Management should hire 25 additional vendors to maximize the number of sodas sold.
Let x be the number of additional vendors that management hires. Then the total number of vendors is 40 + x, and the yield per vendor is 200 - 4x (since the yield decreases by 4 for each additional vendor).
The total number of sodas sold is the product of the number of vendors and the yield per vendor:
Total sodas sold = (40 + x) * (200 - 4x)
To maximize the number of sodas sold, we take the derivative of this expression with respect to x and set it equal to zero:
d/dx [(40 + x) * (200 - 4x)] =
Expanding and simplifying, we get:
-8x² + 120x + 8000 = 0
Dividing both sides by -8, we get:
x² - 15x - 1000 = 0
Using the quadratic formula, we solve for x:
x = (15 ± sqrt(15² + 411000)) / 2
x = (15 ± 35) / 2
x = -10 or x = 25
Since we can't hire a negative number of vendors, the only sensible solution is x = 25. Therefore, management should hire 25 additional vendors to maximize the number of sodas sold.
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Twenty students in A and 20 students in class B were asked how many hours they took to prepare for an exam. The data sets represents their answers
The data sets represent the answers of twenty students in Class A and twenty students in Class B regarding the number of hours they took to prepare for an exam. These data sets are important because they help us understand the study habits and time allocation of the students in each class.
To analyze the data sets, first, collect the data from each student in both classes. Record the number of hours they took to prepare for the exam, ensuring you have 20 responses from Class A and 20 from Class B. Then, you can compute the average, or mean, time spent for each class by summing up the hours reported by all students in each class and dividing by 20.
Next, compare the averages for Class A and Class B to determine if there is a significant difference in the time spent preparing for the exam. Additionally, you can calculate other statistical measures such as median and mode to gain further insight into the data sets.
Furthermore, analyzing the distribution of the data, such as the range, will provide information on the variability of the time spent studying in each class. This can help identify any trends or patterns in the students' preparation time.
In conclusion, the data sets representing the number of hours spent by students in Class A and Class B to prepare for an exam can provide valuable insights into their study habits, the effectiveness of their preparation, and any possible correlations between time spent studying and exam performance.
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Alexandre has two brothers: Hugo and Romain. Every day Romain draws a name out of a hat to randomly select one of the three brothers to wash the dishes. Alexandre suspected that Romain is cheating, so he kept track of the draws, and found that out of
12
1212 draws, Romain didn't get picked even once.
Let's test the hypothesis that each brother has an equal chance of
1
3
3
1
start fraction, 1, divided by, 3, end fraction of getting picked in each draw versus the alternative that Romain's probability is lower.
Assuming the hypothesis is correct, what is the probability of Romain not getting picked even once out of
12
1212 times? Round your answer, if necessary, to the nearest tenth of a percent.
Based on the observed outcome, it is therefore very or highly unlikely that Romain's probability is equal to that of the other brothers, and thus it is possible that Romain is cheating.
What is the probability?Beneath the assumption that each brother has an break even with chance of getting picked in each draw, the likelihood of Romain not getting picked indeed once out of 12 times is:
P(Romain not picked) = (2/3)¹²
= 0.0077
This is one that is less than 1%, which suggests that the observed result is made up of a likelihood less than 1% beneath the given speculation. Therefore, we need to reject the hypothesis that each brother has an equal chance of getting picked in all of the draw.
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See text below
Alexandre has two brothers: Hugo and Romain. Every day Romain draws a name out of a hat to randomly select one of the three brothers to wash the dishes. Alexandre suspected that Romain is cheating, so he kept track of the draws, and found that out of 12 draws, Romain didn't get picked even once. 1 Let's test the hypothesis that each brother has an equal chance of of getting picked in each draw versus 3 the alternative that Romain's probability is lower. Assuming the hypothesis is correct, what is the probability of Romain not getting picked even once out of 12 times? Round your answer, if necessary, to the nearest tenth of a percent. Let's agree that if the observed outcome has a probability less than 1% under the tested hypothesis, we will reject the hypothesis. What should we conclude regarding the hypothesis? Choose 1 answer: We cannot reject the hypothesis. B We should reject the hypothesis.
What rate of interest compounded annually is required to double an investment in 29 years? Round your answer to two decimal places
An interest rate of approximately 2.40% per annum, compounded annually, is required to double an investment in 29 years.
Let "r" be the annual interest rate, then the investment will double after 29 years if (1 + r)^29 = 2. Solving this equation, we get r ≈ 0.0240 or 2.40% (rounded to two decimal places) as the required annual interest rate. This means that if the investment is compounded annually at this rate, it will double after 29 years.
Alternatively, we can use the formula for compound interest, A = P(1 + r/n)^(nt), where A is the future value, P is the present value, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
We want to find the interest rate, r, that will double the investment, so we can set A = 2P, t = 29, n = 1 (compounded annually), and solve for r. This gives us r ≈ 0.0240 or 2.40%.
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Which equations will find the distance between the lions and giraffes? Select all that apply. 11+16 = c 112+ 162 = c2 c2+ 162 = 112 121+ 256 = c2 11(2)+16(2) = 2c
The equations that will find the distance between the lions and giraffes include the following:
B. 11² + 16² = c².
D. 11(2) + 16(2) = 2.
What is distance?In Mathematics and Science, distance can be defined as the amount of ground that is travelled by a physical object or body over a particular period of time and speed, irrespective of its direction, starting point or ending point.
Mathematically, the distance traveled by both the lions and giraffes when they are positioned one (1) unit apart can be calculated by using this equation:
11² + 16² = c²
Additionally, the distance traveled by both the lions and giraffes when they are positioned two (2) unit apart can be calculated by using this equation:
11(2) + 16(2) = c
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A large diamond with a mass of 2138. 7 grams was recently discovered in a mine. If
8
the density of the diamond is 3. 51 cm", what is the volume? Round your answer to
the nearest hundredth. (5 points)
O 1)
141. 84 cm3
2) 609. 3 cm3
3) 717. 06 cm3
O 4
8169. 8 cm3
WILL GIVE BRAINLIEST!!
The volume of the diamond is 609.3 cm³.
To find the volume of the diamond, we can use the formula:
Volume = Mass / Density
Given:
Mass = 2138.7 grams
Density = 3.51 g/cm³
Substituting these values into the formula:
Volume = 2138.7 g / 3.51 g/cm³
Calculating the division:
Volume ≈ 609.3 cm³
Therefore, the volume of the diamond is approximately 609.3 cm³.
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what principal will earn $67.14 interest at 6.25% for 82 days?
Answer: attach an image
Step-by-step explanation:
To find the principal, we can use the formula for simple interest:
I = P*r*t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
We need to convert 82 days to years by dividing it by 365 (the number of days in a year):
t = 82/365
t = 0.2247
Now we can plug in the values we know and solve for P:
67.14 = P*0.0625*0.2247
P = 67.14/(0.0625*0.2247)
P = 1900
Therefore, the principal is $1900.
When you don’t replace the marble for the second draw what kind of probability is it?
If you do not replace the marble after the first draw, the probability calculation depends on whether you are dealing with a dependent or an independent event.
The possibility or chance of an event occurring is measured by probability. It is a number between 0 and 1 (inclusive), where 0 denotes an impossibility and 1 denotes a certainty. By dividing the number of favorable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. The field of mathematics known as probability studies the possibility that a certain event will take place. It is a way to quantify the possibility or likelihood that something will really happen.
For an independent event, assuming that the first draw had no bearing on the outcome of the second draw, in the case of an isolated occurrence, the chance of drawing a specific marble on the second draw would be the same as the likelihood of drawing that same marble on the first draw. For a dependent event, the outcome of the first draw would determine the possibility of drawing a specific marble on the second draw.
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Michael had 8/9 of a spool of yarn. He used 2/5 of his yarn for a project. What fraction of the spool was used for the project?
Answer:16/45 of his yarn
Step-by-step explanation:
8/9 x 2/5 = 16/45
Exercise 11. 3. 1: Applying the pigeonhole principle - heights and times. About Apply the pigeonhole principle to answer the following questions. If the pigeonhole principle can not be applied, give a specific counterexample. (a) A team of three high jumpers all have a personal record that is at least 6 feet and less than 7 feet. Is it necessarily true that two of the team members must have personal records that are within four inches of each other
To apply the pigeonhole principle, we need to determine the number of pigeonholes and the number of pigeons. The pigeonhole principle cannot be applied to this question.
In this case, the" holes" are the high minidresses and the" lockers" are the ranges of particular records. Let's assume that the range of particular records is from 6 bases( 72 elevation) to 7 bases( 84 elevation). The difference between the upper and lower bounds of the range is
84- 72 = 12 elevation.
