What effect do you think the sample size have on the mean of the sampling distribution of the mean?.

For the given condition the x distribution is normal. Option B is correct.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

n=64

√n=8

μ=8

σ=16

The sample size (n > 30) is enough. Using the Central Limit Theorem

¯X∼N(8,16²/64)

The formulas below give the mean and standard deviation of the mean value of x:

The sampling distribution of x has a mean value of 8.

The following equation gives the sampling distribution's standard deviation:

=σ/√n

=16/√64

=16/8

=2

The sample distribution's standard deviation is 2.

Yes, this distribution can be regarded as normal as it roughly follows the normal distribution (By using CLT)

Thus, for the given condition the x distribution is normal. Option B is correct.

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The multiple of 2 and 4 is 48.

A number that is the result of a given number and another natural number is called a multiple of that number. To find the multiple of a number, multiply the number by any whole number.

The given options are A. 50,  B. 58,  C. 54, and D.48.

The multiples of 50 can be written as,

[tex]50=2\times5\times5[/tex]

The multiples of 58 can be written as,

[tex]58=2\times29[/tex]

The multiples of 54 can be written as,

[tex]54=2\times3\times3\times3[/tex]

Therefore, the first three options are not multiples of both 2 and 4.

The multiples of 48 can be written as,

[tex]\begin{aligned}48&=2\times2\times2\times2\times3\\&=4\times2\times2\times3\end{aligned}[/tex]

Therefore, 48 is a multiple of 2 and 4.

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The complete question is -

Which of the following is a multiple of 2 and 4?

A. 50 B. 58 C. 54 D.48

The price of 72 rolls of toilet rolls in each shop is:

The shop with the best value for money is Lidal.

Lidal sells 8 toilet rolls for $2.80 and so if it was to sell 72 rolls, it would sell at a price of:

= Price per 8 rolls x Number of rolls / Number of rolls in packages

= 2.80 x 72 / 8

= 2. 80 x 9

= $25.20

Oldi sells 9 toilet rolls for $3.24 so the cost of 72 rolls would be:

= 3. 24 x 72 / 9

= 3. 24 x 8

= $25. 92

The shop with the best value for money is the cheaper one which is Lidal.

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Answer:

B

Step-by-step explanation:

[tex]\frac{1}{5}[/tex] b - 5( [tex]\frac{2}{5}[/tex] a - [tex]\frac{1}{10}[/tex] b ) + 4a ← distribute parenthesis by - 5

[tex]\frac{1}{5}[/tex] b - 2a + [tex]\frac{1}{2}[/tex] b + 4a ← collect like terms

= 2a + [tex]\frac{1}{5}[/tex] b + [tex]\frac{1}{2}[/tex] b ( express fractions with a common denominator of 10 )

= 2a + [tex]\frac{2}{10}[/tex] b + [tex]\frac{5}{10}[/tex] b

= 2a + [tex]\frac{7}{10}[/tex] b

Answer:

Answer:

FALSE

Step-by-step explanation:

3.6ft is 43.2

3ft 6in is 42 in

..........................................

[tex]\displaystyle\\Answer: \frac{-11-12i}{15}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\\frac{-7+2i}{3-6i}=\\\\\frac{(-7+2i)(3+6i)}{(3-6i)(3+6i)}=\\\\ \frac{-21-42i+6i+12i^2}{3^2-(6i)^2} =\\\\\frac{-21-36i-12}{9+36}=\\\\\frac{-33-36i}{45} =\\\\\frac{3(-11-12i)}{3(15)} =\\\\\frac{-11-12i}{15}[/tex]

The fraction that shows the number of hours Saide's dog sleeps every 4 hours in a day is 1/6.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

It should be noted that there are 24 hours in day. Since the dog sleeps for 4 hours in a day, the fraction will be:

= Number of hours slept / Total hours

= 4 / 24.

= 1/6

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The coordinates of the midpoint of segment FG are (3,-1) which was found using midpoint formula.

When it comes to practical application, the midpoint formula is rather straightforward.

Step 1: Determine the line segment or the two ends.

Step 2: Determine their coordinates.

Step 3: Add the x coordinates of both ends and divide by 2.

Step 4: Adding the y coordinates of both endpoints, divide by 2, and complete the step.

Step 5: As you specify the coordinates of any point, write the values that were acquired in Steps 3 and 4.

Given: Endpoints of a line segment are F(2, -1) and G(-8, -1).

We need to find the coordinates of its midpoint.

Using midpoint formula,

(a,b) = (x₁ + x₂)/2,(y₁ + y₂)/2

       = (2-8)/2,(-1-1)/2

       = 3,-1

So, coordinates are (3,-1)

Therefore, the coordinates of the midpoint of segment FG are (3,-1) which was found using midpoint formula.

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Convergent Series:

A Convergent Series is a series whose partial sums tend to a specific member is called a limit.

  ∑ 1/2n = 1/2+ 1/4 + 1/8 + 1/16 +........

Given an infinite series ∑₁ ∞ an determine the series is convergence. Recall that we can actually do better with geometric series not only we can determine convergence but also divergence. We can also calculate geometric series.

Suppose we are given a series ∑ aₙ which is not quite a geometric series but becomes a geometric series for sufficiently large n. That is we can find an integer N such that aₙ = aₓⁿ for all n > N. we don't have a general formula for aₙ when n ≤ N. The values of aₙ for small n don't effect Sₙ is convergence or not.

As a moment of fact, we never used the fact that aₙ eventually become geometric. More general ∑aₙ is convergent series, we can add a finite number of terms to the be gaining of this series or remove a finite number of terms from the be gaining of the series without affecting the convergence  of the series. For Example: if ∑aₙ convergence then so does

                        10 + 10¹⁰ + 10 ¹⁰⁰ + 10¹⁰⁰⁰ + ∑aₙ

Similarly, if ∑aₙ convergence then,

                a₁₀₀₀ +a₁₀₀₁ +a₁₀₀₂ + ..... = ∑₁₀₀₀ ∞ aₙ

However, the fact that we are only adding finitely many terms to the series is essential. That is, when it comes to determining convergence of a series ∑aₙ , we can see that only the asymptotic  behavior of ∑aₙ matter, that is, only the behavior of the sequence aₙ as n--- ∞ affects convergence.

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Answer:

Opposite sides of a parallelogram are:

1. Congruent

2. Parallel

Step-by-step explanation:

Opposite parallel and congruent sides are the features of a parallelogram and are the criteria for a quadrilateral to be a parallelogram.

Answer: 224/155

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Convert proper Fractions to improper fractions!

-6 2/5/ -4 3/7=

=-32/5/-31/7

2. Multiply by switching Denominator and Numerator of the Fraction!

-32/5/-31/7=

-32/5*-7/31=

224/155=

1 69/155

3. Answer:1 69/155

Answer: Brittany can buy 10 fish

Step-by-step explanation:

If you divide 15 by 1.50 you get 10 meaning Britanny can buy 10 fish. Apologies if this is incorrect.

The correct statement regarding the message in the graph title is of:

a. No, the three candidates were only separated by a margin of about 2%.

The bar graph shows the number of votes obtained by each candidate, which are listed as follows:

These amounts of votes where quite close, however the bar graph has a bad scale, giving the idea that Roberts got about the double number of votes as Johnson and four times as Gomez.

This bad scale is also used to insert the word wide into the text of the article. However, due to the low absolute difference  in the number of votes between these candidates, this work is not correct, and hence, option a is correct.

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150 cm

look at the beginning of the axis. it goes 140 to 160. then 160 to 170. it isnt in order. the missing mumber is 150

The insurance cost now is £449.204.

Given:

Brian pays £465. 98 a year on his car insurance. The insurance company reduces the price by 3. 6%.

Insurance  = 465.98*3.6%

= 465.98*3.6/100

= 465.98*36/10*100

= 46598/100 * 36/1000

= 46598*36 / 100000

= 1677528/100000

= 16.77528

Insurance cost now = 465.98 - 16.77528

= £449.20472

Therefore the insurance cost now is £449.204.

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The lengths of the major and minor axis are 4√6 and 4√3.

A point on a curve is described by an ellipse if its location is such that the sum of the distances between its two focal points is a constant.

(x−h)²/ b² +(y- k)² /a² = 1

Given:

(x−3)²/ 27+(y+4)² /45=1

The above equation can be compared to the standard equation of an ellipse

(x−h)²/ b² +(y- k)² /a² = 1

where, (h, k) = coordinates of the center of the ellipse

a =  length of the semi major axis

b = length of the semi minor axis

By comparison, we have;

(h, k) = (3, -4)

a = √(24) = 2 x√6

b = √(12) = 2 x√3

and, length of the major axis = 2a

length of the minor axis = 2b

Thus, The length of the major axis is

2x a = 2 × 2 x √6 = 4√6

and, length of the minor axis is

2•b = 2 × 2√3 = 4√3

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Answer: 6sqrt(5) and 6sqrt(3)

Step-by-step explanation:

I took the test and these were the correct answers.

the question was already answered but here you go

Based on the rate the number of songs being downloaded is decreasing, in 2030, the number of songs downloaded will be 7,792 songs.

The number of songs downloaded in 2010 is 18,000.

To find the number of downloads in 2030, use the formula:

= Songs in 2010 x ( 1 - Rate of decrease) ^ number of years

Number of years = 2030 - 2010 = 20 years

= 18,000 x (1 - 4.1%)²⁰

= 7,791.92

= 7,792 songs

In conclusion, 7,792 songs will be downloaded in 2030.

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Dan's sales for the next month if he wants his monthly average for the year to be 25,000 is 36430.

Since for the first 11 months of this year , Dan's sales averaged 24,870 a month. The total amount will be:

= 11 × 24870

= 273570

Since Dan's sales for the next month if he wants his monthly average for the year to be 25,000, the amount will be:

= 12 × 25000

= 300000

Therefore, the amount for the next month will be:

= 300000 - 273570

= 26430

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Answer:f^-1(x)= square root x-1 over 4 and square root -square root over 4

Step-by-step explanation:

interchange the variables and solve for y

The vertices of the transformed image D'E'F'G' is D'(0, 4) E' (4, 3) G'(-2, -4) F'(2, -5)

Rectangle DEFG with vertices D(-4, 3), E(0, 2),and G(-6, -5), F(-2,-6),

is transformed into an image as per  (x,y) → (x + 4, y + 1 )

D(-4, 3)

x = -4, y = 3

The image D' will be (x + 4, y + 1) = (-4 + 4, 3 + 1 ) = (0, 4)

E(0, 2)

x = 0, y = 2

The image E' will be (x + 4, y + 1) = (0 + 4, 2 + 1 ) = (4, 3)

G(-6, -5)

x = -6, y = -5

The image G' will be (x + 4, y + 1) = (-6 + 4, -5 + 1 ) = (-2, -4)

F(-2, -6)

x = -2, y = -6

The image F' will be (x + 4, y + 1) = (-2 + 4, -6 + 1 ) = (2, -5)

Therefore, the vertices of the transformed image D'E'F'G' is D'(0, 4) E' (4, 3) G'(-2, -4) F'(2, -5)

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The time elapsed, to the nearest minute, until only 2 grams of the element remains is 15 minutes.

We have an element. The element has a mass of 400 grams. The element decays by 29.8% per minute. We need to find the time duration after which there will be only 2 grams of the element remaining. Let the initial mass of the element, the final mass of the element, the rate of decay, and the time elapsed be represented by the variables m, M, r, and t. We can write the equation as given below.

M = m(1 - r)^t

2 = 400(1 - 0.298)^t

0.005 = (0.702)^t

log(0.005) = t*log(0.702)

t = log(0.005)/log(0.702)

t = 14.97

The time taken, to the nearest minute, is 15 minutes.

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Answer:

Step-by-step explanation:

314 inches  *  (1 foot / 12 inches) * ( 1 meter / 3.28084 foot) * ( 1 kilometer / 1000 meter)

0.0079755997 Km

You walked 16 blocks in a time of 28 minutes. At this rate you walk 1 block in 1 minute 75 seconds.

In Science, distance can be defined as the amount of ground that is covered (travelled) by a physical object over a particular period of time and speed, irrespective of its direction, starting point or ending point.

Mathematically, the distance traveled by a physical object (body) can be calculated by using this formula:

Distance = speed (rate) × time

Note: Let the variable x represent the halfway distance.

Since it takes the same amount of time to walk each block and halfway there, half of the berries are gone. Therefore, we have the following:

At point x, the number of strawberries that is left is equal to 12 strawberries while the distance after walking 3 more blocks, you still have 5 blocks to go would be given by:

1/2 × x = (3 + 5) = 8

1/2 × x = 8

Distance, x = 8 × 2

Distance, x = 16 blocks.

Now, we can determine the rate at which this person walks a block:

Rate (speed) = 28/16

Rate (speed) = 1.75 minutes.

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Answer:

answer -a dilation followed by a translation

-a dilation followed by a reflection

-a reflection followed by a dilation

-a rotation followed by a dilation

Answer:

3n+6 May i pls have the crown

Step-by-step explanation:

If you use the PEMDAS rule

3 * n= 3n

and 3*2= 6

For the given equation the solution would be

                          [tex]r=-7t-3,\:s=\frac{-6t-7}{3}[/tex]

What is the system of linear equations in three variables?

Three-variable equation systems are only slightly more difficult to solve than two-variable equation systems. Substitution and the use of 3x3 matrices are the two most straightforward methods for solving these types of equations.

The given equations are

                  r - 3s + t = 4 ------------(I)

                  3r - 6s +9t = 5 ---------(II)

                  4r - 9s + 10t = 9--------(III)

from equation (I), we get

                  r = 4 + 3s - t ------------(IV)

Now put the value of 'r' in equations (II) and (III), and we get

               3(4 + 3s - t) - 6s + 9t = 5

               4(4 + 3s - t) - 9s + 10t = 9

Solving the above equations, we get

             3s + 6t + 12 = 5 --------(V)

             3s + 6t + 16 = 9 --------(VI)

 Now isolate the value of 's' from equation (IV), we get

              3s = - 6t + 5 -12

             [tex]s=\frac{-6t-7}{3}[/tex]

Now put the value of 's' in equation (IV), and we get

           [tex]r=4 +3s -t\\r=4+3\cdot(\frac{-6t-7}{3}) -t\\ r=4-6t-7-t\\r=-7t-3[/tex]

Hence, For the given equation the solution would be

                   [tex]r=-7t-3,\:s=\frac{-6t-7}{3}[/tex]

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An equation to describe the relationship between g, the number of gems, and c, the number of chests is; g = 300c

In adventure A, when number of gems is 600, we see that number of chests is 2. Thus;

Rate of gems per chests = 600/2 = 300 g/c

In adventure B, when number of gems is 1500, we see that number of chests is 5. Thus;

Rate of gems per chests = 1500/5 = 300 g/c

In adventure C, when number of gems is 4800, we see that number of chests is 16. Thus;

Rate of gems per chests = 4800/16 = 300 g/c

Thus;

There is a constant rate and we can say that the equation that shows the relationship between the two variables is;

g = 300c

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Complete question is;

Lulu the Lucky puts chests of gems into her treasure vault. Each chest holds the same number of gems. The table below shows the number of gems Lulu received from three different adventures and the number of chests she needed to hold the gems.

                      Number of gems(g)     Number of chests(c)

Adventure A    600                            2

Adventure B    1500                           5

Adventure C    4800                          16

Write an equation to describe the relationship between g, the number of gems, and c, the number of chests.