What are the explicit and recursive formulas for the sequence 540, 180, 60, 20, ...?

Answers

Answer 1

Here we have a geometric sequence, the recursive formula is:

Aₙ = (1/3)*Aₙ₋₁

And the explicit formula is:

Aₙ = (1/3)*ⁿ⁻¹*540

How to get the recursive formula?

Here we have the following sequence:

540, 180, 60, 20, ...

This seems to be a geometric sequence, to check this, we need to take the quotients between consecutive terms and see if we get the same thing.

180/540 = 1/3

60/180 = 1/3

20/60 = 1/3

So yes, this is a geometric sequence where the common ratio is 1/3, so each term is (1/3) times the previous one, so the recursive formula is:

Aₙ = (1/3)*Aₙ₋₁

And the explicit formula is:

Aₙ = (1/3)*ⁿ⁻¹*A₁

Where A₁ is the first term, in this case 540, so the formula becomes:

Aₙ = (1/3)*ⁿ⁻¹*540

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Related Questions

Identify the range of the function shown in the graph. 10 8 4 -10-8-4-2 8 10 O A. -2< y < 2 O B. {-2, 2) O C. y is all real numbers OD. Y > 0

Answers

Answer

Option B is correct.

Range: y is all real numbers.

Explanation

The range of a function refers to the region of values where the function can exist. It refers to the values that the dependent variable [y or f(x)] can take on. It is the region around the y-axis that the graph of the function spans.

For this question, we can see that the graph spans over the entire y-axis.

Hence, the range of this function shown in the graph is all real number.

Hope this Helps!!!

If sin A = 3/5 and cos B = 20/29 and angles A and B are in Quadrant 1, find the valueof tan(A + B).

Answers

Our approach is to use SOHCAHTOA to derive values for sine and cosines of both A and B.

[tex]\begin{gathered} \sin A=\frac{3}{5},\text{ cosA=}\frac{\sqrt[]{5^2-3^2}}{5}=\frac{4}{5} \\ \cos B=\frac{20}{29},\text{ sinB=}\frac{\sqrt[]{29^2-20^2}}{29}=\frac{21}{29} \end{gathered}[/tex][tex]\begin{gathered} \tan (A+B)=\frac{\tan A+\tan B}{1-\text{tanAtanB}}\text{ WHERE} \\ \tan A=\frac{\sin A}{\cos A},\tan B=\frac{\sin B}{\cos B} \end{gathered}[/tex][tex]\begin{gathered} \tan (A+B)=\frac{\frac{\frac{3}{5}}{\frac{4}{5}}+\frac{\frac{21}{29}}{\frac{20}{29}}}{1-\frac{\frac{3}{5}}{\frac{4}{5}}\times\frac{\frac{21}{29}}{\frac{20}{29}}}=\frac{\frac{3}{4}+\frac{21}{20}}{1-\frac{3}{4}\times\frac{21}{20}}=\frac{\frac{9}{5}}{1-\frac{63}{80}}=\frac{\frac{9}{5}}{\frac{17}{80}} \\ \tan (A+B)=8.47 \end{gathered}[/tex]

tan (A+B) = 8.47

How many different lineups can Coach Lay create using 10 girls to fill 5 spots on the basketball court. Positions do not matter.

Answers

This is the formula for combinations

In this case, n = 10 and k = 5

C = 10!/(10-5)!(5)! = 3628800/(120)(120) = 3628800/14400 = 252

Answer:

252 different line u

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.

Answers

We will have the following:

[tex]\sin (2\theta)=-\frac{1}{2}\Rightarrow2\theta=2\pi n_1+\frac{7\pi}{6}[/tex][tex]\Rightarrow\theta=\pi n_1+\frac{7\pi}{12}[/tex]

Now, we will solve for the following:

[tex]\Rightarrow\pi n_1+\frac{7\pi}{12}\le2\pi\Rightarrow\pi n_1\le\frac{17\pi}{12}[/tex][tex]\Rightarrow n_1\le\frac{17}{12}[/tex]

This value in degrees is:

[tex]\frac{17}{12}\text{radians}=81.169\text{degrees}[/tex]

So, the solution is located in the interval:

[tex]\lbrack0,81\rbrack[/tex]

The volume, V, of a cube with edge length s cm is given by the equation V=s3.Is the volume of a cube with edge length s=3 greater or less than the volume of a sphere with radius 3?If a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere?Compare the outputs of the two volume functions when the inputs are 2?

