George’s age is three times that of his brother. When you add George’s age to his brother’s, you get 24. How old is each brother?
a) Write an equation that represents the situation. Explain any variable used.
b) Solve the equation from Part (a). Show your work. State your solution as a complete sentence.

In parallelogram SAVE, the value of the angle is m∠SEV = 125° while in parallelogram MORE ∠MOR = 111

A parallelogram is a quadrilateral with equal opposite and parallel sides. Opposite angles are equal.

In parallelogram SAVE:

m∠VAS = m∠SEV

3x - 5 = 2x + 15

x = 20

m∠VAS = 3(20) - 5 = 55 degrees

m∠VAS + m∠SEV = 180 (consecutive interior angles)

55 + m∠SEV = 180

m∠SEV = 125°

In parallelogram MORE:

∠MOR + ∠ORE = 180 (consecutive interior angles)

4x - 5 + 2x + 11 = 180

x = 29

∠MOR = 4(29) - 5 = 111

In parallelogram SAVE, the value of the angle is m∠SEV = 125° while in parallelogram MORE ∠MOR = 111

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Let's find rate of change (slope) of LuCy

\(\\ \sf\longmapsto m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(\\ \sf\longmapsto m=\dfrac{25}{1}=25\)

Troy has greater rate of change

Shaded area = (9 + x)(16 + x) = 198

Expand.

x^2 + 25x + 144 = 198

x^2 + 25x - 54 = 0

(x - 2)(x + 27) = 0

x = 2, -27

but x > 0, so

x = 2 cm

Answer:

The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.

Answer:

-6 x 9 = -54

Explanation:

The best unit of measure for the liquid in family-sized container of apple cider is the liter - True.

The metric unit of volume is known as the litre (international spelling) or liter (American English spelling) (SI symbols L and l,[1] with another symbol also used: ℓ). It is equivalent to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3). A litre or cubic decimetre fills a space of 10 cm × 10 cm × 10 cm (see figure) and is therefore equal to one-thousandth of a cubic metre. One litre of liquid water has a weight of almost precisely one kilogram, because the kilogram was initially defined in 1795 as the weight of one cubic decimetre of water at the temperature of melting ice (0 °C). However, subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact.

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The task is to determine the algebraic expressions for the total number of two-bedroom, one-bedroom, and studio apartments in the building and whether it is possible to design the building with exactly 72 two-bedroom units, 136 one-bedroom units, and 176 studios, and how many different reasonable solutions exist.

Let x, y, and z represent the number of floors for Plans A, B, and C, respectively. Then, the total number of two-bedroom apartments is 5x + 2y + 2z, the total number of one-bedroom apartments is 5x + 6y + 4z, and the total number of studio apartments is 10x + 6y + 5z.

To determine whether it is possible to design the building with exactly 72 two-bedroom units, 136 one-bedroom units, and 176 studios, we can set up the following system of equations:

5x + 2y + 2z = 72

5x + 6y + 4z = 136

10x + 6y + 5z = 176

We can solve this system using Gaussian elimination or matrix inversion. MATLAB can be used to solve the system of equations. After solving, we get x = 8, y = 7, and z = 4, which means that the building can be designed with 8 floors of Plan A, 7 floors of Plan B, and 4 floors of Plan C.

We can verify that this is the only solution by checking that the values of x, y, and z satisfy the original system of equations and that they are non-negative integers. Additionally, we can check that these values result in non-negative values for the total number of two-bedroom, one-bedroom, and studio apartments in the building. Therefore, we can conclude that there is only one reasonable solution, and it is x = 8, y = 7, and z = 4.

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The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.

The volume of the building will be calculated by the formula -

Volume = length × breadth × height

Thus, keeping the value of each component of building in the formula to find the volume of the building.

Volume of building = 255 × 255 × 42

Performing multiplication on Right Hand Side of the equation to find the value of volume

Volume of building = 2,731,050 feet³

Therefore, the volume of the building is 2,731,050 feet³.

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a = 15

b = 23

We would apply the trigonometry SOHCAHTOA

The triangle is right angled:

opposite = side opposite the angle 42° = a

adjacent = 17

hypotenuse = b

To get a, we would use tangent ratio (TOA):

tan 42 = opposite/adjacent

tan 42 = a/17

a = 17 tan 42

a = 17(0.9004)

a = 15.3068

Approximately, to the nearest whole number, a = 15

To get b, we would apply cosine ratio (CAH):

cos 42 = adjacent/hypotenuse

cos 42 = 17/b

b (cos 42) = 17

b = 17/cos 42

b = 17/0.7431

b = 22.877

Approximately to the nearest whole number, b = 23

The null hypothesis would not be rejected and the researcher would fail to find statistical significance at the chosen alpha level of .05.

If a researcher sets the alpha level at .05 and obtains a p-value of .06, it means that the p-value is greater than the chosen significance level. The alpha level, also known as the significance level, represents the threshold for determining whether the results are statistically significant or not.

In hypothesis testing, the null hypothesis assumes that there is no significant difference or relationship between variables.

If the p-value is less than or equal to the alpha level, it suggests that there is enough evidence to reject the null hypothesis and conclude that there is a significant difference or relationship.

However, if the p-value is greater than the alpha level, as in this case with a p-value of .06, it means that the observed data does not provide sufficient evidence to reject the null hypothesis.

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The sum of the given polynomial  \((7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).\)is \(9x^{3} - 8x^{2}\).

Polynomials can be added or subtracted when they contain like terms, which are the same alphabets with the same powers.

Whereas there are no such rules for multiplication, any phrase with any power can be multiplied. The powers of the terms are then modified in accordance with exponentiation principles.

The following polynomial equation is \((7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).\)

Polynomial addition is accomplished by combining 'like terms'.

As a result, sorting and adding

= \((7x^{3} - 4x^{2} ) + (2x^{3} - 4x^{2} ).\)

= \(7x^{3} + 2x^{3} - 4x^{2} - 4x^{2}\)

= \(9x^{3} - 8x^{2}\)

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Complete question:

What is the sum of the polynomials? (7x3 - 4x2) + (2x3 - 4x2)

To find the slope of the curve defined by the implicit equations x = f(t) and y = g(t) at a specific value of t, we can use the implicit differentiation method.

For the first part of the question, to find the slope of the curve x = f(t), y = g(t) at a specific value of t, we can differentiate both equations with respect to t and then calculate dy/dx. The result will give us the slope at that particular value of t.

For the second part, we are given parametric equations x = 4 cos(2t) and y = 4 sin(2t), where 0≤t≤2π. To find the Cartesian equation representing the path of the particle, we can eliminate the parameter t by squaring both equations and adding them together. This will result in x² + y² = 16, which represents a circle with a radius of 4 centered at the origin (0, 0).

The graph of the Cartesian equation x² + y² = 16 is a circle in the xy-plane. Since the parameter t ranges from 0 to 2π, the portion of the graph traced by the particle corresponds to one complete revolution around the circle.

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Answer:

19/36.

Step-by-step explanation:

Shane’s average was 19/36 jumps completed. Here is the equation: (2/3+4/6+1/4) / 3 =a . 4/6 is = ⅔, so ⅔ + ⅔ = 4/3. ¼ is equal to 3/12 and 4/3 is equal to 16/12, and 16/12 + 3/12=19/12. 19/12 divided by three is 19.36, because it is.

Answer: 19/36

Step-by-step explanation:

A mean equation is hidden in this word problem. Focus on the 2 out of 3, 4 out of 6, and 1 out of 4. Those numbers are actually fractions. Shane managed to complete 2/3 of the jumps on the lowest bar, he managed to complete 4/6 of the jumps on the middle bar, and 1/4 of the jumps on the highest bar.

Step 1: Write the mean equation

(2/3 + 4/6 + 1/4)/3 = x

Step 2: Find the common denominator

3, 6, and 4 are all factors of 12, so 12 is your common denominator

4(2/3) = 8/12

2(4/6) = 8/12

3(1/4) = 3/12

Now rewrite the equation with the common denominator

(8/12 + 8/12 + 3/12)/3 = x

Step 3: Sum the fractions

(19/12)/3 = x

Step 4: I

Invert and multiply

(19/12)/3 = 19/12 * 1/3 = 19/36

This is your answer.

Answer:

see below

Step-by-step explanation:

R:B = 8:3

5 ratio marbles is 35 (to make ration 3:3)

1 ratio=7

He originally had 56 red marbles and 21 blue (77 total)

Now he has 21 Red and 21 Blue (42 total)

While a large number of bins can generate noise and obscure the underlying pattern, a limited number of bins can oversimplify the distribution and conceal significant characteristics equation  

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.

Depending on the data and the goal of the presentation, a histogram's ideal number of bins will vary. Nonetheless, as a rule of thumb, the square root of the total number of data points may be used to approximate the number of bins.

In this instance, we have 56 bits of data, and 56 squared is around 7.5. In order to give the histogram a solid foundation, we can start with a range of 7-8 bins.

It's crucial to keep in mind, though, that changing the number of bins might have an effect on how the data are interpreted. While a large number of bins can generate noise and obscure the underlying pattern, a limited number of bins can oversimplify the distribution and conceal significant characteristics.

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Answer:

10, 11 and 12.

Step-by-step explanation:

A number has 5 as one of its factors, when last digit is 5 or 0. Only prime numbers have 1 as the only factor and a number has 2 as one of its factors when last digit is 2, 4, 6, 8 or 0.

Three possible consecutive numbers are 10, 11 and 12. 10 is the product of 2 and 5, 11 is a prime number and 12 is the product of 3 and 2². Therefore, possible choice is 10, 11 and 12.

Answer:

f(x) = 2,600,000(0.989)x

Step-by-step explanation:

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Answer:

See below

Step-by-step explanation:

Odds AGAINST are 3 to5        then odds FOR are  2 to 5

    2/5   = .4 = 40%   chance of winning

The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).

We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;

x⁴ divided by 3x equals 2x³

3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³

subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27

3x³ divided by 3x equals x²

3x + 4 multiplied by x² equals 3x³ + 4x²

subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27

9x² divided by 3x equals 3x

3x + 4 multiplied by 3x equals 9x² + 12x

subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27

-15x divided by 3x equals -5

3x + 4 multiplied by -5 equals -15x - 20

subtract -15x - 20 from -15x + 27 will result to a remainder of 47

using the remainder theorem, x = -4/3 from the the divisor 3x + 4

thus:

f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}

f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27

f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}

f(-4/3) = (5919 - 2112)/81

f(-4/3) = 3807/81

f(-4/3) = 47

Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.

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The number of raindrops hitting a particular region can be modeled using the Poisson distribution. The Poisson distribution is commonly used to describe the number of events occurring in a fixed interval of time or space when these events happen randomly and independently with a known average rate. In this case, the average rate is given as 20 drops per square inch per minute. The probability that the region has no raindrops in a given 6-second time interval is approximately 0.7165

To compute the probability that the region has no raindrops in a given 6-second time interval, we need to convert the rate to match the time interval. Since the rate is given per minute, we can divide it by 60 to get the rate per second: λ = 20/60 = 1/3 drops per square inch per second.

Using the Poisson distribution, the probability of observing exactly k events in a given time interval is given by the formula:

P(X = k) = (e^(-λ) * λ^k) / k!

Where e is Euler's number (approximately 2.71828), λ is the average rate, and k is the number of events.

In our case, we want to find the probability that the region has no raindrops in a 6-second time interval, which corresponds to k = 0.

P(X = 0) = (e^(-1/3) * (1/3)^0) / 0! = e^(-1/3)

Using a calculator, we can evaluate e^(-1/3) ≈ 0.7165.

Therefore, the probability that the region has no raindrops in a given 6-second time interval is approximately 0.7165 or 71.65%.

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Answer: 11,500 grams

Step-by-step explanation: 920/8=115 115*100= 11,500

the arc length indicated by the bolded arc with a radius of 13 inches and a central angle of 30 degrees is (13π/6) inches.

To find the arc length indicated by the bolded arc with a radius of 13 inches and a central angle of 30 degrees, follow these steps:

Convert the central angle to radians: Since there are 360 degrees in a full circle and 2π radians in a full circle, you can use the conversion factor (π/180) to convert the central angle from degrees to radians. So, 30 degrees * (π/180) = (30π/180) = (π/6) radians.

Calculate the arc length using the formula: Arc length (L) = radius (r) * central angle (θ), where r is the radius and θ is the central angle in radians. In this case, r = 13 inches and θ = π/6 radians.

Substitute the values into the formula: L = 13 * (π/6)

Solve for L: L = (13π/6)

Simplify the fraction: L = (13π/6) inches

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Answer:

15,600,000

Step-by-step explanation:

26 x 25 x 24 x 10 x 10 x 10 x 10 = 15,600,000

So, there are 15,600,000 possible license plates that can be constructed if no letter can be repeated.

The focus and directrix of the parabola with equation y = (1/12)x^2 can be determined using the properties of parabolas. The focus is located at the point (0, p), where p is the coefficient of the squared term.

For the given equation y = (1/12)x^2, the coefficient of the squared term is 1/12. Therefore, the focus is located at the point (0, 1/4). The focus is the point on the parabola that is equidistant to both the vertex and the directrix. In this case, since the parabola opens upwards, the focus is above the vertex.

The directrix, on the other hand, is a horizontal line located at a distance of -p from the vertex. In this case, the directrix is located at y = -1/4. It is a line parallel to the x-axis and acts as a mirror for the parabolic curve.

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Answer:

ur screwed but the answer is 110.88

Step-by-step explanation:

:)

Answer:

An equation of the line that passes through the point (-4, -6) and is perpendicular to the line 2x - y = 6 is y = -2x + 10.

Answer:

124.3 ft

Step-by-step explanation:

We solve the above question using the Trigonometric function of Tangent

= tan θ = Opposite/Adjacent

θ = Angle of Elevation = 73°

Adjacent = 38 ft

Opposite = x

Hence

tan 73° = x/38 ft

Cross Multiply

x = tan 73° × 38 ft

x = 124.2923995 ft

Approximately = 124.3 ft

Therefore, Nick is 124.3 ft from the ground.

The probability that at most 15 megatons of snowfall is accumulated over one year in a lake with a gamma distribution a=10 and b=2 is approximately 0.0065.

Given that the annual amount of snowfall x (in megatons) in a lake follows a gamma distribution with a=10 and b=2, we can use the cumulative distribution function (CDF) of the gamma distribution to find the probability that at most 15 megatons of snowfall is accumulated over one year.

The CDF of a gamma distribution with parameters a and b is given by:

F(x;a,b) = 1 - Γ(a, b*x)/Γ(a)

where Γ(a) is the gamma function with parameter a and Γ(a, x) is the incomplete gamma function with parameters a and x

Using this formula, we can calculate the probability that at most 15 megatons of snowfall is accumulated over one year by evaluating the CDF at x=15:

F(15;10,2) = 1 - Γ(10, 2*15)/Γ(10)

≈ 0.0065

Therefore, the probability that at most 15 megatons of snowfall is accumulated over one year in the lake is approximately 0.0065.

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