Step-by-step explanation:
Sp = rs 800
loss = 10%
Cp = ?
we know that,
cp= sp×100÷ 100-L%
= 800×100÷100-10
= 80000÷90
= 888.89#
Answer:
8000/9
Step-by-step explanation:
Loss%=CP-RS/CP*100%------------------------------------------- The formula
Let's substitute
10/100=CP-800/CP
Crisscross it
10*CP=100(CP-800)
10CP=100CP-80000
-90CP= -80000
CP=-80000/-90= So the answer is 8000/9
Notice that I understand "rs" as selling price
2. (15 points) You need to study for your math and physics finals. Your grade on both exams is proportional to the number of hours per day (so capped at 24 total hours) you spend studying that subject times your ability to absorb the material. You estimate that your ability to absorb math material falls from 100% by 4% for every hour you spend studying math and Page 2 of 4 by 3% for every hour you spend studying physics. Similarly, you find your ability to absorb physics material falls by 2% for each hour of studying math and by 5% for each hour of studying physics. (a) Find the optimal number of hours that you should study math and physics to maximize your average grade. Set the problem up and define all the variables and find the answer. (b) If you studied the optimal number of hours you found in part (a), which exam would you be better prepared for? (c) Now assume that your exam scores in both subjects improves by an additional 10% for every hour of the day that you do not study math or physics. Now what is the optimal number of hours spent studying for the two exams? (d) Examine the sensitivity of your answer to the additional 10\% benefit he gets from the time not studying. How would increasing the effect of this benefit affect your average grade?
A. These equations will give us the optimal values of x and y.
B. (b) To determine which exam you would be better prepared for, we compare the Math_grade and Physics_grade using the optimal values obtained in part (a).
C. We can follow the same steps as in part (a) to set up the equations and find the optimal number of hours spent studying for the two exams.
D. the specific impact would depend on the magnitude of the increase and how it interacts with the other variables and constraints in the problem.
(a) Let's define the variables:
Let x represent the number of hours spent studying math.
Let y represent the number of hours spent studying physics.
We want to maximize the average grade, which is proportional to the product of the hours spent studying and the ability to absorb the material.
The math grade is proportional to x * (1 - 0.04x) * (1 - 0.02y)
The physics grade is proportional to y * (1 - 0.03y) * (1 - 0.05x)
We want to maximize the average grade:
Average grade = (math grade + physics grade) / 2
Now, let's set up the optimization problem:
Maximize: (x * (1 - 0.04x) * (1 - 0.02y) + y * (1 - 0.03y) * (1 - 0.05x)) / 2
Subject to:
0 ≤ x ≤ 24 (maximum hours per day)
0 ≤ y ≤ 24 (maximum hours per day)
To solve this optimization problem, we can use calculus or numerical optimization methods.
(b) To determine which exam you would be better prepared for, calculate the average grade for the optimal number of hours obtained in part (a). Compare the average grade of math and physics to determine which one is higher.
(c) Now, assuming the exam scores improve by an additional 10% for every hour not studying, we need to modify the objective function in the optimization problem. Let's redefine the variables:
Let x represent the number of hours spent studying math.
Let y represent the number of hours spent studying physics.
Let z represent the number of hours not spent studying (24 - x - y).
The math grade is proportional to x * (1 - 0.04x) * (1 - 0.02y)
The physics grade is proportional to y * (1 - 0.03y) * (1 - 0.05x)
The additional benefit is 10% * z.
The new objective function to maximize the average grade is:
(x * (1 - 0.04x) * (1 - 0.02y) + y * (1 - 0.03y) * (1 - 0.05x) + 0.1 * z) / 2
Subject to:
0 ≤ x ≤ 24 (maximum hours per day)
0 ≤ y ≤ 24 (maximum hours per day)
z = 24 - x - y
(d) To examine the sensitivity of the answer to the additional 10% benefit from not studying, you can perform sensitivity analysis by changing the percentage value and observing the effect on the average grade. Increasing the effect of this benefit would likely result in a higher average grade as more emphasis is placed on the additional benefit gained from not studying. However, the exact impact would depend on the specific values used and the relationships between the variables and grades.
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Isosceles Triangle BCD has base angles C and D. If m angleB = (13x – 35)°, m angleC = (5x – 19)°, and m angleD = (2x + 14)°, what is the measure of m angleD? Type just the number.