We can divide this range into five subintervals of length2.4 elevation( 72,74.4),(74.4,76.8),(76.8,79.2),(79.2,81.6), and(81.6, 84).
Since there are only five subintervals, but we've three high minidresses, it isn't inescapably true that two of the platoon members must have particular records that are within four elevation of each other. For illustration, if the three high minidresses have particular records of 6 bases 3 elevation( 75 elevation), 6 bases 7 elevation( 79 elevation), and 7 bases( 84 elevation), also none of them have particular records within four elevation of each other.
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evaluate : 20-[5+(9-6]
Answer:
12
Step-by-step explanation:
20-(5+(9-6)) = 20-(5+(3)) = 20-(8) = 12.
Alternatively, rewrite the question without parenthesis.
20-(5+(9-6)) = 20-(5+9-6) = 20-5-9+6 = 12.
In a study of the relationship between birth order and college success, an investigator found that 126 in a sample of 180 college graduates were firstborn or only children; in a sample of 100 nongraduates of comparable age and socioeconomic background, the number of firstborn or only children was 54. estimate the difference in the proportions of firstborn or only children for the two populations from which these samples were drawn. give a bound for the error of estimation.
The difference in the proportions of firstborn or only children for the two populations from which these samples were drawn is 0.16.The bound for the error of estimation is 95% confidence that the true difference in proportions of firstborn or only children for the two populations is between 0.058 and 0.262.
To estimate the difference in the proportions of firstborn or only children for the two populations, we can use the sample proportions and apply the formula:
p1 - p2 = (x1/n1) - (x2/n2)
where p1 and p2 are the true population proportions, x1 and x2 are the numbers of firstborn or only children in the samples, and n1 and n2 are the sample sizes.
Sample of college graduates: x1 = 126, n1 = 180Sample of non-graduates: x2 = 54, n2 = 100The sample proportions,
p1 = x1/n1 = 0.7
p2 = x2/n2 = 0.54
Substituting these values into the formula,
p1 - p2 = (x1/n1) - (x2/n2) = 0.7 - 0.54 = 0.16
Therefore, we estimate that the difference in the proportions of firstborn or only children for the two populations is 0.16.
To find a bound for the error of estimation, we can use the formula:
E = z sqrt(p1*(1-p1)/n1 + p2*(1-p2)/n2)
where E is the margin of error, z is the critical value for the desired level of confidence (we'll use z = 1.96 for a 95% confidence interval), and p1 and p2 are the sample proportions.
Substituting the given values, we get:
E = 1.96sqrt(0.7(1-0.7)/180 + 0.54*(1-0.54)/100) ≈ 0.102
Therefore, we can say with 95% confidence that the true difference in proportions of firstborn or only children for the two populations is between 0.058 and 0.262
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Which scatter plot below would best be modeled by using linear regression?
Answer:
Top
Step-by-step explanation:
The closer the data points come to forming a straight line when plotted, the higher the correlation between the two variables, or the stronger the relationship. Therefore, the top option has the most closest lines to a linear function.
(Ex. 1) Y=4x-2
This example shows the corresponding possibilities of a linear regression because of the way the line is represented as graphed, making a straight line as similar to the top option
(Ex. 2) f(x) = x^2-5+15
This example dialates to a similar option like the third option, which isnt linear regression because of it being a quadratic function.
In a nut shell, all data plotted on the graph that are formed closer together and corresponds to a linear equation is a linear regression
This ladder is extended to a length of 18 feet. The bottom of the ladder is 4. 5 feet from the base of the building. What angle does the ladder make with the ground?
The ladder makes an angle of approximately 82 degrees with the ground when it is extended to a length of 18 feet and the bottom of the ladder is 4.5 feet from the base of the building.
To determine the angle that the ladder makes with the ground, we can use trigonometry. Let x be the height of the ladder when it is leaned against the building. Then, using the Pythagorean theorem, we have: [tex]x^{2}[/tex] + [tex]4.5^{2}[/tex] = [tex]18^{2}[/tex]
Solving for x, we get: x = sqrt([tex]18^{2}[/tex] - [tex]4.5^{2}[/tex]), x ≈ 17.29
Therefore, the ladder makes an angle θ with the ground such that: sin θ = opposite/hypotenuse = x/18, θ = arcsin(x/18)
Substituting x ≈ 17.29, we get: θ ≈ 81.99 degrees
Therefore, the ladder makes an angle of approximately 82 degrees with the ground when it is extended to a length of 18 feet and the bottom of the ladder is 4.5 feet from the base of the building.
