Answer:
0.82% probability the engineer accepts the shipment
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 500, p = 0.04[/tex]
So
[tex]E(X) = np = 500*0.04 = 20[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.04*0.96} = 4.3818[/tex]
What is the probability the engineer accepts the shipment?
Less than 10 defective. Using continuity correction, this is [tex]P(X < 10 - 0.5) = P(X < 9.5)[/tex], which is the pvalue of Z when X = 9.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.5 - 20}{4.3818}[/tex]
[tex]Z = -2.4[/tex]
[tex]Z = -2.4[/tex] has a pvalue of 0.0082
0.82% probability the engineer accepts the shipment
x = 16 18 34 can someone explain please?
Answer:
x = 16
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(x+2) * 2 = 6^2
2(x+2) = 36
Divide each side by 2
x+2 = 18
Subtract 2
x+2-2 = 18-2
x = 16
Answer:
x = 16
Step-by-step explanation:
According to tangent-secant Theorem:
(Tangent)² = (External Part of the secant)(Whole Secant)
(6)² = (2)(2+x)
36 = 4+2x
Subtracting 4 from both sides
36-4 = 2x
=> 2x = 32
Dividing both sides by 2
=> x = 16Which statement best interprets the factor (r+7) in this context?
Answer:
the height of the cylinder is 7 units greater than the radius
Step-by-step explanation:
When you match the forms of the equations ...
[tex]V=\pi r^2(r+7)\\V=\pi r^2h[/tex]
you see that the factor (r+7) corresponds to the height (h) of the cylinder. That is ...
the height of the cylinder is 7 units greater than the radius.
A civil engineer is mapping the overhead clearance of his family’s property on a coordinate grid. The ground is represented by the x-axis and the base of the house is at the origin. There are two trees on the property. One tree is 8 feet from the base of the house and is 14 feet tall. The other tree is 16 feet from the base of the house and is 9 feet tall. What is the distance from the base of the house to the closest treetop? Round your answer to the nearest tenth.
Answer:
15.81
Step-by-step explanation:
Sorry for the delay
Need Help ASAP!!!
Which of the following is a key property of the linear parent function?
O A. It is in quadrants I and III.
B. It does not go through the origin.
C. It has a slope of zero.
O D. It is a curved line.
Answer:
The answer is:
A. It is in the quadrants I and III.
Step-by-step explanation:
I am not sure if this is correct, but I tried my best :)
I hope this helped~
A certain medicine is given in an amount proportional to a patients body weight. Suppose a person weighted 104 pounds requires 156 milligrams of medicine. What is the weight of a patient who requires 207 milligrams of medicine?
Answer:
138 pound
Step-by-step explanation:
Given
A certain medicine is given in an amount proportional to a patients body weight.
thus,
ratio will be
amount of medicine: weight of patient
Given
Suppose a person weighted 104 pounds requires 156 milligrams of medicine.
amount of medicine = 156 milligram
weight of patient = 104 pound
Thus, ratio will be = 156/104
___________________________
What is the weight of a patient who requires 207 milligrams of medicine
Let the weight of weight of patient here be x
thus, ratio in this case will be
207/x
we also know in ratio and proportion that
if two ratio a:b and c:d are equal then a:c = c:d
here also the ratio will be same
Thus,
156/104 = 207/x
=> 156x = 207*104 = 21,528
=> x = 21,528/156 = 138
Thus, weight of patient is 138 pound.
Select all the correct answers.
Which three pieces of information contribute the most to your credit score?
the number of bank accounts you have
the amount of debt you have
your payment history
your ability to make a down payment on a credit purchase
the number of loans you have
W
Answer:
B) the amount of debt you have
C) your payment history
E) the number of loans you have
Step-by-step explanation:
To determine the three pieces of information that contribute the most to your credit score, we have to find the factors that affect credit score calculation.
The major factors that affect a person's credit score calculation include : Payment history:
This is the most important factor that affect your credit score. Lenders want to be sure that you have a reputation back your debt and on time when you apply for new credit.
Amount of Debt :
This is the amount of overall debt you carry. It is the ratio of your credit card balances to your credit limit. Too much debt can hurt your credit score
Credit History:
This is a borrower's track record for repaying debts and how old it is. Opening new accounts within a short time will affect your credit score.
Account Mix: having a diverse portfolio of credit accounts could tell how well you manage different credits.
Credit Inquiries:
Several applications involving inquiries into your credit check within a short duration can affect your credit score.
Therefore the three pieces of information that would contribute the most to your credit score:
B) the amount of debt you have
C) your payment history
E) the number of loans you have
(03.01 MC)
If AXYZ is dilated by a scale factor of 2 about point X, which of the following is true about A'Y'?
Answer:
A'Y' is parallel to AY
Step-by-step explanation:
If X is the center of dilation, the only lines that go through X after the dilation are the ones that go through X before the dilation: XY (and XY'), XZ (and XZ').
Line AY does not go through X, so A'Y' will not go through X. Rather, the line will be moved a distance from X according to the dilation factor. The line A'Y' will be parallel to AY.
-4(-11+4n)-3(-2n+9) simplify to create an equivalent expression
chose 1 answer
-10n-35, -18n+17, -10n-17, or -10n+17
Answer:
the last one is correct
Step-by-step explanation:
hello,
-4(-11+4n)-3(-2n+9) = 44 - 16n + 6n - 27 = -10n + 17
hope this helps
Please help!! Will give 20 points!
Answer:
B. .32
Step-by-step explanation:
I think its B .32
Answer:
A
Step-by-step explanation:
Please answer this correctly
Answer:
3/4
Step-by-step explanation:
The numbers odd or less than 3 are 2, 3, and 5.
3 numbers out of 4.
P(odd or less than 3) = 3/4
Use the addition method to solve the system of linear equations for x. (Enter an exact number.)
3x - 2y = 8
2x + y = 3
Answer:
work is shown and pictured
All boxes with a square base, an open top, and a volume of 220 ft cubed have a surface area given by S(x)equalsx squared plus StartFraction 880 Over x EndFraction , where x is the length of the sides of the base. Find the absolute minimum of the surface area function on the interval (0,infinity). What are the dimensions of the box with minimum surface area?
Answer:
Length of the sides of the base (x) = 7.606 ft
Height (h) = 3.802 ft
The minimum surface area is 173.55 ft²
Step-by-step explanation:
Surface area is given by:
[tex]S(x) = x^2+\frac{880}{x}[/tex]
The value of x for which the derivate of the surface area function is zero, is the length of the sides of the base that minimizes surface area:
[tex]S(x) = x^2+\frac{880}{x} \\\frac{dS(x)}{dx}=0=2x-\frac{880}{x^2}\\x^3=440\\x=7.606\ ft[/tex]
The height of the box is given by:
[tex]V=hx^2\\220 =h*7.606^2\\h=3.802\ ft[/tex]
The dimensions of the box with minimum surface area are:
Length of the sides of the base (x) = 7.606 ft
Height (h) = 3.802 ft
The absolute minimum is:
[tex]S(x) = 7.606^2+\frac{880}{7.606}\\S_{min}=173.55\ ft^2[/tex]
The minimum surface area is 173.55 ft²
Answer:
The absolute minimum of the surface area[tex]=173.55$ ft^2[/tex]
At the minimum surface area,
Base length=7.61 feetHeight of 3.8 feet.Step-by-step explanation:
Volume of the box =220 cubic feet.
[tex]\text{Surface Area, } S(x)=x^2+\dfrac{880}{x}[/tex]
To find the absolute minimum of the surface area function on the interval [tex](0,\infty)[/tex], we take the derivative of S(x) and solve for its critical points.
[tex]S(x)=\dfrac{x^3+880}{x}\\S'(x)=\dfrac{2x^3-880}{x^2}\\$Setting the derivative equal to 0\\S'(x)=\dfrac{2x^3-880}{x^2}=0\\2x^3-880=0\\2x^3=880\\$Divide both sides by 2\\x^3=440[/tex]
Take the cube root of both sides
[tex]x=\sqrt[3]{440}\\ x=7.61$ ft[/tex]
Therefore, the absolute minimum of the surface area function on the interval [tex](0,\infty)[/tex], is:
[tex]S(x)=\dfrac{7.61^3+880}{7.61}\\\\=173.55$ ft^2[/tex]
Since the volume of the box =220 cubic feet
[tex]V=x^2h\\220=7.61^2 \times h\\h=220 \div 7.61^2\\h=3.80 ft[/tex]
The dimensions of the box with the minimum surface area are base length of 7.61 feet and height of 3.8 feet.
if a=2 and b=3 then find the value of 4a^2-4ab+b^2
Answer:
1
Step-by-step explanation:
=> [tex]4a^2-4ab+b^2[/tex]
Where a = 2, b = 3
=> [tex]4(2)^2-4(2)(3)+(3)^2[/tex]
=> 4(4) - 4(6) + 9
=> 16 - 24 + 9
=> -8 + 9
=> 1
Answer:
1.
Step-by-step explanation:
Substituting for a and b we have
4(2)^2 - 4*2*3 + (3)^2
= 16 - 24 + 9
= -8 + 9
= 1.
Please answer this correctly
Answer:
1/6
Step-by-step explanation:
Since the die has 6 sides that are all equally likely to be landed on, the probability of landing on 2 is 1/6, as there is one "favorable" outcome and 6 total outcomes. Hope this helps!
Answer:
1/6
Step-by-step explanation:
Sides of dice = 6
Number 2 in dice = 1
P(2) = 1/6
Question Help The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests positivepositive, given that he or she did not havedid not have the diseas
Answer:
The probability of getting someone who tests positive, given that he or she did not have the disease = P(P|No) = 0.041
Step-by-step explanation:
Complete Question
The data represents the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests positive, given that he or she did not have the disease.
P/N | Yes | No
+ve | 141 | 6
-ve | 11 | 142
Note that +ve and -ve l stands for testing positive and negative respectively.
Yes and No represents whether one has the disease or not respectively.
Solution
Let
- The event of testing positive be P.
- The event of testing negative be N.
- The event of having the disease be Yes.
- The event of not having the disease be No.
The probability of getting someone who tests positive, given that he or she did not have the disease = P(P|No)
The conditional probability of A given B is given mathematically as
P(A|B) = P(A n B) ÷ P(B)
Hence,
P(P|No) = P(P n No) ÷ P(No)
To solve these probabilities, we first define the probability of an event as the number of elements in that event divided by the Total number of elements in the sample space.
P(No) = n(No) ÷ n(Sample space)
n(No) = 6 + 142 = 148
n(Sample Space) = 141 + 11 + 6 + 142 = 300
P(No) = (148/300)
P(P n No) = n(P n No) ÷ n(Sample space)
n(P n No) = 6
n(Sample Space) = 300
P(P n No) = (6/300)
P(P|No) = P(P n No) ÷ P(No)
= (6/300) ÷ (148/300)
= (6/148)
= 0.0405405405 = 0.041 to 3 d.p.
Hope this Helps!!!
this circle is centered at the origin (0,0) the radius is 4, what is the equation?
Answer:
x^2 +y^2 = 16
Step-by-step explanation:
The equation of a circle is given by
(x-h) ^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x-0) ^2 + (y-0)^2 = 4^2
x^2 +y^2 = 16
find P (3) if p(x)=-×^3-2x^2+7
Answer:
-38.
Step-by-step explanation:
p(x) = -x^3 - 2x^2 + 7
p(3) = -(3^3) - 2(3^2) + 7
p(3) = -27 - 2(9) + 7
p(3) = -27 - 18 + 7
p(3) = -45 + 7
p(3) = -38
Hope this helps!
Answer:
p(3) = -38
Step-by-step explanation:
p(x) = -x³ - 2x² + 7
p(3) = -3³ - 2(3)² + 7
p(3) = -27 - 2(9) + 7
p(3) = - 27 - 18 + 7
p(3) = -38
please help me out asap
Answer:
SOLUTION SET={x<-3/2 or x≥48/5} option A
Step-by-step explanation:
12x+7<-11 and 5x-8≥40
solving the both inequalities
12x+7-7<-11-7 and 5x-8+8≥40+8
12x<-18 and 5x≥48
12x/12<-18/12 and 5x/5≥48/5
x<-3/2 and x≥48/5
SOLUTION SET={x<-3/2 or x≥48/5}
i hope this will help you :)
Find [g ° h](x) and [h ° g](x) , if they exist. g(x)=x+6 and h(x)=3x2 YALL PLEASE I NEED HELP :((
Answer:
a) [g ° h](x) = 3x² +6
b) [h ° g](x) =3 x²+36x+108
Step-by-step explanation:
Explanation:-
a)
Given g(x) = x+6 and h(x) = 3x²
Given [g ° h](x) = g(h(x))
= g(3x²) (∵ h(x) =3x²)
= (3x²)+6 (∵ g(x) =x+6)
∴ [g ° h](x) = 3x² +6
b)
Given [h ° g](x) = h (g(x))
= h(x+6) (∵ g(x) =x+6)
= 3 (x+6)² (∵ h(x) =3x²)
= 3 (x²+2(6)x+36) (∵ (a + b)² = a²+2ab+b²)
= 3 (x²+12x+36)
= 3 x²+36x+108)
∴ [h ° g](x) =3 x²+36x+108
Value of the digit 5 in 75 389
Answer:
The value of digit 5 is thousand
Step-by-step explanation:
Digit 5 has thousand value in 75 389
Find the perimeter and total area ? Use 3.14 in
Answer:
Perimeter is when you add up all of the sides, and the area is when you multiply length times width.
The prefix kilo means?
Answer:
one thousand
Step-by-step explanation:
Select the correct answer. Which graph represents this equation? y − 4 = -3(x + 5)
Answer:
I graphed the equation on the graph below.
Step-by-step explanation:
y − 4 = -3(x + 5) Distribute
y - 4 = -3x - 15
+ 4 + 4 Add 4 to both sides
y = -3x - 11 This is the equation in slope-intercept form, which is easier to graph
A line is a one-dimensional shape that is straight. The equation y-4 = -3(x + 5) can be represented on a graph as shown below.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is constant.
If we solve the given equation, the equation will reduce in the form of an equation of a line, therefore, the equation can be written as,
y − 4 = -3(x + 5)
y - 4 = -3x - 15
y = -3x - 15 + 4
y = -3x - 11
Hence, the equation y-4 = -3(x + 5) can be represented on a graph as shown below.
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ2
I NEED HELP PLEASE, THANKS! :)
Answer:
320 square units
Step-by-step explanation:
The four rectangles that approximate the area are shown in the graph. They have heights of 48, 64, 48, and 0. The width of each is 2. Then the total area is the sum of the products of length and width:
2·48 +2·64 +2·48 +2·0 = 2·160 = 320 . . . square units
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The numbers that are 6 or even on the cards are 2, 4, and 6.
3 cards out of a total of 6 cards.
3/6 = 1/2
Answer:
1/2 chance
Step-by-step explanation:
There are 3 numbers that fit the rule, 2, 4, and 6. 3/6 chance of picking one or 1/2, simplified.
Select the correct answer from each drop-down menu.
Answer:
AB = 14AC = 19.8 ≈ 20Step-by-step explanation:
The Pythagorean theorem can be used to find the lengths of the segments at the top of the square. The left one is found from ...
FA² = FE² +EA²
13² -12² = EA² = 169 -144 = 25
EA = √25 = 5
The right one is found from ...
FB² = FE² +EB²
15² -12² = EB² = 225 -144 = 81
EB = √81 = 9
Then the length of the side of the square is ...
AB = AE +EB = 5 +9
AB = 14
__
The length of the diagonal can also be found using the Pythagorean theorem.
AC² = AB² +BC² = 14² +14²
AC = √(196 +196) = 14√2 ≈ 19.7990
Rounded to the nearest integer, AC ≈ 20.
Solve for x in the equation x squared + 11 x + StartFraction 121 Over 4 EndFraction = StartFraction 125 Over 4 EndFraction.
Answer:
x = -13 or 2
Step-by-step explanation:
x² + 11x + ¹²¹/₄ = ¹²⁵/₄
(x + ¹¹/₂)² = ¹²⁵/₄
x + ¹¹/₂ = ±¹⁵/₂
x = -¹¹/₂ ± ¹⁵/₂
x = -13 or 2
Answer: D is the correct answer.
Step-by-step explanation: I took the test :)
What is the solution (q, r) to this system of linear equations? 12q + 3r = 15 –4q – 4r = –44
Step-by-step explanation:
12q+3r=15
-4q-4r=-44
12q+3r=15
-12q-12r=-132
-9r=-117
r= 13
12q + 39 = 15
12q= -24
q= -2
(-2,13)
An equation is formed when two equal expressions. The solution (q, r) to this system of linear equations is (-2,9).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the two equations, Therefore, the solution (q, r) to this system of linear equations can be found as shown below.
12q + 3r = 15...............equation 1
–4q – 4r = –44...........equation 2
Divide the first equation by 3,
4q + r = 5
Solving for r,
r = 5 - 4q
Substitute the value of r in the second equation,
–4q – 4r = –44
–4q – 4(5-4q) = –44
-4q - 20 + 16q = -44
12q = -44 + 20
12q = -24
q = -2
Substitute the value of q in the first equation,
12q + 3r = 15
12(-2) + 3r = 15
-24 + 3r = 15
3r = 15 + 12
3r = 27
r = 9
Hence, the solution (q, r) to this system of linear equations is (-2,9).
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ5
A three-person jury has two members who each have a probability p of making the correct decision in a case. The third member doesnt care and flips a coin for each decision. The ruling is based on a majority vote amongst the jurors
(a) What is the probability that the jury will correctly decide the case?
(b) Suppose two of the jurors quit, one of whom is the juror that doesnt care. Does the rrectly deciding the case i ncrease, decrease, or no at all?
Answer:
(a) p
(b) the probability does not change at all
Step-by-step explanation:
(a) Let A and B be the jurors with probability 'p' of making the correct decision, and C be the juror that doesn't care. The case will be correctly decided if any of the following combinations of jurors decide the case correctly:
AB, AC, BC, ABC.
The probability of one of those outcomes occurring is:
[tex]P=(p*p*0.5)+(p*(1-p)*0.5)+(p*(1-p)*0.5)+(p*p*0.5)\\P=p^2+p-p^2\\P=p[/tex]
The probability is p.
(b) If two of the juros quit, the probability of correctly deciding the case lies on just one juror that correctly decides with probability 'p'. Therefore, the probability of deciding the case does not change at all
Carlos biked miles on Saturday and miles on Sunday. On which day did he ride further and by how much? Carlos rode further on Saturday by miles. Carlos rode further on Saturday by miles. Carlos rode further on Sunday by miles. Carlos rode further on Sunday by miles.
Answer:
He rode farther on Sunday
135/7 - 139/8 = 107/56 or 1 51/56 miles farther
Answer:D
Step-by-step explanation: I got a hundred on my test.