Answer:
76.09 pounds
Step-by-step explanation:
From the information given:
[tex]R_{in} = (\dfrac{1}{2} \ lb/gal ) *(6 \ gal/min)[/tex]
[tex]R_{in} =3 \ lb/min[/tex]
At a slower of 4 gal/min, the solution gets pumped out;
So,
[tex]R_{out} = \dfrac{4A}{100+(6-4)t }[/tex]
[tex]R_{out} = \dfrac{2A}{50+t }[/tex]
The differential of the equation is:
[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A=3 ---(1)[/tex]
For the linear differential equation, the integrating factor is determined as:
[tex]\int_e \dfrac{2}{50 +t}dt = e^{2 In|50+t|[/tex]
[tex]= (50+t)^2[/tex]
Multiplying [tex](50+t)^2[/tex] with the above integration factor;
[tex](50+t)^2 \dfrac{dA}{dt} + 2 (50+t) A = 3(50 +t)^2[/tex]
[tex]\dfrac{d}{dt}[ (50 +t)^2 A] = 3(50+t)^2[/tex]
[tex](50+t)^2 A = (50 +t)^3 + c[/tex]
[tex]A = (50 +t) + c (50 +t )^{-2}[/tex]
By using the given condition:
A(0) = 40
40 = 50 + c (50)⁻²
10 = c(50)⁻²
OR
c = -10 × 2500
c = -25000
A = (50 + t) - 25000(50 + t)⁻²
The number of pounds of salt in the tank after 30 min is:
A(30) = (50+30) - 25000(50 + 30)⁻²
[tex]A(30) = 80 - \dfrac{25000}{6400}[/tex]
[tex]A(30) = 76.09 \ pounds[/tex]
Thus, the number of pounds of salt in the tank after 30 min is 76.09 pounds.
Kim, Mary and Erin made a total of 24 dozen cookies. Mary made twice as many cookes as Erin and Kim made 2 more dozen cookies than Erin. How many cookies did Erin make
Answer:
Erin made 5.5 dozen cookies.
Step-by-step explanation:
Total cookies made by Kim, Mary and Erin = 24 dozen cookies
Let Erin make cookies = x dozens
Mary made cookies = 2x dozens
Kim made cookies = x+2 dozens
Now, we need to find how many cookies did Erin made.
We can write:
[tex]x+2x+x+2=24[/tex]
Solving the equation we get:
[tex]x+2x+x+2=24\\4x+2=24\\4x=24-2\\4x=22\\x=22/4\\x=5.5[/tex]
So, Erin made cookies = x = 5.5 dozens
Mary made cookies = 2x =2(5.5) = 11 dozens
Kim made cookies = x+2 =5.5+2 = 7 dozens
Therefore, Erin made 5.5 dozen cookies.
1. Given that cosθ≈0.646 where θ is in quadrant IV, find the values of sinθ and tanθ to the nearest thousandth
a. sinθ=−0.763; tanθ=−1.181
b. sinθ=−0.763; tanθ=−0.847
c. sinθ=0.763; tanθ=0.847
d. sinθ=0.763; tanθ=1.181
2. Terran’s running rate is 4 miles per hour faster than her walking rate. She can run 21 miles in the same amount of time it takes her to walk 9 miles. What are her walking and running rates in miles per hour? Write and solve a rational equation to answer the question. Let x be Terran’s walking rate
a. 21/x+4=9/x; Terran walks at 2 miles per hour and runs at 6 miles per hour.
b. 21/x=9/x−4; Terran walks at 7 miles per hour and runs at 10 miles per hour.
c. 21/x=9/x−4; Terran walks at 4 miles per hour and runs at 8 miles per hour.
d. 21/x+4=9/x; Terran walks at 3 miles per hour and runs at 7 miles per hour.
Answer:
d.) sinθ=0.763; tanθ=1.181
c. 21/x=9/x−4; Terran walks at 4 miles per hour and runs at 8 miles per hour.
Step-by-step explanation:
Given that:
θ is in the IV quadrant (All is positive) that is sin, cos and tan are all positive.
Cosθ = 0.646
Θ = Cos^-1(0.646)
θ = 49.75930
Hence,
Tanθ = tan(49.75930) = 1.1816365 = 1.182
Sinθ = sin(49.75930) = 0.7633373 = 0.763
2.)
Let
Walking rate = x mph
Running rate = x + 4 mph
21 miles run time = 9 miles walk time
Recall :
Time = distance / speed or rate
21 / (x + 4) = 9 / x
Cross multiply :
21 * x = 9(x + 4)
21x = 9x + 36
21x - 9x = 36
12x = 36
x = 36 /12
x = 4 mph = walking rate
Running rate = x + 4 = 4 + 4 = 8 mph
F(x)=x-7
What is the value of x when f(×) =3
Answer:
3= x - 7 (write out the equation and think of what number with 7 subtracted would be equal to 3)
3= 10-7 (10-7 is equal to three, so that's what x has to be)
x=10
Step-by-step explanation:
Calculate the correlation coefficient, r, for the data below.
This question is incomplete, the complete question is;
Calculate the correlation coefficient, r, for the data below.
X = -10 -8 -1 -4 -6 -7 -5 -3 -2 -9
Y = -15 -13 4 -4 -7 -11 -6 -2 1 -13
Answer: the correlation coefficient, r, for the data is 0.9896
Step-by-step explanation:
Given the data in the question;
correlation coefficient r = ?
we know that, C_Coeff is;
r = [ (Zn(∑xy) - (∑x)(∑y) ] / [ √[( n∑x² - (∑x)²) ( n∑y² - (∑y)²)] ]
so ;
X Y X² Y² XY
-10 -15 100 225 150
-8 -13 64 169 104
-1 4 1 16 -4
-4 -4 16 16 16
-6 -7 36 49 42
-7 -11 49 121 77
-5 -6 25 36 30
-3 -2 9 4 6
-2 1 4 1 -2
-9 -13 81 169 117
∑ -55 -66 385 806 536
now we substitute our values into the formula
r = [ (10×536 - (-55)(-66) ] / [ √[( 10×385 - (-55)²) ( 10×806 - (-66)²)] ]
r = 1730 / √( 825 × 3704 )
r = 1730 / √3055800
r = 1730 / 1748.0846
r = 0.9896
Therefore the correlation coefficient, r, for the data is 0.9896
6. A trail is 13.5 miles long. There are markers every 0.25 mile along the trail, including at the
end of the trail. How many markers are there in all?
a) 4
b) 5
c) 40
d) 54
Answer:
54
Step-by-step explanation:
13.5/0.25=54
simplify:
[tex] \frac{ \sqrt{4} }{ \sqrt[3]{4} } [/tex]
choices:
[tex]4 \frac{5}{6} [/tex]
[tex]4 \frac{1}{6} [/tex]
[tex]4 \frac{3}{2} [/tex]
[tex]4 \frac{1}{3} [/tex]
Step-by-step explanation:
= 4^1/2 /4^1/3
=4^1/2-1/3
=4^1/6
over a 5-year period.
Investment over
5 years
Value of investment (£)
1140
1120
1100
1080
1060
61040
1020
1000
0
0 1 2 3 4 5
Year
Answer:
Year 0 900$
Year 1 1000$
year 2 1080$
Year 3 61040$- (interest comes in)
Year 4 110000$
Year 5 152000$
Step-by-step explanation:
Make sure you put that interest comes in or you will be marked wrong.
You're welcome :D GoodLuck have a good day
For a discrete random variable that takes a value of 8 with probability .75 and a value of -4 with probability of .25, what is the expected value and what is the variance
Answer:
5.20
Step-by-step explanation:
X : ______ 8 ____ - 4
P(X) : ___ 0.75 __ 0.25
The expected mean E(x) :
E(x) = ΣX / n
n = sample size = 2
E(x) = (8*0.75) + (-4*0.25)
E(x) = 6 - 1
E(x) = 5
The standard deviation : sqrt(Var(x))
Var(x) = Σx²p(x) - E(x)²
Var(x) = (8^2 * 0.75) + (-4^2 * 0.25)) - 5^2
Var(x) = ((64 * 0.75) + (16* 0.25)) - 25
Var(x) = (48 + 4) - 25
Var(X) = 27
Standard deviation = sqrt(27)
Standard deviation (x) = 5.1961524
Standard deviation = 5.20
A bag contains 30 lottery balls numbered 1-30. A ball is selected, replaced, then another is drawn. Find each probability.
1. p(even, then odd)
2. p(7 and then a number greater than 16)
3. p(a multiple of 5 and then a prime number)
4. p(two even numbers)
Answer:
17÷3 ok so it was just a compliment sometime soon
2x/3- y +7; x = 9, y=4
Answer:
-5
Step-by-step explanation:
2×9/3 - (4+7)
18/3 -11
18/3 - 33/3
-15/3
-5
Answer:
9
Step-by-step explanation:
2x/3- y +7; x = 9, y=4
plug in the numbers
2(9)/3-(4)+7
simplify 2(9)/3
2 • 9=18
18/3=6
6-4+7
6-4= 2
2+7=9
jester has a piece of wood measuring 1 and 2/3 m.he needs to cut in pieces measuring 3/4 m. long.how many pieces of wood did jester cut.
Answer:
2
Step-by-step explanation:
Given that,
Jester has a piece of wood measuring 1 and 2/3 m = 5/3 m
He needs to cut in pieces measuring 3/4 m
We need to find the number of pieces. Let there are x no. of pieces.
[tex]x=\dfrac{\dfrac{5}{3}}{\dfrac{3}{4}}\\\\=\dfrac{5}{3}\times \dfrac{4}{3}\\\\=2.23\[/tex]
or
x = 2
So, he will cut it into approx 2 pieces.
Is this a function?
Percent is always out of _________ ?
Answer:
Percent is always out of 100
Step-by-step explanation:
Answer:
100
Step-by-step explanation:
QUICK EZ MATH
A bookcase is 4 ft tall. A model of the bookcase is 6 ft tall. What is the ratio of the height of the model bookcase to the height of the real bookcase?
Answer:
4:6
Step-by-step explanation:
The ratio of the height of the model bookcase to the height of the real bookcase will be 3: 2.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
A bookcase is 4 ft tall. A model of the bookcase is 6 ft tall.
The ratio of the height of the model bookcase to the height of the real bookcase is given by the division of the numbers 4 and 6. Then we have
Ratio = 6 / 4
Simplify the ratio, then we have
Ratio = 6 / 4
Ratio = 3 / 2
Ratio = 3: 2
The ratio of the height of the model bookcase to the height of the real bookcase will be 3: 2.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ5
Ravi buys pounds of flour. How many ounces of flour does he buy?
There is 16 ounces in each pound, how ever many pounds it is multiply 16 by the number of pounds,
Step-by-step explanation:
how ever many pounds it is multiply 16 by the number of pounds,
Helpppppppppppppppppp
Answer:
option C
Step-by-step explanation:
Answer:
c number is right anwer .... . .... ..
The natural market sells a 12-ounce jar of peanut butter for $3.96. They also sell bulk peanut butter for $5.50 per pound. The ____ has a cheaper unit rate.
Answer:
The Jar of peanut butter
Step-by-step explanation:
The easiest way to do this is to calculate price per ounce of each unit.
We'll assign the 12 ounce jar to the variable s and the bulk to the variable b.
First create an equation to find the values of each product per ounce.
Since the 12 ounce jar(s) sells for 3.96 we can say it is 3.96 for every 12 ounces, or s = 3.96/12oz.
Simplify this equation and you get s = 0.33 per ounce.
For b we need to convert pounds to ounces.
There are 16 ounces per pound so the equation we get is:
b = 5.50/16oz
Simplified we get:
b = about 0.34/oz
The smaller jar has a rate of $0.33/oz
The bulk has a rate of $0.34/oz
This means the answer is b. The jar of peanut butter has a cheaper unit rate.
Answer:
jar of peanut butter
Step-by-step explanation:
X= What does ×= 88, 89 or 90
Two-thirds of a number is equal to negative one-fifth. What is the number?
-7 1/2
-3/10
-2/15
-3 1/2
Answer:
maybe -3/10? (i did 2/3n = -1/5)
:)
4x-5+2r= -11
What is the value of x?
Help me on this question please
Answer:
the first one:)))
Step-by-step explanation:
8 soccer cards and 4 baseball cards in one box, 6 soccer cards and 3 baseball cards in another box
what is the graph in slope intercept form
Answer: Slope intercept form is y=mx+b, where m is slope and b is the y-intercept. We can use this form of a linear equation to draw the graph of that equation on the x-y coordinate plane.
Step-by-step explanation:
Answer:
Slope intercept form is y=mx+b which is m is slope and b is the y-intercept.
Step-by-step explanation:
Megan is taking the bus from New York City to Montreal. The distance is 380 miles and the bus travels at a steady rate of 76 miles per hour. How long will the bus ride be?
Answer: 5 hours
Step-by-step explanation: 380/76
The bus will take 5 hours to reach Montreal from New York.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Distance between Montreal to New York = 380 miles
Speed of bus = 76 miles per hour
76 miles ⇒ 1 hour
1 mile ⇒ 1/76 hour
Multiply by 380 on both sides
380 miles ⇒ 380/76 hours = 5 hours.
Hence "The bus will take 5 hours to reach Montreal from New York".
For more information about ratio and proportion,
brainly.com/question/26974513
#SPJ2
lines DE and AB intersect at point C.
What is the value of X?
12
25
38
52
ignore the answer i marked, i was guessing around.
Answer:
B
Step-by-step explanation:
∠ACE and ∠ECB form a straight angle whose sum = 180°, hence
2x + 2 + 5x + 3 = 180
7x + 5 = 180 ( subtract 5 from both sides )
7x = 175 ( divide both sides by 7 )
x = 25 → C
Please help!! Will give brainliest!!
Answer:
n=6
Step-by-step explanation:
64(4^n)=262144 then divide it by 64 which is 4^n=4096. divide 4096 by 4 and you get 6
Answer: im sorry bbut i dunno
Step-by-step explanation:
Please help quick!!
Which expression is equivalent to
25?
- 2 + 2 + 2 + 2 + 2
- 5 + 5
- 2 · 2 · 2 · 2 · 2
- 5 · 5
the last one sorry i thought 5 was negative lol
Answer:
5 · 5
Step-by-step explanation:
2 + 2 + 2 + 2 + 2 = 10
5 + 5 = 10
2 · 2 · 2 · 2 · 2 = 32
5 · 5 = 25
A rectangular based prism has a length of
12m a width of 7m and height of 11m. Find
its volume.
Answer:
924m^3 is the volume of the rectangular prism
Round the following numbers to 2 decimal places.
b)
562.6783
Answer:
b is the correct answer i know it is
Please help again!!!!!!!!
Answer:
94.077=90+4+0.07+0.007
Step-by-step explanation:
I hope this answered your question
Answer:
a) 94.077= 90+ 4+ 0.07 + 0.007Step-by-step explanation:
I hope it helps you ❤❤49 – 3m = 4m + 14 please help
Answer:
m=5
Step-by-step explanation:
