Answer:
The probability is 0.8722
Step-by-step explanation:
There are 21 bottles
5 of them are contaminated.
there are 21 - 5 = 16 non-contaminated bottles.
So, if we grab a bottle at random, the probability that this bottle is contaminated will be equal to the quotient between the number of contaminated bottles and the total number of bottles, this is:
p = 5/21
Now we want to find the probability that, for 3 tested bottles, that less than two (0 or 1 ) are contaminated.
Let's see each case on its own.
0 bottles:
The probability of getting a non-contaminated bottle in the first try is equal to the quotient between the number of non-contaminated bottles and the total number of bottles, this is:
p₁ = 16/21
For the second bottle is the same, but because one non-contaminated bottle was drawn before, now there are 15 non-contaminated bottles and 20 bottles in total, so now the probability is:
p₂ = 15/20
and similarly, for the third bottle the probability is:
p₃ = 14/19
The joint probability is the product of the individual probabilities, we get:
P = p₁*p₂*p₃ = (16/21)*(15/20)*(14/19) = 0.4211
Now the case that one bottle is contaminated.
Let's assume that the first one is contaminated.
The probability of getting a contaminated bottle in the first draw is equal to the quotient between the number of contaminated bottles and the total number of bottles, so:
p₁ = 5/21
For the second bottle, we want a non-contaminated one, there are 16 non-contaminated bottles and 20 bottles left, so here the probability is:
p₂ = 16/20
and for the third bottle we have the probability:
p₃ = 15/19
The joint probability is:
p = p₁*p₂*p₃ = (5/21)*(16/20)*(15/19)
Also notice that we only looked at the case where the first bottle is contaminated, we also have the case where the second one is contaminated and the case where the third one is contaminated, so there are 3 permutations, then the probability of having one contaminated bottle is:
Q = 3*p = 3*(5/21)*(16/20)*(15/19) = 0.4511
Then the probability of having less than two contaminated bottles is:
probability = P + Q = 0.4211 + 0.4511 = 0.8722
Question 4 of 10
What else would need to be congruent to show that ABC= AXYZ by SAS?
Answer:
D
Step-by-step explanation:
The correct answer is D. Answered by Gauthmath
My class consists of 8 men and 7 women. I want to pick a group of 6 people for research.
Write each answer using fraction as needed.
a. In how many different ways can I pick this group?
b. What is the probability of having exactly 3 men in the group?
c. What is the probability of all the selected people in group are women?
d. What is the probability of having at least one man in the group?
Answer:
a.5005
b.[tex]\frac{1960}{5005}[/tex]
c.1/715
d.714/715
Step-by-step explanation:
We are given that
Total men=8
Total women=7
Total people, n=8+7=15
r=6
a.
Combination formula:
Selection of r out of n people by total number of ways
[tex]nC_r[/tex]
Using the formula
We have n=15
r=6
Total number of ways=[tex]15C_6[/tex]
Total number of ways=[tex]\frac{15!}{6!9!}[/tex]
Using the formula
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]
Total number of ways=[tex]\frac{15\times 14\times 13\times 12\times 11\times 10\times 9!}{6\times 5\times 4\times 3\times 2\times 1\times 9!}[/tex]
Total number of ways=5005
b. The probability of having exactly 3 men in the group
=[tex]\frac{8C_3\times 7C_3}{15C_6}[/tex]
Using the formula
Probability,[tex]P(E)=\frac{favorable\;cases}{Total\;number\;of\;cases}[/tex]
The probability of having exactly 3 men in the group=[tex]\frac{\frac{8!}{3!5!}\times \frac{7!}{3!4!}}{5005}[/tex]
=[tex]\frac{\frac{8\times 7\times 6\times 5!}{3\times 2\times 1\times 5!}\times \frac{ 7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}}{5005}[/tex]
=[tex]\frac{56\times 35}{5005}[/tex]
The probability of having exactly 3 men in the group
=[tex]\frac{1960}{5005}[/tex]
c. The probability of all the selected people in the group are women
=[tex]\frac{8C_0\times 7C_6}{5005}[/tex]
The probability of all the selected people in the group are women
[tex]=\frac{\frac{8!}{0!8!}\times \frac{7\times 6!}{6!1!}}{5005}[/tex]
The probability of all the selected people in the group are women
[tex]=\frac{7}{5005}=\frac{1}{715}[/tex]
d. The probability of having at least one man in the group
=1- probability of all the selected people in group are women
The probability of having at least one man in the group
[tex]=1-\frac{1}{715}[/tex]
[tex]=\frac{715-1}{715}[/tex]
[tex]=\frac{714}{715}[/tex]
The probability of having at least one man in the group [tex]=\frac{714}{715}[/tex]
the sum of five consecutive number is 45
Answer:
7, 8, 9, 10, 11
Step-by-step explanation:
7+8+9+10+11
7 + 8 = 15
15 + 9 = 24
24 + 10 = 34
34 + 11 = 45
Please help, I’m not sure about this question.
What is the slope of the line that contains these points?
х
-1
0
1
2
y
10
18
26
34
slope:
Answer:
8.
Step-by-step explanation:
The slope =
difference in y coordinates of 2 points / difference in coordinates of corresponding x coordinates.
So taking the first 2 points:
The slope = (18-10) / 0 - (-1)
= 8/1
= 8.
This is confirmed by slope between the second and third points
slope = 26-18/ (1-0) = 8.
An electronics company wants to compare the quality of their cell phones to the cell phones from three of their competitors. They sample 10 phones from each of the four companies and count the number of defects for each phone. If ANOVA was used to compare the average number of defects, then the treatments would be defined as: ______.
Answer:
The treatment should be stated by the four companies,since it more interested in the quality among each of the companies to be compared.
Step-by-step explanation:
Please help , write your answer I will be giving 10 points
Answer:
yes it represents the graph accurately
Can someone help me on 6?
Answer:
66600 ft
Step-by-step explanation:
First draw a rectangle and draw a diagonal line in the middle. The line makes two triangles, and the line itself is the hypotenuse. So, to find hypotenuse, the formula is:
a^2 + b^2 = c^2
The variable c defines the hypotenuse. Therefore:
a = 150
b = 210
Let's solve:
150^2 + 210^2 = c^2
22500 + 44100 = c^2
66600 = c^2
Therefore, in conclusion, the result we are getting is 66600 ft.
Hope This Helps!
Answer:
30√74 ft or 258.070 ft rounded to three decimal places.
Step-by-step explanation:
To find the length of a diagonal, add the square of the width and the square of the length together and find the square root of the sum.
d = √210² + 150²
d = √44100 + 22500
d = √66600
d = 258.069758 ft (This is the answer I got in six decimal places. Rounding it to three, as it says in the question, would be 258.07 ft, as 7 is greater than 5 (the third digit was 9 by the way).)
An exact answer to that, in radical form, is 30√74 ft.
degree and classification of 4x^2+32x+63?
nvm its quadratic trinomial
Answer:
Pertaining to the mathematical expression conveyed, the answer to such proposed interrogate is acknowledged as the following:
Degree: 2nd degree term.
Classification: Quadratic trionomial.
Step-by-step explanation:
Evaluating the Degree:
The degree is acknowledged as the predominating term adjacent to a base of a peculiar value that denotes the particular allocation within a polynomial.
4x^2 has the highest degree of 2.
32x has the degree of one, being that x individually is x^1.
Since polynomials are defined by the term in which obtains the greatest degree, ^2 is referred to as quadratic, whereas ^3 is cubic, ^4…
Classification Evaluation:
Such could be determined by evaluating for the quantity of terms present within the mathematical expression or statement.
4x^2 is the first term.
32x is the second term.
63 is the third term (considered a constant).
Thus, the correct answer is a quadratic trinomial.
*I hope this helps.
Given the similarity statement ΔJKL∼ΔNOP , what’s the corresponding angle of ∠J
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Answer:
∠N
Step-by-step explanation:
J is the first letter listed in the left side of the similarity statement. The corresponding angle is the first letter listed in the right side of the similarity statement: ∠N.
__
Corresponding angles are listed in the same order. The similarity statement means ...
∠J≅∠N
∠K≅∠O
∠L≅∠P
Answer:
<J = <N
Step-by-step explanation:
JKL = NOP
We know the angles match
<J = <N
<K = <O
< L = <P
And we know
JK = NO
KL = OP
JL = NP
A zookeeper perdiceted that the wight of a newborn lion would be 2.8 pounds when the zoo’s lion gave birth ,the newbor. Weight 3.5 pounds what is the zookeeper’s percent error ? Round to nerds err percent
Answer:
20%
Step-by-step explanation:
3.5 - 2.8 = 0.7
0.7 ÷ 3.5 = 0.2
0.2 × 100 = 20
The answer is 20%.
Hope this helped.
Answer:
predicted wight=2.8
Actual wight = 3.5 pounds
(3.5-2.8)/3.5
=0.7/3.5 × 100
=100/5=20%
Answer: 20%
OAmalOHopeO
5-3x<7-2x. Find the range of the values x
[tex] 5-3x<7-2x\\\\5-7<-2x+3x\\\\-2<x\\\\\boxed{\sf{x>-2}}[/tex]
[tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
Answer:
x>-2
Step-by-step explanation:
5-3x<2x+3x
5-7<-2x+3
-2<x
note the sign changes
therefore
x >-2
Please help!! Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
C
Step-by-step explanation:
You start with 6 and add 7 every time
1/2 + 4 5/8 please help
Answer:
[tex]5 \frac{1}{8}[/tex]
Step-by-step explanation:
Remember that [tex]\frac{1}{2} = \frac{4}{8}[/tex], so we want to find [tex]\frac{4}{8} + 4 + \frac{5}{8} = 4 + \frac{9}{8}[/tex]. However, this is not in it's simplest form because [tex]\frac{9}{8}[/tex] should be [tex]1 \frac{1}{8}[/tex]. Therefore, the final answer is [tex]4+1+\frac{1}{8} = 5 \frac{1}{8}[/tex].
Answer:
5 1/8 correct answer to question
Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.)
[tex] \sqrt[3 ]{28} [/tex]
Answer:
Mix fraction: 3 1/27
Improper fraction: 82/27
Decimal approximation: 3.037
Step-by-step explanation:
What value is close to 28 that is a perfect cube...27 which equals 3^3.
So let's find the tangent line to the curve y=cubert(x) at x=27.
We will use this equation to approximate what happens at x=28.
First let's rewrite the radical in our equation;
y=x^(1/3)
Now differentiate
y'=(1/3) x^(1/3-1) by power rule
Simplify
y'=(1/3) x^(-2/3) or (1)/(3x^[2/3])
So the slope of our tangent line at x=27 is (1)/(3(27)^[2/3])=1/(3(3)^2)=1/(3×9)=1/27.
We will also need a point on this tangent line....We know we have the point at x=27 because that is what our tangent line to curve is being found at.
So at x=27, we have y=cubert(27)=3. We used our equation y=cubert(x) here.
So we want to find the equation of the line that contains point (27,3) and has slope 1/27.
Point-slope form is
y-y1=m(x-x1)
Plug in our values
y-3=(1/27)(x-27)
Add 3 on both sides
y=3+(1/27)(x-27)
We will use this linear equation to approximate cubert(28) by replacing x with 28.
y=3+(1/27)(28-27)
y=3+(1/27)(1)
y=3+1/27
You can write that as a mix fraction if you want.
This value is than 3 but super close to 3 since 1/27 is close to 0.
Mix fraction: 3 1/27
Improper fraction: 82/27
Decimal approximation: 3.037
Cubert of 28 when smashed into calculator as is gives approximately 3.0366 which is pretty close to our approximation.
Using a linear approximation method f'(29) ≈ 3.1465.
What is linear approximation method?
A linear approximation is an approximation of a general function using a linear function (specifically, an affine function). They are widely used in the finite difference method to establish first-order methods to solve or approximate the solutions of equations.
Linear approximation, or linearization, is a method by which we can approximate the value of a function at a certain point. The reason linear approximation is useful is that finding the value of a function at a particular point can be difficult. Square roots are a good example of this.
Linear approximated as:
f(x+Δx)≈f (x)+Δx x[tex]f^{'}[/tex](x)
Take x = 28 and Δx = 1
f(x) = [tex]\sqrt[3]{x}[/tex]
Substitute 28for x
f(x) = [tex]\sqrt[3]{28}[/tex]
f(x) = 3.0365
So, we have
f(x+Δx)≈f (x)+Δx x[tex]f^{'}[/tex](x)
f(28+1)≈3.0365+1.[tex]f^{'}[/tex](x)
f(29)≈3.0365+1.[tex]f^{'}[/tex](x)
To calculate f'(x)
We have
f(x)=[tex]\sqrt[3]{x}[/tex]
Rewrite as
f(x)= [tex]x^{\frac{1}{3} }[/tex]
Differentiate
[tex]f^{'}[/tex]= [tex]\frac{1}{3}[/tex][tex]X^{\frac{1}{3}-1 }[/tex]
f' = [tex]\frac{1}{3}[/tex] . [tex]\frac{x^{\frac{1}{3} } }{3x}[/tex]
f'(29) = [tex]\frac{29^{\frac{1}{3} } }{3\times29}[/tex]
f'(29) =9.66/87
f'(29) = 3.22/29
f'(29) ≈ 3.0365+1x 3.22/29
f'(29) ≈3.0365+ 0.1110
f'(29) ≈ 3.1465
To learn more about differential equation, refer;
https://brainly.com/question/14620493
#SPJ2
Find an equation of the line that is the perpendicular bisector of the line segment joining the points (6,2) and (18,6)
Answer:
y= -3x +40
Step-by-step explanation:
Properties of perpendicular bisector:
• perpendicular to the given line
• cuts through the center of the given line
The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y -intercept.
Let's find the gradient of the given line first.
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
Gradient of given line
[tex] = \frac{6 - 2}{18 - 6} [/tex]
[tex] = \frac{4}{12} [/tex]
[tex] = \frac{1}{3} [/tex]
The product of the gradients of perpendicular lines is -1.
m(⅓)= -1
m= -1(3)
m= -3
Substitute m= -3 into the equation:
y= -3x +c
To find the value of c, substitute a pair of coordinates in which the perpendicular bisector passes through into the equation. Since perpendicular bisectors passes through the center of the segment, we can find the point in which the perpendicular bisector passes through using the mid- point formula.
[tex]\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )}[/tex]
Midpoint
[tex] = ( \frac{6 + 18}{2} , \frac{6 + 2}{2} )[/tex]
[tex] = ( \frac{24}{2} , \frac{8}{2} )[/tex]
[tex] = (12,4)[/tex]
y= -3x +c
when x= 12, y= 4,
4= -3(12) +c
4= -36 +c
c= 4 +36
c= 40
Thus, the equation of the perpendicular bisector is y= -3x +40.
Denver's elevation is 5280 feet above sea level. Death Valley is -282 feet. Is Death Valley located above sea level or below sea level???
(plz answer, due date is semtemper)
9514 1404 393
Answer:
below
Step-by-step explanation:
When signed numbers are used to represent elevation with respect to sea level, positive signs are used for values above sea level, and negative signs are used for values below sea level. The given elevation of Death Valley indicates it is 282 feet below sea level.
Answer by any chance?❤️
Step-by-step explanation:
Question 2.[tex] \frac{ \frac{6}{7} }{ \frac{9}{14} } [/tex]
[tex] = \frac{6}{7} \times \frac{14}{9} [/tex]
[tex] = \frac{2}{1} \times \frac{2}{3} [/tex]
[tex] = \frac{4}{3} = 1 \frac{1}{3} (Ans) [/tex]
Question 3.[tex] \frac{18}{x} = \frac{6}{10} [/tex]
[By cross multiplication]
=> 18 × 10 = 6 × x
[tex] = > \frac{18 \times 10}{6} = x[/tex]
=> 3 × 10 = x
=> x = 30 (Ans)
What relationship do the ratios of sin x° and cos y° share? A right triangle is shown with one leg measuring 12 and another leg measuring 5.
How many millitiers are in 4.55 liters?
Answer:
v nnv vb n
Step-by-step explanation:
b ng chfxhc.jx.gc,fhxfgfdkhgvn gghcjfuoctykfd mmyegfiuegfypgerukf khergfuoegrfyurgfirge jgreuyofrgiregvoifgr riygfepiygfreu;k frugfyrfbhrevf rrgfbreuobghfre rgeuherhbgerui freurehuregh ruogysfhurgiugwhlerghre rgiuyrge97grukbgr ker ruipuhrgeugregariyarga ;rskfglfsglgsfuifgryrgljs kjger;ugiergs hope this was helpful good luck!
The ratio of the side lengths of Rectangle A to Rectangle B is 3 to 7. What is the
ratio of their areas?
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Answer:
9 : 49
Step-by-step explanation:
Assuming the rectangles are similar, the ratio of their areas is the square of the ratio of their side lengths.
sides ratio = 3 : 7
areas ratio = 3² : 7² = 9 : 49
I need help with this
Answer:
D
Step-by-step explanation:
The table gives us the squares of certain values, and can be used to find the square root of certain values as well. For example, if 6² = 36, we can say that √36 = 6. Given this information, we can say that √47.6 is 6.9, and √49 = 7. If we look at the square root graph (√x=y), we can see that as x goes up, y goes up, and when x goes down, y goes down.
Therefore, we can say that the square root of 48 is between 6.9 and 7. We don't know exactly where it is, as there is no formula given to find it, so what Gina can do is go through the values between 6.9 and 7.0 and look for √48
⅗ Write the numerator and denominator of each of the following rational numbers
Answer:
1 3 5 7 9 11
Step-by-step explanation:
same like this do the question the answer will come
Can someone please help me with this problem? I tried inputting the numbers into the standard deviation equation but I did not get the right answer. Can someone please help me? Thank you for your time.
Answer:
97.8
Step-by-step explanation:
add together 97.3 +0.5
The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is 2630. Assume the standard deviation is$500 . A real estate firm samples 100 apartments. Use the TI-84 Plus calculator.a) What is the probability that the sample mean rent is greater than $27007?b) What is the probability that the sample mean rent is between $2450 and $2550? c) Find the 25th percentile of the sample mean. d) Would it be unusual if the sample mean were greater than $26457?e) Do you think it would be unusual for an individual to have a rent greater than $2645? Explain. Assume the variable is normally distributed.
Answer:
a) 0.0808 = 8.08% probability that the sample mean rent is greater than $2700.
b) 0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.
c) The 25th percentile of the sample mean is of $2596.
d) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
e) |Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
If |Z|>2, the measure X is considered unusual.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2630. Assume the standard deviation is $500.
This means that [tex]\mu = 2630, \sigma = 500[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{500}{\sqrt{100}} = 50[/tex]
a) What is the probability that the sample mean rent is greater than $2700?
This is the 1 subtracted by the p-value of Z when X = 2700. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2700 - 2630}{50}[/tex]
[tex]Z = 1.4[/tex]
[tex]Z = 1.4[/tex] has a p-value 0.9192
1 - 0.9192 = 0.0808
0.0808 = 8.08% probability that the sample mean rent is greater than $2700.
b) What is the probability that the sample mean rent is between $2450 and $2550?
This is the p-value of Z when X = 2550 subtracted by the p-value of Z when X = 2450.
X = 2550
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2550 - 2630}{50}[/tex]
[tex]Z = -1.6[/tex]
[tex]Z = -1.6[/tex] has a p-value 0.0548
X = 2450
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2450 - 2630}{50}[/tex]
[tex]Z = -3.6[/tex]
[tex]Z = -3.6[/tex] has a p-value 0.0002
0.0548 - 0.0002 = 0.0546.
0.0546 = 5.46% probability that the sample mean rent is between $2450 and $2550.
c) Find the 25th percentile of the sample mean.
This is X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-0.675 = \frac{X - 2630}{50}[/tex]
[tex]X - 2630 = -0.675*50[/tex]
[tex]X = 2596[/tex]
The 25th percentile of the sample mean is of $2596.
Question d and e)
We have to find the z-score when X = 2645.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2645 - 2630}{50}[/tex]
[tex]Z = 0.3[/tex]
|Z| = 0.3 < 2, which means it would not be unusual if the sample mean was greater than $2645.
Which of the following phrases should not be expressed using a negative number?
Answer:
its 1900 Bc. Because BC stand for before chirst
Step-by-step explanation:
Plz I need help on this question
Answer:
11.33
Step-by-step explanation:
First find the markup
8.80 * 25%
8.8 *.25 = 2.20
The new price is 8.80+2.20 = 11
Now find the tax
11*.03
.33
Add the tax to the new price
11+.33
11.33
Answer:
$11.33
Step-by-step explanation:
First divide 25% by 100, 0.25.
Then multiply 8.80 x 0.25 = 11.
Again, divide 3% by 100, 0.03
Then finally take 11.00 and multiply it with 0.03.
11.00 x 0.03=
$11.33
The x - intercept of the function f(x) = x2 + 4x - 12 is:
A) (-4,0)(3,0)
B) (-2,0)(6,0)
C) (-6,0)(2,0)
D)(4,0)(-3,0)
PLEAEE HELP ITS REALLY URGENT AND WILL MARK AS BRAINLIEST!!!
Answer:
C) (-6,0)(2,0)
For x-intercept, f(x) = 0:
[tex]{ \tt{ {x}^{2} + 4x - 12 = 0 }} \\ { \tt{(x - 2)(x + 6) = 0}} [/tex]
Answer:
C) (-6,0)(2,0)
Step-by-step explanation:
f(x)= x²+4x-12
(x-2)(x+6)=0
x=2
x=-6
help !!!! what’s the solution
1/x-2/3=3/2x find x
Answer:
1/x-2/3=3/2x
-2/3=3/2x-1/x
-2/3=(3-2)/2x
-2/3=1/2x
by cross multiplication
-2(2x)=1(3)
-4x=3
x= -3/4
Step-by-step explanation:
I hope this will help
plz mark as brainliest
