A rectangular swimming pool is 15 meters long, 14 1/2 meters wide, and 3 1/2 meters deep. What is its volume? in cubic meters

The expression of the translated function g(x) is gotten as; g(x) = 2x² - 3

We are given the function;

f(x) = 2x² + 3

Now, when we translate a function f(x) downwards, the new function becomes;

g(x) = f(x) - a

where a is the amount of units by which the graph was translated.

Thus for translation of 6 units vertically downwards;

g(x) = 2x² + 3 - 6

g(x) = 2x² - 3

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Answer:

[tex]6644.672~ m^3[/tex]

Step-by-step explanation:

[tex]\text{Volume} = (18.8)^3~ m^3 = 6644.672~ m^3[/tex]

The probability that the next person will be assigned an orchestra seats is 2/5.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, Available Orchestra seats = 8

            Balcony seats = 12

      Total available seats = 12 + 8 = 20

  Probability = Favorable Outcome / Total Outcome

  Probability of getting orchestra ticket = 8/20

                                                                 = 2/5

Thus, the probability that the next person will be assigned an orchestra seats is 2/5.

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Answer:

B.

Step-by-step explanation:

They form a right angle.

Answer:

B

Step-by-step explanation:

if A were true, this hole shape could not be a triangle as AC and BC would be parallel and never have an intersecting point.

C - the line BC intersects the line EC but only at the very end point. but to bisected means to split it in half, so the intersection would have to be in the middle.

D - the line AC is only perpendicular to DE, and while DE is a perpendicular bisector to AC, AC itself does not split anything in half.

Answer:

see photo

Step-by-step explanation:

see photo for answer

sometimes when there is a fraction in the question it's a good idea to keep things as fractions and not decimals

Based on the bar graph, the true statement is that: C. more 36- to 45-year-olds listen to audiobooks than 26- to 35-year-olds.

A bar graph is used for the graphical representation of data, especially by using rectangular bars or vertical columns.

From the information provided, we can deduce the following points about the audiobook listeners:

Age                                 Relative frequency

13 to 17                                      0.08

18 to 25                                     0.15

26 to 35                                    0.23

36 to 45                                    0.45

46 and over                              0.47

Based on the frequency table for the bar graph, we can logically deduce that more 36 to 45-year-olds with a frequency of "0.45" listen to audiobooks than 26 to 35-year-olds with a frequency of "0.23."

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Complete Question:

People of different ages were asked the question "Do you listen to audiobooks?" The bar chart displays the percentage of "yes" responses in each age group. Which of the following statements is correct?

A. More 18- to 25-year-olds listen to audiobooks than 26- to 35-year-olds.

B. Fewer 18- to 25-year-olds listen to audiobooks than 13- to 17-year-olds.

C. More 36- to 45-year-olds listen to audiobooks than 26- to 35-year-olds.

D. Fewer 36- to 45-year-olds listen to audiobooks than 26- to 35-year-olds.

Answer:

5/12

Step-by-step explanation: 2/3 x 5/8 Multiply the numerators ( top numbers) and the denominators ( bottom numbers ) 2x 5= 10 3x8=12 Simplify by 2      Answer=5/12

The student that simplified the expression incorrectly is student 2

The steps are given as:

[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)}[/tex]

Student 1:

Student 2:

As a general trigonometry rule;

[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)} = \sec^2(\theta)[/tex]

This means that student 1 is correct, while student 2 is not

The first error in student 2's workings is in step 2, where we have:

[tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)} = \frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]

The above expression is not justified and cannot be proved by any trigonometry rule

Since the step 2 is incorrect, the other steps cannot be used.

Hence, the student that simplified the expression incorrectly is student 2

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Inequalities help us to compare two unequal expressions. The correct option is A.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Another way of writing the inequality 64 < x < 68, where x represents the height of the actor, is x>64 and x< 68. Hence, the correct option is A.

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Answer:

The 3rd one (y_< 2/3 x + 1/5) If this helps please mark brainiest! :)

Answer:

  1584

Step-by-step explanation:

The sum of this sequence can be found a number of ways. One way is to recast it as the series whose terms are groups of three terms of the given series.

__

The partial sums, taken 3 terms at a time, are

  1+2-3 = 0

  4+5-6 = 3

  7+8-9 = 6

...

  97+98-99 = 96

So the original series is equivalent to ...

  0 +3 +6 +... +96 = 3×1 +3×2 +... +3×32 = 3×(1 +2 +... +32)

That is, the sum is 3 times the sum of the consecutive integers 1..32.

__

The sum of integers 1..n is given by the equation ...

  s(n) = n(n+1)/2

__

Using this to find the sum of our series, we find it to be ...

  series sum = 3 × (32)(33)/2 = 1584

_____

Alternate solution

The given series is the sum of integers 1-99, with 6 times the sum of integers 1-33 subtracted. That is, ...

  1 + 2 - 3 + 4 + 5 - 6 = 1+2+3+4+5+6 -2(3 +6) = 1+2+3+4+5+6 -6(1+2)

Continuing on to ...97 +98 -99 gives the result s(99) -6s(33).

Computed that way, we find the sum to be ...

  (99)(100)/2 -6(33)(34)/2 = 4950 -3366 = 1584

The value of f(9) for the given function is 5

From the question, we are to determine the value of f(9)

The given function is

f(x) = -13 + 2x

To determine f(9), we will put x = 9 in the given function

That is,

f(x) = -13 + 2x becomes

f(9) = -13 + 2(9)

f(9) = -13 + 18

f(9) = 5

Hence, the value of f(9) for the given function is 5

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Step-by-step explanation:

4x + 3y = 3

y = 2x + 6 ->

2x - y = -6

let's multiply the modified second equation by 3 and add both equations :

4x + 3y = 3

6x - 3y = -18

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

10x + 0 = -15

x = -1.5

4x + 3y = 3

4×-1.5 + 3y = 3

-6 + 3y = 3

3y = 9

y = 3

and so the solution is (-1.5, 3).

which is not in the list of your answer options.

so, something must have been wrong in your problem definition.

either you changed something in the 2 equations, or subverting is missing in the answer options, or you even mixed up problem and answer options of 2 different questions.

but I also checked by using the numbers in the 2 equations, but (-1.5, 3) is indeed the correct solution for the given 2 equations.

