Find an equation for the nth term of the arithmetic sequence.
a16 = 21, a17 = -1
Answer:nth term=a1 - 27n + 27
Step-by-step explanation:
first term =a1
common difference=d=-1-21
d=-27
Using the formula
Tn=a1 + d x (n-1)
nth term=a1 + (-27)(n-1)
nth term=a1 - 27n + 27
The scores on one portion of a standardized test are approximately Normally distributed, N(572, 51). a. Use the 68-95-99.7 rule to estimate the range of scores that includes the middle 95% of these test scores. b. Use technology to estimate the range of scores that includes the middle 90% of these test scores.
Answer:
a) The range of scores that includes the middle 95% of these test scores is between 470 and 674.
b) The range of scores that includes the middle 90% of these test scores is between 488.1 and 655.9.
Step-by-step explanation:
68-95-99.7 rule:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Z-score:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Mean [tex]\mu = 572[/tex], standard deviation [tex]\sigma = 51[/tex]
a. Use the 68-95-99.7 rule to estimate the range of scores that includes the middle 95% of these test scores.
By the 68-95-99.7 rule, within 2 standard deviations of the mean.
572 - 2*51 = 470
572 + 2*51 = 674
The range of scores that includes the middle 95% of these test scores is between 470 and 674.
b. Use technology to estimate the range of scores that includes the middle 90% of these test scores.
Using the z-score formula.
Between these following percentiles:
50 - (90/2) = 5th percentile
50 + (90/2) = 95th percentile.
5th percentile.
X when Z has a pvalue of 0.05. So when X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 572}{51}[/tex]
[tex]X - 572 = -1.645*51[/tex]
[tex]X = 488.1[/tex]
95th percentile.
X when Z has a pvalue of 0.95. So when X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 572}{51}[/tex]
[tex]X - 572 = 1.645*51[/tex]
[tex]X = 655.9[/tex]
The range of scores that includes the middle 90% of these test scores is between 488.1 and 655.9.
Daryl wishes to save money to provide for his retirement. He is now 30 years old and will be
retiring at age 64. Beginning one month from now, he will begin depositing a fixed amount into
a retirement savings account that will earn 12% compounded monthly. Then one year after
making his final deposit, he will withdraw $100,000 annually for 25 years. In addition, and after
he passes away (assuming he lives 25 years after retirement) he wishes to leave in the fund a sum
worth $1,000,000 to his nephew who is under his charge. The fund will continue to earn 12%
compounded monthly. How much should the monthly deposits be for his retirement plan?
Answer:
Step-by-step explanation:
Today's Age = 30
Retirement Age = 64
Total Monthly Deposits = ( 64 - 30 ) * 12 = 408
In case of 12% Compounded Monthly , Interest Rate per month = ( 12% / 12 ) = 1%
Effective Interest Rate per year = ( 1 + 0.12/12 )12 - 1 = 1.1268 - 1 = 0.1268 = 12.68%
Present value of Annual 25 Years withdrawal of $100,000 at time of Retirement = $100,000 * PVAF ( 12.68% , 25 )
= $100,000 * 7.4864
= $748,642.20
Present Value of Money for nephew at time of Retirement = $1,000,000 * PVF ( 12.68% , 25 )
= $1,000,000 * 0.050535
= $50,534.52
Now the Present Value of total Amount Required at time of Retirement = $748,642.20 + $50,534.52
= $799,176.70
Now the monthly deposit be X
= X * FVAF ( 408 , 1% ) = $799,176.70
= X * 5752.85 = $799,176.70
X = $138.918
Therefore Monthly Deposit = $138.92
The table shows the number of cups of water required when cooking different amounts of rice.
Amount of
Rice
(cups) Amount of
Water
(cups)
2 5
3 7.5
5 12.5
8 20
Which statements apply to the ratio of rice and water? Choose two options.
The amount of rice is the dependent value.
The amount of water is the dependent value.
The amount of rice is the independent value.
The amount of water is the independent value.
The values cannot be labeled as dependent or independent without a given equation
Answer:
The amount of water is the dependent value.The amount of rice is the independent value.Step-by-step explanation:
The wording "the amount of water required for different amounts of rice" suggests that the "output" value of the table is the amount of water, and the "input" value is the amount of rice.
That makes "water" the dependent variable, and "rice" the independent variable.
The amount of water is the dependent value.
The amount of rice is the independent value.