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HELP NEEDED ASAP!!!!
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:
High Low Q1 Q3 IQR Median Mean σ
Rome 18 1 3 7 4 6.5 6.4 4.3
New York 14 1 4.5 8.5 4 5.5 6.1 3.2
Which of the choices below best describes how to measure the center of these data?
a.Both centers are best described by the mean.
b.Both centers are best described by the median.
c.The Rome data center is best described by the mean. The New York data center is best described by the median.
d.The Rome data center is best described by the median. The New York data center is best described by the mean.
The choice which best describes the measure of center of these data is (d) Rome data center is "best-described" by median and data center of "New-York" is "best-described" by mean.
In the table provided below, we see that the "IQR" for Rome is relatively large compared to the IQR for New York, which suggests that that there may be some skewness in the distribution of the Rome data. So, the median would be a better-measure of center than the mean.
On the other hand, the IQR for "New-York" is relatively small, which indicates that the data is more symmetric and the mean would be a better measure of center.
Therefore, the correct answer is (d).
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The given question is incomplete, the complete question is
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:
High Low Q1 Q3 IQR Median Mean σ
Rome 18 1 3 7 4 6.5 6.4 4.3
New York 14 1 4.5 8.5 4 5.5 6.1 3.2
Which of the choices below best describes how to measure the center of these data?
(a) Both centers are best described by the mean.
(b) Both centers are best described by the median.
(c) The Rome data center is best described by the mean. The New York data center is best described by the median.
(d) The Rome data center is best described by the median. The New York data center is best described by the mean.
4) Your phone needs to be charged every other day and your tablet needs to be charged every third day. If you charge both today, how many days will it be until you need to charge both on the same day?
Answer:
If they were both charged today, it would be on the sixth day that they were actually charging at the same time
In a random sample of 74 homeowners in a city, 22 homeowners said they would
support a ban on nonnatural lawn fertilizers to protect fish in the local waterways. The sampling
method had a margin of error of ±3. 1%.
A) Find the point estimate.
B) Find the lower and upper limits and state the interval
Point estimate is 29.7%.
The confidence interval for the proportion of homeowners who support the ban on nonnatural lawn fertilizers is (26.6%, 32.8%).
A) The point estimate is the proportion of homeowners who support the ban on nonnatural lawn fertilizers.
In this case, 22 out of 74 homeowners support the ban. To find the point estimate, divide the number of supporters (22) by the total number of homeowners in the sample (74):
Point estimate = 22 / 74 ≈ 0.297 or 29.7%
B) To find the lower and upper limits, we need to consider the margin of error (±3.1%). Subtract the margin of error from the point estimate for the lower limit, and add the margin of error to the point estimate for the upper limit:
Lower limit = 29.7% - 3.1% = 26.6%
Upper limit = 29.7% + 3.1% = 32.8%
The confidence interval for the proportion of homeowners who support the ban on nonnatural lawn fertilizers is (26.6%, 32.8%).
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At midnight, the temperature in a city was 5 degrees celsius. the temperature was dropping at a steady rate of 1 degrees celsius per hour.
a. write an inequality that represents t, the number of hours past midnight, when the temperature was colder than -3 degrees celsius.
b. explain or show your reasoning.
The inequality that represents t, the number of hours past midnight, when the temperature was colder than -3 degrees Celsius is t > 8.
The inequality that represents t, the number of hours past midnight, when the temperature was colder than -3 degrees Celsius is t > 8.When the temperature drops at a steady rate of 1 degree Celsius per hour, it will take 8 hours to reach -3 degrees Celsius from the initial temperature of 5 degrees Celsius.
Therefore, any time past 8 hours after midnight will result in a temperature colder than -3 degrees Celsius.
Thus, the inequality t > 8 represents the number of hours past midnight when the temperature was colder than -3 degrees Celsius.
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Victoria has $200 of her birthday gift money saved at home, and the amount is modeled by the function h(x) = 200. She reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1. 05)x−1. Explain how Victoria can combine the two functions to model the total amount of money she will have in her bank account as interest accrues after she deposits her $200. Justify your reasoning.
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The total amount of money Victoria will have in her bank account after x years can be modeled by the function f(x) = 200 * (1.05)ˣ.
How can we model Victoria's bank account growth over time?To model the total amount of money Victoria will have in her bank account after depositing her $200 and accruing interest over time, we can combine the two functions h(x) and s(x).
We can use the following formula to represent the total amount of money Victoria will have in her bank account after x years:
f(x) = h(x) + h(x) * s(x)
where h(x) represents the $200 that Victoria has saved at home, and h(x) * s(x) represents the amount of interest accrued on that $200 in x years according to the function s(x).
The justification for this formula is that the total amount of money Victoria will have in her bank account after x years is the sum of the initial amount of $200 and the interest accrued on that amount over x years.
The interest accrued can be calculated by multiplying the initial amount by the interest rate function s(x).
For example, if Victoria leaves her $200 in the bank for 5 years, the total amount of money she will have in her account can be calculated using the formula:
f(5) = h(5) + h(5) * s(5) = 200 + 200 * (1.05)⁴ ≈ $273.04
Therefore, the total amount of money Victoria will have in her bank account after x years can be modeled using the function f(x) = h(x) + h(x) * s(x).
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At a certain vineyard it is found that each grape vine produces about 10 lb of grapes in a season when about 800 vines are planted per acre. for each additional vine that is planted, the production of each vine decreases by about 1 percent. so the number of pounds of grapes produced per acre is modeled by
a(n) = (800 + n)(10 − 0.01n)
where n is the number of additional vines planted. find the number of vines that should be planted to maximize grape production.
Planting an additional 210 vines will maximize grape production.
How to maximize grape production?To find the number of vines that should be planted to maximize grape production, we need to find the maximum value of the function A(n) = (800 + n)(10 - 0.01n), which represents the number of pounds of grapes produced per acre as a function of the number of additional vines planted. To find the maximum value, we can take the derivative of A(n) with respect to n and set it equal to zero.
A'(n) = -0.01n² + 2.1n + 800
Setting A'(n) = 0, we get
-0.01n²+ 2.1n + 800 = 0
Solving for n using the quadratic formula, we get
n ≈ 210
Therefore, planting an additional 210 vines will maximize grape production.
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Consider the following series: (-1)^ 71n n We will test this series for convergence or divergence. (i) What test(s) is(are) applicable to test this series? Click for List (i) Determine whether this series converges or diverges. O Converges O Diverges (iii) What is the sum of the series? Note: Write the exact answer not the decimal approximation (for example write 1 / not 0.8). Answer: The sum of the series is PO
The series given is (-1)^71n*n. To test for convergence or divergence, the alternating series test as the series alternates in sign. Also, the absolute value of the terms of the series is decreasing as n increases. In conclusion, the given series (-1)^71n * n diverges, and it does not have a finite sum.
According to the alternating series test, if a series alternates in sign, and the absolute value of its terms is decreasing as n increases, then the series converges.
Thus, the series converges.
To find the sum of the series, we use the formula for the sum of an alternating series:
Sum = (-1)^71*1 - (-1)^71*2 + (-1)^71*3 - (-1)^71*4 + ...
= (-1)^71*(1 - 2 + 3 - 4 + ...)
= (-1)^71*(n(n+1)/2)
= 0
Therefore, the sum of the series is 0.
I'd be happy to help you with your question. To determine the convergence or divergence of the series (-1)^71n * n, we can follow these steps:
(i) Since the series has terms that alternate in sign, we can use the Alternating Series Test to test for convergence.
(ii) To apply the Alternating Series Test, we must first verify that the sequence of positive terms is decreasing and has a limit of zero. In this case, the sequence of positive terms is given by "n". As "n" goes to infinity, the sequence increases, not decreases, and the limit is not zero. Therefore, the series (-1)^71n * n does not pass the Alternating Series Test, and it diverges.
(iii) Since the series diverges, it does not have a finite sum.
In conclusion, the given series (-1)^71n * n diverges, and it does not have a finite sum.
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A savings account balance is compounded annually. if the interest rate is 2% per year and the current balance is $1430.00 what will the balance be 8 years from now
Answer:
A = P(1 + r/n)^(nt)
Where:
A = the future balance
P = the present balance ($1430.00)
r = the annual interest rate (2% or 0.02)
n = the number of times the interest is compounded per year (since it's compounded annually, n = 1)
t = the number of years (8 years in this case)
Plugging in the values into the formula:
A = 1430(1 + 0.02/1)^(1*8)
Simplifying the equation:
A = 1430(1.02)^8
Using a calculator or performing the calculations manually:
A ≈ 1430(1.171661)
A ≈ 1674.02
the balance after 8 years will be approximately $1674.02.
