Are these two cylinders similar? The diagrams are not drawn to scale.

The 10th term of the sequence is 1024/729

From the question, we have the following parameters that can be used in our computation:

a2 = 36

a7 = 128/27

The nth term of a geometric sequence is

an = a1 * r^(n -1)

So, we have

a2 = a1 * r = 36

a7 = a1 * r^6 = 128/27

Divide the equations

r^5 = (128)/(27 * 36)

This gives

r = [(128)/(972)]^1/5

So, we have

r = [(32)/(243)]^1/5

r = 2/5

Also, we have

a1 = 128/(27r^6)

The 10th term of the sequence is

a10 = a1 * r^9

So, we have

a10 = 128/(27r^6) * r^9

This gives

a10 = 128/(27) * r^3

This gives

a10 = 128/(27) * [2/3]^3

Evaluate

a10 = 128/27 * 8/27

This gives

a10 = 1024/729

Hence, the 10th term is 1024/729

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We can add 13 and 15, or 49 and 28, or 20 and 47, or 45 and 35 to make 10 in the equations

To add choose 2 numbers to make 10, we can use the fact that 10 is the sum of 6 and 4.

Therefore, we can add a number that is 6 more than 10 and another number that is 4 less than 10.

This gives us the following equations:

13 + 15 = 28, since 13 + 15 = 28 and 10 = 6 + 4

49 + 28 = 77, since 49 + 28 = 77 and 10 = 6 + 4

20 + 47 = 67, since 20 + 47 = 67 and 10 = 6 + 4

45 + 35 = 80, since 45 + 35 = 80 and 10 = 6 + 4

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The probability of the high school baseball player getting at least 2 hits in a game with 8 at bats, given his 0.197 batting average, is approximately 0.378.

To calculate the probability of the player getting exactly 2 hits in the game, we can use the binomial probability formula:

P(X = x) = (n choose x) x pˣ x (1-p)ⁿ⁻ˣ

Where:

P(X = x) is the probability of getting exactly k hits

n is the number of trials (in this case, 8 at bats)

k is the number of successful trials (in this case, 2 hits)

p is the probability of a successful trial (in this case, 0.197)

Using this formula, we can calculate the probability of the player getting exactly 2 hits in the game:

P(X = 2) = (8 choose 2) x 0.197² x (1-0.197)⁸⁻² = 0.214

So the probability of the player getting exactly 2 hits in the game is 0.214.

To calculate the probability of the player getting at least 2 hits in the game, we need to add up the probabilities of getting exactly 2 hits, exactly 3 hits, exactly 4 hits, and so on, up to 8 hits. This can be a bit cumbersome to do by hand, but fortunately, there are tools available to help us with this.

Using a binomial probability calculator or a statistical software program, we can find that the probability of the player getting at least 2 hits in the game is approximately 0.378.

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Pour développer il faut appliquer la distributivité de la multiplication :

7m + 5.5(2+m) = 7m + 5.5 x 2 + 5.5m

= 7m + 11 + 5.5m

Il faut combiner les termes contenant m :

= 7m + 5.5m + 11

= (7 + 5.5)m + 11

= 12.5m + 11

The resistance in the circuit is 9.6 Ohms.

Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.

Given that:

V = √(PR)

Where P is the power and R is the resistance in ohms.

Make the resistance R, the subject of the formula.

V = √(PR)

V² = (√(PR) )²

V² = PR

PR = V²

R = V²/P

Plug in Voltage V = 120V and Power P = 1500 watts

R = V²/P

R = (120)² / 1500

R = 14400 / 1500

R = 9.6 Ω

Therefore, the resistance is 9.6 Ω.

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The solution is:

The equations are;

4(2x + 5) = 3(2x + 8)

x = 2

Perimeter of each shape is 36

Here, we have,

Mathematically;

The perimeter of a square is 4L

while the perimeter of an equilateral triangle is 3L

where L represents the lengths of the sides

Mathematically, from what we have in the question, since the perimeter are equal;

4(2x + 5) = 3(2x + 8)

8x + 20 = 6x + 24

8x-6x = 24-20

2x = 4

x = 4/2

x = 2

The side of the square will measure;

2(2) + 5 = 9

Its perimeter is 4(9) = 36

The side of the triangle will measure

2(2) + 8 = 12

Its perimeter will be 3(12) = 36

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Answer:y=4/3x-14/3

Step-by-step explanation:

1. Find the slope of the original line

3/4x-y=7/2

-y=-3/4+7/2

y=3/4x-7/2

2. Using this find the negative reciprocal

3/4 -------- -4/3

3. Now insert -2,-2 in the equation y=-4/3x

-2=-4/3(-2)

-2=8/3

4. Find the needed intercept to make true.

-2=8/3-14/3

Therefore, y=-4/3x-14/3

Answer: 6.996

Step-by-step explanation:

As given in the problem, V = πr²h

We are given V and r, so all we must do is plug them in and solve for h

[tex]351.68=\pi (4)^2h\\351.68=\pi 16h\\h=6.996[/tex]

The grade of the track between the stations is approximately 1.9%.

The grade of the track is given as a percentage by the change in elevation (climb) divided by the horizontal distance (run) between the two stations:

(climb / run) x 100% = grade

We are given a 5 foot ascent and a 260 foot horizontal distance (run). When we enter these values into the formula, we get:

1.92% = (5/260) x 100% = grade

Rounding to the nearest tenth, the grade of the track between the stations is approximately 1.9%.

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For Matthew, the height is given as [tex]52 + 8 sin (\pi/6t)[/tex]

To express the characteristic repetition of certain actions or events, a sine function is often employed.

This mathematical function links a position on the edge of a unit circle with the height of its corresponding y-coordinates. Conveyed generally as sin(x), it represents angle measurement in radians.

This repeatable pattern attains values between -1 to 1 and reappears once per every 2π radians. There are numerous applications of this type of sinusoidal oscillation pattern, including signal processing, engineering, and physics among others.

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If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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Based on these expected future dividends and the rate of return required by investors, the price of the stock should be $414 in year 1, $476 in year 2, $547 in year 3, $93.24 in year 4, $114.53 in year 5, and $138.49 in year 6.

To calculate the price of the stock, we need to first determine the expected future dividends. We know that the current dividend is $3.60, and we can use the dividend growth rate to calculate the expected future dividends.

For the first three years, we can use the 15% dividend growth rate to calculate the expected dividends as follows:

Year 1: $3.60 x 1.15 = $4.14

Year 2: $4.14 x 1.15 = $4.76

Year 3: $4.76 x 1.15 = $5.47

The Gordon growth model is as follows:

P = D / (r - g)

where:

P = price of the stock

D = expected dividend payment

r = rate of return required by investors

g = expected dividend growth rate

Using the formula, we can calculate the price of the stock as follows:

Year 1: P = $4.14 / (0.16 - 0.15) = $414

Year 2: P = $4.76 / (0.16 - 0.15) = $476

Year 3: P = $5.47 / (0.16 - 0.15) = $547

After year 3, the expected dividend growth rate is 8%, so we can use this rate to calculate the price of the stock beyond year 3.

Year 4: P = $5.47 x 1.08 / (0.16 - 0.08) = $93.24

Year 5: P = $5.96 x 1.08² / (0.16 - 0.08) = $114.53

Year 6: P = $6.47 x 1.08³ / (0.16 - 0.08) = $138.49

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Answer: To solve for x in the equation x/9 = 7/15, we can cross-multiply to get:

15x = 9 * 7

Simplifying the right side, we get:

15x = 63

To solve for x, we can divide both sides by 15:

x = 63/15

Simplifying the fraction on the right side, we get:

x = 4 3/5 or x = 4.2 (rounded to one decimal place)

Therefore, the solution to the equation x/9 = 7/15 is x = 4.2 or x = 4 3/5.

Step-by-step explanation: kinda easy ngl lol but hope this helps :D

The domain and the range of the given function is x ≥ 1 and y ≥ -4 respectively.

Given is a function, y ≤ √(x-1) -4, we need to find the domain and the range,

Domain = all the input values.

Range = all the output values.

So, the function is =

y ≤ √(x-1) -4

The related function can be written as =

y = √(x-1) -4

The function is defined if =

√(x-1) ≥ 0

∴ (x-1) ≥ 0

x ≥ 1,

In the given inequality, the sign of inequality is ≥, it means the points on the boundary line are included in the solution set. Thus, 1 is included in the domain.

So, the domain of the given inequality is x ≥ 1.

Now,

√(x-1) ≥ 0

√(x-1) -4 ≥ 0 - 4

y ≥ -4

The points on the boundary line are included in the solution set. Thus, -4 is included in the range.

So, the range of the given inequality is y ≥ -4.

Hence, the domain and the range of the given function is x ≥ 1 and y ≥ -4 respectively.

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The probability of winning on the first roll is 0.22

Solution-

As in the game of casino, two dice are rolled simultaneously.

So the sample space would be,

|S| = 36

Let E be the event such that the sum of two numbers are 7, so

E = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

|E| = 6

P(E) = 6/36

Let F be the event such that the sum of two numbers are 11, so

F = {(6,5), (5,6)}

|F| = 2

P(F) = 2/36

Now,

P(E∪F)= 0.22

The probability of winning on the first roll is 0.22

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This week, Michelle works 33 hours. She is paid $10 per hour. Her take-home pay is $277.11 after taxes. She pays $ 52.89 in payroll tax.

We know that Michelle works for 33 hours this week and her pay for one hour is $10. So, firstly we will calculate her total pay for this week.

Total pay for week = pay for one hour × hours worked

= 10 × 33

= $ 330

Now, after taxes her pay is $277.11. So,

Tax = Pay before tax - pay after tax

= 330 - 277.11

= $ 52.89

A payroll tax is a tax paid by both employees and employers on wages, tips, and salaries. Employers withhold taxes from employees' paychecks and pay them to the government.

Federal, state, and municipal income taxes, as well as the employee's contribution of Social Security and Medicare taxes (FICA), are all included.

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The lengths of sides a and b are given as follows:

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle B is obtained as follows:

m < B + 81 + 33 = 180

m < B = 180 - 114

m < B = 66º.

Then the relation is:

26/sin(81º) = a/sin(33º) = b/sin(66º).

Then the value of a is obtained as follows:

26/sin(81º) = a/sin(33º)

a = 26 x sine of 33 degrees/sine of 81 degrees

a = 14.3.

The value of b is obtained as follows:

26/sin(81º) = b/sin(66º)

b = 26 x sine of 66 degrees/sine of 81 degrees

b = 24.

The triangle is given by the image presented at the end of the answer.

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The representation of 4.67 on the number line upto 4-decimal places. can be given in image. A picture of numerals along a straight line is called a number line.

A picture of numerals along a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

Just to refresh your memory, the entirety of a number is a collection of numbers that contains both zero (0) and all the numbers that count (1, 2, 3,4,5,6), while the number that is natural is a collection of all counting values (1, 2, 3,4, 5, 6).  The representation of 4.67 on the number line upto 4-decimal places. can be given in below image.

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Your question is incomplete but most probably your full question was,    

Visualise the representation of 4.67 on the number line upto 4-decimal places.​

The solution to the simultaneous equation is x = 6 and y = 3.

To solve this system of equations, we can use the method of elimination. First, we want to eliminate one of the variables, either x or y. In this case, it is easiest to eliminate y. To do so, we can multiply the second equation by 3, which gives us:

6x + 3y = 45

6x - 6y = 18

Now, we can subtract the second equation from the first:

6x + 3y - (6x - 6y) = 45 - 18

Simplifying this expression, we get:

9y = 27

Dividing both sides by 9, we get:

y = 3

Now that we know the value of y, we can substitute it into either equation to find the value of x. Let's use the first equation:

6x + 3y = 45

6x + 3(3) = 45

6x + 9 = 45

Subtracting 9 from both sides, we get:

6x = 36

Dividing both sides by 6, we get:

x = 6

Correct Question :

Solve the following simultaneous equation using algebra

6x+3y=45

2x-2y=6

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The area of the enclosed region is  16√2 - 8 squared units

We have,

The region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π consists of two parts, one above the x-axis and one below the x-axis. We can find the area of each part separately and then add them to get the total area.

First, let's find the x-coordinates of the points where the curves intersect. These are the points where 4 sin(x) = 4 cos(x), or sin(x) = cos(x), which occurs when x = π/4 + kπ/2 for any integer k. Since we are only interested in the intersection points between x = 0 and x = 0.9π, we only need to consider the case k = 0. So the intersection point is x = π/4.

Now, let's consider the part of the region above the x-axis. We need to find the area between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = π/4. This is given by the integral:

A1 = ∫[0, π/4] (4 sin(x) - 4 cos(x)) dx

Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:

A1 = ∫[0, π/4] (4 sin(x) - 4 sin(x + π/2)) dx

 = ∫[0, π/4] (4 sin(x) + 4 sin(x)) dx   (since sin(x + π/2) = sin(x))

 = 8 ∫[0, π/4] sin(x) dx

 = 8 [-cos(x)] [0, π/4]

 = 8 (1 - 1/√2)

 = 8√2 - 8

Next, let's consider the part of the region below the x-axis. We need to find the area between the curves y = 4 cos(x) and y = 4 sin(x) from x = π/4 to x = 0.9π. This is given by the integral:

A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 sin(x)) dx

Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:

A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 cos(x - π/2)) dx

 = ∫[π/4, 0.9π] (4 cos(x) + 4 sin(x)) dx   (since cos(x - π/2) = sin(x))

 = 4 ∫[π/4, 0.9π] (2 cos(x) + 2 sin(x)) dx

 = 4 [2 sin(x) - 2 cos(x)] [π/4, 0.9π]

 = 4 (2/√2 + 2) - 4 (1 - 1/√2)

 = 8√2

So the total area of the region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π is:

A = A1 + A2

A = 8√2 - 8 + 8√2

A = 16√2 - 8 squared units

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[tex]surface \: area = 2\pi {r}^{2} + 2\pi \: rh \\ 2\pi {(6)}^{2} + 2\pi(6)(15) \\ = 2\pi(36) + 2\pi(90) \\ = 72\pi + 180\pi \\ = 252\pi {in}^{2} [/tex]

Answer:

28 KG

Step-by-step explanation:

To find the smallest possible weight, we need to consider the possible range of weights for each suitcase based on the rounding.

The 12 kg suitcase could actually weigh anywhere from 11.5 kg to 12.4 kg (since rounding to the nearest kg means it could be as low as 11.5 kg or as high as 12.4 kg, with 12 kg being the nearest whole number).

The 17 kg suitcase could actually weigh anywhere from 16.5 kg to 17.4 kg.

To get the smallest possible total weight, we want to add the lowest weights of each suitcase:

11.5 kg + 16.5 kg = 28 kg

Therefore, the smallest possible amount that the two suitcases could weigh in total is 28 kg.

17 in binary is 10001.

How to Convert 17 in Binary?

Step 1: Divide 17 by 2. Use the integer quotient obtained in this step as the dividend for the next step. Repeat the process until the quotient becomes 0.

Write the remainder from bottom to top i.e. in the reverse chronological order. This will give the binary equivalent of 17.

Therefore, the binary equivalent of decimal number 17 is 10001.

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Answer:

a= b/2

Step-by-step explanation:

it is in internet

​

The area of each wing to founds the total area as; 26000 square inches

We need to find the area of each wing to founds the total area In square inches

The dimensions are;

Length = 100 + 100 = 200 unit

Width = 70 + 70  = 130

Now the area of the wing

= Length x width

= 200 x 130

= 26000

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Answer:

v = 5

Step-by-step explanation:

Collect like-terms:

[tex]8v = 3v + 25[/tex]

[tex]8v - 3v = 25[/tex]

[tex]5v = 25[/tex]

Divide both sides by 5 to make v the subject:

[tex]v = 5[/tex]

The correct statement about the product of 5/12 and 7 is given as follows:

C. The product is greater than 5/12 but less than 7.

The multiplication operation for this problem is given as follows:

5/12 x 7.

The factors of the operation are given as follows:

5/12 and 7.

When two fractions multiply each other, the product is given by the multiplication of the numerators divided by the multiplication of the denominators, hence:

5/12 x 7 = (5 x 7)/(12 x 1) = 35/12.

35/12 is a number close to 3, which is:

Hence option C is the correct statement.

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Answer:

B 2

Step-by-step explanation:because a quart is 0.25 of a gallon