Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. If it takes the hot water faucet minutes to fill the tub by itself, how long will it take the cold water faucet to fill the tub on its own?
Do not do any rounding.
Answer:
[tex]Cold = \frac{1}{6}\ mins[/tex]
Step-by-step explanation:
The correct given parameters are:
[tex]Both = \frac{1}{4}\ mins[/tex]
[tex]Hot = \frac{1}{12}\ mins[/tex]
Required
Time taken by the cold water faucet
We have:
[tex]Cold + Hot = Both[/tex]
Make Cold the subject
[tex]Cold = Both -Hot[/tex]
So, we have:
[tex]Cold = \frac{1}{4}-\frac{1}{12}[/tex]
Take LCM
[tex]Cold = \frac{3-1}{12}[/tex]
[tex]Cold = \frac{2}{12}[/tex]
Divide by 2
[tex]Cold = \frac{1}{6}[/tex]
The number 0 is a critical point of the autonomous differential equation dx/dt = 7xn, where n is a positive integer. For what values of n is 0 asymptotically stable? Semi-stable? Unstable?
Answer:
a) 0 is stable when n = odd
b) 0 is semi-stable when n = even
c) 0 is unstable when n is odd
Step-by-step explanation:
Th differential equation for this question
dx/dt = x^n
n = positive integer
a) value of n where 0 is stable
0 is stable when x^n is replaced with -x^n
because considering n to be an odd number
-x^n > 0 when x < 0 while -x^n < 0 when x > 0
∴ In this scenerio we can conclude that 0 is stable when n = odd number
b) Value of n where 0 is Semi-stable
assuming n is an even number
x^n > 0 for all the values of x
c) Value of n where 0 is unstable
lets assume n is odd
when n < 0, xⁿ < 0
when n > 0, xⁿ > 0
i.e. 0 is asymptotically unstable when n is an odd number
There are 40 children in a classroom and n of them do not wear spectacles. (4)/(5) of the boys and (2)/(3) of the girls wear spectacles. Express the number of boys who wear spectacles in terms of n.
9514 1404 393
Answer:
b = 80 -6n . . . . boys who wear spectacles
Step-by-step explanation:
We know the ratio of boys who wear spectacles to those who don't is ...
(4/5) : (1 -4/5) = 4 : 1
If we let b represent the number of boys who wear spectacles, then the number who don't is b/4. Then total number of boys is then b +b/4 = 5b/4. The number of girls in the classroom is this number less than 40.
Let's define a few groups:
boys who wear spectacles: bboys who do not wear spectacles: b/4girls who wear spectacles: (2/3)(40 -5b/4)girls who do not wear spectacles (1/3)(40 -5b/4)Then the total of children who do not wear spectacles is ...
n = b/4 +(1/3)(40 -5b/4)
12n = 3b +(160 -5b) = 160 -2b . . . . multiply by 12
2b = 160 -12n . . . . . . . . . . . . . add 2b-12n
b = 80 -6n . . . . the desired relation, b = boys who wear spectacles
_____
Additional comment
The only values of n that make sense in this context are {8, 10, 12}, corresponding to {0, 15, 30} total girls and {40, 25, 10} total boys.
−3 1/2 ÷ 1 1/4
khan academy
answer in simplified proper fraction
or
simplified improper fraction
Answer:
Step-by-step explanation:
Change the mixed numbers to improper fractions.
HELPP PLEASEEEEEEEEEEEEEEEEEEEEEE
The sum of 6 and 12 divided by 9.
Suppose a jar contains 9 red marbles and 40 blue marbles. If 2 marbles are randomly chosen from the jar at
the same time, find the probability that both marbles are red. Round your answer to four decimal places.
Answer:
0.0306
Step-by-step explanation:
I don't know if there is any significance to both being drawn at the same time. I'm going to say there isn't.
The first draw gives
9/49
Their is no replacement. That's because both marbles are drawn together. The second draw is
8/48
P(both red) = 9/49 * 8 / 48 = 3/98 = 0.03061 which rounds to 0.0306
Umm.. Hi there! Can someone please help me out with this? (only for those who know the answer)
Bcoz I really need this rn :(
DUEEEE AFTERRR LUNCHH! :(:(:(:(
If your answer is NONSENSE it will be deleted as soon as possible!
But if your answer is CORRECT, HELPFUL, HAS AN EXPLANATION, I'll chose your answer as the BRAINLIEST ANSWER!
Answer:
The Exterior Angle of triangle LDR is angle d. The Remote Interior Angles are a and b.
The Exterior Angle of triangle PDR is angle 4. The Remote Interior Angles are angles 1 and 2
Explanation:
Interior angles are the angles that are inside the shape. The remote interior angles would be the 2 angles away from the exterior angle.
The exterior angle is the angle, made by the side of the shape and a line drawn out from an adjacent side.
I hope this helps!
Answer:
In LDR
Exterior = d Interior = a, bIn PDR
Exterior = 4Interior = 1, 2Exterior angle of a triangle is formed when one side of the triangle is extended .
Interior remote angles the angles in the triangle that do not lie on the extended side.
Simplify 3/4 + 5/8 over 3/4 - 1/2
Answer:
11/2
Step-by-step explanation:
[tex]\frac{\frac{3}{4} + \frac{5}{8} }{\frac{3}{4} - \frac{1}{2} }[/tex]
= 3/4 + 5/8 = 11/8 (take LCM)
3/4 - 1/2 = 1/4 (take LCM)
11/8 ÷ 1 /4
= 11/8 x 4
= 11/2
Answered by Gauthmath
I need help finding the answer to this question on edge.
Answer:
6
Step-by-step explanation:
We need to evaluate :-
[tex]\rm\implies \displaystyle\rm\sum^4_n (-1)^n (3n + 2 ) [/tex]
Here the [tex]\Sigma[/tex] is the sum operator . And here we need to find the sum from n = 1 to n = 4 . We can write it as ,
[tex]\rm\implies (-1)^1 ( 3*1 +2) + (-1)^2 ( 3*2+2) + (-1)^3(3*3+2) + (-1)^4(3*4+2) [/tex]
Now we know that for odd powers of -1 , we get -1 and for even powers we get 1 . Therefore ,
[tex]\rm\implies -1 ( 3 + 2 ) + 1 (6+2)+-1(9+2)+1(12+2)[/tex]
Now add the terms inside the brackets and then multiply it with the number outside the bracket . We will get ,
[tex]\rm\implies -1 * 5 + 1 * 8 + -1*11 + 1*14 \\\\\rm\implies -5 + 8 - 11 + 14 \\\\\rm\implies\boxed{\quad 6 \quad}[/tex]
Hence the required answer is 6.
find c.round to the nearest tenth
Answer:
we need a picture...
Step-by-step explanation:
. Mildred bought an old
necklace and pair of earrings
while at an antique show. If
the cost of the jewelry is ]
and tax is 7%, which of the
following equations could be
used to find the total cost of
the jewelry?
a. .07 + ]
b. J +.07 x)
C. (.07x)) + ]
d. 7) + ]
Answer:
j * .07 +j
Step-by-step explanation:
The tax on the jewelry is J* .07
Add the tax to the cost of the jewelry to get the total cost
j * .07 +j
Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Surveying 26 people to determine which brand of ice cream is their favorite.
A. Yes
B. No
There are more than two possible outcomes on each trial of the experiment. The experiment does not consist of n identical trials. The trials are dependent.
Answer:
The answer is "No, There are more than two possible outcomes on each trial of the experiment ".
Step-by-step explanation:
When various ice cream products are known. This might surpass 2 brands or more. Thus the number of different results varies considerably.
BINOMIAL DISTRIBUTION:
An investigation with a set set of individual tests, each only with two possible results.
Four conditions are met by the binomial experiment
The set of indicators is fixed.Each attempt is autonomous.2 potential results exist only.In each and every test, the probability of each outcome remains unchanged.What is the answer to this
Answer:
y = -1.5x - 1
Step-by-step explanation:
We can use the general equation of y = mx + c to form our linear equation as seen on this graph.
Choosing two points on the graph (I will choose 0,-1 and 2,-4) we can find the gradient, m, as the distance between these points
[tex]\frac{Rise}{Run} = \frac{(-1)-(-4)}{(0)-(2)} = \frac{3}{-2} =-1.5[/tex]
We can find the c value by seeing where the graph cuts through the y-axis
This point is -1
Therefore our equation is y = -1.5x - 1
Alternatively, you could write it as [tex]y= -\frac{3}{2} x - 1[/tex]
Answer:
y = -1.5x - 1
A bottling machine fills soda bottles with an average of 12.000 ounces of soda. The standard deviation is 0.002 ounces. If the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces, calculate the process capability index of the machine. Group of answer choices Less than or equal to 1 More than 4 More than 2 but less than or equal to 3 More than 1 but less than or equal to 2
Answer:
the process capability index of the machine is 2.5
Option c) [More than 2 but less than or equal to 3] is the correct answer
Step-by-step explanation:
Given the data in the question;
process average ( x') = 12.000 ounces
standard deviation σ = 0.002 ounces
the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces.
so
Upper specification Limit USL = 12.000 + 0.015 = 12.015 ounces
Lower specification Limit LSL = 12.000 - 0.015 = 11.985 ounces
the process capability index of the machine will be;
Cp = ( process average - Lower specification Limit ) / 3σ
so we substitute
Cp = ( 12 - 11.985 ) / ( 3 × 0.002 )
Cp = 0.015 / 0.006
Cp = 2.5
Therefore, the process capability index of the machine is 2.5
Option c) [More than 2 but less than or equal to 3] is the correct answer
I almost got the problem but the problem was the rounding. I believe I rounded right but it is still incorrect. Can someone please help me on the rounding portion of the question? Thank you for your help!!!
Answer: The answer that I got for z was 0.111575, which when you round it to the hundredths place would be 0.11
g Find an equation of the line with slope m that passes through the given point. Put the answer in slope-intercept form. (-4, 8), undefined slope Hint: Any line parallel to Y axis has undefined slope.
Answer:
The equation is x + 4 = 0.
Step-by-step explanation:
Point (-4 , 8)
A line parallel to the Y axis has slope is infinite.
The equation of line is
[tex]y - y' = m (x-x')\\\\y - 8 =\frac{1}{0}(x+4)\\\\x + 4 = 0[/tex]
An oil tanker spills oil that spreads in a circular pattern whose radius increases at a rate of 15 ft/min. Let A be the area of the circle and r be the radius of the circle. How fast is the area increasing when the radius is 30 feet
Answer:
[tex]2827.4 \dfrac{ft}{s}[/tex]
Step-by-step explanation:
[tex] A = \pi r^2 [/tex]
[tex] \dfrac{dA}{dt} = 2 \pi r \dfrac{dr}{dt} [/tex]
[tex] \dfrac{dA}{dt} = 2 \times \pi \times 30~ft \times 15 \dfrac{ft}{s} [/tex]
[tex] \dfrac{dA}{dt} = 2827.4 \dfrac{ft}{s} [/tex]
need assistance with this, thank you
Answer:
B. 1✓3 in.
Search It ok
I see the answer :)
Solve for x.
7(x+2) = 6(x+5)
O x=-44
O X=-16
O x= 44
O x= 16
Answer:
x = 16
Step-by-step explanation:
7(x + 2) = 6(x + 5)
First, to start solving this problem, we have to distribute the "7" to the "x + 2" in the parenthesis and the "6" to the "x + 5" in the parenthesis.
7x + 14 = 6x + 30
Next, let's subtract "6x" from both sides of this equation!
x + 14 = 30
Now, we have to subtract "14" from both sides of the equation.
x = 16
Lastly! Let's make sure our "x=" equation is correct by inputting our value into the "x" values.
7(16 + 2) = 6(16 + 5)
7(18) = 6(21)
126 = 126
Since our equations equal each other we know that our x-value is correct!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Find the slope and then an equation for each line.
hellppp................
Answer:
[tex]B)[/tex]
[tex](-1,1)(-3,3)\\\frac{3-1}{-3+1} =-1\\1=1+b\\b=0\\y=-x[/tex]
OAmayOHopeO
Which of these shapes have the same area?
Answer:
wheres the picture?
Step-by-step explanation:
PLEASE HELP AND BE CORRECT BEFORE ANSWERING
9514 1404 393
Answer:
3
Step-by-step explanation:
The length of A'B' is 3 units.
The length of AB is 1 unit.
The scale factor is A'B'/AB = 3/1 = 3.
help me with my work pls
Answer:
-75/4
Step-by-step explanation:
75 x 100 = 7500
4 x 100 = 400
Express the solution graphically of -1/3(2x+1) <3
Answer:
The first picture is the solution that I worked out and the second is the graph of the two solutions.
The graph of the solution of inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is as shown below.
What is inequality?"It is a mathematical statement of an order relationship (greater than, greater than or equal to, less than, or less than or equal to) between two numbers or algebraic expressions."
For given question,
We have been given a inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex]
We solve above inequality.
[tex]\Rightarrow -\frac{1}{3} (2x+1) < 3\\\\\Rightarrow \frac{1}{3} (2x+1) > -3\\\\\Rightarrow 2x+1 > -9\\\\\Rightarrow 2x > -10\\\\\Rightarrow x > -5[/tex]
so, the solution of the inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is all points on the X-axis which are greater than x = -5.
The graph of the solution of inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is as shown below.
Learn more about the inequality here:
https://brainly.com/question/19003099
#SPJ2
A passenger car will go 455 miles on 17.5 gallons of gasoline in city driving what is the rate in miles per gallon ?
Answer:
26 gallons
Step-by-step explanation:
Take the miles and divide by the gallons
455 miles / 17.5 gallons
26 miles per gallon
Seeds are often treated with fungicides to protect them in poor-draining, wet environments. A small-scale trial, involving six treated and six untreated seeds, was conducted prior to a large-scale experiment to explore how much fungicide to apply. The seeds were planted in wet soil, and the number of emerging plants were counted. If the solution was not effective and five plants actually sprouted.
Required:
What is the probability that all five plants emerged from treated seeds?
Answer:
0.0076 = 0.76% probability that all five plants emerged from treated seeds
Step-by-step explanation:
The plants were chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
6 + 6 = 12 seeds, which means that [tex]N = 12[/tex]
6 treated, which means that [tex]k = 6[/tex]
Five sprouted, which means that [tex]n = 5[/tex]
What is the probability that all five plants emerged from treated seeds?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,12,5,6) = \frac{C_{6,5}*C_{6,0}}{C_{12,5}} = 0.0076[/tex]
0.0076 = 0.76% probability that all five plants emerged from treated seeds
5x³y³z³×6a³x³z²
Find the product
Can someone help me with this question plz
Answer:
Volume is 167.6 yd³
Step-by-step explanation:
[tex]{ \boxed{ \bf{volume = \frac{1}{3}\pi {r}^{2} h}}} \\ { \sf{volume = \frac{1}{3} \times 3.14 \times {(4)}^{2} \times 10}} \\ \\ { \sf{volume = 167.6 \: {yd}^{3} }}[/tex]
Find the midpoint of the line segment with endpoints (7, -12) and (-5, -15).
Answer:
The midpoint is (1,-13.5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2
(7+-5) /2 = 2/2 =1
To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2
(-12+-15) /2 = -27/2 =-13.5
The midpoint is (1,-13.5)
