By using the concept of rate of change, it is obtained that
Water level is falling at the rate of [tex]\frac{2}{9\pi}[/tex] m per minute
What is rate of change?
Suppose there is a function and there are two quantities. If one quantity of a function changes, the rate at which other quantity of the function changes is called rate of change of a function.
Here the concept of rate of change has been used
Let the radius of cone at any point be r m and height be h m
Volume of cone = [tex]\frac{1}{3}\pi\times r^2\times h[/tex]
Now,
By the concept of similarity,
[tex]\frac{r}{h} = \frac{4}{16}\\\\\frac{r}{h} = \frac{1}{4}\\\\r = \frac{1}{4}h[/tex]
Volume of cone (V) =
[tex]\frac{1}{3}\times \pi \times (\frac{1}{4} h)^2\timesh\\\\\frac{1}{48}\times \pi \times h^3\\[/tex]
[tex]\frac{dV}{dt} = \frac{1}{48} \times \pi \times 3h^2\times \frac{dh}{dt}\\\\\frac{dV}{dt} = \frac{1}{16} \times \pi \times h^2\times \frac{dh}{dt}\\\\[/tex]
Now,
[tex]\frac{dV}{dt} = -2,\ h = 12[/tex]
So,
[tex]-2 = \frac{1}{16}\times \pi \times (12)^2 \times \frac{dh}{dt}\\\\\frac{dh}{dt} = -\frac{2 \times 16}{\pi \times 12 \times 12}\\\\\frac{dh}{dt} =- \frac{2}{9\pi}[/tex]
So water level is falling at the rate of [tex]\frac{2}{9\pi}[/tex] m per minute
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Eric rode his small motor bike 5 4/5 miles in 1/3 of an hour what is his average speed per mile
The Average speed is 17.4 mph.
What is Average speed?The average speed is calculated by dividing the total distance travelled by the total amount of motion time.
The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.
Average speed = Distance travelled/ Time taken
Given:
Distance = 5 4/5 = 29/5 miles
Time= 1/3 hours
So, Average speed = Distance travelled/ Time taken
Average speed= 29/5 x 3/1
= 87/5
= 17.4 mph
Hence, the Average speed is 17.4 mph.
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In just two days it will be seven days after three days before Halloween. What is the date today ?
Answer:
November 2nd
Step-by-step explanation:
Halloween = Oct. 31
3 days before Halloween (Oct. 31) is Oct. 28
7 days after that it is Nov. 4
2 days before is November 2nd
Please answer this question, URGENT 50 POINT
Answer: Use your brain aka 12 and 7
Step-by-step explanation:isn't this urgent?
Math trigonometry non right angle help please
ong please guys
well, as I said a while back, Heron's Area formula works for any triangle, so long we have all sides, and in this case we do, since it's not a right-triangle SOH CAH TOA won't work, so let's plug the values in Heron's
[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a = 12\\ b = 8\\ c = 6\\ s=\frac{12+8+6}{2}\\ \qquad 13 \end{cases} \\\\\\ A=\sqrt{13(13-12)(13-8)(13-6)} \implies A=\sqrt{13(1)(5)(7)} \\\\\\ A=\sqrt{455}\implies {\Large \begin{array}{llll} A\approx 21.33 \end{array}}~cm^2[/tex]
5,10,20 Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
The given sequence is geometric sequence not arithmetic.
What is arithmetic sequence?An arithmetic sequence is a sequence in which the difference between every two consecutive terms is constant
What is the geometric sequence?A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. It is found by taking any term in the sequence and dividing it by its preceding term.
Difference between arithmetic and geometric sequence:
An arithmetic sequence has a constant difference between each consecutive pair of terms
while
A geometric sequence has a constant ratio between each pair of consecutive terms.
Here, we have a sequence 5,10,20.
So a₁ = 5, a₂ = 10, a₃ = 20
Difference = a₃- a₂ = 20 - 0 = 10
a₂ - a₁ = 10 - 5 = 5
Since the difference is not constant, therefore the given sequence is not arithmetic.
Now ratio a₃/a₂ = 20/10 =2 and a₂/a₁ = 10/5 =2 which is same which shows the sequence is geometric.
Therefore, the sequence is geometric sequence.
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A certain brand of coffee comes in two sizes. An 11.5-ounce package costs 3.19. A 30.6-ounce package costs 7.98. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
The size that is the better one is 30.6-ounce package costs 7.98.
