Express sin U as a fraction in simplest terms.
S
12
13
5
U

The standard deviation for the given data items is 2.6

The standard deviation of the given data items can be calculated by taking the square root of the variance.

Variance is a measure of variability and it is calculated by taking the average of squared deviations from the mean.

Hence, we will first determine the mean of the given data items.

Mean is simply the average of the numbers.

Therefore mean of the given data items is

[tex]Mean = \frac{9+11+11+16}{4}[/tex]

[tex]Mean = \frac{47}{4}[/tex]

Mean = 11.75

Now, for the variance of the data

[tex]Variance = \frac{(9-11.75)^{2}+(11-11.75)^{2}+(11-11.75)^{2}+(16-11.75)^{2} }{4}[/tex]

[tex]Variance = \frac{(-2.75)^{2}+(-0.75)^{2}+(-0.75)^{2}+(4.25)^{2} }{4}[/tex]

[tex]Variance = \frac{7.5625+0.5625+0.5625+18.0625}{4}[/tex]

[tex]Variance = \frac{26.75}{4}\\[/tex]

∴ Variance = 6.6875

But,

Standard deviation [tex]= \sqrt{Varinace}[/tex]

∴Standard deviation  [tex]=\sqrt{6.6875}[/tex]

Standard deviation = 2.586

Standard deviation ≅ 2.6

Hence, the standard deviation for the given data items is 2.6

Learn more on standard deviation here: https://brainly.com/question/18562832

Answer:

1.33 < 2.67 ; Fail to reject H0 at 0.05

Step-by-step explanation:

Given the data :

Men:

n1= 11

s1= 6.1

Women:

n2= 14

s2= 5.3

The hypothesis :

H0 : σ1² = σ2²

H1 : σ1² > σ2²

To calculate the test statistic ; we use th Ftest statistics ;

F statistic = Larger sample variance / Smaller sample variance

Fstatistic = s1² / s2² = 6.1² / 5.3² = 37.21/28.09 = 1.325

The F critical value at :

df numerator = n - 1 = 11 - 1 = 10

df denominator = n - 1 = 14 - 1 = 13

Using the F distribution table :

F critical = 2.671

Since

F statistic < F critical ; Fail to reject H0 at 0.05

We fail to reject the null hypothesis at significance level of H0 : s1² = s2²

For the men, we have:

For the women, we have:

The null and the alternate hypotheses are:

The numerator and the denominator degrees of freedom are calculated as:

[tex]\mathbf{df = n -1}[/tex]

So, we have:

[tex]\mathbf{df_1 = 11 -1}[/tex]

[tex]\mathbf{df_1 = 10}[/tex] ----- numerator

[tex]\mathbf{df_2 = 14 -1}[/tex]

[tex]\mathbf{df_2 = 13}[/tex] ----- denominator

The test statistic of the f test is:

[tex]\mathbf{t = \frac{s_1^2}{s_2^2}}[/tex]

So, we have:

[tex]\mathbf{t = \frac{6.1^2}{5.3^2}}[/tex]

[tex]\mathbf{t = \frac{37.21}{28.09}}[/tex]

[tex]\mathbf{t = 1.325}[/tex]

The critical values at [tex]\mathbf{t = 1.325}[/tex] and the degrees of freedom is:

[tex]\mathbf{F= 2.671}[/tex]

By comparison, 1.325 is less than 2.671.

Hence, we fail to reject the null hypothesis at H0 : s1² = s2²

Read more about hypothesis at:

https://brainly.com/question/23639322

Answer:

Qualitative data

Neither discrete or continous

Ordinal

Step-by-step explanation:

Qualitative data simply refers to Non-numeric measure, they make use of data labels which are expressed in words rather than figures or numbers.

For a data to be either discrete or continous, then it has to be numeric, since the data is qualitative and non- numeric, then it is neither continous or discrete.

This is an ordinal scale representation of data as data are ordered or ranked in terms of performance, however, there is no measure of difference between each rank or order. The highest level of performance in the scale is Excellent.

Answer:

63m³

Step-by-step explanation:

volume of a cylinder = πr²h

r = 2m, h = 5m

= 22/7 × 2² × 5

= 62.86m³

approx 63m³

Answer:

[tex]\displaystyle y' = \frac{y - 5x}{x + 6y^2}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Product Rule]:                                                                             [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle 5x^2 - 2xy + 4y^3 = 5[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

Answer:

A majority of the data will lie between 38 and 46.

Step-by-step explanation:

It can be said that a majority of the data of a distribution lies within 1 standard deviation of the mean.

In this question:

Mean of 42, standard deviation of 4.

42 - 4 = 38

42 + 4 = 46

A majority of the data will lie between 38 and 46.

