3 11 / 16 simplified

We will have the following:

*First: We would determine the piecewise function that describes the graph.

Since we can see that the function increases by a factor of 2 and decreases by the same factor we would have:

This is:

*Second: We calculate the inverse of the piecewise function:

That is:

From this we can see that the inverse of that graph would in fact represent a function, a non-continuous function. [It will represent a function as long as it follows the parameters stablished in the first point]

Given a Geometric Series:

Where "r" is the ratio.

By definition:

The solution for the given system of equations is x[1] = -1 and x[2] = 2.

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.

Given are the following equations as -

5 x[1] + 5 x[2] = 5

2 x[1] + 3 x[2] = 4

Assume that -

x[1] = a    

x[2] = b

Then, we can write the equations as -

5a + 5b = 5

2a + 3b = 4

Now -

5a + 5b = 5

5(a + b) = 5

a + b = 1

a = 1 - b

So, we can write -

2a + 3b = 4

as

2(1 - b) + 3b =4

2 - 2b + 3b = 4

b = 4 - 2

b = 2 = x[2]

Then

a = 1 - 2

a = -1 = x[1]

Therefore, the solution for the given system of equations is x[1] = -1 and x[2] = 2.

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These angles measure the same they are interior alternate angles.

3x + 14 = 5x + 4

Solve for x

3x - 5x = 4 - 14

Simplify like terms

-2x = -10

x = -10/-2

Result

x = 5

The expression in 4a) is given below

Collecting similar terms using the division rule of indices, we will have

The above expression therefore becomes

Hence,

The final answer = x/3

Given the expression

To find the value of the expression you have to follow the order of operations:

- Parentheses

- Exponents

- Multiplication/Division

- Addition/ Subtraction

• First, you have to solve the operations inside the parentheses term:

Solve the division first and then the sum:

• Write the result on the original expression:

• The next step is to solve the multiplication and finally solve the difference

The value of the expression is 7

From the question, we can deduce the following:

Length = 5.6 meters

Width = 7.3 meters

Height = 4.5 meters

Where:

1 ft = 0.3048 m

1 cubic foot = 7.48 gallons

Let's find the amount of gallons of water in the tank if the tank is filled to 1 foot below the top of the tank.

Let's first sketch the tank.

We have:

Now, let's find the volume of the tank(total amount of water it can carry).

Apply the formula:

Thus, we have:

Now, to find the amount of water presently in the tank since it is filled 1 ft below the top of the tank, we have:

Therefore, the volume of the water in the tank is 171.5 cubic meters.

Now, let'c convert from cubic meters to gallons.

Where:

1 foot = 0.3048 m

Thus, we have:

Now, to convert from cubic feet to gallons, where:

1 cubci foot = 7.48 gallon

We have:

Therefore, there are 45273.86 gallons of water filled in the tank.

Given:

new game cost - $ 64

used game cost - $ 43

Luis spent $ 343

Required:

Number of used games Luis purchased

Solution

Let: x be the number of new games Luis bought

x + 3 be the number of used games Luis bought

Total cost = $ 343

Total Cost = (No. of new games bought)(Cost of new games) + (No. of used games bought)(Cost of used games)

$ 343 = ( x ) ( $ 64 ) + ( x + 3 ) ( $ 43 )

343 = 64x + 43 ( x + 3 )

343 = 64x + 43x + 129

343 - 129 = 107x

214 = 107x

2 = x

x = 2

x be the number of new games Luis bought 2

x + 3 be the number of used games Luis bought 2 + 3 = 5

Answer:

Luis purchased 5 used games

To check:

Substitute x into the equation,

343 = x ( 64 ) + (x + 3 ) (43)

343 = 2 ( 64 ) + (2 + 3)(43)

343 = 2 (64) + (5) (43)

343 = 128 + 215

343 = 343

The computed value of x satisfies the equation, Our answer is correct.

Wednesday's game generated $2020

Let the amount generated by Wednesday's game be x

Let the amount generated by Saturday's game be y

The two games together earn $4920 for the team. That is,

x + y = 4920....................(1)

Wednesday's game generates $880 less than Saturday's game

x = y - 880.................(2)

Make y the subject of the formula in equation (2)

y = x + 880..................(3)

Substitute equation (3) into equation (2)

x + x + 880 = 4920

x + x = 4920 - 880

2x = 4040

Divide both sides by 2

2x/2 = 4040/2

x = 2020

Wednesday's game generated $2020

Here, we want to get what Andre's mistake was and correct it

To answer this, we are supposed to use the division law of indices

We have this as;

Now, in the case of this question, x is 4 and y is -3

So, we have the expression as;

His mistake is thus adding the exponents instead of subtracting

we have that

43.5694 * 22.07=961.576658

therefore

the answer is

961.577 -----> 6 figures

(remember that 43.5694 has 6 figures)

option C

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.

A data set is a group of figures or values related to a specific topic. a list of words, numbers, or symbols, the values of which are frequently the outcomes of an investigation or observation. There are typically multiple variables in data sets.

A dataset is an organized group of data typically connected to a certain body of work. An organized collection of data kept as several datasets is called a database.

In an ordered data set, the median is the value in the middle. The mean is calculated by dividing the sum of all values by the total number of values. The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.

Therefore, the correct answer is option c) The northbound cars were generally faster because the median for the northbound cars is greater than the median for the southbound cars.

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The time on which parents evening was due to finish was 19 hour 20 minutes.

Time is the ongoing pattern of existence and things that happen in what seems to be an irreversible order from the past, through the present, and into the future.

It is a component quantity of various measurements used to order events, compare the length of events or the time gaps between them, and quantify rates of change of quantities in objective reality or in conscious experience. Along with the three spatial dimensions, time is frequently considered a fourth dimension.

The International System of Units is built upon the seven base units of measurement stipulated by the Système International d'Unités (SI), from which all other SI units are derived. The primary unit of time is the second. The second can be shortened using either the letter S or the letter sec.

20 consecutive appointments of 10 mins = 20 × 10 mins

                                                                     = 200 min

                                                                      = 3 hours 20 mins

A break of 15 mins = 3 hours 20 mins + 15 min

                               = 3 hours 35 mins

The time that the parents evening due to finish = 15h 45 min +3h 35 mins

                                                                               = 19h 20min

Thus, the time on which parents evening was due to finish was 19h 20min.

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Using the normal distribution and the central limit theorem, it is found that:

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the glucose levels are given, respectively, by:

[tex]\mu = 85, \sigma = 25[/tex]

The probability of a reading of less than 40 mg/dl(severe excess insulin) is the p-value of Z when X = 40, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (40 - 85)/25

Z = -1.8.

Z = -1.8 has a p-value of 0.0359.

For the mean of two tests, the standard error is:

s = 25/sqrt(2) = 17.68.

Hence, by the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (40 - 85)/17.68

Z = -2.55.

Z = -2.55 has a p-value of 0.0054.

For 3 tests, we have that:

s = 25/sqrt(3) = 14.43.

Z = (40 - 85)/14.43

Z = -3.12.

Z = -3.12 has a p-value of 0.0009.

For 5 tests, we have that:

s = 25/sqrt(5) = 11.18.

Z = (40 - 85)/11.18

Z = -4.03

Z = -4.03 has a p-value of 0.

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Answer:

Explanation:

A bag contains 11 red marbles and 4 blue marbles.

• The total number of marbles = 11+4=15

1 marble of any color is chosen random from the bag with a probability of 1/15.

A situation that can be modeled using such a situation must be one that also has a probability of 1/15.

In Option D,

In order to represent three consecutive odd numbers, we can use the expressions "x", "x+2" and "x+4".

If we add the square of each number, the result is 83, so we can write the following inequality:

Let's solve this quadratic equation using the quadratic formula, with a = 1, b = 4 and c = -21:

If we assume the numbers are positive, the numbers are 3, 5 and 7.

(The other result, with negative numbers, would be -7, -5 and -3).

Given the function:

Find the first derivative:

The first derivative gives us the slope of the tangent line to the graph of the function. When the tangent line is horizontal, the slope is 0, thus:

This is a quadratic equation with coefficients a = 3, b = -8, c = -7.

To calculate the solutions to the equation, we use the quadratic solver formula:

Substituting:

Operate:

Since:

We have:

There are two solutions:

ANSWER

a = √21

EXPLANATION

This is a right triangle, so we have to apply the Pythagorean Theorem to find the value of a.

We know the length of the hypotenuse which is 5, and the length of one of the legs, which is 2. The Pythagorean Theorem for this problem is,

Subtract 2² from both sides,

And take the square root to both sides,

Hence, the value of a is √21.

Answer: f(4) = -18

Step-by-step explanation:

f(4) = -3(4 + 2)

= -3(6)

= -18

The given diagram is a traingle with base 12 units, height 4 units, and one side 9 units.

Since base (b) and height (h) are known, we can use the following formula for the area (A) of the triangle,

Substitute the values and simplify the expression,

Thus, the area of the given triangle is 24 square units.

Answer:

(b) f(2) = 28

(c) f(-2) = -20

Step-by-step explanation:

f(2) = -2^3 + 7 x 2^2 - 2 x 2 + 12           f(-2) = -2^3 + 7 x -2^2 - 2 x -2 + 12

1. Calculate Exponents

-2^3 = -8                                               -2^3 = -8

2^2 = 4                                                  -2^2 = -4

-8 + 7 x 4 - 2 x 2 + 12                           -8 + 7 x -4 - 2 x -2 + 12

2.  Multiply (left to right)

7 x 4 = 28                                               7 x -4 = -28

2 x 2 = 4                                                 2 x -2 = -4

-8 + 28 - 4 + 12                                    -8 - 28 - (-4) + 12

3. Add (left to right)

-8 + 28 = 20                                           -8 + -28 = -36

20 - 4 = 16                                              -36 - (-4)= -32

16 + 12 = 28                                            -32 + 12 = -20

Solution

A coin has two possible outcome

We have 5 marbles

The final answer

Answer:

5(km)/1(hr)

Step-by-step explanation:

You multiply the 30 minutes to make one hour, and with that, you also multiply the 2.5 kilometers to get 5. You multiply the 2.5 because we multiply both sides of an equation.

Uniform line movement.

We have that the data is:

Time (t) = 30 m = 0.5 h

Distance (d)= 2.5 km

Speed (v) = ?

Since it asks us for the speed in Km/h, we make a time conversion, from minutes to hours. Knowing that 1 hr = 60 minutes, then

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{30 \not{m}*\left(\frac{1 \ h}{60 \not{m})\right)=0.5 \ h } } \end{gathered}$}}[/tex]

To calculate the speed, divide the distance by the time. We apply the following formula:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{Speed=\frac{Distance}{Time} } \end{gathered}$}}[/tex]

We substitute our data in the formula and solve:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=\frac{d}{t} } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=\frac{2.5 \ km}{0.5 \ h} } \end{gathered}$}}[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V=5 \ km/h} \end{gathered}$} }}[/tex]

If the Manufacturing Overhead account is closed proportionally to Work in Process, Finished Goods, and Cost of Goods Sold, the related entry will include a Credit to cost of goods sold for $12000

The cost of a good is the total amount that was used in the purchase of a particular good form the market.

we have the manufacturing overhead to be = 30000 dollars

the work in progress = 30000 x 25 %

= 30000 x 0.25

= 7500

The finished goods = 30000 x 35 %

= 30000 x 0.35

= 10500

The cost of good sold = 30000 - 10500 - 7500

= 12000

Hence the cost of good sold is 12000

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Manufacturing overhead applied $ 150,000  

Actual amount of manufacturing overhead costs  120,000  

Amount of overhead applied during the year that is in:    

Work in Process $ 37,500 25 %

Finished Goods  52,500 35 %

Cost of Goods Sold  60,000 40 %

Total overhead applied $ 150,000 100 %

If the Manufacturing Overhead account is closed proportionally to Work in Process, Finished Goods, and Cost of Goods Sold, the related entry will include a ________.

debit to Cost of Goods Sold for $12,000

credit to Cost of Goods Sold for $12,000

credit to Cost of Goods Sold for $30,000

debit to Work in Process for $7,500

The rate at which the distance between the two cars increased four hours later is 30 mi/h.

First of all, we would determine the distances travelled by each of the cars. The distance travelled by the first car after four (4) hours is given by:

Distance, x = speed/time

Distance, x = 24/4

Distance, x = 6 miles.

For the second car, we have:

Distance, y = speed/time

Distance, y = 18/4

Distance, y = 4.5 miles.

After four (4) hours, the total distance travelled by the two (2) cars is given by this mathematical expression (Pythagorean theorem):

z² = x² + y²

Substituting the parameters into the mathematical expression, we have;

z² = 6² + 4.5²

z² = 36 + 20.25

z² = 56.25

z = 7.5 miles.

Next, we would differentiate both sides of the mathematical expression (Pythagorean theorem) with respect to time, we have:

2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)

Therefore, the rate of change of speed (dz/dt) between the two (2) cars is given by:

dz/dt = [x(dx/dt) + y(dy/dt)]/z

dz/dt = [6(24) + 4.5(18)]/7.5

dz/dt = [144 + 81]/7.5

dz/dt = 225/7.5

dz/dt = 30 mi/h.

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Answer:

30 mi / hr

Step-by-step explanation:

First find out how far the cars are apart after 4 hours

24 * 4 = 96 mi = y

18 * 4 = 72 mi = x

Now use the pythagorean theorem

   s^2 =  ( x^2 + y^2 )                shows s = 120 miles apart at 4 hours

Now s^2 = x^2 + y^2     Differentiate with respect to time ( d  / dt )

       2 s ds/dt    =  2x dx/ dt  + 2y dy / dt

             ds/dt    =   (x dx/dt + y dy/dt)/s

                           =  (72(18)  + 96(24)) / 120

               ds/dt   = 30 mi/hr

The price of the chair will be 261.9 $ .

One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. For example, 1 percent of 1,000 chickens equals 1/100 of 1,000, or 10 chickens; 20 percent of the quantity is 20/100 1,000, or 200.

If we say, 5%, then it is equal to 5/100 = 0.05.

To solve percent problems, you can use the equation, Percent · Base = Amount, and solve for the unknown numbers. Or, you can set up the proportion, Percent = , where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion.

Based on given conditions formulate

x = 194 ×(35%+1)

x= 194 ×1.35

x = 261.9 $ .

Thus The price of the chair will be 261.9 $ .

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The algebraic expression which correctly represents the word phrase and it's solution are respectively; 29 equals 11.5 plus m over 2.5; m = 43.75.

It follows from the task content that the algebraic expression of which represents the word phrase is to be determined.

First, the quotient of a number, m and 2.5 can be represented algebraically as; m/2.5.

Therefore, since; Twenty-nine equals the sum of 11.5 and the quotient of a number and 2.5, we have;

29 = 11.5 + (m/2.5)

The solution is therefore as follows;

29 -11.5 = (m/2.5)

17.5 = (m/2.5)

m = 2.5 × 17.5

m = 43.75.

Therefore, the correct answer choice is; 29 equals 11.5 plus m over 2.5; m = 43.75.

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We are asked to find the final expression in exponent for, of the product of two radical expressions as shown below:

We will be addressing each factor at a time, first in the cubic root, and second in the square root.

Cubic root:

notice that the pure number (64) can be written as the perfect cube of the number 4 since 4^3 = 64. That means that a factor 4 will come out of the cubic root, and no factor 4 will be left in the root.

Now we are going to address the variables g and y which are inside the root, and try to find if they contain any perfect cube expression (perfect cubes will cancel out of the cubic root simplifying then the notation).

We notic that g^4 can be written as g^3 times g, so g^3 will come out of the cubic root as "g", and a factor "g" would be left inside the cubic root. Similarly, the factor y^2 cannot get out of the cubic root because it doesn't have a perfect cube in it.

We are then left with the following expression:

Now, we recall the property of fractional exponents associated with roots of a factor:

Using this, the cubic root can be expressed as fractional exponents, as we show below:

Now we proceed to simplify the expression with the square root. This is much simpler, since all factor inside can be written as perfect squares:

64 = 8^2

g^4 = (g^2)^2 (the double square of g)

y^2 is already a perfect square.

Therefore, the square root is simplified entirely and we are left with the following factors:

8 g^2 y

Now we combine via the multiplication what we found for the cubic root and what we found for the square root:

Therefore the power (r) of the factor g is the fraction: 10/3

The power (s) of the factor y is the fraction 5/3

and the constant number "k" is 32.

Answer:

See below and attached Venn Diagram3

Step-by-step explanation:

No need to change Venn diagrams It is perfectly clear

The completed Venn Diagram is attached for your convenience