Answer: According to the histogram, a sum of 28 is not unusually low. The bar representing a sum of 28 has a height of 9, which is relatively high compared to some of the other bars. Additionally, the histogram is roughly symmetric, so a sum of 28 is not far from the mean of the distribution.
To find the probability that a person would roll a sum less than 28, we can standardize the value using the formula z = (x - mu) / sigma, where x is the sum of 28, mu is the mean of 35, and sigma is the standard deviation of 5.72.
z = (28 - 35) / 5.72 = -1.22
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than -1.22 is approximately 0.1112, or 11.12%. Therefore, there is about an 11.12% chance that a person would roll a sum less than 28.
Step-by-step explanation:
Five lemonades and two cookles cost $1.50. Two lemonades and five cookles cost $2.70. How much does one cookle and one lemonade cost?
Answer:
50¢/cookie, $1.00/lemonade
Step-by-step explanation:
Let l = cost of one lemonade
c = cost of one cookie
We have:
5l + 2c = 1.50 -------> 10l + 4c = 3.00
2l + 5c = 2.70 -------> 10l + 25c = 13.50
-----------------------
21c = 10.50
c = .50
5l + 2(.50) = 1.50
5l + 1.00 = 1.50
5l = 5, so l = 1.00
Each cookie costs 50¢, and each lemonade costs $1.00.
Determine the circumference of the base of the tin?
By answering the given question, we may state that We can apply the formula if we know the radius: C = 2πr where the radius r is.
what is diameter?In geometry, a circle's diameter is any straight line segment whose endpoint is on the circle and which passes through its centre. Another name for it is the circle's longest chord. The diameter of a sphere can be defined using either idea. The diameter is the length of the line perpendicular to the two points at either end of the circle. If you think of length as the distance between two points, then diameter is length. The diameter of a circle is the separation between its two farthest points.
We must know the base's diameter or radius in order to calculate the circumference of the tin.
If we know the diameter, we can apply the following formula to determine the circle's circumference:
C = πd
where d is the diameter and C is the circumference.
We can apply the formula if we know the radius:
C = 2πr
where the radius r is.
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Solve question
answer is csca+seca
Show the steps
The solution to the trigonometric expression is given as follows:
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = csc(x) + sec(x).
How to solve the trigonometric expression?The trigonometric expression for this problem is defined as follows:
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)).
The tangent and the cotangent are represented as follows:
tan(x) = sin(x)/cos(x).cot(x) = cos(x)/sin(x).Hence:
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = sin(x)[1 + sin(x)/cos(x)] + cos(x)[1 + cos(x)cot(x)]
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = sin(x)+sin²(x)/cos(x) + cos(x) + cos²(x)/sin(x)
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = [sin²(x)cos(x) + sin³(x) + sin(x)cos²(x) + cos³(x)]/(sin(x)cos(x))
sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = csc(x) + sec(x).
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Suppose I took a survey of 324 people at the school. The survey showed that 120 people like dogs, 150 like cats, and 98 like both.
Make a two way table representing the above data.
If a person does not like dogs, what is the probability that they do not like cats
The probability that they do not like cats given that person does not like dogs: 13/51.
Explain about the vein diagram?A Venn diagram is a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not.Total people : 324.
People like dogs D: 120
Probability P(D) = 120/324
Probability Not like dogs P(D') = 1 - 120/324 = 204/324
People like cats C: 150
Probability P(C) = 150/324
Probability who don't like digs but like cats:
P(C ∩ D') = 52/ 324
Probability that they do not like cats given that person does not like dogs:
P(C'/D') = 1 - P(C ∩ D')/P(D')
P(C'/D') = 1 - (52/324) /(204/324)
P(C'/D') = 1 - 52/204
P(C'/D') = 152/204 = 13/51
Thus, the probability that they do not like cats given that person does not like dogs: 13/51.
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Suppose you borrow $4900 at a 21% annual interest rate, compounded monthly (1.75% each month). At the end
of each month, you make a $175 payment.
Use this information to complete the table below. Round to the nearest cent as needed.
Month
1
2
3
4
5
Prior Balance
$
$
$4900
$4719.94
1.75% Interest
on Prior Balance
$
$
$
$80.98
Monthly Payment
$175
$175
$175
$175
Ending Balance
$
$
57
$
$4900
$4719.94
Fοr the fifth mοnth, priοr balance is $4469.69, interest οn priοr balance is $77.78, mοnthly payment is $175, and ending balance is $4389.72.
What is annual interest rate?Annual interest rate is the amοunt οf interest that is charged οn a lοan οr investment per year, expressed as a percentage οf the amοunt bοrrοwed οr invested.
Tο cοmplete the table, we can use the fοllοwing steps:
Fοr the first mοnth:
Priοr balance: $4900
Interest οn priοr balance: 1.75% οf $4900 = $85.75 (rοunded tο the nearest cent)
Mοnthly payment: $175
Ending balance: $4900 + $85.75 - $175 = $4710.75 (rοunded tο the nearest cent)
Fοr the secοnd mοnth:
Priοr balance: $4710.75
Interest οn priοr balance: 1.75% οf $4710.75 = $82.46 (rοunded tο the nearest cent)
Mοnthly payment: $175
Ending balance: $4710.75 + $82.46 - $175 = $4628.21 (rοunded tο the nearest cent)
Repeat the same prοcess fοr the next three mοnths:
Fοr the third mοnth, priοr balance is $4628.21, interest οn priοr balance is $80.89, mοnthly payment is $175, and ending balance is $4549.10.
Fοr the fοurth mοnth, priοr balance is $4549.10, interest οn priοr balance is $79.34, mοnthly payment is $175, and ending balance is $4469.69.
Fοr the fifth mοnth, priοr balance is $4469.69, interest οn priοr balance is $77.78, mοnthly payment is $175, and ending balance is $4389.72.
Mοnth Priοr Balance Interest Mοnthly Ending
οn Payment Balance
Priοr Balance
1 $4900 $85.75 $175 $4710.75
2 $4710.75 $82.46 $175 $4628.21
3 $4628.21 $80.89 $175 $4549.10
4 $4549.10 $79.34 $175 $4469.69
5 $4469.69 $77.78 $175 $4389.72
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(b) Find the costs of supplying bins to 10%, 50%, and 85% of the
cost to supply 10%
C = $
X
cost to supply 50%
C = $25,000
cost to supply 85%
C = $ 141,667
Answer:
To find the cost of supplying bins to 10%, 50%, and 85% of the cost to supply 10%, we can use proportional reasoning.
Let X be the cost to supply 10%. Then:
The cost to supply 50% is 5 times the cost to supply 10%, so it is 5X.
The cost to supply 85% is 8.5 times the cost to supply 10%, so it is 8.5X.
The cost to supply 10% is X.
To find the cost of supplying bins to 10%, 50%, and 85% of the cost to supply 10%, we can substitute X = $1 and multiply by the appropriate percentages:
The cost to supply bins to 10% of the cost to supply 10% is 0.1 * X = 0.1 * $1 = $0.10.
The cost to supply bins to 50% of the cost to supply 10% is 0.5 * X = 0.5 * $1 = $0.50.
The cost to supply bins to 85% of the cost to supply 10% is 0.85 * X = 0.85 * $1 = $0.85.
Therefore, the costs of supplying bins to 10%, 50%, and 85% of the cost to supply 10% are $0.10, $0.50, and $0.85, respectively.
Answer:
Let the cost to supply 10% of the bins be X dollars.
To find the cost of supplying bins to 50% of the cost to supply 10%, we can set up the following proportion:
10% of the cost = X dollars
50% of the cost = Y dollars
We know that the two costs are proportional, so we can set up the following equation:
10% / 50% = X / Y
Simplifying this equation, we get:
0.1 / 0.5 = X / Y
0.2 = X / Y
Multiplying both sides by Y, we get:
Y * 0.2 = X
Y = X / 0.2
Y = 5X
Therefore, the cost of supplying bins to 50% of the cost to supply 10% is 5 times the cost of supplying bins to 10%.
Substituting X = C/10 (where C is the cost to supply 10% of the bins), we get:
Y = 5X = 5(C/10) = C/2
So the cost of supplying bins to 50% of the cost to supply 10% is C/2 dollars.
To find the cost of supplying bins to 85% of the cost to supply 10%, we can set up a similar proportion:
10% of the cost = X dollars
85% of the cost = Z dollars
We know that the two costs are proportional, so we can set up the following equation:
10% / 85% = X / Z
Simplifying this equation, we get:
0.1 / 0.85 = X / Z
0.1176 = X / Z
Multiplying both sides by Z, we get:
Z * 0.1176 = X
Z = X / 0.1176
Z = 8.5X
Therefore, the cost of supplying bins to 85% of the cost to supply 10% is 8.5 times the cost of supplying bins to 10%.
Substituting X = C/10 (where C is the cost to supply 10% of the bins), we get:
Z = 8.5X = 8.5(C/10) = 0.85C
So the cost of supplying bins to 85% of the cost to supply 10% is 85% of the cost to supply 10%, or 0.85C dollars.
Therefore, the costs of supplying bins to 10%, 50%, and 85% of the cost to supply 10% are:
- 10% of the cost: X dollars = C/10 dollars
- 50% of the cost: Y dollars = C/2 dollars
- 85% of the cost: Z dollars = 0.85C dollars
I'LL MARK THE BRAINLIEST
What is the exact circumference of the circle?
Answer: The circumference would be 62.83
Step-by-step explanation:
C=2πr=2·π·10≈62.83185
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 0\le x \le 150≤x≤15.
x f(x)
0 9
3 39
6 69
9 99
12 129
15 159
So the average rate of change of the function over the interval 0 ≤ x ≤ 15 is 4.4.
What is function?In mathematics, a function is a relationship between two sets of numbers, where each input in the first set (called the domain) corresponds to exactly one output in the second set (called the range). In other words, a function takes an input, performs a specific operation on it, and produces an output. A function is usually denoted by a symbol (often a letter) and is defined by a rule that specifies how to calculate the output value for any given input value.
Here,
To find the average rate of change of the function over the interval 0 ≤ x ≤ 15, we need to calculate the change in the function value divided by the change in x over the interval.
The change in the function value over the interval is f(15) - f(0), which is 159 - 93 = 66.
The change in x over the interval is 15 - 0 = 15.
Therefore, the average rate of change of the function over the interval 0 ≤ x ≤ 15 is:
average rate of change = change in f / change in x
= 66 / 15
= 4.4
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Question 4 of 10
The graphs below have the same shape. What is the equation of the blue
graph?
g(x) = ?
g(x) =
10
|f(x)=x²
6
E
Option B. g(x)=(x-2)²is the equation of blue graph.
A graph: what is it?A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.
The red graph is represented by the function:
f(x)=x²
Also, we need the formula for the blue graph.
We can see that the blue graph is just the red graph with the horizontal axis moved 2 units to the right.
An example of a horizontal transition is:
f(x-h) where h is the quantity we shift (to the right).
h = 2 since we moved two units to the right.
Our new role will thus be:
g(x)=f(x-2)=(x-2)²
Therefore:
g(x)=(x-2)²
Our response is B.
Notes:
A denotes a downward vertical movement of two units.
C (assuming it is x²) denotes a two-unit vertical displacement upward.
And D (if you let h = -2, then f(x - (-2)) = f(x + 2) = (x + 2)²) is a horizontal shift of two units to the left.
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the complete question is:
The graphs below have the same shape. What is the equation of the blue
graph?
f(x) = x2
g(x) = ?
9(x) =
O A. g(x) = x² - 2
B. g(x) = (x - 2)2
c. g(x) = x + 2
D. Q(x) = (x + 2)2
Image is attached below;
Consider the following function.
r(x)=4−32x
Step 2 of 2 : Find two points on the line to graph the function.
We can plot (0, 4) and (1, -28) points on a coordinate plane and draw a straight line passing through both points to graph the function.
What is a coordinate plane?
A coordinate plane, also known as a Cartesian plane, is a two-dimensional plane that is used to plot points and graph mathematical equations. It consists of two perpendicular number lines called the x-axis and the y-axis. The x-axis is the horizontal line, with positive values to the right of the origin (0) and negative values to the left of the origin. The y-axis is the vertical line, with positive values above the origin and negative values below the origin. The x-coordinate gives the horizontal position of the point, and the y-coordinate gives the vertical position of the point. By plotting points on a coordinate plane, we can graph lines, curves, and other mathematical functions. It is a fundamental tool in mathematics, science, and engineering for visualizing and analyzing relationships between variables.
To find two points on the line of the function r(x) = 4 - 32x, we can simply choose any two values of x and find the corresponding values of r(x).
For example, when x = 0:
r(0) = 4 - 32(0) = 4
So one point on the line is (0, 4).
When x = 1:
r(1) = 4 - 32(1) = -28
So another point on the line is (1, -28).
Therefore, we have two points on the line: (0, 4) and (1, -28).
We can plot these points on a coordinate plane and draw a straight line passing through both points to graph the function.
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Find the radius r………………………..
Answer:
r = 3
Step-by-step explanation:
Pythagoras' theorem states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides.
AO^2 = AB^2 + BO^2
(2 + r)^2 = 4^2 + r^2
r^2 + 4r + 4 = 16 + r^2
4r = 12
r = 12/4
r = 3
Margo borrows $1500, agreeing to pay it back with 6% annual interest after 6 months. How much interest will she pay?
Answer:
Step-by-step explanation:
1,500 times 0.06 = 90
90 divided by 2 = 45
Jayla is training for the Seaview sprint race she runs the same route in her neighborhood every day and she makes her go on 80% of the time she plans to run every day for the next 10 days how likely that will she make her goal every day
If Jayla makes her goal 80% of the time, we can say that she has a probability of 0.8 of achieving her goal on any given day.
The probability of Jayla making her goal every day for the next 10 days can be calculated by multiplying the probability of her achieving her goal on each day.
Assuming each day's result is independent of the previous day, the probability of Jayla making her goal every day for the next 10 days is:
0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 = 0.1073741824
So, there is approximately a 10.7% chance that Jayla will make her goal every day for the next 10 days.
How many particles in
9.89 moles of Carbon?
The number of particles in 9.89 moles of carbon is solved to be
5.95 x 10^24 particlesHow to find the number of particles in 9.89 moles of carbonTo determine the number of particles in 9.89 moles of carbon, we can use Avogadro's constant, which is defined as the number of particles (atoms or molecules) in one mole of a substance.
Avogadro's constant is approximately 6.02 x 10^23 particles per mole.
So, the number of particles in 9.89 moles of carbon is:
= 9.89 moles x (6.02 x 10^23 particles/mole)
= 5.95 x 10^24 particles
Therefore, there are approximately 5.95 x 10^24 particles in 9.89 moles of carbon.
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Please help me
Simplify this expression:
(In picture)
The simplified expression for given expression is x⁷/y¹⁰.
What is simplication of a expression?Simplification means reducing the expression in a simpler form using various operations while Approximation is simplifying the mathematical expression to its nearest value but not exactly correct.
Equation:To simplify the expression:
x³y⁻²x/x⁻³y⁸
Applying the properties, we get:
x³y⁻²x/x⁻³y⁸ = x⁽³⁻⁽⁻¹⁾⁾y⁽⁻²⁻⁸⁾/x⁻³x¹y⁰
Simplifying the exponents and the term with y, we get:
x⁴/y¹⁰ * x³ = x⁽⁴⁺³⁾/y¹⁰ = x⁷/y¹⁰
Therefore, the simplified expression is x⁷/y¹⁰.
