The function notation for the volume of the box is V(a) = (L-2a)(W-2a)(a). However, we need to know the dimensions of the paper in order to determine the volume of the box when the cutout length is 0.8 inches.
To represent the volume of the box (in cubic inches) using function notation, we can use V(a) where "a" represents the cutout length (in inches). To determine the volume of the box when the cutout length is 0.8 inches, we simply substitute 0.8 for "a" in the function V(a). However, we need to know the dimensions of the paper in order to determine the function itself.
Let's assume that the length of the paper is "L" inches and the width is "W" inches. When squares of length "x" are cut out from each corner, the length of the box will be L-2x and the width will be W-2x. The height of the box will be x inches. Therefore, the volume of the box will be V(a) = (L-2a)(W-2a)(a). Since we don't know the dimensions of the paper, we cannot determine the exact value of V(0.8).
So, the volume of the box when the cutout length is 0.8 inches is represented by the function f(0.8) = (L - 1.6)(W - 1.6)(0.8) in cubic inches.
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Find the final value of $2000 investment at an interest rate of 2%compounded quarterly (4 times a year) for 8 years
Answer:
[tex]\Huge \boxed{\boxed{\texttt{\bf{\$2346.09} } } }[/tex]
Step-by-step explanation:
We can use the compound interest formula to get the final value of a $2000 investment at an interest rate of 2% compounded quarterly for 8 years, using:
[tex]\LARGE \boxed{\tt{A = P(1 + \frac{r}{n})^{nt}}}[/tex]
The final amount is A.P stands for the initial principal, in this case $2,000The yearly interest rate is given as r (0.02 for 2%).The value of n determines how many times interest is compounded annually (4 for quarterly).t represents the time in years (8 years).Substituting the values:
[tex]\tt{A = 2000(1 + \frac{0.02}{4})^{4 \times 8}}[/tex][tex]\tt{ A = 2000(1 + 0.005)^{32}}[/tex][tex]\tt{A = 2000(1.005)^{32}}[/tex][tex]\texttt{ A $\approx$ 2346.09 (rounded to 2 decimal places)}[/tex]So, the final value of the investment after 8 years would be approximately $2346.09.
________________________________________________________
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Two thirds of a certain number plus five equals ten less than the same number, what is the number?
The calculated value of the number is -45
Calculating the value of the number?From the question, we have the following parameters that can be used in our computation:
Two thirds of a certain number Plus five Equals ten less than the same numberRepresent the number with x
So, we have the following equation
2/3x + 5 = x - 10
Collect the like terms
This gives
2/3x - x = -10 - 5
When the like terms are evaluated, we have
1/3x = -15
So, we have
x = -45
Hence, the value of the number is -45
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2. After running the appropriate statistical tests, Jack finds that life satisfaction was __________ in the older adults (M = 4.9, SD = 1.2) than in middle-aged adults (M = 4.1, SD = 1.8), t(58) = 2.03, p = .047, 95% CI [0.01, 1.59], d = .52. A. From these statistical results, what conclusions can Jack make? Comment on whether there are statistically significant differences between the groups and how you know. B. What should Jack decide about the hypotheses? C. What does the "t(58) = 2.03" tell us? D. What can we conclude from the confidence interval? E. What does the effect size tell us?
A. From the statistical results, Jack can conclude that there is a statistically significant difference between the life satisfaction of older adults and middle-aged adults. This is evidenced by the t-value of 2.03 and p-value of .047, which fall below the standard cutoffs for statistical significance. The 95% confidence interval also supports this conclusion, as it does not include zero.
B. Based on these results, Jack should reject the null hypothesis and accept the alternative hypothesis that there is a difference in life satisfaction between older adults and middle-aged adults.
C. The "t(58) = 2.03" indicates the t-value of the statistical test, which is a measure of the difference between the means of the two groups divided by the standard error of that difference. In this case, the t-value of 2.03 suggests that the difference in life satisfaction between the two groups is larger than would be expected by chance.
D. The confidence interval tells us that there is a 95% chance that the true difference in life satisfaction between the two groups falls within the range of 0.01 to 1.59. This suggests that the difference between the two groups is likely not due to chance.
E. The effect size (d = .52) tells us that the difference in life satisfaction between the two groups is moderate in magnitude. This suggests that the difference is not only statistically significant but also practically meaningful.
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from a population with a variance of 441, s sample of 361 items is selected. what is the margin of error at 95% condifdence
The margin of error at 95% confidence is approximately 2.16.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
To find the margin of error at 95% confidence, we need to use the following formula:
Margin of error = z * (σ/√n)
where:
z = the z-score associated with the desired level of confidence (in this case, 95% confidence corresponds to a z-score of 1.96)
σ = the population standard deviation
n = the sample size
Given that the population variance is 441, the population standard deviation is the square root of 441, which is 21.
So, the margin of error is:
Margin of error = 1.96 * (21/√361)
= 1.96 * (21/19)
= 2.16 (rounded to two decimal places)
Therefore, the margin of error at 95% confidence is approximately 2.16.
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2. Find the area of a rectangle if the length is (x ^ 2 + 7x + 12)/(5x ^ 2 - 45); (10x - 10)/(x ^ 2 + 3x - 4) and the width is Write your answer as a simplified expression and remember to state restrictions!
[NEED ALL WORK]
The area of the rectangle based on the information given is A = 2 / (x - 3)
How to calculate the areaLength: (x² + 7x + 12) / (5x² - 45)
We can factor the numerator and denominator to simplify:
(x + 3)(x + 4) / 5(x - 3)(x + 3)
The (x + 3) factors cancel out, leaving:
(x + 4) / 5(x - 3)
Width: (10x - 10) / (x² + 3x - 4)
We can factor the denominator to simplify:
(x + 4)(x - 1)
So the width becomes:
10(x - 1) / (x + 4)(x - 1)
The (x - 1) factors cancel out, leaving:
10 / (x + 4)
Now we can multiply the length and width to get the area:
[(x + 4) / 5(x - 3)] * [10 / (x + 4)]
The (x + 4) factors cancel out, leaving:
2 / (x - 3)
The area of the rectangle is:A = 2 / (x - 3)
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An ice cream shop ordered waffle cones that have a height of 4 in and volume of 3
�
π
in3. The ice cream shop is trying to determine which size ice cream scoop will be the best fit for the waffle cones. Ice cream scoops come in different sizes and have different diameters. The #12 scoop has a 2. 5 in diameter and the #6 scoop has a 3 in diameter. Unfortunately, they are waiting on their order of waffle cones and they don't know the measure of the diameter
The ice cream shop could order a different size scoop with a diameter closer to 1.732 in for an even better fit.
Ice cream scoop will be the best fit for the waffle cones need to find out the diameter of the cones.
We can use the given height and volume of the cones to calculate the diameter using the formula for the volume of a cone:
V = (1/3) × π × r² × h
V is the volume r is the radius (which is half the diameter) and h is the height.
Rearranging the formula to solve for r we get:
r = √((3V) / (πh))
Substituting the given values of V = 3π in³ and h = 4 in we get:
r = √((3π) / (4π))
= √(3/4)
= 0.866 in
So, the diameter of the waffle cones is approximately 1.732 in (twice the radius).
Now we can compare this diameter to the diameters of the #12 and #6 scoops.
The #12 scoop has a diameter of 2.5 in is larger than the cone diameter of 1.732 in so it may not be the best fit.
The #6 scoop has a diameter of 3 in is larger than the cone diameter but closer in size so it may be a better fit than the #12 scoop.
The ice cream shop could order a different size scoop with a diameter closer to 1.732 in for an even better fit.
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if testing the claim that σ21≠σ22, what do we know about the two samples if the test statistic is f=1?
When testing the claim that σ21≠σ22, the null hypothesis states that the variances of the two populations are equal, while the alternative hypothesis states that the variances are not equal. To test this claim, we use an F-test, which involves calculating the ratio of the variances of the two samples.
If the test statistic is f=1, this means that the ratio of the variances is equal to 1. This indicates that there is no significant difference between the variances of the two populations. In other words, we cannot reject the null hypothesis that the variances are equal.
However, it is important to note that a test statistic of f=1 does not necessarily mean that the two samples are identical. It is possible for two samples to have slightly different variances that still result in a test statistic of f=1. Additionally, a sample size that is too small or too large can affect the accuracy of the F-test.
Overall, if the test statistic is f=1 when testing the claim that σ21≠σ22, we can conclude that there is not enough evidence to support the alternative hypothesis that the variances are different.
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You earn $15 per hour plus a commission equal to x percent of your sales as a cell phone sales representative.
What is your commission percentage (x) if you work 8 hours with sales of $1400 worth of merchandise and your total earnings
for the day is $176?
Using an equation, the commission percentage (x) that you earn if you work 8 hours with sales of $1,400 and total earnings of $176 for the day is 4%.
How the percentage is determined:The commission percentage can be determined by equating the normal earnings for the day and the sales commission to the total earnings.
An equation represents two or more mathematical expressions using the equal symbol.
The hourly rate of earnings = $15
The number of hours worked for the day = 8 hours
The commission percentage = x
The Sales for the day = $1,400
The total earnings for the day = $176
Equation:Total earnings = hourly rate x 8 hours + 1,400x
176 = 15 x 8 + 1,400x
176 = 120 + 1,400x
56 = 1,400x
x = 0.04
x = 4%
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The ages of the employees in Kathy’s office are: 54, 23, 42, 59, 61, 44, 44, 50, 39, 40, 37, 43, 51, 34, 41,
40, 35, 49, 55, 58, 36, 43.
a. What is the median age?
b. How old are the youngest and oldest employees?
c. What are the lower quartile, upper quartile, and interquartile range?
d. Sketch a box plot using the points you found.
a. The Median age is 43
b. Youngest employee: 34
Oldest employee: 61
c. The lower quartile (Q1) is the median of the lower half of the sorted list, and the upper quartile (Q3) is the median of the upper half. The interquartile range (IQR) is the difference between Q3 and Q1.
How to explain the informationa. The median age is the middle value when the ages are sorted. Since there are 21 employees, the median will be the 11th value:
Median age = 43
b. The youngest employee is the first value in the sorted list, and the oldest employee is the last value:
Youngest employee: 34
Oldest employee: 61
c. The lower quartile (Q1) is the median of the lower half of the sorted list, and the upper quartile (Q3) is the median of the upper half. The interquartile range (IQR) is the difference between Q3 and Q1.
Lower quartile (Q1) = Median of the lower half = (36 + 37) / 2 = 36.5
Upper quartile (Q3) = Median of the upper half = (51 + 54) / 2 = 52.5
Interquartile range (IQR) = Q3 - Q1 = 52.5 - 36.5 = 16
d. To sketch a box plot, we can represent the minimum, maximum, Q1, Q3, and median values on a number line:
Minimum: 34
Q1: 36.5
Median: 43
Q3: 52.5
Maximum: 61
The box plot will have a box from Q1 to Q3 with a line inside representing the median. The whiskers will extend from Q1 to the minimum and from Q3 to the maximum.
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if the average value of a continuous function f on the interval [−2, 4 ] is 12, what is ∫4−2f(x)8 dx?
The value of the integral ∫[4,-2]f(x)8 dx is -576.
What is the value of the integral ∫[4,-2]f(x)8 dx?If the average value of a continuous function f on the interval [−2, 4] is 12, it means that the definite integral of f(x) over the interval [−2, 4] is equal to 12 times the length of the interval, which is 6. In other words:
∫[-2,4]f(x) dx = 12(4-(-2)) = 72
Now we can use this information to evaluate the integral ∫[4,-2]f(x)8 dx. We can use the constant multiple rule of integration to pull out the constant 8 from the integral:
∫[4,-2]f(x)8 dx = 8 ∫[4,-2]f(x) dx
Since we already know that ∫[-2,4]f(x) dx = 72, we can evaluate the integral over the interval [4,-2] using the property of definite integrals that says:
∫[a,b]f(x) dx = -∫[b,a]f(x) dx
Therefore:
∫[4,-2]f(x) dx = -∫[-2,4]f(x) dx = -72
Substituting this value back into the original expression, we get:
∫[4,-2]f(x)8 dx = 8 ∫[4,-2]f(x) dx = 8(-72) = -576
Therefore, the value of the integral ∫[4,-2]f(x)8 dx is -576.
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Marine has a 6-inch-wide rectangular photograph. She wants to enlarge the photograph using the scale 1:5. What is the width of the enlarged photograph?
The enlarged photograph will be 30 inches in width and a proportional length.
Marine has a rectangular photograph that measures 6 inches in width. If she wants to enlarge the photograph using a scale of 1:5, this means that the size of the photograph will be increased by a factor of 5 in both width and height.
To determine the new width of the photograph, we can multiply the original width of 6 inches by 5, which gives us a width of 30 inches for the enlarged photograph.
It's important to note that while the width of the photograph will increase, the aspect ratio of the photograph will remain the same.
This means that the length of the photograph will also be increased by the same factor of 5.
Therefore, the enlarged photograph will be 30 inches in width and a proportional length.
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Use the Polygon Angle Sum Theorem to find the measure of x :
The required value of x for this polygon is - 90.
We know that,
Polygons are two-dimensional geometric figures with a fixed number of sides. A polygon's sides are made up of straight line segments that are joined end to end. As a result, the line segments of a polygon are referred to as sides or edges.
The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result.
A triangle with three sides is an example of a polygon. A circle is a plane figure, however it is not regarded a polygon because it is curved and lacks sides and angles.
As a result, we can argue that all polygons are 2d shapes, but not all two-dimensional figures are polygons.
Since,
Sum of interior angles of polygons = 360 degree
Therefore,
130 + x + 20 + 120 + 140 + x - 20 + 150 + x = 360
2x = 360 - 540
x = -180/2
x = -90
Thus,
The value of x = - 90
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find the distance between x and y . question content area bottom part 1 the distance between x and y is enter your response here.
To find the distance between x and y, we need to know their coordinates. Let's assume x is located at point (x1, y1) and y is located at point (x2, y2). The distance between them can be calculated using the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
The distance formula is derived from the Pythagorean theorem and can be used to find the distance between any two points in a plane. The formula involves taking the square root of the sum of the squared differences in x and y coordinates between the two points.
In order to find the distance between x and y, we need to know their coordinates and then apply the distance formula. It is a useful formula to know when working with geometric figures and can be applied in various real-life situations such as calculating the distance between two cities on a map.
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The distance between x and y can be calculated using the distance formula, which is √((x2 - x1)^2 + (y2 - y1)^2).
In order to find the distance between x and y, we need to know the coordinates or positions of x and y. Without this information, we cannot calculate the distance between them. Therefore, we cannot provide a specific answer to this question.
To use this formula, you need the coordinates of the points x and y (x1, y1) and (x2, y2). Plug the coordinates into the formula, then calculate the differences between the x and y values, square them, add them together, and finally, find the square root of the sum. This will give you the distance between x and y.
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7 1/4 divided by 3/8
Answer:
14/3
Step-by-step explanation:
Answer:
58/3
Step-by-step explanation:
7 1/4 ÷ 3/8
= 29/4 x 8/3
= 29 x 2/3
= 58/3
the miller school of business at ball state university claims to have a 73% graduate rate from its online mba program. a happy student believes that the 3-year graduation rate is higher than that. a sample of 500 students indicates that 371 graduated within three years. what is the lower limit for the 95% confidence interval for the true graduation rate? use decimals rather than percentages and round your answer to three decimal places.
The lower limit for the 95% confidence interval for the true graduation rate is 0.704.
What is confidence interval?The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level.
We can use the formula for the confidence interval for a proportion:
lower limit = sample proportion - z * √((sample proportion * (1 - sample proportion)) / sample size)
where z is the z-score corresponding to the desired level of confidence (95% in this case), and sample size is 500.
The sample proportion is 371/500 = 0.742.
The z-score for a 95% confidence level can be found using a standard normal distribution table or calculator, and is approximately 1.96.
Plugging in the values, we get:
lower limit = 0.742 - 1.96 * √((0.742 * 0.258) / 500)
lower limit = 0.704
Rounding to three decimal places, the lower limit for the 95% confidence interval for the true graduation rate is 0.704.
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what is the volume of a 5 sided pyramid with a height of 10 and the length of each bottom side is 8
Answer:
200cm3
Step-by-step explanation:
Volume is LxWxHL=8cm
W=5 cm
H=10cm
=200cm
find a square root of 340 modulo 437
One possible square root of 340 modulo 437 is 281.
To find a square root of a number modulo another number, we can use the Tonelli-Shanks algorithm. First, we check that 340 is a quadratic residue modulo 437 by calculating 340^((437-1)/2) mod 437, which gives 1. Then we can choose a starting value for the square root, such as 281, and use the Tonelli-Shanks algorithm to iteratively improve our estimate. After a few iterations, we should arrive at a more precise square root. Note that there may be multiple square roots, and this is just one example.
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Cross-sections, Surface Areas and Volumes of Solids
1. The surface area of the cone is 252.58 cm' with the radius of 6 cm. What is the slant
height of the cone? Round nearest tenth. Leave your answer in terms of pie
The slant height of the cone is 24 cm.
We are given that the surface area of the cone is 252.58 cm' with the radius of 6 cm.
The surface area of the cone is calculated through the equation as;
A = πr² + πrl
where r is the radius and l is the slant height.
Now Substituting the known values to the equation,
252.58 = π(6 cm)² + π(6 cm)(l)
l = 24 cm.
Thus, the slant height of the cone is 24 cm.
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i need help asap plsssss
Answer:
'x' only has one solution
Step-by-step explanation:
First multiply both sides by 'x^2'
40x = -5x^2
(bring both values to one side and factorize to solve for 'x')
5x^2 +40x=0
5x(x+8)=0
5x= 0 ; x+8 = 0
x=0 ; x=-8
x cannot equal to '0' as zero cannot be a denominator.
Hence, x=-8 is the only correct solution.
So, 'x' only has one solution.
Determine The General Solution
The solution is: The General Solution of the expression is: Cos x = 2/3
Here, we have,
Explanation:
Given expression:
3sinx = 2tanx
Find:
Simplify expression......
Computation:
By taking given trigonometric equation
⇒ 3sinx = 2tanx
Using substitution method...
⇒ sinx = [2/3]tax
⇒ sinx / tanx = 2/3
⇒ sinx / [sinx / cosx] = 2/3
⇒ [sinx × cosx] / sinx = 2/3
⇒ cosx = 2/3
Simplify expression
Cos x = 2/3
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complete question:
Determine the general solution of 3sin x=2tan x
A waterfall is n times the height of its picture on a postcard. Which equation represents the height ,y, of the waterfall picture is 7cm tall
To represent the relationship between the height of the waterfall and the height of its picture on a postcard, we can use the equation y = 7n.The correct answer is option A.
Here, 'y' represents the height of the waterfall, and 'n' represents the factor by which the waterfall is taller than the picture.
The equation states that the height of the waterfall, 'y', is equal to 7 multiplied by 'n'. Since the picture on the postcard is 7 cm tall, multiplying it by 'n' gives us the height of the waterfall.
For example, if the factor 'n' is 3, the height of the waterfall would be 7 cm * 3 = 21 cm. If 'n' is 5, the height would be 7 cm * 5 = 35 cm. The equation allows us to calculate the height of the waterfall for any given factor 'n'.
Using this equation, we can determine the height of the waterfall based on the height of its picture on the postcard, providing a simple and direct relationship between the two.
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The probable question may be:
A waterfall is n times the height of its picture on a postcard. Which equation represents the height, y, of the waterfall if the picture is 7 cm tall?
A. y = 7n
B. y = 7 + n
C. y = n - 7
D. y = 7 / n
some statistics instructors have students use an online homework system and some do not. final exam scores were recorded for a sample of statistic students who used an online homework system and were compared to the final exam scores from a sample of statistic students who did not use an online homework system. is there evidence that the students who used an online homework system did better on the final?
To determine whether there is evidence that the students who used an online homework system did better on the final exam than those who did not, we can perform a hypothesis test.
State the null hypothesis (H0) and alternative hypothesis (Ha)
H0: There is no difference in the final exam scores between students who used an online homework system and those who did not.
Ha: Students who used an online homework system scored higher on the final exam than those who did not.
Determine the level of significance (alpha). Let's assume a significance level of 0.05.
Collect the data and calculate the sample means and standard deviations for the two groups.
Conduct a t-test for independent samples to determine whether the observed difference in means between the two groups is statistically significant.
If the calculated p-value is less than the significance level (alpha), we can reject the null hypothesis and conclude that there is evidence that the students who used an online homework system did better on the final exam than those who did not. If the p-value is greater than alpha, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that there is a difference in the final exam scores between the two groups.
It's important to note that the results of a hypothesis test depend on the sample size, the variability of the data, and the assumptions made about the underlying population. Therefore, it's important to carefully evaluate the data and assumptions before making any conclusions.
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Can someone answer check please
Answer:
you got them all correct! good job :)
Step-by-step explanation:
find an equation of the tangent line to y=7sin(x) at x=π. (use symbolic notation and fractions where needed.)
To find the equation of the tangent line to the curve y = 7sin(x) at x = π, we first need to find the slope of the tangent line.
We can use the derivative of y with respect to x to find the slope:
dy/dx = 7cos(x)
At x = π, the value of the derivative is:
dy/dx = 7cos(π) = -7
So the slope of the tangent line at x = π is -7.
To find the equation of the tangent line, we also need to know the y-coordinate of the point on the curve where x = π.
y = 7sin(π) = 0
So the point on the curve where x = π is (π, 0).
Now we can use the point slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
Plugging in the values we found, we get:
y - 0 = -7(x - π)
Simplifying, we get:
y = -7x + 7π
So the equation of the tangent line to y = 7sin(x) at x = π is y = -7x + 7π.
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(LCM) of 24 and 64
The LCM of 24 and 64 is 192.
a car is driving at 55 kilometers per hour. how far, in meters, does it travel in 3 seconds? myopenmath
The car travels 45.84 meters in 3 seconds.
To solve this problem, we need to convert the speed of the car from kilometers per hour to meters per second since the time given is in seconds.
To do this, we can use the conversion factor that 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds.
So, 55 kilometers per hour is equal to (55 x 1000) / 3600 = 15.28 meters per second.
Now, we can use the formula: distance = speed x time
Plugging in the values, we get distance = 15.28 meters per second x 3 seconds = 45.84 meters.
Therefore, the car travels 45.84 meters in 3 seconds.
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Find the mean of 8,9,1
Answer:
6
Step-by-step explanation:
8+9+1 is 18, and since there are 3 numbers, we must divide 18 by 3, 2 which is 6
Answer: 6
Step-by-step explanation:
8+9+1 = 18
3 numbers
18/3 = 6
The radius of a circle is 3 m. Find its area in terms of pi
Answer:
9π m²
Step-by-step explanation:
area of circle = πr², where r is the radius.
area = π (3)²
= 9π m²
*MUST ANSWER ASAP PLS*
find the work done by f in moving a particle once counterclockwise around the given curve. f=(x−5y)i (5x−y)j c: the circle (x−4)2 (y−4)2=16
The work done by force f in moving a particle counterclockwise around the given curve is zero.
How much work is done by force f on the particle?The given force [tex]f = (x-5y)i + (5x-y)j[/tex] is a conservative force. A conservative force is characterized by having a curl of zero, indicating that it can be derived from a potential function. For conservative forces, the work done over a closed path is always zero.
In this case, the particle moves counterclockwise around the circle defined by [tex](x-4)^2 + (y-4)^2 = 16[/tex]. Since the force f is conservative, the work done by f on the particle is independent of the path taken and depends only on the initial and final positions of the particle.
As the particle completes one counterclockwise revolution around the circle, it returns to its initial position. Therefore, the work done by force f is zero, indicating that the force does not transfer any energy to or from the particle.
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