Answer:
7/2 x 52/3
Step-by-step explanation:
Steps:
Since 1 year = 52 weeks
52*7/2*3= 7/2*52/3
Since 1 year equal 52 weeks meaning we have to times 52 by 7/2 then times by 3 the weeks. The answer is below.
Answer: 7/2 x 52/3
Please mark brainliest
Hope this helps.
Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication. At this rate of decay, how many bacteria will there be in 8 hours?
Answer:
There will be 66 bacteria in 8 hours.
Step-by-step explanation:
The number of bacteria after t hours is given by the following formula.
[tex]P(t) = P(0)(1-r)^{t}[/tex]
In which P(0) is the initual number of bacteria and r is the decay rate.
Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication.
This means that [tex]P(0) = 750000, P(48) = 250[/tex]
We use this to find r. So
[tex]P(t) = P(0)(1-r)^{t}[/tex]
[tex]250 = 750000(1-r)^{48}[/tex]
[tex](1-r)^{48} = \frac{250}{750000}[/tex]
[tex]\sqrt[48]{(1-r)^{48}} = \sqrt[48]{\frac{250}{750000}}[/tex]
[tex]1-r = 0.84637[/tex]
So
[tex]P(t) = 750000(0.84637)^{t}[/tex]
How many bacteria will there be in 8 hours?
8 hours from now, in this context, is 8 + 48 = 56 hours. So this is P(56).
[tex]P(56) = 750000(0.84637)^{56} = 65.83[/tex]
Rounding to the nearest number
There will be 66 bacteria in 8 hours.
Answer:
197,488
Step-by-step explanation:
This problem requires two main steps. First, we must find the unknown rate, k. Then, we use that value of k to help us find the unknown number of bacteria.
Identify the variables in the formula.
AA0ktA=250=750,000=?=48hours=A0ekt
Substitute the values in the formula.
250=750,000ek⋅48
Solve for k. Divide each side by 750,000.
13,000=e48k
Take the natural log of each side.
ln13,000=lne48k
Use the power property.
ln13,000=48klne
Simplify.
ln13,000=48k
Divide each side by 48.
ln13,00048=k
Approximate the answer.
k≈−0.167
We use this rate of growth to predict the number of bacteria there will be in 8 hours.
AA0ktA=?=750,000=ln13,00048=8hours=A0ekt
Substitute in the values.
A=750,000eln13,00048⋅8
Evaluate.
A≈197,488.16
At this rate of decay, researchers can expect 197,488 bacteria.
Name the x-axis of symmetry for the parabola sketched below
Answer:
x=-3
Step-by-step explanation:
The vertex is at x = -3
The axis of symmetry is along the vertex
x=-3
Answer:
x=-3
Step-by-step explanation:
To find the axis of symmetry, you just need to find the x-coordinate of the vertex using this formula: -b/2a=x
*Only when provided a three variable quadratic equation.
For looking at a graph, you find the center of the parabola in which when you reflect it over itself, it will be symmetrical.
According to the graph, x=-3 is the line which you can draw to fold over to the other side and it can fit perfectly.
Can someone please please help me
Answer:
The answer is None
Step-by-step explanation:
Multiply 6 2 and 1 and also multiply 12 4 and 2 separately now divide 96 with 12 and you get 8 which is none of the answer choices
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
According to theorem, "the measure of central angle of minor Arc of a circle is doubleto that of the angle subtended by the corresponding major Arc."
So
m<AOB = 2(m<AZB)
m<AZB = M<AOB / 2
m<AZB = 68/2
m<AZB = 34°
Answer:
34° is right answer
Step-by-step explanation:
correct answer is 34
If the figures below are similar, find the scale factor of Figure B to Figure A.
48
27
60
А
16
B
20
9
Answer:
The scale factor is 3.
Step-by-step explanation
Figure B has side measures 16, 20, and 9. Figure A has side measures 48, 27, and 60. The ratio of each of the corresponding sides is 1:3 (16:48, etc). Therefore, the scale factor of Figure B to Figure A is 3.
Which answer is equivalent to the equation shown below?
7c = 49
A.log7 c = 49
B.c = log49 7
C.logc49 = 7
D.c = log7 49
Answer:
D.
Step-by-step explanation:
The base of a log is also the base of an exponent. So 7 to the c power, our 7 would be the base. To find c, we simply just do log base 7 of 49, which comes out to be 2.
15 POINTS & BRAINLIEST!!!
How do you find the axis of symmery in the form f(x) = 3(x - 4)^2 + 5?
Answer:
so the axis of symmetry is x=4
Answer: X = 4
Explanation: Hope it helps you♡
Dan buys a car for £2300. It depreciates at a rate of 0.2% per year. How much will it be worth in 6 years? Give your answer to the nearest penny where appropriate.
9514 1404 393
Answer:
£2272.54
Step-by-step explanation:
An equation for the value is ...
v = £2300(0.998^t)
Then for t=6, the value is ...
v = £2272.54
_____
Additional comment
The growth factor (0.998) is (1 - decay rate) = (1 -0.002).
Answer:
the answer is 2272.54
Step-by-step explanation:
:))
Solve for x
A) 10
B) 20
C) 30
D) 60
Help me I’m so pretty and funny I need help, worms infesting my brain.
Answer:
Option (2). x = 20°
Step-by-step explanation:
In the figure attached,
ΔABC is an equilateral triangle.
By the property of equilateral triangle, all sides of the triangle are equal and measure of all angles of the triangle is 60°.
By this property,
m∠B = 60°
and y = 46 - 16 = 30
By applying Sine rule in ΔBCD,
[tex]\frac{\text{sin}60}{BD}=\frac{\text{sin}80}{46}=\frac{\text{sin}(\angle CBD)}{DC}[/tex]
[tex]\frac{\text{sin}80}{46}=\frac{\text{sin}(\angle CBD)}{y}[/tex]
sin(∠CBD) = [tex]\frac{30\times \text{sin}80}{46}[/tex]
= 0.6423
m∠CBD = 39.96
≈ 40°
m∠ABD = 60° - 40°
= 20°
Therefore, Option (2). 20° will be the answer.
A random sample of 1,000 StatCrunchU students contains 598 female and 402 males. We analyze responses to the question, "What is the total amount (in dollars) of your student loans to date?" Two sample T confidence interval: μ 1: Mean of Loans where Gender="Female" μ 2: Mean of Loans where Gender="Male" μ 1 − μ 2: Difference between two means (without pooled variances) 95% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit μ 1 − μ 2 516.74334 368.41116 907.34739 -206.29374 1239.7804 What can we conclude from the 95% confidence interval? Check all that apply. Group of answer choices
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
Here, we have,
From the provided 95% confidence interval, we can make the following conclusions:
The point estimate of the difference between the mean student loans for females and males is 516.74334 dollars.
The standard error of the difference between the means is 368.41116 dollars.
The degrees of freedom (DF) associated with the confidence interval is 907.34739.
The lower limit of the confidence interval is -206.29374 dollars.
The upper limit of the confidence interval is 1239.7804 dollars.
The confidence interval does not contain zero.
Since zero is not within the interval, we can conclude that the difference between the mean student loans for females and males is statistically significant at the 95% confidence level.
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
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The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Based on the 95% confidence interval provided for the difference in means between the loans of female and male StatCrunchU students, we can draw the following conclusions:
The sample difference in means is 516.74334.
The standard error of the difference is 368.41116.
The degrees of freedom (DF) for the analysis is 907.34739.
The lower limit of the confidence interval is -206.29374.
The upper limit of the confidence interval is 1239.7804.
Therefore, we can conclude the following:
The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Note: Since the confidence interval includes both positive and negative values, we cannot conclude with certainty whether there is a significant difference or not in the mean student loans between females and males. The confidence interval suggests that the difference could be positive, negative, or even zero.
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Bonita said that the product of 5/6 x 1 2/3 is 7/3. How can you tell that her answer is wrong.
Answer:=
1 7/18
Step-by-step explanation:
Turn the improper fraction into a mixed fraction.
Noaya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read. Let y represent the number of pages left to read after x hours.
Answer: –55x + 570
Step-by-step explanation:
The person above me completely missed the question so this is the right one
A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled "The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes, and depth D is in meters. The report then says, "The regression equation for this bird is: DD = 2.69 + 0.0138D.
1. What is the slope of the regression line?
2. Explain in specfic language what this slope says about this penguin's dives.
A. If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.
B. If the depth of the dive is decreased by one meter, it adds 0.0138 minutes to the time spent under water.
C. If the depth of the dive is increased by 0.0138 meter, it adds one minute to the time spent under water.
3. According to the regression line, how long does a typical dive to a depth of 200 meters last?
4. According to the regression line, how long does a typical dive to a depth of 210 meters last?
5. According to the regression line, how long does a typical dive to a depth of 220 meters last?
6. According to the regression line, how long does a typical dive to a depth of 230 meters last?
7. According to the regression line, how long does a typical dive to a depth of 240 meters last?
8. According to the regression line, how long does a typical dive to a depth of 150 meters last?
9. According to the regression line, how long does a typical dive to a depth of 160 meters last?
10. According to the regression line, how long does a typical dive to a depth of 170 meters last?
11. According to the regression line, how long does a typical dive to a depth of 180 meters last?
12. According to the regression line, how long does a typical dive to a depth of 190 meters last?
Answer:
(1)0.0138
(2)A. If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.
Nos 3-12: See Explanation
Step-by-step explanation:
Given the regression equation for the relation of dive duration (DD) to depth (D).
[tex]DD = 2.69 + 0.0138D\\$Where: Duration DD is measured in minutes\\epth D is in meters.[/tex]
(1)The slope of the regression lie =0.0138
(2)
When D=1, DD = 2.69 + 0.0138(1)=2.7038
When D=2, DD = 2.69 + 0.0138(2)=2.7176
2.7176-2.7038=0.0138
Therefore, If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.
(3) When depth, D =200 meters
DD = 2.69 + 0.0138(200)=5.45 Minutes
(4) When depth, D =210 meters
DD = 2.69 + 0.0138(210)=5.588 Minutes
(5) When depth, D =220 meters
DD = 2.69 + 0.0138(220)=5.726 Minutes
(6) When depth, D =230 meters
DD = 2.69 + 0.0138(230)=5.864 Minutes
(7) When depth, D =240 meters
DD = 2.69 + 0.0138(240)=6.002 Minutes
(8) When depth, D =150 meters
DD = 2.69 + 0.0138(150)=4.76 Minutes
(9) When depth, D =160 meters
DD = 2.69 + 0.0138(160)=4.898 Minutes
(10) When depth, D =170 meters
DD = 2.69 + 0.0138(170)=5.036 Minutes
(11) When depth, D =180 meters
DD = 2.69 + 0.0138(180)=5.174 Minutes
(12) When depth, D =190 meters
DD = 2.69 + 0.0138(190)=5.312 Minutes
A regression line is only a single line that fits the data the best. It tells how steep it is, whereas the intercept reveals where it intersects an axis.
Regression line:For question 1):
By calculating the slope of the regression line we get the slope value that is [tex]= 0.0138[/tex]
For question 2):
Describe whatever this slope means about this penguin's dives in precise terms.
The time spent under liquid increases by 0.0138 minutes whenever the diving depth is raised by one meter, which is equal to "Option A".
For question 3):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times200 = 2.69+2.76 = 5.45\ minutes[/tex]
For question 4):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times210 = 2.69 + 2.898 = 5.588\ minutes[/tex]
For question 5):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 220 = 2.69 + 3.036 = 5.726\ minutes[/tex]
For question 6):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times230 = 2.69 + 3.174 = 5.864 \ minutes[/tex]
For question 7):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times240 = 2.69 + 3.312 = 6.002\ minutes[/tex]
For question 8):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 150 = 2.69 + 2.07 = 4.76\ minutes[/tex]
For question 9):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 160 = 2.69 + 2.208 = 4.898\ minutes[/tex]
For question 10):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 170 = 2.69 + 2.346 = 5.036\ minutes[/tex]
For question 11):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 180 = 2.69 + 2.484 = 5.174 \ minutes[/tex]
For question 12):
Calculated equation:
[tex]\to DD = 2.69 + 0.0138\times 190 = 2.69 + 2.622 = 5.312\ minutes[/tex]
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a consumer affairs company is interested in testing at the 5% level of significance that the average weight of a package of butter is less than 16 oz if the p value is 0.003 the conclusion is
The perimeter of the rectangle is 28 units.
A rectangle with perimeter 28 units is shown. The length of the sides is w, and the length of the top and bottom sides are 2 w minus 1.
What is the value of w?
5 units
7 units
14 units
15 units
Answer:
5 units
Step-by-step explanation:
P=2(w)+2(2w-1)
28=2w+4w-2
30=6w
w=5
Answer:
5
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
In the attached file
A solid lies between planes perpendicular to the x-axis at xequals=0 and xequals=1212. The cross-sections perpendicular to the axis on the interval 0less than or equals≤xless than or equals≤1212 are squares with diagonals that run from the parabola y equals negative 2 StartRoot x EndRooty=−2x to the parabola y equals 2 StartRoot x EndRooty=2x. Find the volume of the solid.
Question:
A solid lies between planes perpendicular to the x-axis at x=0 and x=12. The cross-sections perpendicular to the axis on the interval 0≤x≤12 are squares with diagonals that run from the parabola y=-2√x to the parabola y=2√x. Find the volume of the solid.
Answer:
576
Step-by-step explanation:
Given:
Length of diagonal square:
[tex] D = 2\sqrt{x} - (-2\sqrt{x}) [/tex]
[tex] D = 4\sqrt{x} [/tex]
Here, the diagonal is the hypotenus of a right angle triangle, with leg S, where the square has a side of length S.
Using Pythagoras theorem:
[tex] S^2 + S^2 = D^2 [/tex]
[tex] S^2 + S^2 = (4\sqrt{x})^2 [/tex]
[tex] 2S^2 = 16x [/tex]
Divide both sides by 2
[tex] S^2 = 8x [/tex]
Thus,
Area, A = S² = 8x
Take differential volume, dx =
dV = Axdx
dV = 8xdx
Where limit of solid= 0≤x≤12
Volume of solid, V:
V =∫₀¹² dV
V = 8 ∫₀¹² xdx
V = [4x²]₀¹²
V = 4 (12)²
V = 12 * 144
= 576
Volume of solid = 576
In the rectangular prism, express each of the following in terms of s, t, and u. Give an explanation for each of your answers.
(a) HK
(b) GL
(c)JH
Complete Question
The complete question is shown on the first and second uploaded image
Answer:
a
[tex]\= HK = \= t + \= u[/tex]
b
[tex]\= GL = \= s - \= t[/tex]
c
[tex]\= JH = \= u + \= s[/tex]
Step-by-step explanation:
Now looking at the diagram
Following the direction of the unit vectors [tex]\= u , \= s, \= t[/tex]
[tex]\= {HK} = \= {KI} + \= KL[/tex]
=> [tex]\= HK = \= t + \= u[/tex]
And
[tex]\= GL = \= GH + \= GF[/tex] jjj
=> [tex]\= GL = \= s - \= t[/tex]
Also
[tex]\= JH = \= JG + \= JI[/tex]
=> [tex]\= JH = \= u + \= s[/tex]
luke is 5 years younger than 3 times sydenys age, s in this situation what does 3s represent
3s represents three times Sydney's age. Sydney's age is symbolized with an S.
What is the value of X ? A-17 B-26 C-39 D-41
Answer:
D.
Step-by-step explanation:
It's a right triangle so
[tex]x^2=40^2+9^2[/tex]
x = 41
The mean of 3 numbers is 4
The two numbers are 1,9
what is the missing number?
Answer:
2
Step-by-step explanation:
1+9+2 = 12
12/3= 4
Answer:2
Step-by-step explanation:9+2+1=12
So 12/3=4
ANSWER=2
What is 1.036 that add up to 4
Answer:
2.964
Step-by-step explanation:
Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication a at what time will you need to stop the infusion
Answer:
6 PM
Step-by-step explanation:
125 mg --- 300 mL
500 mg --- x mL
x = 500*300/125 = 1200 mL solution contains 500 mg
rate = 100 mL/h
1200 mL* 1h/100 mL = 12 h
6AM + 12 h = 6 PM
You need to stop infusion at 6 PM
It is found that You need to stop infusion at 6 PM.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication.
125 mg = 300 mL
500 mg = x mL
x = 500*300/125
x = 1200 mL
Here solution contains 500 mg
The rate = 100 mL/h
1200 mL* 1h/100 mL = 12 h
6AM + 12 h = 6 PM
Therefore, You need to stop infusion at 6 PM.
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The relationship between the number of pencil sharpener a company can sell each week and the price of each sharpener p is given by the equation x = 2300 − 100 p At what price should the sharpeners be sold if the weekly revenue is to be $ 12000
Answer:
The price p could be any of $8 or $15 .
Step-by-step explanation:
The equation is a relationship between the numbers of pencil sharpener x can sell each week and the price of each sharpener p.
x = 2300 - 100p
xp = 12000
therefore,
x = 12000/p
insert the value of x in the equation
x = 2300 - 100p
12000/p = 2300 - 100p
12000/p + 100p - 2300 = 0
multiply through by p
12000 + 100p² - 2300p = 0
100p² - 2300p + 12000 = 0
divide through by 100
p² - 23 + 120 = 0
Find the number that we can multiply to give 120 and add to give - 23. The number are -15 and - 8.
p² - 8p - 15p + 120 = 0
p(p - 8) - 15(p - 8) = 0
(p - 8)(p - 15)
p = 8 or 15
x = 2300 - 100p
x = 2300 - 100(8)
x = 2300 - 800
x = 1500 pencil sharpener sold
or
x = 2300 - 100(15)
x = 2300 - 1500
x = 800 pencil sharpener sold
The price could be any of $8 or $15 .
Joseph places $5,500 in a savings
account for 30 months. He earns $893.75
in interest. What is the annual interest
rate?
Answer: About 6.2%
Step-by-step explanation:
He starts with 5500 and gains 893.75 in 2.5 years.
The equation is then 5500*(x)^2.5 = 5500+893.75, or
5500*x^2.5 = 6393.75.
x is about 1.0621, or about 6.2% because it's interest.
Hope that helped,
-sirswagger21
Answer: 137.5%
Step-by-step explanation
Consider the homogeneous second-order linear differential equation y′′+4y′−12y=0. Which of the following pairs gives two solutions to this equation? A. y1=e2x,y2=e−6x B. y1=e3x,y2=e1x C. y1=e2x,y2=e−2x D. y1=e−12x,y2=xe−12x E. y1=cos(−12x),y2=sin(−12x) F. y1=e−4x,y2=e−12x Then for these solutions find a particular solution of the form y=c1y1+c2y2 that satisfies the initial conditions y(0)=−5,y′(0)=0. y = y1 + y2.
1. Use limit comparison test to determine whether the series converges or diverges:
Σ[infinity]_n=1 n^2 + 1 / 2n^3 - 1
2. Use limit comparison test to determine whether the series converges or diverges:
Σ[infinity]_n = 1 n / √n^5 + 5
3. Use direct comparison test to determine whether the series converges or diverges:
Σ[infinity]_n = 1 4 + 3^n / 2^n
Answer:
1. Diverges
2. Converges
3. Diverges
Step-by-step explanation:
Solution:-
Limit comparison test:
- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ). Then the following three conditions are applicable for the limit:
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = c
Where,
1) If c is finite: 0 < c < 1, then both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] either converges or diverges.
2) If c = 0, then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges.
3) If c = ∞ or undefined, then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges.
a) The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{n^2+1}{2n^3-1} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{n^2( 1 + \frac{1}{n^2} )}{n^3 ( 2 - \frac{1}{n^2} ) } ] = [ \frac{( 1 + \frac{1}{n^2} )}{n( 2 - \frac{1}{n^2} ) } ][/tex]
- Apply the limit ( n - > ∞ ):
(n = 1) ∑^∞ [tex][ \frac{1}{2n}][/tex] .... The comparative series ( ∑[tex]b_n[/tex] )
- Both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.
- Compute the limit:
Lim ( n-> ∞ ) [tex][ \frac{n^2 + 1}{2n^3 - 1} * 2n ] = [ \frac{2n^3 + 2n}{2n^3 - 1} ][/tex]
Lim ( n-> ∞ ) [tex][ \frac{2n^3 ( 1 + \frac{1}{n^2} ) }{2n^3 ( 1 - \frac{1}{2n^3} ) } ] = [ \frac{ 1 + \frac{1}{n^2} }{ 1 - \frac{1}{2n^3} } ][/tex]
- Apply the limit ( n - > ∞ ):
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = [tex][ \frac{1 + 0}{1 + 0} ][/tex] = 1 ... Finite
- So from first condition both series either converge or diverge.
- We check for ∑[tex]b_n[/tex] convergence or divergence.
- The ∑[tex]b_n[/tex] = ( 1 / 2n ) resembles harmonic series ∑ ( 1 / n ) which diverges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 1 ≤ 1. Hence, ∑
- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also diverges.
Answer: Diverges
b)
The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{n}{n^\frac{5}{2} +5} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{n( 1 )}{n ( n^\frac{3}{2} + \frac{5}{n} ) } ] = [\frac{1}{( n^\frac{3}{2} + \frac{5}{n} )} ][/tex]
- Apply the limit ( n - > ∞ ) in the denominator for ( 5 / n ), only the dominant term n^(3/2) is left:
(n = 1) ∑^∞ [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] .... The comparative series ( ∑[tex]b_n[/tex] )
- Both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.
- Compute the limit:
Lim ( n-> ∞ ) [tex][ \frac{n}{n^\frac{5}{2} +5} * n^\frac{3}{2} ] = [ \frac{n^\frac{5}{2}}{n^\frac{5}{2} +5} ][/tex]
Lim ( n-> ∞ ) [tex][ \frac{n^\frac{5}{2}}{n^\frac{5}{2} ( 1 + \frac{5}{n^\frac{5}{2}}) } ] = [ \frac{1}{1 + \frac{5}{n^\frac{5}{2}} } ][/tex]
- Apply the limit ( n - > ∞ ):
Lim ( n-> ∞ ) [tex][ \frac{a_n}{b_n} ][/tex] = [tex][\frac{1}{1 + 0}][/tex] = 1 ... Finite
- So from first condition both series either converge or diverge.
- We check for ∑[tex]b_n[/tex] convergence or divergence.
- The ∑[tex]b_n[/tex] = ( [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] ) converges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 3/2 > 1. Hence, ∑
- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also converges.
Answer: converges
Comparison Test:-
- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ).
-Then the following conditions are applied:
1 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) < 0 , then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges
2 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≤ 0 , then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges
c) The given series ∑[tex]a_n[/tex] is:
(n = 1) ∑^∞ [tex][ \frac{4 + 3^2}{2^n} ][/tex]
- We will make an educated guess on the comparative series ∑[tex]b_n[/tex] by the following procedure.
(n = 1) ∑^∞ [tex][ \frac{3^n ( \frac{4}{3^n} + 1 )}{2^n} ][/tex]
- Apply the limit ( n - > ∞ ) in the numerator for ( 4 / 3^n ), only the dominant terms ( 3^n ) and ( 2^n ) are left:
(n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex] ... The comparative series ( ∑[tex]b_n[/tex] )
- Compute the difference between sequences ( [tex]a_n[/tex] - [tex]b_n[/tex] ):
[tex]a_n - b_n = \frac{4 + 3^n}{2^n} - [ \frac{3^n}{2^n} ] \\\\a_n - b_n = \frac{4 }{2^n} \geq 0[/tex], for all values of ( n )
- Check for divergence of the comparative series ( ∑[tex]b_n[/tex] ), using divergence test:
∑[tex]b_n[/tex] = (n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex] diverges
- The first condition is applied when ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≥ 0, then ∑diverges only if ∑[tex]b_n[/tex] diverges.
Answer: Diverges
y = -9x - 2; (4, -37)
A. Yes it satisfies the equation
B. No the ordered pair does not satisfy the equation
Answer:
B. No the ordered pair does not satisfy the equation
Step-by-step explanation:
y = -9x - 2
Substitute the point in and see if it is true
-37 = -9(4) -2
-37 = -36 -2
-37 = -38
This is not true so the point is not a solution
Felicia walks 3 blocks west, 4 blocks south, 3 more blocks west, then
2 blocks south again. How far is Felicia from her starting point?
Answer:
blocks
Answer: i did the question i told you the steps
Step-by-step explanation:
From the starting point move three to the left. Then move four down. Then move three times to the left. Lastly move two down.
In a survey of students, 60% were in high school and 40% were in middle school. Of the high school students, 30% had visited a foreign country. If a surveyed student is selected at random, what is the probability that the student is in high school and has visited a foreign country?
Answer:
The probability that the student is in high school and has visited a foreign country is 0.18.
Step-by-step explanation:
We are given that in a survey of students, 60% were in high school and 40% were in middle school.
Of the high school students, 30% had visited a foreign country.
Let the Probability that students were in high school = P(H) = 60%
Probability that students were in middle school = P(M) = 40%
Also, let F = event that students had had visited a foreign country
So, Probability that high school students had visited a foreign country = P(F/H) = 30%
Now, probability that the student is in high school and has visited a foreign country is given by = Probability that students were in high school [tex]\times[/tex] Probability that high school students had visited a foreign country
= P(H) [tex]\times[/tex] P(F/H)
= 0.60 [tex]\times[/tex] 0.30
= 0.18 or 18%
