One pipe takes 6 hours to fill the pool and the other takes 12 hours.
Pipe A fills 1/x of the pool per hour, and Pipe B fills 1/y of the pool per hour. In other words, A takes x hours to fill the pool and B takes y hours to fill the pool.
Together, they fill 1/x + 1/y of the pool per hour. So, 4 hours times that rate should equal 1 full pool, since together they take 4 hours to fill the pool. That gives you your first equation:
4(1/x + 1/y) = 1
You're also told that if one pipe fills half the pool and the other takes over to fill the rest, it will take 9 hours. We don't know how long Pipe A works, so call that number of hours t. Pipe B must work for 9 - t hours.
So, Pipe A, working for t hours, fills half the pool:
t(1/x) = 1/2
And Pipe B, working for 9 - t hours, fills half the pool:
(9-t)(1/y) = 1/2
You now have a system of three equations (because this is an exceptionally complicated pipe-filling-pool problem):
4(1/x + 1/y) = 1
t(1/x) = 1/2
(9-t)(1/y) = 1/2
Solve for t in that second equation, then plug it into the third equation:
t(1/x) = 1/2
t = x(1/2)
t = x/2
(9 - x/2)(1/y) = 1/2
Now you've got a system of two equations:
4(1/x + 1/y) = 1
(9 - x/2)(1/y) = 1/2
Solve for y in the second equation, then plug that into the first equation:
(9 - x/2)(1/y) = 1/2
(9 - x/2) = y(1/2)
2(9 - x/2) = y
18 - x = y (this is a really nice-looking form of that equation; we'll use it again later)
4(1/x + 1/y) = 1
4(1/x + 1/(18-x)) = 1
4/x + 4/(18-x) = 1
(4(18-x))/(x(18-x)) + (4x)/(x(18-x)) = 1
(4(18-x) + 4x)/(x(18-x)) = 1
4(18-x) + 4x = x(18-x)
72 - 4x + 4x = 18x - x2
72 = 18x - x2
x2 - 18x + 72 = 0
(x - 6)(x - 12) = 0
x - 6 = 0 OR x - 12 = 0
x = 6 OR x = 12
So, Pipe A takes either x = 6 or x = 12 hours to fill the pool alone.
When Pipe A takes 6 hours to fill the pool, Pipe B takes 12. When Pipe A takes 12 hours to fill the pool, Pipe B takes 6.
These cases are equivalent, since the original problem makes no distinction between the pipes.
Hence, one pipe takes 6 hours to fill the pool and the other takes 12 hours.
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$$1,2,2,4,8,32,256,\ldots,$$each term (starting from the third term) is the product of the two terms before it. for example, the seventh term is $256$, which is the product of the fifth term ($8$) and the sixth term ($32$). this sequence can be continued forever, though the numbers very quickly grow enormous! (for example, the $14^{\text{th}}$ term is close to some estimates of the number of particles in the observable universe.) what is the last digit of the $35^{\text{th}}$ term of the sequence?
The last digit of a₃₅ is 8 when each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it.
Given that,
Each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it. For instance, the seventh term, which is the sum of the fifth ($8) and sixth ($32) terms, is $256. Though the numbers very rapidly become large, this series can go on indefinitely! In terms of the number of particles in the observable universe, the $14 term, for instance, is close to some estimations.
We have to find what is the final digit of the sequence's $35 term.
We know that,
Remember the Fibonacci sequence, which goes 1, 1, 2, 3, 5, 8, 13, 21..., where each word is the total of the one before it. Continuing the above pattern, if Fn is the n-th Fibonacci number, we would arrive at
aₙ=a₂ˣₙ₋₁a₁ˣₙ₋₂=2ˣₙ₋₁
A periodic series of residues mod 10 is left behind by the sequence of positive powers of 2:
2≡2(mod 10)
2²≡4 (mod 10)
2³≡8 (mod 10)
2⁴≡16 (mod 10)
2⁵≡32 (mod 10)
2⁶≡64 (mod 10)
And so forth; this series of residues has a 4-year period.
The taken mod 4 period is 6:
34≡4 (mod 6)
F₃₄≡3 (mod6)
2³=8
So, the last digit of a₃₅ is 8.
Therefore, the last digit of a₃₅ is 8 when each phrase (beginning with the third term) in the sequence $$1,2,2,4,8,32,256 is the product of the two terms that came before it.
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(2+8) + 10 ^2 +60 divided 10
Answer: 17
Step-by-step explanation:
Answer:
Step-by-step explanation:
116
i need your help please!!!!!!! and no fake answers please guys
The measure of the LK us 5 units and the measure of the NL is 6 units after applying intersecting secants theorem.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).
It is given that:
A circle:
Applying intersecting secants theorem:
4(4 + 2) = 3(3 + 2x + 5)
8 = 8 + 2x
x = 0
LK = 2x + 5 = 5 units
In the second circle:
4(4 + x - 8) = 3(3 + x - 5)
x = 10
NL = x - 8 + 4 = 10 - 8 + 4 = 6 units
Thus, the measure of the LK us 5 units and the measure of the NL is 6 units after applying intersecting secants theorem.
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compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. (4 points)compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. (4 points)
The slope of a function is defined as the change in y-coordinate with respect to the change in x-coordinate of the line.
m = Δy/Δx
∆y --> net change in the y coordinate
∆x ---> net change in x coordinate
m ---> slope of fution
The y-intercept of both functions 'f' and 'g' are equal and slope of f(x) is less than the slope of g(x). So, the correct option is option (A).
We have given a function, g (x) = 2x + 1
comparing the g(x) with standard equation
y = mx + b
where m is slope of this line
b --> y-intercept
Thus we get m = 2 , b= 1 . So, the slope of g(x) is 2 and y-intersecpt is 1 .
Now, we have a table for function f(x) that is function f(x) passing through all points as given in table. The slope of function passing through (h,k) and (a,b) is expressed as (k-b)/(h-a)
Thus, slope of function 'f' passing through (0,1) and (2,4) = (1-4)/(0-2) = -3/-2
= 3/2
=> f (x) = (3/2)x + b
where , b --> y-intercept
plug the value x= 4 and corresponding to it
f(x) = 7 we get , 7 = 3/2× 4 + b
=> b = 7-6 = 1
Therefore, slope of function g(x) is greater than slope of function f(x) and y-intercept of f(x) is equal to y-intercept g(x) .
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Complete question:
The Table represents the linear function f(x), and the equation represents the linear function g(x). Compare the y-intercepts and the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
x / f(x)
0/1
2/4
4/7
g(x)= 2x+1
A. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
B. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
C. The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
D. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
Solve the inequality
2/7 > b + 5/7
Answer:
-3/7 > b
Step-by-step explanation:
subtract 5/7 on both sides
based on past experience, a hiring manager believes that less than one-third of applicants are actually qualified for an entry-level position. suppose that in a random sample of 144 applicants for this position, 63 are found to be qualified. do the sample data support the manager's belief? test the relevant hypotheses using a
The no. of people qualified is less than the managers belief of 0.265
What is P-value?
The likelihood of receiving outcomes from a statistical hypothesis test that are at least as severe as the actual results provided the null hypothesis is true, is known as the p-value in statistics. The p-value provides the minimal level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by greater evidence when the p-value is lower.
P-value is frequently utilised by government organisations to increase the credibility of their research or reports. The United States Census Bureau, for instance, mandates that any analysis with a p-value higher than 0.10 be accompanied by a statement stating that the difference is not statistically significant from zero.
Here [tex]H_{0}[/tex] - P =1/3=0.3333
Hi - P <0.3333
Given n =144
x = 63
P^=63/144=0.4375
Test Static = [tex]\frac{P^-P}{\sqrt{\frac{PQ}{n} } }[/tex]
= [tex]\frac{0.4375^-0.3333}{\sqrt{\frac{0.3333-(1-0.3333)}{144} } }[/tex]
=0.265
P-value =P(Z<2.65)=0.9960, Given [tex]\alpha[/tex] =0.05
here P-Value >[tex]\alpha[/tex]
So, don't reject [tex]H_{0}[/tex]
There is no evidence to support the manager's Belief That less Than 1/3 of Applications are qualified
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if you good at geometry help pls lol
Dubai, United Arab Emirates set a record temperature for 49 ° C What does the number 49 mean
Answer: It means that the high in Dubai is 49
Step-by-step explanation: When saying about the weather, we always say the highest temperature first, so that mean 49 here is the high temperature in Dubai.
If you can please give me a Brainliest, I only need 1 more to become an Ace, thank you!
Answer:
The mercury is expected to cross the 49°C mark again later today.
Company g also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by company g are 0. 40 and 0. 66, respectively. The fat quarters sell for $5. 00 each, but are discounted by $1. 50 for each defect found. (c) what are the mean and standard deviation of the selling price for the fat quarters sold by company g?
From the given information given, the mean and standard deviation of the probability distribution is; Y will be 0.4899 and 0.699 respectively.
How to create the probability distribution?
From the given probability distribution, it should be noted that the probability distribution for y will be:
Y 0 1. 2
Probability 0.63. 0.25. 0.12
The mean of Y will be:
Mean = (0 × 0.63) + (1 × 0.25) + (2 × 0.12)
Mean = 0 + 0.25 + 0.25
Mean = 0.49
The variance will be 0.4899. Therefore, the standard deviation will be:
standard deviation = ✓0.4899
Standard Deviation = 0.699
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Find the value of ccc so that the polynomial p(x)p(x)p, left parenthesis, x, right parenthesis is divisible by (x+2)(x+2)left parenthesis, x, plus, 2, right parenthesis. P(x) = 4x^3+cx^2+x+2p(x)=4x 3 +cx 2 +x+2p, left parenthesis, x, right parenthesis, equals, 4, x, cubed, plus, c, x, squared, plus, x, plus, 2 c=c=c, equals.
The value of c after solving the equation is 8.
For the polynomial to be divisible by x+2, hence x = -2
Given
p(x) = 4x³+cx²+x+2
p(-2) = 4(-2)³+c(-2)²+(-2)+2
p(-2) = 4(-8) + c(4)-2+2
p(-2) = -32+4c
If p(-2) = 0
0= -32+4c
-4c = -32
c = 32/4
c = 8
Hence we get the value of c as 8.
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When we do a confidence interval for the mean, we use the following distribution to determine the number of standard deviations needed for our confidence:
t-distribution z-distribution
skewed distribution Chi Square distribution
When we do a confidence interval for the mean, we use T-distribution to determine the number of standard deviations needed for our confidence
The T-distribution is a way to describe a collection of observations in which the majority of the observations are close to the mean and the remaining observations are the tails on either side. It is a type of normal distribution that is utilized for data with unknown variance and smaller sample sizes.
We use the T-distribution to obtain the required critical value, which is nothing more than the number of standard deviations from the center taken to obtain the confidence interval, despite the fact that there is no population standard deviation and only sample metrics—the sample mean and standard deviation—are used. As a result, the solution to this problem is T-distribution.
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find the rate of change of the area of a square when the side of the square is 2 meters and the side is growing at a rate of 3 meters per second.
The rate of change of the area of a square is 12m^2/sec.
What do you mean by rate of change?
The term "rate of change" refers to the rate at which one quantity changes in respect to another. Consequently, if y value is the dependent variable and x value is the independent variable.
Rate of Change is equal to [tex]\frac{Change in y}{Change in x}[/tex].
Change rates may be positive or negative. This reflects a change in the y-value between the two data points, either up or down. Zero rate of change is the state where a quantity does not change over time.
Solution Explained:
Given,
S = 2m and ds/dt = 3m/s
So, we use
Area = s^2
dA/dt = 2s ds/dt
= 2 X 2 X 3
Therefore, the rate of change of the area is 12m^2/s.
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I need answers as soon as possible.
Answer:78 feet and 34 cubic feet
Step-by-step explanation:
Let be the vector space of polynomials in with degree less than 3 and be the subspace.
the polynomial will be 2x² + 11x+6, with degree less than 3 and be the subspace.
What is vector space?
A collection of vectors collected collectively and multiplied ("scaled") by scalars forms a vector space, also known as a linear space. Real numbers are typically thought of as scalars. Nevertheless, there aren't many instances of scalar multiplication with vector spaces using rational, complex, etc. numbers. Axioms and other preconditions must be met by the vector addition and scalar multiplication techniques. A space made up of vectors is referred to as a vector space when the addition of vectors is governed by the associative and commutative law and when vectors are multiplied by scalars is governed by the associative and distributive process.
W = span (9x-4-2x²,5+x+2x²)
Now, a(9x42x²)+b(5+x+2x²) = 0
⇒(9a+b)x+(2b-2a)x² + (5b-4a) = 0
⇒9a+b= 0; 2b2a = 0; 5b-4a=0
a = b =0
p(x)=(9x-4-2x²) + 2(5+x+2x²) = 9x-4-2x² + 10 + 2x + 4x² = 2x² + 11x+6
Hence the polynomial will be 2x² + 11x+6.
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use the appropriate normal distribution to approximate the resulting binomial distributions. a convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit. a random sample of 35 customers is made. if the store owner's claim is correct, what is the probability that fewer than 21 customers in the sample buy coffee during their visit on that certain day of the week? a) 0.7486 b) 0.6915 c) 0.7224 d) 0.5987 e) 0.6628 f) none of the above.
The probability that fewer than 21 customers in the sample buy coffee during their visit on that certain day of the week is 0.7224. Hence option C is the correct option.
What is the binomial distribution?
When each trial has the same probability of achieving a given value, the number of trials or observations is summarised using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.
The formula for z-score is z = (x -μ)/σ
Where, μ is mean of the sample, σ is standard deviation of the sample
Given that 55% of the customers buy coffee, hence p = 55% = 0.55
Sample of 35 customers, hence n = 35.
For the binomial distribution μ = np, σ = √[np(1-p)]
The mean and the standard deviation of the approximation are:
μ = 35 ˣ 0.55 = 19.25
σ = √[35 ˣ 0.55(1-0.55)] =2.943
Now calculate the z score where μ = 19.25, σ = 2.943 and X = 21
z = (21 -19.25)/2.943
z = 0.59
The value of p is 0.2776 when z score is 0.59.
The probability is 1 - 0.2776 = 0.7224.
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What is the value of x?
Answer: 2
Step-by-step explanation:
Since both triangles are similar you can set both side lengths to be equal
4x = 16x -24
Isolate x on one side
-12x = -24
Then solve for x
x = 2
For the holidays, Kenji is driving to visit his grandparents who live 402 miles away. Kenji's car
gets 33.5 miles per gallon of gas when he is driving on the highway. In order to budget for
his trip, Kenji wants to know how much gas he will need.
Use an equation to find how much gas Kenji needs for the drive.
Kenji needs
gallons of gas.
By solving a linear equation, it can be calculated that-
Kenji needs 12 gallons of gas for the drive
What is a linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a linear equation needs to be solved
Let Kenji requires x gallons of gas
Kenji's car gets 33.5 miles per gallon of gas when he is driving on the highway.
Kenji can travel 33.5x miles with x gallons of gas
Distance to be travelled = 402 miles
By the problem,
The required linear equation is
33.5x = 402
x = [tex]\frac{402}{33.5}[/tex]
x = 12 gallons
Kenji needs 12 gallons of gas for the drive
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Which graph shows y=2⌈x⌉−3 ???
Answer: the first 1
Step-by-step explanation:
i just did it hope it helps
Write an equation for the line parallel to the given line that contains C.
C(1,5); y= -4x+7
Answer:
y=-4x+9
Step-by-step explanation:
We will find an equation in the form of y = mx + b. We know m must be -4(because the slope must be the same for parallel lines), so we need to solve for b, which is the y-intercept. To do that, we will plug in the point C, giving us [tex]5 = -4 * 1 + b[/tex]. Adding 4 to both sides gives us b = 9, so that is the y-intercept.
Point p’ is the image of p (5,-5) under translation by 2 units left and 5 units up what are the cordinates of p’
Answer: (3,0)
Hope this helps! :)
Step-by-step explanation: Think of graphing, like regular number lines. The numbers are either positive or negative and depending on the integer you add or subtract, the number on the line will either move left or right.
x= 5 (x on a coordinate plane is left to right)
2 units left
5-2=3
y= -5 (y on a coordinate plane is top to bottom)
5 units up
-5+5=0
(3,0)
Answer:
(3,0)
Step-by-step explanation:
x= 5-2 = 3
y= -5+5 =0
solve (x+21)+(2x+9)=90
Answer:
The answer is x=20
Step-by-step explanation:
Answer:
x = 20
Step-by-step explanation:
(x+21)+(2x+9)=90
x + 21 + 2x + 9 = 90
combine numbers on left side:
x + 30 + 2x = 90
combine x terms on left side:
3x + 30 = 90
subtract 30 from both sides:
3x + 30 -30 = 90 - 30
3x = 60
divide both sides by 3:
3x/3 = 60/3
x = 20
An exponential growth function represents a quantity that has a constant
doubling time.
O A. True
OB. False
Answer:
false
Step-by-step explanation:
Hope it helps!
One angle of a triangle measures 75°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?
well, since a triangle has a total of 180° interior angles, that means 180 - 75 = 105 is leftover for the other two remaining angles.
now, they're in a 2 : 5 ratio, well, let's simply divide 105° by (2 + 5) and distribute accordingly.
[tex]2~~ : ~~5\implies 2\cdot \frac{105}{2+5}~~ : ~~5\cdot \frac{105}{2+5}\implies 2\cdot 15~~ : ~~5\cdot 15\implies \text{\LARGE 30~~ : ~~75 }[/tex]
Which additional piece of information would show that quadrilateral WXYZ is a rhombus?
The additional piece of information that is needed to show that the quadrilateral is a rhombus is given as follows:
The angle measures.
What is a rhombus?A rhombus is a quadrilateral, and is a special case of a parallelogram.
For the parallelogram to represent a rhombus, these following conditions need to be respected:
Parallelism of opposite sides.Congruence of opposite angles -> Same measures.All the sides are equal in length.The bisection of diagonals happen at right angles.To verify if two sides are parallel, we need to verify their slopes, which are dependent on their angle measures. Hence these angle measures are the missing piece of information to define if the quadrilateral is a rhombus.
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please help, no idea what to do
Confusing! Plsss Help!!!!!!
Answer:
y = 120°
Step-by-step explanation:
Given a triangle with external angle y and remote internal angles 33° and 87°, you want the measure of y.
External angleThe external angle is the sum of the remote internal angles:
y = 33° +87°
y = 120°
__
Additional comment
Angle x is supplementary to y, so its measure is ...
x = 180° -y = 180° -120°
x = 60°
Hopefully, you notice that the value of x is ...
x = 180° -(33° +87°)
This is the same value you get when you solve the equation for the sum of angles in the triangle:
33° +87° +x = 180°
Effectively, the rule regarding the external angle being the sum of remote internal angles is another way of saying the sum of angles in a triangle is 180°.
The probability that a marksman will hit a target each time he shoots is 0. 89. If he fires 15 times, what is the probability that he hits the target at most 13 times?.
The likelihood that a shooter will hit the target at least 13 times is 27.92%.
Define the phrase "binomial distribution" please.The number of times the target is hit, X, has to be a random variable.The amount of trials ("n") equals 10 as a result of 15 bullets being fired.In such a binomial distribution, "p" symbolizes the probability of success and "q" represents the probability of failure (where q = p - 1)p = 0.89 with q = 0.11 as a result of the 0.89 chance of hitting the target.For such a binomial distribution, the probability density function equals the amount of successes ("x").
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
The required number of achievements is five (i.e., x = 13), as we are keen in the development that the objective will be hit exactly five times.
P(X = 13) = ¹⁵C₁₃. (0.89)¹³ (0.11)²
P(X = 13) = 0.2792
P(X = 13) = 27.92%
Therefore, there is a 27.92% chance that a shooter will hit the target at most 13 times.
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Complete the statement by filling in the blank. When constructing a confidence interval, if the level of confidence increases the margin of error will and the confidence interval will be A larger sample size will improve the accuracy of the confidence interval, therefore margin of error will and the confidence interval will be A) Decrease, wider. Increase, narrower B) Decrease, narrower. Increase, wider C) Increase, wider. Decrease, narrower. D) Increase, narrower. Decrease, wider.
Option-C is correct that is increase, wider. If the level of confidence rises when generating a confidence interval, the margin of error must increase and the confidence interval will get wider.
Given that,
By completing the blanks, the sentence is complete. When generating a confidence interval, the margin of error and the confidence interval will be larger if the level of confidence grows.
We have to find the accuracy of the confidence interval will increase with a larger sample size, so the margin of error and the confidence interval will be-----.
We know that,
If the level of confidence rises when generating a confidence interval, the margin of error must increase and the confidence interval will get wider.
The margin of error is a phrase that conveys how much sampling error there is in the data that was gathered or in the parameter estimates. Accordingly, the credibility of the poll will decrease as the margin of error increases. It displays the degree of estimation accuracy.
Three things determine the margin of error:
Confidence level: The margin of error grows in proportion to the level of confidence.
Sample size: The margin of error gets smaller as the size of the random sample gets bigger.
Population standard deviation: The population's standard deviation is: For a given level of confidence, our interval will be wider the more dispersed the population is.
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a keypad at the entrance of a building has 10 buttons labeled 0 through 9. what is the probability of a person correctly guessing 8 digit entry code
The probability is it that someone will correctly guess an 8-digit entry code is 0.022.
Given that,
A keypad with 10 buttons marked 0 through 9 is located at the building's entrance.
We have to find how much probability is it that someone will correctly guess an 8-digit entry code.
We know that,
Probability is defined as the ratio of the number of required outcomes to the total number of outcomes.
Based on the details provided;
One outcome is expected if the needed number of outcomes is 8-digits.
Since there are 10 numbers and 8 numbers need to be chosen, the total number of outcomes is ¹⁰C₈.
Considering that the lock can only be opened by 8 digits;
The probability that someone will properly guess a 8-digit input code is
P=1/¹⁰C₈
P=1/10!/8!2!
P=1/10×9/2
P=1/45
P=0.022
Therefore, The probability is it that someone will correctly guess an 8-digit entry code is 0.022.
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Wrote an equation with a vertex : (4,-5)
passes through: (2,-1)