What Is The Volume Of This Figure?PLEASE HELP I DONT GETTTT ITTT (2024)

The general solutions of these simultaneous equations for x and y are:

x = t, y = 120 - 3t

x = t, y = 120 - 12t

x = t, y = 1/(40 - 3t)

x = t, y = 476 - 12t

Equation

To find the general solution to these equations, we need to solve for the variables x and y in terms of a parameter (let's call it t).

12x + 4y = 480

Rearranging, we get: y = (480 - 12x)/4

Simplifying, we get: y = 120 - 3x

The general solution is: x = t, y = 120 - 3t

y = 120 - 12x

Rearranging, we get: x = (120 - y)/12

The general solution is: x = t, y = 120 - 12t

y = 1/(40 - 3x)

Rearranging, we get: x = (40 - 1/y)/3

The general solution is: x = t, y = 1/(40 - 3t)

y = 476 - 12x

Rearranging, we get: x = (476 - y)/12

The general solution is: x = t, y = 476 - 12t

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Answer d= -16.2

Step by step

d/6 = -2.7

To cancel out the denominator of the fraction ( a fraction is considered a division), we do the inverse or opposite which is to multiply.

6 * d/6 = - 2.7 * 6

d = - 16.2 is your answer.
I attached the math

Answer:20cm

Step-by-step explanation:

P=4A-4X5=20CM

Answer: P=20cm

Step-by-step explanation: The perimeter of the square will be 5 + 5 + 5 + 5 = 20 cm

The differential equation for the amount of salt in the tank is obtained as [tex]A = \frac{2000}{3} - \frac{2000}{3} \times e^{(\frac{-9t}{250})}[/tex].

What is differential equation?

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.

We can start by finding the rate of change of salt in the tank. Let's call this quantity dA/dt, where A is the amount of salt in the tank.

The salt that enters the tank at a rate of 10 grams per liter, so the amount of salt that enters the tank per minute is -

10 grams/liter × 6 liters/minute = 60 grams/minute

The salt that leaves the tank at a rate of 9 liters per minute, so the amount of salt that leaves the tank per minute is -

A/250 grams/liter × 9 liters/minute = 9A/250 grams/minute

Therefore, the rate of change of salt in the tank is -

dA/dt = 60 - 9A/250

This is a separable differential equation, which we can solve by separating the variables and integrating -

dA/(60 - 9A/250) = dt

Multiplying both sides by (250/9) and integrating, we get -

-250/9 × ln|60 - 9A/250| = t + C

where C is an arbitrary constant of integration.

Solving for A, we get -

[tex]A = \frac{250}{9} \times (60 - e^{(\frac{-9t}{250} + C)})[/tex]

To find the value of C, we can use the initial condition that there are 11 grams of salt in the tank initially (when t = 0) -

A(0) = 11

Substituting t = 0 and A(0) = 11 into the equation above, we get -

[tex]11 = \frac{250}{9} \times (60 - e^C)[/tex]

Solving for C, we get -

C = ln(60 - 9/250 × 11)

C = ln(57.28)

Therefore, the amount of salt in the tank as a function of time t is -

[tex]A = \frac{250}{9} \times (60 - e^{(\frac{-9t}{250} + ln(57.28))})[/tex]

Simplifying this expression, we get -

[tex]A = \frac{2000}{3} - \frac{2000}{3} \times e^{(\frac{-9t}{250})}[/tex]

Therefore, the differential equation is [tex]A = \frac{2000}{3} - \frac{2000}{3} \times e^{(\frac{-9t}{250})}[/tex].

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Answer:

14,770.56

Step-by-step explanation:

The formula that we will use is [tex]V=\pi r^{2} h[/tex]. First, we multiply 14 × 14 = 196. Second, we multiply 196 × 24 = 4,704. Lastly, we multiply 4,704 × 3.14 = 14,770.56.

pi is 3.14r is for radiusV is for volumeh is for height.

Samantha will have at least $300 in her account after Option b- 2 years.

To solve this problem, we can use the formula for compound interest

[tex]A = P(1 + r/n)^(n*t)[/tex]

where A is the amount of money in the account after t years, P is the initial amount (or principal), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).

In this case, P = $250, r = 0.21, n = 1 (since the interest is compounded annually), and we want to find t such that A = $300. So we can set up the equation:

$300 = $250(1 + 0.21/1)

Simplifying the equation:

[tex]1.2 = 1.21^t[/tex]

Taking the logarithm of both sides:

[tex]log(1.2) = log(1.21^t)[/tex]

log(1.2) = t * log(1.21)

T = log(1.2) / log(1.21)

t ≈ 2.15

Therefore, it will take Samantha approximately 2 years and 2 months (rounded to the nearest month) for her account to reach $300 with 21% interest compounded annually.

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Total area painted is 313.5 ft² and the total number of CANS needed is 5.

What is a trapezoid?

A quadrilateral with just one pair of sides that are parallel. It is used in numerous fields and is a common shape in mathematics. A trapezoid's area is determined by multiplying the height by half of the sum of the two bases' lengths.

A trapezoid is a quadrilateral or a four-sided polygon that has one sets of equal sides. In North America, it is also known as a trapezoid. A trapezium's other two sides are usually not parallel and may be different lengths.

We know that the deck is in trapezium figure, So the

Area of trapezium = 1/2 (sum of parallel line) × height

Area of trapezium = 1/2 ( 14 + 24 ) × 16.5

Area of trapezium = 313.5 ft²

Therefore, total area painted = 313.5 ft²

Total number of CANS needed = total area /one can of paint covers

Total number of CANS needed = 313.5/72 = 4.35 = 5 cans needed

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Complete question and its diagram-

The length of A'B'is √13 and the length of BB'is 9

The solution of the question is as follows :-

To solve this problem, we can use the law of sines and the fact that the sum of the angles in a triangle is 180 degrees. Let's start by finding angle BAC:

sin(BAC) = opposite/hypotenuse = AB/AC = 12/9 = 4/3

BAC = sin⁻¹(4/3) = 53.13 degrees

Now we can find angle BAA':

BAA' = 180 - BAC - CA'A = 180 - 53.13 - sin^-1(2/3) = 79.37 degrees

Using the law of sines, we can find A'B':

A'B' / sin(BAA') = A'A / sin(BAC)

A'B' = sin(BAA') * A'A / sin(BAC) = sin(79.37) * 6 / sin(53.13) = 8.5

To find BB', we can use the fact that triangles ABB' and ACB' are similar:

AB' / CB' = AB / AC

AB' / 2 = 12 / 9

AB' = 8/3

Now we can use the Pythagorean theorem to find BB':

BB'² = AB'² - AB²

BB'²= (8/3)²- 12²

BB' = sqrt((64/9) - 144) = sqrt(64/9 - 16/9) = 2sqrt(10/9) = 2sqrt(10)/3

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Answer:

a) 20%

b) 945

c) 2571

Step-by-step explanation:

(a) To find the relative rate of growth of the bacterium population, we need to find the derivative of the given function with respect to time t:

n(t) = 945e^0.2t

Taking the derivative of both sides with respect to t, we get:

dn/dt = 945(0.2)e^0.2t

Simplifying this expression, we get:

dn/dt = 189e^0.2t

Now, we can find the relative rate of growth by dividing the derivative by the original function:

Relative rate of growth = (dn/dt) / n(t)

Substituting the expressions we found earlier, we get:

Relative rate of growth = 189e^0.2t / 945e^0.2t = 0.2

Therefore, the relative rate of growth is 0.2 or 20%.

(b) To find the initial population of the culture, we simply need to substitute t = 0 in the given function:

n(0) = 945e^0.2(0) = 945e^0 = 945(1) = 945

Therefore, the initial population of the culture is 945.

(c) To find the number of bacteria in the culture at time t=5, we simply need to substitute t = 5 in the given function:

n(5) = 945e^0.2(5) = 945e = 945(2.71828) = 2571.2266

Therefore, the culture will contain approximately 2571 bacteria at time t=5.

Answer: your answer should be C

Step-by-step explanation: when you dilate a figure, you are basically multiplying it, so looking and seeing B is at (0,4) if we multiple this by 3 (since its dilated by a scale factor of 3) we will get (0,12)

Answer:

x = 2

Step-by-step explanation:

Add 2/5 to both sides. This makes the equation:

x = 1+3/5+2/5 = 1+1 = 2

x = 2

The slopes of the two lines are the same (-1), and hence the lines are parallel. Option D.

Equation of a straight line

Let's start by putting each equation in slope-intercept form (y = mx + b) to determine their slope and y-intercept.

4x + 4y = -8 can be simplified as:

4y = -4x - 8

y = -x - 2

So, the slope of this line is -1, and the y-intercept is -2.

x + y = -8 can be simplified as:

y = -x - 8

So, the slope of this line is -1, and the y-intercept is -8.

