c. Where would the line y = - 2x + 1 lie? Again, justify your prediction and add the graph of this lineto your graph from part (b).

Answer:

A) 0.35

B) Expected value = 37.4 passengers

C) Standard deviation = 1.24 passengers

Explanation:

Part a.

The sum of all the probabilities should be 1, so we can calculate the missing probability as follows:

0.1 + 0.1 + 0.3 + x + 0.1 + 0.05 = 1

Solving for x, we get:

0.65 + x = 1

x = 1 - 0.65

x = 0.35

Then, the missing probability is 0.35

Part b.

The expected value is equal to the sum of each number of passengers multiplied by its respective probability, so:

E = 35(0.1) + 36(0.1) + 37(0.3) + 38(0.35) + 39(0.1) + 40(0.05)

E = 3.5 + 3.6 + 11.1 + 13.3 + 3.9 + 2

E = 37.4

Therefore, the expected value is 37.4 passengers

Part c.

To find the standard deviation, we first need to calculate the square of the difference between each value and the expected value, so

x (x - E)²

35 (35 - 37.4)² = 5.76

36 (36 - 37.4)² = 1.96

37 (37 - 37.4)² = 0.16

38 (38 - 37.4)² = 0.36

39 (39 - 37.4)² = 2.56

40 (40 - 37.4)² = 6.76

Then, the variance will be the sum of these values multiplied by its probability, so

Variance = 5.76(0.1) + 1.96(0.1) + 0.16(0.3) + 0.36(0.35) + 2.56(0.1) + 6.76(0.05)

Variance = 0.576 + 0.196 + 0.048 + 0.126 + 0.256 + 0.338

Variance = 1.54

Finally, the standard deviation is the square root of the variance

Standard deviation = √(Variance)

Standard deviation = √(1.54)

Standard deviation = 1.24

Therefore, the standard deviation is 1.24 passengers. and it is a measure of the dispersion, it says how far are the numbers from the mean.

Then, the answers are:

A) 0.35

B) Expected value = 37.4 passengers

C) Standard deviation = 1.24 passengers

You have the following function for the profit for selling x units of a product:

f(x) = 15x - 600

in order to determine the profit for 15,600 units, replace x = 15,600 into the previous function and simplify:

f(15,600) = 15(15,600) - 600 = 233,400

Hence, the profit for 15,600 units is $233,400

The general expression for the area of circle with radius r is express as :

In the given circle : radius is 5ft

Substitute radius = 5 ft in the expression for the area of circle :

Answer : Area of circle is 78.5 square feet

The solution set does have only one element: {7000}

Solution:

If the outer diameter is 7, then the outer radius is b=7/2.

On the other hand, if the inner diameter is 3, then the inner radius is a= 3/2.

Now, the surface area of a torus (glazed donut) with inner radius a and outer radius b is given by

Then, applying the data of the problem to the above equation, we can conclude that the surface area of the given glazed donut would be:

so that, the correct answer is:

A bird sits on top of a Lamppost. The angle made by the lamp-post and a line from the feet of the bird to the feet of the Observer standing away from the Lamppost is 55°. the distance from the Lamppost and the Observer is 25 ft. estimate the height of the lamp post ​

we have that

see the attached figure to better understand the problem

so

tan(55)=h/25

solve for h

h=25(tan(55))

Let's begin by listing out the information given to us:

Total utensils = 66

Spoons = 22

Forks = 66 - 22 = 44

The ratio of spoons to the total utensil is given by the ratio of spoons to total utensils. We have:

22:66 ⇒ 1:3

Therefore, the ratio of spoons to total utensils is 1 spoon is to 3 utensils

The ratio of the number of forks to spoon is given by the ratio of forks to spoon. We have:

44:22 ⇒ 2:1

Therefore, the ratio of forks to spoon is 2 to 1. For every 2 forks, there is 1 spoon

6.

(a)

The slope for the side AB is:

The slope for the side BC is:

The slope for the side DC is:

And the slope for AD is:

(b) According to the previous results:

(c) Since it has two pairs of parallel sides, also, The opposite sides are of equal length, we can conclude that this figure is a parallelogram

Answer:

C. Infinite Solutions

Explanation:

Given the equation

First, open the bracket

Since the left-hand side equals the right-hand side, the system has Infinite Solutions.