Answers

We have that the volume of sphere is

[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot r^3 \\ \end{gathered}[/tex]

and the volume of a cube is

[tex]V_c=s^3[/tex]

so if s=r=3. The volume of the sphere is greater.

If they have the same volume, we get that

[tex]\begin{gathered} \frac{4}{3}\pi\cdot r^3=125\rightarrow \\ r^3=\frac{3}{4\cdot\pi}\cdot125\approx29.84\approx30 \\ r=\sqrt[3]{30}\approx3.10 \end{gathered}[/tex]

when s=r=2 we have that

[tex]\begin{gathered} V_s=\frac{4}{3}\pi\cdot8=\frac{32}{3}\pi \\ V_c=8 \end{gathered}[/tex]

so the volume of the sphere is greater

how do you work the problem 3k+16=5k?

Answers

We have the following:

[tex]3k+16=5k[/tex]

solving for k

[tex]\begin{gathered} 5k-3k=16 \\ k=\frac{16}{2} \\ k=8 \end{gathered}[/tex]

The value of k is 8

The dog looked at the cat warily A with interestb viciously c hungrily d with caution

Answers

Answer

Option D is correct.

The dog looked at the cat with caution.

is the same as

The dog looked at the cat warily.

Explanation

The word warily means 'using caution' or 'cautiously'.

Hope this Helps!!!

9. A researcher gathered data on hours of video games played by school-aged children and young adults. She collected the following data:601241215171711409914110131015163915121698131016651717129(a) Complete the frequency distribution for the data.HoursFrequencyRelative Frequency0-23-56-89-1112-1415-17(b) Which of the following is the correct histogram for this data?246810Hours0369121518Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,10);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.2],[0,0.2]); text([0,0],"0","below");line([3,-0.2],[3,0.2]); text([3,0],"3","below");line([6,-0.2],[6,0.2]); text([6,0],"6","below");line([9,-0.2],[9,0.2]); text([9,0],"9","below");line([12,-0.2],[12,0.2]); text([12,0],"12","below");line([15,-0.2],[15,0.2]); text([15,0],"15","below");line([18,-0.2],[18,0.2]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[3,6]);rect([3,0],[6,4]);rect([6,0],[9,5]);rect([9,0],[12,7]);rect([12,0],[15,6]);rect([15,0],[18,10]);]246810121416Hours061218Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,16);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.32],[0,0.32]); text([0,0],"0","below");line([6,-0.32],[6,0.32]); text([6,0],"6","below");line([12,-0.32],[12,0.32]); text([12,0],"12","below");line([18,-0.32],[18,0.32]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[6,10]);rect([6,0],[12,12]);rect([12,0],[18,16]);]2468101214Hours061218Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(0,18,0,14);axes(34,2,1,null,2); fill="blue"; textabs([165,0],"Hours","above");line([0,-0.28],[0,0.28]); text([0,0],"0","below");line([6,-0.28],[6,0.28]); text([6,0],"6","below");line([12,-0.28],[12,0.28]); text([12,0],"12","below");line([18,-0.28],[18,0.28]); text([18,0],"18","below");textabs([0,115],"Frequency","right",90);rect([0,0],[6,12]);rect([6,0],[12,14]);rect([12,0],[18,12]);]2468Hours0369121518

Answers

(a)

Remember that the frequency refers to the number of times a data shows up. In this case, the frequency is the number of data that falls into each interval.la

To find the relative frequency is calculated by dividing each frequency by 38 (the total number of data).

[tex]\begin{gathered} \frac{6}{38}=0.1579 \\ \frac{4}{38}=0.1053 \\ \frac{4}{38}=0.1053 \\ \frac{8}{38}=0.2105 \\ \frac{7}{38}=0.1842 \\ \frac{9}{38}=0.2368 \end{gathered}[/tex]

Let's include the relative frequencies in the table.

On the other hand, the correct histogram has to show the frequencies in the same order. The following histogram shows the correct frequency distribution.

You start at (9,2). you move left 9 units. where do you end

Answers

If you start at (9,2) and then move left 9 units, you'll end up at (0, 2)

What is the length of the arc ? ( Precalc )

Answers

We're going to use the following formula:

[tex]L=2\cdot\pi\cdot r\cdot\frac{\theta}{360}[/tex]

If we replace our values:

[tex]L=2\cdot\pi\cdot3\cdot\frac{60}{360}=\pi[/tex]

Therefore, the length is pi.

Ali borrowed Php22,000 for 3months at the discount rate of 5 ¼ % from a bank. Find the (a) bank’s discount and (b) proceeds.

Answers

If an M amount is borrowed for a time t at a discount rate of r per year, then the discount D is calculated as

[tex]\begin{gathered} D=M\cdot r\cdot t \\ \\ \text{where} \\ r\text{ is expressed in decimals} \end{gathered}[/tex][tex]\begin{gathered} \text{Given} \\ M=22000 \\ r=5\frac{1}{4}\%\rightarrow5.25\%\rightarrow0.0525 \\ t=\mleft(\frac{3}{12}\mright)\text{or }0.25\text{ (3 months out of 1 year or 12 months} \end{gathered}[/tex]

Substitute the following values to get the bank's discount.

[tex]\begin{gathered} D=Mrt \\ D=(22000)(0.0525)(\frac{3}{12}) \\ D=288.75 \end{gathered}[/tex]

Therefore, the bank's discount is Php 288.75.

To calculate for proceeds, subtract the amount borrowed by the bank's discount.

[tex]\begin{gathered} P=M-D \\ P=22000-288.75 \\ P=21711.25 \end{gathered}[/tex]

The proceeds given to Ali is Php 21,711.25.

I need to help finding the length of the arc shown in red..

Answers

We have the next formula to find the length is

[tex]\text{arc length }=\text{ 2}\pi r(\frac{\theta}{360})[/tex]

where

r=10

theta=45°

[tex]\begin{gathered} \text{arc length=}2\pi(10)\frac{45}{360}=\frac{5}{2}\pi \\ \end{gathered}[/tex]

the arc length is 5/2 pi cm

The area of an equilateral triangle is decreasing at a rate of 3 cm2/min. Find the rate (in centimeters per minute) at which the length of a side is decreasing when the area of the triangle is 100 cm2.

Answers

The rate at which the length of a side is decreasing when the area of the triangle is 100 cm² is equal to -0.227 centimeters per minute.

What is rate of change?

Rate of change is a type of function that describes the average rate at which a quantity either decreases or increases with respect to another quantity.

How to calculate the area of an equilateral triangle?

Mathematically, the area of an equilateral triangle can be calculated by using this formula;

A = (√3/4)s²

Where:

A represents the area of an equilateral triangle.s represents the side length of an equilateral triangle.

Next, we would determine the side length of a square by making s the subject of formula as follows:

s = (√4A)/√3

s = (√4 × 100)/√3

Side length, s = 15.20

Note: The rate of change (dA/dt) is negative because it is decreasing.

By applying chain rule of differentiation, the rate of change (dA/dt) in area of this equilateral triangle with respect to time is given by:

dA/dt = (√3/4)(2s)ds/dt

dA/dt = (√3/4) × (2 × 15.20) × -3

dA/dt = -0.227 centimeters per minute.

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Find the 1st term, last term and the sum for the finite arithmetic series.

Answers

Answer:

Given that,

[tex]\sum ^{30}_{n\mathop=2}(3n-1)[/tex]

Simplifying we get,

[tex]\sum ^{30}_{n\mathop{=}2}(3n-1)=\sum ^{30}_{n\mathop{=}2}3n+\sum ^{30}_{n\mathop{=}2}1[/tex][tex]=3\sum ^{30}_{n\mathop{=}2}n+\sum ^{30}_{n\mathop{=}2}1[/tex]

we have that,

[tex]\sum ^n_{n\mathop=1}1=n[/tex]

If n is from 2 to n we get,

[tex]\sum ^n_{n\mathop{=}2}1=n-1[/tex]

Also,

[tex]\sum ^k_{n\mathop=1}n=\frac{k(k+1)}{2}[/tex]

If n is from 2 to n we get,

[tex]\sum ^k_{n\mathop=2}n=\frac{k(k+1)}{2}-1[/tex]

Using this and substituting in the required expression we get,

[tex]=3\lbrack\frac{30\times31}{2}-1\rbrack+30-1[/tex][tex]=3(464)+29[/tex][tex]=1421[/tex]

Answer is: 1421

The table gives a set of outcomes and their probabilities. Let A be the event the outcome is divisible by 3". Find P(A). 12 Outcome Probability Tim elaps 1 0.14 PAUS 2 0.02 3 0.19 Smart out of 4 0.01 5 0.04 7 6 0.17 7 0.15 8 0.28

Answers

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;

[tex]P(A)\text{ = 0.19 + 0.17 = 0.36}[/tex]

All changes saved16. Suppose you invest $7500 at an annual Interest rate of 4.2% compounded continuously. How much will you have in the account after 2 years? Round the solution to the nearest dollar.$8158$17,372$17,373$8157

Answers

We have to use the continuous compound interest formula

[tex]A=P\cdot e^{rt}[/tex]

Where P = 7500, r = 0.042, t = 2. Let's replace and solve

[tex]\begin{gathered} A=7500\cdot e^{0.042\cdot2} \\ A\approx8,157 \end{gathered}[/tex]Hence, the answer is $8,157.

Lesson 6.07: In a random sample of 74 homeowners in a city, 22 homeowners said they wouldsupport a ban on nonnatural lawn fertilizers to protect fish in the local waterways. The samplingmethod had a margin of error of +3.1%. SHOW ALL WORK!A) Find the point estimate.B) Find the lower and upper limits and state the interval.

Answers

Confidence interval is written in the form,

(point estimate +/- margin of error)

The given scenario involves population proportion

The formula for the point estimate is

p' = x/n

where

p' = estimated proportion of success. p' is a point estimate for p which is the true proportion

x represents the number of success

n represents the number of samples

From the information given,

n = 74

x = 22

p' = 22/74 = 0.297

The formula for finding margin of error is expressed as

[tex]\begin{gathered} \text{margin of error = z}_{\frac{\alpha}{2}}(\sqrt[]{\frac{p^{\prime}q^{\prime}}{n}} \\ q^{\prime}\text{ = 1 - p'} \\ q^{\prime}\text{ = 1 - 0.297 = 0.703} \end{gathered}[/tex]

A) The point estimate is 0.297

B) margin of error = +/-3.1% = 3.1/100 = +/- 0.031

Thus,

the lower limit would be 0.297 - 0.031 = 0.266

Expressing in percentage, it is 0.266 x 100 = 26.6%

the upper limit would be 0.297 + 0.031 = 0.328

Expressing in percentage, it is 0.328 x 100 = 32.8%

Thus, the confidence interval is between 26.6% and 32.8%

Please help me I need the answer asap.

Answers

Therefore the right answer is option D = 1. The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation.

What are linear equations?An equation with the form Ax+By=C is referred to as a linear equation. It consists of two variables combined with a constant value that exists in each of them. The values of the variables will be obtained when the system of linear equations is solved; this is referred to as the solution of a linear equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.A two-variable linear equation can be thought of as a linear relationship between x and y, or two variables whose values rely on each other (often y and x) (usually x).

Hence,

The correct Option is D = 1

Given

[tex]x^2+x-1\\[/tex] = 0

[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex] = ?

From  [tex]x^2+x-1\\[/tex] = 0

[tex]x^2 = 1-x[/tex]

Therefore,

[tex]\frac{1-x}{2x^2} +\frac{ x^2}{2x-2}[/tex]  =  [tex]\frac{x^2}{2x^2} + \frac{x^2}{2(x-1)}[/tex]

[tex]\frac{1}{2} + \frac{x^2}{2(x-1)}[/tex]

[tex]\frac{1}{2} + \frac{1}{2}[/tex]

= 1

Therefore the right answer is option D = 1

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The graph of f(a) = > has been transformed to create the graph of g(s) =

Answers

EXPLANATION

The graph of the parent function: f(x) = 1/x has the following form:

Translating the function two units to the left, give us the Image function:

This function is obtained by adding two units to the denominator.

In conclusion, the solution is -2

Find conditions on k that will make the matrix A invertible. To enter your answer, first select 'always', 'never', or whether k should be equal or not equal to specific values, then enter a value or a list of values separated by commas.

Answers

To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible.

What is a matrix?

matrix, a collection of numbers lined up in rows and columns to produce a rectangular array.

In computer graphics, where they have been used to describe picture transformations and other alterations.

The elements of the matrix, also known as the entry, are the numerals.

A matrix will be invertible only and only if the determinant is non-zero.

Given the matrix A.

The determinant of A is that |A| will be,

|A| = -3(8 - 8) - 0(-k + 2) - 3(-4k + 8) ≠ 0

0 + 0 + -3(-4k + 8) |A| ≠ 0

-4k + 8 ≠ 0

-4k ≠ -8

k ≠ 2

Hence "To be a matrix to be invertible the determinant of the matrix must be non zero thus for k ≠ 2 the matrix will be invertible".

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50 Points
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.
Part A: What is the expression that represents the area of the rectangle? Show your work.
Part B: What are the degree and classification of the expression obtained in Part A?

Part C: How does Part A demonstrate the closure property for the multiplication of polynomials?

Answers

The expression that represents the area of the rectangle is 6x²+29x+35.

Given that, a rectangle has sides measuring (2x + 5) units and (3x + 7) units.

What is the area of a rectangle?

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Part A:

Now, area = (2x+5)(3x+7)

= 2x(3x+7)+5(3x+7)

= 6x²+14x+15x+35

= 6x²+29x+35

So, the area of a rectangle is 6x²+29x+35

Part B:

A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.

Here, the degree of the expression 6x²+29x+35 is 2.

Part C:

Closure property of multiplication states that if any two real numbers a and b are multiplied, the product will be a real number as well.

Here, we obtained product of two binomials is trinomial

Therefore, the expression that represents the area of the rectangle is 6x²+29x+35.

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John starting playing video games as soon as he got home from school. He played videogames for 45 minutes. Then, it took John 30 minutes to finish his homework. When Johnfinished his homework, it was 4:25 P.M. What time did John get home from school?

Answers

Given:

After coming from school to home,

He played video games for 45 minutes.

Then he took 30 minutes to finish his homework.

When John finished his homework, it was 4:25 PM.

To find:

The time at which John got home from school

Explanation:

According to the problem,

Total time to play video games and do homework is,

[tex]\begin{gathered} 45mins+30mins=75mins \\ =1hr15mins \end{gathered}[/tex]

So, the time he got home from school will be,

[tex]4:25P.M.-1hr15mins=3:10P.M.[/tex]

Final answer:

The time he got home from school is 3:10 P.M.

Find the equation of the tangent line to the curve y = x^3- 4x - 5 at the point (2, -5).Tangent Line Equation:

Answers

Let's find the derivative of y:

[tex]\begin{gathered} y=x^3-4x-5 \\ \frac{dy}{dx}=3x^2-4 \end{gathered}[/tex]

Evaluate the derivative for x = 2:

[tex]\frac{dy}{dx}\begin{cases} \\ x=2\end{cases}=3(2)^2-4=12-4=8[/tex]

Now, we have the slope, let's use the point-slope formula to find the equation:

[tex]\begin{gathered} y-y1=m(x-x1) \\ _{\text{ }}where\colon \\ (x1,y1)=(2,-5) \\ m=8 \\ y+5=8(x-2) \\ y+5=8x-16 \\ y=8x-21 \end{gathered}[/tex]

Answer:

y = 8x - 21

At a point on the ground 35 ft from base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree. The height of the tree is ___. (ft^3, ft^2, or ft)(Simply your answer. Round to the nearest foot as needed)

Answers

At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree

see the attached figure to better understand the problem

Applying the Pythagorean Theorem

(3h+1)^2=h^2+35^2

9h^2+6h+1=h^2+1,225

solve for h

9h^2-h^2+6h+1-1,225=0

8h^2+6h-1,224=0

Solve the quadratic equation

Using a graphing tool

the solution is

h=12 ft

Anna's room is a rectangle. Its length is 15 feet and its width is 4 yards. What is the perimeter of the room?

Answers

Answer:

38

Step-by-step explanation:

Perimeter is basically each side added together. 15 + 15 + 4 + 4 is 38. Therefore, it's 38.

Through (1,-2) parallel to y=-2x+5

Answers

Answer:

Step-by-step explanation:The line parallel to y = -2x + 5 that passes through the point(1,1)

Has the same slope, m but a different y intercept (0,b)

So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b

y = mx + b

m = -2

1 = -2(1) + b

1 = -2 + b

Add 2 to both sides of the equation to solve for b

1 + 2 = b

3 = b

The line is

y = -2x + 3

11 gallons Blue Car 2 of gas 35.4 miles A gallons 27 miles Silver Car 5 14. You are running a fuel economy study. You want to find out which car can travel a greater distance on 1'gallon of gas. a. What is the gas mileage, in miles per gallon, for the blue car? b. What is the gas mileage, in miles per gallon, for the silver car? c. Which car could travel the greater distance on 1 gallon of gas?

Answers

Answer:

a) 23.67 miles per gallon

b) 34 miles per gallon

c) The silver car could travel a greater distance.

Step-by-step explanation:

a)

Conversion of the mixed numbers to fractions:

[tex]1\frac{1}{2}=\frac{1\ast2+1}{2}=\frac{2+1}{2}=\frac{3}{2}[/tex][tex]35\frac{1}{2}=\frac{35\ast2+1}{2}=\frac{70+1}{2}=\frac{71}{2}[/tex]

Gas mileage:

3/2 gallons - 71/2 miles

1 gallons - x miles

Simplifying the top line by 2.

3 gallons - 71 miles

1 gallon - x miles

3x = 71

x = 71/3

x = 23.67 miles per gallon

b)

Conversion of the mixed number to fraction:

[tex]27\frac{1}{5}=\frac{27\ast5+1}{5}=\frac{135+1}{5}=\frac{136}{5}[/tex]

Mileage:

4/5 gallons - 136/5 miles

1 gallon - x miles

Simplifying the top line by 5

4 gallons - 136 miles

1 gallon - x miles

4x = 136

x = 136/4

x = 34 miles per gallon

c)

Blue car: 23.67 miles per gallon

Silver car: 34 miles per gallon

Silver car could travel a greater distance.

l show how the distributive property can make the arithmetic simpler in the following problems5(108)

Answers

Firstly Example of Distributive property can be shown below.

GIiven: 6(9 - 4)

6 x 9 - 6 x 4

54 - 24 = 30

a) 3(50.15)

3(50 + 0.15)

3x50 + 3 x0.15

150 + 0.45 = 150.45

(b) 5(108)

5(100 + 8)

5x100 + 5x8

500 + 40 = 540

Section 11 - Topic 5Probability and Independence• In your own words, describe what the word independeyou.Now describe dependent..

Answers

In probability , there are two events independent events and dependent events.

Independent Events :

Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur.

Example

. Choosing a marble from a jar AND landing on heads after tossing a coin.

Dependent Events :

If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.

Example

Buying ten lottery tickets and winning the lottery.

Evaluate the expression when m=9 and n=7.
5m +n
Correction: m = 7 and n = 9

Answers

We have the expression:

[tex]5m+n\text{.}[/tex]

We must evaluate the expression for:

• m = 7,

,

• n = 9.

Replacing the values of m and n in the expression above, we get:

[tex]5\cdot7+9=35+9=44.[/tex]

Answer

44

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