I'm kinda stuck rn.
Step-by-step explanation:
Answer:-Its Isosceles
So, base angles is equal.
[tex]13x - 35 = 5x - 19[/tex]
[tex]13x - 5x = -19 + 35[/tex]
[tex]8x = 16[/tex]
[tex]x = 2[/tex]
So, 2x+14 will be
[tex]2 \times 2 + 14[/tex]
So, 18° is the answer.
Hope it HELPS ☃️
a relation is a set of ordered pairs where the first element is called the ranged while the second element is the domain
Answer:
False.
Step-by-step explanation:
We have the statement:
"a relation is a set of ordered pairs where the first element is called the ranged while the second element is the domain"
A relation between two sets maps the elements of the first set into elements of the second set, creating an ordered pair.
So we can have a relation that maps elements X, into elements Y, and the ordered pairs will be (X, Y)
Where the set of the elements X is called the domain, and the set of elements Y is called the range.
Then the statement is false.
[tex]2 \sqrt{3} [/tex]
16 The equation of a circle in the xy-plane is given as x² + y² + 16x-20y = 60. What are the coordinates of the center of this circle? A. (-16, 20) B. (-8, 10) C. (8,-10) D. (16, -20)
The coordinates of the center of the circle with the equation x² + y² + 16x - 20y = 60 are (-8, 10).
To find the center of the circle, we need to rewrite the equation in the standard form (x - h)² + (y - k)² = r², where (h, k) represents the center coordinates and r represents the radius.
To do this, we complete the square for both the x and y terms. We rearrange the given equation as (x² + 16x) + (y² - 20y) = 60.
To complete the square for the x terms, we add (16/2)² = 64 to both sides of the equation. Similarly, for the y terms, we add (-20/2)² = 100 to both sides. This gives us x² + 16x + 64 + y² - 20y + 100 = 60 + 64 + 100.
Simplifying further, we have (x + 8)² + (y - 10)² = 224. Comparing this with the standard form, we can see that the center coordinates are (-8, 10). Therefore, the correct answer is B. (-8, 10).
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If sin?(Łº) + cos²(42) = 1, then what does L equal?
Answer:
Ł=42°
Step-by-step explanation:
We have the equation:
[tex]\sin^2(\L) +\cos^2(42)=1[/tex]
Remember from the Pythagorean Identity that:
[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]
So, the angles within our trig functions must be exactly the same.
Therefore, since the angle within cosine is 42°, this means that our angle within sine, Ł, must also be 42°.
And we're done!
.THIS IS DIFFERENTIALS EQUATION SUBJECT.
THE TOPIC WAS ALL ABOUT APPLICATIONS ON 1ST ORDER OF DIFFERENTIALS EQUATIONS In an episode of How to Get Away with Murder, the intern lawyers were investigating a murder case. During investigation, the forensics informed them that the dead body was found within a closed room of a house where the temperature was 70 F. At the time of discovery the core temperature of the body was determined to be 85 F. One hour later a second measurement showed that the core temperature of the body was 80 F. Assume that the time of death corresponds to * = 0 and the core temperature at that time was 98.6 F. Determine how many hours elapsed before the body was found.Provide what is needed. Show your full solutions, no shorthand. Do notapproximate the value of k, do
approximation after you find your final answer
Approximately 0.456 hours (or about 27.36 minutes) elapsed before the body was found.
To solve this problem, we can use Newton's Law of Cooling, which states that the rate of change of temperature of an object is proportional to the difference between its temperature and the surrounding temperature.
Let's denote T(t) as the core temperature of the body at time t, and T_s as the surrounding temperature (which is 70 F in this case).
According to the problem, at time t = 0, the core temperature of the body is T(0) = 98.6 F. One hour later, at t = 1, the core temperature is T(1) = 80 F.
Using Newton's Law of Cooling, we can set up the differential equation:
dT/dt = k(T - T_s)
where k is the proportionality constant.
Substituting the given values at t = 0 and t = 1, we can find the specific value of k.
