The rate at which the surface area of the sphere is increasing is 16π cm^2/s.(option-c)
To find the rate at which the area of a sphere increases when its radius is increasing at a given rate, we can use the formula for the surface area of a sphere, which is A =\(4πr^2\), where r is the radius of the sphere and A is its surface area. We can then differentiate this with respect to time t to find the rate of change of area with respect to time, which is given as dA/dt.
Given that the radius of the sphere increases at the rate of 0.4 cm/s, we can find the rate of change of area as follows:
- Differentiate the surface area formula with respect to time t:
dA/dt = d/dt \((4πr^2)\)
- Use the chain rule to differentiate\(r^2\)with respect to time t:
d/dt (r^2) = 2r (dr/dt)
- Substitute the value of dr/dt given as 0.4 cm/s, and the radius value as 5 cm:
dA/dt = 4π(5)^2 (2 × 0.4)
- Simplify the expression to get the rate of change of area with respect to time:
dA/dt = 16π \(cm^2/s\)
(option-c)
In circle N with � ∠ � � � = 12 4 ∘ m∠MNP=124 ∘ and � � = 13 MN=13, find the area of sector MNP. Round to the nearest hundredth.
If circle with center N with m∠MNP=124 ∘ and MN=13, the area of sector MNP is approximately equal to 194.86 square units.
To find the area of a sector of a circle, we need to use the formula:
Area of sector = (central angle/360°) x πr²
Where r is the radius of the circle.
In this problem, we know that the central angle m∠MNP is 124° and MN, which is also the radius of the circle, is 13. So we can substitute these values into the formula:
Area of sector = (124/360) x π(13)²
Area of sector ≈ 194.86
Therefore, the area of sector MNP is approximately equal to 194.86 square units.
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7.)
The temperature started out at 6° above zero and dropped 12° during the
Snowstorm that afternoon. By nighttime, the temperature had dropped another 10°.
What was the final temperature for the day?
Answer:
The final temperature for the day was -16 degrees.
Step-by-step explanation:
6-12= -6
-6-10= -16
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26)
Jeff's school is selling raffle tickets for $1 each. Of all the money collected from the sale of raffle tickets, 80% will go
to a scholarship fund, and 20% will go to the winner of the raffle. Jeff boughts of the 750 raffle tickets sold. What is
the expected payoff for Jeff when playing the raffle, and what does it mean?
A)
-$4, which means that Jeff can expect to lose $4
B)
- $1, which means that Jeff can expect to lose $1
C)
-$0.80, which means that Jeff can expect to lose $0.80
D)
-$4, which does not mean that Jeff can expect to lose $4 - only that he
could expect to lose $4 on average if the same scenario were repeated
many times
- $1, which does not mean that Jeff can expect to lose $1 - only that he
could expect to lose $1 on average if the same scenario were repeated
E)
many times
no
Answer:it’s D
Step-by-step explanation:
Make a frequency table using five classes.
class 31-38 39-46 47-54 55-62 63-70
f
11
24
15
7
3
Then estimate the mean and sample standard deviation using the frequency table. (Round s to two decimal places.)
Answer: C
Step-by-step explanation:
Please help! The question is in the image.
Answer:
Step-by-step explanation:
y -7.2 = 8 I need this as explanation and in algebraic show
Answer:
Heyya !
Here's how to do it:-
First write down what's given:-
y -7.2 = 8
Next, we do like this:-
y = 8+ 7.2
We transferred 7.2 to the other side of the ' = ' sign.
When we do so, the sign of the number changes
Here 7.2 was negative first but when we transferred it to the other side, its sign changed to positive.
So,
y = 8 + 7.2
Now, just add it!
8 + 7.2 equals 15.2
So, the value of y is 15.2 I hope the explanation was clear.If you still have doubts, let me know in the comments !(7 points) Briefly explain what perfect multicollinearity is and how it relates to what is often called the "dummy variable trap". This is where if you have multiple binary regressors (variables that are either 0 or 1) to represent a series of groups, you have to leave the variable that represents one of the groups out of the regression.
Find the given attachments
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Using the absolute value function, we have that:
The gasket with a weight of 0.53 lb should be thrown out.The inequality is: |x - 0.6| ≤ 0.06.What is the absolute value function?The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin.
For the batch, the weights are given as follows:
0.58, 0.63, 0.65, 0.53, 0.61.
Hence the mean is:
(0.58 + 0.63 + 0.65 + 0.53 + 0.61)/5 = 0.6.
Weights that are more than 0.06 of the pounds must be thrown out, hence the inequality for the valid weights is given by:
|x - 0.6| ≤ 0.06.
Hence the range of valid weighs is:
x - 0.6 ≥ -0.06 -> x ≥ 0.54.x - 0.6 ≤ 0.06 -> x ≤ 0.66.0.53 is not in the interval, hence the gasket with a weight of 0.53 lb should be thrown out.
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A fence with 2 gates in it surrounds a lion enclosure.
Each gate is 4 m wide.
an image
What is the length of the fence around the enclosure not including the gates?
The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.
Let's assume the length of the rectangle is 'l' and the width is 'w'.
From the given data, we know that each gate is 4 m wide.
Therefore, the width of the rectangle is:
Width = w + (4 m + 4 m) = w + 8 m
The perimeter of the rectangle is:
P = 2l + 2(w + 8 m) = 2l + 2w + 16 m
Now, we need to subtract the combined length of the two gates from the perimeter:
P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m
So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m
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Carla asked students at a lunch table what their main course they liked. Out of these students, 28n liked pizza, 15 liked chicken nuggets, and 8 liked both. what is the probability that a randomly selected student will like pizza but not chicken nuggets?
The probability that a randomly selected student will like pizza but not chicken nuggets is (28n - 8)/(28n + 7), where 28n is the students who like pizza and 8 is students who like both pizza and chicken nuggets.
To find the probability that a randomly selected student will like pizza but not chicken nuggets.
Let P = the number of students who like pizza but not chicken nuggets
Then, P = the number of students who like pizza - the number of students who like both pizza and chicken nuggets
P = 28n - 8
So, the probability that a randomly selected student will like pizza but not chicken nuggets is:
P(Pizza but not nuggets) = P/(Total number of students)
We can find the total number of students who like either pizza or chicken nuggets by adding the number of students who like pizza and the number of students who like chicken nuggets, and then subtracting the number of students who like both:
Total number of students = 28n + 15 - 8 = 28n + 7
So, the probability that a randomly selected student will like pizza but not chicken nuggets is:
P(Pizza but not nuggets) = P/(Total number of students) = (28n - 8)/(28n + 7)
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ok please hep me !!!!!!!!
Answer:
the person who had answer in first is correct
Please help! Ubehebe crater in death Valley has a diameter of a little more than 1/2 a mile. If Latisha walks around its rim at a rate of 2 mph, about how long will it take her to walk all the way around the crater? Round your answer to the nearest tenth. Use 3.14 for pi.
The time required for Latisha to walk around the rim at a rate of 2 mph is 0.235 hours.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
here,
Ubehebe crater in Death Valley has a diameter of a little more than 1/2 a mile.
Circumference of the rim,
= πD
= 3.14 × 1/2
= 1.57 mile
Time = Distance/speed
Time = 1.57 / 2
Time = 0.785 hours
Thus, the time required for Latisha to walk around the rim at a rate of 2 mph is 0.235 hours.
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Scores on a common final exam are normally distributed with mean 71 and standard deviation 9. Department policy is that the top 10% of students receive an A. The minimum exam score to be awarded an A is about:
Answer:
The minimum exam score to be awarded an A is about 8.52.
Step-by-step explanation:
Let X represent the scores on a common final exam.
It is provided that X follows a normal distribution with mean, μ = 71 and standard deviation, σ = 9.
It is provided that according to the department policy is that the top 10% of students receive an A.
That is, P (X > x) = 0.10.
⇒ P (X < x) = 0.90
⇒ P (Z < z) = 0.90
The corresponding z-score is:
z = 1.28
Compute the value of x as follows:
\(z=\frac{x-\mu}{\sigma}\\\\1.28=\frac{x-71}{9}\\\\x=71+(1.28\times 9)\\\\x=82.52\)
Thus, the minimum exam score to be awarded an A is about 8.52.
complete the table for each circle. plz help marking as brainliest
Answer:
written in blue are answer
Step-by-step explanation:
please mark me brainliest
inverse function of f(x)=x-7/x+4
Final Answer: The inverse of f (x)=7x-4 is f^-1 (x)= (x+4)/7
In a fruit basket there are 2 oranges, 3 mangoes, and 5 apples.
What is the theoretical probability of selecting an orange?
Answer:
The answer to your problem is, 20%
Step-by-step explanation:
First add all them:
2 + 3 + 5 = 10
Next find the fraction which is:
\(\frac{2}{10}\) Make it into decimal:
0.2
We have, 0 . 2 = 2 10 × 100% = 20% .
Thus the answer to your problem is 20%
Last year the cost of Tom's train ticket was £42 This year the cost of Tom's train ticket increased to £50 Write down the increase in the cost of Tom's ticket as a fraction of last year's cost. (2 marks
Answer:
19.048%
Step-by-step explanation:
The formula for the increase in cost will be :
[(New cost - Original Cost)÷Original Cost] × 100
So let's substitute values in from the question :
[(50-42)÷42] × 100
[8÷42] × 100
0.19048 × 100
19.048%
Hope this helped and have a good day
You can sand 4/9 square yard of wood in 1/2 hour. How many square yards can you sand in 3.2 hours? Justify your answer.
Answer:
4/9 = 1/2 x
Step-by-step explanation: 2.84 sands
Hello Can Someone Please Answer This Math Question
Answer:
180 cm2
Step-by-step explanation:
if you add all the sides together (10, 10, 4, 5, 5, 5) you'll get the sum of 36. if you divide the answer choices by the number of sides you'll get 36.
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Bananas are 3 for a dollar. Jen has $3. How many bananas can Jen buy?
1 dollar for 3 bananas
so with
3 dollars we will get 3x3 = 9 bananas
If her income is 210 marks, how many bananas can she buy if ... is 4 dollars each and the cost of bananas is 3 dollars per bunch.
Step-by-step explanation:
What is the weight of a 35.01-carat diamond in grams and ounces? Use 1 carat = 0.2 gram, 1 carat = 3.086 grains, and 1 ounce = 437.5 grains.
The weight of a 35.01-carat diamond is
(Round to two decimal places as needed.)
The weight of a 35.01-carat diamond is oz.
The weight of a 35.01-carat diamond in grams and ounces
7.002gram0.247 ouncesHow to determine the weight of a 35.01-carat diamond in grams and ouncesInformation given in the question include
1 carat = 0.2 gram,
1 carat = 3.086 grains,
1 ounce = 437.5 grains.
The conversion of the weight units using the given variables can bbe done as follows
1 carat = 0.2 gram
35.01-carat diamond = ?
cross multiplying gives
1 * ? = 35.01 * 0.2
? = 7.002gram
1 carat = 3.086 grains
35.01-carat diamond = ?
cross multiplying gives
1 * ? = 35.01 * 3.086
? = 108.041 grains
That is 35.01-carat diamond = 108.041 grains
1 ounce = 437.5 grains
? = 108.041 grains
cross multiplying gives
437.5 * ? = 108.041 * 1
? = 108.041 /437.5
? = 0.247 ounces
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What is one fifth of twenty more than half
of 80?
(A) 8
(B) 10
(C) 12
(D) 13
Answer:
(C) 12
Step-by-step explanation:
To solve this problem, we can use the following steps:
Find half of 80: 80/2 = 40
Add 20 to half of 80: 40 + 20 = 60
Find one fifth of the result: 60/5 = 12
Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.
Answer:
(C) 12
Step-by-step explanation:
What is one fifth of twenty more than half of 80
0.5 × 80 = 40
What is one fifth of twenty more than half of 80
40 + 20 = 60
What is one fifth of twenty more than half of 80
1/5 × 60 = 60/5 = 12
love yall again thx for the help
Answer :
Cost of running shoes = $92
Cost of total expenditure = $122
It is given that the four pairs of socks cost the same so if we let the cost of one pair of socks as s then 4 pairs of socks will cost us $ 4s
Thus the equation formed will be ,
4s + 92 = 122Option D is the correct answer
Which expression is equivalent to 6/4
Just a generic answer would by 12/8 or any other multiple of the numbers. If that is a fraction than same goes as above.
