A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0: µ = 12 against H1: µ < 12 using a random sample of n = 4 specimens. Calculate the P-value if the observed statistic is Xbar (average) = 11.25. Suppose that the distribution of the sample mean is approximately normal.

Answers

Answer 1

Answer:

The p-value of the test is 0.0013.

Step-by-step explanation:

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

12 is tested at the null hypothesis:

This means that [tex]\mu = 12[/tex]

Standard deviation of 0.5 kilograms.

This means that [tex]\sigma = 0.5[/tex]

Sample of n = 4 specimens. Observed statistic is Xbar (average) = 11.25.  

This means that [tex]n = 4, X = 11.25[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{11.25 - 12}{\frac{0.5}{\sqrt{4}}}[/tex]

[tex]z = -3[/tex]

P-value:

Probability of finding a sample mean belo 11.25, which is the p-value of z = -3.

Looking at the z-table, z = -3 has a p-value of 0.0013, thus the this is the p-value of the test.


Related Questions

Solve, then check algebraically and graphically. 9x-3=78

Answers

Answer:

[tex]9x - 3 = 78 \\ 9x - 3 + 3 = 78 + 3 \\ 9x = 81 \\ \frac{9x}{9} = \frac{81}{9} \\ x = 9[/tex]

Answer:

[tex]9x - 3 = 78 \\9 x = 78 + 3 \\ 9x = 81 \\ x = \frac{81}{9} \\ x = 9[/tex]

A printing machine 600 books in 3 hours. How many books will the machine print in 5​

Answers

Answer:

1, 000 hrs

Step-by-step explanation:

The machine prints,

in 3 hrs = 600 books

in 1 hr = 600/ 3 hrs = 200 hrs.

in 5 hrs = 200 × 5

= 1, 000 hrs

The printing machine will print 1000 books in 5 hours.

Let's calculate how many books the printing machine will print in 5 hours based on the given information.

To do this, we'll use the concept of rates and proportions.

Given that the printing machine can print 600 books in 3 hours, we can set up a rate equation as follows:

Rate of printing = Number of books / Time taken

Let "x" be the number of books the machine will print in 5 hours. We can set up the proportion:

600 books / 3 hours = x books / 5 hours

To solve for "x," we cross-multiply:

3 * x = 600 * 5

Now, let's solve for "x":

3x = 3000

x = 3000 / 3

x = 1000

So, the printing machine will print 1000 books in 5 hours.

Given: Printing machine prints 600 books in 3 hours.

Let the number of books the machine will print in 5 hours be "x."

Using the rate formula, we can set up the proportion:

600 books / 3 hours = x books / 5 hours

Cross-multiplying:

3 * x = 600 * 5

Solving for "x":

3x = 3000

x = 3000 / 3

x = 1000

Hence, the printing machine will print 1000 books in 5 hours.

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Consider the quadratic function y = 0.3 (x-4)2 - 2.5
Determine the axis of symmetry, x =

Answers

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

We have the quadratic function:

[tex]\displaystyle y=0.3(x-4)^2-2.5[/tex]

And we want to determine its axis of symmetry.

Notice that this is in vertex form:

[tex]y=a(x-h)^2+k[/tex]

Where (h, k) is the vertex of the parabola.

From our function, we can see that h = 4 and k = -2.5. Hence, our vertex is the point (4, -2.5).

The axis of symmetry is equivalent to the x-coordinate of the vertex.

The x-coordinate of the vertex is 4.

Therefore, the axis of symmetry is x = 4.

At what x value does the function given below have a hole?

f(x)=x+3/x2−9

Answers

Answer:

hole at x=-3

Step-by-step explanation:

The hole is the discontinuity that exists after the fraction reduces. (Still doesn't exist for original of course)

The discontinuities for this expression is when the bottom is 0. x^2-9=0 when x=3 or x=-3 since squaring either and then subtracting 9 would lead to 0.

So anyways we have (x+3)/(x^2-9)

= (x+3)/((x-3)(x+3))

Now this equals 1/(x-3) with a hole at x=-3 since the x+3 factor was "cancelled" from the denominator.

