Answer:
125,664 mm³/s
Step-by-step explanation:
V = (4/3)πr³
dV/dt = (4π/3) × 3r² × dr/dt
dV/dt = 4πr² × dr/dt
dr/dt = 4 mm/s
d = 100 mm; r = 50 mm
dV/dt = 4π(50 mm)² × 4 mm/s
dV/dt = 125,664 mm³/s
Mandy owns a car dealership in which her employees earn commission for each car they sell in addition to a weekly salary. One employee sells 5 cars and makes $1,700 that week. A second employee sells 6 cars and makes $1,940 that week.
The equation in slope-intercept form as required is; y = 240x + 500
What is partial variation?This is when the value of the dependent variable depends partly on the value of the independent variable and partly on an initial value that is not 0
According to the statements in the task content;
One employee sells 5 cars and makes $1,700 that week.
A second employee sells 6 cars and makes $1,940 that week.
Hence, it follows from partial variation that;
1700 = 5a + b
1940 = 6a + b
Hence, by solving simultaneously, it follows that;
a = 240
b = 500
Hence, the equation in slope-intercept form as required is; y = 240x + 500
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g(x)=14x2^x
a=_
b=_
identify the initial amount a and the growth fact b in the exponential function
In the exponential function the initial amount a = 14 and the growth fact b = 2.
What is exponential function?One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function.
The simplest kinds of dynamical systems have solutions in the form of exponential functions.
Growth or decay can both be described by an exponential function.
g(x)=14x2^x
It is an exponential function.
g(x)=axb^x
where, a is initial amount and b is growth/decay factor.
Now we will compare the function with this one.
a = 14
b = 2
Hence, The initial amount a=14 and factor b=2
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please look at the attachment
The points for the inequality are plotted on the graph attached below.
What is inequality?
A linear inequality is one that, if the equals relation were used in place of the inequality, would provide a linear equation. When multiplying or dividing both sides by a negative number, the direction of the inequality is reversed when the problem is solved. The solution set for an inequality is the set of all solutions.
We are given an inequality as y ≤ 6x/5 - 6
Now, in order to plot the points, we need to find x and y
So, let y be 0, then
⇒0 ≤ 6x/5 - 6
⇒6 ≤ 6x/5
⇒6 ≤ 6x/5
⇒5 ≤ x
So, we get first point as (5,0).
Now, let x=0, then
⇒y ≤ 6(0)/5 - 6
⇒y ≤ -6
So, we get second point as (-6,0).
From these two points, the graph is plotted which is shown below.
Hence, the graph for the inequality is plotted.
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gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. it forms a pile in the shape of a right circular cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 25 feet high?
Below is the answer
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What is the value of 8.3x10^4
Answer: 83000
Step-by-step explanation:
Lucy says the hypotenuse is 15 Annie says its 117. Timo says it rounds to 11.
Explain who is right. PROVE your answer using Pythagoras visually or numerically.
Answer: Timo is correct; the hypotenuse rounds to 11
Work Shown:
[tex]a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{6^2+9^2}\\\\c = \sqrt{36+81}\\\\c = \sqrt{117}\\\\c \approx 10.81665\\\\c \approx 11\\\\[/tex]
This confirms Timo is correct.
It appears Lucy mistakenly added the side lengths 6 and 9 to get 6+9 = 15, which is not the correct way to get the hypotenuse.
Annie mentioning the 117 seems to suggest that she might have forgotten about the square root, since we got [tex]\sqrt{117}[/tex] earlier in the steps shown above.
If Annie said [tex]\text{The hypotenuse is } \sqrt{117} \text{ units long}[/tex], then she would be correct. Though it's probably better to go with the decimal form (rounding however you want) to get a better sense of how long the hypotenuse is.
given f(x) = 3x^2 - 9, find f(1)
Answer:
Answer is in attached photo.
Step-by-step explanation:
SolutionSolution is in attached photo, this question is testing on function substitution. (Substituting an input to get an output.)
A book sold 32,900 copies in its first month of release. Suppose this represents 9.1% of the number of copies sold to date. How many copies have been sold to date?
The number of copies that have been sold to date approximately is equal to 361,538 copies.
What is a percentage?In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
How many copies have been sold to date?In order to determine the number of copies that have been sold to date, we would develop an expression to multiply the total number of copies (T) by the percentage of the number of copies sold in its first month of release as follows;
9.1/100 × T = 32,900
0.091T = 32,900
Dividing both sides of the equation by 0.091, we have the following:
Total number of copies (T) = 32,900/0.091
Total number of copies (T) = 361,538 copies.
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Sheng drives at a constant speed for 0.2
hours to get to the train station. He then boards a train that takes him 35
miles to downtown. His whole trip is 42
miles long.
How can Sheng determine his driving speed?
The train travels an average 12 miles/hr
We always need to be working in the same units, so lets convert the trains speed to minutes since the time traveled is in minutes.
12 miles / 60 min = 0.2 miles/min
A camera has a listed price of $653.99 before tax. If the sales tax rate is 8.5%, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
Answer:
$709.58
Step-by-step explanation:
The total cost is 100% plus the tax rate of 8.5%, it will be 108.5%
To find the cost of the camera with the sales tax included, we take
$653.99 divided by 100, then times 108.5 = $709.58
So, the cost of the camera with sales tax is $709.58
Please solve this linear equation
7x-3y=-5
3x+2y=11
The value of x and y in the equation are 1 and 4 respectively
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 , 4x − 4y = 4.
7x-3y=-5 equation 1
3x+2y=11 equation 2
using elimination method, we multiply the coefficient of x by both equations
21x- 9y = -15 equation 3
21x +14y = 77 equation 4
subtract equation 3 from 4
23y = 92
y = 92/23
y = 4
substitute 4 for y in equation 1
7x -3(4) = -5
7x -12 = -5
7x = -5+12
7x = 7
x= 7/7= 1
therefore the value of x and y are 1 and 4 respectively
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A rectangle has an area of 174. 8m2
One of the sides is 3. 8m in length.
Work out the perimeter of the rectangle.
The perimeter of the rectangle with area 174.8m² and side-length 3.8m is equal to 99.6 meters.
Area of the rectangle is equal to 174.8 m².
Length of the rectangle is equal to 3.8 m
let us consider 'w' be the width of the rectangle.
area of the rectangle = length × width
⇒ 174.8 = 3.8 × w
⇒ w = 174.8 / 3.8
⇒ w = 46 m
Perimeter of the rectangle = 2 ( length + width )
⇒ Perimeter of the rectangle = 2 ( 3.8 + 46 )
⇒ Perimeter of the rectangle = 2 ( 49.8 )
⇒Perimeter of the rectangle = 99.6 meter.
Therefore, the perimeter of the rectangle with length 3.8m and width 46m is equal to 99.6m.
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You have a recipe that indicates to use 7 parts of sugar for every 6 parts of milk. You use 28 cups of sugar. How much milk do you need?
7/6 = 28/x
To solve for x, you can cross-multiply:
7 * x = 6 * 28
Simplifying:
x = 6*28/7
x = 24
So, you would need 24 cups of milk.
Answer:
28 cups of sugar / 7 parts of sugar = 4 cups
If 4 cups is 1 part, 6 parts of milk would be 4 x 6
4 x 6
= 24
You would need 24 cups of milk.
in hillsboro, the use of landlines has been declining at a rate of 10% every year. if there are 86,652 landlines this year, how many will there be in 12 years?
Answer: A decline of 10% per year means that the number of landlines will be multiplied by 0.9 (100% - 10%) every year.
So, in 12 years the number of landlines will be multiplied by 0.9^12 = 0.531441
So, in 12 years there will be 86,652 * 0.531441 = 46,115.69 landlines.
Rounded to the nearest whole number there will be 46,116 landlines in 12 years.
Step-by-step explanation:
Answer: 24,473
Step-by-step explanation: This is the formula for exponential decay:
y=a(1–r)t
In this formula, a is the initial amount, r is the rate of decrease expressed as a decimal, t is the elapsed time, and y is the final amount.
solve
Plug in 86,652 landlines for the initial amount, 0.1 for the rate of decrease, and 12 years for the time elapsed.
y
= a(1–r)t
y
= 86,652(1–0.1)12 Plug in values
y
= 86,652(0.9)12 Subtract
y
= 86,652(0.28242…) Simplify
y
= 24,473.08419… Multiply
Round to the nearest whole number.
24,473.08419… → 24,473
To the nearest whole number, there will be 24,473 landlines.
{96 divide[36 divide 3-(18x2-30)]} divide(31-16+1)
Note that the answer to the expression {96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) Is: one (1). This problem is solved using PEMDAS.
What is PEMDAS?
PEMDAS is the acronym for parenthesis, exponents, multiplication, division, addition, and subtraction. These operators must be solved exactly in the order given above. Thus:
{96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1)
⇒ {96 ÷ [36÷3-(6)]} ÷ (31-16+1)
⇒ {96 ÷ [12-6]} ÷ (31-16+1)
⇒ {96 ÷ 6} ÷ (31-16+1)
⇒ 16 ÷ 16
⇒ 1
Thus, it is correct to state that the answer to the mathematical expression {96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) is 1 or
{96 ÷ [36÷3-(18 x 2 - 30)]} ÷ (31-16+1) = 1
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Graphs the function. Question c
Answer: Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (3,−4)
Focus: (3,−15/4)
Axis of Symmetry: x = 3
Directrix: y = − 17/4
X Y
1 0
2 -3
3 -4
4 -3
5 0
Step-by-step explanation:
There are 875 hotel rooms in Edwin's city. During a convention, 16% of the hotel rooms were occupied. How many occupied hotel rooms were there during the convention?
The number of occupied rooms is 140 rooms
What is percentage?Percentage can be defined as a ratio or number that is expressed as a fraction of the number, 100.
It is denoted the the percent sign, "%"
Percentage is known as a dimensionless number. This means that is it has no unit of measurement.
They can also be represented in fraction or decimal forms, like 0.3%, 0.5%, etc
From the information given, we have that;
875 hotel rooms were avaliable16% of the rooms were occupiedThe number of occupied rooms is;
= 16/100 × 875
Find the fraction
=0. 16 × 875
multiply the values
= 140 rooms
Hence, the value is 140 rooms
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x^-4/x^3 times x^-7 in equivalent expression
x^-4/x^3 times x^-7 in equivalent expression is x⁻¹⁴
What are index forms?The index form of a number can be defined as the number that is written as an exponential expression.
It is also seen as the single number that is raised to another number.
The rules of index forms are;
Multiplying the index forms when they have the same base, add the exponents or powersDividing indices, in dividing, they must have the same base so subtract the powers Brackets with indices. When there is a power outside the parentheses, then multiply the powersFrom the information given, we have that;
x⁻⁴/x³ × x⁷
Since the denominators are of the same base, add the powers
x⁻⁴/x³⁺⁷
Add the values
x⁻⁴/x¹⁰
Now, subtract the powers
x⁻¹⁴
Hence, the value is x⁻¹⁴
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5) Which number is 10 times less than 45.3?
a) 453.0
b) 45.30
c) 4.53
d) 0.453
Answer: 4.53
Step-by-step explanation:
10 times less than 45.3 means that you will be looking for an answer that is the solution to 45.3 / 10, which equals 4.53.
What is equal to 4 pencils every 2 students
Assignment 2: Room Area
A scientist is developing a new method to reduce the population of a certain invasive insect species. For an experiment, the scientist starts with 2,500 insects. She predicts that her new method will reduce the number of insects in the experiment by 14% each week.
Write an exponential equation in the form y=a(b)x that can model the predicted number of insects, y, in the experiment after x weeks.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential equation to represent the reduce rate of the insects as conducted in the new experiment with initial population of 2500 is given by y(n) = 2500 ( 1 - 0.14 ) ⁿ.
What is Exponential equation ?
Exponential equation can be defined as the equation in which it contains the exponent.
The exponential equation in the 'y' form to represent the reduce rate of the insects 14% as conducted in the new experiment with initial population of 2500 is given by y(n) = 2500 ( 1 - 0.14 ) ⁿ.
As given in the question,
Initial population scientist starts with is given by P₀ = 2500 insects
Rate by which number of insects reduce each week = 14%
= 0.14
Let time be 'n'
Final population of the insects represented by y(t)
Exponential equation to represents the reduce rate each week is given by :
y(n) = P₀( 1 - r ) ⁿ
⇒ y(n) = 2500 ( 1 - 0.14 ) ⁿ
Therefore, the exponential equation to represent the reduce rate of the insects as conducted in the new experiment with initial population of 2500 is given by y(n) = 2500 ( 1 - 0.14 ) ⁿ.
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amy drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 12 hours. when amy drove home, there was no traffic and the trip only took 8 hours. if her average rate was 20 miles per hour faster on the trip home, how far away does amy live from the mountains?
If her average rate was 20 miles per hour faster on the trip home, Amy live 480 miles far from the mountains
Suppose Amy lives x miles from the mountains.
Fill in x as both distances and the times
going and coming 12 hours and 8 hours.
Distance | speed | time
To mountains | x | 8
Coming home | x | 5
Use: speed =distance/ time
to fill in the two rate boxes:
Distance | Speed | time
To mountains | x | x/12 | 8
Coming home | x | x/8 | 5
The equation comes from this sentence:
Her average rate was 20 miles per hour faster on the trip home
Her speed coming home late = Her speed going to the mountains + 20 miles per hour
x/8 = x/12+20
20 = x/8-x/12
20 = x/24
x = 24×20
x = 480
So Amy lives 480 miles from the mountains.
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Katy wants to wrap a present that is 15cm wide, 18cm deep and 4cm high. How much wrapping paper will she need to use?
If Katy wants to wrap a present that is 15cm wide, 18cm deep and 4cm high , then amount of wrapping paper that she need to use is 804 cm² .
Katy is wrapping a gift ,
the dimensions of the box that needs to be wrapped is ⇒
length(l) is = 15cm , width(w) is = 18cm and height(h) is = 4cm .
the present is in shape of cuboid ,
we know that Total Surface Area of cuboid is = 2(lw + wh + hl) ;
substituting values of length , width and height ,
we get ;
Area is = 2(15×18 + 18×4 + 4×15)
= 2( 270 + 72 + 60)
= 2( 402 )
= 804 cm² .
Therefore , Katy will need 804 cm² of wrapping paper to wrap the gift .
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The dot plots below show the number of students present in Mr. King's first and second period classes each day in April.
2 dot plots showing the number of students present in Mr. King's first and second period. X axis is labelled number of students present.
The mean absolute deviation for each class period is 1.4. The difference between the mode number of students present for each class period is how many times the mean absolute deviation?
A.
6
B.
5
C.
7
D.
4
The mode of each data-set is given by the input that has the most dots in the dot plot.
After obtaining the mode, the difference is obtained subtracting the mode from the MAD of 1.4 for each data-set.
How to obtain the modes and the difference?A dot plot shows the number of times that each observation appears in the data-set.
The mode of a data-set is the observation that appears the most times in the data-set, hence it will be given by the observation with the most dots in the dot plot.
The mean absolute deviation is of 1.4, then for each data-set the mode is subtracted by 1.4.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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True or false
The following graph represents a maximum:
f(x)=3x^2+2
Answer:
False
Step-by-step explanation:
Answer come only two
The table shows the decrease in the amount of chicken feed in a farmer's barn over a seven-month period. Let x represent the number of months since March. Write a linear regression equation for the data. Explain what does the linear regression equation for the data represents in the problem situation.
This data's linear regression equation is y = mx + b, where y is the quantity of chicken feed, x is the number of months since March, m is the line's slope (or the rate at which y changes with respect to x), and b is the y-intercept (or the value of y at x = 0).
The pace at which the amount of chicken feed has been decreasing over time is seen by the slope of the line. The beginning quantity of chicken feed in the barn in March is represented by the y-intercept.
Based on the rate of reduction and beginning quantity for each month since March, the linear regression equation may be used to forecast the amount of chicken feed in the barn in the issue situation.
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which part of the expression -2(3 +4) is the sum of two terms
The part containing the sum of two terms in the given expression can be found to be as (3 + 4) and (6 + 8) respectively.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
here, we have,
The given expression is 2(3 + 4).
It can be rewritten as follows,
2(3 + 4)
=2 × 3 + 2 × 4
=6 + 8
or, 2 × 7
Thus, in order to find the expression for sum of two terms in the given expression, there can be two possible ways, the first is (3 + 4) and the other is (6 + 8).
Hence, the sum of two terms in the given expression is found to be as (3 + 4) and (6 + 8) respectively.
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using only the digits $7$, $8$ and $9$, how many positive seven-digit integers can be made that are palindromes?
Using the digits 7,8 and 9, the positive seven-digit integers can be made that are palindromes are 729.
When constructing a seven-digit palindrome out of the digits 7, 8, and 9, the first three digits must be the same as the last three digits in reverse order.
This means that each of the first three digits can be either a 7, 8, or 9. Therefore, the total number of combinations for the first three digits is 3 x 3 x 3 = 27.
Since the last three digits must match the first three, the total number of possible combinations of integers is 27 x 27 = 729.
Thus, the total number of positive seven-digit palindromes that can be created using the digits 7, 8 and 9 is 729.
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from a (western) standard 52-card deck, how many ways are there to draw two cards such that the first card is a spade and the second card is a queen?
So, there are 52 ways to draw two cards such that the first card is a spade and the second card is a queen.
In a standard 52-card deck, there are 13 cards of each suit: spades, hearts, diamonds, and clubs. Each suit has 4 face cards (Jack, Queen, King, and Ace) and 9 numbered cards (2 through 10).
To find the number of ways to draw two cards such that the first card is a spade and the second card is a queen, we first need to determine the number of spades in the deck, and then the number of queens.
There are 13 spades in a standard 52-card deck, so there are 13 ways to draw a spade as the first card.
There are 4 queens in a standard 52-card deck (one from each suit), so there are 4 ways to draw a queen as the second card.
To find the total number of ways to draw two cards such that the first card is a spade and the second card is a queen, we multiply the number of ways to draw each card: 13 * 4 = 52 ways.
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the area of a rectangle field is 7350m to the second power. if the length of the field is 98m, what is its width
Answer:
Step-by-step explanation:
The formula of the area of a triangle is equal to Length multiply by Width[A = L * W]
Therefore:7350m[tex]x^{2}[/tex] = 98 * W.7350m[tex]x^{2}[/tex] = 98W.7350m[tex]x^{2}[/tex]/98 = 98W/98.Thus: 7350 divided by 98 is 75 which is the width.W=75m .