Answers
Answer:
[tex]x = -7[/tex] and [tex]x = 2[/tex]
Step-by-step explanation:
Given
See attachment for graph
Required
Find x, for [tex]f(x)= 1[/tex]
From the graph, we have the following readings
[tex]f(x)= 1[/tex] when:
[tex]x = 2[/tex] and [tex]x = -7[/tex]
Hence, (d) is correct
Related Questions
Plan production for the next year. The demand forecast is: spring, 20,600; summer, 9,400; fall, 15,400; winter, 18,400. At the beginning of spring, you have 69 workers and 1,030 units in inventory. The union contract specifies that you may lay off workers only once a year, at the beginning of summer. Also, you may hire new workers only at the end of summer to begin regular work in the fall. The number of workers laid off at the beginning of summer and the number hired at the end of summer should result in planned production levels for summer and fall that equal the demand forecasts for summer and fall, respectively. If demand exceeds supply, use overtime in spring only, which means that backorders could occur in winter. You are given these costs: hiring, $130 per new worker; layoff, $260 per worker laid off; holding, $21 per unit-quarter; backorder cost, $9 per unit; regular time labor, $11 per hour; overtime, $17 per hour. Productivity is 0.5 unit per worker hour, eight hours per day, 50 days per quarter.
Find the total cost of this plan. Note: Hiring expense occurs at beginning of Fall. (Leave no cells blank - be certain to enter "O" wherever required.) Fall 15,400 Winter 18,400 15,400 30,800 77 18,400 36,800 77 Spring Summer Forecast 20,600 9,400 Beginning inventory I 1,030 Production required 9,400 Production hours required 39,140 18,800 Regular workforce 69 47 Regular production Overtime hours Overtime production Total production Ending inventory Ending backorders Workers hired Workers laid off Spring Summer Fall Winter Straight time Overtime Inventory Backorder Hiring Layoff Total Total cost
Answers
Answer: end of summer
Multiply the monomials:
-11x^2y and 0.3x^2y^3
Answers
Answer:
-3.3x^4y^4
Step-by-step explanation:
-11x^2y and 0.3x^2y^3
-11x^2y * 0.3x^2y^3
Multiply the constants
-11 * .3 = -3.3
Multiply the x terms
We know that a^b*a^c = a^(b+c)
x^2 * x^2 = x^(2+2) = x^2
Multiply the y terms
y * y^3 = y^(1+3) = y^4
Put them all together
-3.3x^4y^4
solve the triangle given 28° angle and adj side of 210
Answers
Answer:
Tan(28) = x/210
Step-by-step explanation:
111.65^2 + 210^2 = hyp^2
opposite = 111.65
hypotenuse = 237.83
Answer:
hypotenuse =237.84
opposite =111.66
Step-by-step explanation:
cos‐¹(210/x)=28
210/x =cos28
210=cos28x
divide by cos28
x=237.84 (hypotenuse)
sin28= x/237.84
x=sin28×237.84
x=111.66 (opposite)
(another way to do it)
the vertex of this parabola is at (2,-4). when the y-value us -3, the x-value is -3. what is the coefficient of the squared term in the parabolas equation?
Answers
Answer:
The coefficient of the squared term is 1/25.
Step-by-step explanation:
We are given that the vertex of a parabola is at (2, -4). We also know that y = -3 when x = -3.
And we want to determine the coefficient of the squared term of the equation.
Since we are given the vertex, we can use the vertex form of the quadratic:
[tex]\displaystyle y = a(x-h)^2+k[/tex]
Where (h, k) is the vertex and a is the leading coefficient. The leading coefficient is also the coefficient of the squared term, so we simply need to find the value of a.
Since the vertex is at (2, -4), h = 2 and k = -4. Substitute:
[tex]\displaystyle y = a(x-2)^2-4[/tex]
y = -3 when x = -3. Solve for a:
[tex]\displaystyle (-3) = a((-3)-2)^2-4[/tex]
Simplify:
[tex]\displaystyle 1 = a(-5)^2\Rightarrow a = \frac{1}{25}[/tex]
Therefore, our function in vertex form is:
[tex]\displaystyle f(x) = \frac{1}{25}\left(x-2)^2-4[/tex]
Hence, the coefficient of the squared term is 1/25.
