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Using the Central Limit Theorem, it is found that the values of the population standard deviation [tex]\sigma[/tex] needed are given by:

a) [tex]\sigma = 32[/tex]

b) [tex]\sigma = 16[/tex]

c) [tex]\sigma = 4[/tex]

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem, we have that n = 16.

Item a:

s = 8, hence:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]8 = \frac{\sigma}{\sqrt{16}}[/tex]

[tex]\sigma = 32[/tex]

Item b:

s = 4, hence:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]4 = \frac{\sigma}{\sqrt{16}}[/tex]

[tex]\sigma = 16[/tex]

Item c:

s = 1, hence:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

[tex]1 = \frac{\sigma}{\sqrt{16}}[/tex]

[tex]\sigma = 4[/tex]

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[tex]~~~\dfrac{d}{dx} f(x) \\ \\=\dfrac{d}{dx} \left(x^3 \cdot \log_6 x \right)\\\\=x^3\dfrac{d}{dx} \left(\log_6 x\right) + \log_6 (x)\dfrac d{dx} x^3 \\\\=x^3 \cdot \dfrac 1{x \ln 6} + \log _6 (x) \cdot 3x^2\\\\=\dfrac{x^2}{\ln 6} + \log_6(x) \cdot 3x^2\\\\\\=x^2 \left(\dfrac 1{\ln 6} + 3\log_6 x \right)[/tex]

[tex]\text{The derivative is now in a form of}~ x^A (B + C \log_D (x))[/tex]

Answer:

B.The answer is incorrect; the plus sign should be a minus sign.

Step-by-step explanation:

[tex]x^2-18x+81\\\\=x^2-2\cdot 9x +9^2\\\\=(x-9)^2\\\\=(x-9)(x-9)[/tex]

Answer:

C

Step-by-step explanation:Only one that makes sence just look at the graph

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=10\\ h=18 \end{cases}\implies V=\cfrac{\pi (10)^2(18)}{3}\implies \stackrel{using~\pi =3.14}{V=1884}[/tex]

Answer:

£252.58

Step-by-step explanation:

$346 × £0.73/$1 = £252.58

Please rate!! I hope this helps!!

Both are supplementary

The answer to your question is =

Danny got 1/16 of the whole pie

An expression is defined as a set of numbers, variables, and mathematical operations. The value(s) for which the rational expression (10w−5)/(2w²+11w+5) is undefined is -1/2 and -5.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value for which the function will not be defined is the value of w which will make the denominator of the rational function zero. This values can be found by factorizing the denominator of the function. Therefore,

2w² + 11w + 5 = 0

2w² + 10w + 1w + 5 = 0

2w(w+5) + 1(w+5) = 0

(2w+1)(w+5) = 0

w = -1/2 , -5

Hence, the value(s) for which the rational expression (10w−5)/(2w²+11w+5) is undefined is -1/2 and -5.

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The height of the pole is  53 m

The angle of elevation is the angle formed between a horizontal line and a line of sight or an upwardly inclined line from an observer to an object or point. It is used to describe the angle at which an object is viewed from a particular position

Let the height of the pole be x

We know that;

Tan 38 = 1.67 + x/70

Tan 38 * 70 = 1.67 + x

x = (Tan 38 * 70 ) - 1.67

x = 53 m

Thus we can see that the height of the pole is about 53 m

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Answer:

x = 60

Step-by-step explanation:

Since this triangle is an isosceles triangle, the angle next to the 60 degrees is 60 as well. The interior angles of a triangle adds up to 180 degrees, so:

60 + 60 + x = 180
120 + x = 180
x = 60
Hope this helps :)

Answer:

2.25 tablespoons of oregano

Step-by-step explanation:

as Diego use 3x more than Tracy, and you know that Tracy use 0.75 tablespoon, so 0.75 x 3 and you will get 2.25

The computation of the equation illustrates that the number will be 46.4.

Let the number be represented as x.

Therefore, the the difference of 3 / 4 and 1 / 6 of a number is 7 will be computed as follows:

(1/6 × x) - 3/4 = 7

0.167x = 7 + 3/4

0.167x = 7.75

x = 7.75/0.167

x = 46.4

Therefore, the number is 46.4.

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Answer:

Cubed root

Step-by-step explanation:

Do the inverse of cubed, cubed root

A candidate received the majority of first-place votes but loses hows that A. The statement does not make sense.

It should be noted that plurality voting simply means when each voter is allowed to vote for only one candidate.

In this case, a candidate received the majority of first-place votes will win the election. Here, the majority of the first place votes using the plurality method is the winner.

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Answer:

C. 80 grapes

Step-by-step explanation:

6 / 3 = 2

Each person gets 2 pounds of grapes.

2 X 40 = 80

1 pound = 40 grapes

2 pound = 80 grapes

Answer:

sorry cant help with that

Step-by-step explanation:

Answer:

Hope the picture will help you

Answer:

  3

Step-by-step explanation:

You want the mean absolute deviation of the set of numbers ...

