Cube roots - The two numbers that are solutions to the equation x³ = 27 are +3 and -3.
What are cube roots?
A number's cube root is a quantity that, when multiplied by itself three or more times, returns the original quantity. The cube root of 27, represented as 327, for instance, is 3 because 3 x 3 x 3 = 27 = 33 when we multiply 3 by itself three times. As a result, we can state that the cube root yields a value that is essentially cubed. Here, 27 is referred to as the ideal cube. We may deduce what the cube's root is from the word "cube root." It denotes the integer that brought about the cube under the root. Typically, we use the prime factorization technique to determine the cubic root of perfect cubes. We can discover the importance of square root in a similar way.
We are given the equation,
[tex]x^{3}[/tex] = 27
taking cube root on both the sides to find the value of x,
we get,
x = ±[tex]\sqrt[3]{27}[/tex]
further solving,
x = ±3.
Hence the two solutions of the x³ = 27 equation will be ±3 or +3 and -3.
Because 3x3x3 Equals 27, the cube root of 27 is 3.
Since 4x4x4 = 64, the cube root of 64 is also 4, and so on.
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HELP
What is the slope of the line?
Answer:
y= 1/2x+3.5
Step-by-step explanation:
Answer:
y= 1/2x+3.5
I took the test this is right
Step-by-step explanation:
an ecologist wishes to mark off a circular sampling region having radius 13 m. however, the radius of the resulting region is actually a random variable r with the following pdf.
The expected area of a circular sampling region is 531.56 m²
Given,
The radius of the circular sampling region = 13m
f(r) = [tex]\left \{ {\frac{3}{4} } \atop {0}} \right.[/tex] [1 - (13 - r)²] 12 ≤ r ≤ 14
We have to find the area of the circular sampling region = E (π r²)
E (π r²) = π E (r²)
Lets find E (r²)
E (r²) =₁₂ [tex]\int\limits^[/tex]¹⁴ r² f(r) dr
= ₁₂∫¹⁴ (3r²/4) (1 - (13 -r)²) dr
= 3/4 ₁₂∫¹⁴ r² (1 - 169 - r² + 26r) dr
= 3/4 ₁₂∫¹⁴ r² (26r³ - r⁴ - 168r²) dr
= 3/4 [ 26r⁴/4 - r⁵/5 - 168r³/3]₁₂¹⁴
= 3/4 [ (26 × 14⁴)/4 - 14⁵/5 - (168 × 14³)/3] - [ (26 × 12⁴)/4 - 12⁵/5 (168 × 12³)/3]
= 3/4 [ (26 × 38416)/4 - 537824/5 - (168 × 2744)/3] - [ (26 × 20736)/4 - 248832/5 - (168 × 1728)/3]
= 3/4 [ 249704 - 107564.8 - 153664] - [ 134784 - 49766.4 - 96768]
= 3/4 [-11524.8] - [-11750.4]
= 3/4 [225.6]
= 169.2
∴ E(r²) = 169.2
Now lets find the expected area of the circular sampling region:
Area = E(π r²) = π E (r²)
Here, E(r²) = 169.2
So, area = π × 169.2 = 531.56 m²
That is, the expected area of a circular sampling region is 531.56 m²
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professor moore forgets to set his alarm with a probability of 0.10. if he sets the alarm, it will wake him on time to make his first class with a probability of 0.95. if he forgets to set the alarm, he wakes up in time for his first class with a probability of 0.25. professor moore was late to his first class. what is the probability that professor moore set his alarm given this information?
Answer: -The probability of setting his alarm is 1-0.1=0.9
-The probability of being in time is therefore calculated as:
0.9 x 0.95 + 0.1 x 0.25
= 0.88
Hence, the probability that the professor shows up in time is 0.88
Step-by-step explanation:
One pound of apples costs $3.25. Five pounds of apples costs $16.25.
Answer:
what do you mean?
Step-by-step explanation:
The population of a city decreases by 1.7% per year. If this year's population is 366,000, what will next year's population be, to the nearest individual?
The population of the city next year, after decreasing, will be 359,778
Here, we are given that the population of a city decreases by 1.7% per year.
This, means that the city's population will decrease by 1.7% in 1 year, (1.7 × 1.7)% in 2 years and so on.
The population of the city this year is given to be 366,000.
Thus, next year, the population will decrease by-
1.7% of 366,000
= 1.7/100 × 366,000
= 17/10 × 3,660
= 17 × 366
= 6,222
Thus, the city's total population next year will be-
366,000 - 6,222
= 3,59,778
Hence, the city's population to the nearest individual comes out to be 359,778.
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100 points give me an explanation.
Dont lie or I will report you.
Answer:
Both ans are attached
The graph of y = f(x) is shown below. Find all values of x where f(x) = 0
The values of x when f(x) = 0 are 2 and 8
Graphs are used mostly to show the relationship between two variables (usually x and y).
The graph of y = f(x) is attached
To get the values of x when f(x) = 0 , we consider where the line of the graph crosses the x-axis.
The graph crosses the x-axis at:
x = 2
x = 8
This means that the values of x when f(x) = 0 are 2 and 8
Therefore, in the graph of y = f(x), the values of x where f(x) = 0 are 2 and 8
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Disclaimer : The question mentined is not provided with a graph, the above solution is done as per the graph attached.
A seafood market sells Maryland crabs for $10.50 per Ib and Alaskan crabs for $8.50 per lb. The owner can bring 500 lbs of crabs to sell at a weekend seafood festival. How much
money can the owner earn at the festival? Show your work and explain your reasoning.
Provided the owner can bring 500 lbs of crabs to sell at the weekend seafood festival, they can earn between $4,250 and $5,250, depending on which type of crabs or their different combinations.
How are the total earnings determined?The total earnings can be determined using mathematical operations of multiplication, division, addition, and subtraction.
The total earnings are the products (multiplication results) of the units of each type of crab and their selling prices.
The selling price of Maryland crabs per Ib = $10.50
The selling price of Alaskan crabs per lb = $8.50
The total quantity of crabs the owner can bring to the seafood festival = 500 lbs
If the owner decides to bring in Maryland crabs, they can earn $5,250 ($10.50 x 500)
If the owner decides to bring in Alaskan crabs, they can earn $4,250 ($8.50 x 500)
If the owner decides to bring a combination of Maryland and Alaskan in the ratio of 50:50, they can earn $4,750 ($10.50 x 250) + $8.50 x 250)
Thus, if the owner sells Maryland crabs, the total earnings are $5,250, but if they sell Alaskan crabs, they earn $4,250.
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Customer number two gives you a
15% off coupon. What is the new cost
of the order? 11.50
Answer:
$8.50 ? let me know if im wrong
Step-by-step explanation:
I need to make sure these are correct thank you in advance!
Using the unit rate, the graphs that best represent the amount they earn for different amount of time is: C.
How to Interpret the Slope?The slope of a graph can be interpreted as the unit rate of the scenario that is being represented by the graph. For example, money earned in dollars per hour worked is the unit rate or slope of the graph given in this scenario.
The larger the unit rate value, the steeper the slope of the line of the graph.
Let Lin's unit rate be represented as x, therefore,
Lin's unit rate = x
Diego's unit rate = 2x
Jada's unit rate = 2(2x) = 4x
This shows that unit rate of Jada is the highest, and therefore, the graph that would represent how much Jada earns would be the steepest, followed by Diego's, and the least is Lin's.
Therefore, the all the graphs would be: C.
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- 1 2/5 - 3 1/3. Please help.
Answer:
-4 11/15
Step-by-step explanation:
The mean of five numbers is 8.2. Four of the numbers are 8, 10, 12 and 10.
Work out the fifth number.
Answer:
1
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
let x be the fifth number , then
[tex]\frac{8+10+12+10+x}{5}[/tex] = 8.2 ( multiply both sides by 5 to clear the fraction )
40 + x = 41 ( subtract 40 from both sides )
x = 1
the fifth number is 1
What is the least common multiple of 34, 17, and 31?
Answer: 31, 34, 17
Step-by-step explanation:
which answer?
pls help
Answer:
1. C: y = 3x - 5
2. B: y = -3x - 9
Step-by-step explanation:
1.
y = 3x + 9; (2, 1) (parallel)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - 1 = 3(x - 2)
y - 1 = 3x - 6
+1 +1
-------------------
y = 3x - 5
----------------------------------------------------------------------------------------------------------
2.
y = (1/3)x - 6 ; (-3, 0) (perpendicular)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - 0 = -3(x - (-3))
y - 0 = -3(x + 3)
y - 0 = -3x - 9
+0 +0
----------------------
y = -3x - 9
I hope this helps!
select the correct answer. a 500-gallon water tank drains at a rate of 50 gallons per minute. the amount of water left in the tank depends on the number of minutes it has been draining. what is the range of this relation? 0 ≤ y ≤ 500 0 ≤ y ≤ 10 y ≤ 500 y ≥ 0
Our range is 0 x 10, We could also graph this with x along with the x-axis and w along the y-axis then every minute 50x gallons are gone
We have 500 gallons of the water tank and it drains at the rate of 50 gallons per minute,
.Let's suppose after 5 minutes,
W = 500 - 50 * 5W = 500 - 250W = 250
After 5 minutes, 250 gallons are left in the water tank.
Here the lowest value is 0 so our maximum time is once the tank emptied, or when w is equal to 0.
0 = 500 - 50x
50x = 500X = 500/50X = 10
So, our range is 0 x 10
We could also graph this with x along with x-axis and w along the y-axis, in the graph the x- intercept where the tank is empty
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lin and her brother earn 15 dollars for shoveling snow for their grandma and 35 dollars for cleaning the garage how much money does lin get if she split the money equally with her brother
Answer:
35+15 =50
50/2= 25 dollars
Hi ! Please help, this came up as one of my questions and I don’t know how to do it well. Thanks!
Answer:
y = (3/2)x + 3
Step-by-step explanation:
Comment
The general equation is
y = mx + b
Finding m
The equation for the slope is
m = (y2 - y1)/(x2 - x1)
Givens
y2 = 3
y1 = 0
x2 = 0
x1 = - 2
m = (3 - 0)/(0 - -2)
m = 3 / 2
m = 3/2
Finding b
b is the y intercept which is (0,3)
x = 0
y = 3
3 = 0*3 + b
b = 3
So the equation is
y = (3/2) x + 3
9. The amount of water used by a washing
machine varies directly with the weight of the
load being washed. The washing machine uses
28 gallons to wash 7 pounds of clothing. How
many gallons of water will the machine
use to wash 24.5 pounds of laundry?
The machine will use 90 gallons of water to wash 24.5 pounds of laundry.
What is Direct Variation?If two quantities change by the same amount, they are said to follow a direct variation. As a result, when one quantity changes, the other follows suit, increasing when the first increases and decreasing when the first decreases. To put it another way, two quantities are said to be directly proportional to one another if the ratio of the first to the second is a constant term. The coefficient or constant of proportionality is the name given to this constant quantity. Assuming that x and y are two quantities that are directly varying, they are stated as follows:y ∝ x
Consequently, y = kx, where k is the proportionality constant.
Given:
The amount of water used by a washing machine varies directly with the weight of the load being washed.
Let's assume,
The amount of water used by a washing machine is y.
The weight of the load being washed is x.
According to the question,
y = 28 gallons
x = 7 pounds
Putting the values we get,
y = kx
28 = k × 7
k = 4
Now, we have to find y when x = 24.5
y = 4 × 24.5 = 98
Hence the machine will use 90 gallons of water to wash 24.5 pounds of laundry.
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what is 10.88+10.88+10.88
Answer:
32.64
Step-by-step explanation:
Two-fifths of a number decreased by 3 is 1. Find the number.
By using the basics of the number system the calculated number from the given statement is 10.
What is number system?
In mathematics, the number system can be used to express the numbers in a way of writing to make the mathematical expression. Basically, it provide the unique representation of the number with the help of the algebraic structures and operations.
According to the question, the expression can be formed by the given statement is as follows:
Let us assume the number be 'a'
Using basics of the number system for the formation of an expression:
Therefore,
(2/5)a - 3 = 1
⇒ (2/5)a = 4
⇒ a = 10
Hence, by using the basics of the number system the calculated number from the given statement is 10.
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this past semester, a professor had a small business calculus section. the students in the class were . suppose the professor randomly selects two people to go to the board to work problems. what is the probability that is the first person chosen to go to the board and is the second?
Given : Professor randomly selects two people to go to board to work on problems.
To find: Probability of chosen first or second person to go to the board.
Let [tex]x[/tex] be the total no. of students.
After the first student is chosen, no of students left = [tex]x[/tex] - 1
Therefore,
the required probability = 1 / total no. of students x no. of students left
⇒ 1 / [tex]x[/tex] ([tex]x[/tex]- 1 )
= 1 / ([tex]x^{2} - x[/tex])
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Amanda is driving a racecar. The table below gives the distance D (1) (in meters) she has driven at a few times t (in seconds) after she startsTimer(seconds)Distance D (1)(meters)
From the question;
we are to calculate average rate of change of distance with respect to time
The average rate of change is given as
[tex]\text{Average rate of change = }\frac{D_2-D_1}{T_2-T_1}[/tex]From the question we are given the table below
a. we are to find the average rate of change of the distance driven from 0 secons to 3 seconds
From the information
we have
[tex]undefined[/tex]Read through the solution below. Then, answer
the questions that follow.
16
6 + d =
[box]*
d
ad=b(de-c)
b
=
ad
de
=e
-C
= b
In the line marked *, what strategy was used?
The expression
fills in the orange box.
Determine the rate of change of the graph (HELP PLEASE)
Activity 4: Fair Share!
Directions: apply the rules in multiplication of integers in answering the following activity.
Answer:
1. P
2. U
3. K
4. A
5. M
6. C
7. E
8. J
9. L
10. I
The 89 members of the Taft School Band spend
a total of $4,628 for tickets to Hammond's
Amusement Park. What is the cost of each
amusement park ticket?
By using division, if 89 members of the Taft school band spend a total of $4628 for tickets to Hammond's amusement park, The the cost of each amusement park ticket is $52
The total number of members of the Taft school = 89 members
The total cost for the ticket to Hammond's amusement park = $4628
The cost of each amusement park ticket = The total cost for the ticket to Hammond's amusement park ÷ The total number of members of the Taft school
Substitute the values in the equation
The cost of each amusement park ticket = 4628/89
= $52
Hence, by using division, if 89 members of the Taft school band spend a total of $4628 for tickets to Hammond's amusement park, The the cost of each amusement park ticket is $52
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Lisa spent $27 on fruit at the grocery store. She spent a total of $30 at the store. What percentage of the total did she spend on fruit?
Lisa spent 90% of the total money on the fruits.
What is Percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
Given is Lisa spent $27 on fruits at the grocery store. She spent a total of $30 at the same store.
Money spent by Lisa on fruits = $27
Total money spent by Lisa = $30
Therefore, percentage of the total money she spend on fruits will be -
(27/30) x 100 = 90%
Hence, Lisa spent 90% of the total money on the fruits.
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A company takes 16 minutes to wash 24 cars. How many cars can be
washed in 1 minute?
Answer:1.5 cars can be washed in 1 minute but realistically only 1 car can be washed
Step-by-step explanation: 24/16 =1.5 and that get you your answer of 1.5 but the correct answer is 1.5 or 1 depending on if they are asking you to round down or not.
A factory adds three red drops and two blue drops of coloring to white paint to make each pint of purple paint. The factory will make 50 gallons of the purple paint.
How many drops of red and blue coloring will the factory need in the 50-gallon batch of purple paint?
Answer: 1200 red and 800 blue
Given m\_EBC = (3x + 20)° and m \_ABC = (17x-40)° find m\_ EBC and m LABC.
Answer:
18. m<EBC = 43°, m<CBD = 47°
19. m<EBC = 50°, m<ABC = 130°
Step-by-step explanation:
18. Find m<EBC and m<CBD
m<EBC = (5x + 8) and m<CBD = (6x + 5)
these two angles add up to a right angle, therefore their sum is 90°
5x + 8 + 6x + 5 = 90
11x + 13 = 90 , 11x = 77 , x = 7
m<EBC: 5(7) + 8 = 43
m<CBD: 6(7) + 5 = 47
19. Find m<EBC and m<ABC
m<EBC = (3x + 20) and m<ABC = (17x - 40)
these two angles are supplementary, meaning that they add up to 180°
3x + 20 + 17x - 40 = 180
20x - 20 = 180, 20x = 200, x = 10
m<EBC: 3(10) + 20 = 50
m<ABC: 17(10) - 40 = 130