Answer:
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by 0.2864 grams of chemical.
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.
Standard deviation 1.6 grams of chemical. Random sample of 100.
This means that [tex]n = 100, s = \frac{1.6}{\sqrt{100}} = 0.16[/tex]
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by how much?
Z multiplied by s, in which Z has a p-value of 1 - 0.0367 = 0.9633, so Z = 1.79.
1.79*0.16 = 0.2864.
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by 0.2864 grams of chemical.
Let V be the set of all 3x3 matrices with Real number entries, with the usual definitions of scalar multiplication and vector addition. Consider whether V is a vector space over C. Mark all true statements (there may be more than one).
a. The scalar closure axiom is satisfied
b. The additive inverse axiom is not satisfied
c The additive inverse axiom is satisfied
d. The additive closure axiom is not satisfied
e. The scalar closure axiom is not satisfied
f. The additive closure axiom is satsified
g. V is not a vector space over C
h. V is a vector space over C
i. The zero axiom is satisfied
j. The zero axiom is not satisfied
Answer:
the Scalar Closure axiom is not satisfiedV is not a Vector Space of CThe Additive Closure axiom is satisfied.Step-by-step explanation:
According to the Question,
Given That, Let V be the set of all 3x3 matrices with Real number entries, with the usual definitions of scalar multiplication and vector addition. Consider whether V is a vector space over C.For V is a vector space over C and V is Set of 3x3 Matrices with Real entries.Then, For any u,w ∈ V ⇒ u+w ∈ V
And u∈V and z∈C ⇒ z u ∈ V
So, If we take any z= i ∈ C
and V be any 3x3 matrices with Real entrices.then, z,v ∉ V ∴z,v Has Complex entries
So, the Scalar Closure axiom is not satisfied
Hence, V is not a Vector Space of C
Any u,w ∈ W ⇒ u+w ∈ V
So, The Additive Closure axiom is satisfied.
Calculate the area of the following Circle
Answer:
324
Step-by-step explanation:
Circles are 100% even. If you add another line going opposite direction you would multiply 18x18. You get 324.
international system of 89643092 in words
Answer:
Eighty nine million six hundred forty three thousand ninety two
Step-by-step explanation:
89,643,092
=> Eighty nine million six hundred forty three thousand ninety two
Determine whether the following event is mutually exclusive or not mutually exclusive.
Choosing a student who is a mathematics major or a business major from a nearby university to participate in a research study. (Assume that each student only has one major.)
Answer:
The event is mutually exclusive.
Step-by-step explanation:
Mutually exclusive events are events that cannot exist simultaneously.
Thus, events that are not mutually exclusive can exist simultaneously.
Since each student only has one major, a single student cannot be both a mathematics major and a business major.
So, the event is mutually exclusive.
he speeds (in MPH) of automobiles traveling in a city are given below:
20, 35, 42, 52, 65, 49, 24, 37, 23, 41, 50, 58
The mean speed of the cars is
Answer:
Mean speed = 41.3 mph
Step-by-step explanation:
Given that,
The speeds of an automobiles are given below:
20, 35, 42, 52, 65, 49, 24, 37, 23, 41, 50, 58
We need to find the mean speed of the cars.
Mean = sum of observations/ no. of observation
[tex]M=\dfrac{20+35+42+52+65+49+24+37+23+41+50+58}{12}\\\\M=41.3[/tex]
So, the mean speed of the cars is equal to 41.3 mph.
The top of the Boulder Dam has an angle of elevation of 1.2 radians from a point on the Colorado River. Measuring the angle of elevation to the top of the dam from a point 155 feet farther down river is 0.9 radi- ans; assume the two angle measurements are taken at the same elevation above sea level. How high is the dam?
Answer:
382.925 feets
Step-by-step explanation:
The solution diagram is attached below :
Converting radian measurement to degree :
radian angle * 180/π = degree angle
1.2 * 180/π = 68.755°
0.9 * 180/π = 51.566°
Height of dam is h:
Using trigonometry :
Tan θ = opposite / Adjacent
Tan 68.755° = h / x
h = x Tan 68.755° - - - (1)
Tan 51.566° = h / (155+x)
h = (155+x) tan 51.566° - - - (2)
Equate (1) and (2)
x Tan 68.755 = (155+x) Tan 51.566
x Tan 68.755 = 155tan 51.566 + x tan 51.566
x Tan 68.755 = 195.32311 + x Tan 51.566
x Tan 68.755 - x Tan 51.566 = 195.32311
x(tan 68.755 - tan 51.566) = 195.32311
x * 1.3120110 = 195.32311
1.3120110x = 195.32311
x = 195.32311 / 1.3120110
x = 148.87307
Using :
h = x Tan 68.755
h = 148.87307 * tan(68.755)
h = 382.92539
h = 382.925 feets
Suppose that g(x)= f(x)+ 6. Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted 6 units down.
B. The graph of g(x) is the graph of f(x) shifted to the right.
C. The graph of g(x) is the graph of f(x) shifted 6 units to the left.
D. The graph of g(x) is the graph of f(x) shifted 6 units up.
Answer:
D
Step-by-step explanation:
The + 6 moves it up 6 units.
The correct answer is (D) "The graph of g(x) is the graph of f(x) shifted 6 units up."
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
When we add a constant to a function, such as in the case of g(x) = f(x) + 6, it will shift the graph of f(x) upward by 6 units.
This is because, for any value of x, the value of f(x) will be added to 6, resulting in a vertical shift of the entire graph.
Option (A) is incorrect because adding 6 to f(x) would shift the graph up, not down.
Option (B) is incorrect because adding a constant to a function does not cause it to shift horizontally.
Option (C) is incorrect because adding 6 to f(x) would shift the graph right, not left.
D. The graph of g(x) is the graph of f(x) shifted 6 units up. Adding a constant term to a function will shift the graph of the function vertically. In this case, adding 6 to f(x) will shift the graph of f(x) upward by 6 units, resulting in the graph of g(x).
Learn more about function here:
https://brainly.com/question/29633660
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A person walks 1/6 mile in 1/18 hour.
The person's speed is _ miles per hour.
This Is What I Got!
Hope This Helps! :)
Have A Good Day!!
And If You Can I Wouldn't Mind A Brainliest! :))
Answer:
Divide 1/6 miles to 1/12hour since u wanna find our miles per hour
So it’ll be : 1/6 / 1/12
= 1/6 x 12/1
= 2 miles
Given points (-3;-6), G(3; -2) and H(6; 1); determine:
(a) The equation of line FG
Answer:
The equation of line FG is [tex]y = \frac{2}{3}x - 4[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
F(-3;-6), G(3; -2)
When we have two points, the slope is given by the change in y divided by the change in x. So
Change in y : -2 - (-6) = -2 + 6 = 4
Change in x: 3 - (-3) = 3 + 3 = 6
Slope: [tex]m = \frac{4}{6} = \frac{2}{3}[/tex]
So
[tex]y = \frac{2}{3}x + b[/tex]
Finding b:
(3; -2) means that when [tex]x = 3, y = -2[/tex]. We use this to find b.
[tex]y = \frac{2}{3}x + b[/tex]
[tex]-2 = \frac{2}{3}(3) + b[/tex]
[tex]2 + b = -2[/tex]
[tex]b = -4[/tex]
The equation of line FG is [tex]y = \frac{2}{3}x - 4[/tex]
Can someone answer with steps and explanation? Thanks.
Answer:
[tex]x=-16\text{ or } x=7[/tex]
Step-by-step explanation:
Since ΔABC is mapped onto ΔDEF, we can write that:
[tex]\Delta ABC\cong \Delta DE F[/tex]
By CPCTC:
[tex]\angle A\cong \angle D[/tex]
And since ΔABC is isosceles with Vertex C:
[tex]\angle A \cong \angle B[/tex]
We are given that:
[tex]m\angle D=34[/tex]
Hence:
[tex]m\angle A=34=m\angle B[/tex]
We are also given that:
[tex]m\angle C=x^2+9x[/tex]
The interior angles of a triangle must sum to 180°. Thus:
[tex]m\angle A+m\angle B+m\angle C=180[/tex]
Substitute:
[tex](34)+(34)+(x^2+9x)=180[/tex]
Simplify:
[tex]68+x^2+9x=180[/tex]
Isolate the equation:
[tex]x^2+9x-112=0[/tex]
Factor:
[tex](x+16)(x-7)=0[/tex]
Zero Product Property:
[tex]x+16=0\text{ or } x-7=0[/tex]
Solve for each case:
[tex]x=-16\text{ or } x=7[/tex]
Testing the solutions, we can see that both yields C = 112°.
Hence, our solutions are:
[tex]x=-16\text{ or } x=7[/tex]
The probability distribution for a random variable x is given in the table X: -5,-3,-2,0,2,3 Probability: .17,.13,.33,.16,.11,.10 Find the probability that X <_-3
Answer:
0.3 probability that [tex]x \leq -3[/tex]
Step-by-step explanation:
The probability distribution is given in the table.
Probability that x <= -3
The values that are -3 or lower are -3 and -5. So
[tex]P(X \leq -3) = P(X = -3) + P(X = -5)[/tex]
From the table:
[tex]P(X = -3) = 0.13, P(X = -5) = 0.17[/tex]. So
[tex]P(X \leq -3) = P(X = -3) + P(X = -5) = 0.13 + 0.17 = 0.3[/tex]
0.3 probability that [tex]x \leq -3[/tex]
Answer:0.3
Step-by-step explanation:
Is 9/54 equivalent to 1/3
Answer: No.
Step-by-step explanation:
9/54 is equal to 1/6
Answer:
no, it is not
Step-by-step explanation:
9/54 can be simplified by dividing both sides by 3, getting 3/18. you can do this again and get 1/6. significantly smaller that l/3
seventy four lakh nine thousand eleven in numeral form
Seventy Four Lakh , Nine Thousand And Eleven=
7409011What is the area of this figure?
Answer:
90km² only if it is parallelogram
Step-by-step explanation:
base = 9km
height=10km
area of parallelogram = b x h
=9km x 10km
=90km²
Answer:
A = 90km2
Step-by-step explanation:
Area of a rhombus is:
1. A = s x h (if given side and height)
2. A = 1/2 a x b (if given lengths of diagonals)
3. A = s^2 sin A (if given side and length)
Therefore from your problem, height and side is given thus, you'll use number 1
A = s x h
A = 9km x 10km = 90km2
andrea is planning a birthday party and wants to include a cheese board with the desserts.
she reads online that she should have 110g of cheese per person ,but the cheese is sold in blocks of 500g
How many blocks of cheese should she buy to ensure that each guest can have 110g of cheese?
Step-by-step explanation:
how many people in the party please ?
Stats question what are the main difference between frequenting and Bayesian
Answer:
The frequentist believes that probability represents long term frequencies of repeatable events (such a flipping a coin). Frequentists do not attach probabilities to hypotheses or unknown values. On the other hand, the Bayesian approach uses probabilities to represent the uncertainty in any event or hypothesis.HOPE IT HELPS
I need help I’ll give u brainlest
Answer:
[tex]V=280[/tex] cubic inches
Step-by-step explanation:
Volume formula for triangular prism is [tex]V=\frac{1}{2} bhl[/tex]
[tex]V=\frac{1}{2} (7)(10)(8)[/tex]
[tex]V=\frac{1}{2}(560)[/tex]
[tex]V=280[/tex]
Hope this helps
How many liters each of a 25% acid solution and a 50% acid solution must be used to produce 80 liters of a 40% acid solution?
Answer:
32 and 48 litersStep-by-step explanation:
Let 25% solution is x liters, then 50% solution is (80 - x) liters.
Acid content is going to be same:
0.25x + 0.5(80 - x) = 80*0.40.25x - 0.5x + 40 = 320.25x = 8x = 8/0.25x = 32 litersSo 32 liters of 25% solution and 80 - 32 = 48 liters of 50% solution
Simplify the expression.
33 · 32 + 12 ÷ 4
Answer:
1059
Step-by-step explanation:
33 · 32 + 12 ÷ 4
PEMDAS
Multiply and divide first from left to right
1056 + 3
Then add
1059
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{33\times32+12\div4}\\\\\mathsf{33\times32= \boxed{\bf 1,056}}\\\\\mathsf{\bold{1,056}+12\div4}\\\\\mathsf{12\div4=\boxed{\bf 3}}\\\\\mathsf{1,056+\bf 3}\\\mathsf{= \boxed{\bf 1,059}}\\\\\\\boxed{\boxed{\large\textsf{Answer: \huge \bf 1,059}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite40:)}[/tex]
what'd the greatest common factor (GCF) for each pair of numbers. 25, 55 The GCE IS
Answer:
5
Step-by-step explanation:
5 l 25,55
l 5,11
Darcy gave her hairstylist a $ 4.90 The tip was 14% of the cost of the haircut . Write an equation to find b, the cost of the haircut.
Answer:
Equation: 4.90/b = 14/100
Solution: b = $35
Step-by-step explanation:
Variable b = cost of the haircut
Solve for b:
4.90/b = 14/100
490 = 14b
35 = b
Check your work:
35 × 0.14 = 4.90
Correct!
11x+7y=17
solve for y
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {\: y = \frac{17 - 11x}{7} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]\\11x + 7y = 17[/tex]
[tex] \\➺ \: 7y = 17 - 11x[/tex]
[tex]\\➺ \: y = \frac{17 - 11x}{7} [/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
I need help k please help gardinuhola
Answer:
Step-by-step explanation:
for circle
diameter = 26 cm
radius = diamtere/2
=26/2
=13 cm
area of circle = πr^2
=3.14^13^2
=3.14*169
=530.66 cm^2
=531 cm^2 (after round off )
area of square= l^2
=5.1^2
=26.01 mi^2
are of rectangle = l *b
=6*5.1
=30.6 m^2
area of triangle = base*height / 2
=9*6.4 / 2
=57.6 / 2
=28.8 yd^2
Simplify:......................................................
Answer:
...
Step-by-step explanation:...
What is the value of the expression 3m-4.2 If m equals 2.1
Answer:
2.1
Step-by-step explanation:
Given :
3m-4.2 where, m=2.1
Now,
3(2.1)-4.2
6.3-4.2
2.1
Answer is 2.1
4(x+9)=8x-7
Solve for x
Answer:
x = 10.75
Step-by-step explanation:
4(x+9)=8x-7
Step 1: Distribute the 4 to the x and 9
4 * x = 4x
4 * 9 = 36
We now have 4x + 36 = 8x - 7
Step 2: add 7 to both sides
36 + 7 = 43
-7 + 7 cancels out
We now have 4x + 43 = 8x
Step 3 subtract 4x from both sides
4x - 4x cancels out
8x - 4x = 4x
We now have 4x = 43
step 4 divide both sides by 4
4x / 4 ( the 4s cancel out and we're left with x )
43/4 = 10.75
We're left with x = 10.75
The diagram shows a right-angled triangle.
xo
26 cm
17 cm
Find the size of angle x.
Give your answer correct to 1 decimal place.
Answer:
Diagram? I don't see a diagram.
Where is the diagram?
Step-by-step explanation:
xác định m để 3 vector sau đây phụ thuộc tuyến tính
u=(m+1,1,m+1),v=(1,1,1),u(2,0,m+2
0
Answer:
i dont know hahaha
Step-by-step explanation:
soryy
What is the average score of runa 140,96 and 13?
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{Formula:}[/tex]
[tex]\mathsf{\dfrac{Sum\ of\ all\ terms}{Total\ number\ of\ values\ in\ the\ data}= your\ mean/average}[/tex]
[tex]\mathsf{\dfrac{140+96+13}{3}}[/tex]
[tex]\mathsf{140+36+13}[/tex]
[tex]\mathsf{140 + 96 = \bf 236}[/tex]
[tex]\mathsf{236 + 13}[/tex]
[tex]\mathsf{ = \bf 249}[/tex]
[tex]\mathsf{\dfrac{249}{3}}[/tex]
[tex]\mathsf{= \bf 83}[/tex]
[tex]\boxed{\boxed{\large\textsf{Possible answer: \huge \bf 83}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
2 divided by 0.75 full divison work i dont just need the answer
Answer:
0.375
Step-by-step explanation:
Check the picture below.
whenever we do division of decimals, we have to mind how many decimals are there on each amount, the dividend as well as the divisor, that way we pad with zeros the other amount accordingly whilst losing the dot, for example, to say divide 3 by 0.123, 3 has no decimals, whilst 0.123 has three decimals, so we can just divide 3000 by 0123, so dividing 3 by 0.123 is the same as dividing 3000 by 123. Another example, if we were to divide say 23.761 by 555.89331, the dividend has 3 decimals, that means 3 zeros the other way, the divisor has 5 decimals, that means 5 zeros the other way while losing the dots, so we'd end up dividing 2376100000 by 55589331000, which we can simplify to just 2376100 by 5589331, as you can see in the picture in this case.
