On a certain hot summer's day, 273 people used the public swimming pool. The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $528.75. How many children and how many adults swam at the public pool that day?

Compute the Laplace transform of [tex]f(t)=t^n[/tex], where [tex]n[/tex] is a non-negative integer.

[tex]\displaystyle L\left\{t^n\right\} = I_n = \int_0^\infty t^n e^{-st} \, dt[/tex]

Integrate by parts with

[tex]u=t^n \implies du = nt^{n-1} \, dt[/tex]

[tex]dv = e^{-st} \, dt \implies v = -\dfrac1s e^{-st}[/tex]

[tex]\displaystyle I_n = \frac ns \int_0^\infty t^{n-1} e^{-st} \, dt = \frac ns I_{n-1}[/tex]

By substitution,

[tex]\displaystyle I_n = \frac ns I_{n-1} = \frac{n(n-1)}{s^2} I_{n-2} = \cdots = \frac{n(n-1)\cdots(n-(k-1))}{s^k} I_{n-k}[/tex]

so that for [tex]k=n[/tex], we end up with

[tex]\displaystyle I_n = \frac{n(n-1)\cdots1}{s^n} I_0 = \frac{n!}{s^n} \int_0^\infty e^{-st} \, dt = \frac{n!}{s^{n+1}}[/tex]

We then have the inverse transform relation

[tex]\displaystyle L^{-1}\left\{ \frac1{s^n} \right\} = \frac{t^{n-1}}{(n-1)!}[/tex]

and so

[tex]L^{-1}\left\{ \dfrac1{s^3} + \dfrac1s \right\} = \dfrac{t^2}{2!} + \dfrac{0!}{t^0} = \boxed{\dfrac{t^2}2 + 1}[/tex]

Answer:

[tex]\sf y =\dfrac{-3}{4}x+16[/tex]

Step-by-step explanation:

Where m is the slope and b is the y-intercept.

   3x + 4y = 64

Subtract 3x from both sides,

           4y = -3x + 64

Now, divide both sides by 4,

      [tex]\sf \dfrac{4y}{4}=\dfrac{-3x}{4}+\dfrac{64}{4}\\\\y = \dfrac{-3}{4}x + 16[/tex]

Standard deviation of population mean is 0.33.

Why is there a standard deviation?

it is shown that 5% values are over 2.1 pounds and 5% are under 1.9 pounds

so stastically that means

P( X > 2.1,  μ; σ) = 0.05 and P( X 1.9; μ; σ) = 0.05

where  μ is mean of the sample and σis the standard deviation of the sample.

so mean can be calculated easily μ = (2.1 + 1.9)/2 = 2.0

and as we can interpret P(1.9 <x < 2.1; 2.0; σ) = 0.90 by normal distribution the Z value for 90% confidence interval is 1.65

so σ = (2.1 -2) /1.65 = 0.06

standard deviation of the sample mean= 0.06

and by that standard deviation of population mean = 0.06 * (30) 0.5  = 0.33

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The complete question is -

A production process is checked periodically by a quality control inspector. the inspector selects simple random samples of 30 finished products and computes the sample mean product weight. If test results over a long period of time show that 5% of the values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process? What is the population mean? (to 1 decimal) What is the population standard deviation (to 2 decimals)?

The decimal is equal to (294117647)/(1000000000).

Answer:

Step-by-step explanation:

246 degrees

Answer:61.5

Step-by-step explanation:

123/2=61.5

61.5+57=118.5

180-118.5=61.5

AE and BE are congruent lines or we can say lines with same length.

What are congruent lines?

Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent.

As given in the question,

AC = BD, and

EC = ED

We can see in the figure that:

AC - EC = AE ___(1)

BD - ED = BE ___(2)

Substituting the value of AC and EC in equation (1):

AE = BD - ED ___(3)

From equations (2) and (3), we can conclude that,

AE = BC

Therefore, AE and BE are congruent lines.

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Answer:

B and C

Step-by-step explanation:

I think that you mean -1 -1.  That would equal -2

-2 is an integer and a rational number.

An integer are the whole numbers 0,1,2,3 and so on and their opposites, -1, -2, -3 ,-4 and so on

Rational number is when you can write a number as an integer over and integer.  You can write -2 as  -2/1

Answer: a,b,c

I did it in the test

Answer:

Option 2

Step-by-step explanation:

Using point-slope form, the line passes through (3, 1).

Option 2 is the only choice that satisfes this.

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

[tex]\qquad \tt \rightarrow \: Graph \:\: 2[/tex]

____________________________________

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

The equation is given in its point slope form :

[tex]\qquad \tt \rightarrow \:y - 1 = \dfrac{2}{3} (x - 3)[/tex]

And the general equation in point slope form is :

[tex]\qquad \tt \rightarrow \:y - y_1 = m(x - x_1)[/tex]

by comparing these two, we can get

And [tex]{ (x_1 , y_1) } [/tex] satisfies the equation, so the line (graph) of this equation should have point (3 , 1) lying on it.

And the only graph satisfying this condition is graph 2, therefore The graph 2 is the required graph.

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The depreciation equation is given by

where x represents the number of years. Here, the initial value of the car corresponds to x=0, then we have

After one year, the car value corresponds to x=1, that is,

Now, let's find the depreciation percentage by means of a rule of three:

so we have

So the difference between 100% and 86% is 14% This means Nichole's car depreciate 14% each year

Answer:

5

Step-by-step explanation:

Since 7 into 42 is six we know the answer can't be 7 because it's too high. We can also rule out 6 because 6 times 7.94 is more than 41. The first answer choice is wrong because if you take away the .94, 7 times 4 is 28 which is pretty far from 41. If you multiply 5 and 7, it comes out to 35. That's significantly closer than four.

Hope this helps! :)

Answer:

yes

Step-by-step explanation:

On subtracting 20 from twice a number we get 50, then the number is 35 in this context.

This is referred to as a type of mathematical operation in which one number is taken or deducted from the other and the sign is ( - ). this expression is used in every facet of life for their daily activities.

We were told that 20 was subtracted from twice a number to give 50 which means that twice the number is 70. The exact number will therefore be 70/2 which will then result in 35 and is therefore the most appropriate choice.

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Answer: 7 units

Step-by-step explanation:

There will  be no interval of time when Josue has more in savings than Arianna, they have same savings is after 4 weeks

Step one:

For Josue

initial savings balance= $70

weekly savings = $9

Let J represent amount of money Josue has saved and  t the number of weeks after the beginning of the year

The total amount in the savings after t weeks is

J=9t+70-------1

For Arianna

initial savings balance= $30

weekly savings = $19

Let A represent the amount of money Arianna has saved and  t the number of weeks after the beginning of the year

The total amount in the savings after t weeks is

J=19t+30---------2

Step two

equation 1 and 2 to find t

9t+70=19t+30

9t-19t=30-70

-10t=-40

divide both sides by 10

t=4

t=4 weeks

so after 4 weeks Josue and Arianna will have the same amount of money

For Josue t=4

J=9(4)+70-------1

J=36+70

J=$106

For Arianna t=4

A=19(4)+30---------2

A=76+30

A=$106

The two equations above shows that after 5 weeks their savings will be $106.

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Answer:

First question mark is 4, second question mark is 64

Step-by-step explanation:

For the first question mark, 7 is half of 14, and half of 8 is 4, so they would be the same ratio, and then for the second, 12 to 24 is just one half, meaning you would need to find double 32, which is just 64

Answer:

its the 3rd option

Step-by-step explanation:

you solve parenthesis then multiply then had to minus which gave you the total

Answer:its D

Step-by-step explanation:

answer-x=π/7+y/7

Step-by-step explanation:

yes

Answer:

11, 110

Step-by-step explanation:

Constant of proportionality: Ratio of distance to time, which is 11.

Distance at 10s: Multiply time by the constant of proportionality, giving 110.

Based on the given, the variable p from the expression 4.45p represent pounds of tomatoes sold.

Algebra is a system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

The cost of the tomatoes for a number of packages = 4.45p

If the store sold 2 1/4 pounds of tomatoes

The cost of the tomatoes for a number of packages = 4.45p

= 4.45(2 1/4)

= 4.45(9/4)

= 4.45(2.25)

= $10.0125

In conclusion, the variable p represent pounds of tomatoes sold in the store.

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Answer:

Option 4

Step-by-step explanation:

Each x-value corresponds to only one y-value

It's (1, 0) - first option

Hope this helps!

Answers to your questions with explanations are below. You can ask a question, feel free. I wish you success!

This answer should be Vertical Angles.

Vertical angles are angles that are opposite of each other when two lines cross and equal each other. [tex](a^o=b^o)[/tex]

A pair of vertical angles is formed when two lines intersect each other at a single point. They are said to be linear if the angles are adjacent after the intersection of the two lines. The sum of the angles of a linear pair is always equal to [tex]180^o[/tex]. Such angles are also known as complementary or supplementary angles.