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Need help with math
Answer:
to find are u need to do it this way: pie r sqare
Step-by-step explanation:
22/7x7x7
22/7 x49
cut 7 and 49
1 and 7
22/1x7
=22x7
=154
please help me i really need this
Answer:
The area is given by the expreesion:
A = 5f + 10
Step-by-step explanation:
Notice the height of the shaded area is 5. But the base is the difference between f+9 and 7
So the length of the shaded area will be f+9-7=f+2
then the area of a rectangle is given by A=height*length
This is
A = 5 (f+2) = 5f+10
Question: Write an expression for the area shaded section of this rectangle. Expand your brackets
The area of shaded section is 5f+10
To calculate the area of the rectangle, it is known that just multiply the measurement of the height by the length.
So, to calculate the value of the area of this rectangle considering that the shaded area is part of it, we would do [tex]\sf f+9\times5[/tex].
The area of the shaded section will be given by the difference between the area of the shaded area and the unshaded area.
That is, [tex]\sf(f+9-7)\times5[/tex]
Let's calculate[tex]\begin{array}{l}\sf(f+9-7)\times5\\\sf(f+2)\times5\\\sf 5f+2\times5\\\therefore \bf 5f+10\end{array}[/tex]
5f+10 is the shaded section area expression
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Which statement is true about the circumstance of a circle?
Answer:
The true statement about the circumference of a circle is: circumference is found by multiplying Pi by the diameter
Step-by-step explanation:
FInd the next three terms of 240,-120,60
The next three terms of the sequence 240,-120,60 are -30, 15 and -7.5
What is the next three terms?240, -120, 60
From observation, the second term is found by halving the first term and multiplying by negative
The third is found by halving the second term and multiplying by negative.
The fourth term = negative third term divided by half
= -(60/2)
= -30
The fifth term = negative fourth term divided by half
= -(-30/2)
= 15
The sixth term = negative fifth term divided by half
= -(15/2)
= -7.5
Hence, the next terms of 240, -120, 60 are -30, 15 and -7.5
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An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the linear regression line for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
Number of TV commercials, x 3
5
11
16
19
Car sales, y (in hundreds) 2
3
8
9
6
According to the given problem, the linear regression line for the given data is y = -0.65 + 0.26x
What is linear regression?
Linear regression is a statistical method used to find the relationship between a dependent variable (y) and one or more independent variables (x). It assumes that there is a linear relationship between the variables, meaning that changes in the independent variable(s) are associated with proportional changes in the dependent variable.
The linear regression model can be represented as a straight-line equation:
y = b0 + b1*x + e
The equation of a linear regression line can be written as:
y = b0 + b1*x
where y is the dependent variable (car sales in this case), x is the independent variable (number of TV commercials), b0 is the intercept, and b1 is the slope of the line.
To find the values of b0 and b1, we need to calculate the following:
n = number of data points = 4
Σx = sum of x values = 54
Σy = sum of y values = 28
Σxy = sum of (x*y) values = 164
Σx^2 = sum of (x^2) values = 689
Using these values, we can calculate b1:
b1 = (nΣxy - ΣxΣy) / (n*Σx^2 - Σx^2)
b1 = (4164 - 5428) / (4*689 - 54^2)
b1 = 0.26 (rounded to two decimal places)
Next, we can use b1 to calculate b0:
b0 = (Σy - b1*Σx) / n
b0 = (28 - 0.26*54) / 4
b0 = -0.65 (rounded to two decimal places)
Therefore, the linear regression line for the given data is:
y = -0.65 + 0.26x
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What are the coordinates of the point on the directed line segment from (-6,4) to
(9,-8) that partitions the segment into a ratio of 5 to 1?
The required point's coordinates are (0,3).
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
Hence, The required point's coordinates are (0,3).
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PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
Answer:
see explanation
Step-by-step explanation:
Part A is correct
Part B
student A solved the system correctly
Part C
student B made the error from step 3 to step 4 , that is
step 3 : 3x - 5x + 150 = 114
step 4 : - 2x + 150 = 114 ( should be - 2x not 2x was the error made )
step 5 : - 2x = 114 - 150 = - 36
step 6 : - 2x = - 36 ( divide both sides by - 2 )
x = 18
substitute x = 18 into y = - x + 30 ( from step 1 )
y = - 18 + 30 = 12
Answer : (18, 12 ) which is the answer student A obtained correctly
-7 2/3 + (-5 1/2) + 8 3/4 =
-4 2/3
6 7/12
-21 11/22
-4 5/12
Answer: -4 5/12
Step-by-step explanation: because -7 2/3+(-5 1/2)= -13 1/6
finally take -13 1/6 + 8 3/4= -4 5/12
If A is True, and B is True, what is C
Answer: True
Step-by-step explanation: That was a complete guess. Did you forget to include an image? Am I missing something?
Consider a sequence generated by the
formula f(n) = 4n - 7 starting with n =3.
Generate the terms f(1), f(2), f(3), f(4), f(5)
Can you please give a detailed explanation so I can understand
The sequence generated by the formula f(n) = (4n - 7) starting with n = 1 is: -3, 1, 5, 9, 13
What is functions?A function is typically denoted by a symbol, such as "f(x)", where "x" is the input value and "f(x)" is the output value. The input value is sometimes referred to as the "argument" of the function.
The formula f(n) = (4n - 7) generates a sequence of numbers when we plug in different values of "n". To generate the terms f(1), f(2), f(3), f(4), f(5) we need to substitute each value of n into the formula and evaluate the expression.
Starting with n = 1, we can generate the terms as follows:
f(1) = (4 × 1 - 7) = -3
f(2) = (4 × 2 - 7) = 1
f(3) = (4 × 3 - 7) = 5
f(4) = (4 × 4 - 7) = 9
f(5) = (4 × 5 - 7) = 13
So the sequence generated by the formula f(n) = (4n - 7) starting with n = 1 is: -3, 1, 5, 9, 13
Each term in the sequence is found by plugging in a different value of "n" into the formula f(n) = (4n - 7). The first term, f(1), is found by plugging in n = 1, the second term, f(2), is found by plugging in n = 2, and so on.
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solve for the value of a
( pls help i dont get this at all)
Answer:
Given that
(5a+6 )°+90°+(7a)°=180°
(angles on a straight line sum up to 180°)
5a°+6°+90°+7a°=180°
5a°+7a°=(180-96)°
12a°=84°
Deviding both sides by 12° gives
a=84/12
a=7°
therefore the value of
a=7°
Part a: Assume that the height of your cylinder is 8
inches. Consider A
as a function of r
, so we can write that as A(r)=2πr2+16πr
. What is the domain of A(r)
? In other words, for which values of r
is A(r)
defined?
Part b: Continue to assume that the height of your cylinder is 8
inches. Write the radius r
as a function of A
. This is the inverse function to A(r)
, i.e., to turn A
as a function of r
into r
as a function of A
.
r(A)=
Change entry mode
Hints:
To calculate an inverse function, you need to solve for r
. Here, you would start with A=2πr2+16πr
. This equation is the same as 2πr2+16πr−A=0
which is a quadratic equation in the variable r
, and you can solve that using the quadratic formula. You will want to keep A
as a variable when you plug the values into the quadratic formula.
If you want to type in 3π+1x+1
in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit.
Part c: If the surface area is 300
square inches, then what is the radius r
? In other words, evaluate r(300)
. Round your answer to 2 decimal places.
Hint: To compute a numeric square root such as 17.3−−−−√
, you could
Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17.3)
Use a browser to connect to the Internet and type in sqrt(17.3) into a search field
Use a calculator
The radius is
Number
inches if the surface area is 300
square inches.
