Answer:
Step-by-step explanation:
From the given information:
ΔG° = -30.5 kJ/mol
By applying the following equation to calculate the value of K.
ΔG° =-RT㏑K
making ㏑ K the subject of the formula:
[tex]\mathtt{ In \ K} = \dfrac{\Delta G^0}{-RT}[/tex]
where;
Temperature at 25° C = (25 + 273)K
= 298K
R = 8.3145 J/mol.K (gas cosntant)
[tex]\mathtt{ In \ K} = \dfrac{-30.5 \times 10^{3}\ J /mol} {-(8.3145 \ J/mol. K \times 298 \ K}[/tex]
[tex]\mathtt{ In \ K} = \dfrac{-30.5 \times 10^{3}\ J /mol} {-2477.721 J/mol }[/tex]
㏑K = 12.309
[tex]K = e^{12.309}[/tex]
K = 221682.17
K = 2.22 × 10⁵
b) The reaction for the metabolism of glucose is given as:
[tex]C_6H_{12} O_6 + 6O_{2(g)} \to + 6CO_{2(g)} + 6H_2O_{(l)}[/tex]
From the above expression, let calculate the Gibbs free energy by using the formula:
[tex]\Delta G^0_{rx n }= \Delta G^0_{product}- \Delta G^0_{reactant}[/tex]
[tex]\Delta G^0_{rx n }= [6 \times \Delta G^0_{f}(CO_2) + 6 \times \Delta G^0_{f}(H_2O)] - [1 \times \Delta G^0_{f}(C_6H_{12}O_6) + 6 \times \Delta G^0_{f}(O_2)][/tex]
At standard conditions;
The values of corresponding compounds are substituted into the equation above:
Thus,
[tex]\Delta G^0_{rx n }= [6 \times (-394) + 6 \times (-237)] - [1 \times (-911) + 6 \times (0)] \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= [-2364-1422] - [-911+0] \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= -3786 +911 \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= -2875 \ kJ/mol[/tex]
[tex]\Delta G^0_{rx n }= -2875000 \ J/mol[/tex]
Now, the no of ATP molecules generated = [tex]\dfrac{\Delta G^0 \text{of metabolism for glucose}}{\Delta G^0 \text{of hydrolysis for ATP}}[/tex]
= (-2875000 J/mol ) / -30500 J/mol
= 94.26
≅ 94 ATP molecules generated
What is a solution to the system? y = x^2 + 2x - 15 y – 4x = -12
9514 1404 393
Answer:
(x, y) = (-1, -16) or (3, 0)
Step-by-step explanation:
Perhaps you want to solve the system of equations ...
y = x^2 +2x -15y -4x = -12Substituting the first expression for y into the second equation gives ...
x^2 +2x -15 -4x = -12
x^2 -2x -3 = 0 . . . . . . . . add 12
(x -3)(x +1) = 0 . . . . . . . factor
Solutions are the values of x that make the factors zero: x = 3, x = -1.
The corresponding values of y are ...
y = -12 +4x
y = -12 +4{-1, 3} = -12 +{-4, 12} = {-16, 0}
The solutions to the system are ...
(x, y) = (-1, -16) or (3, 0)
Need help on this one (listing BRAINLIST and giving points) =)
I hope this is help full to you
Armando works in a research institute and they have collected the following data on a random sample of 500 students,
Gender
GRE score before and after participation in a GRE prep course (GRE is a test you take for entering graduate school)
Armando wants to answer questions the following questions:
1: After taking the GRE preparation course, did women show more improvement on the GRE score or men?
2: After the GRE preparation course, did more women get admitted to the graduate program or men?
3: What statistical method should he use?
a. He should use the one-sample test of the mean to answer question one and the one-sample test of proportion to answer question b.
b. He should use the two-sample test of the mean to answer question one and the two-sample test of proportion to answer question two.
c. He should use the two-sample test of proportion to answer question one and the two-sample test of the mean to answer question b.
d. He should use the paired-sample of the mean to answer question one and two sample test of the mean to answer question two.
Answer:
b. He should use the two-sample test of the mean to answer question one and the two-sample test of proportion to answer question two.
Step-by-step explanation:
Here we have two independent groups, Men and Women, therefore, to show if it is the Men or Women who performed better, this can be determined based the mean scores of each group. Therefore, use the two sample test of mean which is used to test whether the unknown mean of two independent population are equal or not.
In other to determine those who have the greater number of admissions between the two groups, this is determined by comparing the proportion of each group admitted. Hence, rather Than testing for the mean, we compare the proportion. Hence, we use the two sample test of proportion.
Find the 7th term of the geometric sequence
7, 24.5, 85.75, ...
Answer:
12,867.859375
Step-by-step explanation:
24.5/7 = 3.5
Geometric sequence
A_n = 7 * (3.5)^(n - 1)
A_7 = 7 * (3.5)^(7 - 1)
A_7 = 12,867.859375
f(2) 42 g(x) = 2x +3 Find 4) (. Include any restrictions on the domain. O A. 2.2---3 417 2 > 0 B. 47 2 2 r--3, (1) (a) = (4) (a) x A 을 c. (5) (r) = 1,2*0 OD (1) (a= + 2
Answer:
Option D
Step-by-step explanation:
Given f(x) = [tex]\sqrt[3]{4x}[/tex]
g(x) = 2x + 3
Since, [tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
[tex]=\frac{\sqrt[3]{4x}}{2x+3}[/tex]
This function is defined for the denominator is not equal to zero.
(2x + 3) ≠ 0
x ≠ [tex]-\frac{3}{2}[/tex]
Therefore, Option D will be the correct option.
If f(x)= 10 sin(x) – 3 then f (30%) = ?
A) - square root 3/2 -3
B.) 2
C.) -5/2
D.) 4/3 - square root 3/2
Answer:
The value of f(30) is equal to 2.
Step-by-step explanation:
The given expression is :
[tex]f(x)= 10 \sin(x) - 3[/tex]
We need to find the value of f(30)
Put x = 30 in above expression.
So,
[tex]f(x)= 10 \sin(30) - 3\\\\=10\times \dfrac{1}{2}-3\\\\=5-3\\\\=2[/tex]
Hence, the value of f(30) is equal to 2.
Find the value of the trigonometric ratio. Simplify the ratio if possible.
(Hint: You may need to use some pythagorean theorem first!)
Step-by-step explanation:
Given that,
BC = 8
Ac = 15
We can find AB using the pythagoas theorem.
[tex]AB=\sqrt{AC^2+BC^2}\\\\=\sqrt{15^2+8^2}\\\\AB=17[/tex]
We know that,
[tex]\cos\theta=\dfrac{B}{H}[/tex], B is base and H is Hypotenuse
[tex]\cosB=\dfrac{8}{17}[/tex]
Hence, this is the required solution.
Can someone please explain to me a easier way of understanding this please
Step-by-step explanation:
u have solve it by finding slope(m)
and substitute is general eq of straight line
y = mx + c
Answer:
y = 2x - 6
Step-by-step explanation:
These are actually pretty fun to do once you get the hang of it! Here are the steps!
The formula for slope intercept form is y=mx + b.
m is the slope and b is the y-intercept. Let's start with finding the y-intercept (also known as b).
To find the y-intercept, look at where the line crosses the y-axis. In your equation, the line crosses the y-axis at -6. Plug -6 in for b in the equation.
y = mx + (-6)
Now were going to find the slope. To find the slope, you need to find the rise over run. To start, first find a point on the graph where the line goes through an integer (just pick one of the blue dots). Then, count how many squares you go up or down, and how many you go to the left or right before you hit the next blue dot. Divide the rise over the run, and you have your slope! Here are the steps for the problem:
To get from one dot to another, you rise up 2 units, and you run to the right 1 unit. Plugging those integers into rise/run, you get 2/1 which simplifies to 2. That's your slope.
Now all we need to do is plug the slope into the formula, and you have your equation!
Answer: y = 2x - 6
Frank earns 56,600$ one year and receives a 9 % raise in salary. What is his new salary?
Answer:
His new salary would be $61,694
Step-by-step explanation:
y=10x/3+19 find the y-intercept
Answer:
(0, 19)
Step-by-step explanation:
In slope-intercept form, the constant at the end of the equation is the value of the y-intercept.
You can also solve for the y-intercept by letting x = 0. This is because, at the point where the line crosses the y-axis, x will be 0.
y = 10(0)/3 + 19
y = 0 + 19
y = 19
Therefore, the y-intercept is (0, 19).
The y-intercept is (0, 19).
What is the y-intercept?The y-intercept is the point where the graph intersects the y-axis.
Given is an equation of a line, y = 10x/3+19
To solve for the y-intercept,
Put x = 0. This is because, at the point where the line crosses the y-axis, x will be 0.
y = 10(0)/3 + 19
y = 0 + 19
y = 19
Therefore, the y-intercept is (0, 19).
For more references on y-intercept, click;
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Identify a pair of parallel lines in the given figure.
a)p and s
b)r and s
c)r and q
d)r and p
Help!!!! 20 points!!!!!!’
Answer:
option c is the correct answer
first take y raised to the power 4 common then cancel its power by y raised to the power 3
you get your answer
SAT Scores The national average SAT score (for verbal and math) is 1028. Assume a normal distribution with o=92.
0
Round intermediate : -value calculations to two decimal places.
What is the 95th percentile score? Round the answer to the nearest whole number,
The 95th percentile score is ?
Answer:
Similar to your other question. Now, you're looking for the score such that this time, 0.99 corresponds to a z-score of approximately, which means
1. p-4= -9+p
2. 4m-4= 4m
Extra Credit, need help
Answer:
1. No solution
2. No solution
Step-by-step explanation:
1. p-4=-9+p
-4=-9
No solution
2. 4m-4=4m
-4=0
No solution
If this helps please mark as brainliest
A fuel pump at a gasoline station doesn't always dispense the exact amount displayed on the meter. When the
meter reads 1.000 L, the amount of fuel a certain pump dispenses is normally distributed with a mean of 1 L
and standard deviation of 0.05 L. Let X = the amount dispensed in a random trial when the meter reads
1.000 L
Find P(X < 1).
Answer:
P(X < 1) = 0.5
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 1 L and standard deviation of 0.05 L.
This means that [tex]\mu = 1, \sigma = 0.05[/tex]
Find P(X < 1).
This is the p-value of Z when X = 1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1 - 1}{0.05}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5. Thus
P(X < 1) = 0.5
What is the unit rate for the following point?
(7, 1 3/4)
Answer:
Step-by-step explanation:
7
What is the value of m
Answer:
B=34, A=56
Step-by-step explanation:
56 + 90 + B = 180
=) B=34
A is head to head with 56°.
Question 2 of 25
What do both of these functions have in common?
f(x) = |x-71-2
g(x) = 1.5 In (x - 2) +7
A. They have the same vertical shift
B. They have the same end behavior
C. They have the same vertical stretch
O D. They have the same horizontal translation
Answer:they have the same vertical stretch
Step-by-step explanation:
Cuánto es 1/4 mas 1/4
Answer:
0.5
Step-by-step explanation:
1,Convert 24 hours to sec
Answer:
86400 sec
Step-by-step explanation:
24 hour⇒ sec
1 hr = 3600 sec
So,
24×3600
= 86400 sec
The height of a triangle is 7 feet greater than the base. the area of the triangle is 247 ft.² find the length of the base and the height of the triangle
Answer:
Base = 19
Height = 26
Step-by-step explanation:
Given :
Height, h = base, b + 7 feets
The area of triangle, A = 247 ft²
The area of a triangle is given by :
A = 1/2 * base * height
247 = 1/2 * b * (b + 7)
247 = 0.5 * b * (b + 7)
247 = 0.5b² + 3.5b
0.5b² + 3.5b - 247 = 0
Solving the quadratic equation ; using the quadratic equation solver, the roots are :
b = -26 or b = 19
Length of base can't be negative :
Hence,
Base, b = 19
Height, h = base + 7 = 19 + 7 = 26
how to convert 15 cm to mm
I need help on C......
Step-by-step explanation:
[tex]B=100e^{0.592t}[/tex]
c) To solve for t, take the natural logarithm of the above equation:
[tex]\dfrac{B}{100}=e^{0.592t}[/tex]
[tex]\Rightarrow \ln \left(\dfrac{B}{100} \right) = \ln e^{(0.592t)}=(0.592t)\ln e[/tex]
Recall that [tex]\ln e = 1[/tex] so we can rewrite the equation above as
[tex]0.592t = \ln \left(\dfrac{B}{100} \right)[/tex]
Finally, solving for t, we get
[tex]t = \frac{1}{0.592} \ln \left(\dfrac{B}{100} \right)[/tex]
Which of the following will most likely produce sample proportions that are
normally distributed?
A. Many samples of 34 coin flips
B. Many samples of 14 coin flips
C. Many samples of 19 coin flips
D. Many samples of 9 coin flips
Given that ZABC = ZDBE, which statement must be
true?
ZABC - ZABD
ZABD Z CBE
Z CBD , ZDBE
Z CBD - ZABC
Answer:
B abd = cbe
Step-by-step explanation:
ABC = DBE
so
ABC + CBD = DBE + CBD
The statement which is true is ZABC - ZABD, the correct option is A.
What is a solution to a system of equations? (SOLUTION GRAPHICALLY)
For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)
We are given that;
Angle ABC = Angle DBE
Now,
A flowchart proof is a formal proof that is set up with boxes that flow from one to the next with arrows1. The statements, which are true facts that we know, are placed in the boxes, with the reason we know them on a line underneath2. We can prove theorems are true using flowchart proofs.
To justify each step in the flowchart proof, we have to provide a reason for each statement based on definitions, postulates, properties or previously proven theorems. Here is how we can fill in the blanks:
A: Given B: Definition of angle bisector C: Definition of congruent angles
Therefore, graphically the answer will be ZABC - ZABD.
Learn more about finding the solution graphically here:
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which measure of central tendency best describes the situation, the ages of 7 people who auditioned for a role in a play: 17,20,22,12,15,12,21
Answer:
Both the mean and median and they both gives a measure of 17
Step-by-step explanation:
Given the data about the ages of 7 people :
17,20,22,12,15,12,21
Ordered data: 12, 12, 15, 17, 20, 21, 22
To find the median :
Median = 1/2 * (n+1)th term
n = number of observations = 7
Median = 1/2(7+1)th term
Median = 1/2 *8 = 4th term = 17
Mean = Σx / n = (sum of ages) / number of observations
Mean = 119 / 7 = 17
:
PLEAZSEE HELP MEEEJEHSHD
Answer:
First gap:
√1000/16
= 8 seconds
Second gap:
Rearrange formula:
√d = 4t
40=√d
d = 6 meters.
explain why triangles in the figure are similar. then find the missing length x
Answer:
∨∨∨∨see below∨∨∨∨∨∨
Step-by-step explanation: 6 26 18 13
The two outside angles are congruent. The two inside angles are supplemental thus they are equal. The last two angles the high one and the lower one must sum to 180° in their respective triangles so they are equal since their similar angles are equal.
find x
4 is to x as 5 is to 7.5
4/x = 5/7.5 solve for x
4 × 7.5 / 5 = x
30 / 5 = x
6 = x
Teresa received a $90 gift card for a coffee store. she used it in buying some coffee that cost her $8.21 per pound. After buying the coffee, she had $65.37 left on her card. how many pounds of coffee did she buy?
Answer:
3 Pounds of Coffee
Step-by-step explanation:
To find out how much she spent on the pounds of coffee, you would have to takeaway $65.37 away from the total of $90 which will give you $24.63, which is how much she has spent on the coffee. To find out how many pounds of coffee she bought, you would have to divide $24.63 by $8.21 giving you 3, which is how many pounds of coffee Teresa bought.
Much appreciated if this is marked as brainliest :)
the ratio of two complementary angles is 8:17. find the measure of the smallest angle.
Answer:
28.8
Step-by-step explanation:
Multiply each by x
8x : 17x
Complementary angles add to 90
8x+17x = 90
25x = 90
Divide each side by 25
25x/25 = 90/25
x=3.6
The smallest angle is 8x
8*3.6 =28.8