How to calculate the cost?The 11.5-ounce package costs 3.19. The price per package will be:
= 3.19 / 11.5
= 0.27
A 30.6-ounce package costs 7.98. The cost per package will be:
= 7.98 / 30.6
= 0.26
In this case, it should be noted that the cheaper one.is the better buy. This was illustrated as the 30.6-ounce package costs 7.98.
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Find f(x) +g(x) if f(x)=10-3 and g(x)=-x+3
Answer:
10 - x
Step-by-step explanation:
Since f(x) = 10 - 3, we can replace the "f(x)" in the equation with "10 - 3". Likewise, we can replace the "g(x)" in the equation with "-x + 3" because g(x) = -x + 3:
10 - 3 - x + 3
7 - x + 3
10 - x
Boden's account has a principal of $600 and a simple interest rate of 3.5%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
Answer:$84
Step-by-step explanation:
$84 dollars because 3.5 percent of 600 is 21 so if we do 21x4=$84 well atleast that't what i think
Jacob reduced the size of a painting to a width of 3. 2 inches. What would be the new height if the painting was originally 42. 88 inches in width and 33. 5 inches tall?.
The new height of painting by Jacob will be 2.5 inches.
The ratio and proportion will be used to relate the original and reduced dimensions of painting. The original width and height = 42.88/33.5. Let us assume the new height be x. So, new width and height = 3.2/x. Equating these two fractions -
42.88/33.5 = 3.2/x
Rewriting the equation according to x
x = (3.2 × 33.5) ÷ 42.88
Performing multiplication in numerator
x = 107.2 ÷ 42.88
Performing division on Right Hand Side of the equation
x = 2.5
Thus, the new height will be 2.5 inches.
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Show that there exist a rational number a and an irrational number b such that a^b is irrational.
Answer:
In explanation below.
Step-by-step explanation:
Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.
Find the nth term of the sequence 90,81,72,63
Answer: 9.
Step-by-step explanation:
These are all multiples of 9, meaning that they can all be divided by 9 into a whole number.
90/9 =10
81/9 =9
72/9 =8
63/9 =7
Answer:
9:N
Step-by-step explanation:
90-9=81
81-9=72
72-9=63
The same number (9) is used to fing the sum of the next number in the sequence therefore that is your nth term
In Cedarburg, the library is due south of the courthouse and due west of the community
swimming pool. If the distance between the library and the courthouse is 12 kilometers and
the distance between the courthouse and the city pool is 13 kilometers, how far is the library
from the community pool?
kilometers
The library is 5 kilometres far from the community pool.
According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC, where BC² = AB² + AC² is present. The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation.
The distance between the courthouse and the library is 12 kilometres and the distance between the courthouse and the city pool is 13 kilometres. Let the distance between the library and the community pool be x and it can be observed that the Courthouse, library and Community hall form a sort of right-angled triangle
So, using Pythagoras theorem, we get
[tex]13^2=x^2+12^2\\x^2=169-144\\x^2=25\\x=5 km[/tex]
So, the library is 5 kilometres far from the community pool.
Therefore, the distance between the library and the community pool is 5 kilometres.
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Shawn had some nickels in a jar. He put 147 nickels in the jar. Now there are 435 nickels in the jar. How many nickels were in the jar at the start?
Responses
A 288288
B 218218
C 312312
D 398398
Answer:
A
288 nickels
Step-by-step explanation:
There are now 435 nickels, after he put in 147. To find the answer, we need to find what the amount of nickels was before Shawn put in the 147. So, we need to subtract 147 from 435.
435 - 147 = 288
So, there were 288 nickels in the jar at the start.
Please help me please
The value of all the missing angles is in the measure of m∠1 = 88°, m∠2 = 42°, and m∠3 = 113°.
We know that,
Sum of all angles of triangle = 180°.
Therefore, m∠3 + 42° + 25° = 180°.
m∠3 = 180° - 67°
m∠3 = 113°
Vertical angles: Vertical angles are the angles that are opposite to each other when two lines cross.
We know that,
Vertical or opposite angles have equal measures.
So, 42° and m∠2 are vertical or opposite angles.
Therefore, the value of m∠2 = 42°.
Similarly, for m∠3, We know that,
Sum of all angles of triangle = 180°.
∴ ∠1 + ∠2 + 50° = 180°.
=> ∠1 + 42° + 50° = 180°
=> m∠1 = 88°.
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1-8: MathXL for School: Practice & Problem Solving
0 Assignment is past due (10/27/22 11:59pm)
Question Help
The populations of Cities A and B are 3.7 x 105 and 2,115,000, respectively. The population of City C is twice the population
of City B.
The population of City C is how many times the population of City A?
1.8.PS-15
The population of City C is times the population of City A.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest tenth as needed.)
Answer:
11
Step-by-step explanation:
You want the ratio of the populations of city C and city A, given city C is 2 times the 2,115,000 population of city B, and city A's population is 3.7×10⁵.
EvaluationThe ratio of interest is ...
2B/A = 2(2115000)/(3.7×10⁵)
A calculator provides an easy answer to the value of this expression. (See attached.)
City C is about 11 times the population of City A.
__
Additional comment
If you want to work this out "by hand", you will need to find the quotient of ...
4230000/370000 = 423/37 = 11 17/37 ≈ 11
because 17/37 < 1/2.
8x + 5° + 3x + 8° =90
Solve for x pls <3
Answer: x=7°
Combine like terms and divide.
8x+5°+3x+8°=90°
(8x+3x)+(5°+8°)=90°
11x+13°=90°
-13° -13°
11x=77°
[tex]\frac{11x}{11} =\frac{77}{11}[/tex]
x=7°
I need help please!!!!!!!
the slope of the given point is m=9
princeton pretzels picks a package box A 6in 7in 6in box B 3in 8in 9in calculate the volume of each box answer
Answer:
box a - 252 inches squared (6 x 7 x 6)
box b - 216 inches squared (3 x 8 x 9)
Step-by-step explanation:
Which of the following is NOT a solution to -4x + 9 > -3
A: -3
B: -1
C: 3
D:5
Answer:
D
Step-by-step explanation:
-4x + 9 ≥ -3 Subtract 9 from both sides
-4x ≥ -12 Divide both sides by -4. When you divide both sides by a negative number, you must flip the inequality sign.
x ≤ 3
D: 5 is not a solution.
Answer:
D) 5
Step-by-step explanation:
To solve this problem, we must first isolate the variable and simplify the inequality. Isolating the variable means having the variable on one side of an equation or inequality without any other terms?
How do you isolate a variable?
Here's an example.
x+3=18
What can we do to have x on its own side of the equation? Currently, 3 is also with it. If we subtract 3 on both sides, we are leaving the equation with the same answer.
x + 3 - 3= 18 - 3
Combine like terms.
x = 21
That's how you solve for an equation.
Next, an example with division.
3x = 21
How do we solve for x this? Well, we know that 3x = 3 times x. So, to solve for x, we remove the 3. Since its 3 times x, lets divide by 3 on both sides.
[tex]\frac{3x}{3} =\frac{21} {3}[/tex]
Simplify:
3x/3 means 3 times x divided by 3. 3/3 = 1
1x = 21/3
21/3 = 7
x = 7
Now lets get to the problem.
[tex]-4x + 9 \geq -3[/tex]
The first step is to subtract by 9 on both sides so we can work our way to isolating the variable and solving the problem.
[tex]-4x + 9 -9\geq -3 - 9[/tex]
Simplify.
[tex]-4x \geq -12[/tex][tex]-4x \geq -12[/tex]
Now heres the tricky part. To solve for an equation, we must remove -4 from x, or -4 times x. In an equality, which states that:
A [tex]\geq , \leq , > , or < B[/tex]
If you divide or multiply both sides by a negative number, which means the number is less than 0, you must flip the sign!
When you multiply/divide by a negative number or both sides in an equality:
[tex]\leq[/tex] [tex]\geq[/tex]
[tex]\geq[/tex] [tex]\leq[/tex]
> <
< >
So, we currently have:
[tex]-4x \geq -12[/tex]
Divide by -4 on both sides.
[tex]\frac{-4x}{-4} \geq \frac{-12}{-4}[/tex]
Simplify. (Use the rule which states that a negative number multiplied or divided by another negative number equates to a positive number).
[tex]x \geq 3[/tex]
Flip the sign (This is a crucial step!)
[tex]x \leq 3[/tex]
Now, [tex]x \leq 3[/tex] means any number equal to or lower than 3 satisfies the conditions of the inequality.
Is -3 lower than or equal to 3?
Yes; Lower
Is -1 lower than or equal to 3?
Yes;
Is 3 lower than or equal to 3?
Yes; Equal
Is 5 lower than or equal to 3?
No; Greater
D, 5 is your answer as it does not satisfy the inequality.
Given the perimeter of 225 ft. Solve for x and then find the indicated side lengths.
Answer:
X=14
Side GF: 41 ft
Side FE: 58 ft
Side DE: 98 ft
Side DG: 28 ft
Step-by-step explanation:
(13+2x)+(4x+2)+(7x)+(X+14)
6x+15+8x+14
14x+29=225
-29. -29
14x=196
/14. /14
X=14
Fill in 14 for x for each side
13+2(14)
13+28
Side GF: 41 ft
4(14)+2
56+2
Side FE: 58 ft
7(14)
Side DE:98 ft
14+14
Side DG: 28 ft
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a fruit basket contains apples, oranges, and tangerines in the ratio 3:2:5, respectively. what is the total number of apples, oranges, and tangerines in the fruit basket?
The total number of apples, oranges, and tangerines in the fruit basket is in the ratio 10 or 10x
In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.
A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
We know that : the ratio of apples : oranges : tangerines = 3 : 2 : 5.
The total number of apples, oranges, and tangerines in the fruit basket is the total number of ratio, that is 3 + 2 + 5 = 10.
Because of the question is not contain information about the number of pieces, we can describe the dividend with x (or unknown value). So, the total number of apples, oranges, and tangerines in the fruit basket with ratio, that is 10 or 10x.
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if amy has 17 apples and gave 9 to jacob how may does amy hve if she goes to the store and buys 78 more?
Answer:You should have learnt this in kindergarten yet you're in high school, the answer is 86
Dora is paid a salary of $50,000per year. How much would she be paid if she's weekly
Answer:
about 958 dollars
Step-by-step explanation:
50,000÷52.1429 is about 958 dollars weekly
Erin wants to buy a dictionary that costs $12, a dinosaur book that costs $16, and a
children's cookbook that costs $11. She has saved $29 from her allowance. How much
more money does Erin need to buy all three books?
Answer:
Erin would need $10 more dollars in order to buy all three books.
Step-by-step explanation:
Step one: find the cost of all books
12 +16 +11 = 39
Step two: subtract
39 -29 = 10
Step two: Get your Answer!
Erin would need $10 more dollars in order to buy all three books.
g if you randomly select 850 credit card users, what interval will contain the sample proportion for 95% of samples of that size?
The Confidence interval is (0.85,1.05) which contain the sample proportion for 95%of samples size.
Confidence interval is an interval with a confidence level. Confidence interval is always constructed on basis of sample , p = sample statistic - margin of error to sample statistic + margin of error
Confidence interval for a proportion are calculated using the following formula:
p= ( p' - Z√p'(1-q')/n , p'+ Z √p'(1-p')/n ) ---(1)
where, p' ---> sample proportion for sucess
1-p' -----> sample proportion for failure
Z --> Z-value (statistic value)
n---> sample size
we have given that,
sample size ( n)=850 , sample proportion (p') = 0.95 and population proportion= 0.75
a) mean of sample of proportion is same as poplution proportion i.e 0.75 ..
1 -p' = q' = 0.05
Using the formula for margin of error ,
M .E = Z √ p'q'/n ---(2)
as the Z-value for given proportion is 13.46
putting all values in equation( 2) we get,
M.E = 13.45 √0.95×0.05/850 = 0.1005
Now, we shall calculate the confidence interval for given data
confidence interval (p)
= ( 0.95 - 0.100 , 0.95 + 0.100)
p= ( 0.85 , 1.05)
Hence,confidence interval(CI) is (0.85, 1.05).
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Complete Question:
75% of all credit card users carry a balance from month to month. a. If you randomly select 850 credit card users and will compute the sample proportion that carry a balance from month to month, what is the mean of the sample proportion? b. If you randomly select 850 credit card users, what interval will contain the sample proportion for 95% of samples of that size?
Find the value of the variables in the figure. Explain your reasoning.
The value of the variables in the figure is x = 60 degrees and y = 10 degrees.
From the figure:
x + 120 = 180 (since consecutive interior angles equal to 180)
x = 180 - 120
x = 60 degrees.
3y + 40 + 3x - 70 = 180(since supplementary angles = 180)
3y + 3x - 30 = 180
3(y + x) = 180 + 30
y + x = 210/3
y + x = 70
substitute x value
y + 60 = 70
y = 70 - 60
y = 10 degrees.
Therefore the value of the variables in the figure is x = 60 degrees and y = 10 degrees.
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a) 6x(3x+5)-2x(9x-2)=17
b) 2x(3x -1)-3x(2x+11)-70=0
Answer:
a). 18x+30 - 18x+4=17
18x-18x 30+4 =17
34=17
[tex](a) \: { \pink{ \boxed{ \blue{ \sf{x = \frac{13}{30}}}}}}[/tex]
[tex](b) \: { \pink{ \boxed{ \blue{ \sf{x = -2}}}}}[/tex]
Step-by-step explanation:
[tex](a){ \red{ \sf{6x(3x + 5) - 2x(9x - 2) = 17}}}[/tex]
[tex]{ \red{ \sf{ { \cancel{18x}^{2} + 30x \: { \cancel { - 18x}^{2} + 4 = 17}}}}} [/tex]
[tex]{ \red{ \sf{30x + 4 = 17}}}[/tex]
[tex]{ \red{ \sf{30x = 17 - 4}}}[/tex]
[tex]{ \red{ \sf{30x = 13}}}[/tex]
Divide both the sides by 30 then,
[tex]{ \red{ \sf{ \cancel {\frac{30}{30}}}}}{ \red{ \sf{x} = \frac{13}{30}}} [/tex]
[tex]{ \red{ \boxed{ \green{ \sf{x = \frac{13}{30}}}}}} [/tex]
[tex](b) { \red{ \sf{2x(3x - 1) - 3x(2x + 11) - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ { \cancel{6x}^{2} - 2x}}}} \: \: { \red{ \sf{ \cancel { - 6x}^{2} - 33x - 70 = 0}}} [/tex]
[tex]{ \red{ \sf{ - 2x - 33x - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ - 35x - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ - 35x = 70}}}[/tex]
Divide both the sides by -35 then,
[tex]{ \red{ \sf{ \cancel {\frac{ - 35}{ - 35}}}x}}= { \red{ \sf{ { - \frac{ \cancel{70} ^{2} } { \cancel{35_{1} }}}}}}[/tex]
[tex]{ \red{ \boxed{ \green{ \sf{x = -2}}}}}[/tex]
Davis digs a hole at a rate of 3/4 feet every 10 minutes. After digging for 40 minutes, Davis places a bush in the hole that fills exactly 7/8 feet of the hole.
Relative to ground level, what is the elevation of the hole after placing the bush in the hole?
Enter your answer as a simplified fraction. NOT MIXED NUMBER
The elevation of the hole after placing the bush in the hole is 17/8 feet
How calculate the elevation of the hole after placing the bush in the hole?
Given: Davis digs a hole at a rate of 3/4 feet every 10 minutes
After digging for 40 minutes, Davis places a bush in the hole that fills exactly 7/8 feet of the hole
This involves subtraction and multiplication of fractions
Since the rate of digging = 3/4 feet every 10 minutes
Thus, after digging for 40 minutes, the depth will be:
3/4 × 4 = 3 feet
If Davis places a bush in the hole that fills exactly 7/8 feet of the hole, the remaining depth or elevation will be:
3 feet - 7/8 feet = 17/8 feet
Therefore, after placing the bush in the hole, the elevation of the hole is 17/8 feet
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(06.02)
Match the verbal expression (term) with its algebraic expression (definition).
Match
Term
A variable cubed
Quotient of some number and three
Product of an unknown value and three
Three less than a variable
Three more than some number
Definition
A) 3a
B) b + 3
C) z + 3
D) y - 3
E) x³
The values of the statements are x³, b ÷ 3, 3a, y-3, z+3.
What is an Expression?
An expression is a mathematical statement which consists of variables, constants and mathematical operators.
Hence the answer is, the statements are:
A variable cubed : x³
Quotient of some number and three: b ÷ 3
Product of an unknown value and three : 3a
Three less than a variable : y-3
Three more than some number : z+3
Hence the answer is, the values of the statements are x³, b ÷ 3, 3a, y-3, z+3.
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What is the slope of the line represented by the equation 2x-5y=9
The slope of the line represented by the equation 2x - 5y = 9 is 2/5 .
In the question ,
it is given that ,
the equation of the line is 2x - 5y = 9 .
we know that the equation of the line is represented as y = mx + c ,
where slope of the equation is "m" .
So , rewriting 2x - 5y = 9 in the form of y = mx + c ,
w get ,
2x - 5y = 9
5y = 2x - 9
dividing both sides of the equation 5y = 2x - 9 by 5 ,we get
y = 2/5x - 9/5
y = (2/5)x - 9/5
the slope is = 2/5 .
Therefore , The slope of the line represented by the equation 2x - 5y = 9 is 2/5 .
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