A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.


Number of Hours Total Number of Students
0 1
1 3
2 2
3 10
4 9
5 7
6 3


Determine the probability that a student studied for exactly 4 hours. Round to the nearest hundredth.
0.74
0.35
0.26
0.11

Answer:

A. and 3

Step-by-step explanation:

3x+2=8

3x=6

x=2

The inverse of the function is given by x=√y-10

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here;  g(x)= (x+10)²

To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

Thus y=(x+10)²

√y=x+10

x=√y-10

Hence, The inverse of the function is given by x=√y-10

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Answer:  5 : 18 =  10 : 36

Step-by-step explanation:

The ratio is already in lowest terms so we found an equivalent ratio by multiplying both terms by 2.

Answer:

5 to 18

Step-by-step explanation:

Using the arrangements formula, it is found that there is a 0.0178 = 1.78% probability that all the girls are ahead of all the boys.

The number of possible arrangements of the n elements is the factorial of n, that is:

[tex]A_{n} = n![/tex]

The total number of outcomes is the arrangement of 8 elements, hence:

T = 8! = 40320

The desired number of outcomes is all-girls(5!), then all-boys(3!), hence:

D = 5! × 3! =120× 6=720

Hence, the probability is:

p = D/T =720/40320 = 0.0178

There is a 0.0178 = 1.78% probability that all the girls are ahead of all the boys.

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Answer:

Step-by-step explanation:

1. Total number of students in class 8B: 30

2. Number of students studying both German and French: 3

3. Number of students studying only German: 12

4. Number of students studying only French: 15

the rule for x terms is 1.5x - 1.5 and the rule for y terms is 4.5y - 4.5.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, the ordered pairs.(0,0) (1.5,4.5) (3,9) (4.5,13.5)

For x term:

The rule for x term that is 0, 1.5, 3, 4.5

First term = 0

difference = 1.5

From the general formula of Arithmetic sequence:

an = a + (n – 1)d.

thus,

Equation = 0 + (x -1 ) d

Equation = 1.5x - 1.5

For y term:

The rule for y term that is 0, 4.5, 9, 13.5

First term = 0

difference = 4.5

From the general formula of Arithmetic sequence:

an = a + (n – 1)d.

thus,

Equation = 0 + (x -1 ) d

Equation = 4.5x - 4.5

Therefore, The x-term rule is 1.5x-1.5, while the y-term rule is 4.5y-4.5.

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Answer:

7.5qt is the correct answer

Answer:

x = (2, 0), y = (0, -10)

The cost of painting the wall is Rs.48.75 .

The square shape wall whose length is 10m has a door of length 2m and breadth 1m.   It also has a window of length 1m and breadth 0.5m.

Therefore, the cost of painting the wall can be calculated as follows:

cost of painting per meters = Rs0.5 per metre square

Therefore, the area of the wall to be painted will exclude the window and the door.

Hence,

area of wall of the wall to be painted = area of the wall - area of the window - area of the door

Therefore,

area of wall of the wall to be painted = 10² - (1 ×  0.5) - (2 × 1)

area of wall of the wall to be painted = 100 - 0.5 - 2

area of wall of the wall to be painted = 97.5 metres²

Therefore,

1 metres square = Rs0.5

97.5 metres squared = ?

cross multiply

cost to paint the wall = 0.5 × 97.5

cost to paint the wall = Rs.48.75

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Jorimiah score 680 points in the season.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Jorimiah scored 85 points in a basketball game.

That was 1/8 of the points that he scored for the season.

let Jorimiah score x points

So, 1/8 of x= 85

x= 85(8)

x= 680 points.

Hence, he score 680 points.

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Answer:

77.35

Step-by-step explanation:

I'm sorry because I don't know how to explain it...

4 over 6 because when you multiply 2 over 3 by 2 over two the answer is 4 over 6.

Casey went too movie for 4 times and Darnell went to movie for 7 times.

Casey and Darnell went to the movies a total of 11 times last month, Darnell went one less than twice as many times as Casey did.

Let us say that Casey went to movie for X times,

So, the amount of times that Darnel went for movie is 2X-1

It is given that they went for a total of 11 times.

We can make a simple algebraic equation by using the above data.

X + 2X - 1 = 11

3X = 12

X = 4

So, Casey went to movie for 4 times and Darnell went to movie for 7 times.

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The phase shift of the sin function , y = -2 sin (2x - π)-3 is   =π/-3.

Amplitude: The amplitude of a wave is a maximum displacement of a particle from its rest position

Period: The ratio of wavelength to the velocity.

Phase shift: The phase shift represents the amount a wave has shifted horizontally from the the usual position.

here, we have,

The equation of a wave is

f(x) = a sin(bx - c)+d

Where

amplitude = |a|

phase shift = c/d

now,

Given equation of wave is

f(x) =-2 sin (2x - π)-3

Here a=-4, b=2, c = π, d = -3

i.e.

phase shift = c/d

                  =π/-3

Therefore, phase shift   =π/-3.

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The given lines are parallel.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: The two equations given are  y = 3/8x +3 &  y = 3/8x + 8/3

We can observe that both the equations are in slope-intercept form we get

the slope of both the lines m=3/8

Two lines are parallel if their slopes are equal and they have different y-intercepts. In other words, perpendicular slopes are negative reciprocals of each other.

Clearly the two given lines have the same slope and different y intercept

Hence, The two lines are parallel

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The amount of total distance walked has walked by Eric in a man-made circular lake is 75.36 miles.

A circle's circumference is the length of its perimeter. The circumference of a circle can be calculated using length units such as centimeters, meters, or kilometers by opening a circle and measuring the boundary in the same way that we would measure a straight line.

Circumference = D* π

Total distance walked four times = 4.C

= 4 * D * π

= 4 * 6 * 3.14

= 75.36 miles

So, the total distance is 75.36 miles.

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The equation of the graph is (a) [tex]\frac{2x^2-8}{x^2+x-6}[/tex]

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

The graph and the list of options

Next, we test the graph with the options

On the graph, we have:

f(0) = 1.3

f(-1) = -1

From the list of options, the equation that has the above properties is option (a)

Hence, the equation is (a)

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Ohm's Law states that the current passing through a conductor is proportional to the voltage across the conductor, and inversely proportional to the resistance of the conductor.

Mathematically, this can be expressed as:

V = IR,

where V is the voltage, I is the current, and R is the resistance of the conductor. The resistance of a conductor is given by:

R = ρℓ/a,

where ρ is the resistivity of the material, ℓ is the length of the conductor, and a is the cross-sectional area.

From Ohm's Law, we can also derive an expression for the electric field inside the conductor:

E = V/ℓ = IR/ℓ = ρI/a

In the case of conductors 1 and 2, the voltage across both conductors is the same (v2 = v1), so the electric field in conductor 2 can be expressed as:

E2 = V2/ℓ2 = v1/(2ℓ1) = ρI2/a2 = (ρ/2a1)I2

Similarly, the electric field in conductor 1 can be expressed as:

E1 = V1/ℓ1 = v1/ℓ1 = ρI1/a1 = (ρ/a1)I1

Finally, the ratio of the electric fields in conductors 1 and 2 can be calculated as:

E2/E1 = (ρ/2a1)I2 / (ρ/a1)I1 = a1/2a1 = 1/2

So, the ratio of the electric fields, E2/E1, is equal to 1/2. This means that the electric field in conductor 2 is half the electric field in conductor 1, despite the fact that the voltage across both conductors is the same. This happens because the cross-sectional area of conductor 2 is twice that of conductor 1, which compensates for the fact that the length of conductor 2 is also twice that of conductor 1.

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The expanded logarithmic expression is 7log y + log x + 3log z.

The use of a logarithm can be utilised to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. Log interpretation is not that tough. It suffices to know that an exponential equation can also be written as a logarithmic equation in order to comprehend logarithms.

Exponent and logarithm are inverses of one another. This is explained in the section below. John Napier, a mathematician, first developed logarithms as a technique to perform computations simply, and other scientists, engineers, etc. immediately embraced this idea.

The given logarithmic equation is:

log ([tex]y^{7}xz^{3}[/tex])

Now, we can use the properties of logarithms to expand this fully.

Therefore,

log ([tex]y^{7}xz^{3}[/tex]) = log ([tex]y^{7}[/tex]) + log (x) + log ([tex]z^{3}[/tex])

Therefore,

log (y⁷) = 7 log y

log (z³) = 3 log z

Therefore, the expanded logarithmic expression is 7log y + log x + 3log z.

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The monthly Period interest rate is 1.67( nearest hundredth)

Annual percentage rate (APR) refers to the yearly interest rate you'll pay if you carry a balance on your credit card. Some credit cards have variable APRs, meaning your rate can go up or down over time.

To convert annual rate to monthly rate, when using APR, simply divide the annual percent rate by 12.

The APR of the card holder is 19.99%

Therefore the monthly Period interest will be calculated as ;

19.99/12

= 1.67% ( nearest hundredth)

therefore the monthly periodic interest is 1.67%

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The graph shows an inverse relationship between the number of baseballs produced per day and the cost of production. As the number of baseballs produced per day increases, the cost of production decreases.

1. The graph shows a downward-sloping line, which indicates an inverse relationship between the number of baseballs produced per day, q, and the daily cost of production, c.

2. As q increases, c decreases.

3. This inverse relationship means that as the number of baseballs produced per day increases, the cost of production decreases.

The graph shows an inverse relationship between the number of baseballs produced per day and the cost of production. As the number of baseballs produced per day increases, the cost of production decreases.

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If the taco truck were to sell its tacos for $1, it would earn a profit of $267. However, if they were to sell their tacos for $-1, they would incur a loss of $202.

[tex]x | -7x^2 + 32x + 240[/tex]

[tex]-1 | -7(-1)^2 + 32(-1) + 240 = 6 + 32 - 240 = -202[/tex]

[tex]0 | -7(0)^2 + 32(0) + 240 = 240[/tex]

[tex]1 | -7(1)^2 + 32(1) + 240 = -5 + 32 + 240 = 267[/tex]

The optimal price that the taco truck should sell its tacos for is $0. This is because when x is equal to 0, the value of the polynomial expression is at its highest point. This means that the taco truck will earn the most profit when they sell their tacos for $0.

However, it is important to note that this is not a realistic scenario and the taco truck would need to sell its tacos for a positive whole dollar amount.

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Based on given ratio of 10:11:9, the share for each person is as follows:

Ratio is the relative size of one value or variable compared to another.

Ratios show how much each quantity is contained in another.

Ratios are fractional values obtained as the quotient of one value divided by another, and are depicted in fractions, decimals, or percentages.

The total shareable amount =  £300

The sharing ratio = 10:11:9

The sum of ratios = 30

Simon's share =  £100 (10/30 x  £300)

Sarah's share =  £110 (11/30 x  £300)

Matthew's share =  £90 99/30 x  £300)

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The solution of the initial value problem is [tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}[/tex].

Initial value issues are a specific kind of calculus issue. Calculus initial value issues include differential equations with a known beginning condition that identifies the function's value at a certain point. Finding the function that best describes the system is the goal of these puzzles, and this can be accomplished by integrating the differential equation.

There is always an unknown constant present when doing an integration with an indeterminate integral or without initial conditions. The constant of integration is what is commonly indicated by the letter C.

Given that the initial value problem is:

dy/dt= e^(y-t) sec(y)(1+t2)

This can be re written as follows:

dy/ dt = e^(y-t) (1 + t^2) / sec (y)

Separate the derivative in terms of y and t and take integration:

[tex]\int{e^{-y}cos(y)} \, dy = \int {e^{-t}(1 + t^2)} \, dt[/tex]

Integrate the following:

[tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + c\\[/tex]

The initial conditions given are y(0) = 0, substitute the value of the variables as 0:

[tex]\frac{e^{0}}{2} [sin0 - cos0] = -e^{0} [0^2 + 2(0) + 3] + c\\\\\\\frac{1}{2} [-1] = 3 + c[/tex]

c = 5/2

Hence, the solution of the initial value problem is:

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#SPJ4[tex]\frac{e^{-y}}{2} [siny - cosy] = -e^{-t} [t^2 + 2t + 3] + \frac{5}{2}[/tex]

The age of the automobile and the odometer reading will be in direct proportion and both variables will have a strong positive correlation.

The age of automobiles indicates the lifetime of the Automobiles from their manufacturing day to the present workday. For example, if the car was made in 2010 and working till 2020 then the age of the car will be 10 years.  

Odometer is a machine or instrument which is used to calculate the distance traveled by a vehicle in its lifetime. The reading of the Odometer shows the distance covered by the car in the number of milages.  

Here the more age of the automobile increases the more the distance covered by the automobile will increased hence the reading of the Odometer will increase.

As we know in mathematics, if two quantities are in relation such as one quantity is increased then the other quantity will also increase then two quantities are said to be in Direct proportion.      

So here we can conclude that the age of the automobile and the odometer reading will be in direct proportion Since both are increases both variables will have a strong positive correlation.

Therefore,

The age of the automobile and the odometer reading will be in direct proportion and both variables will have a strong positive correlation.

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The formula (y2y1)/(x2x1)  (y 2y1)/(x 2x1) can be used to determine the constant rate of change.

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Based on the information provided the coordinates would be

To know her sequence, let's apply the rule given"Add 1, then multiply by 3"

2 + 1 = 3 x 3 = 9

3+1 = 4 x 3 =12

4 +1 = 5 x 3 =14

5 + 1 = 6x3 = 18

Let's apply the rule given "Add 2, then multiply by 2"

2+ 2 = 4x2= 8

3+2= 5x2= 10

3+3= 6x 2= 12

4+3=7x 12 = 14

Based on this, the coordinates are (2,2), (9,8), (12,10), (14,12), (18,14).

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11. The measure of ∠EBF = 20°

12. The measure of ∠DBE = 32°.

13. The measure of ∠GBC = 56°.

What is the angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that m∠EBF = 60°, m∠EBG = 2m∠EBF

The m∠EBF is the sum of the angles and the angles are m∠EBG and m∠EBF.

Therefore,

m∠EBF =  m∠EBG + m∠EBF

Putting m∠EBF = 60° and m∠EBG = 2m∠EBF in aboue equation:

60° =  2m∠EBF + m∠EBF

3m∠EBF = 60°

Divide both sides by 3:

∠EBF = 20°.

12.

Given that, m∠ABE = 64°.

From the diagram, m∠ABD = m∠DBE.

The m∠ABE is the sum of the angles and the angles are m∠ABD and m∠DBE.

m∠ABE = m∠ABD + m∠DBE

64° = 2m∠DBE

Divide both sides by 2:

m∠DBE = 32°

13.

Given that, m∠GBH = 28°.

From the diagram, m∠GBH = m∠HBC.

m∠HBC = 28°.

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For the function P = 3x + y, there is no solution present to maximize it.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given objective function -

P = 3x + y

Subjected to the constraints -

5x + 7y ≥ 35

3x + 4y ≤ 12

x ≥ 0, y ≤ 0

First consider the inequality 5x + 7y ≥ 35.

The equation of the above inequality is as follows -

5x + 7y = 35

Find two points that satisfies the above equation.

Take x = 0, then -

5(0) + 7y = 35

7y = 35

y = 5

The first point is (0,5).

Take y = 0, then -

5x + 7(0) = 35

5x = 35

x = 7

The second point is (7,0).

Substitute (x,y) = (0,0) and see the direction of the region for 5x + 7y ≥ 35.

5(0) + 7(0) ≥ 35

0 ≥ 35

This is not true.

Therefore, the region is non-origin side.

Now consider the inequality 3x + 4y ≤ 12.

The equation of the above inequality is as follows -

3x + 4y = 12

Find two points that satisfies the above equation.

Take x = 0, then -

3(0) + 4y = 12

4y = 12

y = 3

The first point is (0,3).

Take y = 0, then -

3x + 4(0) = 12

3x = 12

x = 4

The second point is (4,0).

Substitute (x,y) = (0,0) and see the direction of the region for 3x + 4y ≤ 12.

3(0) + 4(0) ≤ 12

0 ≥ 12

This is true.

Therefore, the region is origin side.

Plot the graph.

From the graph it can be seen that there are no corner points and no feasible region.

Therefore, there is no solution for the function.

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So, Ethan gets $38 and Enoch gets $95.

We can find the amount each boy gets by using the ratio to find how much of the total $133 reward belongs to each.

Since the ratio is 2:5, this means that for every 7 parts, 2 of those parts belong to Ethan and 5 of them belong to Enoch.

So, if we divide the total reward of $133 into 7 equal parts, each part would be $133 / 7 = $19.

Since Ethan is entitled to 2 parts of the reward, he would get $19 x 2 = $38.

And since Enoch is entitled to 5 parts of the reward, he would get $19 x 5 = $95.

So, to summarize:

Ethan gets $38

Enoch gets $95

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So, Ethan gets $38 and Enoch gets $95.

We can find the amount each boy gets by using the ratio to find how much of the total $133 reward belongs to each.

Since the ratio is 2:5, this means that for every 7 parts, 2 of those parts belong to Ethan and 5 of them belong to Enoch.

So, if we divide the total reward of $133 into 7 equal parts, each part would be $133 / 7 = $19.

Since Ethan is entitled to 2 parts of the reward, he would get $19 x 2 = $38.

And since Enoch is entitled to 5 parts of the reward, he would get $19 x 5 = $95.

So, to summarize:

Ethan gets $38

Enoch gets $95

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