what is the sum of the geometric series sigma 15,x=0, 2(1/3)x​

Answer:

No

Step-by-step explanation:

A parallelogram may have a right angle (making it a rectangle), but may not.

I see no actual question, but I'm assuming that you want to find the dimensions of the rectangle.

In general, the area of a rectangle with width [tex]w[/tex] and length[tex]l[/tex] is

[tex] A = wl [/tex]

In this case, we know that the width is one-fourth of its length, which means [tex] w = \frac{1}{4}l[/tex]

If we plug this expression for w in the formula for the area, we get

[tex] A = wl = \dfrac{1}{4}l\cdot l = \dfrac{1}{4}l^2 [/tex]

We also know that the area is 9 squared units, so we have

[tex] 9 = \dfrac{1}{4}l^2 [/tex]

If we multiply both sides by 4, we get

[tex] l^2 = 36 [/tex]

Consider the square root of both sides (we only accept the positive solution, since a negative length would make no sense:

[tex] l = \sqrt{36} = 6 [/tex]

So, the length is 6, and the width is one-fourth of 6, i.e.

[tex]\dfrac{1}{4} \cdot 6 = \dfrac{6}{4} = \dfrac{3}{2} = 1.5[/tex]

Answer:

1.5

Step-by-step explanation:

Answer:

[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]

Step-by-step explanation:

Given: [tex]y^2+3y=-1[/tex]

To solve for [tex]y[/tex], we need to get everything on one side of the equal sign and set it to zero. We can do this by adding 1 to both sides. We then get:

[tex]y^2+3y+1=0[/tex]

We can solve for [tex]y[/tex] by using the quadratic formula:

[tex]y=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2a}[/tex] AND [tex]y=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2a}[/tex]

Let's identify our values:

[tex]a: 1\\b: 3\\c: 1[/tex]

Plug in the values and simplify.

[tex]y=\frac{-3+\sqrt{(3)^2-4(1)(1)}}{2(1)}\\y=\frac{-3+\sqrt{5}}{2}\\-------------------------\\y=\frac{-3-\sqrt{(3)^2-4(1)(1)}}{2(1)}\\\\y=\frac{-3-\sqrt{5}}{2}\\[/tex]

Your final answers are:

[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]

answer should be C

let me know if that’s right

Answer:

answer should be C

Step-by-step explanation:

Answer:

The correct answer options are (B) {(-6, 6), (-6, 7), (10, 12)} and (D) {(-6, 4), (10, 5)}.

Step-by-step explanation:

Here, we are given the domain {-6, 10} and we are to determine which of given relations in the options has this domain.

Domain is the set made up of the first elements of each ordered pair (x, y).

For {-6, 10} to be the domain, we will check which of the options have ordered pairs that start with -6 and 10.

If we look at option (B) {(-6, 6), (-6, 7), (10, 12)} and D. {(-6, 4), (10, 5)}, the first (two) ordered pair(s) start with -6 while the last ordered pair starts with 10.

Therefore, B and D are the correct answer option.

Answer:

The correct answer is 3/4

Step-by-step explanation:

This is because if we first change them to using the same unit of measure we get the following.

3 ft/48 in

36 in/48 in

Now we can simplify by dividing both by 12

3/4

Answer:

  B.  -1, 2, -4, 8

Step-by-step explanation:

The characteristic of a geometric sequence is that adjacent terms have a common ratio. Sequence B is the only one.

  2/-1 = -4/2 = 8/-4 = the common ratio: -2

___

Ratios of adjacent terms are different for the other sequences.

Answer:

First account (simple interest)

Step-by-step explanation:

The amount of interest earned by the first account is ...

I = Prt = $2000·0.04·7 = $2000·0.28 = $560

The amount in the second account at the end of 7 year is ...

FV = P·(1+r)^t = $2000·1.02^7 = $2297.37

so you have earned $297.37 in interest on the second account.

$560 is more than $297, so the First Account (simple interest) earns more money.

Answer:

Mason wins after 18 total moves

Step-by-step explanation:

Mason's optimal strategy is to keep the total number of marbles at 11n+1, so he will take 10 marbles to start. For each move Jason makes, Mason will take a number of marbles that makes the sum from the two turns be 11.

