Complete the two-way frequency table below, which shows the relationship between students who enroll in advanced algebra and physics in a particular high school. From a sample of 40 students, it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both. How many students are enrolled in either algebra or physics?

Algebra Not in Algebra Total
Physics 5 9 14
Not in Physics 24 2 26
Total 29 11 40

Answers

Answer 1

it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both using principle of inclusion-exclusion we can say 38 students are enrolled in either algebra or physics.

How to find the number of students enrolled  in either algebra or physics?

To find how many students are enrolled in either algebra or physics, you can use the principle of inclusion-exclusion, which states that the total number of elements in two sets can be found by adding the number of elements in each set and then subtracting the number of elements that are in both sets.

So, the number of students enrolled in either algebra or physics is:

29 (students enrolled in algebra) + 14 (students enrolled in physics) - 5 (students enrolled in both) = 38

So, 38 students are enrolled in either algebra or physics.

It is important to notice that in the table you provided is a two-way frequency table also known as a contingency table, it shows the relationship between two variables, in this case, Algebra and Physics and the frequencies of each combination.

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Related Questions

What is the slope of a horizontal line? Write the equation of an example of a horizontal line.

Answers

The slope of the horizontal line will be zero.

What is a slope?

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope of the line is the ratio of the rise to the run.

The horizontal line always has zero slopes because the y coordinate will always be the same for two points.

The slope is calculated by the formula below,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

y₂ = y₁

Slope = ( y₁  - y₁ ) / ( x₂ - x₁ )

Slope = 0

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The weight of the square is 10 grams. How much heavier is the circle than the square?

Answers

The weight of the circle is heavier than the weight of the square by the weight of the triangle

How to find how much weightier is the circle as compared with the square

Examining the weights, can lead to a linear equation, the equation will have the follows parameters

let t represent triangle

let c represent circle

let s represent square

6s + 3t = 3s + 3c

6s - 3s + 3t = 3s + 3c

3s + 3t = 3c

divide through by 3

s + t = c

10 + t = c

From the equation 10 + t = c we can say that the weight of the circle is a triangle weight more than the square

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PLEASE HELP ME THIS IS DUE RIGHT NOW HELP ASAP

Answers

Answers:  A, D, and E

============================================================

Explanation:

We'll need to find the slope of the line through the two given points.

[tex](x_1,y_1) = (-3,17) \text{ and } (x_2,y_2) = (2,-3)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-3 - 17}{2 - (-3)}\\\\m = \frac{-3 - 17}{2 + 3}\\\\m = \frac{-20}{5}\\\\m = -4\\\\[/tex]

The slope is -4.

Think of -4 as -4/1. The reciprocal is -1/4, and it flips in sign to +1/4 or simply 1/4.

The original slope -4 leads to the perpendicular slope 1/4. The two slopes multiply to -1. This is true of any perpendicular lines where neither is vertical nor horizontal.

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

In short, the answer equation will involve a slope of 1/4. This points us directly to choices A and E as two answers so far.

Something like choice B is not an answer since it has slope 4. Choice C is ruled out because 4x+y = -8 solves to y = -4x-8. It has a slope of -4.

Choice D on the other hand has x-4y = 2 solve to y = (1/4)x - 1/2, and this has a slope of 1/4 that we want. This means choice D is another answer.

Choice F and choice G are ruled out because they involve slopes of 4 and -4 respectively.

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

Summary: The 3 answers are choices A, D and E

Step-by-step explanation:

the slope of a line is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

so for (-3, 17) and (2, -3) we get

x changes by +5 (from -3 to 2).

y changes by -20 (from 17 to -3).

the slope is

-20/+5 = -4/1 = -4

now, a perpendicular slope (90° to the original slope) is putting the slope fraction upside-down and flips the sign :

+1/4 or simply 1/4.

the slope in an equation of the form "y = ..." is always the factor of x.

y + 2 = (1/4)(x - 1)

yes, there are only some constant additions or subtractions to get to a or "y = ..." form, so 1/4 is indeed the factor of x and the slope of this line.

y = 4x + 12

4 <> 1/4, so, no, it is not.

4x + y = -8

y = -4x - 8

-4 <> 1/4, so, no, it is not.

x - 4y = 2

-4y = -x + 2

y = (1/4)x - 2/4

1/4 is indeed 1/4, so, yes, it is.

y = (1/4)x - 15

1/4 is indeed 1/4, so, yes, it is.

y + 3 = 4(x - 2)

similar to the first one, but 4 <> 1/4, so, no, it is not.

y = -4x + 3

-4 <> 1/4, so, no, it is not.

Beverly Hobbs earns $683 a week she is single and claims 2 allowances what amount is withheld weekly for federal income tax

Answers

Therefore, $52.25 is the answer to the inquiry about what percentage of a person's income is withheld each week for federal income tax.

What is percentage?

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Here,

The Federal Insurance Contribution Act is the American legislative framework in use here, and it contains the criteria and guidelines that are utilized to determine payroll taxes on an employee's paychecks. The social security and Medicare programs are funded through taxation, which is paid by both employers and employees.

The amount of federal income tax deducted from the weekly cheque is:

6.2% from Social Security plus 1.45% from Medicare.

= 7.5 percent of the weekly gross salary.

The amount of federal income tax withheld each week from Beverly Hibbs's $683.00 weekly salary is:

= 0.0765 × 683

= $52.25

Therefore, $52.25 is the answer to the inquiry about what proportion of a person's income is withheld each week for federal income tax.

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6x(2x+3)+1(2x+3)
Rewrite the expression

Answers

The answer to this question in particular is 12x^2+20x+3

•15 POINTS• don’t explain

A.neither
B.HL
C.SAS

Answers

Answer:

C

Step-by-step explanation:

2 sides and the included angle of both triangles are congruent, then the triangles are congruent by SAS postulate

A manager at a shopping mall counts 244 males and n females as they enter the mall. The manager realizes that 25% of all males and 25% of all females are children. She writes the expression 0.25n + 61 to represent the number of children who enter the mall. Is the manager correct? Why or why not?
The manager (blank, choose is or is not) correct because the original expression 0.25(n + 244) (blank, choose is or is not) equivalent to the manager’s expression, 0.25n + 61.

Answers

Answer:

The manager is not correct in her calculation.

Step-by-step explanation:

There are 244 males and n females who entered the mall as the manager at the shopping mall counts.

If 25% of all males are children, then the number of male children are .

Again, the 25% of all female are children, then the number of female chilfren are .

Therefore, the total number of children will be (60 + 0.25n).

But the manager gives the number of children to be 0.25n + 61 who entered the mall.

So, the manager is not correct in that calculation. (Answer)

Step-by-step explanation:

if john makes $55 working 2 hours , how much would he make working 8 hours ?

Answers

Answer:

$220

Step-by-step explanation:

Find the amount of money John makes in one hour:

[tex]55\div2=27.5[/tex]
[tex]=27.5[/tex]

John makes $27.50 an hour, now multiply the amount of money earned per hour, by the number of hours he worked.

[tex]27.50\times8=220[/tex]
[tex]=220[/tex]

John made "$220 dollars an hour."

Hope this helps.

evaluate 7 to the 3rd power x 7 to the 3rd power

Answers

Answer:117649

Step-by-step explanation:

Use the diagram to find the indicated angle measures. Please do 1, 2, and 3. Please need ASAP!!!!!!!!!!!!!!! 30 POINTS

Answers

The measures of given figures are m∠ADC is 90 degrees and m∠DAC will be 34 degrees

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given m∠B= 57 degrees

m∠c= 51 degrees

segment AD bisects m∠BAC

then  m∠ADC we need to find.

As AD is perpendicular to BC, the angle of  m∠ADC is 90 degrees.

Given m∠B= 66 degrees

m∠BAD=34 degrees

Now we need to find m∠DAC

m∠DAC will be 34 degrees

Hence, the measures of given figures are m∠ADC is 90 degrees and m∠DAC will be 34 degrees

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How many tens do u need to make 280

Answers

Answer:

28

Step-by-step explanation:

280 divided by 10 = 28

28 because 280/10=28

n% of 28 is 14 `percentage`

Answers

Answer:

The Percentage is 50% because 14 is the half of 28.

Evaluate the expression (42 + 2) -5

Answers

Answer:

39

Step-by-step explanation:

Solve inside of the parenthesis, then open them and solve.

(42 + 2) - 5

(44) - 5

44 - 5

39

Answer:

39

Step-by-step explanation:

42+2−5

=39

Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.

Answers

The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.

The graph is given in the question.

As per the given line, we take two points (0, 4) and (5, 8)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 0, y₁ = 4

x₂ = 5, y₂ = 8

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 4 = (8 - 4)/(5-0 )[x -0]

⇒ y - 4 = (4/5)x

⇒ y = (4/5)x + 4

The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.

So, the equation of the line would be y = (4/5)x + 4.

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each minute your heart pumps 1.5 gallons of blood around your body. How many pints of blood will your heart pump in a day? PLEASE HELP ME

Answers

Answer:

So there are 60 minutes in an hour, and since there are 24 hours in a day you will multiply 60 by 24:

60 * 24 = 1440.

That multiplied by 1.5 is 2160, so that would be your answer.

Step-by-step explanation:

Hope it helps! =D

hello i need help with question 5 please i need help

Answers

a) The total cost of buying the car with HST is given as follows: $36,160.

b) The amount of money saved by the customer leasing the car instead of buying is given as follows: $14,760.

c) The customer should lease a new car, as according to the two options in this problem, leasing is more economic than purchasing a new car.

How to obtain the costs?


The costs are obtained applying the proportions in the context of this problem.

The HST tax is the Ontario Sales Tax, which means that an additional 13% of taxes has to be paid when purchasing the car.

Hence the total cost of buying the car, considering the HST tax, is given as follows:

1.13 x 32000 = $36,160.

The costs for leasing the car are given as follows:

$1,000 down payment.48 payments of $425.

Hence the total cost for leasing the car is given as follows:

1000 + 48 x 425 = $21,400.

Then the amount saved by the customers when he/she decides to lease the car instead of purchase is given as follows:

36160 - 21400 = $14,760.

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i need help right freaking now

Answers

Answer:

a. x^4 - 12x^3 + 2x^2 - 2x + 4

Degree: 4

b. x^4 - 2x^2 - 2x - 4

Degree: 4

Step-by-step explanation:

For part a, all you are doing is adding the polynomials together. They already set up the boxes in standard form, so all you need to do is add each like term as I wrote out in the answer. The degree is then going to be the first exponent that you see once the polynomial is in standard form, which is 4.

For part b, you are now subtracting the polynomials. Again, it is set up for you in standard form. There is no x^3 terms because they cancel out, but you basically subtract each like term from another, and remember to distribute the subtraction sign (it acts as a -1) across the parenthesis. The degree is the first exponent you see, and that is 4.

Raj was getting a 5% commission, but now he's getting 6.5%. How much more money will he make on $24,000 of sales than on his old commission?

Answers

If Raj was getting a 5% commission, he would make 24000 * 5% = $<<240005.01=1200>>1200 on $24,000 of sales.

If he is now getting a 6.5% commission, he will make 24000 * 6.5% = $<<240006.5.01=1560>>1560 on $24,000 of sales.

Thus, Raj will make 1560 - 1200 = $<<1560-1200=360>>360 more on $24,000 of sales with his new commission rate of 6.5% than he did with his old commission rate of 5%.

A camper lights an oil lantern at 12 noon lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant tare of each hour. At 2 p.m., the amount of oil left in the lantern is 63 ounces. At 5 p.m., the amount of oil left in the lantern is 61 1/2 ounces. Based on the average rate of oil burning per hour, how much oil, in ounces, was in the lantern at 12 noon?
Show your work.

Answers

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

The rate at which the oil burns.

1 hour = 2/3 ounce

At 12 noon = 193/3 = 64.33 ounces

At 2 pm = 63 ounces

At 5 pm = 61 ounces

The amount of oil at 12 noon is 64.33 ounces.

What is a unit rate?

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour.

At 2 p.m., the amount of oil left in the lantern is 63 ounces.

At 5 p.m., the amount of oil left in the lantern is 61 ounces.

This means,

Amount of oil burnt in the lantern from 2 pm to 5 pm.

= 63 ounces - 61 ounces

= 2 ounces

Now,

3 hours = 2 ounces

2 hours = 1.33 ounces

1 hour = 0.67 ounces

Now,

The number of hours from 12 noon to 2 pm.

= 2 hours

So,

The amount of oil at 12 noon.

= 63 + 4/3

= (189 + 4) / 3

= 193/3 ounces

Thus,

The amount of oil at 12 noon is 65 ounces.

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3
Use the drawing tool(s) to form the correct answer on the provided graph.
The function f(x) is shown on the provided graph.
Graph the result of the following transformation on f(x).
Drawing Tools
Select
Line
Click on a tool to begin drawing
-10
-8
f(z) + 6
-6
4
-2
10-
8-
6
Delete
Undo
Reset
10 i need help with this

Answers

Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.

what is transformation ?

Four various modifications that can be made to a point, line, or geometric object are referred to as transformations collectively. You must be able to identify which changes have been made and that each alteration has been made. The following guidelines for function translation and transformation: The function is shifted up by b units by F (x) + b. F (x) b causes the function to move downward. The expression f (x + b) causes the function to be moved left b units. Translation, reflection, rotation, and dilation are the four different types of transformations. Transform, reflect, or rotate the geometric shapes that are displayed on a coordinate plane. The transformation, often known as f: X X, is the name given to a function, f, that maps to itself.

given

-1 on the left x-axis and 4 on the right y-axis

Start at -2 on the y-axis, move up the y-axis six times, and you should arrive at 4. However, you must identify the first line in order to complete the puzzle.

Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.

Since you should be at 4, apply the formula rise/run 4/1 to ascend 6 on the y-axis.

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what is the unit rate for meters per second if a car travels 424 meters in 8 seconds

Answers

The unit rate for meters per second if a car travels 424 meters in 8 seconds is 53 meters per second.

How to find the unit rate?

The unit rate meters per second can be determine using this formula

Unit rate meters per second = Number of meters / Numbers of seconds

Where:

Number of meters = 424 meters

Numbers of seconds = 8 seconds

Let plug in the formula

Unit rate meters per second  = 424 meters / 8 seconds

Unit rate meters per second = 53 meters per second

Therefore we can conclude that the Unit rate meters per second  is 53 meters per seconds.

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Find the measure of ∠ 1

Answers

The measure of ∠ 1 is 68.7°

What is linear pair angles?

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

Given is a figure of angles showing the pair of linear angles.

Therefore, by the definition of linear pair angles,

∠ 1 + 111.3° = 180°

∠ 1 = 180° - 111.3°

∠ 1 = 68.7°

Hence, the measure of ∠ 1 is  68.7°

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each minute your heart pumps 1.5 gallons of blood around your body. How many pints of blood will your heart pump in a day?

Answers

The heart pumps around 17280 pints of blood in a day.

To find out how many pints of blood your heart pumps in a day, we need to determine the total volume of blood that your heart pumps in one day.

We know that your heart pumps 1.5 gallons of blood per minute. To find out how much blood your heart pumps in one day, we need to multiply that amount by the number of minutes in a day.

1 day = 24 hours

1 hour = 60 minutes

So, the number of minutes in one day is 24 hours x 60 minutes = 1440 minutes

Now, we can use this information to find out how many gallons of blood your heart pumps in a day.

Gallons of blood pumped per day = 1.5 gallons/minute x 1440 minutes/day

= 2160 gallons

1 gallon = 8 pints

So the number of pints of blood that your heart pumps in a day = 2160 gallons × 8 pints/gallon = 17280 pints.

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your heart pumps 2000 gallons of blood around your body each day.

if your body pumps around 1.5 gallons of blood each minute then a day is 24 hours so yu do that x together which is 20 but as its hours you do it for 2000 and just incase yu need some more info

(1.5 imperial gallons) x 24 hours = 589.173508 m3 s

SORRY IF THIS DONT ALL MAKE SO MUCH SENSE

‐3 + 4(a – 3b + 2) – 5(2 – a + 3b)

Answers

Answer: 15a – 12b – 5.

Step-by-step explanation: To solve this equation, we need to distribute the constants in front of the parentheses. Doing so, we get:

-3 + 4(a – 3b + 2) – 5(2 – a + 3b)

= -3 + 4a – 12b + 8 – 10 + 15a – 15b

= (15a – 12b) + (-10 + 8) – 3

= 15a – 12b + -2 – 3

= 15a – 12b – 5

Thus, the solution to the equation is 15a – 12b – 5.

Which of the following numbers is one fifth of a given number if one fourth of that same number is 20

Answers

Answer:100

Step-by-step explanation:

There is a proportional relationship between the weight and total cost of a bag of lemons. One bag weighs 2.4 pounds and costs $5.28. Another bag weighs 2.7 pounds and costs $5.94. Describe how you would graph the proportional relationship i need help asp

Answers

There is a directly proportional relationship between the weight and total cost of bag of of lemons.

What is constant of proportionality?

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

When two variables are directly or indirectly proportional to one another, their relationship may be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.

As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant.

Given data :

One bag weighs 2.4 pounds and cost $5.28.

Another bag weighs 2.7 pounds and cost $5.94

2.4k = 5.28

k= 2.2

2.7k = 5.94

k = 2.2

k > 1

The weight and total cost of bag of of lemons is directly proportional, so when weight of lemon increases, the cost of lemon also increases.

Therefore, there is a directly proportional relationship between the weight and total cost of bag of of lemons.

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If the sun is 57 degrees above the horizon, find the length of the shadow cast by a building 56 ft tall. Round your answer to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

The Length of shadow  is 35.56 ft.

Given that,

If the sun is 68° above the horizon.

Based on the above information, the calculation is as follows:

tan68° =BC divide AC

tan68° =88 divide b

b =88 divide tan68°

=88 divide 2.475

= 35.56 ft.

Pacquiao has inherited P6,000 from the death of his Grandma . He would like to use this money to buy his mom Dionisia a new bicycle costing P7,000 2 years from now. Will Pacquiao have enough money to buy the gift if he deposits his money in an account paying 8 percent compounded semi-annually?

Answers

Pacquiao will have enough money (a future value of up to P7,000) to buy the gift if he deposits his money (P6,000) in an account paying 8 percent compounded semi-annually.

What is the future value?

The future value is the compounded present value at an interest rate.

The future value can be determined using an online finance calculator, FV table, or FV formula.

N (# of periods) = 4 (2 years x 2)

I/Y (Interest per year) = 8%

PV (Present Value) = P6,000

PMT (Periodic Payment) = P0

Results:

Future Value (FV) = P7,019.15

Total Interest = P1,019.15

Thus, in 2 years' time, Pacquiao will have P7,019 enough to buy his mom a new bicycle.

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A 38 ounce box of cat food costs $1.69 and a 24 ounce box costs $1.29. How much can be saved per ounce by guiding the larger box

Answers

The amount of money that can be saved per ounce by guiding the larger box is $0.009.

What is equation modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is that a 38 ounce box of cat food costs $1.69 and a 24 ounce box costs $1.29.

For the larger box -

38 ounce box of cat food costs $1.69

1 ounce of this box will cost $(1.69/38) = $0.045

For the smaller box -

24 ounce box of cat food costs $1.29

1 ounce of this box will cost $(1.29/24) = $0.054

Money that can be saved per ounce by guiding the larger box -

0.054 - 0.045

0.009

Therefore, the amount of money that can be saved per ounce by guiding the larger box is $0.009.

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URGENT: please help!!!!!!!!!

Answers

Answer:

In the form of y=mx+b:

y = -5/6x-5

Step-by-step explanation:

I'm not that good at explaining, but I'll try:


Slope intercept is y=mx+b, M is the slope of the line which is rise over run, the rise is -5 (distance traveled along y-axis) and the run is 6 (distance traveled along x-axis) found from two points: (-6, 0) and (0, -5). Using this data -5/6 can be plugged in for M, and b is the y variable at (0, _) in this case the y variable is -5. The final answer after plugging everything in is y=-5/6x-5, I hope this wasn't too confusing.

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