The 50th term in the arithmetic sequence starting with 10 and increasing by 3 each time is 157. This is calculated using the standard formula for the nth term of an arithmetic sequence.
The given sequence starts with 10 and increases by 3 each time (10, 13, 16).
To find the 50th term, we need to use the formula for the nth term of an arithmetic sequence:
[tex]a_n = a_1 + (n - 1)d[/tex]
Where [tex]a_1[/tex] is the first term, d is the common difference, and n is the term number.
In this case, [tex]a_1 = 10, d = 3, and ~n = 50[/tex].
Plugging those values into the formula, we get [tex]a_{50} = 10 + (50 - 1)\*3[/tex],
[tex]a_{50} = 10 + 49\*3[/tex]
Calculating further, a_50 = 10 + 147 = 157.
Therefore, the 50th term of the given arithmetic sequence is 157.
Is my answer correct?
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.
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.
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.
Learn more about Range of a Function here:https://brainly.com/question/29145252
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Find the first four terms of the infinite sequence defined explicitly by the following rule.
f(n)= 4n - 2
what are the translation rules in geometry?
Final answer:
The translation rules in geometry involve moving every point in a figure the same distance and direction. For a horizontal translation, add or subtract the same value from the x-coordinate of each point. For a vertical translation, add or subtract the same value from the y-coordinate of each point.
Explanation:
In geometry, translation is a transformation that moves every point in a figure the same distance and direction. The translation rules involve determining the new coordinates of the translated figure.
The translation rules in geometry can be summarized as:
For a horizontal translation, add or subtract the same value from the x-coordinate of each point.For a vertical translation, add or subtract the same value from the y-coordinate of each point.For example, if you have a point with coordinates (2, 3) and you want to translate it 3 units to the right and 2 units up, you would add 3 to the x-coordinate and 2 to the y-coordinate to get the new coordinates of the translated point: (5, 5).
Which undefined term is used to define a ray?
Answer:
Line
Step-by-step explanation:
factorise tis please.
[tex] (x+3)^{2} +2(x+3)[/tex]
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
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
If 32% of a number is 64, what is the number?
A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 0.7m^3/min. How fast is the water level rising when it is 0.8 m?
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.
Linda Frankell pays $50.00 a month for group health insurance. There is a $300 deductible. Her medical bills for the last year were $2,600.00. Linda's insurance company provided payment of 80% of the bills less the deductible.
What was the insurance company's payment? $
What was Linda's total cost (including the monthly premium)? $
what do real number include?
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.
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.
Learn more about Converting Percent to Fraction#SPJ11A store is having a 10% off sale. It gives an additional 20% off for an item that is above $100 after the first 10% discount.A jacket costs $124.99
if you buy the jacket, how much will you save in total?
*SHOW WORK* ...?
To calculate the total amount saved when buying a jacket at a store with a 10% discount and an additional 20% discount, follow these steps: find the savings from the first discount, calculate the price after the first discount, check if the price is above $100, calculate the additional discount, and add both savings together. In this case, the total amount saved is $34.9972.
Explanation:To calculate the total amount saved, we need to use the following steps:
Find the total savings from the first 10% discount: $124.99 * 0.10 = $12.499Find the price of the jacket after the first discount: $124.99 - $12.499 = $112.491Check if the price is above $100. If it is, calculate the additional 20% discount: $112.491 * 0.20 = $22.4982Add the savings from the additional discount to the previous savings: $12.499 + $22.4982 = $34.9972So, the total amount saved is $34.9972.
Final answer:
To find the total amount saved, apply the discounts and add the amounts together. The total amount saved is $35.00.
Explanation:
To find the total amount saved, you need to calculate the discount for each discount percentage. First, apply the 10% discount to the original price of the jacket:
10% of $124.99 = $12.499.
Next, apply the 20% discount to the price after the first discount:
20% of ($124.99 - $12.499) = 20% of $112.491 = $22.4982.
Finally, add the two discounts together to find the total amount saved:
$12.499 + $22.4982 = $34.9972.
Rounding to the nearest cent, the total amount saved is $35.00.
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
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:
tan inverse cos x/1-sin x
write in simplest form? ...?
Boris bought 22 pounds of rice for $10. How many pounds of rice did he get per dollar?
Taxi ride cost $1 plus 80c more for each quarter mile travel. What was the total cost for 2-mile trip
-17x 15 6x - 23 = 10 - 8x
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.
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 .
Line AB is tangent to circle C, AB= 4 inches, and AD = 2 inches. Find the radius of the circle.
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?
If you divide 6! by 4! you are evaluating
P(6, 4)
P(4, 6)
P(6, 2)
what is the 10th term of this geometric sequence?
1,2,4 ,8...
A)128
B)256
C)512
D)1024
Simplify: log base 3 (1/3) ...?