A bottle of ant killer holds 1,5 L of concentrate.
To make up a solution, 5 capfuls are added to 1
L of water. Each capful is 20 mL. How many
litres of solutions can be made if you use the
entire bottle of concentrate? [2]
82,5 L
16,5 L
15 L

Answer: 1/6

Step-by-step explanation:

There are 6 faces in a dice

The faces are labeled as =

1

2

3

4

5

6

This means, there are 6 different outcomes in a dice

So we have to find out the probability of the dice showing 3

Now, out of 6 different possible outcomes, there is only 1 face labeled as 3.

So there is only 1 possible outcome as "3".

We can simply make it a fraction = 1/6 . 

So the answer is 1/6

Probability is expressed as a fraction, percentage and decimal.

Answer:

{ right angle  } triangle          { angle } to the hypotenuse   sin C =   { y / sin (A)  }   sin A = {sin(C) x }    the hypotenuse if not being used in sin we multiply

Step-by-step explanation:

This is because we're adding -6 to each term, i.e. subtracting 6 from each term, to get the next term

and so on. The gap between adjacent terms is the same width. We say that the common difference is d = -6.

By using the fact that the sum of the interior angles must be 180°, we wil see that:

x = 110°.

First, remember that the sum of the interior angles of a triangle is alway equal to 180°.

We also can see that the interior angle that is adjacent to x can be written as:

a = 180° - x

Then the sum of the interior angles will give:

30° + 80° + (180° - x) = 180°

30° + 80° - x = 0

110° - x = 0

110° = x

That is the value of x.

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The number of barrels of crude oil required to run the car for a year is 61.4

The information given is as follows;

Percentage of crude oil processed into gasoline = 45%

The distance achieved per gallon by car = 31 mi/gal

Distance driven per year = 36,000 miles

Hence, the number of Gasoline usage in one year,

\(\text{Gasoline usage in one year} = \dfrac{\text{Distance drievn per year}}{\text{distance achieve per gallon by car}}\)

\(\text{Gasoline usage in one year} = \dfrac{36000 \ \text{miles}}{31\ \text{miles/gallon}}\)

\(\text{Gasoline usage in one year} = 1,161 \ \text{gallons}\)

Here, Percentage of crude oil processed into gasoline = 45%

Hence, where 45% of the crude oil produces 1000, the volume of crude, x, from which the gasoline is sourced becomes;

\(x \times 45\% = 1161\)

\(x \times \dfrac{45}{100} = 1161\)

\(45x = 1161\times 100\)

\(45x = 1,16,100\)

\(x = 2580\) gallons of crude

Since 1 barrel of crude oil is approximately 42 gallons of crude oil.

Hence, we have;

\(2580 \ \text{gallons of crude }\) = \(\dfrac{2580}{42} \text{ barrels of crude}\)

= \(61.4\)  \(\text{ barrels of crude}\)

Hence the number of barrels of crude oil required to run the car for a year = \(61.4\)  \(\text{ barrels of crude}\)

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Approximately 61.44 barrels of crude oil are required to run your car for a year.

To determine the number of barrels of crude oil required to run your car for a year, we'll need to calculate the total amount of gasoline consumed and then convert that into the equivalent volume of crude oil.

Volume of a barrel of crude oil: 42 gallons

Approximately 45% of crude oil is processed into gasoline

Car fuel efficiency: 31 miles per gallon

Distance driven in a year: 36,000 miles

First, let's calculate the total amount of gasoline consumed in a year. We'll divide the total distance driven by the car's fuel efficiency:

Gasoline consumed = Distance driven / Fuel efficiency

Gasoline consumed = 36,000 miles / 31 miles per gallon

Gasoline consumed ≈ 1161.29 gallons

Next, we need to calculate the equivalent volume of crude oil required to produce this amount of gasoline. Since only approximately 45% of crude oil is processed into gasoline, we'll multiply the gasoline consumed by the reciprocal of 45% (or 0.45) to account for this conversion:

Equivalent volume of crude oil = Gasoline consumed / Conversion factor

Equivalent volume of crude oil = 1161.29 gallons / 0.45

Equivalent volume of crude oil ≈ 2580.64 gallons

Finally, to determine the number of barrels of crude oil required, we'll divide the equivalent volume of crude oil by the volume of a barrel (42 gallons):

Number of barrels of crude oil = Equivalent volume of crude oil / Volume of a barrel

Number of barrels of crude oil = 2580.64 gallons / 42 gallons

Number of barrels of crude oil ≈ 61.44 barrels

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The angle in degrees is 873.1843.

Let the measure of the angle be θ in degrees. Therefore, the measure of the same angle in gradians is (θ × π/180).

According to the given information, the number of degrees of a certain angle added to the number of gradians of the same angle is 152.(θ) + (θ × π/180) = 152.

Simplifying the above equation, we get:(θ) + (θ/180 × π) = 152.

Multiplying both sides of the equation by 180/π, we get:

θ + θ = (152 × 180)/π2θ = (152 × 180)/πθ = (152 × 180)/(3.14)θ = 873.1843

Thus, the angle in degrees is 873.1843.

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Answer:

\(y = C_1J_2(3\sqrt{x})+C_2Y_2(3\sqrt{x})\)

Step-by-step explanation:

\(x^{2} \dfrac{d^2 y}{dx^2} + x\dfrac{dx}{dy} + (x-1)y =0\)

Considering \(x=0\) ordinary point we could use Frobenius method assuming

\($y = \sum_{n=0}^{\infty} c_nx^n$\)

and consider the series representation given by the method to solve the equation. I think this way is harder.

In your case, It seems to have something to do with Bessel differential equation

\(x^2 y'' + x y' + (x^2-n^2) y = 0\)

that will have the same representation as the Frobenius method. To get the form \((x^2-n^2)\) as we have \( (x-1)\) in the given equation we can substitute \(x\) and take \(x = \dfrac{t^2}{9}\)

Thus,

\(\dfrac{dy}{dx} = \dfrac{3}{t}\dfrac{dy}{dt} \implies \dfrac{d^2y}{dx^2} = \dfrac{9}{t^2}\dfrac{d^2y}{dt^2}-\dfrac{9}{t^3}\dfrac{dy}{dt} \)

\($\implies \frac{1}{3^2}\left(t^2\frac{{d}^2y}{{d}t^2}+t\frac{{d}y}{{d}t}+(t^2-3^2)y\right) = 0$\)

The solution will have the format

\(y( x) = {C_1}{J_n}( x) + {C_2}{Y_n}( x )\)

such that

\(${J_n}( x ) = \sum\limits_{p = 0}^\infty {\frac{{{{( { - 1} )}^p}}}{{\Gamma ( {p + 1} )\Gamma ( {p + n + 1} )}} {{\left( {\frac{x}{2}} \right)}^{2p + n}}}$ \)

\(${Y_n}\left( x \right) = \frac{{{J_n}\left( x \right)\cos \pi n - {J_{ - n}}\left( x \right)}}{{\sin \pi n}}$ \)

and \(C_1, C_2\) are constants

And the order of the Bessel equation is \(n=2\)

In our case, we can just write

\(y(t) = C_1J_2(t)+C_2Y_2(t)\)

\(y = C_1J_2(3\sqrt{x})+C_2Y_2(3\sqrt{x})\)

Answer:

$12

Step-by-step explanation:

If we stuck with the price of $8, then we end with an income of $2400

Increasing it by $1 will decrease attendance by 20

8 x 300 = 2400

9 x 280 = 2520

10 x 260 = 2600

11 x 240 = 2640

12 x 220 = 2640

13 x 200 = 2600

We're starting to go down, so let's stop there

The ticket price of $11 or $12 appears to give the most income

I would stick with $12 since your still getting more money from one ticket

The price of a ticket stick at $12 since you still get more money from one ticket.

Last year 300 people attended a play with a ticket price of $8.

The school estimates that 20 fewer people attend for each $1 increase in price.

If we keep the price at $8, we'll end up with a $2400 profit.

Increasing it by $1 will result in a 20 percent drop in attendance.

8 × 300 = 2400

9 × 280 = 2520

10 × 260 = 2600

11 × 240 = 2640

12 × 220 = 2640

13 x 200 = 2600

Let's come to a halt here since we're starting to descend.

The $11 or $12 ticket price looks to generate the most revenue.

I'd continue with $12 because you'll still make more money with one ticket.

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Answer:

F(-x) = 0

Step-by-step explanation:

What is F(-x)?

F(-x) = F(-1)

F(x) = x³ + 1                              F(-1)

F(-1) = -1³ + 1

F(-1) = -1 + 1

F(-1) = 0

So, F(-x) = 0

Answer:

f(-1) = 0

Step-by-step explanation:

Evaluating a function for f(-x) is the same as evaluating it for f(-1).

So we plug in -1 instead.

f(-1) = x³ + 1  

      = (-1)³ + 1 (here we cube -1)

      = -1 + 1     (here we subtract)

      = 0           (and, this is the answer)

\(\therefore\) The answer is f(-1) = 0

Answer:

10

Step-by-step explanation:

Miguel will circle 10 counters because 5/8 * 16 = 10.

Answer:

A. 10 is the correct answer.

Step-by-step explanation:

The equation is 5/8 x 16.

Here, there are 16 counters. This is also known as 2 rounds of 8, which is the denominator in our fraction. Since 8 is 1/2 times 16, 5 x 2, or 10, is the correct answer.

Hope this helps! :)

Answer:

37/40

you asked how tho, so I included that in the explanation.

Step-by-step explanation:

desimplify:

the LCD is 40

so:

5/8+3/10=25/40+12/40

which is:

37/40

Answer:

The answers are below

Step-by-step explanation:

1. H0: rho = 0

  H1: rho not equal to 0

2. I will add the scatter plot as an attachment

3. ΣX = 523,

ΣY = 1055

ΣX² = 46023

ΣY²= 430407

ΣXY = 111448

n = 7

The correlation coefficient r =

r = 7(111448)-(523)(1055)/√7(46023)-(523)² × √7(430407)-(1055)²

r = 780136-551765/√322161-273529√3012849-1113025

= 228371/220.53*1378.34

= 228371/303965.32

r = 0.751

4. Test statistics

t = r√n-2/√1-r²

= 0.751√5/√0.5640

= 1.679/0.660

= 2.543

5. P value

Degrees of freedom n-2 = 5

T dist(2.543,5,2)

The p value is less than 0.05 so we reject null hypothesis. There is enough evidence to show a linear correlation between budgets and gross receipts.

Answer:

1,665.25 km

Step-by-step explanation:

There are no possible real values for the first term 'a' that satisfy both equations.

Let's denote the first term of the geometric progression as 'a' and the common ratio as 'r'.

The sum of the first two terms can be expressed as:

a + ar = 16

To find the sum to infinity, we can use the formula:

Sum to infinity = a / (1 - r)

Given that the sum to infinity is 25, we have:

25 = a / (1 - r)

We now have two equations:

a + ar = 16

a / (1 - r) = 25

We can solve these equations simultaneously to find the possible values of 'a'.

From the first equation, we can factor out 'a' to get:

a(1 + r) = 16

Dividing both sides of the second equation by 25, we have:

a / (1 - r) = 1

We can rearrange this equation to get:

a = 1 - r

Substituting this expression for 'a' in the first equation, we get:

(1 - r)(1 + r) = 16

Expanding the equation, we have:

1 - r^2 = 16

Rearranging the terms, we get:

r^2 = -15

Since we are dealing with a geometric progression, the common ratio 'r' must be a real number. However, we observe that r^2 = -15 has no real solutions. Therefore, there are no possible real values for the first term 'a' that satisfy both equations.

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Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.

I prefer Wills method because it is easier and less complicated.

Wills method:

(5x + 6x) - (2x - 1)

Subtract both 2x and -1

5x + 6x - 2x - - 1

5x + 4x + 1

In conclusion, Wills method is preferred when both methods are compared.

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The trigonometric function on the graph is:

f(x)= -cos(x)

So the correct option is B.

Here we can see the graph of a trigonometric function. We can see that the x-intercept is -1.

Notice that:

sin(0)= 0

cos(0) = 1

So the function can be an inversion over the x-axis of the cosine function, we coulod write this as:

f(x) = -cos(x)

That is the graphed function.

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Answer:

Correct option is A

Since it is an equilateral triangle, the lengths of the sides are equal

So, x+3 y=3 x+2 y−2=4 x+

2

1

​

y+1

x+3 y=3 x+2 y−2

y=2 x−2

2 x−y=2 ...(1)

Also, 4 x+

2

1

y+1=x+3 y

8 x+y+2=2 x+6 y

6 x+2=5 y

6 x−5 y=−2   ...(2)

Multiplying e q(1) by  5 we get,

10 x−5 y=10      ...(3)

Subtracting e q(2) from e q(3) we get,

4 x=12⇒x=3

y=2 x−2=4

The length of one side of equilateral triangle = x+3 y =3+3(4)=15 units

If principal is $2,658 and rate of interest 9% then the value of  the account balance is approximately $10,253 by using continuous compound interest formula.

Recurring interest is interest calculated on principal plus all interest and other interest. The idea is that lenders always receive interest, not individually at specific times.

The formula for continuous compound interest :

  A=    Peˣⁿ                          

Where,

A =Amount of money  after a certain amount of time

P= principal or the amount of money you start with

e =Napier's number, which is approximately 2.7183

x =Interest rate

n =Amount of time in years.

Use the continuous compound interest formula :

Given  P= 2658

x =9% =   = 0.09

n = 15

e = 2.7183

By using

A=    Peˣⁿ  

A= (2658)(2.7183)⁰°⁰⁹¹⁵

A =10,253 (approximately)

Hence, the value of account balance after 15 years is approximately $10,253

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The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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Answer:

800 grams flour ÷ 5 grams flour/biscuit = 160 biscuits

160 biscuits × 3 grams butter/biscuit = 480 grams butter

160 biscuits × 2 grams sugar/biscuit = 320 grams sugar

Katie needs 320 grams sugar.

Kate needs 270g of sugar to make the maximum number of biscuits possible.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Now, Based on the ratio of flour, butter, and sugar of 5:3:2, we can determine that Kate needs;

⇒ 800g + 550g

= 1350g of the mixture.

Hence, For find out the amount of sugar needed, we need to determine the proportion of sugar in the mixture.

We can do this by adding up the ratio numbers;

(5+3+2) = 10.

Then we can divide each ratio number by the total (10) to get the proportion of each ingredient.

So the proportion of sugar in the mixture is 2/10. To find out how much sugar Kate needs, we can set up a proportion:

2/10 = x/1350

We can solve for x by cross-multiplying:

2 × 1350 = 10x

2700 = 10x
x = 270

Therefore, Kate needs 270g of sugar to make the maximum number of biscuits possible.

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\(e^{2x} = \ln(y^3)\\\\\implies e^{2x} = 3 \ln y\\\\\implies \dfrac{d}{dx} e^{2x} = 3\dfrac{d}{dx}( \ln y)\\\\\implies 2e^{2x} = 3 \cdot \dfrac 1y \cdot \dfrac{dy}{dx}\\\\\implies 3\dfrac{dy}{dx} = 2ye^{2x}\\\\\implies \dfrac{dy}{dx} = \dfrac{2y}3 e^{2x}\)

Answer:

y=-8x+4

Step-by-step explanation:

Isolate the Y variable by balencing the equation! Khan acadamy has great videos on how to do this!

Answer:

Y=4-8x

OR if you want it more specific (slope intercept form)

y= -8x+4

Same thing

Step-by-step explanation:

SO when asked for y you just have to isolate the y

SO we can do that by subtracting 2x on both sides

1/4y=1-2x

Now to get y isloated we can just divide 1/4 on each sides

y=4-8x

THere you go or if you want it in slope intercept form just reverse the signs when switching the positions becuase y=mx+b

y= -8+4

Answer:

2341.78

Step-by-step explanation:

The number is already rounded to the nearest hundreth

Answer:

48/13

Step-by-step explanation:

To make this into an improper fraction, convert the integer into a fraction using the denominator of the fraction

3 * 13/13 = 39/13

Then add it to the rest of the fraction

39/13 + 9/13

= 48/13

Answer: 48/13

Step-by-step explanation: first multiply 3 x 13 to get 39. do this because you get the fraction for the whole number, 3. then, add 39 to the numerator (9). you will get 48/13. you do this because you are adding the whole number (3) to the fraction so that way it is an improper fraction.

The intersection between the complements of A and B is:

A' ∩ B' = {1, 2}

We have the sets:

A={4, 5, 6, 7}​

B={3, 4, 7}

And we want to find the intersection between the complements, where the complements are all the elements that are in the universal set and not are in the given sets, so:

A' = {1, 2, 3}

B'= {1, 2, 5, 6}

The intersection between two sets is the set of the common elements, so we have:

A' ∩ B' = {1, 2}

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The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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Answer:

150.8

pie(48/2)^2

Okay, here we have this:

Considering the provided information, we obtain the following system:

Now, let's clear x in the first equation:

Let's replace in the second equation:

Solving for y:

Then, x:

Finally we obtain that each encyclopedia measures 1.5 inches and each dictionary 2.5 inches.