Answer:

A = 3.9 in²

Step-by-step explanation:

To find the area of the shaded region, you need to find the (1) area of the entire square, then (2) find the area of the 1/2 circles, then (3) subtract them and divide by 2. Because the 1/2 circles are identical, you can combine them and just use the circle area equation.

Area of the Square:

A = l x w

A = 6 in x 6 in

A = 36 in²

Area of Combined 1/2 Circles:

A = πr²

r = 6 in / 2

r = 3 in

A = π(3)²

A = 9π  ----->  28.3 in²

Area of Shaded Region:

A = (Area Square - Area Circle) / 2

A = (36 in² - 28.3 in²) / 2

A = 7.7 in² / 2

A = 3.9 in²

Answer:Suppose y= cot x is our parent function then remember general rules of transformation.1) y= -f(x), reflects the graph of f(x) across x-axis.2) y= cf(x), stretches the graph of f vertically by factor of c , for c >1.Now, apply these rules to y= -4 cot(x)the -ve sign reflects the graph of cot(x) across x-axis and the number 4 will stretch it vertically by 4 units.The graph of both parent function (y=cot x ) and transformed function (y= -4 cot(x)) are attached below.

Answer: Equation: 27t +700 = w

Total amount of water after 17 minutes: 1159 L

Step-by-step explanation:

Equation: 27t +700 = w

let t = minutes

let w = total amount of water in pond (liters)

Total amount of water after 17 minutes: 1159 L

t = 17

therefore

27(17) +700 = 1159

Answer:

425 l

Step-by-step explanation:

Find 3/5th of the classmates

They are 15 students

Answer:

15 students

Step-by-step explanation:

To find 3/5 of 25 students, simply swap the word "of" for the multiplication symbol and calculate:

[tex]\begin{aligned}\sf \dfrac{3}{5}\:of\:25\:students & = \sf \dfrac{3}{5} \times 25\\\\& = \sf \dfrac{3 \times 25}{5}\\\\& = \sf \dfrac{75}{5}\\\\& = \sf 15\:students\end{aligned}[/tex]

Answer:

area = 28.27

circumference = 18.85

Step-by-step explanation:

Using the formulas for area,

A = πr^2

d = 2r

Solving for area,

A = 1/4 πd^2 = 1/4 × π × 6^2 ≈ 28.27yd²

Using the formulas for circumference,

C = 2 πr

d = 2r

Solving for circumference,

C = πd = π × 6 ≈ 18.85yd

Answer:

Angle1 and Angle2 are supplementary.

Step-by-step explanation:

There are at least 8 pairs and I want to say up to maybe 16 pairs if angles that are supplementary.

Supplementary angles add up to 180°. So any pair that is lying together on a straight line (that's 180°) are supplementary:

1&2

2&4

3&4

1&3

5&6

6&8

7&8

5&7

Since angles don't have to touch in order to be supplementary there are many more pairs.

Answer:

10%

Explanation:

Use future value formula

Future Value =  Present Value ((1+r)^n)

26,600 =  20,000 ((1+r)^3

26,600/20,000 = (1+r)^3

1.33 = (1+r)^3

1.33^1/3 = 1+r

1.0997 = 1+r

1.0997 - 1 = r

r = 0.997 = 9.97% = 10% (rounded of to the nearest whole percentage)

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The amount of bacteria cells that would be in the petri dish after 30 minutes is 73.3

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the number of cells after x minutes, hence:

y = 4.2(1.1)ˣ

After 30 minutes:

y = 4.2(1.1)³⁰ = 73.3

The amount of bacteria cells that would be in the petri dish after 30 minutes is 73.3

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Answer:

I think it's sit and reach sorry if I'm wrong

Answer:

35177.51057 (Rounded - 35177.5)

Step-by-step explanation:

Compound Interest -

- Recalculates how much you should be getting

The format will ALWAYS be y=[tex]ab^x[/tex]

A = Starting Value

B = Multiplier

X = Time (years)

5% = .05

1.00 + .05 = 1.05%

y=25,000(1.05)^7

= 35177.51057

Let me know if i did anything wrong <3

Answer:

Your answer is 368

Step-by-step explanation:

Separate 92 into 90 + 2

4 * 92 = 4 * (90 + 2)

Distribute 4.

= 4 * 90 + 4 * 2

Multiply and Add

= 360 + 8

= 368

Step-by-step explanation:

if you made no typo or left things out, this is very simple :

-x < -29

x > 29

remember that when you multiply an inequality by -1 (or any negative value), the orientation of the inequality changes.

Answer:

10:

7/4π = 5.5(1decimql place)

11:

50π = 157.1(1 decimal place)

Step-by-step explanation:

the equation is (angle/360) X πr^2

Answer:

pattern 0 i believe would be just the 4 red squares

Step-by-step explanation:

its adding a blue square on the 3 sides and adding enough green squares to cover the middle, or however many blue squares there are on the top and side, multiply them together. like in figure 1 i noticed that 1×1=1 so that's how many green squares there are. Figure 2: 2 blue× 2 blue= 4 green. if that makes sense. Figure 3: 3×3=9 i dont know if that made sense. but that's what i could think of!!