The height of the sand is changing when the height of the sand is 5 cm is 0.7848 in cm/sec
What is meant by volume?Volume is a measure of three-dimensional space that is occupied. It is frequently quantified numerically using SI-derived units (such as the cubic metre and litre) or various imperial units (such as the gallon, quart, cubic inch). The definition of length (cubed) is related to volume. The volume of a container is commonly understood to be its capacity; that is, the amount of fluid (gas or liquid) that the container can hold, rather than the amount of space it occupies.
Volume was measured in ancient times using similar-shaped natural containers, and later, standardized containers. Arithmetic formulas can easily calculate the volume of some simple three-dimensional shapes. Volumes of more complicated shapes can be calculated using integral calculus if a formula is provided.
The volume of the cylindrical is,
V = πr²h
V = volume
r = base radius
h = height
Calculate the difference between both sides of the equation in relation to time t. Because the radius r does not change over time, we can consider it a constant:
dv/dt = πr²(dh/dt)
Given,
dv/dt =555 cubic cm per second
r = 15
solve dh/dt:
555 = π(15)²(dh/dt)
dh/dt = 555(7/22)(1/225)
dh/dt =0.7848
The height of the sand is decreasing at a rate of 0.7848 in cm/sec
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decide whether the following situation is looking for part, the percent, or the whole.
81 of 270 pages in a book
PLEASE HELP quick it would help
81 of 270 pages in a book is a part of the situation.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
81 of 270 pages in a book.
Eighty one of two hundred seventy pages in a book.
In the given situation, A book has 270 pages in that we have taken 81 pages which are part of the book.
We have taken pat of the book,
In the given situation, book is whole and 81 is the part.
Hence 81 of 270 pages in a book is a part of the situation.
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Write an equation for the nth term of the arithmetic sequence 4, 7, 10, 13,
The equation for the nth term of the arithmetic sequence 4, 7, 10, 13 is aₙ = 3n + 1
How to find nth term of arithmetic sequence?Arithmetic sequence can be represented with the formula as follows:
aₙ = a + (n - 1)d
where
n = number of termsd = common differencea = first termTherefore, let's write the equation for the nth term of the arithmetic sequence 4, 7, 10, 13..
a = 4
d = 7 - 4 = 3
Therefore,
aₙ = 4 + (n - 1)3
aₙ = 4 + 3n - 3
aₙ = 3n + 4 - 3
aₙ = 3n + 1
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At school, 40% of the sixth grade students said that hip hop was their favorite kind of music. If 100 sixth grade students prefer hip hop music how many sixth graders are at the school
If 100 sixth grade students prefer hip hop music, the number of sixth graders at the school is 250.
How many sixth graders are at the school?Percentage is a measure of frequency that is used to express a number as as a fraction of 100. In order to change a value to percentage, multiply the number by 100. The sign that represents percentage is %.
In order to determine the number of sixth graders, divide the number of sixth graders that prefer hip hop music by the percentage.
Number of sixth graders = number that prefer hip hop / percentage
100 / 40%
100 / 0.4 = 250
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pls help me wit this
Can someone help me with this and a reason why the equation chosen?
2(f-25) = 86 is the equation use to find f, the cost of each drill set at full price.
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Given that, Ariana purchased two drill set from a sale, each of them costs $25 less than its original price,
If f is the original price, then she must have purchased it at (f-25) and for two sets it's 2(f-25)
She paid $86 for her purchase, so,
2(f-25) = $86
Hence, 2(f-25) = 86 is the equation use to find f, the cost of each drill set at full price.
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Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
The formula for nth term in the given arithmetic sequence is 10 - 3n
For an nth term in an arithmetic sequence
U(n) = a + (n - 1)d
Where n is the number of terms
a is the first term
d is the common difference
From the sequence above
a = 7
d = 4 - 7 = - 3
The formula for an nth term is
U(n) = 7 + (n - 1)-3
= 7 - 3n + 3
Hence, the formula for nth term is 10-3n
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Please help me
Slope=
Y- intercept=
Equation=
Slope:
The slope is found with m = (y2 - y1) / (x2 - x1).
You can use any two points, so I'd pick ones with positive x and y values.
Using (1,5) and (3,3):
m = (3 - 5) / (3 - 1) = (-2)/(2) = -1
The slope is -1.
To find the y-intercept, we can go to the point (-1,7) and use the slope of -1. A slope of -1 means that if x goes up by 1, then then y goes down by 1. So if we go from x=-1 to x=0, then the y-value of 7 will go down by 1.
y-intercept (0,6)
The equation in slope-intercept form is y = -x + 6, since we already found the slope and y-intercept.
Which rule explains why these triangles are congruent
Answer:
A
Step-by-step explanation:
∠ A = ∠ P
∠ C = ∠ R
AC = PR
If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.
The included side is the side between the vertices of the 2 angles.
Then the triangles are congruent by the ASA postulate
What is the size of an angle called a revolution
Answer:
Step-by-step explanation:
The size of the angle of one whole revolution is 360 degrees. A revolution describes the angle of a circular surrounding sector as it rotates! This means one full revolution is 360 degrees. And half of a revolution is 180 degrees!
marital status: of women according to the statistical abstract of the united states, 70.3% of females ages 20 to 24 have never been married. choose 5 young women in this age category at random. find the probability that a. none has ever been married
0.1717 is Probability that none has ever been married from selected 5 young women in age category at random.
In the question we have,
the number of females age 20 to 24 has never been married = 70.3%
the number of young women in this age category (20 to 24) at random = 5
We shall find out the probability that none has been maaried from selected group of 5 females.
Probability of female age 20 to 24 has never been married = 0.703
So, the probability that none has been married from selected group of 5 females ( p)= 0.703×0.703×0.703×0.73×0.73
= 0.1717
Therefore, The probability that none has ever been married is 0.1717.
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There is a number written on the board.
One student increased the number by 12.
Another student multiplied the number written
on the board by 3. The first student’s result is 2
greater than the second student's result. What
number is written on the board?
The number written on the board is 2 2/5
What are linear equations?A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0. where, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. where, x and y are variables, A and B are coefficients and C is a constant.
represent the number on the board by x, the result of the second student by y , therefore the result of the first student is 2y
solving for the first student, 12+x= 2y
for the second student , 3x= y
substituting 3x for y in first equation
12+ x= 2(3x)
12+x= 6x
collecting like terms
5x= 12
divide both side by5
x= 12/5= 2 2/5.
Therefore the number on the board is 2 2/5
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astudy showed that 33% of allfirms in couniry a are owned by women. you are phoning local businesses, assuming that the national percentage is true in your area. you call 3 fims. what is the probability that all three are owned by women?
There is a 0.33 percent chance that a woman is the owner of each of the firms identified. Therefore, there is a 0.036 percent chance that women own ALL three of the called businesses.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The probability that each of the firms called is owned by a woman is 0.33. Therefore, the probability that ALL three of the firms called are owned by women is:
percentage=0.33*0.33*0.33
percentage=0.035937
=0.036
There is a 0.33 percent chance that each of the businesses is run by a woman. As a result, there is a 0.036 percent chance that women own ALL three of the businesses mentioned.
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if the 90% confidence limits for the population mean are 45 and 55, which of the following could be the 99% confidence limits a) [48, 55] b) [49, 53] c) [42, 58] d) [46, 51] e) [49, 51] f) none of the above
The 99% confidence limit will be option B which is (45, 55)
90% confidence limits for the population mean are (46,54)
mean = 46+54 / 2 = 50.
the margin of error E = 54-46/2 = 4
For 90% Confidence Z- Critical value is = 1.645
But the margin of error
E = ZS/√n
4=(1.645)S/√n
S/√n = 4 / 1.645
= 2.4316
For 95% confidence Z-critical value is 1.96
A 95% confidence interval is = mean ± E
(50 ± 1.96) S/√n = (50 ± 1.96)×2.4316
= 50+ 4.7660
= 45.2340, 54.7660
= (45, 55)
Hence the correct option is B which is (45, 55) as the 99% confidence limit.
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help me please please please triangle 2222
The surface area of the triangular prism is 936 cm².
How to find the surface area of a triangular prism?In geometry, a triangular prism is a three-sided prism.
Therefore, the surface area of the triangular prism can be calculated as follows:
surface area of triangular prism = bh + L(x + y + z)
where
b and h are the base and height of the triangular baseL is the height of the prism.x, y and z is the side of the triangle.Therefore,
surface area of triangular prism = 24 × 18 + 7(18 + 30 + 24)
surface area of triangular prism = 432 + 7(72)
surface area of triangular prism = 432 + 504
surface area of triangular prism = 936 cm²
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we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can i. change the z value to a smaller number. ii. take a larger sample. iii. take a smaller sample.
Using the concepts of errors and measurement, we got that by taking a larger sample 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence.
In science, experimental errors may be caused due to the human inaccuracies like a wrong experimental setup in the science experiment or choosing the wrong set of people for the social experiment. Systematic error refers to that error which is actually inherent in the system of experimentation.
Hence, if we have calculated a 95% confidence interval for p and would prefer to have a smaller margin of error without losing any confidence. in order to do this, we can take a larger sample.
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WILL MARK BRAINLIEST
Suppose the polynomial function below represents the power generated by a wind turbine, where x represents the wind speed in meters per second and y represents the kilowatts generated. Interpret ƒ(10).
ƒ(x) = 0.08x3 + x2 + x + 0.26
Answer:f(10) or the power generated by the wind turbine at the wind speed of 10 m/s is 190.26 kW
why is it important to create a budget even if you don’t get a lot of money or if you have an irregular income?
Answer:
it is important because this will be helpful for your incomes, tax, bills etc. This also will plan for other things that you might pay like savings.
Step-by-step explanation:
Dennis spends 1.5 hours practicing guitar each
day. What is the total amount of time (in hours)
that Dennis spent practicing guitar after 8 days?
Dennis spent 12 hours practicing.
1.5 hours = 90 mins
90 mins x 8
720 mins = 12 hours
20 plants were measured and their heights were recorded in cm. Here are the heights: draw a frequency polygon to represent the data
(also, I just need b, I've done A)
Which of the following numbers could be the probability of an event?
1, -0.5, 0.29, 0.06, 1.18, 0
Question: The numbers that could be a probability of an event are_
(Use a comma to separate answers as needed.)
The probability of an event is 0.29,0.06. An event's probability is always between 0 and 1.
Explain about the probability?
When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.
-0.5 cant be a probability because it is less than 0
0.29 can be a probability because it is more than zero.
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The numbers that could be a probability of an event are 0.29 and 0.06
What is a probability?An event's probability is always between 0 and 1. (inclusive).
This implies:
There can be just one.
It must be zero or less.
Evaluation of Option (a) - 0.5
This cannot represent probability (b) 0.29 because it is less than 1,
This can be used to represent probability (c) 0.06 since it lies between 0 and 1.
This can be used to indicate probability (d) 1.18 since it is less than 1.
Given that this is larger than 1, it cannot be a probability (e) 0
A probability is not zero.
This ranges from 0 to 1, so it can be used to express probability.
Therefore, 0.29 and 0.06 can be used to indicate probabilities.
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1. the following two points are located on a line (-12, 6). and (4,6), find the slope of the line.
2. Solve for the value of x : 2/8 = 3/x+2
thank you! this assignment is graded on accuracy so please try your hardest!!
The slope of the linear equation is 0, and the solution of the second equation is x = 10.
How to find the slope of the line?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
slope = (y2 - y1)/(x2 - x1)
So if the line passes through (-12, 6) and (4, 6), the slope is:
slope = (6 - 6)/(4 + 12) = 0
The slope is 0.
2) How to solve the equation for x?
Here we have the equation:
2/8 = 3/(x + 2)
If we move the denominators we get:
2*(x + 2) = 3*8
2x + 4 = 24
2x = 24 - 4
2x = 20
x = 20/2 = 10
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write the missing number = 1/2 of 18
please help me !!!!
Answer:
a) 9b) 18Step-by-step explanation:
a) 1/2 of 18 = ?
→ 1/2 of 18
→ (1/2) × 18
→ 18/2 = 9
So, answer is 9.
b) 2/3 of 27 = ?
→ 2/3 of 27
→ (2/3) × 27
→ 54/3 = 18
So, answer is 18.
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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Whats the answer to question 10?
Answer:
[tex]y = |x - 3|+ 5[/tex]
y = |x| is the equation that forms the triangular shape. -3 and 5 reflect the shape to that position.
Solve for x.
x/2 + 1 = √3
The solution of x when solving x/2 + 1 = √3 is :
x is 2√3 - 2 .
What is the solution of x?Find the value of x that would make the equation you see true is what it means to "solve for x." Consider the following formula: x + 1 Equals 3. If you were to attempt to solve it, you would need to identify a value for x such that it yields three when one is added.
Here in the question given equation ,
x/2 + 1 = √3
To find solution,
we have to subtract 1 from LHS and RHS of equation,
⇒ x/2 + 1 - 1 = √3 - 1
⇒ x/2 = √3 - 1
Next multiply both sides by 2
2( x/2) = 2(√3 -1)
By simplifying both sides we get,
x = 2√3 - 2
So the value of x = 2√3 -2.
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Which expression is equivalent to 5(4x+3)-2x
How is the work shown?
Answer:
Step-by-step explanation:
18x+15. Step-by-step explanation: 5(4x+3)-2x. Distribute the 5. 20x +15 - 2x. Combine like terms. 20x-2x +15.
Find the sum of the measures of the interior angles of each convex polygon.
Answer:
Step-by-step explanation:
interior angles of polygons:
180(n-2)
1. =180(11-2)
=180(9)
=1620
2. 180(17-2)
=180(15)
=2700
what is 1/1/2 x 2/23
Answer:
1/23
Step-by-step explanation:
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. Which ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint?
The ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint 4:9.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
A housepainter mixed 5 gal of blue paint with every 9 gal of yellow paint.
So, the ratio of gallons of blue paint to gallons of yellow paint is
= 5 to 9 or 5:9
Now, ratio of gallons of blue paint to gallons of yellow paint will NOT make the same shade of green paint
= 1- 5/9
=4/9
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Calculus Math Minimum and maximum
Answer:
[tex]y_{min}=-17[/tex]
[tex]y_{max}=15[/tex]
Step-by-step explanation:
Given function:
[tex]y=2x^2-12x+1[/tex]
The critical points are those values of x which make the derivative of the function zero.
Differentiate the function:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2 \cdot 2x^{2-1}-12x^{1-0}+0[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=4x-12[/tex]
Set the derivative to zero and solve for x:
[tex]\implies 4x-12=0[/tex]
[tex]\implies 4x=12[/tex]
[tex]\implies x=3[/tex]
To find the y-value of the critical point, substitute the found value of x into the function:
[tex]\implies 2(3)^2-12(3)+1[/tex]
[tex]\implies 2(9)-12(3)+1[/tex]
[tex]\implies 18-36+1[/tex]
[tex]\implies -18+1[/tex]
[tex]\implies -17[/tex]
Therefore, the critical point is (3, -17).
To find the endpoints of the function in the interval [0, 7], substitute x = 0 and x = 7 into the function:
[tex]\begin{aligned} x=0 \implies 2(0)^2-12(0)+1&=0-0+1\\&=1\end{aligned}[/tex]
[tex]\begin{aligned} x=7 \implies 2(7)^2-12(7)+1&=2(49)-12(7)+1\\&=98-84+1\\&=14+1\\&=15\end{aligned}[/tex]
Therefore:
Critical point: (3, -17)Endpoints: (0, 1) and (7, 15)Therefore the minimum y-value is -17 and the maximum y-value is 15 in the given interval [0, 7]
The minimum and maximum y value of the function is -17 and 15 respectively.
This is a basic problem in calculus.
Given function: [tex]y=2x^{2} -12x+1[/tex]
Step 1: First, let's find the derivative of the function
[tex]\frac{dy}{dx} = 2.2x^{2-1} -12x^{1-0} +0\\\frac{dy}{dx} = 4x-12[/tex]
Step 2: Equate the derivative with zero
4x-12=0
x=3
Therefore, x=3 is the critical value for x
Step 3: Find the critical value for y
[tex]y=2x^{2} -12x+1[/tex]
[tex]y=2\times3^{2} -12\times3+1\\y=-17[/tex]
Thus, the critical points for the function [tex]y=2x^{2} -12x+1[/tex] are (3,-17)
Step 4: Find endpoints using the given interval [0,7]
This can be done by substituting x1=0 and x2=7 simultaneously in the given function and finding y1 and y2.
For x1=0,
[tex]y1=2\times0^{2} -12\times0+1\\y1=0+0+1\\y1=1[/tex]
For x2=7,
[tex]y2=2\times7^{2} -12\times7+1\\y2=98-84+1\\y2=15[/tex]
Now, we have both critical points and endpoints.
Therefore, The minimum and maximum y value of the function is -17 and 15 respectively.
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