Need help with my math please. Determine the most probable next term in each list of numbers.
Answers
Answer:
23. 216
24. 56
25. 52
26. -7
27. 5
Step-by-step explanation:
Question 23Work out the differences between the terms until the differences are the same:
[tex]1 \underset{+7}{\longrightarrow} 8 \underset{+19}{\longrightarrow} 27 \underset{+37}{\longrightarrow} 64 \underset{+61}{\longrightarrow} 125[/tex]
[tex]7 \underset{+12}{\longrightarrow} 19 \underset{+18}{\longrightarrow} 37 \underset{+24}{\longrightarrow} 61[/tex]
[tex]12 \underset{+6}{\longrightarrow} 18 \underset{+6}{\longrightarrow} 24[/tex]
As the third differences are the same, the sequence is cubic and will contain an n³ term. The coefficient of n³ is always a sixth of the third difference. Therefore, the coefficient of n³ = 1.
To work out the nth term of the sequence, write out the numbers in the sequence n³ and compare this sequence with the sequence in the question.
[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} n&1 & 2 & 3&4&5 \\\cline{1-6} n^3 & 1 & 8 & 27 & 64 & 125 \\\cline{1-6} \sf sequence & 1 & 8 & 27 & 64 & 125 \\\cline{1-6}\end{array}[/tex]
Therefore, the nth term is:
[tex]a_n=n^3[/tex]
So the next term in the sequence is:
[tex]\implies a_6=6^3=216[/tex]
Question 24Work out the differences between the terms until the differences are the same:
[tex]2 \underset{+4}{\longrightarrow} 6 \underset{+6}{\longrightarrow} 12 \underset{+8}{\longrightarrow} 20 \underset{+10}{\longrightarrow} 30 \underset{+12}{\longrightarrow} 42[/tex]
[tex]4 \underset{+2}{\longrightarrow} 6 \underset{+2}{\longrightarrow} 8 \underset{+2}{\longrightarrow} 10 \underset{+2}{\longrightarrow} 12[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term. The coefficient of n² is always half of the second difference. Therefore, the coefficient of n² = 1.
To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.
[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +1 & +2 & +3 & +4 & +5 & +6 \\\cline{1-7} \sf sequence & 2 & 6 & 12 & 20 & 30 & 42 \\\cline{1-7}\end{array}[/tex]
Therefore, the nth term is:
[tex]a_n=n^2+n[/tex]
So the next term in the sequence is:
[tex]\implies a_7=7^2+7=56[/tex]
Question 25Work out the differences between the terms until the differences are the same:
[tex]4 \underset{+3}{\longrightarrow} 7 \underset{+5}{\longrightarrow} 12 \underset{+7}{\longrightarrow} 19 \underset{+9}{\longrightarrow} 28 \underset{+11}{\longrightarrow} 39[/tex]
[tex]3 \underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7 \underset{+2}{\longrightarrow} 9 \underset{+2}{\longrightarrow} 11[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term. The coefficient of n² is always half of the second difference. Therefore, the coefficient of n² = 1.
To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.
[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +3 & +3 & +3 & +3 & +3 & +3 \\\cline{1-7} \sf sequence & 4&7&12&19&28&39 \\\cline{1-7}\end{array}[/tex]
Therefore, the nth term is:
[tex]a_n=n^2+3[/tex]
So the next term in the sequence is:
[tex]\implies a_7=7^2+3=52[/tex]
Question 26Given numbers:
-1, 2, -3, 4, -5, 6
As the list of numbers does not increase or decrease, we cannot apply the same method as the previous questions.
[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} \sf list & -1 & 2 & -3 & 4 & -5 & 6 \\\cline{1-7}\end{array}[/tex]
From comparing the position of the term to its number in the list, we can see that the nth term is the same as n, but the odd numbers are negative and the even numbers are positive.
Therefore, the rule is:
[tex]\implies a_n=n \quad \textsf{where }n \textsf{ is an even natural number}[/tex]
[tex]\implies a_n=-n \quad \textsf{where }n \textsf{ is an odd natural number}[/tex]
So the next term in the sequence is:
[tex]\implies a_7=-7[/tex]
(since 7 is an odd natural number)
Question 27Given numbers:
5, 3, 5, 5, 3, 5, 5, 5, 3, 5, 5, 5, 5, 3, 5, 5, 5, 5
The pattern of these numbers appears to be an ascending number of 5s with a 3 in between:
One 5, followed by a 3Two 5s, followed by a 3Three 5s, followed by a 3Four 5s, followed by a 3Therefore, the next number of 5s will be five. This means the next number in the list will be 5, since there are only four 5s after the last 3.
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Related Questions
What is the approximate radian measure
of an angle with a degree measure of
59.6°?
Answers
Answer:
The approximate radian measure of the angle. So we have 15 nine 0.6 degrees convert degrees to radiance. You have to multiply by pi over 1 80. So if we did that, that'd be 59.6 pi over 1 80. So if we want to know the approximate value, we're going to use the pi button on our calculator to figure out what 59.6 times pi is. That's approximately 187.2389, Divided by 1 80. So now I would divide that number by 180 and that gives me 1.04 radiance, 1.04 radiance is the answer.
Given: circle k(O) with diameter AB and CD ⊥ AB
Prove: AD·CB=AC·CD
Answers
For a circle k(O) with diameter AB and CD ⊥ AB, it is proved that AD·CB=AC·CD, using similarity of triangles.
Given:
circle k(O) with diameter AB
CD ⊥ AB
To Prove: AD·CB=AC·CD
Proof:
In ΔADC and ΔCDB,
∠ADC = ∠CDB = 90°
[∵Both are right angle triangles]
CB = CB [Common side]
⇒ AC / CB = CD / DB
Thus, ΔACD is similar to ΔCDB by RHS similarity.
Therefore, we can write,
AD/CD = AC/CB [Since corresponding sides of similar triangles are proportional]
⇒ AD·CB = AC·CD
Hence proved.
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Please please please help
In a lottery, the probability of the jackpot being won in any draw is
a What is the probability that the jackpot prize will be won in each of four consecutive draws? 1/60^4
b How many consecutive draws need to be made for there to be a greater than 98% chance that at least
one jackpot prize will have been won?
Answers
The probability that the jackpot prize will be won in each of four consecutive draws is (1/60)⁴.
The number of consecutive draws needed will be, n = 233
What is probability?Probability is the likelihood or chance of an event happening or not.
Probability = number of expected outcomes/number of possible outcomes.From the given question, the probability of the jackpot being won in any draw is 1/60.
The probability that the jackpot prize will be won in each of four consecutive draws will be:
1/60 * 1/60 * 1/60 * 1/60 = (1/60)⁴
b. The number of consecutive draws that needs to be made for there to be a greater than 98% chance that at least one jackpot prize will have been won is calculated as follows:
There is a 100% - 98% chance that that none has been won = 2% that none has been won.
Also, the probability of the jackpot not being won in a draw is = 1 1/60 = 59/60
The number of consecutive draws needed will be (59/60)ⁿ ≤ 0.02
Solving for n by taking logarithms of both sides:
n = 233
In conclusion, probability measures chances of an event occurring or not.
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Ethan bought 3 pints of raspberries for $5 per pint and x pints of blueberries for $3 per pint. The average
15 + 3x
3+x
15+ 3x dollars per pint. If the equation y =
=
is graphed in the
3+x
cost of all the berries he bought was
xy-plane, what quantity will be represented by the y-intercept of the graph?
O The total cost, in dollars, of all the raspberries Ethan bought
O The average cost, in dollars per pint, of all the raspberries Ethan bought
O The total cost, in dollars, of all the blueberries Ethan bought
O The average cost, in dollars per pint, of all the blueberries Ethan bought
Answers
The y-intercept represents the average cost, in dollars per pint, of all the raspberries Ethan bought. Therefore, option B is the correct answer.
Given that, Ethan bought 3 pints of raspberries for $5 per pint and x pints of blueberries for $3 per pint.
The average is (15 + 3x)/(3+x) per pint.
We need to find what quantity will be represented by the y-intercept of the graph.
How to find the y-intercept of the graph?Since the y-intercept always has a corresponding x-value of 0, replace x with 0 in the equation and solve for y. On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.
Now, the graph of y=(15 + 3x)/(3+x)is given below.
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (−5,0)
y-intercept(s): (0,5)
So, the y-intercept represents the average cost, in dollars per pint, of all the raspberries Ethan bought.
Therefore, option B is the correct answer.
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What is the number between 8.1 and 8.24?
Answers
Answer:
8.17Step-by-step explanation:
What is the number between 8.1 and 8.24?
Add the numbers and divide by 2 and you will find the average
(8.1 + 8.24) : 2 =
8.17
8.17 is exactly half way between them.
Rajini throws a die. What is the chance of her getting a number 8?
Answers
Answer:
Hey there!
Step-by-step explanation:
This is ur answer...
0/6She has no chance getting an 8 because 8 doesn't exist in a dice....She can get 1-6 only....Hope it helps!
Brainliest pls!
Have a good day!^^
PLEASE ANSWER QUICKLY
Answers
Answer:
f(x) = 5x - 5
Step-by-step explanation:
f(x) = 5x - 5 is a linear equation as it has no power.
Darren wins a coupon for $4 off the lunch special for each of 5 days. He pays $75 for his 5 lunch specials. Write and solve the equation to find the original price p for one lunch special.
Answers
Answer:
19
Step-by-step explanation: (75/5) + 4= p
15+4=p
19=p
The original price for one lunch meal is $19
p = $15 + $4
p = $19
Find a power series representation for the function. (center your power series representation at x = 0. ) f(x) = 1 9 x f(x) = [infinity] n = 0
Answers
The power series representation for the function, so the interval of convergence is (-9,9).
The definition of convergence refers to 2 or more matters coming together, joining collectively, or evolving into one. An example of convergence is when a crowd of people all move collectively into a unified organization.
Convergence is when two or extra matters come collectively to shape a brand new whole, like the convergence of plum and apricot genes within the plucot. Convergence comes from the prefix con-, meaning collectively, and the verb verge, because of this to show closer to.
The simple concept of convergence permits multiple responsibilities to be accomplished on a single device, which efficiently conserves space and power. for example, as opposed to wearing separate devices – like a cell cellphone, digital camera, and virtual organizer – each era converges on a single tool or telephone.
We have given f(x)=1/(9+x)
f(x)=(1/9)*(1/(1-(-x/9))
f(x)=summation of (n=0 to infinity) [1/9*(-x/9)n]
=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]
f(x)=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]
Let an=(-1)n*(xn/9n+1)
using the Ratio Test
L=lim n-->infinity|an+1/anL=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]/[(-1)n*(xn/9n+1)]|
=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]*[9n+1/(-1)n*(xn)]|
=lim n-->infinity|(-1)*(x)/9)|
=|-x/9|<1
x/9<1 and x>9>-1
x<9 and x>-9
x is -9<x<9
for x=9 the series ,summation of (n=0 to infinity) [(-1)n*(9n/9n+1)] =summation of (n=0 to infinity) [(-1)n*(/9)]
=1/9*summation of (n=0 to infinity) [(-1)n]
By the geometric series this summation of (n=0 to infinity) [(-1)n] diverges
=1/9*diverges
the series diverges for x=9
for x=-9 the series ,summation of (n=0 to infinity) [(-1)n*(-9)n/9n+1)] =summation of (n=0 to infinity) [(-1)2n*(/9)]
=1/9*summation of (n=0 to infinity) [(-1)2n]
which is diverges
so the interval of convergence is (-9,9)
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A nonnative fern species is introduced into an area and quickly begins to spread. The number of plants can be modeled by
P(n) = 1,200(1.68)", where n is the number of months since the ferns were introduced. Use this information to complete the
statements.
Select the correct answer from each drop-down menu.
Based on the model, there were initially
The monthly percent rate of change is
This situation is modeled by an exponential
%.
ferns.
function.
Submit
Answers
Based on the information, there were initially 1200 ferns; the monthly percent rate of change is 68% and this situation is modeled by an exponential growth function
How to complete the information?The given parameters from the question are:
P(n) = 1200(1.68)^n
Where
n represent the number of months
An exponential growth function is represented as:
P(n) = a * (1 + r)^n
Where
a represents the initial value
r represents the rate
By comparison, we have
a = 1200
1 + r = 1.68
This gives
r = 0.68 = 68%
Hence, there were initially 1200 ferns; the monthly percent rate of change is 68% and this situation is modeled by an exponential growth function
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1,200
68
growth
Got it right on Edmentum
A meson when at rest decays 2 μs after it is created. If moving in the laboratory at 0. 99C. Its lifetime according to laboratory clocks would be?
Answers
The lifetime of meson according to laboratory clocks would be 14 μs.
In this question,
Meson decay, Δt = 2μs
Velocity, y = 0.99C, where C is the speed of the light
Time measurement depends on the reference frame of clock.
Time dilation, Δt' = y Δt
⇒ [tex]\frac{\Delta t }{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-\frac{(0.99c)^{2} }{c^{2} } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.99^{2} } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.9801 } } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{0.0199} } }[/tex]
⇒ [tex]\frac{2(10^{-6} ) }{0.1410} } }[/tex]
⇒ 14.18 × 10⁻⁶ ≈ 14 μs
Hence we can conclude that the lifetime of meson according to laboratory clocks would be 14 μs.
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A large company has offices in cities across the country. The facilities director of the company was asked to survey employees about their office furniture. Rather than survey all employees in the company, the director decided to take a sample of employees. Which groups would be most representative of the opinions of all employees in the company? Select each correct answer.
A.
5% of randomly selected employees from each office location
B.
Employees with office phone numbers ending in 3 and 7
C.
Employees who are randomly selected by a computer from a list of all company employees
D.
Employees who have worked for the company for more than 10 years
E.
Randomly selected employees in the cafeteria of one of the offices
F.
Employees answering phone calls in the company’s customer service departme
Answers
The groups which would be most representative of the opinions of all employees in the company are: A sample of 5% of randomly selected employees from each office location, Employees who are randomly selected by a computer from a list of all company employees and Employees who have worked for the company for more than 10 years.
Options (A),(C) and (D) are correct.
A sizable business has locations around the nation. The company's facilities director was tasked with asking employees about their office furnishings. Instead of polling every worker at the company, the director chose to select a sample. We are supposed to find the groups which would be most representative of the opinions of all employees in the company.
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Situation:
An archaelogist in Turkey discovers a
spear head that contains 57%of its
original amount of C-14.
Find the age of the spear head to the nearest
year.
Enter the correct answer.
Answers
Answer:
t = 6162 years
Step-by-step explanation:
This equation takes the form of
We are given everything but the amount of C-14 at time t = 0. But we can figure it out from the info we ARE given. We are told that when the spear head is found it contains 54% of its original amount of C-14. Notice we are dealing in percents. If 54% remains when it is found, it started out with 100% of its amount. That's our N value. Filling in:
Our goal is to get that t down from the exponential position that it is currently in. To do that we will need to eventually take the natural log of both sides, because ln's and e's "undo" each other, much like squaring "undoes" a square, or dividing "undoes" multiplication. So we take the natural log of both sides. On the right side, notice that when we take the natural log, the e disappears; it's "undone", gone. Before that, though, we will simplify by dividing both sides by 54. 100/54 = 1.851851852. So, altogether...
Simplifying by plugging the log of that number into our calculator, we get
.6161861395 = .0001t and
t = 6161.8613
Rounding to the nearest year, t = 6162 years
A submarine is descending to examine the seafloor 2,100 feet below the surface. it takes the submarine 2 hours to make this descent. Write an equation to
represent the relationship between the submarine's elevation and time.
Answers
Answer:
Step-by-step explanation:
x = time
y = elevation
At x = 0 , y = 0
It takes the submarine 2 hours to make descent of 2100 ft
=> x = 2 , y = - 2100
Slope = ( -2100 - 0)/(2 - 0) = -1050
y - 0 = -1050 ( x -0)
=> y = -1050x
1050x + y = 0
represent the relationship between the submarine's elevation and time.
Mr. and mrs. smith plan to roof the cabin on 2 consecutive days. Assuming that the chance of rain is independent of the day, what is the probability that it will rain both days?
Answers
The probability that it will rain both days is [tex]\frac{1}{4}[/tex].
According to the question
Mr. and mrs. smith plan to roof the cabin on 2 consecutive days.
Assuming that the chance of rain is independent of the day
Probability is the chance that some event will happen.
It is the ratio of the number of ways a certain event can occur to the number of possible outcomes.
Probability = Number of ways it can occur/Total number of outcomes
Probability of rain on first day = 1/2
Probability of rain on second day = 1/2
Then
Probability of rain on both days = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = 1/4
Hence,
The probability that it will rain both days is [tex]\frac{1}{4}[/tex].
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Work out the circumference of this circle.
Take it to be 3. 142 and give your answer to 1 decimal place.
4 cm
Answers
The circumference of the given circle is 25.1 cm.
According to the statement
we have given that the the radius of circle which is 4cm.
And we have to find the circumference of the circle.
So, For this purpose
The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center.To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).
The formula to calculate it is
C = 2(pi)r
So, substitute the values in it then
Here use pi value is 3.14
C = 2 *3.14*4
C = 25.12.
The circumference of the given circle is according to one decimal place is 25.12 cm.
So, The circumference of the given circle is 25.1 cm.
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Solve: 25x2 − 30 = 0 round the answer to the nearest hundredth. x = −1.10 and x = 1.10 x = −26.15 and x = 1.15 x = 0 x = −0.83 and x = 0.83
Answers
Answer:
(a) x = -1.10 and x = 1.10
Step-by-step explanation:
A straightforward square root will give the value of x.
SolutionDivide by the coefficient of x^2:
x^2 -30/25 = 0
x^2 -1.20 = 0
Add 1.20, and take the square root.
x^2 = 1.20
x = ±√1.20 ≈ ±1.0954
x ≈ -1.10 and 1.10 . . . . . round to hundredths
__
Additional comment
For small values of x, the root of (1+x) is approximately 1+x/2. For a root accuracy to the nearest hundredth, x < 0.21 (as here). For accuracy to the nearest thousandth, x < 0.064.
Geometry: complete this proof, ASAP!!!!!!!!
Answers
Answer:
1. Given
2. Definition of Congruent Angles
3. Triangle Interior Angle Sum Theorem
4. Transitive Property of Equality
5. Substitution Property of Equality
6. Definition of Congruent Angles
please help I don't understand
Answers
Answer:
Each number is increasing by [tex]\frac{1}{4}[/tex]. The next number would be 1 [tex]\frac{1}{4}[/tex] or [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
I am not sure what the question is. I am wondering if they are asking how is the list growing or what would be the next number.
Each number is increasing by 1/4
[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] + [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{2}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex] To change [tex]\frac{1}{2}[/tex] to [tex]\frac{2}{4}[/tex] you multiple the top and the bottom of [tex]\frac{1}{2}[/tex] by2 to get [tex]\frac{2}{4}[/tex]
[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{4}{4}[/tex] or 1
Find the solution for the system of linear equations by substitution: 2x - y = 3 y − x = 1
Answers
The solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2x- y = 3
y - x = 1
Make y the subject in the second equation, by adding x to both sides of the equation
y - x + x = x + 1
This gives
y = x + 1
Substitute y = x + 1 in 2x- y = 3
2x- x - 1 = 3
Evaluate the like terms
x = 4
Substitute x = 4 in y = x + 1
y = 4 + 1
Evaluate
y = 5
Hence, the solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5
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State what additional information is required in order to know the
triangles are congruent using the theorem or postulate listed.
Answers
Answer: line ZX is congruent to line VX (option 4)
Step-by-step explanation:
We already know <X is congruent to <X, we also know that line YX is congruent to line XW. Now all we need is one more line adjacent to X which is going to be ZX ad VX
What equation can be used to find the sum of 4/10 and 7/100
Answers
Answer:
47/100
Step-by-step explanation:
First you have to make the denominators equal.
4/10 * 10/10 = 40/100
40/100 + 7/100 = 47/100
Consider the line 4x + 2y = 8.
What is the slope of a line perpendicular to this line?
Answers
Answer:
supposed to make the subject y then slope is -2
y = mx + b
Subtract 4x from both side
2y = 8 - 4x
Divided each term by 2
y = 4 - 2x
y = -2x + 4
Using the slope-intercept form, the slope is -2
m = -2
The equation of a perpendicular line to y = -2x + 4 must has a slope that is the negative reciprocal of the original slope.
M perpendicular = - 1/-2
Move the negative infront of the fraction
M perpendicular = 1/2
Which of the graphs below represents the equation 3x-2y=-12?
Answers
Answer:
Graph B
Step-by-step explanation:
Transform the given equation into the slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
3x - 2y = -12
2y = 3x + 12
y = 3/2x + 6
Graph B represents y = 3/2x + 6 because it has a y-intercept at (0,6) and a slope of 3/2.
-2y = -3x -12
Y = 3/2x + 6
Slope = 3/2 Andy intercept is 6
So it’s B.
What is the slope?
What is the slope?
What is the slope?
What is the slope?
What is the slope?
Answers
Answer:
okay it's name is Muhammad Deco alfansia ( ◜‿◝ )
Answer:
Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting.
Step-by-step explanation: Hope this helps you!
You randomly choose a block from each
set in the diagram. What is the probability
that you will choose a block labeled with a
Tor a block labeled with a 6?
Answers
Using it's concept, there is a 0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For each block, there are 8 outcomes, since there are 2 blocks, there are 8² = 64 total outcomes. For the desired outcomes, we have that:
There are 8 outcomes with a T and a block from the second square.Removing the 2 outcomes below with a 6 and a T, as they are already counted, there are 7 outcomes with a six.Hence there are 8 + 7 = 15 desired outcomes, and the probability is given by:
p = 15/64 = 0.2344.
0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.
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what are these questions i need help
177
3 is a root of f(x) = x2–93987. Find the other roots of f(x).
Write your answer as a list of simplified values separated by commas, if there is more than one value.
Answers
The roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987
What are quadratic equations?Quadratic equations are equations that have a second degree and have the standard form of ax^2 + bx + c = 0, where a, b and c are constants and the variable a does not equal 0
How to determine the other roots of the equation?The equation of the function is given as:
f(x) = x^2 - 93987
The above equation is a quadratic equation
Express the equation as a difference of two squares
f(x) = (x - √93987)(x + √93987)
Set the equation of the function to 0
(x - √93987)(x + √93987) = 0
Split the factors of the above function equation as follows
x - √93987 = 0 and x + √93987 = 0
Solve for x in the above equations
x = √93987 and x = -√93987
Hence, the roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987
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really confused about b, how to get the position of w. Hope someone could help me.
Answers
Answer + Step-by-step explanation:
(a)
[tex]\overrightarrow{PQ} =a+\frac{3}{5} b[/tex]
(b)
we are given:
[tex]\left\vert \overrightarrow{RQ} \right\vert =\frac{3}{5} \left\vert \overrightarrow{OP} \right\vert[/tex]
Then
[tex]\left\vert \overrightarrow{WR} \right\vert =\frac{3}{5} \left\vert \overrightarrow{WO} \right\vert[/tex]
and we know that :
[tex]\overrightarrow{OW} = \overrightarrow{OR} + \overrightarrow{RW}[/tex]
Then
[tex]\overrightarrow{OW} = a +\frac{3}{5} \overrightarrow{OW}[/tex]
Then
[tex]\frac{2}{5} \overrightarrow{OW} = a[/tex]
Then
[tex]\overrightarrow{OW} = \frac{5}{2} a[/tex]
help please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111
Answers
Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.
Given solution of a question done by two people.
Jenna's method
5(30+4)
(5)(30)+(5)(4)
150+20=170
Mia's method
5(30+4)
5(34)=170
We are required to find why they have achieved at the same answer.
Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.
Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.
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A flat of plants contains 12 plants. yoshi wants a garden that has three rows with 10 plants per row. write and solve an equation for the number of flats yos should buy.
Answers
Yoshi should buy 3 flats.
What is an equation?The equation is a statement of equality between two expressions that contain variables and/or integers. In essence, equations are questions, and the development of mathematics has been driven by efforts to discover systematic answers to those questions.To find how many flats Yoshi should buy:
First, determine how many plants Yoshi requires in total. Multiply 3 by 10 so the garden will have three rows of ten plants each.3 × 10 = 30 total plantsAfter that, divide this value by the number of plants in a flat.30 / 12 = 2.5 flatsIf Yoshi is unable to purchase half the apartments, this figure must be rounded up to 3 flats.Therefore, Yoshi should buy 3 flats.
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