Neal buys a board game. He pays for the board game and pays \$1.54$1.54dollar sign, 1, point, 54 in sales tax. The sales tax rate is 5.5\%5.5%5, point, 5, percent.
What is the original price of the board game, before tax?

Answers

Answer 1

The original price of the board game for which Neal pays $1.54, which includes a sales tax on the original price of 5.5% (5.5 percent) is about $1.46

What is a percentage?

A percentage is a proportion or rate of an item within a set of items per one hundred (100) units of the set of items.

Percentages indicates the proportion of an item to be selected or received, such that percentage of each item within a set of items can be easily calculated.

The amount Neal pays for the board game = $1.54

The sales tax rate for the purchase = 5.5%

The sales tax is the percentage amount of an original price, each buyer pays when purchasing an item, and which is collected for the government agency by the seller of the item.

The original price of the board game can be found as follows;

Let x represent the original price of the board game, we get;

Therefore, we get;

x + 5.5% of x = 1.54

(1 + 0.055) × x = 1.54

1.055 × x = 1.54

x = 1.54/1.055 ≈ 1.46

The original sale price of the board game is about $1.46

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Related Questions

Brianna wants to buy a digital camera for a photography class. One store offers the camera for $60 down and a payment plan of $10 per month. The payment plan for a second store is described by y 20x + 60, where y is the total cost in dollars and x is the number of months. Which camera is cheaper when the camera is paid off in 12 months? Explain.
Please show your work! I will give brainliest answer quick

Answers

The cost of the camera in the first store is cheaper as the downpayment is the same for both stores but the monthly payment is cheaper in the first store.

What is a linear equation?

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

The total cost for the first store is,

y = 10(12) + 60.

y = 120 + 60.

y = $160.

The total cost for the second store is,

y = 20(12) + 60.

y = 240 + 60.

y = $300.

So, The first store is cheaper.

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PLEASE HELP
Which of the following are solutions to the equation below?
CHECK ALL THAT APPLY.

(image attched

Answers

The solutions to the quadratic equation are;

[tex]x = \frac{ \sqrt{10} + 5 }{2} [/tex]

[tex]x = \frac{ - \sqrt{10} + 5 }{2} [/tex]

The correct answer choice is option A and E

How to solve quadratic equation using formula?

4x² - 20x + 25 = 10

Equate the equation to 0

4x² - 20x + 25 - 10 = 0

4x² - 20x + 15 = 0

Solve the quadratic equation using formula

[tex]4x^2 - 20x + 15 = 0[/tex]

using Quadratic Formula where,

a = 4,

b = -20, and

c = 15

[tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]

[tex]x = \frac{ -(-20) \pm \sqrt{(-20)^2 - 4(4)(15)}}{ 2(4) }[/tex]

[tex]x = \frac{ 20 \pm \sqrt{400 - 240}}{ 8 }[/tex]

[tex]x = \frac{ 20 \pm \sqrt{160}}{ 8 }[/tex]

[tex]x = \frac{ 20 \pm 4\sqrt{10}\, }{ 8 }[/tex]

[tex]x = \frac{ 20 }{ 8 } \pm \frac{4\sqrt{10}\, }{ 8 }[/tex]

[tex]x = \frac{ 5}{ 2 } \pm \frac{ \sqrt{10}\, }{ 2 }[/tex]

Therefore, the solution to the quadratic equation using formula is

[tex]x = \frac{ 5}{ 2 } \pm \frac{ \sqrt{10}\, }{ 2 }[/tex]

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The water level f, in feet, at a certain beach is modeled by the function
[tex]f(t)=2sin(2\pi t)/24[/tex], where is the number of hours since the level was measured.

What is the amplitude of the function? What does it mean in this context?
What is the period of the function? What does it mean in this context?
Sketch a graph of the function over 72 hours.

Answers

Answer:

1. Amplitude = 2 feet (max height level of water on the beach)

2. Periodicity = 24 hours (water level reaches 2 ft max every 24 hours or 0 feet minimum every 24 hours

3. Graph attached with explanation

Step-by-step explanation:

For a sine function, sin(x), the maximum value is 1 when x is π/2, 5π/2, 9π/2...

The minimum value is -1 at x = 0, π, 3π/2, 2π,...

a sin(x) will have the maximum value(amplitude) of |a · 1| = |a|

The given function is
[tex]f(t) = 2 \sin\left(\dfrac{2\pi t}{24}\right)\\\\\dfrac{2\pi t}{24} = \dfrac{\pi t}{12}\\\\\textrm{So the function is:}}\\\\f(t) = 2 \sin \left(\dfrac{\pi t}{12}\right)[/tex]

1. The amplitude is 2 and this is the maximum water level in feet at the beach. This occurs when [tex]\textstyle {\dfrac{\pi t }{12} = \dfrac{\pi}{2}}[/tex]

or, when t = 6. It repeats every 24 hours (see #2)

2. The periodicity of a function is when the function starts repeating itself

The periodicity of sin(x) is 2π i.e. the sinusoidal wave starts repeating itself every 2π radians

Since our sine function has πt/12 as its argument we have that
πt/12 = 2π

or t = 24

So every 24 hours, the water level which starts at 0 feet at 0 hours, becomes 0 again

3) Graph of the function attached. Note that water level cannot be negative which is the sine value from π/2 to 2π so we have to set it equal to 0

Water level goes to zero every 12 hours and stays at zero for 12 hours when it starts rising again.

As can be seen from the graph, every 24 hours, the water level reaches a peak height of 2 feet

I hope that this helps

A farmer operates a tractor on a farm to fertilize crops.



Suppose that shifting into third gear decreased the engine speed (rpm) while increasing the tractor speed (mph). What would be the effect of this change?


A. Both area rate and flow rate would increase.
B. Area rate would increase and flow rate would decrease.
C. Area rate would decrease and flow rate would increase.
D. Both area rate and flow rate would decrease.

Answers

The correct option regarding the area and the flow rate when the engine speed is decreased and the tractor speed is increased is given as follows:

B. Area rate would increase and flow rate would decrease.

How to obtain the effects of each change?

From the first table, when the tractor's speed increases, the area also increases, hence they are direct proportional and the area rate would decrease.

From the second table, when the engine's speed increases, the flow rate also increases, hence if the engine's speed decreases, the flow rate would also decrease, as the variables are also direct proportional.

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janissa has just purchased a new home the house was priced at 125,000, and she chose a 40 - year - mortgage at 5.2% what will her total cost be

Answers

The total cost for Janissa is given by the equation A = $ 297,312

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost for the home by Janissa be represented as A

Now , the equation will be

The initial cost of the house C = $ 125,000

The total number of payments n = 40 x 12

The total number of payments = 480 payments

The monthly rate i = 5.2 % / 12

The monthly rate i = 0.004333

Now , the monthly payment is M = C [ i ( 1 + i )ⁿ ] / [ ( 1 + i )ⁿ⁻¹ ]

Substituting the values in the equation , we get

Monthly payment M = 125000 [ ( 0.00433 ) ( 1.00433 )⁴⁸⁰ ] / [ 1.00433 )⁴⁷⁹ ]

On simplifying the equation , we get

Monthly payment M = $ 619.40

Now , the total cost of the house A = total number of payments x Monthly payment M

Substituting the values in the equation , we get

The total cost of the house A = 480 x 619.40

The total cost of the house A = $ 297,312

Hence , the equation is A = $ 297,312

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PLEASE HELP Determine the x and y intercepts for each indicated line.
1. 2x-4y=8
2. 4x+y= -5
3. 14--7y=-14
4. 2x+6y=10

Answers

Answer:

x = -2/3

y = -7/3

Step-by-step explanation:

2x-4y=8

4x+y= -5

Times the first equation by -2

-4x + 8y = -16

4x + y = -5

9y = -21

y = -7/3

Now put -7/3 back in for y and solve for x

4x - 7/3 = -5

4x - 7/3 = -15/3

4x = 8/3

x = -2/3

Answer:

x: 4, y: -2x: -5/4, y: -5x: -1, y: 2x: 5, y: 5/3

Step-by-step explanation:

You want the x- and y-intercepts of each of the given lines:

2x-4y=84x+y= -514x-7y=-142x+6y=10

Intercepts

The x-intercept is the x-value when y = 0. For an equation of the form ...

  ax +by = c

setting y = 0, we have ...

  ax = c

Solving for x gives ...

  x = c/a . . . . . x-intercept

Similarly, setting x=0 and solving for y gives the y-intercept:

  by = c

  y = c/b

1. 2x -4y = 8

X-intercept: 8/2 = 4

Y-intercept: 8/-4 = -2

2. 4x +y = -5

X-intercept: -5/4

Y-intercept: -5/1 = -5

3. 14x -7y = -14

X-intercept: -14/14 = -1

Y-intercept: -14/-7 = 2

4. 2x +6y = 10

X-intercept: 10/2 = 5

Y-intercept: 10/6 = 5/3

Emilia and Miranda are sisters and their mother just signed them up for a new cell phone plan because they send too many text messengers Using I formation below detriment which sister sends the most text messages how many more text messengers does this sister send per week

Answers

254 because that is the messages that the sisters send

Tenesha is trying to draw a parallelogram and find its area using the two line segments shown.

On a coordinate plane, 2 line segments are formed by points (1, 5), (5, 2), (12, 2).

She begins by finding the missing vertex on the graph to be point (9, 5). Then she calculates the area of the parallelogram. What errors did she make? Check all that apply.


On a coordinate plane, a parallelogram is formed by the points (1, 5), (5, 2), (12, 2). and fourth point unlabeled. A = (8) (5). A = 40.
She did not find the correct vertex; it should be at (8, 5).
She used the wrong area formula; it should be A = one-half b h.
She used the wrong length for the base; it should be 7, like the given base.
She used a side length of the parallelogram for the height instead of a line segment perpendicular to the base; the height should be 3.
She should have found a segment for the top that was not parallel to the bottom.

Answers

The errors she made are She did not find the correct vertex; it should be at (8, 5) and She used the wrong area formula; it should be A = one-half b h, the incorrect options are B and C.

What is standard error?

Error is an estimate of the standard deviation of the sampling distribution. It measures the variability of a considered sample statistic.

Supopse that we're given that:

Population standard deviation =[tex]\sigma[/tex]

Size of sample we're working on = n

Then, the standard error can be calculated as:

[tex]SE = \dfrac{\sigma}{\sqrt{n}}[/tex]

where SE denotes the standard error.

Given;

On a coordinate plane, 2 line segments are formed by points (1, 5), (5, 2), (12, 2).

She begins by finding the missing vertex on the graph to be point (9, 5).

Now,

The parallelogram is a simple quadrilateral with two parallel pairs of sides; The opposite or reverse sides of the parallelogram are of similar duration and the reverse angles of the parallelogram are of equivalent proportion;

The square has two sets of parallel sides, four right angles, and the four sides are identical. It's even a triangle and a parallelogram;

The rhombus is known as a four-sided parallelogram;

Therefore, the error will be in B and C.

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Evaluate 2 over 3 times 6 minus 3 plus 5 over 3 times 3

Answers

Answer: 2/21

Step-by-step explanation:

2/3x6-3+5/3x3

2/18-3+5

2/21

Let x = 120°. What is the second coterminal angle for x that is less than -500°?

Answers

The second coterminal angle for x = 120° that is less than -500° is -620°.

What is angle?

Triangle is geometric figure that can be described as the amount of rotation between two straight line or planes and angle is measured in degree with a full circle being 360° the most common type of angle are the right angles 90° acute angles are less than 90°. Anglican also be classified as either complementary or supplementary depending on how they relate to each other.

Coterminal angles are angles that are the same distance from 0° but in the opposite direction. To find the second coterminal angle for x = 120° we subtract 360° from it. Thus, the second coterminal angle for x = 120° that is less than -500° is -620°.

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Start with the equation 0⋅3=0 to explain why −2⋅3 must equal −6.

Drag descriptions and equations to the table to complete the explanation.

Answers

To complete the explanation, the table needs the following explanations and equations, respectively: (-2 + 2)*3 = 0 Put the distributive property to use. Take 6 away from both sides. -2*3 = -6

How do equations work?

An equal sign is located between the two algebraic expressions to form an equation, which is a mathematical statement. It indicates that the left and right sides of the equation are equal. Mathematical operators, variables, symbols, and integers all appear in algebraic expressions.

The initial stage in this technique is to insert any real number its opposite, which is zero. These results;

(-2 + 2)*3 = 0

The following step is to get using distributive property;

-2*3 + 2*3 = 0

That this next is to remove 6 away from both corners to get at;

-2*3 = 0 - 6

Lastly, we distill to obtain;

-2*3 = -6

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stu dent has 8 different math books, 9 different science books and 14 different engineering books. find the number of ways to pick two books with different subjects.

Answers

The total number of ways to select two books which are of different subject from the given subjects books is equal to 310.

Total number of different Math's books are 8

Total number of different Science books are 9

Total number of different Engineering books are 14

Number of ways to select two books with different subject

= (One Math's One Science ) + (One Math's One Engineering ) +(One Engineering One Science )

= ⁸C₁⁹C₁ + ⁸C₁¹⁴C₁ + ⁹C₁¹⁴C₁

= [ 8! / (8 -1)!1! ]  [ 9! / (9 -1)!1! ] + [ 8! / (8 -1)!1! ]  [ 14! / (14 -1)!1! ] + [ 9! / (9 -1)!1! ]  [ 14! / (14 -1)!1! ]

= (8 × 9) + ( 8 × 14 ) + ( 9 × 14 )

= 72 + 112 + 126

= 310

Therefore, the number of ways to select two books of different subjects are 310.

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Eric and Jennifer both plan to run for a spot on the school board in their city. They must each collect a certain number of signatures to get their name on the ballot. So far, Eric has 20 signatures, but Jennifer just started and doesn't have any yet. Eric is collecting signatures at an average rate of 17 per hour, while Jennifer can get 19 signatures every hour. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How many signatures will they both have? How many hours will have gone by?

Answers

After 20 hours, Eric and Jennifer will each have 340 signatures.

We may begin by constructing an equation that solves for the number of signatures and the number of hours that have passed. Let's name the number of signatures "x" and the number of hours "h" respectively. Then there's:

20 + 17h Eric's signatures

Jennifer's signatures: 19h

We may put their signatures equal to each other because they will eventually have the same amount of signatures:

20 + 17h = 19h

We can now solve for h by removing h from one side of the equation. To begin, remove 19h from both sides:

20 = -h

Then we divide both sides by -1 to get h on its own:

h = 20

So, after 20 hours, Eric and Jennifer will have both gathered the same amount of signatures, which is:

Eric's autographs total 340 (20 + 17 * 20).

Jennifer has 19 * 20 = 380 signatures.

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Does the fact that YZ = WX lead to the proof that XYWZ is a parallelogram? Why or why not?

Answers

Answer:

C. Yes, if both pairs of opposite sides are congruent, they must also be parallel.

Step-by-step explanation:

a parallelogram means a quadrilateral with 2 pairs that are parallel. If one pair is congruent, that means that if it is parallel, the other pair must be congruent as well. That proof can be pretty complex to explain, but i hope this helps.

Answer:

Step-by-step explanation:

B. No; both pairs of opposite sides can be congruent without being parallel.

Pleeeeeeeease I need help answer this for me

Answers

Answer:B I’m not sure if it is correct

Step-by-step explanation:

2/5+1/3= using 15 as the  common denominator 

Answers

Answer:

11/15

Step-by-step explanation:

Which of the following transformations is shown in the graph below?

Answers

Answer:

Red-Blue: Translate 2 units down, and translate 5 units right.

Blue-Red: Translate 2 units up, and translate 5 units left.

Step-by-step explanation:

Hi, I don't know if you want to go from red to blue or blue to red, but I'll answer both ways.

Isabella recently opened her online candle shop, Spectacular Scents. Her sales in the first
week were $86. After advertising her new shop on social media, her sales increased by 20%
the following week and continued to increase at that rate.
Write an exponential equation in the form y = a(b)* that can model Isabella's weekly sales, y,
x weeks after opening her shop.
Use whole numbers, decimals, or simplified fractions for the values of a and b.

Answers

Answer:

Step-by-step explanation:

The required exponential equation that can model Isabella's weekly sales, y, x weeks after opening her shop is y = 86 * (1.20)ˣ.

What is an exponential function?

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Let's let the variable x represent the number of weeks after opening the shop, and let y represent the weekly sales in dollars. We know that in the first week, her sales were $86. After that, her sales increased by 20% each week. This means that her sales in the second week were,

We can see that her sales are increasing by a factor of 1.20 each week. This means that we can model her sales using an exponential equation of the form:

y = a * (1.20)ˣ

Where a is the amount of the initial sales in the first week (which we know is $86).

So the exponential equation that can model Isabella's weekly sales, y, x weeks after opening her shop is:

y = 86 * (1.20)ˣ

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One of the primary goals of constructing a frequency distribution for quantitative data is to summarize:___________

Answers

One of the main goals of making a frequency distribution for quantitative data is to summarize the data in a way that properly depicts data as a whole.

A frequency distribution is a representation of the number of times each value or range of values appears in a set of data. By constructing a frequency distribution, we can get a better understanding of the distribution of values and the overall pattern of the data. This information can help us identify any outliers, the center or average of the data, and the spread or variability of the data.

Additionally, a frequency distribution allows us to compare different sets of data and make informed decisions based on the information presented. For example, if we compare the frequency distributions of two groups, we can determine if there are any significant differences between the two groups. This can be useful in various fields such as market research, psychology, and medicine.

In summary, the goal of constructing a frequency distribution is to summarize the information contained within the data and gain a better understanding of the distribution of values. This information can be used to make informed decisions and compare different sets of data.

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Write the expanded form of the expression.
3
(y+x)
3
(y+x)=[
(Simplify your answer. Use integers or fractions for any numbers in the expression.)

Answers

The expanded form of the expressions is 3y + 3x

What are algebraic expressions?

These are mathematical expressions that are composed of terms, variables, constants and  factors with coefficients,

These expressions are also known to include mathematical or arithmetic operations, such as;

ParenthesesBracketAdditionSubtractionMultiplicationFloor divisionDivision

They could also be made up of fractions and decimlals

We have the expression;

3(y + x)

expand the parentheses

3y + 3x

Hence, the expression is 3y + 3x

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SHOW WORK A snowboarder stands at the edge of a 4.50 m high half-pipe. The mass of the snowboarder is 55.0 kg. What is the gravitational potential energy of the snowboarder thanks

Answers

Answer:

Step-by-step explanation:

The gravitational potential energy (GPE) of an object with mass m at a height h above some reference level is given by the formula:

GPE = mgh

where g is the acceleration due to gravity (which is approximately 9.8 m/s^2 on Earth).

In this case, the snowboarder has a mass of 55.0 kg and is at a height of 4.50 m above some reference level (which is not specified). So the GPE of the snowboarder is:

GPE = (55.0 kg) x (9.8 m/s^2) x (4.50 m) = 2404.5 J

Therefore, the gravitational potential energy of the snowboarder is 2404.5 joules (J).

Answer:

2404.5

Step-by-step explanation:

In the figure below, m1 = (x+84)° and m2 = 2x°.
Find the angle measures.

Answers

Answer: The angle measures cannot be determined from the information given. The equation m1 = (x+84)° and m2 = 2x° only specify a relationship between two angles, but do not specify specific angle measures. To determine the angle measures, additional information or constraints are needed.

Step-by-step explanation:

Write the augmented matrix for the following system of equations 7-6y+8x=0, 6x=-3-2y

Answers

Augmented matrix is a matrix that is composed of the coefficients of the variables of a system of linear equations and the constants on the right side of the equal signs of the linear equation.

For the given system of equations, the augmented matrix is:

|  7  -6  8  |  0  |

|  6  -2  -3 | -3  |

The first row consists of the coefficients of the variables x and y, and the constant 0 from the equation 7-6y+8x=0.

The second row consists of the coefficients of the variables x and y, and the constant -3 from the equation 6x=-3-2y.

The augmented matrix can be written in a short form as:

|  7  -6  8  |  0  |

|  6  -2  -3 | -3  |

This augmented matrix can be used to solve the system of equations by using the Gaussian Elimination Method or the Gauss-Jordan Elimination Method.

The columns of two matrices are combined to create a new matrix, which is known as an augmented matrix. When using matrices to solve straightforward linear equations, the augmented matrix is a crucial tool. The number of variables in the linear equation is the same as the number of rows in the augmented matrix.

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Solve the problem.
The profit made when t units are sold, t > 0, is given by P-t2-30t+200. Determine the number of units to be sold in
order for P> 0 (a profit is made).
A) 20 B) t=30
t = 20 ort=10
(D) t>20 or t < 10

Answers

The number of units sold for a profit to be made is given as follows:

D. t > 20 or t < 10.

How to make a profit?

The quadratic function that models the earnings is given as follows:

P(t) = t² - 30t + 200.

The roots of the quadratic function are obtained as follows:

t² - 30t + 200 = 0

(t - 20)(t - 10) = 0.

Hence:

t - 20 = 0 -> t = 20.t - 10 = 0 -> t = 10.

A profit is made when P(t) > 0, and since P(t) is a concave up function, it is positive to the left of the smallest root and to the right of the largest root, hence the correct option is given by option D.

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need help pls
schoology

Answers

The box in the corner shows that this is a 90 degree angle so take 42 and subtract it from 90 in order to find out what the rest of the angle is which is 48 degrees
This graph displays a complementary angle, meaning all sides add to a sum of 90°. Given that one side equals 42°, we can subtract 90 - 42 to find that the measure of the missing angle is 48°.

solve the ineaquality. 5t+4≥19

Answers

First, subtract 4 from both sides:

[tex]5t\geq 15[/tex]

Now, divide both sides of the equation by 5 to isolate variable t:

[tex]t\geq 3[/tex]

Therefore, we know that t must be greater than or equal to 3 for this inequality to be true!

Solve for x !
[tex] \it( {5}^{2}x + 8(1x)) + 5(9x + 2) - 2[/tex]





Thank You!:)​

Answers

Step-by-step explanation:

(10x + 8x) +( 45x +10)- 2

18x + 45x + 10 - 2

63x + 10 - 2

71x

Step-by-step explanation:

18x + 45x+10-2

63x+8(unlike terms)

The students of three sections of a class have to stand n rows. Each row have equal number of students. If there are 36, 40 and 48 students are in three sections. Find the maximum number of students in each rows.

Answers

Answer:

24

Step-by-step explanation:

The total number of students in the three sections is 36 + 40 + 48 = 124.

To find the maximum number of students in each row, we need to divide the total number of students by the number of rows, rounded down to the nearest integer.

Let's call the maximum number of students in each row "x". Then, we can write the equation:

x * n = 124

To find the maximum value of x, we need to find the maximum value of n such that the result of x * n is less than or equal to 124.

Starting with n = 1, we can increment n and calculate x for each value of n until x * n is greater than 124.

For n = 1, x * n = 124, so x = 124.

For n = 2, x * n = 62, so x = 62.

For n = 3, x * n = 41, so x = 41.

For n = 4, x * n = 31, so x = 31.

For n = 5, x * n = 24.8, which is not an integer, so we round down to 24.

Therefore, the maximum number of students in each row is 24, with a total of 5 rows.

Answer:

Step-by-step explanation:

Let's call the maximum number of students in each row "r". To find this value, we need to divide the total number of students by the number of rows. To ensure that all the students can fit into the rows, the number of students in each section must be divisible by the number of rows.

First, we find the least common multiple (LCM) of the number of students in each section, which will be the total number of students if we arrange them in the same number of rows. The LCM of 36, 40, and 48 is 240.

Next, we divide the LCM by the number of students in each section to find the number of rows:

r = LCM / 36 = 240 / 36= 6.67 (rounded down to 6)

So, the maximum number of students that can be in each row is 24

(2 points) conditional probability. a fair coin is tossed twice. (a) (1 point) what is the probability of two heads if we know that the first toss is a head? (b) (1 point) what is the probability of two heads if we know that at least one toss is a head?

Answers

If we know that the first toss is a head, the probability of two heads is 1/2. The probability of two heads if we know that at least one toss is a head is 2/3.

(a) If we know that the first toss is a head, the probability of two heads is 1/2 because the second toss is still independent and has a 50% chance of being either heads or tails.

(b) If we know that at least one toss is a head, the probability of two heads can be found by adding up the probability of getting two heads on the first and second tosses and then getting heads on the first and tails on the second toss. This can be represented as:

P(two heads | at least one head) = P(two heads) / P(at least one head) = (P(heads on first and heads on second) + P(heads on first and tails on second)) / (1 - P(tails on first and tails on second))

Since each toss has a 50% chance of being heads, the probability of getting two heads on the first and second tosses is 0.5 × 0.5 = 0.25. The probability of getting heads on the first and tails on the second is also 0.5 × 0.5 = 0.25. And the probability of getting tails on both tosses is 0.5 × 0.5 = 0.25.

Therefore, the answer is:

P(two heads | at least one head) = (0.25 + 0.25) / (1 - 0.25) = 0.5 / 0.75 = 2/3

So the probability of two heads, if we know that at least one toss is a head, is 2/3.

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An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 29 feet up. The ladder makes an angle of 71∘
with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

Answers

Answer:

30.7

Step-by-step explanation:

sin 71° = 29/ ladder length

so length = 29/ sin 71° = 30.7

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