Contestants in a dance-a-thon rest for the same amount of time every hour. A couple rests for 25 minutes in 5 hours. How long did they rest in 8 hours?

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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Answer:

11/15

Step-by-step explanation:

Answer:

30.7

Step-by-step explanation:

sin 71° = 29/ ladder length

so length = 29/ sin 71° = 30.7

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

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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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:

The perimeter of the floor in the scale drawing is 30 inches.

The ratio of length and width of floor of classroom will be same as the ratio of scale drawing. Therefore, representing the formula for ratio -

length/width (floor) = length/width (scale drawing)

32/28 = 16/width

Converting the original measurement to inches

1 foot = 12 inches

Length = 384 inches

Width = 336 inches

Rearranging the equation according to width of scale drawing

Width = (16 × 336)/384

Performing multiplication and division on Right Hand Side of the equation

Width = 14 inches

Thus, the width is 14 inches

Now, perimeter = 2(length + width)

Perimeter = 2 (16 + 14)

Perimeter = 2 × 30

Perimeter = 60 inches

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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

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.

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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Multiplication of given polynomials = x³ + 3x² - 22x - 2

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer.

Given,

(x + 6) ( x ^2 - 3x - 4)

Using distributive property

x( x ^2 - 3x - 4) + 6( x ^2 - 3x - 4)

Again using distributive property

x³ - 3x² - 4x + 6x² - 18x - 24

Adding like terms

x³ + 3x² - 22x - 2

Hence, x³ + 3x² - 22x - 24 is multiplication of given polynomials.

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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:

Step-by-step explanation:

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

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

X-intercept: 8/2 = 4

Y-intercept: 8/-4 = -2

X-intercept: -5/4

Y-intercept: -5/1 = -5

X-intercept: -14/14 = -1

Y-intercept: -14/-7 = 2

X-intercept: 10/2 = 5

Y-intercept: 10/6 = 5/3

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.

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

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;

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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Answer: 2/21

Step-by-step explanation:

2/3x6-3+5/3x3

2/18-3+5

2/21

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

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

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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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.

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:

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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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.

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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Answer:

d

Step-by-step explanation:

the sum of the interior angles in a quadrilateral = 360°

sum the angles and equate to 360°

x + 40° + 90° + 127° = 360°

x + 257° = 360° ( subtract 257° from both sides )

x = 103°

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.

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

D. t > 20 or t < 10.

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:

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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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

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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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)

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!

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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