An oil tank is being drained. the volume, V, in litres, of oil remaining in the tank after t minutes can be modeled by the function
V(t) = 0,5 (10 – t)^3
where 0 ≤ t ≤ 10.
a) how much oil is in the tank initially?
b) determine the average rate of change of volume in the first 1 minutes.
c) estimate the instantaneous rate of change of volume at 5 minutes. Do NOT use Calculus.

Answer: 210 ( it hope this is a best answer)

Step-by-step explanation:

2 hours and 20 minutes is 2 and a third hours. Multiply 90 by 2 and a third.

90 × 2.333

209.999

If you round to the nearest kilometer, the answer is 210 km

Answer: The answer would be C

Step-by-step explanation:

If we start from 56,60,64,68 and were adding 4 each time the next numbers would be 72,76,80

The simplification of the radical expression √9. is 3.

Radical expressions are simplified by taking them down to their most basic form and, if feasible, altogether deleting the radical. When a radical expression appears in the denominator of an algebraic expression, the radical expression is simplified by multiplying the numerator and denominator by the appropriate radical expression (for example, conjugate in the case of a binomial and the same radical in the case of a monomial).

The given expression is √9.

The given expression can be written as:

√(3)(3) = 3

Hence, the simplification of the radical expression √9. is 3.

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Answer:

A= 9/20 B= 45% C=0.45 d= 4.5% E= 3/8 F= 0.375 G= 37.5% H= 15.5% I = 0.8 j=80%

We can use the two-point form to find the equation of the line passing through the two given points:

y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)

where (x1, y1) = (1, 7) and (x2, y2) = (3, 3).

Substituting the values, we get:

y - 7 = ((3 - 7)/(3 - 1))(x - 1)

Simplifying the equation, we get:

y - 7 = (-2/2)(x - 1)

y - 7 = -x + 1

Adding 7 to both sides, we get:

y = -x + 8

Therefore, the equation of the line passing through the points (1, 7) and (3, 3) is y = -x + 8.

Hope this helps <3

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plt.plot(x, y_sine)
plt.plot(x, y_cosine)

To compute the x and y coordinates for points on sine and cosine curves, you need to use the trigonometric functions sine and cosine. To plot the sine and cosine graphs in the same figure, you need to create a subplot grid using the plt.subplot() function. This function takes in the number of rows, columns and the active plot you want to plot the graphs in.

To create a subplot grid that has height 2 and width 1 and set the first subplot as active, the code will look like this:
plt.subplot(2, 1, 1)

You can then plot the sine and cosine graphs by using the x and y coordinates calculated from the sine and cosine functions. The code for plotting the graphs will look like this:
plt.plot(x, y_sine)
plt.plot(x, y_cosine)

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Answer: no

Step-by-step explanation:

we can graph s=s(t),v=v(t), and a=a(t) by plotting the equations for s, v, and a as functions of t. The graph of s=s(t) is a sinusoidal curve with a linear trend. The graph of v=v(t) is a sinusoidal curve with a constant value. The graph of a=a(t) is a sinusoidal curve with a zero value.

The velocity v of the pendulum is the first derivative of the distance s with respect to time t. That is, \[ v=v(t)=\frac{ds}{dt} \] Similarly, the acceleration a of the pendulum is the first derivative of the velocity v with respect to time t. That is, \[ a=a(t)=\frac{dv}{dt} \] We can find the velocity v and acceleration a by taking the derivatives of the given equation for the distance s. \[ s=s(t)=0.04 \sin (2 t)+3 t \] The first derivative of s with respect to t is \[ v=v(t)=\frac{ds}{dt}=0.08 \cos (2 t)+3 \] The second derivative of s with respect to t is \[ a=a(t)=\frac{dv}{dt}=-0.16 \sin (2 t) \] Now, we can find the velocity v and acceleration a at the given times t= 8π ,t= 4π , and t= 2π by plugging in the values of t into the equations for v and a. \[ v( 8π )=0.08 \cos (2( 8π ))+3=3 \quad \text{m/s} \] \[ v( 4π )=0.08 \cos (2( 4π ))+3=3 \quad \text{m/s} \] \[ v( 2π )=0.08 \cos (2( 2π ))+3=3 \quad \text{m/s} \] \[ a( 8π )=-0.16 \sin (2( 8π ))=0 \quad \text{m/s}^2 \] \[ a( 4π )=-0.16 \sin (2( 4π ))=0 \quad \text{m/s}^2 \] \[ a( 2π )=-0.16 \sin (2( 2π ))=0 \quad \text{m/s}^2 \] Finally, we can graph s=s(t),v=v(t), and a=a(t) by plotting the equations for s, v, and a as functions of t. The graph of s=s(t) is a sinusoidal curve with a linear trend. The graph of v=v(t) is a sinusoidal curve with a constant value. The graph of a=a(t) is a sinusoidal curve with a zero value.

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Due to length restrictions, we kindly invite to read the explanation to see the lenghts of each 30-60-90 right triangles.

In this problem we find six cases of 30-60-90 right triangles, that is, right triangles whose inner angles have the following measures: 30°, 60°, 90°. The length of sides can be found by the following relationships:

Now we proceed to determine the missing length:

Case 1:

PV = 4 / (1 / 2)

PV = 8

VT = √3 · 4

VT = 4√3

Case 2:

PT = 2 / √3

PT = 2√3 / 3

PV = 2 / (√3 / 2)

PV = 4√3 / 3

Case 3:

PT = (1 / 2) · 3

PT = 3 / 2

VT = 3√3 / 2

Case 4:

PT = 7 / √3

PT = 7√3 / 3

PV = 7 / (√3 / 2)

PV = 14√3 / 3

Case 5:

VT = √3 · (1 / 2)

VT = √3 / 2

PV = (1 / 2) / (1 / 2)

PV = 1

Case 6:

PV = 100

PT = 50

VT = 50√3

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For function fx= -4x2+6x-1

To find f(-1), we need to plug in -1 for x in the function and simplify:
f(-1) = -4(-1)2+6(-1)-1
f(-1) = -4+(-6)-1
f(-1) = -11

To find when fx=0, we need to set the function equal to 0 and solve for x: -4x2+6x-1=0

We can use the quadratic formula to solve for x:
x = (-b ± √(b2-4ac))/(2a)
x = (-(6) ± √((6)2-4(-4)(-1)))/(2(-4))
x = (-6 ± √(36-16))/(-8)
x = (-6 ± √20)/(-8)
x = (-6 ± 2√5)/(-8)
x = (3 ± √5)/4

So, the two values of x that make fx=0 are (3+√5)/4 and (3-√5)/4.

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The line which is not transversal to LR would be Line TK.

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.

Properties of Parallel Lines Cut by a Transversal

The corresponding angles are equal and the vertically opposite angles are equal.

The alternate interior angles are equal and the alternate exterior angles are equal.

Also, pair of interior angles on the same side of the transversal is supplementary.

Since we know that transversal is a line that intersects two or more other lines at different points.

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Line TK is not transversal to line LR.

Parallel lines are the lines that do not intersect or meet each other at any point in a plane. They are always parallel and are at equidistant from each other. Parallel lines are non-intersecting lines. We can also say Parallel lines meet at infinity.

Given,

Line PR and KT are parallel

By the figure,
PR = LR

and KT = TK
PR || KT

∴ LR || TK

Hence, TK is the line, that is not the transversal line to LR.

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Therefore , the solution of the given problem of inequality comes out to be the inequality x -5 is option B.

Regardless of the equal symbol, a connection or group of numbers variables can be an inequality in mathematics. Equilibrium is always followed by equity. Inequality happens when ideals are still incompatible. Differences exist between inequality expression and fairness. We chose to utilize the most prevalent symbol because elements aren't always similar or comparable (). No mater how few or many variations there are, they can all be used to evaluate values.

Here,

Option B) B is the proper response.

We must isolate x on one side of the inequality in order to answer the inequality x + 2 -3. By taking 2 away from both edges, we arrive at:

=> x < -5

According to this inequality, x is any integer that is less than -5. Since x cannot equal -5,

we must create an open circle at this point on the number line and shade to the left of it to represent all the different values of x that could be used.

Looking at the available choices, we can see that the only graph that accurately depicts the inequality x -5 is option B) B.

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The probability of drawing a King, Queen, or Jack from a standard deck of 52 cards is 3/13.

The probability of drawing a King, Queen, or Jack in a standard deck of 52 cards can be calculated by using the formula for the probability of an event happening: P(E) = number of favorable outcomes / total number of possible outcomes.

In this case, the number of favorable outcomes is the total number of Kings, Queens, and Jacks in the deck, which is 4 + 4 + 4 = 12. The total number of possible outcomes is the total number of cards in the deck, which is 52.

So, the probability of drawing a King, Queen, or Jack is:

P(E) = 12 / 52

Simplifying this fraction gives us:

P(E) = 3 / 13

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There are 2 real solutions to the equation [tex]2(x-1)^(2)(2x+3)(x+5)^(3)=.001.[/tex]

To find the real solutions, we can use the zero product property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero. In this case, we can set each of the factors equal to zero and solve for x:

[tex]2(x-1)^(2)=02x+3=0(x+5)^(3)=0[/tex]

Solving each of these equations gives us the following solutions:
[tex]x=1x=-3/2x=-5[/tex]

However, we need to check each of these solutions to see if they satisfy the original equation. Plugging each solution back into the equation gives us:

[tex]2(1-1)^(2)(2(1)+3)(1+5)^(3)=.0012(-3/2-1)^(2)(2(-3/2)+3)(-3/2+5)^(3)=.0012(-5-1)^(2)(2(-5)+3)(-5+5)^(3)=.001[/tex]

The first and third solutions do not satisfy the equation, but the second solution does. Therefore, there are 2 real solutions to the equation [tex]2(x-1)^(2)(2x+3)(x+5)^(3)=.001.[/tex]

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The radius of the first circle is 14.67 cm and the radius of the second circle is 8.11 miles.

The radius of a circle can be found by using the formula s = rθ, where s is the length of the arc, r is the radius, and θ is the central angle in radians. Rearranging the formula, we can find the radius by dividing the length of the arc by the central angle: r = s/θ.

For the first part of the question, we are given an arc length of 88 cm and a central angle of 6 radians. Plugging these values into the formula, we can find the radius:

r = 88 cm / 6 radians = 14.67 cm

For the second part of the question, we are given an arc length of 17 miles and a central angle of 120°. However, we need to convert the central angle from degrees to radians before plugging it into the formula. We can do this by multiplying the angle in degrees by π/180:

120° × π/180 = 2π/3 radians

Now we can plug the values into the formula to find the radius:

r = 17 miles / (2π/3) radians = 8.11 miles

So the radius of the first circle is 14.67 cm and the radius of the second circle is 8.11 miles.

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The solution of the inequality |x+3| < 2 is -5 < x < -1.

And the graph is given in the image below.

The correct option is C.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

To solve the inequality |x+3| < 2, we need to consider two cases:

Case 1: x+3 ≥ 0

In this case, the inequality simplifies to x+3 < 2, which gives us x < -1.

Case 2: x+3 < 0

In this case, the inequality simplifies to -(x+3) < 2, which gives us -x-3 < 2, or -x < 5, or x > -5.

Combining the results from both cases, we get the solution:

-5 < x < -1

To graph the solution, we draw an open circle at x=-3

(since the absolute value is less than 2, not less than or equal to), and shade the region between -5 and -1.

Therefore, the solution is -5 < x < -1.

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The composition of the given functions are:\( (f\circ g)(x) = 6x^2 - 36x + 13 \) and \( (g\circ f)(x) = 36x^2 - 72x + 29 \).

Given functions are \( f(x)=6x−5 \) and \( g(x)=x^2−6x+3 \). Let's find the composition of functions below:\((f\circ g)(x)\)First, we need to substitute \( g(x) \) in place of \( x \) in \( f(x) \). Hence,\( (f\circ g)(x) = f(g(x)) \)\( f(g(x)) = 6g(x) - 5 \)Substitute \( g(x) \) in the above equation,\( (f\circ g)(x) = 6(x^2-6x+3) - 5 \)\( (f\circ g)(x) = 6x^2 - 36x + 13 \)\((g\circ f)(x)\)First, we need to substitute \( f(x) \) in place of \( x \) in \( g(x) \). Hence,\( (g\circ f)(x) = g(f(x)) \)We are given that \( f(x)=6x−5 \) , substitute this in the above equation,\( (g\circ f)(x) = g(6x-5) \)Substitute this in the function \( g(x) \),\( (g\circ f)(x) = (6x-5)^2 - 6(6x-5) + 3 \)\( (g\circ f)(x) = 36x^2 - 72x + 29 \)Hence, the composition of the given functions are:\( (f\circ g)(x) = 6x^2 - 36x + 13 \) and \( (g\circ f)(x) = 36x^2 - 72x + 29 \).

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The coordinates of R are (-15, 8). The solution has been obtained by using Mid point formula.

What is Mid point formula?

The centre point of a straight line can be located using the midpoint formula. If we know the coordinates of the other endpoint and the midpoint, we can use the midpoint formula to obtain the coordinates of the endpoint as well.

We are given that Q is the midpoint of segment PR and point P is (11,-2) and point Q is (-2,3).

Let the coordinates of R be (x₂, y₂)

Using Mid point formula, we get

⇒Point Q = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

⇒(-2,3) = ((11 + x₂) / 2, (-2 + y₂) / 2)

So,

⇒-2 = (11 + x₂) / 2

⇒-4 = 11 + x₂

⇒x₂ = -15  

Similarly,

⇒3 = (-2 + y₂) / 2

⇒6 = -2 + y₂

⇒y₂ = 8

Hence, the coordinates of R are (-15, 8).

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Answer: 23 kg

Step-by-step explanation:

Let's begin by using algebra to solve the problem.

Let x be the number of kilograms of salmon the fish-shop owner bought at the market.

We know that the total cost of the salmon was $400, so we can write:

400 = x * c

where c is the cost per kilogram of salmon.

We also know that all except for 2 kg of the fish were sold at a price per kg that was $10 more than what the owner paid at the market. So the price per kilogram of salmon at the fish shop was c + 10.

The total revenue from the sale of the fish was $540, so we can write:

540 = (x - 2) * (c + 10)

Now we can use these two equations to solve for x.

First, we can use the first equation to solve for c:

c = 400 / x

Then we can substitute this expression for c into the second equation:

540 = (x - 2) * (400/x + 10)

Simplifying this equation:

540 = 4000/x + 10x - 20 - 80/x

Multiplying both sides by x:

540x = 4000 + 10x^2 - 20x - 80

10x^2 - 20x - 4600 = 0

Dividing both sides by 10:

x^2 - 2x - 460 = 0

We can solve for x using the quadratic formula:

x = [2 ± sqrt(4 + 4*460)] / 2

x = [2 ± 44] / 2

Discarding the negative solution, we get:

x = (2 + 44) / 2

x = 23

Therefore, the fish-shop owner bought 23 kilograms of salmon at the market.

Answer:

vydbskehhwbe

Step-by-step explanation:

bshhdvjebheunsns

The white ball is transferring its momentum to the red ball.
The missing blank is "transferring".

The statement "the white ball is transferring its momentum to the red ball" is based on the law of conservation of momentum.

According to this law, the total momentum of a closed system (in which no external forces act on the system) is conserved. This means that the momentum lost by one object in the system must be gained by another object in the system.

So we can conclude that, in the picture, the white ball and the red ball together form a closed system, and the collision between them causes the white ball to transfer some of its momentum to the red ball, in accordance with the law of conservation of momentum.

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2.8889........., 2.8890........, 2.8891...... etc is an irrational number the is between the two rational numbers.

What is a rational number, with an example?

Any number with the pattern p/q, where p and q are integers and q is not equal to 0, is a rational number. Rational numbers include, among others, 1/3, 2/4, 1/5, 9/3, and so forth.

A rational number is a number which is can be represented as the quotient of two numbers without having any remainder i.e., having remainder 0. For example 2.45, 2, 3 etc.

An irrational number has a non zero remainder and has a non terminating quotient. For example the numbers shown in the question 2.888...... and 2.999..... etc.

So the numbers between 2.888... and 2.999... are 2.8889........., 2.8890........, 2.8891...... etc

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The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.

A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.

here, we have,

given that,

Triangle ABC has vertices A (-1, 2), B (5, 2), and C (5,-3)

and triangle XYZ has vertices X(-0.5, 1), Y(2.5, 1), and 2(2.5, "-1.5)."

now, we now that,

distance formula:

d=√(x2−x1)^2+(y2−y1)^2

so, we get,

length of AB = 3√2

and, length of XY = 3

so, scale factor = AB/XY

                          =3√2/3

                          =√2

Hence, The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.

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Step-by-step explanation:

The circumference of the bike tire above is 82.268 inches.

What is the radius of the bike tire? (Use 3.14 for .)

A.

26.2 in

B.

13.1 in

C.

41.13 in

D.

258.32 in

Ps=the answer is B

(1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.

What is Scatter Plot ?

A scatter plot is a graph that shows the relationship between two sets of data. Each dot on the plot represents a single data point, and the position of the dot corresponds to the values of the two variables being plotted.

In this specific scatter plot, we have 10 data points represented by dots. To find the two points that a line of best fit would go through, we want to look for a pattern or trend in the data. Ideally, the line of best fit should pass as close as possible to all of the data points, but this is not always possible.

One common method for finding the line of best fit is to choose two points that seem to be close to the middle of the data and that the line passes through. This is because we want the line to be a good representation of the overall trend in the data.

Looking at the scatter plot provided, we can see that there is a general trend of the data points sloping downward from left to right. If we draw a line that passes through the points (3, 7) and (9, 1), we can see that it closely follows the trend of the data points. Therefore, these are the two points that a line of best fit would go through to best fit the data.

Therefore, (1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.

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The area of the hexagon is 98 sq. m and option 3 is the correct answer.

The closed polygonal form of a regular hexagon has six equal sides and six equal angles. Any regular polygon has equal sides and angles on all sides. Regular pentagons, for instance, have 5 equal sides, while regular octagons have 8 equal sides. When these requirements are not satisfied, polygons might resemble many other asymmetrical forms. A regular hexagon is formed when six equilateral triangles are placed side by side. The regular hexagon's area then increases to six times that of the identical triangle.

Given that,

The scale factor of two similar hexagons is 3:7.

The ratio of the area will thus be,

(3/7)^2 = 9/49.

For the area of the smaller hexagon as 18 we have:

9/49 = 18/A

(9/49)A = 18

Multiplying both sides by 49/9, we get:

A = 98 sq. m

The volume of the hexagon cannot be determined by the given information.

Hence, the area of the hexagon is 98 sq. m and option 3 is the correct answer.

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Alternate interior angles = ∠7 and ∠9.

Corresponding angles = ∠1 and ∠7

Vertical angles = ∠4 and ∠11

∠7 = 60°

∠8 = 120°

∠9 = 60°

When two lines meet, they intersect at an angle. By using the symbol, we may symbolise an angle.

Two lines meet at the common vertex of an angle, which has one common leg. A straight line's one side always has a total angle of 180 degrees. On the other hand, a point's surrounding angles are always added up to 360 degrees.

Here,

We can see that the Alternate interior angles = ∠7 and ∠9.

Corresponding angles = ∠1 and ∠7

Vertical angles = ∠4 and ∠11

Given, ∠1 = 60°

Now similarly, using the angles properties we can ind the rest of the angles.

∠7 = 60°

∠8 = 120°

∠9 = 60°

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The length of the diagonal is between 3 and 4; it is closer to 3.

In Mathematics, the diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.

In any rectangle, each of the two (2) opposite sides are equal and parallel and the two (2) diagonals are equal.

Based on the information provided about the diagonal, we have:

Diagonal = √18

Diagonal = √9 × √2

Diagonal = 3√2 units.

In conclusion, we can logically deduce that the diagonal is closer to 3 units.

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The zeros in the given graph. (the one where its curved pointing downwards) is {-3,1}.

The solutions to the equation p(x) = 0, where p(x) stands for the polynomial, are the zeros of a polynomial. If we plot this polynomial as y = p, we can see that these are the values of x where y = 0. (x). In other words, these are the x-intercepts of the graph.

The polynomial's zeros can be found by locating the locations where its graph contacts or crosses the x-axis.

When f(x) = 0, or when the graph's y-coordinate is equal to 0, the zeroes of the graph are determined.

From the graph we see that, at y = 0 we have the values of x as:

1. x = -3 and x = 1

Hence, the zeros in the given graph. (the one where its curved pointing downwards) is {-3,1}.

2. Roots of the graph are - x = - 2 and x = 4, {-2, 4}

3. solutions to x² + 10x = 24,

x² + 10x - 24 = 0

x² + 12x - 2x - 24

x(x + 12) -2 (x + 12)

(x - 2) (x + 12)

x = 2 or x = -12

{-12,2}

4. solutions to x² + 18x = 4x - 49

x² + 14x + 49

x² + 7x + 7x + 49

x(x + 7) + 7 (x + 7)

(x + 7)(x + 7)

x = -7

{-7}

5.  zeros of x² - 9x = 0

x(x - 9) = 0

Either x = 0 or x = 9,

{0,9}

6. roots of 4x² - 24 = 20x

4x² - 20x - 24 = 0

x² - 5x - 6 = 0

x² -6x + x - 6 = 0

x(x - 6) + 1(x - 6) = 0

(x + 1) (x - 6)

x = -1 and x = 6

{-1,6}

7. correct option is y = x² - x - 6

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Substituting Q = 30 degrees, we get:

Q' = 30 degrees + 45 degrees

Q' = 75 degrees

Therefore, the measure of angle Q' is 75 degrees.

Acute angles are those that range in degree from 0 to 90. Obtuse angles (90°–180°) are those that fall within this range. • A right angle is one with an angle of 90 degrees (= 90°).

If angle Q measures 30 degrees and is rotated 45 degrees, we can find the measure of the new angle Q' as follows:

Q' = Q + 45 degrees

Substituting Q = 30 degrees, we get:

Q' = 30 degrees + 45 degrees

Simplifying, we get:

Q' = 75 degrees

Therefore, the measure of angle Q' is 75 degrees.

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