To find the number of page she read per minute

First let's chenge the 8 hours to minute

8 hours = 8 x 60 = 480 min

Since she read 600 pages

Number of pages read per min = 600/ 480

=1.25 pages

the formula is:

A = P( 1 + r/n )^nt

then solve:

7 ( 1 + 3 )

Solve the sum inside the parentheses ( 1 + 3 = 4 )

7 ( 4 )

multiply

7*4 = 28

Since the sum must equal 28

7 + 21 = 28

Correct option = 7+21

Answer

Options A and C are correct.

The triangle is a Scalen triangle and it is also an Acute triangle.

Explanation

To answer this question, we first explain what these type of triangles are

According to side lengths,

- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.

- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.

- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.

According to the angles,

- Acute triangle has all of the angles in the triangle being less than 90 degrees.

- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.

- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.

For this triangle,

We can see that all of its sides have different lengths. Hence, the triangle is a Scalene triangle.

Also, each of the angles of the triangle is less than 90 degrees. Hence, the triangle is an Acute triangle.

Hope this Helps!!!

she spent 525 on Food

she spent 750 on rent

she spent 775 on others

she spent 450 on fun

Explanation

to find the value of the percentage of any number just use this formula

so

to find the values, apply the formula

Step 1

a) food :21 %

so

it means she spent 525 on Food

Step 2

b) Rent:30 %

so

it means she spent 750 on rent

Step 3

c)other:31 %

so

it means she spent 775 on others

Step 4

d)Fun:18 %

so

it means she spent 450 on fun

I hope this helps you

The number of rolls divided in the two groups so that the ratio is 3 to 5 is 27 and 45 respectively.

According to the question,

We have the following information:

Rolls are being prepared to go to grocery stores.

Now, we have to divide 72 rolls into 2 groups so the ratio is 3 to 5.

Now, let's take the number of rolls given to the first group to be 3x and the number of rolls given to the second group to be 5x.

So, we have the following expression:

3x+5x = 72

8x = 72

x = 72/8

x = 9

So, the number of rolls for the first group:

3x

3*9

27

Now, the number of rolls for the second group:

5x

5*9

45

Hence, the number of rolls divided in the given two group is 27 and 45.

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Hello

We are given a log funtion to solve and see if it have a solution.

Step 1

we apply log rules

Step 2

Solve for x

From the calculation above, the solution of the set is 13; i.e x = 13

The ratio of boy to girl is 3:2. There are 15 boys on the team. The total number of players on the team can be calculated as follows.

Total players = 25

We are given the following equation:

We need to solve for delta, to do that we will first add 8delta on both sides:

Now we add like terms:

Now we subtract 21 on both sides:

Adding like terms:

Therefore delta is 17

The arithmetic series is:

-1 + 2 + 5 + 8 + .....

The first term, a = -1

The common difference, d = 2 - (-1)

d = 3

The number of terms, n = 7

Find the sum of the arithmetic series below

Therefore, the sum of the arithmetic series = 56

To determine which of the given equations represents the function given in the table, let us analyze each of them.

The first two equations do bring not integer numbers in such a way that, if we substitute any of the x values given, we will find a y value which is not an integer. This means that both are not the ones we are looking for.

Now, to determine if the third or the fourth is the one, let us substitute one of the x values on it, and if the y value matches, it means that it might be correct.

Checking the fourth, let's use the values:

Substituting the value of x in the equation of the fourth option, we have:

Because the y value found was not the one given, the option is wrong!

Let's check the third option with the same values of x and y:

It matches. This substitution alone does not assure this is the right answer, but once it can not be anyone of the other three, and once we expect that one of the four is the function, this match becomes enough for our final answer:

C) y = -5x + 6

The probability of birthday being in July is 1/12.

What do you mean by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a numeric value and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is flipping a fair (impartial) coin. The chance of either "heads" or "tails" is half because there are only two possible outcomes (heads or tails), and because the coin is fair, both outcomes (heads and tails) are equally likely.

Probability of birthday being in July = 1/12 (12 months in a year)

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Explanation

The question wants us to obtain all the outcomes possible when a coin and a cube is tossed

A coin has two possible outcomes

A cube has 6 surfaces, so the outcomes are

Thus, we can have the diagram showing the outcomes to be

A.

This is a question of graphical operations with vectors. In order to get the answer, you must draw vector B with inverse direction, and place the tail of said vector on top of the arrow of vector A. Check the attached image.

Hence, the answer that better represent the resulting vector is answer A.

A.

This is a question of graphical operations with vectors. In order to get the answer, you must draw vector B with inverse direction, and place the tail of said vector on top of the arrow of vector A. Check the attached image.

Hence, the answer that better represent the resulting vector is answer A.

option B

The cost of renting per hour = $2

For 1 hour = $2

For each additional hour, it is $1

For 2 hours = First hour + 1(additional hour)

For 2 hours = $2 + $1(1) = 2+1 = $3

For 3 hours = $2 + $1 (2) = 2+2 = $4

For 4 hours = $2 + $1(3) = 2+3 = $5

The graph which shows this rental cost as 2, 3, 4, 5 is option B

The values of given functions f(-2), f(0) and f(7) when f(x) = 1-6x are 13, 1 and -41 respectively.

According to the question,

We have the following function:

f(x) = 1-6x

Now, we can find the values of each function by putting the numbers in place of x.

Now, in order to find the value of f(-2), we will put -2 in place of x in the given function.

f(-2) = 1-6*(-2)

f(-2) = 1+12

f(-2) = 13

Now, in order to find the value of f(0), we will put 0 in place of x in the given function.

f(0) = 1-6(0)

f(0) = 1-0

(We know that when a number is multiplied with 0 then the result is always 0.)

f(0) = 1

Now, in order to find the value of f(7), we will put 7 in place of x in the given function.

f(7) = 1-6*7

f(7) = 1-42

f(7) = -41

Hence, the values of f(-2), f(0) and f(7) are 13, 1 and -41 respectively.

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The future value formula, given by

Can be used to obtain the Principal by substituting other values into the equation and solving for P

Step 1: List out the parameters given

FV =$8,700

r=7%=0.07

n=4 (since there are 4 quarters in a year)

t=6 (since it will be compounded 6 times a year)

Step 2: Substitute the values into the formula

Solving for P

P=$5737.11

Option B is correct

Solution

Note: Laws Of Logarithm To Use

From the question, we have

To evaluate, we have

The answer is

Let:

After the reflection over y = -x:

Instead of describing the constituents of a set, a set-builder notation describes them. The set-builder notation exists A = {x: x is a natural number less than 27}.

A set can be represented by its elements or the properties that each of its members must meet can be described using set-builder notation.

Set-builder notation is a mathematical notation for defining a set by enumerating its elements or by specifying the properties that each of its members must satisfy. It is used in set theory and its applications to logic, mathematics, and computer science.

Let the given inequality be 2x+1 < 27

Subtract 1 from both sides, we get

-2x+1-1 < 27-1

Simplifying the above equation, we get

-2 x < 26

Multiply both sides by - 1 (reverse the inequality)

(-2 x)(-1) > 26(-1)

Simplifying the above equation, we get

2x > -26

Divide both sides by 2

[tex]$\frac{2 x}{2} > \frac{-26}{2}[/tex]

x > -13

Therefore, the set-builder notation exists

A = {x: x is a natural number less than 27}.

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So first of all we should write the three equations in slope-intercept form. This will make the problem easier to solve. Remember that the slope-interception form of an equation of a line looks like this:

Where m is known as the slope and b the y-intercept. The next step is to rewrite the second and third equation since the first equation is already in slope-intercept form. Its slope is 4 and its y-intercept is -1.

So let's rewrite equation (ii). We can begin with substracting 4 from both sides of the equation:

Then we can divide both sides by 8:

So its slope is -1/4 and its y-intercept is -1/2.

For equation (iii) we can add 8x at both sides:

Then we can divide both sides by 2:

Then its slope is 4 and its y-intercept is -1. As you can see this equation is equal to equation (i).

In summary, the three equations in slope-intercept form are:

It's important to write them in this form because when trying to figure out if two lines are parallel or perpendicular we have to look at their slopes:

- Two lines are parallel to each other if they have the same slope (independently of their y-intercept).

- Two lines are perpendicular to each other when the slope of one of them is the inverse of the other multiplied by -1. What does this mean? If a line has a slope m then a perpendicular line will have a slope:

Now that we know how to find if two lines are parallel or perpendicular we can find the answers to question 4.

So for part (a) we must find the pairs of parallel lines. As I stated before we have to look for those lines with the same slope. As you can see, only lines (i) and (iii) have the same slope (4) so the answer to part (a) is: Lines (i) and (iii) are parallel to each other.

For part (b) we have to look for perpendicular lines. (i) and (iii) are parallel so they can't be perpendicular. Their slopes are equal to 4 so any line perpendicular to them must have a slope equal to:

Which is the slope of line (ii). Then the answer to part (b) is that lines (i) and (ii) are perpendicular to each other as well as lines (ii) and (iii).