Answer:
[tex]g=\frac{2\,H}{m+r}[/tex]
Step-by-step explanation:
Starting with :
m g + r g = 2 H
extract "g" as a common factor on the left of the equal sign:
g (m + r) = 2 H
Now, in order to solve for "g" , divide both sides of the equal sign by the binomial (m + r):
g = (2 H )/(m + r)
[tex]g=\frac{2\,H}{m+r}[/tex]
A very large tank initially contains 100L of pure water. Starting at time t = 0 a solution with a salt concentration of 0.8kg/L is added at a rate of 5L/min. The solution is kept thoroughly mixed and is drained from the tank at a rate of 3L/min.
1. Let y(t) be the amount of salt (in kilograms) in the tank after t minutes. What differential equation does y satisfy?
2. How much salt is in the tank after 40 minutes?
Answer:
1. [tex]\dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}[/tex]
2. [tex]y(40) = 110.873 \ kg[/tex]
Step-by-step explanation:
Given that:
A very large tank initially contains 100 L of pure water.
Starting at time t = 0 a solution with a salt concentration of 0.8kg/L is added at a rate of 5L/min.
. The solution is kept thoroughly mixed and is drained from the tank at a rate of 3L/min.
As 5L/min is entering and 3L/min is drained out, there is a 2L increase per minute. Therefore, the amount of water at any given time t = (100 +2t) L
t = (50 + t ) L
Since it is given that we should consider y(t) to be the amount of salt (in kilograms) in the tank after t minutes.
Then , the differential equation that y satisfies can be computed as follows:
[tex]\dfrac{dy}{dt}=rate_{in} - rate_{out}[/tex]
[tex]\dfrac{dy}{dt}=(0.8)(5) -\dfrac{y(t)}{100+2t} \times3[/tex]
[tex]\dfrac{dy}{dt}=(0.8)(5) -\dfrac{3y}{100+2t}[/tex]
[tex]\dfrac{dy}{dt}=4-\dfrac{3y(t)}{100+2t}[/tex]
How much salt is in the tank after 40 minutes?
So,
suppose : [tex]e^{\int \dfrac{3}{100+2t} \ dt} = (t+50)^{3/2}[/tex]
Then ,
[tex]( t + 50)^{3/2} y' + \dfrac{3}{2}(t+50)^{1/2} y = 4(t+50)^{3/2}[/tex]
[tex]( t + 50)^{1.5} y' + \dfrac{3}{2}(t+50)^{0.5} y = 4(t+50)^{3/2}[/tex]
[tex][y\ (t + 50)^{1.5}]' = 4(t+ 50)^{1.5}[/tex]
Taking the integral on both sides; we have:
[tex][y(t + 50)^{1.5}] = 1.6 (t + 50)^{2.5} + C[/tex]
[tex]y = 1.6 (t+50)+C(t+50)^{-1.5}[/tex]
[tex]y(0) = 0 = 1.6(0+50) + C ( 0 + 50)^{-1.5}[/tex]
[tex]0 = 1.6(50) + C ( 50)^{-1.5}[/tex]
[tex]C= -1.6(50)^{2.5}[/tex]
[tex]y(40) = 1.6 (40 + 50)^1 - 1.6 (50)^{2.5}(50+40)^{-1.5}[/tex]
[tex]y(40) = 144 - 1.6 \times 17677.66953 (90)^{-1.5}[/tex]
[tex]y(40) = 144 - 1.6 \times 17677.66953 \times 0.001171213948[/tex]
[tex]y(40) = 144 - 33.12693299[/tex]
[tex]y(40) = 110.873 \ kg[/tex]
Hello, there are three questions and pictures of them in the links If you could solve them that would be awesome, thank you!
Answer:
1. 1 * [tex]x^{3/6}[/tex] = [tex]x^{3/6}[/tex] (it will be equal to the sixth root of x cube)
2. No, the expression [tex]x^{3}[/tex] X [tex]x^{3}[/tex] X [tex]x^{3}[/tex] will be equal to [tex]x^{3 + 3 + 3 }[/tex] since the powers of numbers with the same base are added
3. B and D 1/[tex]x^{-1}[/tex] is the same as 'x'
as mentioned in the last answer, powers of numbers with same base are added. hence, option D will be [tex]x^{3/3}[/tex] which will be equal to x
Google maps has told Juanita that her car trip will be 32 miles. Juanita has already gone 14 miles. How fast, in miles per hour, must Juanita drive to arrive in 16 more minutes?
Answer:
Speed= 67.5 miles per hour
Step-by-step explanation:
Google maps has told Juanita that her car trip will be 32 miles.
Juanita has already gone 14 miles.
Remaining miles left to travel
= 32-14
Remaining miles left to travel
= 18 miles
She has only 16 minutes to reach her destination.
The required speed for her to reach her destination
= Distance/time
Her time = 16 minutes
Her time = 16/60
Her time =4/15 hours
Speed= distance/time
Speed= 18 /(4/15)
Speed=18* 15/4
Speed= 67.5 miles per hour
Juanita needs to drive at 67.5 miles per hour to arrive in 16 more minutes
The total distance (D) is given as:
[tex]\mathbf{D = 32miles}[/tex]
She has traveled 14 miles;
So, the remaining distance (d) is:
[tex]\mathbf{d = D -14}[/tex]
This gives
[tex]\mathbf{d = 32 -14}[/tex]
[tex]\mathbf{d = 18}[/tex]
Speed is calculated as:
[tex]\mathbf{Speed = \frac{distance}{time}}[/tex]
Where: distance = 18 miles and time = 16 minutes
So, we have:
[tex]\mathbf{Speed = \frac{18\ miles}{16\ minutes}}[/tex]
Convert time to hour
[tex]\mathbf{Speed = \frac{18\ miles}{16/60\ hour}}[/tex]
So, we have:
[tex]\mathbf{Speed = \frac{18 \times 60\ miles}{16\ hour}}[/tex]
[tex]\mathbf{Speed = \frac{1080\ miles}{16\ hour}}[/tex]
Divide
[tex]\mathbf{Speed = 67.5\ miles/ hour}[/tex]
Hence, the speed is 67.5 miles per hour
Read more about speed and distance at:
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A partially amortizing loan of $200,000 is made with 4.55% annual interest. A balloon of $20,000 exists on the loan. If the monthly payments are $2,500, in how many years will the loan be fully repaid?
Answer:
7.28 years
Step-by-step explanation:
Given that:
A partially amortizing loan of with a present value = $200000
is made with a 4.55% annual interest rate.
i.e rate (4.55/100) ÷ 12
= 0.0455 ÷ 12
= 0.00379
A balloon of $20,000 exists on the loan
This implies that the Present value of the loan = 20000
If the monthly payments PMT are $2,500
The number of years that it will require for the loan to be fully repaid can be calculated by using the EXCEL FUNCTION (=NPER(0.00379;-2500;200000;-20000;0) )
= 87.3997 /12
= 7.28 years
The Excel computation can be found in the attached file below
Help me please thank you
Answer:
x = 7
Step-by-step explanation:
5x + 9 = 6x + 2
5x - 6x = 2 - 9
-x = -7
x = 7
probe:
5*7 + 9 = 6*7 + 2
35 + 9 = 42 + 2 = 44
Answer:
x = 11
Step-by-step explanation:
The angles shown are alternate exterior angles. If they are equal, then the lines are parallel
5x+9 = 6x-2
Subtract 5x from each side
5x-5x+9 = 6x-5x-2
9 = x-2
Add 2 to each side
9+2 = x
11 =x
A simple random sample of college students was performed recently in which the students were asked to self identify as to whether they are binge drinkers or not. In a 1995 study it was found that about 44% of students were self identified as such and the researcher believed that this number has increased. In this study 7851 of the 17592 students interviewed self identified as binge drinkers. A 90% confidence interval of the estimated binge drinking rate is
Answer:
The 90% confidence interval is [tex]0.445< p < 0.456[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 17592[/tex]
The number of binge drinkers is [tex]k = 7851[/tex]
Given that the confidence level is 90% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 90)\%[/tex]
[tex]\alpha = 0.10[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
The sample proportion is mathematically represented as
[tex]\r p = \frac{ 7851}{ 17592}[/tex]
[tex]\r p = 0.45[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{ \frac{x}{y} } * \sqrt{\frac{\r p(1 - \r p )}{n} }[/tex]
[tex]E =1.645 * \sqrt{\frac{ 0.45 (1 - 0.45 )}{17592} }[/tex]
[tex]E =0.00617[/tex]
The 90% confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
[tex]0.45 -0.00617 < p < 0.45 + 0.00617[/tex]
[tex]0.445< p < 0.456[/tex]
Which of these random samples qualifies as a representative sample to find out what parents think about the levels of college tuition fees in the state? a.) 50 residents of a city in the state b.) 50 parents of college students from another state c.) 50 parents of college students from the state d.) 50 residents of a county in the state
The correct answer is C) 50 parents of college students from the state
Explanation:
The purpose of representative samples is to study a population by only selecting a small group in it. Due to this, the individuals selected as part of the sample need to match the characteristics of the population being studied.
In this context, if the focus is the opinion of parents about college tuition fees in a specific state, it is expected the sample includes parents of college students rather than students, citizens, etc. because the opinion of parents of college students is being evaluated. Moreover, those parents selected should have children in the state being studied. According to this, the correct option is C because this includes individuals who can appropriately represent the population that is being analyzed.
Answer:
50 parents of college students from the state.
Step-by-step explanation:
Sophia Statistics
In order to go to college, Chris goes from working full-time making $30,000 per year to working part-time at half the salary for two years. The cost of his education will be $5,000. If Chris makes $35,000 per year after getting his degree, approximately how many years will it take him to recover his investment?
Answer:
Step-by-steIn order to go to college, Chris goes from working full-time making $30,000 per year to working part-time at half the salary for two years. The cost of his education will be $5,000. If Chris makes $35,000 per year after getting his degree, approximately how many years will it take him to recover his investment? *
it would take him 7 years to recover the 35,000 he invested
p explanation:
he was in college two years and it cost him a total of 5000 and he lost 30000 from the two years he worked part time
Determine whether the relation is a function. {(−3,−6),(−2,−4),(−1,−2),(0,0),(1,2),(2,4),(3,6)}
Answer:
Yes, this is a function
Step-by-step explanation:
This relation is function because 1 x value corresponds to 1 y value
The data below represent the weight losses for people on three different exercise programs.
Exercise A Exercise B Exercise C
2.5 5.8 4.3
8.8 4.9 6.2
7.3 1.1 5.8
9.8 7.8 8.1
5.1 1.2 7.9
If we want to test the claim that the three size categories have the same means, why don't we use three separate hypothesis tests for μ1 = μ2, μ2 = μ3, and μ1 = μ3?
A. The risk of type l error increases and becomes too high.
B. Actually, we do want to use three separate hypothesis tests.
C. The risk of type ll error increases and becomes too high.
D. A hypothesis test for comparing two means does not exist.
Answer:
A. The risk of type l error increases and becomes too high.
Step-by-step explanation:
The overall level of significance increases as the number of t- tests ( used for comparing two, three or four means separately ) increases. This in turn increases the risk of type I error.
We might be tempted to apply the two sample t- test to all possible pairwise comparisons of means. This type of running t- test to several means comparison has the risk of increasing overall level of significance
What is the difference in finding the length of a segment that is drawn on a sheet of blank paper and segment that is drawn on a coordinate plane?
If you have tickmarks on the segment, on a blank piece of paper, then you count out the spaces to get the length of the segment. This is assuming the tickmarks are properly spaced out. If there aren't any tickmarks, then you'll have to use a ruler to find the length. Either way, a ruler is encouraged.
The coordinate plane makes things easier to find the length of any segment. Use either the pythagorean theorem or the distance formula to find the length of the segment.
Consider the following sets. U = {all real number points on a number line} A = {solutions to the inequality 3x + 4 ≥ 13} B = {solutions to the inequality One-halfx + 3 ≤ 4} For which values of x is A ⋃ B = Ø? 2 3
Answer:
2 < x < 3
Step-by-step explanation:
Set A)
3x + 4 ≥ 13
3x ≥ 9
x ≥ 3
Set B)
0.5x + 3 ≤ 4
0.5x ≤ 1
x ≤ 2
Plot it out on a number line, and you'll see that 2 < x < 3
Answer:
It's A
Step-by-step explanation:
What is the value of t?
Answer:
[tex]t=22[/tex]
Step-by-step explanation:
First, note that the entire thing is a square. This is because since two of the opposite angles are right angles, the remaining two must also be right angles.
In a square, all four sides are equivalent.
Therefore, the sides PS an RS are equal to each other. Thus:
[tex]PS=RS\\t+22=2t\\22=t\\t=22[/tex]
Linda Roy received a $200,000 inheritance after taxes from her parents. She invested it at 4% interest compounded quarterly for 3 years. A year later, she sold one of her rental properties for $210,000 and invested that money at 3% compounded semiannually for 2 years. Both of the investments have matured. She is hoping to have at least $500,000 in 7 years compounded annually at 2% interest so she can move to Hawaii. Will she meet her goal?
Answer:
Step-by-step explanation:
Matured amount of $200000 at 4% compounded quarterly after 3 years
= $200000 x ( FVIF , 1 , 12 )
= $200000 X 1. 1268
= $225360 .
Matured amount of $210000 at 3% compounded semiannually after 2 years
= $210000 x ( FVIF , 1.5 , 4 )
= $210000 X 1. 1268
= $225360 x 1.0614
= $239197
Total amount after maturity
= $225360 + $239197
= $464557
Matured amount of $464557 at 2% compounded annually after 7 years
= $464557 x ( FVIF , 2 , 7 )
= $464557 x 1.1487
= $533636.6
This amount is more than his target amount of 500000.00 So she meets the goal .
Find the value of “a”
Answer:
The correct answer is a = 8.
Step-by-step explanation:
To solve this problem, we must remember the formula for slope, which is:
slope = m = (y2 - y1)/(x2 - x1)
Now, we can plug in the values that we are given into the slope formula:
-3/2 = (-3-6)/(a-2)
Now, we should begin to simplify the equation.
-3(a-2) = 2(-9)
We can use the distributive property to eliminate the parentheses on each side of the equation:
-3a + 6 = -18
Then, we can subtract 6 from both sides of the equation to get the variable term alone on the left side of the equation:
-3a = -24
Finally, we should divide both sides by -3 to completely isolate the variable on the left side of the equation:
a = 8
Therefore, the correct answer is a= 8.
Hope this helps!
Sketch the region bounded by the curves, and visually estimate the location of the centroid. Then find the exact coordi nates of the centroid. y=2x, y=0, x=1
Answer:
coordinates of the centroid = [tex](\frac{2}{3} , \frac{2}{3} )[/tex]
Step-by-step explanation:
The curves to be plotted are : y =2x, y = 0, x =1
The coordinates of the centroid ( visually estimated ) can be found by first calculating the area of the region
A = [tex]\int\limits^1_0 {2x} \, dx[/tex] = 2[tex](\frac{x^2}{2} )[/tex] hence A = 1
attached below is the remaining part of the solution
cual es los primeros tres digitos de pi
Answer:
3.14
Step-by-step explanation:
Los primeros tres son 3.14
Evaluate the expression if x=12, y=8, and z=3 4x-yz
Answer:
[tex]\huge \boxed{24}[/tex]
Step-by-step explanation:
Let if x=12, y=8, and z=3.
[tex]4(12)-(8)(3)[/tex]
Evaluate.
[tex]48-24[/tex]
[tex]=24[/tex]
Start by substituting the appropriate numbers in for
your variables, using parenthses as you go.
You'll get 4(12) - (8)(3).
Now think about your order of operations.
Multiplication comes before subtraction.
So first multiply 4(12) to get 48.
So we have 48 - (8)(3).
Now multiply (8)(3) to get 24.
So we have 48 - 24 which is 24.
County had 112 cases on June 22. On July 22 there were 553 cases. At that rate, how many days will it take before there are 1000 cases?
Answer:
30.4 days or 31 days
Step-by-step explanation:
553 - 112 = 441
it took 30 days for 441 cases
30 / 441 = 0.06802721088
1000 - 553 = 447
0.06802721088 x 447 = 30.4081632653
30.4 days or 31 days
What value of c makes x2 − 24x + c a perfect square trinomial? −144 −48 48 144
Answer:
144
Step-by-step explanation:
Hello, please consider the following.
[tex]x^2-24x+c[/tex]
is a perfect square means that the discriminant is 0.
[tex]\Delta = b^2-4ac=24^2-4c=0\\\\<=>24^2-4c =0<=> 4c=576\\\\\text{We divide by 4}\\\\c= \dfrac{576}{4}=144[/tex]
Thank you
The value of c which make a perfect square trinomial is,
⇒ c = 144
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ x² - 24x + c
Now, We can it squared as;
⇒ x² - 24x + c
⇒ x² - 2 × 12x + 144
⇒ x² - 24x + 12²
⇒ (x - 12)²
Thus, The value of c which make a perfect square trinomial is,
⇒ c = 144
Learn more about the mathematical expression visit:
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the martin fruit co charges 7% commission for selling fruit. the commission for selling 516 crates of oranges at 16.30 per crate is:
Answer:
588.76
Step-by-step explanation:
Commission is 7% of total
Total selling price of 516 crates of oranges:
516*16.3 = 8410.8Commission amount:
0.07*8410.8 ≈ 588.76Jana's friend draws a card that shows a 0. Draw a point at 0. What is the opposite of 0?
Explain.
Answer:
There is no opposite of 0.
Step-by-step explanation:
There cannot be a zero the opposite of zero. If there was, then there would be two 0's, and there is only one.
what is the next two sequence -1, 5, -25, 125
Answer:
-625,3125
Step-by-step explanation:
Im not saying this is correct but it looks like its multipling by 25
Stella rewrite -2 1/2+3.7 using the commutative property of addition. Which expression did she write
Answer:
Step-by-step explanation
C
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between and minutes. Find the probability that a given class period runs between and minutes.
Question:
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 55.0 minutes. Find the probability that a given class period runs between 50.75 and 51.5 minutes.. (Round to three decimal places as needed.)
Answer:
[tex]Probability = 0.150[/tex]
Step-by-step explanation:
Given
Type of distribution: Uniform Distribution
Distribution Interval: 50.0 to 55.0
Required
Determine the probability that her class is between 50.75 and 51.5
First, we need to calculate the difference between the distribution interval (D1)
[tex]D1 = 55.0 - 50.0[/tex]
[tex]D1 = 5.0[/tex]
Next is to calculate the difference between the probability interval (D2)
[tex]D2 = 51.50 - 50.75[/tex]
[tex]D2 = 0.75[/tex]
The required probability is calculated by dividing D2 by D1
[tex]Probability = \frac{D2}{D1}[/tex]
[tex]Probability = \frac{0.75}{5.0}[/tex]
[tex]Probability = 0.150[/tex]
Help!!!!!! What is the absolute value of Point A labelled on the number line? Drag and drop the answer into the box to match the correct statement.
Answer:
see below (I hope this helps!)
Step-by-step explanation:
We can see that every 3 tick marks on the line is 1, therefore, the space between 2 tick marks is 1/3. Using this information, we can see that A = [tex]-3\frac{1}{3}[/tex]. The absolute value of a negative number is simply the additive inverse of the number, therefore, our answer is [tex]-(-3\frac{1}{3}) = 3\frac{1}{3}[/tex].
B=3x+9xy solving for x
Answer:
Dear its two variable function so either you should give me other function of x and y or you should give me condition to solve this problem
so see you next time
Step-by-step explanation:
Figure ABCD is a rectangle. Which segment is parallel to AB?
D
A
С
B
Answer:
cd
Step-by-step explanation:
Because if you think of a rectangle the parallel side is CD
Answer:
segment CD would be parallel to segment AB
Step-by-step explanation:
CORRECT ANSWER GET BRAINLIEST!! PLS HELP FAST!!
Answer:
1. 0.5 for x, 3 for y
2. 1.5 for x, 9 for y
3. 2.5 for x, 15 for y
Step-by-step explanation:
I will explain later if you still need help...but you said you need it fast, so I don't want to be too slow. :)
Find the value of 717×213 Although these numbers aren't quite as nice as the ones from the example, the procedure is the same, so the difficulty is the same same excepting the ability to perform the calculation in your head. You may choose to use a calculator.
Answer:
717 * 213 = 152721
Step-by-step explanation:
Given
717 and 213
Required
Multiply
Rewrite in the following form
7 1 7
* 2 1 3
---------------------
Start by multiply 717 by 3
7 1 7
* 2 1 3
---------------------
2 1 5 1
Then multiply 717 by 1
7 1 7
* 2 1 3
---------------------
2 1 5 1
7 1 7
Then multiply 717 by 2
7 1 7
* 2 1 3
---------------------
2 1 5 1
7 1 7
1 4 3 4
Lastly, add the resulting digits
7 1 7
* 2 1 3
---------------------
2 1 5 1
7 1 7
1 4 3 4
--------------------------
1 5 2 7 2 1
Hence; 717 * 213 = 152721