Answer:
n^3 + 1.
Step-by-step explanation:
Each term is 1 more than a perfect cube.
2 = 1^3 + 1
9 = 2^3 + 1
28 = 3^3 + 1
65 = 4^3 + 1
126 = 5^3 + 1
So the explicit formula is n^3 + 1.
The explicit formula that generates the given sequence is indeed aₙ = n³+1.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The nth term of the sequence can be obtained by substituting n = 1, 2, 3, ... into the expression n³+1:
a₁ = 1³+1 = 2
a₂ = 2³+1 = 9
a₃ = 3³+1 = 28
a₄ = 4³+1 = 65
a₅ = 5³+1 = 126
Hence, the explicit formula that generates the given sequence is indeed aₙ = n³+1.
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What is the size of exterior angle of regular polygon which has interior angle of 120 degree?
Answer: 60 degrees
Step-by-step explanation:
An interior angle of a polygon and its corresponding exterior angle are supplementary (add to 180 degrees).
A red team, blue team and green team were playing a game. The 3 people on the red team each lost 15 points. The 6 people on the blue team each gained 14 points. The 5 people on the green team each lost 11 points.
1. What is the total gain/loss for each team? Write your answer as a integer.
Team red:
Team blue:
Team green:
2. The twist in this game is that you need to multiply your final score by -6. Who won the game and what was their final score? The team with the greatest integer wins.
Team————wins with———-points.
If a pet store has 15 puppies 12 kittens and 6 rabbits
This question is down below. Please solve in detail if you know how to solve.
Answer:
8.4 meters tall ( one decimal place)
Step-by-step explanation:
See diagram below:
find distance 'd' as tan 68 = opp / adj = d/6
then d = 6 tan 68 = 14.85 m
Then find h as tan 9 = h / d
d tan 9 = h
14.85 tan 9 = h = 2.35 m tall
add the 6 m height of the house 8.4 m tall
Susie enjoys spending her afternoons kayaking. One afternoon she was kayaking on a river 3 miles upstream, and 3 miles downstream in a total of 4 hours. In still water, Susie can Kayak at an average speed of 2 miles per hour. Based on this information, what a reasonable estimation of the current measured in miles per hour.
Using the relation between velocity, distance and time, it is found that a reasonable estimation of the current is of 1 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
Upstream, against the current, he traveled 3 miles in t hours, hence the equation is:
[tex]2 - c = \frac{3}{t}[/tex]
[tex]c = 2 - \frac{3}{t}[/tex]
Downstream, with the current, he traveled 3 miles in 4 - t hours, hence the equation is:
[tex]2 + c = \frac{3}{4 - t}[/tex]
Hence:
[tex]c = \frac{3}{4 - t} - 2[/tex]
Then, taking the two equal equations:
[tex]2 - \frac{3}{t} = \frac{3}{4 - t} - 2[/tex]
[tex]\frac{3}{4 - t} + \frac{3}{t} = 4[/tex]
[tex]\frac{3t + 12 - 3t}{t(4 - t)} = 4[/tex]
12 = -4t² + 16t
4t² - 16t + 12 = 0
t² - 4t + 3 = 0
(t - 3)(t - 1) = 0.
The current is positive, hence:
[tex]c = 2 - \frac{3}{3}[/tex]
c = 2 - 1
c = 1 mph.
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What part of this question is an hour
Which two factors are needed to calculate the velocity of an object?
A. Speed
B. Direction
C. Mass
D. Acceleration
Do you think any resulting prediction would be more or less reliable than your original one?
No, The resulting prediction would be more or less reliable than your original one.
Importance:
Prediction is a forecast or a prophecy. An example of a prediction is a psychic telling a couple they will have a child soon, before they know the woman is pregnant. A statement of what will happen in the future.
Predictions provide a reference point for the scientist. If predictions are confirmed, the scientist has supported the hypothesis. If the predictions are not supported, the hypothesis is falsified. Either way, the scientist has increased knowledge of the process being studied.
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Rita divides avogadro’s number (approximately 6.02214 times. 1023) by 2.055 to calculate the number of atoms in a sample. which expression gives her result to the correct number of significant figures? 2.93 times. 1023 2.930 times. 1023 2.9305 times. 1023 2.93048 times. 1023
The correct answer is 2.930 × [tex]10^{23}[/tex]
What is Avogadro's number?
Avogadro's number, which is equal to 6.02214076 1023, is the quantity of units in one mole of any material (defined as its molecular weight in grams). Depending on the substance and the nature of the reaction, the units may be electrons, atoms, ions, or molecules (if any).
You have two numbers here. While number 2.0550 is stated with five significant figures, Avogadro's number is supplied with four. This implies that you must provide four significant figures with your result.
(6.022 × [tex]10^{23}[/tex]) / 2.0550 = 2.930 × [tex]10^{23}[/tex]
Therefore, the correct answer is 2.930 ×[tex]10^{23}[/tex] .
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Instructions: Find the surface area of the figure below. Round your answers to the nearest tenth, if necessary.
The surface area of the figure given is of: 61.3 yd².
What is the combined surface area of a figure?The combined surface area of a figure is the area of each figure.
This figure is composed by:
A circle of radius 3 yd.A triangle with base 6 yd and one leg 11.4 yd.The area of the circle is given as follows:
[tex]A = \pi r^2 = \pi \times 3^2 = 9\pi[/tex]
For the triangle, we need to find it's height, which is the leg of a right triangle, in which one of the sides is 3 and the hypotenuse is 11.4, hence:
h² + 3² = 11.4²
[tex]h = \sqrt{11.4^2 - 3^2}[/tex]
h = 11 yd.
Hence the area of the triangle is:
A = 0.5 x 6 x 11 = 33 yd²
The surface area of the figure is:
9pi + 33 yd² = 61.3 yd².
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what is the length and width
Answer:
Step-by-step explanation:
144,72
Answer:
If you cut the rectangle in half, you have two squares of area 144 ft², or side length 12 ft.
The length of the rectangle is 24 ft; its width is 12 ft.
An interior wall is made up of metal studs with 5/8 gypsum board on each side if the actual width of a stud is 3 5/8 what is the total thickness of the wall
What is f[g(7)] for the following functions?
f(x) = 3x2 − 4
g(x) = 2x − 5
f[g(7)] = 9
f[g(7)] = 143
f[g(7)] = 239
f[g(7)] =281
Answer: 239
Step-by-step explanation:
[tex]g(7)=2(7)-5=9\\\\f[g(7)]=f(9)=3(9)^2 - 4=239[/tex]
Which inequality can be used to explain why these three segments cannot be used to construct a triangle? ac ab > cb ac cb < ab ac cb > ab ac ab < cb
The response option that demonstrates why the three segments cannot be combined to form a triangle is AC + CB< AB.
What is triangle inequalities?According to the triangle inequality, the length of any two sides of a triangle added together must be longer than the length of the third side. Since a straight line is the shortest distance between two places, this conclusion follows. If the triangle isn't degenerate, the inequality is strict (meaning it has a non-zero area).
Which inequality explains why a triangle cannot be made from the three segments?Since the length of any two sides of a triangle added together is longer than the length of the third side, it follows from the triangle inequalities theorem that this is the case.
As a result, the necessary inequality is AC + CB AB because the sum of sides AC + CB is less than AB.
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I understand that question you are looking for is:
Which inequality can be used to explain why these three segments cannot be used to construct a triangle?
A. AC + AB > CB
B. AC + CB < AB
C. AC + CB > AB
D. AC + AB < CB
There are 2500 women and 2000 men enrolled in a certain college. The mean height for the women is 64.4 inches, and the mean height for the men is 69.8 inches. 1. Find the sum of the heights of the women. 2. Find the sum of the heights of the men. 3. Find the mean height for all 4500 people. 4. What is the average of the means for men and women
The sum height of men and women is 139600 and 161000 inches respectively. Their mean height is 66.8 inches and the average of their mean is 67.1 inches.
Calculation of the sum and meanNumber of women =2500
Mean height of women = 64.4 inches
So, the total height of 2500 women = 64.4*2500 = 161000 inches
Number of men=2000
Mean height of men = 69.8 inches
So, the total height of 2000 men = 69.8*2000 = 139600 inches
Therefore, the sum height of all 4500 people = 161000+139600 =b
So, their mean height = 300600/ 4500 = 66.8 inches
The sum of mean height of men and women = 64.4 + 69.8 = 134.2 inches
Hence, The average of their mean = 134.2/ 2= 67.1 inches.
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Calculate the (modeled) probability P(E) using the given information, assuming that all outcomes are equally likely.
S = {1, 3, 5, 7, 9}, E = {1, 5, 7}
The probability P(E) is 13/15.
According to the statement
we have given that the S = {1, 3, 5, 7, 9}, E = {1, 5, 7}
And we have to find the probability P(E).
So, For this purpose
Recall the formula for the probability of an event E in case when all outcomes are equally likely:
P(E)= n(E) /n(S)
in which S is the sample space.
But we have the S = {1, 3, 5, 7, 9},
so, n(S) = Sum of all outcomes / number of outcomes
n(S) = 1+3+5+7+9 /5
n(S) = 25 /5
n(S) = 5 and
For n(E) = Sum of all outcomes / number of outcomes
n(E) = 1+5+7 /3
n(E) = 13 /3
n(E) = 13 /3
Substitute these values in the above written formula then
P(E)= n(E) /n(S)
P(E)= (13/3)/ 5
P(E)= 13 /15
So, The probability P(E) is 13/15.
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The chess club started with a membership of only 4 students, but the membership grew at a rate of 2.56% each week. The number of students is modeled by f(x) = 4(1.0256)x.
A: Create a question you could ask that could be answered only by graphing or using a logarithm.
The question that could be answered by using a logarithm is explained below
How to explain the logarithm?The question is: Let your dependent variable in the function be y. Write the function that models the independent variable in terms of y, using logarithms.
The question is asking you to solve y = f(x)
You already did this using a constant for y. Do the same thing with y instead of the constant.
y = 4(1.0256^x)
y/4 = 1.0256^x . . . . . . . divide by 4
log(y/4) = x·log(1.0256) . . . . . take logs
log(y/4)/log(1.0256) = x . . . . . divide by the coefficient of x
Now, you have a model for x in terms of y, which is what the question is asking for.
x = log(y/4)/log(1.0256)
When y=12, this is .x = log(12/4)/log(1.0256) ≈ 43.46 weeks
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It cost Cai $1,80 to send 12 text messages, How much would it cost to send 90 text
messages?
Answer:
$13.5
Step-by-step explanation:
cost of 1 text message= $1.80÷12 =$0.15
cost of 90 messages = $0.15×90 = $13.5
Answer: $13.50 for 90 text messages
Step-by-step explanation:
$0.15×90 = $13.5
$0.15 is the unit rate for 1 text message cost.
Drag the tiles to the correct boxes to complete the pairs.
Given: u = <-2, -7>, v = <3, -4>, and w = <5, 1>.
Based on the components of the given vectors, match each vector subtraction with the graph of the resulting vector.
Please help me figure out the correct pairs, godbless the one who answers! (See images attached)
Performing subtraction operations on the given vectors gives;
Graph 1 → u - vGraph 2 → u - wGraph 3 → w - vGraph 4 → v - u Which method can be used to complete the pairs correctly?
u - v = <-2 - 3, -7 - (-4) > = <-5, -3>
Therefore;
Graph 1 → u - vu - w = <-2 - 5, -7 - 1> = <-7, -8>
u - w = <-7, -8> which corresponds with graph 2
Therefore;
Graph 2 → u - ww - v = <5 - 3, 1 - (-4)> = <2, 5>
w - v = <2, 5> which corresponds with graph 3
Therefore;
Graph 3 → w - vv - u = <3 - (-2), -4 - (-7)> = <5, 3>
v - u = <5, 3> which corresponds with graph 4
Therefore;
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What is the measure of angle g, in terms of x? x° x° x° 90° 180° – x° 180° – 2x°
The measure of angle G in terms of x is x+x degrees
Circle theoremThe measure of angle F and angle D is 90 degrees so that;
<GFD = <GDF = 90 - x
Since the sum of angle in a triangle is 180 degrees, hence;
<G + 90 - x + 90 - x = 180
<G + 180 - 2x = 180
<G = 2x
<G = x + x
Hence the measure of angle G in terms of x is x+x degrees
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Answer:A
Step-by-step explanation: math and me go together like mustard and pees
y
T
N
9
6
U
3
M
What is the value of y?
3√3 units
6√3 units
O
9√3 units
O 12√3 units
The value of y from the given figure is 6√3
Pythagoras theoremFrom the given figure, according to the theorem;
H² = 6² - 3²
H² = 36 - 9
H² = 27
H = 3√3
Determine the value of y using the same theorem;
y² = 9² + ( 3√3)²
y² = 81. + 27
y = √108
y = 6√3
Hence the value of y from the given figure is 6√3
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If h (x)=√49-x², find h (0), h (-7) and h (9).
Answer:
Step-by-step explanation:
f(0) = √49 - x^2
f(0) means that wherever you see an x on the right, you put a zero.
so f(0) = √49 - 0^2
f(0) = √49
f(0) = 7
f(-7) = √49 - x^2
Again the meaning is that where you see an x on the right, you substitute - 7 for that x.
f(-7) = √49 - (-7)^2
f(-7) = 7 - 49
f(-7) = - 42
f(9) = √49 - (9)^2
f(9) = 7 - 81
f(9) = - 74
Which of the following terms are possible in the domain of a sequence? Select all that apply.
The terms that are possible on the domain of a sequence are given as follows:
13, 25, 60.
What is a sequence?A sequence is a list containing numbers, that may be related or not. It has a 1st term, 2nd term, and so on until the nth term.
The domain is the indexes of the terms, which starts at one and goes until n, hence the possible numbers are:
13, 25, 60.
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if f(x)=3^x+10x and g(x)=2x-4 find (f-g) (x) (urgent)
Answer:
(f - g)(x) = [tex]3^{x}[/tex] + 8x + 4
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= [tex]3^{x}[/tex] + 10x - (2x - 4) ← distribute parenthesis by - 1
= [tex]3^{x}[/tex] + 10x - 2x + 4 ← collect like terms
= [tex]3^{x}[/tex] + 8x + 4
PLESSEE HELP ME ASAPP
Answer:
option A. is the midpoint of the graph
Find the h.c.f of {x}^{3} + {y}^{3} \: and \: \: {x}^{2} - xy + {y}^{2}x 3 +y 3 andx 2 −xy+y 2
Factorize the sum of cubes:
[tex]x^3 + y^3 = (x+y) (x^2 - xy + y^2)[/tex]
so [tex]x^2-xy+y^2[/tex] is a factor of [tex]x^3+y^3[/tex]. Then the HCF is [tex]\boxed{x^2 - xy + y^2}[/tex].
29. The table below represents the relationship of the price of carrots to their weight in ounces in a market: Price Weight, in oz. $0.377.4 $0.44 8.8 $0.52 10.4 B Another market sells carrots at a rate of $4.80 for every 3 pounds. Which equation represents the market that sells their carrots at a lower rate per pound? y = 0.8x y = 1.2x ) y = 0,4x y = 1.6x
The proportional relationship that represents the market that sells their carrots at a lower rate per pound is: y = 1.6x.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
From the table, the rate is:
k = $8.8/4.4 = 2.
From the market, the rate is:
k = $4.8/3 = $1.6.
Hence the equation is y = 1.6x.
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Consider triangle DEF. The legs have a length of 36 units each. What is the length of the hypotenuse of the triangle 18 units units 36 units units
Answer:
(っ◔◡◔)っ ♥ 36 square root 2 ♥
Step-by-step explanation:
The length of the hypotenuse of the triangle is approximately 48.99 units.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
We can use the Pythagorean theorem to find the length of the hypotenuse of the triangle:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs.
Substituting the values given in the problem.
c² = 18² + 36²
c² = 324 + 1296
c² = 1620
Taking the square root of both sides.
c = √(1620)
Simplifying.
c = 6 √(90) or approximately 48.99
Therefore,
The length of the hypotenuse of the triangle is approximately 48.99 units.
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please answer both asap!!!
does anyone want to play tarkov and run customs or something lol? add me on disc destructer11#0001
Answer:
Step-by-step explanation:
Mabye later