Consider the following data. The expected value is -2.1.Find the variance, standard deviation, P(X ≥ -1), and P(X ≤ -3).

Part A) To find out the value for x that makes it an identity, (true), we need to solve it.

4(x-4) +6x=14 Distiribute

4x -16 +6x = 14 Combine like terms

2x -16 = 14 Add 16 to both sides

2x = 30 Divide both sides by 2

x =15

Part B) Above explained.

Part C) We can know it by plugging it into the original equation:

4(15 -4) +6(15) = 14

4(11) +90 = 14

44

Answer:

M (-7/2, -7)

Explanation:

Given the coordinates as I(3, - 9) and J(-10, -5), we can go ahead and determine the midpoint of the line segment IJ using the midpoint formula stated below;

So we have that x1 = 3, x2 = -10, y1 = -9, and y2 = -5.

Let's go ahead and substitute the above values into our formula and simplify;

The equation of the perpendicular line is y = -3x - 60

The equation is given as

12y - 4x = 8

Make y the subject

12y= 4x + 8

y = 1/3x + 2/3

The point is also given as

Point = (-10, -30)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 1/3

This means that the slope of 12y - 4x = 8 is 1/3

So, we have

m = 1/3

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the other line is -3

The equation of the perpendicular lines is then calculated as

y = m(x - x₁) +y₁

Where

m = -3

(x₁, y₁) = (-10, -30)

So, we have

y = -3(x + 10) - 30

Evaluate

y = -3x - 30 - 30

y = -3x - 60

Hence, the perpendicular line has an equation of y = -3x - 60

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Consider the following table for interval notation:

First row:

x<0 is the same as:

And the interval notation for that inequality is:

Second row:

-2

The graph of this inequality is:

The interval notation is:

Third row

The inequality that is represented by that interval is:

Its graph is:

Fourth row

The interval represented in that graph is:

The inequality represented by that interval is:

We are given a problem that can be solved using a system of linear equations. Let A, be the number of adults, and S the number of students. Since there are in total 142 people and there were two days, this means that the sum of the number of adults and the number of students must be 284, which can be written mathematically as follows:

This is our first equation. The second equation is found using the total sales of $1948. Since the ticket per adult is $8 and per student is $5, we have the following equations:

To solve this equation we will solve for A in equation (1), by subtracting S to both sides;

Now we will replace this value in equation (2):

Now we will apply the distributive property:

Addins like terms:

Subtracting 2272 to both sides;

Dividing both sides by -3:

Now we replace this value in equation (1), where we have already solved for A:

Therefore, there were sold 108 student tickets and 140 adult tickets.

SOLUTION

Exterior property of a triangle

An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.

Hence,

Simplify and evaluate for x

Therefore,

You have that y is proportional to x. Futhermore, you have y = -0.6 when x = 0.24.

Due to y is proportional to x, you have the following equation:

where k is the constant of proportionality. In order to find the value of x when y = -31.5, you first calculate k.

k is calculated by using the information about y=-0.6 and x=0.24. You proceed as follow:

y = kx solve for k

k = y/x replace by known x and y values

k = -0.6/0.24

k = -2.5

Hence, the constant of proportionality is -2.5.

Next, you use the same formula for the relation between y and x to find the value of x when y = -31.5. You proceed as follow:

y = kx solve for x

x = y/

The form of the exponential function is

a is the initial value (value f(x) at x = 0)

b is the growth/decay factor

Since the function has points (0, 6) and (3, 48), then

Substitute x by 0 and f(x) by 6 to find the value of a

Substitute the value of a in the equation above

Now, we will use the 2nd point

Substitute x by 3 and f(x) by 48

Divide both sides by 6

Since 8 = 2 x 2 x 2, then

Change 8 to 2^3

Since the powers are equal then the bases must be equal

Substitute the value of b in the function

The answer is:

The formula of the exponential function is

Explanation

Given the question

To get the values of x, we will consider two possibilities which are:

And

Therefore, the value of x is

So the correct option is

The first option is correct

Those are similar triangles, which means, they are related by a ratio

For example in this case,

7: 10

to find x

10 / 7 = x/3

x= 10*3 /7

x= 30/ 7

x= 4.29

____________

Given a circle with a radius = r = 10 in

The area of the circle is given by the following formula:

Substitute with r= 10

so, the area will be:

Rounding the answer to the nearest tenth:

So, the answer will be area = 314.3 square inches

We have the measure of angles 1 and angle 2, as we can see from the diagram in the image, angles 1 and 2 added form the right angle (90°) in the figure.

Thus, the sum of x-6 and 5x, must be equal to 90°.

(a) Write an equation:

(b) To find the degree measure of each angle, first we need to solve for the value of x in the equation.

Combining like terms:

Adding 6 from both sides:

Divide both sides by 6:

Now that we have x, we find angle 1:

And the measure of angle 2:

90.32 square inches

Explanation

Step 1

the area of the circle is given by:

Step 2

find the areas

birthday cake

Now, the wedding cake

Step 3

finally, find the difference

so, the answer is 90.32 square inches

The coordinate of point A = (0, 1)

Given:

the line AB is drawn on the grid

To find:

the coordinates of A

The coordinates of a point is in the form: (x, y)

To determine the coordinates of A, we will trace the y axis and x-axis.

At point A, x = 0, y = 1

The coordinate of point A = (0, 1)

The value of x in the equation given is x = -4/7.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The information given will be illustrated as:

9 - (9x - 6) - 9 = 3(4x + 6)

9 - 9x + 6 - 9 = 12x + 18

Collect like terms

-9x + 6 = 12x + 18

-9x - 12x = 18 - 6

-21x = 12

Divide

x = 12/-21

x = -4/7

This illustrates the concept of equations.

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The Solution:

Given the pair of sequences below:

We are asked to write a statement that correctly describes the relationship between the two sequences.

The two sequences are both linear sequences. Their common differences are:

The general formula for the first sequence is

Similarly,

The general formula for the second sequence is

Thus, the relationship between the two sequences is:

Where

Therefore, the correct answer is:

Let:

C(n,m) = Total cost

n = number of t- shirts ordered

m = fee for each color to be printed on the shirts

Therefore, the total cost of the order would be given by the following equation:

C(n,m) = $2n + $50m

Where:

n = 75

C(n,m) = $2(75) + $50m

C(n,m) = $150 + $50m

To be a function, it is nesessary that the values of x correspond to a unique value of y (a value of x cannot correspond to 2 different values of y). The same value of y can correspond to two or more values of x

As in the given data each value of x has just one value of y. Then, it is a function.

Answer:

$160

Step-by-step explanation:

A shop, had a sale. In the sale, normal prices were reduced by 15%. The normal price of a chair was reduced in the sale by $24. Work out the normal price of the chair.

if 15% of normal price equals $24 then:

24/15% or 24/0.15 = $160 normal price

CHECK:

$160 * 0.15 = $24

Answer:

$160

Step-by-step explanation:

We want to know the price of the chair

So:

24 / 0.15 = 160$

or

24 / 15% = 160

In position one, we can have any of the 8 ducks

In position two, we can have 7 ducks, since one has to occupy position one

and so on

then, we have:

the factorial of 8 is 40320

Answer:

B. Infinite

Explanation:

Given that:

This implies that:

From the graph of f(x)=cos(x), we observe that:

Therefore, there are infinitely possible values of y.

The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.

For the given question.

Line m is the line along which reflection of point P is taken.

Then, line m is called the "perpendicular bisector" of line PP'.

P is the object and P' will be the image of the point P.

Thus, the complete definition of the reflection is given as-

The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.

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For the conditions stated, y=1500+2250t and y=1200+1200t, respectively, will be necessary equations because both Rachel and Jeffery are opening savings accounts. Rachel places $1,500 in a savings account that accrues annual compound interest of 1.5%. Jeffery places $1,200 in a savings account that accrues continuously compounded interest of 1% per year.

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.

Here,

according to given condition,

y=1500+1500*1.5t

y=1500+2250t

y=1200+1200*1t

y=1200+1200t

So the required equation will be y=1500+2250t and y=1200+1200t for the conditions given as Rachel and Jeffery are both opening savings accounts. Rachel deposits $1,500 in a savings account that earns 1.5% interest, compounded annually. Jeffery deposits $1,200 in a savings account that earns 1% interest per year, compounded continuously.

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Okay, here we heve this:

We need to combine like terms in the following equation:

Here, we want to get the probability that a selected outcome is divisible by 3

What we have to do here is ti select numbers that are multiples of 3 and add their probabilities

From the given table, the outcomes that are multiples of 3 are;

3 and 6 only

So, we proceed to add the probabilities of these outcomes

Mathematically, we have this as;

Answer:

520<400+15x

15x>120

15x+400>520

Explanation:

Pay of Dan's car wash attendant job =$400 per week

The amount he earns per hour walking dogs = $15

Let the number of hours spent walking dogs in a week = x

Therefore, total earning for walking dogs =$15x

Since he wants to earn more than $520, we have that:

We can rewrite this as:

If we collect like terms, we have:

So the inequalities are:

0. 520<400+15x

1. 15x>120

2. 15x+400>520

To answer this question, we need to evaluate each function in x=66, this way:

In this case, the function that has a greater value at x=66 is the one in the second option:

Answer:

The number will lie between -3 and 11

Step-by-step explanation:

Let the number be 'x'

According to the question,

-15 < 4x - 3 < 41

-12 < 4x < 44 (Adding 3)

-3 < x < 11 (Dividing by 4)