An engineering consulting firm wanted to evaluate the diameter of rivet heads. The following data represent the diameters (in hundredths of an inch) for a random sample of 25 rivet heads:
(20 pts) 6.81 6.79 6.69 6.59 6.65 6.60 6.74 6.70 6.76 6.84 6.81 6.71 6.66 6.76 6.76 6.77 6.72 6.68 6.71 6.79 6.72 6.72 6.72 6.79 6.83
a. Set up a 95% confidence interval estimate of the average diameter of rivet heads (in hundredths of an inch)
b. Set up a 95% CI estimate of the standard deviation of the diameter rivet heads (in hundredths of an inch)
Answer:
a)CI 95 % = ( 6.7063 ; 6.7593) ( in hundredths of an inch)
b) CI 95 % = ( 0.05 < σ < 0.089 ) ( in hundredths of an inch)
Step-by-step explanation:
From the problem statement, we have a manufacturing process and we we assume a normal distribution, from sample data:
x = 6.7328 and s = 0.0644
a) CI 95 % = ( x ± t(c) * s/√n )
t(c) df = n -1 df = 25 - 1 df = 24
CI = 95 % α = 5 % α = 0.05 α /2 = 0.025
Then from t-student table t(c) = 2.060
s/√n = 0.0644/ √ 25 s/√n = 0.01288
CI 95 % = ( x ± t(c) * s/√n ) = ( 6.7328 ± 2.060*0.01288)
CI 95 % = ( 6.7328 ± 0.02653 )
CI 95 % = ( 6.7063 ; 6.7593) ( in hundredths of an inch)
b) CI 95 % of the variance is:
CI 95 % = ( ( n - 1 ) * s² / χ²₁ - α/₂ ≤ σ² ≤ ( n - 1 )*s² / χ²α/₂ )
( n - 1 ) * s² = ( 25 - 1 ) * (0.0644)² = 24* 0.00414
( n - 1 ) * s² = 0.09936
And from χ² table we look for values of
χ² α/₂ ,df df = 24 and α/2 = 0.025
χ² (0.025,24) = 12.40 and χ²₁ - α/₂ = χ² (0.975, 24)
χ² (0.975, 24) = 39.36
Then
CI 95 % = ( 0.09936 / 39.36 ≤ σ² ≤ 0.09936 / 12.40)
CI 95 % = ( 0.0025 ≤ σ² ≤ 0.0080)
Then for the standard deviation, we take the square root of that interval
CI 95 % = ( 0.05 < σ < 0.089 )
Find the area of the composite area
Data with 950 observations are drawn from a bell-shaped distribution with a mean of 78 and a standard deviation of 19. Approximately how many observations are more than 116
Answer: there are 22 observations that are more than 116.
Step-by-step explanation:
Let x be the random variable.
Given: Sample size = 950
Mean = 78
Standard deviation = 19
The probability that the observations are more than 116 is given by :-
[tex]P(X>116)=P(\dfrac{X-mean}{standard \ deviation}>\dfrac{116-78}{19})\\\\=P(Z>2)\\\\=1-P(Z<2)\\\\=1-0.9772\ \ \ [\text{Using p-value calculator}]\\\\=0.0228[/tex]
Number of observations are more than 116 = [tex]0.0228\times950[/tex]
[tex]=21.66\approx22[/tex]
Hence, there are 22 observations that are more than 116.
How many ways can a person toss a coin 16 times so that the number of heads is between 7 and 14 inclusive
50626 ways with a probability of 0.77
Step-by-step explanation:If a coin is tossed once, there are two possible results - a head or a tail. i.e 2¹ = 2
If the coin is tossed twice, there are four possible results - 4 heads no tail, 4 tails no head, 1 head 3tails or 2 heads 2 tails. That is 2² = 4
If the coin is tossed thrice, there are eight possible results. That is 2³ = 8.
Now, if the coin is tossed 16 times, there are 2¹⁶ = 65536 likely results.
From these 16 tosses, let's calculate the number of ways of achieving or selecting 7, 8, 9, 10, 11, 12, 13 or 14 heads. We use the combination formula given as follows;
Cₙ, ₓ = n! ÷ [ (n-x)! (x)! ]
Where;
n = number of tosses
x = number of selection
number of ways of getting 7 heads;
n = 16
x = 7
=> C₁₆, ₇ = 16! ÷ [ (16-7)! (7)! ]
=> C₁₆, ₇ = 16! ÷ [ (9)! (7)! ]
=> C₁₆, ₇ = 11440
number of ways of getting 8 heads;
n = 16
x = 8
=> C₁₆, ₈ = 16! ÷ [ (16-8)! (8)! ]
=> C₁₆, ₈ = 16! ÷ [ (8)! (8)! ]
=> C₁₆, ₈ = 12870
number of ways of getting 9 heads;
n = 16
x = 9
=> C₁₆, ₉ = 16! ÷ [ (16-9)! (9)! ]
=> C₁₆, ₉ = 16! ÷ [ (7)! (9)! ]
=> C₁₆, ₉ = 11440
number of ways of getting 10 heads;
n = 16
x = 10
=> C₁₆, ₁₀ = 16! ÷ [ (16-10)! (10)! ]
=> C₁₆, ₁₀ = 16! ÷ [ (6)! (10)! ]
=> C₁₆, ₁₀ = 8008
number of ways of getting 11 heads;
n = 16
x = 11
=> C₁₆, ₁₁ = 16! ÷ [ (16-11)! (11)! ]
=> C₁₆, ₁₁ = 16! ÷ [ (5)! (11)! ]
=> C₁₆, ₁₁ = 4368
number of ways of getting 12 heads;
n = 16
x = 12
=> C₁₆, ₁₂ = 16! ÷ [ (16-12)! (12)! ]
=> C₁₆, ₁₂ = 16! ÷ [ (4)! (12)! ]
=> C₁₆, ₁₂ = 1820
number of ways of getting 13 heads;
n = 16
x = 13
=> C₁₆, ₁₃ = 16! ÷ [ (16-13)! (13)! ]
=> C₁₆, ₁₃ = 16! ÷ [ (3)! (13)! ]
=> C₁₆, ₁₃ = 560
number of ways of getting 14 heads;
n = 16
x = 14
=> C₁₆, ₁₄ = 16! ÷ [ (16-14)! (14)! ]
=> C₁₆, ₁₄ = 16! ÷ [ (2)! (14)! ]
=> C₁₆, ₁₄ = 120
Therefore, the total number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 heads is the sum of the results above. i.e
11440 + 12870 + 11440 + 8008 + 4368 + 1820 + 560 + 120 = 50626 ways
P(getting number of heads between 7 and 14 inclusive) = [number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 ] ÷ [total number of possible outcomes]
= [tex]\frac{50626}{65536}[/tex]
= 0.77
Simplify the following expression
7-5/6 × 7-7/6
[tex]\longrightarrow{\blue{ 0 }}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex]7 - ( \frac{5}{6} \times 7) - \frac{7}{6} [/tex]
[tex] = 7 - \frac{35}{6} - \frac{7}{6} [/tex]
Since the denominators are unequal, we find the L.C.M (lowest common multiple) for the denominators.
The L. C. M is 6.
Now, multiply the L.C.M. with both numerator & denominator.
[tex] = \frac{7 \times 6}{1 \times 6} - \frac{35}{6} - \frac{7}{6} [/tex]
Now that the denominators are equal, we can add/subtract them.
[tex] = \frac{42- 35 - 7}{6} [/tex]
[tex] = \frac{42 - 42}{6} [/tex]
[tex] = \frac{ 0}{6} [/tex]
[tex] = 0[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
. Cho S là ngoại diên của khái niệm con người, p(x,y) = x yêu thương y.
1) Viết các phán đoán sau đây dưới dạng công thức:
a) Nhiều người yêu thương A. (Thay A bằng chính tên của em).
b) A yêu thương nhiều người. (Thay A bằng chính tên của em).
B làm k cho mình KQ với
An angle measures. What is the measure of its complement? (b) An angle measures 48 . What is measure 26 of its supplement?
Sarah bought a TV for £250
Three years later she sold it for £180
Work out her percentage loss
Answer:
36%
Step-by-step explanation:
Step-by-step explanation:
Loss percentage= loss/cost× 100%
250-180=70
70/180=0.3888
0.3888×100%=39%
A cone has a height of 3 feet. The diameter of the base is 8 feet. What is the approximate volume of the cone in feet to the nearest hundreth?
Answer:
12.56 feet cubed
Step-by-step explanation:
Diameter of 8= radius of 4
4 x 3.14=12.56
12.56x3=37.68
37.68/3=12.56
Given g(x) -x + 4, solve for a when g(x) = 8.
Answer:
x = 12
Step-by-step explanation:
g(x) - × + 4 =0
put g(x) = 8
so, 8 - x + 4 = 0
x = 12
Answer:
x = - 4
Step-by-step explanation:
Given g(x) = - x + 4 and g(x) = 8 , the equate the right sides, that is
- x + 4 = 8 ( subtract 4 from both sides )
- x = 4 ( multiply both sides by - 1 )
x = - 4
Given that a*b = 2ab - 3b. Determine 2*(3*5)
Answer:
15
Problem:
Given that a*b = 2ab - 3b. Determine 2*(3*5)
Step-by-step explanation:
First we find 3*5 using rule a*b = 2ab - 3b.
3*5=2(3)(5)-3(5)
3*5=30-15
3*5=15
Now we are left with 2*15 in which we will still use the rule a*b=2ab-3b.
2*15=2(2)(15)-3(15)
2*15=60-45
2*15=15
Therefore, 2*(3*5)=15.
Sea grass grows on a lake. The rate of growth of the grass is ????????/???????? = ????????, where ???? is a constant.
a. Find an expression for ????, the amount of grass in the lake (in tons), in terms of ????, the number of years, if the amount of grass is 100 tons initially, and 120 tons after one year.
b. In how many years will the amount of grass available be 300 tons?
c. If fish are now introduced into the lake and consume a consistent 80 tons/year of sea grass, how long will it take for the lake to be completely free of sea grass?
Answer:
[tex](a)\ G(t) = 100 *e^{0.1823t}[/tex]
[tex](b)\ t = 6[/tex]
[tex](c)\ t = 1.7[/tex]
Step-by-step explanation:
Given
[tex]G_0 = 100[/tex] --- initial
[tex]G(1) = 120[/tex] --- after 1 year
[tex]r \to rate[/tex]
Solving (a): The expression for g
Since the rate is constant, the distribution of G follows:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]G(1) = 120[/tex] implies that:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]120 = G_0 * e^{r*1}[/tex]
Substitute [tex]G_0 = 100[/tex]
[tex]120 = 100 * e^{r[/tex]
Divide both sides by 100
[tex]1.2 = e^{r[/tex]
Take natural logarithm of both sides
[tex]\ln(1.2) = \ln(e^r)[/tex]
[tex]0.1823 = r[/tex]
[tex]r = 0.1823[/tex]
So, the expression for G is:
[tex]G(t) = G_0 * e^{rt}[/tex]
[tex]G(t) = 100 *e^{0.1823t}[/tex]
Solving (b): t when G(t) = 300
We have:
[tex]G(t) = 100 *e^{0.1823t}[/tex]
[tex]300 = 100 *e^{0.1823t}[/tex]
Divide both sides by 100
[tex]3 = e^{0.1823t}[/tex]
Take natural logarithm
[tex]\ln(3) = \ln(e^{0.1823t})[/tex]
[tex]1.099 = 0.1823t[/tex]
Solve for t
[tex]t = \frac{1.099}{0.1823}[/tex]
[tex]t = 6[/tex] --- approximated
Solving (c): When there will be no grass
Reduction at a rate of 80 tons per year implies that:
[tex]G(t) = 100 *e^{0.1823t}- 80t[/tex]
To solve for t, we set G(t) = 0
[tex]0 = 100 *e^{0.1823t}- 80t\\[/tex]
Rewrite as
[tex]80t = 100 *e^{0.1823t}[/tex]
Divide both sides by 100
[tex]0.8t = e^{0.1823t}[/tex]
Take natural logarithm of both sides
[tex]\ln( 0.8t) = \ln(e^{0.1823t})[/tex]
[tex]\ln( 0.8t) = 0.1823t[/tex]
Plot the graph of: [tex]\ln( 0.8t) = 0.1823t[/tex]
[tex]t = 1.7[/tex]
A business is interested in employees’ job satisfaction. The regional manager places a name card for every employee into a bowl and randomly selects 10 cards. Which sampling method was used?
cluster sampling
simple random sampling
stratified random sampling
systematic random sampling
Answer:
B
Step-by-step explanation:
Answer: simple random sampling
AKA: B
Step-by-step explanation: guy above me is correct :)
3x – 4(x - 4) + 4 = 13
Solve for x step by step
Please answer quickly
Answer:
7
Step-by-step explanation:
3x – 4(x - 4) + 4 = 13
=> 3x - 4x + 16 + 4 = 13
=> - x + 20 = 13
=> - x = 13 - 20
=> - x = - 7
=> x = 7
Answer:
x = 7
Step-by-step explanation:
3x – 4(x - 4) + 4 = 13
3x - 4x + 16 + 4 = 13
-x + 20 = 13
-x + 20 - 20 = 13 - 20
-x = -7
(-x = -7)/-1
x = 7
Hope this helps.
Help me pleassseeeee
Answer:
8x+(-20x)
Step-by-step explanation:
what is the midpoint with the line segments with end points (-4, 6) (2,-1)
Answer:
(-1, 5/2)
Step-by-step explanation:
Midpoint = (-4 + 2)/ 2 , (6 - 1)/2
= (-2/2), (5/2)
= (-1, 5/2)
Answer:
Step-by-step explanation:
The midpoints of two coordinate is = [tex]\frac{x2 + x1}{2}[/tex] , [tex]\frac{y2 +y1}{2}[/tex].
Let x2 = 2
x1 = -4
y2 = -1
y1 = 6
Solution:
[tex]\frac{2+-4}{2} , \frac{-1+6}{2} \\\\\\= (-1,\frac{5}{2})[/tex]
find the equation of the line perpendicular to the given line, through the given point x=-3; (1,8)
Answer:
y = 8
General Formulas and Concepts:
Algebra I
Coordinates (x, y)
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Identify
[Line] x = -3
Point (1, 8)
Step 2: Find Perpendicular Line
A vertical line's slope is undefined.
The negative reciprocal of an undefined slope is 0.
Define perpendicular slope: m = 0Substitute in m [Slope-Intercept Form]: y = 0x + bSimplify: y = bGiven point (1, 8), our y-value is equal to 8.
∴ the perpendicular line is y = 8.
Perimeter of a 14cm,10cm,6cm and 20cm shape?
Answer:
The perimeter is 50 cm.
Step-by-step explanation:
P= 14 + 10 + 6 + 20= 50 cm
Which expression can be used to convert 22 Australian dollars to US dollar
Answer:26.4
Step-by-step explanation:1.2 x22
Please answer part A and B.
Answer:
Percent who walk 45%
Percent in car 22.5%
Step-by-step explanation:
The total number of students is
36+26+18 = 80
Percent who walk is 36/80 = .45 =45%
Percent in car is 18/80 =.225= 22.5%
What is the value of z2 if 3z1 = 6 + 18i and z1 + z2 = 5 + 9i?
Answer:
z2=-3-3i
Step-by-step explanation:
3z1+0z2=6+18i
z1+z2=5+9i (×3)
3z1+3z2=15+27i
3z1+0z2=6+18i (-) =
-3z2=9+9i
z2=-3÷(9+9i)
z2=-3-3i
27. Find the length of the segment LK. (G.CO.C.10)
Show your work! (2pts)
J
1
3x
L
K
X + 6
Click to add speaker notes
Answer:
9
Step-by-step explanation:
the only thing we can say for sure is that JL is splitting the triangle and also its baseline IK in half.
so, both sides of the baseline must be equal :
3x = x + 6
2x = 6
x = 3
=> LK = x + 6 = 3 + 6 = 9
the average of students is 15 years if the age of a teacher is included their average becomes 18 years .what is the age of the teacher ?
Answer:
21; the age of the teacher
Step-by-step explanation:
15+x/2=18
Estimate - I estimated in the 20's because it only averaged up a little bit
Started with 23 and kept going until i got to my answer
21
15+21/2
36/2
18
Please mark brainliest :)
What is the answer. I need it ASAP u have to choose 3 answers
HELP HELP HELP HELP solve this
Answer:
77
Step-by-step explanation:
I need help with this math problem
Answer: A) (x + 12) and (x + 9)
Step-by-step explanation:
You need to get x^2 + 21x + 108.
A) (x + 12) (x + 9) = x^2 + 12x + 9x + 108 = x^2 + 21x + 108
B) (x - 12) (x - 9) = x^2 - 9x - 12x + 108 = x^2 -21x + 108
C) (x - 27) (x - 4) = x^2 - 4x - 27x + 108 = x^2 - 31x + 108
D) (x + 27) (x + 4) = x^2 + 27x + 4x + 31 = x^2 + 31x + 31
So, the answer is A).
Câu ca dao sau đây bị chi phối bởi luật bài trung, Giải thích tại sao?
“Có yêu, thì yêu cho chắc,
Bằng như trúc trắc, thì trục trặc cho luôn”.
Answer:
Hi Are you from Vietnam?
Step-by-step explanation:
Sorry i cant understand
im filipino
Gerald is thinking of a number n, and he wants his sister to guess the number. His first clue is that 7 more than 3 times his
number is at least 10 and at most 28. Write a compound inequality that shows the range of numbers that Isabella might be
thinking of.
Write your answer in interval notation. For example-3
Answer:
(1, 7)
Step-by-step explanation:
The number is n.
7 more than 3 times his
number is at least 10 and at most 28.
Thus;
10 ≤ 3n + 7 ≤ 28
Let's solve individually;
10 ≤ 3n + 7
10 - 7 ≤ 3n
n ≥ 3/3
n ≥ 1
Also,
3n + 7 ≤ 28
3n ≤ 28 - 7
3n ≤ 21
n ≤ 21/3
n ≤ 7
Thus, since n cannot be more than 7 or less than 1, it means in interval Notation, the answer is;
(1, 7)
Please I really need help
=======================================================
Explanation:
The triangular face has area of base*height/2 = 8*2/2 = 16/2 = 8 square feet.
Multiply this with the depth of the prism to get 8*12 = 96 cubic feet
----------
For any prism, the volume formula is
V = (area of base)*(depth of prism)
The term "depth" can be replaced with "height" and it's the same idea.
In this problem, we have a triangular prism because the parallel sides are triangles.
You are riding your bike and notice the square sign above. You mentally draw a
straight line from point A to C. Describe the angle relationship between /_DCA and
/_BCA.
===========================================================
Explanation:
When using the SSS congruence rule, we can prove that triangle DCA is congruent to triangle BCA.
Since the triangles are congruent, the corresponding pieces angle DCA and angle BCA are equal in measure (if they weren't, then the triangles wouldn't be congruent).
Recall that any square has four right angles, ie all angles are 90 degrees each. Angle DCB is cut in half to get 90/2 = 45.
The angles DCA and DCB are 45 degrees each.
