The explicit formula for the arithmetic sequence is: [tex]P_n = 30 + 25n[/tex]
Using the formula, we have that [tex]P_{100} = 2530[/tex].
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
From the recursive formula, we have that:
[tex]a_1 = 30 + 25 = 55, d = 25[/tex]
Hence the explicit formula is:
[tex]P_n = 55 + 25(n-1)[/tex]
[tex]P_n = 30 + 25n[/tex]
Then, when n = 100:
[tex]P_{100} = 30 + 25(100) = 2530[/tex]
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Write the equation of the graph.
Number graph ranging from negative four to four on the x axis and negative two to six on the y axis. A line with a positive slope is drawn on the graph, passing through the point (two, six).
y=12x+5
y−3=−12(x+1)
y−3=12(x+1)
y+3=−12(x−1)
The line which is described as in the task content has equation; (y - 6) = 12 (x-2).
What is the equation of thee line described in the task content?From the task content, it follows that two points which can be used to evaluate the slope of the graph is positive.
Hence, the equation of the line in discuss is which passes through the points given is; (y - 6) = 12 (x-2) in which case, the positive slope number is 12.
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I need some help new topic
Answer:
1160cm squared
Step-by-step explanation:
as for me I've calculated the surface area of a closed cuboid.
this is because we are not informed whether it is open or closed.
and so my teacher told me that if you're not informed, if a cuboid is open or closed, just assume that the cuboid is closed.
and that is what I have done.
hope it helps.
in case of any questions feel free to ask.
She first gave a woman feeding pigeons $100. Next, she gave away half of her remaining money to a child licking an ice cream cone. She gave $50 to an old man riding a rickety bicycle. She bought a homeless woman some shoes for $20. Then she gave half of her remaining money to someone giving a sermon on a soapbox. At this point, she only had $3 left, so she handed it to another woman who lived under a bridge. How much money did the woman have in her purse before she started to give it away in dollars?
Answer:
she hd 173 i think if this is correct
Step-by-step explanation:
if she gave 100 dollars away that would add 100 and then 50 150 and another 20 dollars 170 and she has 3 left so she had 173 dollars
AND PLEASE MARK BRAINLEST
investment of $2000 at 10% simple interest for 9 years
investment of $3000 at 3% simple interest for 20 years
investment of $2000 at 10% simple interest for 3 years
Put them in order from least interest amount to greatest interest amount
Answer:
The last investment (C) has the least interest of $600
The other two investments (A and B) have the same amount of interest of $1800.
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
I = interest earnedP = principalr = interest rate (in decimal form)t = time (in years)Investment A
P = $2000r = 10% = 0.1t = 9 yearsSubstitute the given values into the formula and solve for I:
⇒ I = 2000(0.1)(9)
⇒ I = $1800
Investment B
P = $3000r = 3% = 0.03t = 20 yearsSubstitute the given values into the formula and solve for I:
⇒ I = 3000(0.03)(20)
⇒ I = $1800
Investment C
P = $2000r = 10% = 0.1t = 3 yearsSubstitute the given values into the formula and solve for I:
⇒ I = 2000(0.1)(3)
⇒ I = $600
The last investment (C) has the least interest of $600.
The other two investments (A and B) have the same amount of interest of $1800.
Use the parabola tool to graph the quadratic function f(x)=−(x−3)(x+1).
This is the graph of f(x)=−(x−3)(x+1). Hope it helps!
In how many ways can four people with different heights line up single-file so that exactly two people are taller than the person behind them?
The number of ways by which exactly 2 people are taller than the person behind them is; 6.
What number of ways can they line so that exactly two people are taller than the person behind them?It follows from content that since 4 individuals with different heights are to line up, the 2 individuals who must be taller than the person behind them are represented as one entity and must be in the 1st and 2nd position or the 2nd and 3rd position.
Hence, the number of ways is; 6 upon counting the number of possible outcomes.
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A blue swimsuit costs $42 and a red swimsuit
costs 5/6 as much. How much would the two
swimsuits cost together?
Mark the $42 in the bar model. Mark what is not
known with "?". Solve.
Answer:
$77
Step-by-step explanation:
Hello!
Let's find the cost of the red swimsuit.
Red Swimsuit[tex]R = \frac56*42[/tex][tex]R = \frac{5*42}{6}[/tex][tex]R = \frac{5*7*6}{6}[/tex][tex]R = 5*7[/tex][tex]R = 35[/tex]The cost of the Red swimsuit is $35.
The cost of both swimsuits is $35 plus $42, which gives is $77.
5. [0/0.38 Points]
OG
DETAILS
Find all real solutions of the equation. (Ent
0
www
PRE
-
All the real solutions of the given equation are; x = - 5.61 and x = 1.61
How to find the solutions to an equation?We are given the equation;
x - √(9 - 4x) = 0
Add √(9 - 4x) to get;
x - √(9 - 4x) + √(9 - 4x) = √(9 - 4x)
x = √(9 - 4x)
Square both sides to get;
x² = 9 - 4x
Add 4x to both sides to get;
x² + 4x = 9 - 4x + 4x
x² + 4x - 9 = 0
Using online quadratic equation calculator, we have;
x = - 5.61 and x = 1.61
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MORE HELP :( acellus work
A triangle is a plane shape bounded by three straight sides, thus it has three internal angles. Therefore, the required values are:
i. x = [tex]40^{o}[/tex]
ii. y = [tex]120^{o}[/tex]
A plane shape is a figure bounded by straight sides. Examples are triangles, squares, rectangles, rhombus, kite, trapezium, etc. A triangle is an example of a plane shape that has three sides, thus three angles. also, the sum of angles in a given triangle is [tex]180^{o}[/tex].
Thus the required values of x and y can be determined as follows:
x + 20 + 120 = [tex]180^{o}[/tex]
x + 140 = [tex]180^{o}[/tex]
x = [tex]180^{o}[/tex] - 140
So that,
x = [tex]40^{o}[/tex]
Thus,
y = 20 + 120 (the sum of opposite angles is equal to an exterior angle.)
= [tex]120^{o}[/tex]
Therefore, x = [tex]40^{o}[/tex] and y = [tex]120^{o}[/tex]
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Long-term assets are depreciated over time for which reason?
Step-by-step explanation:
Depreciation of Long Term Assets
As with most types of assets, long term assets needs to be depreciated over the course of their useful life. It is because a long term asset is not expected to generate a benefit for an infinite amount of time.
Answer:
Inflation
Step-by-step explanation:
The rising costs of goods and services mean that $1 in 2022 will be worth more than $1 in 2032. This is called inflation.
Let's just say you put $200,000 in a savings account in 2000. That could've purchased you a 4 bedroom house at the time.
You keep the money in the account for over 20 years. And in 2020, you want to buy a new home with the money you have saved.
However, you can only buy a 2 bedroom house, because the rising costs of the market, increased the cost, or depreciated your savings.
This is called inflation.
To decrease a number by 13%, what decimal should we multiply it by?
Answer:
0.87
Step-by-step explanation:
After decreasing new value would be : 100% - 13% = 87%
87 % = 87/100 = 0.87
To be able to solve equations 3 and 4 by elimination, each equation needs to be multiplied by something, Drag a red number to the red box for equation 3 and a brown number to the brown box for equation 4.
The solution to the equation 3 and 4 by elimination is x = -2 and y = -2
Simultaneous equation2x = 3y + 2. (1)
3x = 5y + 4. (2)
Rewriting the equation2x - 3y = 2. (3)
3x - 5y = 4 (4)
Multiply (3) by 3 and (4) by 26x - 9y = 6. (5)
6x - 10y = 8. (6)
subtract (5) from (6) to eliminate x-10y - (-9y) = 8 - 6
-10y + 9y = 2
-y = 2
y = -2
substitute y = -2 into (3)2x - 3y = 2. (3)
2x - 3(-2) = 2
2x + 6 = 2
2x = 2 - 6
2x = - 4
x = -4/2
x = -2
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Which could be the graph of the function?
The graph of the function y = sin 0.5x is option A. This can be obtained by using period of the graph function.
Which is the required graph?Periodic function is a function that repeats at uniform intervals; the time interval between two waves is called the period.
A function f will be periodic with period n,f (a + n) = f (a), ∀ n > 0.
After first n the function is same that is f(a), after second function is the same, the function is repeated with an interval of n.
For example: the period of sin a is 2π for the reason that the smallest number satisfying sin (a + 2π) = sin a is 2π, for all a.Therefore the formula for period of a function is 2π/|B| when the function is y = A sin(Bx + C) and y = A cos(Bx + C).
For a function y = sin bx, period is given by,
P = 2π/b
Here function is y = sin 0.5x, therefore b = 0.5
P = 2π/0.5
=20π/5
= 4π
Period is 4π. The first graph has period 4π.
Hence the graph of the function y = sin 0.5x is option A.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Which could be the graph of the function y = sin 0.5x?
The digits 0, 1, 2, 3, and 4 are to be used in a four-digit ID card. a) how many different cards are possible? b) If repetition are permitted? c) If repetition are not permitted?
Answer:
a) Varies on b and c
b) 625 combinations
c) 120 combinations
Step-by-step explanation:
a) How many different cards are possible?
Leads to (b and (c
It depends on if repetition are permitted.
↓
in a 4 digit numerical combination, you were given 5 numbers.
b) If repetition are permitted:
you can put any of the given 5 digits to the 1st, 2nd, 3rd, and 4th position.
Each digits would have 5 turns.
This means that you will have 5 x 5 x 5 x 5 If there is repetition,
which is 5⁴ is 625 possible combinations.
c) repetition are not permitted:
This would mean that you have;
5 turns for the first digit,
4 turns for the second digit,
3 turns for the third digit,
2 turns for the fourth digit.
which means you have 5 x 4 x 3 x 2 possible solutions.
5 x 4 x 3 x 2 = 120
There will be 120 possible combinations in total if there's no repetitions.
________________________________________________________
Hope this helped!
Find the future value of $15,000 compounded continuously at 6% for 8 years.
The future value with continuous compounding is $127,420.39.
What is the future value?The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rate15,000 x (e^0.06) x 8 = $127,420.39
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NO LINKS!! Please help me with this problem
Answer:
-8Step-by-step explanation:
[tex] \bf \cfrac{f(x + h) - f(x)}{h} [/tex]
[tex]\bf f(x) -8x + 1[/tex]
[tex]\bf f(x+h) = -8x-8h+1[/tex]
[tex]\bf \cfrac{ - 8x - 8h + 1 + 8x - 1}{h} [/tex]
[tex] \bf =\cfrac{ - 8h}{h} [/tex]
[tex] \bf = - 8[/tex]
▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎
Answer:
Given function:
[tex]f(x) = -8x + 1.[/tex]
Let's find the difference quotient:
[tex]\frac{f(x+h)-f(x)}{h}\\\\= \frac{[-8(x+h)+1] - (-8x + 1)}{h}\\\\= \frac{-8x-8h+1+8x-1}{h}\\\\ = \frac{-8h}{h}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(h\neq 0)\\\\= -8.[/tex]
8 squared plus 6 squared = c squared using Pythagorean theorem for right triangle
Answer:
Hypotenuse of 10
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^{2} +b^{2} = c^{2}[/tex]
So let's plug in the numbers!
[tex]8^{2} +6^{2} = c^{2}[/tex]
Let's start the squaring (8*8 and 6*6)
[tex]64 + 36 = c^{2}[/tex]
Add the numbers to simplify
100 = [tex]c^{2}[/tex]
To reverse/invert a number that is squared, all you have to do is to take the square root of the number. But we have to do the same operations on both sides of the equation.
[tex]\sqrt{100} =\sqrt{c^{2} }[/tex]
We can simplify, and the square of c cancels because of the square root, leaving us with:
10 = c
FINDING THE NUMBER OF REAL AND NONREAL SOLUTIONS ( EDGE 2022 )
How many real and nonreal solutions does the equation have?
x5 – 6x + 4 = 0
By graphing the function, we can see that we have 3 real solutions and 2 non-real solutions.
How many real and nonreal solutions does the equation have?
To check this, we need to graph the equation and see how many times it intersects the x-axis.
Because the degree is 5, we know that there are 5 solutions in total.
Now if we look at the graph, we can see that it intersects the x-axis on 3 points, so there are 3 real solutions. And because there are 5 solutions in total, we conclude that the other 2 solutions are non-real.
So we have 3 real solutions and 2 non-real solutions.
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URGENT!
Positive integers B and C satisfy b^2 - bC-23=0. What is the value of C.
A. 21 b. 22 c.23 d.24
The value of C based on the information given about the integer is C. 22.
How to calculate the value?From the information given,
b² + bc - 23 = 0
Let the assumed value for a = 1
b² + bc - 23 = 0
1² + (1 × c) - 23 = 0
1 + c - 23 = 0
c = 23 - 1
c = 22.
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calling all dazai's ans dazai simps ♡♡♡♡♡♡♡
True or false? in a two-column proof, the right column contains a series of
deductions.
A. True
B. False
Answer: True
Step-by-step explanation:
Answer:False
Step-by-step explanation:I took the test
Casper has some whipping cream that is 18%, percent butterfat, and some milk that is %4, percent butterfat. He wants to make a 500 ML mixture of them that is 12%, percent butterfat.
What does point M represent in this context?
Choose 1 answer:
(Choice A, Checked, Correct)
CORRECT (SELECTED)
The mixture has the intended volume and has more than the intended percent of butterfat.
Explanation: Point M is on line b, so it represents a scenario where the mixture has a volume of exactly 500 ML. Also, point M is above line a, so it represents a scenario where the mixture has more than 12%, percent butterfat.
L represent Option A. The correct answer is that the mixture has the intended volume and has more than the intended percent of butterfat.
What is the graph about?Note that:
The graph shows that the point L is one that is below the blue line of the graph.
Therefore, x + y = 500
Also one need to see that:
0.18x + 0.04y = 500(0.12)
Since that cream is 18% butterfat, milk is 4% butterfat, so L is composed of of 350 ml of cream and 100 ml of milk.
Hence the total amount of butterfat for L is:
0.18 x 350 + 0.04 x 100
= 67ml.
Next, one has to calculate 12% of the volume of L :
12% of 450:
0.12 x 450 = 54ml
So, because 67 is bigger than 54, this implies that the volume of butter fat in L is more than 12 %.
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Beginning with the graph of f(x) = x2, what transformations are needed to form g of x equals one third times the quantity x plus 3 end quantity squared minus 3 question mark?
To transform f(x) into g(x) we need to use addition, subtraction and multiplication.
Given f(x)=[tex]x^{2}[/tex] and g(x)=[tex]x/3+3(x^{2} -3)[/tex]
We need to transform function f(x)into g(x).
A function refers to a relation which expresses relationship between two variables. It contains one value for each value of x. If there are more than one value for one value of x then it is not said to be a function.
f(x)=[tex]x^{2}[/tex], g(x)=[tex]x/3+3(x^{2} -3)[/tex]
To transform f(x) into g(x) we need to follow the following steps:
First subtract 3 from f(x).Then multiply the expression received from above step by 3.Next step is to add x/3 to the expression received from the above step.Now we will get the g(x)=[tex]x/3+3(x^{2} -3)[/tex].Hence we have to use addition, subtraction and multiplication for transformation.
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The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.
Step-by-step explanation:
what year is same if you read it upside down?
Answer:
22/02/2022 ,22 February 2022
Step-by-step explanation:
7. Meghraj divided like this. 1.05 2.1 → 105 210 Do you agree with what he did? Explain your thinking.
Step-by-step explanation:
I guess that means
1.05 / 2.1
or
1.05 ÷ 2.1
both mean the same thing.
so, let's look at
1.05 / 2.1
this is the same as
105/100 / 210/100 = (105×100) / (210×100) =
= (105×100) / (210×100) × (1/100 / 1/100)
as long as we multiply numerator (top) and denominator (bottom) always with the same thing, the general fraction or division is unchanged.
(105×100) / (210×100) × (1/100 / 1/100) =
= (105 × 100/100) / (210 × 100/100) = 105 / 210
so, yes, the division of 105 / 210 is the same as 1.05 / 2.1
If one card is randomly selected from a well-shuffled standard deck of 52 cards, what is the probability that the card selected is not a heart?
Probability helps us to know the chances of an event occurring. The probability that the card selected is not a heart is 3/4.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The probability of the card not being selected is a heart is,
Probability = (Number of cards without heart)/Total number of cards)
Probability = 39/52
Probability = 3/4
Hence, the probability that the card selected is not a heart is 3/4.
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The answer to this problem
Answer:
jdiddbhhuduh9ruruuehgruhrhudhheherj
A number line going from negative 3 to positive 5. a closed circle is at negative 1.5. everything to the left of the circle is shaded. which inequalities have the solution set graphed on the number line? check all that apply. x greater-than-or-equal-to -1.5 x less-than-or-equal-to -1.5 -1.5 less-than-or-equal-to x -1.5 greater-than-or-equal-to x x less-than-or-equal-to -2.5 x greater-than-or-equal-to -2.5 -2.5 greater-than-or-equal-to x
The inequalities which matches the graph are: x ≥ ₋1.5 and ₋1.5 ≤ x
Given, a number line is moving from ₋3 to ₊5 .
Next a mark is made at ₋1.5 and everything to its left is shaded which means not visible.
When we mark the point and shade the left part of it then we can start applying the inequality expressions.
And from that we can match the applicable inequalities while observing the graph.
For the first inequality ₋1.5 ≥ x.Here,x value ranges from ₋1.5 to ₊5, hence we take this as an inequality expression.Next, if we consider x ≤ ₋1.5, then here x value will range from ₋1.5 to ₋3. where the region is shaded. Hence this expression doesn't satisfy the graph.the next expression is ₋1.5 ≤ x. here the value will again range in the shaded area so it is not applicable.₋1.5 ≥ x, here the values will satisfy the graph.remaining inequality expressions does not support the graph.Therefore the only inequalities the graph represents is x ≥ ₋1.5 and ₋1.5 ≤ x
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Help I need the strategies with this one I don’t get it.
The graph of the equation y = 1/4x will pass through which of the following
pairs of points?
A. Point S and (-1,2)
B. Point S and (0,-2)
C. Point T and (0,0)
D. Point T and (0,-2)
Answer:
C. Point T and (0,0)
Step-by-step explanation:
There are more complicated ways to find this answer but the easiest is to go to an online graph maker (I use Desmos) and insert the equation. Then look for each point and see if the line passes through any of these points.
If A and B are 7 x 2 matrices, and C is a 4x7
matrix, which of the following are defined?
A. CA
B. B - A
C. B-C
D. ABT
E. AC
F. CT
Answer:
A, B, D, F
Step-by-step explanation:
Matrix operations require that the matrix dimensions make sense for the operation being performed.
Matrix multiplication forms the dot product of a row in the left matrix and a column in the right matrix. That can only happen if those vectors have the same dimension. That is the number of columns in the left matrix must equal the number of rows in the right matrix.
Matrix addition or subtraction operates on corresponding terms, so the matrices must have the same dimension.
The transpose operation interchanges rows and columns, so reverses the dimension numbers. It is a defined operation for any size matrix.
Defined operationsA. CA ⇒ (4×7) × (7×2) . . . . defined
B. B -A ⇒ (7×2) -(7×2) . . . . defined
C. B -C ⇒ (7×2) -(4×7) . . . undefined
D. AB' ⇒ (7×2) × (2×7) . . . . defined
E. AC ⇒ (7×2) × (4×7) . . . undefined
F. C' ⇒ (7×4) . . . . defined