Answer:
three consecutive integers that add up to 675 are 224, 225, and 226.
Step-by-step explanation:
Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.
∑[infinity]n=17n2−4n+3
12+2n6
Answer:
It means [tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex] also converges.
Step-by-step explanation:
The actual Series is::
[tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex]
The method we are going to use is comparison method:
According to comparison method, we have:
[tex]\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n[/tex]
If series one converges, the second converges and if second diverges series, one diverges
Now Simplify the given series:
Taking"n^2"common from numerator and "n^6"from denominator.
[tex]=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}[/tex]
[tex]\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}[/tex]
Now:
[tex]\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}[/tex]
So a_n is finite, so it converges.
Similarly b_n converges according to p-test.
P-test:
General form:
[tex]\sum_{n=1}^{inf}\frac{1}{n^p}[/tex]
if p>1 then series converges. In oue case we have:
[tex]\sum_{n=1}^{inf}b_n=\frac{1}{n^4}[/tex]
p=4 >1, so b_n also converges.
According to comparison test if both series converges, the final series also converges.
It means [tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex] also converges.
the height of the house is 26 feet what is the height x of each story?
Answer:
1 story=26, 2 stories=13 3 stories= 8.666666 4 stories= 6.5 5 stories=5.2
Step-by-step explanation:
How many whole tens are in 3,200
Answer:
320
Step-by-step explanation:
There are 320 tens in 3,200.
320 x 10 = 3200
Answer:
320
Step-by-step explanation:
3200/10=320
Please explain your work still don’t understand
Answer:
The radius is 5√2.The center is (-3, 4).Step-by-step explanation:
It can be helpful to understand what the square of a binomial looks like:
(a +b)² = a² +2ab +b²
The middle term on the right is twice the product of the terms in the original binomial on the left.
Here, we want to use this relationship to find "b" when we're given "2ab". We recognize that "b" is half the coefficient of "a" in 2ab.
Choosing a value for b² to turn the sum (a² +2ab) into the trinomial (a² +2ab +b²) is called "completing the square" because that trinomial can now be written as the square (a+b)².
__
The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
In order to find the center and radius of the circle from the given equation, you're expected to rewrite the equation in this form. You do that by "completing the square" for both x-terms and y-terms.
__
Given
x² +y² +6x -8y -25 = 0
Regrouping, we have ...
(x² +6x) +(y² -8y) = 25
Adding the squares of half of 6 and half of -8, we can write this as ...
(x² +6x +3²) +(y² -8y +(-4)²) = 25 +3² +(-4)²
And writing the trinomials as squares gives us ...
(x +3)² +(y -4)² = 50 = (5√2)²
Comparing this to the standard form equation above, we see that ...
(h, k) = (-3, 4)
r = 5√2
__
The radius is 5√2.
The center is (-3, 4).
__
The attachment shows that the original equation draws a circle with center (-3, 4) and through points that are 5 units horizontally and vertically from the center, such as the point (2, -1). That is, the radius is 5√2.
( 7m + 1 )( 5m 2 + 4m - 6 ) simplified
Answer:
35m³ + 33m² - 38m - 6
Step-by-step explanation:
simplify ( 7m + 1 )( 5m^2 + 4m - 6 )
= 7m * 5m² + 7m * 4m - 7m * 6 + 5m² + 4m - 6
=7 * 5mm² + 7 * 4mm - 7 * 6m + 5m² + 4m
= 35m³ + 33m² - 38m - 6
Given the figure below, find the values of x and z
Answer:
x=14 z=72
Step-by-step explanation:
(8x-40)+(12x-60)=180
20x-100=180
20x=280
x=14
(12x-60)+z=180
(168-60)+z=180
108+z=180
z=72
Please help me solve this 166=-w+66
Answer:
w = -100
Step-by-step explanation:
Step 1: Write out equation
166 = -w + 66
Step 2: Subtract 66 on both sides
100 = -w
Step 3: Divide both sides by -1
w = -100
Answer:
w=-100
Step-by-step explanation:
We are given the equation:
166= -w +66
To solve for x, we must get x by itself on one side of the equation.
66 is being added to -w. The inverse of addition is subtraction. Subtract 66 from both sides of the equation.
166-66= -w+66-66
166-66= -w
100= -w
-1 and w are being multiplied. The invers of multiplication is division. Divide both sides of the equation by -1.
100/-1= -w/-1
100/-1=w
-100=w
Let's check our solution. Plug -100 in for w.
166= -w+66
166= -(-100)+66
166=100+66
166=166
The statement above is true, so we know our solution is correct.
The solution to 166= -w+66 is w= -100
what is the probability that a randomly selected driver fatality who was female was 55 to 69 years old
Answer:
0.1354
Step-by-step explanation:
Relevant data provided as per the requirement is shown below:-
Female probability of age between 55 to 69 = 2058
Male probability of age between 55 to 69 = 4571
According to the given situation, the calculation of probability is shown below:-
[tex]= \frac{Female\ from\ 55\ to\ 69 }{Total\ female}[/tex]
where,
Total female is
= 143 + 2333 + 4027 + 5178 + 2058 + 1459
= 15,198
And, the female is 2058
So, the probability is
[tex]= \frac{2058}{15,198}[/tex]
= 0.1354
Therefore for computing the probability of female that lies between 55 to 69 we simply applied the above formula.
Answer 9w-4=14 show solving steps pls
Answer:
[tex]w=2[/tex]
Step-by-step explanation:
So we have the equation:
[tex]9w-4=14[/tex]
Add 4 to both sides. The left cancels:
[tex](9w-4)+4=(14)+4\\9w=18[/tex]
Divide both sides by 9.The left cancels:
[tex](9w)/9=(18)/9\\w=2[/tex]
So, the value of w is 2.
And we're done :)
After being arranged and simplified which of the following equations could be solved using the quadratic formula?
Answer:
B. 2x² + x² + x = 30
D. 9x + 3x² = 14 + x - 1
Step-by-step explanation:
2x² + x² + x = 30
simplify
3x² + x - 30 = 0
x can be solve using quadratic equations
x = 3 and x = -10/3
so the answer is B
9x + 3x² = 14 + x - 1
simplify
3x² + 8x - 13 =0
x can be solve using quadratic equations
so the answer is D
Note: options A and C do not qualify for quadratic equation
The solution is Option B , Option D.
The set of quadratic equations are 2x² + x² + x = 30 and 9x + 3x² = 14 + x -1
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
a)
2x² + x² + x = 30 be equation (1)
On simplifying the equation , we get
3x² + x = 30
Subtracting 30 on both sides of the equation , we get
3x² + x - 30 = 0
Now , on factorizing the equation , we get
x = 3 and x = -10/3
b)
9x + 3x² = 14 + x -1 be equation (1)
On simplifying the equation , we get
Subtracting x on both sides of the equation , we get
3x² + 8x = 13
Subtracting 13 on both sides of the equation , we get
3x² + 8x - 13 = 0
Now , on factorizing the equation , we get
x = ( -4/3 ) ± ( √55/3 )
Hence ,
The quadratic equations are 2x² + x² + x = 30 and 9x + 3x² = 14 + x -1
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If you randomly select a letter from the phrase "Sean wants to eat at Olive Garden," what is the probability that you select a vowel
Answer:100%
Step-by-step explanation: Think about it for a second S-ea-n w-a-nts t-o e-a-t a-t o-liv-e g-a-rd-e-n their are vowels in every word
Answer:12/27
Step-by-step explanation:there are 12 vowels in the phrase so the probability is 12:27 or 4:9 (you can write these as fractions too, numerators are on the left)
Find the value of x in the triangle shown below.
12
Answer:
The answer is option CStep-by-step explanation:
Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x
Using Pythagoras theorem we have
c² = a² + b²
where
c is the hypotenuse
From the question x is the hypotenuse
So we have
[tex] {x}^{2} = {5}^{2} + {12}^{2} \\ x = \sqrt{25 + 144} \\ x = \sqrt{169} [/tex]We have the final answer as
x = 13Hope this helps you
In a recent survey, three out of every five students said they would prefer going to a water park for the class trip.
If 105 students were surveyed, how many can be expected to prefer the water park?
O A 21
OB. 35
O c. 63
O D. 70
E. 103
Answer:
the answer is d
Step-by-step explanation:
Just multiply and divide
What is probability?
the quality or state of being probable; the extent to which something is likely to happen or be the case
We have,
Surveyed student = 105
Students would prefer to going to a water park= 3/5
According to question
students who expected to prefer the water park
= 105 × 3/5
= 21×5×3/5
= 21×3
= 63
Hence, students who expected to prefer the water park is 63
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A stock price S is governed where z is a standardized Wiener process. Find the process that governs G(t)
This question is incomplete, the complete question is;
A stock price S is governed by dS = aSdt + bSdz
where z is a standardized Wiener process. Find the process that governs G(t) = S^1/2(t)
Answer:
G = S^1/2
Step-by-step explanation:
Solving the Equation
dS = aSdt + bSdz
First we Take S common from Right hand Side
dS = S(a dt + b dz)
Then we also take S Left Hand Side(LHS) from RHS
dS/S = a dt + b dz
So d = a dt + b dz
now we Take d Common from RHS
d = d(a t + b z)
So
d/d = a t + b z
1 = a t + b z
So, t = (1-b z) / a
Now substitute value of t in equation G(t) = S^1/2(t)
we have
G{(1- b z)/a} = S^1/2 {(1- b z)/a}
(1- b z)/a) from both sides cancels out each other
So we have G = S^1/2
what is the sum of 8.7 + 5.22=
Answer:
8.7+5.22=13.92
Hope it helps you...
Answer:
13.92
Step-by-step explanation:
the red line in the figure is an altitude of triangle ABC. Using right angle trigonometry, write an equation involving sin C
Answer:
[tex]\Large \boxed{\mathrm{\bold{C}}}[/tex]
Step-by-step explanation:
[tex]\sf \displaystyle sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
The side opposite to [tex]\angle C[/tex] is h.
The hypotenuse of the smaller right triangle is a.
[tex]\sf \displaystyle sin(C)=\frac{h}{a}[/tex]
Answer:
sinC = [tex]\frac{h}{a}[/tex]
Step-by-step explanation:
Since the red line is an altitude then the triangles are right, thus
sinC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{h}{a}[/tex]
1. Graph the line y=2x+5 on the graph.
Answer:
See below
Step-by-step explanation:
We can simply use a graphing calculator to carry it out.
See the attached file for more explanation!
Another way is that we can take the values of x as 1,2 and 3 and so on and put it in the equation to get the value of y. We have some coordinates now so we'll plot them in the graph to get the line of y = 2x+5.
Step-by-step explanation:
Hope this helps........
Suppose a deep sea diver dives from the surface to 202 feet below the surface. He then dives down 12 more feet. Use integers to represent this situation. Then find
the diver's present depth.
Which expression best represents the diver's situation.
O A. O + (-202) + 12
OB. 0 + (-202)+(-12)
OC. 0+202 +(-12)
OD. 0+202 + 12
The diver is presently feet below the surface.
(Simplify your answer.)
Answer:
B.) (-202)+(-12)
Step-by-step explanation:
The undersea level is negative then going under again will produce a completely negative answer.
If x=4 what is the value of 2x+18
Answer:
26
Step-by-step explanation:
2x + 18
2(4) + 18
8 + 18
26
Answer:
26
Step-by-step explanation:
We just substitute the value of X and find the answer
Given the sets
A
and
B
expressed in interval notation, find
A
∩
B
.
A
=
(
−
∞
,
−
42
)
∪
(
−
25
,
+
∞
)
B
=
(
−
54
,
70
)
Answer:
Step-by-step explanation:
A∩B=[-54,-42]∪[-25,70]
2. Find the distance between A (-1, 4) and B (1.-1)
5.39
5.19
5.29
5.09
=====================================================
Explanation:
Apply the distance formula.
[tex]d = \sqrt{ (x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{ (-1-1)^2+(4-(-1))^2}\\\\d = \sqrt{ (-1-1)^2+(4+1)^2}\\\\d = \sqrt{ (-2)^2+(5)^2}\\\\d = \sqrt{ 4+25}\\\\d = \sqrt{ 29}\\\\d \approx 5.38516\\\\d \approx 5.39\\\\[/tex]
You could also use the pythagorean theorem which is what the distance formula is based off of.
what is the annual simple interest rate?
I=$17, P=$500, t=2 years
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{1.7 \: \%}}}}}[/tex]
Step-by-step explanation:
Given,
Interest ( I ) = $ 17
Principal ( P ) = $ 500
Time ( T ) = 2 years
Rate ( R ) = ?
Finding the simple Interest rate :
[tex] \boxed{ \bold{ \sf{rate = \frac{interest \times 100}{principal \times time}}}} [/tex]
[tex] \dashrightarrow{ \sf{rate = \frac{17 \times 100}{500 \times 2} }}[/tex]
[tex] \dashrightarrow{ \sf{rate = \frac{1700}{1000} }}[/tex]
[tex] \dashrightarrow{ \sf{ rate = 1.7 \: \%}}[/tex]
Hope I helped!
Best regards! :D
A parallelogram has an area of 20.4 square units. If the height that corresponds to a base is 4 units,what is the base
Answer:
5.1 units
Step-by-step explanation:
A=b x h divide by 2
20.4=4b
b=5.1 units
As a surveyor, you measure an angle of elevation as 35.25 degrees. You are required to record all measurements in fraction form. What is the degree measure of the angle written as a fraction?
Answer:
35 1/4
Step-by-step explanation:
Answer:
B for edge
Step-by-step explanation:
New heat lamps are reported to have the mean lifespan of 100 hours with a standard deviation of 15 hours. Before replacing their current lamp to the new heat lamps for the university, OSU decided to test whether the mean lifetime is equal to 100 or not by sampling 36 heat lamps. They turned them on and recorded the time, in hours, until each lamp failed. The sample provided a mean lifespan is 105.1 hours.
1) What set of hypotheses are correct for this problem?
SET 1 - H0: µ = 100 hours , Ha: µ < 100 hours
SET 2 - H0: µ = 100 hours , Ha: µ > 100 hours
SET 3 - H0: µ = 100 hours , Ha: µ ≠ 100 hours
A) SET 1.
B) SET 2.
C) SET 3.
2) If we assume the null hypothesis to be true, the average of the distribution of sample means, μ x ¯, from a sample size of 36 is:______.
a) 15.
b) 115.
c) 100.
d) 105.1. .
3) According to the Central Limit Theorem, the standard deviation of the distribution of the sample means is:______.
a) 115.
b) 15.
c) 6.
d) 2.5. .
4) What is the approximate probability of observing a sample mean of 105.1 or more from the distribution of sample means, again assuming that the null hypothesis is true?
a) 0.68.
b) 0.025.
c) 0.975.
d) 0.16.
Answer:
1
The correct option is C
2
The correct option is C
3
The correct option is A
4
The correct option is B
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 100[/tex]
The standard deviation is [tex]\sigma = 15[/tex]
The sample size is [tex]n = 36[/tex]
The sample mean is [tex]\= x = 105.1[/tex]
Generally
The null hypothesis is [tex]H_o: \mu = 100 \ hours[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 100\ hours[/tex]
Given that the null hypothesis is true then the distribution of sample means [tex]\mu_{\= x }[/tex], from a sample size of 36 is mathematically represented as
[tex]\mu_{\= x } = \mu[/tex]
=> [tex]\mu_{\= x } = 100[/tex]
According to the Central Limit Theorem the test stated in the question is approximately normally distributed if the sample size is sufficiently large[tex](n > 30 )[/tex] so given that the sample size is large n = 36
Then the test is normally distributed and hence the standard deviation is 15
Generally the standard error of mean is mathematically represented as
[tex]\sigma_{\= x } = \frac{ \sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x } = \frac{15}{\sqrt{36} }[/tex]
=> [tex]\sigma_{\= x } = 2.5[/tex]
Generally the approximate probability of observing a sample mean of 105.1 or more is mathematically represented as
[tex]P( \= X \ge 105.1 ) =1 - P(\= X < 105.1) = 1- P(\frac{\= X - \mu }{\sigma_{\= x }} <\frac{105.1 - 100}{2.5} )[/tex]
=> [tex]P( \= X \ge 105.1 ) =1 - P(\= X < 105.1) = 1- P(Z<2.04 )[/tex]
From the z-table (reference calculator dot net )
[tex]P(Z<2.04 ) = 0.97932[/tex]
So
[tex]P( \= X \ge 105.1 )= 1 - P(\= X < 105.1) = 1- 0.97932[/tex]
[tex]P( \= X \ge 105.1 ) =0.02[/tex]
How do you solve this equation by using the quadratic formula 8x^2+3x-45=0
The 8 is a, the 3 is b and -45 is c
Plug them into the quadratic formula
15. Bradley has a goal to work 28 hours each week at the pizza shop. So far he has
worked 12 hours. How many more hours does he need to work to meet his goal?
70
Limes are on sale. That sale price is 8 limes for $2.00. Why could the unit rate be 4 or 0.25?
Answer:
C.No, because each lime will cost a bit more than 30¢, so 4 limes will cost a bit more than $1.20.Step-by-step explanation:
The unit price of the 8 limes is $0.25 per lime.
The given expression:
The selling price for 8 limes = $2.00
To find:
if the unit price is $4 or $0.25The unit price of the lime is calculated by dividing the total selling price by the total number of limes purchased.
[tex]unit \ price = \frac{total \ amount \ paid \ for \ 8 \ limes }{8 \ limes } \\\\unit \ price =\frac{\$ \ 2}{8 \ limes } \\\\unit \ price = (\frac{1}{4} ) \frac{\$}{lime} \\\\unit \ price = \$0.25 \ per \ lime[/tex]
Thus, the unit price of the 8 limes is $0.25 per lime.
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A market research company wishes to know how many energy drinks adults drink each week. They want to construct a 80% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 0.9. The study found that for a sample of 164 adults the mean number of energy drinks consumed per week is 7.9. Construct the desired confidence interval. Round your answers to one decimal place.
Answer:
The confidence interval = (7.8 , 8.0)
Step-by-step explanation:
Confidence Interval formula =
Mean ± z × Standard deviation/√n
Mean = 7.9
Standard deviation = 0.9
n = number of samples = 164
z = z score of an 80% confidence interval = 1.282
Confidence Interval = 7.9 ± 1.282 × 0.9/√164
= 7.9 ± 0.0900966432
Confidence Interval
= 7.9 - 0.0900966432
= 7.8099033568
Approximately to 1 decimal place = 7.8
7.9 + 0.0900966432
= 7.9900966432
Approximately to 1 decimal place = 8.0
Therefore, the confidence interval = (7.8 , 8.0)
4(x - 3) = 4(2x + 1)
Hi there! :)
Answer:
[tex]\huge\boxed{x = -4}[/tex]
4(x - 3) = 4(2x + 1)
Distribute the coefficient outside of the parenthesis:
4(x)+ 4(-3) = 4(2x) + 4(1)
Simplify:
4x - 12 = 8x + 4
Subtract 4x from both sides:
4x - 4x - 12 = 8x - 4x + 4
-12 = 4x + 4
Subtract 4 from both sides:
-12 -4 = 4x + 4 - 4
-16 = 4x
Divide both sides by 4:
-16/4 = 4x/4
x = -4.
Answer:
x=-4
Step-by-step explanation:
or 4*×-4*3=4*2x+4*1
or 4x-12=8x+4
or 4x-8x=4+12
or -4x=16
or x=16/-4
or =x=-4