Find the first derivative for y = f(x). fox ) 3x² -5x-1 at a Pocat where a = 4​

Answers

Answer:

Step-by-step explanation:

f(x) = 3x² -5x - 1

f'(x) =2*3x - 5*1 +0

     = 6x - 5

f'(4) = 6*4 - 5

      = 24 - 5

      = 19

what is 2x + 4 = x + 40

Answers

[tex]{\boxed{\boxed { ⎆ Answer :- }}} \ [/tex]

[tex]2x + 4 = x + 40 \\ 2x - x = 40 - 4 \\ x = 36[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ ツ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

X=36

Explanation: cause I said what I said

Help me pls, BRAINEST AWARD

Answers

Answer:

x = 3.7

Step-by-step explanation:

By applying sine ratio for the given angle B,

sin(39°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

sin(39°) = [tex]\frac{AD}{AB}[/tex]

0.6293 = [tex]\frac{AD}{7}[/tex]

AD = 4.41

By applying tangent ratio for the given angle C,

tan(50°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

1.19 = [tex]\frac{AD}{x}[/tex]

1.19 = [tex]\frac{4.41}{x}[/tex]

x = 3.7

Please help ❤️
Find the value of x

Answers

Answer:

-2/15

Step-by-step explanation:

14x+x+15=13

Answer:

x = -8

Step-by-step explanation:

based on the picture the top line is equal to 13.

So, 14 + x+ x + 15 = 13

      2x + 29 = 13

      2x = -16

x = -8

2) There are 40 boys and 16 girls in a class of students. What is the ratio of girls to students?

Answers

Add boys and girls together for total students:

40 + 16 = 56 total students

Girls to total students is 16/56

Divide both numbers by 8 to get 2/7

The ratio is 2/7

[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]

There are 40 boys and 16 girls in a class of students. ⠀⠀⠀⠀

[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]

⠀What is the ratio of girls to students?⠀⠀⠀

[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]

In a class,

boys=40

girls =16

So,

The students of the class =

boys+girls 40+1656

According to the question,

we have to find the ratio of girls to the total students

ratio=[tex]\sf{\dfrac{girls}{students} }[/tex]

ratio=[tex]\sf{\dfrac{16}{56} }[/tex]

ratio=[tex]\sf{\dfrac{\cancel{16}}{\cancel{56}} }[/tex]

ratio=[tex]\sf{\dfrac{2}{7} }[/tex]

ratio=[tex]\sf{2:7 }[/tex]

⠀⠀⠀⠀

[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]

⠀⠀⠀⠀

Hence,the ratio of girls to students is 2:7

⠀⠀⠀⠀

A student takes an exam containing 16 true or false questions. If the student guesses, what is the probability that he will get exactly 14 questions right

Answers

Answer:

0.001831055

Step-by-step explanation:

Here, n = 16, p = 0.5, (1 - p) = 0.5 and x = 14

As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 14)

P(x =14) = 16C14 * 0.5^14 *(1-0.5)^2

               = 120 * 0.5^14 *(1-0.5)^2

= 0.001831055

the least value of x²-3x+5 is..​

Answers

11/4

Step-by-step explanation:

to find the minimum value we require to find the vertex and determine if max/min

for a quadratic in standard form ; ax² + bx + c

the coordinate of the vertex is..

xvertex = -b/2a

x² - 3x + 5 is in standard form with a = 1,b = - 3 and c = 5

xvertex = - , -3/2 = 3/2

substitute this value into the equation for y-coordinate

yvertex = ( 3/2 ) ² -3 (3/2) + 5 = 11/4

vertex = ( 3/2, 11/4 )

to determine whether max/min

• if a > 0 then minimum u

• ifa < 0 then maximum n

here a = 1 > 0 hence minimum

minimum value of x² - 3x + 5 is 11/4

hope you understand this :)

In the diagram below, BC is an altitude of ABD. To the nearest whole unit, what is the length of CD?

Answers

Answer:

B. 23

Step-by-step explanation:

BC = 32

CA = 44

To find the length of CD, apply the altitude of right triangle formula, (altitude-on-hypotenuse theorem) which is given as:

h = √(xy)

Where,

h = CB = 32

x = CA = 44

y = CD = ?

Plug in the values

32 = √(44 × CD)

Square both sides

32² = 44 × CD

1,024 = 44 × CD

Divide both sides by 44

1,024/44 = CD

CD = 23 units (nearest whole unit)

Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.

Answers

Answer:

her salary will increase by $ 145 for every week

Step-by-step explanation:

x=1st paycheck (integer).

weekly raise = $ 145.

After completing the 1st week she will get $ (x+145).

Similarly after completing the 2nd week she will get

$ (x + 145) + $ 145.

= $ (x + 145 + 145)

= $ (x + 290)

So in this way end of every week her salary will increase by $ 145.

Could someone help me

Answers

Hello,

I have only found 113 solutions (i have num 15 given)

nb= 1         ::: 27*n +  98= 30*n + 56===> n= 1  4

nb= 2         ::: 28*n +  95= 30*n + 67===> n= 1  4

nb= 3         ::: 29*n +  65= 30*n + 17===> n= 4  8

nb= 4         ::: 29*n +  65= 30*n + 18===> n= 4  7

nb= 5         ::: 29*n +  65= 30*n + 47===> n= 1  8

nb= 6         ::: 29*n +  65= 30*n + 48===> n= 1  7

nb= 7         ::: 29*n +  74= 30*n + 16===> n= 5  8

nb= 8         ::: 29*n +  74= 30*n + 18===> n= 5  6

nb= 9         ::: 29*n +  74= 30*n + 56===> n= 1  8

nb= 10        ::: 29*n +  74= 30*n + 58===> n= 1  6

nb= 11        ::: 30*n +  16= 29*n + 74===> n= 5  8

nb= 12        ::: 30*n +  17= 29*n + 65===> n= 4  8

nb= 13        ::: 30*n +  18= 29*n + 65===> n= 4  7

nb= 14        ::: 30*n +  18= 29*n + 74===> n= 5  6

nb= 15        ::: 30*n +  47= 29*n + 65===> n= 1  8

nb= 16        ::: 30*n +  48= 29*n + 65===> n= 1  7

nb= 17        ::: 30*n +  56= 27*n + 98===> n= 1  4

nb= 18        ::: 30*n +  56= 29*n + 74===> n= 1  8

nb= 19        ::: 30*n +  58= 29*n + 74===> n= 1  6

nb= 20        ::: 30*n +  67= 28*n + 95===> n= 1  4

nb= 21        ::: 36*n +  97= 40*n + 25===> n= 1  8

nb= 22        ::: 38*n +  59= 40*n + 27===> n= 1  6

nb= 23        ::: 38*n +  65= 40*n + 27===> n= 1  9

nb= 24        ::: 38*n +  69= 40*n + 15===> n= 2  7

nb= 25        ::: 39*n +  78= 45*n + 6===> n= 1  2

nb= 26        ::: 39*n +  82= 40*n + 15===> n= 6  7

nb= 27        ::: 39*n +  82= 40*n + 17===> n= 6  5

nb= 28        ::: 39*n +  82= 40*n + 65===> n= 1  7

nb= 29        ::: 39*n +  82= 40*n + 67===> n= 1  5

nb= 30        ::: 40*n +  15= 38*n + 69===> n= 2  7

nb= 31        ::: 40*n +  15= 39*n + 82===> n= 6  7

nb= 32        ::: 40*n +  17= 39*n + 82===> n= 6  5

nb= 33        ::: 40*n +  25= 36*n + 97===> n= 1  8

nb= 34        ::: 40*n +  27= 38*n + 59===> n= 1  6

nb= 35        ::: 40*n +  27= 38*n + 65===> n= 1  9

nb= 36        ::: 40*n +  65= 39*n + 82===> n= 1  7

nb= 37        ::: 40*n +  67= 39*n + 82===> n= 1  5

nb= 38        ::: 46*n +  87= 50*n + 39===> n= 1  2

nb= 39        ::: 46*n +  87= 52*n + 9===> n= 1  3

nb= 40        ::: 47*n +  68= 50*n + 29===> n= 1  3

nb= 41        ::: 47*n +  83= 50*n + 26===> n= 1  9

nb= 42        ::: 47*n +  98= 51*n + 6===> n= 2  3

nb= 43        ::: 47*n +  98= 53*n + 2===> n= 1  6

nb= 44        ::: 48*n +  63= 50*n + 29===> n= 1  7

nb= 45        ::: 48*n +  73= 52*n + 9===> n= 1  6

nb= 46        ::: 49*n +  63= 51*n + 7===> n= 2  8

nb= 47        ::: 49*n +  72= 53*n + 8===> n= 1  6

nb= 48        ::: 49*n +  78= 52*n + 30===> n= 1  6

