There are 3 generations living in one house, Abhilasha, Kalpana and Gouri.
Kalpana is 33 years older than Gouri and 28 years younger than Abhilasha. If Kalpana turned 49 this year, what are the ages of the other two family members?

Answer:

question 1. (20)X = 100

question 2. the last one

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.  20 a yard and made 100. 100/20=5 yards

20x=100

2. Since they don't give the number of yards they did mow, this would be my answer. I would say half the amount. Since they cut their rates in half, they'll have to cut twice as many to even the amount as before. They would have to cut three - four times as many to make over the original amount. They only have one weekend, so that'll be hard.

To find the cost of operating a 200-W lamp continuously for 1 week, we need to first calculate the amount of energy consumed by the lamp.

Energy consumed (in kWh) = Power (in W) x Time (in hours) / 1000

In this case, the power of the lamp is 200 W and the time it is used for is 1 week, which is 7 days x 24 hours/day = 168 hours.

Energy consumed = 200 x 168 / 1000 = 33.6 kWh

Now, to find the cost of this energy, we multiply the energy consumed by the power utility rate of 16 cents/kWh.

Cost of operating the lamp for 1 week = Energy consumed x Power utility rate
= 33.6 x 0.16
= $5.38

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The options that are included in the different system implementation methods are:

a. Phased implementation

b. Project implementation

c. Parallel implementation

e. Pilot implementation

System implementation is the process of introducing a new system or making changes to an existing one. There are several methods for system implementation, each with its advantages and disadvantages.

Phased implementation: This method involves introducing the new system in phases, where each phase is implemented and tested before the next one is started. This approach is suitable for large and complex systems, as it allows for thorough testing and minimizes risks.

Project implementation: This method involves introducing the new system all at once, often after an extensive planning phase. This approach is suitable for smaller systems, where risks can be managed, and a quick implementation is desirable.

Parallel implementation: This method involves running the old and new systems simultaneously for a period of time. This approach allows for a gradual transition to the new system, with minimal disruption to operations.

Pilot implementation: This method involves introducing the new system to a small group of users or departments first. This approach allows for thorough testing and provides an opportunity for feedback and adjustment before a full-scale implementation.

The other options provided, such as planning implementation, perfecting implementation, and plunge implementation, are not commonly used terms in the context of system implementation.

Ultimately, the choice of system implementation method will depend on factors such as the size and complexity of the system, the available resources, and the desired outcomes.

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Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.

Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.

To calculate the number of weeks Londell needs to work, we can set up an equation:

$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)

Simplifying the equation:

$40 + $15 = $400

Subtracting $40 from both sides of the equation:

$15 = $400 - $40

$15 = $360

Dividing both sides of the equation by $15:

= $360 / $15

≈ 24

Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.

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The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.

Given that the population mean, \(\mu\) = 90 wpm

The standard deviation of the population ,\(\sigma\) = 10

Sample size, n = 12

Sample mean, \(\bar x\) = 95

The reading rate of students follows the normal distribution.

Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)

        = \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)

        = 1.732

Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)

                                                                                       = P(z>1.732)

                                                                                       = 1- P(z<1.732)

                                                                                       = 0.4582

[The value 0.4582 found from the area under the normal curve using tables].

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The maximum rate of change of the function f(x,y) at the point (-2,5) is approximately 215.60.

To find the maximum rate of change of the function f(x,y) = 4x1x2y2 - 7y2 at the point (-2,5), we need to calculate the gradient vector and evaluate it at that point. The first paragraph provides a summary of the answer, and the second paragraph explains the details of the calculations.

The gradient vector of a function represents the direction of the steepest increase at any given point. To find the maximum rate of change, we need to calculate the magnitude of the gradient vector at the point (-2,5).

The gradient vector of f(x,y) = 4x1x2y2 - 7y2 is given by:

∇f = (∂f/∂x1, ∂f/∂x2, ∂f/∂y)

To calculate the partial derivatives, we differentiate each term of the function with respect to the corresponding variable:

∂f/∂x1 = 4x2y2

∂f/∂x2 = 4x1y2

∂f/∂y = -14y

Substituting the values x1 = -2, x2 = 5, and y = 5 into the partial derivatives, we can evaluate the gradient vector at the point (-2,5):

∇f(-2,5) = (4(-2)(5)^2, 4(-2)(5), -14(5))

         = (-200, -40, -70)

The magnitude of the gradient vector represents the maximum rate of change of the function at the given point:

Magnitude = |∇f(-2,5)| = √((-200)^2 + (-40)^2 + (-70)^2)

                       = √(40000 + 1600 + 4900)

                       ≈ √46500

                       ≈ 215.60

Therefore, the maximum rate of change of the function f(x,y) at the point (-2,5) is approximately 215.60.

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Salik and Maya are discussing a project that examines the relationship between the number of siblings someone has and their household income. Maya predicts that those with more siblings will have a higher household income. Salik questions whether the number of siblings is a categorical variable since it is a whole number. Our response can be : "In order to conduct this project, we need to choose two quantitative variables, which are variables that can be measured and expressed as numbers. The number of siblings is not a categorical variable because it is a continuous variable that can take on any whole number value."

The number of siblings is a quantitative variable because it can be expressed as a whole number. Household income is also a quantitative variable because it can be measured and expressed as a numerical value. Categorical variables are variables that can be divided into distinct categories or groups, such as gender, race, or occupation. The number of siblings is not a categorical variable because it is a continuous variable that can take on any whole number value.

To examine the relationship between the number of siblings and household income, Maya and Salik could use statistics to analyze their data. They could calculate descriptive statistics such as the mean and standard deviation for each variable, as well as the correlation coefficient to determine the strength and direction of the relationship between the two variables. They could also use probability theory to make predictions about the likelihood of certain outcomes, such as the probability that someone with more siblings will have a higher household income.

The complete question is:

Our classmates, Maya and Salik, are talking about the variables they want to study and how they plan to collect their samples. Here is part of their conversation. Respond in the places that say “your response.”

Double-check that both of their variables are quantitative.

Maya: I want to look at the relationship between the number of siblings someone has and the household income. I predict that those with more siblings have a higher household income.

Salik: We need two quantitative variables for this project. Wouldn’t number of siblings be categorical since it is whole numbers?

Your response:.........

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Answer:

narrower

Step-by-step explanation:

As \(|a|\) increases, the parabola becomes narrower.

As \(|a|\) decreases, the parabola becomes wider.

Answer:

SYMMETRICAL DESIGN: A formal, equilateral triangular design. ROUND DESIGNS: Do not require a focal point. HOOK METHOD: Wiring technique in which the wire is inserted through the flower and a small hook is formed in the wire before it is pulled back into the flower.

Step-by-step explanation:

A triangular arrangement is a formal, equilateral triangular design. Option D

A formal, equilateral triangle pattern is referred to as a triangular arrangement. It entails arranging components or things in a configuration that resembles an equilateral triangle.

In a variety of disciplines, including art, architecture, and landscaping, this arrangement is used. All three sides of the equilateral triangle are identical in length, and all three angles are 60 degrees.

As the equilateral triangle is seen as a stable and aesthetically beautiful shape, the triangular arrangement is frequently employed to establish balance, harmony, and aesthetic appeal in a design.

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It should be B correct me if I'm wrong but it should be B.

Answer:

V = 665,012 cm^2 (centímetros cuadrados)

Step-by-step explanation:

V= (pi) x (r^2) x (h)

V = 3.14 x 1764 x 120cm = 665012 cm^2

Answer:

3 and 4

Step-by-step explanation:

given that the difference is 7, two numbers that add up to 7 are 3 and 4.

Answer:

56.70

Step-by-step explanation:

Answer:

8 and 6

Step-by-step explanation:

If you use x for the first number, and y for the second, you get equations of 3x+5y=54 and x-2=y.

You can substitute the second equation into the first one to solve it. This gives 3x+5(x-2)=54.

The brackets can be expanded to 3x+5x-10=54. Collecting like terms makes it 8x-10=54.

Next, we add 10 to both sides. This gives 8x=64.

From there, we isolate the x by dividing both sides by 8, giving x=8.

To work out the second number, we can sub 8 for x in either equation (I'm using the second one as it's simpler).

This comes to y=8-2, therefore y=6.

**This content is simultaneous equations, which you may wish to revise. I'm always happy to help!

In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

OR 1464 - 1426 = 38 seats

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Thus, if the weather is warm, you can make a total of 20 combinations (5 shirts x 4 pants), and if the weather is cold, you can make a total of 40 combinations (5 shirts x 4 pants x 2 sweaters).

The total combination of clothing items you can wear is 5 shirts, 4 pants, and either 2 neckties or 2 sweaters. If the weather is warm, you can opt to omit the sweater and keep the two neckties. If the weather is cold, then you can omit the neckties and wear the two sweaters. To calculate the total number of clothing combinations you can make, you need to multiply the items you are allowed to wear. For example, if you are wearing a shirt and a pair of pants, you can make 5 x 4 = 20 combinations. If you are wearing a shirt, pants, and either a necktie or a sweater, you can make 5 x 4 x 2 = 40 combinations.

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When given a function f defined as f(x) = ax + b, where a and b are constants, and f(3) = 10 and f(8) = 12, the values of a and b are 0.4 and 0.8, solved using a system of equations. So the right answer is O a = 0.4, b = 8.8.

The values of a and b can be determined as follows:

f(3) = 10 implies that 10 = 3a + bf(8) = 12 implies that 12 = 8a + b

We can solve this system of equations to get the values of a and b.

One way to do this is to use elimination: We can eliminate b by subtracting the first equation from the second equation: 12 - 10 = (8a + b) - (3a + b)2 = 5a

Solving for a, we get a = 2/5.

Substituting this value of a into the first equation, we can solve for b:10 = 3a + bb = 10 - 3a

Substituting the value of a = 2/5, we get: b = 10 - 3(2/5)b = 10 - 6/5b = 44/5

Therefore, the values of a and b are: a = 2/5 and b = 44/5.

The correct answer is: a = 0.4, b = 8.8.

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The correct option would be "None of these" since the projection is an ellipse and not any of the given options (2, 4, 16, or "This option").

To determine the projection of the region D onto the xy-plane, we need to find the intersection curve of the two paraboloids.

First, let's set the two equations equal to each other:

3x² + (12/24)y² = 16 - x²

Next, we simplify the equation:

4x² + (12/24)y² = 16

Multiplying both sides by 24 to eliminate the fraction:

96x² + 12y² = 384

Dividing both sides by 12 to simplify further:

8x² + y² = 32

Now, we can see that this equation represents an elliptical shape in the xy-plane. The equation of an ellipse centered at the origin is:

(x²/a²) + (y²/b²) = 1

Comparing this with our equation, we can deduce that a² = 4 and b² = 32. Taking the square root of both sides, we have a = 2 and b = √32 = 4√2.

So, the semi-major axis is 2 and the semi-minor axis is 4√2. The projection of region D onto the xy-plane is an ellipse with a major axis of length 4 and a minor axis of length 8√2.

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Answer:

C. y=x

Step-by-step explanation:

If you use a graphing calculator and plot the points (-3,5) & (5,-3) and then graph y=x you can see it is the line of reflection.

Also when reflecting over the line y=x, we switch our x and y.

If the mean is greater than the median, the data is likely Right-skewed.

In mathematics, the mean is the average of a set of data, which is calculated by adding all the numbers together and then dividing the result by the total number of numbers. Right-skewed distributions have long right tails and are characterized by having a mean that is greater than the median. There are two different sorts of means that may be calculated: the arithmetic mean and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of integers in the set.

Therefore, the answer is right-skewed. A data set that is skewed to the right is one where the tail to the right of the data clusters is longer than the tail to the left of the data clusters. This means that the data set will have a mean value that is greater than the median.

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Answer:

Parentheses, brackets, and braces are ways of separating parts of a mathematical expression from one another, and they all look quite similar. Parentheses are smooth and curved ( ), brackets are square [ ], and braces are curly { }. In mathematics, they are mostly used for order of operations.

Step-by-step explanation:

Step-by-step explanation:

Since it's a right triangle, you can use Pythagoras

a^2 + b^2 = c^2

We have b and c, we just need a, so let's plug it in

\( {x}^{2} + {24}^{2} = {25}^{2} \)

\( {x}^{2} + 576 = 625\)

\( {x}^{2} = 49\)

\(x = 7\)

Answer: 7ft

Step-by-step explanation:

hypotenuse (h) = 25

perpendicular (p) = 24

base (b) = ?

We know by using Pythagoras theorem

b = √h² - p²

= √ 25² - 24²

= √ 49

= 7 ft

Answer:

The radius of a cylinder(r) = √(V / π × h), where V is the volume of a cylinder, h is the height of the cylinder, and π(Pi) is a mathematical constant with an approximate value of 3.14.

Step-by-step explanation:

hope this helps.

Answer:

33/65

Step-by-step explanation:

Given the following

∠U=90°,

TS = 65 = HYpotenuse

UT = 56 = Opposite

SU = 33 = Adjacent

Cos <S = adj/hyp

Cos <S = SU/TS

Cos <S = 33/65

Hence the required ratio is 33/65

The height of the trapezoid is 98 units

The space enclosed by the boundary of a plane figure is called its area.

A trapeziod is a closed shape or a polygon, that has four sides, four corners/vertices and four angles

The area of a trapezoid is expressed as;

A = 1/2( a+b)h

where a and b are the bases length of the trapezoid.

245= 1/2 ( 14+21)h

490 = 35h

divide both sides by 35

h = 490/35

h = 98 units

Therefore the height of the trapezoid is 98 units

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Answer:

yes

Step-by-step explanation:

it sounds good to me

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Answer:

153

Step-by-step explanation:

You need to find the area of the triangle first which is 63. The you want to find the area of the trapezoid which is 90. Then add them together.