If a1 = 3 and an = 5an-1 + 3 then find the value of a4.

The equations that represent the left side, right side, top side and bottom side are y = 3x+2, y = 3x-10, y = 5 and y = -1 respectively

The slope-intercept form of the equation of a line is y =mx+c,

where m is the slope and c is the y-intercept

slope(m) = y2-y1 / x2-x1

Left side

The line moves from point 1 (-1, -1) to point 2 (1,5)

x1 = -1, y1 = -1 and x2 = 1, y2 = 5

Slope(m) = 5-(-1) / 1-(-1)  = 6/2 = 3

Using the equation of a line for 2 points:

y-y1 = m(x-x1)

y-(-1) = 3(x-(-1))

y+1 = 3(x+1)

y+1 = 3x+3

y = 3x+2

Right side

The line moves from point 1 (3, -1) to point 2 (5,5)

Slope(m) = 5-(-1) / 5-3  = 6/2 = 3

y-(-1) = 3(x-3)

y+1 = 3x -9

y = 3x-10

Top side

y = 5

Bottom side

y = -1

Therefore, equation for the left side : y = 3x+2, equation for the right side: y = 3x-10, equation for the top side: y = 5 and equation for the bottom side: y = -1

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The mean will be increased by 2, and the standard deviation will remain the same (option D).

The first step is to determine the initial mean and standard deviation of the data.

Mean is the average of a set of numbers.

Mean = sum of numbers / total number in the data

(2 + 3 +3 + 5 + 5 + 6) / 6

24 / 6 = 4

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.

Standard deviation of the initial data = √[{(2 - 4)² + (3 -4)² + (3 - 4)² + (5 - 4)² + (5 - 4)² + (6 - 4)²} / 6] = 1.414

Now, determine the mean and the standard deviation of the new data

New data : (2 + 2 =4)

3 + 2 = 5

3 + 2 = 5

5 + 2 = 7

5 + 2 = 7

6 + 2 = 8

Mean = (4 + 5 + 5 + 7 + 7 + 8) / 6 = 6

Standard deviation = √[{(4 - 6)² + (5 - 6)²+ (5 - 6)² + (7 - 6)² + (7 - 6)² + (8 - 6)²} / 6] = 1.41

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The unit rate of the Coca-Cola is $ 1.032 and the unit rate of the Pepsi is $ 1.245.

Given, cost of Coca-Cola is

$1.29 for 1.25L

and cost of Pepsi is

$2.49 for 2L

we have to find the unit rate of each of the following,

As, the cost of Coca-Cola is

$1.29 for 1.25L

$1.29 = 1.25L

1 L = 1.29/1.25

1 L = $ 1.032

Now, the cost of Pepsi is

$2.49 for 2L

$2.49 = 2L

1 L = 2.49/2

1 L = $ 1.245

Hence, the unit rate of the Coca-Cola is $ 1.032 and the unit rate of the Pepsi is $ 1.245.

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The number of small boxes sent is 7 and the number of large boxes sent is 8  .

In the question ,

it is given that ,

the number of books that a small box can hold = 25 books

the number of books that a large box can hold = 35 books .

let the number of small boxes be "s" ,

So , the total number of books in s boxes will be 25s .

since the total number of boxes given is 15 ,

So , the number of large boxes = 15 - s

So , the number of books in the (15-s) large boxes  = 35(15-s),

also given that total books altogether = 455 ,

According to the question ,

the equation becomes

25s + 35(15-s) = 455

25s + 35*15 - 35s = 455

525 - 10s = 455

10s = 525 - 455

10s = 70

s = 70/10

s = 7 boxes

and large boxes = 15 - 7 = 8 boxes .

Therefore , The number of small boxes sent is 7 and the number of large boxes sent is 8  .

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Required inequalities are 0.20x=1.20, 0.10y = 1.20 and 0.20x + 0.10y = 1.20. Combination of fruits open to Kojo are (6,0), (1,10), (2,8), (3,6), (4,4), (5,2), (0,12)

Given,

Kojo is given $1.20 to buy some peaches and apples. Peaches cost 20c each, apples 10c each.

He is told to buy at least 6 individual fruits, but he must not buy more apples than peaches.

Let x be the number of peaches Kojo buys.