nb= 49        ::: 49*n +  87= 56*n + 3===> n= 1  2

nb= 50        ::: 50*n +  26= 47*n + 83===> n= 1  9

nb= 51        ::: 50*n +  29= 47*n + 68===> n= 1  3

nb= 52        ::: 50*n +  29= 48*n + 63===> n= 1  7

nb= 53        ::: 50*n +  39= 46*n + 87===> n= 1  2

nb= 54        ::: 52*n +  30= 49*n + 78===> n= 1  6

nb= 55        ::: 57*n +  92= 63*n + 8===> n= 1  4

nb= 56        ::: 58*n +  72= 60*n + 34===> n= 1  9

nb= 57        ::: 58*n +  73= 60*n + 49===> n= 1  2

nb= 58        ::: 58*n +  79= 60*n + 31===> n= 2  4

nb= 59        ::: 58*n +  97= 60*n + 13===> n= 4  2

nb= 60        ::: 59*n +  47= 62*n + 8===> n= 1  3

nb= 61        ::: 59*n +  71= 60*n + 23===> n= 4  8

nb= 62        ::: 59*n +  71= 60*n + 28===> n= 4  3

nb= 63        ::: 59*n +  71= 60*n + 43===> n= 2  8

nb= 64        ::: 59*n +  71= 60*n + 48===> n= 2  3

nb= 65        ::: 59*n +  74= 63*n + 2===> n= 1  8

nb= 66        ::: 59*n +  78= 61*n + 30===> n= 2  4

nb= 67        ::: 59*n +  84= 61*n + 30===> n= 2  7

nb= 68        ::: 59*n +  87= 61*n + 3===> n= 4  2

nb= 69        ::: 60*n +  13= 58*n + 97===> n= 4  2

nb= 70        ::: 60*n +  23= 59*n + 71===> n= 4  8

nb= 71        ::: 60*n +  28= 59*n + 71===> n= 4  3

nb= 72        ::: 60*n +  31= 58*n + 79===> n= 2  4

nb= 73        ::: 60*n +  34= 58*n + 72===> n= 1  9

nb= 74        ::: 60*n +  43= 59*n + 71===> n= 2  8

nb= 75        ::: 60*n +  48= 59*n + 71===> n= 2  3

nb= 76        ::: 60*n +  49= 58*n + 73===> n= 1  2

nb= 77        ::: 61*n +  30= 59*n + 78===> n= 2  4

nb= 78        ::: 61*n +  30= 59*n + 84===> n= 2  7

nb= 79        ::: 65*n +  89= 70*n + 24===> n= 1  3

nb= 80        ::: 68*n +  59= 72*n + 3===> n= 1  4

nb= 81        ::: 68*n +  91= 70*n + 45===> n= 2  3

nb= 82        ::: 69*n +  43= 70*n + 15===> n= 2  8

nb= 83        ::: 69*n +  43= 70*n + 18===> n= 2  5

nb= 84        ::: 69*n +  43= 70*n + 25===> n= 1  8

nb= 85        ::: 69*n +  43= 70*n + 28===> n= 1  5

nb= 86        ::: 69*n +  48= 72*n + 3===> n= 1  5

nb= 87        ::: 69*n +  52= 70*n + 14===> n= 3  8

nb= 88        ::: 69*n +  52= 70*n + 18===> n= 3  4

nb= 89        ::: 69*n +  52= 70*n + 34===> n= 1  8

nb= 90        ::: 69*n +  52= 70*n + 38===> n= 1  4

nb= 91        ::: 69*n +  54= 71*n + 8===> n= 2  3

nb= 92        ::: 69*n +  58= 73*n + 2===> n= 1  4

nb= 93        ::: 69*n +  82= 75*n + 4===> n= 1  3

nb= 94        ::: 69*n +  85= 74*n + 20===> n= 1  3

nb= 95        ::: 70*n +  14= 69*n + 52===> n= 3  8

nb= 96        ::: 70*n +  15= 69*n + 43===> n= 2  8

nb= 97        ::: 70*n +  18= 69*n + 43===> n= 2  5

nb= 98        ::: 70*n +  18= 69*n + 52===> n= 3  4

nb= 99        ::: 70*n +  24= 65*n + 89===> n= 1  3

nb= 100       ::: 70*n +  25= 69*n + 43===> n= 1  8

nb= 101       ::: 70*n +  28= 69*n + 43===> n= 1  5

nb= 102       ::: 70*n +  34= 69*n + 52===> n= 1  8

nb= 103       ::: 70*n +  38= 69*n + 52===> n= 1  4

nb= 104       ::: 70*n +  45= 68*n + 91===> n= 2  3

nb= 105       ::: 74*n +  20= 69*n + 85===> n= 1  3

nb= 106       ::: 76*n +  93= 80*n + 45===> n= 1  2

