Answer:
Q1 = 33
Q3 = 49.75
D2 = 28.4
D8 = 29.6
67th percentile = 46.10
Step-by-step explanation:
Given the data:
13 13 13 20 26 28 30 34 34 34 35 35 36 37 38
41 41 41 45 46 47 47 49 52 54 54 56 62 67 82
The first quartile (Q1) ;
1/4(n + 1)
Where n = number of observations
n = 30
Q1 = 0.25(30 + 1) = 0.25 × 31 = 7.75
7 : corresponds to 30
0.75 : (34 - 30) × 0.75 = 4 × 0.75 = 3
30 + 3 = 33
Third quartile (Q3) :
3/4(n + 1)
Where n = number of observations
n = 30
Q3 = 0.75(30 + 1) = 0.75 × 31 = 23.25
23 : corresponds to 49
0.25 : (52 - 49) × 0.25 = 3 × 0.25 = 0.75
49 + 0.75 = 49.75
Determine the second decile and the eighth decile.
Second decile (D2)
((n+1) × (2)) / 10
= (30 + 1)(2)/10 = 6.2
6 : corresponds to 28 +
0.2 : (30 - 28 )× 0.20 = 0.4
28 + 0.4 = 28.4
Eight decile (D8)
((n+1) × (8)) / 10
= (30 + 1)(8)/10 = 24.8
24 : corresponds to 52 +
0.8 : (54 - 52 )× 0.80 = 1.6
28 + 1.6 = 29.6
67th percentile :
67% × n = 0.67 × 30 = 20.10
20: corresponds to 46
0.1 : (47 - 46) × (0.1) = 0.1
46 + 0.1 = 46.10
The first quartiles is 33 and third quartiles is 23.25.
The second decile is 24.8 and the eight decile is 29.6
The 67th percentile is 46.10.
Given that,
Sample of the Thomas Supply Company Inc. invoices.13 13 13 20 26 28 30 34 34 34 35 35 36 37 38.
41 41 41 45 46 47 47 49 52 54 54 56 62 67 82
We have to determine,
Determine the first and third quartiles.
Determine the second decile and the eight decile.
Determine the 67th percentile.
According to the question,
The first quartile (Q1) ; [tex]\dfrac{1(n+1)}{4}[/tex]Where n = number of observations
n = 30
Then,
[tex]= \dfrac{1(30+1)}{4}\\\\= 0.2 \times 31\\\\= 6.2[/tex]
Then, 7 : corresponds to 30,
[tex](34 - 30) \times 0.75 = 4 \times 0.75 = 3\\\\30 + 3 = 33[/tex]
And Third quartile (Q3) is; [tex]\dfrac{3(n+1)}{4}[/tex]
Where n = number of observations
n = 30
Then,
[tex]= \dfrac{3(30+1)}{4}\\\\= 0.75 \times 31\\\\= 23.25[/tex]
23 : corresponds to 49
[tex]0.25 : (52 - 49) \times 0.25 = 3 \times 0.25 = 0.75\\\\49 + 0.75 = 49.75[/tex]
To determine the second decile and the eighth decile.
Second decile (D2) ; [tex]\dfrac{2(n+1)}{10}[/tex]
Where n = 30
Then,
[tex]= \dfrac{2(30+1)}{10}\\\\= 0.2 \times 31\\\\= 6.1[/tex]
6 : corresponds to 28,
[tex](30 - 28 ) \times 0.20 = 0.4\\\\28 + 0.4 = 28.4[/tex]
And the Eight decile (D8); [tex]\dfrac{8(n+1)}{10}[/tex]
Where n = 30,
Then,
[tex]\dfrac{(30 + 1)(8)}{10} = 24.8[/tex]
24 : corresponds to 52,
[tex](54 - 52 ) \times 0.80 = 1.6\\\\28 + 1.6 = 29.6[/tex]
To determine the 67th percentile :
67% × n = 0.67 × 30 = 20.10
20: corresponds to 46
0.1 : (47 - 46) × (0.1) = 0.1
46 + 0.1 = 46.10
The 67th percentile is 46.10
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Solve the system of equations.
y=x2-5
y=-2x+3
A. (2-1) and (4.-5)
B. -2.7) and (4-5)
C. (-411) and (2-1)
O D. (-4, 11) and (-27)
Among 6 electrical components exactly one is known not to function properly. If 2 components are randomly selected, find the probability that all selected components function properly?
Answer:
66.67% probability that all selected components function properly
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the components are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Desired outcomes:
2 components which function properly, from a set of 5. So
[tex]D = C_{5,2} = \frac{5!}{2!(5-2)!} = 10[/tex]
Total outcomes:
2 components, from a set of 6. So
[tex]T = C_{6,2} = \frac{6!}{2!(6-2)!} = 15[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{10}{15} = 0.6667[/tex]
66.67% probability that all selected components function properly
Myra wants to save at least $500 by the end of her summer vacation. She currently has $350 saved. She can earn $25 cutting a lawn in her neighborhood. Myra solves an inequality to determine the least number of lawns, n, she must cut to reach her goal.
What number is the minimum number of lawns Myra needs to mow to meet her goal?
Answer:
6 ≤ b.
(6).
Step-by-step explanation:
So, we are given in the question that the amount that Myra wants to say is $500 at the end of her summer vacation and she has saved up to $350. Thus, it remain ($500 - $350 = $150) for completion.
Also, "She can earn $25 cutting a lawn in her neighborhood."
Therefore, the total amount of money she wants to save = a = 500. Then,
Total amount of money, a = 350 + 25b.
500 = 350 + 25b.
=> 500 ≤ 350 + 25b.
Note that the ' =' sign has changed to '≤' sign since she wants that amount(at least). Also, the question specified that she used inequality.
Hence, the amount remaining for it to complete is $150. Therefore;
150 ≤ 25b.
6 ≤ b.
Thus, Myra will have to mow at least 6 lawns
Answer:
6
Step-by-step explanation:
Took the quiz on edge!
Calculate each probability
given that P(A) = 0.2, P(B)
= 0.8, and A & B are
independent.
Complete question:
Calculate each probability given that P(A) = 0.2, P(B) = 0.8, and A & B are independent.
a) compute P(A and B)
b) If P(A|B) = 0.7, compute P(A and B).
Answer:
(a) P(A and B) = 0.16
(b) P(A and B) = 0.56
Step-by-step explanation:
Two events are independent if occurrence of one event does not affect possibility of occurrence of another.
(a) if A and B are independent, then P(A and B) = P(A) x P(B)
= 0.2 x 0.8
= 0.16
(b) If P(A|B) = 0.7, compute P(A and B)
Considering the notations of independent events,
[tex]P(A/B) = P(A)\\\\\frac{P(A \ and \ B)}{P(B)} = P(A)\\\\Thus, P(A/B) = \frac{P(A \ and \ B)}{P(B)}\\\\P(A \ and \ B) = P(A/B) *P(B)[/tex]
= 0.7 x 0.8
= 0.56
Please answer this correctly
Answer:
50 km
Step-by-step explanation:
As the figures are given similar ,
56/v = 84/75
v = 56 × 75/84
v = 50 km
Answer:
v = 50
Step-by-step explanation:
The trapezoids are similar, so set up a proportion like so:
[tex]\frac{56}{v} =\frac{84}{75}[/tex]
→Cross multiply:
[tex]\frac{4200}{84v}[/tex]
→Divide 4200 by 84:
v = 50
what is 42 + 7x + 12x – 8 i really need help
Solution,
42+7x+12x-8
Combine like terms,
= 7x+12x+42-8
Simplify
=19x+34
hope it helps
Good luck on your assignment
Answer:
36+19x
Step-by-step explanation:
Ok, first, combine like terms, so the two values with X.
42 + 7x + 12x – 8
42 +19x – 8
Now, we combine the two values that have no X
42+19x– 8 Imagine there is a plus sign in front of the 42 because it's positive.
So 42-8=36
36+19x
That's your solution, that's the most this can be simplified.
What is the range of g?
Answer:
[-4, 9]
Step-by-step explanation:
The range is the vertical extent of the relation.
__
The minimum value of g is marked by the solid dot at (x, y) = (4, -4). That minimum is -4.
The maximum value of g is the peak at (x, y) = (-2, 9). That maximum is 9.
The function is continuous between these values, so the range includes all values between -4 and +9, inclusive.
range: [-4, 9]
Answer:
Step-by-step explanation:
range: [-4, 9]
In a study in Scotland (as reported by Devlin 2009), researchers left a total of 320 wallets around Edinburgh, as though the wallerts were lost. Each contained contact information including an address. Of the wallets, 146 were returned by the people who found them. With the following steps, use the data to estimate the proportion of lost wallets that are returned, and give a 95% confidence interval for this estimate.
Required:
a. What is the observed proportion of wallets that were returned (rounded to the nearest thousandths)?
b. Calculate p to use in the Agresti-Coull method of calculating a 95% confidence interval for the population proportion rounded to the nearest thousandths).
c. Calculate the lower bound of the 95% confidence interval (rounded to the nearest thousandths)
d. Calculate the upper bound of the 95% confidence interval (rounded to the nearest thousandths)
Answer:
a) The observed proportion of wallets that were returned
p = 0.45625
b) 95% of confidence intervals for Population proportion
0.40168 , 0.51082)
c) The lower bound of the 95% confidence interval = 0.40168
d) The upper bound of the 95% confidence interval = 0.51082
Step-by-step explanation:
Step(i):-
a)
Given data the researchers left a total of 320 wallets around Edinburgh, as though the wallets were lost. Each contained contact information including an address. Of the wallets, 146 were returned by the people who found them
Given sample size 'n' = 320
Given data 'x ' = 146
Sample proportion
[tex]p = \frac{x}{n}[/tex]
[tex]p = \frac{x}{n} = \frac{146}{320} = 0.45625[/tex]
Step(ii):-
b) 95% of confidence intervals for Population proportion
Level of significance = 95% or 0.05%
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]
95% of confidence intervals for Population proportion are determined by
[tex](p - Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p + Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} })[/tex]
[tex](0.45625 - 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} } , 0.45625 + 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} })[/tex]
(0.45625 - 0.05457 , 0.45625 + 0.05457)
( 0.40168 , 0.51082)
c) The lower bound of the 95% confidence interval = 0.40168
d) The upper bound of the 95% confidence interval = 0.51082
Another type of painted ceramic vessel is called three-circle red-on-white ( Mimbres Mogollon Archaeology). At four different sites in an archaeological region, the number of such sherds was counted in local dwelling excavations.
Site I Site II Site III Site IV
16 19 30 19
25 7 20 24
6 33 10 13
24 2 47 34
14 21 11
15 12
Shall we reject or not reject the claim that there is no difference in the population mean three-circle red-on-white sherd counts for the four sites? Use a 5% level of significance.
Answer:
Step-by-step explanation:
Hello!
The objective is to test if the population mean of three-circle red-on-white sheds is equal to the four excavation sites.
To compare the population means you have to apply an ANOVA. For this test the variable of interest is
X: number of three-circle red-on-white sheds.
There is only one factor: "Site" with four treatments "I, II, III; IV"
H₀: μ₁= μ₂= μ₃= μ₄
H₁: At least one population mean is different.
α: 0.05
[tex]F= \frac{MS_{Treatment}}{MS_{Error}} ~~F_{K-1;N-K}[/tex]
Df treatments: k-1= 4-1= 3 (k= nº of treatments)
Df errors: N-K= 21-4= 17 (N= total observations for all treatments)
[tex]F_{H_0}= \frac{102.72}{117.08}= 0.88[/tex]
p-value: 0.4723
Using the p-value approach the decision rule is:
p-value ≤ α, reject the null hypothesis.
p-value > α, do not reject the null hypothesis.
The p-value is greater than the level of significance, the decision is to reject the null hypothesis.
Using a 5% significance level, there is not significant evidence to reject the null hypothesis. Then you can conclude that the population mean three-circle red-on-white sherd count is equal to all the excavation sites.
I hope this helps!
Explain how you could calculate the surface area of a square pyramid
Answer:
calculate the area of a square using the length * width formula, and then add the areas of the other triangles, of which you can calculate by using the base * height formula
Step-by-step explanation:
Answer:
Multiply the side length of the base by the slant height and divide by two. Then, multiply by 4. This will give you the lateral surface area of the pyramid.Step-by-step explanation:
Set up each situation and simplify if possible. Then, choose all situations that are best modeled by a rational inequality.
Answer:
Problem: 3x/5x + 5 ≤ 8 + 2x
Solution: x ≥ -15/7
Step-by-step explanation:
Example of this inequality is:
3x/5x + 5 ≤ 8 + 2x
3x/5x - 2x ≤ 8 - 5
(3x - 10x)/5 ≤ 3
-7x ≤ 15
x ≥ -15/7
Please answer this correctly
Answer:
63.2 = y
Step-by-step explanation:
The perimeter is the sum of all the sides
P = 7.8+ y+37.6 + y
171.8 = 7.8+ y+37.6 + y
Combine like terms
171.8 = 45.4 + 2y
Subtract 45.4 from both sides
171.8-45.4 = 45.4 + 2y -45.4
126.4 = 2y
Divide each side by 2
126.4/2 = 2y/2
63.2 = y
A rectangle measures 9 feet by 6 feet. What is the measure of the diagonal? Round your answer to the nearest tenth.
Answer:
~10.8 (ft)
Step-by-step explanation:
Apply the Pythagorean theorem, you can work out the measure of diagonal.
[tex]Diagonal = \sqrt{9^{2}+6^{2} } =\sqrt{81 + 36} =\sqrt{117} =~10.8(ft)[/tex]
The measure of the diagonal of a rectangle is 10.8 feet.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, a rectangle measures 9 feet by 6 feet.
Let the length of diagonal be x.
x²=9²+6²
x²=81+36
x²=117
x=√117
x=10.8 feet
Therefore, the measure of the diagonal of a rectangle is 10.8 feet.
To learn more about the Pythagoras theorem visit:
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#SPJ3
6+7=73.5
7+8=84
11+12=126
12+24=390.6
24+28=?
Answer:
52
Step-by-step explanation:
24+28 = 52
52 - 24 = 28
(03.04) What is the vertex of the graph of y = −4(x + 2)2 + 5? (1 point) (2, 5) (−2, 5) (5, −2) (5, 2)
Answer:
(-2, 5)
Step-by-step explanation:
The form you're trying to match is the vertex form of the equation of a parabola:
y = a(x -h)^2 +k . . . . . . . vertex (h, k)
You have ...
y = -4(x +2)^2 +5
Comparing forms, you see that a=-4, h=-2, k=5.
Then the vertex (h, k) is (-2, 5).
Answer if you can and help other people out
Solution,
radius=21 cm
Circumference of circle=2 pi r
=2*3.142*21
=131.964 cm
hope it helps
Good luck on your assignment
Solve for the value of x
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = t, y = e−4t, z = 5t − t5; (0, 1, 0) x(t), y(t), z(t) = t,1−4t,5t Illustrate by graphing both the curve and the tangent line on a common screen.