Step-by-step explanation:

jlejej

are u using chrome os

Answer:

0.0698

Step-by-step explanation:

Given :

Population mean, μ = 20

Sample mean, xbar = 21.1

Sample standard deviation, s = 4.3

Sample size, n = 35

The hypothesis :

H0 : μ = 20

H0 : μ > 20

The test statistic :

(xbar - μ) ÷ (s/√(n))

T = (21.1 - 20) ÷ (4.3/√(35))

T = 1.1 ÷ 0.7268326

Test statistic = 1.513

Using the Pvalue calculator :

df = n - 1 = 35 - 1 = 34

Pvalue(1.513, 34) = 0.06976

Pvalue = 0.0698 (4 decimal places)

The p-value is 0.0698 if rounded to 4-decimal places.

It is given that students study an average of more than 20 hours each week and the random sample of 35 students was asked to keep a diary of their activities over a period of several weeks.

The average number of hours that the 35 students was 21.1 hours.

The sample standard deviation is 4.3 hours.

It is required to find the p-value.

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

We can test the hypothesis using the Z test, the formula for the Z-test is given below:

[tex]\rm Z= \frac{(x-u)}{\frac{S}{\sqrt{n} } }[/tex]

Where x is the sample mean

            u is the population mean

            s is the standard deviation

            n is the sample size.

The hypothesis are: H0 : μ = 20  V/s  H1 : μ > 20

We have x = 21.1

               u = 20

               s = 4.3

               n = 35

Putting these values in the above formula, we get:

[tex]\rm Z= \frac{(21.1-20)}{\frac{4.3}{\sqrt{35} } }\\\\\rm Z= \frac{(1.1)}{\frac{4.3}{\sqrt{35} } }\\\\[/tex]

Z = 1.513

difference or df = n -1 ⇒ 35-1 ⇒ 34

P-value at (1.513, 34) =  0.06976  (From the p-value calculator)

P-value = 0.0698 (Rounded to 4-decimal places)

Thus, the p-value is 0.0698 if rounded to 4-decimal places.

Learn more about the standard deviation here:

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(-4/9)*3×(-27/20)*4= 7.2

Step-by-step explanation:

here's the answer to your question

Answer:

7/16

Step-by-step explanation:

7/16>3/8

It would be 7/16 because 3/8 is what is being shown. If you make them both have a common denominator then it would be 6/16.

Answer:

(A)

Step-by-step explanation:

M=-2

therefore

x¹=3, y¹=-12, x²=6 y²=k

M=(y²-y¹)/(x²-x¹)

-2=(k+12)/(6-3)

-2×3=k+12

-6=k+12

k=-18

Answer:

242.7 dB

Step-by-step explanation:

Answer:

x^2 + x - 42

Step-by-step explanation:

use the distributive property:

(x+7)(x-6) = x^2 + x - 42

Answer: x^2 + x - 42

Step-by-step explanation:

Answer:

Last option

Step-by-step explanation:

The slope 3/2 determines the line (although you can plot points to find (0,-4) and (4,2), connecting them, you'll get the equation of the line, and the area it covers will be to the right side, putting x = 0, y<-4, which is below the line, that's how you determine it.

Answered by GAUTHMATH

Answer:

실례합니다 ?

Step-by-step explanation:

이것이 무엇을 의미하는 질문입니까?

회사는 마카로니 상자의 무게를 8% 줄였습니다. 상자의 새 무게가 13.1온스인 경우 상자의 원래 무게는 얼마였습니까? 오른쪽 ?

Answer:

x*0.92 = 13.1

x = 14.24

Step-by-step explanation:

Answer:

$38.25 US dollars.

Step-by-step explanation:

25 / 1 = 25

To find the number of US dollars that can be exchanged for 25 British pounds, multiply 1.53 by 25 to get $38.25 US dollars.

Hope this helps!

if there is something wrong, just let me know.

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

(a) The surface area  consists of the sum of the area of 3 sets of 2 congruent rectangles. The 2 rectangles are on opposite sides of the solid.

= 2(15*15) + 2(5*15) + 2(5&15)

= 450 + 150 + 150

= 750 unit^2.

(b). Similarly to the above:

Surface area = 2(12*6) + 2(4*12) + 2(4*6)

= 144 + 96 + 48

= 288 unit^2.

(c)  Again:

Surface area =  2(25*16) + 2(25*16) + 2(16*16)

= 400 + 400 + 256

= 1056 unit^2.

Answer:

angle bisectors

Step-by-step explanation:

The incentre is where a triangle's three angle bisectors intersect ( an angle bisector is a ray that cuts an angle in half ). The incentre is the centre of a triangle drawn inside the triangle.

Answer:

177.3 feet

This is a classic find the vertex of a parabola question.

if this was a calculus class the solution would be to take the derivative and set it equal to zero... -32t+ 105 = 0

BUT i assume that you are not in a calculus class..

so we try plan "B" the  highest (or lowest) point of parabola is it's vertex

the vertex formula is [-b/2a,f(-b/2a)]

in your problem a = -16, b=105, c= 5

so the "X" (TIME) is located at -(105)/(2*-16) = 3.28

plug in 3.28 into -16(3.28)^2 + 105(3.28) + 5 = 177.27

and you will get

Step-by-step explanation:

Answer:

1/2 jam 30 menit mungkin?

1/2 jam adalah 30 minit

1/2 × 60 = 30 mins

English translation

1/2 an hour is 30 minutes

1/2 × 60 = 30 mins

Answered by Gauthmath must click thanks and mark brainliest

Answer:

A sample of 1699 would be required.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

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

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Standard deviation is known to be $8.2.

This means that [tex]\sigma = 8.2[/tex]

How large of a sample would be required in order to estimate the mean per capita income at the 95% level of confidence with an error of at most $0.39?

This is n for which M = 0.39. So

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

[tex]0.39 = 1.96\frac{8.2}{\sqrt{n}}[/tex]

[tex]0.39\sqrt{n} = 1.96*8.2[/tex]

[tex]\sqrt{n} = \frac{1.96*8.2}{0.39}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*8.2}{0.39})^2[/tex]

[tex]n = 1698.3[/tex]

Rounding up:

A sample of 1699 would be required.

Step-by-step explanation:

thwashm m GB DC GM 3hka it g feeds ygzdkzyzuzjz indin, mi, hn zbe

Answer:

Solution given:

L.H.S

sin²A-cos²B

sin²A=1-cos²A and Cos²B=1-sin²B

replacing value

1-cos²A-(1-sin²B)

1-cos²A-1+sin²B

1-1+sin²B-Cos²A

=sin²B-Cos²A

R.H.S

Answer:

70

Step-by-step explanation:

70 because as the number of trials increase, the actual ratio of outcomes will converge on the expected ratio.

Answer:

1

Explainion show in picture above

Answer:

x=6

Step-by-step explanation:

It should be 8+x+2-5=11

Answer:

(a) [tex]P" = (-4,-3)[/tex]

(b) [tex](x,y) \to (4,-8)[/tex]

Step-by-step explanation:

Given

[tex]P = (4,3)[/tex]

Solving (a): Reflect across x and y-axis.

Reflection across x-axis has the following rules

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex]P' = (4,-3)[/tex]

Reflection across y-axis has the following rules

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]P" = (-4,-3)[/tex]

Hence, the new point is: (-4,-3)

Solving (b): Rx . Do,2 (2,4)

[tex]R_x \to[/tex] reflect across the x-axis

Reflection across x-axis has the following rules

[tex](x,y) \to (x,-y)[/tex]

So, we have:

[tex](2,4) = (2,-4)[/tex] ---- when P is reflected across the x-axis

[tex]D_{o,2} \to[/tex] dilate by a scale factor of 2

The rule is:

[tex](x,y) \to 2 * (x,y)[/tex]

So, we have

[tex](x,y) \to 2 * (2,-4)[/tex]

Open bracket

[tex](x,y) \to (4,-8)[/tex]

Answer:

200 + 2

Step-by-step explanation:

you know that two (2) negatives multiplying each other is = +

=200 +2

=202

Answer:

92.12 seconds

Step-by-step explanation:

According to the poisson probability relation :

P(X =x) = (e^-λ * λ^x) / x!

For no calls to be reveived during the period, x = 0

P(X = 0) = (e^-λ * λ^0) / 0!

P(X = 0) = 0.1

0.1 = (e^-λ * λ^0) / 0!

0.1 = e^-λ

Take the In of both sides

In(0.1) = - λ

-2.303 = - λ

λ = 2.303

The length of call in second, l

l = λ / r ; r = arrival rate

r = 90 per hour ; this means ;

90 / 3600 = 0.025

l = 2.303 / 0.025

l = 92.12 seconds

Answer:

Step-by-step explanation:

H0 = .5 prefer  Democratic candidate

Ha > .5 prefer Democratic candidate

p = .48

z = -1.285179129

0.9006 >= .05 thus we "FAIL TO REJECT THE NULL HYPOTHESES"

Answer: 15328

Step-by-step explanation:

The following can be deduced from the information given:

N = 20000

μ = 80

σ = 11

P(X>72) = 1 - P (X<72)

= 1 - P(Z < 72-80/11)

= 1 - P(Z < -8/11)

= 1 - P(Z < 0.7272)

= 1 - 0.2336 = 0.7664

Therefore, the number of students that were better than Lingard n(X > 72) will be:

= 20000 × 0.7664

= 15328