A swimming pool of 25m long and 20m wide is filled with water to a depth of 5m. what is the volume of water when it is 3/4 full?

Answer:

n = 53

Step-by-step explanation:

the sum to n terms of an arithmetic progression is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 3 and a₅ = 9 , then

3 + 4d = 9 ( subtract 3 from both sides )

4d = 6 ( divide both sides by 4 )

d = 1.5

then solving for n

3 + 1.5(n - 1) = 81 ( subtract 3 from both sides )

1.5(n - 1) = 78 ( divide both sides by 1.5 )

n - 1 = 52 ( add 1 to both sides )

n = 53

there are 53 terms in the progression

Answer:

53 terms

Step-by-step explanation:

Finding common difference :

Solving :

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

[tex]\qquad \tt \rightarrow \: x < -2 \:\: or \:\; x >4[/tex]

____________________________________

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

[tex] \textsf{First Inequality :} [/tex]

[tex]\qquad \tt \rightarrow \: - 2(x + 8) + 6 > x - 4[/tex]

[tex]\qquad \tt \rightarrow \: - 2x - 16 + 6 > x - 4[/tex]

[tex]\qquad \tt \rightarrow \: - 2x - 10 > x - 4[/tex]

[tex]\qquad \tt \rightarrow \: - 10 + 4 > x + 2x[/tex]

[tex]\qquad \tt \rightarrow \: - 6 > 3x[/tex]

[tex]\qquad \tt \rightarrow \: - \cfrac{ 6}{3} > x[/tex]

[tex]\qquad \tt \rightarrow \: - 2 > x[/tex]

[tex]\qquad \tt \rightarrow \: \therefore x < - 2[/tex]

[tex] \textsf{Second Inequality :} [/tex]

[tex]\qquad \tt \rightarrow \: - 3x + 12 < 6(x - 4)[/tex]

[tex]\qquad \tt \rightarrow \: - 3x + 12 < 6x - 24[/tex]

[tex]\qquad \tt \rightarrow \: 12 + 24 < 6x + 3x[/tex]

[tex]\qquad \tt \rightarrow \: 36 < 9x[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{36}{9} < x[/tex]

[tex]\qquad \tt \rightarrow \: 4 < x[/tex]

[tex]\qquad \tt \rightarrow \: \therefore x > 4[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The marked price of the television is Rs. 20,000.

The market price is the current price at which a good or service can be purchased or sold.

Here, let the marked price of the television be Rs. x

          Discount = 16% on MP

          VAT = 13% additional on MP

          Total paid amount = Rs. 18984

Now, according to question;

     MP X (1 - Discount) X (1 + VAT) = 18984

              x (1 - 0.16)(1+0.13) = 18984

              x = 18984/(0.84 X 1.13)

              x = 18984 / 0.9492

              x = 20,000

Thus, the marked price of the television is Rs. 20,000.

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The equation best models the situation 100 + 0.8(x - 100) = 250.

The correct option is (D)

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

The complete question is:

An ongoing promotion at a department store gives customers 20% off the portion of their bill that is over $100. Ruby's total bill at the department store after the promotion has been applied is $250. If x represents the amount of money Ruby would have spent on the same purchase at the department store without the promotion, which of the following equations best models the situation?

A. 0.2x + 100 = 250

B. 0.8x + 100 = 250

C. 100 + 0.2(x - 100) = 250

D. 100 + 0.8(x - 100) = 250

Given:

Department store gives 20 % off the portion of the bill that is over 100 dollars.

Total bill = 250

let x is the amount of money she would have spent without the promotion.

Then, cost after discount applies = 0.8 ( x - 100 ).

Hence, the equation is 100 + 0.8 (x - 100) = 250.

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Answer:

1,600 seats in the theater

Step-by-step explanation:

well it seems like each row is being increased by 8 seats each time.

we start with 4 seats in the 1st row. 12 in the 2nd. and 20 in the 3rd. I will make a chart showing you how many seats are in each row.

4th row - 28  5th row - 36   6th row - 44   7th row - 52   8th row - 60   9th - 68   10th - 76   11th - 84    12th - 92   13th - 100    14th - 108   15th - 116   16th- 124    17th - 132   18th - 140    19th - 148    20th - 156

if we add these all together you will get 1,600

Answer:

1600 seats

Explanation:

1st row = 4 seats, 2nd row = 12 seats, 3rd row = 20 seats

This is arithmetic progression with first term (a) being 4 and common difference (d) of 8 and total term (n) of 20.

