Write the augmented matrix for the following system of equations.
9y-5+9z = 0
7x=-3y+7+z
5x + 7y = 5

Using it's concept, the probabilities are given as follows:

b) P(B|C) = 0.1429.

c) P(not A|B) = 0.8.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

For item b, the conditional probability can be written as follows:

P(B|C) = P(B and C)/P(C).

From the diagram, we have that:

Hence:

P(B|C) = 0.05/0.35 = 0.1429.

For item c, the conditional probability is:

P(not A|B) = P(not A and B)/P(B).

From the diagram, these probabilities are:

Hence:

P(not A|B) = 0.20/0.25 = 0.8.

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If function f(x) = √(x + 1) - 5 is translated three (3) units to the right and two (2) units up, the equation which represents g(x) is: D. f(x) = √(x - 2) - 3

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

Translating f(x) = √(x + 1) - 5 three (3) units to the right and two (2) units up, we have:

f(x) = √(x + 1) - 5

f(x) = √(x + 1 - 3) - 5 + 2

f(x) = √(x - 2) - 3

In Geometry, g(x - 3) simply means shifting a graph three (3) units to the right while adding two (2) to the function simply means moving the graph up.

In this context, we can reasonably infer and logically deduce that the parent function f(x) was shifted 3 units to the right and 2 units up.

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The Domain of the linear function with no restriction is  (-∞,∞)

A linear function is of the form  f(x)  = ax+ b, where a and b are constants , x is independent variable and the graph of such function is a straight line.

Domain of f is the set of all values of x for which function f is defined.

Given that the linear function has no restrictions , means the values of the function can be from anywhere of real line.

-∞  < f(x) < ∞

⇒ -∞  < ax+ b < ∞    , where a≠0

⇒  -∞- b  < ax+ b-b  < ∞ -b

⇒  -∞  < ax < ∞      ( adding or subtracting anything from infinity does not  

                                  make any difference)

⇒ -∞  < x < ∞  

Thus the domain of the linear function which has no restriction is (-∞,∞)

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Step-by-step explanation:

so,

h(x) = f(x) × g(x)

h'(x) = f'(x) × g(x) + f(x)×g'(x)

with f(x) = -2x + 6

f'(x) = -2

so,

h'(-2) = -2 × g(-2) + (-2×-2 + 6) × g'(x) =

= -2 × -4 + 2 × 5 = 8 + 10 = 18

If the sum of two terms = 0, then the 2 terms must have the same value but different signs

That means x and y must have the same value but different signs

Look at the given answers

The 1st, 2nd, and 4th answers are wrong because the solution of this equation must have a value of x and a value of y together

In the 3rd answer

x = 1 and y = -1

Both have the same value and different signs

Then 3rd answer is a solution

In the 5th answer

x = -2 and y = -2

They have the same value with the same signs

The 5th answer is not a solution

In the last answer

x = 0 and y = 0

They have the same value but the zero has no sign

Then substitute them in the equation to check if it is solution or not

2(0)+2(0) = 0

0 + 0 = 0

The 2 sides of the equation are equal, then

The last answer is a solution

The answer is the 3rd and last answers

ANSWER

C. 6x - 16y = -10

EXPLANATION

An equation or a pair of equations has infinite solutions when all numbers are solutions of the equation(s).

The left and right hand side of the equation(s) are the same.

So, we have to look for the equation such that the case happens.

To do that, we have to simply look for an equation that is identical to the given equation:

3x - 8y = -5

By observing keenly, we see that the identical one is:

6x - 16y = -10

Divide both sides by 2, we have that:

3x - 8y = -5

Let us try to solve these equations:

3x - 8y = -5

3x - 8y = -5

Subtract the second from the first:

3x - 8y = -5

- (3x - 8y = -5)

0 + 0 = 0

=> 0 = 0

We see that both sides are identical.

So, the answer is option C.

Answer:

Step-by-step explanation:

if they are working 7 days a week, lunch will cost $2,275

hope this helped :)

Taking into account the definition of a system of linear equations, the system of equations that represents the total amount of money you spent on hotdogs and hotdog buns at each store is

10x + 8y= 80

11x + 7.50y= 81.50

A system of linear equations is a set of linear equations that have more than one unknown, appear in several but not necessarily all of the equations, and are related by the equations.

In the systems of equations, the values of the unknowns must be found, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know that:

The system of equations to be solved is

10x + 8y= 80

11x + 7.50y= 81.50

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(a)

Graphing the function from x = 0 to x = 10:

b)

Evaluate the function for x = 5

Answer:

$2901.41

c)

Let's solve the following inequality:

so:

Approximately after 8.2 years.

d)

Let's solve the previous equation in order to find the rate y:

The depreciation rate is approximately:

It depreciates 22% per year

A = (-3, 1)

B = (2, -2)

First we will calculate the slope of the line

The slope is negative

Now, we are gonna calculate the equation, with (2, -2)

Answer:

There is a chance it could happen. Rare occurrence though.

Step-by-step explanation:

Invasive weed grows at a rate of 0.0011 ft per minute a day

In the above question, it is given as

Invasive weed grows really fast and the rate of its growth is being provided as follows

The rate at which the weed is growing a day is = 1.65 ft

We need to find the, rate at which this weed is growing per minute

So, to do this, we'll find the growth in 1 min

In 24 hours growth is = 1.65 ft

Conversion factors

We know, 1 hour = 60 minutes

In 1 min growth is = [tex]\frac{1.65}{24 . 60}[/tex]

Here, we have multiplied with 60 in the denominator to convert hours into minutes  

After solving the fraction we'll get

Growth in 1 min of the weed = 0.0011 ft

Hence, Invasive weed grows at a rate of 0.0011 ft per minute a day

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y=4x equation represents a proportional relationship between x and y.

Form the question

Only B doesn't have constant

y=4x

x=y/4

So option 2 is correct.

The formula y=kx y = k x can be used to describe a proportional relationship, where k is the constant ratio.

y = k x, where is the proportionality constant, is the equation that depicts a proportional relationship, or a line. Find k and create the equation by using k = y x from a table or graph. Tables, diagrams, and equations can all be used to depict proportional relationships.

The graph of a straight line through the origin with a slope equal to the unit rate can be used to depict a relationship where two quantities are related proportionally. is equal to k, where k is the unit rate, for each point (x, y) on the graph.

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The rate of the given amount 0.001744%

What is Simple Interest?

Simple interest is a quick and easy way to calculate interest on a loan. Simple interest is the daily interest rate multiplied by the principal multiplied by the number of days until the next payment.

Given,

Principal = $5000

Interest = $157

Time = 18years

The formula for simple interest:

I = P x R x T

157 = 5000 x R x 18

R = 157 / 5000 x 18

R =0.001744%

Hence, the annual rate of interest is 0.001744%

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Answer:

the y intercept is -3. it is -3 because it goes through the point (0,-3)

Step 1:

Sum the numbers

Step 2:

Express the number in Hundreds, Tens, and Ones

3 has a value of 300

6 has a value of 60

1 has a value of 1

Therefore, to express 361 in hundreds, tens and ones

If we replace with 10:

10 is a solution.

Let's try with 11:

11 is not a solution.

WIth 12:

12 is not a solution

WIth 13

13 is not a solution.

Therefore, the solution to this equation is 10

The mean (or average) is given as:

where xi is the value of each data and n is the total number of data. In this case we have:

Therefore the average is 1 hour 4 minutes and the answer is B.

The value of g for the given conditions is obtained from linear equations as 2000.

A linear equation in one variable has only one variable of order 1. It has the formula ax + b = 0, where x is a variable. There is only one solution to this equation.

The initial amount is given as g.

400 pounds is added.

2 times 600 pounds is taken out.

The remaining amount is 1200 pounds.

Form a linear equation from the given constraints.

g+400-2(600)=1200

Solve the linear equation using basic mathematical functions.

g+400-1200=1200

g=2400-400

g=2000

So, the value of g is obtained using the linear equation as 2000.

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If we mutiply a positive number with a positive or negative sign we get the answer as number with sign.

If we mutiply a negative number with sign the answer will be,

Thus, if we mutiply a negative to a positive number the sign gets reversed.

Gina's books has 349 fewer pages than Terri's, if Gina's books has 597 pages, Terri's books have 946 pages. In mathematics, an operation is function which takes zero or more input values (also called the "operands" or "arguments") to a well-defined output value. The number of the operands is the arity of the operation.

In mathematics, an operation is function which takes zero or more input values (also called the "operands" or "arguments") to a well-defined output value. The number of the operands is the arity of the operation.

The most commonly studied operations are the binary operations (i.e., the operations of arity 2), such as addition and multiplication, and the unary operations (i.e., the operations of arity 1), such as additive inverse and the multiplicative inverse. An operation of arity zero, or nullary operation, is constant. The mixed product is example of operation of arity 3, also called ternary operation.

Generally, arity is taken to be finite. However, the infinitary operations are sometimes considered, in which case "usual" operations of finite arity are called finitary operations.

A partial operation is defined similarly to operation, but with partial function in place of a function.

Gina's book = 597 pages

Terri's book= (597+349) pages

                   = 946 pages

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All of them would be the answer.

The left side and right side of every equation should be equal. It is essential that both parties are on an even playing field. An equation must contain the following elements: coefficients, variables, operators, constants, terms, expressions, and an equals sign. Any one, some, or all of these terms may circle the equal sign in an equation.

Rule of Thumb for Equation Solving:

Here, we will put the values of x and y coordinates in the equations:

5=3+2

6=4+2

7=5+2  

8=6+2

Hence, the right and left side of the equation is equal.

Thus, all of them are correct answers. It would just be all of them.

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Answer

Amount invested at 6% interest = 17,000

Explanation

The simple interest on an invested principal (P), at a rate, R, for a period of time, T, is given by

Simple Interest = (PRT/100)

Let the amount invested at 6% be x

Let the amount invested at 7% be y

Sum of these amounts is $41,000

x + y = 41000

Simple Interest on x for 1 year

SI = (x × 6 × 1/100) = 0.06x

Simple interest on y for 1 year

SI = (y × 7 × 1/10) = 0.07y

Sum of annual interest = $2,700

0.06x + 0.07y = 2700

Now, we have a simultaneous equation

x + y = 41000

0.06x + 0.07y = 2700

Solving this simultaneously,

x = 17,000

y = 24,000

Hope this Helps!!!

GIVEN:

We are told that a baseball fan is sitting at a point where his eyes are 350 feet vertical distance from the ground. When the fan is looking at the home plate the angle of depression is 30 degrees.

Required;

Find the horizontal distance from the fan to the home plate.

Step-by-step solution;

We begin by making a sketch of the scene to determine the shape and angles formed. This is shown below;

From the sketch above we can see the that the baseball fan has effectively formed a right triangle with the home plate from his position and the dimensions, that is, angles and sides, have been labeled.

We have the reference angle given as 60 degrees and the opposite is x (horizontal distance from the fan to home plate). That means the adjacent side is 350.

We can now use the following trig ratio;

We now cross multiply;

A second way to determine this distance is by using the triangle formed by the angle 30 degrees, in which case the horizontal distance will be the green line as shown in the sketch above. In that case, the vertical distance of 350 feet will be the opposite while the horizontal distance will be the adjacent while the reference angle will be 30 degrees.

For the second scenario, the straight line distance between both sets of eyes is 300 feet, and the angle of depression is 48 degrees. Note that the second fan is being watched at an angle of depression of 48 degrees which means he is at a lower level.

Now we are required to determine the vertical distance between the field level and the eyes of the second fan.

Let us begin by calculating the value of x as indicated in the triangle.

We shall use the trig ratio of;

Now we cross multiply;

Observe carefully that the distance calculated as x (222.9 ft) is the vertical distance between both fans. If we subtract this value from 350 feet we will now derive the vertical distance from the second fan to the field level.

Therefore,

ANSWER:

~ 399.3 $ / w

. The average for the 2 highest-salaried quarters:

(17 500 $ + 18 300 $ ) / 2 = 35 800 $ / 2 = 17 900$

. The 58% compensation representing the total amount Barry will be compensated:

17 900 * 58 / 100 = 10 382 $

. The weekly compensation:

10 382 $ / 26 week ~= 399.307692 $ / w

SOLUTION

The probability of an event occuring is found using the formula

There is only "one" 4, in a die, out of a total of "six" numbers labelled 1 to 6.

So, possible outcome = 1

Total possible outcome = 6, since the die was tossed once.

Probability becomes

Hence the answer is

7 + 3 × (2 × 8) is the expression that uses the commutative property of addition and the associative property of multiplication to rewrite the expression 3 × (2 × 8) + 7.

Given, 3 × (2 × 8) + 7

Following the application of the Commutative property of addition, which stipulates that altering the order of addends does not affect the result.

The expression will be,

7 + (2 × 8) × 3

Then, using the associative principle of multiplication, which states that how elements are arranged in a multiplication issue does not affect the product.

The expression will be,

7 + 3 × (2 × 8)

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We have to find the length of AR.

It will be the same as the length of AS, as they are both radius of the circle:

AS is the hypotenuse of a right triangle with legs AT and TS.

Also, TS has half the length of SQ, so we have:

We then can calculate AS as:

Answer: AR = 10

Answer:

The perimeter of the parallelogram is;

Explanation:

Given the figure of a parallelogram in the attached image.

With sides;

The perimeter of a parallelogram can be calculated using the formula;

substituting the given sides;

Therefore, the perimeter of the parallelogram is;

Given

The function,

To find:

The maximum or minimum value of the function, and where does it occur.

Explanation:

It is given that,

That implies,

Set g(x)=y.

Then,

Here, a=1>0.

Then, the parabola opens up.

And, k is the minimum functional value, it occurs when x = h.

Therefore,

1) g(x) has a minimum value.

2) g(x)'s minimum value is -4.

3) And it occurs at x = -2.