Answer:
15/ 16
Step-by-step explanation: 3/2 x 5/8= 15/16
you flip 2/3 to 3/2 and multiply it
Could -free, automatic faucets actually be housing more bacteris than the old fashioned, manual kind The concern is that decreased water flow may increase the chance that bacteria grows, because the automatic faucets are not being thoroughly flushed through. It is known that 15% of cultures from older faucets in hospital patient care areas test positive for Legionella bacteria. A recent study at Johns Hopkins Hospital found Legionella bacteria growing in 10 of cultured water samples from 20 electronic faucets aIf the probability of Legionella bacteria growing in a faucet is 0.15, what is the prob ability that in a sample of 20 faucets. 10 or more have the bacteria growing (the Johns Hopkins study provide sufficient evidence that the probability of Legionella bacteria growing in electronic faucets is greater than 15%? Explain.
Answer:
Not enough evidence to reject Null hypothesis
Step-by-step explanation:
Solution:-
- A comparative study for bacterial growth in manual and electronic faucets is made.
- It is observed that there is a higher growth in electronic faucets due to slower flow rates, i.e electronic faucets are not thoroughly flushed; hence, giving more resident time for the scaled bacteria to grow.
- It is known that 15% of cultures from older faucets were tested positive for the Legionella bacteria.
- A study at John Hopkins was conducted on a sample n = 20 electronic faucets with the probability of bacteria growing in a faucet is 0.15.
- We will conduct a hypothesis for at-least half proportion of electronic faucets have cultured bacteria.
- State the hypothesis for the proportion of electronic faucets culturing Legionella bacteria:
Null Hypothesis: P = 0.15
Alternate hypothesis: P > 0.15
- To determine the test statistics for the study conducted at John hopkins. We had a sample size of n = 20, and the probability for a bacteria to grow in a faucet is 0.15.
- Denote random variable, X: The number of electronic faucets culturing Legionella bacteria.
- Since, the probability for a bacteria to grow in a faucet is independent for each new faucet. We will assume the RV " X " to follow binomial distribution with probability of success 0.15:
X ~ Bin ( 20 , 0.15 )
- We are to determine that at-least half of the sample is subjected to the said bacteria. This is the probability of P ( X ≥ 10 ).
- The pmf for a binomially distributed random variable X is given below:
[tex]P ( X = r ) = n_C__r * ( p(success) )^r * ( p (fail) )^(^n^-^r^)[/tex]
Where,
p ( success ) = 0.15
p ( fail ) = 1 - p ( success ) = 1 - 0.15 = 0.85
- Use the pmf to determine the required test statistics:
[tex]P ( X \geq 10 ) = 1 - P ( X \leq 9 )\\\\P ( X \geq 10 ) = 1 - [ (0.85)^2^0 + 20*(0.15)*(0.85)^1^9 + 20_C_2 (0.15)^2*(0.85)^1^8 +\\\\ 20_C_3 (0.15)^3*(0.85)^1^7 + 20_C_4 (0.15)^4*(0.85)^1^6 + 20_C_5 (0.15)^5*(0.85)^1^5+\\\\ 20_C_6 (0.15)^6*(0.85)^1^4 + 20_C_7 (0.15)^7*(0.85)^1^3 + 20_C_8 (0.15)^8*(0.85)^1^2 + \\\\ 20_C_9 (0.15)^9*(0.85)^1^1\\\\\\P ( X \geq 10 ) = 1 - [ 0.03875 + 0.13679 + 0.22933 + 0.24282 + 0.18212 + 0.10284 + \\\\ 0.04537 + 0.01601 + 0.00459 + 0.00108 ]\\\\[/tex]
[tex]P ( X \geq 10 ) = 1 - [ 0.997 ] = 0.003[/tex]
- The probability that 10 or more electronic faucets is found to have Legionella bacteria growing is 0.003
- The test proportion of 10 and more electronic faucets have culturing bacteria is p = 0.003.
- Assuming normality of the population, the Z-statistics would be:
[tex]Z-test = \frac{ (p - P) \sqrt{n} }{\sqrt{P*(1 - P )} } \\\\Z-test = \frac{ (0.003 - 0.15) \sqrt{20} }{\sqrt{0.15*(0.85)} } \\\\Z-test = -1.84109[/tex]
- If we were to test the claim to 90% level of confidence:
significance level (α) = 1 - CI = 1 - 0.9 = 0.1
- The rejection region Z-critical is defined by a right-tail:
[tex]Z-critical \geq Z_\alpha \geq Z_0_._2\\\\Z-critical \geq 1.28[/tex]
- Compare the test statistics with the rejection criteria defined by the Z-critical:
Z-test < Z-critical
-1.84 < 1.28
Conclusion:
There is not enough evidence that the probability of Legionella bacteria growing in electronic faucets is greater than 15%.
Vivek plans to survey 10 randomly chosen residence out of the 280 people that live in his community about plans for new neighborhood dog park describe one way he can make the sample to represent the population of residence *hint how will you pick those 10 people*
Step-by-step explanation:
To randomly pick the 10 people needed in the sample, it can be done this way
1. Define the population: in this case, the total population is 280 and expressed as N and since we are interested in everyone in the neighborhood with no exclusion, our sampling frame is thus 280 people.
2. Choose your sample size: As given in the question, our sample size is to randomly pick 10 people expressed as n.
3. List your population and then assign numbers to each unit in the population: Getting the list of all 280 people in the population and then assigning numbers from 1 to N - in this case 1 - 280.
4. Then find random numbers using the random number table to help select your 10 people sample making them a representative of the population in residence.
Find the area underneath the normal distribution between these two Z-Scores.
Z = 1.21 and Z = 0.01
Answer:
03829
Step-by-step explanation:
A suitable calculator is useful for this.
Find the equation of the line. Write the equation of the line in standard form.
Vertical line; through (-4,-8).
Answer:
x = -4
Step-by-step explanation:
The equation of a vertical line in standard form is ...
x = constant
In order for this line to go through the point with x-coordinate -4, the constant must be -4:
x = -4
What’s the correct answer for this?
Answer:
B.
Step-by-step explanation:
Data
Center = (2, -16)
A (2, -13)
P (-1, -16)
Equation
(x - h)² + (y - k)² = r² or
(x₁ - h)² + (y₁ - k)² = (x₂ - h)² + (y₂ - k)²
Substitution
(2 - 2)² + (-13 + 16)² = (-1 - 2)² + (-16 + 16)²
The signs in my equation and the one in the options are different but the results are the same
What is the slope, m, and y-intercept for the line that is plotted on the grid below? On a coordinate plane, a line goes through points (0, 4) and (negative 2, 0).
Answer:
On a coordinate plane, a line (y = mx + b) goes through point A(0, 4), then it has point A as y-intercept (the point with x component is 0). And it goes through B(-2, 0).
Denote that line: y = mx + b
=> m*0 + b = 4 (it goes through A(0, 4))
=> b = 4
=> m*2 + 4 = 0 (it goes through B(-2, 0))
=> m = -2
=> Slope m = 2 and y-intercept (0, 4)
Hope this helps!
:)
Answer:
Slope: 2
y-intercept: 4
Step-by-step explanation:
m = (0-4)/(-2-0) = -4/-2 = 2
y -4 = 2(x - 0)
y = 2x + 4
the perimeter of this quarter circle with radius, r= 23mm.
Give your answer rounded to 1 DP.
Answer:
82.1
Step-by-step explanation:
So the circumference of the whole circle is 46π.
A quarter of that is 11.5π.
11.5π ≈ 36.1283155163
Simplify that to 1 decimal point: 36.1
Then you add 46 to that.
36.1 + 46 = 82.1
State who is correct and explain why
Answer:
12.4+3√7 is irrational
Step-by-step explanation:
12.4 is a rational number
3√7 is an irrational number
The sum of a rational number and an irrational number is irrational.
So, 12.4+3√7 is irrational
Neeed Help ASAP Quick
Answer:
4; 7
Step-by-step explanation:
Small box = 25 and Large box = 50
small box = x and large box = x+3
25x+50(x+3)=450
25x+50x+150=450
75x=300
x=4
Large box = 4+3 = 7
Therefore, 4; 7
I hope this helped and have a good rest of your day!
What is the quotient?
(6 * 108) = (1.5 * 10-4)
4 x 1012
4 x 104
4 x 10-32
410-2
Answer:
(A)[tex]4X10^{12}[/tex]
Step-by-step explanation:
Given the quotient:
[tex]\dfrac{6*10^8}{1.5*10^{-4}}[/tex]
To evaluate, we first separate the given expression as follows.
[tex]=\dfrac{6}{1.5}X\dfrac{10^8}{10^{-4}}[/tex]
Next, we apply the division law of indices to the powers of 10.
Division Law of Indices: [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
[tex]=4X10^{8-(-4)}\\=4X10^{8+4}\\=4X10^{12}[/tex]
Therefore, our quotient is [tex]4X10^{12}[/tex].
The correct answer is A.
How is 3 help me please
Step-by-step explanation:
Square root 8 = 2 square root 2
CALC HELP!!! WILL MARK BRAINLIEST
Consider the parametric equations below.
x = t2 − 2, y = t + 1, −3 ≤ t ≤ 3
(a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.
(b) Eliminate the parameter to find a Cartesian equation of the curve. for −2 ≤ y ≤ 4
Answer:
(a) In attachment
(b) x = y² - 2y - 1, −2 ≤ y ≤ 4
Step-by-step explanation:
(a)
The graph of the given parametric equation is given in the attachment.
The direction in which the curve is traced as t increases, is indicated by black arrows.
(b)
To eleminate the parameter t, we simultaneously solve both the equations.
So, we have the equations:
x = t² - 2 ----- equation (1)
y = t + 1 ----- equation (2)
So, from equation (2), we have:
t = y - 1
Substituting this in equation (1), we get:
x = (y - 1)² - 2
x = y² - 2y + 1 - 2
x = y² - 2y - 1
Now, for limits of y, we use equation (2)
For initial limit, t = -3
y = - 3 + 1 = - 2
For final limit, t = 3
y = 3 + 1 = 4
Therefore, the final relation after eliminating t is:
x = y² - 2y - 1, −2 ≤ y ≤ 4
The Cartesian equation of the curve after eliminating the parameter t is expressed below.
[tex]x=y^2-2y-1[/tex]
For, the y values of, [tex]-2 \leq y \leq 4[/tex]
What is a parametric equation?The parametric equation is the type of equation in which the variable which is in depended on on is known as parameter. The dependent function in this equation is defined as the continuous function of that variable.
The first equation given in the problem is,
[tex]x = t^2 - 2 \\t^2=x+2[/tex]
The second equation given in the problem is,
[tex]y = t + 1\\t=y-1[/tex]
Put the values of t in the modified first equation as,
[tex](y-1)^2=x+2\\y^2+1-2y-2=x\\x=y^2-2y-1[/tex]
The values of t are between -3 to 3.
[tex]-3 \leq t \leq 3[/tex]
The value of t is -3 then the value of y will be -2 and when the value of t is 4 then the value of y will be 4 from equation 2.
Hence, the Cartesian equation of the curve after eliminating the parameter t is expressed below.
[tex]x=y^2-2y-1[/tex]
For, the y values of, [tex]-2 \leq y \leq 4[/tex]
Learn more about the parametric equation here;
https://brainly.com/question/21845570
A couple plans to have no more than three children, and they will keep having children until they have a girl. So, if their first child is a girl, they will stop and have only one child. However, if their first child is a boy, they will try again and have a second child. As it turns out, the probability of having a boy is slightly greater than having a girl. Here is the probability distribution for the number of boys the couple could have. Boys 0 boys 1 boy 2 boys 3 boys Probability 0.490 0.250 0.127 0.133
What is the expected number of boys the couple will have? (Recall: the expected value is the mean). 0.903 1.5 0.228
Answer:
0.903.
Step-by-step explanation:
Okay, from the question we are given the following information or data or parameters:
''couple plans to have no more than three children, and they will keep having children until they have a girl. So, if their first child is a girl, they will stop and have only one child"
Additionally, from the question we are given that; ''However, if their first child is a boy, they will try again and have a second child".
Also, the probability distribution is given as Boys 0, boys 1 , boy 2, boys 3 boys with Probability 0.490, 0.250, 0.127, 0.133 respectively.
That is, we now have:
Number of boys × probability.
Boys 0 = 0 × 0.490 = 0.
Boys 1 = 1 × 0.250 = 0.250.
Boys 2 = 2 × 0.127 = 0.254.
Boys 3 = 3 × 0.133 = 0.399.
The addition of the products for each Number of boys × probability gives us the expected value. That is to say;
0 + 0.250 + 0.254 + 0.399 = 0.903 = mean.
Write the formula to calculate how much dough is prepared in x hours.
10 kilograms of prepared dough in 5 hours
Answer: D(x) = 2kg/h*x
where x is the number of hours.
Step-by-step explanation:
The information that we have is:
in 5 hours, we can prepare 10kg of dough.
With this, we can find the rate per hour, to do this we find the quotient:
R = 10kg/5h = 2kh/h
This meeans that in one hour, we can make 2kg of dough.
Then, in x hours, we can make x times 2kg of dough, then the equation will be:
D(x) = 2kg/h*x
where x is the number of hours.
Solve: 3(2d - 1) – 2d = 4(d– 2) + 5
The right answer is No solution.
Look at the attached picture
Hope it will help you
If 8=10 and 1=7,which describes all the lines that must be parallel?
Only lines rand s must be parallel.
Only lines tand u must be parallel.
Lines rand s and lines t and u must be parallel.
Neither lines r and s nor lines t and u must be parallel.
Answer:
C: Lines r and s and lines t and u must be parallel.
Step-by-step explanation:
The true statement is (c) Only lines r and s must be parallel.
How to determine the true statementFrom the figure, we can see that:
Lines r and s point in the same direction, while lines t and u point in the same direction
If angle 8 = angle 10 and angle 1 = angle 7, then it means that:
Lines r and s must be parallel.
Line t and u may or may not be parallel.
Hence, the true statement is (c) Only lines r and s must be parallel.
Read more about parallel lines and transversal at:
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Circle B is shown. Line segments C B, D B, and E B are radii. Angle C B E is 52 degrees and angle E B D is 160 degrees. What is the measure of Arc C E D? 106° 108° 148° 212°
Answer it would be 212 :)
Step-by-step explanation:
The measure of arc CED in the circle given is: D. 212°.
What is the Measure of an Arc of a Circle?Measurement of an arc of a circle = measure of its central angle.
Thus:
Measure of arc CED = angle CBE + angle EBD
Substitute
Measure of arc CED = 52 + 160
Measure of arc CED = 212°
Therefore, the measure of arc CED in the circle given is: D. 212°.
Learn more about measure of arc on:
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I need some assistance on this
Answer:
1650
Step-by-step explanation:
The shape is a pyramid on top of a prism.
Volume of a pyramid is V = ⅓ Ah, where A is the area of the base and h is the height of the pyramid.
Volume of a prism is V = Ah, where A is the area of the base and h is the height of the prism.
The base of both shapes is a right triangle. The area is:
A = ½ bh
A = ½ (22) (10)
A = 110
The height of the prism is 6. The height of the pyramid is 33 − 6 = 27. The total volume is:
V = (110) (6) + ⅓ (110) (27)
V = 1650
12m by 7m what is the area
Answer:
multiply 12*7
Step-by-step explanation:
Answer:
84 m²
Step-by-step explanation:
12 times 7 (for a rectangle)
Grace swam 0.6 kilometers during her first week of training and 0.25 kilometers during her second week of training. How many kilometers did she swim in all?
A.3.1 kilometers
B.8.5 kilometers
C.0.31 kilometers
D.0.85 kilometers
Answer:
she will cover a distance of 0.85 km.
Step-by-step explanation:
We have,
Grace swam 0.6 kilometres during her first week of training and 0.25 kilometres during her second week of training.
It is required to find total distance covered by her in all.
It can be calculated simply adding the distance covered in first and second week of training. So,
Total distance, D = 0.6 km +0.25 km = 0.85 km
Hence, she will cover a distance of 0.85 km.
If Josh invests $500 in a 5-year fixed interest savings bond that pays 5% per annum, how much will his entire investment be worth at the end of the term?
Answer:
$638.14
Step-by-step explanation:
Our equation is [tex]p*(1+x)^{t}[/tex], with p being the starting amount, x being the interest rate, and t being the time. Plugging our variables in, we get
[tex]500*(1+0.05)^{5}[/tex] = around 638.14
Josh will receive $638 at the end of the term.
Josh invests $500 in a 5-year fixed interest savings bond that pays 5% per annum,
What is cost price?Cost price is that price for buyer which he pays to seller for an object or product.
Principle amount = $500
Rate = 5 %
Tenure = 5 years
Amount = principle (1+R)^tenure
= 500 (1+5/100)^5
= $638
Thus, Josh will receive $638 at the end of the term.
Learn more about cost price here:
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What is the circumference of a circle with a radius of 91 mm? (use 22/7 for pi; show your work in numbers)
Answer:
[tex] \boxed{Circumference \: of \: circle = 572 \: mm} [/tex]
Step-by-step explanation:
Radius (r) = 91 mm
[tex]Circumference \: of \: circle = 2\pi r \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times \frac{22}{7} \times 91 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 22 \times 13 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 44 \times 13\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 572 \: mm[/tex]
The product of a rational number
(Other than zero) and an irrational number is always irrational true or false
Answer:
I think it's true. hope this helps!!
8
17. Find the area of the shaded
portion of this figure, which
consists of a parallelogram
enclosing a right triangle
and a circle. Dimensions are
in feet. (Round off answer to
the nearest tenth of a foot.)
Answer:
37.4 ft^2
Step-by-step explanation:
The area of the parallelogram is given by ...
A = bh = (8 ft)(7 ft) = 56 ft^2
The area of the right triangle is given by ...
A = (1/2)bh = (1/2)(3 ft)(4 ft) = 6 ft^2
The area of the circle is given by ...
A = πr^2 = π(2 ft)^2 = 4π ft^2 ≈ 12.6 ft^2
__
The shaded area is the area of the parallelogram less the areas of the unshaded triangle and circle:
(56 ft^2) -(6 ft^2) -(12.6 ft^2) = 37.4 ft^2 . . . . shaded area
Which expression is equivalent to 25a+5b-13
1/2 cup serving provides 180 calories and 6 grams. How many calories and grams of fiber are in 1/3 cup serving
Answer:
1/3 cup Serving will provide 120 calories and 4 grams of fibre
Step-by-step explanation: one gram = 7.716 calories
1/2 cup serving provides 180 calories and 6 grams.
One cup serving with you provide 360 calories and 12 grams
So
1/3 cup Serving will provide 360/3 calories and 12/3 grams
1/3 cup Serving will provide 120 calories and 4 grams of fibre
Please answer quick
Taylor is playing a board game with two friends, using a single dice, one friend rolled a one, and the other friend rolled a three. Taylor need to roll a number higher than both friends in order to win the game, and she wants to calculate her probability of winning. What is the sample space for Taylor’s calculation?
A. [4,5,6]
B. [2,4,5,6]
C. [1,3]
D. [1,2,3,4,5,6]
Answer:
it is a
Step-by-step explanation:
its the only possible answer. :)
let me know if i am wrong!
S500 invested at 4% compounded annually for 10 years.
Hello there!
$500 invested at 4% compounded annually for 10 years
time: 10 years
compound: annually
interest: 4%
y = 500(1.04)^10
1.04^10 = 1.48
500 x 1.48 = 740
Value after 10 years: $740
Answer:
$740.12
Step-by-step explanation:
The amount is multiplied by 1.04 each year, so after 10 years, the balance will be ...
$500(1.04^10) = $740.12
Log 3 base 6 + log 8 base 6 - log 4 base 6
Step-by-step explanation:
Refer The attachment.
a desert tray has three slices of cake, three key lime pies, and four ice cream sundaes. What is the probability of the next two customers both select key lime pie?
Answer:
The probability of the next two customers both select key lime pie is 1/15
Step-by-step explanation:
No. of slices of cakes = 3
No. of key lime pies = 3
No. of ice cream sundaes = 4
Total deserts = 3+3+4=10
We are supposed to find The probability of the next two customers both select key lime pie
Probability of selecting key lime pie by first customer =[tex]\frac{3}{10}[/tex]
So,Total deserts =10-1=9
No. of key lime pies = 3-1=2
So,Probability of selecting key lime pie by second customer = [tex]\frac{2}{9}[/tex]
So,the probability of the next two customers both select key lime pie=[tex]\frac{3}{10} \times \frac{2}{9} =\frac{1}{15}[/tex]
Hence the probability of the next two customers both select key lime pie is 1/15