Chris saved x dollars and spent half of his savings buying video games. After earning an additional $20 cutting grass, he had $60. If the equation one half times x plus 20 equals 60 represents the scenario, how much did he start with in his savings?.

The maximum volume of the cylinder is 27147.355 cm² at the maximum point.

What is volume of cylinder?

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula r2h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. The substance could be a liquid amount or something else that can be evenly put into the cylinder.

The formula for the volume of the cylinder v = [tex]\pi r^2[/tex]h,

To find the maximum volume of the cylinder we apply the condition of maxima [tex]\frac{dv}{dr}[/tex]  = 0.

Let r cm be the radius and h cm be the height of the closed cylinder.

Then, Total surface area of the cylinder = [tex]2\pi r(r+h)[/tex]

                                                   5000      = [tex]2\pi r^{2} +2\pi rh[/tex]

                                                    h     =    [tex]\frac{5000-2\pi r^{2} }{2\pi rh}[/tex]............(1)

Volume of the cylinder v = [tex]\pi r^2h[/tex]

Substitute the value of h  in the above equation

                                      = [tex]\pi r^2[/tex] × [tex]\frac{5000-2\pi r^{2} }{2\pi rh}\\[/tex]

                                      = [tex]\frac{r}{2}[/tex] ×  [tex]5000-2\pi r^2[/tex]

                                   v = [tex]2500r-\pi x^{3}[/tex] ..............(2)

Now, for the maximum volume of the cylinder   dv/dr= 0

                                                      [tex]\frac{d(2500r-\pi x^{3})}{dr}[/tex]         =0

                                                            [tex]3\pi r^{2} =2500[/tex]

                                                               [tex]r^{2} =\frac{2500}{3\pi }[/tex]

                                                              r=[tex]\frac{50}{\sqrt{3\pi } }[/tex]

                                                           r= 27147.355

Hence, The maximum volume of the cylinder is 27147.355 at the maximum point r= [tex]\frac{50}{\sqrt{3\pi } }[/tex].

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Answer:

Step-by-step explanation:

Let x be the number of black ink cartridges sold and y be the number of color ink cartridges sold. We know that:

x + y = 36 (total number of cartridges sold)

18.99x + 22.99y = 723.64 (total amount of money earned)

We can use the first equation to solve for one variable in terms of the other and substitute that expression into the second equation to get a single equation in one variable, which can then be solved. For example:

y = 36 - x

18.99x + 22.99(36 - x) = 723.64

18.99x + 827.64 - 22.99x = 723.64

-4x = -104

x = 26

So, 26 black cartridges were sold and 36 - 26 = 10 color cartridges were sold.

Answer:

slope: -3/2  y-intercept: -1

Answer: -32

Step-by-step explanation:

Aurther have jump 0.50575 feet more to break the record.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

The high school jump record = 24 ft 5 1/4 inch

                                                 = 24 ft 21/4 inch = 24.4375 ft

and, Aurther jump is = 23.958 ft

So, Aurther have jump

= 24.46375 - 23.958

= 0.50575 feet more

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The solution of the differential equation is [tex]y = (48/t - 6t)^{-1/2}.[/tex]

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives.

In this particular differential equation, the dependent variable is y and the independent variable is t. The equation states that the rate of change of y with respect to t is equal to

=> y²(6 + t).

To find the solution to this differential equation, we first need to separate the variables and integrate both sides.

This gives us an equation of the form

[tex]= > y = (C/t - 6t)^{-1/2}[/tex]

where C is an arbitrary constant.

To find the value of C, we use the initial condition y = 8 when t = 1. Plugging in these values, we find that

=> C = (8)² * 1 - 6 = 48.

So, the solution to the differential equation is

=> [tex]y = (48/t - 6t)^{-1/2}.[/tex]

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Yes, an object can have zero velocity and immobile be accelerating together. While participating the object, you will find that the object will continue to move ahead for some time and then stops instantly.

Then the object will start to move in the reverse direction.

at all the velocity is constant, the acceleration is zero. For example, a car traveling at a constant 80 km/h in a straight line has nonzero velocity and zero acceleration.

If acceleration is 0, the velocity is not converted. If the velocity is constant (0 acceleration) then the object will continue needing slowing down or speeding up.

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Answer:

option 2

Step-by-step explanation:

The numeric values for the function y = 4x² are given as follows:

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function in this problem is given as follows:

y = 4x².

Hence, to obtain the numeric value at x = -3, we replace the lone instance of x by -3, hence:

y = 4(-3)² = 4 x 9 = 36.

The same procedure is applied to obtain the other numeric values.

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The meaning of the point (1,10) on the graph of the function is given as follows:

10 gallons of gas in the tank after one hour.

All the points in the graph of a function have the format presented as follows:

(x,y).

In which:

For this problem, the input and output variables are given as follows:

Hence the interpretation of point (1,10) is that there are 10 gallons of gas in the tank after one hour.

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The expressions with powers are ( -7 )³ and   [tex]3^{-2}[/tex]

What is an expression?

A mathematical expression is a phrase containing a minimum of two numbers or variables and a minimum of one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression)

The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication, and division (left to right), addition and subtraction (from left to right).

a) -7 is taken 3 times. so raise power as 3

( -7 )³

b) 1/(3²) = [tex]3^{-2}[/tex]

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The solution is Option C , Option D.

The inequality equation is x > 5

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the equation will be

Substituting the values in the equation , we get

-3 ( 2x - 5 ) < 5 ( 2 - x )

On simplifying the equation , we get

-3 ( 2x ) - 3 ( -5 ) < 10 - 5x

-6x + 15 < 10 - 5x

Adding 6x on both sides of the equation , we get

x + 10 > 15

Subtracting 10 on both sides of the equation , we get

x > 5

Hence , the inequality equation is x > 5

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The probability that two grandchildren of the woman who are first cousins to one another will each inherit the dominant allele is 1/16.

To determine the probability that two grandchildren of a woman who are first cousins to one another will each inherit the dominant allele, we first need to understand the pattern of inheritance for dominant and recessive alleles.

Assuming the woman has two dominant alleles (D) and two recessive alleles (d), the probability of passing on a dominant allele to each grandchild is 1/2. For two first cousins to each inherit a dominant allele, we need both of their parents to pass on a dominant allele to them. The probability of both parents passing on a dominant allele is (1/2) * (1/2) = 1/4.

So, the probability of two first cousins each inheriting a dominant allele is 1/4 * 1/4 = 1/16. This means that there is a 1 in 16 chance that both first cousins will each inherit the dominant allele.

To summarize:

P(inheriting dominant allele) = 1/2

P(both parents passing on dominant allele) = 1/2 * 1/2 = 1/4

P(two first cousins each inheriting dominant allele) = 1/4 * 1/4 = 1/16

Therefore, the probability that two grandchildren of the woman who are first cousins to one another will each inherit the dominant allele is 1/16.

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The probability that two grandchildren of the woman who are first cousins to one another will each inherit the dominant allele is 1/16.

To determine the probability that two grandchildren of a woman who are first cousins to one another will each inherit the dominant allele, we first need to understand the pattern of inheritance for dominant and recessive alleles.

Assuming the woman has two dominant alleles (D) and two recessive alleles (d), the probability of passing on a dominant allele to each grandchild is 1/2. For two first cousins to each inherit a dominant allele, we need both of their parents to pass on a dominant allele to them. The probability of both parents passing on a dominant allele is (1/2) * (1/2) = 1/4.

So, the probability of two first cousins each inheriting a dominant allele is 1/4 * 1/4 = 1/16. This means that there is a 1 in 16 chance that both first cousins will each inherit the dominant allele.

To summarize:

P(inheriting dominant allele) = 1/2

P(both parents passing on dominant allele) = 1/2 * 1/2 = 1/4

P(two first cousins each inheriting dominant allele) = 1/4 * 1/4 = 1/16

Therefore, the probability that two grandchildren of the woman who are first cousins to one another will each inherit the dominant allele is 1/16.

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You can resolve the equation by completing the square. first, subtract 0.33 from both sides of the equation. Add 968.15/0.33 to both sides after that. The resulting equation will be x2 + 189.94 x = 2113.58. Divide both sides by 189.94, then multiply both sides by 0.5.  To find x=-93.97, square root both sides of the equation.

-0.33x^2 + 63.78x - 968.15 = 0

x2 + 189.94x = 2113.58 after subtracting -0.33 from both sides.

Multiply both sides by 189.94 to get 11.27 (x + 94.97).

To all sides, add 0.5: x + 94.97 + 0.5 = 11.77

Add up both sides and subtract 94.97: x + 0.5 = 11.77 - 94.97

Add 0.5 on either side to get the result: x = 11.27 - 94.97 x = -93.97

By completing the square, the equation -0.33x2 + 63.78x - 968.15 = 0 can be resolved. first, subtract 0.33 from both sides of the equation. As a result, the equation x2 + 189.94x = 2113.58 will be produced. Divide both sides by 189.94, then multiply both sides by 0.5. The outcome will be (x+94.97)2=2403.55. Square root both sides of the equation to finish. As a result, x + 0.5 = 11.27 - 94.97 will be obtained. The result of deducting 0.5 from both sides and then 94.97 from both sides is yield x = -93.97.

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The correct answer is option 4. The equation that is equivalent to 12 3/x + 15 = 36 is 3/x + 15 = 24.

To isolate x in the equation, we need to subtract 15 from both sides, which gives us 3/x = 9. Then, we need to multiply both sides by x, which gives us 3 = 9x. Finally, we divide both sides by 9 to get x = 1/3. This means that the value of x that makes the equation true is 1/3. To verify, we can plug this value back into the original equation and see if both sides are equal.

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Neither Ahmed's conclusion nor Adel's conclusion is entirely true or false. Adel's conclusion is closer to being true than Ahmed's conclusion, as it is only false in one case.

The truth table would look like this:

Egg broken? Egg boiled? Khalid's statement Ahmed's conclusion Adel's conclusion

No No True False False

No Yes False True False

Yes No True False True

Yes Yes False False False

From the truth table, we can see that Ahmed's conclusion is only true in one case (when the egg is boiled and not dropped), but false in two cases (when the egg is not boiled or when it is dropped). Adel's conclusion is only false in one case (when the egg is boiled and not dropped), but true in two cases (when the egg is not boiled or when it is dropped).

So, neither Ahmed's conclusion nor Adel's conclusion is entirely true or false. Adel's conclusion is closer to being true than Ahmed's conclusion, as it is only false in one case.

Therefore, Neither Ahmed's conclusion nor Adel's conclusion is entirely true or false. Adel's conclusion is closer to being true than Ahmed's conclusion, as it is only false in one case.

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The variance of the error anticipated value should therefore be constant when plotting each individual error against the expected value.

What is regression line?

A regression line is a line that in statistics best depicts the behavior of a set of data. It is, in other words, a line that best fits the trend of the data at hand.

The standard deviation and variance of the residuals are assumed to be constant for all values of independent variables in regression analysis under the concept of constant variance.

The variance of the error anticipated value should therefore be constant when plotting each individual error against the expected value.

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The total number of blue jewelry is 52, whereas the total number of green jewelry is 13.

In algebra, a percentage is really a number any ratio that is presented as a part of 100. Often, the acronyms "percent growth.," "percentage points," and "personal computer" are utilized as well. But it is commonly indicated by the percent sign, "%." The % amount will have no dimensions. Percentages are essentially fractions when the denominator is 100. Can use percent sign (%) to indicate that perhaps a number is a percentages by placing it next to it. For instance, you score a 75% if you properly answer 75 out of 100 respondents on a test (75/100). Divide the payment by the aggregate and multiply the results by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.

given

80 percent of the jewelry in the equation is blue:

80/100 * 65 = 52.

Let the quantity of blue jewelry be x and the number of green jewelry be y.

20% of the jewelry is green, so

20/100 * 65, or 13

The total number of blue jewelry is 52, whereas the total number of green jewelry is 13.

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To mark the bisector of the AB make an arc above and below AB one from the point A and another arc from point B. Hence, option D is the answer.

A line known as a bisector divides an angle or a line into two equally sized segments. A segment's midpoint is always contained in the segment's bisector. Based on the geometric shape that they bisect, there are two different sorts of bisectors.

Bisector of Line Segments (Perpendicular Bisector Theorem)

Bisector of angles (Triangle Bisector Theorem)

To mark the bisector of the AB make an arc above and below AB one from the point A and another arc from point B.

Hence, option D is the answer.

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a) Two vectors are proportional then compa b = compa a

b) Two vectors are parallel when proja b = proja a

A vector is a mathematical object with both magnitude and direction. In this problem, we have two vectors, a and b, which are assumed to be nonzero

(a) For two vectors a and b, the dot product (also known as the scalar product or inner product) is a scalar quantity that measures the extent to which the vectors are pointing in the same direction. The dot product of two vectors is defined as

=> compa b = ||a|| ||b|| cos(θ), where ||a|| and ||b|| are the magnitudes of the vectors and θ is the angle between them.

Hence,

=> compa b = compb a

if and only if the vectors are equal or parallel, meaning they have the same direction or are pointing in opposite directions.

(b) The projection of a vector onto another vector is the vector that points in the same direction as the second vector and has the same magnitude as the component of the first vector that lies in that direction. The projection of a vector a onto a vector b is given by

=> proja b = (compa b / compb b) b.

Since the dot product is commutative, it follows that

=> proja b = proj b

if and only if the vectors are equal.

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The average decrease in temperature of the liquid from 1:00 p.m. to 10:00 p.m. is approximately 0.8°C per hour.

The concept used in this calculation is average rate of change. The average rate of change is the change in a quantity (in this case, temperature) over a certain time period (in this case, 9 hours), expressed as a ratio or per unit of time. In this calculation, we are finding the average decrease in temperature per hour.

To find the average decrease, we need to find the difference between the starting temperature (14.7°C) and the final temperature (-6.8°C), and then divide by the number of hours that passed, which is 9 hours.

Therefore:

(14.7°C - (-6.8°C)) / 9 hours = 21.5°C / 9 hours = 2.39°C per hour

Rounding to the nearest whole number, we have:

2.39°C per hour ≈ 2.4°C per hour = 0.8°C per hour.

So, The average decrease in temperature of the liquid from 1:00 p.m. to 10:00 p.m. is approximately 0.8°C per hour.

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The average rate of change is the idea used in this calculation. The change in a number (in this case, temperature) over a predetermined amount of time (in this case, 9 hours), expressed as a ratio or per unit of time, is known as the average rate of change. We are calculating the average temperature drop per hour in this computation.

We must calculate the difference between the initial temperature (14.7°C) and the final temperature (-6.8°C) and divide it by the number of hours that elapsed, which is 9 hours, to determine the average decrease.

Therefore:

(14.7°C - (-6.8°C)) / 9 hours = 21.5°C / 9 hours = 2.39°C per hour

Rounding to the nearest whole number, we have:

2.39°C per hour ≈ 2.4°C per hour = 0.8°C per hour.

The value of area of a rectangular garden is, (8x² + 42x + 55).

The perimeter of the garden is, (12x + 32).

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

The side lengths of a rectangular garden are,

⇒ (4x + 11) and (2x + 5)

Now, We know that;

Area of rectangle = Length × Width

Thus, The value of area of a rectangular garden is,

⇒ Area = (4x + 11) × (2x + 5)

           = (8x² + 20x + 22x + 55)

           = (8x² + 42x + 55)

And, The perimeter of rectangle = 2 (Length + Width)

Thus, The perimeter of the garden is,

⇒ Perimeter = 2 (4x + 11 + 2x + 5)

                    = 2 (6x + 16)

                    = (12x + 32)

Thus, The value of area of a rectangular garden is, (8x² + 42x + 55).

And, The perimeter of the garden is, (12x + 32).

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To find the height of a right cone if we are given the diameter and the slant:

The characteristics of cones include:

The properties of cones, including:

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Answer:

Yes

Step-by-step explanation:

Yes, because 6.9 > 0.95

Answer:

Yes

Step-by-step explanation:

Yes....about 7 times faster because   6.9 >> .95 meters

The height of the kite is equal to 9.19 feet.

In Mathematics, the law of sines is sometimes referred to as sine rule and it can be modeled by this mathematical expression:

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex] or Sinθ = opposite/hypotenuse

Since the reference angle lies between the ground and the string of the kite  (hypotenuse), the side opposite the reference angle would be denoted by x and calculated as follows;

Sinθ = opposite/hypotenuse

Sin(50) = x/12

x = 12 × sin(50)

x = 12 × 0.7660

x = 9.19 feet.

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F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using fibonacci numbers definition is proved.

What is a Fibonacci  sequence ?

The Fibonacci sequence is a number sequence in which each subsequent number is formed by adding the two numbers that came before it. The series is named after the Italian mathematician who devised it.

Fibonacci numbers are defined as follows:

F(0) = 0

F(1) = 1

F(n) = F(n-1) + F(n-2) for n ≥ 2

Now, let's prove that F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using this definition:

F(n + 1) = F(n) + F(n - 1) (by definition)

F(n – 2) = F(n - 3) + F(n - 4) (by definition)

Adding these two equations, we get:

F(n + 1) + F(n – 2) = F(n) + F(n - 1) + F(n - 3) + F(n - 4)

Now, using the definition of F(n) = F(n-1) + F(n-2), we can substitute F(n-1) + F(n-2) for F(n):

F(n + 1) + F(n – 2) = F(n) + F(n) = 2F(n)

Therefore, F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3, which is the desired result.

Hence, F(n + 1) + F(n – 2) = 2F(n) for n ≥ 3 using fibonacci numbers definition is proved.

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Answer:3

Step-by-step explanation: the closest multiple of for is 16 then reminder 3

Answer:

9

Step-by-step explanation:

one side of a triangle =x

the other two sides measure = (x-4) each

perimeter = 19

therefore :

perimeter of a triangle = x + (x-4) + (x-4)

I.e = x+x+x-4-4=19

= 3x -8=19

= 3x = 19+8

3x=27

divide both sides by 3

x=9

3.17 is the meaning of the x - value when y = 81. This equation can be solved using the concept of equation solving.

A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Graphs and mathematical equations of the type y = mx + b can both be used to represent linear connections. The quantity of hours worked in relation to income is an illustration of a linear connection. The independent variable would be the number of hours worked, and the dependent variable would be the amount of money made.

Linear relationship can be represented by the equation y = 62 + 6x where y represents the expected quiz score and x represents hours spent on homework that week.

when y = 81, then: y = 62 + 6x

or, 81 = 62 + 6x

or, 6x = 19

or, x = 3.17

3.17 is the meaning of the x - value when y = 81.

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The derivative of the expression is y' = [tex]-\frac{-y}{x}[/tex].

What is derivative?

Differentiation refers to the method of determining the derivative. Anti-differentiation is the term for the opposite process. We'll calculate the derivative of the function y = f. (x). It represents the rate at which the value of y varies in relation to the change in the variable x. It is referred to as the "f" derivative with regard to the variable x.

Here the given expression is [tex]x^2y^2=10[/tex] then

=> f(x,y) = [tex]x^2y^2-10[/tex]

To find [tex]\frac{dy}{dx}[/tex] by using the formula [tex]\frac{dy}dx}=-\frac{f_x}{f_y}[/tex] and first find [tex]f_x , f_y[/tex]

Now ,

=> [tex]f_x =\frac{d}{dx}x^2y^2-10[/tex]

=> [tex]f_x=2xy^2[/tex]

Now,

=> [tex]f_y=\frac{d}{dy}x^2y^2-10[/tex]

=> [tex]f_y=2x^2y[/tex]

Now substitute into formula then

=> [tex]y' = -\frac{2xy^2}{2x^2y}[/tex]

=> y' = [tex]-\frac{-y}{x}[/tex]

Hence the derivative of the expression is y' = [tex]-\frac{-y}{x}[/tex].

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The approximate amount of granola that can be held in the container is B. 5,464 cm³.

The amount of granola held in the container can be calculated by finding the volume of cylinder. The formula to be used for volume calculation is -

V = πr²h, where V is volume of cylinder r is radius and h refers to height of cylinder.

Radius = diameter/2

Radius = 20/2

Radius = 10 cm

V = 22/7 × 10² × 17.4

Performing multiplication on Right Hand Side of the equation

V = 5464 cm³

Thus, the volume of the cylinder is 5464 cm³.

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