The circumference of a circle is 20 m. What is the area, in square meters? Express
your answer in terms of pi?

Answer:

8.8 gallons left in the gas tank.

Step-by-step explanation:

180 x 0.04 = 7.2

16 - 7.2 = 8.8

The series is convergent. This is determined by using the ratio test and simplifying the expression to a limit as n approaches infinity, which results in a value less than 1.

To determine whether the given series is convergent or divergent, we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of the (n+1)th term to the nth term is less than 1, then the series is convergent. If the limit is greater than 1 or equal to 1, then the series is divergent.

Applying the ratio test to the given series, we can find the nth term by substituting n for n+1, giving us: (-1)^(n+1-1) * 8(n+1) * 5(n+1)/(n+1)^3 * (-1)^(n-1) * 8n * 5n/n^3

Simplifying this expression, we get: (-1) * 8 * 5 * (n+1)/(n+1)^3 * 8 * 5/n^3

Canceling out the common factors, we get: -40/n^2(n+1)

Taking the absolute value, we get: 40/n^2(n+1)

Now, we can calculate the limit of this expression as n approaches infinity, which gives us: lim n→∞ 40/n^2(n+1) = 0

Since the limit is less than 1, the series is convergent. Therefore, the series is convergent and an cannot be identified as a specific value as the series does not converge to a single value.

To learn more about convergent click here: brainly.com/question/29258536

#SPJ11

The area of the parking lot is 4606 square meter.

What is parallelogram?

It is a special type of quadrilateral that has both the pairs of opposite sides parallel and equal.

What is the area of parallelogram?

The area of a parallelogram is the product of its base and height.

We have,

length of two adjacent sides are 70meters and 100meters.

And base of parallelogram is 70m.      (length of parallelogram is its base)

Angle between the adjacent sides is 70 degrees.

Let, side AB and BC be the two adjacent sides whose lengths are 70m and 100m.And h be the height of the parallelogram.

For the height of the parallelogram

In ΔADE, we have

\(sin70=\frac{DE}{AD}\)           \((sinx=\frac{perpendicular}{hypotenuse})\)

⇒ \(0.9397=\frac{h}{70}\)

⇒ \(0.9397\)×70\(=h\)

⇒ h=65.8m

Formula to find the area of parallelogram:

Area= base× height

so, the area of parking lot=base × height

substitute the value of base and height of the parallelogram in the above formula.

Therefore,

\(Area=65.8\)×\(70\)

\(Area=4606m^{2}\)

Hence, the area of the parking lot is 4606 square meter.

Learn more about area of parallelogram here:

https://brainly.com/question/21576252

#Tag #SPJ2

In ridge regression, the penalty strength parameter, represented by \lambda», controls the trade-off between fitting the training data well and keeping the model coefficients small.

When a very large penalty strength is chosen, it results in a higher degree of shrinkage of the regression coefficients towards zero. This means that the model becomes less complex and less likely to overfit the training data. However, it also means that the model may become too biased towards the null hypothesis, leading to underfitting and decreased predictive power. Therefore, choosing the right value of \lambdaλ is crucial for achieving optimal performance in ridge regression.
In ridge regression, choosing a very large λ (lambda) penalty strength results in a higher regularization effect, which helps to reduce overfitting by shrinking the coefficients of the independent variables towards zero. This helps to create a more generalized model by controlling the complexity of the model. However, choosing a λ value that is too large can also result in underfitting, as the model may become too simple to capture the underlying relationships in the data effectively.

Visit here to learn more about ridge regression:

brainly.com/question/31436095

#SPJ11

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

To know more about function visit:

brainly.com/question/30721594

#SPJ11

Answer:

(0,3) and (0,11)

Step-by-step explanation:

A tip for next time is that if the "0" is first, then it is the y-axis. And if the "0" is second, it is the x-axis.

Answer:

45.27feet

Step-by-step explanation:

Given the height of the balloon (in feet) represented by the equation h=−16t2+28.7t+32.4, where t is the time (in seconds)

Note that the velocity of the balloon at maximum height is zero, hence;

v = dh/dt =0

-32t+28.7 = 0

-32t = -28.7

t = 28.7/32

t = 0.897secs

Get the maximum height

Recall that h=−16t²+28.7t+32.4

h = -16(0.897)²+28.7(0.897)+32.4

h= -12.87+25.74+32.4

h = 45.27feet

Hence the maximum height reached is 45.27feet

Answer:

f = 2

Step-by-step explanation:

10 = 6 + 2f

subtract 6 from both sides

4 = 2f

divide both sides by 2

2 = f

Answer:

1) x < -1

2) x ≥ -1

3) x ≤ -1

4) x < -1 and x > 0

5) -1 < x < 0

Explanation:

(1) f(x) > 0

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x-2 > \:0\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x > \:2\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x > \:2^{-1}\)

\(\sf \rightarrow x < -1\)

(2) f(x) ≤ 0

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x-2 \leq \:0\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x \leq \:2\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x \leq \:2^{-1}\)

\(\sf \rightarrow x\geq -1\)

(3) g(x) ≥ 0

\(\sf \rightarrow -\dfrac{2}{x}-2 \:\geq \:0\)

\(\sf \rightarrow -\dfrac{2}{x} \:\geq \:2\)

\(\sf \rightarrow \dfrac{1}{x} \:\geq \:-1\)

\(\sf \rightarrow x \: \leq \:-1\)

(4) g(x) < 0

\(\sf \rightarrow -\dfrac{2}{x}-2 \: < \: 0\)

\(\sf \rightarrow x < -1 \ or \ x > 0\)

Observe the graphs a find solution for g(x) < 0

(5) f(x) < g(x)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x-2 < -\dfrac{2}{x}-2\)

\(\sf \rightarrow -1 < x < 0\)

Answer:

a. 3/10

b. 1/10

c. 4/10 or 2/5

Step-by-step explanation:

There is 4 brown, 3 green, 2 red, and 1 purple if you add those all up you get 10. Since there is a total of 10 marbles in the bag and 3 of those are green 3/10 of the marbles are green. Same goes with purple, 1 of the 10 marbles in the bag is purple.

To solve for green and purple you must add them. Since there is 3 green and 1 purple that gives you 4. 4 out of 10 marbles are green or purple. 4/10 can also be simplified to 2/5

The volume of the rectangular prism is 243 cm³

given that

The top face of the cube has an area of 9 cm²

since All the faces of the cube are squares

therefore The top face is a square

∵ Area of any square = L² , where L is the length of the side of

 the square

∵ Area of the top face is 9 cm²

∴ L² = 9 ⇒ take √ for both sides

∴ L = 3 cm

∵ The volume of any cube = L³

∵ L = 3 cm

∴ The volume of the cube = (3)³ = 27 cm³

- We will use 9 cubes to make a rectangle prism

∴ The volume of the rectangle prism is equal to the volume of

 the 9 cubes

∴ The volume of the prism = 9 × volume of a cube

∵ The volume of the cube is 27 cm³

∴ The volume of the prism = 9 × 27 = 243 cm³

* The volume of the rectangular prism is 243 cm³

learn more about of rectangular prism here

https://brainly.com/question/13066534

#SPJ9

The statement that compares the graph of g(x) with f(x) is that the graph of g(x) is shifted 3 units up.

A variable y is said to be a function of the independent variable x if there is a relationship between them such that whenever a numerical value is assigned to x, there is a rule that determines a specific value of y.

If we have the equation:

G(x) = F(x) + 3

Then, the graph of G(x) will be composed of  3 units above the graph of F(x).

Vice versa, the difference between F(x) and G(x) at any particular value of x will always be 3.

To know more about variables visit:

https://brainly.com/question/17344045

#SPJ9

Answer:

W(2) = 5

Step-by-step explanation:

Because when you look at the graph, the y value is 5 when the x value is 2.

Answer:

w(2) = 5

Step-by-step explanation:

by using rise over run to find the slope easily, you get a slope of 4 and an equation of w(x) = 4x - 3, -3 being the y-intercept

to calculate w(2):

w(2) = 4(2) - 3

w(2) = 8 - 3

w(2) = 5

or you could just look at when y is 2 and see that the corresponding x value is 5 but i wanted to provide a longer explanation in case :)

Answer:

Step-by-step explanation:

Triangle ABC is congruent to Triangle CDA using the SSS rule.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

SSS rule states that,

If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.

To prove:

ΔABC ≅ ΔCDA.

AB = DC ( given)

AD = BC (given)

AC = AC (common to both the triangles)

ΔABC ≅ ΔCDA ( By SSS rule )

Thus,

ΔABC ≅ ΔCDA by SSS rule.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

It is true, as The term "ecological correlation" refers to correlations based on rates or averages that frequently appear in political science or sociology and tend to exaggerate the significance of a link.

Correlations describe the connections between different variables. Strong, weak, positive, or negative expressions are all possible. 1 = Causation need not always follow from correlation. A statistical measure of the linear relationship between two variables is called correlation (that is, do they change at a constant rate). Without defining cause and effect, this is a common method for illustrating straightforward connections. To illustrate the connection between two quantitative variables, statistical language employs correlation. Additionally, we consider that this connection is linear. In other words, when one variable changes by a given amount, the other variable also changes by a fixed amount, but only by one unit.

The term "ecological correlation" refers to correlations based on rates or averages that frequently appear in political science or sociology and tend to exaggerate the significance of a link.

So, it is true.

To know more about correlation visit:

https://brainly.com/question/30016867

#SPJ4

As it is a rectangle and we know that its diagonal bisects each other therefore PT=TR i.e. 10 units

PS = 20 units  

1. Area of rectangle = PQ x PS

Area = 100√3

2. angle PRS is 30°                                 {sum of interior angle of a triangle}

sin30° = PS/PR

1/2 x 20 = PS

PS= 10 units

3. angle PRQ is 60°                                     {Alternate interior angle}

cosine60°=QR/PR

1/2 x 20 = QR

QR= 10 unit

4. cosQSR = 10/20

cosQSR=1/2

angle QSR = 60°

Thus angle PQS is 30°

tanPQS = 1/√3

PQ= 10√3

Learn more about Area of rectangle from the link below

https://brainly.com/question/20693059

#SPJ1

The sum of the given infinite series is \(\frac{3}{5}\)

To find the value of the sum from n=0 to infinity of (-2/3)^n, we need to use the formula for the sum of an infinite geometric series. The formula is:

\(Sum = \frac{a} { (1 - r)}\)

where 'a' is the first term in the series, and 'r' is the common ratio between the terms. In this case, a = (-2/3)^0 = 1 and r = -2/3. Now, we can plug these values into the formula:

\(Sum =\frac{ 1}{ (1 - (-2/3))}\\Sum ={ 1}{ (1 + 2/3)}\\Sum ={ 1}{ / (3/3 + 2/3)}\\Sum = 1 / (5/3)\\Sum = 1 * (3/5)\\\\Sum = 3/5\)
So, the value of the sum of the series is 3/5.

learn more about sum of series

https://brainly.com/question/30647793

#SPJ11

Applying the definition of congruent triangles:

1. QS = 57 units; TV = 57 units

2. m∠B = 3°; m∠Q = 3°

The triangles that are congruent to each other have corresponding parts that are congruent, that is their corresponding sides and angles are equal to each other.

1. Given that triangles QRS and TUV are congruent triangles, therefore:

QS = TV [corresponding congruent sides]

QS = 4v + 5

TV = 5v - 8

Therefore:

4v + 5 = 5v - 8

4v - 5v = -5 - 8

-v = -13

v = 13

QS = 4v + 5 = 4(13) + 5 = 57 units

TV = 5v - 8 = 5(13) - 8 = 57 units

2. Given that triangles ABC and PQR are congruent, therefore:

m∠B = m∠Q

m∠B = 2v + 1

m∠Q = 8v - 5

Therefore:

2v + 1 = 8v - 5

2v - 8v = -1 - 5

-6v = -6

v = -6/-6

v = 1

m∠B = 2v + 1 = 2(1) + 1 = 3°

m∠Q = 8v - 5 = 8(1) - 5 = 3°

Learn more about congruent triangles on:

https://brainly.com/question/1675117

#SPJ1

The area of the rectangular base of his friend's tank is 468.75 square inches. So, Option D is correct.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

One of Julian's friends also has a rectangular aquarium.

The dimensions of his friend's tank are each exactly 1 1/4 times the dimensions of Julian's tank.

Let x be the length of Julian's tank.

Let y be the width of Julian's tank.

So, the Area of Julian's tank = length × Width

                                               = xy

Since we are given

300 = xy

Now we are given that the dimensions of his friend's tank are each exactly times the dimensions of Julian's tank.

So, the length of his friend's tank = 5/4 x

So, the width of his friend's tank = 5/4 y

So, Area of his friend's tank = ( 5/4 x) (5/4 y)

                                           = 25 / 16 xy

                                           = 25 / 16 (300)

                                           = 468.75

Hence the area of the rectangular base of his friend's tank is 468.75 square inches.

So, Option D is correct.

Learn more about the area;

https://brainly.com/question/1658516

#SPJ1

Answer:

−1.01

Step-by-step explanation:

Simplify the expression!

Answer: -1.01

Step-by-step explanation:

a double negative equals a positive. -(-1.9) = 1.9

-0.85 + 1.9 = 1.05

when you have a positive number and add a negative number you just subtract the negative number from the positive.

1.05 + - 2.06 = 1.05 - 2.06

1.05 - 2.06 = -1.01

the answer is -1.01

hope this wasn’t confusing!

Answer:

The larger angle is 143

Step-by-step explanation:

x + y = 180 (This is the meaning of supplementary. Two angles make up 180 degrees)

4x - 5 = y

x + (4x - 5) = 180            Remove the brackets.

x + 4x - 5 = 180

5x - 5 =  180                  Add 5 to both sides

5x - 5 +5 = 180 + 5       Combine

5x = 185                        Divide by 5

5x/5=185/5

x = 37

y = 4*37 - 5

y = 148 - 5

y = 143

Answer:

1. unknow

2. mean median range spread average

3. the bike Ville is more expensive in everything

Using Average, the prices of bicycles at two stores are compared.

Average is the" sum of observations divided by total number of observations".

According to the question,

The price of bicycles at two stores are shown.

Bikeville:                  140 160 800 235   250 450 80 115 220 250 96  290

Discount Bicycles:   50  180  300  110   120  150 155 285 120 200 70 175 95

Average of bikeville = \(\frac{sum of observations}{Total number of observation}\)

= 140 + 160 + 800 + 235 + 250 + 450 + 80 + 115 + 220+250+96+29

= 3086

Average of bikeville= 3086/12

= 257.167

Average of Discount of bicycles:

( 50 +180+100+110+120+150+155+285+

120+150+155+285+120+200+70+175+95)     =2720

= 2720/15

=181.33

Average of Discount of bicycles is 181.33.

Hence, using Average the prices of bicycles at two stores are compared.

Learn more about average here

https://brainly.com/question/13191507

#SPJ2

Answer:

(7x+18)°+(5x-6)° =180° adjacent angles sum up to 180°

7x+5x+18-6=180

12x+12=180

12x=180-12

12x=168

dividing through by 12

x=14

(3y+11)°=(7x+18)° corresponding angles

3y+11=7(14)+18

3y+11=98+18

3y+11=116

3y=116-11

3y=105

dividing through by 3

y=35

The correct option is (C) His friend’s statement is not accurate. The percent increase will be less than 2%.

Jason’s friend tells him that the average hourly earnings for construction workers will rise by 2% from 2009 to 2012. Based on the data below, assuming that the projected hourly earnings are correct, Jason’s friend’s statement is not accurate.

What is the reason?

The given data is about the average hourly earnings of the construction industry for the years 2000-2009.

The average hourly earnings in 2009 were $22.4.

We are to find the percentage increase in hourly earnings from 2009 to 2012, assuming the projected hourly earnings of $24.50 to be correct.

We have to find the percentage increase in the average hourly earnings of the construction industry from 2009 to 2012.= $24.50 − $22.4 / $22.4 × 100%

= $2.10 / $22.4 × 100%≈ 9.375%

Hence, the percentage increase in hourly earnings from 2009 to 2012 is approximately 9.375%.

Therefore, the statement of Jason’s friend is not accurate. The percent increase will be less than 2%.

To know more about percent visit:

https://brainly.com/question/31323953

#SPJ11