After each of Mason's 9 turns, the number of remaining marbles will be ...

89, 78, 67, 56, 45, 34, 23, 12, 1

It doesn't matter how many marbles Jason takes. He will lose on his 9th turn.

Mason's best strategy is to stay the overall variety of marbles at 11n+1, thus he can take ten marbles to begin. for every move Jason makes, Mason can take variety of marbles that creates the add from the 2 turns be eleven.

After every of Mason's nine turns, the amount of remaining marbles are

89, 78, 67, 56, 45, 34, 23, 12, 1

It doesn't matter what number marbles Jason takes. He can lose on his ninth flip.

mason will win after 18 moves

Answer:

t = 58x or t + 7x = 65x

The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as: Method 1: Total Cost = $65 - $7 per hour. Method 2: Total Cost = $65 - ($7 per hour x Number of hours)

The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as:

Method 1 calculates the total cost by applying the discount of $7 per hour directly to the base rate of $65. Method 2 calculates the total cost by multiplying the discount per hour ($7) by the number of hours and subtracting it from the base rate of $65.

https://brainly.com/question/3200361

#SPJ2

Answer:

standard deviation will remain unchanged at 3.5

Step-by-step explanation:

Subtracting 2 from each of the values in the data set will only change the origin of the data set. The mean of the values will change but the variance and consequently the standard deviation will remain unchanged

Answer:

standard deviation of the resulting data will be 3.5

Step-by-step explanation:

When we add or subtract each values of the data set by some constant then the mean will change by the same amount whereas the there is no change in the standard deviation.

So, when we subtract 2 from each values of the data set, the standard deviation of the resulting data will be also 3.5.

Answer:

s= 15x+3x and s=18x

Step-by-step explanation:

Answer:

The total cost for the special would be $15.45

Step-by-step explanation:

One equation would be 15 x 1.03 = 15.45

Second equation would be (15 x .03) + 15 = $15.45

sadly i haven’t learned this so i can’t help you with the answers themselves but a graphing utility you could use is a graphing calculator or a graphing calculator online i know one called desmos.com just not sure if it has the intersect feature so i recommend graphing calculator

The percent that Container A is full after pumping its water into Container B until it is full is that Container A is 49.1% full after pumping water to Container B.

The problem asks us to determine what percent of Container A is full after Container B is full when water is transferred from Container A to Container B. We start by calculating the volume of both cylinders. The volume of a cylinder is given by the formula V = π r² h where V is volume, r is radius, and h is height.

Container A has a radius of 13 feet and a height of 13 feet, so:

π r² h ≈ 6985.3 cubic feet

Container B has a radius of 9 feet and a height of 14 feet, so:

π r² h≈ 3553.0 cubic feet

After filling Container B completely, the volume of water left in Container A is the original volume of Container A minus the volume of Container B. Therefore, the remaining volume in Container A is (6985.3 - 3553.0) cubic feet ≈ 3432.3 cubic feet.

To find the percentage full, we divide this remaining volume by the total volume of Container A and multiply by 100:

Percentage = (3432.3 / 6985.3) * 100 ≈ 49.1%.

After the pumping is complete, Container A is 48.4% full.

Calculate the volume of each container

The volume  of a cylinder is given by the formula:

[tex]\[V = \pi r^2 h\][/tex]

Volume of Container A

- Radius [tex]\( r_A = 13 \)[/tex]feet

- Height [tex]\( h_A = 13 \)[/tex] feet

[tex]\[V_A = \pi (13)^2 (13) = \pi (169)(13) = 2197\pi \text{ cubic feet}\][/tex]

Volume of Container B

- Radius [tex]\( r_B = 9 \)[/tex]feet

- Height [tex]\( h_B = 14 \)[/tex] feet

[tex]\[V_B = \pi (9)^2 (14) = \pi (81)(14) = 1134\pi \text{ cubic feet}\][/tex]

Calculate the remaining volume of water in Container A

Since Container A is initially full and the water is pumped into Container B until Container B is full, the remaining volume of water in Container A is:

[tex]\[V_{\text{remaining}} = V_A - V_B = 2197\pi - 1134\pi = (2197 - 1134)\pi = 1063\pi \text{ cubic feet}\][/tex]

Calculate the percent of Container A that is still full

The percent of Container A that is full is given by:

[tex]\[\text{Percent full} = \left( \frac{V_{\text{remaining}}}{V_A} \right) \times 100\%\][/tex]

Substituting the volumes we calculated:

[tex]\[\text{Percent full} = \left( \frac{1063\pi}{2197\pi} \right) \times 100\% = \left( \frac{1063}{2197} \right) \times 100\%\][/tex]

Simplifying the fraction:

[tex]\[\text{Percent full} = 0.484 \times 100\% = 48.4\%\][/tex]

(-9,11) This one is eleven units from the y-axis

(10,15) is fifteen units away

(5,-12) is 12 units away

(-4,14) is 14 units away

so the one closest to the y-axis is (-9,11)

Please mark me as brainliest

The above answer is wrong. Once graphing the lines you will see the -4 and 14 is the closet to the y axis

The [tex]z[/tex]-score for a height of 16.4 feet is

[tex]z=\dfrac{16.4-14.2}{2.15}\approx1.023[/tex]

So

[tex]P(\text{height}>16.4\,\mathrm{ft})=P(Z>1.023)=1-F_Z(1.023)\approx0.153[/tex]

where [tex]F_Z(z)=P(Z\le z)[/tex] is the cumulative distribution function for the standard normal distribution.

[tex]\bf a^{2b}\implies a^{2\cdot b}\implies (a^2)^b\implies (a^b)^2\qquad \boxed{a^b=x}\qquad (x)^2\implies x^2[/tex]

Answer:

The fractional part of the original pizza is  [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Let

x-----> the original pizza (complete pizza)

we know that

Half a pizza represent ------> [tex]\frac{x}{2}[/tex]

Divide half a pizza by three people

[tex](\frac{x}{2})/3=\frac{x}{6}[/tex]

therefore

The fractional part of the original pizza is  [tex]\frac{1}{6}[/tex]

Consider the attached figure. The height CD cuts the triangle exactly in half. This means that

[tex]\overline{AD}=\overline{BD}=\dfrac{1}{2}\overline{AB}=10[/tex]

Moreover, since CD is the height of the triangle, we know that ACD is a right triangle. We know the hypothenuse AC to be 20 feet because it is a side of the triangle, and we just found out that AD is 10. We can use the pythagorean theorem to deduce

[tex]\overline{CD}=\sqrt{\overline{AC}^2-\overline{AD}^2}=\sqrt{400-100}=\sqrt{300}[/tex]

So, the area is

[tex]A=\dfrac{bh}{2}=\dfrac{\overline{AB}\cdot\overline{CD}}{2} = \dfrac{20\cdot\sqrt{300}}{2}=10\sqrt{300}\approx 173[/tex]

Well to start off all sides are gonna be 20. To find area it’s lxw so 20•20=400

Dives 400 by 12 and you get 33.333333333 so you round that to the nearest whole foot and you get 33 feet

Answer:

Both plans last for 1.25 hours (1 hour 15 minutes)

Step-by-step explanation:

Let x hours be the time needed for plan A and y hours be the time needed for plan B.

On Wednesday there were 5 clients who did Plan A and 3 who did Plan B. Thus, 5x+3y=10.

On Thursday there were 2 clients who did Plan A and 6 who did Plan B. Thus, 2x+6y=10.

Solve the sytem of two equation. Multiply the first equation by 2, the second by 5 and subtract them:

[tex]10x+6y-10x-30y=20-50,\\ \\-24y=-30,\\ \\y=\dfrac{30}{24}=\dfrac{5}{4}=1.25\ hours.[/tex]

Therefore,

[tex]5x+3\cdot 1.25=10,\\ \\5x=10-3.75=6.25,\\ \\x=1.25\ hours.[/tex]

Answer:

y = x^2 +2x -35

Step-by-step explanation:

Multiply the binomials. The distributive property is helpful.

y = x(x -5) +7(x -5) . . . . the terms of the first binomial multiplied by the second

= x^2 -5x +7x -35 . . . . eliminate parenthses

y = x^2 +2x -35 . . . . . . collect terms

Answer:

B) 11:35 a.m.

Final answer:

The bottle will be half full at 11:50 PM, which is ten minutes before it is completely full at midnight, due to the exponential growth doubling the contents every ten minutes.

Explanation:

The question involves understanding exponential growth, specifically the doubling time of a population or, in a more tangible sense, the filling of a jar (or bottle). Given that a bottle doubles the amount inside every ten minutes and is full at midnight, we can calculate when the bottle will be half full by working backwards from the endpoint.

If the bottle is full at midnight, then it was half full at 11:50 PM, since the contents double every ten minutes. This reveals a common misunderstanding in our intuition about exponential growth, where significant change occurs in the final moments before reaching capacity.

In summary, to find out when the bottle will be half full, simply subtract a single doubling interval (ten minutes) from the time when the bottle is known to be full.

Answer:

1/4

Step-by-step explanation:

3 x 1 = 3

4 x 3 = 12

3/12 simplified is 1/4

The quotient of the numbers 3/4 and 1/3 will be 9/4.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The numbers are given below.

3/4 and 1/3

The quotient of the numbers 3/4 and 1/3 is given by the number 3/4 divided by 1/3. Then we have

⇒ (3/4) / (1/3)

Simplify the expression, then we have

⇒ (3/4) x (3/1)

⇒ 9 / 4

The quotient of the numbers 3/4 and 1/3 will be 9/4.

More about the division link is given below.

https://brainly.com/question/369266

#SPJ2

Answer:

430

Step-by-step explanation:

All you have to do is add up all the sides So 80+80+250+20=430 And there you have it!

Answer:

-1/2=x

Step-by-step explanation:

-9 + x = 5x - 7

     -x      -x

-9=4x-7

+7         +7

-2=4x

-2/4 =4x/4

-1/2=x

Answer:

You need to find the number of times x goes into 3x^2 which is 3x, so you write 3x as the beginning of the quotient to start the division.

Answer:

3x^2 / x.

Step-by-step explanation:

The first step is to divide 3x^2 by the first term of x - 2 ( that is x).

Answer:

  x = 7.5

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relationship between the angle and the sides of interest is ...

  Tan = Opposite/Adjacent

  tan(37°) = x/10 . . . . fill in given values

Multiplying by 10, we get ...

  x = 10·tan(37°) ≈ 7.5

Answer:

3) 2/3

4) an = 162·(1/3)^(n-1)

Step-by-step explanation:

3) A geometric sequence has a common ratio between adjacent terms. Here, that ratio is ...

r = 54/162 = 18/54 = 6/18 = 1/3

Then the next two terms can be found by multiplying by the common ratio:

6 · 1/3 = 2

2 · 1/3 = 2/3 . . . . . the sixth term

____

4) The generic expression for the n-th term of a geometric sequence with first term a1 and common ratio r is ...

an = a1·r^(n-1)

We can put in the numbers for a1 and r, and we have ...

an = 162·(1/3)^(n-1)

Answer:

Step-by-step explanation:

After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...

  V = πr²·h = 2πr³ = 39 in³

Then the radius is ...

  r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in

  h = 2r = 3.67557 in ≈ 3.68 in

_____

The total surface area of a cylinder is ...

  S = 2πr² + 2πrh

For a given volume, V, this becomes ...

  S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r

The derivative of this with respect to r is ...

  S' = 4πr -2V/r²

Setting this to zero and multiplying by r²/2 gives ...

  0 = 2πr³ -V

  r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r

__

If we substitute the equation for V into the equation just above this last one, we have ...

  0 = 2πr³ - πr²·h

Dividing by πr² gives ...

  0 = 2r - h

  h = 2r . . . . . generic solution for cylinder optimization problems

A random supporter roots the home team with probability 0.9, and the away team with probability 0.1.

Choosing 6 out of 8 supporters who root for the home team has probability

[tex]\displaystyle\binom{8}{6}\cdot 0.9^6\cdot 0.1^2 = 28\cdot0.531441\cdot 0.01=0.14[/tex]