Answer:
a) 0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg.
b) The weight that is exceeded by 98% of the bags is of 45.9 kg.
c) 0.0125 = 1.25% probability that two weigh more than 53kg and one weighs less than 53kg.
Step-by-step explanation:
The first two questions are solved using the normal distribution, while the third is solved using the binomial distribution.
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.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
The weight X kg of a bag can be modeled by a normal distribution with mean 50kg and standard deviation 2kg.
This means that [tex]\mu = 50, \sigma = 2[/tex]
a. Find the probability that a randomly selected bag weighs more than 53kg.
This is 1 subtracted by the p-value of Z when X = 53. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{53 - 50}{2}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
1 - 0.9332 = 0.0668.
0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg.
b. Find the weight that is exceeded by 98% of the bags.
This is the 100 - 98 = 2nd percentile, which is X when Z has a p-value of 0.02, so X when Z = -2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.054 = \frac{X - 50}{2}[/tex]
[tex]X - 50 = -2.054*2[/tex]
[tex]X = 45.9[/tex]
The weight that is exceeded by 98% of the bags is of 45.9 kg.
c. Three bags are selected at random. Find the probability that two weigh more than 53kg and one weighs less than 53kg.
0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg means that [tex]p = 0.0668[/tex]
3 bags means that [tex]n = 2[/tex]
Two above 53kg, which means that we want P(X = 2). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{3,2}.(0.0668)^{2}.(0.9332)^{1} = 0.0125[/tex]
0.0125 = 1.25% probability that two weigh more than 53kg and one weighs less than 53kg.
3.3.C-1
If one tablet of calcium pantothenate contains 0.5 gram, how much is contained in
n 2 1/4 tablets? How many tablets are needed to make up 2.3 grams?
A fraction calcium pantothenate contains 0.5 gram of a tablet 5 tablets to make up 2.3 grams.
To calculate the amount of calcium pantothenate contained in a given number of tablets, use the given information that one tablet contains 0.5 grams.
Amount in n 2 1/4 tablets:
To calculate the amount of calcium pantothenate in n 2 1/4 tablets, we need to calculate the total amount for each part (whole tablets and the fraction of a tablet) and then sum them up.
Amount in n whole tablets: n tablets × 0.5 grams/tablet
Amount in 1/4 tablet: (1/4)× 0.5 grams
So, the total amount in n 2 1/4 tablets would be:
Total amount = n ×0.5 + (1/4) ×0.5 grams
Tablets needed to make up 2.3 grams:
To calculate the number of tablets needed to make up 2.3 grams of calcium pantothenate, set up a proportion using the given tablet amount (0.5 grams/tablet).
Let x be the number of tablets needed.
0.5 grams/tablet = 2.3 grams / x tablets
Cross-multiply:
0.5 × x = 2.3
x = 2.3 / 0.5
x = 4.6
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uog;;ooooooooooooooooooooooooooooooooooo ml
Answer:
D
Step-by-step explanation:
2. Write the numeral for four thousand and twelve
The terminal side of θ passes through the point (8,−7).
What is the exact value of cosθ in simplified form?
Answer:
8√113 / 113
Step-by-step explanation:
Representing the information on a triangle :
From trigonometry :
Cos θ = Adjacent / hypotenus = AC / AB
AB = hypotenus :
Using Pythagoras :
AB² = AC² + BC²
AB² = 8² + (-7)²
AB² = 64 + 49
AB = √113
Cos θ = AC / AB = 8 / √113
RATIONALIZE :
8/√113 * √113/√113 = 8√113 / 113
Multiply the monomials:
-11x^2y and 0.3x^2y^3
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
√12 + √10 − √2) is
(a) A positive rational number
(b) Equal to zero
(c) An irrational number
(d) A negative integer
Hello!
[tex] \bf \sqrt{12} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \sqrt{ {2}^{2} \times 3} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \sqrt{ {2}^{2} } \sqrt{ 3} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \boxed{ 2 \sqrt{3} + \sqrt{10} - \sqrt{2}} [/tex]
Answer: (c) An irrational number
Good luck! :)
Which of the following is a geometric sequence where a1 = 4 and r = 3?