  {9, 2, 9, 9, 5, 4, 9, 1, 4, 10}

The mean of this 10-number set of data is 6.2. The mean absolute deviation (MAD) is found by subtracting that from the members of the dataset, taking the absolute values of the result, and finding the means of those.

The attachment shows those calculations.

The MAD of this set of data is 3.

__

Additional comment

The period (decimal point) in the column of numbers suggests this is a 6-number dataset, and the last 4 numbers are answer choices. If that is the case, none of those answer choices is correct. That is why we assumed that this problem has a 10-number dataset.

When you're calculating this by hand, you only need to consider the values for which the deviation is negative. The MAD is twice their total absolute value, divided by the number of numbers in the dataset. Here, that is 2(4.2+2.2+5.2+2.2+1.2)/10 = 3. (Numbers 2, 5, 4, 1, 4 are less than the mean of 6.2.)

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[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=24\\ \theta =135 \end{cases}\implies s=\cfrac{(135)\pi (24)}{180}\implies s=18\pi ~cm[/tex]

Answer:

B) 18π cm

Step-by-step explanation:

Step 1

Given:

   Central angle θ=135°

    Radius of circle r=24 cm

    Length of arc CD =θ360°(2πr)

Step 2

  l=135°360°×2π×24

    l=38×2×π×24

    l=3×2π×3

      l=18π cm

Therefore

  Length of arc CD =18π cm

Thus, option B is correct.

Answer:

A function is defined as a relation between a set of inputs having one output each..

Step-by-step explanation:

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

¿Qué es la función explicar?

Una función se define como una relación entre un conjunto de entradas que tienen una salida cada una. En palabras simples, una función es una relación entre entradas donde cada entrada está relacionada exactamente con una salida. Cada función tiene un dominio y un codominio o rango. Una función generalmente se denota por f(x) donde x es la entrada.

Answer:

Θ = (π/6) + πn

Θ = (5π/6) + πn

Step-by-step explanation:

4sin²Θ + 4 = 5

            -4    -4

4sin²Θ = 1

÷4         ÷4

sin²Θ = (1/4)

√sin²Θ = √(1/4)

sinΘ = (1/2), (-1/2)

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

Θ = arcsin (1/2)

Θ = (π/6)

to find the quadrant subtract π

Θ = π - (π/6)

Θ = (5π/6)

Find the period

2π / |b|

b = 1

2π/1 = 2π

The sin Θ function is 2π, so values will repeat 2π in both directions.

Θ = (π/6) + 2πn (n is the variable)

Θ = (5π/6) + 2πn

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

sin Θ = (-1/2)

Θ = arcsin (-1/2)

Θ = (-π/6)

To find the second function add π

Θ = 2π + (π/6) + π

Θ = (7π/6)

Find the period

2π/|b|

2π/1

2π

(-π/6) + 2π

2π       6         π

----- ×  ----- -  -----

1           6        6

Θ = (11π/6) will repeat every 2π in both directions

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

Θ = (π/6) + 2πn

Θ = (5π/6) + 2πn

Θ = (7π/6) + 2πn

Θ = (11π/6) + 2πn

(π/6) + π = (7π/6)

(5π/6) + π = (11π/6)

Θ = (π/6) + πn

Θ = (5π/6) + πn

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

I hope this helps!

Answer:

403π/9 or 140.67

Step-by-step explanation:

First, you have to find the circumference of the circle

Circle circumference equation:

Circumference = dπ (Circumference = diameter x pi)

You have a radius of 31 which is equal to 62 diameter (diameter is double the radius)

So:

C = 62π

Now, you need to know that a full circle is 360 degrees and we want only 200 degrees of that,

So in other words, you want 200/360 of the circle's circumference.

You can find the measure of the 200 degree arc by doing

62π x [tex]\frac{200}{360}[/tex] = [tex]\frac{403pi}{9}[/tex] or 140.67

Answer:

44 represents months

x*y

$77

x

x*y

Answer:

-38

Step-by-step explanation:

i hope this helps you

good luck on your quiz or lesson!

Answer:

-38

Step-by-step explanation:

[tex]\frac{1}{4} = 0.25[/tex]

[tex]\frac{1}{4} -41\frac{1}{4} +3[/tex]

[tex]0.25-41.25+3[/tex]

[tex]-41+3[/tex]

[tex]-38[/tex]

Answer:

it is proportional because there is a roc of +5 bc as one hour increases 5 dollars is added to the initial cost

Answer:

Step-by-step explanation:

hello :

the sum is : Sn = n/2(U1 + Un )     and U n = U1+(n-1)r    

given :    U1 = 1      r=4-1=7-4=...= 3      n= 32

so :  U 32 = 1+(32-1)3= 94

S32 = 32/2 (1+94) = 1520

Answer:

x is greater than -2 and less than or equal to 3

Step-by-step explanation:

so the 3x + 1 is greater than -5

so 3x is greater than -6

we divide both sides by 3

then we find out that x is greater than -2

we also know that 3x + 1 is less than or equal to 10

so 3x is less than or equal to 9

we divide both sides by 3

then we find out that x is less or equal to 3

so we can say that x is greater than -2 and less than or equal to 3