find the value of $a 2 a 4 a 6 \dots a {98}$ if $a 1, a 2, a 3, \dots$ is an arithmetic progression with common difference 1, and $a 1 a 2 a 3 \dots a {98}

Creative Section - B

7. a) The average of daily income of a plumber from Sunday to Friday is Rs 1,300

in the last week. If he earned Rs 2,000 on Saturday, find

income of the week.

Given: x = -2; y = -3; z = 5

It is clear that a numerical term can only be evaluated from an expression filled with numbers (no variables). In the expression provided, we have two variables, where y is being subtracted from x.

The expression can't be simplified because there is no like terms in the expression. However, since there are specific numerical values for each variable, we can substitute the numerical values for the variables in the expression and simplify the expression.

As planned, let's substitute the variables into the expression

Here, we know that x = -2 and y = -3.

If -2 is being subtracted by a negative integer, the negative integer will become positive, and the "minus sign" will be converted to a "plus sign".

We can conclude that 1 is the solution to the expression.

Answer:

x = 7.2 , y = 57 , z = 10.8

Step-by-step explanation:

the sum of the 3 angles in the outer triangle = 180° , that is

y + 88 + 35 = 180

y + 123 = 180 ( subtract 123 from both sides )

y = 57

------------

the outer and inner triangles are similar ( AA postulate ) then the ratios of corresponding sides are in proportion, that is

[tex]\frac{x}{12}[/tex] = [tex]\frac{9}{9+6}[/tex] = [tex]\frac{9}{15}[/tex] ( cross- multiply )

15x = 108 ( divide both sides by 15 )

x = 7.2

and

[tex]\frac{z}{18}[/tex] = [tex]\frac{9}{15}[/tex] ( cross- multiply )

15z = 162 ( divide both sides by 15 )

z = 10.8

The monetary value of gold, silver and bronze is $0.5, $0.35 and $0.25 respectively.

The given conditions in the question are-

Let the monetary value of gold be 'a'.

Let the monetary value of silver be 'b'.

Let the monetary value of bronze be 'c'.

The total monetary value is $20.

The equation will be;

14 gold, 20 silver, and 24 bronze

14a + 20b + 24c = 20      .......eq1

20 gold, 15 silver, and 19 bronze

20a + 15b + 19c = 20   .......eq 2

30 gold, 5 silver, and 13 bronze.

30a + 5b + 13c = 20       .....eq 3.

Solving equation 1,2 and 3 by elimination method.

a = 1/2

b = 7/20 and

c = 1/4

Thus, the monetary value of gold, silver and bronze is $0.5, $0.35 and $0.25 respectively.

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Based on the beginning balance to Jackie's account and the deposits as well as the checks written, the balance at the end of the month was $644.86

At the end of the month, the simple formula to determine Jackie's balance is:
= Beginning balance + Cash inflows - Cash outflows

This means that to calculate the balance on Jackie's account at the end of October gives:

= Beginning balance + Deposits + Interest earned - Checks written - maintenance fee

= 432.23 + 752.34 + 3.42 - 532.13 - 11

= $644.86

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Amount of water produced in 6 days is 15.6×10⁶.

We will simply perform multiplication to find the amount of water produced in 6 days.

Amount of water produced in 6 days = amount of water produced in one day × 6

Amount of water produced in 6 days = 2.6×10⁶×6

Performing multiplication to find the amount of water produced in 6 days

Amount of water produced in 6 days = 15.6×10⁶

The answer is in scientific notation as 15.6 is coefficient, 10 is base and 6 is exponent. Therefore, amount of water produced by plant in 6 days is 15.6×10⁶.

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The answer is x = 1, assuming that the space is meant to be an equal sign.

Answer:

year 7 have 135 students

year 9 have 45 students

Step-by-step explanation:

200=total students

360=value of the whole chart

1/2×360

=180

year 8 have 180students

360-180=180

the students remain are 180

1/4×180

=45

year 9 have 45 students

180-45

=135

year7 have 135 students

Answer:

275-234 = 41

41/275 times 100

4100/275

=14.90909

=15%

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:\pm b + 9 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given expression is :

[tex]\qquad \tt \rightarrow \: |b + 1| + 8[/tex]

[tex]\qquad \tt \rightarrow \: |b| + 1 + 8[/tex]

[ as 1 is a positive number, it can come out of modulus function as it is ]

[tex]\qquad \tt \rightarrow \: |b| + 9[/tex]

Now, there are two cases possible.

