This sign is 50 centimeters high and 40 centimeters along the base. What is it’s area?
height =50
base=40
area of triangle =1/2b*h
1/2*40*50
1000
Canine Crunchies Inc. (CCI) sells bags of dog food to warehouse clubs. CCI uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 45 kilograms and a standard deviation of 1.2 kilograms.
Requried:
a. What is the probability that a filled bag will weigh less than 49.5 kilograms?
b. What is the probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms?
c. What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled?
d. CCI is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that no more than 2% of all filled bags weigh more than 52 kilograms?
Answer:
a) 0.9999 = 99.99% probability that a filled bag will weigh less than 49.5 kilograms
b) 0.0018 = 0.18% probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms.
c) 46.24 kilograms
d) The standard deviation would have to be of 3.41 kilograms.
Step-by-step explanation:
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.
Mean of 45 kilograms and a standard deviation of 1.2 kilograms.
This means that [tex]\mu = 45, \sigma = 1.2[/tex]
a. What is the probability that a filled bag will weigh less than 49.5 kilograms?
This is the pvalue of Z when X = 49.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49.5 - 45}{1.2}[/tex]
[tex]Z = 3.75[/tex]
[tex]Z = 3.75[/tex] has a pvalue of 0.9999
0.9999 = 99.99% probability that a filled bag will weigh less than 49.5 kilograms
b. What is the probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms?
This is the pvalue of Z when X = 51 subtracted by the pvalue of Z when X = 48.5.
X = 51
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{51 - 45}{1.2}[/tex]
[tex]Z = 5[/tex]
[tex]Z = 5[/tex] has a pvalue of 1
X = 48.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{48.5 - 45}{1.2}[/tex]
[tex]Z = 2.92[/tex]
[tex]Z = 2.92[/tex] has a pvalue of 0.9982
1 - 0.9982 = 0.0018
0.0018 = 0.18% probability that a randomly sampled filled bag will weight between 48.5 and 51 kilograms.
c. What is the minimum weight a bag of dog food could be and remain in the top 15% of all bags filled?
This is the 100 - 15 = 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.037 = \frac{X - 45}{1.2}[/tex]
[tex]X - 45 = 1.037*1.2[/tex]
[tex]X = 46.24[/tex]
46.24 kilograms.
d. CCI is unable to adjust the mean of the filling process. However, it is able to adjust the standard deviation of the filling process. What would the standard deviation need to be so that no more than 2% of all filled bags weigh more than 52 kilograms?
X = 52 would have to be the 100 - 2 = 98th percentile, which is X when Z has a pvalue of 0.98, so X when Z = 2.054. We would need to find the value of [tex]\sigma[/tex] for this.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.054 = \frac{52 - 45}{\sigma}[/tex]
[tex]2.054\sigma = 7[/tex]
[tex]\sigma = \frac{7}{2.054}[/tex]
[tex]\sigma = 3.41[/tex]
The standard deviation would have to be of 3.41 kilograms.
help please and explain (no links and random answers for points)
Answer:
No 2 answer is 6\8 i.e 3\4 for the one eaten and 2\8 i.e 1\4 for the left over
The volume of a fish tank is 70 cubic feet. If the density is 0.4 fish over feet cubed, how many fish are in the tank?
175
88
28
14
Answer:
28 fish is the correct answer
Step-by-step explanation:.
The number of fish in the fish tank will be 28.
What is a volume?Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of the Cuboid.
The density of the fish is defined as the number of fish per unit volume of the tank.
Given that volume of a fish tank is 70 cubic feet and the density is 0.4 fish over feet cubed.
The number of fish is calculated as below:-
Number = Volume of tank x Density of fish
Number = 70 x 0.4
Number = 28 fish
Therefore, the number of fish in the fish tank will be 28.
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please help me with this as soon as you can
9514 1404 393
Answer:
14.14
Step-by-step explanation:
The diagonal of a square is √2 times the side length.
AC = AB×√2
AC = 10√2 ≈ 14.14
_____
The diagonal of a square is the hypotenuse of an isosceles right triangle. If the sides of that are s and the diagonal is d, the Pythagorean theorem tells us ...
d² = s² + s²
d² = 2s²
d = (√2)(√s²) = s√2
This relation holds for any isosceles right triangle, not just for the diagonal of this square. It is useful to remember.
What is the factored form of x^3 - x^2 - 30x?
Answer:
x(x − 6) (x + 5)
Step-by-step explanation:
this is the factored form of x^3 - x^2 - 30x
hope this helps and is right :)
Someone please want to do my algebra assignments all due at 11 tn I need help at least ;(
Answer:
-48
Step-by-step explanation:
I think!! :)
A bank wants to estimate the difference in the proportion of its "big" customers who have a second account with a different bank and the proportion of its "small" customers who also have an account with another bank. Of the 200 "big" customers randomly selected, 160 claimed to also bank elsewhere. Of the 300 "small" customers randomly selected, 120 claimed to also bank with other banks. Check the conditions for constructing a confidence interval for the difference in proportions.
Answer:
Kindly check explanation
Step-by-step explanation:
To construct confidence interval for difference in proportion ; the following conditions must be met :
1.) The selected samples must have been randomly chosen or selected from a larger population. This is essential in other to eliminate bias.
Each group of samples must be independently chosen. That is, the samples of bug customers chosen must be independent of the sample of small customers selected.
The population from which the samples are drawn must be considerably larger than the sample size. Sample size, n should be ≤ 10% of the population size.
p1 = 160 / 200 = 0.8 ; (1 - p1) = 0.2
p2 = 120 / 300 = 0.4 ; (1 - p2) = 0.6
(p1 - p2) ± Zcritical * sqrt[(p1(1 - p1) /n1) + (p2(1 - p2) / n2)]
Answer: A
Step-by-step explanation:
PLEASE PLEASE HELP
find the value of y
Answer:
Step-by-step explanation:
y=108/2=54°
Answer:
Y = 54
Step-by-step explanation:
Easy Work! Please look at the picture and yes it’s easy for other people but not for me for people asking please and thank you.
2.6 cm = .........................mm
Answer:
26 mm
Step-by-step explanation:
1 cm is equal to 10 mm
2.6 cm
> 2.6 x 10
> 26 mm
Someone please help me asnwer this!!
Answer:
89 cm
Step-by-step explanation:
By Pythagoras Theorem,
c² = 80² + 39²
c² = 6400 + 1521
c² = 7921
c = 89 cm
Hope it helps :)
helpppp meeee! pleaseeee!
Answer:
9
11
17
25
Step-by-step explanation:
Input the x into the equation
Answer:
2×2+5=9
2×3+5=11
2×6+5=17
2×10+5=25
Which expression is equivalent to 6x-9•3
A bag contains 8 red marbles and 4 blue marbles. You randomly pick a marble and then pick a second marble without returning the first marble to the bag. What is the probability that both marbles are red?
Answer:
0.50%
Step-by-step explanation:
What's the surface area?
Answer:
Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area
Step-by-step explanation:
Answer:
of what
Step-by-step explanation:
Please help, I’m confused
Answer:
220/221
Step-by-step explanation:
cos math
Solve for x.
7(x + 2) = 6(x + 5)
X=-44
x = -16
x = 16
X= 44
Look in picture
Help please
Answer:
x= 16
Step-by-step explanation:
First, you want to distribute each side! (you're gonna wanna learn this because you will be having to do it for the next 3 years no joke it sucks)
7(x+2) can be distributed as 7x+14 after multiplying 7 times x and 7 times 2, and 6(x+5) can be distributed as 6x+30.
Now, you have to get the x on one side to solve for x (so like x=__).
To do this, look at the equation as of now. 7x+14=6x+30.
We can minus 14 and bring that to the right, and minus 6x and bring that to the left to separate the x's and the regular numbers.
Now we have 16=x (or x=16).
Please I need helpppp
Seven cards are drawn from an ordinary deck. In how many ways is it possible to draw (b) only 8's, 's and (c) no 's, 's and (d) exactly 2 or ; (e) spades and hearts? (a) Number of ways to draw only 's = 0 (b) Number of ways to draw only 's, 's, and 's = 924 (c) Number of ways to draw no 's, 's, and 's = 3838380 (d) Number of ways to draw exactly 2 s or s = 3,801,028 (e) Number of ways to draw spades and hearts = 55770 Question is complete. Tap on the red indicators to see incorrect answers.
Complete question :
Seven cards are drawn from an ordinary deck. In how mnat ways is it possible to draw (a) only 5s (b)only 8s, 9s, and 10s, (c) no 8s, 9s, and 10s (d) exactly 2 jacks or kings, (e) 5 spades and 2 hearts?
Answer:
0; 792 ; 100396 ; 30408224 ; 18643560 ;
Step-by-step explanation:
Number of cards in a deck = 52
Number of cards to be drawn = 7
Using combination:
nCr = n! ÷ (n-r)!r!
A.)
Number of 5's in a deck = 4
4C7 = 0
(B.)
only 8s, 9s, and 10s,
Number of 8, 9 and 10's = 4 *3 = 12
12C7 = 12! ÷ 5!7! = 792
(C)
no 8s, 9s, and 10s ;
Number of cards to select from = 52 - (3(4)) = 40C7 = 18643560
(D)
exactly 2 jacks or kings,
Number of jack or king in deck = 8 ; other 5 could be any of the rest : (52 - 8) = 44
8C2 * 44C5 = 28 * 1086008 = 30408224
(e) 5 spades and 2 hearts?
Number of spades = 13
Number of hearts = 13
13C5 * 13C2
1287 * 78 = 100396
Bob and Venessa share $52. if Bob gets three times what Venessa gets, how much does he get?
PLEASE HELPP!!!!!! FOR 10 POINTS. Am I right? Show work if I’m wrong
Answer:
you are correct, they are supplementary
Step-by-step explanation:
Answer:
Yes! You are correct! The angles added together produce 180degrees, therefore, is supplementary. Just like the fellow above me said :)
Step-by-step explanation:
Would anyone please help me with these if they can?
Answer:
12) F.0
13) 3/2
Step-by-step explanation:
12)
(5, 0) and (10, 0)
Slope:
m=(y2-y1)/(x2-x1)
m=(0-0)/(10-5)
m = 0
13)
(3, 2) and (-1, -4)
Slope:
m=(y2-y1)/(x2-x1)
m=(-4-2)/(-1-3)
m=(-6)/(-4)
m= 3/2
Before starting to play the roulette in a casino you want to look for biases that you can exploit. Youtherefore watch 100 rounds that result in a number between 1 and 36 and you count the number ofrounds for which the result is odd. If the count exceeds 55, you decide that the roulette is not fair.Assuming that the roulette is fair, find an approximation for the probability that you will makethe wrong decision.
Answer:
[tex]P(n>55)=0.1357[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size n=100
Sample space n'=36
Generally the equation for the mean number of times odds appears is mathematically given by
[tex]\=x_o=hp[/tex]
[tex]\=x_o=100*0.5[/tex]
[tex]\=x_o=50[/tex]
Generally the equation for standard deviation is mathematically given by
[tex]\sigma=(hp(1-p))^{1/2}\\\sigma=(50(0.5))^{1/2}[/tex]
[tex]\sigma=5[/tex]
Therefore probability to make wrong decision P(n>55)
[tex]P(n>55)=1-P(z<50.5/5)\\P(n>55)=1-P(z<1.1)\\P(n>55)=1-0.86[/tex]
[tex]P(n>55)=0.1357[/tex]
An approximation for the probability that you will make the wrong decision is 0.1587.
ProbabilityS=Number of time that the result was odd
n=100
p=0.5
Hence:
E[S]=100×0.5
E[S]=50
Standard deviation=√100×0.5×0.5
Standard deviation√25
Standard deviation=5
Using normal approximation to the binomial
P(S≥55)=P(S-50/5 ≥ 55-50/5)
P(S≥55)=1-P(z ≤ 1)
P(S≥55)=1-0.8413
P(S≥55)= 0.1587
Inconclusion an approximation for the probability that you will make the wrong decision is 0.1587.
Learn more about probability here:https://brainly.com/question/24756209
Find mZDOC.
A)
22°
B)
44°
C)
107
D)
126
Answer: [tex]107^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle DOC=\frac{170+44}{2}=\boxed{107^{\circ}}[/tex]
10. Find the measure of angle x.
11. Find the measure of angle ?
9514 1404 393
Answer:
10. 28°
11. 65°
Step-by-step explanation:
10. The two angles are complementary, so the unknown angle is ...
x = 90° -62° = 28°
__
11. The three angles total 180°, so the unknown angle is ...
? = 180° -55° -60° = 65°
15 cm
15 cm
16 cm
20 cm
57 cm
What is the perimeter of the polygon?
Answer:
C.
Step-by-step explanation:
15 x 16=240 x 2= 480
57 x 20= 1140
1140 + 480 = 1620
Given f x please help me
Try math-way, it gives you the answers to stuff in mathematics, in this case algebra. Also there's no - between the two words, I had to do this because of brainly.
In a lab experiment, 290 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 26 hours. How long would it be, to
the nearest tenth of an hour, until there are 330 bacteria present?
GUYS NEED HELP I HAVE A MATH TEST
Answer:
4.8
Step-by-step explanation:
Please help me and no links or sites! Please
Answer:
B
Step-by-step explanation:
By using the fraction strip, if you think about it:
Pretend to color in 5/6 on the yellow side, and do the same to the 1/12 part, instead pretend to shade in 5/12. If you see how much remaining you have, you get 5/12.