Answer:
-5
Step-by-step explanation:
from a p e x
PLEASE ANSWER!!
What is the remainder for the synthetic division problem below?
2/ 3 1 2 -7
A. 25
B. 17
C. -29
D. -39
Answers
A: 25.
Explanation: Check the attached image.
For synthetic division, you just need to multiply the 1st number of the polynomial by the divisior, and then, add it up to the next number; then, the coefficient will be multiplied by the divisor, and so on and so forth until you reach the last number... that last coefficient at the end is the reminder that you've been asked for
A sofa is on sale for $703, which is 26% less than the regular price what is the regular price?
Answers
$950
Step-by-step explanation:
26% less than the regular price = 74%
set up the dimensions as:
part/whole = part/whole
$703 goes in part 74% goes in part
703/? = 74%/100%
Then multiply 100 by 703
100 x 703 = 70300
Finally divided by 74
70300 divided by 74 = 950
••••••••••••••••••••••••••••••••••••
The regular price = $950
703/950 = 74%/100%
Omar keeps his sneaker collection carefully arranged on the floor of his closet. 8 pairs of
sneakers fit perfectly side-by-side from one end of the closet to the other. The closet is 60
inches wide.
How wide is each pair of sneakers?
Answers
Answer:
7.5 inches wide. I wasnt wrong. for a second i thought it was asking for the width of each individual sneaker.
Answer:
each pair of sneakers are 7.5 inches wide
the cost of 2 pairs of trousers and 3 shirts is $825 it shirt cost $50 less than the trouser. find the cost of each shirt and trouser
Answers
Answer:
a pair of trousers cost = x = 195 $
one shirt costs = x - 50 = 145 $
Step-by-step explanation:
let the cost of trouser be x.cost of shirt = (x - 50)2 pairs of trousers cost = 2x 3 shirts cost = 3(x - 50)= 3x- 150
2 trousers and 3 shirts cost = 825
=> 2x + 3x - 150 = 825
=> 5x = 975
x = 195
a pair of trousers cost = x = 195 $
a pair of trousers cost = x = 195 $ one shirt costs = x - 50 = 145 $
It cost $52 to use 800 kWh of electricity. How much will 650 kWh cost?
Answers
Hello!
$52 ..... 800kWh
$x ..... 650kWh
_____________
52/x = 800/650 <=>
<=> 52 × 650 = 800x <=>
<=> 33800 = 800x <=>
<=> 800x = 33800 <=>
<=> x = 33800/800 <=>
<=> x = 338/8 <=>
<=> x = 169/4 <=>
<=> x = 42,25$
Good luck! :)
find the differential equation of this function and indicate the order y = e^3x (acos3x +bsin3x)
Answers
Answer:
y"-6y'+18y=0
Second order
Step-by-step explanation:
Since there are 2 constants, the order of the differential equation will be 2. This means we will need to differentiate twice.
y = e^(3x) (acos3x +bsin3x)
y'=3e^(3x) (acos3x+bsin3x)
+e^(3x) (-3asin3x+3bcos3x)
Simplifying a bit by reordering and regrouping:
y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)
y"=
3e^(3x) cos3x (3a+3b)+-3e^(3x) sin(3x) (3a+3b)
+3e^(3x) sin3x (3b-3a)+3e^(3x) cos(3x) (3b-3a)
Simplifying a bit by reordering and regrouping:
y"=
e^(3x) cos3x (9a+9b+9b-9a)
+e^(3x) sin3x (-9a-9b+9b-9a)
Combining like terms:
y"=
e^(3x) cos3x (18b)
+e^(3x) sin3x (-18a)
Let's reorder y like we did y' and y".
y = e^(3x) (acos3x +bsin3x)
y=e^(3x) cos3x (a) + e^(3x) sin3x (b)
Objective is to find a way to combine or combine constant multiples of y, y', and y" so that a and b are not appearing.
Let's start with the highest order derivative and work down
y"=
e^(3x) cos3x (18b)
+e^(3x) sin3x (-18a)
We need to get rid of the 18b and 18a.
This is what we had for y':
y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)
Multiplying this by -6 would get rid of the 18b and 18a in y" if we add them.
So we have y"-6y'=
e^(3x) cos3x (-18a)+e^(3x) sin3x (-18b)
Now multiplying
y=e^(3x) cos3x (a) + e^(3x) sin3x (b)
by 18 and then adding that result to the y"-6y' will eliminate the -18a and -18b
y"-6y'+18y=0
Also the characteristic equation is:
r^2-6r+18=0
This can be solved with completing square or quadratic formula.
I will do completing the square:
r^2-6r+18=0
Subtract 9 on both sides:
r^2-6r+9=-9
Factor left side:
(r-3)^2=-9
Take square root of both sides:
r-3=-3i or r-3=3i
Add 3 on both sides for each:
r=3-3i or r=3+3i
This confirms our solution.
Another way to think about the problem:
Any differential equation whose solution winds up in the form y=e^(px) (acos(qx)+bsin(qx)) will be second order and you can go to trying to figure out the quadratic to solve that leads to solution r=p +/- qi
Note: +/- means plus or minus
So we would be looking for a quadratic equation whose solution was r=3 ×/- 3i
Subtracting 3 on both sides gives:
r-3= +/- 3i
Squaring both sides gives:
(r-3)^2=-9
Applying the exponent on the binomial gives:
r^2-6r+9=-9
Adding 9 on both sides gives:
r^2-6r+18=0
Question 14 please show ALL STEPS
Answers
List of possible integral roots = 1, -1, 2, -2, 3, -3, 6, -6
List of corresponding remainders = 0, -16, -4, 0, 0, 96, 600, 1764
Check out the table below for a more organized way to represent the answer. The x values are the possible roots while the P(x) values are the corresponding remainders.
====================================================
Explanation:
We'll use the rational root theorem. This says that the factors of the last term divide over the factors of the first coefficient to get the list of all possible rational roots.
We'll be dividing factors of 6 over factors of 1. We'll do the plus and minus version of each. Since we're dividing over +1 or -1, this means that we're basically just looking at the plus minus of the factors of 6.
Those factors are: 1, -1, 2, -2, 3, -3, 6, -6
This is the list of possible integral roots.
Basically we list 1,2,3,6 with the negative versions of each value thrown in as well.
---------------------------------
From there, you plug each value into the P(x) function
If we plugged in x = 1, then,
P(x) = x^4 - 3x^3 - 3x^2 + 11x - 6
P(1) = (1)^4 - 3(1)^3 - 3(1)^2 + 11(1) - 6
P(1) = 1 - 3 - 3 + 11 - 6
P(1) = 0
This shows that x = 1 is a root, since we get a remainder 0. Do the same for the other possible rational roots listed above. You should find (through trial and error) that x = -2 and x = 3 are the other two roots.
B
15x+7
6x+2y|
y +3
2y + 1
С
E
The triangles are congruent. Find the length of each hypotenuse.
A. 3
B. 5
C 17
Answers
Answer:
Hypothenus = 22
Step-by-step explanation:
From the question given above, we were told that the triangles are congruent (i.e same size). Thus,
AC = EF
BC = DE
To obtain the length of each Hypothenus, we shall determine the value of y and x. This can be obtained as follow:
For y:
AC = y + 3
EF = 2y + 1
AC = EF
y + 3 = 2y + 1
Collect like terms
3 – 1 = 2y – y
2 = y
y = 2
For x:
BC = 5x + 7
DE = 6x + 2y
y = 2
DE = 6x + 2(2)
DE = 6x + 4
BC = DE
5x + 7 = 6x + 4
Collect like terms
7 – 4 = 6x – 5x
3 = x
x = 3
Finally, we shall determine the length of each Hypothenus. This can be obtained as follow:
Hypothenus = BC
Hypothenus = 5x + 7
x = 3
Hypothenus = 5x + 7
Hypothenus = 5(3) + 7
Hypothenus = 15 + 7
Hypothenus = 22
OR
Hypothenus = DE
DE = 6x + 2y
y = 2
x = 3
Hypothenus = 6(3) + 2(2)
Hypothenus = 18 + 4
Hypothenus = 22
Shirley has a collection of 50 stamps and adds 4 stamps daily to her collection. Model this situation as a function of number of days (d).
Answers
Answer:
N = 50 +4d
Step-by-step explanation:
Take the original number of stamps and add the stamps per days times the number of days
N = 50 +4d
What's the equivalent expression.
(2-7. 5)² =?
