The volume of a cylinder is 50πx
We know that
The volume (V) of a cylinder is,
V = πr²h
where
r is the radius of the cylinder
h is the height of the cylinder
From the question, we have
a cylinder with diameter 10 and height of 2x.
r = 10/2 =5
V = πr²h
V = π*5²*2x
V = 50πx
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Suzette ran and biked for a total of 50 mi in 4 h. Her average running speed was 5mph and her average biking speed was 15 mph.
Let x= total hours ran
Let y= total hours biked
How many hours did suzette run?
How many hours did she bike?
In total 4 hours Suzette ran for 1 hour and biked for 3 hours having average speed 5mph and 15mph respectively.
What is Average Speed?
Average speed is defined as total distance covered by the body divided by the time taken.
Average speed = Total distance covered/ total time taken
According to the given question:
Let x = total hours ran and y = total hours biked
Total time she ran and biked = 4h
∴ x + y = 4 ----- 1)
Total distance she biked and ran = 50 miles
Now, average running speed = 5 mph
Distance she ran = 5x
Similarly average biking speed = 15 mph
Distance she biked = 15y
∴ 5x + 15y = 50 ----- 2)
Solving 1) and 2) to get the values of x and y
Substituting x = 4 - y from 1) in 2)
5 (4 - y) + 15y = 50
On solving further we get y = 3
Substituting y = 3 to get x
x = 4 - 3
x = 1
Hence the Suzette ran for 1h and biked for 3h.
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the breaking strengths of a random sample of 20 bundles of wool fibers have a sample mean 436.5 and a sample standard deviation 11.9. (a) construct 90%, 95%, and 99% confidence intervals for the average breaking strength of the wool fibers. (b) compare the widths of the three confidence intervals. at which level of confidence do you have the widest interval? (c) do you think it is plausible that the average breaking strength is equal to 450?
With the help of standard deviation we can conclude our answer.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD.acc to our question-
total sample of wool fibres = 20thus the sample mean = 436.05hence the sd= 11.9learn more about standard deviation here:
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The geometric mean of a number and nine times the number is 30. What is the number?
What are the correct set of factors for the given equation?
1. 4x² - 11x - 3=0 18
A (2x + 1)(2x − 3)
B (4x + 1)(x − 3)
C (4x − 3)(x + 1)
Give the numerical coefficient of the term.
xw
The numerical coefficient is _____.
Answer:
x
Step-by-step explanation:
The numerical coefficient is x.
Given m || n, find the value of x.
(8x+9)°
81⁰
I need help I don’t understand how it’s wrong
==========================================
Explanation:
If it is possible to draw a single vertical line through more than one point on the blue graph, then that graph is not a function. We consider it failing the vertical line test. Such a thing happens in the middle of the top row (graph 2). A vertical line intersects the sideways parabola at more than one point.
Recall a function is when any given input leads to exactly one output. We can't have the input x = 4 lead to both y = 1 and y = -3 at the same time for instance.
Graph 4 is another instance where we don't have a function for similar reasoning. This graph fails the vertical line test. So does graph 6.
The other graphs (1, 3, and 5) all pass the vertical line test since it's not possible to draw a single vertical line to intersect through more than one blue point.
a sample of 1,400 american households was asked if they planned to buy a new car next year. of the respondents, 34% indicated they planned to buy a new car next year. construct a 90% confidence interval of the proportion of american households who expect to buy a new car next year.
The proportion of American households who expect to buy a new car next year is[0.3191, 0.3609].
The Four answer choices:
[0.3152, 0.3648]
[0.3191, 0.3609]
[0.3394, 0.3406]
[0.3354, 0.3446]
According to the survey, 1,400 American households are expected to buy a new car next year. According to respondents, 34% plan on buying a new car next year.
The confidence interval for a population proportion is given by the following equation for large random samples
Sample proportion ± z × [tex]\frac{\sqrt{(sample proportion(1-sample proportion)}}{n}[/tex]
whereas z is a multiplier number that comes from the normal curve and determines the level of confidence.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
When using re-grouping to solve 21 x 43, what are the four products that would be calculated and then added?
800 + 40 + 6 + 3
80 + 40 + 60 + 3
800 + 40 + 60 + 3
800 + 3
Using re-grouping to solve 21 x 43, the four products that would be calculated and then added is: 800 + 40 + 60 + 3.
How to find the products?Given data:
21 x 43
Now let make use of re-group to find the for product
21 x 43
So,
20 +1 = 21
40 + 3 =43
Hence,
(20+1) × (40+3)
Expand
(20 × 40) + (1 × 40) + (20 ×3) + (1 ×3)
800 + 40 + 60 + 3
= 903
Check:
21 x 43 = 903
800 + 40 + 60 + 3 =903
Therefore the correct option is C.
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Members of the track team can run 400 meters in an average time of 58.2 sec. The fastest and slowest times varied from the average by 6.4 sec.
Write an absolute value equation to model this equation.
The absolute value equation modelling this situation is presented as follows:
|x - 58.2| = 6.4.
What is the absolute value of a number?The function giving the absolute value of another function is defined by the piece-wise rule presented as follows:
|f(x)| = f(x), f(x) ≥ 0.|f(x)| = -f(x), f(x) < 0.The result is never negative, as the function gives the distance of the function f(x) from the origin, which is the point in which f(x) = 0.
The difference between both the fastest and the slowest time from the average time of 58.2 seconds is of 6.4 seconds, hence the absolute value equation is given as follows:
|x - 58.2| = 6.4.
Which can be solved applying these following rules:
x - 58.2 = -6.4.x - 58.2 = 6.4.To find the fastest and slowest times, respectively.
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which is a net for this triangular prism
Answer:
this One...............
The handle of a car jack is moved 75cm and the car is lifted 2.5 cm. What is the ideal mechnical advantage of this car
Jack?
The ideal mechanical advantage of this car Jack: 30cm
What is Ideal mechanical advantage?
The length of the effort arm of a lever divided by the length of the resistance arm represents the optimal mechanical advantage. The IMA is typically calculated as the resistance force (Fr) divided by the effort force (Fe). IMA is also equal to the product of the load's travel distance (dr) and the distance over which the effort is applied (de).
The Handle of the car jack = 75cm
The car lifted by the jack = 2.5cm
According to the formula:
Ideal mechanical advantage = The resistance force / The effort force
or, (Fr/Fe)
IMA = 75 / 2.5
IMA = 30cm
Hence, Ideal mechanical advantage of the car jack = 30cm
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Serena just started working at the local salon. She is paid $9.85 per hour and earns, on
average, $58.50 in tips each day. Roseline just started working at a bank. Since she
does not receive tips, she earns $16.35 an hour. The system of equations
{y=9.85x+58.50 y=16.35x can be used to represent the amount of money earned, y,
each day for working x hours.
Determine the number of hours Serena and Roseline have to work to earn the same
amount of money.
The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Serena recently began working at the nearby salon. By and large, $58.50 in tips every day. Roseline recently began working at a bank. Since she doesn't get tips, she procures $16.35 60 minutes. The arrangement of conditions {y = 9.85x + 58.50 and y = 16.35x} can be utilized to address how much cash is procured, y, every day for working x hours.
The number of hours Serena and Roseline have to work to earn the same amount of money will be given as,
16.35x = 9.85x + 58.5
6.5x = 58.5
x = 9 hours
The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.
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can someone help pls
What is the value of -2|6x - y| when x = -3 and y = 4?
O-44
O-28
O 28
O 44
Answer:
-44
Step-by-step explanation:
-2|6 * -3 - 4|
-2|-18-4|
-2|-22|
-2 * 22
-44
Show that a sum of the angles of a polygon could be 1800 and not 2000
Answer:
150
Step-by-step explanation:
The sum of the interior angles, in degrees, of a regular polygon is given by the formula 180(n – 2), where n is the number of sides. The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be 180(12 – 2) = 180(10) = 1800.
Can anyone write the equation of the graph?
The equation of given graph is y = |x - 3| + 5.
The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.
Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.
As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.
So, by putting the value of vertex in general equation we get the equation of the graph,
y = |x - 3| + 5
Therefore, the equation of given graph is y = |x - 3| + 5.
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if our circadian clocks are not reset each morning by exposure to light, they: a. tend to run a cycle that is a little longer than 24 hours b. tend to run a cycle that is a little shorter than 24 hours c. tend to run on a 12-hour cycle d. still run exactly on a 24-hour cycle
If our circadian clocks are not reset each morning by exposure to light, they a. tend to run a cycle that is a little longer than 24 hours.
Chronobiology, the study of the body's circadian rhythms, contends that our daily routine, including when we eat, exercise, go to bed, and are exposed to light, may have a significant impact on how our bodies function on a day-to-day basis.
According to the National Institute of General Medical Sciences, circadian rhythms are the normal physical, mental, and behavioral changes that take place in the body on a 24-hour cycle, typically in reaction to light and darkness. One illustration is resting at night and remaining awake during the day.
You might not be able to avoid daytime sleep and evening work if you work an overnight shift or other irregular hours. According to Wright, those people should pay extra close attention to making other healthy decisions a priority, such as getting enough exercise and quitting smoking.
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Mariyah wants to enlarge a triangle with sides of 3 inches, 6 inches, and 6 inches. If the shortest side of the new triangle is 13 inches, how long will the other two sides be?
The other sides of the new triangle are 13, 26 and 26 inches as calculated by the properties of similarity.
We know that when two triangles are similar then the ratio of the sides are also equal.
Let the original triangle be ΔABC and the new triangle be ΔXYZ
So from the property of similarity.
AB/XY = BC /YZ = CA/ ZX
Now it is given AB = 3 inches
XY = 13 inches
Hence AB/XY = 13/3
Hence YZ = 13 / 3 × 6 =26 inches
Again ZX = 26 inches
Similar triangles have parallel sides that are proportional to one another and parallel angles that are identical to one another.
Triangles can have different diameters despite having comparable exteriors. Triangles that are congruent and similar to each other usually don't match up.
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25) If a number, n, divided by 8 equals 2.5, what is n?
26) The sum of a number, n, and 6.05 is 12.4. What is n?
27) Stacy is one-fourth as old as her mother. If Stacy's mother is 36, how old is Stacy?
28) One-third of a painting job takes 24 hours. How long will it take to finish the entire job?
The solutions for the equations in each of the questions given are as follows;
25). The number, n in which case equals 2.5 when divided by 8 is; n = 20.26). The number n which sums up with 6.05 to equal 12.4 is; n = 6.35.27). Stacy's age as required is; 9 years.28). The entire job takes 72 hours.What is the solution for the given equations?It follows from the task content that the solution for all of the given word problems are to be determined.
25. If a number, n, divided by 8 equals 2.5, what is n?
The algebraic representation is; n/8 = 2.5.
Hence, the value of n is; n = 8 × 2.5 = 20.
26. The sum of a number, n, and 6.05 is 12.4. What is n?
The algebraic representation is; n + 6.05 = 12.4.
Hence, the value of n is; n = 12.4 - 6.05 = 6.35.
27. Stacy is one-fourth as old as her mother. If Stacy's mother is 36, how old is Stacy?
The algebraic representation is; 36/4 = n.
Hence, Stacy's age, n is; n = 9.
28. One-third of a painting job takes 24 hours. How long will it take to finish the entire job?
The algebraic representation is; n/3 = 24.
Hence, the value of n is; n = 3 × 24 = 72 hours.
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can you please help me find the measure of an exterior angle of a regular hexagon?
thanks
The measure of each exterior angles of a regular hexagon is 60 degrees
The interior angle of the regular polygon is
d = 180(n - 2) / n
Where d is the measure of interior angle
n is the number of sides
The number of sides in a regular hexagon
d = 180(6 - 2) / 6
= 180×4 / 6
= 720 / 6
=120 degrees
The each interior angle of the regular hexagon is 120 degrees
The measure of exterior angle = 180 - The measure of interior angle
= 180 - 120
= 60 degrees
Hence, the measure of each exterior angles of a regular hexagon is 60 degrees
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dean halverson recently read that full-time college students study 20 hours each week. she decides to do a study at her university to see if there is evidence that students study an average of more than 20 hours each week. a random sample of 31 students were asked to keep a diary of their activities over a period of several weeks. it was found that the average number of hours that the 31 students studied each week was 22.4 hours. the sample standard deviation of 3.7 hours.find the p -value. the p -value should be rounded to 4-decimal places.
Dean halverson recently read that full-time college students study 20 hours each week. 0.000519 is the p -value.
How to find the p-value ?
Given :
Population mean, μ = 20
Sample mean, xbar = 22.4
Sample standard deviation, s = 3.7
Sample size, n = 31
The hypothesis :
H0 : μ = 20
H0 : μ > 20
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (22.4 - 20) ÷ (3.7/√(31))
T = 2.4*5.6 ÷ 3.7
Test statistic = 3.632
Using the Pvalue calculator :
df = n - 1 = 31 - 1 = 30
Pvalue(3.632, 30) = .000519.
The p-value is .000519.
The result is significant at p < .05
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PLEASE HELP MEE!
Solve x2 – 2x = 15 by applying the quadratic formula.
victor, a student at um, conducted a similar survey among undergraduate students at the university of michigan using a random sample of the same size from the study conducted at cornell university and obtained the same sample proportion. the undergraduate student body at the university of michigan is almost twice as large as the undergraduate student body at cornell university. victor is concerned that the computation of the margin of error for a confidence interval for the population proportion will be affected by the population size. do you agree with victor's concern?
Yes, Victor needs to have similar portion of the population in the sample.
What is population size?
The number of objects inside a geographical area that has been arbitrary assigned as the population size.
In a fair, unbiased poll
Population proportion plus random error equals sample proportion.
According to the Normal Approximation, the standard deviation of the distribution of these random mistakes across all feasible samples is
[tex]\sqrt{\frac{\text{Population proportion}(1-\text{Population proportion})}{n}}[/tex]
The sample estimate's variance from the actual population value is known as the random error. Numerous alternative summaries, such as sample averages or discrepancies between two sample proportions or averages, are likewise consistent with the observation that random mistakes follow the normal curve.
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Find the perimeter of the parallelogram. (please answer asap! ty!)
Perimeter of the parallelogram is 20 units.
According to question,
3 + x = 2a - 4
x = 2a - 4 - 3
x = 2a - 7
Diagonals in a parallelogram bisects each other.
Therefore, 2a - 7 = 3
2a = 3 + 7
2a = 10
a = 10/2
a = 5
a - 1 = 4b - 6
5 - 1 = 4b - 6
4 = 4b - 6
4b = 4 + 6
4b = 10
b = 10/4
b = 5/2
Opposite sides of a parallelogram are equal.
Therefore, c - 2 = 2b
c - 2 = 2(5/2)
c - 2 = 5
c = 5 + 2
c = 7
Sides of parallelogram,
Side 1 = 12 - c
= 12 - 7
= 5
Side 2 = c - 2
= 7 - 2
= 5
Perimeter of parallelogram = 2(length of side 1 + length of side 2)
= 2(5 + 5)
= 2 * 10
= 20
Hence, perimeter is 20 units.
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According to the fundamental theorem of algebra, how many zeros does the function f(x) = 5x - 9 have?
The algebraic fundamental theorem states that there are 12 zeros in the function f(x) = 15x12 + 41x9 + 13x2 10.
What is fundamental theorem?Theorem that connects the ideas of differentiating a function (calculating the gradient) and integrating a function is known as the fundamental theorem of calculus (calculating the area under the curve). With the exception of a constant value that depends on where one starts to compute area, the two procedures are inverses of one another.One of the antiderivatives (also known as an indefinite integral), let's say F, of some function f, may be derived as the integral of f with a variable bound of integration, according to the first section of the theorem, which is frequently referred to as the first fundamental theorem of calculus. This indicates that continuous function antiderivatives existacc to our question-
The degree that we need to identify in a polynomial is the largest exponent used in the equation. In this case, 15x¹², has the largest exponent. It is the degree of n used to determine the number of zeros.Thus, n = 12 so number of zero is also 12.hence,there are 12 zeros
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i need help with this asap please!!!
Answer:
54°
Step-by-step explanation:
m and the 54° angle are VERTICAL ANGLES. That means they are the same measure.
Answer:
Step-by-step explanation:
54 degree
f(x) = −3 x 2+ 18x − 27
Answer:
18x−33−f(x)=0
Step-by-step explanation:Solve for f by simplifying both sides of the equation, then isolating the variable.
. Kendra has a painting canvas that is 23 inches wide by 33 inches high. She painted a red
rose, which covered 30% of the canvas. What was the area of the canvas which was
covered by the red rose?
Answer:
227.7 in²
Step-by-step explanation:
You want to know the area that is 30% of a canvas that is 23 inches by 33 inches.
AreaThe area of the canvas is the product of its length and width.
A = LW
A = (33 in)(23 in) = 759 in²
RoseThe rose covers 30% of that area, so an area of ...
rose = 0.30 × 759 in² = 227.7 in²
The area of the canvas covered by the rose was 227.7 square inches.
