Answer:
The juice bar can sell 3 more cups of the passion juice than the berry juice (last one)
Step-by-step explanation:
Passion: 768/16=48
Berry: 810/18=45
passion can fill 48 cups while berry can fill 45 cups, so passion fills +3
:)
A campsite provides a locking, rectangular box with the dimensions shown to secure
food from bears. What is the volume?
(PUT NUMBER ONLY)
3 feet
2 feet
5 feet
Answer:
30 feet^3
Step-by-step explanation:
2*5*3=30
V= bhw
A machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%). Prior to shipment produced parts are passed through an automatic inspection machine, which is supposed to be able to detect any part that is obviously defective and discard it. However, the inspection machine is not perfect. A part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input. Slightly defective parts are marked as defective and discarded 40% of the time, and obviously defective parts are correctly identified and discarded 98% of the time.
Required:
a. What is the total probability that a part is marked as defective and discarded by the automatic inspection machine?
b. What is the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped?
c. What is the probability that a part is 'bad' (obviously defective) given that it makes it through the inspection machine and gets shipped?
Answer:
(a) 0.0686
(b) 0.9984
(c) 0.0016
Step-by-step explanation:
Given that a machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%).
Let A, B, and C be the events of defect-free, slightly defective, and the defective parts produced by the machine.
So, from the given data:
P(A)=0.90, P(B)=0.03, and P(C)=0.07.
Let E be the event that the part is disregarded by the inspection machine.
As a part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input.
So, [tex]P\left(\frac{E}{A}\right)=0.02[/tex]
Now, from the conditional probability,
[tex]P\left(\frac{E}{A}\right)=\frac{P(E\cap A)}{P(A)}[/tex]
[tex]\Rightarrow P(E\cap A)=P\left(\frac{E}{A}\right)\times P(A)[/tex]
[tex]\Rightarrow P(E\cap A)=0.02\times 0.90=0.018\cdots(i)[/tex]
This is the probability of disregarding the defect-free parts by inspection machine.
Similarly,
[tex]P\left(\frac{E}{A}\right)=0.40[/tex]
and [tex]\Rightarrow P(E\cap B)=0.40\times 0.03=0.012\cdots(ii)[/tex]
This is the probability of disregarding the partially defective parts by inspection machine.
[tex]P\left(\frac{E}{A}\right)=0.98[/tex]
and [tex]\Rightarrow P(E\cap C)=0.98\times 0.07=0.0686\cdots(iii)[/tex]
This is the probability of disregarding the defective parts by inspection machine.
(a) The total probability that a part is marked as defective and discarded by the automatic inspection machine
[tex]=P(E\cap C)[/tex]
[tex]= 0.0686[/tex] [from equation (iii)]
(b) The total probability that the parts produced get disregarded by the inspection machine,
[tex]P(E)=P(E\cap A)+P(E\cap B)+P(E\cap C)[/tex]
[tex]\Rightarrow P(E)=0.018+0.012+0.0686[/tex]
[tex]\Rightarrow P(E)=0.0986[/tex]
So, the total probability that the part produced get shipped
[tex]=1-P(E)=1-0.0986=0.9014[/tex]
The probability that the part is good (either defect free or slightly defective)
[tex]=\left(P(A)-P(E\cap A)\right)+\left(P(B)-P(E\cap B)\right)[/tex]
[tex]=(0.9-0.018)+(0.03-0.012)[/tex]
[tex]=0.9[/tex]
So, the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped
[tex]=\frac{\text{Probabilily that shipped part is 'good'}}{\text{Probability of total shipped parts}}[/tex]
[tex]=\frac{0.9}{0.9014}[/tex]
[tex]=0.9984[/tex]
(c) The probability that the 'bad' (defective} parts get shipped
=1- the probability that the 'good' parts get shipped
=1-0.9984
=0.0016
A cylinder has a radius of 3 feet and a height of 7 feet. Which of the following can be used to calculate the volume of a cone that fits exactly inside the cylinder?
(3.14)(7%)(3)
03(3.14373)(3)
(3.14)(3)(7)
O
0|(3.1413307
Volume of a cylindre = area base x height
Volume of a cone = 1/3 x area base x height
V cone = 1/3 x pi x r² x h = 1/3 x 3,14 x 3² x 7
In Table 2, at this rate, how much would it cost to buy 9 books?
Answer:
There is no table attached, if you attach is I will gladly help :)
Step-by-step explanation:
Solve for m please I will give brainliest
Answer:
m-4n=8 divide both sides by 4.
m-n=2
There are two variables, so this is the simplest form.
help please!
I need to prove this using identities
show all steps
cos(pi/2+x)/cos(pi+x)=tanx
Answer: see proof below
Step-by-step explanation:
Use the Sum & Difference Identity: cos (A + B) = cos A · cos B - sin A · sin B
Recall the following from Unit Circle: cos (π/2) = 0, sin (π/2) = 1
cos (π) = -1, sin (π) = 0
Use the Quotient Identity: [tex]\tan A=\dfrac{\sin A}{\cos A}[/tex]
Proof LHS → RHS:
[tex]\text{LHS:}\qquad \qquad \dfrac{\cos \bigg(\dfrac{\pi}{2}+x\bigg)}{\cos \bigg(\pi +x\bigg)}[/tex]
[tex]\text{Sum Difference:}\qquad \dfrac{\cos \dfrac{\pi}{2}\cdot \cos x-\sin \dfrac{\pi}{2}\cdot \sin x}{\cos \pi \cdot \cos x-\sin \pi \cdot \sin x}[/tex]
[tex]\text{Unit Circle:}\qquad \qquad \dfrac{0\cdot \cos x-1\cdot \sin x}{-1\cdot \cos x-0\cdot \sin x}[/tex]
[tex]=\dfrac{-\sin x}{-\cos x}[/tex]
Quotient: tan x
LHS = RHS [tex]\checkmark[/tex]
A food safety guideline is that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city. Construct a 99% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi?
0.57 0.68 0.10 0.93 1.29 0.55 0.86
What is the confidence interval estimate of the population mean mu?
_ppm < mu < _ ppm
Answer:
hi there friend
Step-by-step explanation:
CI=(0.431,1.0376)CI=(0.431,1.0376)
Explanation:
Given that:
The sample size , n = 7
The mean of the observation:
Mean = Sum of observation / Total number of observation
= (0.56+ 0.72+ 0.10 + 0.99 + 1.32 + 0.52 + 0.93) / 7 = 0.7343
The standard deviation:
S.D. = \sqrt {\frac {\sum_{i=1}^{i=7}(x_i-\bar{x})^2}{n-1}}S.D.=
n−1
∑
i=1
i=7
(x
i
−
x
ˉ
)
2
Calculating SD as:
S.D. = \sqrt {\frac {(0.56-0.7343)^2+(0.72-0.7343)^2+.....+(0.52-0.7343)^2+(0.93-0.7343)^2}{7-1}}S.D.=
7−1
(0.56−0.7343)
2
+(0.72−0.7343)
2
+.....+(0.52−0.7343)
2
+(0.93−0.7343)
2
SD = 0.3928
Degree of freedom = n-1 = 6
The critical value for t at 2% level of significance and 6 degree of freedom is 2.043.
So,
90 \% \ confidence\ interval=Mean\pm Z\times \frac {SD}{\sqrt {n}}90% confidence interval=Mean±Z×
n
SD
So, applying values , we get:
CI=0.7343\pm 2.043\times \frac {0.3928}{\sqrt {7}}CI=0.7343±2.043×
7
0.3928
CI=(0.431,1.0376)CI=(0.431,1.0376)
9,874.35 - 6490.02
step by step
Answer:
[tex]9874.35 \\ 6490.02 \\ 3384.33[/tex]
How many pairs does a liminal have?
Answer:the answer to your intresting question is 3
Step-by-step explanation:
add me to brainiest if you want
All the prime numbers
Answer:
13 23 43
Step-by-step explanation:
Prime numbers are numbers that are divisible by 1 and itself or numbers that have only 2 factors which is 1 and itself.
What's a non-included angle?
Answer:
It is the side where the rays of the angles overlap. The "non-included" side in AAS can be either of the two sides that are not directly between the two angles being used.
factorise [8x^{2}-30x-27=0
Answer:
Step-by-step explanation:
8x² - 30x - 27 = 0
8 = 4 * 2
-27 = -9 * 3
-30 = 4*(-9) + 2*3
so (4x + 3)(2x - 9) = 0
A small can contain 2 cups of soup. do 3 small cans have a greater amount than a 1 - quart container of soup.
Answer:
quarts. 11. fluid ounces = —. 1. 4. — quart. 12. quarts = 6 gallons. 13. 16 pints = gallons. 14. ... How many times must a 1-cup measuring cup be filled to equal 4 pints? 2. Leroy has 2 containers. ... can hold. Write cup, pint, quart, or gallon. 15. a bathtub. 16. a container of orange juice. 17. a juice box. 18. a small milk carton. 1
Step-by-step explanation:
The 16th term of an AP is three times the 5th term.If the 12th term is 20 more the 7th term.Find the first term and the common difference
Let's take the first term as a and the common difference be d
The formula to find the nth term of an arithmetic progression is given by :
an = a + ( n - 1 ) dAccording to question, we have :
16th term of an AP is three times the 5th term.➝ a16 = 3 ( a5 )
➝ a + ( 16 - 1 )d = 3 ( a + ( 5 - 1 )d )
➝ a + 15d = 3 ( a + 4d )
➝ a + 15d = 3a + 12d
➝ 15d - 12d = 3a - a
➝ 3d = 2a
➝ 2a = 3d
➝ a = 3d/2ㅤㅤㅤ⸻ ( 1 )
And, the 12th term is 20 more the 7th term.➝ a12 - ( a7 ) = 20
➝ a + ( n - 1 )d -( a + ( n - 1 )d ) = 20
➝ a + ( 12 - 1 )d - + a + ( 7 - 1 )d ) = 20
➝ a + 11d - ( a + 6d ) = 20
➝ a - a + 11d - 6d = 20
➝ 5d = 20
➝ d = 20/ 5
➝ d = 4
Using equation ( 1 )➝ a = 3d / 2
➝ a = ( 3 × 4 ) / 2
➝ a = 12 / 2
➝ a = 6
A parabola has an axis of symmetry at x = 0.5 and one of the x-intercepts is at x=-3. Where is
the other x-intercept?
Answer:
4
Step-by-step explanation:
distance from .5 to -3 is 3.5
now add the same distance to the other side
.5 plus 3.5 is 4
In January, the depth of a lake was 1,178 feet. In August, the depth of the lake was 1,001.3 feet. What is the percentage decrease of the depth of the lake from January to August?
Answer:
15%
Step-by-step explanation:
decrease in depth = 1,178 - 1,001.3 = 176.7
percentage decrease = 176.7/1,178 = 0.15 = 15%
Help!
What is the answer to this question?
Answer:
b = 73°
Step-by-step explanation:
They are vertical angles to each other.
What is 2.95 expressed as a fraction?
5920
11880
33640
40118
2.95 expressed as a fraction is 59/20.
What is the fraction equivalent?The decimal is made up of a whole number and a non-integer. In order to convert the decimal to a fraction, divide the non-integer by 100 and add it to the whole number.
2 + 95/100
2 19/20
Now multiply the whole number by the denominator, add the numerator and then divide by the denominator. The result is:
59/20
To learn more about decimals, please check: https://brainly.com/question/15287678
Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 9 ounces. The process standard deviation is 0.15, and the process control is set at plus or minus 1 standard deviation. Units with weights less than 8.85 or greater than 9.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)
Answer:
[tex]1-P(8.85 < X < 9.15)=0.3173[/tex]
Step-by-step explanation:
We need to first calculate the probability that a unit between the weight of 8.85 and 9.15 ounces is NOT a defect, then subtract it from 1.
It just so happens that 8.85 and 9.15 are both 1 standard deviation from the mean of 9, so by the Empirical Rule, [tex]P(8.85 < X < 9.15)=0.6827[/tex].
Thus, the probability of a unit being a defect is [tex]1-P(8.85 < X < 9.15)=1-0.6827=0.3173[/tex]
Please i need your help
Answer:
it okay I can help you with that
Patrick usually jogs 1 1/2 miles each day but yesterday he jogged only 1/3 as far. How far did he run yesterday?
Answer:
You need to divide 11/2 by 1/3 and you will have you answer
Step-by-step explanation:
what is the elapse time between 10:35am and 1:10pm
2 hours, 35 minutes, and 0 second
Step-by-step explanation:
10 am to 1 pm is 2 hours
and you have the 35 in which you add there for giving you the answer 2 hours, 35 minutes, and 0 second
Answer:
2 hours 35 minutes
Step-by-step explanation:
On a map, Peach Street is modeled by the equation 4x - y = 7. Apple Street is perpendicular to Peach Street and passes through the point
(12, 2). Find the equation that models Apple Street (1 point)
A. Y=1/4x+5
B. Y=-1/4x-1
C. Y=1/4x-1
D. Y=-1/4x+5
Did you ever get the answer
You want to buy an ice cream cone but you want to make sure it’s worth your money, the cone has a radius of 1.4 inches and a height of 4.5 inches. How much ice cream will fit inside?
30 points please show work thanks so much :)
The amount of ice cream that can fit into the cone is about 9.24 in³.
What is volume?
Volume is the amount of space occupied by a three dimensional shape and object. The volume of a cone is given by:
Volume (V) = (1/3) * π * radius² * height
From the dimensions of radius = 1.4 in and height = 4.5 in, hence:
V = (1/3) * π * 1.4² * 4.5 = 9.24 in³
The amount of ice cream that can fit into the cone is about 9.24 in³.
Find out more on volume at: https://brainly.com/question/12410983
Using the volume of the cone, it is found that 9.24 cubic inches of ice cream will fit inside.
What is the volume of a cone?The volume of a cone of radius r and height h is given by:
[tex]V = \frac{\pi r^2h}{3}[/tex]
In this problem, the cone has a radius of 1.4 inches and a height of 4.5 inches, hence r = 1.4, h = 4.5, then:
[tex]V = \frac{\pi 1.4^2(4.5)}{3} = 9.24[/tex]
9.24 cubic inches of ice cream will fit inside.
More can be learned about the volume of a cone at https://brainly.com/question/14281550
find the slope and the y-intercept for the graph of y = -4.
a -4;none
b 1;-4
c 0; -4
d -4;0
thank you for the help
Answer:
C, 0;-4
Step-by-step explanation:
y=-4 means that no matter what the x value is, the y value will ALWAYS be -4. It does not change based on what x is, and we can tell that just by looking at it because x isn't even in the equation. I've attached an image of that the graph would look like.
The slope of the graph references how many units the y value increases for each increase in the x value. For example, a slope of 1/2 means that each time the x value increases by 2, the y value would increase by 1. But because y's value never changes, the slope is 0. No matter how much the x value changes, the increase in y values will be 0.
Since the y-axis is at where x=0, the y-intercept basically asks, "What is y's value when x is 0?" But like I mentioned before y's value never changes. It's always -4, no matter what the x value is. Therefore, the y-intercept is at -4.
In Ben's apartment complex, residents are fined $9 per day each day the rent is late. Last month, Ben wrote the apartment complex a check for $702 when his monthly rent is only $585. How many days late was Ben's rent?
Answer:
13 days late-poor guy
Step-by-step explanation:
(702-585)/9
117/9
13
“Firms will loss _?_ if the firm shuts down in the short run”
Answer:
The correct answer was C!
Step-by-step explanation:
Griffin bought 1.2 pounds of almonds for $6.60. His friend, Sam, bought almonds for $0.70 per pound cheaper. Which equation represents the cost, c, Sam paid for x pounds of almonds?
A.c = 4.80x
B. c = 5.50x
C. c = 5.90x
D. c = 7.30x
Answer:
Step-by-step explanation:
A
Answer: C
Step-by-step explanation:
0.70 divided by 1.2=0.59
0.59*1.2= 0.70
c=5.90x
Please help me with this I need it now :)
Answer:
reverse it x-15=4 do 15+4=x
Step-by-step explanation:
which algebraic expression is correct on this mathematical phrases?the qoutient of a and b multiplied by the difference of t and s
A.(axb)-(s-t) B. (axb)+(t-s) C.(a÷b)-(sxt) D.6a+2
please answer this fast i need it right now i'll give you brainleist
Answer:
D
Step-by-step explanation:
quotient of a and b: a ÷ b
multiplied: ×
difference of t and s: t - s
Therefore: (a ÷ b) × (t - s)
Answer:
D. (a/b) x (t-s)
Step-by-step explanation:
Given :-
The quotient of a and b multiplied by the difference of t and s.
Solving :-
Quotient of a and b = a/b
Difference of t and s = t - s
Multiplied together :-
(a/b) x (t-s)
Solution :-
D. (a/b) x (t-s)