Case 1 :

[tex]\qquad \tt \rightarrow \: b + 9[/tex]

[ if b is a positive number, it will come out of modulus as it is ]

Case 2 :

[tex]\qquad \tt \rightarrow \: - b + 9[/tex]

[ if b is a negative number, it will come out of modulus with a negative sign, to make the overall term out of modulus positive ]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Below in bold.

Step-by-step explanation:

3/20

We divide 3 by 20:-

3 / 20 = 0 so we divide 30 by 20 and proceed as below:

20)3.00 ( 0.15

     20

      100

      100

       ......

The answer is 0.15 which is terminating.

5/11

If we divide as above we get 0.45454545....

The 45 keeps repeating

2/15

Dividing gives 0.133.........

Repeating

7/8 = 0.875

terminating.

9/16

= 0.5625

terminating.

Answer:

3/20 = 0.15 (Terminating)

5/11 = 0.45454 (Repeating)

2/15 = 0.13333 (Repeating)

7/8 = 0.875 (Terminating)

9/16 = 0.5625 (Terminating)

Explanation:

The definition of Terminate means to bring to an end. This would also apply to the decimals. To find whether a fraction is terminating or not, is to simply divide and you will get a decimal, unless it is mixed fraction. Terminating will bring an end, Ex: 1/2 ( 1 ÷ 2 ) which would equal = 0.5 This is an example of a terminating decimal. A repeating decimal is a decimal that never ends of its repetition, Ex: 0.13333333 (Continuous).

I hope this helps my grammar might bit a bad sorry.

Hope you get an A ^^

Have a great day

The distributive property should be used to rewrite each expression without parenthesis as follows:

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a specific number, the same output (result) would be produced as when each addend is multiplied respectively by the number, and the products are added together.

Mathematically, the distributive property of multiplication is given by this expression:

a(b + c) = ab + ac.

In conclusion, the distributive property of multiplication can be used to evaluate and rewrite a mathematical expression as shown above.

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The fraction of the reading assignment done by Tuesday night is 1/2.

Given:

Let the total reading assignment be x.

Fraction of the reading assignment finished by Tori on Monday afternoon = (1/6)x

Fraction of the reading assignment finished by Tori on Tuesday afternoon = (1/3)x

The fraction of the reading assignment done by Tuesday night is,

Total - Fraction of the reading assignment completed by Tori

= [tex]x -(\frac{x}{6} + \frac{x}{3} )[/tex]

= [tex]x -(\frac{x+ 2x}{6} )[/tex]

= [tex]x - \frac{3x}{6}[/tex]

= [tex]x -\frac{x}{2}[/tex]

= [tex]\frac{2x-x}{2}[/tex]

= [tex]\frac{x}{2}[/tex]

So, 1/2 of the reading assignment(x) was done by Tuesday night.

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Answer: 16 drops

Step-by-step explanation: For every 2 drops is 5 ounces. We can set up an equation such as: 2/5*8/8=16/40. If you divide 40/5 you get 8, and now multiply by 2, you get 16.

The percentage of customers who chose whole wheat bread with turkey are 19 %.

Given that:-

Percentage of customers who preferred white bread = 55 %

Percentage of customers who preferred turkey with white bread = 46 % of those who like white bread.

Percentage of customers who preferred ham with whole wheat bread = 55 %

We have to find the percentage of customers who chose whole wheat bread with turkey.

Let the total number of customers at the local sandwich shop be 100x.

Percentage of customers who preferred whole wheat bread = (100-55) % = 45 %

45 % of 100x = 45x.

Percentage of customers who preferred turkey with whole wheat bread = (100-58) % of 45x = 42 % of 45x.

42 % of 45x = 18.9x ≈ 19x.

19x is 19 % of 100x.

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Answer: The answer is A, 19%

Step-by-step explanation: I had the same question.

Answer:

y = 5

Step-by-step explanation:

2(40 - 5y) : 80 - 10y

10y + 5(1 + y) : 5y + 5

80 - 10y = 5y +5

-10y = 5y -75

-10y - 5y = 5y - 75 - 5y

-15y/-15 = -75/-15

-15y/-15 : y

-75/-15 : 5

Hence, The answer should be 5

Answer:

y=-5x+6

Step-by-step explanation:

the two lines are parallel so they have the same slope and if you put the like in y=mx+b it would be y=-5x+1 so the slope is -5

Then you need to put it into point slope for to figure it out y-y1=m(x-x1)

y-1=-5(x-1) (simplify)

y-1=-5x+5 (add 1 to both sides)

y=-5x+6

Answer: 9.77 m

Step-by-step explanation:

xyz

The sales in 2012 is estimated to be $40546.5 million if we use the midpoint formula assuming that the sales followed a linear pattern.

Midpoint is a term used in geometry and can be described as the center or middle point of a line segment. It enables you to take two endpoints, and then by using these endpoints you can find the point that is midway between them in the line segment.

Considering,

[tex]P_{1} = (x_{1},y_{1})[/tex]

[tex]P_{2} = (x_{2},y_{2})[/tex]

Here;

[tex]x_{1}[/tex] = 2010

[tex]x_{2}[/tex] = 2014

[tex]y_{1}[/tex] = $35,109 million

[tex]y_{2}[/tex] = $45,984 million

The formula for the midpoint is given as;

[tex]P_{m}[/tex] = {( [tex]x_{1} + x_{2}/2[/tex] ), ( [tex]y_{1} + y_{2} / 2[/tex] )}

[tex]P_{m}[/tex] = {(2010 + 2014 / 2), (35109 million + 45984 million / 2)}

[tex]P_{m}[/tex] = {(4024 / 2), (81,093 million / 2)}

[tex]P_{m}[/tex] = {2012 , 40546.5 million}

Therefore, the sales in 2012 are calculated to be $40546.5 million by using the midpoint formula.

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Employee's gross pay is their salary before any payroll deductions such as taxes, benefits, and other expenses are made.

Her goss weekly pay is $409.13.

Before taxes, benefits, and other payroll deductions are deducted, an employee's gross pay is what they are paid.

Net pay, often known as take-home pay, is the sum that is left over after all deductions have been taken into consideration.

Federal income tax:

306.36+ 43 = 349.36

Medical insurance:

349.36 + 22.35 = 371.71

Credit union:

371.71 + 25 = 396.71

State tax:

396.71 increased by 1.5% is 396.71 * (1.015) = 402.66

Local tax:

402.66 increased by 1.5% is 402.66 * (1.015)= 409.13

Her goss weekly pay is $409.13.

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Answer:

Step-by-step explanation:

answer:

I hope the solution is helpful.

Ai) 5575 Swedish kronor      500*11.15

Aii) 312.50 swiss frans      250*1.25

B) £345     407.10/1.18

Hope this helps, have a great day!!

Ratio of number of boys to total number of children is 3:4 and number of girls is 8

The comparison of two values using the same unit is called a ratio. Divide the first amount by the second to get it. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0.

Let the number of boys be 3x and girls be x.(As they are in ratio of 3:1)

a) Total number of children = 3x + x = 4x

Ratio of number of boys to total number of children = [tex]\frac{3x}{4x}[/tex]

= 3:4

b) As, number of boys are 24

3x = 24

x = 8

, number of girls = x = 8

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Swimmer is 47 dm away from the sailboat.

The mentioned problem will use cosine trigonometric functions to find the distance between swimmer and sailboat. Assuming the distance between lifeguard and swimmer be x and the distance between lifeguard and sailboat be y.

Taking the triangle between swimmer and lifeguard -

cos theta = base/hypotenuse

cos 32 = x/36.5

x = 0.8×36.5

x = 29.2 dm

Taking the triangle between lifeguard and sailboat -

cos 13 = y/84.7

y = 0.9×84.7

y = 76.23 dm

Therefore, the distance between sailboat and swimmer is y - x

Distance = 76.23 - 29.2

Performing subtraction

Distance = 47.03 dm

Round to nearest tenth

Distance = 47 dm

Thus, the sailboat and swimmer are 47 dm apart.

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As a result, angle M's supplement is 167 degrees, while angle M's complement is 77 degrees.

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. The sum of complimentary angles is 90 degrees. If the two additional angles are combined, they create a straight line and an angle.

Complementary angles are those whose combined angle is 90 degrees or less. To put it another way, two angles are said to be complimentary if they combine to make a right angle. In this case, we say that the two angles work well together.

So as per the given information:

we know that

a).  180-angle M=supplement of angle M

180-13=167 degree

b).  90-angle M=compliment of angle M

    =77 degree

Therefore, the supplement of the angle M is 167 degree and the complement of angle m is 77 degree.

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Answer: 7 -(-3)=7+3=10

Step-by-step explanation:

If you multiply a negative sign be a negative number in parenthesis, then it becomes positive. So, -(-3) = 3

Can also be seen as -1*-3 = 3