Andrew would like to put six different Rubik's cubes onto 3 shelves. The order of the cubes does not matter.
In how many ways can Andrew do this if a shelf can have zero cubes?
What if each shelf must have at least one cube?

The values of a, b and c are a = 2, b = -10 and c = -20

The equation is given as

(ax + 2)(5x + b) = 10x^2 + bx + c

Open the brackets

So, we have

5ax^2 + 10x + abx + 2b = 10x^2 + bx + c

By comparing the above equation.

We have the following set of equations

5a = 10

10 + ab = b

2b = c

By solving the equations, we have

a = 2

Substitute a = 2 in 10 + ab = b

10 + 2b = b

So, we have

b = -10

Substitute b = -10 in 2b = c

2(-10) = c

Evaluate

c = -20

Hence, the values of the variables are a = 2, b = -10 and c = -20

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Answer:

[tex]\frac{41}{100}[/tex]

Step-by-step explanation:

It cannot be simplified.

Ex: 50% can be simplified to [tex]\frac{1}{2}[/tex]

architecture, invest money so that I can pay fr fees

Answer: [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex]

Step-by-step explanation:

If the numbers have at least one 2 and at least one 5, then they are multiples of 10 (since [tex]10=2 \times 5[/tex]).

So, these numbers are [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex].

In the above question, we need to from 3 probability questions and then give solutions for them

Example 1 : A coin is tossed three times. What is the probability of getting at least one head?

Solution : A coin is tossed 3 times then

Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]

Total number of ways = 2 × 2 × 2 = 8

Favorable Cases = 7

P (A) = 7/8

OR

Probability (of getting at least one head) = 1 – P (no head)⇒ 1 – (1/8) = 7/8

Example 2 : Three red and four black balls are contained in a bag. Randomly, one ball gets taken out of the bag. Determine the probability that the drawn ball is

(i) black

(ii) not black

Solution :

Total number of balls in the bag are = 3 + 4 = 7 balls

Number of favorable outcomes or number of black balls in the bag = 4

(i) Probability getting black balls = [tex]\frac{number of favorable outcomes}{number of total outcomes}[/tex]

P(black ball) = [tex]\frac{4}{7}[/tex]

(ii)  Probability getting no black balls = 1 - P(black ball)

= 1 - [tex]\frac{4}{7}[/tex]

= [tex]\frac{3}{7}[/tex]

Example 3 : Given two dice, what is the likelihood of receiving the number 7?

Mathematical probability - There are 36 ways in all, or 6 times 6. Favorable scenarios are (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3), etc., in six different ways. P (A) = 6/36 = 1/6

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Answer:

  4.  (d)

  5.  (b)

Step-by-step explanation:

You want to apply the secant and chord rules to the circles given in the diagram.

The secant rule is "the product of distances from the point of intersection of secants to the two points of intersection of the secant with the circle is the same for both secants." A tangent can be considered to be a secant that has both points of intersection with the circle in the same place.

The chord rule is similar to the secant rule: "The product of distances from the point of intersection of the chords to their intersection with the circle is the same for both chords."

The diagram shows a tangent of length 12, so the product of distances to the two points of intersection with the circle is 12(12).

The secant has length 8 to the near point of intersection, and (x+8) to the far point of intersection. That product is the same as for the tangent:

  8(x +8) = 12(12) . . . . . . matches choice D

One chord has lengths of 14 and x, so the product of those is 14x.

The other chord has lengths of 12 and 21, so the product of those is 12(21).

The product is the same for both chords, meaning ...

  14x = 12(21) . . . . . . matches choice B

__

Additional comment

We have purposely tried to write the rules in "parallel" fashion, because we find them easier to remember that way. Considering a tangent to be a secant with the points of intersection with the circle merged means the same rule can be used for all three cases:

The farmer will purchase five bags of kind A and six bags of type B.

Per bag, Type A includes 9 pounds of oats and 3 pounds of maize.

