The sigma notation for the sequence 22, 28, 34, 40, 46 is as follows:
[tex]\sum_{n = 0}^{n = 4} 22 + 6n[/tex]
How to represent a notation in sigma notation?A sequence is represented in sigma notation according to the following rule:
[tex]\sum_{n = 0}^{n = N-1} a + bn[/tex]
In which the parameters are described as follows:
N is the number of terms in the sequence.a is the first term of the sequence.b is the common difference between the terms of the sequence.In the context of this problem, the sequence is:
22, 28, 34, 40, 46.
Hence the values of these parameters are given as follows:
N = 5, as there are 5 terms in the sequence.a = 22, which is the first term of the sequence.b = 6, as the difference between each term of the sequence is.Hence the sigma notation of the sequence is given by:
[tex]\sum_{n = 0}^{n = 4} 22 + 6n[/tex]
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what is Vivian's new account balance?
Answer: 218.65 US$
Step-by-step explanation: $187.56+$49.73= $237.29
237.29 US$- $18.64
Answer:
$218.65
Step-by-step explanation:
She starts with a balance of $187.56. When she deposits money she is adding to the account.
$187.56 + $49.73 = $237.29
When she spends money money is being subtracted from her account.
$237.29 - $18.64 = $218.65
Look at the table below. Which of the following is the constant rate of change?
Given data:
The first value of x is a=-16.
The first value of y is b=20.
The second value of x is c=-12.
The second value of y is d=15.
The expression for the rate change is,
x=(d-b)/(c-a)
Substitute the given values in thhe above expression.
x=(15-20)/(-12+16)
=-5/4
Thus, he constant rate of change is -5/4.
ASAP please Hurry
The number of issues of books from a library are given for the years 2001–2011. The numbers are in hundreds of thousands.
Answer:
See attached graph.
Step-by-step explanation:
Use DESMOS graphing software. Free.
due in an hour pls help!!
just tell me where to put the points
Translation is defined as an interpretation into another language or context. The Spanish word "bueno," which translates to "good," serves as an illustration. A translation can involve explaining to a parent the significance of their teen's expression.
What is the translational equation?The translation equation or formula is written as g(x) = f(x+k) + C.
Example
(x -3, y - 2)
x - 3 y - 2 ;
x-3 y-2
x-3y - 2
x² - x - 6 =0
-x + 3 > 2x + 1
line(1, 2),(3 ,1)
f(x) = x³
prove tan²(x) - sin ²(x) = tan²(x) sin²(x)
d /dx(3x + 9/2 -x)
(sin²(0))
sin (120)
lim(x -> 0 (xln(x))
= 0 3/2n.
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2 Four friends go to the ice cream shop to purchase frozen
yogurt. Each friend gets a part strawberry and part
vanilla.
• Lucas gets 0.25 strawberry.
Adrianna gets % strawberry.
Ricardo gets 0.8 strawberry.
Jasmine gets % strawberry.
•
•
Arrange the friends in order from least to greatest amount of
strawberry in their yogurt.
Least
Greatest
Answer:
12
Step-by-step explanation:
Provide an example and explain the steps to convert a fraction into a percent.
If the cost of an 800 number is $29.95 per month plus 28 cents per minute, then the monthly cost varies directly as the number of minutes.TrueFalse
We have the monthly cost is fixed: $29.95.
The cost varies directly as the number of minutes since the total cost per month will be:
[tex]29.95+\frac{28}{100}x[/tex]If we make a call and spend 30 minutes. We need to add this cost to the payment:
[tex]undefined[/tex]18. An 80-pound grass seed mixture is 30% bluegrass seed. How many pounds of seed
containing no bluegrass seed (0%) should be added to the seed mixture for a resulting
blend that is 20% bluegrass seed? Construct a table, then solve.
Step-by-step explanation:
what table is your teacher taking about ?
in any case this is resistive easy to solve
80 pounds of 30% with x pounds of 0% result in 80+x pounds of 20% :
80×0.3 + x×0 = (80 + x)×0.2 = 80×0.2 + x×0.2
80×0.1 = x×0.2
x = 80×0.1/0.2 = 80/2 = 40 pounds
so, 40 pounds of 0% have to be added to the 80 pounds of 30% to get a mixture of 20% (80+40 = 120 pounds).
13+14=3×f;f=9 helppp
Answer: 3x=13+14
3x=27
x=27/3
x=9
Step-by-step explanation: Maybe.
explain how you got the answer please
Answer:
I cannot include a picture, but the slope is -2/3, and the y-intercept is (0, 3).
Step-by-step explanation:
When given an equation like this, remember the formula y=mx+b that you should have learned. This formula is the slope-intercept formula that you can use. The m is the slope and the b is the intercept. In the equation, the x is what we are trying to find.
y=-2/3x+3
y=mx+b
m=-2/3
b= (0,3)
So, graph the slope as -2/3 and the y-intercept as (0,3).
Hope this helps!
The lateral surface area of cone A is equal to the lateral surface area of
cylinder B.
A
2h
A. True
B. False
The lateral surface area of cone A is equal to the lateral surface area of
cylinder B. This is true.
How to illustrate the information?Lateral area of cone is given by: πrl
where r is the radius and l is the slant height
Here r=r and l=2h
Hence, lateral area of cone A= π×r×2h = 2πrh
Lateral area of cylinder is given by: 2πrh
where r is the radius and h is the height
Lateral area of cylinder B=2πrh
Clearly, both the lateral areas are equal. Therefore, it's true.
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Whats the Point-Slope Equation for the line that goes through
(-3, 5) and (-7, 4)
A pet boarder keeps a dog-to-cat ratio of 5:2. If the boarder has room for 98 animals, then how many of them can be dogs in a ratio
Answer:We have 70 dogs
Step-by-step explanation:
dogs: cats: total5 2 7We want 98 animals98/7 =14We need to multiply each number by 14dogs: cats: total…
hope this helps
Photo plus charges $2 for each print plus a $6 processing fee. Picture time charges $3 for each print plus a $4 processing fee. for what number of prints is the price the same at both stores
10) Find DF if LF = 2X - 8 and LD = X - 3
Answer:
DF = 4
Step-by-step explanation:
You want DF when L is the midpoint, LD = x-3 and LF = 2x-8.
Congruent segmentsSegments DL and LF are marked the same, so are congruent. Using the given expressions, we have ...
LF = LD
2x -8 = x -3
x = 5 . . . . . . . . add 8-x to both sides
Then the measures of the segments are ...
LF = 2(5) -8 = 2
LD = 5 -3 = 2
DF = DL +LF = 2 +2 = 4
The length of DF is 4 units.
The sum of 4 consecutive integers is 170. What is the largest number in the group?
The largest number when the sum of 4 consecutive integers is 170 will be 44.
According to the question,
We have the following information:
Sum of four consecutive integers = 170
Now, let's take the first integer to be x.
So, the next 3 integers will be (x+1), (x+2) and (x+3) respectively.
Now, the largest number will be (x+3).
Adding 4 consecutive integers:
x+ (x+1) + (x+2) + (x+3) = 170
4x+6 = 170
4x = 170-6 (Moving 6 from the left hand side to the right hand will result in the change of the sign from plus to minus.)
4x = 164
x = 164/4
x = 41
So, the next three consecutive integers will be 42, 43 and 44.
Hence, the largest of the four consecutive integers is 44.
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describe the transformation of f represented by G then graph each function
Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.
5)
Transformation 2: the function is shifted 2 units up
Explanation
[tex]f(x)=x^4[/tex]Step 1
the first transformation is the function multiplied by a constant ( 1/2)
If the function is multiplied by a value less than one, all the values of the equation will decrease, leading to a “shrunken” appearance in the vertical direction
so
[tex]\begin{gathered} f(x)=x^4\Rightarrow\frac{1}{2}x^4 \\ \frac{1}{2}is\text{ smaller than 1, so} \end{gathered}[/tex]Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.
5)
Step 2
the second transformation is add 5
[tex]f(x)=x^4\Rightarrow\frac{1}{2}x^4\Rightarrow g(x)=\frac{1}{2}x^4+5[/tex]If a positive number is added, the function shifts up the y-axis by the amount added.
so,
Transformation 2: the function is shifted 2 units up
I hope this helps you
Greg is at his house he gets in his car drives north 8. 9 miles and stops at a store then he turns around and drives south 7. 7 miles to his friends house how far is the friends house from Greg’s houses?
His friend's house is 1.2 miles away from his house.
How do you know his friend's house is 1.2 miles away from his house?Well, the solution to this math problem is very simple. We just need to remove a number away from another. In other words, we only need to do some subtraction.
Subtraction is one of four main arithmetic operations in which we use to take away a number or an amount from another number or amount. Remember that the commutative law doesn't apply to subtraction, so we really need to be careful to pick what number is subtracted by the other number.
The distance from Greg's house to the store is 8.9 miles away. That's the number that is going to be subtracted. His friend's house is 7.7 miles away from the store. This is the number that we're going to subtract from the previous number. Mathematically, we can express this as:
8.9 - 7.7 = 1.2
We're left with 1.2, which is the distance in miles from Greg's house to his friend's house.
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2. What is the equation of a line that passes through the points (-0.92, 2.49) and (-5.62, 9.76)? Write your answer in point-slope form.
Answer:
Step-by-step explanation:
-0.92 2.49
-5.62 9.76
Rise = 9.76 - 2,49 = 7.27
Run: -5.62 - (-0.92) = -4.7
Slope (Rise/Run) = (7.27.`-0.92) = -1.55
The line has the form:
y = 1.55x + b
We need to find a value of b that forces the line through both point, Use one of the points and solve for b. I'll use (-0.92, 2.49).
y = 1.55x + b
2.49 = 1.55(-0.92) + b
b = 2.49 - 1.426 = 1.064
The equation is y = 1.55x + 1.0
what is 4.5=m + 2.75
4.5 = m + 2.75
Solving for m:
Subtract 2.75 from both sides:
4.5 - 2.75 = m + 2.75 - 2.75
1.75 = m
m = 1.75
Which of the binomials below is a factor of this expression?
25x^2-4y^2z^2
answer- 5x-2yz
The binomials 5x-2yz are a factor of this expression
25x^2-4y^2z^2
This is further explained below.
What are binomials?Generally, A binomial is a kind of polynomial that is used in algebra and is defined as the sum of two terms, each of which is a monomial.
After monomials, this is the sort of sparse polynomial that is the easiest to understand.
The word "binomial" refers to an algebraic expression that consists of just two different terms. This is a polynomial with two terms.
25 x^2-4 y^2 z^2
Rewrite 25 x^2 as (5 x)^2.
(5 x)^2-4 y^2 z^2
Rewrite 4 y^2 z^2 as (2 y z)^2.
(5 x)^2-(2 y z)^2
Since both terms are perfect squares, factor using the difference of squares formula, a^2-b^2=(a+b)(a-b) where a=5 x and b=2 y z.
(5 x+2 y z)(5 x-(2 y z))
Simplify.
(5 x+2 y z)(5 x-2 y z)
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A normal distribution has = 32 and = 5.
(a) Find the z score corresponding to
x = 27.
(b) Find the z score corresponding to
x = 43.
(c) Find the raw score corresponding to
z = −3.
(d) Find the raw score corresponding to
z = 1.1.
a) z score corresponding to x = 27 is -1
b) z score corresponding to x = 43 is 2.2
c) Raw score corresponding to z = -3 is 17.
d) Raw score corresponding to z = 1.1 is 37.5
Given,
Normal distribution with μ = 32 and σ = 5
a) z score corresponding to x = 27
z = (x - μ) / σ
Then,
z = (27 - 32) / 5 = -5/5 = -1
That is, z score corresponding to x = 27 is -1.
b) z score corresponding to x = 43
z = (x - μ) / σ
Then,
z = (43 - 32) / 5 = 11/5 = 2.2
That is, z score corresponding to x = 43 is 2.2
c) Raw score corresponding to z = -3
z = (x - μ) / σ
Then,
-3 = (x - 32) / 5
-3 × 5 = x - 32
-15 = x - 32
x = 32 - 15 = 17
That is, raw score corresponding to z = -3 is 17.
d) Raw score corresponding to z = 1.1
z = (x - μ) / σ
1.1 = (x - 32) / 5
1.1 × 5 = x - 32
x = 32 + 5.5 = 37.5
That is, raw score corresponding to z = 1.1 is 37.5
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On what day does frank first get charged an overdraft fee? a. wednesday b. thursday c. friday d. saturday
Frank first get charged an overdraft fee on Wednesday
Frank has $66.50 in his account as of Sunday.
He made a debit of $60.33 on Monday (66.50 - 60.33), leaving him with a balance of $6.17. He added $80.75 to the account on that same Monday (6.17 plus 80.75). He has $86.92 left over as of Monday.
Frank had a balance of $86.92 on Tuesday when he made a $54.45 debit (86.92 - 54.45). The remaining balance is $32.47.
Frank had a balance of $32.47 at the beginning of the day on Wednesday. He subsequently made withdraw of $49.20. debit(32.47 - 49.20). Frank has overdrawn and will be assessed an overdraft fee following the debit because his balance is -$16.73. Frank still has a negative balance even after making a deposit of $15.
Therefore, Frank was therefore assessed an overdraft fee on Wednesday.
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what is the size of the angle between south and south east
The angle between north and south = 180°. The angle between East and South = 90°. The angle between South and West is 90° and between South and East is also 90°. So the sum of these two angles is equal to 180°. Since these two angles are adjacent to each other so they form a linear pair.
Triangle ABC is shown below, with the angle measures as marked.
What is the measure of Angle A and B?
The measure of Angle A and Angle B are 54° and 122° respectively.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In triangle ABC,
The measure of angle A = (n + 20)°
The measure of angle B = (3n - 10)°
The measure of angle C = n°
Now,
The sum of all the angles of the triangle = 180°
So, we can formulate;
(n + 20)° + (3n - 10)° + n° = 180°
Solve for n as;
n + 20 + 3n - 10 + n = 180
5n + 10 = 180
5n = 180 - 10
5n = 170
Divide by 5, we get;
n = 170/5
n = 34
Thus, The measure of angle A = (n + 20)°
= 34 + 20
= 54°
And, The measure of angle B = (3n - 10)°
= 3 x 34 + 20
= 102 + 20
= 122°
Therefore,
The measure of Angle A and Angle B are 54° and 122° respectively.
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Find the slope of the line that passes through the following points: (-4,-2) and (-3,5)
What is -2=-1+n/8? I’ve been stuck on it for a while
Answer: n= -8
Step-by-step explanation:
1. -2 = -1 + [tex]\frac{n}{8}[/tex]
2. -1 = [tex]\frac{n}{8}[/tex]
3. -8 = n
Door prizes for entrants in a young inventors competition are $100, $50, $25 and $10. In how many ways can the door prizes be awarded if there are 23 entrants?.
There are 212 520 ways that the door prizes can be awarded if there are 23 entrants
To solve this problem the formula and the permutation procedure we must use is:
nPr = n! / (n-r)!
Where:
nPr = permutationn = total number of objectsr = number of selected objects! = factorial of the numberInformation about the problem:
n = 23 (entrants)r = 4 (prizes )23P4 =?Applying the permutation formula we have:
nPr = n! / (n-r)!
23P4 = 23! / (23-4)!
23P4= 23! / 19!
23P4 = 23*22*21*20*19! / 19!
23P4 = 23*22*21*20
23P4 = 212520
What is permutation?It is the ordered arrangement of members belonging to a set with no repeats.
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The impact of new entrants, new products, channel conflicts, and regulation would all be associated with the external opportunities and threats dimension of a SWOT website design analysis.
In summary, the impact of new entrants, new products, channel conflicts, and regulation are all factors that fall under the external opportunities and threats dimension of a SWOT website design analysis. 1. New entrants: When new companies enter the market offering similar website design services, it can increase competition and potentially affect the market share of existing website design businesses. This is an external threat as it poses challenges and risks to the current players in the industry. 2. New products: The introduction of new and innovative website design products can create opportunities for businesses to attract more customers and gain a competitive edge. This is an external opportunity that can be leveraged to improve market position.
3. Channel conflicts: Channel conflicts refer to conflicts or disputes that arise between different distribution channels. In the context of a SWOT analysis for website design, channel conflicts can impact how products and services are delivered to customers. For example, if a website design company relies heavily on a specific distribution channel and that channel experiences conflicts or disruptions, it can affect the company's ability to reach its target market. This is an external threat that needs to be considered.
4. Regulation: Regulations imposed by governing bodies can have a significant impact on website design businesses. For example, regulations related to data privacy, accessibility, or internet governance can affect how websites are designed and operated. Compliance with regulations is crucial to avoid penalties or legal issues. This is an external threat that businesses need to navigate.
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According to the rules of significant figures 7.898 + 5.23 = 13.13. This is because the least precise value in the problem is 5.23, which is precise only to the hundredths digit, so the answer must also be rounded to the nearest hundredths.True or False
The given expression is
[tex]7.898+5.23=13.13[/tex]It's important to know that the rules of significant figures state that the resulting number of a sum of decimal numbers may have no more significant numbers than the least number of significant figures.
In other words, the answers can't be more precise than the least precise number in the sum.
Therefore, the given statement is true.
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