examples of compound events

Answer:

Totally number of coaches needed is 12

Step-by-step explanation:

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Answer:

  lies in the shaded regions of both the top and bottom inequalities

Step-by-step explanation:

For a point to be a solution of two inequalities, it must lie in both solution sets. It ...

  lies in the shaded regions of both the top and bottom inequalities

We want to define when a point is a solution of a system of inequalities, we will see that the correct option is: "lies in the shaded regions of both the top and bottom inequalities."

Just like in a system of equations, a solution of the system is must be a solution of both equations.

Here, a solution ot the system of inequalities must be at the same time a solution of each inequality.

Remember that the solutions of the inequalities are represented by shaded regions, so the point must belong to the intersection of the two shaded regions.

So the correct option is:

"lies in the shaded regions of both the top and bottom inequalities."

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Answer:

0.02275

Step-by-step explanation:

We use the z score formula to solve for this

z-score is given as: z = (x-μ)/σ

where x is the raw score,

μ is the population mean

σ is the population standard deviation

In the above question:

mean of μ=500

a standard deviation of SD=100

raw score x = 700

Hence, z score = (700 - 500)/ 100

= 200/100

= 2

z score = 2

Using the z score table of normal distribution to find the Probability of z = 2

P( x = z)

= P(x = 700)

= P( z = 2)

= 0.97725

P(x>700) = 1 - P(x = 700)

= 1 - 0.97725

= 0.02275

Therefore, the probability of randomly selecting an individual from this population who has an SAT score greater than 700 is 0.02275

Answer:

X=13

Step-by-step explanation:

Answer: g(x) f(x) h(x)

Step-by-step explanation:

The order of the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3] is is g(x) >f(x) > h(x)

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.

It is a measure of how much the function changed per unit, on average, over that interval.

Given,

[tex]f(x) = 16(\frac{1}{2})^{x}[/tex]

interval = [0,3]

[tex]f(0)= 16(\frac{1}{2})^{0} =16 \\f(3)= 16(\frac{1}{2})^{3} =2[/tex]

Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Average rate of change= [tex]\frac{2-16}{3-0}=-4.67[/tex]

Consider the function g(x)

g(0)=21

g(3)=1

Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Average rate of change =[tex]\frac{1-27}{3-0}=-8.67[/tex]

Consider the exponential function

at x=0 the exponential function h =4

at x=0 the exponential function h =-3

Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Average rate of change =[tex]\frac{-3-4}{3-0}=-2.33[/tex]

Hence, the order of the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3] is g(x) >f(x) > h(x)

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Answer:

[tex]slope=3[/tex]

Step-by-step explanation:

Use the following equation the find the slope:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change in the x-axis from one point to the other. This is also known as the "slope". Insert the known values:

[tex](-10_{x1},8_{y1})\\\\(-15_{x2},-7_{y2})\\\\\\\frac{-7-8}{-15-(-10)}\\\\\frac{-7-8}{-15+10}[/tex]

Solve:

[tex]\frac{-7-8}{-15+10}=\frac{-15}{-5}[/tex]

Simplify. Two negatives make a positive:

[tex]\frac{-15}{-5}=\frac{15}{5}[/tex]

Simplify fraction by dividing top and bottom by 5:

[tex]\frac{15}{5}=\frac{3}{1} =3[/tex]

The slope is 3.

:Done

The slope of the line that passes through the points (-10, 8) and  (-15, -7) is 3 and thsi can be determined by using the point-slope formula.

Given :

The line that passes through the points (-10, 8) and  (-15, -7).

The following steps can be used in order to determine the slope of the line that passes through the points (-10, 8) and  (-15, -7):

Step 1 - The slope formula when two points are given is:

[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

where m is the slope and [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the line.

Step 2 - Substitute the known terms in the above formula.

[tex]\rm m = \dfrac{-7-8}{-15+10}[/tex]

Step 3 - Simplify the above expression.

[tex]\rm m = \dfrac{15}{5}[/tex]

m = 3

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Answer:

The correct option is;

A. The total points Shelly earned

Step-by-step explanation:

The given details are;

The number of tasks completed by Shelly and Terrence in the game = x

The total points scored by Terrence = 20 less than the total point scored by Shelly

The expression for Terrence's total point is 90·x - 20

Let the total points Shelly earned = Y

Therefore since the total points scored by Terrence = 20 less than the total point scored by Shelly, we have;

The total points scored by Terrence = Y - 20

Comparing the two expressions for the total points scored by Terrence which are;

90·x - 20 and Y - 20 we have;

90·x - 20 = Y - 20

Adding 20 to both sides of the equation gives;

90·x - 20 + 20= Y - 20 + 20

Which gives;

90·x = Y

Therefore, the first term of the expression 90·x - 20, which is 90·x is equal to Y, which is the total points Shelly earned

The correct option is therefore the total points Shelly earned.

Answer:

A. The total points Shelly earned

Step-by-step explanation:

Hope this helps!

Have a great day! :)

Answer:

The point is at -0.58

Step-by-step explanation:

If you count each line, they each represent 0.1, so -0.55, -0.56, -0.57 and -0.58 is the 4th line

Answer:

-0.58

Step-by-step explanation:

Each division is 1/100  or 0.01

-(0.55 + 0.01) = - 0.56

-(0.56 +0.01) = -0.57

-(0.57 + 0.01) = -0.58

this is simplify? I think it's simplify so I can give you an answer

Answer:

x=4       -3/2 =x

Step-by-step explanation:

y = (x – 4)(2x + 3)

To find the x intercepts set y=0 and solve for x

0 = (x – 4)(2x + 3)

Using the zero product property

0= x-4    0= 2x+3

x=4        -3 = 2x

x=4       -3/2 =x

Answer:

We can find the x intercepts by setting this equation equal to 0.

So we have:

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

So we get:

x-4 = 0, x = 4

2x+3 = 0, x = -3/2

The x intercepts are 4 and -3/2

Hope this helps!

Answer:

4[tex]\sqrt{2}[/tex] cm

Step-by-step explanation:

The diagonal divides the square into 2 right angles with legs s and the diagonal as the hypotenuse.

Using Pythagoras' identity in the right triangle , then

s² + s² = 8²

2s² = 64 ( divide both sides by 2 )

s² = 32 ( take the square root of both sides )

s = [tex]\sqrt{32}[/tex] = 4[tex]\sqrt{2}[/tex]

Answer:

Given :

To Find :

Using Formula :

Here is the formula to find the side of square if diagonal is given :

[tex]\implies{\sf{a = \sqrt{2} \dfrac{d}{2}}} [/tex]

Where :

Solution :

Substituting the given value in the required formula :

[tex]{\dashrightarrow{\pmb{\sf{ \: a = \sqrt{2} \dfrac{d}{2}}}}}[/tex]

[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times \dfrac{8}{2}}}}[/tex]

[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times \cancel{\dfrac{8}{2}}}}}[/tex]

[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times 4}}}[/tex]

[tex]{\dashrightarrow{\sf{ \: a = 4\sqrt{2}}}}[/tex]

[tex]{\dashrightarrow{\sf{\underline{\underline{\red{ \: a = 5.65 \: cm}}}}}}[/tex]

Hence, the length of the side of square is 5.6 cm.

[tex]\underline{\rule{220pt}{3pt}}[/tex]

Answer:

y = -2/5x - 4

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]a = b[/tex]

Required

Match proper type of equality

Each of the equality properties can easily be identified with their names; For multiplication property of equality, same term must be multiplied on both sides;

For addition, same term  must be added on both sides;

Same thing implies for division and subtraction

Multiplication:

[tex]a(c) = b(c)[/tex]

Subtraction

[tex]a - c = b - c[/tex]

Addition

[tex]a + c = b + c[/tex]

Division

[tex]a/c = b/c[/tex]

Answer:

111

Step-by-step explanation:

Reducing the given expression:

74(6)       37(6)           111

--------- =  ----------  =  ---------- = 111

   4              2                1

Answer:

Step-by-step explanation:

[tex] \mathsf{(74) \times ( \frac{6}{4} )}[/tex]

To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term.

⇒[tex] \mathsf{ \frac{74 \times 6}{4 \times 1} }[/tex]

⇒[tex] \mathsf{ \frac{444}{4} }[/tex]

⇒[tex] \mathsf{111}[/tex]

[tex] \mathrm{Hope \: I \: helped !} [/tex]

[tex] \mathrm{Best \: regards !}[/tex]

Answer:

3 chocolate bars, and 2 graham crackers

Someone forgot the marshmallows...... :P

Step-by-step explanation:

Chocolate bars = 8 pack

Graham Crackers = 12pack

To have no crackers or chocolate left over, we need to find LCM

Factors of 8:

8, 16, 24, 32, 40, 48, 56, 72....

Factors of 12:

12, 24, 36, 48, 60, 72

The smallest LCM is 24

Chocolate bars:

24/8 = 3

Graham Crackers:

24/12 = 2

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Answer:

3 packs of chocolate and 2 packs of crackers

Step-by-step explanation:

the lowest common multiple of 8 and 12 is 24. We can determine this by prime factorization:

Prime factors of 8: 2 x 2 x 2

Prime factors of 12: 2 x 2 x 3

multipyling the bottom rungs of our factor tree we get: 2 x 2 x 2 x 3 = 24.

If you need me to draw the factor tree, just ask.

Answer: Option 4 (Hexagon)

Step-by-step explanation:

A equilateral triangle, square and hexagon can be used to form a tessellation.

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find the cost of the painting of a rectangular box of length 6m breadth 4m and height 3m at the rate of rs.25 per meter square

According to the question, first we need to get the T.S.A. or Total Surface Area of the cuboid then dividing it by ₹ 0.25 we can get the cost. After solving the concept will be more clear.

Let's start :

Here,

l represents length

b represents breadth

h represents height

Now, putting the values of all these we get

Now, we are given that cost of every square metre costs ₹ 0.25

So, for 108 m² it will cost = ₹ 108 × 0.25 = ₹ 27

Hence, cost of painting the rectangular box is ₹ 27

Answer:Rs.2700

Step-by-step explanation:step1is 2[6*3]+2[6*4]=84

step2is 2[3*4]=24

24+84=108*25=2700

Answer:

l=30

or

22 it is the coret anser

Answer:

The answer is

[tex] \sqrt{65} \: \: \: units[/tex]

Step-by-step explanation:

To find the distance between two points we use the formula

[tex] \sqrt{ ({x1 - x2})^{2} + ( {y1 - y2})^{2} } [/tex]

where

( x1 , y1) and ( x2 , y2) are the points

From the question the points were

(-8,5), (-1.1)

Substitute the values into the above formula

That's

[tex] \sqrt{ ({ - 8 + 1})^{2} + ({5 - 1})^{2} } [/tex]

[tex] \sqrt{ ({ - 7})^{2} + {4}^{2} } [/tex]

[tex] \sqrt{49 + 16} [/tex]

We have the final answer as

[tex] \sqrt{65} \: \: units[/tex]

Hope this helps you

Answer:

All positive Real numbers

Answer:

  7/6

Step-by-step explanation:

You have correctly graphed the line, so you know that the rate of change is ...

  ∆d/∆t = 7/6

d changes by 7/6 units for each unit change in t.

Answer:

This is marked evenly from 0 to 100

This means that the total number of possible outcomes is:

D = 101

and the set of possible outcomes is:

O = {0, 1, 2, 3, ..., 100}

Now, the probability to geting between 42 and 72 seconds is equal to the quotient between the number of outcomes between 42 and 72, and the total possible outcomes.

The number of outcomes between 42 and 72 is:

72 - 42 = 30

Then the probability is:

P = 30/101 = 0.297

Then, out of the 100 players, we can expect that:

0.297*100 = 29.7 ≈ 30

(we rounded to the next whole number)

30 of them get between 42 and 72 seconds.

Answer:

  40

Step-by-step explanation:

Angles ABO, BAO, and AOB are the angles of isosceles triangle AOB. The angles at A and B are equal, so we have ...

  AOB +2ABO = 180° . . . . . sum of angles in the triangle

  100° +2ABO = 180° . . . . . . use the given value

  50° +ABO = 90°  . . . . . . . . divide by 2; next, subtract 50°

  ∠ABO = 40°

Answer:

either 2 or 2 1/2

Step-by-step explanation:

Since the pre-image gets bigger, the scale factor is larger than 1.

Answer:

8x^2-4x+5

Step-by-step explanation:

(3x^2+4)-(-5x^2+4x-1)

Let's start by removing the parentheses.

3x^2+4-(-5x^2)-4x+1

Now let's reorder the equation to make it easier to combine like terms.

3x^2+5x^2-4x+1+4

Combine like terms.

8x^2-4x+5

Answer:

The answer is below

Step-by-step explanation:

a) Weekly gross salary is the product of the number of hours worked per week and earnings per hour. It is given as:

Weekly gross salary = number of hours worked per week × earnings per hour = 30 hrs / week × $12.08/hr = $362.4

b) Using claim code 2 for the weekly gross salary, Federal tax = $16.05, CPP = $14.61, provisional income tax = $0.6 and EI = $6.27

Total deductions = $16.05 + $14.61 + $0.6 + $6.27 = $37.53

Weekly net pay = Weekly gross salary - Total deductions = $362.4 - $37.53 = $324.87

c) Yearly net pay = weekly net pay × number of weeks in a year = $324.87 × 52 = $16893.24

d) percent of his gross income deducted yearly = weekly deductions / weekly gross income × 100% = 37.53 / 362.4 × 100% = 10.4%

Answer: 11136 grams

≈ 11.14 kilograms  

Step-by-step explanation:

Given, Each package has 126 grams of granola, 245 grams of chocolate chip cookies , and 325 grams of nuts in it.

Total weight of each package =  126 grams + 245 grams +  325 grams

= 696 grams

If they have 16 care packages, then total weight of packages = 16 x (Total weight of each package)

= 16 x 696 grams

=  11136 grams

≈ 11.14 kilograms   [ 1 kilogram = 1000 grams]

Options :

A. Each roll has a 0.117 probability of being divisible by 3.

B. Each roll has a 0.333 probability of being divisible by 3.

C. Each roll has a 0.5 probability of being divisible by 3. D. Each roll has a 0.667 probability of being divisible by 3.

Answer: B. Each roll has a 0.333 probability of being divisible by 3.

Step-by-step explanation:

Sample space for a six-sided number cube :

1, 2, 3, 4, 5, 6

Number of outcomes divisible by 3:

(3, 6) = 2

Probability of an event = Number of required outcomes / total number of possible items

Probability (getting a number divisible by 3):

(Number of outcomes divisible by 3 / total outcomes in sample space)

Probability (getting a number divisible by 3):

2 / 6 = 1/3

= 0.333

Answer:

63

Step-by-step explanation:

pie multiply 2 sq. 2 multiply with 5