4−1+1/4−1/16+... Find the sum of the infinite geometric series, if it exists.

12x10=120 now 120x30=3,600 so your answer is 3600

The area of Shen's rectangular garden is 120 square feet. Given that a bag of fertilizer covers 30 square feet, Shen will need 4 bags of fertilizer to cover his garden.

This question relates to the area of a rectangle and unit conversion. The area of a rectangle can be calculated by multiplying its length and its width. In this case, the garden is a rectangle with a length of 12 feet and a width of 10 feet. By multiplying these two dimensions, we get an area of 120 square feet.

A single bag of fertilizer covers 30 square feet. To calculate the number of bags required to cover the garden, we can divide the total area of the garden (120 square feet) by the area that one bag of fertilizer can cover (30 square feet).

So, 120 ÷ 30 = 4. Therefore, Shen will need 4 bags of fertilizer to cover his garden.

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Answer:

V≈1231.5in³

Step-by-step explanation:

ANSWER

[tex]Volume = 1231.5 {in}^{3} [/tex]

EXPLANATION

The volume of the cylinder is

EXPLANATION

The volume of a right cylinder is given by the formula:

[tex]Volume = \pi \: {r}^{2} h[/tex]

From the given information, the height of the cylinder is 2 inches and the base radius is 14 inches.

This implies that, r=14 inches and r=2 inches.

We plug in the values into the formula to get;

[tex]Volume = \pi \times {14}^{2} \times 2[/tex]

[tex]Volume = \pi \times 196 \times 2[/tex]

[tex]Volume =392 \pi [/tex]

[tex]Volume = 1231.5 {in}^{3} [/tex] to the nearest tenth.

Looks like your figure is missing...

Could you repost it with the figure next time?

Someone will solve it for sure.

Regards;

Leukonov.

Answer:A dot plot.

Step-by-step explanation: it shows the 5 number summary.

The correct answer is dot plot!

Answer:

Part 1) [tex]x=-0.07[/tex]

Part 2) [tex]y=2.48[/tex]

Step-by-step explanation:

Part 1) we have

[tex]15^{-9x} =6[/tex]

Solve for x

Apply log both sides

[tex]log(15^{-9x})=log(6)[/tex]

[tex]-x*(9log(15))=log(6)[/tex]

[tex]x=-log(6)/(9log(15))[/tex]

[tex]x=-0.07[/tex]

Part 2) we have

[tex]e^{y}=12[/tex]

Apply ln both sides

[tex]ln(e^{y})=ln(12)[/tex]

[tex]y*ln(e)=ln(12)[/tex]

Remember that

[tex]ln(e)=1[/tex]

[tex]y=ln(12)[/tex]

[tex]y=2.48[/tex]

Answer with explanation:

The two equations which we have to solve for x and y and the way of finding it's solution is

   [tex]1.\rightarrow 15^{-9x}=6\\\\\text{Taking log on both sides}\\\\\rightarrow -9x \log 15=\log 6\\\\\rightarrow x \log 15^{-9}=\log 6\\\\\rightarrow x=\frac{\log 6}{\log 15^{-9}}}\\\\\rightarrow x=\log_{15^{-9}} 6\\\\2.\rightarrow e^y=12\\\\\text{Taking log on both sides}\\\\\rightarrow y \log e=\log 12\\\\\rightarrow y= \log 12[/tex]

The answer is the first option

[tex]\frac{3^{2}(-2)^{6}}{5^{4}}[/tex]

Quick tips to help you the next time

Multiply the exponents

Add the exponents

Answer:

the first person is right but...

Step-by-step explanation:

you should censor out your name!! Safety!

Answer:

15 ounces of red beans

Step-by-step explanation:

So, we know Kim's soup contains a total of 75 ounces of beans, including red beans (r) and black beans (b), so r + b = 75

Then we know that for each ounce of red beans, there are 4 ounces of black beans, 1b = 4r

Then we merge both equations by replacing b's value in the first equation by its equivalent (b = 4r), since we are looking for the count of red beans.

r + b = 75

r + 4r = 75

5 r = 75

r = 15

There are 15 ounces of red beans in Kim's soup, that looks a lot like the last chili I made :-)

[tex]\bf (2x^2-11x-9)-(14x^2+8x-4)\implies (2x^2-11x-9)-14x^2-8x-4 \\\\\\ 2x^2-14x^2-11x-8x-9-4\implies -12x^2-19x-5~~\checkmark \\\\[-0.35em] ~\dotfill\\\\ 2(x-1)-3(4x^2+7x+1)\implies 2x-2-12x^2-21x-3 \\\\\\ -12x^2+2x-21x-2-3\implies -12x^2-19x-5~~\checkmark \\\\[-0.35em] ~\dotfill\\\\ 3(x-5)-2(6x^2+9x+5)\implies 3x-15-12x^2-18x-10 \\\\\\ -12x^2+3x-18x-15-10\implies -12x^2-15x-25~~\bigotimes \\\\[-0.35em] ~\dotfill\\\\ (4x^2-13x-7)-(16x^2+9x-5)\implies 4x^2-13x-7-16x^2-9x+5[/tex]

[tex]\bf 4x^2-16x^2-13x-9x-7+5\implies -12x^2-22x-2~~\bigotimes \\\\[-0.35em] ~\dotfill\\\\ (-16x^2+10x-3)+(4x^2-29x-2)\implies -16x^2+10x-3+4x^2-29x-2 \\\\\\ -16x^2+4x^2+10x-29x-3-2\implies -12x^2-19x-5~~\checkmark \\\\[-0.35em] ~\dotfill\\\\ (-15x^2+9x-10)+(3x^2-10x-5)\implies -15x^2+9x-10+3x^2-10x-5 \\\\\\ -15x^2+3x^2+9x-10x-10-5\implies -12x^2-x-15~~\bigotimes[/tex]

To find the original amount of sugar in each cake recipe, we can set up a proportion and solve for x. The original amount of sugar in each cake recipe was 7/6 cups.

To solve this problem, we can use a proportion to find the original amount of sugar in each cake recipe. Let x represent the original amount of sugar in each cake recipe. We know that reducing the amount of sugar by 1/2 cup from 1 cake results in 4 cups of sugar for 6 cakes. So we can set up the proportion:

(x - 1/2) / 1 = 4 / 6

Cross-multiplying, we get (x - 1/2) * 6 = 4 * 1. Simplifying further, we have 6x - 3 = 4. Adding 3 to both sides, we get 6x = 7. Finally, dividing both sides by 6, we find that x = 7/6 cups of sugar.

Therefore, the original amount of sugar in each cake recipe was 7/6 cups.

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Answer:

The simplified form is 1 over the quantity x plus 2 times the quantity

x minus 5 ⇒ 1/(x+2)(x-5) ⇒ last answer

Step-by-step explanation:

* Lets write the product of the two fraction

∵ [tex]\frac{x+4}{x^{2}-3x-10} *\frac{x-3}{x^{2}+x-12}[/tex]

- At first factorize the denominators

# x² - 3x - 10

∵ x² = x × x ⇒ 1st term in the 1st bracket and 1st term in the

  2nd bracket

∵ -10 = 2 × -5 ⇒ 2nd term in the 1st bracket and 2nd term in the

  2nd bracket

∵ x × - 5 = -5x ⇒ ext-reams

∵ x × 2 = 2x ⇒ means

∵ 2x + -5x = -3x ⇒ middle term

∴ x² - 3x - 10 = (x + 2)(x - 5)

# x² + x - 12

∵ x² = x × x ⇒ 1st term in the 1st bracket and 1st term in the

  2nd bracket

∵ -12 = -3 × 4 ⇒ 2nd term in the 1st bracket and 2nd term in the

  2nd bracket

∵ x × 4 = 4x ⇒ ext-reams

∵ x × -3 = -3x ⇒ means

∵ 4x + -3x = x ⇒ middle term

∴ x² + x - 12 = (x - 3)(x + 4)

* Lets write the fractions after factorization

∴ [tex]\frac{x+4}{(x+2)(x-5)}*\frac{x-3}{(x-3)(x+4)}[/tex]

- lets simplify the fractions by cancel (x - 3) up with (x - 3) down

 and cancel(x + 4) up with (x + 4) down

∴ [tex]\frac{1}{(x+2)(x-5)}*1=\frac{1}{(x+2)(x-5)}[/tex]

* The simplified form is 1 over the quantity x plus 2 times the

  quantity x minus 5

Answer:

(x,y)=(85/562, -20/281)

Step-by-step explanation:

4x+2y=-6.5y=-30x+5

{4x+2y=-30x+5

{-6.5y=-30x+5 simplify the expression

{34x+2y=5

{300x-65y=50 multiply

{2210x+130y=325

{600x-1307=100 eliminate on evariable by adding the equations

2810x=425 divide both sides by 2810

x=85/562 substitute the value of x into the equation

34*85/562+2y=5 solve the equation

y=-20/281 a possible solution

(x,y)=(85/562,-20/281) check the solution

4*85/562+2*(-20/281)=-6.5*(-20/281)=-30*85/562+5 simplify the expression

130/281=130/281=130/281 the orderred pair is a solution

Answer:

A. [tex]3r-14=78[/tex]

Step-by-step explanation:

We are given the equation

[tex]3r=78+14[/tex]

If we subtract 14 from each side we get

[tex]3r=78+14\\\\3r-14=78[/tex]

This is what is shown in answer A

The equation equivalent to 3r = 78 + 14 is Option(A) 3r - 14 = 78 .

The given equation is 3r = 78 + 14 .

Thus, rearranging the given equation, we have

3r - 14 = 78 .

which gives us Option(A).

Therefore, the equation equivalent to 3r = 78 + 14 is Option(A) 3r - 14 = 78 .

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Answer:

Step-by-step explanation:

167.31 is 33% of 507

180 is 48% of 375

216.6 is 76% of 285

238.8 is 60% of 398

133.5 is 89% of 150

111.8 is 26% of 430

174.96 is 81% of 216

29.2 is 5% of 584

130.5 is 18% of 725

2.3 is 2% of 115

136.8 is 90% of 152

77.88 is 12% of 649

118.8 is 55% of 216

46.44 is 43% of 108

227.95 is 97% of 235

33% of 507 = 167.31

48% of 375 = 180

76% of 285 = 216.6

60% of 398 = 238.8

89% of 150 = 133.5

26% of 430 = 111.8

81% of 216 = 174.96

5% of 584 = 29.2

18% of 725 = 130.5

2% of 115 = 2.3

90% of 152 = 136.8

12% of 649 = 77.88

55% of 216 = 118.8

43% of 108 = 46.44

97% of 235 = 227.95

Answer:

x ≤ -4

Step-by-step explanation:

Less than or equal to ≤

x ≤ -4

Answer:

1947

Step-by-step explanation:

This is the answer

Answer:

Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.

Step-by-step explanation:

Joni put $200 in an interest-bearing account with an annual compound interest rate of 5%. Joni determined that after 3 years, she will have a total balance of $230.

Step 1: P = 200, r = 5, t = 3

Step 2: I = 200*0.05* 3

Step 3: I = 30

Step 4: 30 + 200 = 230

Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.

Above it is given, that annual compound interest rate of 5%

So, she should have calculated using the compound interest formula.

[tex]A=p(1+r/n)^{nt}[/tex]

So, amount becomes :

[tex]A=200(1+0.05)^{3}[/tex]

[tex]A=200(1.05)^{3}[/tex] = $231.53.

Answer:

Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.

Step-by-step explanation:

Just did it

Answer:

51

Step-by-step explanation:

113-62=51

Answer:

[tex]\boxed{\bold{66k+9}}[/tex]

Explanation:

Expand [tex]\bold{5\left(10k+1\right): \ 50k+5}[/tex]

= [tex]\bold{50k+5+2\left(2+8k\right)}[/tex]

Expand [tex]\bold{2\left(2+8k\right): \ 4+16k}[/tex]

= [tex]\bold{50k+5+4+16k}[/tex]

Simplify [tex]\bold{50k+5+4+16k: \ 66k+9}[/tex]

= [tex]\bold{66k+9}[/tex]

Mordancy.

Equivalent expressions are expressions that work the same even though they look different. The equivalent expression 5(10k+1)+2(2+8k) is 66k+9. So option A is correct.

The given expression is 5(10k+1)+2(2+8k). We need to find equivalent expression.

Equivalent expressions are expressions that work the same even though they look different.

The given expression is 5(10k+1)+2(2+8k)

Multiply 5 with 10k+1 and 2 with 2+8k

50k+5+4+16k

Add the terms with k coefficient.

66k+9

Therefore 66k+9 is equivalent expression of 5(10k+1)+2(2+8k).

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Answer: in doing transformations, the pre-image is the image you start with. The task is to move the pre-image so that it is contiguous with the (target) image. This is typically done by translation, rotation or reflection or a combination of those moves.

Hope that helps

Step-by-step explanation:

Image is a related term of preimage. Preimage is a derived term of image.

In context terms the difference between preimage and image is that preimage is the set containing exactly every member of the domain of a function such that the member is mapped by the function onto an element of a given subset of the codomain of the function formally, of a subset b'' of the codomain ''y'' under a function ƒ, the subset of the domain ''x defined by while image is the subset of a codomain comprising those elements that are images of something.

As nouns the difference between preimage and image is that preimage is the set containing exactly every member of the domain of a function such that the member is mapped by the function onto an element of a given subset of the codomain of the function formally, of a subset b'' of the codomain ''y'' under a function ƒ, the subset of the domain ''x defined by while image is an optical or other representation of a real object; a graphic; a picture.

Answer:

4+3 squared 3 equals 9.19 and 4-3 squared 3 equals -1.19

Step-by-step explanation:

Answer:

g(x) = (x + 9)2

Step-by-step explanation:

I am sorry but I am not 100% sure this is correct but it might be.. x = 80.3848

Answer:

B. Plane and Line

Step-by-step explanation:

Answer :FDG AND IGJ

Step-by-step explanation: Since EGF is 90 degrees then and EGD equals 38 degrees you need to subtract 38 from 90 and you are left with 52 degrees for angle FGD. The alternate interior angle to FGD is IGJ which would make the angles congruent.

The measure of angle IGJ is 38 degrees.

Let's derive the measure of angle IGJ step by step:

Given: Angle EGD = 38 degrees

To find: Angle IGJ

In triangle IGJ, we know that the sum of the interior angles is 180 degrees. Therefore, we can write:

Angle I + Angle G + Angle J = 180 degrees

Now, let's focus on angle G. Angle G is opposite to angle EGD in triangle EGD. According to the angle opposite to the side in a triangle theorem (or the angle opposite to the side is equal in a triangle theorem), we can say:

Angle G = Angle EGD

Given that Angle EGD = 38 degrees, we have:

Angle G = 38 degrees

Now, let's substitute this value into the equation for triangle IGJ:

Angle I + 38 degrees + Angle J = 180 degrees

Now, let's isolate angle I and angle J by subtracting 38 degrees from both sides:

Angle I + Angle J = 180 degrees - 38 degrees

Angle I + Angle J = 142 degrees

Now, we have an equation relating angle I and angle J. However, we need more information to determine the measure of either angle. But, we know that the sum of the angles in triangle IGJ is 180 degrees. Therefore, we can conclude that:

Angle I + Angle G + Angle J = 180 degrees

Angle I + 38 degrees + Angle J = 180 degrees

Angle I + Angle J = 180 degrees - 38 degrees

Angle I + Angle J = 142 degrees

Since the sum of angles I and J is 142 degrees, and we know that angle G is 38 degrees, the remaining angle (IGJ) must be equal to angle G:

Angle IGJ = Angle G = 38 degrees

Therefore, the measure of angle IGJ is 38 degrees.

Complete question

If angle EGD=38 degrees, what is angle IGJ?

Answer:

The domain by the interval notation is (-∞ , 3)∪(3 , 4)∪(4 , ∞) ⇒ 3rd answer

Step-by-step explanation:

* Lets revise how to find the domain of the function

- The domain is all values of  x  that make the expression defined

- To find where the expression is undefined put the denominator

  equal 0, to get the values of x which make denominator equal to 0

- The domain will be all the real number except those values

* Now lets solve the problem

∵ f(x) = (x² - 9)/(x² - 7x + 12)

- Let the denominator x² − 7x + 12  equal to  0

∵ x² − 7x + 12 = 0 ⇒ factorize it

- Consider the form  x² + bx + c

- Find a pair of integers whose product is c and whose sum is b

- In this case, whose product is 12 and whose sum is −7

- They are -3 and -4

- Write the factored form using these integers.

∴ (x -3)(x - 4) = 0 ⇒ put each bracket = 0

∴ x - 3 = 0 or x - 4 = 0

∵ x - 3 = 0 ⇒ add 3 to both sides

∴ x = 3

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∴ The domain of f(x) is all real number except 3 and 4

* The domain by the interval notation is

 (-∞ , 3)∪(3 , 4)∪(4 , ∞)

The probability of grabbing a diet soda and a snack bag of Cheetos is 42%.

The question is asking to find the probability of selecting a diet soda and a bag of Cheetos at a party. To calculate this probability, we need to look at the total number of each item and determine how many favorable outcomes there are based on the selections made.

64 is the correct answer

Answer: [tex]A = 201.06\ in^2[/tex] or [tex]A = 64\pi\ in^2[/tex]

Step-by-step explanation:

The surface area of a sphere is calculated by the following formula

[tex]A = 4\pi r^2[/tex]

Where r is the radius of the sphere

In this case we know that the diameter d of the sphere is

[tex]d=8\ inches[/tex]

So the radius r is:

[tex]r=\frac{d}{2}\\\\r=\frac{8}{2}\\\\r=4\ inches[/tex]

So the surface area of the sphere is:

[tex]A = 4\pi (4)^2[/tex]

[tex]A = 64\pi[/tex]

[tex]A = 201.06\ in^2[/tex]

A. 34 square rooted

[tex]lm = \sqrt{34} [/tex]

it would be 112.5 times times 3 and then multiply by 1000

I got the same answer that user said

Answer:

Olive oil contains Vitamin E, which improves blood circulation and facilitates nail growth. Heat up some olive oil and massage it into your nails and cuticles for about five minutes. Wear gloves and let it sit overnight. Alternatively, you can soak your nails in warm olive oil for fifteen to twenty minutes.

Step-by-step explanation:

Answer:

tea tree oil can work  and to stop biting your nails use gel nail polish

Step-by-step explanation: