Therefore, the volume is changing at a rate of 54 cm3/s when each edge is 3 cm and at a rate of 1014 cm3/s when each edge is 13 cm.
The volume of a cube is given by the formula V = e3, where V is the volume and e is the length of each edge. Therefore, the rate of change of the volume with respect to the edge length is given by the derivative of the volume with respect to the edge length:
dV/de = 3e2
Since the edges are expanding at a rate of 2 cm/s, we can use the chain rule to find the rate of change of the volume with respect to time:
dV/dt = dV/de × de/dt = 3e2 × 2 = 6e2
(a) When each edge is 3 cm, the rate of change of the volume is:
dV/dt = 6(3)2 = 6(9) = 54 cm3/s
(b) When each edge is 13 cm, the rate of change of the volume is:
dV/dt = 6(13)2 = 6(169) = 1014 cm3/s
Therefore, the volume is changing at a rate of 54 cm3/s when each edge is 3 cm and at a rate of 1014 cm3/s when each edge is 13 cm.
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Solve for the solution to a system of equations using the following matrices and Cramer’s rule. Show your work.
A= [2 1] X= [5 1] Y= [2 5]
[1 3] [5 3] [1 5]
I WILL MARK BRAINLIEST INSTANTLY.
Answer:
2 * 1 ==> 1st option
Step-by-step explanation:
Matrix dimensions are:
number of rows by number of columns
The number of rows is 2 : ( 2 and 12 are the rows)
The number of columns is 1 : ( 2
12 )
Hence, the dimensions is 2 * 1.
Listed below is a table showing the number of employees. 20 years or older by gender in the United states
The total number of workers that were studied can be found to be 139,340,000.
The percent of workers unemployed would be 5. 4 %.
Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.
How to find the employment figures ?Number of employed workers :
= 74,624,000 + 64, 716, 000
= 139,340,000
Percentage unemployed :
= ( 4, 209,000 + 3,314,000 ) / 139,340,000
= 5. 4 %
Percentage of unemployed men :
= 4,209,000 / 74,624,000
= 5.6 %
Percentage of unemployed women:
= 3,314,000 / 64, 716, 000
= 5. 1 %
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The full question is:
a. How many workers were studied?
b. What percent of the workers were unemployed?
c. Compare the percent unemployed for the men and the women.
−0.22+�−0.33−0.22x+x−0.33x?
The answer to the equation −0.22x + x − 0.33x is 0.11x.
The answer is 0.11x. To solve this, we can start by rearranging the terms of the equation. The equation can be written as:
−0.22x + x − 0.33x = −0.22 + 0.33x
We then subtract x from both sides of the equation, resulting in:
−0.22x − x = −0.22 + 0.33x − x
We then combine like terms on the left side of the equation, resulting in:
−1.22x = −0.55
Finally, we divide both sides of the equation by -1.22 to solve for x, resulting in:
x = 0.11
Therefore, the answer is 0.11x.
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Complete question
What is the value of -0.22+−0.33−0.22x+x−0.33x?
Please help me on average rate of change!
The averge rate of change on the interval -1≤x≤5 for the given function f(x)= -3|x+2|-1 is -3.
In the given question we have to find the averge rate of change on the interval -1≤x≤5 for the given function.
Thegiven function is f(x)= -3|x+2|-1
The interval [a,b]=[-1,5]
As we know that the average rate of change of function f(x) on [a,b] is given by
R = {f(b)-f(a)}/(b-a)
As we know that a= -1 and b=5.
R = {f(5)-f(-1)}/(5-(-1))...........................(1)
Firstly we finding the f(-1) and f(5)
Now put x= -1 in the given function.
f(-1)= -3|-1+2|-1
f(-1)= -3|1|-1
f(-1)= -3-1
f(-1)= -4
As we know that b= 5.
Now put x= 5 in the given function.
f(5)= -3|5+2|-1
f(5)= -3|7|-1
f(5)= -3*7-1
f(5)= -21-1
f(5)= -22
Now putting the value in equation 1.
R = (-22-(-4))/(5+1)
R = (-22+4)/6
R = -18/6
R = -3
Hence, the averge rate of change on the interval -1≤x≤5 for the given function f(x)= -3|x+2|-1 is -3.
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Help. I’ll give more points and brainiest
Answer:
18
Step-by-step explanation:
13.5 / 3 = 4.5
so 4 x 4.5 = 16 + 2 = 18
You pick a marble, roll a die, and pick a card. How many outcomes are possible?
The total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.
How to determine How many outcomes are possibleTo determine the number of possible outcomes, we need to consider the number of outcomes for each event and then multiply them together.
1. Picking a marble: Let's assume there are n marbles to choose from. If there are n marbles, then the number of outcomes for this event is n.
2. Rolling a die: A standard die has 6 sides numbered 1 to 6. Therefore, the number of outcomes for this event is 6.
3. Picking a card: A standard deck of cards has 52 cards. Hence, the number of outcomes for this event is 52.
To find the total number of possible outcomes, we multiply the number of outcomes for each event together:
Total number of outcomes = (number of outcomes for picking a marble) × (number of outcomes for rolling a die) × (number of outcomes for picking a card)
Total number of outcomes = n × 6 × 52
Therefore, the total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.
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Suppose there is a simple index of two stocks, stock A and stock B. Stock A opens on Monday with 5000 shares at $2.75 per share. Stock B opens on Monday with 3000 shares at $4.30 per share. Stock A opens on Tuesday at $3.10 per share, and stock B opens on Tuesday at $4.85 per share. Both stocks have the same number of shares that they opened with on Monday. What is the rate of change of this simple index over 1 day?
The rate of change of the simple index over one day is approximately 12.78%.
To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.
On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:
Total value of Stock A on Monday = 5000 * $2.75 = $13,750
Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:
Total value of Stock B on Monday = 3000 * $4.30 = $12,900
The total value of the index on Monday is the sum of the values of Stock A and Stock B:
Total value of the index on Monday = $13,750 + $12,900 = $26,650
On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.
The total value of Stock A on Tuesday is:
Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500
The total value of Stock B on Tuesday is:
Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550
The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:
Total value of the index on Tuesday = $15,500 + $14,550 = $30,050
To calculate the percent change in the index, we use the formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%
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In Math town,60% of the population are males and 30% of them have brown eyes. Of the total math town population 28 % have brown eyes. What percentage of the females in math town have brown eyes?
25% percent of the females in Math town have brown eyes. To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes
what is percent ?
A percent is a way of expressing a number as a fraction of 100. The symbol for percent is %, which means "per hundred".
In the given question,
Let's assume that there are 100 people in Math town.
60% of them are males, so there are 60 males and 40 females.
Out of the 60 males, 30% have brown eyes, so there are 18 males with brown eyes.
28% of the entire population have brown eyes, so there are 28 people with brown eyes.
To find the number of females with brown eyes, we need to subtract the number of males with brown eyes from the total number of people with brown eyes:
28 - 18 = 10
So, there are 10 females with brown eyes.
Out of the 40 females in Math town, what percentage have brown eyes?
10 brown-eyed females out of 40 females is:
10/40 = 0.25 or 25%
Therefore, 25% of the females in Math town have brown eyes.
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At a real estate agency, an agent sold a house for $361,000. The commission rate is 6.5% for the real estate agency and the commission rate for the agent is 20% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
Answer:
$23,465
$4,693
Step-by-step explanation:
To find a percent of a number, multiply the percent by the number.
6.5% of $361,000 = 0.065 × $361,000 = $23,465
20% of $23,465 = 0.2 × $23,425 = $4,693
please i need help so bad
Dilbert invests $2,000 at 6% simple interest for 1 year. How much is in the account at the end of the 1 year period?
Answer:
$2,120
Step-by-step explanation:
Simple interest formula
A = P(1 + rt)
where:
A = final amountP = principalr = interest rate (in decimal form)t = time (in years)Given:
P = $2000r = 6% = 0.06t = 1 yearSubstitute the given values into the formula and solve for A:
⇒ A = 2000(1 + 0.06(1))
⇒ A = 2000(1.06)
⇒ A = 2120
Therefore, there will be $2,120 in the account at the end of the 1 year period.
13-18 Express the quantity as a single logarithm.
13. \(2 \ln x+3 \ln y-\ln z\)
\(2 \ln x+ 3 \ln y - \ln z\\\\=\ln x^2 + \ln y^3 - \ln z\\\\=\ln(x^2 y^3) - \ln z\\\\=\ln \left( \dfrac{x^2y^3}{z} \right)\)
solve for o 9=5+o i need this for math like asap
Answer: its 4
Step-by-step explanation:
Answer:
o = 4
Step-by-step explanation:
So we have to do the whole inverse operation thingy so our equation is:
9 - 5 = 4
So o = 4
hope this helps:)
solve the equation
what does x equal to
46+x÷6−21=25+6
Answer:
×=36
Step-by-step explanation:
46+1/6X-21=31
25+1/6X=31
1/6X=31-25
1/6X=6
X=36
Find the balance in the account after the given period.
