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What is the probability that a boy selected at random is a Junior?

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Please begging of some help to finish this due today

What is the probability of randomly choosing a student who is a Junior and a boy?

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B)= Answer

Answer:

7°

Step-by-step explanation:

The three angles of a triangle should sum up to 180°

→   m∠1 + 121 + 52 = 180

→   m∠1 + 173 = 180

→   m∠1 = 180 - 173 = 7°

The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2). (Correct choice: E)

In this problem we find five different points of the form (x, y), each of which has to be checked in the linear equation given in the statement. A point is a solution of the linear equation if and only an equality exists, that is, the reflexive property of equalities is guaranteed by evaluating the expression.

Now we proceed to check the expression for each case:

(x, y) = (1, - 5)

- 5 + 4 = (3 / 5) · (1 - 2)

- 1 = (3 / 5) · (- 1)

- 1 = - 3 / 5     (FALSE)

(x, y) = (- 8, - 12)

- 12 + 4 = (3 / 5) · (- 8 - 2)

- 8 = (3 / 5) · (- 10)

- 8 = - 30 / 5

- 8 = - 6    (FALSE)

(x, y) = (- 3, - 8)

- 8 + 4 = (3 / 5) · (- 3 - 2)

- 4 = (3 / 5) · (- 5)

- 4 = - 3    (FALSE)

(x, y) = (12, 10)

10 + 4 = (3 / 5) · (12 - 2)

14 = (3 / 5) · 10

14 = 30 / 5

14 = 6     (FALSE)

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

- 1 + 4 = (3 / 5) · (7 - 2)

3 = (3 / 5) · (5)

3 = 3    (TRUE)

The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2).

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The value of the x means hypotenuse according to the Pythagoras is 12.8.

According to the statement

We have to find that the value of the x.

So, For this purpose, we know that the

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

From the given information:

The perpendicular length is 12.

And The base is a 4.5

And we have to find that the hypotenuse value.

Then

According to the theorem

Perpendicular^2 + base^2 = Hypotenuse^2

And substitute the value then

12^2 + 4.5^2 = Hypotenuse^2

144 + 20.25 = Hypotenuse^2

Then

Hypotenuse^2 = 144 + 20.25

Hypotenuse^2 = 164.25

Hypotenuse = 12.8.

So, The value of the x means hypotenuse according to the Pythagoras is 12.8.

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Answer:

g(f(x)) = 4x^2 + 8x + 4

Step-by-step explanation:

If f(x) = 2x + 1 and g(x) = x² + 2x + 1, find g(f(x)).

You are asked to find g of f of x.

This means your x value for the equation g(x) is f(x), hence g(f(x)).

g(2x+1)=(2x+1)^2 + 2(2x+1) +1

g(2x+1) = 4x^2 + 4x + 1 +4x + 2 + 1

Combine like terms.

g(2x+1) = 4x^2 + 8x + 4

g(f(x)) = 4x^2 + 8x + 4

The solution to the given system of equations is x = 1, y = 1. That is, (1, 1)

From the question, we are to solve the given system of equations.

The given system of equations is

y = -2x + 3y  ------------- (1)

y = 5x - 4      ------------- (2)

Substitute equation (2) into equation (1)

y = -2x + 3y

5x - 4 = -2x + 3(5x - 4)

5x - 4 = -2x + 15x - `12

Collect like terms

-4 + 12 = -2x + 15x - 5x

Simplify

8 = 8x

∴ x = 8/8

x = 1

Substitute the value of x into equation (2)

y = 5x - 4

y = 5(1) - 4

y = 5 - 4

y = 1

Hence, the solution to the given system of equations is x = 1, y = 1. That is, (1, 1)

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The time it would take Kim running the same distance is 15 minutes.

Ratio is used to show the relationship between two or more numbers. It shows the frequency that one value is contained within other value(s). The sign that is used to represent ratio is :.

Speed = distance / time

The first step is to determine the time spent by Richard running:

(4 x 1/8) / 5 = 1/10 or 10 minutes

The second step is to determine the time spent by Kim running:

(2 x 1/10) / 3 = 1/15 =  15 minutes

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39.16 approx. is the value of x in  [tex]e^{\frac{x}{4} -8}[/tex] = 6 solved by using natural logarithm

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

We have been asked to find x in [tex]e^{\frac{x}{4} -8}[/tex] = 6 using natural logarithm

⇒  [tex]e^{\frac{x}{4} -8}[/tex] = 6

⇒ [tex]\frac{x}{4} - 8[/tex] = ㏑6

⇒  [tex]\frac{x}{4}[/tex] = ㏑6 + 8

⇒ x = ln(1296) + 32

      = 39.16 approx.

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Use natural logarithms to solve each equation.

[tex]e^{\frac{x}{4} -8}[/tex] = 6

This version is much shorter, and more simpler, compared to 5 x 10^6 millimeters. It's more appropriate to use millimeters with very small objects or distances.

Note: 5 x 10^6 = 5,000,000 = 5 million

The value of a calculated by Noemi is not correct as the correct value is

     a = -1/45

We know that the general form of the quadratic equation is given as

                        y = ax² + bx + c

where, a and b are coefficients of the variable x and c is the constant term.

Now according to the question the path of the golf ball is parabola whose coordinates will be

       (0,0) = origin where it starts

       (60,80) = vertex or the maximum point

       (120,0) = end point

Now putting the value of (x,y) in the above formula to find the value of a,b and c

when (x,y) = (0,0)

       0 = a0² + b0 +c

       c = 0

when (x,y) = (60,80)

      80 = a60² + b60 +c

       80 = 3600a + 60b + 0        (1)

when (x,y) = (120,0)

      0 = a120² + b120 +c

      0 = 14400a + 120b + 0      

       120b = -14400a

          b = -120a

Putting the value of a in equation (1) we get

    80 = 3600a + 60(-120a)

    80 = 3600a - 7200a

    80 = -3600a

     a = - 1/45

 ⇒ b = 8/3

Hence the equation will be         y = -1/45x² + 8/3x

and the value of a calculated by Noemi is not correct as the correct value is a = -1/45

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The expression that represents the temperature of the water after Raul added the ice cubes is 72.3°F + (72.3°F)

From the question, we are to write an expression that represents the temperature of the water after Raul added ice.

From the given information,

The initial temperature is 72.3°F

and

The change in temperature was -39.1°F

Thus,

The expression that represents the temperature of the water after Raul added the ice cubes is

72.3°F + (72.3°F)

Hence, the expression written as the sum of two numbers is 72.3°F + (72.3°F)

Here is the complete question:

Raul is performing an experiment. He pours water into a glass and measures the temperature of the water at 72.3°F. Then he adds a few ice cubes to the glass of water. He measures the temperature of the water again and finds that it has changed by -39.1°F. Write an expression that represents the temp of the water after Raul added the ice cubes. Write the expression as the sum of two numbers.

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Answer:    14 min

Step-by-step explanation:

After 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A computer is rendering two scenes. The computer has already rendered 540 thousand pixels (kpx) of a kitchen scene and renders another 90kpx each.

Let after t minutes the scene will have the same amounts rendered.

The linear equation in one variable can be framed as:

540 + 90t = 960 + 60t

After solving the above linear equation in one variable:

90t - 60t = 960 - 540

30t = 420

t = 14 minutes

Thus, after 14 minutes more the scene will have the same amounts rendered if the computer is rendering two scenes.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

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For the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.

We are given the logarithm expression as:

1 / 4 log₃ 2 + 1 / 4 log₃ x

Now, take 1 / 4 common from the expression:

1 / 4 ( log₃ 2 + log₃ x)

Now, we know that log₃ a + log₃ b = log₃ ( a b)

So, we get that:

1 / 4 ( log₃ ( 2 x) )

1 / 4 log₃ 2 x

Therefore, for the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.

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After solving the equation, x = -1 is the value of x in [tex]3^{(-2x)+2} = 81[/tex]

⇒ [tex]3^{(-2x)+2} = 81[/tex]

⇒ [tex]3^{(-2x)+2} = 3^4[/tex]

⇒ -2x + 2 = 4

⇒ -2x = 2

⇒ x = 2/(-2)

⇒ x = -1

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

m = -3

Step-by-step explanation:

Jack spent first a total of AED 1282.04 and when he bought the box it cost AED 205.96

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the total cost Jack spend before bought the box:

Total cost = (No. drill bits*cost of drill bits) +  (No. washers  *cost of washers ) +  (No. hammers *cost of hammers)

Total cost = (8 drill bits * AED 11.22/ drill bits) + (10 washers * AED 10.11 / washers) + (2 hammers * AED 545.59 / hammers)

Total cost = AED 89.76 + AED 101.1 + AED 1091.18

Total cost = AED 1282.04

Calculating the box cost:

Balance = Paid - (Total cost + box cost)

Balance = Paid - Total cost - box cost

box cost = Paid - Total cost - Balance

box cost = AED 1500 - AED 1282.04 - AED 12

box cost = AED 205.96

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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The solution of the equation solved for a is (D)  y c-x b / x

As it is given that

x / y = c / a + b

Calculating for a

(a + b)x = cy

a + b = cy / x

a = (cy / x) - b

a = (cy - bx) / x

a = (yc - xb) / x

The solution of the equation solved for a is (D)  y c-x b / x

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The summation of f (x) and g (x) = x ² + 3 x + 3

Given,

f (x) = x ² + 4

g (x) = 3 x - 1

The question states to find the summation of the function f, that is, f (x) = x ² + 4, and function g, that is, g (x) = 3 x - 1

Performing the addition operation on these functions is just like simple addition.