nb= 107       ::: 79*n +  45= 82*n + 6===> n= 1  3

nb= 108       ::: 79*n +  54= 83*n + 6===> n= 1  2

nb= 109       ::: 80*n +  45= 76*n + 93===> n= 1  2

nb= 110       ::: 87*n +  64= 90*n + 25===> n= 1  3

nb= 111       ::: 87*n +  65= 90*n + 23===> n= 1  4

nb= 112       ::: 90*n +  23= 87*n + 65===> n= 1  4

nb= 113       ::: 90*n +  25= 87*n + 64===> n= 1  3

plsssssssssssssssssssssssssssssssssssssssssssss quick

Answers

Answer:

D

y = mx + b

-10 is b because it´s the y intercept (the y value when x is 0).

now, the slope (m) is rise/run:

this is easier graphed, but you can see that the run is 3 (moving sideways on the x axis) and the rise is 2 (going up or down) so its 2/3.

because we are going down on the y axis, the slope is negative (so is the y intercept).

So y = -2/3 -10 is the answer.

I.- Sean los polinomios:
P(x) = 5x5 +4x3 –x +2 Q (X) = -3x4 -7x3 +9x -6 R(x) = 7x5 +3x2 + 8x -2
Halla:
1) P(X) + Q(X) 2) R (X) - P(X) 3) P(X) + R(X) - Q(X)
II.- Resuelve:
1) M= (x-1) (x-1) (x-1) - x3 +1

2) W= (x2 +x +1) (x2 -x +1)

Answers

Answer:

Step-by-step explanation:

M

What is the ratio of 2:5

Answers

Step-by-step explanation:

The ratio is 2 to 5 or 2:5 or 2/5. All these describe the ratio in different forms of fractions. The ratio can consequently be expressed as fractions or as a decimal.

A ratio of 2 : 5 states a comparison between two quantities.

What are ratio and proportion?

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, a ratio 2 : 5.

Suppose it is a ratio of no. of pens to no. of pencils.

So, a ratio 2 : 5 states for every 2 pens there are 5 pencils out of 7 pen and pencils.

We can also write no. of pens = 2/(2+ 5) = 2/7 and for pencils it is 5(2+5)

= 5/7.

Generally, ratios are in simplest form we can have more pens and pencils here but it must be in the multiple of 7.

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Which ordered pairs are in the solution set of the system of linear inequalities?

y > Negative one-thirdx + 2

y < 2x + 3

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 2) and (6, 0. Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (negative 3, negative 3) and (0, 3). Everything above the line is shaded.

Answers

Options:

(2, 2), (3, 1), (4, 2)

(2, 2), (3, –1), (4, 1)

(2, 2), (1, –2), (0, 2)

(2, 2), (1, 2), (2, 0)

Answer:

A. (2, 2), (3, 1), (4, 2)  

Step-by-step explanation:

Given

[tex]y > -\frac{1}{3}x + 2[/tex]

[tex]y < 2x + 3[/tex]

Required

Solve for x and y

To solve this, we make use of graphical method (see attachment for graph)

All points that lie on the shaded region are true for the inequality

Next, we plot each of the given options on the graph

A. (2, 2), (3, 1), (4, 2)

All 3 points lie on the shaded region.

Hence, (a) is true

Answer:

A. (2, 2), (3, 1), (4, 2)  

Step-by-step explanation:


what ordered pair makes both inequalities true
-3,5
-2,2
-1,-3
0,-1

Answers

Answer:

(-2, 2)

Step-by-step explanation:

(-2, 2) is the only ordered pair that makes both inequalities true.

Answer:

B

Step-by-step explanation:

got it right

Which of the following are best described as lines that meet to form a right
angle?

Answers

Answer:

Two lines that intersect and form right angles are called perpendicular lines.

Answer:

perpendicular lines

Step-by-step explanation:

Definition of perpendicular lines:

Two lines that intersect forming a right angle are perpendicular lines.

Answer: perpendicular lines

Janie can stuff 30 envelops in one minute. Find an expression for the number of envelopes she can stuff in n hours?

Answers

Answer: 30(60n) or 30*60*n

I NEED AN ANSWER ASAP
WILL GIVE BRAINLY THING

Answers

Answer:

1) C

2) D

3) A

4) B

hope it helps

a bag contain 3 black balls and 2 white balls.
1. A ball is taken from the black and then replaced, a second is taken. what is the probabilities that.

(a) there are both black,
(b)one is black one is white,
(c) at lease one is black,
(d) at most one is one is black.

2. find out if all the balls are chosen without replacement.

please kindly solve with explanation. thank you.​

Answers

Answer:

Step-by-step explanation:

Total number of balls = 3 + 2 = 5

1)

a)

[tex]Probability \ of \ taking \ 2 \ black \ ball \ with \ replacement\\\\ = \frac{3C_1}{5C_1} \times \frac{3C_1}{5C_1} =\frac{3}{5} \times \frac{3}{5} = \frac{9}{25}\\\\[/tex]

b)

[tex]Probability \ of \ one \ black \ and \ one\ white \ with \ replacement \\\\= \frac{3C_1}{5C_1} \times \frac{2C_1}{5C_1} = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}[/tex]

c)

Probability of at least one black( means BB or BW or WB)

 [tex]=\frac{3}{5} \times \frac{3}{5} + \frac{3}{5} \times \frac{2}{5} + \frac{2}{5} \times \frac{3}{5} \\\\= \frac{9}{25} + \frac{6}{25} + \frac{6}{25}\\\\= \frac{21}{25}[/tex]

d)

Probability of at most one black ( means WW or WB or BW)

[tex]=\frac{2}{5} \times \frac{2}{5} + \frac{3}{5} \times \frac{2}{5} \times \frac{2}{5} + \frac{3}{5}\\\\= \frac{4}{25} + \frac{6}{25} + \frac{6}{25}\\\\=\frac{16}{25}[/tex]

2)

a) Probability both black without replacement

  [tex]=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}[/tex]

b) Probability  of one black and one white

 [tex]=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}[/tex]

c) Probability of at least one black ( BB or BW or WB)

 [tex]=\frac{3}{5} \times \frac{2}{4} + \frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{6}{20} + \frac{6}{20} \\\\=\frac{18}{20} \\\\=\frac{9}{10}[/tex]

d) Probability of at most one black ( BW or WW or WB)

 [tex]=\frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{1}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{2}{20} + \frac{6}{20} \\\\=\frac{14}{20}\\\\=\frac{7}{10}[/tex]

The coordinator of the vertices of the triangle are (-8,8),(-8,-4), and

Answers

Answer with Step-by-step explanation:

Complete question:

The coordinates  of the vertices of the triangle are (-8,8),(-8,-4), and. Consider QR the base of the triangle. The measure of the base is b = 18 units, and the measure of the height is h = units. The area of triangle PQR is square units.

Let

P=(-8,8)

Q=(-8,-4)

QR=b=18 units

Height of triangle, h=Length of PQ

Distance formula

[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the formula

Height of triangle, h=[tex]\sqrt{(-8+8)^2+(-4-8)^2}=12units[/tex]

Area of triangle PQR=[tex]\frac{1}{2}\times base\times height[/tex]

Area of triangle PQR=[tex]\frac{1}{2}\times 18\times 12[/tex]

Area of triangle PQR=108 square units

Length of QR=18units

Let the coordinates of R(x,y)

[tex]\sqrt{(x+8)^2+(y+4)^2}=18[/tex]

[tex](x+8)^2+(y+4)^2=324[/tex]

[tex]x^2+64+16x+y^2+8y+16=324[/tex]

[tex]x^2+y^2+16x+8y=324-64-16[/tex]