Hence, in answering the stated question, we may say that We know, equation however, that r must be positive, therefore we take the positive square root: [tex]r(A) = -4 + square root(64 + 2A) /[/tex]
What is equation?A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to describe the relationship between the two sentences on opposite sides of a letter. In usually, the logo and the programme are the same. For instance, 2x - 4 equals 2.
Part a: Because the radius of a cylinder must be a positive real integer, the domain of A(r) is the set of all real numbers greater than zero.
As a result, the domain of A(r) is:
{r ∈ ℝ | r > 0}
Part b: To determine the inverse function r(A), solve the equation A = 2r2 + 16r for r expressed in terms of A.
To begin, we may simplify the equation by removing 2r:
A = 2πr(r + 8)
Hence, using the quadratic formula, we can find r:
[tex]r = (-16 \sqrt((16)2 - 4(2 )(-A)) / 2(2 )\\r = (-16 \sqrt(2562) + 8A) / 4 r = -4 \sqrt(64 + 2A) /[/tex]
We know, however, that r must be positive, therefore we take the positive square root:
[tex]r(A) = -4 + square root(64 + 2A) /[/tex]
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The radius is apprοximately 11.51 inches when the surface area is 300 square inches.
What is equatiοn?A math equatiοn is a methοd that links twο claims and represents equivalence using the equals sign (=). An equatiοn is a mathematical statement that establishes the equivalence οf twο mathematical expressiοns in algebra.
Part a: The dοmain οf A(r) is the set οf all real numbers greater than οr equal tο zerο since the radius οf a cylinder cannοt be negative.
Dοmain οf A(r): r ≥ 0
Part b: Tο find the inverse functiοn r(A), we start with the equatiοn fοr A(r), set it equal tο A, and sοlve fοr r using the quadratic fοrmula:
[tex]2 \pi r^2 + 16 \pi r - A = 0[/tex]
[tex]r = [-16 \pi \± \sqrt{((16 \pi)^2 - 4(2 \pi)(-A))}] / 2(2 \pi)[/tex]
[tex]r = [-16\pi \± \sqrt{(256\pi^2 + 8 \pi A)}] / 4\pi[/tex]
Simplifying this expressiοn, we get:
[tex]r = (-4 \± \sqrt{(64 + 2A)}) / 2[/tex]
[tex]r(A) = -2 \± \sqrt{(32 + 0.5A)[/tex]
Since the radius οf a cylinder cannοt be negative, we take the pοsitive square rοοt:
[tex]r(A) = -2 + \sqrt{(32 + 0.5A)[/tex]
Part c: Tο find the radius when the surface area is 300 square inches, we plug in A = 300 intο the expressiοn fοr r(A) and simplify:
[tex]r(300) = -2 + \sqrt{(32 + 0.5(300))[/tex]
r(300) = -2 + sqrt(182)
r(300) ≈ 11.51
Therefοre, the radius is apprοximately 11.51 inches when the surface area is 300 square inches.
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multiply in clumns 5824×45
Answer:
Step-by-step explanation:
5824×45
5824
x 45
29120
23296 x
262080
Factor the expression
ax+ay+az +3x+3y+3z
Justin flips a coin and rolls a number cube with sides labeled 1, 2, 3, 4, 5, and 6. He repeats this experiment 40 times. How many times would you expect him to flip tails and roll an even number?
You expect him to flip tails and roll an even number 10 times
How many times would you expect him to flip tails and roll an even number?From the question, we have the following parameters that can be used in our computation:
Sample space 1 = 1, 2, 3, 4, 5, 6
Sample space 2 = H, T
Using the above as a guide, we have the following:
P(Even) = 3/6
P(Tail) = 1/2
So, we have
P(Even and Tail) = 3/6 * 1/2
P(Even and Tail) = 1/4
In 40 times, we have
Expected = 1/4 * 40
Expected = 10
Hence, the number of times is 10
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