6 Marks Questions 13. 2076 GIE Set B Q.No. 12 Sum to n terms of the following senes: 34 +222 +23 + Ans: [6]​

Answer:

a) 0.0281

b) 0.6924

c) 0.3081

Step-by-step explanation:

Probability that one of those sampled saying that Roosevelt was the best president since World War II = 345/2055 = 0.17

Probability that one of those sampled don't mention Roosevelt = (2055 - 345)/2055 = 1710/2055 = 0.83

a) The probability that both adults picked say Franklin Roosevelt was the best president since World War II = (345/2055) × (344/2054) = 0.0281

b) The probability that neither of the two adults say Franklin Roosevelt was the best president since World War II = (1710/2055) × (1709/2054) = 0.6924

c) The probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II = Probability that one of the two adults mention Roosevelt + Probability that the two adults mention Roosevelt

Probability that one of the adults mention Roosevelt = [(345/2055) × (1710/2054)] + [(1710/2055) × (345/2054)] = 0.280

Probability that two of the adults mention Roosevelt has been done in (a) and it is equal to 0.0281

Probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II = 0.280 + 0.0281 = 0.3081

Answer:

7/9 becuase Jerry already have 2/3 of a cake and Mandy gave him a 5/6 so it's 7/9

Answer: 1 1/2

Step-by-step explanation:

2/3+5/6= 4/6+5/6

= 9/6

= 3/2 = 1 1/2

Answer:

because a= 1,1 then 1+1 = 2

Answer:

180 m²

Step-by-step explanation:

The tennis court has a length of 25 meters and a width of 10 meters. The faulty tennis ball machines are placed at both ends of the court length.

The green ball machine has a range of 5 meters to 20 meters from the green machine's side while the yellow ball machine has a range of  2 meters to 16 meters from the yellow machine's.

Therefore the area of the tennis court with balls on it, has a range of 2 meters from the yellow machine and 5 meters from the green ball machine. Hence:

length of court with balls = 25 m - (5 m + 2 m) = 25 m - 7 m = 18 m

width of court = 10 m

Therefore,  the area of the tennis court that has balls of either color on it = length of court with balls * width of court with balls = 18 m * 10 m = 180 m²

All three approaches yield the same result: AED4,600,000 (Expenditure Approach), AED1,600,000 (Income Approach), and AED1,800,000 (Production Approach). This consistency demonstrates that the three approaches provide equivalent measures of GDP.

To calculate the contributions to GDP of the given transactions, we can use the three approaches: the expenditure approach, income approach, and production approach. Let's calculate the GDP using each approach and demonstrate that they give the same answer.

Expenditure Approach:

GDP is calculated as the sum of all final expenditures. In this case, the final expenditures are the sales of the supercomputers.

GDP = Sales of supercomputers

= (3 * AED1,000,000) + (1 * AED800,000)

= AED3,800,000 + AED800,000

= AED4,600,000

Income Approach:

GDP can also be calculated by summing up all the incomes earned during production. In this case, the incomes include wages, interest, and taxes.

GDP = Wages + Interest + Taxes

= (Labour costs for ABC + Labour costs for Jumbo) + (Interest on debt for ABC) + (Taxes for ABC + Taxes for Jumbo)

= (AED1,000,000 + AED200,000) + AED100,000 + (AED200,000 + AED100,000)

= AED1,200,000 + AED100,000 + AED300,000

= AED1,600,000

Production Approach:

GDP can also be calculated by summing the value added at each stage of production. In this case, the value added is the sales price minus the cost of components purchased.

GDP = Sales price of supercomputers - Cost of components

= (3 * AED1,000,000) + (1 * AED800,000) - (4 * AED500,000)

= AED3,000,000 + AED800,000 - AED2,000,000

= AED1,800,000

As we can see, all three approaches yield the same result: AED4,600,000 (Expenditure Approach), AED1,600,000 (Income Approach), and AED1,800,000 (Production Approach). This consistency demonstrates that the three approaches provide equivalent measures of GDP.

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Answer:

$45.60 per month

Step-by-step explanation:

She owes the dentist $342.00

you take $342.00 divided by 7.5(the amount of months)

and get $45.60 per month

Answer:

45/100 or 9/20.

Step-by-step explanation:

Divide 45 by100. This can simplify to 9/20

Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

Answer:

b and e

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation: Because grant had his age added by 6, therefore add 6 to 4 for 10.

Answer:

I think it would be 22

Step-by-step explanation:

The point at which the lines k(x) = 5x - 1 and h(x) = -3x - 1 meet is (0, -1)

Given: k(x) = 5x - 1, h(x) = -3x - 1

We need to find the point(if any) at which these two lines k and h meets.

To find point of intersection(if any), we need to set the functions equal as at the point of intersection the (x, y) value will be same for both of the lines.