Answer:
The amount of water is the dependent value.
The amount of rice is the independent value.
Step-by-step explanation:
Please help if you can
Answer:
4
Step-by-step explanation:
We just have to find the corresponding d(t) value when t=2. From the graph, we can see that when t = 2, d(2) = 4. Hope this helps!
How to add or subtract this polynomial
Answer:
18x^2 + 9x - 5
Step-by-step explanation:
Combine like terms:
(9x^2-8) + (9x^2+9x+3)
= 9x^2 + 9x^2 + 9x - 8 + 3
= 18x^2 + 9x - 5
Can somebody please solve this? I'm confused
Answer:
9
Step-by-step explanation:
Not sure if it is right, don't at me :)
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 18, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B
One-half of the dogs in each shelter are between which weights?
between 8 and 30 pounds in shelter A; between 10 and 28 pounds in shelter B
between 8 and 17 pounds in shelter A; between 10 and 16 pounds in shelter B
between 21 and 30 pounds in shelter A; between 18 and 28 pounds in shelter B
between 28 and 30 pounds in shelter A; between 20 and 28 pounds in shelter B
Answer:
the 2nd one
i am pretty sure
Step-by-step explanation:
The difference of two supplementary angles is 70 degrees. Find the measures of the angles.
Answer:
DUEDY A. 32 degrees
Step-by-step explanation:
PATROLLING WEE WOOO
Xd
Answer:
55 125
Step-by-step explanation:
Let the smaller angle = x
Let the larger angle = x + 70
They are supplementary so the total of the two angles, by definition must be 180 degrees. Note that you should understand that any number of angles can but supplementary as long as they all add up to 180 degrees.
x + x + 70 = 180
2x + 70 = 180
2x + 70 - 70 = 180 - 70
2x = 110
2x/2 = 110/2
x = 55
the smaller angle = 55 degrees
The larger angle = 55 + 70 = 125
A bedroom wall is to be painted around a window as shown below.
A rectangle with length 11 feet and width 10 feet. A smaller rectangle with length 3 feet and width 2 feet is cut out of the larger rectangle.
What is the area of the wall that will be painted?
A.6 feet squared
B.104 feet squared
C.110 feet squared
D.116 feet squared
Answer:B.104 feet squared
Step-by-step explanation:
First find the area of the rectangle 11×10=110 then find the area of the window 3×2=6 then subtract 110-6=104
Answer:
B
Step-by-step explanation:
A bookstore had 60 copies of a magazine. Yesterday, it sold 1/3 of them. Today, it sold 1/4 of what remained. How many copies does the bookstore have left?
Answer:
30
Step-by-step explanation:
1/3 of 60 is 20
40 would be left
1/4 of 40 is 10 so 30 would be left
Johanna wrote the system of equations.
4x-3y=1, 5x+4y=9
If the second equation is multiplied by 4, what should the first equation be multiplied by to eliminate the x-variable by addition?
Answer:
-5
Step-by-step explanation:
If the second equation is multiplied by 4, the coefficient of the x-variable will be 5·4 = 20. To eliminate the x-variable by addition, the first equation needs to be multiplied by a value that will result in an x-coefficient of -20. If that value is k, then we have ...
4k = -20
k = -20/4 = -5
The first equation should be multiplied by -5 to eliminate the x-variable by addition.
_____
Comment on general case
In general, if you have ...
ax +by = c
dx +ey = f
to eliminate the x-variable by addition, you can multiply the second equation by "a" and the first equation by "-d". In the problem above, those numbers are 4 and -5.
Answer:
-5
Step-by-step explanation:
The object below is a cubical lunch box having each edge as 10 cm.
Find its surface area.
A
600 cm2
B
360 cm2
C
300 cm2
D
36 cm2
Answer:
B
Step-by-step explanation:
The total surface area of a cubical lunch box having each edge as 10 cm is 600 square centimeter. Therefore, option A is the correct answer.
What is surface area of a cube?The surface area of the cube all six faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added six times to itself. The formula to find the surface area of a cube is 6a², where a is edge.
Given that, the cubical lunch box having each edge as 10 cm.
Here, surface area = 6×10²
= 600 square centimeter
Therefore, option A is the correct answer.
Learn more about the surface area of a cube here:
brainly.com/question/23273671.
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How many sundaes did the shop make if they used 32 spoonfuls of sprinkles?
Answer:
32?
Step-by-step explanation:
Answer:
Depends on how many spoonfuls of sprinkles per sundae. Is there more details to this question?
The function fff is given in three equivalent forms. Which form most quickly reveals the zeros (or "roots") of the function? Choose 1 answer: Choose 1 answer: (Choice A) A f(x)=-3(x-2)^2+27f(x)=−3(x−2) 2 +27f, (, x, ), equals, minus, 3, (, x, minus, 2, ), squared, plus, 27 (Choice B) B f(x)=-3(x+1)(x-5)f(x)=−3(x+1)(x−5)f, (, x, ), equals, minus, 3, (, x, plus, 1, ), (, x, minus, 5, )(Choice C) C f(x)=-3x^2+12x+15f(x)=−3x 2 +12x+15f, (, x, ), equals, minus, 3, x, squared, plus, 12, x, plus, 15 Write one of the zeros. xxx =
Answer:
(B) [tex]f(x)=-3(x+1)(x-5)[/tex]
x=5
Step-by-step explanation:
Given the three equivalent forms of f(x):
[tex]f(x)=-3(x-2)^2+27\\f(x)=-3(x+1)(x-5)\\f(x)=-3x^2+12x+15[/tex]
The form which most quickly reveals the zeros (or "roots") of f(x) is
(B) [tex]f(x)=-3(x+1)(x-5)[/tex]
This is as a result of the fact that on equating to zero, the roots becomes immediately evident.
[tex]f(x)=-3(x+1)(x-5)=0\\-3\neq 0\\Therefore:\\x+1=0$ or x-5=0\\The zeros are x=-1 or x=5[/tex]
Therefore, one of the zeros, x=5
Answer:
i dont think the one above is correct. here is the correct answer
Step-by-step explanation:
Trust me,I will give braineist. I swear to god.
Answer:
= 1696m^3
Step-by-step explanation:
V = πr²h
= 3.14 x 6 x 6 x 15
= 3.14 x 540
= 1695.6 m^3
= 1696m^3
Find the first five terms of the geometric sequence defined by a (n)=10
(.1)^n
Answer:
Step-by-step explanation:
a(1) = 10(.1)^1 = 1
a(2) = 10(.1)^2 = 10(0.01) = 0.1
a(3) = 10(.1)^3 = 10(0.001) = 0.01
a(4) = 0.001
a(5) = 0.0001
What is the value of 5x+3 when x = 4?
Answer:
Step-by-step explanation:
5(4)+ 3
20+3
23
A polynomial function has a root of -5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the
function has a negative leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (-0, 5).
The graph of the function is negative on (-5, 3)
The graph of the function is positive on (-0, 1).
The graph of the function is negative on (3,co)
Mark this and return
Save and Exit
Sabem
Answer:
The graph of the function is negative on (3, ∞)
Step-by-step explanation:
The function starts negative at the left side of the graph, crosses the x-axis at x = -5, touches the x-axis at x = 1, again crosses into negative values at x = 3.
The function is positive on the open intervals (-5, 1) and (1, 3). It is negative on the open intervals (-∞, -5) and (3, ∞). The latter description matches the last answer choice:
the graph of the function is negative on (3, ∞).
$32 for a 14 2/19 km taxi ride
Answer:
What about it? If you need to know how much that is per km, it would be about $2.27 per km
Step-by-step explanation:
how do I simplify this
Answer:Use Distributive property
whats the answer for 45 meters every 5 seconds = meters per second
Answer:
9 meters every second
Step-by-step explanation:
45/5=9
5/5=1
9:1
plzz help i hav a test after i need the answer quick plzz.
Answer:Oop
Step-by-step explanation:
A child is laying on the ground relaxing and looking up at a plane that is passing by. If the plane’s altitude is 33,500 feet and the child’s eyes are located 8,200 feet away from a point on the ground directly beneath the plane, what is the angle of elevation for the child’s line of sight to the plane?
Answer:
about 76.2°
Step-by-step explanation:
The geometry can be modeled by a right triangle with the given dimensions being the side opposite the angle (height = 33,500 ft) and the side adjacent to the angle (8,200 ft). The fact that you know these two sides suggests the inverse of the tangent function may be useful.
Tan = Opposite/Adjacent
tan(angle) = (33,500/8,200)
angle = arctan (335/82) ≈ 76.246°
The angle of elevation is about 76.2°.
PLS HELP ME!
Um doing venn digrams so u have to set one up for it to work... TWENTY POINTS
Answer:
Creating a diagram..
Step-by-step explanation:
Alrighty, I've made a diagram. I've even uploaded it so everyone can see how good at drawing I am (not)
a. 7 do not own anything.
b. the probability that someone owns a bone or a stick is 50%.
c. the probability that someone owns a rock and a bone is 14%.
d. the probability that someone owns at least 2 items is 42%.
e. the probability that someone owns only 1 of these items is 51%.
Please tell me if im wrong! im only a student .m.
A boathouse costs $2750 a month to operate, and it spends $650 each
month for every boat that it docks. The boathouse charges a monthly fee of
$900 to dock a boat. If n is the number of boats, which equation represents
the profit function of the boathouse?
O A. p = 2750n + 250
O B. p= 900n + 2750
O c. p = 250n- 2750
O D. p = 650n + 2750
Answer: P=250n-2750
Step-by-step explanation:
The profit function of the boathouse is given as follows p = 250n- 2750.
What is the profit function?The profit function is a mathematical function that reflects a company's or business's profit as a function of the number of products or services produced and sold.
The revenue generated by the boathouse with n boats is given by the monthly fee per boat multiplied by the number of boats, which is $900n.
The total cost to operate the boathouse with n boats is the fixed cost of $2750 plus the variable cost of $650 per boat, which is $2750 + $650n.
Therefore, the profit function of the boathouse is given by the revenue minus the cost:
p = 900n - (2750 + 650n)
Simplifying this expression, we get:
p = 250n - 2750
Thus, the answer is (c) p = 250n - 2750.
Learn more about the profit function here:
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50 POINTS!!!!!!! WILL MARK BRAINLIEST! NO COPY/PASTE! TWO TO THREE SENTENCES AND EXPLAIN! WILL REPORT STUPID ANSWERS! According to Nikita Khrushchev, Premier of the Soviet Union, which of the three events had the potential to advance Soviet interests the most? The three events are the Cuban Missile Crisis, The Space Race, and The Berlin Wall.
Answer: Soviet leader Nikita Khrushchev had gambled on sending the missiles to Cuba with the specific goal of increasing his nation's nuclear strike capability.
Step-by-step explanation:
The Soviet Union signed a treaty with Hitler, the U.S. kept the atomic bomb a secret, and the U.S. took a long time to attack Hitler. France, Britain, and the United States wanted to reunify Germany, so they combined their areas into West Germany. Soviets cut off transportation to West Berlin. This lead to the United States and Britain using the Berlin airlift to bring food/supplies into the isolated part of Soviet occupied West Berlin.Which equation represents the line that passes through points (1, –5) and (3, –17)?
A. y = -6x + 1
B. y = 6x + 1
C. y = -6x - 1
D. y = 6x - 1
Answer:
C
Step-by-step explanation:
I’m rusty with my math, so I’m not 100% sure this is correct. My best attempt.
(1,-5) & (3,-17)
1=1x, -5=1y, 3=2x, -17=2y
Formula is y2-y1/x2-x1
-17 - -5 = -12
3 - 1 =2
So -12/2 = -6
Formula for the line is
y-y1 = m (x-x1)
In this equation m=-6
Y - -5 = -6 ( x - 1 )
Answer:C
Step-by-step explanation:
Find the compound interest on GHS 50,200 invested at 13% p.a. compounded annually for 3 years ( to the nearest
GHS).
Select one:
A. GHS 19,578
B. GHS 69,778
O
C. GHS 72,433
D. GHS 22.233
Answer:
D
Step-by-step explanation:
First found amount yielded
A = P(1+r)^nt
P is amount deposited 50,200
r is interest rate 13% = 13/100 = 0.13
t = 3
A = 50,200(1+0.13)^3
A = 50,200(1,13)^3
A = 72,433.42939999998
A is approximately 72,433.43
interest = A - P = 72,433.43-50,200 = 22,233.43= 22,233 to the nearest GHS
................................................
Answer:
V =108 ft^3
Step-by-step explanation:
The volume is found by
V = Bh where B is the area of the base
B = the area of the trapezoid
B = 1/2 (b1+b2)*h of the trapezoid
B = 1/2(4+6)*4 = 1/2(10)*4 = 20
Now we can find the volume
V = 20* 9
V =108 ft^3
