Answer:
The probability that it came from A, given that is defective is 0.362.
Step-by-step explanation:
Define the events:
A: The element comes from A.
B: The element comes from B.
C: The element comes from C.
D: The elemens is defective.
We are given that P(A) = 0.25, P(B) = 0.35, P(C) = 0.4. Recall that since the element comes from only one of the machines, if an element is defective, it comes either from A, B or C. Using the probability axioms, we can calculate that
[tex]P(D) = P(A\cap D) + P(B\cap D) + P(C\cap D)[/tex]
Recall that given events E,F the conditional probability of E given F is defined as
[tex]P(E|F) = \frac{P(E\cap F)}{P(F)}[/tex], from where we deduce that
[tex]P(E\cap F) = P(E|F)P(F)[/tex].
We are given that given that the element is from A, the probability of being defective is 5%. That is P(D|A) =0.05. Using the previous analysis we get that
[tex] P(D) = P(A)P(D|A)+P(B) P(D|B) + P(C)P(D|C) = 0.05\cdot 0.25+0.04\cdot 0.35+0.02\cdot 0.4 = 0.0345[/tex]
We are told to calculate P(A|D), then using the formulas we have
[tex] P(A|D) = \frac{P(A\cap D)}{P(D)}= \frac{P(D|A)P(A)}{P(D)}= \frac{0.05\cdot 0.25}{0.0345}= 0.36231884[/tex]
3(12−5)+(8x8)-45? Answer?
Answer:
its 40
Step-by-step explanation:
i think
A fraction that is equivalent to 6/-5?
Answer:
12/-10
Step-by-step explanation:
Any multiple of a fraction is the equivalent of the original fraction, the only difference is that it wont be fully simplified. If we multiply the original fraction (6/-5) by 2, both the numerator and denominator, you will get 12/-10.
Answer:
12/-10
Step-by-step explanation:
6/-5
6×2= 12
-5×2=-10
12/-10
Brittany Monroe is a legal secretary. Her biweekly salary is $1,650.00 what is her annual salary?
Answer:
$42,900 a year
Step-by-step explanation:
so there are 26 bi-weeks in a year. (fun fact)
you take $1,650 and multiply that biweekly to get her annual salary.
1650*26=42,900
Equations
What is the solution of the system of linear equations?
-3x + 4y = -18
2x - y = 7
(-2,-3)
(-2,3)
(2, -3)
(2, 3)
Answer:
Step-by-step explanation:
-3x + 4y = -18
8x - 4y = 28
5x = 10
x = 2
4 - y = 7
-y = 3
y = -3
(2, -3)
The solution of the system of linear equations given is (2,-3), the correct option is C.
What is System of Linear Equation?The system of linear equation is set of equations which have a common solution.
The equations are
-3x+4y = -18
2x-y =7
The linear equations can be solved using substitution method
y = 2x -7 from equation 2 will be substituted in equation 1
-3x +4 ( 2x -7) = -18
-3x +8x -28 = -18
5x = 10
x = 2
y = 2 * 2 -7 = -3
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what is the degree of x^4-3x+22
Answer:
4
Step-by-step explanation:
The degree is the highest power on the exponent when they are lined up from highest to lowest
The degree is 4
6
An ordinary fair dice is thrown once.
(a) On the probability scale mark with a cross (X) the probability ti
the dice lands on an even number.
1
2
(b) Write down the probability that the dice lands on a number les
than 3.
Answer:
(a) 1/2(b) 1/3Step-by-step explanation:
(a) 3 of the 6 numbers on the die are even, so the probability that one of them will show is 3/6 = 1/2.
__
(b) 2 of the 6 numbers on the die are less than 3, so the probability that one of them will show is 2/6 = 1/3.
help plz now quick if right brain list
Answer:
c= 5 yards.
Step-by-step explanation:
4*1.5=6
30/6= 5
Is the statement "The solution set of a linear system involving variables x 1 comma ... comma x Subscript n is a list of numbers (s 1 comma ... comma s Subscript n Baseline )that makes each equation in the system a true statement when the values s 1 comma ... comma s Subscript n are substituted for x 1 comma ... comma x Subscript n Baseline comma respectively" true or false? Explain. A. True, because the list of variables (x 1 comma ... comma x Subscript n Baseline )and the list of numbers (s 1 comma ... comma s Subscript n Baseline )have a one-to-one correspondence. B. False, because the description applies to a single solution. The solution set consists of all possible solutions.
Answer:
B. False, because the description applies to a single solution. The solution set consists of all possible solutions.
Step-by-step explanation:
The choice of true or false revolves around whether a linear system can have more than one solution.
The problem statement does not say the equations are independent, a condition that must be satisfied if there is to be only one solution. Hence we must assume that the system may be dependent or even inconsistent, leading to zero, one, or an infinite number of solutions. The answer above carries its own explanation.
False, for the reason given
which of the following is an expression for”doubling a number n and dividing by 3”?
Answer:
2n/3
Step-by-step explanation:
hope this helps!! moo
256 divided by -16 with steps.
Answer:
256÷-16=16
Step-by-step explanation:
The complete expression is 256 divided by -16 is -16
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
256 divided by -16 = what
When represented as an equation, we have
Result = 256 divided by -16
Make the result the subject of the formula
So, we have
Result = 256/-16
Rewrite as
Result = -256/16
Evaluate the quotient
Result = -16
Hence, the number is -16
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Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
Answer:
A. p + q = b
D. p · q = c
Step-by-step explanation:
It's best to look at an example, such as this:
[tex]x^2 - 12x + 35[/tex]
And it's factored form is:
(x - 5) (x - 7)
As you can see, if you add -5 (p) and -7 (q), you get -12 (b). Then, if you multiply -5 (p) and -7 (q), you get 35 (c).
Answer:
A and D
Step-by-step explanation:
STOP REPORTING MY ANSWER!!
Kono Dio Da!!!
Which fraction is in simplest form 4/20 6/9 5/13 14/21
Answer: 5/13
Step-by-step explanation:
Answer:
5/13 is in simplest form, because it cannot be reduced any further.
Step-by-step explanation: 4/20 can be reduced to 1/5, 6/9 to 1/3, and 14/21 can be reduced to 2/3
How to factor this trinomial(a=1)?
Answer:
The answer is (x+8)(x-3) .
Step-by-step explanation:
First, you have to elaborate out :
[tex] {x}^{2} + 5x - 24[/tex]
[tex] = {x}^{2} - 3x + 8x - 24[/tex]
Next, you can factor out the like terms :
[tex] {x}^{2} - 3x + 8x - 24[/tex]
[tex] = x(x - 3) + 8(x - 3)[/tex]
[tex] = (x - 3)(x + 8)[/tex]
Answer:(x-3)(x+8)
Step-by-step explanation:
x^2+5x-24
We first find two numbers whose product is -24 and whose sum is 5,the two numbers are 8 and -3,we then removed +5x from the equation and replace it with +8x-3x
x^2+8x-3x-24
We factorise
x(x+8)-3(x+8)
We factorise the like terms which is (x+8)
(x-3)(x+8)
Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 43.5 and standard deviation of 4.1 while the second sample has a mean of 40.1 and standard deviation of 3.2. A researcher would like to test if there is a difference between the population means at the 0.05 significance level. What can the researcher conclude?
Answer:
[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]
The degrees of freedom are
[tex]df=20+20-2=38[/tex]
And the p value is given by:
[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]
Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different
Step-by-step explanation:
When we have two independent samples from two normal distributions with equal variances we are assuming that
[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]
And the statistic is given by this formula:
[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}[/tex]
Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:
[tex]S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]
The system of hypothesis on this case are:
Null hypothesis: [tex]\mu_1 = \mu_2[/tex]
Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]
We have the following data given:
[tex]n_1 =20[/tex] represent the sample size for group 1
[tex]n_2 =20[/tex] represent the sample size for group 2
[tex]\bar X_1 =43.5[/tex] represent the sample mean for the group 1
[tex]\bar X_2 =40.1[/tex] represent the sample mean for the group 2
[tex]s_1=4.1[/tex] represent the sample standard deviation for group 1
[tex]s_2=3.2[/tex] represent the sample standard deviation for group 2
First we can begin finding the pooled variance:
[tex]\S^2_p =\frac{(20-1)(4.1)^2 +(20 -1)(3.2)^2}{20 +20 -2}=13.525[/tex]
And the deviation would be just the square root of the variance:
[tex]S_p=3.678[/tex]
The statistic is givne by:
[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]
The degrees of freedom are
[tex]df=20+20-2=38[/tex]
And the p value is given by:
[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]
Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different
Using the t-distribution, as we have the standard deviation for the sample, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.
What are the hypothesis tested?At the null hypothesis, it is tested if there is no difference, that is:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternative hypothesis, it is tested if there is a difference, that is:
[tex]H_a: \mu_1 - \mu_2 \neq 0[/tex]
What is the mean and the standard error of the distribution of differences?For each sample, we have that they are given by
[tex]\mu_1 = 43.5, s_1 = \frac{4.1}{\sqrt{20}} = 0.9168[/tex]
[tex]\mu_2 = 40.2, s_2 = \frac{3.2}{\sqrt{20}} = 0.7155[/tex]
Hence, for the distribution of differences, the mean and the standard error are given by:
[tex]\overline{x} = \mu_1 - \mu_2 = 43.5 - 40.2 = 3.3[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.9168^2 + 0.7155^2} = 1.163[/tex]
What is the test statistic?It is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{3.3 - 0}{1.163}[/tex]
[tex]t = 2.84[/tex]
What is the decision?Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 20 + 20 - 2 = 38 df, the critical value is of [tex]|z^{\ast}| = 2.0244[/tex].
Since the absolute value of the test statistic is greater than the critical value, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.
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Sara goes on a slingshot ride in an amusement park. She is strapped into a spherical ball that has a radius of centimeters. What is the volume of air in the spherical ball? Use this formula: , where r is the sphere’s radius.
A.
B.
C.
D.
Answer:
A. 4×π×3²×[tex]10^{6}[/tex]
Step-by-step explanation:
r = 3×10² = 3×100 = 300
[tex]\frac{4}{3}[/tex]×π×300³=
[tex]\frac{4}{3}[/tex]×π×27,000,000=
[tex]\frac{108,000,000}{3}[/tex]×π=
36,000,000π
Answers solved:
A. 36,000,000π
B. 108,000,000π
C. 3,600,000π
D. 32,400,000π
The solution is Option A.
The volume of the air in the spherical ball is given by the equation
V = 4π ( 3 )² ( 10 )⁶ cm³
What is a Sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the volume of the sphere be represented as V
Now , the radius of the spherical ball be r
The value of r = 3 ( 10 )² cm
So , the volume of the spherical ball = ( 4/3 ) πr³
Substituting the values in the equation , we get
Volume of the spherical ball V = ( 4/3 ) x π x [ 3 ( 10 )² ]³
On simplifying the equation , we get
Volume of the spherical ball V = ( 4/3 ) x π x ( 3 )³ ( 10 )⁶
Volume of the spherical ball V = 4 x π x ( 3 )² ( 10 )⁶
Therefore , the value of V is 4π ( 3 )² ( 10 )⁶
Hence , the volume of the spherical ball is 4π ( 3 )² ( 10 )⁶
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A local retailer claims that the mean waiting time is less than 8 minutes. A random sample of 20 waiting times has a mean of 6.3 minutes with a standard deviation of 2.1 minutes. At α = 0.01, test the retailer's claim. Assume the distribution is normally distributed. Round the test statistic to the nearest thousandth.
Answer:
The claim is not true
Step-by-step explanation:
We are given that A local retailer claims that the mean waiting time is less than 8 minutes.
[tex]H_0:\mu=8[/tex]
[tex]H_a:\mu<8[/tex]
A random sample of 20 waiting times has a mean of 6.3 minutes with a standard deviation of 2.1 minutes.
[tex]\bar{x}=6.3[/tex]
s = 2.1
n = 20
Since n <30 and population standard deviation is unknown
So,we will use t test
So,[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t=\frac{6.3-8}{\frac{2.1}{\sqrt{20}}}[/tex]
t=-3.62
α = 0.01
Degree of freedom = df=n-1=20-1=19
[tex]t_{df,\frac{\alpha}{2}}=t_{19,\frac{0.01}{2}}=2.861[/tex]
t calculated < t critical
So, we failed to reject null hypothesis
Hence the claim is not true
what is the best college to go to?
Answer:
The the best college to go to is the one where you feel comfortable.
Step-by-step explanation:
It is so important to understand the sence of what is actually "the best" college to go to.
You can look at that from a viriety of perspectives, and it is debatable to just go for the college which holds the highest rank on some site.
There are a lot of factors to consider, and what is generally considered the best college does not necassarilly the right one for you.
Ask your loved ones for advice and if you can take a look at yourvtop thee collages.
The the best college to go to is the one where you feel comfortable.
Factor x2 – 8x + 15.
Which pair of numbers has a product of ac and a sum of b?
Answer:
(x - 5)(x - 3)
Step-by-step explanation:
[tex] {x}^{2} - 8x + 15 \\ = {x}^{2} - 5x - 3x + 15 \\ = x(x - 5) - 3(x - 5) \\ = (x - 5)(x - 3) \\ \\ ac = ( - 5) (- 3) = 15 \\ a + c = - 5 - 3 = - 8[/tex]
Classify this triangle.
Acute scalene triangle
Obtuse isosceles triangle
Right isosceles triangle
Right scalene triangle
Answer: right isosceles
Step-by-step explanation:
the angle at the bottom is right therefore you need to figure out the lengths of the sides to conclude if it is isosceles or scalene. because two of the sides are the same length and the other is not it is isosceles
Please help ASAP! Will give BRAINLIEST! Please read the questionTHEN answer correctly! No guessing.
Answer:D
Step-by-step explanation:
(4/5)^0
4^0/5^0=1/1=1
a clock chimes once at 1, twice at 2
Answer:
3 times at 3
Step-by-step explanation:
What is the slope of a line that is parallel to the line
represented by the equation y- 4x = 1?
Answer:
m=4
Step-by-step explanation:
First get the equation in slope intercept form
y -4x =1
Add 4x to each side
y - 4x+4x = 4x+1
y = 4x+1
This is in the form
y = mx+b where m is the slope and b is the y intercept
The slope is 4
Parallel lines have the same slope
m =4
What is the volume of this cube with a side length of 6 centimeters
6 cm
Answer:
V = 216 cm^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length
V = (6)^3
V = 216 cm^3
Answer:216 cm^3
Step-by-step explanation:
In cube, the length of all sides are equal
length of side=6cm
Volume of cube=length x length x length
Volume of cube=6 x 6 x 6
Volume of cube=216
Volume of cube=216 cm^3
A line with a slope of -7 passes through the points (10,v) (9,4) What is the value of V?
Answer:
-3
Step-by-step explanation:
An increase in x-value from 9 to 10 is an increase of 1 unit. The slope of -7 tells you that the corresponding change in y will by -7 units:
v = 4 -7 = -3
The value of v is -3.
_____
Alternate solutions
You can see this easily on a graph, or you can use the equation of the line. We have a point and a slope, so the point-slope form is useful.
y = m(x -h) +k
y = -7(x -9) +4
For x=10, the value of y is ...
v = -7(10 -9) +4 = -7 +4
v = -3
EASY
A broken thermometer reads 33° F, but Kira knows that the temperature is at least 33° F, if not even colder. Which of the following inequalities, shows the possible temperatures?
t ≤ 33° F
t ≥ 33° F
t > 33° F
t < 33° F
Answer: t ≥ 33
Step-by-step explanation:
So the temperature has to equal to 33 or less than 33.It can't be greater than 33.
Help ASAP giving BRAINLIEST! Am i correct?
Answer:
You are correct
Step-by-step explanation:
x - 8 < 23
Add 8 to both sides
x - 8 + 8 < 23 + 8
Simplify
x < 31
Yes, you are correct.
How many seconds would it take to fill up one gallon
Answer:
5 seconds
Step-by-step explanation:
(60 / seconds = GPM)
60 / 5 = 12 GPM
12 GPM = 60 seconds
Simplified
1 Gallon is 5 seconds
Answer:
5
Step-by-step explanation:
Joe earns $750 each week working his full time job. His employer has a
9.75% tax deduction on all monies earned each week.
Answer:
After tax deduction he makes $676.875 a week
Step-by-step explanation:
9.75% of 750 is 71.125
750-71.125 is 676.875
Employees that work at a fish store must measure the level of nitrites in the water each day. Nitrite levels should remain lower than 5 ppm as to not harm the fish. The nitrite level varies according to a distribution that is approximately normal with a mean of 3 ppm. The probability that the nitrite level is less than 2 ppm is 0.0918.
1. Which of the following is closest to the probability that on a randomly selected day the nitrite level will be at least 5 ppm?
(A) 0.0039
(B) 0.0266
(C) 0.0918
(D) 0.7519
(E) 0.9961
Answer: .0039
Step-by-step explanation:
Using the information below, Solve for x. Show Your Work with your answer.
X + 2y = 5
2x + y = 12
-2(x + 2y = 5)
-2x - 4y = - 10
-2x - 4y = -10
2x + 6y = 12
_____________
2y = 2
————————
2 2
y=1
[insert answer here]
Step-by-step explanation:
