Solve the following literal equation for y. -5x+8y=15

a) In fractions the probability that a teenager selected at random is female and their favorite hobby is watching films is given as: 1/4, while

b) if  the teenager from the question above rejoins the group and another teenager is picked at random, the probability that the teenager picked at random is male and their favorite hobby is playing video games is 1/6.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

With regard to problem (a),

There is a total of 32 teenagers.

Of those, 8 are female with a favorite hobby of watching films.

Thus,

Related Probability = 8/32; divide both numerator and denominator by 8 to get;

= 1/4

With regard to problem (b), the probability that the teenager picked at random is male and their favorite hobby is playing video games is:

P = (14/32) x  (2/14)

P = 2/32; thus

P = 1/16.

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Full Question:

A group of teenagers are asked about their favourite hobbies. The results are shown in the following table: Sports Playing video games Watching films Total

Male 9 2 3 14

Female 7 3 8 18

Total 16 5 11 32

Q6a. In fractions, what is the probability that a teenager selected at random is female and their favorite hobby is watching films? You can simplify this fraction if you wish.

Q6b. the teenager from the question above rejoins the group and another teenager is picked at random what is the probability that the teenager picked at random is male and their favourite hobby is playing video games? you can simplify this fraction if you wish

Refer to the images attached. Please let me know if you have any questions regarding how I did things or why.

Yes, because it is a graph of a straight line with y = 1.625x, y changes for every value of x.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, Value set for x and y.

Since it asked if the given equation is linear or not

The general formula for the line:

y = mx +c

where,

m is slope

and c is constant

m = (y₂ - y₁)/(x₂ - x₁)

in our case

m = 26 - 13 / 16 -8

m = 13/8

Thus the equation of a line:

y = 13/8x + c

putting any of the given coordinates in the given equation:

c = 0

Thus, the equation of a line

y = 1.625x

Therefore, yes, y varies for every value of x since it is a graph of a straight line y = 1.625x

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Answer:

108 students

Step-by-step explanation:

Just multiply the amount of students in each group by the number of groups (6)(18)=108

so there are 108 students

Question 17

Opposite angles of a parallelogram are congruent, so [tex]3y+2=62 \implies y=20[/tex].

Adjacent angles of a parallelogram are supplementary, so [tex]62+5x+3=180 \implies x=23[/tex].

Question 18

Diagonals of a parallelogram bisect each other.

[tex]3y+9=2y+16 \implies y=7\\\\10x-24=5x-4 \implies x=4[/tex]

Answer:

x = [-3, 1]

Step-by-step explanation:

I wrote it in interval notation but if x can be any whole number between those two it can literally be -3, -2, 1, 0 or 1. Unless there are further restrictions or some sort of equation, there is no one number answer. Pick your poison, write it like x = {-3, -2, 1, 0, 1} if you'd like or the way I wrote it.

We will use the triple integral in cylindrical coordinates to calculate the integral across the surface of the box in the illustration.

The integral is given by:

[tex]∫∫∫ {ze}^{2x} + y dzdydx[/tex]

Where x, y, and z are the coordinates and the limits of integration are

[tex]0 <= x <= 2, 0 <= y <= 3, and 0 <= z <= {ze}^{2x} + y[/tex]

We can change the integral into cylindrical coordinates by using the following change of variables:

x = rcosθ

y = rsinθ

z = z

The integral becomes:

[tex]∫(0 to 2)∫(0 to 3)∫(0 to ze^(2r cosθ) + r sinθ) rze^(2r cosθ) + r^2sinθ dzdrdθ[/tex]

Although the integral is challenging to calculate, this method will assess it. The region of integration can be determined by knowing the bounds of z, which would be beneficial given that the box is in rectangular coordinates.

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The equation of the square coop is 4x = 20 and the length is 5yd .

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

20yd of fencing to build the walls of a square coop.

Therefore, the perimeter of the square coop is 20 yd .

Then the equation of the perimeter of the square coop is 4x = 20.

Solving the equation,

4x = 20

We get,

x = 5yd

The equation of the square coop is 4x = 20 and the length is 5yd .

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Answer: 61 cm.

Step-by-step explanation: The perimeter of any shape is the total distance of the exterior. This means that the sum of all side lengths of a shape is the perimeter. For a rectangle, the sum of both lengths and widths is the perimeter.

You can use the formula 2L+2W=P to solve this problem. 308 is P or the perimeter and 93 is L or the length. We can substitute these values and we get 2(93)+2(w)=308. We then subtract 2(93) or 186 from both sides to get 2W= 122. We then divide by two to get W or the width is equal to 61 cm.

A graph of triangle ABC after a translation of 1 unit left and 7 units down is shown in the image attached below.

In Mathematics, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

By translating the pre-image of triangle ABC vertically down by 7 units and horizontally left by 1 unit, the coordinates of the image of triangle A'B'C' include the following:

(x, y)                               →                  (x - 1, y - 7)

Coordinate A = (-6, 7)   →    Coordinate A' (-6 - 1, 7 - 7) = (-7, 0)

Coordinate B = (-8, 1)   →    Coordinate B' = (-8 - 1, 1 - 7) = (-9, -6)

Coordinate C = (-1, 2)   →     Coordinate C' = (-1 - 1, 2 - 7) = (0, -5)

Next, we would use an online graphing calculator to construct (plot) triangle A'B'C' on a cartesian coordinate based on its vertices after a translation.

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Answer:

follow me if this helped you

Step-by-step explanation:

The Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Therefore, c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

The estimated regression equation is d. ŷ = 145 + 20x₁ – 18x₂ + 4x₃

This equation is obtained from the coefficients given in the table. It is the equation that best predicts the value of the dependent variable (y) based on the values of the independent variables (x₁, x₂, and x₃).

The equation is in the form of y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε, where β₀, β₁, β₂, and β₃ are the coefficients of the independent variables and ε is the error term. These coefficients represent the change in the dependent variable for a unit change in the independent variable, holding all other independent variables constant.

From the table, we can see that the value of β₀ = 145, which represents the predicted value of y when all independent variables (x₁, x₂, and x₃) are equal to zero.

The value of β₁ = 20 represents the change in the predicted value of y for a unit change in x₁, holding x₂ and x₃ constant. Similarly, the value of β₂ = -18 represents the change in the predicted value of y for a unit change in x₂, holding x₁ and x₃ constant, and the value of β₃ = 4 represents the change in the predicted value of y for a unit change in x₃, holding x₁ and x₂ constant.

So, the estimated regression equation is: ŷ = 145 + 20x₁ – 18x₂ + 4x₃.

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Using the percentage method the amount of flour used this month in the bakery for bread orders is 240 kg.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

The amount of flour used last month is, a = 300 kg

The percentage of flour less used is = 20%

Calculate the 20 percent of 300 kg flour -

b = 20% × 300

b = 20/100 × 300

b = 60 kg

The amount of flour used this month = a - b

The amount of flour used this month = 300 - 60

The amount of flour used this month = 240 kg.

Therefore, this month 240 kg of flour was used.

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The area of the hexagon is approximate, Area = (150 √3) m².

What is a formula of a hexagon?

A Regular hexagon has six sides and angles that are congruent and is made up of six equilateral triangles. The formula to find out the area of a regular hexagon is as given:

Area = (3√3 s²)/ 2

where 's' represents the length of a side of the regular hexagon.

A hexagon is a six-sided polygon. The area of a hexagon can be calculated using the formula:

Area = (3 * √3 * (side length)^2) / 2

In this case, the hexagon is 10m by 5m, so the side length of the hexagon is 10m. Plugging this into the formula, we get:

Area = (3 * √3 * (10m)^2) / 2

Area = (3 * √3 * 100m^2) / 2

Hence, the area of the hexagon is approximate:

Area = (150 √3) m².

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Answer:

Okay so, if he is getting a console for $17.50, then you first want to do is subtract that from the total amount that he has which is $49.

49 - 17.50 = $31.50

Now each game costs $5.25

You can either just keep adding 5.25 by itself until you get to 31.50, or you can just divide 31.50 by 5.25, but I am going to just multiply then by certain numbers until I get the result.

5.25 * 5 = 26.25 so we know he can buy more than 5.

5.25 * 6 = 31.50

He can buy 6 games!

Step-by-step explanation:

Hope it helps! =D

Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.

Thus, all angles are equivalent to 60 degrees.

So, for a triangle, we know that Interior angle + neighbouring outside angle = 180°, 60° + x = 180°, and x = 180° - 60° = 120°.

Thus, a triangle's x value is 120°.