Per bag, Type B includes 2 pounds of oats and 10 pounds of maize.

The farmer is looking for a blend that comprises at least 57 pounds of oats and 75 pounds of maize.

Allow the farmer to mix type A feed = x pounds.

and feed type B = y pounds

(9x + 2y) pounds of oats when blended

Corn amount when combined: (3x + 10y) pounds

Oats equation: 9x + 2y = 57 ———— (1)

Corn equation: 3x + 10y = 75 ————- (2)

Subtract equation (2) from equation (2) by multiplying it by three (1)

3(3x + 10y) - (9x + 2y) = 75×3 - 57

9x + 30y - 9x - 2y = 225 - 57

28y = 168

y = 6 bags

derived from the equation (1)

9x + 2×6 = 57

9x + 12 = 57

9x = 57 - 12

9x = 45

x = 5 bags

Because the business has 15 bags of each sort, each bag costs $4.

As a result, the cost of 5 bags of type A and 6 bags of type B is = (54) + (64)

= 20 + 24

= $44

The farmer intends to buy five bags of kind A and six bags of type B.

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A car salesman earns a 3% commission on sales. If he sells a car for $27,990, how much commission will he earn?

($27,990)*(0.03) = $839.70

The Jones family will pay their insurance broker a commission of $1,750.00.

Commission is an amount of money paid to an employee or company as an incentive to sell more. A straight commission is a percentage of sales.

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Answer: The value of the house when it was purchased was 120,000

Step-by-step explanation:

1) Set up the equation. Let x be the house.

x-x*35%= 78,000

First, the house decreases 35% of the cost of the original house. It now costs 78,000.

2) Solve the equation.

x-x*0.35 = 78,000

x-0.35x=78,000

0.65x = 78,000

x= 120,000

The coordinate that represent the solution of the equation -

x² - 3x = x² - 1 is (0.333, -0.8889).

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given is the following equation -

x² - 3x = x² - 1

In order to solve it using intersect method, we will plot the graphs of both functions and find the point of intersection of graphs of both the equations.

Assume -

f(x) = x² - 3x

g(x) = x² - 1

Now, the point of intersection of both the graphs will be the solution to the equation given by -

f(x) = g(x)

It can be seen from the graph that, both the graphs intersect at the coordinate (0.333, -0.8889). This coordinate will be the solution set of the equation -

f(x) = g(x)

Therefore, the coordinate that represent the solution of the equation -

x² - 3x = x² - 1 is (0.333, -0.8889).

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Answer:

Step-by-step explanation:

x cannot be -3 or 2

Step-by-step explanation:

f(g(x)) = 1 / (( x-2) +5)

        = 1/ (x+3)

g(x) cannot have x=2

The domain is restricted where

f(x) has an restriction that x cannot be 5

so g(x) cannot be -5

-5 = x-2

Add 2 to each side

-5+2 = x

-3

Answer:

40

Step-by-step explanation:

5*(2^3)=40

Answer:

It is arithmetic, the common difference is 5

Step-by-step explanation:

What an arithmetic sequence has to have is a common difference meaning you are adding or subtracting the same number each time, in this case you are adding 5 every time so it is arithmetic

y=-1/3-4

Step-by-step explanation:

point slope form!

y-y=m(x-x)

with the point (-6,-2) and the slope (-1/3) replace the 2nd variables of each variable and replace m with the slope

y-(-2)=-1/3(x-(-6))

then solve that normally

y-(-2)=-1/3(x-(-6))

y+2=-1/3x -2

y=-1/3x-4

I didnt use officially math symbols but i hope you can still read it!

The US GDP for the first quarter of 2020 was 21.54 trillion dollars, and the US GDP for the second quarter of 2020 was 19.49 trillion dollars.

The personal consumption expenditures for the first quarter of 2020 are 13.02 trillion dollars.

the personal consumption expenditures for the second quarter of 2020 are 11.82 trillion dollars.

What are the personal consumption expenditures?

Personal consumption expenditures are the price that citizens of the US pay for goods and services. This is a crucial index that indicates inflation or deflation and consumer behavior over some time.

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Answer: A = 452.16 ft²

Step-by-step explanation:

      This gives us the formula to solve for the area.

                     A = πr²

      The radius (r) is the same as the diameter divided by 2.

                     24 ft / 2 = 12 ft

      We will input these given values and solve.

A = πr²

A = (3.14)(12)²

A = 452.16 ft²

Answer:

452.16 ft²

Step-by-step explanation:

To find the radius, you divide the diameter (24) by 2, which equals 12. The area of a circle formula is πr². To find area, you do 12² * 3.14. That equals 144 * 3.14, which equals 452.16.

Answer:

1. 12hrs

2. 2hrs

Step-by-step explanation:

4:00pm is 2 hrs from 6:00pm

5:00am is 12hrs from 5:00pm

At 1000 seconds the graph shows the height of 3500 meter.

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

Following the creation of a research question, data is continuously gathered through observation. The information is subsequently arranged, condensed, categorised, and visually portrayed.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Usually, data that varies over time is represented with a line graph.

Given:

The graph gives the relation between Elevation and Time.

As, if at 400 seconds the height is 6500 meters.

and, at 800 seconds the height is 4500 meters.

Thus, at 1000 seconds the graph shows the height of 3500 meter.

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Answer:

k<-8.82

Step-by-step explanation:

k/1.8<-4.9

k<-8.82

Answer:k<-8.82

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

n ≥ -5

Step-by-step explanation:

-2n ≤ 10

Divide both sides by -2. Remember to flip ≤ to ≥.

-2n/(-2) ≥ 10/(-2)

n ≥ -5

using calculator

Area right to the right of the 2=2.12

P(Z > 2.12)

• P(Z < -2.12)

= 0.0170

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (4500)(0.08)(1) \implies I = 360~\hfill \underset{monthly~payment}{\stackrel{360 ~~ \div ~~ 12}{\text{\LARGE 30}}}[/tex]

c.

PRT/100

4500×8×1/100=360

per month=360÷12

=30

The unit price per ounce at Price-Club is $0.29 per ounce and the unit price per ounce at Shop Mart is $0.21 per ounce.

The unit price can be determined by dividing the total cost by the total ounce that is purchased.

Division is the process of putting a number into  equal groups using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. The result of the division process is known as the quotient. Other mathematical operations include addition, subtraction and multiplication.

Unit price = total cost / total ounce sold

Unit price of Price-Club = $3.44 / 12 = $0.29 per ounce

In order to determine the unit price of Shop Mart, pounds have to be converted to ounces

1 pound = 16 ounces

To convert 2 1/2 pounds to ounces, multiply 2 1/2 by 16. Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

16 x 2 1/2

16 x 5/2 = 40 ounces

Unit price of Shop Mart = $8.35 ÷ 40 = $0.21 per ounce

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Triangle LMN is an obtuse angle then, the angle at vertex L is acute, the angle at vertex N is acute.

The triangle LMN is an obtuse angle at the vertex M. So by the definition of obtuse angle triangle LMN is an obtuse angle.

As ∠M is an obtuse angle

So 90° < m∠M < 180°

By the property of a triangle,

m∠L + m∠M + m∠N = 180°

m∠M = 180° - (m∠L + m∠N)

90° < 180° - (m∠L + m∠N) < 180°

90° - 180° < -(m∠L + m∠N) < 0

-90° < -(m∠L + m∠N) < 0

90° >(m∠L + m∠N) > 0

90° > m∠L  and 90° > m∠N

Therefore both angles L and N are acute angles.

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Answer:

1, 2 and 5

Step-by-step explanation:

see picture

Answer:

39 dollars

Step-by-step explanation: 20 perrcent of 52