A track has the dimensions shown.
36.5 m
ISTAN
SAMANT
men komm
84.4 m
Ta
inside of track
outside of track
. The track has 8 lanes
• Each lane is 2.1 meters wide
36.5 m
O
TI
16. To the nearest tenth of a meter, what is
the perimeter of the outside of the
track?
Byp
*REQUIRED
ANA
1
√x
Sign out
Answer:
Step-by-step explanation:
Zola wrote the area of the rectangle as `2a+3a+4a`.
amir wrote the area as `(2+3+4) a.
explain why they are both correct
please help as quickly as possible
assp
Both Zola and Amir are correct in writing the area of the rectangle. They have simply used different ways of expressing the same value.
Zola and Amir have both written the area of a rectangle using different algebraic expressions.
Zola wrote the area of the rectangle as `2a + 3a + 4a`, which can be simplified using the distributive property of multiplication:
2a + 3a + 4a = (2 + 3 + 4)a
Therefore, Zola's expression simplifies to `(2 + 3 + 4)a`, which is the same as Amir's expression.
Amir wrote the area of the rectangle as `(2 + 3 + 4) a`, which can also be simplified:
(2 + 3 + 4) a = 9a
Therefore, Amir's expression simplifies to `9a`, which is the same as the sum of the terms in Zola's expression.
Therefore, both Zola and Amir are correct in writing the area of the rectangle. They have simply used different ways of expressing the same value.
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Cuál es el valor de la razón del cambio cuando metemos un vaso de agua al tiempo al congelador por 15 minutos?
The value of the rate of change when we put a glass of water at room temperature is 1/3.
The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one thing by the equal amount of change in another.
The connection defining how one quantity changes in response to the change in another quantity is given by the rate of change formula. The formula for calculating the rate of change from y coordinates to x coordinates is y/x = (y2 - y1)/. (x2 - x1 ).
Rate of change = change in temperature / time
= 10-5/15
=5 / 15
= 1/3
Therefore, the Rate of change is 1/3.
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Complete question;
What is the value of the rate of change when we put a glass of water at room temperature in the freezer for 15 minutes, what is its temperature at 5 minutes and then at 10 minutes.
At the start of an observation, there are 7286.9 grams of a radioactive element present. The number of years t that must pass before N grams remain is given by the natural logarithm equation
t = 7,286.9 - 1,252 In(IV).
, dit
Find dt/dn When N = 15. Round to 2 decimal places, if necessary.
The value of dt/dN when N = 15 is -0.00509.
We are given the equation t = 7,286.9 - 1,252 ln(N/IV) which relates the number of years t that must pass before N grams of a radioactive element remain. We want to find the rate of change of t with respect to N, i.e., dt/dN when N = 15.
We can start by taking the derivative of both sides of the equation with respect to N:
dt/dN = -1252 / (N*ln(2))
Now we can substitute N = 15 into this equation to get:
dt/dN = -1252 / (15*ln(2))
Evaluating this expression, we get dt/dN ≈ -0.00509 (rounded to 2 decimal places). Therefore, the rate of change of t with respect to N when N = 15 is approximately -0.00509 years per gram.
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pls solve this asap
Step-by-step explanation:
perimeter of triangle=22 cm
AB+BC+CA=22cm
AB+4+AB =22cm (given,AB=AC)
2AB+4cm=22cm
2AB=22-4cm
2AB=18
AB=18÷2
AB=9cm
Part 3
sales tax is 8%
basketballs are 20% off
you have two customers john and david. john has $250 and
david has $150. john is coaching a baseball team and wants
to buy 10 baseball bats for his team. david wants to buy 3
pairs of running shoes for his kids. will each person be able
to buy the items that they want? explain.
baseball bats are 5% off
running shoes are 15% off
i
tax
with
discount
total
cost
john
david
John will be able to buy the 10 baseball bats for his team with some money left over is -$6.50 and David will be able to buy the 3 pairs of running shoes for his kids with some money left over is $12.30.
Based on the given information, we can calculate the total cost for each customer after factoring in the sales tax and discounts.
For John:
The cost of 10 baseball bats without any discounts or tax would be 10 * $25 = $250.
Since baseball bats are 5% off, John will get a discount of 0.05 * $250 = $12.50.
So, the cost of 10 baseball bats after discount is $250 - $12.50 = $237.50.
Adding 8% sales tax to this amount, the total cost for John will be $237.50 + (0.08 * $237.50) = $256.50.
For David:
The cost of 3 pairs of running shoes without any discounts or tax would be 3 * $50 = $150.
Since running shoes are 15% off, David will get a discount of 0.15 * $150 = $22.50.
So, the cost of 3 pairs of running shoes after discount is $150 - $22.50 = $127.50.
Adding 8% sales tax to this amount, the total cost for David will be $127.50 + (0.08 * $127.50) = $137.70.
Therefore, John will be able to buy the 10 baseball bats for his team with some money left over ($250 - $256.50 = -$6.50) and David will be able to buy the 3 pairs of running shoes for his kids with some money left over ($150 - $137.70 = $12.30).
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Scientists estimate that the mass of the sun is 1. 9891 x 10 kg. How many zeros are in this
number when it is written in standard notation?
A 26
B 30
C 35
D 25
There are 30 zeros in the mass of the sun which is 1.9891 x 10³⁰ kg when it is written in standard notation. The correct answer is option B.
To determine how many zeros are in the mass of the sun (1.9891 x 10³⁰ kg) when it is written in standard notation, you first need to recognize that the provided mass is not written correctly. It should be written as 1.9891 x 10^n kg, where n is an integer representing the exponent.
The actual mass of the sun is 1.9891 x 10³⁰ kg. When written in standard notation, this number would be:
1,989,100,000,000,000,000,000,000,000,000 kg
There are 30 zeros in this number when written in standard notation.
So, the correct answer is B) 30.
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find a constant b so that y(t) = e^2t [1 4 b] is a solution of y′ = [4 1 3 2 3 3 −2 −1 −1]y.
We have found a value of b that makes y(t) = [tex]e^2t[/tex] [1; 4; -1/2] a solution of y′ = [4 1 3; 2 3 3; −2 −1 −1]y. To check if y(t) is a solution of y′ = Ay, we need to substitute it into the differential equation and see if it holds.
Let's start by finding y′:
y′(t) = [[tex]2e^2t, 8e^2t, 4be^2t[/tex]]
Now, let's find Ay:
Ay = [4 1 3; 2 3 3; −2 −1 −1] [1; 4; b] = [4+4b; 14; -5-b]
We want y(t) = e^2t [1; 4; b] to satisfy y′ = Ay, so we set them equal:
y′ = Ay
[[tex]2e^2t; 8e^2t; 4be^2t] = [4+4b; 14; -5-b] e^2t[/tex] [1; 4; b]
Expanding this equation, we get:
[tex]2e^2t[/tex]= (4+4b)[tex]e^2t[/tex]
[tex]8e^2t[/tex] = 14 [tex]e^2t[/tex]
[tex]4be^2t[/tex]= (-5-b) [tex]e^2t[/tex]
The second equation is always true, so we can ignore it. For the first equation, we can cancel out [tex]e^2t[/tex] on both sides to get:
2 = 4+4b
Solving for b, we get:
b = -1/2
Finally, we can substitute b = -1/2 back into the third equation to check if it holds:
4be^2t = (-5-b) [tex]e^2t[/tex]
-2e^2t = (-5 + 1/2)[tex]e^2t[/tex]
This equation is true, so we have found a value of b that makes y(t) = [tex]e^2t[/tex] [1; 4; -1/2] a solution of y′ = [4 1 3; 2 3 3; −2 −1 −1]y.
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Which relationship does not represent a direct proportion?
A. y = −
3
8
x
B.
Pounds Cost
3 $3.87
5 $6.45
8 $10.32
C. A dog groomer charges $15 per hour.
D.
The correct relationship which does not represent a direct proportion is,
⇒ A dog groomer charges $15 per hour.
Given that;
The graph is shown relation between number of minutes and Distance.
Take two points on the line are,
(2, 100) and (4, 150)
Hence, From graph we get;
The equation of line is,
⇒ y - 100 = (150 - 100)/ (4 - 2) (x - 2)
⇒ y - 100 = 25 (x - 2)
⇒ y - 100 = 25x - 50
⇒ y = 25x - 50 + 100
⇒ y = 25x + 50
Thus, The correct relationship which does not represent a direct proportion is,
⇒ A dog groomer charges $15 per hour.
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