The rate at which the water level is rising when the water level is 5 cm is;
dh/dt = 1.6 cm/s
What is a PYRAMID?A structure with triangle outside surfaces that converge to a single step at the summit is referred to as a pyramid (from Greek: pyrams)]. This shape is roughly a pyramid in the geometric sense. A pyramid foundation might be triangular, quadrilateral, or any other type of polygon. A pyramid therefore has at least three triangular exterior surfaces (at least four faces including the base). A typical variation is the square pyramid, which has a square base and four triangular exterior surfaces.Because a pyramid is built with the pyramidion at the top and the remainder of the weight closer to the ground[3], less material will be pressing down from above. Early civilizations could build stable structures thanks to this weight distribution.Acc to our question-
length of square side; s = 4 cmheight of pyramid; h = 8 cmvolumetric rate; dV/dt = 30 cm³/sSince the base is square shaped and we know that area of a square = s², then we can say that;Volume of pyramid = ¹/₃s²hThe pyramid has a height of 8 cm and length of its' square base side is 8 cm.Now, regardless of the water height, the surface of the water will always be square shaped. This implies that the ratio of the height to the top side of square will always be the same. Thus, we can say that; s = 4/8 h = h/2Thus, Volume is;V = ¹/₃ × (h/2)² × hV = ¹/₃ × h³/4V = h³/12dV/dt = (3h²/4) dh/dtPlugging in the relevant values gives;30 = (3 × 5²/4) dh/d120 = 75 dh/dtdh/dt = 120/75dh/dt = 1.6 cm/sHence,The rate at which the water level is rising when the water level is 5 cm is; dh/dt = 1.6 cm/s
learn more about pyramid click here:
https://brainly.com/question/13697843
#SPJ4
suppose that 47% of americans are iphone users. (a) if a random sample of 100 americans are surveyed, what is the probability that the proportion of the sample who are iphone users is between 45% and 50%? (b) if a random sample of 50 americans are surveyed, what is the probability that more than 50% of americans are iphone users?
The probability that the proportion of the sample who are iphone users is between 45% and 50% be 22.87%.
The probability that more than 50% of americans are iphone users be 11.12%.
(a)We know, p = 0.47 and n = 100. First, we should check our conditions for the sampling distribution of the sample proportion.
np = (100)(0.47) = 47 and n(1 - p) = (100)(1 - 0.47) = 53
Since, X will have a sampling distribution that is approximately normal with mean = 0.47
and
standard deviation = √(0.47)(0.53)/100 ≈ 0.05
P(0.45<X<0.50) = P((0.45 - 0.47)/0.05 < Z < (0.50-0.47)/0.05)
P(0.45<X<0.50) ≈ 0.2287
Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 22.87% chance that we would see a sample proportion between 45% and 50% when the sample size is 100.
(b) Now, p = 0.47 and n = 50.
np = (50)(0.47) = 23.5 and n(1 - p) = (50)(1 - 0.47) = 26.5
Since, X will have a sampling distribution that is approximately normal with mean = 0.47
and
standard deviation = √(0.47)(26.5)/50 ≈ 0.25
P(X>0.50) = P(Z > (0.50-0.47)/0.25)
P(X>0.50) ≈ 0.1112
Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 11.12% chance that we would see a sample proportion more than 50% when the sample size is 50.
Learn more about Probability here https://brainly.com/question/13604758
#SPJ4
Find the length of each side of triangle XYZ, then classify the triangle by its side: X(7,6), Y(5,1), Z(9,1) show work, please!!!
Answer:
(9,1), Z(5,1)
Step-by-step explanation:
Hey I would rlly appreciate if someone can help IVE been stuck on this and pls make sure to find measure BCD
Answer:
140
Step-by-step explanation:
2x+5x+40=180
7x+40=180
7x=140
x=20
5x+40=BCD
5(20)+40
100+40
140
Can someone teach me how to do this?
sin^-1(-1/2) enter directly into a calculator and you'll find your answer
suppose that 10 green balls and 14 purple balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn? a) 0.1224 b) 0.6250 c) 0.8333 d) 0.4167 e) 0.5833 f) none of the above.
The probability that the second ball drawn is a purple ball is (e) 0.5833
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Green balls = 10
Purple balls = 14
This means that the total number of balls is
Total = 10 + 14
Evaluate the equation
So, we have
Total = 24
From the question, we understand that the ball is replaced
So, the probability that the second ball is purple ie
P(second purple) = purple/total
This gives
P(second purple) = 14/24
Evaluate
P(second purple) = 0.5833
Hence, the probability is (e) 0.5833
Read more about probability at
https://brainly.com/question/251701
#SPJ1
How to find correlation coefficient? I'm stuck pls help me
(0,1132), (1,1107), (2,1000), (3,1019)
The correlation coefficient of the data (0,1132), (1,1107), (2,1000), (3,1019) is -0.89
How to determine the correlation coefficient?Correlation coefficients are used to measure how strong a relationship is between two variables
Given: (0,1132), (1,1107), (2,1000), (3,1019)
x >>>> y >>>> x² >>>> y² >>>> xy
0 1132 0 1281424 0
1 1107 1 1225449 1107
2 1000 4 1000000 2000
3 1019 9 1038361 3057
................................................................................................
6 4258 14 4545234 6164
.................................................................................................
The formula for the correlation coefficient is:
r = ( n∑xy -(∑x)(∑y) ) / ( √(n∑x² - (∑x)²) .√(n∑y² - (∑y)²) )
From the table:
∑x = 6, ∑y = 4258, ∑x² = 14, ∑y² = 4545234 and ∑xy = 6164
n = 4 (number of data points)
Substituting the values into the formula will give:
r = ( 4×6164 -(6)(4258) ) / ( √(4×14 - (6)²) .√(4×4545234 - (4258²) )
r = 24656-25548 / √(20).√(50372)
r = -892/√(1007440)
r = -0.89
Therefore, the correlation coefficient is -0.89
Learn more about correlation coefficient on:
https://brainly.com/question/27842223
#SPJ1
Which of the following is the independent variable of F(G(x))?
O A. V
• B. x
• C. F(x)
• D. F(G(x))
Answer:
D
Step-by-step explanation:
Clay asks Donte to play the following number puzzle:
Pick a number
Add 4
Multiply by 2
Subtract 3
Add your original number
Donte’s final result is 32. Which number did he start with?
Group of answer choices below
A. 7
B. 9
C. 4
D. 23
E. 0
1 3/4 divided by 3
Please helppp
Answer:
= 7/12
Step-by-step explanation:
1 3/4 = 1 + 3/4 = 4/4 + 3/4 = (4+3)/4 = 7/4
(7/4)÷3 = 7/(4*3) = 7/12
A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. The professor has informed us that 8. 75 percent of her students received grades of a. What is the minimum score needed to receive a grade of a?.
The minimum score needed to receive a grade of A is 88.51
Let, X, be the scores of the student's
X follows Normal Distribution with mean = μ = 73 and standard deviation = σ = 11
The professor has informed us that 7.93 percent of her students received grades of A.
That is P( X > a ) = 7.93% = 0.0793 .
We have to find a.
P( X > a ) = 7.93% = 0.0793
So, P( X <= a ) = 1 - 0.0793 = 0.9207
Using function = NORMINV( probability , μ ,σ )
a = NORMINV( 0.9207, 73 , 11 ) = 88.51
The minimum score needed to receive a grade of A is 88.51
We have to find P( X <= 57.93 )
Using function = NORMDIST( x, μ , σ , 1 )
P( X <= 57.93 ) =NORMDIST( 57.93 , 73 , 11 , 1 ) = 0.0853 = 8.53%
8.53 percent of students failed the course
To learn more about statistics, mean, median, and mode,
https://brainly.com/question/15323584
#SPJ4
over the past month, george the tortoise has been flipped onto his back 146 times by angie the tortoise. george has been able to get back on his feet without help 3 times. what's the empirical probability that george will be able to get back on his feet without help the next time angie flips him over?
The empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.
Describe the term empirical probability?The likelihood of an event is closely related to an empirical probability, also described as an experimental probability. Empirical probability bases its evaluation of the likelihood that a specific result will recur on the number of instances of that outcome together within sample set.For the given question.
We include George the turtle, who Angie has successfully turned over 146 times the turtle.3 times George has used the assistance to get back up on his feet. The empirical probability is really what we seek.Therefore, it follows that we are doing an experimental calculation based on the observation whether George will indeed be able to stand again the following time.
empirical probability = 3/146
Thus, the empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.
To know more about the empirical probability, here
https://brainly.com/question/27541895
#SPJ4
how many 4-letter passwords can be formed using the letters a, b, c, d, e, f, g if repetition of letters is not allowed and the first letter can only be a, b or c?
840 are 4-letter passwords can be formed using the letters by permutation .
What are some examples of permutation?
A permutation is a set up of things in a specific order. In this arrangement, the components or components of sets are organized in a linear or sequential order. The permutation of the set A=1,6 is 2, for instance, 1,6, and 6,1. The components of set A cannot be arranged in any other way, as you can see.We are to count all possible 4-letter passwords that can be generated from the letters a, b, c, d, e, f, g .
There are 7 letters in total.
n = 7 r = 4
P(n , r ) = 7!/( n - r )!
P( 7 ,4 ) = 7!/( 7 - 4)!
= 7!/3!
= 7 * 6 * 5 * 4 * 3 * 2 * 1/3!
= 7 * 6 * 5 * 4
= 840
Learn more about permutation
brainly.com/question/1216161
#SPJ4
If g(x)=8x^6 and f(x) = log4 (2x) then f(g(x)) = ?
Answer:
f(g(x))= log4(2(8x^6))
or log4(16x^6)
Step-by-step explanation:
3/8 - 5/6 Please put a step by step
Answer:
(-11/24)
Step-by-step explanation:
3 5
------- - -------
8 6
3(3) 5(4)
------- - -------
8(3) 6(4)
9 20 - 11
------- - ------- = -------
24 24 24
I hope this helps!
A baseball is thrown from the pitcher's
mound at 40 m/s. It takes 0.46 seconds for
the ball to reach home plate. What is the
distance between the mound and home
plate?
Answer:
Step-by-step explanation:
Velocity = distance / time
In this problem, we need to calculate for distance, knowing time and velocity.
multiply time on both sides, on the right side the time will cancel out leaving time alone.
velocity * time = distance
40m/s * 0.46s = distance
distance = 18.4 meters
Hope it helped!
Brandon invested $7,900 in an account paying an interest rate of 6\tfrac{1}{8}6 8 1 % compounded daily. Jacob invested $7,900 in an account paying an interest rate of 6\tfrac{5}{8}6 8 5 % compounded monthly. After 15 years, how much more money would Jacob have in his account than Brandon, to the nearest dollar?
Using the properties of compound interest we can calculate that Jacob will have $1485 more than Brandon in his account.
Brandon invested $7,900 at the rate of 6 1/8% compounded daily.
Principal = $7900
Time = 15 years
Rate = 6 1/8% = 49/8 %
Amount earned after n years:
[tex]A=P (1+\frac{r}{n})^{nt}[/tex]
Now we will use these values to find the amount at the end of 15 years.
P = 7900
r = 0.06625
n = 365
t = 15
[tex]A=P (1+\frac{.06125}{365})^{15\times 365}[/tex]
or, A = 19797.104...
or, A ≈ 19797.1
Again, Jacob invested the same sum at compound interest monthly at
6 5/8% .
Amount earned after 15 years:
P = 7900
r = 6.125
n = 12
t = 15
[tex]A=P (1+\frac{.06625}{12})^{15\times 12}[/tex]
or, A = 21282.383..
or, A ≈ 21282.38
Amount earned by Jacob more than Brandon
= $21282.38 - $19797.1
= $148785.283..
≈ $1485
Hence Jacob will have $1485 more than Brandon in his account.
To learn more about compound interest visit:
https://brainly.com/question/13155407
#SPJ1
Find all rational roots.
x(3x − 4) (x − 5) = 0
The rational roots of the given equation x(3x − 4) (x − 5) = 0 are x = 0, 4/3 and 5
What is Rational Number?
Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.
So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that numerator or denominator doesn't have common divisible.
x(3x − 4) (x − 5) = 0
So we can put every term equal to zero to find it's root.
1st case, x = 0
2nd, 3x-4 = 0
3x = 4
x= 4/3
3rd, x-5 = 0
x = 5
Hence, the rational roots of the given equation are x = 0, 4/3 and 5
Learn more about Rational Number , by the following link
https://brainly.com/question/12088221
#SPJ1
A rectangle plot of land has a width of 3x+5 feet, and a length of 2x-1 feet.
A- express the area of the plot as a function of x.
B- express the perimeter of the plot as a function of x
A- the area of the plot as a function of x. is 6 x^2 +10x-5
B- the perimeter of the plot as a function of x is 10x+8
A rectangle plot of land has a width of 3x+5 feet,
and a length of 2x-1 feet.
A) the area of the plot as a function of x is given by
A= length * width
= ( 2x-1) * ( 3x+5)
=6 x^2 +10x-5
B) the perimeter of the plot as a function of x
P = 2( l+ W)
= 2 (( 2x-1) +( 3x+5))
= 2( 5x +4)
= 10x +8
learn more about of rectangle here
https://brainly.com/question/15019502
#SPJ4
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.
From the graph:
vertex:
The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.
here vertex = (-2,2)
Axis of symmetry:
The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric.
x = -2.
Parabola:
It is clearly visible that the parabola is facing downward so it is a downward parabola.
Therefore the vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.
Learn more about the parabola here:
https://brainly.com/question/11911877
#SPJ1
can someone please solve (iii)
The point on a line that is at an equal distance from either end.
Hence, the equation of the line [tex]Q[/tex] to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].
What is midpoint ?
The point on a line that is at an equal distance from either end.
Here, the coordinates of [tex]A(1,-1),P(3,7),Q(\frac{-1}{2},\frac{7}{2})[/tex]
The general formula of the midpoint is
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+t_2}{2})[/tex]
The equation of [tex]AP[/tex] is
[tex]AP=(\frac{1+3}{2},\frac{7-1}{2})\\AP=(\frac{4}{2},\frac{6}{2})\\AP=(2,3)\\[/tex]
The equation of the line [tex]Q[/tex] to the midpoint of [tex]AP[/tex] is
where [tex]AP(2,3),Q(\frac{-1}{2},\frac{7}{2})[/tex].
[tex](AP,Q)=(\frac{2+\frac{-1}{2}}{2},\frac{3+\frac{7}{2}}{2})\\(AP,Q)=(\frac{\frac{4-1}{2}}{2},\frac{\frac{6+7}{2}}{2})\\(AP,Q)=(\frac{\frac{3}{2}}{2},\frac{\frac{13}{2}}{2})\\\\(AP,Q)=(\frac{3}{4},\frac{13}{4})\\[/tex]
Hence, the equation of the line [tex]Q[/tex] to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].
To know more about the midpoint
https://brainly.com/question/28224145
#SPJ1
2) What is the slope of the line from the following table? (Please show your work)
Answer:
pick any two points
im going to chose (1,3) and (3,7)
so the equation y2-y1/x2-x1
1 = x1
3=y1
3=x2
7=y2
so 7-3/3-1 is 4/2
which is 2
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k
The given function is f(x)=7x^2.
The given vertex = (3,5)
The equation of the parabola with the vertex of (h,k) is
y=a(x-h)^2+k
On comparing we get; a=7, h=3, k=5
Now putting the value
f(x)=7(x-3)^2+5
Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.
To learn more about parabola link is here
brainly.com/question/4074088
#SPJ1
How do I know where to shade on this graph?
y≤-3x+4 has lesser than or equal to symbol so we shade the below line.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Relationship between two expressions or values that are not equal to each other is called 'inequality.
y≤-3x+4 is the given inequality.
The sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.
In the inequality we have lesser than or equal to symbol so we shade the below line.
Hence, y≤-3x+4 has lesser than or equal to symbol so we shade the below line.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
the weight of bags of all purpose flour is normally distributed with expected value 10 pounds and standard deviation 0.2 pounds. the heaviest 2.5% of the bags packaged by the flour company are labeled as overweight. what is the probability that of 10 randomly chosen bags of flour at least 2 are overweight?
The probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68.
Given, that the weight of bags of all purpose flour is normally distributed with expected value 10 pounds and standard deviation 0.2 pounds.
As, we know that
P(X) = (1/s√2π)exp(-1/2((X-m)/s)^2)
where, m is the expected value
and s is the standard deviation.
Now, we have Expected value 10 pounds
and Standard Deviation 0.2 pounds
So, the probability that of 10 randomly chosen bags of flour at least 2 are overweight be
P(X=0) + P(X=1) = (1/0.2√2π)exp(-1/2((0-10)/0.2)^2) + (1/0.2√2π)exp(-1/2((1-10)/0.2)^2)
P(X=0) + P(X=1) = 0.32
So, Required Probability be 0.68.
Now, the probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68
Learn more about Probability here https://brainly.com/question/13604758
#SPJ4
Mr. Williams is planting a garden. It measures 30 meter along one side. He makes a mark every 1/5 meter. What is the total number of marks that Mr. Williams will make?
Answer:
150 marks
Step-by-step explanation:
Every meter has 5 marks.
30 meters × 5 marks = 150 marks
What is the value sine?
5/12
5/13
12/13
13/5
Answer:
(C.) 5/13
Step-by-step explanation:
The sine proportion is opposite / hypotenuse
Given the reference angle, the side measuring 5 units is the opposite side and the side measuring 13 units (and opposite of the right angle) is the hypotenuse
Thus, sine is 5/13
what is 315.00 divided by 30.
Answer:
Step-by-step explanation:
Answer 10.5
the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 2.3 days. what is the probability of spending more than 2 days in recovery? (round your answer to four decimal places.)
When the patient recovery time from a specific surgical procedure is normally distributed, with a mean of 5.2 days and a standard deviation of 2.3 days, the probability of spending more than 2 days in recovery will be 0.61.
What is probability?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. Information about the likelihood that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is used in epidemiology to comprehend the connection between exposures and the risk of health effects.
Here,
z=(X-μ)/σ
X=2
μ=5.2
σ=2.3
Z=(2-5.2)/2.3
Z=-1.39
-1.39+1
=0.39
1-0.39=0.61
The probability of spending more than 2 days in recovery will be 0.61 when the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 2.3 days.
To know more about probability,
https://brainly.com/question/11234923?referrer=searchResults
#SPJ4
there are 5 yellow flowers there are red flowers.how many are in there all togerther
The total number of flowers is 8 flowers.
How to calculate the addition?From the information given, there are 5 yellow flowers there are 3 red flowers.
It should be noted that in order to get the total value of the flowers, we have to add them. This will be:
Yellow flowers = 5
Red flowers = 3
Total flowers = Yellow + Red
= 5 + 3
= 8
The total flowers is 8.
Learn more about flowers on:
brainly.com/question/957208
#SPJ1
Complete question
There are 5 yellow flowers there are 3 red flowers.how many are in there all togerther
Container A has 200 L of water, and is being filled at a rate of 6 liters per minute. Container B has 500 L of water, and is being drained at 6 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
It will take 25 minutes for the two containers to have the same amount of water .
In the question ,
it is given that ,
water present in container A = 200L
water present in container B = 500L
rate at which the water is filling in container A= 6 liter/minute
rate at which the water is draining in container B = 6 liter/minute
let the time taken = m minutes ,
So , According to the question ,
the equation representing the situation is
200 + 6m = 500 - 6m
Simplifying further , we get
6m + 6m = 500 - 200
12m = 300
m = 300/12
m = 25
Therefore , It will take 25 minutes for the two containers to have the same amount of water .
Learn more about Equations here
https://brainly.com/question/13304287
#SPJ1