Answer:
7.5 ft³/min
Step-by-step explanation:
Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.
Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²
So, V = Ah = 2h = 2(10 - x)
The rate of change of volume is thus
dV/dt = d[2(10 - x)]/dt = -2dx/dt
Since dV/dt = 15 ft³/min,
dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min
Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt
= -dx/dt
= -(-7.5 ft³/min)
= 7.5 ft³/min
And the height at this point when x = 8 inches = 8 in × 1 ft/12 in = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft
A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 101 feet and the radius of the hemisphere is r feet. Express the volume of the silo as a function of r.
Answer:
[tex]V(r) =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]
Step-by-step explanation:
Given
Shapes: cylinder and hemisphere
[tex]h = 101[/tex] --- height of cylinder
Required
The volume of the silo
The volume is calculated as:
Volume (V) = Volume of cylinder (V1) + Volume of hemisphere (V2)
So, we have:
[tex]V_1 = \pi r^2h[/tex]
[tex]V_1 = \pi r^2 * 101[/tex]
[tex]V_1 = 101\pi r^2[/tex] --- cylinder
[tex]V_2 = \frac{2}{3}\pi r^3[/tex] ---- hemisphere
So, the volume of the silo is:
[tex]V =V_1 + V_2[/tex]
[tex]V =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]
Write as a function
[tex]V(r) =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]
Where: [tex]\pi = \frac{22}{7}[/tex]
The area of a rectangular piece of land is 5/16 square mile. .
One dimension is 1/2 mile. How long is the other side?
Answer:
Step-by-step explanation:
Area = L * W
L = 1/2
Area = 5/16
5/16 = 1/2 * w You could do this using decimals
5/16 = 0.3125
1/2 = 0.5
0.3125 = 0.5 * w
w = 0.3125/0.5
w = 0.625
w = 5/8
The other way is done by fractions
[tex]\frac{\frac{5}{16} }{\frac{1}{2} } = \frac{5}{16}*\frac{2}{1} =\frac{5}{8}[/tex]
There are a couple of notes
First, you invert and multiply the denominator (the bottom fraction). It becomes 2/1Second the 2 and 16 cancel 5/16 becomes 5/8Cars arrive at a toll booth according to a Poisson process with mean 90 cars per hour. Suppose the attendant makes a phone call. How long, in seconds, can the attendant's phone call last if the probability is at least 0.1 that no cars arrive during the call
Answer:
92.12 seconds
Step-by-step explanation:
According to the poisson probability relation :
P(X =x) = (e^-λ * λ^x) / x!
For no calls to be reveived during the period, x = 0
P(X = 0) = (e^-λ * λ^0) / 0!
P(X = 0) = 0.1
0.1 = (e^-λ * λ^0) / 0!
0.1 = e^-λ
Take the In of both sides
In(0.1) = - λ
-2.303 = - λ
λ = 2.303
The length of call in second, l
l = λ / r ; r = arrival rate
r = 90 per hour ; this means ;
90 / 3600 = 0.025
l = 2.303 / 0.025
l = 92.12 seconds
help please i’ll give brainliest
Answer:
b
Step-by-step explanation:
b intercepts the y axis
Identify the first 4 terms in the arithmetic sequence given by the explicit formula ƒ(n) = 8 + 3(n – 1).
Step-by-step explanation:
simple formula application :
a1 = 8 + 3×(1-1) = 8
a2 = 8 + 3×(2-1) = 11
a3 = 8 + 3×(3-1) = 14
a4 = 8 + 3×(4-1) = 17
...
For an avid bird watcher, the probability of spotting a California Condor while birdwatching in the Grand Canyon area is 0.3. The probability of being able to take a clear picture of the bird suppose one is able to spot it is 0.8. What is the probability that the bird watcher is able to take a clear picture of a California Condor
Answer:
the probability of taking a clear picture of a California candor is .24
Dividing integers
7. (-154) ➗ (-14) =
11. (-40) ➗10=
15. 90 ➗ (-15)=
16. 108 ➗ (-9)=
17. (-48) ➗ (-6)=
18. (-105) ➗ 7=
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =11
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-4
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-415. 90 ➗ (-15)=-6
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-415. 90 ➗ (-15)=-616. 108 ➗ (-9)=-12
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-415. 90 ➗ (-15)=-616. 108 ➗ (-9)=-1217. (-48) ➗ (-6)=8
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-415. 90 ➗ (-15)=-616. 108 ➗ (-9)=-1217. (-48) ➗ (-6)=818. (-105) ➗ 7=-15
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.here,7. (-154) ➗ (-14) =1111. (-40) ➗10=-415. 90 ➗ (-15)=-616. 108 ➗ (-9)=-1217. (-48) ➗ (-6)=818. (-105) ➗ 7=-15hope it helps you...........
What is the more formal name used for describing the corporate-finance decision concerning which projects to invest in?
Answer:
i hope it will help you
Step-by-step explanation:
Working capital management is how companies are able to manage finances and continue operations.
Find the volume of the prism.
