10+12+14+...+(2n)=90 n=?
Answers
Answer:
n=10
Step-by-step explanation:
The given equation is
\(10+12+14+...+2n=90\) ...(1)
Let nth term is 2n.
We need to find the values of n.
It is clear that \(S_n=10+12+14+...+2n\) is sum of A.P., whose first term is 10 and common difference is 2.
Sum of A.P. is
\(S_n=\dfrac{n}{2}[2a+(n-1)d]\)
where, a is first term and d is common difference.
Substitute a=10 and d=2 in the above formula.
\(S_n=\dfrac{n}{2}[2(10)+(n-1)2]\)
\(10+12+14+...+2n=n[10+n-1]\)
\(10+12+14+...+2n=n[9+n]\) ...(2)
From (1) and (2), we get
\(n(9+n)=90\)
\(n^2+9n-90=0\)
Splitting middle term, we get
\(n^2+15n-6n-90=0\)
\(n(n+15)-6(n+15)=0\)
\((n+15)(n-6)=0\)
\(n=-15,6\)
Since, n represents the number of terms so n cannot be a negative number, therefore number of term is 6.
Note: nth term and variable n both are different.
\(a_n=a+(n-1)d\)
\(a_6=10+(6-1)2=10+10=20\)
Sixth term is 20. So,
\(2n=20\)
\(n=10\)
Therefore, the value of n is 10.
Related Questions
The length of each side of an equilateral triangle is 4 cm longer than the length of each side of a square. If the perimeter of these two shapes is the same, find the area of the square.
Answers
The area of the square is 144 \(cm^{2}\).
Let x be the side of the square. Then the length of the triangle is (x+4). Perimeter is the length of all sides of a geometric figure combined. For an equilateral triangle, it's equal to thrice the length of one side. For a square, it's four times the length of one side. The Perimeter of the Triangle is 3(x+4) & the Perimeter of the square is 4x.
We know, both these perimeters are equal. Hence,
4x = 3(x+4)
To further simplify the above equation.
4x = 3x + 12
x = 12
Hence, the length of one side of the square is 12 cm. The area of the square can be calculated as follows:
Area = \((side)^{2}\)
Area = 12 * 12
Area = 144 \(cm^{2}\)
Hence, the Area of the Square is 144 \(cm^{2}\)
To know more about Linear Algebra:
https://brainly.com/question/30894110
What is the value of f(x) = 4x -9
Answers
Answer:
F= 1 /4 y+ 9 /4
Step-by-step explanation:
brainliest?
What is true as the spread of scores around the arithmetic mean gets smaller? A. The coefficient of variation gets smaller B. The interquartile range gets smaller. C. The standard deviation gets smaller D. All of the above
Answers
The correct answer is D. All of the above. When the spread of scores around the arithmetic mean gets smaller, it means that the data points are closer to the mean.
This has several implications:
A. The coefficient of variation (CV) gets smaller: The coefficient of variation is the ratio of the standard deviation to the mean. When the standard deviation decreases (due to smaller spread of scores), the CV also decreases.
B. The interquartile range (IQR) gets smaller: The IQR represents the range between the first quartile and the third quartile. When the spread of scores decreases, the values at the first and third quartiles are closer together, resulting in a smaller IQR.
C. The standard deviation gets smaller: The standard deviation measures the average distance of data points from the mean. As the spread of scores decreases, the data points are closer to the mean, resulting in a smaller standard deviation.
In summary, when the spread of scores around the arithmetic mean gets smaller, the coefficient of variation, interquartile range, and standard deviation all decrease.
To know more about the arithmetic mean, visit:
https://brainly.com/question/29445117
#SPJ11
Slope = -1/5, y-Intercept = -1/4
Answers
Answer:
\(\sf y =\dfrac{-1}{5}x-\dfrac{1}{4}\)
Step-by-step explanation:
Slope y-intercept form of equation: y =mx +bHere, m is the slope and b is the y-intercept.
Substitute the values of m and b in the above equation.
\(\sf m = \dfrac{-1}{5} \\\\b = \dfrac{-1}{4}\)
Slope y-intercept form:
\(\sf \boxed{y=\dfrac{-1}{5}x - \dfrac{1}{4}}\)
5. A theater wants to take in at least $2000 for the matinee. Children's
tickets cost $5 each and adult tickets cost $10 each. The theater can seat
up to 350 people. Select all the combinations of children and adult tickets
that will make the $2000 goal.
There are several possible answers.
A- (80, 150)
B- (40, 200)
C- (60, 150)
D- (70, 160)
E- (90, 200)
F- (200, 100)
Answers
The required number of children and adults for sitting in the theater are 300 and 50 respectively.
Explain linear equation of two variable.A equation is supposed to be linear equation in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an a and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight equation in two factors.
According to question:Let be consider number of children be x and that of adults is y.
We have,
x + y = 350-------(1)
y = 350 - x
And 5x + 10y = 2000------------------(2)
Put value of y in equation (2)
5x + 10( 350 - x) = 2000
5x + 3500 - 10x = 2000
-5x = -1500
x = 300
Then
y = 350 - x = 350 - 300 = 50
Thus, There will be 300 children and 50 adults in the theater .
To know more about equation of two variable visit:
brainly.com/question/29209545
#SPJ1
What are the first 3 consecutive odd numbers?
Answers
The first 3 consecutive odd numbers are 1,3,5. x and x + 2 are consecutive odd numbers if x is an odd number.
Consecutive numbers are those that always appear in the same order, from smallest to largest.
For instance:
The numbers 1, 2, 3, 4, 5, 6, and so on are consecutive.
consecutive odd numbers:
Let's call the odd number "x." The subsequent term becomes "x + 4" and the next consecutive odd number becomes "x + 2."
Numbers that begin with 1, 3, 5, 7, or 9 are considered odd. 1, 3, 5, 7, 9, 11, 13, 15, and so on are examples of consecutive odd numbers.
Know more about Consecutive numbers here: https://brainly.com/question/29775116
#SPJ4
X
Frequency
50
3
60
8
70
15
80
30
90
29
100
15
Distribution Type 1: Normal distribution with mean = 75 and std.
dev = 25
Distribution Type 2: Uniform Distribution U[50,100]
Distribution
Answers
The second is a Uniform distribution with a minimum value of 50 and a maximum value of 100, where all values have equal frequencies.
Frequency distribution is a statistical representation of the number of occurrences of each value in a set of data. Let's consider the given set of values and describe two types of distributions for it.
Distribution Type 1: Normal Distribution with mean = 75 and standard deviation = 25.
This distribution follows a bell-shaped curve that is symmetric around the mean value of 75. The standard deviation of 25 indicates that the data is spread out with a moderate amount of variability. The highest frequency occurs at the mean value of 75, and as we move away from the mean in either direction, the frequency gradually decreases. The distribution provides information about how the values are distributed around the mean.
Distribution Type 2: Uniform Distribution U[50, 100].
This distribution is characterized by a rectangular shape, where all values have the same frequency. In this case, the minimum value is 50, and the maximum value is 100, resulting in a range of 50. The frequencies are uniform throughout the distribution, meaning that each value has the same frequency. In this case, since there are seven values in the set, each value has a frequency of 1/7.
To summarize, the given set of values can be represented by two different distributions. The first is a Normal distribution with a mean of 75 and a standard deviation of 25, which shows the overall pattern and spread of the data.
Learn more about standard deviation
https://brainly.com/question/29115611
#SPJ11
An arithmetic sequence has u10 = 16 and u30 = 156.
a Find the value of 50
Answers
Answer: u50=296
Step-by-step explanation:
30-10=20
50-30=20
u30-u10=
156-16=140
u50=u30+140
u50=156+140
u50=296
Help Math question Write ur answers
Answers
Answer:
this can be solved by simple unitary method
\(time \: taken \: to \: remove \: \frac{5}{9} \: tons \: of \: dirt \: = 1 \: hr \\ time \: taken \: to \: remove \: \frac{31}{6} \: tons \: of \: dirt \: = \frac{31}{6} \times \frac{9}{5} \: hr \\ = \frac{93}{10}hr \\ = 9 \times \frac{3}{10} hr\)
find the minimum or maximum value of the function. h(x)=-4x^2-4x+24
Answers
Answer:
the maxium value is 25 you can see this in the picture
Hope This Helps!!!
simplify polynomials -3x²+2x-x³+4-7x²
Answers
Answer:
-(x^2 + 10x^2 - 2x - 4)
Step-by-step explanation:
Which function has real zeros at x = 3 and x = 7?
f(x) = x2 + 4x - 21
Cf(x) = x2 - 4x - 21
Cf(x) = x2 - 10x + 21
f(x) = x2 - 10x - 21
Answers
Answer:
f(x) = x2 – 10x + 21
Step-by-step explanation:
I got it because you substract and add the last part
Help ASAP! Question 12 points)
05.02 MC
The angles below are supplementary. What is the value of x? (5 points)
5
7.5
15
30
Answers
Answer:
D
Step-by-step explanation:
supplementary means two angles that there sum will be 180. and 30 x 4 = 120 + 20 = 140 and if you add the other angle 40 that's 180.
For the distribution of student suspensions from school from Week 2, assume that these can be used to derive empirical estimates of probabilities.
a. (1 point) What is the probability that a randomly selected student will be suspended sometime during the year?
b. (1 point) What is the probability that a randomly selected student will be suspended at least twice during the year?
c. (2 points) What is the probability that a randomly selected student will be suspended at least twice during the given that he or she is suspended at least once?
d. (2 points) If two students (Student A and Student B) are selected at random, what is the probability that Students A and B are both are suspended sometime during the year? Are these events independent? Explain.
e. (2 points) If two students (Student A and Student B) are selected at random, what is the probability that either Student A or Student B is suspended sometime during the year? Are these events mutually exclusive? Explain.
Answers
a. To find the probability that a randomly selected student will be suspended sometime during the year, we need the total number of students who were suspended during Week 2. The probability can be estimated by dividing this number by the total number of students in the population.
b. To find the probability that a randomly selected student will be suspended at least twice during the year, we need to determine the number of students who were suspended twice or more during Week 2. Again, this probability can be estimated by dividing this number by the total number of students in the population.
c. To find the probability that a randomly selected student will be suspended at least twice during the year given that he or she is suspended at least once, we can use conditional probability. We need to calculate the number of students who were suspended at least twice during Week 2 and were also suspended at least once during that time. Then, we divide this number by the total number of students who were suspended at least once during Week 2.
d. To find the probability that both Student A and Student B are suspended sometime during the year, we need to consider the probability of each student being suspended individually and the assumption of independence between the events. We multiply the probability of Student A being suspended by the probability of Student B being suspended, assuming independence. Whether these events are independent depends on the specific context and factors that might influence the suspension of students.
e. To find the probability that either Student A or Student B is suspended sometime during the year, we consider the probability of each student being suspended individually and subtract the probability of both students not being suspended. Whether these events are mutually exclusive depends on the specific context and factors that might influence the suspension of students. If a student can be suspended multiple times, the events may not be mutually exclusive as both students can be suspended.
Know more about probability here:
https://brainly.com/question/31828911
#SPJ11
Which of the following are mathematical sentences? Check all that apply.
O A. 9
O B. 4+3 = 7
OC. 7
OD. 2 <3
O E. 5-d=9
a
OF. 5-V
70
SUBMIT
Answers
Answer:
B D E F
Step-by-step explanation:
a mathematical sentence makes a statement about TWO expressions. it can also use symbols or words like equals, greater than, or less than.
Please Help me ni️️as
Answers
Answer: see below
Step-by-step explanation:
Multiply the coefficient by the exponent and reduce the coefficient by 1.
1) f'(x) = 10
2) f'(x) = 12x³ + 4x - 5
3) f'(x) = 6x² + 7
4) f'(x) = 20x + 20
5) f'(x) = 20x + 23
...............need help
Answers
Answer:
3472
Step-by-step explanation:
pls mark brainiest I solved it.
Answer:
3.572
Step-by-step explanation:
I don't know what to explain or how
Table 9: Drivers of retaining graduates in regional areas: regression results Consider model 2 in Table 9 on page 51. Assume there is no intercept coefficient (or that the intercept =0 ). What is the predicted % of bachelor degree graduates living in the same region where there is a local university presence (=3) and log (Population )=1.2 30.48% 54.84% 4.2% 51.4%
Answers
Consider the given scenario,Given model 2 in Table 9 on page 51,If we assume that there is no intercept coefficient (or that the intercept =0).
Hence, the correct option is 4.2%.
To answer the above question we need to know that:\hat{y} = b_1x_1 + b_2x_2Where, y is the predicted response value, b1 is the slope, x1 is the value of the predictor variable, and b2 is the slope of the predictor variable, and x2 is the value of the predictor variable. From the given scenario, the predicted % of bachelor degree graduates living in the same region where there is a local university presence and log(Population) = 1.2.
The values of X1 and X2 are given as:X1 = 3 (value of predictor variable where there is a local university presence)X2 = 1.2 (value of predictor variable log (Population) = 1.2)To find out the predicted value of % of bachelor degree graduates living in the same region, we need to substitute the values in the above equation: \hat{y} = b_1x_1 + b_2x_2
\hat{y} = -0.239(3) + 0.24(1.2)
\hat{y} = -0.717 + 0.288
\hat{y} = -0.429
Therefore, the predicted % of bachelor degree graduates living in the same region where there is a local university presence (=3) and log (Population) = 1.2 is 4.2%.
To know more about predicted visit:
https://brainly.com/question/31828911
#SPJ11
Brian is building a sandbox that is 6 feet wide, 3 feet long, and 15 feet high. How many cubic feet of sand with the box hold?
Answers
Answer:
270 cubic feet
Step-by-step explanation:
3 * 6 * 15 = 270 cubic feet
Which of the following is equivalent to the complex number i^7
Answers
Answer:-i
Step-by-step explanation: :)
During the Dallas marathon, a helicopter monitors the racers at a height of 527 feet. The pilot can see the runners that are in first and second place. The angle of elevation from the runner in first place to the helicopter is 45 degrees. The angle of elevation from the runner in second place to the helicopter is 60 degrees. What is the distance from the runner in 2nd place to the point directly below the helicopter? Round your answer to the hundredths place.
Answers
The distance from the runner in 2nd place to the point directly below the helicopter is given as follows:
304.26 feet.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The parameters for this problem are given as follows:
Distance of x adjacent to the angle of 60º.Opposite side of 527 feet, which is the height.Hence the distance is obtained applying the tangent function as follows:
tan(60º) = 527/x
x = 527 / tangent of 60 degrees
x = 304.26 feet.
More can be learned about trigonometric ratios at brainly.com/question/24349828
#SPJ1
If (-2,11) and (9,22) are two
anchor points on the trend line,
then find the equation of the line.
y = [ ? ]x + [
Answers
Answer:
The equation of the line is- y = x + 13
What is 12*6-1????????????????????????
Answers
Answer:
71
Step-by-step explanation:
what is pemdas? algebra 1
Answers
Answer:
p=Parentheses
e=Exponents
m=Multiplication
d=Division
a=Addition
s=Subtraction
its an order of solving a equation
In your own words, what is a radical expression?
Answers
Answer:
In mathematics, a radical expression is defined as any expression containing a radical (√) symbol. Many people mistakenly call this a 'square root' symbol, and many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root, or higher. When the radical symbol is used to denote any root other than a square root, there will be a superscript number in the 'V'-shaped part of the symbol. For example, 3√(8) means to find the cube root of 8. If there is no superscript number, the radical expression is calling for the square root.
The term underneath the radical symbol is called the radicand.
I hope it's helpful!
Elena’s backyard is in the shape of a rectangle. She created a triangular-shaped flower bed (shown as the shaded region) to plant flowers in. The area of the triangular flower bed is square feet. The area of her backyard that does not include the flower bed is square feet.
Answers
Answer:
Area of background without flower bed = 575 feet²
Step-by-step explanation:
Given:
Length of rectangle ground = 35 feet
Width of rectangle ground = 20 feet
Height of triangle bed = 10 feet
Base of triangle bed = 25 feet
Find:
Area of background without flower bed
Computation;
Area of background without flower bed = Area of rectangle - Area of triangle
Area of background without flower bed = [l x b] - (1/2)(b)(h)
Area of background without flower bed = [35 x 20] - (1/2)(25)(10)
Area of background without flower bed = 700 - 125
Area of background without flower bed = 575 feet²
Answer:
125 for the backyard with the flower bed, and the backyard that does not include the flower bed is 575 square feet :)
HELP NOW IT IS 6th GRADE MATH HELPPPPPP
Answers
Answer:
S=2t
or
T=1/2 S
A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table, and a dotplot of the differences is given. A 4-column table with 10 rows. Column 1 is labeled volunteer with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Column 2 is labeled Treatment A with entries 10, 13, 13, 9, 13, 12, 14, 10, 8, 7. Column 3 is labeled Treatment B with entries 19, 18, 19, 15, 20, 16, 16, 16, 13, 17. Column 4 is labeled difference (A minus B) with entries negative 9, negative 5, negative 6, negative 6, negative 7, negative 4, negative 2, negative 6, negative 5, negative 10. A dotplot. A number line labeled Difference (A minus B) in time to experience relief (minutes) goes from negative 10 to negative 2. Negative 10, 1; negative 9, 1; negative 7, 1; negative 6, 3; negative 5, 2; negative 4, 1; negative 2, 1. The researchers would like to construct a 99% confidence interval for the mean difference (A – B) in the time it took to experience relief. Are the conditions for inference met? No, the random condition is not met. No, the 10% condition is not met. No, the Normal/large sample condition is not met. Yes, the conditions for inference are met.
Answers
"A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. " For the question "Are the conditions for inference met?" we say No, the 10% condition is not met. This is further explained below.
What is a confidence interval?Generally, the confidence interval is simply defined as a predetermined interval across which some parameter has a certain chance of falling
In conclusion, with a resultant confidence interval of; confidence interval ( -8.373, -3.627) For the hypothesis test question "Are the inference requirements met?" Our company is certain that the 10% threshold has not been reached.
Read more about confidence interval
https://brainly.com/question/24131141
#SPJ1
$1,554.31 With an 30% discount
Answers
Answer:
Original: $1,554.31
You Pay: $1088.02
You Save: $466.29
If the sum of an infinite geometric series is \( \frac{15625}{24} \) and the common ratio is \( \frac{1}{25} \), determine the first term. Select one: a. 625 b. 3125 c. 25 d. 125
Answers
The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.
We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).
learn more about geometric series here here
https://brainly.com/question/30264021
#SPJ11