To find the average speed of an object, we find the change in distance divided by the time over which that change occurs. For the instantaneous speed, we must make the time interval very _______, so that the speed does not change appreciably.

The radius of the inner and outer circles is 5 miles and 10 miles. Then the area of the shaded region will be 235.5 square miles.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

Both circles have the same center. The circumference of the inner circle is 31.4 miles. Then the radius of the inner circle is given as,

2πr = C

2 x 3.14 x r = 31.4

r = 5 miles

Then the ratio of the outer circle to the inner circle is 2. Then the radius of the outer circle is given as,

R/r = 2

R / 5 = 2

R = 10 miles

The area of the shaded region is given as,

A = πR² - πr²

A = 3.14 x 10² - 3.14 x 5²

A = 3.14 x (100 - 25)

A = 3.14 x 75

A = 235.50 square miles

The area is 235.50 square miles.

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After dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.

When two figures are congruent, it means they have the same shape and size, whereby, all pairs of corresponding angles and sides of both figures are congruent or equal in measure.

The image attached below shows a dilated figure.

Dilation is a transformation that enlarges a figure or reduces the figure.

After dilation, the new figure maintains the same shape of the original figure.

However, after dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.

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The probability of getting at least 1 red is 6/7

Probability is the likelihood of a desired event happening.

Theoretical probability is the theory behind probability. To find the probability of an event, an experiment is not required. Instead, we should know about the situation to find the probability of an event occurring.

The probability that the first is blue and the second is blue

p(First blue, Second blue) = 3/7 × 2/6 = 1/7

Thus, the probability of getting at least 1 red, is the complement of getting both blue

That is, P(At least 1 red) = P'(both blue) = 1 - P(Both blue) = 1 - 1/7 = 6/7

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The volume of the composite figure is equal to 3425.333 cubic feet.

In this problem we need to determine the volume of a composite figure, that is, the sum of the volumes of a right prism and a pyramid, whose formulae are described below:

Right prism

V = 0.5 · w · l · h

Pyramid

V = (1 / 3) · (0.5 · w · l) · h

Where:

Now we proceed to determine the volume of the composite figure:

V = 0.5 · (8 ft) · (7 ft) · (12 ft) + (1 / 3) · 0.5 · (8 ft) · (7 ft) · (7 ft)

V = 3425.333 ft³

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The zeros of f(x) are:

Here we have the polynomial:

f(x) = 6*(x - 9)*(x - 7)*(x + 13)^2*(x + 5)^3

In each factor of the form:

(x - k)^n

the zero is x = k

and the multiplicity is n.

Then:

The zeros x = 9 and x = 7 have multiplicity 1.

The zero x = .13 has multiplicity 2.

The zero x = -5 has multiplicity 3.

These are the zeros of the polynomial.

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Answer:

Step-by-step explanation:

The formula to calculate the future value of an investment with compound interest is:

FV = PV * (1 + (r/n))^(n*t)

Where:

PV is the present value (the initial investment)

r is the annual interest rate

n is the number of compounding periods per year

t is the number of years

For Investment A:

PV = $4,000

r = 6% = 0.06

n = 2 (semiannual compounding)

t = 5 years

FV = $4,000 * (1 + (0.06/2))^(2*5) = $4,000 * (1.03)^10

FV = $4,000 * 1.664131669 = $6,656.53

So, the total amount of Investment A is $6,656.53 (rounded to the nearest cent).

Answer:

1st question:

10°, 80°, 90°

2nd question:

76°, 52°, 52°

Step-by-step explanation:

For both of these questions we will use the idea that the three angles of a triangle add up to 180°.

In the triangle on the left, two angles are marked and the third is a right angle. The tiny square marking on the third angle means it is a right angle, so it is 90°.

We can write an equation.

x + 8x + 90° = 180°

combine like terms

9x + 90 = 180

subtract 90

9x = 90

divide by 9

x = 10

So the angles are x, 8x and 90°

Since x = 10

the 3 angles are 10°, 80° and 90°

For the second question, two sides are marked to show they are congruent (same, equal) that means the two angles on the base (base angles) are congruent (the same)

One angle is 3x+1 and both the other two angles are 2x+2. Write an equation.

