Two laboratory technicians are running product quality tests. One technician takes 6 minutes less than the
other. What equation would give the amount of time, t, it would take to run the tests if the technicians work
together to split the work on the different tests?
Answers
Answer:
The time it will take will be ;
t = (2x -6)/(x^2-6x)
Where x is the amount of time
in minutes taken by the technician who is slower
Step-by-step explanation:
We want to write the time it would take to run the tests if the technicians work together.
Let the time taken by the first technician be x minutes
The time that would. taken by the second is 6 minutes less which is (x -6) minutes
So if they work together, how long will it take?
That would be ;
t = 1/x + 1/(x-6)
t = (x + x -6)/(x(x-6))
t = (2x -6)/(x^2 -6x)
The time it will take if they both work together is ;
t = (2x -6)/(x^2-6x)
where x minutes is the amount of time taken by the technician who is slower of the two
Related Questions
Question 3 Let X1, X2,..., Xn be independent random variables, each having a uniform distri- bution over (0,1). Let M = maximum (X₁, X₂,..., Xn). Show that the distribution function of M, FM(-), is given by FM(x)=x, 0≤x≤1 What is the probability density function of M?
Answers
The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.
The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.
In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.
For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).
The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).
To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.
The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.
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New game You pay 10 and roll a 6 die. If you get a you win 50 If not, you get to roll again. If you get a 6 this time, you get your 10 back.a) Create a probability model for this game.b) Find the expected value and standard deviation of your prospective winnings.c) You play this game five times. Find the expected value and standard deviation of your average winnings.d) 100 people play this game. What's the probability the person running the game makes a profit?
Answers
The probability mode for the given value is created. The expected value and standard deviation of prospective winnings are -$0.28 and $18.33. The expected value and standard deviation if the game is played five times are -$1.40 and $40.99. The probability that the person running the game makes a profit is 0.561.
Probability is a way to determine how likely something is to happen. It is computed by dividing the frequency of the event by the total number of outcomes. The formula then becomes P(X) = frequency of the event÷total number of outcomes.
The product of the probabilities determines the likelihood that two or more occurrences will coincide. This is given by, P(A and B) = P(A)P(B).
a) To create a probability model follow the steps. Let X is an occurrence of an event. The table is attached here.
b) The expected value is calculated using the formula, E(X) = μ = ∑ x P(x).
\(\begin{aligned}E(X)=\mu&=x_1p_1+x_2p_2+x_3p_3\\&=40\left(\frac{1}{6}\right)+0\left(\frac{5}{36}\right)+(-10)\left(\frac{25}{36}\right)\\&=-\$ 0.28\end{aligned}\)
Also,
\(\begin{aligned}E(X^2)&={x_1}^{2}p_{1}+{x_2}^{2}p_{2}+{x_3}^{2}p_{3}\\&=(40)^2\frac{1}{6}+(0)\frac{5}{36}+(-10)^2\frac{25}{36}\\&=(1600)\frac{1}{6}+(0)\frac{5}{36}+(100)\frac{25}{36}\\&=266.67+69.44\\&=336.11\end{aligned}\)
And the standard deviation is calculated using the formula, σ=√Var[X].
\(\begin{aligned}\sigma=\sqrt{\text{Var}(X)}&=\sqrt{E(X^2)-E(X)^2}\\&=\sqrt{336.11-0.08}\\&=\sqrt{336.03}\\&=\$18.33\end{aligned}\)
c) The expected value and standard deviation for playing the game 5 times are calculated as follows.
The expected value is,
\(\begin{aligned}5\times E(X)&=5(-\$0.28)\\&=-\$1.40\\\end{aligned}\)
The standard deviation is,
\(\begin{aligned}\sigma&=\sqrt{5\times\tex{Var}(X)\\&=\sqrt{5\times336.03\\&=\sqrt{1680.15}\\&=\$40.99\end{aligned}\)
d) The dice rolling is random and the winning chance is independent. The probability the person running the game makes a profit (P(x<0)) is given by,
The population mean, μ(Y) = -$0.28
The standard deviation for a population of 100 is,
\(\begin{aligned}\sigma&=\sqrt{\frac{\text{Var}(X)}{n}}\\&=\frac{18.33}{\sqrt{100}}\\&=1.83\end{aligned}\)
The z-score for mean winning is,
\(\begin{aligned}z&=\frac{x-\mu}{\sigma}\\&=\frac{0-(-0.28)}{1.83}\\&=0.153\end{aligned}\)
For a person to make a profit, the mean winning of the player should be less than the z-score. Then,
The P-value from the z-table, P(z<0.153)=0.5608
The answer is 0.561.
The complete question is -
You pay $10 and roll a die. If you get a 6, you win$50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What’s the probability the person running the game makes a profit?
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Factor using the GCF. 7x + 35
1 point
O 7x + 35 Prime (cannot be factored)
O 7(x + 35)
O 7(7x + 5)
O 7(x + 5)
x
Answers
Explanation: factor out 7 from the expression as 35 divided by 7 is 5 therefore 7(x+5) is the answer and to check it you just distribute the 7 through the parenthesis.
Hope that helps! Have a good day:)
How do I find the values of x, y, and z?
Answers
Pythagorean theorem:
\(\begin{gathered} hypotenuse^2=Leg1^2+Leg2^2 \\ Leg1^2=hypotenuse^2-Leg2^2 \end{gathered}\)Use the pythagorean theorem above to find the values of x, y and z as follow:
1. From the triangle in the right find the value of y^2 (Leg 1)
\(y^2=z^2-\left(x+1\right)^2\)2. From the triangle in the left find the value of y^2 (Leg 1):
\(y^2=\left(x+2\right)^2-x^2\)3. From the big triangle find the value of z^2 (Leg 1):
\(\begin{gathered} z^2=\left(x+\left(x+1\right)\right)^2-\left(x+2\right)^2 \\ \\ z^2=\left(2x+1\right)^2-\left(x+2\right)^2 \end{gathered}\)3. Equal the expressions of y^2 (step 1 and step 2):
\(z^2-\left(x+1\right)^2=\left(x+2\right)^2-x^2\)4. Substitute the z^2 in the equation above by the value of z^2 you get in step 3:
\(\lparen2x+1)^2-\left(x+2\right)^2-\left(x+1\right)^2=\left(x+2\right)^2-x^2\)5. Solve x in the equation above:
\(\begin{gathered} Subtract\text{ \lparen x+2\rparen}^2\text{ in both sides of the equation:} \\ \lparen2x+1)^2-\left(x+2\right)^2-\left(x+2\right)^2-\left(x+1\right)^2=\left(x+2\right)^2-\left(x+2\right)^2-x^2 \\ \lparen2x+1)^2-2\left(x+2\right)^2-\left(x+1\right)^2=-x^2 \\ \\ Add\text{ x}^2\text{ in both sides of the equation:} \\ \lparen2x+1)^2-2\left(x+2\right)^2-\left(x+1\right)^2+x^2=-x^2+x^2 \\ \lparen2x+1)^2-2\left(x+2\right)^2-\left(x+1\right)^2+x^2=0 \\ \\ Simplify: \\ \left(4x^2+4x+1\right)^2-2\lparen x^2+4x+4)-\left(x^2+2x+1\right)+x^2=0 \\ 4x^2+4x+1-2x^2-8x-8-x^2-2x-1+x^2=0 \\ 2x^2-6x-8=0 \end{gathered}\)Use quadratic formula to solve x:
\(\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ \\ x=\frac{-\left(-6\right)\pm\sqrt{\left(-6\right)^2-4\left(2\right)\left(-8\right)}}{2\left(2\right)} \\ \\ x=\frac{6\pm\sqrt{36+64}}{4} \\ \\ x=\frac{6\pm\sqrt{100}}{4} \\ \\ x_1=\frac{6-10}{4}=\frac{-4}{4}=-1 \\ \\ x_2=\frac{6+10}{4}=\frac{16}{4}=4 \end{gathered}\)As x cannot be a negative value (a side of a triangle cannot be negative) the value of x is 4
6. Use the value of x to solve y in the equation in step 2:
\(\begin{gathered} y^2=(x+2)^2-x^2 \\ \\ y^2=\left(4+2\right?^2-\left(4\right?^2 \\ \\ y^2=6^2-16 \\ y^2=36-16 \\ y^2=20 \\ y=\sqrt{20} \\ y=2\sqrt{5} \end{gathered}\)7. Use the value of x to solve z in the equation in step 3:
\(\begin{gathered} z^{2}=(2x+1)^{2}-(x+2)^{2} \\ \\ z^2=\left(2\left(4\right)+1\right)^2-\left(4+2\right)^2 \\ z^2=\left(8+1\right)^2-6^2 \\ z^2=9^2-6^2 \\ z^2=81-36 \\ z^2=45 \\ z=\sqrt{45} \\ z=3\sqrt{5} \end{gathered}\)Then, the values of x, y and z are:
\(\begin{gathered} x=4 \\ y=2\sqrt{5} \\ z=3\sqrt{5} \end{gathered}\)PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Answers
Answer:
D. The over 30s have a larger range and interquartile range than the under 30s
Step-by-step explanation:
In a data set, the range is the difference between the maximum and minimum. So, the range for under 30s is 20, while the range for over 30s is 24. Additionally, the interquartile range is the difference between Q3 and Q1. For a boxplot, Q3 is the line where the box ends and Q1 is the line where the box begins. Therefore, the IQR for the under 30s is 8, and the IQR for over 30s is 11. So, D must be correct.
The following cone has a slant height of 17
cm and a radius of 8
cm.
What is the volume of the cone?
Responses
480π
320π
544π
Answers
The formula for the volume of a cone is:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is pi.
In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:
h² = s² - r²
h² = 17² - 8²
h² = 225
h = 15
Now that we have the height, we can plug in the values for r and h into the formula for the volume:
V = (1/3)π(8²)(15)
V = (1/3)π(64)(15)
V = (1/3)(960π)
V = 320π
Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.
Solve for m.
4 + | 7 - m | = 5
a.) m = 16 or m = -2
b.) m = 6 or m = 8
c.) m = 2 or m = -8
d.) m = 2 or m=16
Answers
Answer:
m = 6 .......................
Answer:
\(4 + | 7 - m | = 5\)
\(4+\left|7-m\right|-4=5-4\)
\(\left|7-m\right|=1\)
\(7-m=-1\: or \:7-m=1\)
\(m=6\: or \:m=8\)
Michelle was found not guilty of armed robbery and then put on trial for the same crime right after the verdict. Which amendment was violated?
Group of answer choices
5th Amendment
1st Amendment
3rd Amendment
4th Amendment
Answers
How many complex and real roots are in the problem (x+10)^9.
Answers
Answer:
9 roots
Step-by-step explanation:
(x+10)^9 = 0
If you would multiply it out, the highest power is x^9 so the equation has 9 roots
Solving (x+10)^9 =0
Taking the 9th root of each sdie
x+10 = 0
x = -10
The root is -10 with multiplicity of 9
4. A prism has an area of cross-section of 89 cm². The volume of the prism is
4895 cm?. Find the height of the prism.
Answers
Answer:
55 cm
Step-by-step explanation:
height = 4895/89 = 55 cm
The ratio of inmates to guards at the
asylum is 6:1. If there are 108 guards at
the prison how many inmates are there?
Answers
Answer:
648
Step-by-step explanation:
108X1=108 so 108X6=648
the thin-walled pipe has an inner diameter of 0.5 in and a thickness of 0.025 in.
Answers
The outer diameter of the thin-walled pipe can be calculated by adding twice the thickness to the inner diameter. Therefore, the outer diameter is 0.5 in + 2(0.025 in) = 0.55 in.
A thin-walled pipe is a hollow cylinder with a relatively small thickness compared to its inner and outer diameters. In this case, the inner diameter of the pipe is given value as 0.5 in, and the thickness is 0.025 in.
To find the outer diameter, we add twice the thickness to the inner diameter. This is because the thickness is divided equally on both sides of the inner diameter. So, the outer diameter can be calculated as 0.5 in + 2(0.025 in) = 0.55 in.
The outer diameter is an important parameter in determining the overall size and structural integrity of the pipe. It affects the flow capacity, strength, and compatibility with other pipe fittings.
Knowing the outer diameter allows for proper sizing and fitting of the thin-walled pipe in various applications, such as plumbing, HVAC systems, or fluid transportation.
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12/-3 Enter your answer as a number, like this: 42
Answers
Answer:
-4
Step-by-step explanation:
12/-3=-4
Help me please answer both ...
Answers
I cant see any question on the attachment it is just a black screen
a.
1. One side of a rectangle is 5 inches long. Another side of the rectangle is 8 inches long. What
are the lengths of the other two sides of the rectangle?
5 inches and 5 inches
b. 8 inches and 5 inches
c. 8 inches and 8 inches
d. They could be any length
Answers
Answer:
B. 8 inches and 5 inches
Step-by-step explanation:
Rectangles: opposite sides are parallel and equal and adjacent sides form right angles.
Help me I need this answer really fast
Answers
Answer:
the last option
Step-by-step explanation:
50+25+x=180
x=105
50+105+x=180
x=25
Find the slope of the line that passes through the given points. (0,10) and 24,6). Be sure to simplify. Also in picture.
Answers
(6-10)/(24-0) = -4/24 = -1/6
find the area of the following figure. solve and show your solution
help pls!
Answers
Answer:
Step-by-step explanation:
1)sol;
perpendicular=15cm
base=25
now,
area of right angled triangle=1/2 p*b
=1/2*15*25
=187.5cm^2
2)sol;
length=12cm
now,
area of square=l^2
=(12)^2
=144cm^2
3)sol;
radius=20cm
now,
area of circle=\(\pi \\ \)r^2
=\(\pi \)*(20)^2
1257.14cm^2
5)sol;
length=9cm
now,
area of square=l^2
=(9)^2
=81cm^2
Use the work shown to find the image of point F(–1, 6) after a 90° counterclockwise rotation.
(x, y) → (–y, x)
Switch the x- and y-coordinates: (6, –1)
Multiply the new x-coordinate by –1: (6(–1), –1)
Simplify.
What are the coordinates of F’?
Answers
Aloioi
Step-by-step explanation:
Answer:
C (-6, -1)
Step-by-step explanation:
if the minimum charge of 175 calls is Rs 180 and Rs 1.50 per calls for additional calls then find the cost of calls including the charge of TSC 10% and VAT 13% as the former reading the total calls a land line phone is 5577 and the present reading 7577.Also,find the amount of payment including 20% fine
Answers
The total amount of payment for calls is Rs 648
How to find the total amount for paymentFrom the problem, the following information is deduced to help solve the problem
the minimum charge of 175 calls is Rs 180 and Rs 1.50 per calls for additional calls
The total call reading
= present reading - former reading
= 7577 - 5577
= 2000
the number of 175 calls in 2000
= 2000 / 175
= 11 3/7 approximately 12
Total cost of calls
175 calls = Rs 180 + Rs 1.50 * 12
= 180 + 1.50 * 12
= Rs 180
Adding other charges to Rs 180
= 180 * 1.1 + 180 * 1.3 + 180 * 1.2
= Rs 648
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Angles X and Y are complementary. The measure of Angle Y is 55.5 degrees. What is the measure of Angle X?
Answers
25 points
Matthew is planning a party and found pizzas for $5 each and drinks for $1 each.
Write an expression that represents how much he will spend. (p = pizza, d = drinks)
Answers
The expression that represents how much he will spend would be = y ( 5p + 1d)
How to derive the expression that shows how much he will spend?The amount of money that each pizza(p) is sold = $5 each.
The amount of money that each drink(d) is sold = $1.
The total money that Matthew may spend on the party is represented by = y.
Therefore the expression that will show how much he will spend would be = y ( 5p + 1d).
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y = x4 - 3x2 + 4
Does the equation above represent a relation, a function, both a relation and a function, or neither a relation nor a function?
A.
neither a relation nor a function
B.
both a relation and a function
C.
function only
D.
relation only
Answers
The equation as given in the task content above can be said to represent; Choice C; function online.
What is the equation given in the task content representing?By definition, a function from a set X to a set Y assigns to each element of X exactly one element of Y.
A relation, on the other hand defines the relationship between sets of values of ordered pairs.
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What will the volume of the box be if you cut 1 inch by 1 inch squares out of each corner (Notice that you have to subtract 1 inch from each side twice? Remember volume is length times width times height. Discuss how you found the length, the width, and the height of the box in order to calculate the volume.
Answers
Answer:
324 cubic inches
Step-by-step explanation:
The dimensions are now 18 x 18 x 1, since you are cutting an inch off each side.
324 cubic inches
The vertices of a triangle are listed below.
What is the area of the triangle?
A. 16 square units
B. 32 square units
OC. 19.3 square units
OD. 8 square units
L(2, 2), M(6, -2), N(2, -6)
Answers
The area of the triangle from the vertices of the triangle is B. 32 square units
What is the area of the triangle from the vertices of a triangleFrom the question, we have the following parameters that can be used in our computation:
The vertices of a triangle are
L(2, 2), M(6, -2), N(2, -6)
The area of the triangle is calculated using
Area = 1/2 * |Lx * (My - Ny) + Mx * (Lx - Ny) + Nx * (Lx - My)|
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * |2 * (-2 + 6) + 6 * (2 + 6) + 2 * (2 + 2)|
Evaluate
Area = 32
Hence, the area is B. 32 square units
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Find the circumcenter of the triangle.
(-1, 1)
(4,-2)
(-1, -2)
Answers
What is the volume of this sphere?
Use a = 3.14 and round your answer to the nearest hundredth.
8 mm
cubic millimeters
Answers
Answer:
Volume = 2,143.57 mm³
Step-by-step explanation:
Given:
radius (r) = 8 mm
π = 3.14
Required:
Volume of the sphere
Solution:
Volume of the sphere = ⁴/3πr³
Plug in the values
Volume = ⁴/3 × 3.14 × 8³
= ⁴/3 × 3.14 × 512
= 6,430.72/3
Volume = 2,143.57333
Volume = 2,143.57 mm³ (nearest hundredth)
After a shift in the aggregate demand curve, which variable adjusts to restore general equilibrium? A.real interest rate B.investment spending C.consumption spending D.price level
Answers
In order to restore general equilibrium, price adjustments are undertaken. In the short run, prices increase, and when expectations rise above actual inflation, prices continue to climb until they do. answer is option (d). price level.
What is aggregate demand?The term "aggregate demand" in macroeconomics refers to the overall demand for locally produced commodities, including capital goods, consumer products, and services. Aggregate demand is calculated as the total of spending by consumers, corporate and governmental investment spending, and net imports and exports.
The overall demand of final products and services in an economy at any particular time is known as aggregate demand, often referred to as domestic final demand. Effective demand is a frequent word for it, however occasionally this phrase is used to distinguish between two things. This is the demand for a nation's gross domestic product.
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Fifty-five petcent of people in a survey said that they do exercise on a fairly regular basis. If 12,000 people were sureveyed, how many of them exercised on a fairly regular basis? A. 5,000 B. 5,500 C. 6000 D. 6,600
Answers
Hope it helps : )
what is the last digit of 3 with a power of 2011
Answers
So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.