[tex]x^2+y^2+16x+8y=244[/tex]   ......(1)

Using Pythagoras theorem

[tex]H=\sqrt{P^2+B^2}[/tex]

[tex]H=\sqrt{(18)^2+(12)^2}[/tex]

[tex]H=6\sqrt{13}[/tex]units

[tex](6\sqrt{13})^2=(x+8)^2+(y-8)^2[/tex]

[tex]x^2+64+16x+y^2+64-16y=468[/tex]

[tex]x^2+y^2+16x-16y=468-64-64=340[/tex]

[tex]x^2+y^2+16x-16y=340[/tex] .....(2)

Subtract equation (2) from (1) we get

[tex]24y=-96[/tex]

[tex]y=-96/24=-4[/tex]

Using the value of y in equation (1)

[tex]x^2+16x+16-32=244[/tex]

[tex]x^2+16x=244-16+32[/tex]

[tex]x^2+16x=260[/tex]

[tex]x^2+16x-260=0[/tex]

[tex]x^2+26x-10x-260=0[/tex]

[tex]x(x+26)-10(x+26)=0[/tex]

[tex](x+26)(x-10)=0[/tex]

[tex]x=-26, x=10[/tex]

Hence, the coordinate of R (10,-4) or (-26,-4).

From a set of 5 nickels, 10 dimes and 15 quarters, six coins are removed at random without replacement.
a. Find the probability of not removing 6 quarters.
b. Find the probability of removing exactly 2 nickels, 2 dimes and 2 quarters.

Answers

Answer:

(a) 1 - (15 C 6) / (30 C 6)

(b)  (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)

Step-by-step explanation:

Number of  nickels = 5

Number of dimes = 10

Number of quarters = 15

(a) The probability of getting 6 quarters  

= (15 C 6) / (30 C 6)

So, the probability of not getting 6 quarters = 1 - (15 C 6) / (30 C 6)

(b) Probability of getting 2 nickels , 2 dimes and 2 quarters

= (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)

Tim and Al are bricklayers. Tim can construct an outdoor grill in 5 days. If Al helps Tim, they can build it in only 3 days. How long
would it take Al to build the grill alone? Write your answer as an integer, simplified fraction, or mixed number.
It would take Al
days to build the grill alone.

Answers

Answer:

It would take Al 7.5 days to build the grill alone.

Step-by-step explanation:

Since Tim and Al are bricklayers, and Tim can construct an outdoor grill in 5 days, and if Al helps Tim, they can build it in only 3 days, to determine how long would it take Al to build the grill alone should be done the following calculation:

1/5 + X = 1/3

0.20 + X = 0.333

X = 0.333 - 0.20

X = 0.1333333

X = 1 / 7.5

Therefore it would take Al 7.5 days to build the grill alone.

A statistician calculates that 7% of Americans are vegetarians. If the statistician is correct, what is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%

Answers

Answer:

0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A statistician calculates that 7% of Americans are vegetarians.

This means that [tex]p = 0.07[/tex]

Sample of 403 Americans

This means that [tex]n = 403[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.07[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.07*0.93}{403}} = 0.0127[/tex]

What is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%?

Proportion below 7 - 3 = 4% or above 7 + 3 = 10%. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them, and multiply by 2.

Probability the proportion is below 4%

p-value of Z when X = 0.04.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.04 - 0.07}{0.0127}[/tex]

[tex]Z = -2.36[/tex]

[tex]Z = -2.36[/tex] has a p-value of 0.0091

2*0.0091 = 0.0182

0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.

Write an expression for the sequence of operations described below.

divide s by q, add r to the result, then triple what you have

Do not simplify any part of the expression.

Answers

Answer:

3( [tex]\frac{s}{q}[/tex] + r)  

Find the intersection of the parabola y=x^2+4x+3 and the line x-y=-1

Answers

Answer:

1

Step-by-step explanation:

BRE
What is the radius of a circle whose equation is (x - 7)2 + (y - 10)2 = 4?
2 units
ОО
4 units
8 units
16 units

Answers

Answer:

2

Step-by-step explanation:

The equation of a circle is given as:

    (x-h)^2 + (y-k)^2 = r^2

so r^2 = 4

r = sqrt(4)

r = 2

Answer:

A

Step-by-step explanation:

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