Now we can answer the given question based on this information:

The lines share the same y-intercept. False, as the y-intercepts of the two lines are different (-2 and -8).

Both lines intersect at point (0, -8). False, as the line 4x + 4y = -8 passes through the point (-2, 0) and the line x + y = -8 passes through the point (-4, -4).

The lines are perpendicular. False, as the slopes of the two lines are the same (-1).

The lines are parallel. True, as the slopes of the two lines are the same (-1), and hence the lines are parallel.

Therefore, the correct answer is (D) The lines are parallel.

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The probability is

1. 2/11

2. 11/500

3. 41/500

4. 0

What is probability?

Probability is a measure of the likelihood of a certain event occurring. It is commonly expressed as a fraction, decimal, or percentage.

The probability that the consumer is 18-24 years of age, given that he/she dislikes Crunchicles is 2/11.

The probability that the selected consumer dislikes Crunchicles is 11/500. The probability that the selected consumer is 35-55 years old or likes Crunchicles is 41/500.

If the selected consumer is 70 years old, then the probability that he/she likes Crunchicles is 0 as there are no consumers in this age group that like Crunchicles.

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Question:

Five hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.

18–24 25–34 35–55 55 and over Total

Liked Crunchicles 2 15 12 25 54

Disliked Crunchicles 2 5 113 1 11

No Preference 48 113 34 240 435

Total 52 133 49 266 500

One consumer from the survey is selected at random. Use reduced fractions for your responses to each of the following questions.

What is the probability that the consumer is 18–24 years of age, given that he/she dislikes Crunchicles?

What is the probability that the selected consumer dislikes Crunchicles?

What is the probability that the selected consumer is 35–55 years old or likes Crunchicles?

If the selected consumer is 70 years old, what is th probability that he/she likes Crunchicles?

Answer:

No

Step-by-step explanation:

There are no numbers that can multiply by itself to get 50

Example of some perfect square:

4, 9, 16, 25, 36, 49, 64, 81, etc.

The fraction of the jar that is filled would be = 3/8

How to calculate the fraction of the jar that is filled?

The quantity of pound of flour that the jar can hold = ¾

That is the whole jar can contain flour of quantity = 3/4 pound.

The amount of flour that was emptied into the jar = ½

The fraction of the jar that is filled with the flour when 1/2 is emptied into it = 1/2of 3/4 = 3/8 of the jar.

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Step-by-step explanation:

The steps that Inga can use to solve the quadratic equation 2x^2 + 12x - 3 = 0 are:

Use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a = 2, b = 12, and c = -3.

Factor out the greatest common factor (GCF) from the quadratic expression: 2(x^2 + 6x - 3/2) = 0. Then, use either the zero product property or divide both sides by the GCF of 2 to solve for x.

Complete the square by adding and subtracting the square of half the coefficient of x from both sides: 2(x + 3)^2 - 27 = 0. Then, isolate the squared term and take the square root of both sides to solve for x.

Answer:

2(x² + 6x) = 32(x² +6x +9) = 3 +18x +3 = ±√(21/2)

Step-by-step explanation:

You want to know which steps Inga could use to solve the quadratic equation 2x² +12x -3 = 0.

Completing the square

The offered steps are those used to solve the quadratic by completing the square.

2x² +12x = 3 . . . . . . . . . separate the constant from the variable terms

2(x² +6x) = 3 . . . . . . . . . matches choice 3

2(x² +6x +9) = 3 +18 . . . . matches choice 1

2(x +3)² = 21

(x +3)² = 21/2

x +3 = ±√(21/2) . . . . . . . matches choice 4

x = -3 ±√(21/2)

__

Additional comment

In the third step above, we have added the square of half the x-coefficient inside parentheses, and an equivalent amount on the other side of the equal sign: (6/2)² = 9, and 2(9) = 18.

The length of the common tangent LK is approximately 34.43.

What is the length?

To solve this problem, we can draw a line segment from the center of circle O to point L on line LK, and draw a line segment from the center of circle P to point K on line LK.

We can then use the Pythagorean theorem to find the length of the line segment from the center of circle O to point L:

(OL)² = (OP)² - (LP)²

(OL)² = 26² - 10²

(OL)² = 576

OL = 24

Similarly, we can use the Pythagorean theorem to find the length of the line segment from the center of circle P to point K:

(PK)² = (OP)² - (OP - LP)²

(PK)² = 26² - 20²

(PK)² = 156

PK = 2 * √(39)

Now that we know the lengths of OL and PK, we can find the distance between L and K:

LK = OL + PK

LK = 24 + 2 * √(39)

Therefore, the length of the common tangent LK is approximately 34.43

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The identity to find the value of the expression is D. sin² (pi/4) + cos² (pi/4) = 1

How to explain the expression

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

The correct identity to use here is the Pythagorean identity, which states that sin²(x) + cos²(x) = 1 for any value of x.

Substituting x = pi/4, we get:

sin² (pi/4) + cos² (pi/4) = 1

Therefore, the value of the expression is 1.

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Use an identity to find the value of the following expression.

sin^2 (pi/4) + cos^2 (pi/4)

sin^2 (pi/4) + cos^2 (pi/4) = 0

sin^2 (pi/4) + cos^2 (pi/4) = 1/2

sin^2 (pi/4) + cos^2 (pi/4) = 2

sin^2 (pi/4) + cos^2 (pi/4) = 1

Since the wall's base is b = 1.0b in length, a quart of paint will cover a wall that is 8 feet by 1.0b feet in size.

what is equation ?

In algebra, an equation is a document that presents the equality among both two expressions. It contains a set, constants, and mathematical calculations such as addition, subtraction, cell growth, and division. The goal of trying to solve an equation is really to find the value or beliefs of the variables that make the calculation true. Equations are used to model a broad variety of phenomena in science, architecture, economics, among other fields

given

The base length of the rectangular wall that Jasmine wishes to paint is represented by the variable "b" in the equation 8b/100. This equation is used by Jasmine to calculate how much wall space one quart of paint will fill. By dividing 8b by 100, Jasmine can find the number of quarts required to paint the entire wall.

To solve the equation for "b", we need to isolate the variable on one side of the equation. We can do this by multiplying both sides of the equation by 100/8 or 12.5, which gets us:

b = (100/8) / (100/8) * 8b/100

b = 12.5 * 8b/100

b = 1.0b

Since the wall's base is b = 1.0b in length, a quart of paint will cover a wall that is 8 feet by 1.0b feet in size.

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The complete question is:- Jasmine is redecorating her bedroom and wants to paint one wall with an accent color. She has 1 quart of accent color paint and is trying to figure out how much of the wall the quart will cover. The walls in Jasmine's room are 8 feet tall. The area of the rectangular wall can be represented by the expression 8b, where b is the length of the base.

The paint container says that each quart will cover an area of 100 square feet, so Jasmine uses the equation b the area of wall that the quart of paint will cover.

In this equation, the variable b is by Because division is the opposite of to get the variable by itself on one side of the equation. In other multiplication, we'll divide by words, we'll the variable. 8b 100 =

Remember that the property of equality states that we must both sides of the equation by to keep a balanced equation.

After subtracting the scholarship amount from the tuition cost, we still need to pay $8,000 towards your tuition cost after receiving the scholarship and federal loan.

Define Subtracting ?

The procedure for calculating the difference between two quantities or quantities is known as subtraction. Yet, the phrase "taking one quantity aside from another" is used to refer to subtracting one number from another. In any subtraction problem, the terms of the numbers are minimum, minimum plus, and difference.

After subtracting the scholarship amount of $500 from the tuition cost of $10,500, the remaining amount to be paid is:

$10,500 - $500 = $10,000

Since you are eligible for a $2,000 subsidized federal loan, you subtract this amount from the remaining tuition cost to determine how much more you need to pay:

$10,000 - $2,000 = $8,000

Therefore, you still need to pay $8,000 towards your tuition cost after receiving the scholarship and federal loan.

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From the graph of the function 3√(x + 3) it can be deduced that

Minimum: 0Maximum: 8.49

How to find the minimum and maximum points

To find the minimum and maximum values of the function on the interval [-11, 5], we just need to find the lowest and highest points on the graph within that interval.

From the graph, we can see that

the minimum value occurs at x = -3, where the function is 0, and the maximum value occurs at x = 5, where the function is 6sqrt(2).

Therefore: we can express the minimum and maximum in the form

Minimum: 0

Maximum: 6√(2) = 8.485

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He payed $29.92 for his gas.

11.6 x 2.58= 29.92

I hope this helps!

