The water level increases by 0.608 meters per minute when the water is 3.5 m deep
How to determine the rate?The given parameters are:
Radius, r = 3Height, h = 7Rate in, V' = 4.3m^3/minThe relationship between the radius and height is:
r/h = 3/7
Make r the subject
r = 3h/7
The volume of a cone is;
[tex]V = \frac 13\pi r^2h[/tex]
This gives
[tex]V = \frac 13\pi (\frac{3h}{7})^2h[/tex]
Expand
[tex]V = \frac{3h^3}{49}\pi[/tex]
Differentiate
[tex]V' = \frac{9h^2}{49}\pi h'[/tex]
Make h' the subject
[tex]h' = \frac{49}{9\pi h^2}V'[/tex]
When the water level is 3.5.
We have:
[tex]h' = \frac{49}{9\pi * 3.5^2}V'[/tex]
Also, we have:
V' = 4.3
So, the equation becomes
[tex]h' = \frac{49}{9\pi * 3.5^2} * 4.3[/tex]
Evaluate the products
[tex]h' = \frac{210.7}{346.36}[/tex]
Evaluate the quotient
h' = 0.608
Hence, the water level increases by 0.608 meters per minute
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Find the GCF of 12a and 18a²
Answer:
6
Step-by-step explanation:
the blue factors are all the factors 12 and 18 have in common.
. The two bottles are similar in shape. The larger bottle holds 100 m/ of perfume. Calculate how many millilitres of perfume the smaller bottle holds.The length of the larger bottle is 10cm.the length of the smaller bottle is 5cm
Answer:
The smaller bottle holds 12.5 ml of perfume.
====================
GivenTwo bottles of similar shape;Larger bottle has volume of 100 ml;The length of larger bottle is 10 cm;The length of smaller bottle is 5 cm.To find The volume of smaller bottle.SolutionFind the scale factor, the ratio of corresponding dimensions:
[tex]k = 5/10 = 1/2[/tex]We know the volume is the function of three dimensions, therefore the ratio of volumes is the cube of the scale factor:
[tex]V_{small}/V_{large} = k^3\\[/tex]Substitute the known values and find the volume of small bottle:
[tex]V_{small}/100= (1/2)^3\\[/tex][tex]V_{small}/100= 1/8[/tex][tex]V_{small}= 1/8*100=12.5[/tex]The smaller bottle holds 12.5 ml of perfume.
The smaller bottle holds 12.5 ml of perfume.
I solved it and came with this result.
The product of the length of 2 unequal poles before cutting 2 cm from each was 285 cm. Their present sum after cutting 2cm from each is 30cm. What is the length of the shorter pole? The product of the length of 2 unequal poles before cutting 2 cm from each was 285 cm . Their present sum after cutting 2cm from each is 30cm . What is the length of the shorter pole ?
Answer:
15 cm
Step-by-step explanation:
The length of the shorter pole can be found by forming and subsequently solving 2 equations.
Start by defining the variables that are going to be used in the working.
Let the original length of the shorter pole be a cm and that of the longer pole be b cm.
'Product' refers to the multiplication operation.
ab= 285 -----(1)
On the other hand, 'sum' refers to the addition operation.
Length of shorter pole after cutting= a -2
Length of longer pole after cutting= b -2
(a -2) +(b-2)= 30
a +b -4= 30
Adding 4 to both sides:
a +b= 30 +4
a +b= 34 -----(2)
From (2):
a= 34 -b -----(3)
Let's solve by substitution:
Substitute (3) into (1):
b(34 -b)= 285
Expand:
34b -b²= 285
b² -34b +285= 0
Factorise:
(b -15)(b -19)= 0
b -15= 0 or b -19= 0
b= 15 or b= 19
Substitute into (1):
a(15)= 285 or a(19)= 285
a= 285 ÷15 or a= 285 ÷19
a= 19 or a= 15
Since a <b, a= 15 and b= 19.
Thus, the length of the shorter pole is 15 cm.
-3 5/7 X -2 1/2
I really don't understand
Answer:
[tex] - 3 \frac{5}{7} x - 2\ \frac{1}{2} [/tex]
[tex] \frac{ - 26}{7} - \frac{5}{2} [/tex]
LCM of 7 and 2 is 14
Multiplying (-26/7) with 1/2 (to make the denominator 14) and -5/2 with 1/7
[tex] \frac{ - 26}{7} \times \frac{1}{2} - \frac{5}{2} \times \frac{1}{7} [/tex]
[tex] \frac{ - 26}{14} - \frac{5}{14} [/tex]
[tex] \frac{ - 26 - 5}{14} [/tex]
[tex] - \frac{31}{14} [/tex]
parallelogram
b=12 cm, h=10 cm, a=
solve the following inequality, algebra 1.
will give brainliest answer !!
Answer:
See below
Step-by-step explanation:
r/6 <-6 multiply both sides by 6 to get
r < - 36
or 4r+2 > 18 subtract 2 from both sides of the equation
4r > 16 divide both sides by 4
r > 4
Step-by-step explanation:
[tex] \frac{r}{6} < - 6 \: \: \: \: \: \: \: \: \: \: ... 1[/tex]
[tex]4r + 2 > 18 \: \: \: \: \: \: \: \: \: \: ...2[/tex]
Solving for inequality 1:
[tex] \frac{r}{6} < - 6 \: \: \: \: \: \: \: \: \: \: ... 1[/tex]Multiplying both sides by 6:
6 * 1/6 r < -6*6r < -36Hence the solution is r < -36
Solving for inequality 2:
4r + 2 > 18Subtract 2 from both sides:
4r + 2 - 2 > 18 - 24r > 16Divide both sides by 4:
[tex] \cfrac{4r}{4} > \cfrac{16}{4} [/tex][tex]r > 4[/tex]Hence the answer is r > 4.
HELP PLS 100 POINTS PLS BRAINLY IF CAN
find the domain y=[tex]\frac{2-3x}{12-|x-12|}[/tex]
Step-by-step explanation:
hope you can understand
5. Find the quadratic equation with root alpha and beta,given that alpha-beta=2 and alpha^2-beta^2=3.
Answer:
[tex]x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]
Step-by-step explanation:
[tex]\begin{cases}\alpha -\beta =2\\ \alpha^{2} -\beta^{2} =3\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \left( \alpha +\beta \right) \left( \alpha -\beta \right) =3&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \alpha +\beta =\frac{3}{2} &\end{cases}[/tex]
Then
2α = 2 + 3/2 = 7/2
2β = (3/2) - 2 = -1/2
Then
Then
α = 7/4
β = -1/4
Then
a quadratic equation with root α and β can be :
[tex]\left( x+\frac{1}{4} \right) \left( x-\frac{7}{4} \right) =0[/tex]
[tex]\Longrightarrow x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]
I really need help on this question. Im stuck any help?
Answer:
170
Step-by-step explanation:
[tex]x+40=210\\x=170[/tex]
If a number, x, is increased by 40 (+40) and is now equal to 210 (=210), then the number, x, is equal to 170.
Out of 310 racers who started the marathon, 289 completed the race, 18 gave up, and 3 were disqualified. What percentage did not complet
Answer:
7.1%
Step-by-step explanation:
Those that did not complete the race either gave up or were disqualified. This means that 18 + 3 = 22 people did not complete the race. The percentage is 22/310 × 100% = 7.1%
Help please confused
Answer:
AB : y=1/5x+12
CB : y=-3x+10
CD : y=1/2x-1
DA : y=-2x+1
Brad wants to buy flowers for his friend
with $33. The daisies are $1 each and
the roses are $2 each. He buys 3 more daisies than roses.
how much did the roses cost?
Answer:
20
Step-by-step explanation:
Answer:
20$ For the Roses
Step-by-step explanation:
Think about it like this. For each daisy (1$), the price is double for roses (2$).
Brad has a limit of 33$. And he bought 3 more daisies than roses.
If each daisy is 1$, and he bought 3+ over roses, take away 3$ to get 30$. If he bought 10 (excluding 3+) Daisies, He must have bought 10 roses.
(10 Daisies = 10$) + (10 Roses = 20$) = 30$
30$ + (3 Daisies = 3$) = 33$
Write the domain and range using interval notation
The domain of the graph is [-3, 2) and the range is (-4, 5]
How to determine the domain and the range?From the given graph, we have the following highlights:
Minimum x value = -3 (closed circle)Maximum x value = 2 (open circle)Minimum y value = -4 (open circle)Maximum y value = 5 (closed circle)Open circles are represented with () while closed circles are represented with []
Hence, the domain of the graph is [-3, 2) and the range is (-4, 5]
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Which of the following are square roots of the number below? Check all that
apply.
4
A. 41/2
B. 8
C. -41/2
D. 2
E. -2
F. 16
Answer:
D. 2
E. -2
Step-by-step explanation:
Find the area of the trapezoid. TOP 11ft, RIGHT4√3ft , BOTTOM 15ft ,LEFT 8ft
Answer:
[tex]52\sqrt{3} ft^{2}[/tex]
Step-by-step explanation:
Please refer to the attached picture.
First we will find the area of rectangle BCDE.
Area of Rectangle = Length x Breadth = DE x CD
= 11 x [tex]4\sqrt{3}[/tex]
[tex]=44\sqrt{3} ft^{2}[/tex]
Next we will find Area of Triangle ABE.
Area of Triangle = 0.5 x Base x Height
[tex]0.5*4*4\sqrt{3} \\=8\sqrt{3} ft^{2}[/tex]
Area of Trapezoid = Area of Rectangle + Area of Triangle
[tex]=44\sqrt{3} +8\sqrt{3} \\=52\sqrt{3} ft^{2}[/tex]
Answer:
A = 52[tex]\sqrt{3}[/tex] ft² ≈ 90.1 ft²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height and b₁ , b₂ the parallel bases
here h = 4[tex]\sqrt{3}[/tex] , b₁ = 15 , b₂ = 11 , then
A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{3}[/tex] × (15 + 11)
= 2[tex]\sqrt{3}[/tex] × 26
= 52[tex]\sqrt{3}[/tex] ft²
≈ 90.1 ft² ( to the nearest tenth )
I need help with question 12
The value of the integral over limit is 20, the average is 1.73
The signed area is shown in the graph attached.
What is a Function ?A function is a mathematical statement used to find a relation between two variable.
To Evaluate the definite integral between
f(x) = 5 if 4≤x ≤9
f(x) = -1 if 9≤x≤14
[tex]\rm \int_{4}^{14}f(x) dx = \int_{4}^{9} 5 dx +\int_{9}^{14} (-1)dx\\\\\int_{4}^{14}f(x) dx = (5x)^{9}_{4} -(x)^{14}_{9}\\\\\int_{4}^{14}f(x) dx = 5*(9-4) - (14-9)\\\\\int_{4}^{14}f(x) dx = 20[/tex]
The average value of the interval is
= (5+5+5+5+5-1-1-1-1-1-1)/ 11 = 1.73
Therefore the average is 1.73.
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When we're solving minimum or maximum problems, are we h or the constant k? looking for the constant
In solving minimum and maximum problems, result we are looking for would be the constant, k.
What is being solved for in minimum and maximum problems?When looking for the minimum functional value, we are looking for the constant, k because it can be thought of as the absolute minimum value.
An open parabola would then have k as the maximum functional value which means that the constant k is the value being sought.
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46. Machine A produces 500 springs a day. The number of defective springs produced by this machine each day is recorded for 60 days. Based on the distribution given below, what is the expected value of the number of defective springs produced by Machine A in any single day?
F. 0.00
G. 0.45
H. 0.70
J. 1.00
K. 1.50
Answer:
G. 0.45
Step-by-step explanation:
To find expected value, you simply multiply the value of each outcome (the numbers in the left column) by its probability
(the numbers in the right column) and then add them all together.
0(0.7) + 1(0.2) + 2(0.05) + 3(0.05)
0 + 0.2 + 0.1 + 0.15 = 0.3 + 0.15 = 0.45
The expected value is 0.45. Thus, the correct option is G.
What is the expected value?In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
The expected value is calculated as,
E(x) = 0 x 0.70 + 1 x 0.20 + 2 x 0.05 + 3 x 0.05
E(x) = 0 + 0.20 + 0.10 + 0.15
E(x) = 0.45
Thus, the correct option is G.
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What grade is middle school geography?
Answer:
5th or 6th grade
Step-by-step explanation:
The reason why we learn geography in 5th grade is to prepare us for 6th grade geography. The reason why we learn geography in 6th grade is because Geography helps us understand basic physical systems that affect everyday life. In other words, geography is a nice skill to have when you're learning about the water cycle or rock formations, or the moving of the tectonic plates (and other natural disasters). It's also a very important skill to have when you want to start traveling.
Use the Distributive Property to find $(n-6)(n-4)$ .
Answer:
n^2 -10n + 24
Step-by-step explanation:
Given expression:
(n-6)(n-4)
Solution:
Apply distributive property,then simplifying using PEMDAS,we obtain
n^2 - 4n - 6n + 24n^2 -10n +24Hence,n^2 -10n -24 is the answer.
if you put 25ml of concentration in a glass, how much water should be added
Answer:
50 ml
Step-by-step explanation:
50 ml
Find the distance between the parallel lines y=x-5 and y=x+6
Answer:
11
Step-by-step explanation:
i don't know
Giving a test to a group of students, the grades and gender are summarized below
Grades vs. Gender
A B C
Male 17 18 5
Female 12 3 14
If one student was chosen at random,
find the probability that the student was female.
Probability = (Round to 4 decimal places)
Evaluate.
-|a+bl
2-c
when a = 1, b = -2, and c = -7
Enter your answer as a simplified fraction in the box.
Answer:
-9
Step-by-step explanation:
-|1-2|2+7
-|-1|9
-9×1
-9
Write 4 1/7 as an improper fraction?
Answer:
29/7
Step-by-step explanation:
4 1/7 = 4 + 1/7
4 = 28/7
then:
4 1/7 = 28/7 + 1/7 = (28+1) / 7
= 29/7
A sample has a sample proportion of 0.3. Which sample size will produce the
widest 95% confidence interval when estimating the population parameter?
A. 46
B. 68
C. 56
D. 36
Using the z-distribution, the sample size that will produce the widest confidence interval is given by:
D. 36.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The widest interval has the highest margin of error, and since the margin of error is inversely proportional to the sample size, a lower sample size generates a higher margin of error, hence option D is correct.
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Which of the following is the midpoint between (6, 3) and (-2, -5)
Answer:
( 2, -1)
Step-by-step explanation:
(X1 + X2)/2 , (Y1 + Y2)/2
(6-2)/2 , (3-5)/2
4/2 , -2/2
2 , -1
Answer:
(2, -1)
Step-by-step explanation:
(x1, y1)=(6, 3)
(x2, y2)=(-2, -5)
[(6+(-2))/2, (3+(-5))/2]
=(4/2, -2/2)
=(2, -1)
PLS HELP ME ASAP!! TEN POINTS!!! Select each correct answer.
Answer:
It's 3
Step-by-step explanation:
if you go to desmos graphing calculator it'll help you get the solutions for these if you type it in every number and letter and for exponents type ^ its shift then type 6.
You are choosing between two different cell phone plans. The first plan charges a rate of
21 cents per minute. The second plan charges a monthly fee of $44.95 plus 11 cents per
minute. How many minutes would you have to use in a month in order for the second
plan to be preferable?
Answer:
at least 450 minutes
Step-by-step explanation:
Find an expression for the cost of each plan as a function of the number of minutes. Set the expressions equal to each other, and solve for the number of minutes.
Let x = number of minutes.
First plan:
cost (in dollars) = 0.21x
Second plan:
cost (in dollars) = 0.11x + 44.95
Set the expressions equal:
0.21x = 0.11x + 44.95
Subtract 0.11x from both sides.
0.1x = 44.95
Divide both sides by 0.1
x = 44.95/0.1
x = 449.5
Since you cannot have a fraction of a minute, the answer is 450 minutes.
Sid makes a graph for estimating the y-value.He wants to compare it to the table before he turns it in. Do the table and the graph represent the same function?
Answer:
No
Step-by-step explanation:
The graph and the table do not show the same function as none of the y values on the graph correspond to the y values on the table.