3x+1 + 2x+2 + 2x+2 = 180°

combine like terms

7x + 5 = 180

subtract 5

7x = 175

divide by 7

x = 25

Calculate the angle measures using x = 25

3x+1 = 3(25)+1 = 76°

2x+2 = 2(25)+2 = 52°

The 3 angles of the triangle are 76°, 52° and 52°

Answer:

5 x 10^9

Step-by-step explanation:

= ( 5x1) X (10^(6+3) ) = 5 x 10^9

Answer:

12 1/30

Step-by-step explanation:

Sum is the term used for the total amount of something when two or more numbers are added.

In order to add the two fractions, they must have the same denominator.

To do this, we need to find a common denominator.

Multiples of 3:  3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 10:  10, 20, 30

Both 3 and 10 have 30 in common, so this is the common denominator.

In order to get to 30, 3 must be multiplied by 10.  Whatever you do to the bottom must be done to the top and vice versa.

7 1/3 becomes 7 10/30.

4 7/10 becomes 4 21/30

Now, we add the whole numbers.

7 + 4 = 11

Now, add the fractions.

10/30 + 21/30 = 31/30

Put it all together.

11 31/30

This is an improper fraction, so we must make it a proper fraction.  To do this, we divide 30 into 31.  It can only go in evenly one time and has a remainder of one.  The remainder is added to the whole numbers and the numerator of the fraction takes the evenly divided one.

11 + 1 1/30  This is adding the remainder to the whole number.

12 1/30  This is the result of adding the remainder and fixing the fraction.

12 1/30 is the answer.

The simplification of the  algebraic expression gives:

(5m² + 3mn - 3n²) - (m² - n²) = 4m² + 3mn - 2n²

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

(5m² + 3mn - 3n²) - (m² - n²) = 5m² + 3mn - 3n² - m² + n²

                                              = 5m²- m² + 3mn - 3n²+ n²

                                              = 4m² + 3mn - 2n²

Therefore, (5m² + 3mn - 3n²) - (m² - n²) simplifies to 4m² + 3mn - 2n²

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The least squares regression line for the corrected data would be shifted upwards compared to the original data, indicating that increasing the amount of time spent studying would likely have a greater impact on a student's grades.

The least squares regression line for the corrected data would be shifted upwards compared to the least squares regression line for the original data, since the corrected data point has a higher value than the original data point. This shift in the regression line would indicate that, in general, increasing the amount of time spent studying would have a greater impact on the student's grades than the original data indicated.

The least squares regression line for the corrected data would be shifted upwards compared to the original data, indicating that increasing the amount of time spent studying would likely have a greater impact on a student's grades.

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Answer: 24 Daisies

Step-by-step explanation:

14 flowers are normal and the other 8 are daisies, there are currently 22 flowers.

To fill 66 plots, she'd need to plant 3 times as many flowers as there are now, so there'd be 14*3 non daisies and 8*3 daisies. 8*3 = 24.

Answer:

24

Step-by-step explanation:

[tex]\frac{daisies}{total flowers}[/tex] = [tex]\frac{daisies}{total flowers\\}[/tex]

[tex]\frac{8}{22}[/tex] = [tex]\frac{d}{66}[/tex]

22 x 3 = 66

8 x 3 = 24

Answer:

I can if you post the question...

Step-by-step explanation:

Answer: 0.5 inches of rain per hour or 0.5/1

Step-by-step explanation:

divide 3/6 gets you 0.5

Answer: The best estimate for 2/5 hour is 1/2 hour and the best estimate for 5/8 hour is 1/2 hour. So, the total time spent would be 1/2 hour + 1/2 hour = 1 hour.

Therefore, the best estimate for the total time Maria spent with her little sister is 1 hour.

Step-by-step explanation:

The function that models the mass of the carbon-14 sample remaining {t} years since the initial measurement is → M{t} = 960 - 0.012t.

Given is that Carbon-14 is an element which loses (1/10) of its mass every 871 years. The initial mass of a sample of Carbon-14 is 960 grams. The mass of a sample of carbon-14 can be modeled by a function {M} which depends on its age {t} (in years).

(1/10) x 96 = 96/10 = 9.6 grams.

Carbon - 14 looses 9.6 grams in 871 years.

In 1 year, Carbon - 14 will loose (9.6/871) = 0.012 gram.

We can write the function {M} as -

M{t} = 960 - 0.012t

Therefore, the function that models the mass of the carbon-14 sample remaining {t} years since the initial measurement is → M{t} = 960 - 0.012t.

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The expression is equivalent to the given polynomial expression is

-7[tex]m^4[/tex]n + 18mn - 8m².

In particular, an expression must not contain any square roots of variables, any fractional or negative powers on the variables, and any variables in any fractions' denominators in order to qualify as a polynomial term.

These are trinomials, binomials, and monomials. A polynomial can be categorised into 4 categories based on its degree. The four are the cubic polynomial, linear polynomial, and polynomial of zero.

From all the options the equivalent polynomial expression as

-7[tex]m^4[/tex]n + 18mn - 8m²

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The Question attached here is incomplete, the complete question is

Which expression is equivalent to the given polynomial expression?

(9mn – 19m4n)19m4n) - (8m2 + 12m4n + 9mn)

A.-7mtn + 8m2

B.-7m4n + 18mn - 8m2

C.-31m 4n – 8m2

D.-31m 4n + 18mn

8m2

The total monthly payments is  $2169.49

You should understand that a mortgage is a home loan that is secured by the property the borrower finances with the loan funds.

The mortgage payment is

 A = (210,000·0.95)(0.045/12)/(1 -(1 +0.045/12)^(-12·15)) ≈ 1526.16

The monthly set-aside for taxes is

 3.5%*200,000/12 = 583.33

The monthly set-aside for insurance is

 720/12 = 60

So the total of P&I + taxes + insurance will be

In conclusion, the monthly payment is given by :

 $1526.16 +583.33 +60.00 = $2169.49

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Answer: I'm sorry, but the statement "the answer to the meaning of life that is squared by two" is not a coherent or meaningful concept. The meaning of life is a philosophical question that has been debated by scholars, theologians, and thinkers throughout history and has no single, universally agreed-upon answer. Additionally, squaring by two does not have any inherent relationship to the meaning of life.

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be it shares an angle with triangle DEF that is equal in measure to angle F.

If a triangle has four quadrants or more, it is referred to as a polygon. It has a straightforward rectangular shape. The letters ABC when combined form a right-angled triangular. A new parallelogram with rectangular shape corners is created by Euclidean geometry when the limits are incompatible. Due to their three edges but also three points, triangles are categorised as polygons. The location of a triangle's corners is determined by where its three edges meet. The sum of the angles on the inside of a trapezoid is 180.

Here,

Part A: To determine if triangle DEF is similar to triangle DBC, we need to check if their corresponding angles are equal in measure and if their corresponding sides are proportional. If both conditions are satisfied, the triangles are similar. Since BC is parallel to EF, we know that angle DBC and angle DEF are corresponding angles and are therefore equal in measure.

Part B: The line segment on triangle DBC that corresponds to line segment EF is the side opposite to angle DBC, which is segment DC. This is because segment DC is parallel to segment EF and shares an angle with triangle DEF that is equal in measure to angle DBC.

Part C: The corresponding angle to angle F in triangle DBC is angle BCD. This is because angle BCD is opposite to side BC, which is parallel to EF and shares an angle with triangle DEF that is equal in measure to angle F.

Therefore , the solution of the given problem of triangle comes out to be it shares an angle with triangle DEF that is equal in measure to angle F.

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Answer:

Infinity divided by infinity is undefined because infinity is not a number and cannot be treated as one in mathematical operations. In mathematics, division is a process that involves finding the ratio between two numbers. However, infinity is not a number and has no finite value, so it cannot be used as the denominator or numerator in a division operation.

When dividing infinity by infinity, you are asking for the ratio of two quantities that are both infinite, and the result is not well-defined. The concept of infinity can be useful in certain mathematical contexts, such as limits and calculus, but it cannot be used as a number in the usual sense.

In mathematical terms, the expression infinity divided by infinity is considered indeterminate and has no defined value. This is why it is undefined in mathematical analysis.

Step-by-step explanation:

We have the differential equation, [tex]y''+5y'+4y=2e^{-2x}[/tex]. The question asks to find the particular solution to the DE.

To find the particular solution look at the right-hand-side and make a “guess” of what the solution could be.

Since we have [tex]2e^{-2x}[/tex] we can guess that the particular solution could be in the form [tex]Ae^{-2x}[/tex], where [tex]A[/tex] is some unknown constant.

Now finding the value of the unknown constant, [tex]A[/tex]. Lets say [tex]g(x)=Ae^{-2x}[/tex], find [tex]g'(x)[/tex] and [tex]g''(x)[/tex].

[tex]g(x)=Ae^{-2x}[/tex]

=> [tex]g'(x)=-2Ae^{-2x}[/tex]

=> [tex]g''(x)=4Ae^{-2x}[/tex]

Now plug [tex]g(x)[/tex], [tex]g'(x)\\[/tex], and [tex]g''(x)[/tex] into the given differential equation.

=> [tex]y''+5y'+4y=2e^{-2x}[/tex]

=> [tex](4Ae^{-2x})+5(-2Ae^{-2x})+4(Ae^{-2x})=2e^{-2x}[/tex]

=> [tex]4Ae^{-2x}-10Ae^{-2x}+4Ae^{-2x}=2e^{-2x}[/tex]

=> [tex]8Ae^{-2x}-10Ae^{-2x}=2e^{-2x}[/tex]

=> [tex]-2Ae^{-2x}=2e^{-2x}[/tex]

Compare the coefficients,

=>[tex]-2A=2[/tex]

=>[tex]A=-1[/tex]

So we can say our "guess" to the particular solution of the given differential equation is, [tex]y_{p} =-e^{-2x}[/tex].

Answer: To find the distance between Earth and the star in miles, we need to multiply the number of light-years by the number of miles in a light-year.

33.7 light-years * 6,000,000,000,000 miles/light-year = 2.022 x 10^17 miles

So, the distance between Earth and the star is approximately 2.022 x 10^17 miles, written in scientific notation.

Step-by-step explanation:

A possible vector function that represents the curve of intersection of the two surfaces is r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))

The cylinder x^2 + y^2 = 25 represents the set of points in 3D space where the distance from the origin to the point (x, y, z) is equal to 5. The surface z = xy represents the set of points in 3D space where the height of the point (x, y, z) is equal to its x-y coordinate.

The curve of intersection of the two surfaces is given by the set of points in 3D space that are simultaneously on the cylinder and on the surface z = xy. This means that for any point on the curve of intersection, the distance from the origin to the point must be equal to 5, and the height of the point must be equal to its x-y coordinate.

We can find a vector function that represents the curve of intersection by parameterising the points on the curve in terms of a scalar parameter t. For example, a possible parameterization of the curve of intersection is:

r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))

where t is a scalar parameter that ranges over all values between 0 and 2π. The values of x, y, and z are given by 5 cos(t), 5 sin(t), and 5 cos(t) sin(t), respectively, and represent a point on the curve of intersection for each value of t.

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The equation of line M is given by y = 3x + 6 , where the slope is m = 3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

x + 3y = 18   be equation (1)

when x = 0 , y = 6

So , one point is P ( 0 , 6 )

Now , the line L has the points A , E and B

where ABCD is a rectangle , so AD is perpendicular to the line L

So , the product of slopes of the perpendicular line will be = -1

On simplifying the equation (1) , we get

Subtracting x on both sides of the equation , we get

3y = -x + 18

Divide by 3 on both sides of the equation , we get

y = -( 1/3 )x + 6

Substituting the values in the equation , we get

Slope of line L x Slope if line M = -1

The slope of line L = -1/3

So , the slope of line M = 3

Now , the equation of line L is given by

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 6 = 3 ( x - 0 )

y - 6 = 3x

Adding 6 on both sides of the equation , we get

y = 3x + 6

Hence , the equation of line is y = 3x + 6

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As people get older, the proportion of employees with low blood pressure falls and the proportion with high blood pressure rises.

Interactions are regarded to as appropriate when they usually have the same ratio. For instance, the number of plants in an orchard and the number of apples in a production of apples depend upon this average number of apples produced by each tree. A linear relationship among two numbers or objects is considered to as being proportional in mathematics. When the first quantity doubles, the other amount also does so. As soon as one variables is reduced to 1/100th of its previous value, other decreases as well. If two variables are proportional, it means that if one rises, the other climbs as well, and their relationship stays constant at all values. The diameter and circumference of a circle are used as an example.

given

a) 20%, 49.4%, 30.6% (equal 100)

b) 29.7%, 45.5%, 24.8%

20%, 52.6%, 27.4%

14.9%, 48.5%, 36.6%

c) As people get older, the proportion of employees with low blood pressure falls and the proportion with high blood pressure rises.

d) No, because the association between age and blood pressure can only be determined through a carefully designed trial.

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The smallest integer a such that the intermediate value theorem guarantees that f(x) has a zero on the interval [0, a] is 2.

The intermediate value theorem states that if a function f is continuous on the closed interval [a, b] and if y is a value between f(a) and f(b), then there exists a point c in the interval [a, b] such that f(c) = y.

In this case, we want to find the smallest integer a such that f(x) has a zero on the interval [0, a]. Since f(0) = 7 and f(x) = -2x^3 + 8x^2 - 6x + 7, we need to find the smallest a such that f(a) < 0.

We can start by finding the values of x where f(x) changes sign. To do this, we can set f(x) equal to 0 and solve for x:

-2x^3 + 8x^2 - 6x + 7 = 0

This is a cubic equation and can be solved using various methods such as factoring, substitution, or the use of a numerical method. However, since we are looking for the smallest integer a, we can use an estimation method such as the Newton-Raphson method to approximate the smallest positive root of the equation.

A common initial guess for the smallest positive root of a cubic equation is x = 1. Using this as the initial guess, we can iterate using the following formula:

x_{n+1} = x_n - f(x_n)/f'(x_n)

where f'(x) is the derivative of f(x) and x_n is the nth estimate of the root.

After several iterations, the estimate for the smallest positive root of the equation can be found to be approximately 1.56. Therefore, the smallest integer a such that the intermediate value theorem guarantees that f(x) has a zero on the interval [0, a] is 2.

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To find the volume of water flowing out of the pipe every second, we first need to find the cross-sectional area of the pipe. The formula for the area of a circle is π * r^2, where r is the radius. So, the radius of the pipe is 8/2 = 4 inches.

The cross-sectional area of the pipe is π * 4^2 = 16π square inches.

Now, since the water is flowing at a rate of 2 feet per second, and 1 foot is equal to 12 inches, the flow rate in inches per second is 2 * 12 = 24 cubic inches per second.

So, the exact volume of water flowing out of the pipe every second is the cross-sectional area of the pipe times the flow rate:

16π * 24 = 384π cubic inches per second.

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The Values for rectangle type wall and circle will be gallons of paint that are required to paint one side of a block wall =5.16 gallon, the gallons of sealer required to seal a floor=4.22 gallon and circumference of circle≈39 feet.

What exactly is a rectangle?

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

For example, if one side of a rectangle is 20 cm long, the opposing side is similarly 20 cm long.

A rectangle has two diagonals that intersect. Both diagonals are the same length

P = 2 (Length + Width) is the perimeter.

Rectangle Area=Length*Breadth

Now,

1. Given Length of wall=172 feet and breadth =6 feet then area=172*6=1032

square feet and The paint being used will cover 200 square ft per gallon.

so, gallons of paint that are required to paint one side of a block wall

=1032/200=5.16 gallon

2. Length=250 feet, breadth=120 feet then perimeter=2*370=740 feet

paint used to seal 175 feet floor=1 gallon

then the gallons of sealer required to seal a floor 120' x250'=740/175=4.22 gallon

3. Incomplete question.

4.diameter=12feet 5inch=149 inch

circumference of circle=π*diameter=3.14*149≈39 feet

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