Step-by-step explanation:
Consider the problem
Let, E 1 and E 2
be the respective events of items produced by machine A and B.
And let x be the event that the produced item was found to be defective.
Therefore,
Probability of items produced by machine A,P (E 1)=60%= 53
Probability of items produced by machine B,P (E 2)=40%= 52
And,
Probability that machine A produced defective items, P( E 1 x)=2%= 1002
Probability that machine B produced defective items, P( E 2 x)=1%= 1001
So, the probability that randomly selected items was from machine A is given by P( x E 1)
Now, Apply Bayes' Theorem
P( x E 1)= P(E 1)P( E 1x )+P(E 2)P( E 2x)P(E 1)P( E 1x)= 52× 1001 + 5
3× 1002
53× 100
2= 2+5
6= 11
6
Hence, the required probability of machine A is
11
6
The required answers are,
A.) The probability that the unit is defective is 0.046
B.) The probability that it was manufactured by machine M2 is 0.4
What is probability?Probability is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases.
Now given that,
Product produced by machine M1 = 60%
⇒ P(M1) = 60% = 0.6
Defective units = 5%
⇒ P(D1) = 5% = 0.05
Product produced by machine M2 = 40%
⇒ P(M2) = 40% = 0.4
Defective units = 4%
⇒ P(D2) = 4% = 0.04
Now, a unit is selected at random from the whole product
So, probability that it is defective is given as,
P(D) = P(D|M1) * P(D1) + P(D|M2) * P(D2)
⇒ P(M1|M2) = (0.6 X 0.05) + (0.4 X 0.04)
⇒ P(M1|M2) = 0.03 + 0.016
⇒ P(M1|M2) = 0.046
And probability that it was produced on the first machine(M2).
P(M2|D1) = P(M2∩D1) / P(D1)
⇒ P(M2|D) = (0.4 X 0.04)/0.04
⇒ P(M2|D) = 0.016 / 0.04
⇒ P(M2|D) = 0.4
Thus, the required answers are,
A.) The probability that the unit is defective is 0.046
B.) The probability that it was manufactured by machine M2 is 0.4
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Give 0.25ml twice a day for 8 days what is the quantity to dispense
Answer:
4 mL
Step-by-step explanation:
Multiply .25 by 2 because you are dispensing it twice a day.
.25 x 2 = .5, so you dispense .5 mL a day.
Now, multiply .5 mL a day x 8 days.
.5 x 8 = 4
Therefore, you should dispense 4 mL.
Please answer the questions below:
1. 3(16x+2)
2. 2(18+24x)
3. 4(12x+8)
4. 6(6+8x)
Thanks for helping♥️
Answer:
1. 48x+6
2.36+48x
3.48x+32
4.36+48x
I think it will help you.
People attending a basketball game either supported the home team or the visiting team. If 576 of the people attending supported the home team and 1224 supported the visiting team, what percentage supported the home team?
Answer:
32%
Step-by-step explanation:
1224 + 576 = 1800
100% = 1800
1% = 18 (divide by 100)
576 / 18 = 32
32% = 576
Answer:
32%
Step-by-step explanation:
576+1224=1800
576/1800=32/100
32%
For what value of x is the given parallelogram a rhombus ?
Answer:
x = 6
Both the angles are equal
7x + 4 = 9x - 8
9x - 7x = 4 + 8
2x = 12
x = 6
Solution:
We know that:
Both angles are equivalent.This means that:
[tex](7x + 4) = (9x - 8)[/tex]Step-by step calculations:
Open the parenthesis:
[tex](7x + 4) = (9x - 8)[/tex]=> [tex]7x + 4 = 9x - 8[/tex]Subtract 7x both sides:
=> [tex]7x - 7x + 4 = 9x - 8 - 7x[/tex]=> [tex]4 = 2x - 8[/tex]Add 8 both sides:
=> [tex]4 + 8 = 2x - 8 + 8[/tex]=> [tex]12 = 2x[/tex]Divide 2 both sides:
=> [tex]\frac{12}{2} = \frac{2x}{2}[/tex]=> [tex]x = 6[/tex]Tutorial
A cylinder has a height of 17 centimeters and a radius of 15 centimeters. What is its volume?
Use 3.14 and round your answer to the nearest hundredth.
Answer:
Volume of the cylinder is 12016.5 cm³[tex] \\ [/tex]
Step-by-step explanation:
Using formula:
[tex] \: \: \: \: \: \: \: \: \: \: {\underline{\boxed {\pmb{ \sf{Volume \: of \: cylinder = \pi r^2h}}}}} \: \pink\star [/tex]
[tex] \\ [/tex]
Where,
Height of cylinder is 17 cmRadius of the cylinder is 15 cm.Value of π = 3.14[tex] \\ [/tex]
Substituting the required values in the above formula :
[tex] \\ [/tex]
[tex] \dashrightarrow \sf \: \: Volume = 3.14 \times {(15)}^{2} \times 17 \\ \\ [/tex]
[tex]\dashrightarrow \sf \: \: Volume = 3.14 \times 225 \times 17 \\ \\ [/tex]
[tex]\dashrightarrow \sf \: \: Volume = 706.5 \times 17 \\ \\ [/tex]
[tex]\dashrightarrow~~{\boxed {\pink{\pmb{\sf {Volume = 12016.5 \: {cm}^{3}}}}}} \\ \\ [/tex]
Hence,
Volume of cylinder is 12016.5 cm³Answer :
12000 cm³⠀
Explanation :
We know,
[tex]{ \longrightarrow \qquad{\boldsymbol {\pmb{ Volume_{(cylinder)} = \pi {r}^{2} h \: }}}}[/tex]
Where,
r is the radius of the cylinder. Here, the radius is 15 cm . h is the height of the cylinder. Here, height is 17 cm Here, we will take the value of π as 3.14 approximately .⠀
Substituting the values in the formula :
[tex]{ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \times ({15})^{2} \times 17 \: }}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \: \times 225 \times 17}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \times 3825 }}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ \pmb{ \sf{ Volume_{(cylinder)} = 12010.5 }}}}[/tex]
⠀
Therefore,
The volume of the cylinder is 12000 cm³ . (Rounded to nearest hundredth)The area of a trapezoid is 30 cm². If the bases measure 9 cm and 11 cm, what is the height of the trapezoid?
Answer:
3cm
Step-by-step explanation:
uhh i drew it but i cant show picture hope this is right tho!!!
A tank contains 340 liters of water when it begins to leak at a rate of 6 liters per minute into an empty container. Which equation shows the number of minutes, x, it will take for the tank and
the container to have the same amount of water?
The equation that shows the number of minutes, x, it will take for the tank and the container to have the same amount of water will be 340 - 6x = 6x.
Based on the information given, the equation that shows the number of minutes, x, it will take for the tank and the container to have the same amount of water will be 340 - 6x = 6x. Therefore, the number of minutes will be:
340 - 6x = 6x
Collect like terms
340 = 6x + 6x
340 = 12x
x = 340/12
x = 28.33 minutes.
In 28.33 minutes, they'll have the same content.
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An internet company charges $12 per gigabyte of data plus a monthly service charge of $18. Last month, Niki's bill was $78. Write an equation to find how many gigabytes of data Niki used last month.
Answer:
5 gigabytes
Step-by-step explanation:
gb = gigabytes
bill - monthly service charge = gigabytes only bill
gigabytes only bill divided by charges per gigabyte = gb of data used
78 - 18 = 60
60 divided by 12 = 5
18
78
What is the value of 3 to the power 2 over 3 to the power 4?
1 over 81
1 over 27
1 over 9
1 over 3
Answer:
1 over 9
Step-by-step explanation:
3^2= 9 =1
3^4= 81 =9
Ans:1over9
The area of a triangle is 64 in2. The base of the triangle is twice as long as the height. The base of the triangle is and the height of the triangle is
Answer:
Step-by-step explanation:
Area=bh/2=64, b=2h --->h2=64 --> h=8 (positive root) and b=16.
solve: |x-1|=1
can someone help fast im confused
Answer:
The equation has two answers
X = 0
X = 2
Step-by-step explanation:
The answer is absolute value or positive or negative, So it is
[tex] |x - 1| = 1[/tex]
[tex] |x - 1| = - 1[/tex]
We solve the equations and the answer is obtained
Hey there!
|x - 1| = 1
TRANSLATE:
x - 1 = 1 or x - 1 = -1
SOLVING for: x - 1 = 1
x - 1 = 1
ADD 1 to BOTH SIDES
x - 1 + 1 = 1 + 1
CANCEL out: -1 + 1 because it give you 0
KEEP: 1 + 1 because it help solve for the current x-value
NEW EQUATION: x = 1 + 1
SIMPLIFY IT!
x = 2
Thus, your answer is: x = 2
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
SOLVING for: x - 1 = -1
x - 1 = -1
ADD 1 to BOTH SIDES
x - 1 + 1 = -1 + 1
CANCEL out: -1 + 1 (the LEFT SIDE) because it give you 0
KEEP: -1 + 1 (the RIGHT SIDE) because it give you the current x-value
NEW EQUATION: x = -1 + 1
SIMPLIFY IT!
x = 0
Thus, your answer is: x = 0
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
Therefore, your overall answer is:
x = 2 or x = 0
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Can anyone tell me why I got this wrong?
-3(x+2)>15 or x-3 ≤ -1
my answer was ( -7, 2 )
The options are
A. ( - infinity, 2)
B. (-7, -2)
C. [ - 7, infinity)
D. ( -7, 2)
Answer:
The answer should be A. [tex]x \in (-\infty,\, 2)[/tex].
Step-by-step explanation:
Start with the second inequality, which is more straightforward than the first. Add [tex]3[/tex] to both sides of this equation to separate [tex]x[/tex] from the numbers:
[tex]x - 3 + 3 \le -1 + 3[/tex]. The direction of the inequality sign shall stay the same.
[tex]x \le 2[/tex].
On the other hand, simplifying the first inequality takes a bit more work. Start by dividing both sides by [tex](-3)[/tex]. However, keep in mind that dividing or multiplying both sides of an inequality with a negative number will invert the direction of the inequality sign. For example, the left-hand side of an inequality might have been greater than the right-hand side. When both sides are multiplied with a number less than zero, the new left-hand side would become smaller than the new right-hand side.
Because [tex](-3)\![/tex] is a negative number, dividing both sides of the first inequality inequality by [tex](-3)[/tex] will turn the "greater-than" sign into a "less-than" sign.
The inequality used to be:
[tex]-3\, (x + 2) > 15[/tex].
After dividing both sides by the negative number [tex](-3)[/tex], it becomes:
[tex]\displaystyle \frac{(-3)\, (x + 2 )}{(-3)} < \frac{15}{(-3)}[/tex].
[tex]\displaystyle (x + 2) < -5[/tex].
[tex]x < -7[/tex].
The question connected the two original inequalities with "or". Therefore, the conditions will be satisfied as long as either of at least one of the two inequalities is true. Note, that [tex]x < 2[/tex] is true whenever [tex]x <-7[/tex] is true. Therefore, any real number that is smaller than [tex]2[/tex] will meet the requirements- not just those that are smaller than [tex](-7)[/tex].
The corresponding interval will be [tex](-\infty,\, 2)[/tex].
You need a 40% alcohol solution. On hand, you have a 540 mL of a 10% alcohol mixture. How much pure alcohol will you need to add to obtain the desired solution?
Answer:
270 mL of pure alcohol is needed.
Step-by-step explanation:
In 540 mL of the mixture, you have 540*10% = 54 mL of pure alcohol.
If you add x mL pure alcohol, then you have (540 + x) mL solution, in it there is (54 + x) mL of pure alcohol
so (54 + x)/(540 + x) = 40%
Then
54 + x = 0.4(540 + x)
54 + x = 216 + 0.4 x
0.6x = 216 - 54 = 162
x = 162/0.6 = 270 mL
GIVING BRAINLIST ON TIMER
✏️VOLUME
Solution:
Figure #1.
Since the given is a rectangular prism, use the formula:
V = lwhWhere:
l - lengthw - widthh - heightGiven:
l = 15 in.w = 6 in.h = 8 in.» Substitute the givens on the formula.
V = lwhV = (15 in.)(6 in.)(8 in.)V = (90 in.²)(18 in.)V = 1 620 in.³Therefore, the volume of the rectangular prism is 1 620 in.³
Figure #2
Since the given a cube, use the formula:
e³Where:
e - edgeGiven:
e = 9 in.» Substitute the given on the formula.
e³(9 in.)³(9 in.)(9 in.)(9 in.)729 in.³Therefore, the volume of the cube is 729 in.³
Figure #3
Since the given is a cylinder, use the formula:
V = πr²hWhere:
π - pi (3.14)r - radiush - heightGiven:
r = 8 in.h = 14 in.» Substitute the givens on the formula.
V = πr²hV = (3.14)(8 in.)(14 in.)V = (25.12 in.)(14 in.)V = 351.68 in.³Therefore, the volume of the cylinder is 351.68 in.³
Answer:
Number #1
1 620 in.³Number #2
729 in.³Number #3
351.68 in.³•••••••••••••••••••••••••••••••••••••••••••••••••
#CarryOnLearning
Please help I'll mark brainliest
Answer:
The correct answer is 2:1 :)
Answer:
4:2
Step-by-step explanation:
1. The data set represents the amounts of time (in minutes) spent watching
online videos each day for a random sample of 30 college students.
Assume the population standard deviation is 2.4 minutes. (Adapted from
the Council for Research Excellence)
5.0 6.25 8.0 5.5 4.75 4.5 7.2 6.6 5.8
4.2 5.4 6.75 9.8 8.2 6.4 7.8 6.5 5.5
3.8 6.75 9.25 10.0 9.6 7.2 6.4 6.8 9.8 10.2
(a) Find the point estimate of the population mean.
(b) Find the margin of error for a 95% confidence level.
(c) Construct a 95% confidence interval for the population mean.
Interpret the results.
5.5
6.0
Never gonna give you up, never gonna let you down, never gonna run around and dessert you.
Workout the solution for the equation: 3a = 15
Please help as soon as possible :D
Answer:
a = 5
Step-by-step explanation:
a = 5
all you have to do is divide both sides by 3
Answer:
A=5
Step-by-step explanation:
Divide each term by 3 and simplify :)
Hope I helped!
Cindy is driving 345 miles. She put 16 gallons in her car to fill it up. What is her average MPG?
21.5
16
18.75
20
Answer:
MPG is miles per gallon so we just need to divide the miles by the gallons
345/16=21.56
so i guess a?
i mean thats rounded wrong but its the closes one
a
Hope This Helps!!!
If x equals 8 - (-2.25) and y equals 6 - 4.2 - (-4.9), what is the value of x - y?
Answer:
3.55
Step-by-step explanation:
This is simply combining like terms.
First, lets evaluate the terms separately.
x = 8 - (-2.25)
x = 8 + 2.25 (Negative signs cancel out)
x = 10.25 (Combine like terms)
y = 6 - 4.2 - (-4.9)
y = 6 - 4.2 + 4.9 (Negative signs cancel out)
y = 6.7 (Combine like terms)
Now, lets plug in these values to x - y.
(10.25) - (6.7)
3.55
The value of x - y is equal to 3.55.
How do I find the value of X
Answer:
x = 12
Step-by-step explanation:
ΔABC is a right triangle, therefore we can use Pythagoras' Theorem to find the value of x.
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Therefore,
a = xb = 16c = 20Substitute these values into the equation and solve for x:
⇒ x² + 16² = 20²
⇒ x² + 256 = 400
⇒ x² = 400 - 256
⇒ x² = 144
⇒ x = √(144)
⇒ x = ±12
As length is positive, x = 12 units (only)
Which of the following is the inverse of f(x) = 3-x/5
Answer:
The correct answer is, F-1(x) = 5(x-3)/3
Step-by-step explanation:
The inverse of given function f(x) = 3-x/5 would be equal to 3(x - 5)/5
What is the inverse of a function?Suppose that the given function is [tex]f:X\rightarrow Y[/tex]Then if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is ;
[tex]f^{-1}: Y \rightarrow X[/tex]
We have been given a function of x as ; 3-x/5.
To find the inverse we will just switch x and function of x with each other.
That means we have;
x = 5/3 f(x) + 5
5/3 f(x) = x - 5
f(x) = 3(x - 5)/5
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The ratio of children to adults at a play is 2:3. The ratio of children under 10 to those over 10 is 7: 3. What % are younger children?
Answer:
28%
Step-by-step explanation:
Let number of children be 2x, then number of adults be 3x
Total number is 5x
Let number of children under 10 be 7y, number of children be 3y,
then total number of children is 10y
so 2x = 10y, x = 5y, y/x = 1/5
younger children = children under 10, number is 7y
so the % is 7y/5x = 7/5 * y/x = 7/5 * 1/5 = 7/25 = 28/100 = 28%
shapes th
7. Hilary flew from Denver to Atlanta for
business. From Atlanta, she flew to Chicago
to visit her aunt. From Chicago, she flew
back home to Denver. Classify the triangle
made by her complete flight path.
this pro
8. How many miles complete the triangle made
by Hilary's flight path?
7 and 8 please
Hilary trip is an illustration of a scalene triangle
The triangle that represents Hilary's trip can be classified as a scalene triangleHilary completed 2717 milesClassify the triangleThe triangle that represents Hilary's trip can be classified by the side lengths.
From the figure, the side lengths of the triangles are:
919 miles, 586 miles and 1212 miles
The lengths are not equal.
Triangles that do not have equal side lengths are scalene triangles
Hence, the triangle that represents Hilary's trip is a scalene triangle
The miles completed by HilaryTo do this, we simply calculate the perimeter of the triangle.
So, we have:
P = 919 miles + 586 miles + 1212 miles
P = 2717 miles
Hence, Hilary completed 2717 miles
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A fish tank has 240240240 quarts of water. Levi adds another 120120120 quarts to the tank.
How many gallons of water are in the fish tank? HURRY PLS :(
Answer:
90090090 quarts to fill the fish tank
At the beginning of a certain study of a group of persons, 15% were classified as heavy smokers, 30% as light smokers, and 55% as nonsmokers. In the five-year study, it was determined that the death rates of the heavy and light smokers were five and three times that of the nonsmokers, respectively. A randomly selected participant died over the five-year period: calculate the probability that the participant was a nonsmoker.
The probability that the participant was a nonsmoker is 25%.
ProbabilityGiven that at the beginning of a certain study of a group of persons, 15% were classified as heavy smokers, 30% as light smokers, and 55% as nonsmokers, and in the five-year study, it was determined that the death rates of the heavy and light smokers were five and three times that of the nonsmokers, respectively, to calculate, if a randomly selected participant died over the five-year period, the probability that the participant was a nonsmoker, the following calculation must be performed:
15 x 5 = 7530 x 3 = 9055 = 5555 + 90 + 75 = 220220 = 10055 = X55 x 100 / 220 = x5500 / 220 = X25 = XTherefore, the probability that the participant was a nonsmoker is 25%.
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How many lines of symmetry does the picture have ?
Answer:
A. 3Step-by-step explanation:
Salamat po ikaw na pong bahala kung Tama po
what is the mean of these numbers
5
4
1
8
5
Answer:
4.6
Step-by-step explanation:
to find mean you add up all the numbers then divide by how many numbers there are. 5+4+1+8+5= 23 Since there are 5 numbers you divide 23 by 5 which equals 4.6
Find the perimeter 4cm 8 cm 4cm
Answer:
perimeter= a+b+c
Step-by-step explanation:
perimeter= 4+8+4= 16cm
How do I find the left side of BC
"bc is twice half of angle D"
A rectangular prism with a volume of 10 cubic units is filled with cubes with side length of 1/2 unit
We know that:
[tex]1. \space\ V_{Rectangular \space\ prism} = 10 \text\] units^{3}\\\\2. \space\ L_{Small \space\ cube} = \frac{1}{2} \space\ units\\\\ 3. \space\ V_{Small \space\ cube} = L ^{3}[/tex]
Step-1: Find the volume of the small cube.
[tex]V_{Small \space\ cube} = L ^{3}[/tex]
[tex]V_{Small \space\ cube} = (\frac{1}{2}) ^{3}[/tex]
[tex]V_{Small \space\ cube} = (\frac{1}{2}) (\frac{1}{2}) (\frac{1}{2})[/tex]
[tex]V_{Small \space\ cube} = \frac{1}{8} \space\ units^{3}[/tex]
Step-2: Divide.
[tex]\frac{10}{\frac{1}{8} }\\\\ \Rrightarrow(10)(8)\\ \\ \Rrightarrow 80[/tex]
Hence, 80 cubes can be fit in the rectangular prism.
volume of rectangular prism = 10 units³
volume of each cube = [tex]\frac{1}{2} \times\frac{1}{2} \times\frac{1}{2} = \frac{1}{8} units^3[/tex]
required cubes = [tex]\frac{10}{ \frac{1}{8} }= 80[/tex]