A rumour spreads exponentially through a college. 100 people have heard it by noon, and 200 by 1 p.m. How many people have heard it (a) by 3 p.m., (b) by 12.30 p.m., (c) by 1.45 p.rn.?
a) people have heard it by 3 p.m is 800 people
b) people have heard it by 12.30 p.m is 141 people
c) people have heard it by 1.45 p.m is 530 people
Let's analyze this rumor spread problem. Each person who hears the rumor is assumed to spread it to exactly two other people.
a) By 3 p.m.: The rumor spreads for 3 hours after noon. Starting with 100 people at noon, by 3 p.m. it would be 100 * 2^3 = 100 * 8 = 800 people.
b) By 12:30 p.m.: The rumor spreads for half an hour after noon. That's 30 minutes or 0.5 hours. Since the rumor spreads exponentially, in half an hour, the number of people who hear it doubles once. So, by 12:30 p.m., it would be 100 * 2^0.5 = 100 * √2 ≈ 100 * 1.41 ≈ 141 people.
c) By 1:45 p.m.: The rumor spreads for 1 hour and 45 minutes after noon, which is 1.75 hours. So, by 1:45 p.m., it would be 100 * 2^1.75 ≈ 100 * 5.3 ≈ 530 people.
In summary:
a) 800 people
b) 141 people
c) 530 people
The repeating decimal, 0.27..., is converted to the fraction 0.27..=3/x
what is the value for x in the fraction
Answer:
The required number in the fraction is x=11
Step-by-step explanation:
Given : The repeating decimal, 0.27..., is converted to the fraction [tex]0.27....=\frac{3}{x}[/tex]
To find : What is the value for x in the fraction ?
Solution :
Let [tex]y=0.272727...[/tex] ....(1)
Multiply both side by 100,
[tex]100y=27.2727...[/tex] .....(2)
Subtract (1) and (2),
[tex]100y-y=(27.2727....)-(0.272727...)[/tex]
[tex]99y=27[/tex]
[tex]y=\frac{27}{99}[/tex]
[tex]y=\frac{3}{11}[/tex]
On comparing with [tex]0.27....=\frac{3}{x}[/tex]
The value of x is 11.
Therefore, The required number in the fraction is x=11.
Suppose the concentration of a certain pollutant is uniformly distributed in the range of 4 to 20 ppm (parts per million). if a concentration in excess of 15 ppm is considered toxic, what is the probability that a specimen will yield a toxic concentration level
Rachel bought a book for $5.49 And a game for $10.98. She paid with a $20 bill. Which is the best estimate of the amount of change she should receive?
If x has a continuous uniform distribution on the interval (0,5), what is the 25th percentile for x?
Find the extreme values of the function f(x, y) = 4x + 8y subject to the constraint g(x, y) = x2 + y2 − 5 = 0.
Can u simplify and convert these please and thank you
Andreus made $625 mowing yards. He worked for 5 consecutive days and earned the same amount of money each day. How much money did Andreus earn per day
which expression would give the thirteenth term Given the sequence 8, 16, 32, 64, ...,
813
8 · 213
8 · 212 ? 813 8 · 213 8 · 212
Write a real-life situation that can be modeled by the expression 5 x 3/4
3/4 is a fraction
Kesha sharpened 4 colors of pencils for her teacher. She sharpened equal amounts of red and green pencils. Then she sharpened twice as many blue and yellow pencils in equal amounts. How many of the 42 pencils were yellow?
Answer:
Step-by-sstep explanation:
Ted used a $150 check to pay for some books. Where in his checkbook register should he write this amount? in the PAYMENT or WITHDRAWAL AMOUNT column in the DEPOSIT AMOUNT column in the BALANCE column in the FEE column NextReset
Answer:
Ted should write the amount in the PAYMENT column of the checkbook register.
Step-by-step explanation:
When we want to withdraw money from the account then we need to mention the amount in the WITHDRAWAL column of the checkbook register.
When we want to deposit money to the account then we need to mention the amount in the DEPOSIT column of the checkbook register.
When we want to pay money to the someone else's account then we need to mention the amount in the PAYMENT column of the checkbook register.
So, Ted must write the amount in the PAYMENT column of the checkbook register.
match the top cards to the bottom cards to show doubles plus 1
This question is all about doubles. The given bottom cards 5
2 3 4 and the top cards are 1 4 3 2.
The problem is asking to match the top cards to the bottom ones then adding 1
to get the doubles.
So 1 should be corresponding to two. Since 1 + 1 = 2
4 should be corresponding to 5. Since 4 + 1 = 5
3 should be corresponding to 4. Since 3 + 1 = 4
And lastly, 2 should be corresponding to 3. Since 2 + 1 = 3
A jar holds 128 fluid ounces of juice. The label says the jar has 16 servings. How many fluid ounces are needed for 80 servings?
Answer: 640 fluid ounces
Step-by-step explanation:
We assume that the fluid ounces in jar is directly proportional to the number of servings.
Given : A jar holds 128 fluid ounces of juice. The label says the jar has 16 servings.
Ratio of fluid ounces of juice to number of servings =[tex]\dfrac{128}{16}[/tex] (1)
Let x denotes the fluid ounces are needed for 80 servings.
Ratio of fluid ounces of juice to number of servings =[tex]\dfrac{x}{80}[/tex] (2)
From (1) and (2) , we have
[tex]\dfrac{x}{80}=\dfrac{128}{16}[/tex] [in direct variation ration remains constant.]
[tex]x=\dfrac{128\times80}{16}=640[/tex]
Hence, 640 fluid ounces are needed for 80 servings.
Which shows the expressions in the order they would appear on a number line from least to greatest?
17 over 9, square root of 6, square root of 15, square root of 30, 3 to the power of 3
3 to the power of 3, square root of 30, square root of 15, square root of 6, 17 over 9
3 to the power of 3, square root of 6, square root of 15, 17 over 9, square root of 30
17 over 9, square root of 30, square root of 15, 3 to the power of 3, square root of 6
SOMEONE PLEASE HELP!!
Answer:
A
Step-by-step explanation:
write 129.04 in words
Smith High School offers a baseball camp that is $75 for 4 days of camp and a basketball camp that is $100 for 5 days of camp. Which camp is a better deal and by how much?
If n + 3 = 13, then n = 4.33333... B
During the 1998-1999 Junior Hockey League season, the Sharks played 66 games. Together, their wins and losses totaled 59. They tied 14 fewer games than they lost. How many games did they win that season?
The volume of a rectangular prism can be found by multiplying the base area, B, times the height. If the volume of the prism is represented by 15x2 + x + 2 and the height is x2, which expression represents B, the area of the base?
Merritt is driving to mount Shasta. On her map, she is a distance of 7.75 inches away. The scale on the map is .5 inch = 50 Miles. How far must Merritt travel to reach her destination?
What is X+.07x=44.94
What is the distributive property of 27 + 60
(−5k
3
−6k+1)+(−6k
2
+5k)
Remove unnecessary parenthesis.
-5k 3 - 6k +1 - 6k 2 + 5k (simplify each term) -15k - 6k + 1 - 12k +5k = -28k +1
Answer: 28k + 1
Step-by-step explanation:
−5k
3
−6k
2
−k+1
Is 9/6, 21/14 proportional?
The fractions 9/6 and 21/14 are proportional because both simplify to the same value, which is 1.5. Cross-multiplication also confirms their proportionality as the cross products are equal.
Explanation:To determine if the fractions 9/6 and 21/14 are proportional, we can simplify each fraction or cross-multiply to see if we end up with an equivalent value. If two ratios are proportional, this means they are equivalent to each other when reduced to simplest form, or the cross products are equal.
Simplifying 9/6, we get 1.5, and simplifying 21/14, we also get 1.5. Since both simplified fractions result in the same value, 9/6 and 21/14 are indeed proportional.
We can also cross multiply to verify: (9×14) should be equal to (6×21). This results in 126 = 126, confirming that both ratios are indeed proportional.
Final answer:
The ratios 9/6 and 21/14 are proportional because both simplify to the same ratio 3/2, and cross-multiplication yields equal products, confirming proportionality.
Explanation:
To determine if the ratios 9/6 and 21/14 are proportional, we simplify each ratio. The ratio 9/6 simplifies to 3/2 and the ratio 21/14 simplifies to 3/2 as well. Since both simplified ratios are equal, we can confirm that 9/6 and 21/14 are indeed proportional ratios.
Another way to check for proportionality is to cross-multiply and see if the products are equal. Multiplying 9 times 14 and 6 times 21 gives us 126 in both cases, which reaffirms our conclusion. Thus, based on these methods, the given ratios are proportional.
Find the intervals of convergence for the function. f(x)=sum_(n=1)^infinity x**n/n**2 32324243232 incorrect: your answer is incorrect. (b) find the intervals of convergence for f '.
Find the derivative of the function F(x) = (x4 + 9x2 − 5)4
The required derivative of the function (x⁴ + 9x² − 5)⁴ is f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x).
As per the question we have to determine the derivative of the f(x) = (x⁴ + 9x² − 5)⁴.
What is derivative?A derivative is defined as the rate of change of the function with respect to the respective variables.
Here,
According to the question,
f(x) = (x⁴ + 9x² − 5)⁴
Differentiate both sides with respect to x.
f'(x) = d[(x⁴ + 9x² − 5)⁴] / dx
f'(x) = 4 (x⁴ + 9x² − 5)³ × (4x³ + 9×2x)
f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x)
Thus, the required derivative of the function (x⁴ + 9x² − 5)⁴ is f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x).
Learn more about derivatives here:
https://brainly.com/question/25324584
#SPJ2
Consider two identical iron nails: one nail is heated to 95 °c, the other is cooled to 15 °c. the two nails are placed in a coffee cup calorimeter and the system is allowed to come to thermal equilibrium. what is the final temperature of the two nails
In this case, the final temperature of the two nails will be an average of their initial temperatures, which is 55 °C.
Explanation:When two objects at different temperatures come into contact, heat is transferred from the object with higher temperature to the object with lower temperature until they reach thermal equilibrium.
In this case, the heated iron nail at 95 °C will transfer heat to the cooled iron nail at 15 °C when they are placed in the coffee cup calorimeter.
The final temperature of the two nails will be an average of their initial temperatures, which is (95 °C + 15 °C) / 2 = 55 °C.
A rectangular field is to be bounded by a fence on 3 sides and a straight stream on the 4th side. Find the dimensions of the field with maximum area that can be enclosed using 1000 ft of rope. This is in the applied maximum and minimum chapter btw.
To maximize the area of the rectangular field, express the area in terms of one variable, derive the area function, and set it to zero for solving. The sides of the field yielding the maximum area are obtained using these calculations.
Explanation:This question involves optimization in calculus, specifically related to finding the maximum area of a rectangle. In such a problem, the first step is to express the area (A) of the rectangle in terms of one variable. Given a fence that is 1000 ft in length, if we name the side perpendicular to the stream as 'x', and the side parallel to it (bounded by the fence) as 'y', the perimeter of the field is 2x + y = 1000.
We can express y in terms of x: y = 1000 - 2x. The area of the rectangle, A = x*y = x*(1000 - 2x).
To find the maximum area, we find the first derivative of A with respect to x, set it to zero and solve for x. The second derivative test will confirm if it's a maximum. Based on the solutions, the maximum area is achieved with the dimensions of the rectangular field being specific values of x and y that you compute.
Learn more about Optimization here:https://brainly.com/question/33322941
#SPJ3
Write the value of 1710 in standard form