Express 31% as a fraction in its lowest form
To express 31% as a fraction in its lowest form, divide 31 by 100 and simplify the resulting fraction.
Explanation:To express 31% as a fraction in its lowest form, we need to convert the percent to a decimal first. We do this by writing 31% as a fraction with a denominator of 100 and dividing the numerator by the denominator: 31/100. To reduce the fraction to its lowest form, we find the greatest common divisor (GCD) of the numerator and denominator, which is 1. Dividing both the numerator and denominator by 1, we get the fraction 31/100 in its lowest form.
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Write an exponential function to model this situation: a population of 420 animals decreases at an annual rate of 21%. Then predict the value of the function after 5 years (to the nearest whole number).
Answer:
[tex]y=420\cdot (0.79)^x[/tex]
The value of the function after 5 years would be 129.
Step-by-step explanation:
We have been that a population of 420 animals decreases at an annual rate of 21%. We are asked to write an exponential function for our given problem.
We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,
a = Initial value,
b = For decay b is in form [tex]1-r[/tex], where, r represents decay rate in decimal form.
[tex]r=21\%=\frac{21}{100}=0.21[/tex]
[tex]y=a\cdot (1-r)^x[/tex]
[tex]y=420\cdot (1-0.21)^x[/tex]
[tex]y=420\cdot (0.79)^x[/tex]
Therefore, our required function would be [tex]y=420\cdot (0.79)^x[/tex].
To find the value of the function after 5 years, we will substitute [tex]x=5[/tex] in our function.
[tex]y=420\cdot (0.79)^5[/tex]
[tex]y=420\cdot 0.3077056399[/tex]
[tex]y=129.236368758[/tex]
[tex]y\approx 129[/tex]
Therefore, the value of the function after 5 years would be 129.
Translate the phrase into a math expression. twenty divided by the sum of 4 and 1.
A room in the shape of a rectangular prism measures 15 feet by xx feet by 12 feet. Write a simplified expression for the volume (in cubic feet) of the room.
Volume ==
ft3
The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s = 180(n – 2), where n is the number of sides. Benita solves this equation for n and writes the equivalent equation n = s/180 + 2.
Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°?
_______ sides
the answer is 9 hope it helps
Lian and her younger sister Ella are 4 years apart. The sum of their ages is 20. Let l be Lian’s age in years and let e be Ella’s age in years. The system of linear equations that models the scenario is: l – 4 = e l + e = 20 How old is each sister?
Answer:
Lian is 12 years old and Ella is 8 years old.
Step-by-step explanation:
Lian and her younger sister Ella are 4 years apart.
The sum of their ages is 20.
Let L be Lian’s age in years.
Let E be Ella’s age in years.
The system of linear equations that models the scenario is:
[tex]L-4=E[/tex] this gives [tex]L=E+4[/tex]
[tex]L+E=20[/tex]
Putting L=E+4 in the second equation
[tex]E+4+E=20[/tex]
[tex]2E=20-4[/tex]
[tex]2E=16[/tex]
So, [tex]E=8[/tex]
Now we have , L+E=20
[tex]L+8=20[/tex]
So, [tex]L=12[/tex]
Therefore, Lian is 12 years old and Ella is 8 years old.
What is the slope of a line parallel to 10x - 5y = 8?
What is the slope of a line parallel to 4x + 2y = 5?
What is the slope of a line perpendicular to x - 3y = 9?
What is the slope of a line perpendicular to x - 5y = -10?
What is the slope of a line parallel to 4x + y = -1?
A) m = -5
B) m = 2
C) m = -3
D) m = -4
E) m = -2
Ruby bought 15 cell phone cases for a total of $145.80. she sells them for $19.50 each, but she is only able to sell 5 of them. what is ruby's net profit or loss?
what is the 10th term of this geometric sequence?
1,2,4 ,8...
A)128
B)256
C)512
D)1024
Rewrite the following without an exponent ₋7⁻¹.
The potential energy of an object is jointly related with the mass of the object and the height of the object. A 40-kg object is 2 meters off the ground. The potential energy of the object is 784 joules. A 10-kg object is 3 meters off the ground. What is the potential energy of the 10-kg object?
Answer:
The potential energy of the 10-kg object is 294 joules .
Step-by-step explanation:
As given
The potential energy of an object is jointly related with the mass of the object and the height of the object.
Let the potential energy of an object is denoted by P.E .
Mass of the object = m
Height of the object = h
Than
[tex]P.E \propto mh[/tex]
P.E = mgh
Where g is the accleration due to gravity .
As given
A 40-kg object is 2 meters off the ground. The potential energy of the object is 784 joules.
Put the value in the P.E = mgh
784 = g × 2 × 40
784 = 80g
[tex]g = \frac{784}{80}[/tex]
g = 9.8 joules per kg meter .
As given
A 10-kg object is 3 meters off the ground.
Put the value in P.E = mgh
P.E = 10 × 9.8 × 3
P.E = 294 joules
Therefore the potential energy of the 10-kg object is 294 joules .
Find the first four terms of the infinite sequence defined explicitly by the following rule.
f(n)= 4n - 2
Scott and Harry went cycling every day. They increased the number of minutes of cycling every week as described below:
Scott: Cycled for 10 minutes every day in the first week, 15 minutes in the second week, 20 minutes in the third week, and 25 minutes in the fourth week.
Harry: Cycled for 10 minutes every day in the first week, 20 minutes in the second week, 40 minutes in the third week, and 80 minutes in the fourth week.
Which statement best describes the methods used by Scott and Harry to increase the time they spent cycling?
A. Scott's method is linear because the number of minutes increased by an equal number every week.
B. Harry's method is linear because the number of minutes increased by an equal factor every week.
C. Both Harry's and Scott's method is exponential because the number of minutes increased by an equal factor every week.
D. Both Harry's and Scott's method is exponential because the number of minutes increased by an equal number every week.
Answer:
(A)
Step-by-step explanation:
Scott cycled for 10 minutes in first week, 15 minutes in second week,20 minutes in third week and 25 minutes in the fourth week which maintains a consistency in the line as there is consistent slope when drawn on a graph.
On, the other hand, harry cycled for 10 minutes in first week, 20 minutes in second, 40 minutes in third and 80 minutes in fourth week in which there is no consistency in the timings according to the weeks. Therefore, only, scott's method is linear as the number of minutes increased by an equal factor every week.
If you divide 6! by 4! you are evaluating
P(6, 4)
P(4, 6)
P(6, 2)
Which undefined term is used to define a ray?
Answer:
Line
Step-by-step explanation:
A punch recipe calls for cups of orange juice, cup of pineapple juice, and cups of mango juice. How many total cups of fruit juice does the recipe make?
Answer:I can't answer it without measurements. Sorry
Step-by-step explanation:
The Tools Plus Company is planning to produce drills. The company has rented space for its manufacturing operation at $5,000 per month. Each drill requires $61 worth of materials and $36 worth of labor.
Find the total cost if Tools Plus Company makes 460 drills. ...?
Answer:
Step-by-step explanation:
69d+5,000
What is the range of the function f(x) = 3x2 + 6x – 9
The range of a function is the set of all possible output values. For the quadratic function f(x)=3x²+6x-9, because it forms an upward opening parabola, its range will start from its vertex point and continue to infinity. The range of this function will be y ≥ -6.
Explanation:This student is asking about the range of a given quadratic function. In the context of mathematics, the term 'range' refers to the set of all possible output values (y-values) of a function. For your function, f(x) = 3x² + 6x - 9, this is a quadratic function, so it forms a parabola when graphed. Given the positive coefficient of x², the parabola opens upwards.
Therefore, the lowest point (also known as the vertex) of the parabola will provide the minimum value of the range - since the parabola continues indefinitely upwards, there's no maximum value. For a quadratic function in the form f(x) = ax² + bx + c, you can find the x-coordinate of the vertex using the formula -b/2a.
Applying this to your function, we get x = -6 / (2*3) which simplifies to -1. You can then substitute this x-value into the function to find the minimum y value: f(-1) = 3*(-1)² + 6*(-1) - 9 = -6. Thus, the range of the function f(x) = 3x² + 6x - 9 is y ≥ -6.
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tan inverse cos x/1-sin x
write in simplest form? ...?
If 32% of a number is 64, what is the number?
Is the fraction 1/15 a terminating or repeating decimal?
The fraction 1/15 is a repeating decimal because, when converted, it results in the repeating pattern 0.0666..., where the digit 6 repeats indefinitely.
When the fraction 1/15 is converted to a decimal, it results in the repeating decimal 0.0666..., where the digit 6 repeats indefinitely.
This happens because 1 divided by 15 gives a quotient of 0.0666..., and the 6 in the decimal representation repeats infinitely.
In other words, the division process doesn't terminate or end, and the same pattern of digits repeats endlessly after the decimal point.
This repeating pattern signifies that the fraction 1/15 cannot be expressed as a finite decimal and will always have repeating digits when written in decimal form.
Therefore, 1/15 is classified as a repeating decimal rather than a terminating one.
Line AB is tangent to circle C, AB= 4 inches, and AD = 2 inches. Find the radius of the circle.
Boris bought 22 pounds of rice for $10. How many pounds of rice did he get per dollar?
factorise tis please.
[tex] (x+3)^{2} +2(x+3)[/tex]
what is an estimation of 492.6 divided by 48
Answer:
10.
Step-by-step explanation:
We are asked to find the estimation of 492.6 divided by 48.
First of all, we will round 492.6 to nearest hundreds and 48 to nearest tens.
Since tens digit of 492.6 is greater than 5, so we will round up to nearest hundred as: [tex]492.6\approx 500[/tex]
Since ones digit of 48 is greater than 5, so we will round up to nearest tens as: [tex]48\approx 50[/tex].
Now, we will find the quotient as:
[tex]\frac{500}{50}=10[/tex]
Therefore, an estimation of 492.6 divided by 48 would be 10.
Taxi ride cost $1 plus 80c more for each quarter mile travel. What was the total cost for 2-mile trip
what do real number include?
-17x 15 6x - 23 = 10 - 8x
Which type of cause and effect graphic organizer would be best to identify why we use gasoline in our cars today and what we might use as fuel in the future?
a. Timeline
b. Flow chart
c. Both of these
d. None of these
Answer: The answer is (a) Timeline.
Step-by-step explanation: We are given four options out of which one is the cause and effective graphic organiser that best identifies why we use gasoline in our cars today and what we might use as fuel in the future.
The best option is Timeline, because they show the order of events, an event's place in history and identify events which lead up to, or cause, other events.
Flowcharts does not serve the purpose, because they do not clearly identifies the cause.
Thus, the correct option is (a).
A flow chart would be the best graphic organizer to identify why we use gasoline in our cars today and potential future fuels, as it clearly presents causes and effects in a non-linear way.
Explanation:The type of cause and effect graphic organizer that would be most effective in identifying why we use gasoline in our cars today and what we might use as fuel in the future is a flow chart. A timeline would be helpful in demonstrating a chronological progression of fuels, but a flow chart allows you to clearly lay out causes and effects in a non-linear way, which is more suitable for this topic as it involves multiple possibilities for future fuels. It can visually present the reasons why we use gasoline now and the different options we have for future fuels, alongside their possible effects or outcomes.
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Gretchen and Ezia received equal scores on a test made up of multiple choice questions and an essay. Gretchen got 18 multiple choice questions correct and received 19 points for her essay. Ezia got 15 multiple choice questions correct and received 31 points for her essay.
How many points was each multiple choice question worth?
Answer:
Each question had 4 points.
Step-by-step explanation:
Let the questions be x points each. As both Gretchen and Ezia received equal scores, we can write the equation as:
18x+19=15x+31 (Let the questions be x points each)
Solving for x;
[tex]18x-15x=31-19[/tex]
=> [tex]3x=12[/tex]
Dividing both sides by 3;
x = 4
Hence, each question had 4 points.