Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 3 liters of natural oil for every 4 liters of synthetic oil. In order to make 497
liters of Petrolyn oil, how many liters of natural oil are needed?

Answer:

No solution

Step-by-step explanation:

1. Distribute the right side.

8w+5=8w+4

2. This has no solution.

Multiply both sides by \(x^{-3}\) to get a homogeneous equation.

\((2xy^2 - x^3) \, dy + (y^3 - 2yx^2) \, dx = 0 \\\\ \implies \left(2\dfrac{y^2}{x^2} - 1\right) \, dy + \left(\dfrac{y^3}{x^3} - 2\dfrac yx\right) \, dx = 0\)

Substitute \(y=vx\) and \(dy = x\,dv + v\,dx\). This makes the equation separable.

\((2v^2 - 1) (x\,dv + v\,dx) + (v^3 - 2v) \, dx = 0\)

\(x (2v^2 - 1) \,dv + (2v^3 - v) \, dx + (v^3 - 2v) \, dx = 0\)

\(x (2v^2 - 1) \,dv + (3v^3 - 3v) \, dx = 0\)

Separate the variables.

\(x (2v^2 - 1) \, dv = (3v - 3v^3) \, dx\)

\(\dfrac{2v^2-1}{3v-3v^3} \, dv = \dfrac{dx}x\)

\(\dfrac13 \dfrac{1 - 2v^2}{v(v-1)(v+1)} \, dv = \dfrac{dx}x\)

Expand the left side into partial fractions.

\(\dfrac{1-2v^2}{v(v-1)(v+1)} = \dfrac av + \dfrac b{v-1} + \dfrac c{v+1} \\\\ \dfrac{1-2v^2}{v(v-1)(v+1)} = \dfrac{a(v^2-1) + bv(v+1) + cv(v-1)}{v(v-1)(v+1)} \\\\ 1-2v^2 = (a+b+c) v^2 + (b-c) v - a\)

Solve for the coefficients \(a,b,c\).

\(\begin{cases} a + b + c = -2 \\ b-c = 0 \\ -a = 1 \end{cases} \implies a=-1, b=c=-\dfrac12\)

Thus our equation becomes

\(\left(-\dfrac1{3v} - \dfrac1{6(v-1)} - \dfrac1{6(v+1)}\right) \, dv = \dfrac{dx}x\)

Integrate both sides.

\(\displaystyle \int \left(-\dfrac1{3v} - \dfrac1{6(v-1)} - \dfrac1{6(v+1)}\right) \, dv = \int \dfrac{dx}x\)

\(\displaystyle -\frac13 \ln|v| - \frac16 \ln|v-1| - \frac16 \ln|v+1| = \ln|x| + C\)

Solve for \(v\) (as much as you can, anyway).

\(\displaystyle -\frac16 \left(2\ln|v| + \ln|v-1| + \ln|v+1|\right) = \ln|x| + C\)

\(\displaystyle \ln\left|\frac1{\sqrt[6]{v^2(v^2-1)}}\right| = \ln|x| + C\)

\(\displaystyle \frac1{\sqrt[6]{v^4-v^2}} = Cx\)

\(\sqrt[6]{v^4-v^2} = \dfrac Cx\)

\(\left(\sqrt[6]{v^4-v^2}\right)^6 = \left(\dfrac Cx\right)^6\)

\(v^4-v^2 = \dfrac C{x^6}\)

Put the solution back in terms of \(y\).

\(\left(\dfrac yx\right)^4-\left(\dfrac yx\right)^2 = \dfrac C{x^6}\)

\(y^4 - x^2y^2 = \dfrac C{x^2}\)

\(\boxed{x^2y^4 - x^4y^2 = C}\)

which is about as simple as we can hope to get this.

The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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angle J = 45°

angle K = 83°

angle L = 52°

A word problem is a math problem written out as a short story or scenario. These statements are interpreted in into mathematical equation or expression.

Representing angle L by x

therefore, J = x-7

and K = 2x -21

The sum of angle in a triangle is 180°

therefore,

x +x-7+2x-21 = 180

4x -28 = 180

4x = 180+28

4x = 208

x = 208/4

x = 52°

therefore angle J = 52-7 = 45°

angle K = 2 ×52 -21

= 104-21

= 83°

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Answer:

...

Step-by-step explanation:

To find the number of calories Davis burns while running for 30 minutes, we can use the information that he burns 1080 calories running for 2.5 hours.

We know that 30 minutes is 1/120 of 2.5 hours. So, we can divide the total number of calories by 120 and we get the calorie burn for 30 minutes:

1080 calories / 120 = 9 calories

The number of calories Davis burns while swimming for 30 minutes can be determined by using the equation y = 266x, where x represents the number of hours he swims. We know that he swims for 30 minutes, or 1/120 hours, so we can plug that value into the equation:

y = 266(1/120) = 2.216 calories

So, Davis burns 7 calories more running for 30 minutes than swimming for 30 minutes, assuming the rates remain constant.

The figure attached is composed of a cylinder and an sphere. Then:

Surface Area = Total Area of the Sphere + Side Area of the Cylinder.

Hence:

Now, the side area of the cylinder:

Finally:

ANSWER

The surface area is 1432.6 cm²

Now, to find the volume:

Total Volume = Volume of the Sphere + Volume of the Cylinder

Volume of the Sphere:

Volume of the Cylinder:

Finally:

ANSWER

The volume is 4657.9cm³

11.2% of the mass of a water molecule is hydrogen

As water is composed of two parts hydrogen and one part oxygen, the total mass of a single molecule may be determined by ascertaining the following:

The Total Mass of Water = (2 x Mass of Hydrogen) + (1 x Mass of Oxygen)

Total Mass of Water = (2 x 1.01u) + (1 x 16.00u)

Total Mass of Water = 18.02u

Consequently, the overall mass of one molecule of water is determined to be 18.02 atomic mass units (u).

% mass of hydrogen = (mass of hydrogen / total mass of water) × 100

% mass of hydrogen = (2.02u / 18.02u) × 100

% mass of hydrogen = 11.2%

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Answer:

Therefore, the total amount of money saved with a 42% trade discount on an order of 500 dozen microwavable serving bowls at a list price of $425 per set is $1,071,000.

Step-by-step explanation:

To calculate the amount of money saved with a 42% trade discount, we first need to find the discount amount.

The list price of the microwavable serving bowls is $425 per set. The trade discount is 42%, which means that the vendor is offering a discount of 42/100 x $425 = $178.50 per set.

To find the total savings for an order of 500 dozen sets (1 dozen = 12 sets), we need to multiply the discount per set by the number of sets and then by the number of dozens:

Total savings = Discount per set x Number of sets x Number of dozens

Total savings = $178.50 x 500 x 12

Total savings = $1,071,000

Answer:

1. r1 || r2 because of the same side or consecutive interior theorem

2. l1 || l2 because they are corresponding angles

The angle formed between two parallel lines having a common transversal have several common properties

The correct responses are;

1.  Lines r₁ and r₂ are parallel

2. Lines, l₁ and l₂ are parallel

lines r₁ and r₂, are parallel

The reason why the given lines are parallel are as follows:

1. The given figures are presented as shown in the attached diagram

From the diagram, we have that the same side interior angles formed by the common transversal l₂ the lines r₁ and r₂ are 63° and 117°, which are supplementary angles (63° + 117° = 180°)

Therefore, lines r₁ and r₂ are parallel given that same side interior angles formed by two parallel lines having the same transversal are supplementary

2. From the attached diagram, we have;

The alternate exterior angles formed between the lines, l₁ and l₂ that have the common transversal r₁ are equal, therefore;

Lines, l₁ and l₂ are parallel, given that the alternate exterior angles formed by two parallel lines having a common transversal are equal

From the diagram, we also have that the other angle of the linear pair angle with the 63° angle is 117°, and the second angle of the linear pair angle is both either corresponding angle and alternate interior angle with the given 117°

Therefore, lines r₁ and r₂, are parallel given that corresponding angles and the alternate interior angles formed between parallel lines having a common transversal are equal

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Without the exact Number of bread slices and people in each category, we cannot determine the specific number of sandwiches Rosa and Clarice can make

Step 1: Identify the number of leftover bread slices.
Unfortunately, the question doesn't provide the exact number of leftover bread slices. Let's assume Rosa and Clarice have "B" bread slices in total.

Step 2: Determine the number of sandwiches needed.
We know that they are making sandwiches for the custodian, librarian, and office staff. We need to know the number of people in each category to calculate the total number of sandwiches required. Since this information is not provided, let's assume there are "C" custodians, "L" librarians, and "O" office staff members.

Step 3: Calculate the number of sandwiches required.
Each sandwich typically requires 2 slices of bread. Therefore, the total number of sandwiches required can be calculated using the following formula:

Total Sandwiches = (C + L + O)

Step 4: Determine if there is enough bread.
We can now compare the total number of sandwiches required with the number of bread slices available. If there are enough bread slices (B >= 2 * Total Sandwiches), Rosa and Clarice can make sandwiches for everyone. Otherwise, they will not be able to make enough sandwiches for everyone.

In conclusion, without the exact number of bread slices and people in each category, we cannot determine the specific number of sandwiches Rosa and Clarice can make. To answer the question accurately, please provide the missing information.

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Answer:42, 3, 2, 15

Step-by-step explanation:

Answer:

f(x)= -3x + 400

Step-by-step explanation:

\(\frac{x-x_{1} }{x_{2}-x_{1} } = \frac{y-y_{1} }{y_{2}-y_{1} }\)

\(\frac{x-3}{13-3} =\frac{y-391}{361-391}\)

-3 ( x-3 ) = (y - 391 )

-3x + 400

Answer:

he is correct

Step-by-step explanation:

Answer:

Its B

Step-by-step explanation:  By calling people from around the country

Answer:The answer is B

Step-by-step explanation: I had this on my test

Answer:

Step-by-step explanation:

m = -4 ; (x₁ , y₁) = (2, -7)

Point slope form: y - y₁ = m(x - x₁)

y - [-7] = (-4)(x - 2)

y + 7  =(-4)(x - 2)

Answer:

Explanation:

Here, we want to check if the given function is even or odd

To do that, we find g(x) and g(-x)

If g(x) equals g(-x), the the function is even. Otherwise, the function is odd

We find the functions as follows:

Finally:

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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In Jameson's drawing, the nose cone has an area of 5 square inches. Each of the fins has an area of 3 square inches and the total area of the drawn rocket is 22 square inches.

From the question, we have the following parameters that can be used in our computation:

The drawing (see attachment)

The area of the nose cone is

Area = 1/2 * 5 * 2

Area = 5 square inches

For the fin, we have

Fin = 1/2 * 3 * 2

Fin = 3 square inches

Lastly, we have

Total area = (4 + 2 + 1) * 2 + 5 + 3

Total area = 22 square inches

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The angle from the options given that is shown in the drawing is: D. <LIJ.

An angle is a geometric figure that is formed by two rays that share the same endpoint, called the vertex. The rays are called the sides of the angle, and the endpoint is called the vertex.

In the drawing given,  IJ and LI are two segments that have a common endpoint called vertex I.

Points L, I, and J forms an angle whose vertex is at I, as shown in the image given. Thus, the angle shown in the drawing is: D. ∠LIJ.

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Using normal distribution, We may determine the crucial value tc using a statistical calculator. For instance, we may use the qt function in R programmed as follows:

\(> qt(0.9, 11) \\[1] 1.795885\)

A continuous probability distribution is exemplified by the normal distribution, in which the majority of data points are clustered about the middle of the range and the remaining ones decline symmetrically towards one of the extremes. The distribution's mean is another name for the range's midpoint. Data that are close to the mean are more frequent than data that are far from the mean, according to the normal distribution, also known as the Gaussian distribution, which is symmetrical about the mean. I'm getting an individual student's SAT scores from a brand-new test preparation program using heuristics in normal distribution. The data have a mean (M) of 1150 and a standard deviation (SD) of 150, and they are regularly distributed.

We determine the critical value to be tc=1.796 using a t-distribution table with 11 degrees of freedom (n-1=12-1=11) and a two-tailed test (since we are looking for a critical value for a confidence interval).

As an alternative, we may determine the crucial value tc using a statistical calculator. For instance, we may use the qt function in R program as follows:

\(> qt(0.9, 11) \\[1] 1.795885\)

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Answer:

we need a pic of the graph to be able. to work this out.

THANK YOU

Answer:

It's 5.

Step-by-step explanation:

8-3= 5

Answer:

8. d = 20.62

9. d = 47.42

10. (69, -28)

Step-by-step explanation:

                         (x₁, y₁)                        (x₂, y₂)

8. Ferris wheel: (2, 20) Water Ride: (-17, 12)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-17 - 2)² + (12 - 20)²

d = √(-19)² + (-8)²

d = √361 + 64

d = √425

d = 20.62

                              (x₁, y₁)                        (x₂, y₂)

9. Roller Coaster: (26, -8) Water Ride: (-17, 12)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-17 - 26)² + (12 - (-8))²

d = √(-17 - 26)² + (12 + 8)²

d = √(-43)² + (20)²

d = √1849 + 400

d = √2249

d = 47.42

10. Use the Midpoint formula to find the endpoint (aka the exit).

                           x₁ + x₂            y₁ + y₂

Midpoint =      (  ------------ )  ,  ( --------- )

                               2                   2

Since we know the Midpoint is the Roller Coaster (26, -8) and the beginning point is the Water Ride (-17, 12) we need to plug in the numbers.                                           (x₁, y₁)

                           -17 + x₂                      12 + y₂

Midpoint =      (  ------------ ) = 26(2) ,  ( --------- ) = -8(2)

                               2(2)                           2(2)

Get rid of the denominator by multiplying 2 with the number on the other side of the equal ( = ) sign.

Midpoint =      (  -17 + x₂ = 52 )  ,  ( 12 + y₂ = -16 )

                          +17          +17        -12           -12

Midpoint =      (  x₂ = 69 )  ,  ( y₂ = -28 )

The exit is located at point: (69, -28)

I hope this helps!

Answer:

Step-by-step explanation:

The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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Recall that Speed is the rate of change of distance with time

This may be expressed mathematically as

Speed = Distance / time

Hence given that

speed = 45 mph

Time = 0.45 hours

Distance = speed * time

= 45 * 0.45

= 20.25 miles

The train traveled 20.25 miles.

Answer:

b

Step-by-step explanation:

Answer:

The answer is B! :)

Step-by-step explanation:

Using the expression 5t + 16, the height of the tree after 7 years it was planted is: 51 inches.

To evaluate implies that we find the value of the expression by plugging in the value of the variable and simplify accordingly.

Given that t represents the number of years after a tree is planted, and the expression, 5t + 16 represents the approximate height of the tree, to find its height after 7 years, substitute t for 7 into the expression and evaluate:

5(7) + 16

35 + 16

= 51

Thus, the height of the tree after 7 years it was planted is: 51 inches.

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Answer:

×=14

Step-by-step explanation:

24÷16=1.5

21÷1.5=14

Answer:

Step-by-step explanation:

3/4 : 1/8 =

3/4 x 8 =

24/4 =

6

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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