Answer:
The general rule is [tex]a_n = -2 - 5(n-1)[/tex]
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.
The general rule of an arithmetic sequence is given by:
[tex]a_{n} = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term and d is the common difference.
We can also find the nth term as a function of a term m, using:
[tex]a_n = a_m + (n-m)d[/tex]
a3 = -12 and a8 = -37
First we find the common difference. So
[tex]a_n = a_m + (n-m)d[/tex]
[tex]a_8 = a_3 + (8-3)d[/tex]
[tex]-37 = -12 + 5d[/tex]
[tex]5d = -25[/tex]
[tex]d = -\frac{25}{5}[/tex]
[tex]d = -5[/tex]
So
[tex]a_n = a_1 - 5(n-1)[/tex]
Finding the first term:
[tex]a_n = a_1 - 5(n-1)[/tex]
Since [tex]a_3 = -12[/tex]
[tex]a_n = a_1 - 5(n-1)[/tex]
[tex]a_3 = a_1 - 5(3-1)[/tex]
[tex]a_1 = a_3 + 10 = -12 + 10 = -2[/tex]
So the general rule is:
[tex]a_n = a_1 - 5(n-1)[/tex]
[tex]a_n = -2 - 5(n-1)[/tex]
What type of data display is shown below?
Student Grades
60
69
99
82
92
60
70
HA
100
80
90
O A. Histogram
O B. Box-and-whisker plot
C. Stem-and-leaf plot
O D. Scatterplot
Answer:
B) Box-and-Whisker plot
I WILL GIVE 50 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT. The zeros of a function H are -2,3 and -4 which of the following could be h(x)
Answer:
a
Step-by-step explanation:
kkkkkkkkkkkkkkkkkkkkkkk
Answer:
a. h(x)=(x+2) (x-3) (x+4)
Step-by-step explanation:
The zeros of the function are -2, 3 and -4:
(x=-2) (x=3) (x=-4)
(x+2) (x-3) (x+4)
Enter the number that belongs in the green box as you solve for P.
Answer:
2p=18
2p=2p the answer is p=9
Step-by-step explanation:
Help me find the value of x plss
Answer:
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Answer:
What do we see in triangle -- adj and hyp
cosine since it is SOH CAH TOA
cos(14)/1 =x/480
Answer = 465.74 the real rounding is 466
NO LINKS OR WILL BE REPORTED
The table below shows the numbers of tickets sold at a carnival and the amounts of money in dollars collected Cost of Carnival Tickets
Number of Tickets. Amount $ Collected.
5 $15
10. $30
15. $45
20. $60
25. $75
Which equation represents the relationship
A y = x + 10
B y = 5x
C y = x + 15
D y = 3x
One earthquake has MMS magnitude 3.2. If a second earthquake has 390 times as much energy (earth
movement) as the first, find the magnitude of the second quake.
my sister is 12 years older than i am. the sum of our ages is 38. find our ages.
Answer:
you are 13 and she is 25
Step-by-step explanation:
Math
An investor wants to invest up to $100,000 as follows:
X amount into a Certificate of Deposit (CD) that yields an expected annual return of 1% with a risk index of 1,
Y amount into a Bond with an expected annual return of 3% and a risk index of 4,
Z amount into a Stock with an expected annual return of 7% and a risk index of 8.
The investor’s objective is to maximize the total expected annual return of the investment.
However, to be prudent, the investor requires that:
The fraction of the total investment in X must be at least 20%.
The fraction of the total investment in Z must not exceed 50%.
The combined portfolio risk index must not exceed 5.
Required:
a. Set up this investment problem as a linear program, which has 3 variables, 3 basic constraints, and 4 special constraints.
b. Use an LP software to find the maximum expected annual return in dollars and the dollar values of X, Y, and Z for this best investment.
c. From the software solution, show the values of the dual variables for the four special constraints.
Answer:
a-The Linear Model is as follows:
[tex]X+Y+Z\leq 100,000\\{0.001X}\geq 20\\{0.001Z}\leq 50\\0.00001X+0.00004Y+0.00008Z\leq5\\X\geq0\\Y\geq0\\Z\geq0[/tex]
b-The values are
X=$33,333.33
Y=$16,666.67
Z=$50,000.00
Leading to a total expected return of $4333.33.
