tickets for admission to a high school football game cost $3 for students and $5 for adults. During one game, $2995 was collected from the sale of 729 tickets. Write and solve a system of linear equations to find the number of tickets sold to students and the number of tickets sold to adults.

The probability of selecting either a multiple of 4 or a multiple of 5 is [tex]\frac{11}{25}[/tex] or 0.44

Solution:

Given that, A number is chosen at random from 1 to 50

selecting either a multiple of 4 or a multiple of 5

Sample space is given as:

{ 1, 2, 3, ................, 50 }

Muliples of 4 = 4, 8, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52

Favorable outcomes = 12

Muliples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Favorable outcomes = 10

The probability is given as:

[tex]Probability = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}[/tex]

[tex]probability = \frac{12}{50} + \frac{10}{50}\\\\probability = \frac{12+10}{50}\\\\probability = \frac{22}{50}\\\\probability = \frac{11}{25} \text{ or } 0.44[/tex]

Thus probability of selecting either a multiple of 4 or a multiple of 5 is [tex]\frac{11}{25}[/tex] or 0.44

The probability of selecting either a multiple of 4 or a multiple of 5 is 11/25.

A multiple of a number is the product of an integer and that number.

The first step is to determine the numbers that are a multiple of 4. They are  4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48.  There are 12 numbers.

The second step is to determine the numbers that are a multiple of 5. They are : 5, 10 15, 20, 25, 30, 35, 40, 45, 50. There are 10 numbers.

Probability of picking a multiple of 4 or 5 = 12/50 + 10/50 = 22/50 = 11/25

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Step-by-step explanation:

[tex]cos \: x = sin \: (2x + 57) \\ \\ \therefore \: sin(90 \degree - \: x) = sin \: (2x + 57) \\ \\ \therefore \:90 - \: x = 2x + 57 \\ \\ 90 + 57 \: = 2x + 3 \\ \\ \therefore \:3x = 147 \\ \\ \therefore \: x = \frac{147}{3} \\ \\ \huge \orange{ \boxed{\therefore \: x = 49 \degree}}[/tex]

Check the picture below.

well, then we know that (3x-5) + (4x+10) = 180, so

[tex]\bf (3x-5)+(4x+10)=180\implies 7x+5=180\implies 7x=175 \\\\\\ x = \cfrac{175}{7}\implies x = 25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{~\hfill \measuredangle BEC}{3x-5\implies 3(25)-5\implies 70} \\\\\\ \stackrel{~\hfill \measuredangle ABE}{180 - (x-5)\implies 180-(25-5)\implies 180-20\implies 160}[/tex]

Answer:

5/12

Step-by-step explanation:

Answer

pi*R^2

Step-by-step explanation:

Answer:

Pi feet squared

Step-by-step explanation:

area of circle formula is pi radius squared substitute radius as 1²

Answer:

391

Step-by-step explanation:

product of 49and 13= 49x13

sum of 92 and 164 =92+164

the difference of them =

49x13-(92+164)

=49x13-256

=637-256

=381

It will take 3 hours 6 minutes 40 seconds for the cars to be 420 miles apart.

Step-by-step explanation:

Step 1; The cars are traveling in the opposite direction at different speeds. One is going north at a speed of 75 mph while the other is going 60 mph. So for every hour, the cars are traveling they increase the distance between in between themselves by 75 miles + 60 miles = 135 miles.

Step 2; Assume that in x hours the distance between them is 420 miles. To calculate x we divide the distance to be traveled by the distance being traveled every hour.

x = distance to be covered / distance being traveled every hour

= 420 / 135 = 3.11 hours

We multiply the 0.11 hours with 60 to convert it into minutes. 0.11 × 60 = 6.66 minutes and if we do the same for seconds, 0.66 minutes × 60 = 40 seconds.

Answer:

The graph in option 3 will be the correct one.

Step-by-step explanation:

We have to choose the graph from the given options that shows the equation V = 4 + 2t, where V is the total volume of water in a bucket and t is the elapsed time in minutes.

Now, the graph in option 3 will be the correct one.

On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). A straight line with a positive slope begins at point (0, 4) and ends at point (6, 16). (Answer)

Answer:

C

Step-by-step explanation:

Answer:

y=3

Step-by-step explanation:

Step 1: Subtract from both sides

3y+39-16y=16y-16y

-13y+39=0

Step 2: Subtract 39 from both sides

-13y+39-39=0-39

-13y=-39

Step 3: Divide Both sides by -13

-13y/-13=-39/-13

y=3

Numbers are 4 and 8

Step-by-step explanation:

Step 1:

Let the numbers be x and y. Given that their sum is 12 and difference is 4. Form equations for this data.

⇒ x + y = 12 ------ (1)

⇒ x - y = 4 -------- (2)

Subtract eq (2) from (1)

⇒ 2x = 8

⇒ x = 4

Step 2:

Find y.

⇒ y = 12 - x = 12 - 4 = 8

Answer:

[tex]9x^{5}y^{5}[/tex] yards.

Step-by-step explanation:

Given that the area of a rectangle (A) is [tex]45x^{8}y^{9}[/tex] square yards.

If the length of the rectangle (L) is given to be [tex]5x^{3}y^{4}[/tex] yards, then we have to find the width (W) of the rectangle in yards.

Now, A = L × W

⇒ [tex]W = \frac{A}{L} = \frac{45x^{8}y^{9}}{5x^{3}y^{4}} = (\frac{45}{5})\times (\frac{x^{8}}{x^{3}}) \times (\frac{y^{9}}{y^{4}}) = 9x^{8 - 3}y^{9 - 4} = 9x^{5}y^{5}[/tex] yards. (Answer)

Answer:

1161/100

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

40 x 76 is the equation by 4x4 of 86 and the 36

Answer:28×5=$140.00

Step-by-step explanation:

The ball reaches the ground after 7.76 s

Step-by-step explanation:

The motion of the ball along the vertical direction is a free fall motion, which is affected by the force of gravity only; therefore it is a uniformly accelerated motion (=constant acceleration), so we can use the following suvat equation:

[tex]s=ut-\frac{1}{2}gt^2[/tex]

where

s is the displacement

u is the initial vertical velocity

[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity

t is the time

In this problem,

u = 38 m/s

Also, we want to find the time t at which the ball hits the ground again: so, when the displacement becomes zero again,

s = 0

Therefore the equation becomes:

[tex]0=38t-\frac{1}{2}9.8t^2\\0=38t-4.9t^2[/tex]

And solving for t,

[tex]t(38-4.9t)=0[/tex]

we have two solutions:

t = 0 (instant at which the ball is kicked)

[tex]38-4.9t=0\\t=\frac{38}{4.9}=7.76 s[/tex]

which is the solution to the problem.

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Answer:

  B.  T<-4, -2>, r(90°, O)

Step-by-step explanation:

Point A' is 4 units left and 2 units down from point A, so the translation is T<-4, -2>.

Segment C"D" is on the -x axis, 90° counterclockwise from segment C'D' on the +y axis. Since rotation angles are measured the same way other angles are measured (positive is CCW), the rotation is +90° about the origin.

The congruence transformation that maps the quadrilateral ABCD to A''B''C''D'' is [tex]T_{ < -4, \, -2 > } \circ T_{90^{\circ}}, origin > (ABCD)[/tex] which corresponds with the option B.

B. [tex]T_{ < -4, \, -2 > } \circ T_{90^{\circ}}, origin > (ABCD)[/tex]

A congruent transformation, which is also a rigid transformation is one in which the size and shape of the original figure is preserved.

The coordinates of the vertices of the quadrilaterals ABCD and A'B'C'D' indicates that the transformation from the quadrilateral ABCD to the quadrilateral A'B'C'D' is a translation of 4 units to the left and 2 units downwards, which can be expressed as T<-4, -2>

The side D'C' in the quadrilateral A'B'C'D' is vertical while the side D''C'' in the quadrilateral A''B''C''D'' is horizontal and due to the order of the letters D'' and C'' in D''C'' arranged from left to right suggesting a 90° counterclockwise rotation about the origin, which is a T90°, origin

The congruence transformation that maps ABCD to A''B''C''D'' therefore is the option B, [tex]T_{ < -4, \, -2 > }\circ T_{90^{\circ}}, origin > (ABCDE)[/tex]

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Answer:

y = -3x + 3

Step-by-step explanation:

Parallel lines have the same slope.

The given line has a slope of -3, its parallel line will also have a slope of -3... m = -3

y = -3x + c

When x = 1, y = 0

0 = -3(1) + c

c = 3

y = -3x + 3

Answer:

  all non-negative real numbers, [0, ∞)

Step-by-step explanation:

Replacing x in the parent function √x with (x+5) shifts the graph horizontally, but has no effect on the vertical extent of the graph. It still ranges from 0 to +∞.

The range of √(x+5) is [0, ∞).

x - 2y = -4 is the standard form of equation

Solution:

Given equation is:

[tex]y = \frac{1}{2}x + 2[/tex]

We have to write the equation in standard form

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

From given,

[tex]y = \frac{1}{2}x + 2[/tex]

Simplify the above equation

[tex]y = \frac{x+4}{2}\\\\2y = x + 4[/tex]

Shift the variable terms to the left side of the equation and everything else to the right side

[tex]x - 2y = -4[/tex]

Thus the standard form of equation is found

Answer :after four years the price of car depreciate

Final answer:

It will take approximately 4 years for the car to depreciate to $4520 using the declining-balance method of depreciation with a depreciation rate of 30%.

