Answer:
a) 0% probability that one car chosen at random will have less than 49.5 tons of coal
b) 0% probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this question, we have that:
[tex]\mu = 56, \sigma = 1.1[/tex]
a. What is the probability that one car chosen at random will have less than 49.5 tons of coal?
This is the pvalue of Z when X = 49.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49.5 - 56}{1.1}[/tex]
[tex]Z = -5.9[/tex]
[tex]Z = -5.9[/tex] has a pvalue of 0
So 0% probability that one car chosen at random will have less than 49.5 tons of coal.
b. What is the probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal?
Now we have [tex]n = 35[/tex], applying the Central limit theorem [tex]s = \frac{1.1}{\sqrt{35}} = 0.1859[/tex]
This is the pvalue of Z when X = 49.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{49.5 - 56}{0.1859}[/tex]
[tex]Z = -35[/tex]
[tex]Z = -35[/tex] has a pvalue of 0
So 0% probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal
Please please help
Find the measure of the missing angle.
63°
Answer:
27 degrees
Step-by-step explanation:
Answer:
a = 27° ______
Step-by-step explanation:
~~~~~~~~~~
landscape designer has 4/5 ton of mulch to divide equally among 8 customers. how much mulch will each customer get?
Answer:
1/10
Step-by-step explanation:
4/5x1/8=4/40=1/10
Need a problem showing how to to divide beach toys into equal groups. Solve it too.
Answer:
ok
Step-by-step explanation:
Solve 10 + 6(–9 – 4x) = 10(x – 12) + 8.
A)
x = –6
B)
x = 2
C)
x = 17
D)
x = –18
Answer: x = 2
Step-by-step explanation:
first, we remove the parentheses.
10 - 54 - 24x = 10x - 120 + 8
then, we just calculate that out.
-44 - 24x = 10x - 112
next, we move the terms.
-24x - 10x = -112 + 44
then, we collect the like terms and calculate it.
-34x = -68
finally, we divide both sides.
x = 2
Please help. I need to know the answer. I will give brainliest
9514 1404 393
Answer:
1 4 8 9Step-by-step explanation:
blank 1
Locate x = 7 and find the y-value where the blue curve crosses.
f(7) = 1
blank 2
Locate x = -9 and find the y-value where the red curve crosses.
g(-9) = 4
blank 3
Locate y = 0 (the x-axis) and find the x-value where the blue curve crosses.
f(8) = 0
blank 4
Locate y = 2 and find the x-value where the red curve intersects.
g(9) = 2
11/12 x 6/11 in simplest form
the points (3,17) and (5,23) give us an m value of how much?
(3, 17) and (5,23)
23-17= 6
5-3=2
y-17=m(3-x)
m=3
Plz help me with this
Answer:
interest = $5040
total= $6090
Step-by-step explanation:
1050 × .16 = 168
168 × 30 = $5040
$1050+ $5040 = $6090
Find the angles a, b, c and d.
Answer:a b and c are 6
Step-by-step explanation:
Solve for t in terms of u, v, w, and x.
Answer:
there's no image lol
Step-by-step explanation
20 points need help math equation
Answer:
47.3
Step-by-step explanation:
180-90-42.7=47.3
Answer:
47.3
Step-by-step explanation:
this is a right triangle, which means that Angle O is 90°
90 + 42.7 = 132.7
180 - 132.7 = 47.3
Are these correct please help
Answer:
x=x+1 is correct, -6x=-5(x-1)-1x is correct, 7(x-5)=x+13 is correct, x=x is correct, x+4=x+4 is correct.
5(x+2)=25 should go in one solution.
2x+2=2(x+1) should go into infinite solutions.
2x+3=2x+5 should go into no solution.
9x+1=9x should go into no solution.
2x+8=16 should go into one solution.
3x+1=31 should go into one solution.