This implies, adding the two functions f (x) and g (x), we get

f (x) + g (x) = x ² + 4 + 3 x - 1

=> f (x) + g (x) = x ² + 3 x + 3

This assumes that the summation or addition of the two functions f (x) and g (x) gives x ² + 3 x + 3

Therefore, we get the summation of f (x) and g (x) as x ² + 3 x + 3

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Answer:

8.8 x 10^3

Step-by-step explanation:

8.8  *  1 x 10^3  = 8.8 x 10^3      <=====  done

In the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85

In the right triangle XYZ, angle X and angle Y are complementary angles.

The complementary angle is either of two angles whose sum is 90 degrees

Therefore,

Angle X + Angle Z = 90 degrees

In trigonometry,

sinθ = Opposite side / Hypotenuse

sin z= 36/85

z= [tex]sin^{-1}(\frac{36}{85} )[/tex]

z= 25.06

Then the value of cos z is

cos 25.06 = 77/85

Hence, in the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85

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Answer:

Step-by-step explanation:

The coordinate of the midpoint of the segment is -10

We have been given,

The coordinate of the endpoints of the segment are , -16 and -4

We need to find the coordinate of the midpoint of the segment.

Using the midpoint formula,

m = (-16-4)/2

   = -20/2

   = -10

Therefore, the coordinate of the midpoint of the segment is -10

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Answer:

Slope: 2/1

equation: y=2/1x+2

Answer:

z+2y

Step-by-step explanation:

z is the only z there so dont have to change

-3y+5y=2y

so u get z+2y

Hey there!

z - 3y + 5y

= 1z - 3y + 5y

COMBINE the LIKE TERMS:

= (-3y + 5y) + (1z)

= -3y + 5y + 1z

= 2y + 1z

= 2y + z

Therefore, your answer should be:

2y + z

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The answer to the given logarithm expression is  log₁/₂ 1/2 = 1

Another technique to clarify exponents in mathematics is through logarithms. A base number's logarithm equals another number.

For instance, log10 100 = 2 if 102 = 100. A logarithm is defined as an influence by which variety must be raised to receive another value. this is often the foremost convenient thanks to represent large numbers. Logarithms have several important properties that prove that logarithmic multiplication and division is written because the logarithm of addition and subtraction. The log is named the logarithm of base e. The logarithm is represented by ln or loge. where 'e' represents Euler's constant,  approximately capable 2.71828. as an example, the log of 76 is written as ln 76. The log defines what percentage times 'e' must be multiplied to induce the required output.

Using log property logₐ a = 1log₁/₂ 1/2 = 1

Hence , we evaluated the logarithm which is log₁/₂ 1/2 = 1

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Answer:

y = 85

Step-by-step explanation:

6x - 25 = 4x + 15

(Subtract 4x from both sides)

2x - 25 = 15

(Add 25 to both sides)

2x = 40

(Divide 40 by 2)

x = 20

6(20) - 25 = 4(20) + 15

(Solve)

95 + 95 = 190

(Subtract 360 from 190)

360 - 190 = 170

(Divide 170 by 2)

85

y = 85

The solution of the given equation by rounding off it to the nearest ten-thousandth is 0.0872.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation log 8(2x - 1) = 1/3

We are given a logarithmic expression: log 8(2x - 1) = 1/3

We know that e^(log b) = b

a log b = (log b)^a

log a + log b = log (ab)

Using exponential on both sides, we have

e^(log 8(2x - 1)) = e^(⅓)

8(2x - 1) = 1.3956

(2x - 1) = 1.3956 / 8

2x = 0.17445

x = 0.0872

Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 0.0872.

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Answer:  22.8888888889 but rounded 22.9

Step-by-step explanation: This is so because when you turn 23 to ninths you get 207/9 - 1/9 then put into decimal form, 22.8888888889 or 2.9

Answer:

y=-3x-17

Step-by-step explanation:

y=mx+b   (slope-intercept form)           b=y-intercept= (0,?)  m=slope

y=-3x+b  substitute values

y+3x=b isolate b to find b

1+3(-6)=b substitute given ordered pair

-17=b

y=-3x-17