The sum οf 100 numbers in arithmetic sequence is 5445.
What is sequence?The fundamental cοncepts in mathematics are series and sequence. A series is the tοtal οf all elements, but a sequence is an οrdered grοup οf elements in which repetitiοns οf any kind are permitted. One οf the typical examples οf a series οr a sequence is a mathematical prοgressiοn.
Here the given arithmetic sequence [tex]a_1=10[/tex] , common difference d =1.1.
Now using arithmetic sequence sum οf n numbers formula,
=> [tex]S_n = \frac{n}{2}[2a_1+(n-1)d][/tex] where n=100 then,
=> [tex]S_{100}=\frac{100}{2}[2\times10+(100-1)(1.1)][/tex]
=> [tex]S_{100} = 50[20+99\times1.1][/tex]
=> [tex]S_{100}=50[20+108.9][/tex]
=> [tex]S_{100}=50[128.9][/tex] = 5445.
Hence the sum οf 100 numbers in arithmetic sequence is 5445.
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What is the slope of the line through point B, and perpendicular to line k?
Answer:
To find the slope of the line through point B and perpendicular to line k, we need to first find the slope of line k.
If we have the equation of line k in slope-intercept form, y = mx + b, then the slope of line k is simply the coefficient of x, which is m.
Assuming we don't have the equation of line k, we can find its slope by using the slope formula, which is:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are two points on line k.
Let's say line k passes through points P and Q. Then we can write the slope of line k as:
m = (yQ - yP)/(xQ - xP)
Now, we want to find the slope of the line through point B and perpendicular to line k. We know that the product of the slopes of two perpendicular lines is -1. That is:
m1 * m2 = -1
where m1 is the slope of line k, and m2 is the slope of the line through point B and perpendicular to line k.
Therefore, we can write:
m2 = -1/m1
So we just need to find the slope of line k, and then we can use this formula to find the slope of the line through point B and perpendicular to line k.
Once we have the slope of the line through point B, we can write its equation in point-slope form:
y - yB = m2(x - xB)
where (xB, yB) is the point B.
Hope this helps with you with your question (it's not a direct answer, I think?) I'm sorry if it doesn't! If you need more help, ask me! :]
I dont know how to do this
the answer isnt 4
pls answer if u know with simple working
Answer:25 sticks
Step-by-step explanation:
1st=5 sticks
2nd=9 sticks
3rd=13 sticks
4th=17 sticks
5th=21 sticks
6th=25 sticks
The picture shows a container that Rene uses to freeze water:
A container is shown with a base diameter of 8 centimeters and a height of 10 centimeters.
What is the minimum number of identical containers Rene would need to make 2,000 cm3 of ice? (Use π = 3.14.)
a
2
b
4
c
1
d
12
The minimum number οf identical cοntainers Rene wοuld need tο make 2,000 cm³ οf ice is 4. Optiοn b is the cοrrect οptiοn.
What is a cylinder?A cylinder is a three-dimensiοnal sοlid in mathematics that maintains, at a fixed distance, twο parallel bases cοnnected by a curved surface. These bases typically have a circular shape (like a circle), and a line segment knοwn as the axis cοnnects the centers οf the twο bases.
The base οf a cοntainer is 8 centimeters. The height οf the cοntainer is 10 centimetres.
The radius οf a shape is half οf its diameter.
The radius οf cοntainer is 8/2 = 4 cm.
The vοlume οf a cylinder is πr²h.
The vοlume οf a cοntainer is π×4²×10
= 160 × 3.14
= 502.4 cm³
Assume that Rene needs x number οf cοntainers.
The vοlume οf x number οf cοntainers is 502.4 x.
Accοrding tο the questiοn:
502.4 x = 2,000
Divide bοth sides by 502.4:
x = 2000/502.4
x = 3.98
x ≈ 4
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Here are the first 6 terms of a quadratic sequence -5,1,11,25,43,65 find an expression, in terms of n, for the nth term of this sequence
The expression for the nth term of the sequence is, Tn = 3n^2 - 7n - 1
To find an expression for the nth term of a quadratic sequence, we need to find a quadratic function that describes the sequence.
Let the nth term of the sequence be denoted by Tn. We can use the method of finite differences to determine the degree of the quadratic function that describes the sequence.
The first differences between the terms are 6, 10, 14, 18, 22. The second differences between these first differences are all equal to 4. This tells us that the sequence is quadratic, since the second differences are constant.
To find the quadratic function that describes the sequence, we can use the formula for the nth term of a quadratic sequence,
Tn = an^2 + bn + c
where a, b, and c are constants to be determined.
We can use the first three terms of the sequence to form a system of three equations,
T1 = a + b + c = -5
T2 = 4a + 2b + c = 1
T3 = 9a + 3b + c = 11
Solving this system of equations, we get:
a = 3
b = -7
c = -1
Therefore, the expression for the nth term of the sequence is
Tn = 3n^2 - 7n - 1
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The first number minus the second number equals to 26. When the first number is added to 3 times the second number, the result is 194. What are the two numbers
4x0 pls help i weally newd tis madly imb int da fiwst gwade
Answer:it’s 0
Step-by-step explanation:
Alan and Bill at the amount of money they each have and it comes to a total of 250 kroner. Bill and Cassie also at the amount of money they each have that comes to a total of 475 kroner. If all three of them together have a total of 520 kroner how much money does bill have?
If all three of them together have a total of 520 kroner then bill would have 205 kroner
amounts of money that Alan, Bill, and Cassie have:
Let A be the amount of money that Alan has.
Let B be the amount of money that Bill has.
Let C be the amount of money that Cassie has.
From the problem, we know that:
A + B = 250 (equation 1)
B + C = 475 (equation 2)
A + B + C = 520 (equation 3)
We want to solve for B, the amount of money that Bill has.
One way to do this is to use equation 1 to solve for A in terms of B:
A = 250 - B
We can then substitute this expression for A into equations 2 and 3:
(250 - B) + B + C = 520
Simplifying this equation, we get:
C = 270
Substituting this value of C into equation 2, we get:
B + 270 = 475
Solving for B, we get:
B = 205
Therefore, Bill has 205 kroner.
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In a mountain range of California, the percent of moisture that falls as snow rather than rain can be approximated by the function p(h) = 82 in (h) - 649.
where h is the altitude in feet and p(h) is the percent of an annual snow fall at the altitude h. Use the function to approximate the amount of snow at the
altitudes 3000 feet and 6000 feet
Approximately 491351% of the annual moisture at an altitude of 6000 feet falls as snow.
According to the given function, the percent of annual snowfall at an altitude of h feet is given by p(h) = 82 in (h) - 649. To approximate the amount of snow at the altitudes of 3000 feet and 6000 feet, we can simply plug these values into the function and solve for p(h).
At an altitude of 3000 feet, we have:
p(3000) = 82 in (3000) - 649
p(3000) = 246000 - 649
p(3000) = 245351
Therefore, approximately 245351% of the annual moisture at an altitude of 3000 feet falls as snow.
Similarly, at an altitude of 6000 feet, we have:
p(6000) = 82 in (6000) - 649
p(6000) = 492000 - 649
p(6000) = 491351
Therefore, approximately 491351% of the annual moisture at an altitude of 6000 feet falls as snow.
It's important to note that these values represent percentages and not the actual amount of snowfall in inches. To convert these percentages to the actual amount of snowfall, we would need to know the total annual moisture at each altitude. Nonetheless, we can use the given function to approximate the percentage of snowfall at different altitudes in the mountain range of California.
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Find the measure of
x=12°
so:(2x+1°)°+(5x+5)°+90°=180°
7x=180°-1°-5°-90°
7x=84°
x=84°÷7
x=12°
i don't know if it is x that you wanted but the it is
B b) The diagram shows a circle centre O. A, B and Care points on the circumference. DCO is a straight line and DA is a tangent to the circle. Angle ADO = 34° a) Work out the size of angle AOD. (1) 34° Work out the size of angle ABC. Give a reason for your answer. D
let's recall that the point of tangency for a tangent line to a radius in a circle is alway a right-angle, also let's notice that ∡AOD as well as ∡ABC are both intercepting the same arc.
