Answers
Answer:
There are six terms in the series
Step-by-step explanation:
We can see that n starts from 0, and ends at 5. There are therefore 6 terms in this series - as 0 is included. Therefore there will be 6 terms in this series, not 5.
There are six terms in the given series.
Related Questions
Solve the inequality 7a + 13 < 48.
Answers
Hi there! :)
Answer:
[tex]\huge\boxed{a < 5}[/tex]
Given:
7a + 13 < 48
Isolate the variable "a" by subtracting 13 from both sides:
7a - 13 < 48 - 13
7a < 35
Divide both sides by 7:
7a/7 < 35/7
a < 5.
Answer:
a < 5
Step-by-step explanation:
7a + 13 < 48
Subtract 13 from each side
7a + 13-13 < 48-13
7a < 35
Divide each side by 7
7a/7 < 35/7
a < 5
The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 12 cm and the width is 5 cm, how fast is the area of the rectangle increasing?
Answers
Answer:
129 [tex]cm^2/s[/tex]
Step-by-step explanation:
Increasing rate of length, [tex]\frac{dl}{dt}[/tex]= 9 cm/s
Increasing rate of width, [tex]\frac{dw}{dt}[/tex] = 7 cm/s
Length, l = 12 cm
Width, w = 5 cm
To find:
Rate of increase of area of rectangle at above given points.
Solution:
Formula for area of a rectangle is given as:
[tex]Area = Length \times Width[/tex]
OR
[tex]A = l \times w[/tex]
Differentiating w.r.to t:
[tex]\dfrac{d}{dt}A = \dfrac{d}{dt}(l \times w)\\\Rightarrow \dfrac{d}{dt}A = w \times \dfrac{d}{dt}l +l \times \dfrac{d}{dt}w[/tex]
Putting the values:
[tex]\Rightarrow \dfrac{dA}{dt} = 5 \times 9 + 12 \times 7\\\Rightarrow \dfrac{dA}{dt} = 45 + 84\\\Rightarrow \bold{\dfrac{dA}{dt} = 129\ cm^2/sec}[/tex]
Hey! i've been working on these questions but I have no idea how to solve this one, could anybody help me? Thanks in advance!
Answers
Answer:
1) [tex]\boxed{p(x) = x^3-x^2+x-1}[/tex]
2) [tex]\boxed{p(x) = x^2+x-2}[/tex]
3) [tex]\boxed{p(x) =- 2x^2+2x+4}[/tex]
4) [tex]\boxed{p(x) = 2x^2+x-4}[/tex]
Step-by-step explanation:
Part (1)
[tex]p(x) = x^3-x^2+x-1[/tex]
As we have to determine it by ourselves, this is the polynomial having a degree of 3. p(x) with a degree of 3 means that the highest degree/exponent of x should be 3.
Part (2)
[tex]p(x) = x^2+x-2[/tex]
This can be the polynomial having the factor x-1 because if we put:
x - 1 = 0 => x = 1 in the above polynomial, it gives us a result of zero which shows us that (x-1) "is" a factor of the polynomial.
Part (3)
[tex]p(x) = -2x^2+2x+4[/tex]
This can be the polynomial for which p(0) = 4 and p(-1) = 0
Let's check:
[tex]p(0) =- 2(0)^2+2(0)+4\\p(0) = 0 + 0+4\\p(0) = 4[/tex]
[tex]p(-1)= -2(-1)^2+2(-1)+4\\p(-1) = -2(1)-2+4\\p(-1) = -2-2+4\\p(-1) = 0[/tex]
So, this is the required polynomial determined by "myself".
Part (4):
[tex]p(x) = 2x^2+x-4[/tex]
This is the polynomial having a remainder 6 when divided by (x-2)
Let's check:
Let x - 2 = 0 => x = 2
Putting in the above polynomial
[tex]p(x) = 2(2)^2+(2)-4\\Given \ that \ Remainder = 6\\6 = 2(4) +2-4\\6 = 8+2-4\\6 = 10-4\\6 = 6[/tex]
So, Proved that it has a remainder of 6 when divided by (x-2)
Salaries of 42 college graduates who took a statistics course in college have a mean, , of . Assuming a standard deviation, , of $, construct a % confidence interval for estimating the population mean .
Answers
Answer:
The 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).
Step-by-step explanation:
The complete question is:
Salaries of 42 college graduates who took a statistics course in college have a mean, [tex]\bar x[/tex] of, $64, 100. Assuming a standard deviation, σ of $10,016 construct a 99% confidence interval for estimating the population mean μ.
Solution:
The (1 - α)% confidence interval for estimating the population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
The critical value of z for 99% confidence interval is:
[tex]z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.57[/tex]
Compute the 99% confidence interval for estimating the population mean μ as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=64100\pm 2.58\times\frac{10016}{\sqrt{42}}\\\\=64100+3987.3961\\\\=(60112.6039, 68087.3961)\\\\\approx (60112.60, 68087.40)[/tex]
Thus, the 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).
where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50. (Round your answer to two decimal places.)
Answers
THIS IS THE COMPLETE QUESTION BELOW
The demand equation for a product is p=90000/400+3x where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50.
Answer
$168.27
Step by step Explanation
Given p=90000/400+3x
With the limits of 40 to 50
Then we need the integral in the form below to find the average price
1/(g-d)∫ⁿₐf(x)dx
Where n= 40 and a= 50, then if we substitute p and the limits then we integrate
1/(50-40)∫⁵⁰₄₀(90000/400+3x)
1/10∫⁵⁰₄₀(90000/400+3x)
If we perform some factorization we have
90000/(10)(3)∫3dx/(400+3x)
3000[ln400+3x]₄₀⁵⁰
Then let substitute the upper and lower limits we have
3000[ln400+3(50)]-ln[400+3(40]
30000[ln550-ln520]
3000[6.3099×6.254]
3000[0.056]
=168.27
the average price p on the interval 40 ≤ x ≤ 50 is
=$168.27
nishan bought 7 marbles Rs.x per each. if he gave Rs.100 to the shop keeper. what is the balance he would receive?
Answers
What’s the largest fraction: 7/8, 5/8, 7/13, and 11/19
Answers
Answer:
7/8
Step-by-step explanation:
7/8 = 0.875
5/8 = 0.625
7/13 = 0.538
11/19 = 0.579
So 7/8 is the largest
A car dealer recommends that transmissions be serviced at 30,000 miles. To see whether her customers are adhering to this recommendation, the dealer selects a random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles. By finding the P-value, determine whether the owners are having their transmissions serviced at 30,000 miles. Use α = 0.10. Are the owners having their transmissions serviced at 30,000 miles?
Answers
Answer:
No, the owners are not having their transmissions serviced at 30,000 miles.
Step-by-step explanation:
We are given that a car dealer recommends that transmissions be serviced at 30,000 miles.
The car dealer selects a random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles.
Let [tex]\mu[/tex] = true average mileage of the automobiles serviced.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 30,000 miles {means that the owners are having their transmissions serviced at 30,000 miles}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 30,000 miles {means that the owners are having their transmissions serviced at different than 30,000 miles}
The test statistics that will be used here is One-sample z-test statistics because we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample average mileage serviced = 30,456 miles
[tex]\sigma[/tex] = population standard deviation = 1684 miles
n = sample of customers = 40
So, the test statistics = [tex]\frac{30,456-30,000}{\frac{1684}{\sqrt{40} } }[/tex]
= 1.71
The value of z-statistics is 1.71.
Also, the P-value of the test statistics is given by;
P-value = P(Z > 1.71) = 1 - P(Z [tex]\leq[/tex] 1.71)
= 1 - 0.9564 = 0.0436
For the two-tailed test, the P-value is calculated as = 2 [tex]\times[/tex] 0.0436 = 0.0872.
Since the P-value of our test statistics is less than the level of significance as 0.0872 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.
Therefore, we conclude that the owners are having their transmissions serviced at different than 30,000 miles.
Explain why within any set of ten integers chosen from 2 through 24, there are at least two integers with a common divisor greater than 1 g
Answers
Step-by-step explanation:
Here are some examples of ten integers (in this case prime numbers) chosen from 2 to 24;
2, 3, 5, 7, 9, 15, 17, 19, 21, 23
Lets take for example the integers 15 and 21, they have a common divisor 3 which is greater than 1. Which implies that the number 3 can divide through 15 and 21 without a remainder, that is, 21 ÷ 3 = 7, 15 ÷ 3 = 5. Also note that 3 is a divisor of 9.
Therefore, we could right say that within any set of ten integers chosen from 2 through 24, there are at least two integers with a common divisor greater than 1.
if a flight to europe takes about 13 hours and you make one round trip flight per month how many total days do you travel in a year
Answers
Answer:
13 days
Step-by-step explanation:
Given that a one-way flight to europe will take 13 hours
A round trip will take = 13 hrs x 2 = 26 hours
Also given that we make one round trip per months for 12 months (1 year)
We will take a total of 12 round trips per year
Number of hours taken for 12 round trips
= 26 hours per round trip x 12 round trips
= 26 x 12
= 312 hours
Recall that there are 24 hours in a day, hence to convert 312 hours into days, we have to divide this by 24.
Number of days = number of hours ÷ 24
= 312 ÷ 24
= 13 days
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 18% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Required:a. Find the probability that both generators fail during a power outage.b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital?c. Is that probability high enough for the hospital?
Answers
Answer:
a. 0.36
b. 0.1296
c. No.
Step-by-step explanation:
1. Note the probability of emergency backup generators to fail when they are needed = 18% or 0.18. Thus,
a. Probability of both emergency backup generators failing = P (G1 and G2 fails) where G represents the generators.
= P (G1 falls) x P ( G2 fails)
= 0.18 x 0.18
= 0.36
b. The probability of having a working generator in the event of a power outage = G1 fails x G2 works + G2 works x G2 fails
= 0.36 x 0.18 + 0.18 x 0.36
= 0.1296
c. Looking at the probability of any of the generators working, it is not meeting safety standards as lives could be lost if the backup generators needed to perform an emergency surgery operation fails.
A graph is shown below: A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, and 10. The values on the y axis are 0, 4, 8, 12, 16, and 20. Points are shown on ordered pairs 0, 16 and 2, 12 and 4, 8 and 6, 4 and 8, 0. These points are connected by a line. What is the equation of the line in slope-intercept form?
Answers
Answer:
Graph is image, and equation is from the work result below:
Step-by-step explanation:
Take two points find the slope and y-intercept:
Slope = -2
Y-intercept = (0,16)
Equation =
y = − 2 x + 16
check work for one point (to make sure equation works):
(2,12)
y = -2x + 16
12 = -2(2) + 16
12 = -4 + 16
12 = 12
The equation is correct: y = − 2 x + 16
Image below are the points given:
please this is easy show working out and please get correct
Answers
Answer:
$ 180,000
Step-by-step explanation:
All we are being asked to do in this question is take the simple interest, given a principle value of $100,000, with 8 percent interest each year over a course of 10 years. This is given the simple interest formula P( 1 + rt ).
Simple Interest : P( 1 + rt ),
P = $ 100,000 ; r = 8% ; t = 10 years,
100,000( 1 + 0.08( 10 ) ) = 100,000( 1 + 0.8 ) = 100,000( 1.8 ) = 180,000
Therefore you will have to pay back a total of $ 180,000
A function y = g(x) is graphed below. What is the solution to the equation g(x) = 3?
Answers
Answer:
See below.
Step-by-step explanation:
From the graph, we can see that g(x)=3 is true only when x is between 3 and 5. However, note that when x=3, the point is a closed circle. When x=5, the point is an open circle. Therefore, the solution is between 3 and 5, and it includes 3 but not 5.
In set-builder notation, this is:
[tex]\{x|x\in \mathbb{R}, 3\leq x<5\}[/tex]
In interval notation, this is:
[tex][3,5)[/tex]
Essentially, these answers are saying: The solution set for g(x)=3 is all numbers between 3 and 5 including 3 and not including 5.
Chapter: Simple linear equations Answer in steps
Answers
Answer:
6x-3=21
6x=24
x=4
........
6x+27=39
6x=39-27
6x=12
x=2
........
8x-10=14
8x=24
x=3
.........
6+6x=22
6x=22-6
x=3
......
12x-2=28
12x=26
x=3
.....
8-4x=16
-4x=8
x=-2
.....
4x-24=3x-3
4x-3x=24-3
x=21
....
9x+6=6x+12
9x-6x=12-6
3x=6
x=2
Answer:
Step-by-step explanation:
1. 3(2x - 1) = 21
= 6x - 3 = 21
= 6x = 24
= x = 24/6 = 4
------------------------------
2. 3(2x+9) = 39
= 6x + 27 = 39
= 6x = 39 - 27
= 6x = 12
= x = 12/6 = 2
--------------------------------
3. 2(4x - 5) = 14
= 8x - 10 = 14
= 8x = 14+10
= x = 3
-------------------------------
The data represent the membership of a group of politicians. If we randomly select one politician, what is the probability of getting given that a was selected?
Answers
Complete Question
The data represent the membership of a group of politicians. If we randomly select one politician, what is the probability of getting a Republican given that a male was selected?
Republican Democrat Independent
Male 11 6 0
Female 70 17 7
The probability is approximately_____?
Answer:
The probability is [tex]P(k) = 0.647[/tex]
Step-by-step explanation:
From the question we are told that
The sample size of male is [tex]n_m = 11 + 6 =17[/tex]
The number of male Republican is [tex]k = 11[/tex]
Generally the probability of getting a Republican given that a male was selected is
[tex]P(k) = \frac{k}{n_m}[/tex]
substituting values
[tex]P(k) = \frac{ 11}{17}[/tex]
[tex]P(k) = 0.647[/tex]
if the numbers x+3,2x+1and x-7are in AP then find x
Answers
Answer:
-3
Step-by-step explanation:
If these numbers are part of an arithmetic progression, their differences are the same:
(x -7) -(2x +1) = (2x +1) -(x +3)
-x -8 = x -2
-6 = 2x
-3 = x
___
The numbers in the sequence are 0, -5, -10.
Answer:
x = -3.
Step-by-step explanation:
As it is an Arithmetic Progression the differences between successive terms are common, so:
2x + 1 - (x + 3) = x - 7 - (2x + 1)
2x - x + 1 - 3 = x - 2x - 7 - 1
x - 2 = -x - 8
2x = -8 + 2 = -6
x = -3.
Robert is putting new roofing shingles on his house. Each shingle is 1 2/3 feet long. The north part of the house has a roof line that is 60 feet across. How many shingles can be placed (side by side) on the north part of the house?
Answers
Answer: 36 shingles can be placed on the north part of the house.
Step-by-step explanation:
Given: Length of each shingle = [tex]1\dfrac23[/tex] feet = [tex]\dfrac53[/tex] feet.
The north part of the house has a roof line that is 60 feet across.
Then, the number of shingles can be placed on the north part of the house = (Length of roof line in north part) ÷ (Length of each shingle)
[tex]=60\div \dfrac{5}{3}\\\\=60\times\dfrac{3}{5}\\\\=12\times3=36[/tex]
Hence, 36 shingles can be placed on the north part of the house.
A. f(x) = -x^2 - x - 4
B. f(x) = -x^2 + 4
C. f(x) = x^2 + 3x + 4
D. f(x) = x^2 + 4
Answers
Answer:
B: -x^2 + 4
Step-by-step explanation:
If the equation was [tex]f(x)=x^2[/tex], then the vertex would be at 0, and the "U" would be facing straight up. Here, the "U" is upside down, so that means the "x^2" would have to be a negative number ([tex]-x^2[/tex]) to get the upside-down "U". Then, we could see that the vertex is at positive 4, so that means that the parabola moved up 4 units, so the equation should end in +4.
Our answer is:
B: -x^2 + 4
I NEED ALGEBRA HELP! Can you solve a system of equations using the substitution by solving one equation for x or y and then using the substitution method? x + 6y = 6 and 7x - 5y = -5
Answers
Answer:
let x be y
NOW,
X+6Y=6
Y+6Y=6
7Y=6
Y=0.87
The rate of change in sales S is inversely proportional to time t (t > 1), measured in weeks. Find S as a function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively.
Answers
Answer:
S = 250/tStep-by-step explanation:
If the rate of change of sales is inversely proportional to the time t, this is expressed mathematically as ΔS ∝ 1/Δt
ΔS = k/Δt where k is the constant of proportionality
If ΔS = S₂-S₁ and Δt = t₂-t₁
S₂-S₁ = k/ t₂-t₁
If the sales after 2 and 4 weeks are 162 units and 287 units respectively, then when S₁ = 162, t₁ = 2 and when S₂ = 287, t₂ = 4.
On substituting this values into the given functions, we will have;
287 - 162 = k/4-2
125 = k/2
cross multiplying
k = 125* 2
k = 250
Substituting k = 250 into the function ΔS = k/Δt
ΔS = 250/Δt
S = 250/t
Hence the value of S as function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively is expressed as S = 250/t
What is the best way you learn math?
Answers
Answer:
to provide interest in the subject
As per my experience,I used to hate math and always scored less marks,the moment I was going to high school I realized the importance of math towards the future, see you'll find maths in nearly all subjects like the 3 sciences, economics, geography, business e.t.c
Why did you write this question at first?, just take some free time and think about it,the only best way to learn maths is to take maths positively as the best and most valuable subject,if you want to ace math you have to race it, challenge math like you'd challenge anyone to a game, practice math if it's your weakest point, practice is very much needed to skill maths and never be shy to ask your teachers whether you are studying online/offline. You'll need to get the shy behaviour out of you whether you like /don't like your teacher or your an average student.
Concentrate while learning math, whether there's noise in you background or not, Nothing can stop you in excelling math if you have full concentration, positiveness and the "will" to do so.
if you're next to your exams then just one thing, Start now!!
hope this helps!
Find the equation of the line passing through the point (–1, –2) and perpendicular to the line y = –1∕2x + 5. Question options: A) y = –1∕2x – 5∕2 B) y = 1∕2x – 5∕2 C) y = 2x D) y = –1∕2x
Answers
Answer:
The answer is option CStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question
y = - 1/2x + 5
Comparing with the general equation above
Slope / m = -1/2
Since the lines are perpendicular to each other the slope of the other line is the negative inverse of the original line
That's
Slope of the perpendicular line = 2
Equation of the line using point (–1, –2) and slope 2 is
y + 2 = 2( x + 1)
y + 2 = 2x + 2
y = 2x + 2 - 2
We have the final answer as
y = 2xHope this helps you
Answer:
C) y = 2x
Step-by-step explanation:
I got it right in the test !!
Pregnancy length in horses. Bigger mammals tend to carry their young longer before giving birth. The length of horse pregnancies from conception to birth varies according to a roughly Normal distribution, with mean 336 days and standard deviation 3 days. Use the 68–95–99.7 rule to answer the following questions.Required:What percent of horse pregnancies are longer than 339 days?
Answers
Answer:
16%
Step-by-step explanation:
The difference between the time of interest (339 days) and the mean (336 days) is 3 days, which is exactly 1 standard deviation.
The 68-95-99.7 rule tells you that 68% of pregnancies will be within 1 standard deviation. The remaining 32% will be evenly split between pregnancies that are longer than 339 days and ones that are shorter than 333 days. So, half of 32%, or 16%, will be longer than 339 days.
Sean earned 20 points. Charles earned p more points than Sean. Choose the expression that shows how many points Charles earned.
Answers
Therefore, the expression to show how many points Charles earned would be:
p + 20
Answer:
the person above is correct if i did this correct
Step-by-step explanation:
Angles One angle is 4º more than three times another. Find
the measure of each angle if
a. they are complements of each other.
b. they are supplements of each other.
Answers
[tex] \Large{ \boxed{ \bf{ \color{purple}{Solution:}}}}[/tex]
Let the smaller angle be x
Then, Larger angle would be x + 4°
Case -1:❍ They are complementary angles.
This means, they add upto 90°So,
➙ x + x + 4° = 90°
➙ 2x + 4° = 90°
➙ 2x = 86°
➙ x = 86°/2 = 43°
Then, x + 4° = 47°
So, Our required answer:
Smaller angle = 43°Larger angle = 47°Case -2:❍ They are supplementary angles.
This means, they add upto 180°So,
➙ x + x + 4° = 180°
➙ 2x + 4° = 180°
➙ 2x = 176°
➙ x = 176°/2 = 88°
Then, x + 4° = 92°
So, Our required answer:
Smaller angle = 88°Larger angle = 92°✌️ Hence, solved !!
━━━━━━━━━━━━━━━━━━━━
AB||CD. Find the measure of
Answers
Answer:
135 degrees
Step-by-step explanation:
3x+15 = 5x - 5 because of the alternate interior angles theorem.
20 = 2x
x = 10
3(10) + 15 = 30+15 = 45
Remember that a line has a measure of 180 degrees. So we can just subtract the angle we found from 180 degrees to get BFG.
180-45 = 135.
The ball bearing have volumes of 1.6cm cube and 5.4cm cube . Find the ratio of their surface area.
Answers
Answer:
64 : 729
Step-by-step explanation:
Ratio of surface area
= (ratio of linear dimensions) ^2
= 1.6^2 : 5.4^2
= 256 : 2916
= 64 : 729
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
Answers
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Assume that when adults with smartphones are randomly selected, 57% use them in meetings or classes. If 8 adult smartphone users are randomly selected, find the probability that exactly 4 of them use their smartphones in meetings or classes. The probability is
Answers
Answer:
≈ 0.2526
Step-by-step explanation:
The number of combinations of 4 out of 8:
8C4 = 8!/(4!(8-4)!)= 8*7*6*5/(1*2*3*4)= 70Success factor is:
57% = 0.57and failure factor is:
(100 - 57)%= 43%= 0.43Probability:
0.57⁴*0.43⁴*70 ≈ 0.2526