Answer:
Step-by-step explanation:
At the point (0, 1,0) t = 0
Find the tangent vector:
[tex]\frac{dx}{dt}= 1[/tex]
[tex]\frac{dy}{dt}= -4e^{-4t}[/tex]
[tex]\frac{dz}{dt}=5-5t^4[/tex]
The tangent vector for all points [tex]\vec v(t)[/tex] is
[tex]\vec v(t) = \hat {i}-4e^{-4t}\hat{j}+(5-5t^4)\hat{k}[/tex]
[tex]\rightarrow \vec v (0)= \hat{i}-4\hat{j}[/tex]
The vector equation of the tangent line is
[tex](x,y,z) = (0,1,0)+s(\hat{i}-4\hat{j})[/tex]
The parametric equation for this line are
[tex]x= s[/tex]
[tex]y=1-4s[/tex]
[tex]z=0[/tex]
Parametric equations for the tangent line to the curve with the given parametric equations at the specified point are
x=s
y=1-4s
z=0
What is the parametric equation?In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.
At the point (0, 1,0) t = 0
Find the tangent vector:
[tex]\dfrac{dx}{dt}=1[/tex]
[tex]\dfrac{dy}{dt}=-4e^{-4t}[/tex]
[tex]\dfrac{dz}{dt}=5-5t^4[/tex]
The tangent vector for all points is
[tex]v(t)=i-4e^{-4t}j+(5-5t^4)k[/tex]
[tex]v(0)=i-4j[/tex]
The vector equation of the tangent line is
[tex](x,y,z)=(0,1,0)+s(i-4j)[/tex]
The parametric equation for this line is
[tex]x=s\\\\y=1-4s\\\\z=0[/tex]
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25. If the area of a circle is 144cmthen find
a. lts diameter
b. Its circumference
Answer:
a. lts diameter = 13.540550005146 cm
b. Its circumference = 42.538892421732 cm
Step-by-step explanation:
suppose A the area ; d the Diameter ; P the circumference and r the radius
A = πr²
P = d×r = 2πr
then
r² = A/π = 144÷π = 45.836623610466
then
→ r = √(45.836623610466) = 6.770275002573
d = 6.770275002573×2 = 13.540550005146
→ P = 13,.540550005146×π = 42.538892421732
If 24 tomatoes cost $3.55 how much does 6 tomatoes cost?
Will mark brainlest for correct answer!
Answer:
0.89
Step-by-step explanation:
First, let’s find out what one tomato costs. To do this, we need to find the unit rate.
To find the unit rate, divide the cost by the number of tomatoes.
cost/number of tomatoes
It costs $3.55 for 24 tomatoes.
cost=3.55
number of tomatoes=24
Substitute these values in.
3.55/24
0.147916666666667
Each tomato costs $0.147916666666667
Now, we have to find out what 6 tomatoes cost.
Multiply the number of tomatoes by the cost of one tomato
number of tomatoes * cost of one
number of tomatoes=6
cost of one= 0.147916666666667
Substitute these values in.
6* 0.147916666666667
0.8875
Round to the nearest cent or hundredth.
The 7 in the thousandth place tells us to round the 8 in the hundredth place up to a 9.
0.89
6 tomatoes will cost about 0.89.
If the frame of a Ferris wheel is a circle with a 10 meter diameter, what is the circumference of this circle?
Answer:
C = 10π
Step-by-step explanation:
C = Dπ
D = 10
C = 10π
Answer:
see below
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d
C = 10 pi m
We can approximate pi by 3.14
C = 3.14 * 10
C =31.4m
or we can approximate pi by using the pi button
C =31.41592654m
What’s the correct answer for this?
Answer:
x = 5
Step-by-step explanation:
Since TV bisects (equally divides) EF hence <EKT = 90°
Also <EKT = 5x+65
So
5x+65 = 90
5x = 90-65
5x = 25
Dividing both sides by 5
x = 5
Please answer this correctly
Answer: Rectangular pyramid
Step-by-step explanation:
When you think about it, a pyramid has 3 faces that are triangular!
If you found this answer helpful, give it a five-star rating and a thanks! I would really appreciate it!
You can even give it a brainliest if you want! ;)
1. Michel buys a leash for his dog. The leash is 6 ft 3 inches. How long, in inches, is the leash?(1 ft = 12 inches)
A) 48 inches
B) 51 inches
C) 72 inches
D) 75 inches
2. What is the area of a triangular garden with base of 6 ft and a height of 9 ft? (A = 1/2BH)
A) 27 square feet
B) 48 square feet
C) 54 square feet
D) 24 square feet
Answer:
1. D) 75 inches
2. A) 27 square feet
Step-by-step explanation:
1. You need to convert 6 feet to inches. In one foot, there are 12 inches. Multiply 6 by 12 to find the number of inches in 6 feet. Add 3 inches to the product to find the total number of inches.
6 × 12 = 72
72 + 3 = 75
You will have 75 inches in total.
2. Use the formula to solve. You are given the base and the height already. Simply plug in and solve.
A = 1/2BH
A = 1/2(6)(9)
A = 3(9)
A = 27 ft²
The area is 27 ft².
Answer:
Step-by-step explanation:
What’s the correct answer for this?
Answer:
BC = 67
Step-by-step explanation:
Since both tangents are originating from a single point, they are equal, rest in the attached file
The cost of 12 pairs of shoes is $960. what is the cost of 1 pair of shoes?
Answer:
$80 for 1 pair of shoes
divide $960 by 12
Abigail had a fish tank that was in the shape of a box. The dimensions were 1 foot deep by 24 inches wide, by 18 inches tall. How many cubic inches of water will it take to completely fill the tank?
Answer:
volume= 5,184 cubic inches
Step-by-step explanation:
Answer with explanation.
Answer:
D
Step-by-step explanation:
Write the following product in scientific notation: (12.3 × 10^8)(1.06 × 10^−7).
Answer:
[tex] 1.3038 \times {10}^{2} [/tex]
Step-by-step explanation:
[tex] (12.3\times 10^8) (1.06\times 10^{-7})\\ = 12.3 \times 1.06 \times {10}^{8} \times {10}^{ - 7} \\ = 13.038 \times {10}^{8 - 7} \\ = 13.038 \times {10}^{1} \\ = 1.3038 \times {10}^{2} [/tex]
Answer:
[tex]1,3038 . 10^{2}[/tex]
Step-by-step explanation:
(12.3 × 10^8)(1.06 × 10^−7)
12.3 × 10^8 × 1.06 × 10^−7
12.3 × 1.06 × 10^8 × 10^−7
Rule : [tex]a^{b} . a^{c} = a^{b + c}[/tex]10^8 × 10^−7 = 10^(8 -7) = 10^1
12.3 × 1.06 × 10^8 × 10^−7 = 12.3 × 1.06 × 10^1
12.3 × 1.06 =13.038
13.038 × 10^1 = 1,3038 × 10^2
Hope this helps ^-^
The graph of F(x), shown below, has the same shape as the graph of
G(X) = x2, but it is shifted up 3 units and to the right 1 unit. What is its
equation?
Answer:
The answer is A.
Step-by-step explanation:
First, recall the vertex form of a quadratic equation: [tex]f(x)=a(x-h)^2+k[/tex], where [tex]h[/tex] represents the horizontal change and [tex]k[/tex] represents the vertical change.
The original equation is [tex]g(x)=x^2[/tex], or, in other words, [tex]g(x)=1(x-0)^2+0[/tex].
We are told that the graph is shifted up 3 and right 1. Thus, both values are positive (right and up). Note that up 3 corresponds to a positive vertical change of 3 while right 1 represents a positive horizontal change of 1.
Thus, put these back into the equation in place of [tex]h[/tex] and [tex]k[/tex].
We have:
[tex]f(x)=1(x-(+1))^2+(+3)[/tex]
Or, simplified:
[tex]f(x)=(x-1)^2+3[/tex]
The answer is A.