The answer is [tex]2^{nd}+4^{th}+5^{th}[/tex]

The answer is the first option. Adjacent angles. The rule is simple. If [tex]a+b=90^o[/tex] if they're adjacate angles.

The answer is the third option. Supplementary angles. The rule is simple. If [tex]a+b=180^o[/tex] if they're supplementary angles.

9. Option b. The two lines are perpendicular to each other

  Given:

   6x+10y = 20

   5x- 3y = 21

Consider the first line,

10 y = -6x+ 20

y = -3/5 x + 2

This is of the form y = mx+ b

where, slope =m = - 3/5

Consider the second line,

5x- 3y = 21

3y = 5x- 21

y = 5/3 x - 21

This is of the form y = mx+ b

where, slope= m = 5/3

Since the slopes of the two lines are negative reciprocals ,they are perpendicular.

10. Option a. The equation of the line  passing through (2, -9) with a slope -5 is y = - 5x + 1

Given:

slope = m= -5

point = (2,-9)

We know that ,the slope -intercept form is given by ,

y = mx+ b ---(1)

Substituting the given values in (1)

-9 = -5(2)+b

10- 9 = b

b = 1

Substituting m and b in (1)

y = -5x+1

Thus, the slope-intercept form equation of the line is y = -5x + 1

11. The  equation of the line perpendicular to y= -2x+8 and passing through the point (4,-7) is y = 1/2x- 9

Given:

line = y = -2x+8

point = (x, y)= (4, -7)

The given equation is of the form,

y = mx+ b  ---- (1)

m = -2

The line perpendicular to this line will have a negative reciprocal slope,

m = 1/2  

The new line is of the form,

y = 1/2 x+ b   ----(2)

Substituting the given point (4, -7) in (2)

- 7= 2 + b

b = - 9

Substituting b in (2)

y = 1/2x- 9 is the perpendicular line equation

12.  The  equation of the line parallel to 3x- 2y = 14 and passing through the point (-6,-11) is y = 3/2 x -2

Given:

line = 3x- 2y = 14

point = (x, y)= (-6,-11)

The slope - intercept form of the given line is ,

2y = 3x- 14

y = 3/2x - 7  

slope = m = 3/2

The line parallel to this line will have the same slope,

m = 3/2  

The new line is of the form,

y = 3/2 x+ b   ----(1)

Substituting the given point (-6, -11) in (1)

- 11= -9 + b

b = - 2

Substituting b in (1)

y = 3/2 x -2 is the parallel line equation.

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well, her husband makes "x" in salary, hmmm hers is 16% more than that, so

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of x}}{\left( \cfrac{16}{100} \right)x}\implies 0.16x[/tex]

so she really makes x + 0.16x = 1.16x, and we know their total is 72,360, so

[tex]\stackrel{husband}{x} + \stackrel{hers}{1.16x} = 72360\implies 2.16x=72360\implies x=\cfrac{72360}{2.16}\implies \boxed{x = 33500}[/tex]

Answer:

(i) 7 + 4√2  cm^2.

(ii) 50 - 8√2  cm^2.

Step-by-step explanation:

(i)

Area = (3 + √8)(5 - 4/√2)

= 3(5 - 4/√2) + √8(5 - 4/√2)

= 15 - 12/√2 + 5√8 - 4√4

= 15 - 8 -( 12√2)/2 + 5*(2√2)

= 7 - 6√2 + 10√2

= 7 + 4√2.

(ii)

Area of the square

= AC^2

= (3 + √8)^2 + (5 - 4/√2)^2            (By Pythagoras)

= 9 + 6√8 + 8 + 25 - 40/√2 + 16/2

= 9 + 8 + 8 + 25 + 12√2 - 20√2

= 50 - 8√2.

The largest number of rods that the pole can be cut into is 86.

Given:

Length of Metal Pole = 500 cm

The pole is cut into rods.

Length of each rod = 5.8 cm

To determine the number of rods we can divide the total length of the pole by the length of each rod.

Number of rods that the pole can be cut into = (Length of Metal Pole) ÷ (Length of each rod )

⇒ Number of rods = 500 ÷ 5.8 = 86.2 ≈ 86

Therefore, the largest number of rods that the pole can be cut into is 86.

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Answer: irelating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten:

Step-by-step explanation: