Tim+is+attempting+to+bike+a+12+mike+race+he+knows+at+every+third+of+the+race+he+will+need+to+take+a+break+to+stretch+his+leg+how+many+miles+wo

The volume of the solid generated by revolving about the line y=-1 is 324π cubic units and the volume of the solid generated by revolving about the line y=-2 is 216π cubic units.

To find the volume of the solid generated by revolving the region bounded by the parabola y=-(x^2)/9 and the lines y=-1 about a line, we can use the method of cylindrical shells.

a) The line y=-1 is the axis of revolution, so the volume of the solid generated by revolving the region about this line is:

V = ∫[(-1-(x^2)/9)^2 - (-1)^2] * 2πx dx

where the integral is taken over the interval for which the parabola y=-(x^2)/9 is above the line y=-1. So the limits of the integral are from -3 to 3, the volume is:

V = ∫[(-1-(x^2)/9)^2 - (-1)^2] * 2πx dx from -3 to 3 = 324*π cubic units

b) The line y=-2 is the axis of revolution, so the volume of the solid generated by revolving the region about this line is:

V = ∫[(-2-(x^2)/9)^2 - (-2)^2] * 2πx dx

where the integral is taken over the interval for which the parabola y=-(x^2)/9 is above the line y=-2. So the limits of the integral are from -3 to -sqrt(92) = -3 to -3sqrt(2) and 3*sqrt(2) to 3 , the volume is:

V = ∫[(-2-(x^2)/9)^2 - (-2)^2] * 2πx dx from -3 to -3sqrt(2) + ∫[(-2-(x^2)/9)^2 - (-2)^2] * 2πx dx from 3sqrt(2) to 3 = 216*π cubic units

c) The line y=1 is not on the same side of the parabola y=-(x^2)/9 as the region bounded by the parabola and the lines y=-1 so there is no solid generated by revolving about this line.

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a. The value of k from augmented matrix [tex]\left(\begin{array}{ccc}3&- 5&k\\- 9&15&3\end{array}\right)[/tex] is - 1.

b. The value of k from augmented matrix [tex]\left(\begin{array}{ccc}k&1&- 6\\5&- 1&6\end{array}\right)[/tex] is - 5.

The complete question is in the attachment. The augmented matrix is a consistent linear system if

a. The augmented matrix [tex]\left(\begin{array}{ccc}3&- 5&k\\- 9&15&3\end{array}\right)[/tex]

Making the second row become zero R₂ = R₂ + 3R₁

[tex]\left(\begin{array}{ccc}3&- 5&k\\- 9 \:+\: (3 \times 3)&15 \:+\: (3 \times - 5)&3 \:+\: (3 \times k)\end{array}\right)[/tex]

[tex]\left(\begin{array}{ccc}3&- 5&k\\- 9 \:+\: 9&15 \:+\: (- 15)&3 \:+\: 3k\end{array}\right)[/tex]

[tex]\left(\begin{array}{ccc}3&- 5&k\\0&0&3 \:+\: 3k\end{array}\right)[/tex]

From the second row

0x + 0y = 3 + 3k

For the system to be consistent, then

3 + 3k = 0

3k = - 3

k = - 3/3

k = - 1

b. The augmented matrix [tex]\left(\begin{array}{ccc}k&1&- 6\\5&- 1&6\end{array}\right)[/tex]

Making the second row become zero R₂ = R₂ + R₁

[tex]\left(\begin{array}{ccc}k&1&- 6\\5 \:+\: k&- 1 \:+\: 1&6 \:+\: (- 6)\end{array}\right)[/tex]

[tex]\left(\begin{array}{ccc}k&1&- 6\\k \:+\: 5&0&0\end{array}\right)[/tex]

From the second row

(k + 5)x + 0y = 0

For the system to be consistent, then

k + 5 = 0

k = - 5

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Answer:

Step-by-step explanation:oc (6,5), (3,2), (2,4) (6, 3), (1, 0)

Answer:  Option (E)

4,  4√3

===========================================================

Reason:

The hypotenuse is 8. Half of that is 8/2 = 4, which is the value of "s".

This is the short leg of the right triangle. The short leg is opposite the 30 degree angle. Smallest side opposite the smallest angle.

Then use this 30-60-90 triangle template formula

[tex]\text{long leg} = (\text{short leg})*\sqrt{3}\\\\\text{long leg} = 4\sqrt{3}\\\\[/tex]

For any k ∈ (-∞, o), function f is strictly decreasing on the interval (-1, 1).

In mathematics, a function is a relationship or mapping between two sets of elements, known as the domain and the codomain, that assigns each element from the domain to a unique element in the codomain. It describes how inputs from the domain are transformed or related to corresponding outputs in the codomain.

The given function is f = [tex]\frac{kx}{x^2+1}[/tex] ...(1),

Differentiate (1) w.r.t. x,

[tex]\dfrac{d}{dx}f = \dfrac{d}{dx}\frac{kx}{x^2+1}[/tex]

f' = [tex]k\frac{1-x^2}{(x^2 + 1)^2}[/tex]

Since f is decreasing on (-1, 1),

therefore

f' < 0 on (-1, 1),

[tex]k\frac{1-x^2}{(x^2 + 1)^2}[/tex] < 0 on (-1, 1).

As [tex]\frac{1-x^2}{(x^2 + 1)^2}[/tex] > 0 on (-1, 1),

k < 0 for f' < 0.

Therefore, k ∈ (-∞, o) for f to be strictly decreasing on (-1, 1).

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The complete question is as follows:

Let f be the function given by [tex]\frac{kx}{x^2+1}[/tex], where k is a constant. For what values of k, if any, is f strictly decreasing on the interval (-1, 1)?

Answer:

10/10/10

Step-by-step explanation:

Answer: 7/12 can't be simplified anymore. Have a nice day ;)

Answer:

The equation Jared can use to find the rate at which he drove is:

rate (r) = distance (d) / time (t)

So in this case, Jared can plug in the values he knows into the equation:

r = 15 miles / 0.5 hours

Solving for r, he can find the rate at which he drove:

r = 30 miles per hour.

So Jared drove at a rate of 30 miles per hour.

Step-by-step explanation:

PLEASE GIVE BRAINLIEST

A function is a rule that generates one unique output value for every specified input value. Therefore, the fourth statement is true.

In mathematics, the function is something that relates an input to an output. The output obtained will somehow be related to the input. We write the function as f(x). For example, consider f(x) = x². This means that the function f takes the value of x and squares this value. Like when we input x=4. Then the output is f(x)=4²=16.

So, here see the function assigns a single and a unique output value of 16 for the input value of 4. Therefore, option 4 is correct. That is function gives every input value a unique, separate output value.

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The associative property shows that the value of 8/9 / 7/5 x 3/16 is 5/24.

The associative property states that the way in which we group the numbers or variables in an arithmetic operation does not affect the result. In other words, we can change the grouping of the numbers or variables by using parentheses without changing the outcome of the calculation.

In this problem, we can use the associative property to group the fractions in a way that makes it easier to simplify.

= 8/9 ÷ 7/5 x 3/16

= (8/9) ÷ (7/5) x 3/16

= 8/9 x 5/7 x 3/16

= 8/9 x 15/112

= 120/1008

= 5 / 24

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Answer:  To find the mean test score, we need to calculate the sum of the product of each score and its corresponding frequency, and divide it by the total number of students.

To estimate the mean mathematics test score, we can use the midpoint of each data class as the value for each score and multiply it by the corresponding frequency.

For the first class, 550 to 599, the midpoint is (550+599)/2 = 574.5

For the second class, 600 to 649, the midpoint is (600+649)/2 = 624.5

For the third class, 650 to 699, the midpoint is (650+699)/2 = 674.5

For the fourth class, 700 to 749, the midpoint is (700+749)/2 = 724.5

For the fifth class, 750 to 799, the midpoint is (750+799)/2 = 774.5

The mean test score is:

(5574.5 + 11624.5 + 14674.5 + 12724.5 + 7*774.5) / 49 = 669.3

Therefore, the estimate of the mean mathematics test score for the students in the study is 669.3.

Step-by-step explanation:

The migration matrix that has been found is

                [0.98033     0.00179

                 0.01967      0.99821 ]       by matrix method.

The 2012 populations of California and the US minus California are 38,041,430 and 275,872,610, respectively, according to the exercise statement. Let's represent these quantities by the variables c and u. What we want are two vectors m1 and m2 such that

cm 1+um 2 ​=     [ 2013 population of California

                       2013 population of US minus California ]

m1 = [ 0.98033   0.01967 ]      and    m2 = [ 0.00179   0.99821]

Now that we have the two vectors for equation ,we use the fact that a vector equation of the form

                             au + bv = w

is equivalent to a matrix equation of the form  

                              [ u  v ] [a b] = w

to get our migration matrix for this system.

[0.98033     0.00179

0.01967      0.99821 ]

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The complete question is :

In 2012 the population of California was 38,041,430, and the population living in the United States but outside California was 275,872,610. During the year, it is estimated that 748,252 persons moved from California to elsewhere in the United States, while 493,641 persons moved to California from elsewhere in the United States. Set up the migration matrix for this situation, using five decimal places for the migration rates into and out of California. Let your work show how you produced the migration matrix.

​

Answer:

Option A) [tex]132ft[/tex]

Step-by-step explanation:

It is given that,

Radius of a circle = 21ft

We know that π = [tex]\frac{22}{7}[/tex]

So the circumference of a circle = 2πr

Substituting the values,

= [tex]2X\frac{22}{7} X 21[/tex]

So we get,

[tex]= 2X22X3[/tex]

[tex]= 132ft[/tex]

The required circumference of the circle is 132 feet.  Option A is correct.

To find the circumference of a circle, we use the formula C = πd, where C is the circumference, π is the mathematical constant pi (approximately equal to 3.14), and d is the diameter of the circle.

Here,
The circumference of a circle with a radius of 21 feet can be found using the formula:

C = 2πr

where "C" is the circumference, "r" is the radius, and "π" is the mathematical constant pi, which is approximately equal to 22/7.

Substituting the values given, we have:

C = 2 x (22/7) x 21

C = 132 feet

Therefore, the circumference of the circle is 132 feet. Answer: 132 feet.

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The line represents 1 foot, so 4 feet would require a line that is 4 times as long as the 1/4 inch line, which is 1 inch.

The formula for finding the length of a line to represent a certain number of feet is L = (1/4)*F, where L is the length of the line, and F is the number of feet. In this case, to find the length of a line to represent 4 feet, the calculation would be L = (1/4)*4 = 1. Therefore, the line would need to be 1 inch long to represent 4 feet. This is because 1/4 inch of the line represents 1 foot, so 4 feet would require a line that is 4 times as long as the 1/4 inch line, which is 1 inch.Therefore, to represent a length of 4 feet on the same drawing, a line 1 inch long needs to be drawn. The calculation is as follows: 1/4 inch line = 1 foot, therefore 4/4 inch line = 4 feet. Therefore, 1 inch line = 4 feet.

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Answer: According to Mars, the makers of M&Ms, their factory produces 25% blue, 25% orange, and 12.5% for each of the remaining colors, which are yellow, green, brown, and red.

The observed values based on the entire lasso are 25 blue, 25 orange, 12.5 yellow, 12.5 green, 12.5 brown, and 12.5 red. These values match the expected values according to the manufacturer, which is 25% blue, 25% orange, and 12.5% for each of the remaining colors.

So, the observed values based on the entire lasso compare to the expected values from the manufacturer. The proportion of colors in the observed sample is the same as the proportion of colors that the factory produces, meaning that the factory is producing the expected ratio of colors.

Step-by-step explanation:

The length in yards, of the carpet needed for this room is 128 yards.

length of the room = 32 ft

breadth of the room = 27 ft

so we find area now,

area = length X breadth

area = 32 X 27

area = 864ft^2

The width of the carpet in feet is = 2.25ft

so , to find the length of the carpet needed, you must apply the formula for calculate the area of a rectangle and solve for the length, as following,

area = length X width

864 = length X 2.25

length = 864/ 2.25

length = 384ft

length = 128yards

so the length, in yards, of the carpet needed for this room is 128 yards.

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The accurate of the function is calculated using the fomula O(n).

Function in math is known as an equation that has only one answer for y for every x and it assigns exactly one output to each input of a specified type.

Here we have given that maximum distance is less than 10%.

As we all know that the basic approach is to check only consecutive pairs of x and y.

Here we have given that for every element x or y, then we have to check the index of the previous occurrence of x or y and if the previous occurring element is not similar to current element update the minimum distance.

Here we have a question arises what if an x is preceded by another x and that is preceded by a y for that situation we have to know how to get the minimum distance between pairs.

Hereby analyzing closely it can be seen that every x followed by a y or vice versa can only be the closest pair so ignore all other pairs.

Complete question:

Write the function to calculate the accuracy? show that maximum distance is less than 10%.

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The measure of the length HL will be 18.5 units for the given figure.

One of the earliest areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

Given that in the quadrilateral the two sides are Jk = 12 and GF = 25. The value of HL can be calculated by the theorem,

HL = ( 1 / 2 ) x GF x JK

HL = ( 1 / 2 ) x 25 x 12

HL = 18.5

Therefore, the length of section HL will be 18.5 units.

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The company, under the new president, is most likely, earning a profit of $ 10, 000 per month.

When a person is said to have done a 180, it means that they are now doing the opposite of what they used to do. For example, a person who was eating only fast foods doing a 180 would end up eating only healthy food.

This means that the new president doing a 180, means that the company is doing the opposite of what they were doing and instead of making losses of $ 10, 000 monthly, they are making profits of $ 10, 000 every month.

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The dimensional analysis conversion of 100 inch to feet is 8.33 feet.

Dimensional analysis is the study of the relationships between different physical quantities in engineering and science by identifying their base quantities and units of measurement and tracking these dimensions as calculations or comparisons are performed. when there is insufficient information to set up precise equations, a method of analysis in which physical quantities are expressed in terms of their fundamental dimensions. Dimensional Analysis (also known as the Factor-Label Method or the Unit Factor Method) is a problem-solving strategy that takes advantage of the fact that any number or expression can be multiplied by one without changing its value.

Here,

100 inch to feet,

=100/12

=8.33 feet

The conversion of 100 inch to feet using dimensional analysis is 8.33 feet.

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The area of the circle is πr², where r is the radius. The area of the shaded region is half the area of the circle.

The area of the circle is πr², where r is the radius. The area of the shaded region is half the area of the circle.

Therefore, Area of the shaded region = πr²/2

Given that minor arc AD measures 2π, the radius of the circle is 2.

Therefore, Area of the shaded region = π(2)²/2 = 4π = 72

The area of the shaded region is half the area of the circle, which is πr²/2. The minor arc AD measures 2π, so the radius of the circle is 2, and the area of the shaded region is 4π, or 72.

The area of the circle is πr², where r is the radius. The area of the shaded region is half the area of the circle.

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Answer: 1

Step-by-step explanation:

1 + 0 = 1

Answer: When a polynomial is divided by x-1, the quotient is of the form of ax^2 + bx + c and the remainder is of the form of r. The quotient and the remainder are related by the formula:

f(x) = (x-1)(ax^2 + bx + c) + r

Given that the quotient is 1x^2+x-8 and the remainder is -2, we can substitute these into the above equation:

f(x) = (x-1)(1x^2+x-8) + (-2)

f(x) = x^3 - 9x^2 + (1-8)x +(-2)

f(x) = x^3 - 9x^2 - 7x - 2

Therefore the function f(x) is x^3 - 9x^2 - 7x - 2 in standard form.

Step-by-step explanation:

The value of P(x < 1) is 0.5.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Mean = 1

Standard deviation = 0.05

The P-value of Z when x = 1.

z = (x - mean) / standard deviation

z = (1 - 1)/0.05

z = 0

The P-value when z = 0 is 0.5.

So,

P(x < 1) = 0.5

Thus,

P(x < 1) is 0.5.

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The coordinates of X are (-6.4, 5.75)

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

A = (-10,7)

B = (8,-5).

m : n = 1 : 4

The coordinate is then calculated as

X = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

X = 1/5 * (1 * 8 + 4 * -10, 1 * -5 + 4 * 7)

Evaluate

X = (-6.4, 5.75)

Hence, the coordinate is (-6.4, 5.75)

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Complete question

given directed line segment ab determine point x on the graph such that x partitions the segment from a(-10,7) to b(8,-5) in the ratio 1:4 and give it's coordinates

Answer: 38 toys

If each of the smaller boxes has 10 toys, and Martin's mom added 28 more toys into only one of the boxes, that box would have a total of 38 toys.

10 + 28 = 38 toys

Answer:

Step-by-step explanation:

1/3 is 2/6

2/6 + 1/6 = 3/6

3/6 = 1/2

answer 1/2 or half

Answer:

It is 1/2

Step-by-step explanation:

You make 1/3 the same denominator so it becomes 2/6.

2/6+1/6=3/6

Now when you simplify this you get 1/2.

The estimate of the total number of computers that needed repairing last year in Point City is given as follows:

Between 132,000 and 328,000 computers.

The estimate is obtained applying the proportions in the context of this problem.

The confidence interval is given as follows:

1.15 plus/minus 0.49.

Hence the bounds of the interval are given as follows:

Hence, out of 200,000 households, the lower bound of the estimate is given as follows:

0.66 x 200,000 = 132,000.

The upper bound is of:

1.64 x 200,000 = 328,000.

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The simplification of the trigonometric function tan x csc x is;  sec x

The six trigonometric functions are defined as;

sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Now, we know that;

cot x = cos x/sin x

sec x = 1/cos x = (cos x)⁻¹

csc x = 1/sin x = (sin x)⁻¹

tan x = sin x/cos x

Thus;

tan x csc x = (sin x/cos x) * (1/sin x)

= 1/cos x = (cos x)⁻¹

= sec x

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