6.
We know area of circle is
[tex]\pi r^2[/tex]Radius increases at a rate of 4.
So, we can write:
[tex]\frac{dr}{dt}=4[/tex]We want rate of change of area. Thus,
[tex]\begin{gathered} A=\pi r^2 \\ dA=2\pi\text{rdr} \\ \frac{dA}{dt}=2\pi r\frac{dr}{dt} \end{gathered}[/tex]We want dA/dt at r = 7, so substituting all that we know:
[tex]\begin{gathered} \frac{dA}{dt}=2\pi r\frac{dr}{dt} \\ \frac{dA}{\text{dt}}=2\pi(7)(4) \\ =56\pi \end{gathered}[/tex]The correct answer: 56*pi m^2/min
On Monday, your English teacher gives you a list of twenty-five vocabulary terms to be memorized. You memorize all of them Monday night and do not look at the list again. Because you do not study again, you forget 6% of the list each day.a. Does this problem represent exponential growth or decay? How do you know?b. Which exponential formula below will you use for this problem? Why?(Your choices are f(x) = a (1 + r) or f(x) = a (1-ry')c. Write the formula for this specific problem. Explain how you know where each number goes in the formula.d. How many terms will you remember seven days later for the test? Show all your work and explain your computations.
Answer:
a. Exponential decay
b. f(x) = a (1 - r)^x
c. f(x) = 25(1 - 0.06)^x
d. 16 terms
Explanation:
a. Does this problem represent exponential growth or decay? How do you know?
Each day the number of terms that you know is less than the day before, so there is a decrease in the vocabulary terms memorized. It means that the problem represents exponential decay.
b. Which exponential formula below will you use for this problem? Why?
The formula for the exponential decay is:
[tex]f(x)=a(1-r)^x[/tex]Where a is the initial value and r is the rate of decay.
So, the formula that you will use is f(x) = a (1 - r)^x
c. Write the formula for this specific problem. Explain how you know where each number goes in the formula.
The initial value is 25 terms and the decay rate is 6%, so the specific equation is:
[tex]f(x)=25(1-0.06)^x[/tex]d. How many terms will you remember seven days later for the test? Show all your work and explain your computations.
Now, we need to replace the value of x by 7, so:
[tex]\begin{gathered} f(7)=25(1-0.06)^7 \\ f(7)=25(0.94)^7 \\ f(7)=25(0.6485) \\ f(7)=16.21 \end{gathered}[/tex]Therefore, you will remember 16 terms seven days later.
A company manufactures calculators and sells them at $50 each. The fixed costs are $4000 per month and the variable costs per unit are $32. Calculate the number of units that need to be manufactured and sold per month to break even.
The number of units that is needed to be manufactured and sold per month by the company to break even is 222 units
How to calculate the number of units needed to break even ?The first step is to write out the parameters given in the question
The sales price per unit is $50
The fixed cost per month is $4000
The variable cost per unit is $32
The formula for calculating the units needed to break even can be expressed as follows
Fixed Costs ÷ (Sales price per unit – Variable costs per unit)
4000/(50-32)
= 4000/18
= 222.2
Hence 222 units are needed to be manufactured per month
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what is the ratios of 29:1, and the math eqation.
The ratio of 29: 1 is 29
The mathematical equation is 29/1
A ratio can simply be defined as an ordered pair of numbers, say x and y, written in the form x / y where of the denominator is note equivalent to zero.
It is known to explain how many times a given number contains another number in a proportion.
It is seen as the comparison of two numbers , elements or quantities having the same units and moving further to explain how much of one of the element or quantity is present in the another one.
This is achieved based on their magnitude or sizes.
A proportion is a mathematical equation with which two ratios are set equivalent to each other.
A ratio is expressed mathematically as;
x/y
Given the ratio;
29: 1
The equation is = 29/1 = 29
Hence, the ratio is 29
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Increase 10kg by 20%
I'm genuinely tonta right now please help
When 10kg is increased by 20%, the number becomes 24%
What is the result of the percentage increase?
Percentage is a measure of frequency that is used to express a quantity as a number out of 100. The sign that is used to represent percentages is %. In order to convert a number to a percentage, multiply the number by 100.
The new increased number = (100% + percentage increase) x initial number
(100 + 20%) x 20%
120% x 20%
1.20 x 20% = 24%
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Solve: (6x2 + 5x + 1) ÷ (x + 2).
A.) 6x - 7
B.) 6x - 7 - x/15 + 2
C.) 6x + 8
D.) 6x - 7 + 15/ x+ 2
Answer:
d
Step-by-step explanation:
Divide
6x2+5x+1
x+2
=6x−7+
15
x+2
NO LINKS!!! Part 2 Please help me with this Similarity Practice
Answer:
C' = (15, 7)
Dilation by a scale factor of 3 with the origin (0, 0) as the center of dilation, followed by a translation of 1 unit up.
Step-by-step explanation:
If two triangles are said to be similar, their corresponding angles are congruent and their corresponding sides are in the same ratio.
Given vertices of triangle ABC:
A = (0, 0)B = (1, 4)C = (5, 2)To maintain similarity (and thus keep the corresponding angles of both triangles the same) but not maintain congruence, dilate triangle ABC.
Given:
B' = (3, 13)If ΔABC is dilated by a scale factor of 3, with the origin as the center of dilation, B' = (3, 12). If the triangle is then translated 1 unit up, B' = (3, 13), which matches the given coordinate of point B'.
Therefore, the series of transformations is:
Dilation by a scale factor of 3 with the origin (0, 0) as the center of dilation.Translation of 1 unit up.Mapping Rule: (x, y) → (3x, 3y + 1)
Therefore, the coordinates of point C' are:
⇒ C' = (3(5), 3(2) + 1) = (15, 7)
Molly grows corn on her farm to sell for pig feed. one of her fields produced 176.4 bushels of corn this year . if corn is currently selling 3.75 per bushel, how much will molly earn from this field
This year, one of her fields yielded 176.4 bushels of corn. $661.5 will Molly make from this field if corn is now selling for $3.75 per bushel.
Given that,
On her farm, Molly raises corn that she sells for pig food. This year, one of her fields yielded 176.4 bushels of corn.
We have to find how much will Molly make from this field if corn is now selling for $3.75 per bushel.
We have to multiply
=176.4×3.75
=661.5
Therefore, $661.5 will Molly make from this field if corn is now selling for $3.75 per bushel.
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In the high school band there are two percussionist to every seven marching instruments at the high school bad has a total of 180 members that how many percussionists are on the sidelines
The number of percussionists on the sidelines is 40.
What is a proportion?A proportion is an equation that equalizes two ratios. By dividing the provided values, we may determine the missing value. One way to express the proportion formula is as a: b::c : d = a/b = c/d. Here, a and d are the extreme terms and b and c are the mean terms.Given:
Total number of members in high school band = 180
Let's assume "x" is the number of percussionists that are on the sidelines.
According to the question, there are two percussionists to every seven marching instruments. Then,
Number of members = 7 + 2 = 9
You can write the following proportion knowing that there are 180 total members of the high school band:
[tex]\frac{x}{180} = \frac{2}{9}[/tex]
Solving the proportion to get the value of x,
[tex]x = \frac{2}{9} * 180[/tex]
x = 40
Therefore, there are 40 percussionists on the sidelines.
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These box plots show the basketball scores for two teams.Bulldogs55708090105Wolverines355580 8596ㅏ30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110Basketball scoresCompare the shapes of the box plots.
Solution
The bullfdng dataset has its median close to the center of the boxplot.
- This implies that the dataset is symmetric.
- The wolverine dataset has its median moved to the right at 80, implying that it is NOT symmetric.
- However, because there is a skew to the left of datapoints, we say that the dataset is negatively skewed
Final Answer
OPTION A
Solve for x.
(x - 2)² = 2
The value of x is 4 and 0
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. A simple algebraic equation is 2x + 4 = 8. Algebraic expressions are the result of performing operations on variables and constants, such as addition, subtraction, multiplication, division, etc. Consider that James and Natalie came up with the notion to arrange matchsticks into numerical patterns when they were fiddling with them.
Given that : [tex](x-2)^{2} = 2[/tex]
[tex](x-2)^{2} = 2[/tex]
(x-2)=±2
x= 4
x=0
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Let f(x)=x+1 and g(x)=x^2-x. Find and simplify the expression. (f+g)(-5)
Answer:
26
Step-by-step explanation:
(f+g)(-5)=
f(-5)+g(-5)=
-5+1+(-5)^2-(-5)=
-4+25+5=
-4+30=
30-4=26
2. Solve the following addition problem. Remember to carry as necessary.
6 cu yd 9 cu ft
134 cu in
+ 1 cu yd 12 cu ft
200 cu in
The solution to the given addition problem is 150.6 ft^9.
Converting everything to the same unit is the simplest solution to this problem.
The conversions are:
1 cubic yard = (27 cubic feet)
1 cubic inch = (0.000578704 cubic feet)
The addition can be performed as,
(6 cu yd × 9 cu ft × 134 cu in) + (1 cu yd × 12 cu ft × 200 cu in)
= [6(27 cu ft) × 9 cu ft × 134(0.000578704 cu ft)] + [1(27 cu ft) × 12 cu ft × 200(0.000578704 cu ft)]
= 150.6 ft^9
The result of the addition is 150.6 ft^9.
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Rewrite the expression 26 + 8 as the product of the GCF (greatest common factor) and a sum. Then, simplify the expression. Show all of your steps. pls help due today
The expression 26+8 as the product of the GCF and a sum is:
2(13+4).
Given we have the expression as 26+8
We need to find the greatest common factor of the numbers 26 and 8.
26 = 2 × 13
8 = 2 × 2 × 2
Multiply all the prime factors that both numbers share in order to determine the GCF:
Therefore, GCF = 2
Now we can write the expression as:
26 + 8
=2(13 + 4)
=2×17
=34
Hence we get the required expression as 2(13 + 4).
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a bag contains 3 red marbles, 3 white marbles,, and 5 blue marbles. only white marbles will be added to the bag. how many white marbles should be added to the bag to make the probability of pulling a white marble 50%?
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
a 50% probability means 1/2 or 0.5.
that means
desired cases = 1/2 × totally possible cases
at start we have
3 red
3 white
5 blue
that makes 5 + 3 + 3 = 11 totally possible cases and 3 desired cases.
so, the starting probability to pull a white marble is
3/11.
now, we need to say
(3 + x) = 1/2 × (11 + x) (= (3+x)/(11+x) = 1/2)
to make is simpler we multiply both sides by 2 (so we get rid of the 1/2 fraction).
6 + 2x = 11 + x
6 + x = 11
x = 5
we need to add 5 white marble to give us a 50% probability to pull a white marble.
we have then
3 red
3 + 5 = 8 white
5 blue
that makes 5+8+3 = 16 totally possible cases and 8 desired cases.
so, the probability is
8/16 = 1/2
=> our calculation was correct
The number of white marbles should be added to the bag to make the probability of pulling a white marble 50% will be 5.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
A bag contains 3 red marbles, 3 white marbles, and 5 blue marbles. only white marbles will be added to the bag.
Let 'x' be the number of white marble added. Then the equation is given as,
0.50 = (x + 3) / (x + 3 + 3 + 5)
Simplify the equation, then we have
0.50 = (x + 3) / (x + 3 + 3 + 5)
0.50 = (x + 3) / (x + 11)
0.50x + 5.5 = x + 3
0.50x = 2.5
x = 5
The number of white marbles should be added to the bag to make the probability of pulling a white marble 50% will be 5.
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Consider the graph of the function f(x) = 2^x Which statements describe key features of function g if g(x) = f(x + 2)?
The statements that describe key features of function g if g(x) = f(x + 2) are;
a. y-intercept at (0,4)
b. domain of {x|-∞ < x < ∞}
c. horizontal asymptote of y = 0
What are the features of the Function?We are given the function f(x) = 2^(x)
We want to find the features of the function g if;
g(x) = f(x + 2)
Let us first find f(x + 2);
g(x) = f(x + 2) = 2^(x + 2)
The y-intercept is when x = 0;
g(0) = 2^(0 + 2)
g(0) = 4
Some features in a function that limit the x values are: roots, fractions, etc.
g(x) = 2^(x + 2) does not have any restricting value of x.
This means the value of x ranges from negative infinity to positive infinity.
Hence, the domain is: (-∞, ∞)
Next, calculate the horizontal asymptote.
To do this, we plot the graph of g(x) --> see attachment
Then we trace a horizontal line from the horizontal part of the curve of g(x) till it gets to the y-axis.
From the attached graph of g(x), the line touches the y-axis at y = 0
So, the horizontal asymptote is: y = 0
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The missing options are;
a. y-intercept at (0,4)
b. domain of {x|-∞ < x < ∞}
c. horizontal asymptote of y = 0
d. horizontal asymptote of y=2
e. y-intercept at (0,1)
Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
The perimeter of the rectangle below is 104 units. Find the length of side RS
Write your answer without variables
Answer:
24
Step-by-step explanation:
Opposite sides on a rectangle are equal
So 2(3x+3)+2(4x)=104
Now expand, so 6x+6+8x=104
Simplify like terms, 14x+6=104
14x+6-6=104-6
14x=98
14x/14=98/14
x=7
Now just substitute the 7 in for the 3x+3 as thats what we are looking for.
3×7+3=24
which of the following is the rational algebric expression of the verbal phrase below? the ratio of the sum of 2x and 4y and the difference of 8x and 10y.
638x636y73637zy
Answer:
Because first multiple and divide and Again Multiple and ans
What is the value of x that makes this equation true?4x+5=x+14
Explanation:
To solve for x first we have to put all terms that contain x together:
[tex]4x+5=x+14[/tex]Substract x from both sides:
[tex]\begin{gathered} 4x-x+5=x-x+14 \\ 3x+5=14 \end{gathered}[/tex]Now substract 5 from both sides:
[tex]\begin{gathered} 3x+5-5=14-5 \\ 3x=9 \end{gathered}[/tex]And finally divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{9}{3} \\ x=3 \end{gathered}[/tex]Answer:
x = 3
Find the derivative of the function. F(x) = (5x² + 2x³)^4
Answer:
Derivative of y=(x⁴-2x³+5x²-4)³
Step-by-step explanation:
ASAP!! The Brown family baked 3 pies for Thanksgiving. They made a pumpkin pie, an apple pie, and a cherry pie. They ate 0.75 of the pumpkin pie, 0.5 of the apple pie, and 0.6 of the cherry pie How many pies did the Brown family eat in all? Record your answer as a decimal number.
Answer: The Brown family ate 1.85 pies in all
Step-by-step explanation: If you think about it all you have to do is 0.75+0.5= 1.25 and then you do 1.25+ 0.6 and then get 1.85 so they ate 1.85 pies in all
Hope this helped!!!!
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 12 miles per hour slower than the westbound train. If the two trains are 300 miles apart after 2 hours, what is the rate of the westbound train?
Answer:
81 mph
Step-by-step explanation:
2x+2(x-12) = 300
The slope of a line is
Answer:
-2
Step-by-step explanation:
You have to use rise over run. For example, to go from (-1,0) to (-2,2), you have to go up 2 squares and go left 1. That gives you 2/-1, which is -2. Hope this helps!
Gus has skydived 4 more times than Nico. Emma has skydived 16 times, how many times has Gus skydived?
We know that Emma has skydived 16 times, and also Emma has skydived twice as many times as Nico, so Nico has skydived:
[tex]\begin{gathered} \text{Emma}=2\cdot\text{Nico} \\ 16=2\cdot Nico \\ Nico=\frac{16}{2}=8 \end{gathered}[/tex]So, Nico has skydived 8 times.
Finally, we know that Gus has skydived 4 more times than Nico, so:
[tex]\begin{gathered} Gus=\text{Nico}\cdot4 \\ \text{Gus}=8\cdot4=32 \end{gathered}[/tex]Gus has skydived 32 times.
ALGEBRA 1 HW!! PLEASE HELP WILL GIVE BRAINLYEST please only answer b
Answer:
20
Step-by-step explanation:
Every 1 hour it cost $20
You can find this by using the equation y2-y1 divided by x2-x1
y2 is 40 y1 is 20
x2 is 2 and x1 is 1
40-20 divided by 2-1 equals 20
I need help with question #8
I Need the answer in 2 minutes
Answer: [tex]\frac{1}{1024}[/tex]
Step-by-step explanation:
[tex]4^{-3} = (2^{2} )^{-3} = 2^{-6}[/tex]
[tex]\frac{2^{-6} }{2^{4} } = 2^{-6-4} = 2^{-10} = \frac{1}{2^{10} } = \frac{1}{1024}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{4^{-3}}{2^4}}[/tex]
[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{2\times2\times2\times2}}[/tex]
[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{4\times4}}[/tex]
[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{16}}[/tex]
[tex]\mathsf{= \dfrac{1}{1,024}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{1}{1,024}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
6 + root 27over 4 - root 3
When the expression given as 6 + √27/4 - √3 is simplified, the value is 6 - 1/4√3
How to determine the value of the expression?The expression is given as
6 + root 27over 4 - root 3
Mathematically, the expression can be represented as
6 + √27/4 - √3
Expand 27 as the product of 9 and 3
So, we have the following equation
6 + √27/4 - √3 = 6 + √(9 * 3)/4 - √3
Expand the products in the above equation
So, we have the following equation
6 + √27/4 - √3 = 6 + √9 * √3/4 - √3
Evaluate the square root of 9 in the above equation
So, we have
6 + √27/4 - √3 = 6 + 3/4√3 - √3
Evaluate the like terms in the above equation
So, we have the following equation
6 + √27/4 - √3 = 6 - 1/4√3
Hence, the value of the expression given as 6 + √27/4 - √3 is 6 - 1/4√3
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what is the domain of y-x^2-1
The domain of the function y = x² - 1 in interval notation is (-∞, + ∞).
What is defined as the domain of the function?A function is simply object that accepts input, appears to apply a rule to it, and returns the result. A function can be thought of as a machine that receives in a number, performs some operation(s), and then outputs the result. The essential thing regarding functions is that they consistently apply the rule. As a result, if the same value is passed through the same function, the output will remain the same. The domain of a function is the collection of all its inputs. Its codomain is the collection of all possible outputs. The range refers to the outputs which are actually used.The given is y = x² - 1.
The domain of the function is;
Except when the expression is undefined, the domain of the representation is all real numbers. Given that there is no real number in this case, the expression is undefined.Thus, the domain of the function in interval notation is (-∞, + ∞).
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I need the answer to this with an explanation. This is ratio.
Given that 2500 students entered the Teacher Education Program.
[tex]\text{Number of male students + Number of female students = 2500}[/tex]20% of the students are male. Thus,
[tex]\begin{gathered} \text{Number of male students = 20\% of 2500} \\ \Rightarrow\frac{20}{100}\times2500 \\ \text{Number of male students = 500} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \text{Number of male students + Number of female students = 2500} \\ 500\text{ + Number of female students =2500} \\ \Rightarrow Number\text{ of female students = 2500 -500 = 2000 } \end{gathered}[/tex]Thus, the ratio of the number of males to the number of females is evaluated as
[tex]\begin{gathered} \text{Number of female : Number of male} \\ 2000\text{ : 500} \\ reducing\text{ to the lowest term gives} \\ 4\colon1 \end{gathered}[/tex]Hence, the ratio of the number of females to the number of males is thus 4:1
QUESTION DOWN BELOW! PLEASE HELP WILL GET 100 POINTS IM STUCK PLEASE HELP EXPLAIN ITS DUE SOON!!
many thanks!!!
ITS DUE SOON!
1) given
2) base angles theorem
3) PN=QN
4) [tex]\angle 3=\angle 4[/tex]
5) MP=OQ
7) PQ, QP
8) MQ=PO
9) ASA