Answer:
Step-by-step explanation:
the Laplace transform of the function f(x) = e^(ax) is 1/(a-s).
The definition of the Laplace transform of a function f(t) is given by:
L{f(t)} = F(s) = ∫_0^∞ e^(-st) f(t) dt
where s is a complex number.
If f(x) = 0, then we have:
L{f(x)} = L{0} = ∫_0^∞ e^(-st) 0 dt = 0
Therefore, the Laplace transform of the zero function is zero.
If f(x) = 1, then we have:
L{f(x)} = L{1} = ∫_0^∞ e^(-st) dt
Using integration by parts, we get:
L{1} = ∫_0^∞ e^(-st) dt = [-e^(-st)/s]_0^∞ = [0 - (-1/s)] = 1/s
Therefore, the Laplace transform of the constant function 1 is 1/s.
If f(x) = x, then we have:
L{f(x)} = L{x} = ∫_0^∞ e^(-st) x dt
Using integration by parts again, we get:
L{x} = ∫_0^∞ e^(-st) x dt = [(-e^(-st) x)/s]_0^∞ + (1/s) ∫_0^∞ e^(-st) dt
Since e^(-st) x approaches zero as t approaches infinity, the first term evaluates to zero. We can then simplify the second term using the result from part 2:
L{x} = (1/s) ∫_0^∞ e^(-st) dt = 1/s * (1/s) = 1/s^2
Therefore, the Laplace transform of the function f(x) = x is 1/s^2.
If f(x) = e^(ax), then we have:
L{f(x)} = L{e^(ax)} = ∫_0^∞ e^(-st) e^(ax) dt
Simplifying the integrand, we get:
L{e^(ax)} = ∫_0^∞ e^((a-s)t) dt
We can evaluate this integral using the formula:
∫_0^∞ e^(-bx) dx = 1/b
Setting b = a - s, we get:
L{e^(ax)} = ∫_0^∞ e^((a-s)t) dt = 1/(a-s)
Therefore, the Laplace transform of the function f(x) = e^(ax) is 1/(a-s).
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Use the given acceleration function and initial conditions to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 9. a(t) = −cos ti − sin tj v(0) = j + k, r(0) = i v(t) = r(t) = r(9) =
find the position at time t = 9. a(t) = −cos ti − sin tj v(0) = j + k, r(0) = i v(t) = r(t) = r(9) = This gives you the position vector r(9) as a function of sin(9) and cos(9).
To find the velocity vector v(t) and position vector r(t), we need to integrate the given acceleration function a(t) and apply the initial conditions. Here's a step-by-step explanation:
1. Given acceleration function: a(t) = -cos(t)i - sin(t)j
2. Integrate a(t) with respect to t to find v(t):
v(t) = ∫(-cos(t)i - sin(t)j) dt = (sin(t)i + cos(t)j) + C, where C is a constant vector.
3. Apply initial condition v(0) = j + k:
v(0) = sin(0)i + cos(0)j + C = j + k
C = -i + j + k
4. The velocity function is: v(t) = sin(t)i + cos(t)j - i + j + k
Now let's find the position vector r(t):
5. Integrate v(t) with respect to t to find r(t):
r(t) = ∫(sin(t)i + cos(t)j - i + j + k) dt = (-cos(t)i + sin(t)j + t(k) + D, where D is another constant vector.
6. Apply initial condition r(0) = i:
r(0) = -cos(0)i + sin(0)j + 0(k) + D = i
D = i
7. The position function is: r(t) = -cos(t)i + sin(t)j + tk + i
Finally, let's find the position at time t = 9:
8. r(9) = -cos(9)i + sin(9)j + 9k + i
This gives you the position vector r(9) as a function of sin(9) and cos(9).
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In a recent report, Joe's, a Memphis-style barbecue chain, states that 11% of its customers order for delivery. A random sample of 6 Joe's customers is chosen. Find the probability that at most 1 of them order for delivery. " Do not round your intermediate computations, and round your answer to three decimal places.
P(X ≤ 1) = P(X = 0) + P(X = 1) ≈ 0.901
So the probability that at most 1 customer in the sample orders for delivery is approximately 0.901, rounded to three decimal places.
To solve this problem, we can use the binomial distribution since we have a fixed number of trials (6) and each trial can result in one of two outcomes (ordering for delivery or not).
Let X be the number of customers in the sample who order for delivery. Then X follows a binomial distribution with parameters n = 6 and p = 0.11 (the probability of ordering for delivery).
We want to find the probability that at most 1 customer orders for delivery. This can be written as:
P(X ≤ 1) = P(X = 0) + P(X = 1)
To calculate these probabilities, we can use the binomial probability formula:
P(X = k) = (n choose k) *[tex]p^k[/tex]*[tex](1 - p)^(n - k)[/tex]
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.
Using this formula, we can calculate:
P(X = 0) = (6 choose 0) * 0.11^0 * [tex]0.89^6[/tex] ≈ 0.530
P(X = 1) = (6 choose 1) * 0.11^1 * 0.89^5 ≈ 0.371
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What three-dimensional figure is formed when the triangle shown is rotated around the dashed line?
A. cone
B. cylinder
C. double cone
D. hemisphere
Answer: C
Step-by-step explanation: after rotating, if you split it in half horizontally, you have two cones
The three-dimensional figure formed when the triangle is rotated around the dashed line through B and C is a cone.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.
When we rotate a two-dimensional shape around an axis, we create a three-dimensional solid. This process is known as "revolution" or "rotational symmetry".
In this particular case, we have a triangle that can be rotated around the line segment that connects points B and C. If we were to rotate the triangle around this axis, we would create a three-dimensional solid. To figure out what kind of solid this is, we can think about the cross-sections that would be created if we were to slice through the solid perpendicular to the axis of rotation.
If we were to slice through the solid perpendicular to the axis of rotation, we would get a circle. This means that the solid created by rotating the triangle is a cylinder.
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450 cubic centimetres of wood is used to make a solid cylindrical ornament. the radius of the base of the ornament is 5 centimetres. what is the height of the cylindrical ornament? (formula = π x radius² x height)
a) 4.5 cm
b) 5.7 cm
c) 6.3 cm
d) 7.5 cm
The height of the cylindrical ornament is approximately 5.7 centimetres (option b).
To find the height of the cylindrical ornament given that 450 cubic centimetres of wood is used and the radius of the base is 5 centimetres, you can use the formula for the volume of a cylinder: V = π × radius² × height.
Step 1: Write down the given values.
Volume (V) = 450 cubic centimetres
Radius (r) = 5 centimetres
Step 2: Plug the given values into the formula.
450 = π × (5)² × height
Step 3: Solve for the height.
450 = π × 25 × height
450 = 78.54 × height
Step 4: Divide both sides by 78.54 to find the height.
height = 450 / 78.54
height ≈ 5.7 centimetres
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The ratio of Adults to Girls in a tennis club is 5:1
The ratio of Girls to Boys in the same club is 3:4
What is the ratio of adults to boys?
The ratio of adult to boys is 35:24
What is ratio?A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. For example, if the ratio of boys to girls in a class is 4:1. This means that the for every 4 boys therefore is a girl.
Represent the total number of adult, boys and girls in the club by x
This means number of boys = 4/7× x
number of adult = 5/6 × x
Therefore the ratio of adults to boys will be
5x/6 : 4x/7
= 5/6 : 4/7
multiply through by 42
= 35 : 24
therefore the ratio of adult to boys is 35: 24
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A garden hose can normally fill a child's inflatable pool in 30 minutes.
The pool has a small hole in it, and water is secretly leaking out. This leak could empty the
pool in two hours (120 minutes).
How long would it take, from start to finish, until the pool is full of water?
2a) Clearly write out the equation you would use to answer the question.
2b) Answer the question. How long would it take? Please write your answer as a
complete sentence with appropriate units.
2a) The equation used to answer the question is (1/Time to fill the pool) = (1/Time taken by hose) - (1/Time taken by leak).
2b) It would take 40 minutes to fill the pool with water when there is a small hole causing a leak.
To solve this, we can use the concept of rates of work.
2a) The equation we would use to answer the question is:
(1/Time to fill the pool) = (1/Time taken by hose) - (1/Time taken by leak)
2b) Let's plug in the values given in the question:
(1/Time to fill the pool) = (1/30 minutes) - (1/120 minutes)
To find the time to fill the pool, we first need to find a common denominator for the fractions. The common denominator is 120, so we can rewrite the fractions as:
(1/Time to fill the pool) = (4/120) - (1/120)
Now, add the fractions on the right side:
(1/Time to fill the pool) = (3/120)
Next, take the reciprocal of both sides to solve for the time to fill the pool:
Time to fill the pool = 120/3
Time to fill the pool = 40 minutes
So, it would take 40 minutes to fill the pool.
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What is the value of the expression below? (3 1/2 - 9 3/4) entre (-2.5)
PLEASE HELP
Answer:
Let's solve this in steps:
1. Convert mixed numbers to fractions:
```
3 1/2 = 7/2
9 3/4 = 39/4
```
2. Perform the subtraction:
```
7/2 - 39/4 = -11/4
```
3. Divide by -2.5:
```
-11/4 / -2.5 = 4.4
```
Therefore, the value of the expression is **4.4**.
An engineer is using computer-aided design (CAD) software to design a component for a space shuttle. The scale of the drawing is 1 cm: 60 in. The actual length of the component is 12. 75 feet. What is the length of the component in the drawing?
The length of the component in the drawing is 2.125 centimeters.
How to find the length of the component represented in a CAD?To find the length of the component in the drawing, we convert the given length from feet to inches. Since 1 foot is equal to 12 inches, the actual length of 12.75 feet is equivalent to 12.75 x 12 = 153 inches.
Next, we apply the scale of the drawing, which is 1 cm: 60 in. This means that for every 60 inches in reality, the drawing represents it as 1 centimeter. To find the length in centimeters, we set up a proportion:
1 cm / 60 in = x cm / 153 in
Cross-multiplying and solving for x, we get:
x = (1 cm * 153 in) / 60 in = 2.55 cm
Rounding to three decimal places, the length of the component in the drawing is approximately 2.125 centimeters.
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Tyler rides his bike from his house to his cousin's house. He bikes a total of 1.8 kilometers to get there and back. What is the distance, in meters, between Tyler's house and his cousin's house?
Answer:
Step-by-step explanation:
Total of rides from Tyler's house to Cousin's house and Cousin's house to Tyler's house = 1.8km = 1800m
So, the distance from Tyler's house to his cousin's house is
= 1800m ÷ 2 = 900m
find the exact area of a square with a diagonal of 8 inches
Answer:
(8/√2)^2 = 64/2 = 32 square inches
I have no congruent sides. One of my angles has a measure of 100 degrees. Answer with drawing of the triangle
I am a(n and triangle
You are an scalene triangle.
How can you identify the type of triangle when given the information that it has no congruent sides and one angle measuring 100 degrees?You are a scalene triangle.
A scalene triangle is a type of triangle where all three sides have different lengths, and no two angles are congruent. In this case, you mentioned that one of the angles has a measure of 100 degrees.
Here's a simple diagram of a scalene triangle to help illustrate:
\
\
\
\
\
\
In the diagram, the angles are not drawn to scale, but it represents a scalene triangle where one angle measures 100 degrees. The sides of the triangle would have different lengths, distinguishing it from an equilateral or isosceles triangle where at least two sides are congruent.
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69x 10x 6969x 8008x696969696969
Y’all I’m so confused, I got 38792.3. What am I doing wrong?
Answer:
38,772.72
Step-by-step explanation:
The formula for a sphere is
V=4/3 pi r^3
=4/3 3.14 21^3
=4/3 3.14 9,261
=4/3 29,079.54
=38,772.72
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=42 \end{cases}\implies V=\cfrac{4\pi (42)^3}{3}\implies \stackrel{ using~\pi =3.14 }{V\approx 310181.76}[/tex]
50 PONTS Triangle LMN has vertices at L(−1, 4), M(−1, 0), and N(−3, 4) Determine the vertices of image L′M′N′ if the preimage is rotated 90° clockwise about the origin.
L′(4, 1), M′(0, 1), N′(4, 3)
L′(−1, −4), M′(−1, 0), N′(−3, −4)
L′(−4, −1), M′(0, −1), N′(−4, −3)
L′(1, −4), M′(1, 0), N′(3, −4)
The coordinates of the resulting triangle are L'(4, 1), M'(0, 1), and N'(4, 3)
What are the coordinates of the resulting triangle?From the question, we have the following parameters that can be used in our computation:
Triangle LMN has vertices at L(−1, 4), M(−1, 0), and N(−3, 4
This means that
L(−1, 4), M(−1, 0), and N(−3, 4Rotation rule = 90° clockwise around the origin.The rotation rule of 90° clockwise around the origin is
(x,y) becomes (y,-x)
So, we have
Image = (y, -x)
Substitute the known values in the above equation, so, we have the following representation
L'(4, 1), M'(0, 1), and N'(4, 3)
Hence, the coordinates of the resulting points, are L'(4, 1), M'(0, 1), and N'(4, 3)
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Answer:L′(4, 1), M′(0, 1), N′(4, 3)
Step-by-step explanation:
I am in the middle of taking the quiz and I believe this is the correct answer!
Here is a set of data showing the test scores for US History class:
56, 88, 70, 72, 90, 85, 99, 65, 66, 54, 74, 85, 91, 92, 72, 88, 97, 62, 88 Create a stem and leaf plot to show this data. Hint: Decide how many stems you will need.
can somebody help me ?
Hi! I'd be happy to help you create a stem and leaf plot using the provided set of data for US History class test scores.
Step 1: Arrange the data in ascending order.
54, 56, 62, 65, 66, 70, 72, 72, 74, 85, 85, 88, 88, 88, 90, 91, 92, 97, 99
Step 2: Determine the range of the data.
The data ranges from 50s to 90s, so we will need 5 stems: 5, 6, 7, 8, and 9.
Step 3: Create the stem and leaf plot using the stems and corresponding leaves (the units digits of the data).
5 | 4 6
6 | 2 5 6
7 | 0 2 2 4
8 | 5 5 8 8 8
9 | 0 1 2 7 9
Here is the completed stem and leaf plot for the US History class test scores. The stems represent the tens digits (50s, 60s, 70s, 80s, 90s), and the leaves represent the units digits of the scores in each range.
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Qn in attachment
.
..
Answer:
option d
Step-by-step explanation:
24
pls mrk me brainliest (*￣(ｴ)￣*)
A study is designed to test the hypotheses h0: m $ 26 versus ha: m , 26. a random sample of 50 units was selected from a specified population, and the measurements were summarized to y 5 25.9 and s 5 7.6. a. with a 5 .05, is there substantial evidence that the population mean is less than 26
The p-value for a t-score of -0.92 is approximately 0.18 and since it is greater than the significant level, the null hypothesis is rejected.
The first step in testing this hypothesis is to calculate the test statistic, which in this case is a t-score. The formula for the t-score is (y - mu) / (s / sqrt(n)), where y is the sample mean, mu is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
In this case, the sample mean is 25.9, the hypothesized population mean is 26, the sample standard deviation is 7.6, and the sample size is 50. Plugging these values into the formula, we get a t-score of -0.92.
Next, we need to find the p-value associated with this t-score. We can use a t-table or a calculator to do this. Using a t-table with 49 degrees of freedom (since we have a sample size of 50 and one parameter estimated from the sample), we find that the p-value for a t-score of -0.92 is approximately 0.18.
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. In other words, we do not have substantial evidence to conclude that the population mean is less than 26. However, it is important to note that the sample mean is slightly below the hypothesized population mean, and the p-value is relatively close to the significance level. Therefore, it may be worthwhile to conduct additional studies with larger sample sizes or different populations to further investigate this question.
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The function models the amount of money a new business has made over x months. Negative values represent debt. Over what interval is the amount increasing?
If the line has a positive slope, it means that the amount is increasing, and if it has a negative slope, it means that the amount is decreasing.
Based on the given information, the function models the amount of money a new business has made over x months. Therefore, we can assume that the function is a linear function, and its graph is a straight line.
Given that negative values represent debt, we can assume that the slope of the line is positive over the interval where the function takes positive values. Therefore, the interval over which the amount is increasing is from zero to infinity, which means that the business is making money and not in debt.
It's essential to note that if the function has a negative slope over any interval, then the amount is decreasing, and the business is losing money. However, we cannot determine this information from the given function's information.
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$3,900 at 1% compounded
annually for 6 years
_____________________________
A = P (1 + 1%) n = 3,900 (1 + 1%) ⁶= $4,139.92_____________________________
Among 130 pupils, 30 liked both biscuits and chocolates, 10 liked neither and twice as many as liked biscuits liked chocolates.
I) How pupils liked: chocolates, biscuits and exactly one of the two.
The number of pupils who liked both biscuits and chocolates is 30.
The number of pupils who liked neither biscuits nor chocolates is 10.
Let's assume that the number of pupils who liked only biscuits is x, and the number of pupils who liked only chocolates is y.
According to the problem, twice as many pupils liked chocolates as those who liked biscuits. Mathematically, we can write this as:
y = 2x
Now, let's find the total number of pupils who liked at least one of the two:
Total = P(Biscuits) + P(Chocolates) - P(Biscuits and Chocolates)
Total = x + y + 30
Total = x + 2x + 30
Total = 3x + 30
We know that the total number of pupils is 130, and the number of pupils who liked neither is 10. Therefore,
Total = P(All pupils) - P(Neither)
130 = x + y + 30 + 10
130 = x + y + 40
130 - 40 = x + y
90 = x + y
We can now solve these two equations to get the values of x and y:
3x + 30 = 90
3x = 60
x = 20
y = 2x = 40
Therefore, 20 pupils liked only biscuits, 40 pupils liked only chocolates, and 30 pupils liked both biscuits and chocolates. And, 40 pupils liked exactly one of the two.
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A newspaper for a large city launches a new advertising campaign focusing on the number of digital subscriptions. the equation s(t)=31,500(1.034)t approximates the number of digital subscriptions s as a function of t months after the launch of the advertising campaign. determine the statements that interpret the parameters of the function s(t).
"t" increases, and the number of digital subscriptions grows exponentially at a rate of 3.4% per month.
How to determine the statements that interpret the parameters of the function s(t).The function s(t) = 31,500(1.034)^t gives an approximation of the number of digital subscriptions s as a function of t months after the launch of the advertising campaign.
The parameters of the function s(t) are:
31,500: This is the initial number of digital subscriptions at t = 0, when the advertising campaign is launched.
1.034: This is the growth rate of the number of digital subscriptions per month. It represents the percentage increase in the number of subscriptions each month due to the advertising campaign. Specifically, each month the number of subscriptions is multiplied by 1.034, which is the same as increasing it by 3.4%.
t: This is the time in months after the launch of the advertising campaign. It is the independent variable of the function that determines the number of digital subscriptions at any given time t.
Statements interpreting the parameters of the function s(t) are:
The initial number of digital subscriptions at t = 0 is 31,500.
For every month after the launch of the advertising campaign, the number of digital subscriptions increases by 3.4%, or a factor of 1.034.
The parameter t represents the time in months after the launch of the advertising campaign. As t increases, the number of digital subscriptions grows exponentially at a rate of 3.4% per month.
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In a hypothesis test for a mean in one population, where you have H subscript 0 colon space mu space equals space 40 comma space H subscript A colon space mu space not equal to space 40 and the population standard deviation is sigma space equals space 12, what are the critical value(s) of the sample mean x with bar on top if your sample size is 36 and the significance level alpha = 0. 05?
Group of answer choices
Using the t-distribution table with a sample size of 36 and a significance level of 0.05, we find the critical t-value to be ±2.03 (with 34 degrees of freedom, which is n-1).
What are the critical values of the sample mean for a hypothesis test with a sample size of 36, population standard deviation of 12, significance level of 0.05, and null hypothesis of μ = 40?
To explain, we use the t-distribution to find the critical values because the population standard deviation is known. Since the alternative hypothesis is two-tailed (H_A: μ ≠ 40), we need to find two critical values.
With a sample size of 36, the degrees of freedom are 34 (n-1), so we use a t-distribution table with 34 degrees of freedom and a significance level of 0.05. From the table, we find the critical t-value to be ±2.03.
Therefore, if the calculated t-value falls outside of this range, we can reject the null hypothesis H0: μ = 40 in favor of the alternative hypothesis H_A: μ ≠ 40.
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The target to the right is in your backyard. What is the probability of hitting the bulls eye (center circle) when you shoot an arrow? The radius of the bulls eye is 2ft and the radius of the target is 6ft. (Use 3. 14 for pi)
The probability of hitting the bulls eye (center circle) when we shoot an arrow with radius of the bulls eye is 2ft and the radius of the target is 6ft is 11.1%.
Assuming that we are shooting randomly at the target and the arrow can land anywhere within the target area, the probability of hitting the bull's eye (center circle) can be calculated as the ratio of the area of the bull's eye to the area of the entire target.
The area of the bull's eye can be calculated as follows:
Area of bull's eye = π x (radius of bull's eye)²
Area of bull's eye = 3.14 x 2²
Area of bull's eye = 12.56 square feet
The area of the entire target can be calculated as follows:
Area of target = π x (radius of target)²
Area of target = 3.14 x 6²
Area of target = 113.04 square feet
Therefore, the probability of hitting the bull's eye can be calculated as:
Probability of hitting bull's eye = Area of bull's eye / Area of target
Probability of hitting bulls eye = 12.56 / 113.04
Probability of hitting bulls eye = 0.111 or approximately 11.1%
So, the probability of hitting the bull's eye (center circle) when we shoot an arrow randomly at the target is approximately 11.1%.
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4. Question: How can an antiderivative of a velocity function be used to find displacement of the body? Question: If velocity is negative, how does this impact the problem of finding displacement? 5.
If velocity is negative,The body is moving backwards instead of forwards, so the displacement will be measured as a negative value.
An antiderivative of a velocity function can be used to find displacement of the body by integrating the velocity function over a given time interval. The result of this integration will give the total displacement of the body over that time interval.
If the velocity is negative, it means that the body is moving in the opposite direction to the positive direction of the coordinate system. This has an impact on the problem of finding displacement because the displacement will also be negative. In other words, the body is moving backwards instead of forwards, so the displacement will be measured as a negative value.
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can someone help me please
The circumference of a circle is the distance around the edge or perimeter of the circle.
What is the circumference of a circle?1) Radius = 5cm/2 = 2.5 cm
2) Radius = 28 mm/2 = 14 mm
3) Radius = 3 1/2 m * 1/2 = 3/4 m
4) diameter = 2 * 6cm = 12 cm
5) diameter = 2 * 2m = 4 m
6) diameter = 2 * 0.8 ft = 1.6 ft
Circumference can be calculated using the formula:
C = 2πr
7) circumference = 2πr = 2 * 3.14 * 10/2 = 31.4 in
8) circumference = 2 * 7 * 3.14 = 43.96 in
9) Circumference = 2 * 3.14 * 18/2 = 56.52 in
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Triangle XYZ undergoes a transformation to produce triangle XYZ. The coordinates of both triangles are shown.
X'(6,-1)
X(6, 1)
Y(3,4) Y'(3.-4)
Z(-2,0)→ Z'(-2,0)
Which of the following best describes the transformation?
The transformation of the triangle is reflection over the x-axis
Given data ,
Let the transformation be represented as A
Now , the triangle is given as XYZ
where the coordinates are X ( 6 , 1 ) , Y ( 2 , 4 ) and Z ( -2 , 0 )
Now , the coordinates of the transformed triangle is
X' ( 6 , -1 ) , Y' ( 3 , -4 ) and Z' ( -2 , 0 )
The reflection of point (x, y) across the x-axis is (x, -y)
Hence , the transformation is reflection over x-axis
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Mr. vara is designing post caps in the shape of a square pyramid for a fence that he just built in his backyard. the caps are solid wood and each one has a volume of 94.5 cubic centimeters.
If Mr. Vara's square pyramid post caps have a volume of 94.5 cubic centimeters, and he assumes that the height and side length are equal, then the side length of each cap should be approximately 6.04 centimeters.
Mr. Vara is designing post caps in the shape of a square pyramid for his fence. The caps are solid wood and have a volume of 94.5 cubic centimeters. To calculate the dimensions of the pyramid, we need to use the formula for the volume of a square pyramid, which is V = (1/3)bh, where b is the area of the base and h is the height of the pyramid.
Since the caps are square pyramids, the base is a square. Let's call the side length of the base s. Then the area of the base is s². We can rearrange the formula for volume to get h = (3V)/b. Plugging in the given volume of 94.5 cubic centimeters, we get:
h = (3 x 94.5) / s²
h = 283.5 / s²
We still need to find the side length s. We can use the fact that the volume of the pyramid is also equal to [tex](1/3)s^{2h[/tex]. Plugging in the volume and height from above, we get:
94.5 = (1/3)s²(283.5 / s²)
94.5 = 94.5
This equation simplifies to 1 = 1, which doesn't give us any information about s. However, we can make an assumption about the dimensions of the pyramid. Let's say that the height h is equal to the side length s. Then we can solve for s using the volume formula:
[tex]94.5 = (1/3)s^{2s[/tex]
94.5 = (1/3)s³
283.5 = s³
s = 6.04
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CAN somebody pl help
The expression 8(4 - π) yd² is the area of the of the shaded region in terms of π.
How to evaluate for the area of the shaded regionThe area of the shaded region is the area of the semicircle subtracted from the area of the rectangle
radius of the semicircle is also the width of the rectangle, so;
area of the rectangle = 8 yd × 4 yd = 32 yd²
area of the semicircle = (π × 4 yd × 4 yd)/2
area of the semicircle = 8π yd²
area of the shaded region = 32 yd² - 8π yd²
area of the shaded region = 8(4 - π) yd²
Therefore, the expression 8(4 - π) yd² is the area of the of the shaded region in terms of π.
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bacteria in a dirty glass triple every day. if there are 25 bacteria to start, how many are in the glass after 15 days
Answer:
Step-by-step explanation:
25x3x15
HELP ME PLEASE I DON'T UNDERSTAND
Answer:
34/73
Step-by-step explanation:
37 + 34 + 2 = number of customers = 73
73 is our denominator.
34 is the number of people who used a credit card.
34 is our numerator.
Put the two together, and you get 73! Enjoy!