Sum of arithmetic series:

[tex]\sf S_n = \dfrac{n}{2} ( 2a + (n-1)d)[/tex]

insert values

[tex]\sf S_{20} = \dfrac{20}{2} ( 2(4) + (20-1)8)[/tex]

[tex]\sf S_{20} = 1600[/tex]

Answer: The two imaginary solutions with rational coefficients are +/- 4i and the two imaginary solutions with irrational coefficients are +/- 1.414213562i.

Step-by-step explanation:

I would recommend using pascal's triangle to solve this problem.

*Note: This is more of a quick answer, I can show a detailed step-by-step procedure if you need, just comment.

Answer:

y = 7/25x

Step-by-step explanation:

For a proportional relationship, we have

y ∞ x.

Let k = constant of proportionality = 7/25

Removing the proportionality sign, we have

y = k x

Therefore, the answer is  

y = 7/25x

Instead of y= x + 7/25

So, the error is that x should be multiplied by 7/25 and not added.

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The trigonometric function for an angle [tex]\dfrac{\pi}{4}[/tex] is

[tex]tan\theta =1\ \ \ \ Cos \theta=\dfrac{\sqrt{2}}{2}\ \ \ \ Sin\theta = \dfrac{\sqrt{2}}{2}[/tex]

The trigonometric function for an angle [tex]\dfrac{\pi}{6}[/tex] will be:-

[tex]tan\theta = \dfrac{1}{\sqrt3}}\ \ \ \ \ Sin\theta = \dfrac{1}{2} \ \ \ \ \ Cos \theta = \dfrac{\sqrt{3}}{2}[/tex]

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

The trigonometric function for an angle [tex]\dfrac{\pi}{4}[/tex] is

[tex]tan\theta = tan\dfrac{\pi}{4}=1\ \ \ \ Cos \theta=Cos\dfrac{\pi}{4}=\dfrac{\sqrt{2}}{2}\ \ \ \ Sin\theta =Sin\dfrac{\pi}{4}= \dfrac{\sqrt{2}}{2}[/tex]

The trigonometric function for an angle [tex]\dfrac{\pi}{6}[/tex] will be:-

[tex]tan\theta=tan \dfrac{\pi}{6}= \dfrac{1}{\sqrt3}}\ \ \ \ \ Sin\theta =Sin\dfrac{\pi}{6}= \dfrac{1}{2} \ \ \ \ \ Cos \theta = Cos\dfrac{\pi}{6}= \dfrac{\sqrt{3}}{2}[/tex]

Therefore the trigonometric function for an angle [tex]\dfrac{\pi}{4}[/tex] is

[tex]tan\theta =1\ \ \ \ Cos \theta=\dfrac{\sqrt{2}}{2}\ \ \ \ Sin\theta = \dfrac{\sqrt{2}}{2}[/tex]

The trigonometric function for an angle [tex]\dfrac{\pi}{6}[/tex] will be:-

[tex]tan\theta = \dfrac{1}{\sqrt3}}\ \ \ \ \ Sin\theta = \dfrac{1}{2} \ \ \ \ \ Cos \theta = \dfrac{\sqrt{3}}{2}[/tex]

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Answer:

pls yo give the full question

Answer:

2, 3

Step-by-step explanation:

See attached images for work.

Answer:

Roots of the equation are  (−3−√7) , (−3+√7)

Step-by-step explanation:

For solving a quadratic equation using completing the square method:

given equation:

y = x^2 - 6x +2

0 = x^2 - 6x + 2

0 = x^2 - 3^2 + 3^2 -6x +2

0 = (x-3)^2 -7

7 =  (x-3)^2

±[tex]\sqrt{7}[/tex] = x-3

±[tex]\sqrt{7}[/tex] + 3 = x

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The height of the tree is the man's height plus x.

[tex]\tan 26^{\circ}=\frac{x}{16}\\x = 16 \tan 26^{\circ}[/tex]

So, the height of the tree is [tex]\boxed{(16 \tan 26^{\circ}+1.8) \text{ m}}[/tex]

The graph is shown below

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

As, the equation x² + y² < 25 represents equation of circle.

So, the graph will be of the form circle.

and,  y² <6x is the equation to represent parabola

So, the graph will represent a parabola.

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The equation which represent the problem is 14.5 = 469.8k.

An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.

Here, As given in question

The number of gallons of gas Connie’s car, g, uses is directly proportional with the number of miles she drives, m.

                                    g α m

                                     g = km     ............(i)

g = 14.5 gallons of gas          m = 469.8 miles

                                  14.5 = k X 469.8

                                  14.5 = 469.8k

Thus, the equation which represent the problem is 14.5 = 469.8k.

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Answer:

450 in^2

Step-by-step explanation:

Width = 15       Length is twice as much = 30 in

Area = L * W   = 15 * 30 = 450 in^2

The minimum and maximum percentages of voters who could vote Republicans are 40% and 44% respectively, while Green are 0% and 4%

The attached circle graph represents the missing information in the question.

From the graph, we have:

Republicans = 42%

Green = 2%

The actual percentage is given as: ±2%

So, we have:

Republicans = 42% ± 2% = (40%, 44%)

Green = 2% ± 2% = (0%, 4%)

Hence, the minimum and maximum percentages of voters who could vote Republicans are 40% and 44% respectively, while Green are 0% and 4%

We have:

The actual percentage is given as: ±2%

Let the number of votes be on the circle graph be x and the range be y.

So, we have:

y - x = ±2%

Express as absolute value equation

|y - x| = 2%

For Republicans, we have:

|y - 42%| = 2%

For Green, we have:

|y - 2%| = 2%

Hence, the absolute value equations are |y - 42%| = 2% and |y - 2%| = 2%

In (a), we have:

Republicans = 42% ± 2% = (40%, 44%)

Hence, the party of candidate that receives 44% vote is Republican

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Answer:

339

Step-by-step explanation:

Exponential Function

General form of an exponential function: [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given information:

Therefore:  [tex]y=240b^x[/tex]

To find an expression for the population after 1 hour, substitute x = 1 into the found equation:

[tex]\implies y=240b^1[/tex]

[tex]\implies y=240b[/tex]

We are told that the population after 9 hours is double the population after 1 hour.  Therefore, make y equal to twice the found expression for the population after 1 hour, let x = 9, then solve for b:

[tex]\implies 2(240b)=240b^9[/tex]

[tex]\implies 480b=240b^9[/tex]

[tex]\implies 480=240b^8[/tex]

[tex]\implies 2=b^8[/tex]

[tex]\implies b=\sqrt[8]{2}[/tex]

[tex]\implies b=2^{\frac{1}{8}}[/tex]

Therefore, the final exponential equation modelling the given scenario is:

[tex]\implies y=240(2^{\frac{1}{8}})^x[/tex]

[tex]\implies y=240(2)^{\frac{1}{8}x}[/tex]

To find how many bacteria there will be after 4 hours, substitute x = 4 into the found equation:

[tex]\implies y=240(2)^{\frac{1}{8}(4)}[/tex]

[tex]\implies y=240(2)^{\frac{1}{2}}[/tex]

[tex]\implies y=339 \:\: \sf (nearest\:whole\:number)[/tex]

Therefore, there will be 339 bacteria (rounded to the nearest whole number) after 4 hours.

The value of the sin theta will be equal to [tex]Sin\theta =\sqrt{\dfrac{2}{3}}[/tex]

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

Given that:-

The value of Sin will be calculated as:-

[tex]Sin^2\theta +Cos^2\theta = 1\\\\Sin^2\theta + \dfrac{\sqrt{3}}{2}=1\\\\Sin^2\theta = 1 -\dfrac{1}{3}\\\\Sin\theta = \sqrt{\dfrac{2}{3}}[/tex]

We can see that the value of sin is less than zero therefore

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Using the binomial distribution, it is found that there is a 0.242 = 24.2% probability that exactly 2 are dressed inappropriately.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are given as follows:

n = 40, p = 0.07.

The probability that exactly 2 are dressed inappropriately is given by P(X = 2), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{40,2}.(0.07)^{2}.(0.93)^{38} = 0.242[/tex]

0.242 = 24.2% probability that exactly 2 are dressed inappropriately.

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Answer:

Step-by-step explanation:

I'm assuming you meant "David at 78% of his chocolate bar" which means he at 78/100 of his chocolate bar. So if Jane ate more she could've eaten n/100 of her chocolate bar where [tex]78 < n \leq 100[/tex]. Greater than 78 since David at 78/100 and less than or equal to 100 since 100/100 means Jane at the entire thing at 101/100 wouldn't make any sense.

Answer:

17.20465053

Step-by-step explanation:

17.20465053 or

17.2 (to 1 dp)

Answer:

Third side has to be greater than 4 and less than 24.

Step-by-step explanation:

A triangle is valid if the sum of two sides is greater than the third side. That has to be the case for each of the sides. So let the sides of triangle be a, b and c.

a + b > c

a + c > b

b + c > a

Given:

a = 10

b = 14

We are looking for the third side, c.

First inequality:

a + b > c

10 + 14 > c

24 > c

This tells us that c has to be less than 24.

Second inequality:

a + c > b

c > b - a

c > 14 - 10

c > 4

This tells us that c has to be grater than 4.

Third inequality:

b + c > a

c > a - b

c > 10 - 14

c > -4

This tells us that c has to be greater than -4. But we also know that c has to be greater than 4, so we take 4 as the minimal value for c.

Final answer:

4 < c < 24

Third side has to be greater than 4 and less than 24.

Answer:

186

Step-by-step explanation:

x/200 = 0.93

x = 200(0.93)

x = 186

The number of problems that Indigo did answer correctly in the final exam is 186.

Given that:

Indigo earned a grade of 93% on her multiple-choice history final which had a total of 200 problems.

Total number of problems = 200

So, 100% grade = 200 problems

Let x be the number of problems which is answered correctly to get 93%.

Using the proportional concept,

[tex]\frac{x}{200} =\frac{93}{100}[/tex]

Cross multiply,

100x = 93 × 200

Dividing whole by 100,

x = 93 × 2

x = 186

Hence, the number of problems that are answered correctly is 186.

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Answer:

The constant of proportionality is 6. This makes the relation y = 6x.

Step-by-step explanation:

Concept: As the number of apples are increasing, the number of slices are also increasing. Given that x is the number of apples and y is the number of slices. This means that y is directly proportional to x.

y ∝ x

Let the constant of proportionality be k.

y = kx

For x = 1, y = 6. So, k = 6.

For x = 2, y = 12. So, k = 6.

This follows for all the values.

Clearly, the constant of proportionality is 6.

The relationship will become y = 6x.

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Answer:

Step-by-step explanation:

The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.

Diagonal = 5 * 2 = 10

P = 2√2 * 10

P = 20√2

Answer:

x = -3 when f(x) = -5

f(0) = 3

Step-by-step explanation:

When f(x) = -5, that means they have told you the y value. When y = -5, x = -3.

If the number is in the parentheses of the function, they are giving you the x value. When x  = 0, y = 3

You work for a lending institution and are tasked with whether or not to approve a home loan, its  Somewhat likely; that recurring debt is very close to what is allowed. Option B.

Generally,  any payment that is utilized to repay debt obligations that occur on a continuous basis is said to be recurrent debt.

In conclusion, Recurring debt consists of payments that cannot be readily canceled at the request of the payer. Examples of this kind of debt include alimony, child support, and loan installments.

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Answer:

its B

Step-by-step explanation:

The measure of the side RS from the figure is 4.6 units

Midpoint theorem of a trapezium

The given figures are trapezoid. Given the following parameters

PQ = 4RS

We need to determine how PR is equivalent to 4.6

Since PQ = 18.4 from the diagram, hence;

18.4 = 4RS

RS = 18.4/4

RS = 4.6 units

Hence the measure of the side RS from the figure is 4.6 units

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The correct Option is Option C: The radius of the cardboard tube of 85th loop of paper is 4.92cm

The arithmetic sequence is the sequence where every term is increased or decreased by a fixed number from the previous number.

Here the outer radius of the tube is 2.4 cm

the thickness of the paper is 0.3mm= 0.03cm

i.e. in every loop the increase in the radius of the loop is 0.03cm

then the radius in every sequence will be  2.40, 2.43, 2.46, 2.49, 2.52, .....

so here it is clear that it is an arithmetic sequence with a common difference of 0.03.

nth term of the sequence, aₙ = a₁ + (n - 1)d where a₁ is the first term, n is the index of the loop, and d is a common difference.

here a₁ =2.40

d=0.03

n=85

the radius of tube of the 85th loop will be= r= 2.40+(85-1)0.03= 2.40+ 2.52= 4.92

Therefore The radius of the cardboard tube of the 85th loop of paper is 4.92cm

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The number of balloons needed to fill the classroom are  46240 balloons (approx)

Concept: Fermi process is the technique that helps to formulate an answer to a problem based on a series of logical assumptions.

No. of balloons = Volume of rectangular prism/ Volume of each sphere (balloon)

Given: The classroom is a rectangular prism with a length of 38 ft, a width of 52 ft, and a height of 12 ft, and the balloons are spheres with a radius of 0.35 ft.

No. of balloons = Volume of rectangular prism/ Volume of each sphere (balloon)

No. of Balloons = 38*52*12/3.14*0.35*0.35*(4/3)

No. of Balloons = 23712/0.5128 = 46240 balloons (approx)

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