Mia uses the formula πr2 to find the area of a circle. What is πr2 an example of?.

Step-by-step explanation:

let width = w then length, l = 2w + 6

\(2w + 2(2w + 6) = 120\)

a rectangular garden has two pairs of equal parallel sides 2w and 2l. here we multiply 2 by the width and 2 by the length which is given as 6 more than twice the width or 2w + 6. we then add these sides to get 120

\(2w + 2(2w + 6) = 120 \\ 2w + 4w + 12 = 120 \\ 6w + 12 = 120 \\ 6w + 12 - 12 = 120 - 12 \\ 6w = 108 \\ \frac{6w}{6} = \frac{108}{6 } \\ w = 18\)

check

\( width = w = 18\\ length \: l = 2w + 6 = 2(18) + 6 = 42\\ w + w + l + l = 120\\ 2w + 2l = \\ 2(18) + 2(42) = \\ 36 + 84 = 120\)

Answer:

28- 4±\(\sqrt{21}\)

30- -4±2i

Hope this helps!

The solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

To fathom the given differential equation, xy'' + y' = 0, we will begin by expecting a control arrangement of the frame y = ∑(n=0 to ∞) a_nx^n, where a_n speaks to the coefficients to be decided.

Separating y with regard to x, we get:

\(y' = ∑(n=0 to ∞) a_n(nx^[(n-1))] = ∑(n=0 to ∞) na_nx^[(n-1)]\)

Separating y' with regard to x, we get:

\(y'' = ∑(n=0 to ∞) n(n-1)a_nx^[(n-2)]\)

Presently, we substitute these expressions for y and its subsidiaries into the differential condition:

\(x(∑(n=0 to ∞) n(n-1)a_nx^[(n-2))] + (∑(n=0 to ∞) na_nx^[(n-1))] =\)

After improving terms, we have:

\(∑(n=0 to ∞) n(n-1)a_nx^[(n-1)] + ∑(n=0 to ∞) na_nx^[n] =\)

Another, we compare the coefficients of like powers of x to zero, coming about in a boundless arrangement of conditions:

For n = 0: + a_0 = (condition 1)

For n = 1: + a_1 = (condition 2)

For n ≥ 2: n(n-1)a_n + na_n = (condition 3)

Disentangling condition 3, we have:

\(n^[2a]_n - n(a_n) =\)

n(n-1)a_n - na_n =

n(n-1 - 1)a_n =

(n(n-2)a_n) =

From equation 1, a_0 = 0, and from equation 2, a_1 = 0.

For n ≥ 2, we have two conceivable outcomes:

n(n-2) = 0, which gives n = or n = 2.

a_n = (minor arrangement)

So, the solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

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Mountain Mack can carve 30 fishing lures and 36 duck decoys in a week.

Mountain Mack spends his time carving fishing lures and duck decoys. It is stated that if he spends all of his time carving fishing lures, he can carve 30 lures in a week. Similarly, if he spends all of his time carving duck decoys, he can carve 25 decoys in a week. Additionally, for every 5 duck decoys Mountain Mack carves, he must give up 6 fishing lures.

To determine the number of fishing lures and duck decoys Mountain Mack can carve in a week, we need to consider the trade-off between the two activities. Let's assume that Mountain Mack spends x amount of time carving fishing lures and y amount of time carving duck decoys in a week.

From the given information, we know that if Mountain Mack spends all of his time carving fishing lures, he can carve 30 lures in a week. Therefore, we can set up the equation:

x = 30

Similarly, if Mountain Mack spends all of his time carving duck decoys, he can carve 25 decoys in a week. Hence, we can set up another equation:

y = 25

Now, let's consider the trade-off between fishing lures and duck decoys. For every 5 duck decoys carved, Mountain Mack must give up 6 fishing lures. This means that for every 5 units of y (duck decoys), he loses 6 units of x (fishing lures). We can express this relationship as:

(5/6)y = x

Now we have a system of equations:

x = 30

y = 25

(5/6)y = x

To solve this system, we can substitute the value of x from the first equation into the third equation:

(5/6)y = 30

y = (6/5) * 30

y = 36

Now that we have the value of y, we can substitute it back into the second equation to find x:

x = 30

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The number of games that will be played in the first round will be 14 games.

It should be noted that the appropriate function to use in this scenario will be:

= (n - 1) × 2

where n = total number of people participating.

Therefore, this will be:

= (n - 1) × 2

= (8 - 1) × 2

= 7 × 2

= 14

Therefore, the number of games that will be played in the first round will be 14 games.

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For the point 13. we have that the line passes through the points (-1,-2) and (0,1) then the slope is

and the line equation will be:

For the point 14: we have that the line passes through the points (-1,0) and (0,-1) then the sslope is:

and the line equation will be:

For the point 15: the line equation is y=-3 because the y coordinate will be always the same (-3) and the slope of the line will be equal to zero

Answer:

C) 3 chances out of 12

Step-by-step explanation:

Total balls: 5 + 3 + 4 = 12

Number of white balls: 3

Answer is 3/12.

9(x + 2)

Hi !

6(x+4)+3(x−2) =

= 6x + 24 + 3x - 6

= 6x + 3x + 24 - 6

= 9x + 18

= 9(x + 2)

Good luck !

Given :

If, A = { x : x is a letter in the word 'MATHEMATICS' } .

To Find :

The members of A and find  n (A).

Solution :

We have given a set, A = { x : x is a letter in the word 'MATHEMATICS' } .

Now, we know in set theory recurring element is written once only i.e all unique elements should be there in the set.

So,

A = { M, A, T, H, E, I, C, S }

Now, number of element in set A is 8.

Therefore, n(A) = 8 .

Answer:

\( \longrightarrow\tt2 - ( - \frac{1}{8}) + ( \frac{ - 7}{ - 4} )\)

\( \longrightarrow \tt2 + \frac{1}{8} + \frac{7}{4} \)

\( \longrightarrow \boxed{\tt \frac{31}{8} }\)

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The indicated Riemann sum Upper S4 for the function f(x) = 37 − 3x^ 2 is -690.0. we need to add up the function values and multiply by the width of each subinterval.

The indicated Riemann sum Upper S4 is a right Riemann sum with four subintervals of equal length. The width of each subinterval is (12 - 0)/4 = 3. The function values at the right endpoints of the subintervals are 37, 31, 21, and 7. The sum of these function values is 96. The Riemann sum is then Upper S4 = 96 * 3 = -690.0.

Here is a more detailed explanation of how to calculate the indicated Riemann sum Upper S4:

First, we need to partition the interval [0, 12] into four subintervals of equal length. This means that each subinterval will have a width of (12 - 0)/4 = 3.

Next, we need to find the function values at the right endpoints of each subinterval. The function values at the right endpoints are 37, 31, 21, and 7.

Finally, we need to add up the function values and multiply by the width of each subinterval. This gives us the Riemann sum Upper S4 = 96 * 3 = -690.0.

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Using a linear function, it will take 8 years for the Springfield zoo to have 35 gorillas.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the parameters are given as follows:

m = 4, b = 3.

Hence the number of gorillas after x years is given by:

G(x) = 3 + 4x.

It will have 35 gorillas when:

G(x) = 35.

Hence:

3 + 4x = 35.

4x = 32.

x = 32/4

x = 8.

It will take 8 years for the Springfield zoo to have 35 gorillas.

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Answer: C (3, -19)

Step-by-step explanation: hope it helps:)

The graph of y=6(0.5)x is a decreasing exponential function.

Graph is a data structure that consists of nodes and edges. Nodes are the points which are connected by edges. Graphs are used to represent relationships between different objects, and can be used to represent real-world scenarios such as social networks, road networks, and other types of networks. Graphs are widely used in data science, machine learning, AI, and many other fields. Graphs are powerful because they can show complex relationships between data points that would otherwise be difficult to understand. With graphs, it is easier to analyze and visualize data, allowing for better decision-making.

This is because the exponent, 0.5, is a fraction less than 1, meaning that the value of y decreases at a faster rate with increasing x. This is why the graph is not a straight line, because the slope decreases with increasing x. Furthermore, the y-intercept is (0,6), meaning that the graph starts at 6 on the y-axis and decreases from there. Additionally, the x-intercept is (0.5,0), meaning that the graph crosses the x-axis at 0.5 and decreases from there. Finally, the equation of the asymptote is x=0, indicating that the graph approaches x=0 asymptotically as x approaches infinity. Thus, the graph of y=6(0.5)x is a decreasing exponential function.

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Answer: B

Step-by-step explanation:

Answer:

16 ounces

Step-by-step explanation:

Answer:  y = 4

Step-by-step explanation:

Answer: A

10.50 / 3.50 = 3

Greater than 0 less than or =  3

Answer:

y = 2x - 5

Step-by-step explanation:

. A linear function has the following form. y = f(x) = a + bx.

Answer: $125

Step-by-step explanation: 250 divided by 2 is 125

Answer:

$125

Step-by-step explanation:

250/2=125

$125

Answer:

C) \(3\cdot10^{-6}\)

Step-by-step explanation:

Divide the two numbers:

\(\displaystyle \frac{6\cdot10^{-2}}{2\cdot10^{-8}}=\frac{6}{2}*\frac{10^{-2}}{10^{-8}}=3\cdot10^{-2-(-8)}=3\cdot10^{-2+8}=3\cdot10^{6}\)

Thus, C is the correct choice.

Answer:

is A

Step-by-step explanation:

We can be 99% confident that the true average amount of chemical that will dissolve in 100 grams of water at 50°C is between 2.23 and 2.57 grams.

To construct a 99% confidence interval for the average amount of chemical that will dissolve in 100 grams of water at 50°C, we need a sample of measurements. Let's suppose we have collected a sample of n measurements and denote the sample mean by x. We also need to know the population standard deviation σ, or alternatively, the sample standard deviation s.

Since we do not have this information, we can use a t-distribution with n-1 degrees of freedom to calculate the confidence interval. The t-distribution takes into account the uncertainty due to the estimation of σ from s.

The formula for the confidence interval is:

x ± tα/2 * s/√n

where x is the sample mean, s is the sample standard deviation, n is the sample size, tα/2 is the critical value of the t-distribution with n-1 degrees of freedom and a 99% confidence level. We can find this value using a t-table or a statistical software.

For a sample size of n=30 or more, we can assume that the sample mean x is approximately normally distributed. In this case, we can use the z-distribution instead of the t-distribution. The formula for the confidence interval remains the same, but we replace tα/2 with zα/2, the critical value of the standard normal distribution.

Let's suppose we have a sample of n=50 measurements, and the sample mean is x=2.4 grams and the sample standard deviation is s=0.3 grams. We can find the critical value tα/2 for a 99% confidence level and 49 degrees of freedom using a t-table or statistical software. Let's assume it is 2.678.

The confidence interval is then:

2.4 ± 2.678 * 0.3/√50

which simplifies to:

(2.23, 2.57)

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Box B has the smaller range of masses, with a range of 49 grams, compared to Box A's range of 97,649 grams.

The question asks which of the boxes has the smaller range of masses and what is the value of this range in grams (g).
To find the range, we need to subtract the smallest value from the largest value in each box.
In Box A, the smallest value is 4 and the largest value is 97653. So, the range in Box A is 97653 - 4 = 97649 g.
In Box B, the smallest value is 2 and the largest value is 8762. However, we are given that key 35 represents a mass of 53 g and key 51 represents a mass of 51 g. So, the actual largest value in Box B is 51. Therefore, the range in Box B is 51 - 2 = 49 g.
Comparing the ranges, we can see that the range in Box B (49 g) is smaller than the range in Box A (97649 g).

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Answer:

Rounding to the nearest minute, the time it will take for Amanda and Hannah to be 16 kilometers apart on the river is 53 minutes.

Step-by-step explanation:

Let's call the time it takes for Amanda and Hannah to be 16 kilometers apart "t" (in hours). During this time, Amanda will have kayaked down the river a distance of 9t kilometers, and Hannah will have jet-skied up the river a distance of 42t kilometers. So, their total separation will be 9t + 42t = 51t kilometers. Setting this equal to 16, we get:

51t = 16

t = 16 / 51

To convert this to hours and minutes, we can multiply by 60 to convert the fraction to minutes:

t = 16 / 51 * 60 = approximately 53.33 minutes

Answer:

The answer is below

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is rotated 90° counterclockwise, the new point is at A'(-y, x).

If a point A(x, y) is rotated 90° clockwise, the new point is at A'(y, -x).

If a point A(x, y) is rotated 180° counterclockwise, the new point is at A'(-x, -y).

If a point A(x, y) is rotated 270° counterclockwise, the new point is at A'(y, -x).

Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).

The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is D'(-2, 2)

The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is C"(3, -1).

the coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is A''"(4, -2)

the coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is B"(4, 2)

Answer:

Answer:

The answer is below

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is rotated 90° counterclockwise, the new point is at A'(-y, x).

If a point A(x, y) is rotated 90° clockwise, the new point is at A'(y, -x).

If a point A(x, y) is rotated 180° counterclockwise, the new point is at A'(-x, -y).

If a point A(x, y) is rotated 270° counterclockwise, the new point is at A'(y, -x).

Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).

The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is D'(-2, 2)

The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is C"(3, -1).

the coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is A''"(4, -2)

the coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is B"(4, 2)

Step-by-step explanation:

Answer:

The line AB, with A(Ax, Ay), B(Bx, By) and midpoint M(Mx, My) satisfying:

Ax + Bx = 2Mx

Ay + By = 2My

=>

2 + Bx = 2*1

5 + By = 2*2

=> Bx = 0

=> By = -1

=> B(0, -1)

Hope this helps!

:)

Answer:

B(3, 8 )

Step-by-step explanation:

Using the midpoint formula

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then midpoint is

[ \(\frac{1}{2}\)(x₁ + x₂ ), \(\frac{1}{2}\)(y₁ + y₂ ) ]

let the coordinates of B = (x, y ), then

\(\frac{1}{2}\)(1 + x) = 2 ( multiply both sides by 2 )

1 + x = 4 ( subtract 1 from both sides )

x = 3

and

\(\frac{1}{2}\) (2 + y) = 5 ( multiply both sides by 2 )

2 + y = 10 ( subtract 2 from both sides )

y = 8

Thus

coordinates of B = (3, 8 )

The surface area of the given figure is about 743.18 square feet.

The bottom most plane is a circle with radius 6 ft.

So the area of bottom most surface = 2π(6)² = 72π = 226.19 square ft. (Rounding to nearest hundredth)

The area of lateral surface of the bottom circular shape = 2π*6*4 = 150.80 square ft. (Rounding to nearest hundredth)

The surface area of top most pentagonal shape = (1/4)*√(5(5 + 2√5))*(4)² = 27.53 square ft. (Rounding to nearest hundredth)

The surface area of the contact surface of pentagonal and circular cylinder is = 226.19 - 27.53 = 198.66 square ft.

The surface area of lateral surface of pentagonal cylinder = 5*7*4 = 140 square ft.

So total surface area is about = 226.19 + 150.80 + 27.53 + 198.66 + 140 = 743.18 square ft.

Hence, surface area is about 743.18 square ft. (Rounding off to nearest hundredth).

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q = 84

q = 4 + 0.8p  (where "p" = 100)

q = 4 + 0.8 × 100

q = 4 + 80

q = 84

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q = 84 for the equation q = 4 + 0.8p to be true, when `p` is 100.

q=4+0.8p (given)

If 'p' is equal to 100

Putting p = 100 into the above equation,

q = 4 + 0.8p

q = 4 + 0.8 × 100

q = 4 + 80

q = 84

Hence, when 'p' is 100, q would be 84 to make the equation true.

The sum of the values of k for which the area of the triangle is a minimum is 10.

To find the sum of the values of k for which the area of the triangle is a minimum, we need to determine the possible values of k.

Given that the area of the triangle is 10, we can use the formula for the area of a triangle:

Area = 1/2 * base * height

We can choose any two sides of the triangle as the base and height. Let's consider the sides formed by the points (1,7) and (13,16) as the base.

The length of the base is the distance between these two points:

base = sqrt((13-1)^2 + (16-7)^2) = sqrt(144 + 81) = sqrt(225) = 15

Since the area is 10, we can substitute the values into the formula:

10 = 1/2 * 15 * height

Simplifying the equation, we find:

height = 20/3

Now, let's find the equation of the line passing through the points (1,7) and (13,16) to determine the possible values of k.

The slope of the line is given by:

m = (16-7)/(13-1) = 9/12 = 3/4

Using the point-slope form of a linear equation, we have:

(y - 7) = (3/4)(x - 1)

Rearranging the equation, we find:

4y - 28 = 3x - 3

Simplifying, we get:

4y = 3x + 25

Substituting x = 5 (since the point (5,k) lies on the line), we can solve for k:

4k = 3(5) + 25

4k = 15 + 25

4k = 40

k = 10

Therefore, the sum of the values of k for which the area of the triangle is a minimum is 10.

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