Check the picture below.
a quadratic function has a discriminant with a value of -4 what type of solution does the quadratic equation have ?
Answer:
Complex or Imaginary solutions
Step-by-step explanation:
In the Quadratic Formula, the discriminant is the part that is inside of the radical (square root symbol).
So there are three cases, the discriminant can be:
-positive, OR
-zero, OR
-negative
If its positive, there are two real solutions.
If its zero, there is one real solution.
If its negative, there are two complex (imaginary) solutions.
Calculate the distance between the points N and C in the coordinate plane.
Give an exact answer (not a decimal approximation)..... How would i solve something like this?
Applying the distance formula, the distance between points N and C in the coordinate plane is calculated as: 5 units.
How to Calculate the Distance between Two Points on a Coordinate Plane?To calculate the distance between two points on a coordinate plane, the distance formula can be applied which is given as:
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the two points lie on the coordinate plane as the following coordinates:
N = (-8, 9)
C = (-4, 6)
Therefore, we will have:
d = √[(−4 − (−8))² + (6−9)²]
d = √[(4)² + (−3)²]
d = √(16 + 9)
d = √25
d = 5 units
Thus, the distance between points N and C is calculated as: 5 units.
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Compare two functions, f(x) and g(x). f(x) is given by the following equation
and g(x) is shown in the graph below. Which of the following statements below is true?
f [x] = 0.5^x - 3
Both functions have the same y-intercept.
f(x) is an increasing exponential function.
g(x) has a greater y-intercept.
f(x) has a greater y-intercept.
Answer:
True answers:
f(x) is an increasing exponential function.
f(x) has a greater y-intercept
Step-by-step explanation:
Option 1:
Both functions have the same y-intercept is FALSE
The y-intercept of f(x) is found by plugging in 0 for x
[tex]f(0) = 5^0 - 3 = 1 - 3 = -2[/tex]
The intercepts are different, so option 1 is FALSE.
Option 2:
f(x) is an increasing exponential function is TRUE
the largest term is positive and exponential.
Option 3:
g(x) has a greater y-intercept. is FALSE
The y-intercept of g(x) is -3, and the y-intercept of f(x) is -2. -2 > -3
Option 4:
f(x) has a greater y-intercept is TRUE
The y-intercept of g(x) is -3, and the y-intercept of f(x) is -2. -2 > -3
The ratio of boys and girls in a class is 3:5. There are 32 students in the class.
How many students are girls?
Using ratios, we can find that the number of girls in the class are 20.
What are ratios?If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. A proportion is an equation that equalises two ratios.
For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls) There are 3 out of 4 girls and 1 out of 4 guys.
Now in the question, total students in class = 32.
The ratio between the boys and girls is 3:5.
So, total parts from the ratio = 3+5=8
Now 5/8 students in the class are girls.
= 5/8 × 32
= 5 × 4
= 20.
Therefore, the number of girls in the class are 20.
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The second angle of the triangle is 30 degrees larger than the first, while the third angle of the triangle is 3 times the second. How big is the first angle?
Answer:
45 degrees
Step-by-step explanation:
The first angle of the triangle is 45 degrees. This can be determined by the given information that the second angle is 30 degrees larger than the first and the third angle is 3 times the second. Since the second angle is 30 degrees larger than the first, the first angle must be 15 degrees, and the third angle must be 3x15=45 degrees.
What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest form.
Answer:
67.5
Step-by-step explanation:
4 1/2x6= 27 27x2 1/2=67.5
Do what the picture says.If the answer is right,I will give you brainilest!!!!
Answer:
63.25
Step-by-step explanation:
You need to calculate each figure separately.
The diameter of the circle = 4 + 3 + 3 = 10
=> radius = 5
area of 1/2 circle = 1/2πr^2 = 1/2π(5)^2 = 1/2(3.14)(25) = 39.25
area of the top rectangle = 3 x 6 = 18
area of the bottom rectangle = 2 x 3 = 6
total area = 39.25 + 18 + 6 = 63.25
Answer:Hi
Step-by-step explanation:
PLEASE HELP I HAVE TO FINISH BY TODAY WILL MARK BRAINLIEST
What is the period of the function?
A) 2π
B) 4π
C) 6π
D) 8π
Answer:
d
Step-by-step explanation:
What is the best way to design a study to determine how much traffic there is during the morning rush
hour along a city street?
A. Send a survey to the local businesses surrounding the street, asking them how many times they
drive and how many times they take transit to work each year.
OB. Survey local car dealerships to see how many cars are sold in the area over the past year.
X
O C. Make video recordings of the street during rush hour every day for year and count the numbers
of vehicles that pass a certain point.
OD. Count the number of cars that pass a particular point during rush hour over 3 days, and then
take the average
The best way to design a study to measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year and count the number of vehicles that pass a certain point, then calculate the average using the given formula.
The best way to accurately measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year. After recording the video, count the number of vehicles that pass a specific point in the video. Then, calculate the average number of vehicles that pass the point each day during one year by using the following formula: Average = (Number of vehicles per day1 + Number of vehicles per day2 + ... + Number of vehicles per dayn) / n, where n is the number of days the video recording was made. This method is the most reliable way to measure the amount of traffic during the morning rush hour since it provides an average based on the data collected over a full year.
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Solve the equation by using the Square Root Property.
(x+2) 2=64
Answer:
x=-2+-8
Step-by-step explanation:
If you mean (x+2)^2=64
take the sqrt of both sides and get x+2 = +-8
then subtract 2 to get -2+-8 = x
The quotient of 42 and the sum of a number and five equals seven 
Answer:
Step-by-step explanation:
[tex]\frac{42}{x+5} =7[/tex]
[tex]42=7(x+5)[/tex]
[tex]42=7x+35[/tex]
[tex]7x=-7[/tex]
[tex]x=-1[/tex]
A sample of n=25 observations is drawn from a normal population with μ=100 and σ=2,. Find the following. i) P( X <96) ii) P(96< X <105)
Part b) ( 8 marks) The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours. i) What is the probability that a professor works for more than 60 hours per weeks? ii) Find the probability that the mean amount of work per week for three randomly selected professors is more than 60 hours? Part a) (7 marks) Calculate the value of the test statistic, set up the rejection region, undertaking hypothesis test and interpret the result.
P(X > 60) = P(Z > 1.7321) = 0.0418
When answering questions on Brainly, it is important to be factually accurate, professional, and friendly. Additionally, answers should be concise and relevant to the question being asked. When possible, provide a step-by-step explanation using the following terms: sample, observation, and probability. In this particular question, the following information is provided:Part a) A sample of n=25 observations is drawn from a normal population with μ=100 and σ=2. Find the following: i) P(X < 96) ii) P(96 < X < 105)Part b) The amount of time university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours. Find the probability that a professor works for more than 60 hours per week. Find the probability that the mean amount of work per week for three randomly selected professors is more than 60 hours.Part a) Calculate the value of the test statistic, set up the rejection region, undertake the hypothesis test, and interpret the result.
i) P(X < 96)First, we calculate the z-score as follows:z = (X - μ) / σ = (96 - 100) / 2 = -2P(X < 96) = P(Z < -2) = 0.0228ii) P(96 < X < 105)We first calculate the z-scores for both X values as follows:z1 = (X1 - μ) / σ = (96 - 100) / 2 = -2z2 = (X2 - μ) / σ = (105 - 100) / 2 = 2.5Next, we look up the area between these two z-scores using a standard normal distribution table. We have: P(96 < X < 105) = P(-2 < Z < 2.5) = 0.9944 - 0.0228 = 0.9716b) i) Probability that a professor works for more than 60 hours per weekWe first calculate the z-score as follows:z = (X - μ) / σ = (60 - 52) / 6 = 1.3333Using a standard normal distribution table, we find the area to the right of the z-score as follows:P(X > 60) = P(Z > 1.3333) = 0.0912ii) Probability that the mean amount of work per week for three randomly selected professors is more than 60 hoursLet X be the random variable representing the mean amount of work per week for three randomly selected professors. We know that X ~ N(μ, σ / sqrt(n)), where μ = 52, σ = 6, and n = 3. We calculate the z-score as follows:z = (X - μ) / (σ / sqrt(n)) = (60 - 52) / (6 / sqrt(3)) = 1.7321Using a standard normal distribution table, we find the area to the right of the z-score as follows:P(X > 60) = P(Z > 1.7321) = 0.0418Part a) Calculate the value of the test statistic, set up the rejection region, undertake the hypothesis test, and interpret the result.No information is provided about the hypothesis test in Part a of the question, so it is not possible to provide an answer to this part. Please provide more information or clarify the question if possible.
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A side of the triangle below has been extended to form an exterior angle of 136°. Find the value of � x. 136° x° Answer: � = x=
x°=46
Step-by-step explanation:
There are two methods of solving this question
Method 1:
x°+90°=136° the theorem states that "the sum of two opposite interior is equal to the exterior"
x°=136°-90°
x°=46°
or
Method 2:
136° is on a straight line which is 180°
so, let the other side of the straight line be a.
therefore, 136°+a°=180° theorem {Angle on a straight line}
a°=180°-136°
a°=44°
so, in the triangle is the sum of 180°
a°+90°+x°=180° theorem {Sum of angles in a triangle}
44°+90°+x°=180°
x=180°-134°
x°=46°
1, 6, 6, 6, 7, 7, 8, 9, 13, 10, 17 Calculate the upper limit
(Upper Bound) to determine if there are any outliers on the high
end.
Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.
what is Median?
The median is a statistical measure that represents the central value of a dataset.
To calculate the upper limit for outliers, we can use the interquartile range (IQR) and the formula:
Upper Limit = Q3 + 1.5 * IQR
where Q3 is the third quartile, and IQR is the interquartile range.
First, we need to find the values for Q1, Q2 (median), and Q3:
1, 6, 6, 6, 7, 7, 8, 9, 13, 10, 17
Arranging the data in order:
1, 6, 6, 6, 7, 7, 8, 9, 10, 13, 17
The median is the middle value. Since there are 11 values, the median is the average of the 6th and 7th values:
Median = (7 + 8) / 2 = 7.5
To find Q1 and Q3, we need to find the medians of the lower and upper halves of the data, respectively:
Lower half: 1, 6, 6, 6, 7
Upper half: 8, 9, 10, 13, 17
Q1 is the median of the lower half, which is 6.
Q3 is the median of the upper half, which is 10.
Next, we can calculate the interquartile range:
IQR = Q3 - Q1 = 10 - 6 = 4
Finally, we can calculate the upper limit for outliers:
Upper Limit = Q3 + 1.5 * IQR = 10 + 1.5 * 4 = 16
Any value above 16 can be considered a potential outlier on the high end of the data.
Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.
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The mayors of old town and newborn were having a disagreement about which city was more popular. They made the table below to show the population of their cities for the past several years.
Therefore, based on the data provided, Oldtown is more popular than Newburg.
How to solve thisTo determine which city is more popular, we need to compare their populations for each year.
In 2015, Oldtown had a population of 1518, which is significantly larger than Newburg's population of 100. Therefore, Oldtown was more popular in 2015.
In 2016, Oldtown's population increased to 1643, while Newburg's population increased to 110. Again, Oldtown had a larger population and was more popular.
In 2017, Oldtown's population increased to 1768, while Newburg's population increased to 121. Once again, Oldtown had a larger population and was more popular.
In 2018, Oldtown's population increased to 1893, while Newburg's population increased to 133. Yet again, Oldtown had a larger population and was more popular.
Therefore, based on the data provided, Oldtown is more popular than Newburg.
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The mayors of old town and newborn were having a disagreement about which city was more popular. They made the table below to show the population of their cities for the past several years.
2015 Newburg Population 100. Oldtown Population 1518
2016 Newburg Population 110. Oldtown Population 1643
2017 Newburg Population 121. Oldtown Population 1768
2018 Newburg Population 133. Oldtown Population 1893
Which city is more popular?
Shuffle: Charles has seven songs on a playlist. Each song is by a different artist. The artists are Celine Dion, Phil Collins, Elton John, Mariah Carey, Joey Meintyre, Kavana, and Adam Rickilt. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Adam Rickitt and the second song is by Phil Collins? Write vour answer as a fraction or a decimal, rounded to four decimal places.
0.0002
The required probability can be calculated as follows:Explanation:There are 7 different songs from 7 different artists, thus there are 7! ways of shuffling these songs. In other words, there are 7! = 5040 different playlists in which these songs can be shuffled.We need to calculate the probability of Adam Rickitt's song being played first and Phil Collins' song being played second. This can be done in two steps.Step 1: We place Adam Rickitt's song at the beginning of the playlist. There is only one way to do this. After Adam Rickitt's song has been placed, we are left with 6 remaining songs that can be shuffled. Thus, there are 6! = 720 different playlists.Step 2: We place Phil Collins' song as the second song on the playlist. There is only one way to do this as well.Therefore, the probability that Adam Rickitt's song is played first and Phil Collins' song is played second is given by the product of the probabilities of the two steps as follows:P = 1/5040 × 1 = 1/5040 = 0.000198 rounded to 4 decimal places. Thus, the probability is approximately 0.0002. Therefore, the probability that the first song is by Adam Rickitt and the second song is by Phil Collins is 0.0002.
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quadratic function in vertex form y=x^2+4x+6
Answer:
y = (x + 2)² + 2
Step-by-step explanation:
a quadratic function in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
y = x² + 4x + 6
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² + 4x
y = x² + 2(2)x + 4 - 4 + 6
= (x + 2)² + 2 ← in vertex form
Select the correct answer. If x + 12 ≤ 5 − y and 5 − y ≤ 2(x − 3), then which statement is true?
The correct answer is:
x + 12 ≤ 5 − y ≤ 2(x − 3)
Explanation:
From the given inequalities:
x + 12 ≤ 5 − y ... (1)
5 − y ≤ 2(x − 3) ... (2)
We can see that 5 - y is common in both inequalities. We can isolate this term by subtracting 5 from both sides of (1) and (2):
x + 7 ≤ -y ... (3)
-y ≤ 2(x - 8) ... (4)
Multiplying (3) by -1, we get:
y - 7 ≥ x ... (5)
Substituting this value of x in (4), we get:
y - 7 ≤ -2(7 - y)
y - 7 ≤ -14 + 2y
y ≤ 7
Substituting this value of y in (5), we get:
0 ≤ x + 7 ≤ 14
Subtracting 7 from all sides, we get:
-7 ≤ x ≤ 7
Therefore, the statement x + 12 ≤ 5 − y ≤ 2(x − 3) is not true, but the statement -7 ≤ x ≤ 7 is true.
a poll showed that 60.4% of americans say they believe that some people see the future in their dreams. what is the probability of randomly selecting someone who does not believe that some people see the future in their dreams.
The probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.
Probability is an area of mathematics that deals with the study of chance events.
We have, A poll showed that 60.4% of Americans say they believe that some people see the future in their dreams.
Therefore, the probability of randomly selecting someone who does not believe that some people see the future in their dreams can be calculated as follows:
P(A) = 1 - P(B)
Where,
P(A) = Probability of selecting someone who does not believe that some people see the future in their dreams.
P(B) = Probability of selecting someone who believes that some people see the future in their dreams.
P(A) = 1 - P(B)
⇒ 1 - 60.4/100
⇒39.6/100
⇒ 0.396 or 39.6%
Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.
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can someone tell me the algebraic representation pls
Answer:
Triangle XYZ is shifted 9 units to the right, then 4 units down.