Answer:

29.92

Step-by-step explanation:

Answer:

Step-by-step explanation:

(6^3)^5= 216^5 = 4,70 *(10 ^11)

The line-of-sight distance from the television camera to the base of the stadium is approximately 5300 meters.

What is angle of depression ?

The angle of depression is the angle between a horizontal line and the line of sight to an object that is below the horizontal line. This angle is formed by drawing a line from the observer's eye to the object and another line from the observer's eye to the horizontal line. The angle of depression is the angle between these two lines.

For example, imagine standing on a cliff and looking down at a boat in the water below. The angle of depression is the angle between the horizontal line (which represents the level of the water) and the line of sight from your eye to the boat.

According to the question:
In this diagram, point A represents the television camera, point B represents the base of the stadium, and point C represents the blimp. Angle ACB is the angle of depression, which is given as 6 degrees.

We want to find the distance AB, which is the line-of-sight distance from the television camera to the base of the stadium. We can use the tangent function to relate the angle of depression to the distance AB:

tan(θ) = opposite/adjacent = AB/500

Rearranging this equation, we get:

AB = 500 * tan(θ)

Substituting the given angle of depression of 6 degrees, we get:

AB = 500 * tan(6°)

Using a calculator, we find:

AB ≈ 53.16 m

Rounding to the nearest hundred meters, we get:

AB ≈ 5300 m

Triangle STU is mapped to triangle PQR by a dilation with center (0,0) and scale factor 2, along with a reflection across the x-axis.

What is a dilation?

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The resulting image is a larger or smaller version of the original object, depending on whether the scale factor is greater than or less than 1, respectively.

For this problem, we have that the coordinates of each vertex of the original triangle is multiplied by two, hence the scale factor of the dilation is of two.

Then the orientation of the figure was changed, from the third quadrant to the second quadrant, meaning that the figure was reflected over the x-axis.

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The probability that the number of successes x is exactly 2 in this binomial distribution is approximately 0.01536 or 1.536%.

Given that:

Trials: n=6

Probability of success: p=0.80

To find the probability that the number of successes x is exactly 2 in a binomial distribution with n=6 trials and a probability of success p=0.80, use the binomial probability formula:

[tex]P(x) = ^nC _x \times p^x \times (1 - p)^{n - x}[/tex]

Where:

P(x) is the probability of getting exactly x successes.

n is the number of trials.

x is the number of successes want to find the probability for.

p is the probability of success in a single trial.

In this case, x = 2.

Let's calculate the probability:

[tex]P(2) = ^6C _2 \times 0.80^2 \times (1 - 0.80)^{6-2}[/tex]

First, calculate (6 choose 2):

[tex]^6C_2 = 6! / (2! \times (6 - 2)!)\\ ^6C_2 = 6! / (2! \times 4!)\\ ^6C_2 = (6 \times 5) / (2 \times1)\\ ^6C_2 = 15[/tex]

Now, calculate the probability:

[tex]P(2) = 15 \times 0.80^2 \times (1 - 0.80)^{4}\\P(2) = 15 \times 0.64 \times 0.0016\\P(2) = 0.01536[/tex]

So, the probability that the number of successes x is exactly 2 in this binomial distribution is approximately 0.01536 or 1.536%.

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The value of the given expression as required to be determined in the task content is; 6w + 8.

What is the value of the given expression?

As evident from the task content; it follows that the simplified form of the given expression is required to be determined.

Since the given expression is; w + w + w + w + w + w + 15 - 7 = ?

By first summing up the variable w, we have that;

6w + 15 - 7

= 6w + 8.

Ultimately, the value of the expression as required is; 6w + 8.

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We can find that the number of natural numbers he wrote would be:

(v - 9) + 1 = v - 8.

Define natural numbers?

Natural numbers are countable and arranged positive integers (1, 2, 3, and so forth). They are commonly referred to as counting numbers and are the most basic type of number in mathematics. Natural numbers do not include negative numbers, fractions, or decimals, but they start with one and go on forever.

Bill wrote all the natural numbers between 9 and 15 (where 15>9), which implies he wrote all the positive integers between 9 and 15, inclusive. Bill would have written the numbers 9, 10, 11, 12, 13, 14, and 15 if v was 15.

If Bill wrote all the natural numbers between 9 and v, then the number of numbers he wrote would be equal to the difference between v and 9 plus one (since he included both 9 and v). Therefore, the number of numbers he wrote would be (v - 9) + 1 = v - 8.

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