Explanation:

To calculate the number of years it would take for the car to depreciate to $4520, we can use the declining-balance method of depreciation. The declining-balance method is based on a fixed percentage of the remaining value of the asset. In this case, the rate of depreciation is 30%, so the car's value will decrease by 30% each year.

Let's start by finding the value of the car after one year. We can use the formula:

Value after one year = Initial value - (Rate of depreciation * Initial value)

Plugging in the values, we get:

Value after one year = $18820 - (0.3 * $18820) = $18820 - $5646 = $13174

Now, let's find the value after the second year:

Value after two years = $13174 - (0.3 * $13174) = $13174 - $3952.2 = $9221.8

We continue this process until we reach a value of $4520. By the time the car's value reaches $4520, it will have taken approximately 4 years.

Answer:

1 13/32

Step-by-step explanation:

Answer:

Option B, y = 4.6x + 5.2

Step-by-step explanation:

Slope-intercept form:  y = mx + b

Step 1:  Use those two points to get slope

m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

m = [tex]\frac{42 - 19}{8 -3}[/tex]

m = [tex]\frac{23}{5}[/tex]

m = 4.6

Step 2:  Find the y - intercept

Use point slope formula:  (y - y1) = m(x - x1)

(y - 19) = 4.6(x - 3)

y - 19 + 19 = 4.6x - 13.8 + 19

y  = 4.6x + 5.2

Answer:  Option B, y = 4.6x + 5.2

[tex]$-\frac{1}{2}\cdot2=-1[/tex]

Slope of the line h is 2.

The equation for line h is y = 2x + 4.

Solution:

General equation of a line is y = mx + c,

where m is the slope of the line and c is the y-intercept.

In the given image, line g and line h are intersecting lines and perpendicular to each other.

Equation of line g is [tex]y=-\frac{1}{2} x+2[/tex].

Slope of the line g ([tex]m_1[/tex]) = [tex]-\frac{1}{2}[/tex]

If two lines are perpendicular, then the product of the slopes is –1.

⇒ [tex]m_1 \cdot m_2=-1[/tex]

To find the slope of the line h:

[tex]$\Rightarrow-\frac{1}{2} \cdot m_2=-1[/tex]

[tex]$\Rightarrow m_2=-1 \times(-2)[/tex]

[tex]$\Rightarrow m_2=2[/tex]

Slope of the line h is 2.

To find the equation of a line h:

Line h passing through the point (0, 4) and slope 2.

Point-slope formula:

[tex]\left(y-y_{1}\right)=m\left(x-x_{1}\right)[/tex]

[tex]\left(y-4)=2\left(x-0\right)[/tex]

[tex]y-4=2x[/tex]

[tex]y=2x+4[/tex]

The equation for line h is y = 2x + 4.

The system of equations representing the amounts of Drink A and B made by the company is 1) a = b + 30 and 2) 0.20a + 0.15b = 100.5, where a is the amount in liters of Drink A and b is the amount in liters of Drink B.

Let's denote the number of liters of Drink A by the variable a and the number of liters of Drink B by the variable b. Based on the information given, we can establish a system of two equations in two variables that express the relationships between a and b. The first equation is a = b + 30, expressing the fact that the company makes 30 more liters of Drink A than Drink B.

The second equation is 0.20a + 0.15b = 100.5, which expresses the fact that the sum of 20% of a (the amount of real fruit juice in Drink A) and 15% of b (the amount of real fruit juice in Drink B) equals the total amount of real fruit juice used by the company, which is 100.5 liters.

So the system of equations is:

1) a = b + 30

2) 0.20a + 0.15b = 100.5

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To determine the number of liters of Drink A and Drink B made, we can set up a system of equations using the given information.

To write a system of equations, we need to define the variables that represent the number of liters of Drink A and Drink B. Let's use:

A = number of liters of Drink A made

B = number of liters of Drink B made

From the given information, we can create the following equations:

A = B + 30 (since there are 30 more liters of Drink A than Drink B)

0.20A + 0.15B = 100.5 (since the company used 100.5 liters of real fruit juice)

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Answer:

Step-by-step explanation:

4 A + 7K= $83

5 A + 7 K= +7= $90

It means one adult ticket costs 7 more than a kid ticket. If I replace A with K+7 in equation one,  it'll look like

4(K+7) + 7 K= $83

=> 4 K +28+ 7 K= $83

=> 11 K= 83-28= 55

K=5

A= 12

Answer:

The ball would be at its peak at 8 feet from the basket.

Step-by-step explanation:

The basketball should be at its maximum height when it is 10 feet away from the player.

We have,

In a standard basketball shot, the path of the ball follows a parabolic arc. The maximum height is reached at the peak of this arc, which occurs halfway between the player and the basket.

The distance at which the basketball should be at its maximum height is half the distance between the player and the basket.

Half of 20 feet is 10 feet.

Therefore,

The basketball should be at its maximum height when it is 10 feet away from the player.

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The correct inequality among the given options is -a > -c. Thus, option A is correct.

To determine the correct inequality among the given options, we need to compare the values of the variables a, b, and c in the number line.

Given: a = -4, b = 1, and c = 7

Let's evaluate each option:

A. -a > -c:

Substituting the values, we have -(-4) > -(7), which simplifies to 4 > -7.

This is true.

B. -a < -b:

Substituting the values, we have -(-4) < -(1), which simplifies to 4 < -1.

This is false.

C. a > 0:

Substituting the value, we have -4 > 0. This is false since -4 is not greater than 0.

Based on the comparisons, the correct inequality is A. -a > -c.

Therefore, the correct answer is A. -a > -c.

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Answer:

The length of an edge of the cube = x = [tex]\sqrt[3]{1000}[/tex] = 10 feet

Step-by-step explanation:

i.) A cube has a volume of 1000 cubic feet.

ii) A cube has edges which are all the same length, let us say that the length of an edge of the cube = x feet.

iii) therefore the volume of the cube is = [tex]x^{3}[/tex] = 1000 cubic feet

iv) therefore the length of an edge of the cube = x = [tex]\sqrt[3]{1000}[/tex] = 10 feet

Final answer:

The length of an edge of a cube with a volume of 1000 cubic feet is 10 feet. If each smaller cube has linear dimensions one tenth those of the larger cube, then the volume of each smaller cube is 1 cubic foot.

Explanation:

The volume of a cube is calculated by raising the length of one of its edges to the power of three (cubing it). Since we know the volume of the cube is 1000 cubic feet, we can determine the length of an edge by finding the cube root of the volume. The cube root of 1000 cubic feet is 10 feet, so the length of an edge of the cube is 10 feet.

To find the volume of the smaller cubes mentioned, we note that if their dimensions are one tenth of the larger cube, then each side of a smaller cube will be 10 feet divided by 10, which is 1 foot. The volume of each small cube is then 1 foot cubed, which is 1 cubic foot.

For a visual reference, imagine a larger cube divided evenly into smaller cubes, where the length of each side of the big cube is ten times that of the smaller ones. The result is that each smaller cube's volume is the original volume divided by the cube of 10 (since there are 10 layers of small cubes along each dimension of the big cube).

Answer:

x = 5

Step-by-step explanation:

Given

2x - 2 + 5 = 13, that is

2x + 3 = 13 ( subtract 3 from both sides )

2x = 10 ( divide both sides by 2 )

x = 5

Answer:

(-1/2,2)

Step-by-step explanation:

2(4x+y=0)=8x+2y=0

8x+2y=0

-(8x-y=6)

3y=6

Divide both sides y=2

4x+2=0

4x=-2

divide both sides x=-1/2

To solve the system of equations, we can use the matrix tool. The solution to the system of equations is (1, 1.5) as an ordered pair.

To solve the system of equations using matrices, you can represent the coefficients and constants as matrices and then use matrix operations. The system of equations can be represented in matrix form as:

[A] [X] = [B],

Where:

[A] is the coefficient matrix,

[X] is the variable matrix (containing x and y),

[B] is the constant matrix.

For the given system of equations:

4x + y = 0

8x - y = 6

The coefficient matrix [A], variable matrix [X], and constant matrix [B] are:

[A] = [[4, 1],

[8, -1]]

[B] = [[0],

[6]]

Now, to solve for [X], you can use matrix multiplication:

[A] [X] = [B]

[X] = [A]⁻¹ [B]

First, calculate the inverse of [A]:

[A]⁻¹ = [[-1/12, -1/12],

[1/4, 1/4]]

Now, multiply [A]⁻¹ by [B]:

[X] = [[-1/12, -1/12],

[1/4, 1/4]] [0, 6]

[tex][X] = [(-1/12 \times 0 + -1/12 \times 6),[/tex]

[tex](1/4 \times 0 + 1/4 \times 6)][/tex]

Simplify:

[X] = [-(-1), 1.5)]

[X] = [1, 1.5]

So, the solution to the system of equations is (1, 1.5) as an ordered pair.

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Answer:

14

Step-by-step explanation:

Answer: Area = 14 [tex]units^{2}[/tex]

Step-by-step explanation:

The formula for calculating the area of Triangle is given by :

Area = [tex]\frac{1}{2}[/tex] x base x height

From the given triangle

base = 4

height = 7

substituting into the formula

Area = [tex]\frac{1}{2}[/tex] x 4 x 7

Area = [tex]\frac{1}{2}[/tex] x 28

Area = 14 [tex]units^{2}[/tex]