Let y be the number of apples Kojo buys.

(a)Since Kojo has $1.20 to buy peaches and apples; and each peach and apple costs 20c and 10c respectively.

We have the following inequalitites:

0.20x = 1.20

0.10y = 1.20

0.20x + 0.10y = 1.20

(b)Possible combinations of fruits are as follows:

x = 1.20/0.20 = 6

y = 1.20/0.10 = 12

x = 1,2,3,4,5 ; y = 10,8,6,4,2

Thus, Required inequalities are 0.20x=1.20, 0.10y = 1.20 and 0.20x + 0.10y = 1.20. Combination of fruits open to Kojo are (6,0), (1,10), (2,8), (3,6), (4,4), (5,2), (0,12)

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Answer:

$1.50

Step-by-step explanation:

first, find the unit rate which is 0.3 (7.2/24)

then multiply that by 5

Answer:

y=-4x+5;

Step-by-step explanation:

the linear functions are represented by the power of x as 1

Answer:

y=-4x+5

Step-by-step explanation:

the degree of the variable(x) in the function is 1.

Answer:

h(3)=4

Step-by-step explanation:

After solving the value of x is 14.048.

Given:

KM represents an angle bisector.

Let y be the length of KM.

From the figure:

[tex]12.3^{2} = 5.4^{2} +y^{2}[/tex]

151.29 - 29.16 = [tex]y^{2}[/tex]

130.13 = [tex]y^{2}[/tex]

y = 11.407

[tex]x^{2} =8.2^{2} +11.407^{2}[/tex]

= 67.24 + 130.13

= [tex]\sqrt{197.37}[/tex]

x = 14.048.

Therefore After solving the value of x is 14.048.

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The value x is 1 and y is 3.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x+ y = 4

y= 3x

Now solving above equations

x+ 3x = 4

4x = 4

x= 1

and, y = 3x = 3

Hence, the value x is 1 and y is 3.

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Answer:

[tex]l=\frac{A}{W}\\[/tex]

Step-by-step explanation:

Sometimes we have to manipulate a variable this is often easier to do when we solve for the variable we want and input numbers into the rest of the equation

Let's say A=16 and w=8

Solving for l would me using the A=lw and inputing those values

A=lw

16=l(8)

[tex]\frac{16}{8}=\frac{8l}{8}[/tex]

[tex]l=\frac{16}{8} \\[/tex]  or [tex]l=2[/tex]

If A = 16 and w = 8, we could substitute those values into the original equation(A=lw) and say that

[tex]l=\frac{A}{W}[/tex]

Sometimes we have to manipulate a variable.

This is often easier to do when we solve for the variable we want and input numbers into the rest of the equation.

I hope this explanation is helpful :)

Answer:

c) [-16, 4]

Step-by-step explanation:

Given equation,

→ 2 + |t + 6| = 12

Now the value of t will be,

→ 2 + |t + 6| = 12

→ 2 + t + 6 = 12 || → 2 -(t + 6) = 12

→ t + 8 = 12 || → -t - 4 = 12

→ t = 12 - 8 || → -t = 12 + 4

→ [ t = 4 ] || → [ t = -16 ]

Hence, value of t is 4 (or) -16.

Answer:

2

Step-by-step explanation:

first turn the fractions improper to get 16/3 divided by 8/3

then keep the first fraction the same but flip the second fraction and change divide to multiply to get 16/3 times 3/8

last multiply across to get 48/24 then simplify to get 2

2

Step-by-step explanation:

[tex] \frac{ 5\frac{1}{3} }{2 \frac{2}{3} } [/tex]

[tex] = \frac{ \frac{15 + 1}{3} }{ \frac{6 + 2}{3} } [/tex]

[tex] = \frac{ \frac{16}{3} }{ \frac{8}{3} } [/tex]

Shift denominator term i.e. 8/3 to numerator. Then, the fraction will be get reciprocal i.e. 8/3 to 3/8.

[tex] \frac{16}{3} \times \frac{3}{8} [/tex]

[tex] = { \red{ \tt{ \frac{ \cancel{48^{2}}}{ \cancel {24}_{1}}}}}[/tex]

= 2

By using the box plots, the statement that is most appropriate comparison of the spread is option D. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25.

Box plot

A box plot refers the a type of chart often used in explanatory data analysis and it visually show the distribution of numerical data and skewness through displaying the data quartiles (or percentiles) and averages.

Given,

Here we have the box plot that contains the details about the comparison of spread.

Now, we have to find the statement is the most appropriate comparison of the spreads

In the given box plots, we have identified that the

Lower quartile of A = 70

Upper quartile of A = 80

Similarly,

Lower quartile of B = 25

Upper quartile of B = 50

Then the inter quartile is calculated as,

Brand A has interquartile range = 80- 70 =10,

Where as

Brand B has interquartile range = 50 - 25 = 25.

Therefore, the option D is correct.

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The classification of each game as fair or not, using probabilities, is given as follows:

1. Fair.

2. Fair.

A fair game is a game in which each competitor will have the same chance of winning the game.

These changes are calculated using probabilities, which is the number of desired outcomes in the context of the experiment divided by the number of total outcomes.

The probability of two tails when two fair coins are tossed is:

p = 1/2 x 1/2 = 1/4.

The probability of one head and one tail when two fair coins are tossed is:

p = 1/2 x 1/2 = 1/4.

In game 1, the two players have the same probability of winning, hence it is a fair game.

When two dice are thrown, there are 36 possible outcomes. The number of outcomes regarding the sums are given as follows:

Same probabilities, hence game 2 is also fair.

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There doesn't seem to be enough information to answer problem 1.

I would ask your teacher for clarification.

=============================================

Problem 2

--------------------------

Explanation

x = number of cards, which is some positive whole number.

Your teacher has provided these facts:

which I'll call "fact 1", "fact 2", "fact 3" in that order.

For now I'll focus on fact 3.

Recall that multiples of 5 either end with 0 or 5. Example: 25 is a multiple of 5, and so is 60.

Fact 3 says that we get a remainder 2 when dividing by 5. Therefore, x must be something like 25+2 = 27 or 60+2 = 62. I added 2 to each previous example mentioned earlier.

In short, the value of x must end with 2 or 7.

-------------------

Now focus on fact 1.

The multiples of 4 are {4, 8, 12, ...} all of which are even since 2 is a factor of each.

Add remainder 3 to each item to get {7, 11, 15, ...} and it should be fairly obvious that all of these items are odd.

What does this mean? It means we know 100% that x ends with 7 in the units digit. If x has 2 in the units digit, then x would be even, but it's not in the set {7, 11, 15, ...}

So this is very useful info that x ends with 7.

x could be any of these: {7, 17, 27, 37, ...}

-------------------

We've looked at facts 1 and 3 so far. The only thing left is fact 2.

List the multiples of 3 to get

{3, 6, 9, 12, 15, 18, ...}

then add on the remainder 2 giving this new updated set

{5, 8, 11, 14, 17, 20, ...}

We see that 17 is in that set which fits the criteria of "the number ends with 7". So it's possible that 17 is the answer.

But 17/4 = 4 remainder 1 which doesn't fit fact 1 (since we want remainder 3 instead).

But we can add on multiples of 3*5 = 15 to extend to this new set of

{17, 32, 47, 62, 77, ...}

then erase stuff that ends with 2 to get

{17, 47, 77, ...}

Through guess and check, 47 will work out as shown in the next section below. Therefore, 47 is the final answer.

-------------------

Check:

We get the proper remainders mentioned earlier, so the answer has been confirmed.

-------------------

Side note: The convention for problems like this is to use the Chinese Remainder Theorem. However, I decided not to use it because I wasn't sure if your teacher has covered modulo arithmetic yet or not. If s/he has covered it, then I recommend using that method instead of what I posted above. It's a much more efficient option.

Answer:

6×6

Step-by-step explanation:

6×6=36 and so it would be 6 rows and 6 columns.

Answer:

7.2 weeks

Step-by-step explanation:

12 + [tex]\frac{7}{3}[/tex] x = 42 - [tex]\frac{11}{6}[/tex]x  Multiply all the way through by 6 to clear the fractions

72 + 14x = 252 -11x  Add 11x to both sides

72 + 25x = 252  Subtract 72 from both sides

25x = 180  Divide both sides by 25

x = 7.2

The X and Y angles created by lines intersection in the pictures are 18° and 54°.

Based on the picture, angle ∠MON is a right angle hence it has an 90° angle. We then know that the ∠MOA is 72°. Because angle ∠MOA lies within the angle ∠MON, hence we can write the following formula:

∠MON = ∠MOA +∠AON = 90°

∠MON = 72° + ∠AON = 90°

∠AON = 18° ... (i)

If we focus on the line CD being intersected by the line AB, hence we can conclude that the angles form by this intersection will follow these rules:

∠AOD = ∠BOC

∠AOC = ∠BOD

∠AOD + AOC = 180°

∠BOC + ∠BOD = 180°

Based on the picture, we know that:

∠BOC = x

∠AOC = ∠MOA + ∠MOC

∠AOC = 72° + y ...(ii)

∠AOD = ∠AON + ∠NOD

∠AOD = 18° +2x

∠BOC = 3x ... (iii)

Because we already know that ∠BOC = AOD, hence we could rewrite the formula into:

∠BOC = ∠AOD

3x = 18° + 2x

x = 18° ... (iv)

To find the value of y, we need to focus on angle ∠AOC. Based on the previous calculations and formulas, we  know that:

∠AOC + ∠BOC = 180° ... (v)

Input equations (ii) and (iv) into (v)

∠AOC + ∠BOC = 180°

(72° + y) + 3x = 180°

72° + y + 3(18°) = 180°

126° + y = 180°

y = 54° ... (vi)

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An integer between 1000 and 9999 inclusive is called balanced if the sum of its two leftmost digits equals the sum of its two right most digit. Therefore, there are 615 balanced integers .

If the common sum of the first two and last two digits is n ,

such that 1 ≤n ≤ 9 , there are n choices for the first two digits and n +1 choices for the second two digits (since zero may not be the first digit).

This gives:

            ∑⁹ₙ₋₁ n(n+1) balanced numbers.

If the common sum of the first two and last two digits is n, such that:

                   10≤ n ≤ 18

there are 19 - n choices for both pairs.

This gives : ∑ₙ ₁₀¹⁸ ( 19 - n)²

               = ∑₁⁹ n²

               = 285balanced numbers.

Thus, there are in total 330 + 285 = 615 balanced numbers.

Both summations may be calculated using the formula for the sum of consecutive squares, namely:

        ∑₁ⁿ k² = n (n+1) (2n + 1) / 6

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Answer:

Mikhail is 42 years old

Step-by-step explanation:

Answer:

Step-by-step explanation: I don’t know if this is what your asking for but 26, 37, 48.

Answer:

I think 24

Step-by-step explanation:

-6 + 24 =18

Answer: ? = 50, same side interior angles

? = 84, alternate interior angles

Step-by-step explanation:

130 + x = 180

-130   =    -130

x = 50

alternate interior angles are congruent

50° is the value of the missing angle.

Since u and v lines are parallel so the angle asked and the angle with the value of 130° are alternate interior angle.

Alternate interior angles have the following characteristics:

Therefore,

x+130 = 180

x =180-130

x =50°

therefore, the missing angle is 50°.

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The number of pages Giovanni can read in 2 hours is approximately 103.

Giovanni can read 300 words per minute. There are approximately 350 words on a page.  

The number of pages he can read in 2 hours can be calculated as follows:

Therefore,

1 hour = 60 minutes

2 hours = 120 minutes.

Therefore,

1 minute = 300 words

120 minutes = ?

cross multiply

number of words he can read in 2 hours = 120 × 300 = 36000

350 words = 1 page

36000 words = ?

cross multiply

number of pages he read in 2 hours = 36000 / 350

number of pages he read in 2 hours = 102.857142857

Therefore, he read about 103 pages in 2 hours.

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Marcelo will have to take 50 shots in order to miss 30 shots because the ratio of shots to missed shots is 5:3

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

To solve this question, we can simply compare the ratio or proportion of shots to the number of missed shots.

In every 25 shots taken, he made 10 shots. This implies he lose 15 shots.

So, for every 25 shots, he lost 15 shots.

How many shots did he take to miss 30 shots.

25 shots = 15 missed shots

x shots = 30 missed shots

crossed multiply both sides and solve for x

x = (30 * 25) / 15

x = 50 shots.

Marcelo took 50 shots.

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