Answers
Answer:
The Answer of the above question is 30.25
Step-by-step explanation:
Hope it helps you.
Step 1: Rewrite equation
To start off, I find it helpful to rewrite the equation. This will give you a better understanding of the problem. Let’s do this now.
(2-7.5)²
Step 2: Understand PEMDAS
Now that we have written down the equation, let’s solve using PEMDAS. In case you are unfamiliar, I will write down what each letter stands for. Keep in mind that the letters go in the order you need to solve.
P- Parentheses
E- Exponent
M- Multiplication
D- Division
A- Addition
S- Subtraction
Step 3: Solve
Finally, we can solve the equation. Using the knowledge from step 2, we will be able to solve in the correct order. Let’s start with parentheses, and find the answer for 2-7.5.
(2-7.5)²
-5.5²
Now let’s move on to the next letter and solve using the exponent. We will multiply -5.5 by itself. This will be the final step; although there are other letters in PEMDAS, the equation will end after this step since we will already have the answer.
-5.5²
30.25
Hope this helps! Comment below for more questions.
2. Write the numeral for four thousand and twelve
Answers
4012
Step-by-step explanation:
Four Thousand and Twelve
First set it up as separated numbers
• Four Thousand = 4000
• Twelve = 12
Then combine 4000 and 12 to make the number
• 4012
4,012
Have a good day
write your answer in simplest radical form
Answers
9514 1404 393
Answer:
n = 2
Step-by-step explanation:
The ratio of side lengths in a 30°-60°-90° triangle is ...
1 : √3 : 2
We have the ratio ...
n : 2√3 : hypotenuse
from which we can see the basic ratio has been multiplied by 2. That is, n = 2 so the sides of the triangle shown have the ratio ...
2 : 2√3 : 4
Does the point (0, 0) satisfy the equation y = 2x?
Answers
Answer:
It does.
Step-by-step explanation:
y=2x
(0)=2(0)
0=0
Answer:
Yes, the point satisfies the equation
Step-by-step explanation:
Hi there!
We want to see if the point (0,0) will satisfy the equation y=2x
In other words, we want to see if the point will pass through the equation of the line
If a point passes through the equation, the values of the point will create a true statement if they are substituted into the equation
So substitute 0 for x and 0 for y to see if it will create a true statement
0=2(0)
multiply
0=0
The end result is a true statement, so the point passes through the equation
Hope this helps!
Two buses leave towns 576 kilometers apart at the same time and travel toward each other. One bus travels 12
h
slower than the other. If they meet in 3 hours, what is the rate of each bus?
km
Rate of the slower bus:
Rate of the faster bus:
Answers
Answer:
Rate of slower bus; 90 km/h
Rate of faster bus; 102 km/b
Step-by-step explanation:
We know that formula do distance is;
Distance = speed/time
We are told that One bus travels 12h slower than the other.
Let speed of slower bus be x.
Thus;
Speed of faster bus = x + 12
Speed of slower bus = x
After 3 hours, distance by faster bus = 3(x + 12)
Speed of slower bus = 3x
Since the towns are 576 km apart, then;
3(x + 12) + 3x = 576
Divide through by 3 to get;
x + 12 + x = 192
2x + 12 = 192
2x = 192 - 12
2x = 180
x = 180/2
x = 90 km/h
Faster bus speed = 90 + 12 = 102 km/h
Evaluate the following expressions using the chip method. SHOW ALL WORK!!!
Answers
Answer:
a. -7 b. -20c. 7Step-by-step explanation:
a. -9+2, in this case, it is -7 because you take the bigger number and subtract it by the lower number. If the bigger number is negative your answer will be negative, if the bigger number is positive it will be positive it is just really a basic subtraction problem just add the sign.b. In multiplication +++=+ ++-=- and a -+-=+ do your problem without thinking about the signs and then add the signs with the formula I showed you.c. ---=+Hope this helps :)!
You decide to move out of your college's dorms and get an apartment, and you want to discuss the budget with your roommate. You know that your monthly grocery bill will depend on a number of factors, such as whether you are too busy to cook, whether you invite guests for meals frequently, how many special holiday meals you will cook, etc. In particular, G will have an approximate normal distribution with a variance of 2500 and a mean:
μ=300+10M−100B+50H
Where M is the number of meals to which you invite guests, and E[M]=8. B is a measure for how busy you are and assume it is U[0,1]. H is a variable that takes on the value 1 for holiday months of November, December, and January and 0 otherwise.
a. What is the mean of G in a November, where M=10 and B=0.5?
b. What is E(G)?
Answers
answer:
a. 400
b. 342.5
Step-by-step explanation:
The mean in this question has been given as
μ=300+10M−100B+50H
where M = 10
B = 0.5
H = 1
we put these into the formula of the mean above
μ=300+10(10)−100(0.5)+50(1)
μ = 300 + 100 - 50 + 50
= 400
So the mean of G in november is = 400
b. We are to find E[G] here
= E[ 300+10M−100B+50H]
m = 8
B = 0.5 or 1/2
h = 1/4
E[ 300+10x8−100x0.5+50*0.25]
= 300+80-50+12.5
= 342.5
the value for E[G] is therefore 342.5
thank you
Hi can someone answer this question please thank you
Answers
Answer:
25
Step-by-step explanation:
5:20
We want to get the second number to 100
100/20 = 5
Multiply each term by 5
5*5 : 20*5
25 : 100
x is 25
Given that,
→ 5 : 20 :: x : 100
Then we have to,
find the second number to 100.
→ 100/20
→ 5
Now multiply each term by 5 in 5:20,
→ 5 × 5 : 20 × 5
→ 25 : 100
→ x = 25
Now these ratio will be,
→ 5 : 20 :: 25 : 100
Hence, the value of x is 25.
If the number of observations for each sample is 150 units, what is the 3-sigma upper control limit of the process
Answers
Complete Question
Complete Question is attached below
Answer:
[tex]UCL= 0.25[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size[tex]n=150[/tex]
Sample Variants [tex]s=7[/tex]
Sigma control limits [tex]Z = 3[/tex]
Therefore
Total number of observations is Given as
[tex]T_o=n*s[/tex]
[tex]T_o=150 *7[/tex]
[tex]T_0=1050[/tex]
Generally
Summation of defectivee
[tex]\sum np=23+34+15+30+25+22+18[/tex]
[tex]\sum np= 167[/tex]
Generally the equation for P-bar is mathematically given by
[tex]P-bar=\frac{\sum np}{T_o}[/tex]
[tex]P-bar=\frac{167}{1050}[/tex]
[tex]P-bar=0.16[/tex]
Therefore
[tex]Sp=\sqrt{\frac{P-bar(1-P-bar)]}{ n}}[/tex]
[tex]Sp=\sqrt{\frac{[0.159(1-0.159)]}{150}}[/tex]
[tex]Sp=0.03[/tex]
Generally the equation for 3-sigma upper control limit of the process is mathematically given by
[tex]UCL = P-bar + Z*Sp[/tex]
[tex]UCL= 0.16 + 3*0.03[/tex]
[tex]UCL= 0.25[/tex]
for every 5 people who bought $9.75 tickets to the football game, 3 people bought $14.50 tickets. If each of 35 people bought a $9.75 ticket, how many people bought the more expensive ticket?
Answers
9514 1404 393
Answer:
21
Step-by-step explanation:
The number who bought expensive tickets is 3/5 of the number who bought cheap tickets.
(3/5)(35) = 21
21 people bought the more expensive ticket.
Answer:
21 people
Step-by-step explanation:
$9.75 $14.50
5 people to 3 people
35 people to ? people
consider the proportions: 5/3 = 35/?
we need the equivalent fraction of 5/3 that has 35 on the denominator
so 5/3 = (5/3)(7/7) because 7/7 =1, and 5*3 =35
5/3 = 5*7/3*7 = 35/21
How far will fiona jog (in feet)
Answers
Answer:
1780 ft
Step-by-step explanation:
We need to find the perimeter of the rectangle, given by
P= 2(l+w) where l is the length and w is the width
The units need to be the same
Change 230 yds to ft
230 yd * 3 ft/ y = 690 ft
P = 2(690+200)
P = 2(890)
P =1780
You have a dog-walking business. You charge $12 per hour. Let's define n as the amount you earn and h as the number of
hours you work. You want to make $30, so you figure you need to work 2.5 hours.
Sort the solution methods by whether they are correct or incorrect methods to solve the problem.
Answers
Answer:
[tex]n = 12h[/tex]
Step-by-step explanation:
Given
[tex]r = 12/hr[/tex] --- rate
[tex]h \to hours[/tex]
[tex]n \to amount[/tex]
Required
Determine which solution is correct or incorrect
The solutions are not given. So, I will provide a general explanation
The amount (n) is calculated as:
[tex]n = r * h[/tex]
So, we have:
[tex]n = 12 * h[/tex]
[tex]n = 12h[/tex]
The above is the general equation to solve for the amount, given h hours
When h = 2.5, we have:
[tex]n = 12*2.5[/tex]
[tex]n = 30[/tex]
Answer:
going to add a picture
Step-by-step explanation:
:)
Uuannsnnsnndn d. DND. D
Answers
Answer:
im so confused
Step-by-step explanation:
Answer:
what is this goat saying
A psychologist suspects that heroin addicts have a different assessment of self-worth than others in the general population. On a test designed to measure self-worth, the mean for the general population is 48.6. The psychologist obtains a random sample of 40 test scores produced by heroin addicts and found the sample mean and the sample standard deviations are 45.5 and 8.5, respectively. Do these data indicate the self-worth of heroin addicts is less than that of the general population?
Answers
Answer:
The p-value of the test if 0.0131, which is less than the standard significance level of 0.05, meaning that these data indicates that the self-worth of heroin addicts is less than that of the general population.
Step-by-step explanation:
On a test designed to measure self-worth, the mean for the general population is 48.6.
At the null hypothesis, we test if the mean is of 48.6, that is:
[tex]H_0: \mu = 48.6[/tex]
A psychologist suspects that heroin addicts have a different assessment of self-worth than others in the general population. Test if it is lower.
At the alternative hypothesis, we test if the mean is lower, that is:
[tex]H_1: \mu < 48.6[/tex]
The test statistic is:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
48.6 is tested at the null hypothesis:
This means that [tex]\mu = 48.6[/tex]
The psychologist obtains a random sample of 40 test scores produced by heroin addicts and found the sample mean and the sample standard deviations are 45.5 and 8.5, respectively.
This means that [tex]n = 40, X = 45.5, s = 8.5[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{45.5 - 48.6}{\frac{8.5}{\sqrt{40}}}[/tex]
[tex]t = -2.31[/tex]
P-value of the test:
The p-value of the test is a one-tailed test(mean lower than a value), with t = -2.31 and 40 - 1 = 39 df.
Using a t-distribution calculator, this p-value is of 0.0131.
The p-value of the test if 0.0131, which is less than the standard significance level of 0.05, meaning that these data indicates that the self-worth of heroin addicts is less than that of the general population.
I need help please. Show work
Answers
Answer:
28
Step-by-step explanation:
10/14 mph no wind
20 wind
14 x 2 = 28
28 mph with wind
Simplify the given equation.
5x+ 2(x-3) = -2(x - 1)
0 7 x-6=-2 X-2
0 7 x - 6 = -2 x + 2
0 7 X - 3 = -2 x-1
i’m sorry:/
Answers
Answer:
7x - 6 = -2x + 2
Step-by-step explanation:
Hi! First we are going to distribute our "2" and "-2" values to the values in parenthesis.
5x + 2x - 6 = -2x + 2
Now, we can combine our like terms, "5x" and "2x".
7x - 6 = -2x + 2
Since our problem's answers are left in this form, not completely combined our answer is 7x - 6 = -2x + 2.
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 88 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean µ = 88 tons and standard deviation σ = 0.5 ton.
Required:
a. What is the 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?
Answers
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
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.
In this question:
[tex]\mu = 88, \sigma = 0.5[/tex]
a. What is the probability that one car chosen at random will have less than 49.5 tons of coal?
This is the p-value of Z when X = 49.5, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49.5 - 88}{0.5}[/tex]
[tex]Z = -77[/tex]
[tex]Z = -77[/tex] has a p-value of 0.
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 [tex]n = 35, s = \frac{0.5}{\sqrt{35}}[/tex]
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 - 88}{\frac{0.5}{\sqrt{35}}}[/tex]
[tex]Z = -455.5[/tex]
[tex]Z = -455.5[/tex] has a p-value of 0.
0% probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal
