Try adding up the first few odd numbers and see if the numbers you get satisfy some sort of pattern. Once you find the pattern, express it as a formula. Give a geometric verification that your formula is correct.

Answer:

i- 72000 * π radians per hour,  ii- 65,940 miles per hour.

Step-by-step explanation:

(i) To find the car's angular speed in radians per hour, we need to find the number of radians the wheel rotates in one revolution, then multiply that by the number of revolutions per second. The number of radians in one revolution is equal to the circumference of the wheel divided by the wheel's radius. The wheel's circumference is given by 2 * π * r, where r is the wheel's radius (18 inches / 2 = 9 inches). Then, the number of radians per revolution is:

2 * π * r / r = 2 * π

So, the number of radians per second is:

2 * π * 10 revolutions per second = 20 * π radians per second

Finally, to convert radians per second to radians per hour, we multiply by 3600 (the number of seconds in an hour):

20 * π * 3600 seconds/hour = 72000 * π radians per hour

(ii) To find the car's linear speed in miles per hour, we need to multiply the wheel's circumference by the number of revolutions per hour. The wheel's circumference is given by 2 * π * r, so the linear speed is:

2 * π * r * 10 revolutions per second * 3600 seconds/hour = 18 * π * 10 * 3600 miles per hour

The answer is approximately equal to 65,940 miles per hour.

The volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis is 8π/3 cubic units.

The volume of the solid generated by revolving this region about the x-axis can be found using the method of cylindrical shells. The volume is given by:

V = ∫[0, 2] 2πx(2 - 2√x) dx

Evaluating the definite integral:

V = π ∫[0, 2] (4x - 4x^(3/2)) dx

= π [2x^2 - 4/3 x^(3/2) ] |_0^2

= π [4 - (4/3)(2^(3/2))]

= 8π/3.

Therefore, the volume of the solid generated by revolving the region bounded by the lines y = 2 and y = 2√x and the x-axis about the x-axis is 8π/3 cubic units.

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--The question is incomplete, answering to the question below--

"Find the volumes of the solids generated by revolving the regions bounded by the lines and curves about the x-axis

y=2√x, y=2, x=0"

After the 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit is at 20 on number line.

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.

A rabbit started at point 0 and made 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit we do not know the direction of either jump where on the line could the rabbit be.

Now, Rabbit is at 10 on number line

If rabbit made same jumps, rabbit will be at

10+3+4+2+1

= 20

Therefore, after the 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit is at 20 on number line.

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Answer:

[tex]r = \sqrt{\frac{24}{h}}[/tex] inches

Step-by-step explanation:

Volume of a cone = [tex]\frac{1}{3} \pi r^{3}h[/tex]

 where: r = radius of cone

             h = perpendicular height of the cone

Provided volume of cone = 8π cubic inches

[tex]8\pi = \frac{1}{3}\pi r^{2} h[/tex]

Cross multiplication is applied and 'r' is isolated:

[tex]3(8\pi ) = \pi r^{2} h[/tex]

[tex]24\pi =\pi r^{2} h[/tex]

[tex]r^{2} h = \frac{24\pi}{\pi}[/tex]

[tex]\pi[/tex] in the numerator and denominator cancel each other out completely:

[tex]r^{2} h = 24[/tex]

[tex]r^{2} = \frac{24}{h}[/tex]

Taking the square root on both sides of the equation in order to get rid of the square:

[tex]r = \sqrt{\frac{24}{h}}[/tex] inches

At the end of two years if prices increase 5 percent the family needs to spend a total of $56227.50 on their annual living expenses.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Given that, the family spends $51,000 a year.

The first increase of 5% is given as:

A = (51000) (1 + 5/100)

A = 51000 (105/ 100) = 53550

For the second year increase:

A = 53550 (105 / 100) = 56227.50

Hence, at the end of two years the family needs to spend a total of $56227.50 on their annual living expenses.

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When h is very small, then the slope would be equal to 6

We have

m = y2 - y1 / x2 - x1

where 2.97² - 3² / 2.97 - 3

we would have

-0.1791 / -0.03

m = 5.97

We have to do the same for   x = 3.001

3.001² - 3² / 3.001 - 3

m = 6.001

finally we have to solve for x = 3 + h

m = [tex]\frac{(3 + h)^2-(3)^2}{3+h-3}[/tex]

m = [tex]\frac{9+h^2+6h-9}{h}[/tex]

m = [tex](\frac{h}{h})*(\frac{h+6}{1} )[/tex]

m = h + 6

if h is close to 0 then m = 6

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Answer:

838,200

Step-by-step explanation:

960x5x184 =838,200

The number of acres that will be pollinated by the bees in 18 beehives is given as follows:

D. 48.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

From the table, the constant is obtained as follows:

3k = 8

k = 8/3.

Hence the equation is of:

y = 8x/3.

The number of acres that will be pollinated by 18 beehives is then given as follows:

y = 8(18)/3

y = 48 acres.

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Answer: D. 48.

Step-by-step explanation:

because the table shows 3k = 8k = 8/3. y = 8x/3. So then it turns into y = 8(18)/3 = y = 48 acres.

Answer:

Step-by-step explanation:

Total marbles = 0
Number of green marbles = 6
so,
Probability of getting 2 green marbles = 2/20 = 1/10

The probability that Jerod selects two green marbles at random from the bag is 1/10

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that Jerod has a bag of 20 marbles containing 12 red, 6 green, and 2 blue marbles.

Total marbles = 0

Number of green marbles = 6

Therefore,

Probability of getting 2 green marbles ;

= 2/20 = 1/10

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There are 0.0496 Gg/hr in 8.34 x 10^6 tons/week

To convert from tons/week to Gg/hr:

you need to divide the number of tons by the number of hours in a week and then multiply by 1 Gg/ton.

There are 168 hours in a week, so:

8.34 x 10^6 ton/wk / 168 hrs/week = 49642.85 ton/hr

And 1 Gg = 1,000,000 ton, so:

49642.85 ton/hr * 1 Gg/1,000,000 ton = 0.0496 Gg/hr

So, 8.34 x 10^6 tons/week is equivalent to 0.0496 Gg/hr.

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Answer:

there is a 1 in 24 chance

Step-by-step explanation:

1(3)/6x4= 1/24

Shaded region in venn diagram is the common area of set A and set B. It represent A∩B.

How to present a set can also be expressed with a picture or diagram called a Venn Diagram. The Venn diagram was introduced by a British mathematician named John Venn (1834 – 1923).

Instructions for creating a Venn diagram include:

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Answer:

Step-by-step explanation:

The formula for the area of a triangle is:

1/2×base×height

If you know the area of the triangle and height you can apply the area formula:

A=1/2×base×height

in reverse to calculate the length of the base:

b=2A/h

given, h=60dam

A=18

so, b=2×18/60

b=36/60

b=0.6

The answer is 0.6

Answer:

Step-by-step explanation:

To find the equation of a line that is parallel to another line, we can use the same slope for both lines. The slope of the line with the equation -14x + 3y = -4 can be found by rearranging the equation into slope-intercept form:

y = -14/3x - 4/3

The slope of this line is -14/3.

To find the equation of a line that passes through the point (2,-6) with the same slope, we can use the point-slope form of a line:

y - y1 = m(x - x1)

Where:

m is the slope of the line

(x1, y1) is a point on the line

Plugging in the values from the given information:

m = -14/3

x1 = 2

y1 = -6

y - (-6) = -14/3 (x - 2)

y + 6 = -14/3x + 14

So the equation of the line through the point (2,-6) that is parallel to the line with the equation -14x + 3y = -4 is:

y + 6 = -14/3x + 14.

Answer:

[tex]x=16\sqrt{30}; \ y=16\sqrt{10}.[/tex]

Step-by-step explanation:

1. if the angles in the given triangle are 30°-60°-90°, then

[tex]2. \ x=32\sqrt{10} *cos[30 к]; \ = > \ x=32\sqrt{10} *\frac{\sqrt{3}}{2} =16\sqrt{30};[/tex]

[tex]3. \ y=0.5*32\sqrt{10}=16\sqrt{10};[/tex]

4. finally, x=16√[30]; y=16√[10].

Answer:

Below

Step-by-step explanation:

y - y1   = m ( x - x1 )     is point slope form of a line  m = slope

For point ( -1,3) :

y-3 = 3 (x- -1)

y -3 = 3x + 3        add 3 to both sides

y = 3x + 6         The underlined equations are the same line just different forms....you'll need to pick the one you need

The percentage of increase is given by the equation A = 85 %

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage change be represented as P

Now , the equation will be

The initial value be represented as A = 40

The final or increased value be B = 74

So , the percentage change P = [ ( | A - B | ) / A ] x 100

Substituting the values in the equation , we get

The percentage change P = [ ( 34 ) / 40 ] x 100

The percentage change P = 0.85 x 100

The percentage change P = 85 %

Hence , the percentage change is 85 %

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The next two elementary row operations that should beRow4=Row4-4*Row3. This will make the element zero. The second step is we divide 8 by -2 to get 4th unknown as d=8/(-2)=-4.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.

Presently 3rd element in Row 3 is the pivot element,

For solving the matrix, we need to make 3rd element of fourth row as zero,

Hence, we do the operation Row4=Row4-4*Row3.

This will make the element zero.

The second step is we divide 8 by -2 to get 4th unknown as d=8/(-2)=-4.

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Below is a function which takes some number of degrees, positive or negative, and returns the reduced equivalent in the interval [0 , 360 )

Below is a Python function that takes an angle in degrees and returns its equivalent in the interval [0, 360):

def deg_reduce(degrees):

   return degrees % 360

The % operator in Python is the modulo operator, which returns the remainder of a division. By using degrees % 360, the function returns the reduced equivalent of degrees in the interval [0, 360).

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Answer:

25people =90days

? =15days

cross multiply

25×15÷90

=375÷90

=4.16666666

approximately =4.2

150 people needed to complete the work in 15 days.

Given that 25 people take 90 days to do a job.

Relation between number of people and number of days needed to complete a work when work quantity is fixed is inversely proportional.

That is, if number of people is less then the work needs more time and vice versa.

To complete a job in 90 days the number of people required is = 25

To complete that same job in 1 days the number of people needed is = 25 * 90 = 2250

To complete the same job in 15 days the number of people needed is = 2250/15 = 150.

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Answer:

Step-by-step explanation:

Assuming the sides are equal:

-3x - 6 = 4x + 15

-3x - 6 -15 = 4x + 15 - 15

-3x - 21 = 4x

-3x + 3x - 21 = 4x + 3x

-21 = 7x

-21/7 = 7x /7

-3 = x

The period of time during which the projectile is at least 240 feet above the ground is 3 seconds <= t <= 5 seconds.

What is time of projectile motion?

Vertical motion totally determines the time for projectile motion.

The height of the projectile above the ground after t seconds is given by s = -16t^2 + 128t. To find the period of time during which the projectile is at least 240 feet above the ground, we need to find the values of t for which s >= 240.

Solving for t:

-16t^2 + 128t >= 240

-16t^2 + 128t - 240 >= 0

t^2 - 8t + 15 >= 0

(t - 5)(t - 3) >= 0

So t must be between 3 and 5 seconds, inclusive.

Therefore, the period of time during which the projectile is at least 240 feet above the ground is 3 seconds <= t <= 5 seconds.

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The phrase "3 over 1" would be used to describe the proportion of vehicles to trains. The (C) option is that.

A ratio in mathematics shows how many times one quantity is present in another.

For instance, if a dish of fruit's fully oranges and six lemons, the ratio of oranges and lemons is eight to six.

This ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons and oranges is 6:8.

Two quantities are compared to form a ratio.

An equality of two ratios is a percentage.

So, the following are some of the car models that Alex has collected:

There are 8 airplanes.

There are 4 trains in all.

There are 12 vehicles.

Consequently, the car-to-train ratio is 12:4.

This is further simplified to its most basic form:

= 12:4

= 3:1

Therefore, the phrase "3 over 1" would be used to describe the proportion of vehicles to trains. The (C) option is that.

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Complete question:

Alex has a collection of vehicle models. He built 8 model airplanes, 4 model trains, and 12 model cars. Write a ratio to represent the ratio of cars to trains.

A. 12:24 FAST HELP

B. 1:3

C. 3 over 1

D> 4 to 12

a. Her AGI is under the assumption she sells all of the stock now after receiving $1,000 dividends from the stock. is $34500.

b. The computation under the assumption she sells only half of the stock this year and also receives $1,000 in dividends from the stock is $21000.

All of the shares used to divide ownership of a corporation or company constitute stock in the financial world. A single share of stock represents a fractional ownership interest in the company based on the total number of shares.

Compute her AGI under the assumption she sells all of the stock now after receiving $1,000 dividends from the stock.

This will be the addition of the taxable pension, half of the social security benefits, stock gain, and the dividend received. This will be:

= $10000 + ($7000 × 50%) + $20000 + $1000

= $10000 + $3500 + $20000 + $1000.

= $34500

The computation is under the assumption she sells only half of the stock this year and also receives $1,000 in dividends from the stock.

= $10000 + $10000 + $1000

= $21000

The correct question is given below.

Lucia is a 69-year-old single individual who receives a taxable pension of $10,000 per year and Social Security benefits of $7,000. Lucia is considering the possibility of selling stock she has owned for years and using the funds to purchase a summer home. She will realize a gain of $20,000 when she sells the stock, which has been paying $1,000 of dividends each year. Lucia says her brother recommended that she sell half the stock this year and half next year because selling all of the stock at once would affect the tax treatment of her Social Security benefits.

a) Computer her AGI under the assumption she sells all of the stock now after receiving $1,000 dividends from the stock.

b) Repeat the computation under the assumption she sells only half of the stock this year and also receives $1,000 in dividends from the stock.

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Answer:

       For the first picture:

[tex]\frac{1}{3} < \frac{2}{6}[/tex] is false because [tex]\frac{1}{3} x 2 = \frac{2}{6}[/tex]

[tex]\frac{1}{3} > \frac{2}{6}[/tex] is also false because [tex]\frac{1}{3} x 2 = \frac{2}{6}[/tex]

[tex]\frac{1}{3} =\frac{2}{6}[/tex] is true, so the 3rd is the correct option.

       For the second picture:

[tex]\frac{3}{6} ?\frac{1}{4}[/tex] using the LCM method, of 6 and 4 = 12

then it will be [tex]\frac{6}{12} > \frac{3}{12}[/tex] so the symbol will be > (1st option)

      For the third picture:

[tex]\frac{2}{5} =\frac{1}{2}[/tex] is false

[tex]\frac{2}{5} < \frac{1}{2}[/tex] is true, so the 2nd is the correct option.

[tex]\frac{2}{5} > \frac{1}{2}[/tex] is false

      For the forth picture:

The correct answer is the 3rd option ([tex]\frac{5}{8} > \frac{1}{2}[/tex])

Have a wonderful day! :-)

Each side of the given figure measures 2yd and the area of the polygon is A = 8 + 8√2 square units, and apothem is 8 + 8√2 units.

A polygon is a closed, two-dimensional (2-D) figure formed of segments of straight lines. The octagon is an 8-sided polygon in geometry. An octagon is referred to as a regular octagon if all of its sides and angles have equal lengths. In other words, an ordinary octagon has congruent sides. In a standard octagon, the inside angle is 135 degrees, and the outer angle is 45 degrees. A preset set of formulas known as the "octagon formula" can be used to calculate the area and perimeter of a regular octagon.

Given that the perimeter of the octagon is 16yd.

The perimeter is the sum of all the segments or boundaries. So, the perimeter of the octagon is:

P = 8s

16 = 8s

s= 2yd.

The area of a regular octagon is given as:

A = 2a²(1 + √2)

A = 2(2)²(1 + √2)

A = 8 + 8√2

The apothem is given by:

A = 1/2 (s)(a)

8 + 8√2 = 1/2 (2)(a)

a = 8 + 8√2

Hence, each side of the given figure measures 2yd and the area of the polygon is A = 8 + 8√2 square units, and apothem is 8 + 8√2 units.

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Answer:

21.1 minutes

Step-by-step explanation:

Time for first mile + second + third

6.75+ 7.1+ 7.25

21.1 minutes or (21.1 * 60) seconds = 1266 seconds

Answer:

The ratio of ozone used to the total amount of water treated per day can be calculated as follows:

Ozone used = 25,000 mg

Amount of water treated = 16,000,000 liters = 16,000,000 x 1000 ml = 16,000,000 x 1000 x 1000 mg = 16,000,000,000,000 mg

Ratio of ozone used to water treated = 25,000 / 16,000,000,000,000 = 1.5625 x 10^-11

So, the ratio of ozone used to the total amount of water treated per day is approximately 1.5625 x 10^-11.

[tex]15.625*10^{-4}[/tex] miligrams of ozone / liter of water.

16,000,000 liters of water

25,000 milligrams of ozone

A ratio is basically telling how much of one thing corresponds to a unit of another thing. Hence, let's express this as a division in the following fashion:

[tex]\frac{25,000}{16,000,000} =\\ \\\frac{0.0015625}{1} =\\ \\\frac{15.625*10^{-4} }{1}[/tex]

[tex]15.625*10^{-4}[/tex] miligrams of ozone / liter of water.