two boys received equal amounts of pocket money .after one had spent N$15 and the other had spent N$21,they had N$64 together .what were their original allowance?

Answer:

292.4

Step-by-step explanation:

Answer:

292.4

Step-by-step explanation:

Use the mean formula: sum of elements / number of elements

Plug in the numbers:

(300 + 222 + 285 + 310 + 345) / 5

1462 / 5

= 292.4

So, the mean is 292.4

Answer:

a) \(n = 4 + 7\cdot i\), \(\forall\, i \in \mathbb{N}_O\), b) \(n = 2 + (i+1)^{2}\), \(\forall \,i\in \mathbb{N}_{O}\)

Step-by-step explanation:

a) The sequence is representative for an arithmetic sequence, whose key characteristic is that difference is between two consecutive elements is the same. In particular, the sequence has a difference of 7 between any two consecutive elements and the initial element is 4. Hence, we can derive the following formula:

\(n = n_{o} + r\cdot i\), \(\forall\, i \in \mathbb{N}_O\) (1)

Where:

\(n_{o}\) - Initial element.

\(r\) - Difference between two consecutive elements.

\(i\) - Index.

If we know that \(n_{o} = 4\) and \(r = 7\), then the expression for the n-th term of the sequence is:

\(n = 4 + 7\cdot i\), \(\forall \,i\in\mathbb{N}_{O}\)

b) In this case, we have a geometric sequence described by the following equation:

\(n = 2 + (i+1)^{2}\), \(\forall \,i\in \mathbb{N}_{O}\)  (2)

The constant element (\(2\)) represents the two extreme squares, whereas the second order binomial represents the total of squares in the middle (\((i+1)^{2}\)) and emulates the area formula of the square.

Answer:

Step-by-step explanation:

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The proportional relationships for these problems are given as follows:

18. y = 0.5x, with constant k = 0.5.

22. y = -0.4x, with constant k = -0.4.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In item 18, we have that when x = 2, y = 1, hence the constant is:

k = y/x = 1/2 = 0.5.

Hence the equation is:

y = 0.5x.

In item 22, we have that when x = -5, y = 2, hence the constant is:

k = y/x = -2/5 = -0.4.

Hence the equation is:

y = -0.4x.

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Answer:

17 / 10

Step-by-step explanation:

pmz make me btainlieat

Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

The mean and standard deviation of the data sets are;

a. 60.83, 15.11

b. 44, 4.03

c. 7.2, 3.7

d. 114.4, 10.74

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The mean of a data is the average of the data across the points.

a. data set; 35, 50, 60, 75, 65, 80

mean = 60.83

standard deviation = 15.11

b. data set; 51, 48, 47, 46, 45, 43, 41, 40, 40, 39

mean = 44

standard deviation = 4.03

c. data set; 11, 7, 14, 2, 8, 13, 3, 6, 10, 3, 8, 4, 8, 4, 7

mean = 7.2

standard deviation = 3.7

d. data set; 135, 115, 120, 110, 110, 100, 105, 110, 125

mean = 114.4

standard deviation = 10.74

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Answer:

Even Numbers -2, 2, 4, 6, 8, 10, 12

Step-by-step explanation:

Odd numbers - 3,-1,1,3,5,7,9,11

112.34375%

215.7 is 112.34400% of 192

The equation represents the parabola is x² = 6y.

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here.

The general equation of a parabola is given by y = a(x – h)² + k

We have equations.

The graph's parabola is a vertical parabola that is open vertically and has its vertex at the origin.

So, the equation of the parabola is equal to

x² = 4ay...............(1)

and, the equation of the directrix is y= -a.

her, the directrix is y= -1.5

Now, the equation for the parabola is

x² = 4(1.5)y

x² = 6y

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Answer:

v=πr^2(h)

Step-by-step explanation:

the general formula is this

Answer:

x=4

Step-by-step explanation:

18=3(3x-6)

Divide each side by 3

18/3=3/3(3x-6)

6 = 3x-6

Add 6 to each side

6+6 = 3x-6+6

12 = 3x

Divide by 3

12/3 = 3x/3

4 =x

Answer:

Let's assume that Shawant's daily earning is "x" rupees. Then, his earning for 4 days would be 4x rupees.

According to the given information, his weekly earning is 4500 more than the earning of four days. Therefore, his weekly earning can be expressed as:

Weekly earning = Earning of 4 days + 4500

Weekly earning = 4x + 4500

We know that a week has 7 days, so his daily earning can be calculated by dividing his weekly earning by 7:

Daily earning = Weekly earning / 7

Daily earning = (4x + 4500) / 7

Therefore, Shawant's daily earning is (4x + 4500) / 7 rupees.

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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9514 1404 393

Answer:

Step-by-step explanation:

The shaded area contains area A and two of area B. The expression for that area can be written ...

  Area of trapezoid = A + 2×B

__

The overall rectangle has an area of D. The areas labeled C can be subtracted from that to leave the shaded area. The expression for that is ...

  Area of trapezoid = D - 2×C

The centerline (X) is 76.2143°F,

The upper control limit (UCL) is 76.6763, and

The lower control limit (LCL) is 75.7523°F.

Thus, option C is correct.

To construct a cantrol chart for the process mean, we need ta find the centerline (X), the upper control limit (UCL), and the lawer control limit (LCL). We can use the formula:

X = Grand Mean

UCL = X + A2 * R

LCL = X - A2 * R

where A2 is a constant factor based on the sample size (n) and R is the mean range.

From the given data, we can calculate:

Grand Mean (X) = (77.4 + 75.5 + 76.1 + 76.8 + 75.2 + 75.9 + 76.7 + 75.6 + 76.2 + 77.1) / 10 = 76.2143°F

Mean Range (R) = 1.5°F

Sample Size (n) = 10

We can look up the value of A2 for n = 10 in a statistical table or use a calculator to find A2 = 0.577.

Now we can calculate the control limits:

UCL = 76.2143 + 0.577 * 1.5 = 76.6763°F

LCL = 76.2143 - 0.577 * 1.5 = 75.7523°F

Therefore, the centerline (X) is 76.2143°F,

the upper control limit (UCL) is 76.6763, and

the lower control limit (LCL) is 75.7523°F.

We can use these values to construct a control chart for the process mean and monitor the temperatures on the floor to ensure they are within acceptable limits.

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Answer:

130 square metres

Step-by-step explanation:

The shaded area is a trapezium.

Therefore, the rule for its area is base1+base2/2xh

base1=6

base2=14

height = 13

Therefore, 6+14/2 x 13

= 130

Hope that helped!!! k

To start, write a paragraph:

Describe your position as a common man. Your name should be in the first sentence of your self-introduction.

Please describe your professional background and major achievements.

Finish with a transition into the following discussion point.

Then with the topic, you as a citizen want to raise your voice on or on specific problems you see on a daily basis.

Do not be misled; a good citizen is someone who fulfils all of her obligations to her city or county. duties such as making sure their nation or city is tidy and clean; everyone who lives there is happy and problem-free, etc.

A nice neighbour usually makes sure that their neighbourhood is kept tidy and clean. So they can live happily and disease-free if their neighbourhood is clean. Due to the fact that people do not always check to see if a place is clean. Several diseases entered their home as a result of the rubbish. due to the stench and bugs that emanated from the waste. When flies sit on food, bacteria from the food attach to their legs and cause a variety of illnesses in us.

Hence, it is our responsibility as decent citizens to maintain the cleanliness of the city in which we reside. If we begin at home, other people will think about it as well. And after all, is said and done, everyone considers how to keep their home cleaner and more orderly than the city or county. And after viewing the entire state, possibly the entire world!

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Answer:

d

Step-by-step explanation:

Answer:

"2.660503478" would be the right answers to the key statement.

Step-by-step explanation:

Drawing 5 balls out of 69 can be done in (\(\frac{69}{5}\))

=  \(\frac{69\times 68\times 67\times 66\times 65}{5!}\)

Drawing 1 ball out of 26 red balls can be done in (\(\frac{26}{1}\))

= \(26\)

Then the chance of drawing 5 out of 69 balls including 1 out of 26 red balls and then both matching the jackpot  

= \(\frac{1}{11238513\times 26}\)

= \(\frac{1}{292201338}\)

Since the sum of the jackpot is $193-106 and then one ticket costs $2, the estimated value of buying one ticket again for jackpot is $2.

= \(\frac{1}{292201338}\times 193\times 10^6+\frac{292201338-1}{292201338}\times 2\)

= \(2.660503478\)

The even integers are 10,12 and 14.

Concept:  An integer is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.

Let x,x+2,x+4 be the least, middle and greatest integer respectively.

According to the question,

15< x+x+2+x+4< 21

(3x+6)/2> 15      and    (3x+6)/2< 21

30< 3x+6                      3x+6> 42

24<3x                            3x<36

8<x                                x>12

x=10

x+2=12

x+4=14

Hence, The even integers are 10,12 and 14.

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Information is needed to evaluate the project's financial viability, considering factors such as the initial investment, expected cash flows, cost of capital, and project duration.

To calculate the year 1 operating cash flows (OCF), we need to subtract the year 1 costs from the year 1 revenues:

OCF = Year 1 Revenues - Year 1 Costs

OCF = $192,000 - $125,000

OCF = $67,000

To find the depreciation expense in year 3, we need to determine the depreciation method. The provided information is incomplete regarding the depreciation method, so we cannot calculate the depreciation expense in year 3 without knowing the specific method.

The change in Net Working Capital (NWC) in year 2 can be determined by multiplying the Net Working Capital percentage (given as a percentage of t+1 revenues) by the year 1 revenues and subtracting the result from the year 2 revenues:

Change in NWC = (Year 2 Revenues - Net Working Capital percentage * Year 1 Revenues) - Year 1 Revenues

Without the specific Net Working Capital percentage or Year 2 Revenues values, we cannot calculate the exact change in NWC in year 2.

The net cash flow from salvage (ATSV) is calculated by multiplying the Salvage Value percentage by the Initial Cost:

ATSV = Salvage Value percentage * Initial Cost

ATSV = 28% * $390,000

ATSV = $109,200

To calculate the project's NPV, we need the cash flows for each year, the cost of capital, and the project duration. Unfortunately, the information provided does not include the cash flows for each year, so we cannot calculate the project's NPV.

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The complete question is:

Below are your numerical inputs for the problem: 4 & Initial Cost (\$) & 390000 5 & Year 1 Revenues (\$) & 192000 6 & Year 1 Costs (\$) & 125000  7 & Inflation & 2.75% 8 & Project Duration (years) & 6 9 & Depreciation Method & 10 & Tax Rate & 11 & Net Working Capital (\% oft+1 Revenues) & MACRS 12 & Salvage Value (\$) & 28.00% 13 & Cost of Capital & 15.00% & 245000 How much are the year 1 operating cash flows (OCF)? How much is the depreciation expense in year 3 ? What is the change in Net Working Capital (NWC) in year 2? What is the net cash flow from salvage (aka, the after-tax salvage value, or ATSV)? What is the project's NPV? Would you recommend purchasing the ranch? Briefly explain.

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

The two most important parts of a vehicle in preventing traction loss are the tires and the traction control system.

Tires: Tires are the primary point of contact between the vehicle and the road surface. The quality and condition of the tires greatly influence traction. Tires with good tread depth and appropriate tread pattern are essential for maintaining grip on the road. Tread depth helps to channel water, snow, or debris away from the tire, preventing hydroplaning or loss of traction. Additionally, tire pressure should be properly maintained to ensure even contact with the road. Choosing tires suitable for the specific driving conditions, such as all-season, winter, or performance tires, is crucial for optimal traction and handling.

Traction Control System: The traction control system is a vehicle safety feature that helps prevent the wheels from slipping or spinning on low-traction surfaces. It uses various sensors to monitor the speed and rotation of the wheels. If the system detects a loss of traction, it will automatically reduce engine power and apply braking force to the wheels that are slipping. By modulating power delivery and braking, the traction control system helps maintain traction and prevent wheel spin, especially in challenging conditions like slippery roads or during quick acceleration.

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

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Answer:

Step-by-step explanation:

Let x be the number

I hope this helps!

The median of the given list of numbers is 87.

To find the median of a list of numbers, we arrange them in ascending order and identify the middle value.

If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

First, let's arrange the numbers in ascending order:

65.9, 68, 70, 74, 75, 78, 84, 86, 87, 90, 93, 93, 95, 96, 97, 380, 486, 680

There are 17 numbers in the list, which is an odd number. The middle number is the 9th number in the list, which is 87.

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Answer:

No

Step-by-step explanation:

According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third ...

18 + 21   = 38   are not more than 39  

Answer:No,the side of lengths 18m,21m and 39m could not form a

Step-by-step explanation:

To form a triangle, the sum of any two sides must be greater than the third side.

here,

18m + 21m = 39m

the sum to two side is equal to third side that is 39m

that's why these three sides cannot form any triangle

Answer:

u got this bro come on

x28

Answer:

Statistical inference

Step-by-step explanation:

Answer:

6 gallons of punch, 24 quarts of punch.

Step-by-step explanation:

1. Multiply 32 and 3. That is 96.

2. Divide 96 by 16 because there are 16 cups in a gallon. The answer is 6 so they need 6 gallons of punch.

3. Multiply 6 by 4 because there are 4 quarts in a gallon. The answer is 24.

1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces

32 people x 3 cups = 96 cups

96 cups : 16 = 6 gallons

6 gallons x 4 = 24 quarts