Therefore, k(x) = h(x)

=> 5x - 1 = -3x - 1

=> 8x = 0

=> x = 0

k(x=0) = 5 * 0  - 1 = -1

Hence the point at which the lines k(x) = 5x - 1 and h(x) = -3x - 1 meet is (0, -1)

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Answer:

24 minutes

Step-by-step explanation:

1. Turn it into an equation.

60% of 40

2. Create a proportion.

x/40 = 60/100

3. Cross multiply

40 x 60 = 2400

x x 100 = 100x

4. Divide

2400/100x = 24x

Answer:

I think A because we can't see the thing

Answer:

x=1

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

PQ + QR = PR

substituting the values we have:

8 + 7x = 9x

8 + 7x - 7x = 9x - 7x

8 = 2x

8/2 = 2x/2

4 = x

Now, for the value of PR:

9 x 4

36

Answer:

4(x+8)

or

4x + 8

Step-by-step explanation:

four times sum of x and 8

which means a number is four times x+8

Answer:

270cm2

Step-by-step explanation:

you have to split the figure into 2.

the triangle above is = 1/2 x20cmx13cm=130cm2

the rectangle is = 20cmx7cm=140cm2

total area=140cm2+130cm2

               =270cm2

The diagram which best represents the hiking track of the hiker is attached below.

As time increases, speed is constant, i.e., 214 miles per hour

So, the distance increases with an increase in time.

Speed = Distance/Time

Let, Distance = D and Time = T,

214 = D / T

D = 214T

Let, D = Y coordinate, Time = X coordinate

y = 214 x→→Equation of the line passing through the origin and slope 214.

For the given situation, the equation is a linear equation and the equation will be on the y-axis.

Hence, a diagram that represents this information is:  

Correct question :

A hiker began hiking from the 0-mile mark of a trail. The hiker walked at a steady rate of 214 miles per hour. Draw the diagram which best represents this information?

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Answer:

D;the last answer

Step-by-step explanation:

The more negative a fraction or decimal, the lower that actual value.

Therefore since -1 1/5 is the lowest it should go first, and D is the only answer like this! Hope this helps ^^

Answer: -1 \(\frac{1}{5}\), -1, 0.25, \(\frac{1}{2}\) , 0.75

Step-by-step explanation:

    I will turn all of these numbers into numbers that are not fractions since most of the numbers are already this way.

0.75 -> 0.75

-1 -> -1

\(\frac{1}{2}\) -> 0.5

-1 \(\frac{1}{5}\) -> -1.2

0.25 -> 0.25

    First of all, the negative numbers are smaller than the positive numbers. Then, we can order them least to greatest by number.

-1.2, -1, 0.25, 0.5, 0.75

   Putting the numbers into what they were originally given as gives us this:

-1 \(\frac{1}{5}\), -1, 0.25, \(\frac{1}{2}\) , 0.75

    The answer is the last option, -1 \(\frac{1}{5}\), -1, 0.25, \(\frac{1}{2}\) , 0.75.

Answer:

10.5 feet is the length. im not too sure what part b means but mayybbbeeee 1 inch = 3.5 feet

Step-by-step explanation:

2 inches = 7

A= half of 7 is 3.5 so that would equal to 1 inch.  7 feet + 3.5 feet  is 10.5 feet

B= (maybe) 1 inch=3.5 feet

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

46.8 cm²

Step-by-step explanation:

The diagonal of the square has length \(\sqrt{6^2+10^2}=2\sqrt{34}\). Therefore, the radius of the circle is \(\sqrt{34}\), meaning the area is \(\pi(\sqrt{34})^2 \approx 34(3.14)=106.76\).

The area of the rectangle is \((6)(10)=60\) cm².

Subtracting the areas, the answer is 46.76 cm², which is 46.8 cm² to the nearest tenth.

Answer:

Fred's dog weighed 33.75 pounds at the appointment in March

Step-by-step explanation:

First you need to convert 25% to a decimal by moving the percent sign twice to the left and you will get 0.25.

Then you multiply 45 by 0.25 to find 25% of 45.

45 x 0.25= 11.25

After multiplying, you just have to subtract the product (11.25) by 45.

45 - 11.25 = 33.75

This is the same was doing 45-25%

Answer:

956

Step-by-step explanation: jiuufliu

Answer:

x > 22

Step-by-step explanation:

Hey there!

Well to solve,

52 - 3x < -14

we need to single out  x

52 - 3x < -14

-52 to both sides

-3x < -66

Divide both sides by -3

x > 22

The < changes to > because the variable number is a - being divided.

Hope this helps :)

Answer:

x > 22

Step-by-step explanation:

First, rearrange the equation

Then, pull out the like terms:

Next, apply algebra to the equation by dividing each side by -3. It should now look like this: x > 22.

Therefore, the solution set of the inequality would be x > 22.

The radius of the cylinder is 7. 9 in

First, we need to know the formula for volume of a cylinder

The formula for calculating the volume of a cylinder is expressed as;

V = πr²h

Such that the parameters of the formula are expressed as;

From the information given, we have that;

Substitute the values

196 = 3.14 × 1 × r²

Divide both sides by the values

r² = 62. 42

Find the square root of both sides

r = 7. 9 in

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Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3