function f(x,y) = 2 + y
The minimum value are f(√5, √5) = 2 + √5.
Lagrange multipliers:To find the minimum value of the function f(x,y) = 2 + y subject to the constraint xy=5 using Lagrange multipliers,
we first set up the Lagrangian function:
L(x,y,λ) = f(x,y) - λ(xy - 5)
Taking partial derivatives with respect to x, y, and λ, we get:
∂L/∂x = 0 = -λy
∂L/∂y = 1 - λx
∂L/∂λ = xy - 5
Solving for λ from the first equation and substituting into the second equation, we get:
x/y = 0/λ
1 - λx = 0
xy - 5 = 0
From the first equation, we see that either x = 0 or y = 0. But since xy = 5, neither x nor y can be zero.
Therefore, we have:
λ = 0
1 - λx = 0
xy - 5 = 0
Solving for x and y from the last two equations, we get:
x = 5/y
y = ±√5
We take the positive root for y since we are looking for a minimum value of the function.
Substituting y = √5 into x = 5/y, we get x = √5.
Therefore, the minimum value of f(x,y) = 2 + y subject to the constraint xy=5 is:
f(√5, √5) = 2 + √5.
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The function f(x) = 2x + 7x{-1} has one local minimum and one local maximum. This function has a local maximum at x = with value and a local minimum at x = with value
The function has a local maximum at x = -√(2/7) with value -3√14 and a local minimum at x = √(2/7) with value 3√14.
To find the local maximum and minimum of the function f(x) = 2x + 7x⁻¹, we need to find the critical points of the function and then use the second derivative test to determine if they are local maxima or minima.
First, we find the derivative of f(x):
f'(x) = 2 - 7x⁻²
Setting f'(x) = 0, we get:
2 - 7x⁻² = 0
Solving for x, we get:
x = ±√(2/7)
Next, we compute the second derivative of f(x):
f''(x) = 14x⁻³
At x = ±√(2/7), we have:
f''(±√(2/7)) = ±∞
Since f''(±√(2/7)) has opposite signs at the critical points, ±√(2/7), we conclude that f(x) has a local maximum at x = -√(2/7) and a local minimum at x = √(2/7).
To find the values of the local maximum and minimum, we plug them into the original function:
f(-√(2/7)) = 2(-√(2/7)) + 7/(-√(2/7)) = -3√14
f(√(2/7)) = 2(√(2/7)) + 7/(√(2/7)) = 3√14
Therefore, the function has a local maximum at x = -√(2/7) with value -3√14 and a local minimum at x = √(2/7) with value 3√14.
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FFind the equation(s) of tangent(s) to the curve y - 3x? - 5x - 7that passes through the bint (0-10).
2. Ryan is writing the program for a video game.
For one part of the game he uses the rule (x,y)â(x-3,y+8) to move points on the screen.
(a) What output does the rule give when the input is (-7,-3)? Show your work.
(b) What output does the rule give when the input is (10,-5)? Show your work
(a) When the input is (-7,-3), the rule (x,y) → (x-3,y+8) moves the point 3 units to the left and 8 units up.
So we can apply this rule to the input (-7,-3) as follows:
(-7,-3) → (-7-3,-3+8)
(-7,-3) → (-10,5)
Therefore, the output is (-10,5).
(b) When the input is (10,-5), the rule (x,y) → (x-3,y+8) moves the point 3 units to the left and 8 units up. So we can apply this rule to the input (10,-5) as follows:
(10,-5) → (10-3,-5+8)
(10,-5) → (7,3)
Therefore, the output is (7,3).
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What is the 5280th digit in the decimal expansion of 5/17
The second digit after the decimal point is 9. We repeat this process until we have found the 5280th digit:
```
0.294117647058823529...
50
Calculate the decimal expansion?To find the 5280th digit in the decimal expansion of 5/17, we need to find the first 5280 digits of the decimal expansion and then look at the 5280th digit.
To do this, we can use long division to divide 5 by 17. We start by dividing 5 by 17 to get the first digit after the decimal point:
```
0.294117647058823529...
```
We can see that the first digit after the decimal point is 2. To get the second digit, we multiply the remainder (5) by 10 and then divide by 17:
```
5 * 10 = 50
50 / 17 = 2 remainder 16
```
The second digit after the decimal point is 9. We repeat this process until we have found the 5280th digit:
```
0.294117647058823529...
50
-----
5 * 10 = 50 | 16.0000000000000000000000000000000000000000000000000000000000000000000000...
0
---
160
153
---
70
68
--
20
17
--
30
17
--
130
119
---
110
102
---
80
68
--
120
119
---
10
8
--
20
17
--
30
17
--
130
119
---
110
102
---
80
68
--
120
119
---
10
8
--
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--
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--
130
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---
110
102
---
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120
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110
102
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120
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110
102
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120
119
---
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8
--
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---
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---
80
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--
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119
---
10
8
--
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--
30
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5+8(3+x) simplified please
Answer: 8x +29
Step-by-step explanation:
5+8(3+x)
5+8(x+3)
__________
5 + 8(x+3)
5+ 8x +25
_________
5+8x+ 24
29+8x
____
8x+29
Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.
Maximize: f(x, y, 2) = xyz
Constraint: × + y + z - 6 = 0
f = _____
To use Lagrange multipliers, we need to set up the Lagrangian function, Therefore, the maximum value of f(x,y,2) = xyz subject to the constraint x+y+z-6=0 is f(2,2,2) = 8.
L(x,y,z,λ) = xyz + λ(x+y+z-6)
Then we need to find the critical points of L by setting its partial derivatives equal to zero:
∂L/∂x = yz + λ = 0
∂L/∂y = xz + λ = 0
∂L/∂z = xy + λ = 0
∂L/∂λ = x + y + z - 6 = 0
Solving this system of equations, we get:
x = y = z = 2
λ = -4
This critical point satisfies the constraint, since 2+2+2-6 = 0. To check whether it is a maximum or minimum, we need to use the second partial derivative test:
∂²L/∂x² = 0, ∂²L/∂y² = 0, ∂²L/∂z² = 0
∂²L/∂x∂y = z, ∂²L/∂x∂z = y, ∂²L/∂y∂z = x
The Hessian matrix is:
| 0 z y |
| z 0 x |
| y x 0 |
At the critical point (2,2,2), the Hessian matrix is:
| 0 2 2 |
| 2 0 2 |
| 2 2 0 |
The eigenvalues of this matrix are -4, -4, and 8. Since the eigenvalues are not all positive or all negative, we cannot conclude whether the critical point is a maximum or minimum.
Therefore, the maximum value of f(x,y,2) = xyz subject to the constraint x+y+z-6=0 is f(2,2,2) = 8.
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Shapes A and B are similar.
a) Calculate the scale factor from shape A to shape B.
b) Find the value of w.
Give each answer as an integer or as a fraction in its simplest form.
4 cm
7 cm
A
12 cm
3 cm
w cm
B
9 cm
The ratios of successive numbers in the Fibonacci sequence eventually get closer to which number?
a.
1. 61
c.
2. 3
b.
1. 46
d.
1
The ratios of successive numbers in the Fibonacci sequence eventually get closer to a. 1.61
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2.
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1 (0, 1, 1, 2, 3, 5, 8, 13, ...). When you take the ratio of successive numbers in the sequence (e.g., 5/3 or 8/5), it converges to approximately 1.618, also known as the Golden Ratio or Phi.
The closest option in your list is 1.61, which is option (a).
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Maryam scored 86. 7% on a test with 30 questions on
it. How many questions did Maryam get wrong?
Help!
Maryam answered 26 questions correctly and got 4 questions wrong on the test with 30 questions.
How many questions did Maryam answer incorrectly?To find how many questions Maryam got wrong, we need to first determine how many questions she got right. Since she scored 86.7%, we can multiply the total number of questions by the percentage to get the number of questions she answered correctly.
86.7% of 30 questions is (86.7/100) * 30 = 26.01 questions.
Since Maryam cannot have answered a fractional number of questions correctly, we round down to the nearest whole number. Thus, she answered 26 questions correctly.
To find out how many questions she got wrong, we can simply subtract the number of questions she got right from the total number of questions. Therefore, Maryam got 30 - 26 = 4 questions wrong.
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Jamie McAllister is a wonderful rebounder for her high school basketball team. Of
her final 10 games, here are her rebound totals for each game:
8 12 8 11 15 6 9 8 10 13
1.
2.
From the collected data, what
is the mean number of
rebounds Jamie had per
game?
From the collected data, what
is the median number of
rebounds Jamie had for her
final 10 games?
Step-by-step explanation:
1. To find the mean number of rebounds Jamie had per game, we need to add up all the rebounds she had and then divide by the total number of games played:
Mean = (8 + 12 + 8 + 11 + 15 + 6 + 9 + 8 + 10 + 13) / 10
Mean = 100 / 10
Mean = 10
Therefore, the mean number of rebounds Jamie had per game was 10.
2. To find the median number of rebounds Jamie had for her final 10 games, we need to first arrange the data in order from least to greatest:
6, 8, 8, 8, 9, 10, 11, 12, 13, 15
Since there are an even number of data points, the median will be the average of the two middle values, which are 9 and 10:
Median = (9 + 10) / 2
Median = 9.5
Therefore, the median number of rebounds Jamie had for her final 10 games was 9.5.
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HELP!! A surfer recorded the following values for how far the tide rose, in feet, up the beach over a 15-day period.
5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24
Which of the following histograms best represents the data collected?
Answer:
Graph 2
Step-by-step explanation:
There is 1 from 1-5
There are 4 from 6-10
There are 5 from 11-15
There is 1 from 16-20
There are 4 from 21-25
What is the height of the cylinder rounded to the nearest tenth? The figure * 1 point is not drawn to scale . V = 284.7 inches cubed
The height of the cylinder is 3.6 inches.
What is the height of the cylinder?We know that the volume of a cylinder of radius R and height H is:
V = pi*R²*H
where pi = 3.14
We know that the radius is R = 5in and the volume is 284.7 inches cubed, replacing that in the formula above we will get:
284.7 in³= 3.14*(5 in)²*H
Solving that for H we will get:
H= (284.7 in³)/ 3.14*(5 in)²
H = 3.6 inches.
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The math team wants to visit the Museum of Mathematics
to celebrate Pi Day. They have $210 to spend. They need to
buy 14 student tickets and 1 adult ticket. A student ticket
costs $12, and an adult ticket costs $17. The team also
wants to buy sugar-free fruit pies. Each pie costs $6. How
many whole pies can the team buy? Show your work.
Answer:
4
Step-by-step explanation:
14 student tickets times $12 = 168
168 + $17 = 185
210-185=25
6*4=$24
so they can buy 4 pies with 1 dollar left over
sorry if I am wrong
Suppose that you measure the flow rate of blood in an artery. You find that your measurements are well-fit be the equation dᏙ /dt =10 - 2 cos(120t)
in units of milliliters per second.
a) What volume of blood flows through the artery in 10 seconds? (include units)
b) What volume of blood flows through the artery in one minute? (include units)
The volume of blood flow through the artery in one minute is 600 milliliters.
We can integrate the given equation to get the volume of blood flow.
a) Integrating both sides of the equation with respect to time from 0 to 10 seconds, we get:
∫dᏙ = ∫(10 - 2cos(120t)) dt
ΔᏙ = [10t - (1/60)sin(120t)] from 0 to 10
ΔᏙ = [(10 x 10) - (1/60)sin(1200)] - [(10 x 0) - (1/60)sin(0)]
ΔᏙ ≈ 100 - 0
So, the volume of blood flow through the artery in 10 seconds is 100 milliliters.
b) To find the volume of blood flow through the artery in one minute, we need to integrate the given equation from 0 to 60 seconds:
∫dᏙ = ∫(10 - 2cos(120t)) dt
ΔᏙ = [10t - (1/60)sin(120t)] from 0 to 60
ΔᏙ = [(10 x 60) - (1/60)sin(7200)] - [(10 x 0) - (1/60)sin(0)]
ΔᏙ ≈ 600 - 0
So, the volume of blood flow through the artery in one minute is 600 milliliters.
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Patrons in the children's section of a local branch library were randomly selected and asked their ages. the librarian wants to use the data to infer the ages of all patrons of the children's section so he can select age appropriate activities.
In this case, it's important for the librarian to make sure that the sample of patrons who were randomly selected is representative of the larger population of patrons in the children's section, and that any assumptions made in the statistical inference process are valid.
Find out the ages of all patrons of the children's section?To infer the ages of all patrons in the children's section of the library, the librarian should use statistical inference techniques such as estimation or hypothesis testing.
If the librarian wants to estimate the average age of all patrons in the children's section, they can use a point estimate or an interval estimate. A point estimate would involve calculating the sample mean age of the patrons who were randomly selected and using that as an estimate for the population means age. An interval estimate would involve calculating a confidence interval around the sample mean, which would give a range of likely values for the population means.
Alternatively, if the librarian wants to test a hypothesis about the ages of patrons in the children's section, they can use a hypothesis test. For example, they could test whether the average age of patrons in the children's section is significantly different from a certain value (such as the national average age of children), or whether there is a significant difference in age between male and female patrons.
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PLEASE HELPPP
MEEE LAST QUESTION FOR THE DAY!
Answer:
There are 16 unit squares on the geoboard. Each unit square represents 5 meters, so the total area is 16*5 = 80 square meters.
Here is a diagram of the geoboard with the unit squares labeled:
[Image of a geoboard with 16 unit squares labeled]
I hope this helps! Let me know if you have any other questions.
What is the area of the figure?
Answer: 27 inches sq.
Step-by-step explanation:
3*3=9
2*9=18
18+9=27
A number cube has sides numbered 1 through 6. the probability of rolling a 2 is 1/6
what is the probability of not rolling a 2?
enter your answer as a fraction, in simplest form, in the box.
a calculator is allowed on this quiz.
question 1 options:
56
16
23
76
A number cube has sides numbered 1 through 6. the probability of rolling a 2 is 1/6. The probability of not rolling a 2 on a number cube with sides numbered 1 through 6 is 5/6 (in simplest form). The correct answer is 5/6.
The probability of not rolling a 2 on a number cube with sides numbered 1 through 6 can be calculated as follows:
Determine the total number of outcomes, which is 6 (1, 2, 3, 4, 5, and 6).
Determine the number of favorable outcomes, which is 5 (1, 3, 4, 5, and 6), since you're looking for the probability of not rolling a 2.
Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes.
The probability of not rolling a 2 on a number cube with sides numbered 1 through 6 is 5/6 (in simplest form).
So, the correct answer is 5/6.
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What is the equation of the line that best fits the given data? A graph has points (negative 3, negative 3), (negative 2, negative 2), (1, 1. 5), (2, 2), (3, 3), (4, 4). A. Y = 2 x + 1 c. Y = x + 1 b. Y = x d. Y = negative x Please select the best answer from the choices provided A B C D Mark this and return
The equation of the line that best fits the given data is y = (5/6)x + 1/3
The equation of the line that best fits the given data can be found by using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (1, 1.5) and (4, 4), we get:
m = (4 - 1.5) / (4 - 1) = 2.5 / 3 = 5/6
Now we can use one of the given points to find the y-intercept. Let's use the point (2, 2):
y = mx + b
2 = (5/6)(2) + b
2 = 5/3 + b
b = 2 - 5/3
b = 1/3
Therefore, the equation of the line that best fits the given data is:
y = (5/6)x + 1/3
The best answer is C. Y = x + 1.
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In a city of 72,500 people, a simple random sample of four households is selected from the 25,000 households in the population to estimate the average cost on food per household for a week. the first household in the sample had 4 people and spent a total of $150 in food that week. the second household had 2 people and spent $100. the third, with 4 people, spent $200. the fourth, with 3 people, spent $140.
required:
identify the sampling units, the variable of interest, and any auxiliary info mation associated with the units.
In this scenario, the sampling units are four households, the variable of interest is the average food cost, and auxiliary information associated with the units is the number of people in each household and total food cost.
Sampling Units: The sampling units are the four households selected from the 25,000 households in the population.
They are as follows:
1. Household with 4 people that spent $150 on food
2. Household with 2 people that spent $100 on food
3. Household with 4 people that spent $200 on food
4. Household with 3 people that spent $140 on food
Variable of Interest: The variable of interest is the average cost on food per household for a week.
Auxiliary Information: The auxiliary information associated with the units includes the number of people in each household and the total amount spent on food for that week.
To estimate the average cost on food per household for a week, follow these steps:
1. Calculate the total cost on food for all four households: $150 + $100 + $200 + $140 = $590
2. Divide the total cost by the number of households: $590 / 4 = $147.50
So, the estimated average cost on food per household for a week is $147.50.
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The snow globe below is formed by a hemisphere and a cylinder on a cylindrical
base. The dimensions are shown below. The base is slightly wider than the globe
with a diameter of 10cm and height of 1cm.
10 cm
4cm
3cm
1cm
Part D: The globes are ordered by the retail store in cases of 24. Design a rectangular
case to hold 24 globes packaged in individual boxes. What is the minimum
dimensions and volume of your case.
The minimum dimensions of the box will be; 7 cm × 6 cm × 6 cm
Since the dimension is described as the measurement of something in physical space such as length, width, or height.
Given that the there will be maximum dimension when the height of the cylinder and the radius of the hemisphere are aligned together.
Maximum height = 4 cm + 3 cm = 7 cm
Maximum diameter = 2 × 3 cm = 6 cm
Therefore, we can see that the minimum dimensions of the box are :
7 cm × 6 cm × 6 cm.
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Determine whether the series n² - 5 na tn - 6 n=1 is convergent or divergent using the Limit Comparison Test.
To use the Limit Comparison Test, we need to find a series whose behavior is well-known and similar to the given series. Let's consider the series aₙ = n². We have:
limₙ→∞ (aₙ / (n² - 5naₙ - 6)) = limₙ→∞ (n² / n²) = 1
Since this limit is finite and positive, and aₙ is a convergent series (by the p-series test with p = 2), we can apply the Limit Comparison Test and conclude that the given series is convergent.
To determine if the series ∑(n² - 5n) from n=1 to infinity is convergent or divergent using the Limit Comparison Test, we need to find a comparable series and then calculate the limit of the ratio between the two series as n approaches infinity.
Let's compare the given series to a simpler series ∑n² (n=1 to infinity). Now, we'll find the limit of the ratio:
Limit (n→∞) [(n² - 5n) / n²]
As n approaches infinity, the -5n term becomes insignificant compared to the n² term. So, the limit becomes:
Limit (n→∞) [n² / n²] = 1
Since the limit is a finite, nonzero value (1 in this case), the given series and the comparison series will have the same convergence behavior. We know that the series ∑n² (n=1 to infinity) is a divergent series, as it is a p-series with p=2 (less than or equal to 1). Therefore, the given series ∑(n² - 5n) from n=1 to infinity is also divergent.
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Now that you are commuting to work every day, you are considering buying a new car. However, you are undecided if you should invest in a new car or just keep the one you have. You have heard that cars depreciate a lot, and you don't want to waste your hard earned money.
Let's do a little investigating to see if cars really do depreciate and if so, by how much.
Decide on a used automobile that you would like to purchase. Find the auto in an advertisement in the newspaper, car magazine, or internet. You must attach a copy of the advertisement to your work. The vehicle must be at least 3 years old
It's essential to consider the depreciation rate when deciding whether to invest in a new car or keep your current one.
Cars typically depreciate, and the amount can vary depending on factors such as make, model, and age.
For this example, let's assume you're interested in purchasing a 3-year-old used Honda Accord. I found an advertisement for this vehicle online, but since I cannot attach a copy here, please search for a similar advertisement and include it with your work.
It's common for new cars to depreciate by approximately 20-30% in the first year, and around 10-15% each subsequent year. So, a 3-year-old car may have already experienced around 40-60% of its total depreciation.
After researching, the used 3-year-old Honda Accord is priced at $18,000. If you compare it to the price of a new Honda Accord, which starts around $25,000, you can see that there has been a considerable depreciation in value.
In conclusion, cars do depreciate, and the rate can vary depending on the vehicle's age and other factors. In this case, a 3-year-old Honda Accord has already experienced significant depreciation, making it a more affordable option compared to buying a brand new car.
Considering depreciation can help you make an informed decision when deciding between a new or used car.
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The number of hours julie practices her violin each week, y, is 3 hrs more than the numbers of hours she studies, x. write an equation to show the relationship of the two activities.
The equation is y = x + 3 which shows the relationship of the two activities.
The equation to show the relationship between the number of hours Julie practices her violin each week (y) and the number of hours she studies (x) is:
y = x + 3
This means that the number of hours Julie practices her violin each week is equal to the number of hours she studies, plus three additional hours.
A linear equation is an equation that represents a straight line on a graph. It can be written in the form:
y = mx + b
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Use the given circumference to find the surface area of the spherical object.
a pincushion with c = 18 cm
To find the surface area of a spherical object, we need to know the radius of the sphere. However, in this case, only the circumference of the pincushion is given, which is not enough information to directly determine the radius.
The formula relating the circumference (c) and the radius (r) of a sphere is:
c = 2πr
To find the surface area (A) of the sphere, we can use the formula:
A = 4πr^2
Since we don't have the radius, we need to solve the circumference formula for the radius first:
c = 2πr
Divide both sides of the equation by 2π:
r = c / (2π)
Now we can substitute the value of c = 18 cm into the equation to find the radius:
r = 18 cm / (2π)
r ≈ 2.868 cm (approximately)
Now that we have the radius, we can calculate the surface area using the formula:
A = 4πr^2
A = 4π(2.868 cm)^2
A ≈ 103.05 cm² (approximately)
Therefore, the surface area of the pincushion is approximately 103.05 square centimeters.
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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thank you !!!!!!!! (Choose ALL answers that are correct)
Answer:
a and b
Step-by-step explanation:
Garden canes have lengths that are normally
distributed with mean 208. 5cm and standard
deviation 2. 5cm. What is the probability of the length
of a randomly selected cane being between 205cm
and 210cm? Correct to 3 decimal places
The probability of the length of a randomly selected cane being between 205cm and 210cm is approximately 0.645 (rounded to 3 decimal places).
To find the probability of the length of a randomly selected cane being between 205cm and 210cm, we need to calculate the z-scores for these values and then use the standard normal distribution.
The z-score formula is given by:
z = (x - μ) / σ,
where x is the observed value, μ is the mean, and σ is the standard deviation.
For 205cm:
z1 = (205 - 208.5) / 2.5 = -1.4
For 210cm:
z2 = (210 - 208.5) / 2.5 = 0.6
Now, we can use a standard normal distribution table or a calculator to find the probability between these two z-scores.
Using a standard normal distribution table or a calculator, we find that the probability associated with z1 = -1.4 is approximately 0.0808, and the probability associated with z2 = 0.6 is approximately 0.7257.
To find the probability between these two z-scores, we subtract the probability corresponding to z1 from the probability corresponding to z2:
P(205cm < length < 210cm) ≈ P(z1 < z < z2) ≈ P(z < 0.6) - P(z < -1.4) ≈ 0.7257 - 0.0808 ≈ 0.6449.
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What is the value of x in the solution to this system of equations 5x-4y=27
y=2x+3
The value of x in the solution to this system of equations 5x - 4y = 27 and y = 2x + 3 is -13.
To find the value of x in this system of equations, we can use substitution method to find the its solution. Start by isolating x in one of the equations and then substituting that value into the other equation.
Let's start by isolating x in the second equation:
y = 2x + 3
Subtracting 3 from both sides:
y - 3 = 2x
Dividing both sides by 2:
(1/2)y - (3/2) = x
Now we can substitute this expression for x into the first equation:
5x - 4y = 27
5((1/2)y - (3/2)) - 4y = 27
Simplifying:
(5/2)y - 15/2 - 4y = 27
Combining like terms:
-(3/2)y = 69/2
Dividing by -(3/2):
y = -23
Now we can substitute this value of y back into the expression we found for x:
x = (1/2)y - (3/2)
x = (1/2)(-23) - (3/2)
x = -13
Therefore, the solution to this system of equations is x = -13, y = -23.
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Isabella grows two types of pepper plants. The following dot plots show the numbers of peppers, rounded to the nearest
5
55, per plant for each type. Each dot represents a different plant. Compare the typical number of peppers per plant. In general, the
had more peppers, with
per plant
The possible values of x that satisfy the equation |x+5| = c are x = c - 5 and x = -c - 5.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.