Answer:
32.1 g
Step-by-step explanation:
In each 3 grams of C, there are 2 grams of A and 1 gram of B. So, for some amount C, the amount remaining of A is 40 -(2C/3), and the amount remaining of B is (50 -C/3). Since the reaction rate is proportional to the product of these amounts, we have ...
C' = k(40 -2C/3)(50 -C/3) = (2k/9)(60 -C)(150 -C) . . . for some constant k
This is separable differential equation with a solution of the form ...
ln((150 -C)/(60 -C)) = at + b
We know that C(0) = 0, so b=ln(150/60) = ln(2.5). And we know that C(10) = 20, so ln(130/40) = 10a +ln(2.5) ⇒ a = ln(1.3)/10
Then our equation for C is ...
ln((150 -C)/(60 -C)) = t·ln(1.3)/10 +ln(2.5)
__
For t=20, this is ...
ln((150 -C)/(60 -C)) = 2ln(1.3) +ln(2.5) = ln(2.5·1.3²) = ln(4.225)
Taking antilogs, we have ...
(150 -C)/(60 -C) = 4.225
1 +90/(60 -C) = 4.225
C = 60 -90/3.225 ≈ 32.093 . . . . . grams of product in 20 minutes
In 20 minutes, about 32.1 grams of C are formed.
The organization that Jones works for is running for a father son dinner for those employees is invited to attend along with his youngest son. If Jones is known to have two children, what is the condition probability that they are both boys given that he is invited to the dinner?
Answer:
25%
Step-by-step explanation:
The probability of having a boy is 50%
To calculate the probability of him having 2 boys, multiply the probabilities together
0.5(0.5) = 0.25
The graph of y = 1/2 x2 + 2x + 3 is shown. What are the solutions to the equation 1/2 x2 + 2x + 3 = x + 7?
Answer:
Step-by-step explanation:
Let's organise our information :
the function is (1/2)x²+2x+3we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7
Now the trick is to write this expression as a quadratic equation with zero at one side :
(1/2)x²+2x+3=x+7 (1/2)x²+2x+3-x-7=0(1/2)x²+x-4=0Now let's solve this equation :
a= 1/2b= 1c= -4Δ=1²-4*(1/2)*(-4)
= 9
So we have two solutions :
[tex]\left \{ {{y=\frac{-1-3}{2*0.5} } \atop {x=\frac{-1+3}{2*0.5} }} \right.[/tex]y= -4x= 2So the solutions are -4 and 2
T or F? Is 3y=5x If x is 3 and y is 5?
Answer:
True
Step-by-step explanation:
3y=5x
Put x as 3 and y as 5.
3(5) = 5(3)
15 = 15
Hence, true.
Answer:
trueX=3
y=15
[tex]3y = 5x \\ 3 \times 5 = 5 \times 3 \\ 15 = 15[/tex]
Proved.
Hope it helps..
Kurtis is a statistician who claims that the average salary of an employee in the city of Yarmouth is no more than $55,000 per year. Gina, his colleague, believes this to be incorrect, so she randomly selects 61 employees who work in Yarmouth and records their annual salaries. Gina calculates the sample mean income to be $56,500 per year with a sample standard deviation of 3,750. Using the alternative hypothesis Ha:μ>55,000, find the test statistic t and the p-value for the appropriate hypothesis test. Round the test statistic to two decimal places and the p-value to three decimal places.
Degrees of Freedom
0.0004 0.0014 0.0024 0.0034 0.0044 0.0054 0.0064
54 3.562 3.135 2.943 2.816 2.719 2.641 2.576
55 3.558 3.132 2.941 2.814 2.717 2.640 2.574
56 3.554 3.130 2.939 2.812 2.716 2.638 2.572
57 3.550 3.127 2.937 2.810 2.714 2.636 2.571
58 3.547 3.125 2.935 2.808 2.712 2.635 2.569
59 3.544 3.122 2.933 2.806 2.711 2.633 2.568
60 3.540 3.120 2.931 2.805 2.709 2.632 2.567
Answer:
Test statistic t = 3.12
P-value = 0.001
As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year (Gina's claim).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=55000\\\\H_a:\mu> 55000[/tex]
The significance level is 0.05.
The sample has a size n=61.
The sample mean is M=56500.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3750.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3750}{\sqrt{61}}=480.138[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{56500-55000}{480.138}=\dfrac{1500}{480.138}=3.12[/tex]
The degrees of freedom for this sample size are:
df=n-1=61-1=60
This test is a right-tailed test, with 60 degrees of freedom and t=3.12, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>3.12)=0.001[/tex]
As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.
A department store chain is expanding into a new market, and is considering 13 different sites on which to locate 5 stores. Assuming that each site is equally likely to be chosen, in how many ways can the sites for the new stores be selected?
Answer:
Hope it helps you :)
And i hope you understand
For store 1, it can be placed on 16 sites. Store 2 can be placed on 15 sites( since store 1 is already on site 1). Store 3 can be placed on 14 sites and so on until store 5 which has 12 sites.
Therefore the number of way is
C= 16*15*14*13*12
c=524,160 possibilities
In the morning, Marco sold 12 cups of lemonade for $3. By the end of the day, he had earned $9. How many cups of lemonade did he sell in all? Kaycee wrote the proportion 12/3=9/c for this situation identifly the error and give tow ways to write the proportion correctly
Answer:
36 cups
3/12 = 9/c
Step-by-step explanation
3 ÷ 12 = .25
each cup = 25 cents
9 ÷ .25 = 36
Marco sold 36 cups of lemonade.
3/12 = 9/c
Answer:
36 cups
Step-by-step explanation:
We can set up a proportion:
12/3=c/9
Cross multiply.
12*9=3*c
108=3c
Divide both sides by 3.
c=36
The error that the proportion Kaycee set up was
cups/price=price/cups
This is not proportionate.
Possible proportions include:
cups/price=cups/price
price/cups=price/cups
cups/cups=price/price
price/price=cups/cups
will give brainliest help plz i can't get back on the password won't go to my email and my little brother changed the password I am scared I lost everything PLZ HELP ME
simplify the expression into form a+bi, where rational numbers
(4-i)(-3+7i) - 7i(8+2i)
Answer:
-12+28i+3i-7i-65i+28
14 -41i
How many gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze? Use the six step method.
Answer:
x = 270 gallons
270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze
Step-by-step explanation:
Let x represent the number of gallons of the 50% antifreeze solution.
The volume of the 10% antifreeze is = 90 gallons
The volume of the mixture that is 40% antifreeze = 90+x
The amount of antifreeze in the two solutions must be equal to the amount of anti freeze in the mixture;
50% of x + 10% of 90 = 40% of (90+x)
0.50(x) + 0.10(90) = 0.40(90+x)
0.50x + 9 = 36 + 0.40x
Collecting the like terms;
0.50x - 0.40x = 36-9
0.10x = 27
x = 27/0.10
x = 270 gallons
270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze
Randomthing2143 help me please! Range of: 1, 2, 3, 1, 5, 2, 1, 8, 9, 7?
Answer:
8solution,
Highest score=9
lowest score=1
now,
range= highest score-lowest score
=9-1
=8
Hope this helps...
Answer:
8
Step-by-step explanation:
The range of the sequence is the largest number - the smallest number.
The largest number is 9.
The smallest number is 1.
9 - 1
= 8
The range of the sequence is 8.
helppppppppp hurryyyyyyyyyyyyyyyyyyyyyyyy
Answer:
2
Step-by-step explanation:
I would have to say it is two bc Everitt had 30% where Desery had 20%.
ALGEBRA Identify the similar triangles. Then find each measure.
FG
S
G
6
х
R
4
T
F
10
H
ARST - AFGHFG = 11
ARST - AFGHFG = 14
ARST - AFGH FG = 15
ARST- AFGH FG = 18
Answer:
fg t f h 10
Step-by-step explanation:
4) →BRAINLIEST & 10+ POINTS! ← A wheel with diameter 44 cm completes four revolutions in 0.5 seconds. Find the linear speed of the edge of the wheel in cm per second. ⇒Round to the nearest whole number. Linear speed = ____ cm/s
Answer:
352 cm/s
Step-by-step explanation:
circ = 44pi
speed = distance * time
distance = circ * 4 = 176pi
speed = 176pi/0.5
Answer:
≈ 1106 cm/s
Step-by-step explanation:
linear speed = angular speed x radius of the rotation
v = ωr
v = linear speed (m/s)
ω = angular speed (radians/s)
r = radius of the rotation (m)
------------
Given:
d= 44 cm ⇒ r= 44/2 cm= 22 cmω= 4 rev/0.5 s= 8 rev/s= 8*2π/s= 16π/s (converted rev to radians)Linear speed is:
v= 22*16π cm/s ≈ 1106 cm/s (rounded to full number)Juanita wants to buy 12.5 pounds of stones to decorate her garden. The stone normally sells for $1.80 a pound. The salesman offers her a total price of $21.25. How much is she saving per pound with the salesman’s offer? Round to the nearest hundredth.
Answer:
She is saving 10 cents per pound
Step-by-step explanation:
First, we need to find how much she would pay without the sale:
12.5(1.8) = 22.5
Now, we can calculate how much she saved:
22.5 - 21.25 = 1.25
To find how much she's saving per pound, we divide the difference by the number of pounds:
1.25/12.5 = 0.1
She is saving 10 cents per pound
Answer:
A
Step-by-step explanation:
I took the test and got it right
Evaluate. Write your answer as a fraction or whole number without exponents. 3^–3 =
Answer:
The answer is 1/27
Step-by-step explanation:
According to the rules of indices
a^-b can be written as 1/a^b
So 3^- 3 can be written as 1/3³
And
1/3³ = 1/27
Hope this helps you
Select the correct answer. If g = 8, what is the value of the expression g/2+3 ? A. 8/5 B.11/2 C. 7 D. 19
Answer:
7Option C is the correct option
Step-by-step explanation:
g = 8 ( given )
Now,
[tex] \frac{g}{2} + 3[/tex]
Plugging the value of g
[tex] \frac{8}{2} + 3[/tex]
[tex] \frac{8 + 3 \times 2}{2} [/tex]
[tex] \frac{8 + 6}{2} [/tex]
[tex] \frac{14}{2} [/tex]
[tex]7[/tex]
Hope this helps...
Good luck on your assignment...
Look at the picture for the question ........................
Answer:
53/28
Step-by-step explanation:
100 g jam
19 g strawberries53 g blackberriesSugar= 100-(19+53)= 28 gBlackberry / sugar= 53/28
Answer:
53:28Solution,
Amount of sugar=100-(19+53)
=100-72
=28 gram
Ratio of blackberries to sugar=53/28
=53:28
Hope this helps..
Good luck on your assignment..
A group of 4 friends went to lunch and spent a total of $40, which included the $34 food bill and the tip. They decided to split the bill and tip evenly among themselves.
One of the friends used the equation One-fourth (t + 34) = StartFraction 40 over 4 EndFraction to represent the situation, where t represents the total amount of the tip. Which describes the amount each friend paid for the food and for the tip?
Answer:
The individually paid $1.5 for the tip and $8.5 for the food
Step-by-step explanation:
Total money spent = $40
Food bill = $34
if the situation is represented by the equation [tex]\frac{1}{4}(t+34) = \frac{40}{4}[/tex] where t is the amount of the tip, the amount for the tip can be calculated as shown;
[tex]\frac{1}{4}(t+34) = \frac{40}{4}\\ t+34 = 40\\t = 40-34\\t = 6[/tex]
Amount of the tip = $6
If they decided to split the bill and tip evenly among themselves, amount paid by each friend for the food and the tip can be gotten using the equation representing the situation where t = $6 as shown;
[tex]= \frac{1}{4}(t+34) \\= \frac{1}{4}(6+34)\\= \frac{1}{4}(6)+\frac{1}{4}(34)\\= 1.5+8.5\\[/tex]
From the result above, it can be seen that each friend paid $1.5 for their tip and $8.5 for their food
Answer:
A) Each friend paid $8.50 for the food and $1.50 for the tip.
A student earned grades of B, B, A, C, and D. Those courses had these corresponding numbers of credit hours: 4, 5, 1, 5, 4. The grading system assigns quality points to letter grades as follows: Aequals=4, Bequals=3, Cequals=2, Dequals=1, and Fequals=0. Compute the grade point average (GPA) and round the result to two decimal places.
Answer:
1.69Step-by-step explanation:
Let the five courses with their corresponding credit hours be represented as shown;
FST 201 = 4
FST 203 = 5
FST 112 = 1
FST 219 = 5
FST 223 = 4
If a student earned grades of B, B, A, C, and D respectively in those courses with the following grading system A =4, B =3, C =2, D =1, and F =0, before we can get the student GPA, we need to know the total credit point for the five courses.
Credit point for each course = Number of credit hour * point for each grade
FST 201 = 4 * 4 = 16points (A)
FST 203 = 5 * 4 = 20points (A)
FST 112 = 1 * 4 = 4points (A)
FST 219 = 5 * 4 = 20points (A)
FST 223 = 4 * 4 = 16points (A)
Total credit point = 16+20+4+20+16 = 76points
Total credit point gotten by the student is calculated as thus;
FST 201 = 4 * 3 = 12points (B)
FST 203 = 5 * 3 = 15points (B)
FST 112 = 1 * 4 = 4points (A)
FST 219 = 5 * 2 = 10points (C)
FST 223 = 4 * 1 = 4points (D)
Total credit point gotten by the student = 45points.
student's Grade Point Average (GPA) = Total credit point/Total credit point gotten by the student = 76/45 = 1.69 (to 2dp)
Find the value of x
Answer:
8
Step-by-step explanation:
the value of x is 8 because the sides are the same
Which of the following represents the ratio of the hypotenuse to the given side?
Answer:c
Step-by-step explanation:
hyp=6[tex]\sqrt{2}[/tex]
adj=6
hyp:adj=6[tex]\sqrt{2}[/tex] :2
hyp:adj=[tex]\frac{6\sqrt{2} }{6} \\[/tex]
[tex]=\frac{\sqrt{2} }{1} \\hyp:adj=\sqrt{2} :1[/tex]
Write 6 17/20 as a decimal
Answer:
6.85
Step-by-step explanation:
6 17/20
Convert to improper fraction.
137/20
Divide.
= 6.85
Answer:
6.85
Step-by-step explanation:
17/20 = 85/100
17 x 5 = 85
20 x 5 = 100
so,
6 + 85/100 = 6.85
Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 17.5 customer contacts per week. The sample standard deviation was 4.2.
Required:
Provide 90%90% and 95%95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel.
Answer:
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]
And replacing we got
[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]
[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]
For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]
[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]
[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]
Step-by-step explanation:
Information given
[tex]\bar X¿ 17.5[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s¿4.2 represent the sample standard deviation
n¿65 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=65-1=64[/tex]
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]
And replacing we got
[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]
[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]
For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]
[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]
[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]
which of the following descriptions represent the transformation shown in the image? Part 3c
Answer: c) rotation of 180° & shift right 1 unit and down 2 units
Step-by-step explanation:
Rotation of 180° changes the signs of x and y
(x, y) → (-x, -y)
Shift right one unit adds 1 to x, Shift two down subtracts 2 from y
(-x, -y) → (-x + 1, -y - 2)
(x, y) (-x + 1, -y - 2)
(-1, -2) → (2, 0)
(-4, -1) → (5, -1)
(-4, -3) → (5, 1)
In the figure, a//b, and both lines are intersected by transversal t. Complete the statements to prove that m<1=m<5.
Answer:
Transitive Property of EqualityAlternate Interior Angles TheoremStep-by-step explanation:
a) You're trying to justify that two sums equal to 180° are equal to each other. The Transitive Property of Equality is that justification.
__
b) You're trying to justify that angles 3 and 6 are congruent. These are between the parallel lines, so are "interior" angles. They are on opposite sides of the transversal, so are "alternate" angles. They do not share a vertex, so cannot be vertical angles. The applicable theorem is the Alternate Interior Angles Theorem.
Answer:
Step-by-step explanation:
For the data set represented by this box plot, what is the value of the maximum? maximum:
Answer:
140
Step-by-step explanation:
The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84
Answer:
the other person is correct!
Step-by-step explanation:
Kajol has $75. This is 3/8 of the amount she earned. How much did she earn?
Answer:
$200
I hope this helps!
Answer:
200rupees
Step-by-step explanation:
according to the question ,kajol has 75 rupees
amount earned=3/8* amount earned
=75/3*8
=200 rupees
Need Help!!!! What is 1495486+73940426 Thanks!
Answer:
75435912
Step-by-step explanation:
1495486+73940426
= 75435912
Answer:
75,435,912
Step-by-step explanation:
=> 1495486 + 73940426
Using Calculator
=> 75,435,912
5x is equal to 8X raise to power - 1/3
Answer:
No solutions.
Step-by-step explanation:
5x = 8x^-1/3
Divide 8 into both sides.
5/8x = x^-1/3
Divide both sides by x.
5/8 = x^-4/3
Multiply both sides by the exponent -3/4.
5/8^-3/4 = x
1.422624 = x
Plug in 1.422624 for x to check.
It does not work. There are no real solutions.
Select all that apply. A direct variation equation is graphed. The point (6, 4) is on the graph. Which of the following points are also on the graph of the equation? (3, 2) (-9, -6) (-12, 8) (-6, -3)
Answer:
(3,2)
(-9,-6)
Step-by-step explanation:
Given that the graph is a direct variation.
The equation of variation is:
[tex]x=ky[/tex]
Since point (6, 4) is on the graph
[tex]6=4k\\\\k=\dfrac64[/tex]
Therefore, the equation connecting x and y is:
[tex]x=\dfrac64y[/tex]
[tex]\text{When y=2},x=\dfrac64 \times 2 =3\\\\\text{When y =}-6,x=\dfrac64 \times -6 =-9\\\\\text{When y =}8,x=\dfrac64 \times 8 =12\\\\\text{When y =}-3,x=\dfrac64 \times -3 =-4.5[/tex]
Therefore, the points that are also on the graph are:
(3,2) and (-9,-6)
Answer:
(-9, -6) and (3, 2)
Step-by-step explanation: