Find the sum of the first 100
terms of the arithmetic
sequence.
a₁ 15 and a100=307
Answers
The sequence is arithmetic, so there is a constant difference d between consecutive terms such that
\(a_{100} = a_{99} + d\)
\(a_{100} = (a_{98} + d) + d = a_{98} + 2d\)
\(a_{100} = (a_{97} + d) + 2d = a_{97} + 3d\)
and so on, down to
\(a_{100} = a_1 + 99d\)
(notice the pattern of 100 = 99 + 1 = 98 + 2 = 97 + 3 = … = 1 + 99)
Solve for d :
\(307 = 15 + 99d \implies 99d = 292 \implies d = \dfrac{292}{99}\)
Now, the sum of the first 100 terms of this sequence is
\(\displaystyle \sum_{n=1}^{100} a_n = \sum_{n=1}^{100} \left(15 + \frac{292}{99}(n-1)\right) = \boxed{16100}\)
which follows from the well-known sums
\(\displaystyle \sum_{n=1}^N 1 = N\)
\(\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2\)
Related Questions
The concerns about the impact of technology on our lives are growing. There have been
recent research reports about the negative impact of digital technology usage on stress,
work productivity, happiness, and overall well-being. In light of these concerns, a polling
organization asked technology experts about their opinion on our digital life and found
that 29% of the experts believe that in the future our lives will be more harmed than
helped by their digital environment. In an effort to confirm these results, a local tech
company decides to ask 215 randomly selected customers their opinions about their
digital life. Answer parts a through c below.
A
a. What is the probability that 35 or more people from this sample are concerned about
the digital environment?
The probability is
(Round to four decimal places as needed.)
Answers
The probability that 35 or more people from the sample of 215 customers are concerned about the digital environment is 0.7043.
To calculate the probability that 35 or more people from the sample of 215 customers are concerned about the digital environment, we can use the binomial distribution formula.
The binomial distribution is applicable here because we have a fixed sample size (215 customers) and each customer can be categorized as either concerned or not concerned.
Let's denote p as the probability that a randomly selected customer is concerned about the digital environment.
From the given information, we know that 29% of technology experts believe our lives will be more harmed than helped, so p = 0.29.
The formula for the probability mass function of the binomial distribution is:
\(P(X = k) = C(n, k) \times p^k \times (1 - p)^{(n - k)\)
Where:
P(X = k) is the probability of k successes (in this case, customers concerned about the digital environment)
C(n, k) is the number of combinations of n items taken k at a time
\(p^k\) is the probability of k successes
\((1 - p)^{(n - k)\) is the probability of (n - k) failures
Now, let's calculate the probability of having 35 or more customers concerned:
P(X ≥ 35) = P(X = 35) + P(X = 36) + ... + P(X = 215)
Using this formula, we can calculate the probability using a cumulative approach:
P(X ≥ 35) = 1 - P(X ≤ 34)
Calculating this probability requires summing up a large number of individual probabilities, which can be time-consuming.
Therefore, it is more practical to use statistical software or calculators to obtain an accurate answer.
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help please 20 points
Answers
Answer:
48.3
Step-by-step explanation:
How high is a person from the ground when they are at the very top of the ferris wheel? Explain.
Answers
We have the function for the height:
\(h(t)=58+50\sin (\frac{\pi}{2}t-\frac{\pi}{2})\)We have to find the maximum height.
If we look at the function, we see that the first term, 58, is fixed.
The second term is a factor of 50 multiplying a sine function.
This sine function will take values within -1 and 1.
So we can conclude that the maximum height will happen when the sine function takes a value of 1.
NOTE: This is the case because the term has a positive term (50). If not, it would be when the sine function takes a value of -1.
Then, if the sine function has a value of 1, the maximum height will be:
\(h_{\max }=58+50\cdot1=58+50=108\)Answer: the maximum height is 108 feet.
5 members or 20% of the math league did not come to the meet. how many total members are there
Answers
a. Use the product rule to find the derivative of the given function.
b. Find the derivative by expanding the product first.
h(z)= (3-2²) (2³-2z+3)
Answers
Answer:
h'(z) = 2
Step-by-step explanation:
(b) First, let's expand everything so our equation is easier to look at.
h(z) = (3-4)(8-2z+3)
(-1)(-2z+11)
2z-11
Now, let's find the derivative:
h'(z) = 2
United Airlines' flights from Boston to Dallas are on time 80 % of the time. Suppose 7 flights are randomly selected, and the number on-time flights is recorded. 1.The probability that at least 3 flights are on time is
Answers
Answer: 14.5
Step-by-step explanation:
Given data:
Success rate = 80% = 0.8
No of flights = 7
No of failures = 1 – 0.8 = 0.2
Solution
at least 3 flights are on time is
= 7C3 * (0.80)^3 * (0.80)^1 + 7C7 * (0.80)^7 * (0.80)^1
= 35 * 0.512 * 0.8 + 1 * 0.21 * 0.8
= 14.336 + 0.168
= 14.5
deon swam 4 kilometers against the current
Answers
Answer:
DEON is awesome at swimming
Step-by-step explanation:
good job deon
The length of a rectangle exceeds the width by 2 cm . If the diagonal is 10 cm long , find the width of the rectangle .
Answers
Length = 8cm
Out of 35 students in Miss Stacey's class, 21 have a pet. What percent of the students in Miss Stacey's class have a pet? Please Hurry!!
Answers
Answer:
60%
Step-by-step explanation:
21/35 = 3/5
= 0.6
=60%
convert 8 7/9 yard into in
Answers
Answer:
316.08 inches
Step-by-step explanation:
There are 3 feet in a yard, and there is 12 inches in 1 foot, so there are 36 inches in one yard. If there is 8 7/9 yards it is the same at 8.78 yards, and 8.78 x 36 = 316.08 inches. Therefore 8 7/9 yards = 316.08 inches.
A mason is a person who builds structures with bricks, stone, cement block, or wee. A mason usually uses, mortar to hold the bricks together. A general rule of thumb in masonry is that 2 1/2 bags of mortar are needed for every 100 cement blocks. Use a double number line to determine each answer.
Answers
By using the concept of unitary method, it can be calculated that
a) For 350 blocks of cement, \(8\frac{3}{4}\) bags of mortar are required
b) For 50 blocks of cement, \(1\frac{1}{4}\) bags of mortar are required
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, unitary method will be used
The double number line has been shown below-
a) For 100 blocks of cement, \(2\frac{1}{2}\) bags of mortar are required
For 1 block of cement, \(\frac{5}{2} \times \frac{1}{100}\) bags of mortar are required
For 350 blocks of cement, \(\frac{5}{2} \times \frac{1}{100} \times 350\) bags of mortar are required
For 350 blocks of cement, \(\frac{35}{4}\) bags of mortar are required
For 350 blocks of cement, \(8\frac{3}{4}\) bags of mortar are required
b) For 100 blocks of cement, \(2\frac{1}{2}\) bags of mortar are required
For 1 block of cement, \(\frac{5}{2} \times \frac{1}{100}\) bags of mortar are required
For 50 blocks of cement, \(\frac{5}{2} \times \frac{1}{100} \times 50\) bags of mortar are required
For 50 blocks of cement, \(\frac{5}{4}\) bags of mortar are required
For 50 blocks of cement, \(1\frac{1}{4}\) bags of mortar are required
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A sociologist sat married couples down in her office and asked some survey questions for her statistical study on marriage. The first married couple was Bonnie and Clyde. Bonnie sat down next to her husband while the sociologist sat across the table from them both. The sociologist asked each the question, if you could return to the past, would you marry your spouse all over again?" This was continued for several other married couples. This is not a good way to conduct this survey and most likely will not give representative results of all married couples. Why not?
Answers
Answer:
Step-by-step explanation:
I am married. I can tell you, I'd never give any answer but yes, no matter how I felt about her at the time.
Why hurt her feelings?Why lock her answer in? As soon as she hears my answer, she knows what her answer needs to be. Or she's pressured into giving that answerBecause the answer is so likely to be the same way, how would this question pick up on the couples that despise each other?What is the unit price of 12 gallons of gasoline that costs $39.48 ?
Answers
The unit price of 12 gallons of gasoline that costs $39.48 is $3.29 per gallon
How to determine the unit price?The given parameters are:
Gallons = 12
Cost = $39.48
The unit price is calculated as:
Unit = Cost/Gallon
So, we have:
Unit = $39.48/12
Divide
Unit = $3.29
Hence, the unit price of 12 gallons of gasoline that costs $39.48 is $3.29 per gallon
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PLEASE HELP WILL GIVE BRAINLIEST
The number of automobiles in a certain town was 1,890 in 2015, and it was 2,420 in 2020. If we were to make a linear model that gives the number of automobiles in this town as a function of the number of years since 2015, what would be the y-intercept?
Answers
The y-intercept of the linear model is 211,400, which represents the estimated number of automobiles in the town in the year 2015 (when the independent variable is zero).
To find the y-intercept of the linear model, we need to determine the value of the dependent variable (the number of automobiles) when the independent variable (the number of years since 2015) is equal to zero.
Let's first find the slope of the line, which represents the rate of change of the number of automobiles per year:
slope = (change in number of automobiles) / (change in number of years)
slope = (2420 - 1890) / (2020 - 2015) = 106 automobiles per year
Now we can use the point-slope form of a linear equation to find the y-intercept:
y - y1 = m(x - x1)
where y1 is the value of the dependent variable when the independent variable is x1. In this case, x1 = 2015, y1 = 1890, and m = 106 (the slope we just calculated).
y - 1890 = 106(x - 2015)
To find the y-intercept, we can set x = 0:
y - 1890 = 106(0 - 2015)
y - 1890 = -213,290
y = 211,400
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Suppose there are 106 (1 million) asteroids that are 0.87 km in radius. If they were all combined into a single sphere, calculate the radius of this sphere in km.
Answers
Answer:
87km
Step-by-step explanation:
Volume is proportional to radius cubed, so radius is proportional to the cube root of volume.
Increase volume by a factor of 10^6 and radius increases by a factor of the cube root of 10^6, which is 10^(6/3) = 10^2 = 100.
100 * 0.87 km = 87 km
simplify the expresion: 8(x^4 y^3)2/3
Answers
Answer:
Answer is this or not
Step-by-step explanation:
16x^4y^3/3
If in a right triangle, the given legs are a = 10 and b=16, then by using the Pythagorean Theorem find the hypotenuse, c.
The hypotenuse is c = ?
(Simplify your answer. Type an exact answer, using radicals as needed.)
Answers
Answer:
\(c=2\sqrt{89}\)
Step-by-step explanation:
Pythagorean theorem is:
\(c^{2} =a^{2} +b^{2}\)
\(c^{2}=10^{2}+16^{2} \\c^{2} =100+256\\c^{2}=356\\c=\sqrt{356} \\c=2\sqrt{89}\)
Solve the Quadratic Below:
y=2x²-7x-4x
Answers
The solution to the quadratic equation 2x² - 7x - 4x is x = 0 and x = 11/2.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, y = 2x² - 7x - 4x.
y = 2x² - 11x.
y = x(2x - 11).
Or,
x(2x - 11) = 0.
x = 0 Or 2x - 11 = 0 ⇒ 2x = 11 ⇒ x = 11/2.
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Help! First one to answer I’ll mark brainliest
Answers
Answer:
p=38
Step-by-step explanation:
hope that helps!
A gardener measures the dimensions of a rectangular garden that is 9 meters wide by 12 meters long. If the gardener draws a blueprint of the garden, where each meter is equivalent to
inch, which statements are true?
Select ALL that apply.
The area of the blueprint is square inches
The area of the blueprint is 108 square inches
The length of the blueprint is 6 meters
The perimeter of the blueprint is 28 inches.
The width of the blueprint is 8 meters
Calculator
Answers
Answer:
Catalog Name:*Shimmering Chic Earrings*
Base Metal: Alloy
Plating: Gold Plated
Stone Type: Cubic Zirconia/American Diamond
Type: Jhumkhas
Multipack: 1
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*Proof of Safe Delivery! Click to know on Safety Standards of Delivery Partners- https://ltl.sh/y_nZrAV3
The statements are true:
The area of the blueprint is square inches
The area of the blueprint is 108 square inches
What is Area of rectangle?The Area of Rectangle is product of its length to its width.
So, Area of Rectangle = length x width
Given:
length= 12 inch
and width= 9 inch
Area of Blue print = l x w
= 12 x 9
= 108 square inches.
Perimeter of Blue print = 2 ( l+ w)
= 2( 12+ 9)
= 42 inches
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190 is what percent of 360
Answers
Answer:
190 / 360 = 0.52777777
0.527777 x 100 = 52,78%
A line is drawn so that it passes through the points(-4,0) and (2,6) what is the slope of the line
Answers
Answer:
Slope is 1
Step-by-step explanation:
To find the slope
m = ( y2-y1)/(x2-x1)
= ( 6-0)/(2 - -4)
= 6/ ( 2+4)
= 6/6
=1
Answer:
Slope = 1
Step-by-step explanation:
Now we have to,
→ find the slope of the line.
Formula we use,
→ (y2 - y1)/(x2 -x1)
Now the slope will be,
→ (y2 - y1)/(x2 -x1)
→ (6 - 0)/(2 -(-4))
→ (6 - 0)/(2 + 4)
→ 6/6 = 1
Hence, the slope is 1.
A pet store is selling dogs for $140 and cats for $70. If 28 pets were sold and the
receipts were $3360, how many cats were sold?
Answers
8
Step-by-step explanation:
8 × $70 = $560
20 × $140= $2800
$560 + $2800 = $3360
Who’s feeling the makeup look? cause i am!
Answers
Answer:
not me because its not my color
Answer the question with an algebraic expression.
The perimeter of a square is m meters. How long, in centimeters, is each side of the square?
Answers
The length of the square in centimetres in algebraic expression is 25m
How to find the side length of a square?The perimeter of a square is m meters.
The length of the each side of the square in centimetres can be represented in an algebraic expression as follows:
Therefore,
perimeter of a square = 4l
where
l = side lengthTherefore,
m = 4l
where
m = perimeter of the squarel = m / 4 meters.
Therefore, the side length of the square in centimetres is as follows:
1 meters = 100 cm
m / 4 meters = ?
cross multiply
length of the square in meters = m / 4 × 100
length of the square in meters = 100m / 4
length of the square in meters = 25m
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Marianna finds an annuity that pays 8% annual interest, compounded quarterly. She invests in this annuity and contributes $10,000 each quarter for 6 years. How much money will be in her annuity after 6 years? Enter your answer rounded to the nearest hundred dollars.
Answers
The amount of money in Marianna's annuity after 6 years will be approximately $300,516.
To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:
A = P * ((1 + r/n)^(n*t) - 1) / (r/n)
Where:
A = the final amount in the annuity
P = the regular contribution (each quarter) = $10,000
r = annual interest rate = 8% = 0.08
n = number of compounding periods per year = 4 (since it's compounded quarterly)
t = number of years = 6
Plugging in the values:
A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)
Calculating this expression:
A ≈ 10000 * ((1.02)^24 - 1) / 0.02
A ≈ 10000 * (1.601032449136241 - 1) / 0.02
A ≈ 10000 * 0.601032449136241 / 0.02
A ≈ 10000 * 30.05162245681205
A ≈ 300,516.22
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Answer:
304200
Step-by-step explanation:
To find the value of P6, use the savings annuity formula
PN=d((1+r/k)N k−1)r/k.
From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives
P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).
Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.
Rounding as requested, our answer is 304200.
The set of all numbers greater than 2
Answers
Daejan has a fish tank shaped like the rectangular prism shown below. The fish tank is made of glass, except for the top which is covered by a plastic lid. a. Find the surface area of the glass surfaces of the fish tank. b. Find the surface area of the plastic lid.
Answers
(a) The surface area of the glass surfaces of the fish tank is 2108.50 in^2.
(b) The surface area of the plastic lid is 408 in^2.
Daejan has a fish tank shaped like the rectangular prism.
From the diagram given below:
length of the box , l = 32 inch
width, w = 12.75 inch
and height, h = 19 inch
a) We have to find the surface area of the glass surfaces of the fish tank.
Total surface area of the fish tank = 2(lh + lw + wh)
Total surface area of the fish tank = 2(32*19 + 32*12.75 + 12.75*19)
Total surface area of the fish tank = 2516.50 in2
Dimensions of the plastic lid on top only includes the length and width, so,
Area of the plastic lid = l*w
Area of the plastic lid = 32*12.75
Area of the plastic lid = 408 in^2
Therefore, Surface area of the glass surfaces = 2516.50 - 408
Surface area of the glass surfaces = 2108.50 in^2
b) We have to find the surface area of the plastic lid
Surface area of the plastic lid = 408 in^2.
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Does anyone know where i can get work and answers for this paper if you do it ill give brainliest Thank you so much if you can help : )
Answers
Answer:
I think maybe search Gina Wilson (All things Algebra), 2014 in google, look at the tiny letters at the bottom of the page.
Step-by-step explanation:
47.1 48.2 48.3 47.5 48.5
48.1 47.2 48.2 48.4 48.3
1. What proportion of the reactions were above the 48 grams threshold?
2 .Other chemists typically get 65% of their reactions to produce more than 48 grams. Should the engineer say that she was able to increase the useful product when compared to the other chemists?
Group of answer choices
Answers
Answer:
1. 0.7 since 7 of the 10 reactions had more than 48 grams of the useful product.
2. She could be optimistic, but her proportion does not seem far from what others have done. She should run more reactions to be more sure of the improvement. With only 10 values in her data set, 0.7 (and 0.6) is as close to 0.65 as she could get.
Step-by-step explanation:
Just trust me