Find the 8th term of the geometric sequence 3, 12, 48, ...

Answer:

(a) [tex]\sigma = 7.04[/tex]

(b) [tex]\sigma = 14.1[/tex]

(c) The population standard deviation is multiplied by k

Step-by-step explanation:

Given

[tex]Dataset: 12, 7, 18, 23, 24, 27[/tex]

Solving (a): The population standard deviation

Start by calculating the mean

[tex]\mu = \frac{\sum x}{n}[/tex]

[tex]\mu = \frac{12+7+18+23+24+27}{6}[/tex]

[tex]\mu = \frac{111}{6}[/tex]

[tex]\mu = 18.5[/tex]

The population standard deviation is:

[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]

This gives:

[tex]\sigma = \sqrt{\frac{(12-18.5)^2 + (7 - 18.5)^2 + (18-18.5)^2 + (23-18.5)^2 + (24 - 18.5)^2 + (27 - 18.5)^2}{6}}[/tex]

[tex]\sigma = \sqrt{\frac{297.5}{6}}[/tex]

[tex]\sigma = \sqrt{49.5833}[/tex]

[tex]\sigma = 7.04[/tex]

Solving (b): Double the dataset and calculate the new population standard deviation

The new dataset is:

[tex]Dataset: 24, 14, 36, 46, 48, 54[/tex]

Start by calculating the mean

[tex]\mu = \frac{\sum x}{n}[/tex]

[tex]\mu = \frac{24+ 14+ 36+ 46+ 48+ 54}{6}[/tex]

[tex]\mu = \frac{222}{6}[/tex]

[tex]\mu = 37[/tex]

The population standard deviation is:

[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]

This gives:

[tex]\sigma = \sqrt{\frac{(24-37)^2 +(14-37)^2 +(36-37)^2 +(46-37)^2 +(48-37)^2 +(54-37)^2}{6}}[/tex]

[tex]\sigma = \sqrt{\frac{1190}{6}}[/tex]

[tex]\sigma = \sqrt{198.33}[/tex]

[tex]\sigma = 14.1[/tex]

Solving (c): What happens when the dataset is multiplied by k

In (a), we have:

[tex]\sigma = 7.04[/tex]

In (b), when the dataset is doubled,

[tex]\sigma = 14.1[/tex]

This implies that when the dataset is multiplied by k, the population standard deviation will be multiplied by the same factor:

i.e.

[tex]New \sigma = k * \sigma[/tex]

Answer:

A

Step-by-step explanation:

Hi I don't usually upload pictures but I was too lazy to type so I did it on paper. I had to get the numbers in the parenthesis out so I multiplied the + by everything in the parenthesis following the negative and positive multiplication rules. Then, I combined and subtracted like terms.

Hope this helps !!

-Ketifa

Answer:

<1=62

<2=83

<3=35 this is the answer of this question

9514 1404 393

Answer:

  -2/5, -6

Step-by-step explanation:

We assume you're asking for solutions to ...

  (5x -(-2))(x +6) = 0

This can be simplified to ...

  (5x +2)(x +6) = 0

__

The solutions are the values of x that make the factors zero. (The product can only be zero if a factor is zero.) Here, we'll find the zeros of the factors one at a time.

  5x +2 = 0

  5x = -2 . . . . . subtract the constant

  x = -2/5 . . . . divide by the x-coefficient

__

  x +6 = 0

  x = -6 . . . . . .subtract the constant

The solutions of the equation are x = -2/5 or -6.

__

The graph shows the x-values that make the product zero.

Answer:

a) ≈ 0.1

b) ≈ 0.2

c) ≈ 0.9

Step-by-step explanation:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

SOLUTION :-

a) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{0.1}{0.995}[/tex] ≈ 0.1

b) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{-0.158}{-0.987} = 0.16 (appx)[/tex] ≈ 0.2

c) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{0.631}{0.776} = 0.81 (appx)[/tex] ≈ 0.9

Sales Tax = $3.00

The total amount paid by the group was $48.15

The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:

Sales tax = $37.50 * 8% = $3.00

The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:

Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15

So the total amount paid by the group was $48.15.

Answer:

D

Step-by-step explanation:

i did a test with the same question

The representative sample of the population displayed by the dot plot is: dot plot D.

The representative sample of a population can be described as a subset of a particular population which displays or exhibit similar characteristics of the larger population group.

From the image given, the dot plot that reflects the characteristics of the dot plot of the population is the dot plot in option D.

Dot plot D is a representative sample.

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The result of the product of the given complex numbers as required to be determined is; Choice C; -5 + 14i.

It follows from the task content that the result of the product of the given complex numbers is to be determined.

On this note, since the required product to be evaluated is; (–4 + i) (2 – 3i).

We can therefore multiply as follows;

-8 + 12i + 2i - 3i².

However, it is noteworthy to know that; i² = -1.

Hence, we have that;

-8 + 14i + 3

= -5 + 14i

On this note, it follows that the result of the product of complex numbers as required is; -5 + 14i.

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Answer:

75 : 225

Step-by-step explanation:

[tex]\frac{\frac{1}{4} }{\frac{3}{4} } :\frac{75}{y}[/tex]

0.25 × y = 0.75 × 75

0.25y = 56.25

0.25y ÷ 0.25 = 56.25 ÷ 0.25

y = 225

Answer:

14.1 inches

Step-by-step explanation:

The formula to be used to find the arc length is Ф = s(arc length) / r(radius)

First we rearrange the formula to find the arc length which would be s = Ф * r

This formula only works in radians so the first step is converting 135° to radians so we would do 135° * π radians/180° which would give us 3π/4

We would then multiply 3π/4 * 6 and get 18π/4,  plugging that value into a calculator returns us a value of ≈ 14.137

We then round to the nearest tenth and get an answer of 14.1 inches for the arc length of the circle below

Answer:

Years = {log(total) -log(Principal)} ÷ log(1 + rate)

Years = [log (200,000) -log (20,000)] / log (1.09)

Years = [5.3010299957 -4.3010299957] /  0.037426497941

Years = 1 / 0.037426497941

Years = 26.7190374471

*************************************************

Finding Doubling Time : (We'll calculate $100 becoming $200)

Years = {log(total) -log(Principal)} ÷ log(1 + rate)

Years = log (200) -log (100) / log(1.09)

Years =  (2.3010299957 -2) / 0.037426497941

Years = .3010299957 / 0.037426497941

Years 8.0432317278

It takes 8.0432317278 years for money to double at 9% per year.

Source:

http://www.1728.org/compint2.htm

Step-by-step explanation:

Answer:

No because 9.307 is less than due the facts that the seven in 9.307 is in the thousandth while the seven in 9.37 is in the hundredths

Answer:

The answer is C

Step-by-step explanation:

You have to divide both numerators then the denominater.

So, it would look like:  160 over 90 x 100 over 290

160x100=16   90x290=25     16/25

Answer:

ffyftxrrxrrxcvcmuvcyztzxvujgyh

Step-by-step explanation:

✋☝☝✊✋❤❤❤

On solving the provided question, we can say that - by doing the fraction we have 3/12 = 1/4

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

balloons is 12

blew up is  1/3

friend blew up is  5

1/3*12 = 4

4+5 = 9

3/12 = 1/4

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Answer:

1. A

2. C

Step-by-step explanation:

Answer:

Shift down 15 units

Step-by-step explanation:

the number on the right is the one that determines where the line intersects through the y axis

You can get 3/8 from 13/8 by subtraction. The solution is 10 / 8

In order to get 3/8 from 13/8 we would have to carry out a subtraction of fractions.

That is we would have: 13/8 - 3/8

take the lcm of the denominator

[tex]\frac{13 - 3}{8}[/tex]

= 10 / 8

Hence when we take 3 / 8 from 13 / 8, the solution that we would have would be from subtraction. This is 10 / 8

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9514 1404 393

Answer:

  2) true

  3) X = -19/48

  4) Y = 27/56

Step-by-step explanation:

3) Subtract 5/6 from both sides

  X = 7/16 -5/6 = (7·6 -16·5)/(16·6) = (42 -80)/96

  X = -19/48

__

4) Subtract 1/7 from both sides

  Y = 5/8 -1/7 = (5·7 -8·1)/(8·7)

  Y = 27/56

Answer:

x = 20°

Step-by-step explanation:

x = 180 - (70 + 90)

x = 180 - 160

x = 20°

Hope this helps!

Answer: in explanation

Step-by-step explanation

Sandi can perform  1/9 of the task in a day

Eva can perform 1/5 of the task in a day

Working together, they can perform

                                                            1/9 + 1/5 of the task per day

                                                            = 5/45 + 9/45 = 14/45 of the task in a day

or                                                             45/14 days in the task = 3.2 days

So

          It would take about 3.2 days to complete the task working togethe

Answer:

( a + 2 ) ( x - y )

Step-by-step explanation:

2 ( x - y ) - a ( y - x )

= 2 ( x - y ) + a ( x - y )

= ( 2 + a ) ( x - y )

= ( a + 2 ) ( x - y )

Hence factorised.

Answer:

width = 10 yds

Step-by-step explanation:

perimeter = 2L + 2W

74 = 2(27) + 2W

74 = 54 + 2W

subtract 54 from both sides of the equation:

2W = 20

divide both sides by 2:

W = 10

The width of the yard whose length is 27 yards and perimeter is 74 yards is evaluated to be 10 yards

For a rectangle with length and width L and W units, we get:

Perimeter of the rectangle = [tex]2(L + W) \: \rm units[/tex]

For this case, let we assume that:

The width of the considered rectangular field = W yards

Then, as we're provided that:

Putting these in the formula for perimeter of a rectangle, we get;

[tex]Perimeter = 2( L + W)\\74 = 2(27 + W)\\\\\text{Dividing both the sides by 2}\\\\\dfrac{74}{2} = \dfrac{2(27+W)}{2}\\\\37 = 27 + W\\\\\text{Subtracting 27 from both the sides}\\\\37 - 27 = W\\W = 10 \: \rm yards[/tex]

Thus, the width of the yard whose length is 27 yards and perimeter is 74 yards is evaluated to be 10 yards

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Here we go...

= 2x² - y² = 17

= 2x² = 17 + y²

= x² = 17 + y²/2

= x = √17+y²/2

= x + 2y = 1

= x = 1 - 2y

___________________

Sry,if i misunderstood the question.. do let me know in the comment section

Answer:

yeah it's true

Step-by-step explanation:

............THANKS.........

Answer: Choice A

angle GAF = angle TAE is the lie (aka false statement)

========================================================

Explanation:

Let's go through each answer choice to see which is true or which is false.

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

Choice A

The markers for angles GAF and TAE are different. Both would need to have a single angle marker, or a double angle marker. The differing markers indicates the angles aren't the same.

Also, note that angle TAG isn't a 180 degree angle, or that point G isn't on line TA. We need this to be the the case, so that two vertical angles form. However, such a thing doesn't happen.

So that's why angles TAE and GAF aren't the same measure.

Choice A is the answer. You can stop here if you wanted.

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

Choice B

Let

x = measure of angle TAE

y = measure of angle TAH

z = measure of angle HAF

We can see that x+y+z = 180, since angle EAF is a straight angle. The diagram gives y = 90 and z = 50, so,

x+y+z = 180

x+90+50 = 180

x+140 = 180

x = 180-140

x = 40

Angle TAE is 40 degrees. It adds with angle FAH to get 40+50 = 90, showing that the two angles are indeed complementary.

Choice B is a true statement, so we can rule it out.

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

Choice C

Angle TAF is composed of angles TAH and HAF

Adding the two angles gets us 90+50 = 140, which is larger than 90.

Therefore angle TAF is obtuse.

Choice C is a true statement, and it can be ruled out as well.

Technically you could have stopped at choice A once you found the lie, but I figured to show why choices B and C could be ruled out.

Step-by-step explanation:

please refer to the 3 pages of sketch for details