At t = 0: dT/dt = k(98.6 - 70)
At t = 1: dT/dt = k(80 - 70)
Integrating both sides of the equation, we get:
∫ dT/(T - T_s) = ∫ k dt
Applying the natural logarithm, we have:
ln|T - T_s| = kt + C
Simplifying the equation, we get:
T - T_s = Ce^(kt)
Substituting the values at t = 0, we have:
98.6 - 70 = Ce^(k * 0)
Solving for C, we get:
C = 28.6
Now we can rewrite the equation as:
T - 70 = 28.6e^(kt)
At t = 1, we have:
80 - 70 = 28.6e^(k * 1)
Simplifying the equation, we get:
10 = 28.6e^k
Dividing both sides by 28.6, we have:
e^k = 10/28.6
Taking the natural logarithm of both sides, we get:
k = ln(10/28.6)
Now, we can use this value of k to determine how many hours elapsed before the body was found.
We want to find the value of t when T(t) = 85. Substituting this value into our equation, we have:
85 - 70 = 28.6e^(ln(10/28.6) * t)
15 = 28.6(10/28.6)^t
Dividing both sides by 28.6, we get:
15/28.6 = (10/28.6)^t
Taking the natural logarithm of both sides, we have:
ln(15/28.6) = t * ln(10/28.6)
Dividing both sides by ln(10/28.6), we can solve for t:
t = ln(15/28.6) / ln(10/28.6)
Calculating this expression, we find:
t ≈ 0.456 hours
Therefore, approximately 0.456 hours (or about 27.36 minutes) elapsed before the body was found.
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I'm studying for a quiz but I don't know how to do these two questions! Can someone explain them to me?
Answer:
11. m∠ABD = 28°
Other Q. m∠1 = 61°
Step-by-step explanation:
11) Extend line BE. Because of the Alternate Interior Angles Theorem, ∠ABE is congruent to ∠BEF. m∠BEF = 118°, so m∠ABD + m∠DBE = 118°. Because ∠DBE is a right angle, it equals 90°. So m∠ABD + 90° = 118°. So m∠ABD = 28.
Other Q.) Looking only at line a, line b, and the line next to angle 3 and angle 1. ∠3 is congruent to ∠1 + 74° by the Corresponding Angles Theorem. Now, we have:
m∠3 = m∠1 + 74°
So we have to find the measure of angle 3.
Angle 3 is supplementary to 45°, meaning their sum is 180°, because they're linear pairs.
180 - 45 = m∠3
= 135°
Now, plug in the values to the previous:
m∠3 = m∠1 + 74°
135° = m∠1 + 74°
m∠1 = 135 - 74
= 61°
Joshua sold his bike for 10% less than he paid for it. If he sold the bike for $585, how much did he pay for it?
Answer:
He payed $643.50 for the bike
Step-by-step explanation:
Because $585 + 10% = $643.50
(Sorry if wrong!)
Answer:
he paid $643.5 for it originally
585 x .1 = 58.5
585+58.5= 643.5
hope this helps
Step-by-step explanation:
Please help ASAP
Will mark brainliest!
Answer:
x = 13
I hope that is what your looking for, my explanation will make no sense to you because it's so messy. So sorry no explanation
Answer:
x=13
Step-by-step explanation:
jhjsjdbdjdjndjdidbd
Which system of equations is consistent and dependent?
Answer:
Step-by-step explanation:
if you multiply 2 to both sides, 2(3x+2y)=2*3, having 6x+4y=6
thus, the two equations are same (consistent), having infinite number of solutions (dependent).
Answer:
The answer is A
Step-by-step explanation:
EDGE2021
please help a humanoid out
Answer:
false
Step-by-step explanation:
false people inthe world use diffrent different names with j
The population of Cook island has always been modeled by a logistic equation P′=k(M−P) with growth rate k=3 and carrying capacity M=6000 with time t in years. Starting in the year 2000, 7 citizens of Cook island have left every year to become mathematicians, never to return. What is the new differential equation modeling the population of the island P?
The new differential equation modeling the population of the island P is P′=3(M−P)−7.
Given, the population of Cook island is modeled by a logistic equation
P′=k(M−P) with growth rate k=3 and carrying capacity M=6000 with time t in years.
Starting in the year 2000, 7 citizens of Cook island have left every year to become mathematicians, never to return.To determine the new differential equation modeling the population of the island P, we need to modify the logistic equation as follows:
For every year since 2000, the population has decreased by 7.
Therefore, the equation that models the decrease in population is -7, and it has to be subtracted from the original equation.
Therefore, we obtain the new differential equation as P′=3(M−P)−7.
The above equation models the rate of change of population for Cook island.
Thus, the new differential equation modeling the population of the island P is P′=3(M−P)−7.
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Let p: It is raining
Let q: Robert is laughing.
Assume p is true. Select two statements that must logically be true.
p ∨ q
p ∧ q
q → p
p → q
q ↔ p
HELP IK ITS THE FIRST ONE WHATS THE SECOND ONE!!!
Answer:
1) [tex]p\,\lor\,q[/tex], 2) [tex]q\implies p[/tex].
Step-by-step explanation:
We selected the following two statements based on the fact that [tex]p[/tex] is true: 1) [tex]p\,\lor\,q[/tex], 2) [tex]q\implies p[/tex]. We proceed to explain the reason behind each selection:
1) [tex]p\,\lor \,q[/tex]: Because the entire proposition is logically true when any of the two proposition is true.
2) [tex]q \implies p[/tex]: Because the entire proposition is logically true when the conclusion of the condition is true.
Answer:
1,3
Step-by-step explanation:
Customers can rent canoes from Bob’s Boats for $40 per day with a deposit fee of $30. Ned’s Water World charges $55 per day with no deposit fee. When will the cost be the same for both places?
Answer:
ill help
Step-by-step explanation:
help me pleasee, my brain won't work
The given fractions have equal value, so Liam is correct.
How to find the equivalent fractions?Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.
Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.
Thus, we can say that:
The fraction -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.
The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient
The fractions have equal value, so Liam is correct
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What should the expression xy - 2x + z look like when you substitute in the values x
= 4, y = -1, and z = 2 ?
2- 10+ x = 6 -8 + 12
Please answer ASAP :)
Answer: X=18
Step by Step:
2−10+x=6−8+12
Step 1: Simplify both sides of the equation.
2−10+x=6−8+12
2+−10+x=6+−8+12
(x)+(2+−10)=(6+−8+12)(Combine Like Terms)
x+−8=10
x−8=10
Step 2: Add 8 to both sides.
x−8+8=10+8
x=18
Answer:
[tex]x = 18[/tex]
Step-by-step explanation:
[tex]2 - 10 + x = 6 - 8 + 12 \\ - 8 + x = - 2 + 12 \\ - 8 + x = 10 \\ x = 10 + 8 \\ x = 18[/tex]
What is three over two x plus three equal to zero
QUESTION → [tex]\frac{3}{2}x + 3 = 0[/tex]
Start by subtracting 3 from both sides to get [tex]\frac{3}{2}x = -3[/tex].
Now multiply both sides by the reciprocal of 3/2, which is 2/3.
On the left, we have x, and on the right, -3(2/3) is -2.
So we have x = -2.
Answer:
x = -2
Step-by-step explanation:
Over means a fraction.
Equal means "="
3/2x + 3 = 0
~Subtract 3 to both sides
3/2x = -3
~Multiply 2/3 to both sides
x = -2
Best of Luck!
Hi please help! I already got the 1st answer and the 3rd one I just need help on B and D thank you!!
Step-by-step explanation:
Try for B - 0.0000000009 or one less zero
Try for D - 0.00000000006 or one less zero.
Hoped this helped.
9. sonja is cutting wire to construct a mobile. she cuts 100 inches for the first piece, 80 inches for the second piece. and 64 inches for the third piece. assuming the pattern continues, write an explicit formula for the nth piece. sonja only has 40 feet of wire to use for the project and wants to cut 20 pieces total for the mobile using her pattern. will she have enough wire? justify your answer.
Total length of wire = 8.33 + 6.67 + 5.33 + ...20 terms= 100[2 - 0.8^20] / [1.2]≈ 80.99 feet Since the total length of wire required is less than the available wire, Sonja will have enough wire.
Given, Sonja cuts 100 inches for the first piece, 80 inches for the second piece, and 64 inches for the third piece. We need to find the explicit formula for the nth piece.We can see that Sonja is cutting wire in decreasing order of 20%.So, the explicit formula for the nth piece can be given by an = a1 * r^(n-1)where a1 = 100 and r = 0.8 Thus, the explicit formula for the nth piece can be given byan = 100 * (0.8)^(n-1)Now, we need to find if Sonja has enough wire for the mobile as she only has 40 feet of wire to use for the project and wants to cut 20 pieces total for the mobile using her pattern.We know that 1 inch = 0.0833 feet 100 inches = 100 * 0.0833 feet = 8.33 feet80 inches = 80 * 0.0833 feet = 6.67 feet64 inches = 64 * 0.0833 feet = 5.33 feet Now, we can find the total length of wire Sonja needs to cut 20 pieces. Therefore, she can complete the mobile using the given pattern.
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If α and β are the zeros of the quadratic polynomial f(x) = 2x² -5x + 7, find a polynomial whose zeros are 2α+ 3β and 3α+ 2β?
Answer
pizza
Step-by-step explanation:
me
Hal had c coins in his piggy bank. He gave 6 of the coins to his cousin. This left 20 coins in the bank. What equation can help you find c, the original number of coins?
1. 4, 16.64,
Common ratio
Answer:
4
Step-by-step explanation:
1, 4, 16,64,
1*4=4
4*4=16
16*4=64
The common ratio is what we are multiplying by
We are multiplying by 4 so the common ratio is 4
What is the answer and can you explain why please
Answer:
f⁻¹(x) = (x + 3) / 2
Step-by-step explanation:
y = 2x − 3
To find the inverse, switch x and y, then solve for y.
x = 2y − 3
x + 3 = 2y
y = (x + 3) / 2
What is the nature of the roots of the quadratic equationsbif the value of its discriminant is 0
If the discriminant is 0, then you'll have exactly one root. This is a double root since the root repeats itself.
Example: y = (x-5)^2 = x^2-10x+25 has a double root at x = 5
The cost, in dollars, of parking a car in a busy downtown area for h hours is $10 + $3h.
Which statement is correct?
A.
For every hour the car is parked, the cost increases by $10.
B.
For every hour the car is parked, the cost increases by $7.
C.
For every hour the car is parked, the cost increases by $13.
D.
For every hour the car is parked, the cost increases by $3.
Answer:
c
Step-by-step explanation:
the area add that to the number of hours
manny’s pizza shows declining sales over the last few months. their net profit in hundreds of dollars follows the arithmetic sequence 4, 1, −2, −5, …, −56. what is their total profit over this time period?
Answer:
The total profit over this period is -546
Step-by-step explanation:
Given
Sequence: 4, 1, −2, −5, …, −56
Required
Determine the total profit
To do this, we simply calculate the sum of terms (Sn)
[tex]S_n = \frac{n}{2}(a + T_n)[/tex]
But first, we need to determine the value of n using
[tex]T_n = a + (n - 1)d[/tex]
Where:
[tex]T_n = -56[/tex]
[tex]a = 4[/tex]
[tex]d = 1 -4= -3[/tex]
Substitute these values in the above formula, we have:
[tex]-56 = 4 + (n - 1) * -3[/tex]
[tex]-56 = 4 -3n +3[/tex]
Collect Like Terms
[tex]3n = 56 + 4 + 3[/tex]
[tex]3n = 63[/tex]
[tex]n = 63/3[/tex]
[tex]n = 21[/tex]
Recall that:
[tex]S_n = \frac{n}{2}(a + T_n)[/tex]
This gives:
[tex]S_n = \frac{21}{2}(4 - 56)[/tex]
[tex]S_n = \frac{21}{2}(-52)[/tex]
[tex]S_n = 21 * -26[/tex]
[tex]S_n = -546[/tex]
The total profit over this period is -546
Need help on this Advanced algebra problem
Answer:
8 m, 17 m and 22 m
Step-by-step explanation:
The first side is x
The second is 1 more than twice the first = 2x + 1
The third is 2 less than 3 times the first = 3x - 2
Sum the 3 sides and equate to 47
x + 2x + 1 + 3x - 2 = 47, that is
6x - 1 = 47 ( add 1 to both sides )
6x = 48 ( divide both sides by 6 )
x = 8
Thus
side 1 = 8 m
side 2 = 2x + 1 = 2(8) + 1 = 16 + 1 = 17 m
side 3 = 3x - 2 = 3(8) - 2 = 24 - 2 = 22 m
select the two equations that represent lines perpendicular to the line graphed below.
y = -4/3X - 10
y = -3x +1
y = 3/4X + 7
Answer:
Step-by-step explanation:
elect the two equations that represent lines perpendicular to the line graphed below.
y = -4/3X - 10
y = -3x +1
y = 3/4X +
