How to simplify this expression??

Answer:

The standard error decreases and the width of the confidence interval also decreases.

Step-by-step explanation:

The standard error of a distribution (E) is given as:

[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }[/tex]

Where n is the sample size, [tex]z_{\frac{\alpha}{2} }[/tex] is the z score of he confidence and [tex]\sigma[/tex] is the standard deviation.

The sample size is inversely proportional to the standard error. If the sample size is increased and everything else is constant, the standard would decrease since they are inversely proportional to each other. The confidence interval = μ ± E = (μ - E, μ + E). μ is the mean

The width of the confidence interval = μ + E - (μ - E) = μ + E - μ + E = 2E

The width of the confidence interval is 2E, therefore as the sample size increase, the margin of error decrease and since the width of the confidence interval is directly proportional to the margin of error, the width of the confidence interval also decreases.

Answer:

The same mean  ⇒  the same symmetry axis

Bigger standard deviation major spread

Step-by-step explanation: See Annex

The annex shows two different normal curves:

1.-  N (μ₀ ; σ₁ )

2.- N (μ₀ ; σ₂ )

Where   σ₁  > σ₂

They both have the same symmetry  axis ( they have the same mean and both curves have to be symmetrically related to the mean )

Normal distribution curves spread symmetrically at both sides of the mean, but the wider curve is the one that has the bigger standard deviation.  Standard deviation is a measure of the spread of the curve.

Whenever deviation is high, the data is more dispersed than when deviation is low.

Let the mean be 2.

Let the standard deviation be 0.3 for first graph. The data is more clustered around mean.

Let the standard deviation be 0.6 for second graph. The data is less clustered more dispersed from mean.

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The base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.

Triangle is the closed shaped polygon which has 3 sides and 3 interior angles. The height of the triangle is the dimension of the elevation from the opposite peak to the length of the base.

Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.

In the given figure, three triangles is shown with base and height. Here,

Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.

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Answer:

$34000

Step-by-step explanation:

We can set up a systems of equations, assuming [tex]h[/tex] is the husbands income and [tex]w[/tex] is the wife's income.

h + w = 84000

h = 2w - 18000

We can substitute h into the equation as 2w - 18000:

(2w - 18000) + w = 84000

Combine like terms:

3w - 18000 = 84000

Add 18000 to both sides

3w = 102000

And divide both sides by 3

w = 34000

Now that we know how much the wife earns, we can also find out how much the husband earns by substituting into the equation.

h + 34000  = 84000

h = 50000

Hope this helped!

Answer:

Hi, sorry, please could you resend the question again this isn't clear enough to properly answer your question .

maybe you should type in the steps before it is answered. thanks

Answer:

answer= C

Step-by-step explanation:

Answer:

The median is 1.84 and the difference between the first and third quartile is 0.34

Step-by-step explanation:

When you write them out 1.84 is the median (middle number). To find the difference I just subtracted the third quartile (2.09) by the first quartile (1.75)

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

Explanation:

Original data set = {1.96, 2.09, 1.79, 1.61, 1.75, 2.11, 1.84}

Sorted data set = {1.61, 1.75, 1.79, 1.84, 1.96, 2.09, 2.11}

Notice that 1.84 is in the middle of the sorted set. Three values are smaller than it, and three values are larger than it.

Therefore, 1.84 is the median.

The values {1.61, 1.75, 1.79} are smaller than the median. We'll call this set L for lower set.

The values {1.96, 2.09, 2.11} are larger than the median. We'll call this set U for upper set.

From set L = {1.61, 1.75, 1.79}, the median here is 1.75. This is the value of the first quartile Q1

The value of Q3 is 2.09 as it is in the direct middle of set U = {1.96, 2.09, 2.11}

The interquartile range (IQR) is the difference of Q3 and Q1

IQR = Q3 - Q1

IQR = 2.09 - 1.75

IQR = 0.34

Answer: blank 1:  3   Blank 2:  8   blank 3:  1.5    blank 4:   0.25

Step-by-step explanation:

5 times 8=15

4 times 8=32

6 times 1.5=9

12 times 0.25=3

The complete equation is

5⋅____3__=15

4⋅___8___=32

6⋅___1.5___=9

12⋅__0.25____=3

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.

Multiplication Formula

The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where:

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Answer:

its multiple choice

A. 26inches (1inch/25.4mm)

B. 26inches (25.4mm/1inch)

C. 25.4inches (1mm/26inch)

D. 26inches (1mm/25.4inch)

and its b

Answer:

Amount = $6614 and 19 cent

Step-by-step explanation:

Formula for compound interest is

A= p(1+r/n)^(nt)

Compounded daily

So n= 365*2= 730

T= 2

r= 0.13

P= 5100

A= p(1+r/n)^(nt)

A= 5100(1+0.13/730)^(730*2)

A= 5100(1+1.78082*10^-4)^(1460)

A= 5100(1.000178082)^1460

A= 5100(1.2969)

A= 6614.19

Amount = $6614 and 19 cent

Answer:

Step-by-step explanation:

8-2=6

answer is 6

Answer:

2 x 4

Step-by-step explanation:

She need to travel 4 times before she reach the same points again

Answer:  2.5 seconds

Step-by-step explanation:

x refers to time. Since we want to know how long it is in the air, we need to find the time (x) for the ball to land on the ground (y = 0)

0 = -10x² + 25x

0 = -5x(2x - 5)

0 = -5x     0 = 2x - 5

[tex]0 = x\qquad \dfrac{5}{2}=x[/tex]

x = 0 seconds is when the ball was kicked

x = 5/2 --> 2.5 seconds is when the ball landed on the ground

Answer:

Option (G)

Step-by-step explanation:

Volume of the real cane = 96 in³

Volume of the model of a can = 12 in³

Volume scale factor = [tex]\frac{\text{Volume of the model}}{\text{Volume of the real can}}[/tex]

                                 = [tex]\frac{12}{96}[/tex]

                                 [tex]=\frac{1}{8}[/tex]

Scale factor of the model = [tex]\sqrt[3]{\text{Volume scale factor}}[/tex]

                                          [tex]=\sqrt[3]{\frac{1}{8}}[/tex]

                                          [tex]=\frac{1}{2}[/tex]

Therefore, scale factor of the model of a can = [tex]\frac{1}{2}[/tex] ≈ 1 : 2

Option (G) will be the correct option.

Answer:

2.83

Step-by-step explanation:

For a normally distributed data :

Mean = 3.1 inches

Standard deviation = 0.4 inches

Find the value of the quartile Q1:

The quartile Q1 represents the first quartile which is the Lower 25% of the distribution

25% = 0.25

Using the z-table :

0.25 = - 0.68

The z- score formula

Z-score = ( x - mean / standard deviation)

-0.68 = ((x - 3.1) / 0.4)

x - 3.1 = (-0.68 * 0.4)

x - 3.1 = - 0.272

x = - 0.272 + 3.1

x = 2.828

x = 2.83

Answer:

D

Step-by-step explanation:

The fastest way to solve this probelm would be to plug in each x value into these equations untill it outputs the correct two y values.

When you plug 3 into equation D the entire right side it will become.

y-1=0

y=1, which is true.

When you plug 6 into that equation.

y-1=5

y=6 which is also true.

im sorry but the thing is i cant translate these words but the answer is D

Answer:The probability Val will win is 1/5 or 10/50 or 2/10

Step-by-step explanation:

Answer:

9 x =108

Step-by-step explanation:

Let the number of candies be x.

According to the question,

x=108/9

We can also write it as,

9 x=108

By the way ,each child will get 12 candies.

Thank you!

Answer:

18.90

Hope i got it right

Answer:

Hey there!

The first graph is the correct answer. A point on the parabola is equally far from the focus as it is to the directrix.

Let me know if this helps :)

The graph that  accurately displays a parabola with its directrix and focus is the first graph.

Suppose the considered function whose graph is to be made is  f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values  f(x) are plotted on the vertical axis.

They are together plotted on the point  (x,y) = (x, f(x))

This is why we usually write the functions as:  y = f(x)

A point shown in the graphs on the parabola is equally far from the focus as it is to the directrix.

Therefore, The first graph is the correct answer.

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Answer:

5/12

Step-by-step explanation:

(5 * 2^1/4)/4 * 162^1/4) = (5 * 2^1/4)/4 * 3 *2^1/4)

multiply top and bottom by 2^3/4

(5 * 2)/4 * 3 * 2) = 10/24 = 5/12

Answer:

36.143

Step-by-step explanation:

143/1000=0.143

36+0.143=36.143

Answer:

20 gallons of the 40% solution, 60 gallons of the 80% solution

Step-by-step explanation:

Let x = the gallons of the 40% solution, and y = the gallons of a 80% solution. The first thing we want to do here is to convert each percentage into decimal form - including the ​70% solution mixture.

40% = 0.40,

80% = 0.80, respectively 70% = 0.70

As you can tell, 0.40 is associated with x gallons, 0.80 is associated with y gallons, and the mixture contains 0.70 [tex]*[/tex] 80 solution, as 0.70 is associated with 80. Therefore we can formulate the following expression,

0.40x + 0.80y = 0.70 [tex]*[/tex] 80

At the same time x + y = 80, as the solution ( mixture ) is present with 80 gallons. Isolating x, x = 80 - y. Let us plug that into our expression, solving for y, following by x gallons.

[tex]0.40\left(\:80\:-\:y\:\right)\:+\:0.80y\:=\:0.70\:\cdot \:80[/tex]

[tex]0.4\left(80-y\right)+0.8y=56[/tex] ( Multiply either side by 10 )

[tex]4\left(80-y\right)+8y=560[/tex] ( Expand )

[tex]320-4y+8y=560[/tex]

[tex]320+4y=560[/tex]

[tex]4y=240[/tex]

[tex]y = \frac{240}{4} = 60[/tex] ( Substitute to solve for x )

[tex]x = 80 - y = 80 - 60 = 20[/tex]

As you can see there are 20 gallons of the 40% solution, and 60 gallons of the 80% solution.

Answer:

No, each outcome is equally likely regardless of the previous outcome.

A

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Answer: I just took the test and it is D

Answer:

[tex]p(a\ or\ b) = 0.65[/tex]

Step-by-step explanation:

Given

[tex]p(a) = 0.60[/tex]

[tex]p(b) = 0.20[/tex]

[tex]p(a\ and\ b) = 0.15[/tex]

Required

[tex]p(a\ or\ b)[/tex]

The relationship between the given parameters and the required parameters is as follows;

[tex]p(a\ and\ b) = p(a) + p(b) - p(a\ or\ b)[/tex]

Substitute values for the known parameters

[tex]0.15 = 0.60 + 0.20 - p(a\ or\ b)[/tex]

[tex]0.15 = 0.80 - p(a\ or\ b)[/tex]

Collect Like Terms

[tex]p(a\ or\ b) = 0.80 - 0.15[/tex]

[tex]p(a\ or\ b) = 0.65[/tex]

Hence;

[tex]p(a\ or\ b) = 0.65[/tex]

Answer:

[tex] Area = 240 m^2 [/tex]

Step-by-step explanation:

The area of the right triangle above = [tex] \frac{1}{2}*base*height [/tex].

Where,

base = 16 m

height = 30 m

Plug in the above values into the area formula:

[tex] Area = \frac{1}{2}*16*30 [/tex]

[tex] Area = 8*30 [/tex]

[tex] Area = 240 m^2 [/tex]

Refer to the attachment for solution.

Answer:

B. $30

Step-by-step explanation:

First, find the amount of the tip.

Multiply the tip rate and taxi fare.

tip rate * taxi fare

The tip rate is 15% and the taxi fare is $25.50

15% * 25.50

Convert 15% to a decimal. Divide 15 by 100 or move the decimal place two spots to the left.

15/100=0.15

15.0 ---> 1.5 ---> 0.15

0.15 * 25.50

3.825

The tip amount is $3.825

Next, find the total amount she paid.

Add the taxi fare and the tip amount.

taxi fare + tip amount

The taxi fare is $25.50 and the tip amount is $3.825

$25.50 + $3.825

$29.325

Round to the nearest dollar. Typically, this would round down to $29, but that is not an answer choice. So, if we round up, the next best answer is $30.

Therefore, the best answer choice is B. $30

Answer:

The answer is

Step-by-step explanation:

The statement

y varies inversely with x is written as

[tex]y = \frac{k}{x} [/tex]

where k is the constant of proportionality

To find k substitute the values of x and y into the equation

From the question

y = 4

x = 6

We have

[tex]4 = \frac{k}{6} [/tex]

Cross multiply

k = 4 × 6

k = 24

So the formula for the variation is

Hope this helps you

Answer: 5

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

it makes the most senses the lower the discount the higher the chance

Step-by-step explanation:

First we need to find out what they all 3 equal, with multiplication.

5×5=25

10×5=50

20×5=100

In each of these problems, the answer is multiplying itself by 2 in order to get to the next answer. So this is how they are related

Answer:

the profit is $8

Step-by-step explanation:

so Susan started with 0, lost 11, equals -11

earned 18, =7

lost 7, =0

earned 8, =$8 for the final answer