In circle G, r = 3 units. Maria draws a circle with double the area of circle G.
What is the area of Maria’s circle?

Answer:

The sum of the first nine terms of the sequence is 74.44.

Step-by-step explanation:

Geometric sequence concepts:

The nth term of a geometric sequence is given by the following equation.

[tex]a_{n+1} = ra_{n}[/tex]

In which r is the common ratio.

This can be expanded for the nth term in the following way:

[tex]a_{n} = a_{1}r^{n-1}[/tex]

In which [tex]a_{1}[/tex] is the first term.

Or even:

[tex]a_{n} = a_{m}r^{n-m}[/tex]

The sum of the first n terms of a geometric sequence is given by:

[tex]S_{n} = \frac{a_{1}(1 - r^{n})}{1 - r}[/tex]

Finding the common ratio:

[tex]a_{3} = 3.645, a_{8} = 15[/tex]

[tex]a_{n} = a_{m}r^{n-m}[/tex]

[tex]a_{8} = a_{3}r^{8-3}[/tex]

[tex]a_{3}r^{5} = a_{8}[/tex]

[tex]3.645r^{5} = 15[/tex]

[tex]r^{5} = \frac{15}{3.645}[/tex]

[tex]r = \sqrt[5]{\frac{15}{3.645}}[/tex]

[tex]r = 1.327[/tex]

Finding the first term:

[tex]a_{3} = a_{1}r^{2}[/tex]

[tex]a_{1} = \frac{a_{3}}{r^{2}}[/tex]

[tex]a_{1} = \frac{3.645}{(1.327)^{2}}[/tex]

[tex]a_{1} = 2.07[/tex]

Sum of the first nine terms:

[tex]S_{9} = \frac{2.07*(1 - (1.327)^{9})}{1 - 1.327} = 74.44[/tex]

The sum of the first nine terms of the sequence is 74.44.

Answer:

S₉ = 9.84

Step-by-step explanation:

In a geometric series, the general formula for nth term is:

an = a₁rⁿ⁻¹

where,

an = nth term

a₁ = first term

r = common ratio

From this formula, we have:

a₃ = a₁r² = 3.645   --------- equation (1)

a₈ = a₁r⁷ = 15    ----------- equation (2)

dividing both of these equations, we get:

a₁r⁷/a₁r² = 15/3.645

r⁵ = 4.115

r = (4.115)^1/5

r = 1.33

Now, put this value in equation (1), we get:

a₁(1.33)² = 3.645

a₁ = 0.27

Now, the formula for the sum of geometric series upto nth term is:

Sn = a₁(rⁿ - 1)/(r - 1)

therefore,

S₉ = (0.27)(1.33⁹ - 1)/(1.33 - 1)

S₉ = 9.84

c number answer is the correct answer

Answer:

The intercepts of the line: 9x - 7y = 14

For x-intercept, in this case: y = 0, => 9x = 14 => x = 14/9

=> x-intercept (14/9, 0)

For y-intercept, in this case: x = 0, => -7y = 14 => y = -2

=> y-intercept (0, -2)

Hope this helps!

:)

Answer:

Yes 0 is a natural number

Step-by-step explanation:

I googled it

Step-by-step explanation:

Zero is not positive or negative Even though zero is not a positive number it is still considered a whole number yes it is a natural number because it is on the number line

Answer:

Volume of the mold is [tex]6.93\ \text{yards}^3[/tex].

Step-by-step explanation:

The volume of the mold is 186 cubic feet concrete. It is to be sold by cubic yard. It means that we need to convert cubic feet to cubic yard.

1 feet = 0.334 yards

[tex]186\ \text{feet}^3=186\times (0.334\ \text{yards})^3\\\\V=6.93\ \text{yards}^3[/tex]

So, the volume of the mold is [tex]6.93\ \text{yards}^3[/tex].

Answer:

The central angle measure of the sector in radians is [tex]\theta=\frac{13}{9}[/tex].

Step-by-step explanation:

A sector of a circle is the portion of a circle enclosed by two radii and an arc. It resembles a "pizza" slice.

The area of a sector when the central angle is in radians is given by

                                                    [tex]A=(\frac{\theta}{2})\cdot r^2[/tex]

where

r = radius

θ = central angle in radians

We know that the area of the sector is [tex]26 \:cm^2[/tex] and the radius is 6 cm. Applying the above formula and solving for the central angle ([tex]\theta[/tex]) we get that

                                                   [tex]26=(\frac{\theta}{2})\cdot (6)^2\\\\\left(\frac{\theta}{2}\right)\left(6\right)^2=26\\\\\frac{\frac{\theta}{2}\cdot \:6^2}{36}=\frac{26}{36}\\\\\frac{\theta}{2}=\frac{13}{18}\\\\\theta=\frac{13}{9}[/tex]

Answer:2k-13

Step-by-step explanation:

Answer:

2k-13.

Step-by-step explanation:

We can simplify this equation using the Distributive Property:

-3(2 + 4k) + 7(2k-1) becomes

-6 - 12k + 14k -7

Combining like terms gets us:

2k-13.

Answer:

4,775.329156626506‬

Step-by-step explanation:

Answer:

(x-8)(x^2-2)

Step-by-step explanation:

take x common from the first 2 terms and take -2 common from the last two terms. Then, take (x-8) common.

x^2(x-8)-2(x-8) = (x-8)(x^2-2)

Answer:

x = 2, y =7

Step-by-step explanation:

4x - 2y = -6

-6x + 2y = 2

Add the equations together

4x - 2y = -6

-6x + 2y = 2

-----------------------

-2x = -4

Divide each side by -2

-2x/-2 = -4/-2

x = 2

now find y

-6x+2y =2

-6(2) +2y =2

-12+2y =2

Add 12 to each side

-12+12+2y = 2+12

2y =14

Divide by 2

2y/2 =14/2

y =7

Answer:

The smallest angle of the triangle is 33.030°.

Step-by-step explanation:

The angles of triangle can be determined with the help of the Law of Cosine and the fact that sum of all angles equals to 180°:

[tex]\cos A = -\frac{6^{2}-9^{2}-11^{2}}{2\cdot (9)\cdot (11)}[/tex]

[tex]\cos A = 0.838[/tex]

[tex]A \approx 33.030^{\circ}[/tex]

[tex]\cos B = -\frac{9^{2}-6^{2}-11^{2}}{2\cdot (6)\cdot (11)}[/tex]

[tex]\cos B = 0.575[/tex]

[tex]B \approx 54.847^{\circ}[/tex]

[tex]C = 180^{\circ} - A - B[/tex]

[tex]C = 180^{\circ} - 33.030^{\circ} - 54.847^{\circ}[/tex]

[tex]C = 92.123^{\circ}[/tex]

The smallest angle of the triangle is 33.030°.

Answer:

95​% confidence interval for the mean difference in leisure time between adults with no children and adults with children (μ1 - μ2).

(0.4144 , 2.3256)

Step-by-step explanation:

Given sample size 'n' =n₁ = n₂ = 40

The mean of the first sample  (x₁⁻) = 5.69 hours

The standard deviation of the first sample (S₁)= 2.42 hours

The mean of the second sample( x₂⁻) = 4.32 hours

The standard deviation of the second sample (S₂)= 1.83 hours

95% of confidence intervals for (μ₁ - μ₂)are determined by

[tex](X^{-} _{1} - X^{-} _{2} - t_{\frac{\alpha }{2} } Se(X^{-} _{1} - X^{-} _{2} ) , X^{-} _{1} - X^{-} _{2} + t_{\frac{\alpha }{2} } se(X^{-} _{1} - X^{-} _{2} ))[/tex]

where

The standard error of the difference between two means

[tex]se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{\frac{S^{2} _{1} }{n_{1} }+\frac{S^{2} _{2} }{n_{2} } }[/tex]

[tex]se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{\frac{(2.42)^2 }{40 }+\frac{(1.83)^2 }{40 } }[/tex]

[tex]se(X^{-} _{1} - X^{-} _{2} ) = \sqrt{0.2301325} = 0.47972[/tex]

Degrees of freedom γ = n₁ +n₂ -2 = 40+40 -2 =78

[tex]t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } = t_{0.025}[/tex]

t₀.₀₂₅ = 1.992

95% of confidence intervals for (μ₁ - μ₂)are determined by

[tex](X^{-} _{1} - X^{-} _{2} - t_{\frac{\alpha }{2} } Se(X^{-} _{1} - X^{-} _{2} ) , X^{-} _{1} - X^{-} _{2} + t_{\frac{\alpha }{2} } se(X^{-} _{1} - X^{-} _{2} ))[/tex]

(5.69 -4.32)- 1.992(0.47972)), (5.69-4.32)+1.992(0.47972))

(1.37 -0.9556 , 1.37+0.9556)

(0.4144 , 2.3256)

Conclusion:-

95​% confidence interval for the mean difference in leisure time between adults with no children and adults with children (μ1 - μ2).

(0.4144 , 2.3256)

Following are the calculation to the confidence interval:

Given:

[tex]\bar{x_1}= 5.69\\\\\bar{x_2}= 4.32\\\\s_1=2.42\\\\s_2=1.83\\\\n_1=40\\\\n_2=40\\\\[/tex]

To find:

confidence interval=?

Solution:

[tex]\to a=0.1\\\\ \to Z(0.05)=1.645[/tex]            (from standard normal table)

Calculating the confidence interval when its value is [tex]95\%[/tex]:

[tex]\to (\bar{x_1}-\bar{x_2}) \pm Z \times \sqrt{(\frac{s^2_{1}}{n_1}+ \frac{s^2_{2}}{n_2})}[/tex]  

[tex]\to (5.69-4.32)\pm 1.645 \times \sqrt{(\frac{2.42^2}{40}+\frac{1.83^2}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{5.8564}{40}+\frac{3.3489}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{5.8564+3.3489}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{(\frac{9.2053}{40})}\\\\\to (1.37)\pm 1.645 \times \sqrt{0.2301325}\\\\\to (1.37)\pm 1.645 \times 0.4797212 \\\\\to (1.37)\pm 0.789\\\\\to (2.159, 0.581 )[/tex]

Therefore, the final answer is "(2.159 and 0.581)".

Learn more about the confidence interval:

brainly.com/question/24131141

Answer:

Athena = 10,265 km

Vesta = 102,650 km

Juno = 102,650 km

Ceres = 2,053,000 km

Apollo = 1,026,500 km

Step-by-step explanation:

Athena = 20,530 / 2 = 10,256

From there, you can work out the rest by multiplying accordingly.

Hope this helps and made sense! :)

Answer:

-2+2x=y

Step-by-step explanation:

got it correct on imagine math

the percent difference is 60%

Step-by-step explanation:

[tex](3x-2)(5x^2-3x+4)[/tex]

[tex]15x^3-9x^2+12x-10x^2+6x-8[/tex]

Now, combine like terms.

[tex]15x^3-19x^2+18x-8[/tex]

Answer:

Option C is correct

Step-by-step explanation:

The equation, when graphed with the given  equation (y = -x + 4), will form a system that has an infinite number of solutions MUST have same form as given equation.

y = (-1/2)(2x - 8) = (-1/2)*2x + (-1/2)*8 = -x + 4 (same form as given equation)

Hope this helps!

:)

Answer:

There are two limo companies that charge based on the number of people, x, that they carry. Limo A charges $30 plus $4 per person. Limo B charges $70 plus $2 per person. How many people can ride to make the two companies charge the same amount?

Step-by-step explanation:

The correct situation is the third one, this is because the expression we have is:

[tex]30+4x=70+2x[/tex]

let's take the left side as the charge of the company limo A, and the left side as the charge of limo B.

Since 'x' is the number of people, the left side tells us that limo A charges $4 per person (hence the 4x) and adds an additional $30 (hence the 30 added on the left side).

And the right side tells us that limo B charges $2 per person (hence the 2x) and adds an additional $70 (hence the 70 added on the right side).

And since we have an equal sign this means that the expression represents the number of people that can ride and will pay an equal amount in each company.

This is the situation that the third option describes:

There are two limo companies that charge based on the number of people, x, that they carry. Limo A charges $30 plus $4 per person. Limo B charges $70 plus $2 per person. How many people can ride to make the two companies charge the same amount?

Answer:

$0.08

Step-by-step explanation:

Take 0.23 and divide it by 3 to get an individual cost and round to the nearest tenth.

Answer:

Step-by-step explanation:

.23 ÷3=.076

Rounded up .08

Answer:

[tex]\frac{5(x+y)}{-8x}[/tex]

Step-by-step explanation:

Given the description below;

-The expression is quotient of 2 quantities

-The numerator of the expression is 5 and the sum of x and y

-The denominator is the product of -8 and x

Let the given two quantities be a and b

The quotient of the expression will be expressed as [tex]\frac{a}{b}[/tex] where 'a' is the numerator and 'b' is the denominator

If the numerator of the expression is 5 and the sum of x and y , then;

[tex]a = 5(x+y)[/tex]

If the denominator is the product of -8 and x, then;

[tex]b =-8x[/tex]

The quotient of both expression will be [tex]\frac{a}{b} = \frac{5(x+y)}{-8x}[/tex]

The expression that fits the description is [tex]\frac{5(x+y)}{-8x}[/tex]

Answer:

[tex]32[/tex]

Step-by-step explanation:

[tex] {2}^{5} \\ 2 \times 2 \times 2 \times 2 \times 2 \\ 4 \times 4 \times 2 \\ 16 \times 2 \\ = 32[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

The right answer is 32.

Look at the attached picture

hope it will help you

good luck on your assignment

Answer:

7 + 5a

Step-by-step explanation:

3-(- 2a -4)+3a = 3+2a +4 +3a = 7 + 5a

Answer:

The solution is: [tex](-\infty, \infty)[/tex], that is, all real values of x.

Step-by-step explanation:

The modulus of a value x(|x|) is the distance of x to the origin.

A distance is a positive measure, or zero, so |x| is never a negative value.

In this problem:

|10x| > -2

Remembering that the modulus is never negative, which means that for every value of x in the real set, |10x| > -2.

So the solution is: [tex](-\infty, \infty)[/tex], that is, all real values of x.

Answer:

The answer is D. Range Hopefully this helps!

Answer:

D

Step-by-step explanation:

Hope this helps

Answer:

976

Step-by-step explanation:

this is literally the exact same question

Answer:

  7,854 cm squared

Step-by-step explanation:

The formula for the area of a circle is ...

  A = πr^2

Filling in the given radius gives you ...

  A = π(50 cm)^2 = 2500π cm^2 ≈ 7854 cm^2

Answer:

x = 2, y = 1

Step-by-step explanation:

2x+3y = 7

y = 6x -11

Substitute the second equation in for y in the first equation

2x +3( 6x - 11) = 7

Distribute

2x+18x - 33 = 7

Combine like terms

20x - 33 = 7

Add 33 to each side

20x -33+33= 7+33

20x = 40

Divide each side by 20

20x/20 = 40/20

x= 2

Now find y

y = 6x-11

y = 6*2-11

y = 12-11

y =1

Answer:

B (2,1)

Step-by-step explanation:

X = 2, y = 1

Look at the attached picture

Hope it will help you

Answer:

Mean, m = 72

Step-by-step explanation:

It is given that, Carl earned grades of 62, 78, 59, and 89 on four math tests.

It is required to find the mean of his grades.

Mean of a data is given by :

[tex]m=\dfrac{\text{sum of observations}}{\text{total no of observations}}[/tex]

Sum of observations is 62 + 78 + 59 + 89 = 288

Total no of observations are 4

So, mean of his grades is :

[tex]m=\dfrac{288}{4}\\\\m=72[/tex]

So, the mean of his grades is 72.

Option C is correct. If Carl earned grades of 62, 78, 59, and 89 on four math tests, the mean of his grades is 72

Mean is the average of the given data. It is expressed mathematically as:

[tex]\overlibe x=\frac{\sum x}{N}[/tex]

[tex]\sum x[/tex] is the sum of the variables

N is the total test taken

[tex]\sum x = 62 + 78 + 59 + 89\\\sum x = 288\\\\N = 4[/tex]

Substitute the resulting values into the mean formula:

[tex]\overline x = \frac{288}{4}\\ \overline x =72[/tex]

This shows that the mean of his grades is 72

Learn more here:https://brainly.in/question/2401311