If the median is 3.5, we can assume the mean is ____________than 3.5
We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
What is mean?The mean is a measure of central tendency that represents the average value of a set of numbers. It is also called the arithmetic mean or simply the average.
According to question:We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
The mean and the median are two different measures of central tendency, and they can have different values depending on the distribution of the data. In general, if a data set is symmetric and bell-shaped, the mean and the median are close to each other. However, if the data set is skewed, the mean and the median may be different.
For example, consider the following two data sets:
Set 1 data: 1, 2, 3, 4, and 5.
The median is 3.
The mean is (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3.
Data set 2: 1, 2, 3, 4, 10
The median is 3.
The mean is (1 + 2 + 3 + 4 + 10) / 5 = 20 / 5 = 4.
In data set 1, the mean is the same as the median. In data set 2, the mean is greater than the median because the value 10 is an outlier that pulls the mean up.
Therefore, without additional information about the distribution of the data, we cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
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What is the value of r
Step-by-step explanation:
Vertical angles are equal r = 70 degrees
9. (10 points) Find all values of b such that
3x² - 2bx
to nieme
x ≥-3
-3x² + 5x +4bx x < -3
f(x) =
is continuous at x = -3. What type of discontinuity exists at x = -3
when b is not equal to this value(s)? Explain your answer(s).
In the function given, the type of discontinuity that exists at x = -3 when b is not equal to 11/6 is a jump discontinuity.
What is the value of bFor the function f(x) to be continuous at x = -3, the limit of f(x) as x approaches -3 from both the left and the right must be equal to f(-3). That is:
lim x→-3+ f(x) = f(-3) = lim x→-3- f(x)
Since x < -3 for the second part of the function, we can calculate the left-hand limit as:
lim x→-3- f(x) = -3(-3)² + 5(-3) + 4b(-3) = 9 + (-15) - 12b = -6 - 12b
And the right-hand limit as:
lim x→-3+ f(x) = 3(-3)² - 2b(-3) = 27 + 6b
Therefore, we must have:
-6 - 12b = 27 + 6b
Solving for b, we get:
b = 33/18 = 11/6
So when b = 11/6, the function is continuous at x = -3.
Now let's consider the case where b is not equal to 11/6. In this case, the left-hand limit and right-hand limit are not equal, which means the function has a jump discontinuity at x = -3. The value of the function at x = -3 from the left-hand side is:
f(-3-) = -3(-3)² + 5(-3) + 4b(-3) = 9 - 15 - 12b = -6 - 12b
And the value of the function at x = -3 from the right-hand side is:
f(-3+) = 3(-3)² - 2b(-3) = 27 + 6b
Therefore, the type of discontinuity that exists at x = -3 when b is not equal to 11/6 is a jump discontinuity.
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it takes 1 minute to bake 6 cookies how many cookies could you bake in 2 minutes
The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 8% per day. A sample of this radioactive substance has an initial mass of 2.43 kg. Find the mass of the sample after three days. Round your answer to two decimal places.Note: This is a continuous exponential decay model.And though the decay rate parameter is 8% per day, the actual decay is not 8% each day.
Given:
Decay rate = 8% per day = 0.08
Initial mass = 2.43 kg
Let's find the mass of the sample after 3 days.
Apply the exponential decay formula:
\(A=P_oe^{-rt}\)Where:
A is the final amount
Po is the initial amount = 2.43
r is the rate = 0.08
t is the time = 3 days.
Thus, we have:
\(\begin{gathered} A=2.43e^{-0.08*3} \\ \\ A=2.43(0.78662) \\ \\ A=1.91 \end{gathered}\)Therefore, the mass of the sample after 3 days is 1.91 kg.
ANSWER:
1.91 kg
the weighted-average method is best used for
A. heterogeneous
B. fuels only
C. grains only
D. homogeneous products