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Answer: 104

Step-by-step explanation:

Angles at a line are equal to 180 degrees so:

180 = 72 + (x + 4)

180 = x + 76

180 -76 = x + 76 -76

104 = x

Answer:  -2 1/2

Step-by-step explanation

if the equation is + but a number is negative, remember that +- = - which means 5/12 + (-2 11/12) = 5/12 - 2 11/12

2 11/12 is bigger than 5/12, so we'll switch it around and it'll become

2 11/12 - 5/12

2 11/12 - 5/12 = 2 6/12

Because 2 11/12 is originally a negative number, +- = -

which means the answer will be negative, so it is  -2 6/12.

but we're not done yet, we need to simplify it by dividing it with 6

so the final answer is -2 1/2

if it didn't make any sense at all heres an equation version :

5/12 + (-2 11/12)

= 5/12 - 2 11/12

= 2 11/12 - 5/12

= 2 6/12 (2 11/12 is originally negative so the ans will be negative)

= - 2 6/12 (divide by 6 to simplify)

= - 2 1/2

Answer:

[tex]l = \frac{P}{2} - w[/tex]

Step-by-step explanation:

[tex]P= 2(l+w)[/tex]

[tex]\frac{P}{2} = l +w[/tex]

[tex]l = \frac{P}{2} - w[/tex]

Answer:

Identify the x-value in the ordered pair and plug it into the equation. When you simplify, if the y-value you get is the same as the y-value in the ordered pair, then that ordered pair is indeed a solution to the equation.

Step-by-step explanation:

Equation of the tangent to the curve at point (-1,1) is: y=2x+3

Given,

x=cos(t)+cos(2t)

y=sin(t)+sin(2t)

P(-1,1)

For the point(-1,1), the value of t satisfy the equations x=cos(t)+cos(2t) and y=sin(t)+sin(2t) is pi/2.

To find an equation of the tangent to the curve at the given point (x,y) where x=cos(t)+cos(2t) and y=sin(t)+sin(2t) and t= pi/2, we need to first find the slope of the tangent line at this point. To do this, we need to take the derivative of the x and y functions with respect to t:

dx/dt = -sin(t) + 2sin(2t)

dy/dt = cos(t) - 2cos(2t)

Now we can use this information to find the slope of the tangent line at the given point (x,y) where x=cos(t)+cos(2t) and y=sin(t)+sin(2t) and t= pi/2:

slope = dy/dx = (cos(t) - 2cos(2t)) / (-sin(t) + 2sin(2t)) evaluated at t = pi/2

slope = (cos(pi/2) - 2cos(2pi/2))/(-sin(pi/2) + 2sin(2pi/2)) = 0 - (-2)/0 + 0 = 2

Now, we can use this slope to find the equation of tangent using:

(y-y1)= m(x-x1)

=> y-1=2(x+1)

=>y=2x+3

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Answer:

  about 9 years

Step-by-step explanation:

You want to know the doubling time for money earning an interest rate of 8%.

The rule of 72 tells you the doubling time is about ...

  72/(interest rate %) = 72/8 = 9 . . . . years

The sum will double in about 9 years.

__

Additional comment

The actual period will depend on the way interest is compounded. When compounded annually, the time is ...

  log(2)/log(1.08) ≈ 9.01 . . . years

Compounded monthly, the time is ...

  log(2)/(12·log(1 +.08/12)) ≈ 8.69 . . . years

The solution of the given system of equations is (-2, -2).

What is addition method?

Using the Addition Method to Solve Systems of Equations in Two Variables. The addition method, also known as the elimination method, is a third strategy for resolving linear equation systems. With this approach, we add two terms that share the same variable but have opposing coefficients, resulting in a sum of zero.

Consider, the given system of equations

-5x - 9y = 28             ..(1)

-4x + 5y = -2              ..(2)

Multiply equation (1) by 5 and multiply equation (2) by 9.

-25x - 45y = 140         ..(3)

-36x + 45y = -18          ..(4)

Adding equation (3) and (4), we get

     -25x - 45y = 140

+   -36x + 45y = -18

______________________

     -61x + 0  = 122

-61x = 122

   x = -2

Plug x = 2 in equation (1)

-5(-2) - 9y = 28

    10 - 9y = 28

           9y = -18

             y = -2

Hence, the solution of the given system of equations is (-2, -2).

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The dog moves quickly through 250-meter passes

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

dog run =11 metres per second

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Answer:

The answer is 6x²+x+7

Step-by-step explanation:

(3x²+3) + (3x²+x+4)

3x²+3 + 3x²+x+4

COLLECT LIKE TERMS

3x²+3x²+x+3+4

ADD UP LIKE TERMS

6x²+x+7

The relation which is a function among the given answer choices are Choices A and D.

It follows from the task content that the answer choices which represent a function be identified as required.

By definition, a function is a relation in which case, no one input value is assigned more than one output.

On this note, for Choice A; all input values have only one output value assigned to them and for Choice D; the graph represents a quadratic function in which case, each input value, x is assigned only one output value, y.

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Answer:

34.

Step-by-step explanation:

The value of 7u + 6

=3u - 8 = 4

=3u = 4 + 8

=3u = 12

=3u/3 = 12/3

u = 4.

therefore u = 4

=7u + 6

=7(4) + 6

=28 + 6

=34.