A quantity with an initial value of 390 decays continuously at a rate of 5% per decade. What is the value of the quantity after 51 years, to the nearest hundredth?
Answers
The value of the quantity after 51 years, rounded to the nearest hundredth, is 499.92.
Since a decade is a period of 10 years, a decay rate of 5% per decade can be converted to a continuous decay rate as follows:
Continuous decay rate = (1 + decay rate per decade\()^{(1/10)\) - 1
In this case, the decay rate per decade is 5%, which can be expressed as 0.05.
Continuous decay rate = (1 + 0.05\()^{(1/10)\) - 1
Continuous decay rate ≈ 0.0048767
Now we can use the formula for continuous decay:
A = A0\(e^{rt\)
In this case, the initial value A0 is 390, the continuous decay rate r is 0.0048767, and the time elapsed t is 51 years.
Substituting these values into the formula, we have:
A = 390 \(e^{(0.0048767)( 51)\)
A ≈ 499.9202826
Therefore, the value of the quantity after 51 years, rounded to the nearest hundredth, is 499.92.
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Related Questions
Verify whether x ≤ 3 is the solution to the inequality 7x ≥ 20x - 39.
Answers
Answer:
Yes, it is correct.
Step-by-step explanation:
7x≥20x-39
39≥13x
x≤39/13
x≤3
if the variance of the population a is 10 and the variance of the population b is 15, does it mean that population a has less variability than population b?
Answers
Yes, the given statement is true if the variance of the population 'a' is smaller than the variance of population 'b' it represents that population 'b' is more variable than 'a'.
Population variance represents the measurement of spread of group data points.It shows the average squared deviation from the given mean.Whenever data points are very near to the mean then the variance has smaller value.And when data points are far away to the mean then it has larger value of variance.Here variance of population 'a' is 10 which is smaller than the variance of population 'b' .It represents population 'a' is less variable than population 'b'.Therefore, the given statement is true for the variance of population 'a' and 'b'.
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A town operates two recycling centers. Each day that Center I is open, 300 lbs. of glass, 200 lbs.
of paper, and 100 lbs. of aluminum are deposited there. Each day that Center II is open, 100 lbs.
of glass, 600 lbs. of paper, and 100 lbs. of aluminum are deposited there. The town has
contracted to supply at least 1200 lbs. of glass, 2400 lbs. of paper, and 800 lbs. of aluminum per
week to a salvage company. Supervision and maintenance at Center I costs $40 each day it is
open, and Center II costs $50 each it is open. How many days a week should each center remain
open so as to minimize the total weekly cost for supervision and maintenance, yet allow the
town to fulfill its contract with the salvage company?
Answers
Answer:
Step-by-step explanation:
hmm im trying to slve this rn
this half my grade i cant fail help
Answers
Let's see what to do buddy....
\(T = b + \frac{d}{2f} \\ \)
Subtract sides b
\(T - b = b - b + \frac{d}{2f} \\ \)
Simplification
\(T - b = \frac{d}{2f} \\ \)
Multiply sides by 2f
\((T - b)(2f) = d\)
So ;
\(d =( T - b) \times (2f)\)
We're done but i wanna go one step more...
\(d = T \times 2f - b \times 2f\)
\(d = 2Tf - 2bf\)
_________________________________
Hope helped buddy....♥️♥️♥️♥️♥️
Good luck :)
A math test has 25 multiple choice questions. Each question has 4 possible answers.
Which is the best way to simulate getting a 100% on this test?
Answers
GET THEM ALL RIGHT!?
Assume tuition at Penn State cost $6,142 (per semester) in 2007 and $7,562 in 2012. If the price index was 207.34 in 2007 and 226 in 2012, then we could say:
Answers
Based on the given information, we can conclude that tuition at Penn State has increased more rapidly than inflation.
The price index measures the average change in prices of a basket of goods and services over time. In this case, the price index increased from 207.34 in 2007 to 226 in 2012, indicating an overall inflation rate of approximately 9% over that period. On the other hand, tuition at Penn State increased from $6,142 to $7,562, representing an increase of approximately 23%.
When comparing the rates of increase, we can see that tuition has outpaced inflation. This implies that the cost of education at Penn State has been rising more rapidly than the general increase in prices for goods and services. It suggests that factors specific to the education industry, such as rising costs of resources, facilities, and personnel, have contributed to the higher tuition rates.
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The complete question is:
Assume tuition at Penn State cost $6,142 (per semester) in 2007 and $7,562 in 2012. If the price index was 207.34 in 2007 and 226 in 2012, then we could say:
has increased more slowly than inflation.suffers from menu costs due to inflation,has increased more rapidly than inflation.has increased at about the same rate as inflation.is an inferior good.For the product (8x-6)(2x + 5). does anyone know how I would get the answer for A and B?
Answers
Answer:
A=16x^2
B=-12x
Step-by-step explanation:
I think this question is asking you to use box method. If so, imagine 8x times 2x is 16x^2, which would be the A value. Then, 2x times -6 is -12x, which is the B value. I'm sorry if thats not what the question is asking. Hope this helps though!
the linear correlation coefficient is always between
Answers
The formulas return a value between -1 and 1, where:
• 1 indicates a strong positive relationship. A correlation coefficient of 1 means that for every positive increase in one variable, there is a positive increase of a fixed proportion in the other.
• -1 indicates a strong negative relationship. A correlation coefficient of -1 means that for every positive increase in one variable, there is a negative decrease of a fixed proportion in the other.
• A result of zero indicates no relationship at all. Zero means that for every increase, there isn’t a positive or negative increase. The two just aren’t related.
Therefore, the correct answer is: The linear correlation coefficient is always between -1 and 1.
Please mark my answers as the Brainliest if my explanations were helpful :)
Rickey bought a 35 pound bag of dog food . His dog eats an average of 3.5 pounds a day . How many pounds will remain in the bag after 8 days
Answers
Answer:
7 pounds
Step-by-step explanation:
3.5×8=28 pounds
35-28=7 pounds
so 7 pounds will b left
sum of the first nth term of a series is given by Sn = n (3n-4). Show that the terms of the series are in arithmetic progression
Answers
Answer:
see explanation
Step-by-step explanation:
Using the sum to n terms formula, then
S₁ = 1(3 - 4) = 1(- 1) = - 1 ⇒ a₁ = - 1
S₂ = 2(6 - 4) = 2(2) = 4, then
a₂ = S₂ - S₁ = 4 - (- 1) = 4 + 1 = 5
S₃ = 3(9 - 4) = 3(5) = 15, then
a₃ = S₃ - S₂ = 15 - 4 = 11
S₄ = 4(12 - 4) = 4(8) = 32 , then
a₄ = S₄ - S₃ = 32 - 15 = 17
S₅ = 5(15 - 4) = 5(11) = 55 , then
a₅ = S₅ - S₄ = 55 - 32 = 23
The first 5 terns of the series are
- 1, 5, 11, 17, 23
There is a common difference (d) between consecutive terms
d = 5 - (- 1) = 11 - 5 = 17 - 11 = 23 - 17 = 6
Thus the series is in arithmetic progression
what is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations? (round your answer to three decimal places.)
Answers
0.003 is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations
To calculate the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations.The mean is the expected number of calls involving a fax transmission, while the standard deviation is the measure of variability in the distribution. We then use this information to calculate the probability of exceeding the expected number by more than 2 standard deviations, which can be done using the z-score formula. The z-score for values more than 2 standard deviations away from the mean is 2.33, which corresponds to a probability of 0.003. Thus, the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations is 0.003.
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Last winter Carrie wrote down the number of days it snowed in February. She noticed that for every 2 snow days , there were 5 days it did not snow. There are a total of 28 days in February, how many days did it snow in February. How many days did it not snow?
Answers
No snow days = 20
what is the volume of this triangular prism?
15 points :)
Answers
Answer:
c)5676.16
Step-by-step explanation:
formula =0.5 X A X BX H
= 0.5 * 22.4*22.8*18.1
Please help! In desperate need :(
Answers
y=6
\(z=3\sqrt{13} \\x=2\sqrt{13}\)
Jeanette uses 2 1/2 more balls of yarn to knit a blanket than she uses to knit a sweater. Knitting a sweater requires three times as much yarn as knitting a hat. Jeanette uses 1 1/2 balls of yarn to knit a scarf, which is 1/2 ball more than shes uses for a hat
Answers
Jeannette needs 5 1/2 balls of yarn or 5.5 balls of yarn to knit a blanket.
How to calculate the number of balls of yarn that Jeannette needs?This question requires finding the number of balls that are necessary to knit a blanket based on the information provided.
Yarn to knit a hat:
It is known knitting a hat requires 1/2 ball of yarn less than knitting a scarf that requires 1 1/2.1 1/2 - 1/2 = 1 ball of yarnTherefore, Jeannette uses 1 ball of yarn to knit a hat.
Yarn to knit a sweater:
Knitting a sweater requires three times the yarn to knit a hat.1 ball of yarn x 3 = 3 balls of yarnTherefore, Jeannette uses 3 balls of yarn to knit a sweater.
Yarn to knit a blanket:
A blanket requires 2 1/2 more balls than a sweater.3 + 2 1/2 = 5 1/2 balls of yarn or 5.5 balls of yarnTherefore, Jeannette uses 5 1/2 balls of yarn or 5.5 balls of yarn to knit a sweater.
Note: This question is incomplete; here is the possible missing part.
How many balls of yarn does Jeannette use to knit a blanket?
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Find the probability of randomly selecting a red, then a free marble from a bag of 5 red, 8 green, and 3 marbles when (a) you replace the first marble before drawing the second, and (b) you do not replace the first marble. Then, compare the probability. Round your answers to four decimals places
Answers
The probability of randomly selecting a red, then a free marble from a bag of 5 red, 8 green, and 3 marbles
a) 0.1563
b) 0.1667
Since we are given with bag of 5 red, 8 green, and 3 marbles. so, r=5, g=8 and b= 3. For the first case, we replace the first marble before drawing the second, the total number of marble = 5 + 8 + 3 = 16. So, the probability of drawing a red marble at the 1st attempt is: 5/16. Then, the first marble is replaced back into the bag before making the second draw. Probability of drawing green marbles at the second draw is: 8/16= 1/2, Therefore the probability of selecting a red, then a green marble is: 5/16 * 1/2 = 5/32 =0.1563
For the second case , we do not replace the first marble, the probability of drawing a red marble at the 1st draw is:5/16 . Since we don't replace the balls so the number of marbles remaining in the bag is: 16-1 =15 ,the probability of drawing green marbles at the second draw is: 8/15, therefore the combined probability of selecting a red, then a green marble is: 5/16 * 8/15 =0.1667
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answer plzzzzzzzzzzzzzzz
Answers
Answer:
25
Step-by-step explanation:
They are relevant
3x=75
x=75/3
x=25
(1) An architect firm uses an average of 60 boxes of copier paper a day. The fim operates 280 days a year. Storage and handling costs for the paper are $30 a year per box, and its costs approximately $60 to order and receive a shipment of paper. (a) What quantity order size would minimize the total annual inventory cost? (b) Determine the minimum total annual inventory cost. (c) The office manager is currently using an order size of 300 boxes. The partners of the firm expect the office to be managed "in a cost-efficient manner." Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes):
Answers
Part a: What quantity order size would minimize the total annual inventory cost? Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying Cost At minimum Total Annual Inventory Cost, the formula for the Economic Order Quantity (EOQ) is used. EOQ formula is given below: EOQ = sqrt((2DS)/H)Where, D = Annual DemandS = Ordering cost
The company should place an order for 168 boxes at a time in order to minimize the total annual inventory cost.Part b: Determine the minimum total annual inventory cost.Using the EOQ, the company can calculate the minimum total annual inventory cost. The Total Annual Inventory Cost formula is:Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying CostAnnual Ordering Cost = (D/EOQ) × S = (16,800/168) × $60 = $6,000Annual Carrying Cost = (EOQ/2) × H = (168/2) × $30 = $2,520Total Annual Inventory Cost = $6,000 + $2,520 = $8,520Therefore, the minimum Total Annual Inventory Cost would be $8,520.Part c: Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes)
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On certain highways the speed limit is 75 mph, at this rate how far would you travel in 2.5 hours.
Answers
Answer:
187.5mph
Step-by-step explanation:
If 1 hour= 75mph
what about 2.5 hours
you cross multiply
A random sample of 64 sat scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. the 95onfidence interval for the population mean sat score is: ________
a. 1.96. b. 1.998.
c. 1.645. d. 1.28.
Answers
The 95% confidence interval for the population mean SAT score is given as follows:
(1340, 1460).
How to calculate the confidence interval?The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.
The bounds are obtained according to the equation defined as follows:
\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)
In which the variables of the equation are presented as follows:
\(\overline{x}\) is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.In the context of this problem, the values of these parameters are given as follows:
\(\overline{x} = 1400, n = 64, s = 240\)
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.
Then the lower bound of the interval is of:
1400 - 1.998 x 240/sqrt(64) = 1340.
The upper bound of the interval is of:
1400 + 1.998 x 240/sqrt(64) = 1460.
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Evaluate: Question(2): Z+8-6(z-2a)+5z
Answers
Answer:
Z+12a−z+8+12−+8
Step-by-step explanation:
Z+8−6(z−2a)+5z
+8−6(−2)+5
Z+8−6(−2a+z)+5z
+8−6(−2+)+5
Z+8−6(−2a+z)+5z
+8−6(−2+)+5
Z+8+12a−z+8+12−
Answer:
Z + 8 + 12a − z
12a + 8
Step-by-step explanation:
someone help please.
Answers
Answer:
9
Step-by-step explanation:
Special right triangle
this is a 45, 45, 90 triangle
Meaning that whatever the hypotenuse is
that it will be the same for x
PLEASE HELP FAST ILL GIVE BRAINLIEST AJGSAJSJDH 2) Maria Louisa looks at a sequence of shapes and records the number of
vertices in each of the shapes in the sequence. The first shape has 3
vertices, the second shape has 5 vertices, and the third shape has 7
vertices.
If Maria Louisa assumes that the number of vertices in the sequence of
shapes follows the same pattern, how many vertices would she expect the
twenty-first shape to have?
A.
39
B.
41
C.
43
D.
45
Answers
What is y-8=3(x+1) in standard form
Answers
Answer: 3x - y= -11
Step-by-step explanation: just rewrite in youre standard form equation
A contractor is required by a county planning department to submit anywhere from one to five forms (depending on the nature of the project) in applying for a building permit. Let r.v. X = the number of forms required of the next applicant. The probability that x forms are required is known to be proportional to x; that is, pX(x) = cx for x = 1, . . . , 5.
(a) (1 mark). What is the value of c?
(b) (1 mark). What is the probability that at most three forms are required?
(c) (1 mark). What is the probability that between two and four forms (inclusive) are required?
(d) (2 marks). Could pX(x) = x^2/50 for x = 1, . . . , 5 be a probability distribution of X? Explain.
Answers
The probability that x forms are required is known to be proportional to c = 1/15. c= 2/5 c= 3/5, c= 1.1
(a) Since the probabilities must sum to 1, we have:
pX(1) + pX(2) + pX(3) + pX(4) + pX(5) = c(1 + 2 + 3 + 4 + 5) = 15c
Therefore, c = 1/(1 + 2 + 3 + 4 + 5) = 1/15.
(b) The probability that at most three forms are required is:
P(X ≤ 3) = pX(1) + pX(2) + pX(3) = c(1 + 2 + 3) = 6c = 2/5.
(c) The probability that between two and four forms (inclusive) are required is:
P(2 ≤ X ≤ 4) = pX(2) + pX(3) + pX(4) = c(2 + 3 + 4) = 9c = 3/5.
(d) No, because the probabilities do not sum to 1:
Σ pX(x) from x = 1 to 5
= (1/50)(1 + 4 + 9 + 16 + 25)
= 55/50
= 1.1
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what is the perimeter
Answers
Answer:
16
.................
Consider triangle ABC where AB=X+5, BC=X-2, area is 30cm squared. Find X by solving X^2+3X-70=0, and find the perimeter.
Answers
Answer:
What the hell AC is not given so you can't find the Perimeter
Step-by-step explanation:
x^2+3x-70=0(x-7)(x+10)=0x-7=0x+10=0
x=7x=-10
AB=x+5
AB=12AB=-5
BC=x-2
BC=5BC=-12
Area of ABC = 30cm2
Perimeter of ABC = AB+BC+AC
find 24+3-(2×8)÷3
a. Zero
b. 1.37
c. 13.7
d. 1
Answers
In ΔF G H, ∠G is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. f=3, h=9
Answers
The remaining sides and angles in triangle ΔFGH are approximately:
FG ≈ 8.5 units (rounded to the nearest tenth)
∠F ≈ 19.5° (rounded to the nearest tenth)
∠H ≈ 70.5° (rounded to the nearest tenth)
To find the remaining sides and angles in triangle ΔFGH, given that ∠G is a right angle (90°) and f = 3, h = 9, we can use the Pythagorean theorem and trigonometric ratios.
Using the Pythagorean theorem, we know that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
So, we have:
f^2 + g^2 = h^2
Substituting the given values:
3^2 + g^2 = 9^2
9 + g^2 = 81
g^2 = 81 - 9
g^2 = 72
g = √72 ≈ 8.49
Therefore, the length of side FG (g) is approximately 8.5 units when rounded to the nearest tenth.
Now, let's find the remaining angles using trigonometric ratios:
To find ∠F, we can use the sine ratio:
sin(∠F) = opposite/hypotenuse = f/h = 3/9 = 1/3
∠F = arcsin(1/3) ≈ 19.5° (rounded to the nearest tenth)
To find ∠H, we can use the cosine ratio:
cos(∠H) = adjacent/hypotenuse = f/h = 3/9 = 1/3
∠H = arccos(1/3) ≈ 70.5° (rounded to the nearest tenth)
Therefore, the remaining sides and angles in triangle ΔFGH are approximately:
FG ≈ 8.5 units (rounded to the nearest tenth)
∠F ≈ 19.5° (rounded to the nearest tenth)
∠H ≈ 70.5° (rounded to the nearest tenth)
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78 15 6
94 13 4
59 14 ?
Answers
Answer:
12 45 17 98
Step-by-step explanation:
12 36 78