4 m
5 m
19 m
Answer:
19×5×4=380
answer: 380 m³
[tex]\boxed{\sf Volume=2(LB+BH+LH)}[/tex]
[tex]\\ \sf\longmapsto Volume=2(5\times 4+4\times 19+5\times 19)[/tex]
[tex]\\ \sf\longmapsto Volume=2(20+76+95)[/tex]
[tex]\\ \sf\longmapsto Volume=2(191)[/tex]
[tex]\\ \sf\longmapsto Volume=382m^3[/tex]
Which is the graph of the equation y- 1 =} (x 3)?
10
06
6 4
(9,5)
3.1)
1
-10-A-22
2 4 6 8 10 x
4
od
wo
10
6
Two metal spheres of diameter 2.3cm and 3.86cm are melted. The molten material is used to cast equal cylindrical slabs of radius 8mm and length 70mm. If 1/2 of the metal is lost during casting. Calculate the number of complete slabs casted.
Answer:
4
Step-by-step explanation:
If 1/20 of the metal is lost during casting. Calculate the number of complete slabs casted. (4mks)
What unit of measurement would you use to measure the capacity of a juice box?
Juice in a juice box is usually measured in ounces.
Desde cierto paradero se transportan 300 pasajeros en
4 microbuses. ¿Cuántos micros se deben aumentar para
que por cada 3 micros se transporten 90 pasajeros?
Se necesitan 10 micros si queremos que cada 3 micros transporten 90 pasajeros.
En principio, sabemos que 300 pasajeros pueden transportarse en 4 microbuses.
Entonces, el numero de pasajeros que va por cada micro será el cociente entre el numero de pasajeros y el numero de micros:
N = 300/4 = 75
Queremos responder:
¿Cuántos micros se deben aumentar para que por cada 3 micros se transporten 90 pasajeros?
Definamos X como el numero de grupos de 3 micros que tendriamos en esta situación.
Entonces 300 sobre X, debe ser igual a 90 (el numero de pasajeros que va en cada grupo de 3 micros)
300/X = 90
300 = 90*X
300/90 = X = 3.33...
Notar que el número total de micros sera 3 veces X:
3*X = 3*3.33.... = 10
Se necesitan 10 micros.
Si queres leer más sobre el tema, podes ver.
https://brainly.com/question/23854869
Can some help with the answer please it’s very much needed and apprIeciated
Answer:
A
Step-by-step explanation:
The degree of the Polynomial is 3
Line L has a slope of 1/2 . The line through which of the following pair of points is perpendicular to L?
The line which crosses through L must have an intersect point with L to become perpendicular.
Gien slope is positive 1/2.
What is a straight line graph?The graph follows a straight line equation shows a straight line graph.equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the lineslope(m)=tan∅=y axis/x axis.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.
Learn more about the straight lines here:-https://brainly.com/question/14323743
#SPJ2
I need help answering this question thank guys
A rectangular painting is to have a total area (including the frame) of 1200 cm2. If the painting is 30 cm long and 20 cm wide, find the width of the frame
Answer:
5 cm
Step-by-step explanation:
Let x = width of frame.
The width of the frame is added all around the painting, so you must add 2x to the length of the painting and 2x to the width of the painting to find the total length and width including the frame.
painting length: 30
total length: 2x + 30
painting width: 20
total width: 2x + 20
total area = LW
total area = (2x + 30)(2x + 20)
total area = 1200
(2x + 30)(2x + 20) = 1200
(x + 15)(x + 10) = 300
x^2 + 10x + 15x + 150 = 300
x^2 + 25x - 150 = 0
(x - 5)(x + 30) = 0
x - 5 = 0 or x + 30 = 0
x = 5 or x = -30
The width of the frame cannot be a negative number, so we discard the solution x = -30.
Answer: 5 cm
PLSSSSSSSSSSSSSS HELPPPPPPPPPPPP
Answer:
Point D
Step-by-step explanation:
CD and MD share a common point, so it is the intersection
D
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Y<3/2•x-4
Match the equation to a graph.
Answer:
Last option
Step-by-step explanation:
The slope 3/2 determines the line (although you can plot points to find (0,-4) and (4,2), connecting them, you'll get the equation of the line, and the area it covers will be to the right side, putting x = 0, y<-4, which is below the line, that's how you determine it.
Answered by GAUTHMATH
Given the data, identity the type of data for each variable. (For example, determine whether the variable Day is categorical or quantitative data). Which variable is most appropriate to summarize using ungrouped frequency distributions
Answer:
Kindly check explanation
Step-by-step explanation:
The variables in the heavenly chocolate dataset is attached below :
Variables are classed as either Categorical or Quantitative.
Categorical variables are used for non - numeric variables which are used to group values based on labels whole quantitative variables are those which are numeric.
Therefore, the variables ;
Customer = Quantitative (represented with number values)
Day = Categorical (Non-numeric)
Browser = Categorical (Non - numeric)
Time = Quantitative (contains numeric values)
Pages viewed = Quantitative (contains numeric values)
Amount spent = Quantitative (contains numeric values)
Quantitative variables are most appropriate to summarize using ungrouped frequency as the attributed of the data can be adequately ibtia Ed without have to seperates or place data into categories.
Which of the following is the graph of…
Answer:
A
Step-by-step explanation:
Try graphing the function on desmos
Help needed! Thank you!
Which of the following is correct based on this picture?
A. sinD=3124
B. cosK=3124
C. tanK=3124
D. tanD=3124
Answer:
C but see below.
Step-by-step explanation:
If I'm reading this correctly, you mean 31/24. It really can't be much else. The sine and cosine are both incorrect because both involve the hypotenuse which must be calculated in order for them to be considered. In addition 31/24 is greater than one which is impossible for both the Sine and the Cosine.
That leaves K and D
Tan(D) = 24/31 which is not an option.
That leaves C.
tan(K) = 31/24 which is what you have to choose. If your choice is not written this way, then there is no answer.
Answer:
The answer to this problem is C. tanK=3124
look at the image below
Jacqueline will spend a fair spinner with the numbers 0 1 2 3 and 4 a total of three times if event a spinner lands on numbers are greater than 2 and event be total sum of 9 which of the following best describes event A and B
Events are said to be INDEPENDENT if the occurence of one does not rest or depend on the outcome of another. Therefore, since the outcome of event A and B does not depend on each other, then both events are INDEPENDENT
Giving a brief description of the options given :
• Dependent events are simply events where the outcome of one event affects the occurence of the other. This is usually related to selection without replacement, where the number of subjects changes after each selection.
• Mutually Exclusive events simply refers to a scenario whereby two events cannot occur simultaneously. For instance, obtaining a head and a tail simultaneously during a single coin throw.
• Complement events describes two exactly opposite events. For instance, the Complement of obtaining a 4 on a 6 - sided die roll is (1, 2, 3, 5, 6)
For the event described above , the occurrence of A does not hinder the occurrence of the other (not a dependent event ) and it is possible to have both events simultaneously (not Mutually exclusive) (If we have 3 in all throws then both events have occurred )
Therefore, the best description for events A and B is that both events are INDEPENDENT.
Learn more about independent events :
https://brainly.com/question/1393117
Answer: the answer is dependent
Step-by-step explanation:
Events are independent if the knowledge of one event occurring does not affect the chance of the other event occurring. In this case, the chance of Event B occurring is greater if Event A occurs, so these events are dependent. Since the spinner could land on 3, 3, and 3, the events are not mutually exclusive.
Which of the following is a geometric sequence? a. 5,-25,125,-625 b.2,4,16,48 c. 13,16,19,22 d. 100,50,0,-50
Answer:
a
Step-by-step explanation:
B isn't a geometric sequence as it's last term doesn't follow the rule
C is an arithmetic sequence
D is an arithmetic sequence too
A line passes through the point (-2,4) and has a slope of 7. Write an equation for this line
Answer: y = 7x + 18
Step-by-step explanation:
y = mx + b, (-2,4), m = 7
4 = 7(-2) + b
4 = -14 + b
b = 18
y = 7x + 18
find the value of the trigonometric ratio. make sure to simplify the fraction if needed
Answer:
3/5
Step-by-step explanation:
sin=opp/hyp
sinc=24/40=3/5
The football coach randomly selected 10 players and timed how long each player took to perform a certain drill. The result has a sample mean of 9.48 minutes and sample standard deviation of 2.14 minutes. Round answers to two decimals. The 95% confidence interval for the mean time for all players is : __________
Answer:
The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 10 - 1 = 9
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.2622\frac{2.14}{\sqrt{10}} = 1.53[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 9.48 - 1.53 = 7.95 minutes.
The upper end of the interval is the sample mean added to M. So it is 9.48 + 1.53 = 11.01 minutes.
The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).
How do I solve for y:
x²y² = 12/z²
Answer:
Y=Srt(12xs^2/z^2)
Step-by-step explanation:
Firstly
We multiply both sides with 1/x^2
We get
Y^2=12/z^2*1/x^2
Y^2=12x^2/z^2
Next: introduce a srt root
We have
Y=srt(12x^2/z^2)
Please show your work this question what made you come to the conclusion. Thank you
Answer:
B the range, the x- and y-intercept
Step-by-step explanation:
the domain stays the same : all values of x are possible out of the interval (-infinity, +infinity).
but the range changes, as for the original function y could only have positive values - even for negative x.
the new function has a first term (with b) that can get very small for negative x, and then a subtraction of 2 makes the result negative.
the y-intercept (x=0) of the original function is simply y=1, as b⁰=1.
the y-intercept of the new function is definitely different, because the first term 3×(b¹) is larger than 3, because b is larger than 1. and a subtraction of 2 leads to a result larger than 1, which is different to 1.
the original function has no x-intercept (y=0), as this would happen only for x = -infinity. and that is not a valid value.
the new function has an x-intercept, because the y-values (range) go from negative to positive numbers. any continuous function like this must therefore have an x-intercept (again, y = the function result = 0)
[tex] 3 {b}^{x + 1} = 2[/tex]
[tex] {b}^{x + 1} = 2 \div 3[/tex]
[tex] log_{b}(2 \div 3) = x + 1[/tex]
[tex]x = log_{b}(2 \div 3) - 1[/tex]
