The possible number of letter arrangements of 15 letter with 5 a's, 5 b's and 5 c's have no a's in the first 5 letters, no b's in the next 5 letters and no c's in the last 5 letters are equal to 2252.
Total number of letters for arrangement are 15 in count. Arrangment of 5 A's, 5 B's and 5 C's have no A's in the first 5 letters, no B's in the next 5 letters and no C's in the last 5 letters. In other words, we say that the first five letters must be B's or C's, the next five letters must be C's or A's, and the last five letters must be A's or B's. If there are k number of B's in the first five letters, then there must be (5-k) C's in the first five letters, like that there must be k C's and (5 - k ) A's in the next five letters, and k A's and (5-k) B's in the last five letters. That is number of each letter in each group of five letters is determined completely by knowing the number of B's in the first 5 letters. The number of ways to arrange, 15 letters with this restriction is [tex]$\binom{5}{k}^3$[/tex](since there are [tex]$\binom{5}{k}$[/tex]
ways to arrange k B's and 5-k C's that is arrangements ( 1B + 4C , 2B+ 3C , 3B+2C, 4B+ 1C ),similarly for next five arrangements (1A + 4C , 2A+ 3C , 3A+2C, 4A+ 1C ), ( 1B + 4C , 2B+ 3A , 3B+2A, 4B+ 1A ) and ( 5B, 5C, 5A), ( 5C,5B,A). Thus, the final answer for arrangement is [tex]$\sum_{k=0}^{5}\binom{5}{k}^{3}$[/tex]
Solve the above bionomial expression,
[tex]= \binom{5}{0}^{3} + \binom{5}{1}^{3} + \binom{5}{2}^{3} + \binom{5}{4}^{3} + \binom{5}{5}^{3} \\ [/tex]
[tex]= (\frac{ 5!}{5! 0!})^{3} + (\frac{ 5!}{4! 1!})³ + (\frac{5!}{3! 2!})³ + (\frac{5!}{2! 3!})³ + (\frac{5!}{1! 4!})³ + (\frac{5!}{0! 5!})³ \\ [/tex]
= 1 + 5³ + 10³ + 10³ + 5³ + 1
= 2252
Hence, required value is 2252.
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Tiffany’s mother bought a car for $9000 five years ago. She wants to sell it to Tiffany based on a 15% annual rate of depreciation.
Part A. Identify each feature of the problem as it relates to the context and the exponential growth formula: y=a(1−r)t
.
a=
r=
Part B. Which equation correctly models the context of the problem?
Choose : A. y=9000(0.15)t
or B. y=9000(0.85)t
Answer : The equation is
Part C.
Tiffany wants to buy the car from her mother now. (t = 5)
A fair price for the car will be about $
in 5 years.
A) The correct features is,
⇒ a = 9000
⇒ r = 15%
B) The equation correctly models the context of the problem is,
⇒ y = 9000 (0.85)ˣ
We have to given that;
Tiffany’s mother bought a car for $9000 five years ago.
And, She wants to sell it to Tiffany based on a 15% annual rate of depreciation.
Now, We have;
the exponential growth formula is,
⇒ y = a(1 − r)ˣ
Here, We have;
⇒ a = 9000
⇒ r = 15%
Thus, We get;
The equation correctly models the context of the problem is,
⇒ y = a(1 − r)ˣ
⇒ y = 9000 (1 - 0.15)ˣ
⇒ y = 9000 (0.85)ˣ
Therefore, We get;
A) The correct features is,
⇒ a = 9000
⇒ r = 15%
B) The equation correctly models the context of the problem is,
⇒ y = 9000 (0.85)ˣ
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6(5x−3) what is the equation with the fewest symbols?
The equation with the fewest symbols is 30x - 18, which represents the simplified form of the given expression.
Equation calculation.An equation is a mathematical statement that shows the equality between two expressions. The given expression is not an equation since there is no equality sign present. However, we can simplify the expression to get an equivalent equation with the fewest symbols.
To simplify the expression, we use the distributive property of multiplication over addition/subtraction. We multiply 6 with each term inside the parentheses, i.e., 5x and -3. This gives us:
6(5x - 3) = 6(5x) - 6(3) = 30x - 18
This simplified expression is an equation that shows the equality between the left-hand side (LHS) and the right-hand side (RHS). The LHS is 30x - 18, and the RHS is also 30x - 18, which means that they are equal.
Therefore, the equation with the fewest symbols is 30x - 18, which represents the simplified form of the given expression.
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Based on the picture, Planter B is 9 inches by 3 inches by 3 inches. What is its volume?
Answer:
81
Step-by-step explanation:
for the volume you just multiple length, height, and depth
Answer: 81.
Step-by-step explanation:
9 x 3 x 3 . LxWxH brother!
Describe how the graph of ()=(.)− compares to the graph of ()=(.)f of open x close equals 4 . open 0.5 close to the x.
Enter your answer.
Every point on the graph of g(x) is 1 unit higher than the corresponding point on the graph of f(x).
Describing how the graph comparesGiven that
f(x) = 4(0.5)^x and g(x) = 4(0.5)^x + 1
The graphs of the functions f(x) = 4(0.5)^x and g(x) = 4(0.5)^x + 1 are both exponential functions with a base of 0.5.
The only difference between these two functions is the addition of a constant term of 1 to the second function.
This constant term shifts the graph of g(x) vertically upward by 1 unit compared to the graph of f(x).
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Complete question
Describe how the graph of f(x) = 4(0.5)^x compares to the graph of g(x) = 4(0.5)^x +1
What is this Please someone help me
So the measure of angle HLK is 45 degrees.
What is arc?In geometry, an arc is a part of a curve that is typically a segment of a circle. It is defined by any two points on the curve, which are called its endpoints, and by all the points that lie along the curve between those two endpoints. An arc can be measured by its degree measure, which is the measure of the central angle that intercepts the arc, or by its length, which is the distance between its endpoints along the curve. In the context of a circle, an arc is also called a circular arc.
Here,
Since the measure of minor arc HK is 90°, we know that angle HJK is also 90°, since it is an inscribed angle that intercepts the same arc.
By the inscribed angle theorem, the measure of angle HLK is half the measure of arc HK. Therefore,
measure of angle HLK = 1/2 * measure of arc HK
= 1/2 * 90°
= 45°
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Sara paid $15. 95 to become a member at a gym. She then paid a monthly membership fee. Her total cost for 12 months was $735. 95. How much was the monthly fee? Write and Solve an equation
According to the equation, the monthly fee that Sara paid was $60.
Let's start by assigning some variables. Let x be the monthly fee that Sara paid and let y be the number of months that Sara was a member of the gym. We know that Sara paid $15.95 to become a member, so her total cost can be represented by the equation:
Total Cost = Initial Cost + Monthly Fee x Number of Months
$735.95 = $15.95 + x x y
Now we have an equation with two variables. To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting $15.95 from both sides of the equation:
$720 = x x y
Next, we need to solve for x. Since we don't know the value of y, we can't solve for x directly. However, we do know that Sara was a member for 12 months, so we can substitute y = 12 into the equation:
$720 = x x 12
Now we can solve for x by dividing both sides by 12:
$60 = x
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A trapezoid has an area of 35 mm². the ywo bases are 8mm and 6mm. What is the height of the trapezoid?
Using the height formula of the trapezoid, we know that the height is 5000m respectively.
What is Trapezoid?In geometry, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American and Canadian English or a trapezium in British and other forms of English.
In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.
The bases of the trapezoid are the parallel sides.
There are four sides to a trapezoid.
A trapezium is another name for a trapezoid.
It features two parallel sides that are not equal and two nonparallel sides.
So, find the height of the trapezoid as follows:
Formula: h = 2A/a+b
a = 8mm, b = 6 mm
A = 35 mm²
Unit conversion:
a = 8*10⁻³mm
b = 6*10⁻³mm
Using the formula:
h = 2A/a+b
h = 2*35/8*10⁻³+6*10⁻³
h = 5000m
Therefore, using the height formula of the trapezoid, we know that the height is 5000m respectively.
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Jason is making 30 sundaes with mint, chocolate, and vanilla ice cream. 1/5 of the sundaes are mint ice cream and 1/2 of the remaining sundaes are chocolate. The rest will be vanilla. How many sundaes will be vanilla?
Hi
1/5 is mint : so 30*1/5 = 6
1/2 of what remain is chocolate : which mean (30-6) /2 = 24/2 = 12
So vanilla will be : 30-6-12 = 30-18 = 12
recap : 6 mint, 12 chocolate and 12 vanilla.
Using the Standard Normal Table, what is the area to the left of z < -2.34?
The Standard Normal Table is a tool that is used to calculate probabilities associated with the standard normal distribution.
When using the Standard Normal Table, we can find the area to the left of z < -2.34 by first locating the value -2.3 in the left-hand column of the table and the value -0.04 in the top row of the table.
Then, we find the intersection of the row and column to locate the corresponding value of 0.0099. This value represents the area to the left of -2.3 on the standard normal distribution.
To find the area to the left of -2.34, we need to adjust the value by subtracting the area to the left of -2.34 from the area to the left of -2.3.
The standard normal distribution is symmetric around the mean of 0. It means the area to the right of -2.3 is the same as the area to the left of 2.3.
Therefore, the area to the left of z < -2.34 is the area to the left of -2.3 (0.0099) minus the area between -2.34 and -2.3 (0.0040), which equals 0.0059. So, the area to the left of z < -2.34 is 0.0059.
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If the temperature increases and the amount of water vapor in the air remains unchanged, how has the RH (relative humidity) changed?
When the temperature increases and the water vapor content in the air stays the same, the relative humidity decreases. This is because warmer air can hold more moisture than colder air, and therefore the ratio of the actual amount of water vapor in the air to the maximum amount of water vapor that the air can hold decreases as the air temperature increases.
Relative humidity depends on two factors: the amount of water vapor present in the air and the maximum amount of water vapor that the air can hold at a given temperature. As the temperature rises, so does the amount of water vapor that the air can hold, since warm air has more energy to hold the water molecules in vapor form. This reduces the ratio of the actual amount of water vapor in the air to the maximum amount of water vapor the air can hold, resulting in lower relative humidity.
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Question 15(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
Based on the medians, we can conclude that Bus 47 typically has a faster travel time than Bus 18. The median travel time for Bus 47 is 16 minutes, which is 3 minutes faster than the median travel time for Bus 18, which is 13 minutes.
Travel time calculation.
To determine which bus typically has the faster travel time, we need to compare the measures of center for each data set. Since the data sets are relatively small and appear to have some outliers, the median is the more appropriate measure of center to use in this case, as it is less affected by extreme values than the mean.
For Bus 47, the median is 16, which means that half of the students take less than 16 minutes to travel to school on that bus, and half take more than 16 minutes.
For Bus 18, the median is 13, which means that half of the students take less than 13 minutes to travel to school on that bus, and half take more than 13 minutes.
Therefore, based on the medians, we can conclude that Bus 47 typically has a faster travel time than Bus 18. The median travel time for Bus 47 is 16 minutes, which is 3 minutes faster than the median travel time for Bus 18, which is 13 minutes.
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4. The usual 110-V household alternating current varies from -155 V
to 155 V with a frequency of 60 cycles/ sec (frequency is the
reciprocal of period). Assume the current starts at rest and then
rises.
Make a sketch of the curve.
Write an equation to describe the curve:_
Determine the value of y when t = 1/90 sec.:_
Approximate the value of t when y = 100 for the first time:_
Answer:
The equation for the alternating current can be described by: y = 155 sin(120πt)
Where y is the voltage in volts (V) and t is the time in seconds (s).
To find the value of y when t = 1/90 s:
y = 155 sin(120π(1/90))
y ≈ 30.8 V
To approximate the value of t when y = 100 V for the first time, we need to solve the equation for t:
100 = 155 sin(120πt)
sin(120πt) = 100/155
t = arcsin(100/155)/(120π)
t ≈ 0.001 s
Therefore, the value of t when y = 100 V for the first time is approximately 0.001 seconds
Given: sin (alpha) =(5)/(13) in Quadrant I and cos(beta) = (-12)/(13) in Quadrant II; evaluate the following expression:
sin(alpha + beta ) =
1) -120/169
2) -1
3) 0
If sin (α) =(5)/(13) in Quadrant I and cos(β) = (-12)/(13) in Quadrant II, then sin(α + β ) = -120/169 .So, the answer is option 1).
To evaluate sin(α + β), we can use the trigonometric identity:
sin(α + β) = sin α cos β + cos α sin β
First, we need to find cos α. Since sin α is positive and in Quadrant I, we can use the Pythagorean identity to find cos α:
cos α = √(1 - sin² α) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13
Next, we need to find sin β. Since cos β is negative and in Quadrant II, we can use the Pythagorean identity to find sin β:
sin β = -√(1 - cos² β) = -√(1 - (-12/13)²) = -√(1 - 144/169) = -√(25/169) = -5/13
Now we have all the values we need to evaluate sin(α + β):
sin(α + β) = sin α cos β + cos α sin β
= (5/13)(-12/13) + (12/13)(-5/13)
= -60/169 - 60/169
= -120/169
Therefore, the answer is option 1) -120/169.
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anyone know these?? i need help
Answer:
[tex]\frac{12}{5}[/tex] = 12 ÷ 5
[tex]\frac{1}{4}[/tex] = 1 ÷ 4
[tex]\frac{3}{8}[/tex] = 3 ÷ 8
[tex]\frac{9}{2}[/tex] = 9 ÷ 2
Use a linear regression algorithm to determine the equation for the line of best fit for the data in the table.
a. Identify the correlation coefficient.
b. What type of correlation exists for the data?
a. The correlation coefficient: ≈ -0.184
b. The correlation coefficient r ≈ -0.184, which is close to 0. This suggests that there is a weak negative correlation between the x and y values in the data.'
How to solve
To find the line of best fit using a linear regression algorithm, we need to find the slope (m) and y-intercept (b) of the equation in the form y = mx + b.
We will start by calculating some statistics from the given data.
First, let's find the means of x and y:
x_mean = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) / 9 = 45 / 9 = 5
y_mean = (8 + 4.037 + 7.200 + 4.180 + 4.763 + 1 + 1.047 + 2.436 + 1.844) / 9 ≈ 34.507 / 9 ≈ 3.834
Next, we need to find the sum of the product of the differences between each point and the mean for both x and y:
Σ((x - x_mean) * (y - y_mean)) = (1 - 5) * (8 - 3.834) + (2 - 5) * (4.037 - 3.834) + ... + (9 - 5) * (1.844 - 3.834) ≈ -8.311
We also need to find the sum of the squared differences between each x and the mean of x:
Σ((x - x_mean)^2) = (1 - 5)^2 + (2 - 5)^2 + ... + (9 - 5)^2 = 60
Now, we can calculate the slope (m):
m = Σ((x - x_mean) * (y - y_mean)) / Σ((x - x_mean)^2) ≈ -8.311 / 60 ≈ -0.1385
To find the y-intercept (b), use the formula:
b = y_mean - m * x_mean ≈ 3.834 - (-0.1385) * 5 ≈ 4.525
Now we have the line of best fit equation:
y = -0.1385x + 4.525
a. To find the correlation coefficient (r), we need to divide the covariance of x and y by the product of the standard deviations of x and y.
First, let's find the covariance:
cov(x, y) = Σ((x - x_mean) * (y - y_mean)) / (n - 1) ≈ -8.311 / 8 ≈ -1.039
Next, find the standard deviations of x and y:
sd_x = sqrt(Σ((x - x_mean)^2) / (n - 1)) = sqrt(60 / 8) ≈ 2.738
sd_y = sqrt(Σ((y - y_mean)^2) / (n - 1))
sd_y = sqrt((8 - 3.834)^2 + (4.037 - 3.834)^2 + ... + (1.844 - 3.834)^2) / 8 ≈ sqrt(33.904) / 8 ≈ sqrt(4.238) ≈ 2.058
Now we can calculate the correlation coefficient:
r = cov(x, y) / (sd_x * sd_y) ≈ -1.039 / (2.738 * 2.058) ≈ -0.184
b. The correlation coefficient r ≈ -0.184, which is close to 0. This suggests that there is a weak negative correlation between the x and y values in the data.'
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Consider the equation: x² + 10x + 22 = 13 1) Rewrite the equation by completing the square. Your equation should look like (x + c)2 = dor (x - c)² = d. 2) What are the solutions to the equation? Choose 1 answer: A x=5±4 x = -5±4 x = 5±16 x = -5±16
The solutions to the equation x² + 10x + 22 = 13 are: x = -5 ± 4
Solving the equation by completing the squareTo rewrite the equation by completing the square, we need to isolate the constant term on one side and group the x-terms together. Starting with:
x² + 10x + 22 = 13
Subtracting 13 from both sides:
x² + 10x + 9 = 0
Next, we add and subtract the square of half of the coefficient of x (which is 5 in this case) to complete the square:
x² + 10x + 25 - 25 + 9 = 0
x² + 10x + 25 - 16 = 0
Factor the perfect square trinomial:
(x + 5)² - 16 = 0
Now that we have rewritten the equation in the form (x + c)² = d, we can solve for x by taking the square root of both sides:
(x + 5)² - 16 = 0
Taking the square root of both sides and solving for x, we get:
x + 5 = ±4
So, we have
x = -5 ± 4
So the solutions to the equation are:
x = -5 + 4 = -1
x = -5 - 4 = -9
Therefore, the answer is x = -5 ± 4.
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Find the value of x. If a segment looks like a tangent, it is a tangent.
We got x = 149.53 by using Pythagorean theorem.
What is the Pythagorean theorem in plain English?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90°.
[tex]172^2=85^2+x^2[/tex]
[tex]29584=7225+x^2[/tex]
[tex]x^2=29584-7225[/tex]
[tex]=22359[/tex]
[tex]x=\sqrt{22359}[/tex]
[tex]\boxed{\bold{x=149.53}}[/tex]
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Marilyn needs to buy two Series EE savings bonds as graduation gifts for her cousins. She has $75 to spend. What could be the face value on each bond? (Hint: The face values of the bonds she can buy are $50, $75, and $100. )
Marilyn has $75 to spend on two Series EE savings bonds as graduation gifts. The face values of the bonds she can buy are $50, $75, and $100. Therefore, she could buy two $50 bonds.
Since Marilyn has $75 to spend and she needs to buy two bonds, the total face value of the bonds she can purchase must be equal to $75.
Let x be the face value of the first bond, then the face value of the second bond must be 75 - x.
The face values of the bonds are $50, $75, and $100, so we can set up the following three equations
x + (75 - x) = 75 (since the total face value must be $75)
x = 50 (since the face value must be $50, $75, or $100)
x = 100 (since the face value must be $50, $75, or $100)
Solving these equations, we find that the possible face values for each bond are $50 and $25, $75 and $0, or $100 and $-25 (which is not a valid option).
Therefore, Marilyn could buy two bonds with face values of $50 each, or one bond with a face value of $75 and the other with a face value of $0 (which essentially means she would only be buying one bond).
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I hope everyone has a great day and can someone solve this will mark brainlist
y=8x-9
y=7
Answer:
x=2
Step-by-step explanation:
This is a system of equations that we can solve by using substitution.
We know that y=7. We know that y is also equal to 8x-9.
Since y is equal to both 7 and 8x-9, this must mean that 7 is also equal to 8x-9.
Let's set them equal and solve for x, like so:
[tex]y=8x-9=\\7=8x-9=\\16=8x=\\2=x[/tex]
So, x=2.
Patricia is buying new kitchen cabinets, which are shaped as rectangular prisms. The cabinets are 34 inches tall, 24 inches deep, and 16 inches wide. What is the volume of the cabinets?
If the cabinets are 34 inches tall, 24 inches deep, and 16 inches wide, the volume of the kitchen cabinets is 16,384 cubic inches.
To find the volume of the rectangular prisms-shaped kitchen cabinets, we need to multiply the three dimensions: height, depth, and width. We are given the following measurements:
Height = 34 inches
Depth = 24 inches
Width = 16 inches
So the formula for the volume is:
Volume = Height x Depth x Width
Substituting the given values, we get:
Volume = 34 x 24 x 16
Volume = 16,384 cubic inches
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Please answer asap
It would be helpful
The answer of the given question based on the cylinder is , the volume of the solid = 929.44 inch³ . , the mistake is student may have only calculated the volume of the inner cylinder.
What is Volume?Volume is amount of three-dimensional space occupied by object or substance. It is a physical quantity that is measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of an object can be calculated by measuring its dimensions and using a mathematical formula specific to its shape.
To find volume of solid, we need to subtract volume of inner cylinder from volume of outer cylinder.
Volume of the outer cylinder = πr²h
where r = radius of the outer cylinder = 4 inches (diameter is given as 8 inches)
h = height of the outer cylinder = 23 inches
Volume of the outer cylinder = π(4)²(23) = 368π in³
Volume of the inner cylinder = πr²h
where r = radius of the inner cylinder = 2 inches
h = height of the inner cylinder = 18 inches
Volume of the inner cylinder = π(2)²(18) = 72π in³
So, the volume of the solid = Volume of the outer cylinder - Volume of the inner cylinder
= 368π - 72π
= 296π
= 929.44 inch³
The student's answer of 988.05 in³ is significantly higher than the correct answer, suggesting that the student may have only calculated the volume of the inner cylinder instead of subtracting it from the volume of the outer cylinder. This mistake may have arisen due to misreading the problem or misunderstanding the instructions.
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Provide a detailed example. How lessons from Micah chapter 2 can be pacifically apply toward our lives today.
PLEASE ANSWER ASAP
IT WOULD BE HELPFUL
The answer of the given question based on the cylinder is , the volume of the solid = 929.44 inch³ . , the mistake is student may have only calculated the volume of the inner cylinder.
What is Volume?
Volume is amount of three-dimensional space occupied by object or substance. It is physical quantity that is measured in cubic units, like cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of object can be calculated by measuring its dimensions and using mathematical formula specific to its shape.
To find volume of solid, we need to subtract volume of inner cylinder from volume of outer cylinder.
Volume of the outer cylinder = πr²h
where r = radius of the outer cylinder = 4 inches (diameter is given as 8 inches)
h = height of the outer cylinder = 23 inches
Volume of the outer cylinder = π(4)²(23) = 368π in³
Volume of the inner cylinder = πr²h
where r = radius of the inner cylinder = 2 inches
h = height of the inner cylinder = 18 inches
Volume of the inner cylinder = π(2)²(18) = 72π in³
So, the volume of the solid = Volume of the outer cylinder - Volume of the inner cylinder
= 368π - 72π
= 296π
= 929.44 inch³
The student's answer of 988.05 in³ is significantly higher than the correct answer, suggesting that the student may have only calculated the volume of the inner cylinder instead of subtracting it from the volume of the outer cylinder. This mistake may have arisen due to misreading the problem or misunderstanding the instructions.
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Gail averages 153 points per bowling game with a standard deviation of 14.5 points. Suppose Gail's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X ∼ N ( 153 , 14.5 ) . z-score when x = 108 is _____. The mean is 153 . The z-score tell you that x = 108 is _____ standard deviations to the left of the mean.
x = 108 is 3.10 standard deviations to the left of the mean.
What is standard deviation?The standard deviation (SD, also written as the Greek symbol sigma or the Latin letter s) is a statistic that is used to express how much a group of data values vary from one another.
The z-score when x = 108 is:
z = (108 - 153) / 14.5
z = -3.10
This tells us that x = 108 is 3.10 standard deviations to the left of the mean.
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A 3 column table with 4 rows. The first column is labeled Satellite with entries, A, B, C, D. The second column is labeled mass in kilograms with entries, 375, 250, 50, 500. The last column is labeled Distance from Earth in kilometers with entries, 320, 320, 320, 320. Which satellite has the greatest gravitational force with Earth? Earth and Satellite A Earth and Satellite B Earth and Satellite C Earth and Satellite D
Since the gravitational force is directly proportional to the mass, we can see that Satellite D has the greatest mass and therefore the greatest gravitational force with Earth. Therefore, the correct option is D.
To determine which satellite has the greatest gravitational force with Earth, we need to use the formula for gravitational force, which is:
force = (G x m1 x m2) / r^2
where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the objects.
Since the mass of Earth is much greater than any of the satellites, we can assume that the distance between Earth and each satellite is the same. Therefore, we can compare the gravitational force of each satellite with Earth by calculating:
force = (G x Earth's mass x satellite's mass) / distance^2
Using this formula and plugging in the given values, we get:
For Satellite A: force = (G x Earth's mass x 375 kg) / (320 km)^2
For Satellite B: force = (G x Earth's mass x 250 kg) / (320 km)^2
For Satellite C: force = (G x Earth's mass x 50 kg) / (320 km)^2
For Satellite D: force = (G x Earth's mass x 500 kg) / (320 km)^2
Therefore, the correct option is D.
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HELP PLEASE I NEED IT LIKE NOW
What is the volume of a rectangular prism with a length of 14 1/5 yards, a width of 7 yard, and a height of 8 yards?
795 1/5
739 1/5
452 4/5
226 2/5
A1=3. 1 and a4=2. 86
write a function rule for the nth term of the sequence. And find the 10th term of the sequence
According to the function, the 10th term of the sequence is 2.038.
We can now use the values of A1, A4, A2, and A3 to find the value of d. Substituting A2 and A3 into the expression for A4 - A3, we get:
A4 - A3 = d
2.86 - (A1 + 2d) = d
Solving for d, we get:
d = -0.12
Now that we know the common difference between consecutive terms, we can write the function rule for the nth term of the sequence as:
An = A1 + (n - 1)d
Substituting A1 = 3.1 and d = -0.12, we get:
An = 3.1 - 0.12(n - 1)
To find the 10th term of the sequence, we simply plug in n = 10 into the formula:
A10 = 3.1 - 0.12(10 - 1) = 2.038
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Find the number of minutes between 17:53 and 7:26
There are 813 minutes in between 17:53 to 7.26 .
Time can be represented in two formats, that is in a twelve - hour format and in a twenty four - hour format.
Here the time 17:53 and 7:26 is represented in twenty four - hour format where the day is divided in twenty four hours and time runs from midnight and ends at midnight.
(If the time 17:53 and 7:26 was represented in twelve - hour format then it would have AM and PM to denote if the time is from midnight till noon or noon till midnight, which is clearly not the case.)
Thus, from 17:53 to 7.26 there is 13 hours and 33 minutes.
We know one hour has 60 minutes. Therefore by method of conversion of hours to minutes we get,
Number of minutes between 17:53 to 7.26 = {(13*60) + 33} = 780+33 = 813
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the water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. they would like the estimate to have a maximum error of 0.15 gallons. a previous study found that for an average family the variance is 3.61 gallons and the mean is 17.3 gallons per day. if they are using a 90% level of confidence, how large of a sample is required to estimate the mean usage of water? round your answer up to the next integer.
We need to round up to the nearest integer, the required sample size is 76 households.
To estimate the required sample size, we can use the formula:
[tex]n = (z^2 * s^2) / E^2[/tex]
Where:
z is the z-score corresponding to the confidence level (90% = 1.645)
s is the standard deviation of the population (square root of the variance, so s = sqrt(3.61) = 1.898)
E is the maximum error allowed (0.15 gallons)
Plugging in the values, we get:
[tex]n = (1.645^2 * 1.898^2) / 0.15^2[/tex]
n = 75.57
Since we need to round up to the nearest integer, the required sample size is 76 households.
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write the ratio 5x10^-1 :2:3x10^-10 in its simplest form