$4000 principal earning 7% compounded annually, 8 years
The balance in the account after the given period is \(\$6,872.74\)
we know that
The compound interest formula is equal to
\(\text{A}=\text{P}(1+\frac{\text{r}}{\text{n}})^{\text{nt}}\)
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
\(\text{t}= 8 \ \text{years}\)
\(\text{P}=\$4,000\)
\(\text{r}=0.07\)
\(\text{n}=1\)
substitute in the formula above
\(\text{A}=\$4,000(1+\frac{0.07}{1})^{1\times8}=\$6,872.74\)
Worth 100 points if answered: 2 PARTS!
Answer: The answer is 18 bread pieces
Step-by-step explanation:
SECOND ONE he will need 9 loafs of bread because 108 divided by 12 equals 9 so he will ned 9 loafs
is this graph a negative association or positive association
Answer:
This graph is positive
Step-by-step explanation:
Hi please help on question! . If answer is correct I'll rate you five stars a thanks and maybe even brainliest! You will even get 39 pts!!
Here is a function machine.
Input : multiply by 6. Subtract 80: output
The input is the same as the output. Find the input.
Also can you please show me an easy to work out these type of questions
The input (x) that satisfies the condition of being multiplied by 6 and then Subtracted by 80 to give the same value as the output is 16.
The input as "x." According to the given information, the input (x) is multiplied by 6 and then subtracted by 80, resulting in the output. In mathematical terms, this can be expressed as:
Output = (6 * x) - 80
The problem states that the input and output are the same. Therefore, we can set up the equation:
x = (6 * x) - 80
To solve for x, we'll rearrange the equation and isolate the variable:
x - 6 * x = -80
Combine like terms:
-5 * x = -80
Divide both sides by -5:
x = (-80) / (-5)
Simplifying the division:
x = 16
Hence, the input (x) that satisfies the condition of being multiplied by 6 and then subtracted by 80 to give the same value as the output is 16.
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58 children go into the hall for a concert. There are six seats in a row. How many rows are needed to seat everyone?
To seat all 58 children in the hall for the concert, 10 rows are needed.
1. Determine the number of children per row: Since there are 6 seats in a row, each row can accommodate 6 children.
2. Divide the total number of children by the number of children per row: Divide 58 (the total number of children) by 6 (the number of children per row).
58 ÷ 6 = 9 with a remainder of 4
This means that 9 full rows can be formed, and there will be 4 children left after the last full row.
3. Check if there are any remaining children: Since there are 4 children remaining, they cannot form a complete row by themselves.
4. Calculate the number of rows needed: Add 1 to the number of full rows to account for the remaining children.
9 full rows + 1 row for the remaining children = 10 rows in total.
Therefore, to seat all 58 children in the hall for the concert, 10 rows are needed.
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Use the information given below to find tan(a + B)
cos a = 3/5, with a in quadrant IV
tan B = 4/3, with B in quadrant I I I
Give the exact answer, not a decimal approximation.
tan(a + B) = ?
let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said
\(\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill\)
\(\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}\)
NEED HELP ASAP!!
f(x)=|6x|-2; reflection over y axis
Translated equation is g(x)= ???
Answer: \(g(x)=-|6x|+2\)
Step-by-step explanation:
\(g(x)=-f(x)\\\\=-(|6x|-2)\\\\=-|6x|+2\)
List all the three elements sunsets of the set {1,2,3,4,5}
A list of all the three-element subsets of the given set include the following:
{1, 2, 3} {1, 2, 4} {1, 2, 5} {1, 3, 4} {1, 3, 5} {1, 4, 5}{2, 3, 4} {2, 3, 5} {2, 4, 5}{3, 4, 5}How to determine the three element subsets?In order to determine the three-element subsets from the given set {1, 2, 3, 4, 5}, we would have to calculate the number of ways to choose the three (3) elements by applying a mathematical model referred to as combination.
Mathematically, combination is given by this mathematical equation:
\(_nC_r = \frac{n!}{r!(n-r)!}\)
Where:
n is the number of elements.r is the number of times of choosing elements.Substituting the given parameters into the formula, we have;
Number of ways = ⁵C₃
Number of ways = 5!/(3! × (5 - 3)!)
Number of ways = 5!/(3! × 2!)
Number of ways = [5 × 4 × 3 × 2 × 1]/[3 × 2 × 2 × 1]
Number of ways = 120/12
Number of ways = 10 ways.
Therefore, there are 10 three-element subsets of this set.
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Complete Question:
List all the three-element subsets of the set {1, 2, 3, 4, 5}
Can't help me??
x/4 - 9 = 7
solve the equation... use transposing method
The Answer Is x = 64.
Explanation.x/4 - 9 = 7
x/4 = 7 + 9
x/4 = 16
x = 16 × 4
x = 64
_________________
Class: High School
Lesson: Equation
\(\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}\)
Answer:
x = 64
Step-by-step explanation:
x/4 - 9 =7
Step 1: Add 9 to both sides
x/4 - 9 + 9 = 7 + 9
x/4 = 16
Step 2: Multiply right side by 4
x/4= 16 x 4
x = 64
Step 3: Prove your x-value
64/4 = 16 - 9 = 7
64/4 - 9 = 7
So x = 64
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Can someone explain these problems to me please
Answer:
I think your suppose to solve the exponents
Step-by-step explanation:
for example:8^3•8^6
would be 64^9
a statistics student is trying to decide whether she should take a gamble and play bingo. the average bingo player earns $9 per game, distributed normally, with a population standard deviation of $8. if a sample of 25 bingo players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.
Select all that apply: 0; = $0.32 0; = $8 O = $1.60 Mi = $9 Hi = $1.80
The expected mean of the sampling distribution and the standard deviation of the sampling distribution is $29.50.
Standard deviation
In statistics, standard deviation refers the square root of variance by determining each data point's deviation relative to the mean.
Given,
Here we know that a statistics student is trying to decide whether she should take a gamble and play bingo. And the average bingo player earns $9 per game, distributed normally, with a population standard deviation of $8.
And we need to find if a sample of 25 bingo players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.
0; = $0.32 0; = $8 O = $1.60 Mi = $9 Hi = $1.80
Here the standard deviation of the sample distribution is calculated as,
=> σₓ = √1.80 = 1.34
Here we know that the distribution is normal then the mean of the sampling distribution is equal to the mean of the population, based on this theory, the resulting value is $29.50.
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y= - 1/2x+2I have to graph the linear equation
Answer
Explanation
To plot a graph, given the equation of the straight line, we simply obtain the intercepts (x and y intercepts) and connect those to plot.
x-intercept
This is the point where the graph crosses the x-axis and it is the value of x when y = 0.
y = -½x + 2
when y = 0
0 = -½x + 2
Multiply through by 2
0 = -x + 4
x = 4
So, first point, (4, 0)
y-intercept
This is where the graph crosses the y-axis and it is the value of y when x = 0
y = -½x + 2
when x = 0
y = -½(0) + 2
y = 0 + 2
y = 2
So, the second point, (0, 2)
So, this graph is plotted and presented under 'Answer'
Hope this Helps!!!
seb buys 1 gallon of paint that covers 400 square feet
The least amount of paint that is needed to paint the walls of a room with a rectangular prism shape is 1. 8 gallons.
How to find the amount of paint ?There would be two walls with 10 x 16 dimensions so the area is :
= 2 x 10 x 16
= 320 square feet
Two walls with 20 x 10 dimensions :
= 2 x 20 x 10
= 400 square feet
The total area is :
= 400 + 320
= 720 square feet
One gallon of paint can cover 400 square feet so the number of gallons needed is:
= 720 / 400
= 1. 8 gallons
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Full question is:
One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 20 feet, a width of 16 feet, and a height of 10 feet? Write your answer as a decimal.
Write and solve an inequality to find the possible values of x.
The inequality tha calculates the possible values of x is x < 2
How to determine the inequality tha calculates xFrom the question, we have the following parameters that can be used in our computation:
The figure
Where, we have
3x + 2 < 10
And, we have
2x + 6 < 10
Evaluate the expressions
So, we have
3x < 8 and 2x < 4
Evaluate
x < 8/3 and x < 2
Hence, the inequality tha calculates x is x < 2
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Please answer this question
Step-by-step explanation:
arithmetic sequence :
a1 = 7
d = 3
an = an-1 + d = a1 + (n-1)×d
the formula for the sum of an arithmetic sequence is
n/2 × (2×a1 + (n-1)×d)
40 is a12 (n = 12), as 40-7 = 33, 33/3 = 11, 11 plus 1 from a1 is 12.
we have the sum of 12 terms.
12/2 × (2×7 + 11×3) = 6 × (14 + 33) = 6×47 = 282
so, we have :
the sum = 282
A = 12
B = 7 + (n-1)×3 = 7 + 3n - 3 = 4 + 3n
If y varies directly as x, and y = 8 when x = 4, find y when x = 24.
The value of y is 48
How to calculate the value of y in the variation ?y= kx
let's solve for k which is the constant
y= 8 , x= 4
k= 8/4
k= 2
Next is to calculate the value of y when x is 24
y = 2 × 24
y= 48
Hence the value of y is 48
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