Step-by-step explanation:
Explanation(s):
5(x+2)=25:
One value of x will equal 25, which is 3. You can solve this in two ways, calculations or graphing. I will show you both ways. You'll get 5x+10 from 5(x+2). Then you can subtract ten from both sides to isolate x, 5x=15. Then divide both sides by five to find what x equals, which is three. By graphing both the equations 5x+10 and y=25, you'll find that both of the lines intersect at (3,25), the x value of the coordinate is what x will equal, and there's only one intersection so there's only one solution.
2x+2=2(x+1):
The equation will be the exact same on both sides, which means all values of x will be a solution. If you were to graph both equations, they'd overlap perfectly, resulting in an infinite amount of intersections.
2x+3=2x+5:
The equation cannot be simplified any further, and 2x+5 is transformed two units above the equation 2x+3. If you were to graph both of these equations, they will never intersect for any value of x, which means no solutions.
9x+1=9x:
The equation cannot be simplified any further, and 9x+1 is transformed one unit above the equation 9x. If you were to graph both of these equations, they will never intersect for any value of x, which means no solutions.
2x+8=16:
Subtract eight from both sides, then divide both sides by two to get x=4. This means that there is only one solution for the equation. Alternatively, you could graph 2x+8 and y=16, and they will intersect at the point (4,16), which is only one solution.
3x+1=31:
Subtract one from both sides, divide by three to get x=10. There is only going to be one solution for the equation. Graph 3x+1 and y=31 to find that both the lines intersect at (10,31).
3
Solve for x.
-2x + 6 + 4x = -12
HELP ME PLS I WILL CRY I HAVE SO MUCH TESTS AND ESSAYS DUE PLS SHOW WORK
Answer:
180 minutes
Step-by-step explanation:
60x3
If you add Natalie's age and Fred's age, the result is 38. If you add Fred's age to 4 times Natalie's age, the result is 74. Write and solve a system of equations to find how old Fred and Natalie are.
Answer:
hmmhhhhhhhhbmmmmhhhm
Answer:
Fred is 26 and Natalie is 12
Step-by-step explanation:
X= Fred's age
Y= Natalie's age
x+y=38
x+4y=74
Use the first equation and isolate the variable x to one side.
x+y=38
-y= -y
x=38-y
Now use this equation and subsitute it into the second equation.
(38-y) + 4y = 74
Simplify to find y
38+3y=74
-38 =-38
3y=36
÷3 ÷3
y= 12
Now that we know y, input it into the second equation to find x.
x+12=38
-12 -12
x= 26
Fred is 26 and Natalie is 12
hope this helps :)
Got this one wrong can someone help me solve it
Answer:
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Step-by-step explanation:
of evidence from seismic waves heat flow in meteoritesof of evidence from seismic waves heat flow in meteorites from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteoritesof evidence from seismic waves heat flow in meteorites
In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?
(a) n = 10, p = 0.5
(b) n = 40, p = 0.88
(c) n = 100, p = 0.2
(d) n = 100, p = 0.99
(e) n = 1000, p = 0.003
Answer:
(c) n = 100, p = 0.2
Step-by-step explanation:
To approximate to use the normal distribution for a binomial, we need that:
[tex]np \geq 10, n(1-p)\geq 10[/tex]
So, for each option
(a) n = 10, p = 0.5
[tex]np = 10*0.5 = 5 < 10[/tex]
So not appropriate
(b) n = 40, p = 0.88
[tex]np = 40*0.88 = 35.2 > 10[/tex]
[tex]n(1-p) = 40*0.12 = 4.8 < 10[/tex]
So not appropriate.
(c) n = 100, p = 0.2
[tex]np = 100*0.2 = 20 > 10[/tex]
[tex]n(1-p) = 100*0.8 = 80 > 10[/tex]
So appropriate
(d) n = 100, p = 0.99
[tex]np = 100*0.99 = 99 > 10[/tex]
[tex]n(1-p) = 100*0.01 = 1 < 10[/tex]
So not appropriated
(e) n = 1000, p = 0.003
[tex]np = 1000*0.003 = 3 < 10[/tex]
So not appropriate
A Normal distribution to approximate probabilities for a binomial distribution with the given values of n = 100 and p = 0.2.
Given that,
Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p.
We have to determine,
In which of the following situations would it be appropriate to use a normal distribution to approximate probabilities for a binomial distribution with the given values of n and p.
According to the question,
Probabilities for a binomial distribution with the given values of n and p.
(a) n = 10, p = 0.5
(b) n = 40, p = 0.88
(c) n = 100, p = 0.2
(d) n = 100, p = 0.99
(e) n = 1000, p = 0.003
To approximate to use the normal distribution for a binomial is given as,
[tex]np\geq 10 , \ n(1-p)\geq 10[/tex]
When n = 10 and p = 0.5,[tex]= np \geq 10\\\\= 10 \times 0.5 = 5<10[/tex]
The normal distribution is less than 10 so, this not appropriate.
When n = 40 and p = 0.88,[tex]= n.p \geq 10\\\\= (40).(0.88) \geq 10\\\\= 35.2\geq 10\\\\Then,\\=n(1-p) = 40(1-0.88) \geq 10 \\\\= 40\times 0.12 \geq 10 = 4.8\leq 10[/tex]
The normal distribution is less than 10 so, this not appropriate.
When n = 100 and p =0.2,[tex]= n.p \geq 10\\\\= (100).(0.2) \geq 10\\\\= 20\geq 10\\\\Then,\\=n(1-p) = 100(1-0.2) \geq 10 \\\\= 100\times 0.8\geq 10 = 80\geq 10[/tex]
The normal distribution is greater than 10 so, this appropriate.
When n = 100 and p = 0.99,[tex]= n.p \geq 10\\\\= (100).(0.99) \geq 10\\\\= 99\geq 10\\\\Then,\\=n(1-p) = 100(1-0.99) \geq 10 \\\\= 100\times 0.01\geq 10 = 1\leq 10[/tex]
The normal distribution is less than 10 so, this not appropriate.
When n = 1000 and p = 0.003,[tex]= np \geq 10\\\\= 1000 \times 0.003 = 3<10[/tex]
The normal distribution is less than 10 so, this not appropriate.
Hence, A Normal distribution to approximate probabilities for a binomial distribution with the given values of n = 100 and p = 0.2.
To know more about Binomial Distribution click the link given below.
https://brainly.com/question/16776778
4 times 4 times 4 times 4 times4 times 4. Using exponents, the expression is?
Answer:
It will have a 4 and then a five on the top right of it.
Step-by-step explanation:
4^5
Answer:
4^{5}
Step-by-step explanation:
Just basically what the other person said.
4 exponent 5
A coffee shop sells refill mugs for $7.50 each. Each coffee refill costs $1.75. Last month, Cody spent $42.50 on a mug and refills. Which equation can you use to find how many refills Cody bought. (Let x = the number of refills) How many refills did Cody buy last month? 10, 12, 20, or 25
Answer:
cannot see equations to select from but I got '7.50 + 1.75x = 42.50'
20 refills
Step-by-step explanation:
7.50 + 1.75x = 42.50
1.75x = 35
x = 35 / 1.75
x = 20
Step1. Formulate two real-life problems involving system of linear inequalities in
two variables.
Step2. Solve the problems you formulated accurately. Show complete solution then
graph.
╱╱▏┈┈╱╱╱╱▏╱╱▏
▇╱▏┈┈▇▇▇╱▏▇╱▏
▇╱▏▁┈▇╱▇╱▏▇╱▏▁
▇╱╱╱▏▇╱▇╱▏▇╱╱╱
▇▇▇╱┈▇▇▇╱┈▇▇▇╱
//////////////////////////////
Answer:
27
Step-by-step explanation:
9³÷3³=729÷27
= 27
Answer:
the answer is 3
Step-by-step explanation:
which expression is equivalent to 2 (3/4n+8+1/4n-12)?
a. 2n+8
b.2n-8
c.2n+10
d.n-4
Answer:
b. 2n-8
Reason
Distribute the 2.
6/4n +16 + 2/4n -24
Simplify
6/4n + 2/4n = 8/4n = 2n
16 - 24= -8
Then you get 2n-8
Answer:2N-8
Step-by-step explanation: I got it right
Let
P be a polynomial function, and
P(x) = 23 – dx2 - 4x – 20. If
(2 – 2) is a factor of the polynomial, what is the value of
d?
Answer:
The value of d = -5
The polynomial function x³ +5 x² - 4x -20 =0
Step-by-step explanation:
Explanation
Given that the equation is third degree polynomial
p(x) = x³ - d x² - 4x -20
Given factors x= 2 and x=-2
Substitute 'x' = 2 in given polynomial
8 -d(2²)-4(2) - 20 =0
⇒ 8 - 4 d - 8 -20=0
⇒ - 4 d-20 = 0
⇒ - 4 d = 20
⇒ d = - 5
The value of d = -5
Verification:-
After substitution d =-5 in given polynomial
x³ - (-5) x² - 4x -20 =0
put x=2
8 +5(4)-8-20 =0
20 =20
The factors are x= 2 and x=-2 of the given polynomial
you buy a shirt that costs 9.99 dollars what is the price with a tax sales is 6 percent
Answer:
$10.59
Step-by-step explanation:
6% of 9.99 is 0.5994, so you round it to 0.60, then add it to 9.99.
A tool manufacturer has fixed costs of $68.00 a day and variable costs of $1.00 per screwdriver
produced. The company gets $2.50 per screwdriver sold. How many screwdrivers must be produced
daily to break even? Your answer should be a number only.
Answer:
46
Step-by-step explanation:
To breakeven, the total cost of the company which is the sum of the fixed and variable cost will be equal to the total sales of the company such that the profit/loss is zero.
Let x be the number of screwdriver that must be produced daily to break even
Then
68 + 1 * x = 2.5 * x
68 + x = 2.5x
collect like terms
68 = 2.5x - x
1.5x = 68
Divide both sides by 1.5
x = 68/1.5
= 45.33
This would be approximated to 46 screws
The letters from the word MATHEMATICS are placed in a hat. What is the probability of selecting an M and then selecting a T if the letters are selected at random and not replaced?
At the start of the school year, there were 72 boxes of coloring pencils in the art room, with each box containing 12 packs. During the school term , 58 boxes were used. How many packs of coloring pencils were left?
Answer:
Take away the 58 boxes from the 72 boxes and you will have 14 boxes left.
Then you have to multiply the 14 boxes left, by the 12 packs of pencils what gives you 168 packs of colouring pencils left.
What is the value of ⅝ ÷ ⅖
Answer:
25/16
Step-by-step explanation:
Remember, keep-change-flip
Turn this into a multiplication equation
[tex]\frac{5}{8} * \frac{5}{2}[/tex]
Multiply to get 25/16
Game stop buys a game for $28 and marks the game up 64%. How much will you pay for the game?
Explain it and answer it please.
-1<9+n<17 and graph the answer after
Answer:
We get [tex]\mathbf{n>-10\:\:and\:\:n<8}[/tex]
Or we can write as: [tex]\mathbf{-10<n<8}[/tex]
The graph is shown is figure attached below:
Step-by-step explanation:
We need to solve the inequality [tex]-1<9+n<17[/tex] and graph the answer.
Solving the inequality
[tex]-1<9+n<17[/tex]
We know that if a<u<b then we can write a<u and u<b
So, we can write
[tex]-1<9+n \:and\: 9+n<17[/tex]
Solving these equations and finding values of n
[tex]-1<9+n \:and\: 9+n<17\\9+n>-1\:and\:9+n<17\\n>-1-9\:and\:n<17-9\\n>-10\:and\:n<8[/tex]
So, we get [tex]\mathbf{n>-10\:\:and\:\:n<8}[/tex]
We can write it as: -10< n and n<8
Overlapping we get: [tex]\mathbf{-10<n<8}[/tex]
The graph is shown is figure attached below: