the base of a solid is the region bounded by the ellipse $$. find the volume of the solid given that cross sections perpendicular to the $$-axis are:

After 27 years, you would have $4800 in the account.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and x is the time period.

Given:

Investment double every 9 years,

and you start with $600 investment.

So, by the exponential growth function,

y = 600(1+r)ˣ,

To find the growth rate:

1200 = 600(1 + r)⁹

r = 1.08006

So, the equation is,

y = 600(1+0.8006)ˣ

After 27 years,

y = 600 x 8

y = $4800

Therefore, $4800 is the required amount.

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We can acquire a number of kites of 6 kites for a total price of $ 30 in both stores (Kites-R-Fun, Windy Kites).

In this problem we find the case of two lines being represented on Cartesian plane, both have a point of intersection that represents the solution to the system. Each line represents a price function for a kite model sold in a store, where the horizontal axis represents the number of kites and the vertical axis represents the total cost.

According to the given figures, we can acquired a number of kites of 6 kites at a total price of $ 30 in both stores.

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Step-by-step explanation:

First find 1/4 of 72 runners. To do this divide by 4.

So

72/4=18

Now take 72 and subtract 18 to get 54

Next find 1/3 of 54 runners

54/3=18

Because it is 2/3 you need to multiply 18 by 2

So

18 x 2 = 36

So

54-36=18 runners that finished the race

If needed in fraction form

18/72

Now simplify

9/16 of the runners finished

The complex number z = 4√3 - i 4 has a norm 8 and a direction 330°. Its representation is in the image shown below.

In this question we find the definition of complex number in rectangular form, whose definition is shown below:

z = a + i b, where a, b are real numbers.

Where:

Graphically speaking, the real component is associated to the horizontal axis of Cartesian plane and the imaginary component is associated to the vertical axis of that plane. The norm (r) and direction (θ) of the complex number are, respectively:

Norm

r = √(a² + b²)

Direction

θ = tan⁻¹ (b / a)

The norm and the direction of the complex number are, respectively:

r = √[(4√3)² + (- 4)²]

r = 8

θ = tan⁻¹ [(- 4) / (4√3)]

θ ≈ 330°

Lastly, we represent the complex number with the help of a graphing tool.

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Answer:

D

Step-by-step explanation:

7 x 1,000,000,000 + 5 x 1,000,000 + 9 x 10,000+ 9 x 100 + 7 x 1

=7,000,000,000

+        5,000,000

+              90,000

+                    900

+                         7

answer is D

If Mei has earned 30 points, the multiplication equation to find how many books she needs to read is 30=5x.

Let x represent the number of books she needs to read.

So,

The equation to find the number of books she need to read is:

30=5x

Let solve for x

30 =5x

Divide both side by 5x

x = 30/5

x = 6 books

Therefore the number of books is 6 books.

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The volume of a cuboid will be, V =  2x² If it has one side of 2 meters and the other two sides are of equal length.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

We know, The volume of a cuboid is (length×width×height).

Assuming the height of the cuboid to be 2 meters and it has a square base of 'x' meters.

Therefore, The volume of the cuboid V = 2×x×x.

V = 2x².

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There exist 108,900 possible results.

Since there are 22 students in the class and half of them are men, there are 22/2 = 11 men. And since half of the students are women, there are 11 women.

When choosing 4 men and 4 women to pair off, the number of results possible is the number of combinations of 4 men from 11, which is C(11, 4), multiplied by the number of combinations of 4 women from 11, which is C(11, 4).

So, the number of results possible is C(11, 4) * C(11, 4) = 330 * 330 = 108900.

Therefore, there are 108,900 possible results.

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Answer: 1,403

Step-by-step explanation: None

Answer:

1403

Step-by-step explanation:

First you find out how many minutes is each episodes at that is 23

Then you multiple 23 by 61 and you get 1403

Answer:

x = 56

Step-by-step explanation:

64 + x + 60 = 180

124 + x = 180

x = 56

The missing angle x of the diagram is; x = 56°

In geometry, we know that the sum of angles on a straight line sums up to 180 degrees.

Now, in the given image we see that the three angles we are concerned with all form a straight line and as such they will all add up to 180 degrees. Thus;

64 + x + 60 = 180

124 + x = 180

x = 180 - 124

x = 56°

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Answer: is A

Step-by-step explanation: if you do the problem youd get 2 root 3x^2

Answer:

(6, -2)

Step-by-step explanation:

The only option that satisfies both equations is (6, -2).

Answer:

23.8888888889 that's the answer

Answer:

215/9=23.8888888889

Step-by-step explanation:

The equation of the line parallel to 8x+5y=1 passing through the point (1,−3)

is y = (-8/5)x - (7/5).

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line is y = m(1)x + c

Now,

The equation of the line parallel to 8x+5y=1 passes through the point (1, -3).

This means,

8x + 5y = 1

5y = - 8x + 1

y = (-8/5)x + 1/5

This is in the form of y = m(2)x + c

m(2) = (-8/5)

Now,

Since the line is parallel.

m(1) = m(2) = (-8/5)

So,

y = (-8/5)x + c

Now,

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

-3 = (-8/5) x 1 + c

c = -3 + 8/5

c = (-15 + 8) / 5

c = -7/5

So,

y = (-8/5)x - (7/5)

Thus,

The equation of the line is y = (-8/5)x - (7/5).

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The required equivalent expression to the given expression is Lima invests $1000 in a mutual fund which gives her a return of 12% per year this situation can be modeled as y = 1000(1.2)ⁿ.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
An expression is given in the question that is,
[tex]Z(t) = 4000(12^{2t +2})[/tex]

We have to form a problem that represents the format of a function same as shown above.

Expression and problem is given as, Lima invests $1000 in a mutual fund which gives her a return of 12% per year this situation can be modeled as y = 1000(1.2)ⁿ.

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Jane's error was that she assumed that the mean of the data set would represent a midpoint, where half of the cats weighed more and half weighed less.

This is not necessarily the case, as the mean is only an average of the data set and does not necessarily represent any particular point within the data set. For example, if the data set was composed of 8 cats that all weighed 8.48 pounds, then the mean would be 8.48, but none of the cats would weigh less than 8.48 pounds.

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The distance from Antrim to Randalstown is 6 5/6 miles.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Martin is walking from Antrim to Randalstown.

Randalstown 3 1/3 miles, Toome is 9 1/4 miles Antrim 3 1/2 miles.

Therefore, the distance from Antrim to Randalstown is the sum of their distances which is,

= 3 1/3 + 3 1/2 miles.

= 10/3 + 7/2 miles.

= (20 + 21)/6 miles.

= 41/6 miles.

= 6 5/6 miles.

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The pressure in the tyre when the volume is 140 cubic inches will be 30 pounds.

Boyle's law states that at a constant temperature, the pressure is inversely proportional to the volume. It means that the product of the pressure and the volume will remain constant for the given system.

Given that when air is pumped into an automobile tire, the pressure is inversely proportional to the volume. If the pressure is 35 pounds when the volume is 120 cubic inches.

The pressure will be calculated as:-

P₁V₁ = P₂V₂

( 35 x 120 ) = 140 x P₂

P₂ = ( 35 x 120 ) / 140

P₂ = 30 pounds

Therefore, when the volume is 140 cubic inches, the tire's pressure will be 30 pounds.

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The probability that a man will test positive on two successive tests if he has the disease 81%.

In mathematical terms, probability can be represented as the ratio of the number of favorable outcomes to the number of possible outcomes. The formula for probability is as follows:

P(E) = n(E) / n(S)

Where:

P(E) is the probability of event E occurring

n(E) is the number of favorable outcomes for event E

n(S) is the number of possible outcomes in the sample space S

Let's assume the probability of a man testing positive for a disease if he has it is represented by the symbol "P".

If the tests are independent, meaning that the outcome of one test does not affect the outcome of the other, then the probability of a man testing positive on two successive tests can be calculated as the product of the probabilities of each individual test.

Therefore, the probability of a man testing positive on two successive tests if he has the disease is P * P, or P².

If the probability of a man testing positive for a disease if he has it is 90%, represented by P = 0.9, then the probability of him testing positive on two successive tests is 0.9 * 0.9 = 0.81, or 81%.

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In linear equation, the unit rate of tickets at the skating rink is; 11.95 per ticket.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                  The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

We have been given Adela paid $71.70 for 6 tickets at the skating rink.

We need to find the unit rate per ticket.

Total amount = 71.70

Number of tickets = 6

Unit rate = Total amount/ Number of tickets

Unit rate =  70.70/ 6

Unit rate = 11.95/1

Therefore, the unit rate of tickets at the skating rink is; 11.95 per ticket.

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Answer:B

Step-by-step explanation:

PART A) Janet needs only three cups of sugar to make three batches of chocolate chip cookies.

PART B) One cup of sugar will be left over after making three batches of cookies.

What is the unit price?

A unit price is the cost of a single object or unit of measurement, such as a pound, a kilogram, or a pint, and it is used to compare the prices of similar products offered in various weights and quantities. Selling more than one unit of the same product at a discount from its unit price is known as multiple pricing.

Given that Janet needs One cup of sugar to make one batch of chocolate chip cookies.

Part A:

Let The number of cups of sugar Janet needs to make three batches of cookies be 'x'.

Now,

1 batch/ 1 cup = 3 batch/ x cups

x= 3

Therefore, Janet needs only three cups of sugar to make three batches of chocolate chip cookies.

Part B:

Given that Janet has four cups of sugar.

From part A, we found that she only need three cups of sugar.

Available - Needed = Excess

4-3=1

So, one cup of sugar will be left over after making three batches of cookies.

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A mathematical description of hexagon is given above.

In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

The segments of a polygonal circuit are called its edges or sides.

Given is hexagon.

In geometry, a hexagon is a six-sided polygon creating the outline of a cube. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.

A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).

Therefore, a mathematical description of hexagon is given above.

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Answer: The last option would be correct p=  75 + 5a. The reason being the last option is the right one is because the expression represents the additional points plus her original 75 she had on her homework assignments.  

Answer:

Step-by-step explanation:

=22.068

Answer:

5

Step-by-step explanation:

actual answer 4.69766713281

The original price of the PlayStation 5 is $500 and there is a 30% discount, calculated as $500 x 30/100 = $150. The sale price is $500 - $150 = $350.

The calculation of the sale price of the PlayStation 5 involves finding the amount of the discount first. The original price of the PlayStation 5 is $500. The discount is 30%, which means that 30% of the original price will be taken off. To find the amount of the discount, we multiply the original price by the discount rate (30% or 0.30).

$500 x 0.30 = $150

Next, we subtract the discount from the original price to get the sale price:

$500 - $150 = $350

So, the sale price of the PlayStation 5 is $350.

The sale price of the PlayStation 5 is an important aspect for customers who are looking for a good deal. By knowing the original price and the discount, one can easily find the sale price. This type of calculation is common in retail and commerce, and is used to determine the savings that a customer can make on a particular item during a sale. Understanding these concepts is crucial for consumers to make informed decisions about their purchases, and for businesses to effectively promote their products and attract customers.

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Answer:

1.03 hours

Step-by-step explanation:

Let x be the time taken to travel from office to seashore at 62mph

Distance traveled = speed x time = 62x miles

Since both trips together took 2 hours, the time taken for the same distance from seashore to office = 2 - x hours

At a speed of 66 mph, the distance traveled = 66(2-x) = 132 - 66x

Since the distances on each trip are equal:
62x = 132 - 66x

Add 66x to both sides => 62x + 66x = 132 =-66x + 66x

128x = 132

x = 132/128 = 1.03125 hours = 1.03 hours rounded to 2 decimal places

The perimeter of this triangular park is equal to: 3x² 37x - 4 feet.

Mathematically, the perimeter of a triangle can be calculated by using this mathematical expression:

P = a + b + c

Where:

P represents the perimeter of a triangle.

a, b, and c represents the length of sides of a triangle.

Substituting the given parameters into the perimeter of a triangle  formula, we have the following;

Perimeter of triangle, P = 12x + (15x + 4) + (10x + 3x² - 8)

Perimeter of triangle, P = 12x + 15x + 4 + 10x + 3x² - 8

Perimeter of triangle, P = 3x² 37x - 4 feet.

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Answer:

4xy + 2xy - 3xy +5xz - yz

4xy - 3xy + 2xy + 5xz - yz

1xy+2xy + 5xz - yz

3xy + 5 xz - yz