A sequence is a list of numbers that follow a specific pattern. Each number in the sequence is called a term. Sequences can be finite (meaning they have a specific number of terms) or infinite (meaning they continue without end).
Arithmetic sequences are a type of sequence where each term is found by adding a constant value to the previous term. This constant value is called the common difference, denoted as d. The formula for the nth term (or any term) of an arithmetic sequence is:
an = a1 + (n-1)d
an is the nth term of the sequencea1 is the first term of the sequencen is the position of the term we want to find (e.g. n=5 means we want to find the 5th term)d is the common difference between terms
In other words, we can find any term of an arithmetic sequence by adding the common difference to the previous term.
(i) The next term in the sequence is 27.
(ii) To get this answer, we can see that each term is 6 greater than the previous term
b) To find the tenth term we can write the formula for the nth term of the sequence using the common difference d = 6 and the first term a1 = 3:
an = a1 + (n - 1)d
Substituting n = 10, a1 = 3, and d = 6, we get:
a10 = 3 + (10 - 1)6
a10 = 3 + 54
a10 = 57
Therefore, the 10th term of the sequence is 57
Romi and her friends ran in a terrain race. Their distance, in miles, from the starting line over time, in minutes, is shown on the graph.
graph titled Romi's Terrain Race with the x axis labeled time in minutes and the y axis labeled distance in miles with line segments going from 0 comma 0 to the 20 comma 2 to 40 comma 2 to 80 comma 4 to 100 comma 4 and to 180 comma 0
Which of the following descriptions could represent the graph?
From the starting line, Romi ran 4 miles in 40 minutes, rested for 20 minutes, jogged back 2 miles toward the starting line in 40 minutes, rested for 20 minutes, and walked the last 2 miles back to the starting line.
From the starting line, Romi ran 4 miles in 40 minutes, rested for 40 minutes, jogged back 1 mile toward the starting line in 20 minutes, rested for 20 minutes, and jogged the last 3 miles back to the starting line.
From the starting line, Romi ran 2 miles in 20 minutes, rested for 20 minutes, jogged 2 more miles away from the starting line in 40 minutes, rested for 20 minutes, and jogged the last 4 miles back to the starting line.
From the starting line, Romi ran 2 miles in 20 minutes, rested for 40 minutes, jogged 1 more mile away from the starting line in 40 minutes, rested for 20 minutes, and jogged the last 4 miles back to the starting line.
Answer:
(c) From the starting line, Romi ran 2 miles in 20 minutes, rested for 20 minutes, jogged 2 more miles away from the starting line in 40 minutes, rested for 20 minutes, and jogged the last 4 miles back to the starting line.
Step-by-step explanation:
You want the description that fits the attached graph of the race run by Romi and her friends.
GraphThe graph shows distance increasing for 20 minutes to a distance of 2 miles. 20 minutes later, it shows distance increasing again by 2 miles to a total distance of 4 miles. Again, after 20 minutes, the distance from the starting line is shown decreasing by 4 miles back to zero.
The best description is choice C:
From the starting line, Romi ran 2 miles in 20 minutes, rested for 20 minutes, jogged 2 more miles away from the starting line in 40 minutes, rested for 20 minutes, and jogged the last 4 miles back to the starting line.
__
The graph was drawn using Desmos.
<95141404393>
The best description of the graph is that Romi ran 2 miles in 20 minutes, rested for 20 minutes, ran another 2 miles in 40 minutes, rested for 20 minutes, and then ran 4 miles back to the start. This corresponds exactly to the line segments depicted on the graph.
Explanation:The description that best matches the graph of Romi's terrain race is: from the starting line, Romi ran 2 miles in 20 minutes, rested for 20 minutes, jogged 2 more miles away from the starting line in 40 minutes, rested for 20 minutes, and jogged the last 4 miles back to the starting line. This is consistent with the line segments on the graph that correspond to the distance and time of each part of the race.
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What is the value of x in this equation -4x=42
the answer would be -10.5
you just divide 42 by -4
In a class of 70 students, 10 students passed mathematics, biology or chemistry, 30 pass mathematics, 30 pass biologi, and 25 pass mathematics if 11 pass mathematics or biology 10 pass biology and chemistry and 7 pass mathematics and. Chemistry how many pass all three subjects (i) pass mathematics or chemistry bt not biology, biology or chemistry bt not chemistry, pass at least one subject
For (A ∪ C) - B: 30 + 25 - 7 - 3 = 45
For (B ∪ C) - A: 30 + 25 - 10 - 3 = 42
For A ∪ B ∪ C: 10 students pass at least one subject.
How to solve
The existing details provide that among 10 students taking tests, groups A, B, and C have 30, 30, and 25 students respectively.
Additionally, scores overlap between pairings of the three groups - 11 students in groups A and B got a similar score, similarly, for students in groups B and C it was 10, while for those in groups A and C there were 7 who scored alike.
To indicate those passing all three exams, one can use the inclusion-exclusion principle and determine that 3 students did so.
Accounting for circumstances where individuals are themselves part of multiple categories,
(A ∪ C) - B gets us 45 and (B ∪ C) - A goes to 42.
On the whole, from A through C, no less than 10 test-takers ended up passing at least one exam.
In summary:
For (A ∪ C) - B: 30 + 25 - 7 - 3 = 45
For (B ∪ C) - A: 30 + 25 - 10 - 3 = 42
For A ∪ B ∪ C: 10 students pass at least one subject.
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HELP ME PLEASE 20 POINTS
Which of the following equations represents a line that passes through the points (-3,-3) and (-2,0)
|. y=3x+6
||. 6x+2y=-12
I WILL GIVE YOU THE BRAINLIST THINGY CROWN IF YOU GET IT RIGHT
Answer:
The correct answer is: y = 3x + 6
Circle all the transformation rules that will result in similar figures.
a.) (x-3, y + 4)
b.) (3x, y)
d.) (6x, y)
e.) (x+2, 2y)
c.) (5x, 5y)
Answer:
b.) (3x, y)
d.) (6x, y)
e.) (x+2, 2y)
c.) (5x, 5y)
All these transformation rules involve only dilation, reflection or translation, which are the basic similarity transformations.
Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through (-7,6) and parallel to the line whose equation is 2x - 7y-6=0
The equation of the line in point-slope form is
(Type an equation. Use integers or fractions for any numbers in the equation.)
The equation of the line in point-slope form is y = 2x/7 + 8.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Since the line is parallel to 2x - 7y-6=0, the slope is given by;
7y = 2x - 6
y = 2x/7 - 6/7
Slope, m = 2/7.
At data point (-7, 6) and a slope of 2/7, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 6 = 2/7(x + 7)
y = 2x/7 + 2 + 6
y = 2x/7 + 8
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Fatima set her aircon at 28. 6 degree Celsius. At 11:30 am, she lowered the setting by 3.5 degree celsius . After an hour, she set it at 19 degree celsius. by how many degrees did she lower down the setting of the aircon 12:30 pm? and how(Like how you got the answer)
Fatima lowered the setting down by 6.1 degrees Celsius.
We have,
Fatima lowered the setting of her aircon from 28.6 degrees Celsius to 28.6 - 3.5 = 25.1 degree Celsius at 11:30 am.
After an hour, she set it to 19 degrees Celsius, so she lowered the setting down by 25.1 - 19 = 6.1 degrees Celsius.
To get the answer, we simply subtracted the final temperature (19 degree Celsius) from the temperature at 11:30 am (25.1 degrees Celsius) to find the difference, which is the amount that the setting was lowered.
Therefore,
Fatima lowered the setting down by 6.1 degrees Celsius.
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Which statement is true about this cube?
Answer: D perfect cube
Step-by-step explanation: same number multiplied 3 times
The brightness of illumination, l, of an object varies inversely as the square of its distance , d, from the source of illumination, if l = 18 luxes when d= 4m, find l if d =3m
The value of source of illumination (I) is 32 luxes when the distance d = 4 m.
The brightness of illumination that is denoted by I of ab object varies inversely as the square of of its distance which is denoted by variable 'd'.
So, I ∝ 1/d²
Therefore, I = k/d².......... (i), where k is a non zero proportionality constant.
It is given that if the source of illumination I = 18 luxes when d = 4 m.
Substituting I = 18 and d = 4 in the equation (i) we get,
18 = k/4²
k/16 = 18
k = 18*16 = 288
Now we have to find the value of I when d = 3m.
Now the relation becomes. I = 288/d²
Substituting the value d = 3 in equation (ii) we get,
I = 288/3² = 288/9 = 32 Iuxes.
Hence the source of illumination now is 32 Iuxes.
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Angle is in Quadrant III and sin 0 = − 11/61
. What is the value of cos 0?
Answer: -60/61
Step-by-step explanation:
Use pythagorean to solve for x first
61²=11²+x²
x=-60 It's negative because x in the 3rd quadrant is neg
so
cos∅=-60/61
The principal represents an amount of money deposited in
a savings account subject to compound interest at the given
rate.
***
Principal
$10,000
A. Find how much money there will be in the account after the given number of years.
B. Find the interest earned.
i Click the icon to view some finance formulas.
A. The amount of money in the account after 3 years is $
(Round to the nearest hundredth as needed.)
Rate
2%
Compounded
annually
Time
3 years
Answer:
10612.08
Step-by-step explanation:
10000 + 2% of 10000 = 10200
10200 + 2% of 10200 = 10404
10404 + 2% of 10408 = 10612.08
Solve the word problem using a formula. Be sure to develop an algebraic equation that represents the problem and state the solution clearly. Luz an Amity owe $600 interest on a loan after 5 years. The rate of simple interest was 7.5%. Find the amount of the loan.
The amount of the loan was $1600.
Given that the Luz an Amity owe $600 interest on a loan after 5 years. The rate of simple interest was 7.5%. We need to find the amount of the loan.
So,
SI = principal × rate × time / 100
Therefore,
600 = principal × 5 × 7.5 / 100
60000 = principal × 37.5
Principal = 60000 / 37.5
Principal = 1600
Hence the amount of the loan was $1600.
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How to solve. If the loan agency requires a down payment of 20%, what will your down payment be? If the selling price is 437,250?
The down payment that will be required if the selling price is $437,250 is 87,450
According to the question,
Down payment = 20%
Selling price = $437,250
The down price can be calculated by calculating 20% of the selling price. This can be done as follows:
We convert the percent into decimal form, this can be done by dividing the percent by 100
Thus the value of a 20% downpayment is 0.20
Then we multiply the decimal by the selling price and get the down payment.
Down payment = 0.20 * 437,250
= 87,450
Thus, the amount paid in down payment is 87,450
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Question 21
< >
In a large population, 60% of the people have been vaccinated. If 3 people are randomly selected, what is
the probability that at least one of them has been vaccinated?
Give your answer as a decimal to 4 places.
Question Help: Message instructor
Submit Question
4
Answer: 0.9360
Step-by-step explanation: To find the probability that at least one of the three people has been vaccinated, we need to find the probability that none of them have been vaccinated and then subtract that from 1.
The probability that a person has not been vaccinated is 1 - 0.6 = 0.4. Therefore, the probability that all three people have not been vaccinated is:
P(no one vaccinated) = 0.4 × 0.4 × 0.4 = 0.064
So, the probability that at least one of the three people has been vaccinated is:
P(at least one vaccinated) = 1 - P(no one vaccinated) = 1 - 0.064 = 0.936
Therefore, the probability that at least one of the three people has been vaccinated is 0.936 (to 4 decimal places).
Answer: 0.9360
Mrs. Monroe weighs 165 lb and is prescribed a med with a dosage of 0.8 mg/kg in 2 divided doses. How many milligrams will Mrs. Monroe receive per day? Select one:
The quantity of medication that Mrs Monroe would be given = 60 mg of the medication.
How to calculate the drug dosage for Mrs Monroe?The weight of Mrs Monroe = 165 Ib
To convert pounds (lb) to kg = 165/2.2 = 75kg
If 0.8 mg = 1 kg
X mg. = 75 kg
Make X the subject of formula;
X = 75×0.8/1
= 60 mg
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A box contains 20 black and 30 green balls. One ball is drawn at random, its colour noted and the ball is then replaced in the box for the next draw. The process continues. a) find the probability that first green ball is drawn at the 4 th draw. b) find the probability that the sequence of draws has the third green ball in the sixth draw
Answer:
a)
Step-by-step explanation:
a) The probability of drawing a green ball on any given draw is 30/50 (since there are 30 green balls out of a total of 50 balls). Since the ball is replace....
Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.26cm and a standard deviation of 0.43cm. Using the empirical rule, what percentage of the apples have diameters that are less than 8.12cm?
Answer:
95%
Step-by-step explanation:
Upper limit = 8.09 cm
Lower limit = 6.41 cm
Distribution mean = 7.25 cm
Standard deviation = 0.42 cm
The number of standard deviations from the mean of the upper and lower limits are, respectively:
Both limits are two standard deviations away from the mean.
According to the empirical rule, in normal distributions, 95% of the data falls within two standard deviations of the mean. Therefore, 95% of the apples have diameters that are between 6.41cm and 8.09 cm.
Given f(x) = -7x + 3, find the
domain if the range is 10.
Answer:
1 <= x
Step-by-step explanation:
Domain = x values
It can be 10 or below 10.
10 >= -7x + 3
7 >= -7x
/ -7. /-7
1 <= x
Sign switched since divided by negative #. I'm in calc 2 so just double-check this. Kinda forget how to do math like this at times.
Given the relation {(−3,−1),(x,0),(5,4),(6,13)} , which value for x would make the relation NOT a function?
There is no value of x that would make the relation not a function.
What is function?The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h.
To determine whether the relation is a function or not, we need to check if there are any repeated x values with different y values. If there are, then the relation is not a function.
So, if we substitute each x value in the relation, we get:
When x = -3, the y value is -1.When x = x, we don't know the y value yet.When x = 5, the y value is 4.When x = 6, the y value is 13.Since we don't know the y value for x, there is no repeated x value with different y values. Therefore, the relation is a function for any value of x, including x.
So, there is no value of x that would make the relation not a function.
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An electronics store sells about 80 drones per month for $120
each. For each $6 decrease in price, the store expects to sell eight more drones. The
revenue from drone sales is given by the function R(n) = (unit price) (units sold), or
R(n): = (120 - 6n) (80 +8n), where n is the number of $6 price decreases.
a. How much should the store charge to maximize monthly revenue?
The store should charge $__
b. Using a different revenue model, the store expects to sell five more drones for each
$4 decrease in price. Which revenue model results in a greater maximum monthly
revenue?
The _____ revenue model results in a greater maximum monthly revenue.
a. The store should charge $90
b. The first revenue model results in a greater maximum monthly revenue.
How to solve for the revenuea. We have
R(n) = (120 - 6n)(80 + 8n)
using product ruile
δr/δn = (120 - 6n)(8) + (80 + 8n)(-6)
δr/δn = 960 - 48n - 480 - 48n
δr/δn = -96n + 480
Now, we set the derivative to zero and solve for n:
0 = -96n + 480
96n = 480
n = 5
we put n as 5 in the equation
120 - 6x 5
= 120 - 30
= 90
To maximize the revenue then $90 is charged.
b. For the 4 dollar decrease in price R'(n) = (120 - 4n)(80 + 5n)
Using the product rule, we have:
dR'/dn = (120 - 4n)(5) + (80 + 5n)(-4)
this is = 600 - 20n - 320 - 20n
= -40n + 280
equate to 0
-40n + 280 = 0
n = 7
The new price would then be
120 - 4 * 7
= 120 - 28
= 92 dollars
The maximum revenue calculation(120 - 65)(80 + 85)
= 90(120)
= $10,800
(120 - 47)(80 + 57)
= 92(115)
= $10,580
The first revenue model results in a greater maximum monthly revenue.
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Darnell has a discount card to use the local coffee shop . When he shows his card, he can save $0.75 off every purchase. Complete the table too show how much he pays (p) after using his discount card for each cup of coffee (c)
In the space below use words numers and/or symbols to explain how you found your answer
Answer:
First, it’s a loyalty program. They are rewarding their loyal customers with a lower price. This is good for building long term clients and maximizing lifetime revenue of a customer. However, as a loyalty program it has a pretty big flaw. After the customer gets his free coffee, he is back to ground zero and has no built up financial incentive to return. Of course he does still know he gets a lower price if he buys 10 more.
The Phi Theta Kappa honor society is holding a raffle to raise funds for a service project. They are selling raffle tickets for $5 each and the prizes are as follows: A Thanksgiving dinner for four valued at $120, four pumpkin pies from the culinary school valued at $25 each, and ten turkey sandwiches for the Monday after break, valued at $6 each. PTK ends up selling 122 tickets total. If someone gives you one of those 122 tickets without your having to pay for it, what is the expected value of
the ticket?
The expected value of the raffle ticket is $0.98.
How to determine the expected value of the ticketLet's first calculate the probability of winning each prize.
Thanksgiving dinner: There is only one prize, so the probability of winning is 1/122.
Pumpkin pies: There are four prizes, so the probability of winning is 4/122.
Turkey sandwiches: There are ten prizes, so the probability of winning is 10/122.
Now, let's calculate the expected value:
Expected value = (probability of winning Thanksgiving dinner * value of Thanksgiving dinner) + (probability of winning pumpkin pie * value of pumpkin pie) + (probability of winning turkey sandwich * value of turkey sandwich)
Expected value = (1/122 * 120) + (4/122 * 25) + (10/122 * 6)
Expected value = 0.98
Therefore, the expected value of the raffle ticket is $0.98.
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Determine whether each statement is true or false.
1. In figure A,
2. In figure B,
3. In figure B, m
4. In figure C,
1. In figure A, ∠XTK is congruent to ∠HTR is True
2. In figure B, ∠WLN is complementary to ∠NLB is False
3. In figure B, m∠WLY+ZYLB = 180° is True
4. In figure C, ∠FMD is adjacent to DMS is True.
What are congruent and complementary angles?Complementary angles are angles that add up to 90°.
The theory of complementary angles states that whether they are adjacent angles or not, angles that complement one another are congruent angles.
Congruent angles are angles that are equal in measure to each other.
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Sarah has $120 to spend on
invitations and favors for a
birthday party. The equation
3x+12y = 120 models the
combinations of invitations, x, and favors, y, for $120.
Part A
How many invitations can Sarah purchase if she does not buy any party favors?
Part B
How many party favors can Sarah purchase if she does not buy any invitations?
a) The number of invitations Sarah can purchase if she does not buy any party favors is: 40
b) The number of party favors Sarah can purchase if she does not buy any invitations is: 10
How to solve Linear Equations?
We are given the linear equation as:
3x + 12y = 120
Where:
x is the number of invitations for the birthday
y is the number of favors for the birthday
a) If she does not buy any party favors, then y = 0 and we have:
3x + 12(0) = 120
3x = 120
x = 40 invitations
b) If she does not buy any invitations, then x = 0 and we have:
3(0) + 12y = 120
12y = 120
y = 10 favors
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Mr Adams is painting the outside of his son’s toy box, including the top and bottom. The toy box measures 4 feet long, 1.5 feet wide, and 2 feet high.
The area that Mr. Adams needs to paint is 34ft².
Given that the toy box measures 4 feet long, 1.5 feet wide, and 2 feet high. Since the area that mr Adams needs to paint is the outside area of this box, therefore, the area he needs to paint is the total surface area of the toy box.
Surface area of the box
= 2 [ (Length×Width) + (Height×Width) + (Length×height)]
= 2[ (4 ft ×1.5 ft) + (2ft × 1.5 ft) + (4 ft × 2 ft)]
= 2( 6 ft² + 3 ft² + 8 ft² )
= 34 ft²
Hence, the area is 34ft².
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The complete question must be:
Mr Adams is painting the outside of his son’s toy box, including the top and bottom. The toy box measures 4 feet long, 1.5 feet wide, and 2 feet high. What is the total area that Mr Adams needs to paint?
What is the volume of a rectangular prism with l = 412
cm, w = 312
cm, and h = 6 cm, in cubic cm?
90 1/2
94 1/2
95
95 1/2
94.5 cubic cm is the volume of the rectangular prism.
The following formula determines a rectangular prism's volume V:
L x W x H = V
where w stands for width, l for length, and h for height.
Inputting the values provided yields:
V is equal to 4.5cm × 3.5cm x 6 cm.
V= 94.5 cubic centimeters
When we round to the nearest half, we obtain:
V = 94.5 cubic cm
Hence, the rectangular prism has a volume of around 94.5 cubic cm.
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Order the side lengths
Ordering the side lengths of the triangle, we have FG < FH < GH
Ordering the side lengthsFrom the question, we have the following parameters that can be used in our computation:
The triangle
The general rule is that
The length opposite the gretaest angle is the greatest length
The length opposite the least angle is the least length
Using the above as a guide, we have
<G = 180 - 43 - 77
<G = 60
So, we have
43 < 60 < 77
For the side lengths, we have
FG < FH < GH
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Truman's father is designing a toy car ramp for him. His dad determined that the measure of angle x needs to be increased by 20.
160
What is the measure of the new angle?
The measure of the new angle x on the ramp is 40 degrees
Calculating the measure of the new angle?The figure represents the given parameter such that the toy car is on a ramp
As a general rule, we have
The sum of angles on a straight line equals 180
substitute the known values in the above equation, so, we have the following representation
x = 160 = 180
So, we have
x = 20
Increasing x by 20, we have
x + 20 = 40
Hence, the angle is 40 degrees
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John has 12 pounds of dog food and is going to separate it into 3/4 pound portions.
How many portions of dog food will he have?
03
04
08
O16
Doug has 8 square pieces of wood. Each piece of wood has a side length of s centimeters. The total area of all eight pieces of wood is 200 square centimeters. Create a quadratic equation Dounfg can use to find the side length of each piece of wood.
The quadratic equation Dounfg can use to find the side length of each piece of wood is:
8s² - 200 = 0
How to create a quadratic equation Dounfg can use to find the side length of each piece of wood?A quadratic equation is an algebraic equation of the second degree in the given variable (e.g. x).
The quadratic equation in its standard form is ax² + bx + c = 0,
where a, b and c are constant
Each piece of wood has a side length of s centimeters. Thus, the area of each piece of wood will be:
s * s = s²
And the total area of all eight pieces of wood will be:
8 * s² = 8s²
Also, the total area of all eight pieces of wood is 200 square centimeters. Thus, we have:
8s² = 200
8s² - 200 = 0
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