c-The values of constraints are as follows
X+Y+Z=33333.33+16666.67+50000=100,000
X=33%, Y is 16.67% and Z is 50%
Risk component of X is 0.33
Risk component of Y is 0.66
Risk component of Z is 4.00
Step-by-step explanation:
a
From the conditions, the first special constraint is the total amount which is that the sum of investments must not be more than the total available amount of $100,000 so
[tex]X+Y+Z\leq 100,000[/tex]
The second special constraint is that the percentage of X must be at least 20% So
[tex]\dfrac{X}{100,000}\times100 \geq20\\\dfrac{X}{1000} \geq20\\{0.001X}\geq 20[/tex]
The third special constraint is that the fraction of total investment of Z must not exceed 50% So
[tex]\dfrac{Z}{100,000}\times100 \leq50\\\dfrac{Z}{1000}\leq 50\\0.001Z\leq50[/tex]
The fourth special constraint is that the combined portfolio risk index must not exceed 5 so
[tex]\dfrac{X}{100,000}\times1+\dfrac{Y}{100,000}\times4+\dfrac{Z}{100,000}\times8\leq5\\0.00001X+0.00004X+0.00008Z\leq5[/tex]
As the investments cannot be negative so three basic constraints are
[tex]X\geq0\\Y\geq0\\Z\geq0[/tex]
The maximization function is given as
[tex]f(X,Y,Z)=\dfrac{X}{X+Y+Z}\times1\%+\dfrac{Y}{X+Y+Z}\times3\%+\dfrac{Z}{X+Y+Z}\times7\%\\f(X,Y,Z)=\dfrac{X}{X+Y+Z}\times0.01+\dfrac{Y}{X+Y+Z}\times0.03+\dfrac{Z}{X+Y+Z}\times0.07[/tex]
b
By using an LP solver with BigM method the solution is as follows:
X=$33,333.33
Y=$16,666.67
Z=$50,000.00
Leading to a total expected return of $4333.33.
c
The values of constraints are as follows
X+Y+Z=33333.33+16666.67+50000=100,000
X=33%, Y is 16.67% and Z is 50%
Risk component of X is 0.33
Risk component of Y is 0.66
Risk component of Z is 4.00
When electricity (the flow of electrons) is passed through a solution, it causes an oxidation-reduction (redox) reaction to occur. If the solution contains a metal cation such as Ag+, the flow of electrons will reduce the silver ion, causing solid silver to plate onto the electrode. The amount of metal plated depends on the number of electrons passed. The total charge of a mole of electrons is 96, 485 coulombs (C) and 1 ampere = 1 coulomb/second (C/s).
What mass of Cu(s) is electroplated by running 28.5 A of current through a Cu2+ (aq) solution for 4.00 h? Express your answer to three significant figures and include the appropriate units.
How many minutes will it take to electroplate 37.1 g of gold by running 5.00 A of current through a solution of Au+(aq)? Express your answer to three significant figures and include the appropriate units.
Answer:
a. 135 g
b. 60.6 min
Step-by-step explanation:
a. What mass of Cu(s) is electroplated by running 28.5 A of current through a Cu2+ (aq) solution for 4.00 h? Express your answer to three significant figures and include the appropriate units.
The chemical equation for the reaction is given below
Cu²⁺(aq) + 2e⁻ → Cu(s)
We find the number of moles of Cu that are deposited from
nF = It where n = number of moles of electrons, F = Faraday's constant = 96485 C/mol, I = current = 28.5 A and t = time = 4.00 h = 4.00 × 60 min/h × 60 s/min = 14,400 s
So, n = It/F = 28.5 A × 14,400 s/96485 C/mol = 410,400 C/96485 C/mol = 4.254 mol
Since 2 moles of electrons deposits 1 mol of Cu, then 4.254 mol of electrons deposits 4.254 mol × 1 mol of Cu/2 mol = 2.127 mol of Cu
Now, number of moles of Cu = n' = m/M where m = mass of copper and M = molar mass of Cu = 63.546 g/mol
So, m = n'M
= 2.127 mol × 63.546 g/mol
= 135.15 g
≅ 135 g to 3 significant figures
b. How many minutes will it take to electroplate 37.1 g of gold by running 5.00 A of current through a solution of Au+(aq)?
The chemical equation for the reaction is given below
Au⁺(aq) + e⁻ → Au(s)
We need to find the number of moles of Au in 37.1 g
So, number of moles of Au = n = m/M where m = mass of gold = 37.1 g and M = molar mass of Au = 196.97 g/mol
So, n = m/M = 37.1 g/196.97 g/mol = 0.188 mol
Since 1 mol of Au is deposited by 1 moles of electrons, then 0.188 mol of Au deposits 0.188 mol of Au × 1 mol of electrons/1 mol of Au = 0.188 mol of electrons
We find the time it takes to deposit 0.188 mol of electrons that are deposited from
nF = It where n = number of moles of electrons, F = Faraday's constant = 96485 C/mol, I = current = 5.00 A and t = time
So, t = nF/It
= 0.188 mol × 96485 C/mol ÷ 5.00 A
= 18173.30 C/5.00 A
= 3634.66 s
= 3634.66 s × 1min/60 s
= 60.58 min
≅ 60.6 min to 3 significant figures
Which ordered pair
describes a point
with location in the
second quadrant?
A. (-6, -5)
B. (-6, 5)
C. (6, 5)
D. (6, -5)
Answer:
B) (-6,5)
Step-by-step explanation:
Quadrant I: (+,+)
Quadrant II: (-,+)
Quadrant III: (-,-)
Quadrant IV: (+,-)
Y(2.5+7)+y-2
10.5y-2
Answer:
−200y − 2
Step-by-step explanation:
y(2.5 + 7) + y −210.5y − 2
=9.5y + y + −210.5y + −2
=(9.5y+ y + −210.5y) + (−2)
−200y − 2
Mark me brainllest
The table shows the probability distribution of siblings of students in a high
school with 1500 students. What is the expected value for the number of
siblings of a randomly chosen student?
Number of siblings
0
1
2
3
4
5
Probability
0.18
0.65
0.09
0.05
0.02
0.01
A. 1.08
B. 2.5
C. 1.11
D. 1.29
Answer:
Step-by-step explanation:
1.11
The expected value for the number of siblings of a randomly chosen student is 1.11.
The correct answer is C. 1.11.
To calculate the expected value for the number of siblings of a randomly chosen student, we need to multiply each possible number of siblings by its corresponding probability and sum up the results.
Expected Value = (0 x 0.18) + (1 x 0.65) + (2 x 0.09) + (3 x 0.05) + (4 x 0.02) + (5 x 0.01)
Expected Value = 0 + 0.65 + 0.18 + 0.15 + 0.08 + 0.05
Expected Value = 1.11
Therefore, the expected value for the number of siblings of a randomly chosen student is 1.11.
Learn more about Probability here:
https://brainly.com/question/31828911
#SPJ5
Graph the line passing through (4, -1) whose slope is m = 4/3
9514 1404 393
Answer:
graph is attached
Step-by-step explanation:
With the given slope, the intercepts will not be at integer values. The best way to graph this by hand is to start at the point (4, -1) and use the slope to identify other points on the line.
The slope of 4/3 tells you the graph will rise 4 units for each 3 units to the right. So, another point will be (4, -1) + (3, 4) = (7, 3). A point in the other direction will be (4, -1) -(3, 4) = (1, -5). These points are sufficient for you to draw the desired line.
A 12 foot ladder leans against a building and reaches a window 10 feet above ground. What is the measure of the angle, to the nearest degree, that the ladder forms with the ground ?
Answer:
56
Step-by-step explanation:
Sinx = 10/12
x = 56
A store pays $35 for a fish tank. The markup is 20%. What is the selling price?
Find the measure of Angle I.
Answer:
I think 5?................
Helpppppppppppppppppppp
Answer:
192.5 m²
Step-by-step explanation:
The formula for calculating the area if a circle
= πr²
Find the area of the larger circle first, then subtract the area of the smaller circle.
The area of the larger circle
= π×(21÷2)²
= 346.4 m² (rounded to the nearest tenth)
The radius of the smaller circle
= 21÷2 - 3.5
= 7 m
The area of the smaller circle
= π×7²
= 153.9 m² (rounded to the nearest tenth)
The area of the shaded region
= 346.4 - 153.9
= 192.5 m²
Examine the figure of two parallel lines cut by a transversal.
What is the value of x?
Answer:
x=17
Step-by-step explanation:
The angles present are Alternative interior angles. That means that they are congruent. Meaning 4x+7 = 75. To solve for 7, you subtract 7 from both sides. That leaves you with 4x=68. Then you divide both sides with 4. Then you get x=17.
Hope this helps!
BTS!!
Answer:
x = 17
Step-by-step explanation:
75° and (4x + 7)° are alternate interior angles.
If two lines are cut by a transversal, then the alternate interior angles are congruent.
75 = 4x + 7
=> 4x = 68
=> x = 17
Is 35.336 an irrational number?
yes or no
Answer:
No
Step-by-step explanation:
Hello, 35.336 is would not be an irrational number because irrational numbers are messy numbers that go on forever like 3.14159..... A rational number is a number with clean numbers like 1.222222....., 35.336, ect. I hope this helped you!
A car is driving at 40 kilometers per hour. How far, in meters, does it travel in 2 seconds?
Answer:
i think its 22.22 thats my guess
Answer:
[tex]\frac{1}{45}[/tex] kilometers
Step-by-step explanation:
60 minutes = 3600 seconds
[tex]\frac{40}{3600} =\frac{y}{2}[/tex]
3600y = 80
3600y ÷ 3600 = 80 ÷ 3600
[tex]y=\frac{1}{45}[/tex]
Upon studying low bids for shipping contracts, a microcomputer manufacturing company finds that intrastate contracts have low bids that are uniformly distributed between 22 and 31, in units of thousands of dollars. Find the probability that the low bid on the next intrastate shipping contract is in excess of $28,000.
Answer:
0.111
Step-by-step explanation:
It is given that a manufacturing company found out that the intrastate contracts having a low bid which are [tex]$\text{uniformly}$[/tex] distributed between [tex]$22$[/tex] and [tex]$31$[/tex] [tex]$\text{units of thousands}$[/tex] of dollars.
Therefore, the probability that a low bid on the [tex]$\text{next intrastate}$[/tex] shipping contract is in excess of [tex]$\$ 28,000$[/tex] is given by :
P(x ≥ 30) = 1 - P(X ≤ 30)
[tex]$=1-\frac{30-22}{31-22}$[/tex]
[tex]$=1-\frac{8}{9}$[/tex]
[tex]$=\frac{1}{9}$[/tex]
= 0.111
Tino and Ramona are planning to go to Washington, D. C. for 4 days. The travel options are shown below. Which travel option is the most expensive?
Answer:
54 grams
Step-by-step explanation:
To hard to explain.
Answer: A
Step-by-step explanation: I am a big brain pro
Find the probability that a randomly selected point within the circle falls in the red shaded area (square). Round to the nearest tenth of a percent.
Answer:
probability of selecting the square is 63.7% approximately
Step-by-step explanation:
First of all, the probability of the point of choice is within the red square can be obtained with this formula
probability = expected outcome / total number of possible outcomes
In this case, we are not dealing with discrete values which can be counted. instead, we are dealing with areas.
We are to go about this problem by finding the area of the internal square and dividing it by the area of the circle.
Area of the square
Area of the square = [tex]l^2[/tex]
where length = [tex]4\sqrt{2}[/tex]
Area = [tex](4\sqrt{2}) ^2 = 32cm^2[/tex]
Area of the circle
Area of the circle = [tex]\pi r^2[/tex]
area of circle =[tex]\pi \times 4^2 =50.26cm^2[/tex]
Probablity of selecting the square =
32/50.26 = 0.6366
To express this as a percentage, we multiply our answer by 100.
This will give us 0.6366 X 100 = 63.7% approximately
HELP! Does the pythagorean theorem work for every triangle or just for right triangles?
a. everytriangle
b. only right triangles
Answer:
This is so easy!
ONLY RIGHT TRIANGLES
Did you really ask this question?
Tip: You should learn the basics first.
Which is greater, (1/2)⁴² or (1/2)⁴⁵? Why?
Answer:
1/2^42 because the 45 will be dividing it b half 3 more times
Step-by-step explanation:
14. If a woman is just about to ski down a steep mountain, She estimates the
angle of depression from where she is now to the flag at the bottom of the
course to be 24". She knows that she is 800 feet higher than the base of the
course. How long is the path that she will ski? (Round to the nearest foot)
I need help with this
9514 1404 393
Answer:
x = 32y = 51Step-by-step explanation:
Angle U = angle N = 180° -142° -24° = 14°
The expression for angle U tells us the value of x.
2x -50 = 14
x -25 = 7 . . . . . divide by 2
x = 32 . . . . . . . .add 25
__
The measure of side SU is the same as that for side PN.
13 = (2x -y)
y = 2x -13 = 2(32) -13 . . . . solve for y, substitute for x
y = 51
What is my answer the missing numbers
please please please help
find the median
72 82 92 93 94 97 98 102
find the median
53 59 64 65 65 66 67 69
find the mean absolute deviation (MAD)
72
82
93
98
102
97
92
94
find the mean absolute deviation (MAD)
53 59 64 65 65 66 67 69
Answer:
median = 93.5
median = 65
MAD = 7.125
MAD = 3.75
Step-by-step explanation:
The median is the middle value when the values of the data set are placed in order from smallest to largest.
Data set: 72 82 92 93 94 97 98 102
As the number of values in the data set is even, the median is the mean of the middle two values.
[tex]\implies \sf median=\dfrac{93+94}{2}=93.5[/tex]
Data set: 53 59 64 65 65 66 67 69
As the number of values in the data set is even, the median is the mean of the middle two values.
[tex]\implies \sf median=\dfrac{65+65}{2}=65[/tex]
To find the Mean Absolute Deviation (MAD):
1. calculate the mean (by summing the data values and dividing by the number of values)
2. Subtract the mean from each value in the data set and take the absolute value of each result.
3. Sum the absolute values from step 2.
4. Divide by the number of values.
Data set: 72, 82, 93, 98, 102, 97, 92, 94
[tex]\sf Mean=\dfrac{72+82+93+98+102+97+92+94}{8}=91.25[/tex]
|72 - 91.25| = 19.25
|82 - 91.25| = 9.25
|93 - 91.25| = 1.75
|98 - 91.25| = 6.75
|102 - 91.25| = 10.75
|97 - 91.25| = 5.75
|92 - 91.25| = 0.75
|94 - 91.25| = 2.75
Sum of absolute values = 57
[tex]\sf MAD=\dfrac{57}{8}=7.125[/tex]
Data set: 53 59 64 65 65 66 67 69
[tex]\sf Mean=\dfrac{53 +59+ 64+ 65+ 65+ 66+ 67+ 69}{8}=63.5[/tex]
|53 - 63.5| = 10.5
|59 - 63.5| = 4.5
|64 - 63.5| = 0.5
|65 - 63.5| = 1.5
|65 - 63.5| = 1.5
|66 - 63.5| = 2.5
|67 - 63.5| = 3.5
|69 - 63.5| = 5.5
Sum of absolute values = 30
[tex]\sf MAD=\dfrac{30}{8}=3.75[/tex]
An education researcher would like to test whether 2nd graders retain or lose knowledge during the summer when they are presumably not in school. She asks nine 2nd graders to take a comprehension exam at the end of the school year (May), and then asks those same students to come back after the summer (late August) to retake a different but equivalent exam, to see if their level of comprehension has changed. Using the data below, test this hypothesis using an alpha level of .05.
May August
90 100
65 80
78 92
50 60
89 90
92 98
75 70
90 96
65 87
a) What is the appropriate test? Is it a one or two tailed test?
b) State the null hypothesis (in words and using means).
c) State the alternative hypothesis (in words and using means).
d) Find the critical value.
e) Calculate the obtained value by hand. What does your decision mean?
Answer:
See step by step explanation
Step-by-step explanation:
From the problem statement, we understand that we need to investigate if 2nd graders RETAIN OR LOSE knowledge comparing information concerning two different months, therefore we are going to find out if the information gives us enough evidence of a difference in the two groups
a) The test should be a two tail-test
Sample sizes are small ( n₁ = n₂ = 9 ) which means we have to use t-student test
b and c) Test Hypothesis:
For Null Hypothesis H₀, we establish that the two means are equal, which in this case means that the two samples´ means are equal. And as Hypothesis alternative Hₐ that the H₀ is not true, or that the samples mean are different.
Null Hypothesis H₀ x₁ - x₂ = 0 or x₁ = x₂
Alternative Hypothesis Hₐ x₁ - x₂ ≠ 0 or x₁ ≠ x₂
d) Significance level α = 0,05 then α/2 = 0,025
then t(c) with α/2 = 0,025 and degree of freedom
df = n₁ + n₂ - 2 df = 9 + 9 -2 df = 16
From t s-tudent table we find t(c) = 2,12
e) Calculating:
x₁ and σ₁
x₂ and σ₂
σₓ = [ ( n₁ - 1 )* σ₁² + ( n₂ - 1 )*σ₂² ]/ n₁ + n₂ - 2
Using a calculator:
x₁ = 77,11 σ₁ = 13,86
x₂ = 85,89 σ₂ = 12,74
σₓ = [ ( 8*(13,86)² + 8*( 12,74 )² ] / 16
σₓ = (8* 192,1) + 8* ( 162,31) / 16
σₓ = (1536,8 + 1298,48 ) / 16
σₓ = 177,205
t(s) = ( x₁ - x₂ ) /√ σₓ²/ n₁ + σₓ²/ n₂
t(s) = ( 77,11 - 85,89 )/ (177,205)²/n₁ + (177,205)²/n₂
t(s) = - 8,78 / √3489,07 + 3489,07
t(s) = -8,78 / 83,54
t(s) = - 0,11
Comparing t(s) and t(c)
|t(s)| < |t(c)|
0,11 < 2,12
t(s) is in the acceptance region. We accept H₀