Answer:
4, 12, 36, 108.... continue multiplying by 3
Plsss HELP!!!
*image included
The total number of vertices adjacent to the vertex is called?
Answer:
The degree of vertex is the total number of vertices adjacent to the vertex .
The total number of vertices adjacent to the vertex is called degree of the vertex.
What is vertex?" Vertex is defined as when two adjacent side meet at one point."
According to the question,
The degree of a vertex is always as the total number of adjacent side to the vertex.
If adjacent sides far away from each other degree is more.
If adjacent sides near to each other degree is less.
Hence, the total number of vertices adjacent to the vertex is called degree of the vertex.
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how many itegers from 15 to 85, inclusive are multibles of 8
Answer:
9 multiples
Step-by-step explanation:
16,24,32,40,48,56,64,72,80
9
Write the equation of the line that passes through the points (1,-7)(1,−7) and (-6,-9)(−6,−9). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
6x+6)(6+4)
Step-by-st(ep explanation:
nbpbf wefqlbwpoi
Answer:
y+7=2/7x-2/7
Step-by-step explanation:
So we first want to find the slope. It's calculated by taking the difference in y values and dividing it by the difference in x values.
-9-(-7)/-6-1
=-9+7/-7
=-2/-7
=2/7.
This is the m in the point-slope equation.
Next, we just plug in the points. We only need 1 point so I will use the (1,-7)
y-y1=m(x-x1)
y-(-7)=2/7(x-1)
y-(-7)=2/7x-2/7
y+7=2/7x-2/7
I've never really seen fully reduced point-slope form, but I'm assuming the above is it because if I keep simplifying it's going to turn into slope-intercept form.
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
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 $
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.
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:
:)
: Find the value of the trigonometric ratio. Make sure to simplify the If needed
Answer:
24/7
Step-by-step explanation:
tan A = opp/adj
For angle Z, the adjacent leg is 14, and the opposite leg is 48.
tan Z = 48/14
tan Z = 24/7
Avery made 6 litres of hot chocolate for the 4th annual bonfire with his family. If
each cup holds of a litre of liquid, how many cups can Avery fill?
Answer:
Avery can hold 6 cups
Step-by-step explanation:
so you have a 6 litre of hot chocolate and for every cup you remove 1 litre of hot chocolate wich makes you get 6 cups of hot chocolate
Find x on this triangle
X is the hypotenuse. Using the given angle and side dimension use the law of sins.
Sin( angle) = opposite leg/ hypotenuse
Sin(30) = 5/2 / x
X = 5/2 / sin(30)
X = 5
The answer is x = 5
Karissa determines the area of her desk by multiplying 45.72 centimeters and 60.95 centimeters. She states that the area is 2786.634 square centimeters. Which best describes the reasonableness of Karissa’s solution?
A. The solution is unreasonable because 50 times 60 is 3,000, not 2,786.
B. The solution is reasonable because 50 times 60 is 3,000, which is close to the computed area.
C. The solution is unreasonable because there are four decimal places in the factors and only three decimal places in the product.
D. The solution is reasonable because there are four numbers to the left of the decimal in the factors and four numbers to the left of the decimal in the product.
Helppp
Answer:
b
Step-by-step explanation:
45.72*60.95 =2786.634, which means that the solution is reasonable.
in b, they used the method of estimation which is a quick method to check if the answer is right.
d doesnt make sense as the decimal places do not have to remain the same number after u multiply them, moreover there's only 2 dp in the factors
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)?
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
Can anyone help with problem 5?
Answer:
Other leg: 25 cm
Hypotenuse: 25√2 cm
Step-by-step explanation:
Hi there!
We are given a 45°-45°-90° triangle, and one leg (a side that makes up the right triangle) measures 25 cm
We want to find the length of the other sides
First, let's find the length of the other leg
A 45°-45°90° triangle is actually an isosceles triangle, and if it was to be drawn, the base angles are 45 and 45 degrees
That means the legs of the right triangle are actually the legs in the isosceles triangle as well
So the other leg is also 25 cm
Now, let's find the length of the hypotenuse, which is the side OPPOSITE from the 90° angle
You can solve for the other side using Pythagorean Theorem if you wish, however, there is a shortcut to finding the hypotenuse
In a 45°-45°-90° triangle, if the length of the legs are a, then the hypotenuse is a√2 cm
So that means the length of the hypotenuse in this case is 25√2 cm
Hope this helps!
How far will fiona jog (in feet)
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
write your answer in simplest radical form
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
A sofa is on sale for $703, which is 26% less than the regular price what is the regular price?
This table shows the ratio of number of people to liters of Find the missing values in the ratio table
ginger ale needed.
A=
People
Ginger Ale
Answer:
A= 2 B= 6
Step-by-step explanation:
What point slope form equation could be produced with the points(-3,-6)and (3,-3)
Answer:
y+6=1/2(x+3)
Step-by-step explanation:
Hi there!
We want to find the equation of the line in point-slope form that passes through (-3, -6), and (3, -3)
Point-slope form is given as y-[tex]y_{1}[/tex]=m(x-[tex]x_{1}[/tex]) where ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) is a point and m is the slope
We don't know the slope of the line, so let's find it
The formula for the slope (m) calculated from two points is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex], [tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) are points
We have two points, but let's label their values to avoid any confusion
[tex]x_{1}[/tex]=-3
[tex]y_{1}[/tex]=-6
[tex]x_{2}[/tex]=3
[tex]y_{2}[/tex]=-3
Now substitute into the formula (remember: the formula has SUBTRACTION)
m=[tex]\frac{-3--6}{3--3}[/tex]
simplify
m=[tex]\frac{-3+6}{3+3}[/tex]
m=[tex]\frac{3}{6}[/tex]
m=1/2
So the slope of the line is 1/2
Now that we have everything needed for point-slope form (a point and the slope), substitute the values into the formula (remember: the formula has SUBTRACTION)
y-[tex]y_{1}[/tex]=m(x-[tex]x_{1}[/tex])
y--6=1/2(x--3)
simplify
y+6=1/2(x+3)
Hope this helps!
Of the delegates at a convention, 60% attended the breakfast forum, 70% attended the dinner speech and 40% attended both events. If a randomly selected delegate is known to have attended the dinner speech, the probability that he also attended the breakfast forum is
Answer:
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Attended the dinner speech.
Event B: Attended the breakfast forum.
70% attended the dinner speech
This means that [tex]P(A) = 0.7[/tex]
40% attended both events.
This means that [tex]P(A \cap B) = 0.4[/tex]
The probability that he also attended the breakfast forum is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.7} = 0.5714[/tex]
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
Question 14 please show ALL STEPS
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.
Karl wants to raise money for charity. He designs a game for people to play.
Karl uses a ten sided dice for the game. The dice is numbered 1 to 10.
Each person will roll the dice once. A person wins the game if the dice lands on a multiple of 4.
Ali plays the game once,
a) Work out the probability that Ali will win the game.
(2 m
Answer:
0.2 = 20% probability that Ali will win the game.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Total outcomes:
The 10 sides that the dice can land, which means that [tex]T = 10[/tex]
Desired outcomes:
Sides that are multiple of 4, that is, side 4 and side 8, so [tex]D = 2[/tex]
Work out the probability that Ali will win the game.
[tex]p = \frac{D}{T} = \frac{2}{10} = 0.2[/tex]
0.2 = 20% probability that Ali will win the game.
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
If Bob gains 15 pounds, then the ratio of Bob's weight to Tom's weight would be 7 to 5. If Tom weighs 115 pounds, what is Bobs weight now?
Answer:
Step-by-step explana:
-115/5= 23
-23x7=16 1
-161-15=146
Answer:
146 pounds.
Step-by-step explanation:
7 : 5 = 12
? : 115 = ?
115 / 5 = 23
23 x 7 = 161
161 - 15 = 146
The answer is 146.
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?
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
