect

Step-by-step explanation:

Every positive integer cannot be expressed as the sum of three or fewer perfect squares.

Supposing the number 7 only squares less than are 0, 1  and   4

Clearly 7 can not be written using three or fewer of these numbers

It is proved

By taking Cube root of 7

\(\sqrt[3]{7}\) = 1.912931183

Now By taking  

\(\sqrt{7}\) = 2.64575131

So both values 1.912931183 and 2.64575131 are not positive integers.

Hence the statement is incorrect.

Answer:

3.8

Step-by-step explanation:

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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Answer:70%

Step-by-step explanation:you have 7/10.SO u times the whole fraction by 10( 7 times 10 =70 and 10 times 10 =100) which means 70/100 so the percent is 70.

Hope it helps

1) The best way to tackle this question is by plotting the graph of this function and then performing the horizontal line test.

So let's sketch out the following function:

Note that this function is a one-to-one function for a horizontal line hits the graph only once.

2) Since, invertible functions can only come from Bijective functions (one-to-one and surjective functions simultaneously) then we can write out this and find the inverse of that inverse function, swapping the variables and then isolating the x on the left side

Answer:

22 1/2

Step-by-step explanation:

The result of  the expression 2 + 5^3 is 127.

To solve the expression 2 + 5^3, you need to follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

In this case, the exponentiation should be performed first.

Step 1: Calculate 5^3

5^3 means raising 5 to the power of 3, which is equivalent to multiplying 5 by itself three times: 5 * 5 * 5 = 125.

Step 2: Add 2 to the result from Step 1.

2 + 125 = 127.

Therefore, the result of 2 + 5^3 is 127.

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The average rate of change of the function over the interval is -6

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

The graph

The interval is given as

From x = 2 to x = 4

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(2) = -3

f(4) = -15

Next, we have

Rate = (-15 + 3)/(4 - 2)

Evaluate

Rate = -6

Hence, the rate is -6

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Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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Answer:

3 eighth pound for $2.28

Step-by-step explanation:

quarter pound = 1.5 three eighth pound

1.49×1.5 = 2.235

We get the function notation as aₙ = 15 - 4 n for the arithmetic sequence beginning with 11, 7,...

We are given an arithmetic sequence:

11, 7, …

We get from the sequence that:

a = 11  ( initial term )

d = 7 - 11 = - 4   ( common difference )

Now the nth term will be given as:

aₙ = a + (n - 1) d

aₙ = 11 + (n - 1) ( - 4 )

aₙ = 11 - 4 n + 4

aₙ = 15 - 4 n

Third term = 7 - 4 = 3

Fourth term = 3 - 4 = - 1

Fifth term = - 1 - 4 = - 5

Therefore, we get the function notation as aₙ = 15 - 4 n for the arithmetic sequence beginning with 11, 7,...

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Answer:

329 miles

Step-by-step explanation:

Create a proportion where x is the distance the car can travel on 14 gallons of gas:

\(\frac{70.5}{3}\) = \(\frac{x}{14}\)

Cross multiply and solve for x:

3x = 987

x = 329

So, the car can travel 329 miles on 14 gallons of gas

Answer:

329 miles

Step-by-step explanation:

We can write a ratio to solve

70.5 miles      x miles

--------------- = ------------

3 gallons          14 gallons

Using cross products

70.5 * 14 = 3x

987=3x

Divide each side by 3

987/3 = 3x/3

329=x

329 miles

Answer: 1 & 4 4&5 6&7

Step-by-step explanation:

Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

To determine the number of pounds of raw materials that should be purchased in July, we need to calculate the raw materials production needs for August and then consider the inventory policies given in the information provided.

Each unit of finished goods requires 5 pounds of raw materials. The budgeted unit sales for August are 19,000 units. Therefore, the raw materials production needs for August would be 19,000 units multiplied by 5 pounds per unit, which equals 95,000 pounds.

The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Therefore, the desired ending raw materials inventory for July would be 10% of 95,000 pounds, which is 9,500 pounds.

To calculate the raw materials purchases for July, we need to consider the payment terms provided. Thirty-five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.

Let's assume the raw materials purchases for July are X pounds. Then the payment for 35% of X pounds will be made in July, and the payment for 65% of X pounds will be made in August.

The payment for raw materials purchases in July (35% of X pounds) will be:

0.35 * X pounds

The payment for raw materials purchases in August (65% of X pounds) will be:

0.65 * X pounds

Since the raw materials purchases for July should cover the desired ending raw materials inventory for July (9,500 pounds), we can set up the following equation:

Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

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The positions will be filled in 56,280 ways

There are 11 qualified candidates applying for 7 positions. The order of the positions does not matter. after choosing a position the number of persons drop so we solve as follows

For the position of president

11 combination 1 = 11

For the position of secretary

10 combination 1 = 10

For the position of treasurer

10 combination 1 = 10

For the position of three directors

8 combination 3 = 56 ways

the total number of ways to fill these positions is

11 x 10 x 9 x 56 = 56,280.

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Answer:

To find the x-intercepts and y-intercepts of a function, we need to find the values of x and y at which the function crosses the x-axis or y-axis.

X-intercepts:

The x-intercepts occur when y = 0, so we can set f(x) = 0 and solve for x:

3x³-12x²-15x = 0

This is a cubic equation, we can use factoring, synthetic division or use a numerical method like the Newton-Raphson method to solve for x.

Y-intercepts:

The y-intercepts occur when x = 0, so we can substitute x = 0 into the function to find the y-intercept:

f(0) = 3(0)³ - 12(0)² - 15(0) = 0

So the y-intercept of the graph is at the point (0,0)

In summary, the x-intercepts are the solutions of the equation 3x³-12x²-15x = 0 and the y-intercept is (0,0)

Please note that, if the equation has complex roots, the graph will not cross the x-axis and hence it will not have any real x-intercepts.

Step-by-step explanation:

The value of k is 4.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Volume= 16

Width = 4

So, we can write the relation as

Volume= k (width)

k = Volume/ width

k= 16/4

k = 4

Hence, the value of k is 4.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The equation of the line that passes through the point (-8, -3) and has a slope of -6 is y = -6x - 51.

To find the equation of a line that passes through the point (-8, -3) and has a slope of -6, we can use the point-slope form of the equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1),

where (x1, y1) represents a point on the line, and m represents the slope.

Substituting the values (-8, -3) for (x1, y1) and -6 for m, we have:

y - (-3) = -6(x - (-8)).

Simplifying the equation, we have:

y + 3 = -6(x + 8).

Expanding the expression, we get:

y + 3 = -6x - 48.

To isolate y, we can subtract 3 from both sides of the equation:

y = -6x - 48 - 3.

Simplifying further, we have

y = -6x - 51.

Therefore, the equation of the line that passes through the point (-8, -3) and has a slope of -6 is y = -6x - 51.

This equation represents a line with a negative slope of -6, indicating that the line has a downward slope. The intercept of -51 on the y-axis implies that the line crosses the y-axis at the point (0, -51). The line is a straight line that decreases by 6 units in the y-direction for every 1 unit increase in the x-direction.

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According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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Answer:

The graph of f is shifted 3 units up to create the graph of g.

Here we have a problem with translations, where we define a translation as an operation that moves the graph of a function in a given direction.

We will see that the correct option is A.

"The graph of f is shifted 3 units up to create the graph of g."

To get this, we first need to describe vertical translations.

For a function f(x) we define a vertical translation (or vertical shift) of N units as:

g(x) = f(x) + N

If N is positive, the translation is upwards

if N is negative, the translation is downwards.

So here we have:

g(x) = f(x) + 3

So we can see that this is a translation of 3 units upwards, then the correct option is A, the graph of f(x) is shifted (or translated) 3 units up to greater the graph of g(x).

And the graphs of g(x) = x + 3 and f(x) = x can be seen below, where you can see this, where the grey line is g(x).

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Answer:

80 points

Step-by-step explanation:

If score in English is x points and score in math is 5% higher then score in math

y = x + 0.05x

where 0.05 = 5% expressed as decimal

0.05x refers to the 5% increase in score

y = math score

y = x(1 + 0.05)

y = 1.05x

Given score in math = 84 this becomes

84 = 1.05x

x = 84/1.05

x = 80

So Emily's score in English was 80 points

Someone can't pay exactly 87 to have their windows washed.

A company charges a 5 flat fee plus 3 per window to wash windows. Therefore, let's find if someone can pay exactly 87 units to have there window washed.

Hence, using equation,

y = 5 + 3x

where

Using the equation, let's find if someone can use exactly 87 units for the service.

87 = 5 + 3x

87 - 5 = 3x

82 = 3x

divide both sides by 3

x = 82 / 3

x = 27.33

Therefore, someone can't use exactly 87 units because the number of windows washed is in decimal.

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Answer:

85 cents

Step-by-step explanation:

34÷40= .85

adding characters to get to 20