Since you know the sequence is quadratic, we can find constants a, b, and c such that the n-th term of the sequence (denoted by f(n)) is
[tex]f(n) = an^2 + bn + c[/tex]
We're given f(1) = 3, f(2) = 11, and f(3) = 25. (We have three unknowns, so we only need three conditions.) Solve for the constants:
[tex]\begin{cases}f(1) = a + b + c = 3 \\ f(2) = 4a + 2b + c = 11 \\ f(3) = 9a + 3n + c = 25 \end{cases} \implies a=3, b=-1, c=1[/tex]
Then the n-th term of the sequence is
[tex]f(n) = \boxed{3n^2 - n + 1}[/tex]
The area of a triangle is 273 square centimeters. If the base is 21 centimeters what is the height?
Th anwse is d) :B k .............
A coin is flipped 8 times. Find the probability of the event: exactly 5 heads a. 0.625 b. 0.03125 c. 0.219 d. 0.0039
The probability of the event of getting exactly 5 heads in 8 tosses of a coin(assuming unbiased coin) is given by: Option C: 0.219 (approximately).
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]
For this case, we've got:
A coin is flipped 8 times.To find: P(getting exactly 5 heads)Each coin flip is a bernoulli distribution as it has two possible outcomes (assuming any other outcome like coin landing standing straight etc ignored). Take success = getting head in a flip, and failure = not getting success= not getting head = getting tail as the outcome of the flip.
Now, each of those 8 flips are independent in terms of result of each other (assuming coin stays unbiased).
If we take:
X = number of heads out of those 8 flips = number of successes in those 8 bernoulli trials, then:
[tex]X \sim B(n = 8, p)[/tex]
where p is the probability of success = P(Getting head in an unbiased coin with head or tail as only possible outcomes) = 1/2 = 0.5 (as head can come in 1 way, and total outcomes is 2, all equally likely).
Thus, we get:
[tex]X \sim B(n = 8, p=0.5)[/tex]
Now, P(Exactly 5 heads in those 8 flips) = P(X = 5)
Using the probability function of the binomial distribution, we get:
[tex]P(X = 5) = \: ^8C_5(0.5)^5(0.5)^{8-5} = \dfrac{8\times 7\times 6\times 5\times 4}{5 \times 4 \times 3\times 2 \times 1} \times (0.5)^8 \approx 0.219[/tex]
Thus, the probability of the event of getting exactly 5 heads in 8 tosses of a coin(assuming unbiased coin) is given by: Option C: 0.219 (approximately).
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50 POINTS NO LINKS
An object is launched at 39.2 meters per second (m/s) from a 42.3-meter tall platform. The equation for the objects height s at time t seconds after launch is s(t)=-4.9t^2+39.2t+42.3, where s is in meters. Create a table of values and graph the function. Approximately what is the maximum height of the object?
Convert into vertex form y=a(x-h)²+k
y=-4.9t²+39.2t+42.3After calculating
y=-4.9(x-39.2)²+42.3Vertex at
(39.2,42.3)Max height=42.3m
Graph attached
What us the value of x? This question is pretty easy…. My brain has just given out!
Answer: 10
Step-by-step explanation:
if sid has 15 mangoes and sera has 6 apples , what is the total number of fruits with sidra ?
[tex] \\ \\ \\ [/tex]
thankyou ~
[tex] \huge \mathfrak \red{HeY \: ThErE♡}[/tex]
Given,No. of mangoes sid has = 15
No. of apples sera has = 6
Therefore, we gonna add them-,-Total no. of fruits Sidra will have = 15 + 6 = 21
Therefore,Sidra will have 21 fruits.[tex] \huge \mathfrak \red{HoPe \: It \: HeLpS♤}[/tex]
estimate 259+372 by rounding each number to the nearest 10
Answer: ok well the answer is 631 if it were rounded it would be 630
Now if u mean those 2 numbers they would be 259:260 and 372:370 there hope it helps bye!
The table of values represents a continuous function. Which type of function describes g(x)?
Rational
Polynomial
Logarithmic
Exponential
A logarithimic function is a function of the sort; loga(a^x) = x. The function that is described by g(x) is a logarithmic function.
What is a lograithimic function?A logarithimic function is a function of the sort; loga(a^x) = x. We now have to look at this table to ascertain of this condition is met.
Given this condition, we can see that each of the entries in the table satisfies this basic criterion of a logarithmic function hence, the function that is described by g(x) is a logarithmic function.
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Answer:
Exponential
Step-by-step explanation:
The function g(x) described by the given table of values is most likely an exponential function because x increases by a constant factor and the values of g(x) increase or decrease by a consistent factor. This behavior aligns with the characteristics of an exponential function, where the variable x appears in the exponent. I put polynomial as my answer on the test and got it incorrect and then realized the answer was exponential.
Which expression is equivalent to 4(2n) + n?
A : 8n
B : 9n
C : 6n + n
D : 8n + n
Answer:
B and D.
Step-by-step explanation:
4(2n) + n
= 8n + n
= 9n.
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
[tex] \large\underline{ \boxed{ \sf{✟\:Important\: point's✟ }}}[/tex]
we can easily check whether the given expression is equivalent or not by simply solving the expression by fôllowling algebraic rule→ Your given expression:- 4(2n)+n
★ Let's solve:-➤4(2n)+n➤distributing 4 with 2n gives you ➤8n+n➤then adding like terms➤9n☆ Hence option b (9n) is right ans
[tex]\pink{\underline{ \underline{ \boxed{ \sf{✰\: Option.\:B✓ }}}}}[/tex]
Hope it helps !
A camera has a listed price of 643.99 before tax. If the sales tax rate is 9.75%, find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answer: $1,271.88
Step-by-step explanation:
The total cost of the camera with sales tax included will be 100% plus our sales tax:
100% + 9.75% = 109.75%
Dividing a percent (%) by 100 gives us a decimal:
109.75% / 100 = 1.975
We can multiply this decimal by the listed price of the camera to find our answer
643.99 * 1.975 = $1,271.88
The camera will cost $1,271.88 with sales tax.
compare 2 1/4 ? 3 1/4
A) >
B) <
C) =
Answer:
B
Step-by-step explanation:
EZ
Match the verbal expression (term) with its algebraic expression (definition).
Match Term Definition
Four less than an unknown value A) y − 4
Quotient of a variable and four B) b + 4
Some number to the power of four C) a4
Four times an unknown value D) 4x
Four more than some number E) z ÷ 4
A) y − 4
Four less than an unknown value
B) b + 4
Four more than some number
C) a^4
Some number to the power of four
D) 4x
Four times an unknown value
E) z ÷ 4 =
Quotient of a variable and four
2/5+3/8 5th grade Math. Please help.
Answer:
31/40
Step-by-step explanation:
Given expression:
[tex]\dfrac{2}{5} + \dfrac{3}{8}[/tex]
Note: Both fractions must have same denominators if we want to perform addition, subtraction, multiplication, or division.
The only way to simplify this expression is to have a common denominator, which can be determined by the LCM of 5 and 8.
⇒ Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45...⇒ Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72...Multiply the denominators with such a number that is equivalent to 40.
Note: The number you are multiplying should also be multiplied to the numerator.
[tex]\rightarrow \dfrac{2 \times 8}{5 \times 8} + \dfrac{3 \times 5}{8 \times 5}[/tex]
[tex]\rightarrow \dfrac{16}{40} + \dfrac{15}{40}[/tex]
Finally, simplify the expression to determine the solution.
[tex]\rightarrow \dfrac{31}{40}[/tex]
Since 31 is a prime number, we can't simplify this fraction. Thus, the final answer is 31/40.
Ah yes, adding fractions! Adding fractions can be a bit of a pain.
So, we have [tex]\frac{2}{5} + \frac{3}{8}[/tex].
To add fractions, the bottoms, or denominators, must be the same number. So we must multiply the fractions by certain numbers to make the denominators the same number. So let's go easy and make the denominator 40, because 8 goes into 40 and so does 5. So, to make 8 become 40, we'll multiply the whole fraction by 5. For 5, we'll multiply by 8.
[tex]5 * \frac{3}{8} = \frac{15}{40}[/tex]
[tex]8 * \frac{2}{5} = \frac{16}{40}[/tex]
Now we'll add the two fractions. When we add fractions we only add the tops, the numerators.
[tex]\frac{15}{40}+\frac{16}{40} = \frac{31}{40}[/tex]
Then we must reduce (or try to reduce). This fraction cannot be reduced, so the answer is simply [tex]\frac{31}{40}[/tex].
I hope this helps you understand.
-Toremi
Use the expression 4(8 + 3x) to answer the following: Part A: Describe the two factors in this expression. (4 points) Part B: How many terms are in each factor of this expression? (4 points) Part C: What is the coefficient of the variable term? (2 points)
Given : 4(8 + 3x)
To Find : Describe the two factors in this expression
How many terms are in each factor of this expression
coefficient of the variable term
Solution:
4(8 + 3x)
two factors in this expression are
4 and ( 8 + 3x)
terms in each factor of this expression
1 term in 4
2 terms in (8 + 3x)
coefficient of the variable term is 3 in factorized form
4(8 + 3x) = 32 + 12x
and coefficient of the variable term is 12 in expanded form
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Using factor theorem, factorize each of the following polynomial ...
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Factorise: 1. a3 – 4a2 + 12 – 3a 2. a3x – x4 + a2x2
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Richard owns a restaurant. He needs to buy at least 300 glasses. Tall glasses cost $2.50. Short glasses
cost $2.10. He can spend at most $670. Which system of inequalities can Richard use to find the possible
numbers of tall glasses, I, and short glasses, s, he can buy?
Answer:
l+s≥300
2.5l+2.1s≤670
Step-by-step explanation:
Hii can you help me? 6/2(1+2)
I really stink at math :(
Answer:
6/2(1+2)
First lets simplify whats in the parentheses
6/2(3)
So thats 6/2 * 3
6/2 = 3
3*3 =
9
Answer:
9
Step-by-step explanation:
first, you do (1+2) which is 3 and then you do 6/2 which is 3 then 3x3 is 9
Suppose the dimensions of a rectangle with a perimeter of 18 inches are quadrupled. Find the perimeter of the new rectangle in inches
The new perimeter of the rectangle if the dimensions are quadrupled would be 72 inches.
What are the side lengths of the first triangle?The perimeter is always obtained by adding all the sides. This means the possible side lengths of the original rectangle are:
5 inches + 5 inches + 4 inches + 4 inchesWhat are the side lengths of the new triangle?5 inches x 4 = 20 inches
4 iches x 4 = 16 inches
What is the new perimeter?20 + 20 + 16 +16= =72 inches
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x= -1/8y2
The focus of the parabola is:
O (0, -2)
O (2, 0)
O (-2, 0)
x=-1/8y²
Interchange x and y
y=-1/8x²Compare to Vertex form y=a(x-h)²+k
a=-1/8Now
1/4a1/4(-1/8)-2.So
Focus (-2,0)
Answer:
(-2, 0)
Step-by-step explanation:
Standard form of a parabola with a horizontal axis of symmetry:
[tex](y-k)^2=4p(x-h)\quad \textsf{where}\:p\neq 0[/tex]
[tex]\textsf{Vertex}=(h, k)[/tex]
[tex]\textsf{Focus}=(h+p,k)[/tex]
Given equation:
[tex]x=-\dfrac18y^2[/tex]
Rewrite in standard form:
[tex]\implies (x-0)=-\dfrac18(y-0)^2[/tex]
[tex]\implies -8(x-0)=(y-0)^2[/tex]
[tex]\implies (y-0)^2=-8(x-0)[/tex]
Comparing with the general standard form:
k = 0h = 04p = -8 ⇒ p = -2Therefore:
[tex]\textsf{Vertex }(h,k)=(0,0)[/tex]
[tex]\textsf{Focus }(h+p,k)=(0-2,0)=(-2,0)[/tex]
Year Speed 1 38 2 46 3 52 4 57 5 61 3) During which time period was the ANNUAL rate of increase of the speed the GREATEST? HELP FAST
A) from year 1 to year 2
B) from year 1 to year 3
C) from year 1 to year 4
D) from year 1 to year 5
Answer: A) from year 1 to year 2
Step-by-step explanation: subtract 46-38=8, I also just took the K12 test and got it right.
Answer:
A) from year 1 to year 2
Step-by-step explanation:
A politician wants to estimate the proportion of constituents favouring a controversial piece of proposed legislation. Suppose that a 99% confidence interval that extends at most 0.05 on each side of the sample proportion is required. How many sample observations are needed?
Answer:
I pressed this by an accident
What is the perimeter?
Answer:
i believe your answer is 41,
Step-by-step explanation:
because to find perimeter, you simply have to add up all of the sides unlike area where you have to multiply, giving you 18+18+2+2=41 for your answer
Answer:
41
Step-by-step explanation:
add up all the sides total to 41
Please help I'll mark brainliest
Answer:
The godsStep-by-step explanation:
Heroes in Greek Mythology were men or women of special strength, courage, or ability. They were often of divine ancestry and noted for superhuman courageous acts.
What makes a hero in Greek Mythology?
Having one immortal parent. Being born into royalty. Having an unusual conception or birth. Being favored by the gods. Being the subject of a prophesy. Being abandoned at birth or while very young. Performing an amazing feat at a young age. Going on a quest.Help help help math math
Answer:
5a + 1
Step-by-step explanation:
3a + 2a = 5a
2 - 1 = 1
So now we rewrite the problem.
5a + 1
combine like variables and combine whole numbers
2+3a-1+2a
2-1 is 1
and 3a+2a is 5a
so this is 5a+1
Hope this helped
What amount of Interest will be charged on $6500 borrowed for 5 months at a simple
Interest rate of 6%
Answer:
162.50
Step-by-step explanation:
6500 * 5/12 * .06 =
can someone help with this please
Y=mx+b form:
y<2/5x+2
y ≥ -1/2x+3
I forgot how to do the inequalities :)
Step-by-step explanation:
26. The solutions given by the quadratic formula are
integers. (1 point)
O sometimes
O always
O never
Show that the set a = (1, 2, 1); b = (0, 1, 0); c = (-2, 0, 2) is linearly dependent.
By definition of linear independence, the vectors in the set {a, b, c} are independent if
[tex]k_1\vec a+k_2\vec b+k_3\vec c=\vec0[/tex]
can only be obtained with the choice of k₁ = k₂ = k₃ = 0.
This vector equation corresponds to the system of linear equations
[tex]\begin{cases}k_1 - 2k_3 = 0 \\ 2k_1 + k_2 = 0 \\ k_1 + 2k_3 = 0\end{cases}[/tex]
The first equation says k₁ = 2 k₃, while the third one says k₁ = -2 k₃. This can only be possible if k₁ = k₃ = 0, and from the second equation it follows that k₂ = 0. So the given set is linearly independent (and *not* dependent).
The hopper bin in the picture below is modeled by the two-dimensional figure beside it. The hopper bin is
composed of a cylinder, and 2 EQUAL cones. Let d be the center of the base of the cone.
52° cylinder cones
The diameter of the hopper is 36 ft and the height of the cylindrical portion is 20 ft. The measure of the acute
angle formed by the slant height of the cone and its base is 52°, determine and state, to the nearest cubic foot,
the volume of the hopper bin.
The hopper bin was constructed to hold a maximum of 500,000 pounds of feed. If feed weighs 22 pounds per cubic foot, can the carnival tent be filled to 85% of its volume and not exceed the weight limit? Justify your
answer.
The volume of the hopper bin is the amount of feed in it
The volume of the hopper bin is 35974 cubic feetThe carnival tent can be filled to 85% of its volume and not exceed the weight limitThe volume of the hopper bin
The given parameters are:
Height of cylinder, H = 20 ftDiameter of cylinder, D = 36 feetAngle, θ = 52°Start by calculating the radius (r) of the cones.
r = D/2 -------- because the cones and the cylinder have equal diameters.
So, we have:
r = 36/2 = 18
The height (h) of the cones is:
tan(θ) = h/r
This gives
tan(52) = h/18
Make h the subject
h = 18 * tan(52)
Evaluate
h = 23.04
The volume is then calculated as:
Volume = Volume of cylinder + 2 * Volume of cone
This gives
Volume = πr^2H + 2 * 1/3πr^2h
Volume = πr^2H + 2/3πr^2h
Factor out πr^2
Volume = πr^2(H + 2/3h)
Substitute known values
Volume = 3.14 * 18^2 * (20 + 2/3 * 23.04)
Evaluate
Volume = 35973.85 cubic feet
Hence, the volume of the hopper bin is 35974 cubic feet
The weight limit of the hopper binThe given parameters are:
Maximum weight = 500000 poundsFeed weight = 22 pounds per cubic feetFor a feed that weighs 22 pounds per cubic feet, the weight of the hopper bin would be:
Weight = 22 * 35974 pounds
Weight = 791428 pounds
At 85% full, the weight wuld be:
Weight = 85% * 791428 pounds
Weight = 672713.8 pounds
672713.8 pounds is greater than the weight limit of 500000 pounds.
Hence, the carnival tent can be filled to 85% of its volume and not exceed the weight limit
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Please solve and show work!!! Need by tomorrow look at attached photo!!<44
Answer:
1.
First, I would solve for ACB.
Calculations:
63° = y?
I would do that because I know that angle 'y' is vertical to 63°, which is given. (Also vertical angles are congruent, meaning that the measure the same degrees).
2.
Second, I would solve for BAC.
Calculations:
x + 63 + 85 = 180
x + 148 = 180
-148 -148
x = 32°
I would do that because I know that there are two given angles so I could easily solve for the leftover angle, 'z', using the a + b + c = 180° formula.
3.
Next, I would solve for CED.
Calculations:
x + 130 = 180
-130 -130
x = 50°
I would do that because I know finding this angle will help me find angle CDE.
4.
Finally, I would solve for CDE.
Calculations:
x + 63 + 50 = 180
x + 113 = 180
-113 -113
x = 67°
I would do that because I know there are now two given angles so I could easily solve for the leftover angle, x, using the a + b + c = 180° formula.
please help me find the answer
Answer:
the angle is equal to 60 degree
Calculate the distance between the points G=(-2, 2) and C = (5, -1) in the coordinate plane.
=
Give an exact answer (not a decimal approximation).
Answer: sqrt(58)
Step-by-step explanation: