A sample of 46 observations is selected from one population with a population standard deviation
of 4.1. The sample mean is 102.0. A sample of 48 observations is selected from a second
population with a population standard deviation of 5.8. The sample mean is 100.1. Using the 0.05
significance level, is there a difference between the two samples?

Answer:

Option C

Step-by-step explanation:

In this question measure of two sides and and the angle between these sides of a triangle is given.

We have to calculate the measure of third side.

By applying cosine rule in the given triangle.

BC² = AB² + AC² - 2(AB)(AC)cos(A)

BC² = (18)² + (12)² - 2(18)(12)cos(62°)

BC² = 324 + 144 - 202.81

BC² = 265.19

BC = 16.28

BC ≈ 16 units

Therefore, Option C will be the correct option.

Answer:

domain of function refers to the various values that can be passed through to the function.

Step-by-step explanation:

Answer:

[tex]CV=0.2[/tex] ---- dataset 1

[tex]CV = 7.2[/tex] --- dataset 2

Step-by-step explanation:

Given

[tex]A: 30500, 27500, 31200, 24000, 27100,28600, 39100, 36900, 35000, 21400, 37900, 27900, 18700,[/tex][tex]33100[/tex]

[tex]B: 4.29, 4.88, 4.34, 4.17, 4.52, 4.80, 3.28, 3.79, 4.84, 4.77, 3.11[/tex]

Required

The coefficient of variation of each

Dataset A

Calculate the mean

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

[tex]\mu = \frac{30500+ 27500+31200+24000+ 27100+28600+ 39100+ 36900+ 35000+ 21400+ 37900+ 27900+ 18700+33100}{14}[/tex][tex]\mu = \frac{418900}{14}[/tex]

[tex]\mu = 29921.43[/tex]

Next, calculate the standard deviation using:

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

So, we have:

[tex]\sigma= \sqrt{\frac{(30500 - 29921.43)^2 +.................+ (18700- 29921.43)^2 + (33100- 29921.43)^2}{13}}[/tex]

[tex]\sigma= \sqrt{\frac{487723571.42857}{14}}[/tex]

[tex]\sigma= \sqrt{34837397.959184}[/tex]

[tex]\sigma= 5902.32[/tex]

So, the coefficient of variation is:

[tex]CV=\frac{\sigma}{\mu}[/tex]

[tex]CV=\frac{5902.32}{29921.43}[/tex]

[tex]CV=0.2[/tex] --- approximated

Dataset B

Calculate the mean

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

[tex]\mu = \frac{4.29+ 4.88+ 4.34+ 4.17+ 4.52+ 4.80+ 3.28+ 3.79+ 4.84+ 4.77+ 3.11}{11}[/tex]

[tex]\mu = \frac{46.79}{11}[/tex]

[tex]\mu = 4.25[/tex]

Next, calculate the standard deviation using:

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

[tex]\sigma = \sqrt{\frac{(4.29 - 4.25)^2 + (4.88- 4.25)^2 +.........+ (3.11- 4.25)^2}{11}}[/tex]

[tex]\sigma = \sqrt{\frac{3.859}{11}}[/tex]

[tex]\sigma = \sqrt{0.35081818181}[/tex]

[tex]\sigma = 0.593[/tex]

So, the coefficient of variation is:

[tex]CV=\frac{\sigma}{\mu}[/tex]

[tex]CV = \frac{4.25}{0.5903}[/tex]

[tex]CV = 7.2[/tex] -- approximated

Answer:

1.71 = BC

Step-by-step explanation:

take 70 degree as reference angle

using cos rule

cos 70 = adjacent / hypotenuse

0.3420 = BC / 5

0.3420*5 = BC

1.71 = BC

Answer:  a+b+c/3

Step-by-step explanation:

mean= sum of all values/number of values

Answer:

The radius is approximately 14 cm

Step-by-step explanation:

The circumference

C = 2 * pi *r

88 = 2 * pi *r

Divide by 2

44 = 3.14 *r

Divide by 3.14

44/3.14 = r

14.01273885=r

Answer:

c I think that's the right answer

Step-by-step explanation:

a rectangle which has a length which was three times the width could be

3 x 9 - this would give a total of just 27 feet.....so we know its bigger than this.....but essentially this starting place puts us in the right ballpark

following on from this....

if we do.....3.11 x 9.33 - this gives us 29.0163

and we have a rectangle which meets the criteria

Answer:

Step-by-step explanation:

Bạn vẽ 1 tức giác ABCD lồi sau đó nối AB và CD cắt nhau tại E, AD và BC cắt nhau tại F, AC và BC cắt nhau tại G. Trồng 7 cây vào các điểm ABCDEFG  l. Ta có sáu hàng là ABE, DCE, BCF, ADF, ACG, BDG

[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]

Radius of the circle "[tex]r[/tex]" = 5.5 yd

[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]

The area of the given figure.

[tex]\sf \bf {\boxed {\mathbb {SOLUTION :}}}[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {b. \:47.5\:sq\:yd.}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

We know that,

[tex]\sf\pink{Area\:of\:a\:semi-circle}[/tex] = [tex]\frac{\pi \: {r}^{2} }{2} [/tex]

Using 3.14 for π, we have

[tex] = \frac{3.14 \times ( {5.5 \: yd})^{2} }{2} \\[/tex]

[tex] = \frac{3.14 \times 5.5 \times 5.5 \: {yd}^{2} }{2}\\ [/tex]

[tex] = \frac{94.985 \: {yd}^{2} }{2} \\[/tex]

[tex] = 47.5 \: {yd}^{2} \\[/tex]

Using [tex]\frac{22}{7} [/tex] for π,

[tex] = \frac{22 \times 5.5 \times 5.5 \: {yd}^{2} }{7 \times 2} \\[/tex]

[tex] = \frac{665.5 \: {yd}^{2} }{14}\\ [/tex]

[tex] = 47.5 \: {yd}^{2} \\[/tex]

Therefore, the area of the semi-circle is [tex]47.5\: yd²[/tex].

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]

Answer:

a

Step-by-step explanation:

Answer:

33 squares of chocolate need

Answer:

33 Biscuits

Step-by-step explanation:

Uni method

How much biscuits do we need for 1 square of chocolate?

22/16 = 1.3

For 1 square of chocolate she needs 1.3 Biscuits.

So for 24 biscuits,

24 * 1.3

=33 biscuits

Answer: 180 degrees rotation, center (1.5, -0.5)

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

Explanation:

Notice how point (1,-1) on triangle A moves to (-2,0) and then that rotates to (2,0)

Form a line segment from (1,-1) to (2,0) to show the beginning and end states. The equation of the line through these two points is y = x-2

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

Similarly, the point (1,-4) moves to (-2,-3) after applying the translation vector, then it rotates to (2,3). Draw a line through (1,-4) and (2,3). The equation of this line is y = 7x-11

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

We have this system of equations

[tex]\begin{cases}y = x-2\\y = 7x-11\\\end{cases}[/tex]

Equate the right hand sides and solve for x

7x-11 = x-2

7x-x = -2+11

6x = 9

x = 9/6

x = 3/2

x = 1.5

which leads to

y = x-2 = 1.5-2 = -0.5

or

y = 7x-11 = 7(1.5)-11 = 10.5-11 = -0.5

Either way, x = 1.5 leads to y = -0.5

We get the ordered pair (x,y) = (1.5, -0.5)

This is the center of rotation when rotating figure A to have it match up with triangle C (the triangle in the upper right quadrant)

Notice in the diagram below point D is that center of rotation. Also, notice that if we use the distance formula, you should find that

AD = A''D

BD = B''D

CD = C''D

Answer: We can conclude that at least one of the population means has a different value than the other population means.

Step-by-step explanation:

When the null hypothesis is rejected for an analysis of variance, we can then conclude that at least one of the population proportions has a different value.

For one-way analysis of variance, it should be noted that the null hypothesis is rejected when there is sufficient evidence which is used in making the conclusion that not all the means are equal and that there is a different value.

Answer:

C. 47 deg

Step-by-step explanation:

m<A = 180 - 94 - 39 = 47

m<D = m<A = 47

Answer:

15 gallons of milk at 3 week

15/3= 5

for a month 5 * 4 =20

in a year 12 * 20 = 240

Step-by-step explanation:

Answer:

4) 93°

5) 1°

6) 51°

7) 6°

Step-by-step explanation:

4)

180 - 36 - 51 =  93

93 °

5)

(4x + 27 ) = 180 - 64 - 85

4x + 27 = 31

x = 1

6)

theory of exterior angles in a triangle:

21 + 30 = x

x = 51

7)

3x + 42 = 46 + 44

3x + 42 = 90

3x = 48

x = 16

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer: this is a continuation starting in number 4 (use the same steps as example 3)

Step-by-step explanation:

-12

45

-12

14

32

-2

5

Step-by-step explanation:

The given equation can be further simplified into

[tex]2x^{2}+2x-12=0[/tex]

The roots of a quadratic equation is given by

[tex]x = \dfrac{ - b \: \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

where a = 2, b = 2 and c = -12. Putting these into the roots equation, we get

[tex]x = \dfrac{ - 2 \: \pm \: \sqrt{4 \: - \: 4(2)( - 12)} }{2(2)} = \dfrac{ - 2 \: \pm \: 10}{4}[/tex]

This gives us two possible roots:

x = 2, x = -3

Since the condition is that p < q, we see that p = -3 and q = 2. Therefore,

[tex]q - p = 2 - ( - 3) = 5[/tex]

Answer:

43.82 mph

266.67 feet

Step-by-step explanation:

Given :

S = √30fl

S = speed of car

f = drag Coefficient

l = Length of skid mark

If f = 0.8 ; l = 80 feets

s = √30fl

s = √(30*0.8*80)

s = √1920

s = 43.817

s = 43.82 mph

B.)

s = 80 mph

f = 0.8

s = √30fl

80 = √30*0.8*l

80 = √24l

Square both sides

80² = 24l

6400 = 24l

l = 6400/24

l = 266.67 feets

Answer:

0.8 you yes both of them has the same answer , so it is a true portion

Step-by-step explanation:

Answer:

Yes.

Step-by-step explanation:

[tex]\frac{4}{5} =\frac{48}{60}[/tex]

This is a true proportion because when you cross multiply you get the same product.

[tex]48*5=240[/tex]

[tex]4*60=240[/tex]

Answer: 22

Step-by-step explanation: 44:2=22

Answer:

2h

Step-by-step explanation:

f(3 + h) = 2(3 + h)^2 + 1

= 2(3^2 + h^2) + 1

= 2(9) + 2h^2 + 1

= 18 + 2h^2 + 1

= 2h^2 + 19

f(3) = 2(3)^2 + 1

= 2(9) + 1

= 18 + 1

= 19

2h^2 + 19 - 19 / h

2h^2 / h

2h

Answer:

D. 56

Step-by-step explanation:

The general solution for the number of combinations with repetition is represented by the following expression:

[tex]x = \frac{(n + r - 1)!}{r!\cdot (n-1)!}[/tex] (1)

Where:

[tex]n[/tex] - Total number of elements.

[tex]r[/tex] - Number of the sample.

If we know that [tex]n = 6[/tex] and [tex]r = 3[/tex], then the number of combinations with repetition:

[tex]x = \frac{(6+3-1)!}{3!\cdot (6-1)!}[/tex]

[tex]x = 56[/tex]

Hence, correct answer is D.

Answer:

Step-by-step explanation:

let the coordinates of P be (x,y)

[tex]x=\frac{mx2+nx1}{m+n} \\y=\frac{my2+ny1}{m+n} \\x=\frac{2(5)+3(-3)}{2+3} \\x=\frac{10-9}{5} =\frac{1}{5} =0.2\\y=\frac{2(0)+3(-4)}{2+3} \\y=\frac{0-12}{5} =\frac{-12}{5} =-2.4\\[/tex]

so coordinates of P are (0.2,-2.4)

Answer:

7 hours

Step-by-step explanation:

9 : 30 to 17:00 = 7 hours 30 minutes

Minus 30 minutes = 7 hours

Answer:

The p-value of the test statistic from the standard normal table is 0.0017 which is less than the level of significance therefore, the null hypothesis would be rejected and it can be concluded that there is sufficient evidence to support the claim that less than 20% of the pumps are inaccurate.

Step-by-step explanation:

Here, 1304 gas pumps were not pumping accurately and 5689 pumps were accurate.

x = 1304, n = 1304 + 5689 = 6993

The level of significance = 0.01

The sample proportion of pump which is not pumping accurately can be calculated as,

The claim is that the industry representative less than 20% of the pumps are inaccurate.

The hypothesis can be constructed as:

H0: p = 0.20

H1: p < 0.20

The one-sample proportion Z test will be used.

The test statistic value can be obtained as:

[tex]Z=\frac{\hat{p}-P}{\sqrt{\frac{P(1-P))}{n}}}\\\\Z=\frac{0.186-0.20}{6993}\\\\Z=-2.927[/tex]

Answer:

8xy+12y/5

Step-by-step explanation:

write the division as a fraction

4(2x+3)/5 y

Calaucte the product

4y(2x+3)/5

Distbtute 4y through the parentheis  

8xy+12y/5

which gives you 8xy+12y/5

Answer:

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

[tex] \frac{x}{7} - 4 = 6 \\ \frac{x}{7} = 6 + 4 \\ \frac{x}{7} = 10 \\ x = 10 \times 7 \\ x = 70[/tex]

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