Answer and Step-by-step explanation:
Alot of these can be solved with the table up above the problems.
A, B, and C.
According to the table, every time a value has an exponent of 0, it would equal to 1. Since all A B and C values follow the 0 exponent, their value is 1.
D.
According to the table, when we have a negative exponent, the number gets turned into a fraction of \(\frac{1}{x^x}\)
Since our value is 9^-2, do as followed :
\(\frac{1}{9^2}\)
Solve what is 9^2 :
\([\frac{1}{81} ]\)
E.\(\frac{1}{x^{-5} }\)
This question is different, since we have to go backwards, we have to switch the negative exponent to a positive exponent and rid the fraction.
\(x^5\)
F.\(5a^3b^{-2}\)
Since we have one negative exponent, follow the fraction rule but instead of having one as the numerator, have 5a^3.
\(\frac{5a^3}{b^{2}}\)
Fill in the table :\(-3^4 = -3*-3*-3*-3=-81\)
Since -3 is in parenthesis, we can rid the negative along with the parenthesis :
\((-3)^4=3^4=3*3*3=81\)
Follow the negative exponent rule :
\((-3)^{-4}=\frac{1}{(-3)^4} =\frac{1}{3^4} =\frac{1}{3*3*3*3}= \frac{1}{81}\)
Follow the negative exponent rule yet again :
\(-3^{-4}=-\frac{1}{3^4} =-\frac{1}{3*3*3*3} =-\frac{1}{81}\)
Convert 25 centimeters to inches
Answer:
9.84252 inches the conversion of centimeters to inches is cm/2.54=in
Step-by-step explanation:
9.45in
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find an equation of the line passing through the given points use function notation to write the equation (2, 0) and (4, 6)
ANSWER
f(x) = 3x - 6
EXPLANATION
The equation of a line is:
\(f(x)=mx+b\)where m is the slope and b is the y-intercept.
The formula for the slope of a line passing through points (x1, y1) and (x2, y2) is:
\(m=\frac{y_1-y_2}{x_1-x_2}\)So the slope for this line is:
\(m=\frac{0-6}{2-4}=\frac{-6}{-2}=3\)For now we have :
\(f(x)=3x+b\)To find the y-intercept b we have to replace with one of the points and solve for b:
\(\begin{gathered} f(2)=0=3\cdot2+b \\ 0=6+b \\ b=-6 \end{gathered}\)So the equation is:
\(f(x)=3x-6\)what is 19ft in diameter
assume the random variable x is normally distributed with mean μ=90 and standard deviation σ=15. compute the probability p(x>102)
The probability that x is greater than 102 is approximately 0.2119.
We need to standardize the random variable x before finding the required probability.
The standardized random variable Z is given by:
Z = (x - μ) / σ
Here, x = 102, μ = 90, and σ = 15.
So,
Z = (102 - 90) / 15 = 0.8
Now, we need to find P(Z > 0.8). We can use a standard normal distribution table or calculator to find this probability.
Using a standard normal distribution table, we find that the probability of Z being greater than 0.8 is approximately 0.2119.
Therefore,
P(x > 102) = P(Z > 0.8) ≈ 0.2119
So, the probability that x is greater than 102 is approximately 0.2119.
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What are the correct answers
NEED ANSWER ASAP PLEASE
Answer:
Step-by-step explanation:
4) A photograph costs $20, so the cost of x photographs is 20x.
Similarly, the cost of y prints is $25.
So the total cost is 20x+25y, and this has to be less than or equal to 400, so C.
5) just plug each pair in.
For example for the first option, x=5 and y=10, and since 20(5)+25(10)=100+250. which is less than or equal to 400, it works.
Elmhurst School organized an ice cream social for the incoming sixth graders. At the social, 7 students chose vanilla ice cream for every 5 that chose chocolate ice cream.
Pick the diagram that models the ratio in the story.
If 84 students chose vanilla ice cream, how many students chose chocolate ice cream?
students
60 students chose chocolate ice cream If 84 students chose vanilla ice cream.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, Elmhurst School organized an ice cream social for the incoming sixth graders. At the social, 7 students chose vanilla ice cream for every 5 that chose chocolate ice cream.
Since,
The ratio of students who choose vanilla ice cream to chocolate ice cream is: 7/5
Thus,
for every students choose chocolate ice cream = 5/7 student who chooses vanilla ice cream
If 84 students chose vanilla ice cream
Thus, students choose chocolate ice cream = 5/7 * 84
students choose chocolate ice cream = 12* 5
students choose chocolate ice cream = 60
Therefore, If 84 students chose vanilla ice cream, 60 students chose chocolate ice cream.
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Practice Your Skills
1. Find the five-number summary for each data set.
a. (5,5, 8, 10, 14, 16, 22, 23, 32, 32, 37, 37, 44, 45, 50}
MIN:
Q1:
MEDIAN:
Q3:
MAX:
HELP PLEASE THIS IS HARD!!!
Solve and check
6x - 5x + 7x = 34
Answer:
Step-by-step explanation:
6x-5x+7x=34
x+7x=34
8x=34
x=\(\frac{34}{8}\)
Answer:
X= 5 2/3
Step-by-step explanation:
Combine Like terms
6x=34
Inverse Operation
x=35/6
Simplify
X=5 2/3
The speed of a powerboat in still water is 35 mi/h. It is traveling on a river that flows directly south
at 8 mi/h.
a. The boat heads directly west across the river. What are the resulting speed and direction of the boat? Round answers to the nearest thousandth.
(DONE)
b. At what angle should the boat head upriver in order to travel directly west?
??????
wouldn’t it still be west??
a) The resultant speed is 35.9 mi/hr
c) The angle is 77 degrees
What is the resultant speed?Resultant speed refers to the speed of an object when it is moving in a particular direction as a result of two or more velocities acting upon it. The resultant speed is the vector sum of the individual velocities.
The concept of resultant speed is important in physics and engineering, where it is used to analyze the motion of objects and to calculate their trajectories and velocities.
The resultant speed can be c;
c^2 = 35^2 + 8^2
c = √35^2 + 8^2
c = 35.9 mi/hr
Then angle is;
Tan-1(35/8)
= 77 degrees
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What is the product of -3 and 5?
0-15
0 -8
O 15
- 3 × 5 = - 15
.....................
A family buys 5 airline tickets online. The family buys travel insurance that costs $18 per ticket. The total cost is $875. Let x represent the price of one ticket. What is the price of one ticket?
157 dollars per ticket
Show work
5 tickets times 18 dollars equals 90 dollars
875 minus 90 dollars in insurance equals 785
785 dollars divided by 5 tickets equals $157
Hey i just need some help with this question thanks :)
Let's factor by grouping.
2n^2 + 7n + 5
2n^2 + 2n + 5n + 5
(2n^2 + 2n) + (5n + 5)
2n(n + 1) + 5(n + 1)
(2n+5)(n+1)
If 2n^2+7n+5 is prime, then one of the factors 2n+5 or n+1 must be 1. This is because a prime number can only be factored into 1 times itself. Example: 7 = 7*1.
Let's set each factor equal to 1 and see what happens.
2n+5 = 1 leads to n = -2. But it was stated that n > 0. So we rule out this case.n+1 = 1 leads to n = 0. This is ruled out as well since n > 0.It is impossible for (2n+5)(n+1) to be prime since none of the factors is 1. Therefore, (2n+5)(n+1) = 2n^2+7n+5 is composite for positive integers n = 1, 2, 3, ...
--------------
Another way to think about it:
2n^2 + 7n + 5 = (2n+5)(n+1)
Since n > 0 both 2n+5 and n+1 are larger than 1.
This means we have two different positive factors. These factors may be prime or composite. They multiply to some composite value.
Example: If n = 4 then
(2n+5)(n+1) = (2*4+5)(4+1) = 13*5 = 65
Answer:
There are no positive integer solutions for n.
Step-by-step explanation:
A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. Therefore, the factors of a prime number are limited to 1 and the number itself.
To find all positive integers n such that 2n² + 7n + 5 is a prime number, first factor the quadratic.
\(2n^2+7n+5\)
\(= 2n^2+2n+5n+5\)
\(= 2n(n+1)+5(n+1)\)
\(= (2n+5)(n+1)\)
As the factors of a prime number are limited to 1 and the number itself, set each factor to 1 and solve for n:
\(\begin{aligned}2n+5&=1\\2n&=-4\\n&=-2\end{aligned}\) \(\begin{aligned}n+1&=1\\n&=1-1\\n&=0\end{aligned}\)
Since -2 and 0 are not positive integers, it is therefore not possible for 2n² + 7n + 5 to be a prime number for any positive integer value of n.
Hence, there are no positive integer solutions for n in this case.
Write the point-slope form of the equation for a line that passes through (6, –1) with a slope of 2.
The value of x1 is
.
The value of y1 is
.
The point-slope form of the equation is
Answer: See photo for details.
Step-by-step explanation:
If I1 ⊇ I2 ⊇ .... In ⊇... is a nested sequence of intervals and if In = [an; bn], show that a1 ≤ a2 ≤ ....... ≤ an ≤ ........ and b1 ≤ b2 ≤..... bn ≤ ......
The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:
1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.
To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.
First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.
Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.
We can continue this process for all the intervals in the sequence, until we reach In. So we have:
a1 ≤ a2 ≤ ... ≤ an-1 ≤ an
and
b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn
This shows that the endpoints of the intervals are ordered in the same way.
Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:
Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:
1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.
Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .
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Can someone help to solve this
6x^3 / x^2 =?
Answer:
6x^3
x^2
Canceling the power we get
6x
1
Hence the answer is 6x
A bicycle has a listed price of $563.95 before tax. If the sales tax rate is 8.75%, find the total cost of the bicycle with sales tax included.
Round your answer to the nearest cent, as necessary.
Answer:
$613.30
Step-by-step explanation:
8.75% = 0.0875
8.75% of $ 563.95 is $ 0.0875*563.95
$ 0.0875*563.95 is tax in dollars
the total cost = $ 563.95 + $ 0.0875*563.95 = $ 613.295 = $613.30
Find an equation for the plane consisting of all points that are equidistant from the points (1,0,-2) and (3,4,0).
The midpoint formula and the normal vector of the plane can be used to determine the equation of the plane that contains all points equidistant from the points (1,0,-2) and (3,4,0).
How is this determined?Given by: The midpoint of the two points is:
M = [(1 + 3)/2, (0 + 4)/2, (-2 + 0)/2] = (2, 2, -1) (2, 2, -1)
The following vector runs between the two points:
V = (3 - 1, 4 - 0, 0 - (-2)) = (2, 4, 2) (2, 4, 2)
The cross product of two non-parallel plane vectors yields the normal vector to the plane. The midpoint M to a point on the plane is one such vector, while the other is the vector V. Consider the point P = (2, 2, -1) + t(2, 4, 2) as an illustration, where t is a scalar.
The normal vector is then provided by:
N = V x (P - M) = (2, 4, 2) x (2t, 4t, 2t -1), which equals (12t, -8t, 4t + 2)
The point-normal form, which makes use of the normal vector N and the point M, can be used to determine the equation for the plane:
(x - 2) * 12t = (y - 2) * -8t = (z + 1) * 4t + 2
The final equation of the plane is obtained by multiplying both sides of the equation by t and setting t 0.
12(x - 2) = -8(y - 2) = 4(z + 1) + 2
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Norma is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a total of $89. Norma will be earning a base salary of $57 per month from the gym, plus an additional $4 for every class she teaches. If Norma teaches a certain number of classes during her first month as an instructor, she will earn back the amount she spent on certification. How much will Norma's expenses and earnings be? How many classes will that take?
Norma's expenses and earnings will both be $89, and she needs to teach 8 classes during her first month to earn back her certification cost.
To calculate Norma's expenses and earnings, we need to first determine how many classes she needs to teach to earn back her certification cost.
Let x be the number of classes Norma teaches in her first month.
Her earnings for the first month will be her base salary plus the additional amount per class, which can be represented as 57 + 4x.
To find out how many classes Norma needs to teach to cover her certification cost, we can set up the equation:
57 + 4x = 89
Now, we need to solve for x:
4x = 89 - 57
4x = 32
x = 8
So, Norma needs to teach 8 classes to earn back her certification cost.
Now, we can calculate Norma's total expenses and earnings for the first month.
Her expenses are the certification cost, which is $89.
Her earnings are the base salary plus the additional amount per class:
Earnings = 57 + 4 * 8
Earnings = 57 + 32
Earnings = $89.
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1.-En una estación de autobuses de la Ciudad de México hay dos líneas que llevan a Cuautla, Morelos. Ambas tienen salidas desde las 6:00 am, la primera, tiene salidas cada 15 minutos y la segunda cada 20. Si los primeros camiones de ambas líneas salen a las 6:00, ¿a qué hora coincidirán nuevamente en la salida?
2.-Tita está haciendo unos recuerdos y está colocando dulces en ellos. Tiene 48 paletas de malvavisco y 32 bolsitas de lunetas. Quiere repartirlos en partes iguales y que a cada familiar le toque el número mayor de dulces y de manera exacta. Calcula el número máximo que le puede tocar a cada persona, cuánto le toca a cada uno y hasta cuántos recuerdos puede hacer.
Answer:
1) 7 : 00 am, 2) 3 paletas de malvavisco, 2 bolsitas de lunetas, 16 recuerdos.
Step-by-step explanation:
(Both exercises are written in Spanish. Hence, explanations will be held in that language)
1) Las ecuaciones que describen el tiempo transcurrido en función del número de salidas de cada línea son, respectivamente:
Primera Línea
\(t_{1} = 15\cdot n_{1}\)
Segunda Línea
\(t_{2} = 20\cdot n_{2}\)
Donde t se mide en minutos. La siguiente relación se obtiene a partir de de igualar y sustituir el tiempo de ambas ecuaciones.
\(15\cdot n_{1} = 20\cdot n_{2}\)
La siguiente relación es construida:
\(n_{1} = \frac{20}{15}\cdot n_{2}\)
\(n_{1} = \frac{4}{3}\cdot n_{2}\)
Tanto \(n_{1}\) como \(n_{2}\) son números naturales, si \(n_{2} = 3\), entonces:
\(n_{1} = 4\)
Finalmente, el tiempo transcurrido es:
\(t_{1} = 15\cdot (4)\)
\(t_{1} = 60\,min\)
En consecuencia, las salidas coincidirán a las 7 : 00 am.
2) El máximo número de recuerdos es determinado por el menor número de determinados dulces. Las bolsitas de lunetas representan el limitante, la razón de paletas de malvavisco a bolsitas de lunetas es:
\(x = \frac{48\,m}{32\,l}\)
\(x = \frac{3\,m}{2\,l}\)
La proporción óptima es de 3 paletas de malvavisco por cada 2 bolsitas de lunetas. Entonces, el máximo número de recuerdos es:
\(y = \frac{32}{2}\)
\(y = 16\)
El máximo número de recuerdos es 16.
Please help, having trouble with geometry word problems. Tysm if you do :)
Hi!
So let's start with some variables.
w is width
L is length.
The length is 4 less than 5 times the width. Let's put that into an equation.
L = 5w - 4
The perimeter is 76.
The perimeter is L + L + w + w or
perimeter = 2L + 2w.
Which means that 1/2 of the perimeter = L + w.
We know the perimeter is 76, so half of 76 is 38.
38 = L + W.
Let's put length in terms of width and plug in the previous equation.
38 = 5w - 4 + w
Add the same variables
38 = 6w - 4
simplify
42 = 6w
w = 7
And plug that into the length equation that we had above to get
L = 35 - 4
L = 31
The correct answer is C: 7, 31
Answer:
1. C. 7, 31 cm
2. A. 43°, 137°
Step-by-step explanation:
1.
A. 14+14+66+66=160 (incorrect)
B. 7+7+27+27= 68 (incorrect)
C. 7+7+31+31= 76 (correct)
D. 7+7+39+39= 92 (incorrect)
For this question, they give you a red herring. Since it's a multiple choice question, you can just add their length and width and see if they add up to 76. Only C. 7, 31 cm dimensions add up to have a perimeter of 76.
2.
Supplementary angles add up to 180°
The formula is x° × 5 = y° × 2 - 59
A. 43° × 5 = 137° × 2 - 59 (correct)
B. 41° × 5 ≠ 139° × 2 - 59 (incorrect)
C. 39° × 5 ≠ 141° × 2 - 59 (incorrect)
D. 37° × 5 ≠ 143° × 2 - 59 (incorrect)
For this question, you can't add up the angle measurements because they all equal 180°. Since it's a multiple choice question, you can just try them and see which one fits. Only A. 43°, 137° has angles that fit our formula.
Which equation represents a line which is perpendicular to the line y=-2x-3y=−2x−3?
Answer:
y=1/2x
y=−2x−3y=-2x-3
Choose a point that the perpendicular line will pass through.
(0,0)
Use the slope-intercept form to find the slope.
m=−2
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
mperpendicular=−1−2
Simplify −1−2 to find the slope of the perpendicular line.
mperpendicular=1/2
Find the equation of the perpendicular line using the point-slope formula.
y+0=12⋅(x+0)
Write in y=mx+b.
y=1/2x
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pleaseeee I beg you helpppppp thank youuuuuu :)))
Answer: 1) 4%/40% 2)4%/40% 3)5%/50% 4)4%/40%
Step-by-step explanation:
i think those are the answers
A car travels on a straight road with a velocity of 25km/hour in first one hour and in the
next one hour it changes its speed to 35km/hour. What is the average velocity of the car?
The Average Velocity (A.V) of car
is 8.33m/s .
This is a Right answer...
ANSWER ASAP PLEASE WILL GIVE BRAINLIEST
In a picture, there are 65 apples, and 60% of the apples are in the trees How many apples are in the trees? Use a 10-squares model to explain your answer
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. The probability that the sample contains 2 female voters is.
The probability that the sample contains 2 female voters is 0.31104
Binomial distribution uses two values; n and p. n represent the counts of sample that are being collected. On the other hand, p represents the chances of being successful on any trial. Using the two values, the probabilities are computed for binomial distribution.
Probability that a random voter is female is 0.40(p).
Sampled voters are 6(n).
Let X be the number of females in the sampled voters.
Then,
X∼ Bin (n, p)
∼Bin (6,0.4)
Probability that the sample contains exactly 2 female voters is,
P (X =2) = 6C2 (0.4)2 (1−0.4)6−2
=0.31104
Therefore, the probability that the sample contains exactly 2 female voters is 0.31104
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ou are taking a quiz that has 12 multiple-choice questions. if each question has 3 possible answers, how many different ways are there to answer the test?
(っ◔◡◔)っ ♥ Answer:
⁎ 531441
Explanation:
⁎ ᗩᒪᒪ I ᔕIᗰᑭᒪY ᗪIᗪ ᗯᗩᔕ - 3^12 ᗯᕼIᑕᕼ ᗰEᗩᑎᔕ 3
TO TᕼE ᑭOᗯEᖇ Oᖴ 12
*If you couldn't read * -
- 3^12 3 12
A word from me:
- Please mark me brainiest, trying to achieve the next rank!
- Hope you have a wonderful & great day! ♥ ヾ(•ω•`)o
Percy has a coin collection. He has five pennies for every 33 dimes. If Percy has 1515 pennies what is the total number of coins in his collection?
Answer:
1515
Step-by-step explanation:
Solve for b
a) 2b x 3 = 6 c) 6 + 7b = 41
b) 32 - 3b = 2 d) 100/ 5b = 2
a) The solution for b in the equation 2b × 3 = 6 is b = 1.
b) The solution for b in the equation 32 - 3b = 2 is b = 10.
c) The solution for b in the equation 6 + 7b = 41 is b = 5.
d) The solution for b in the equation 100/5b = 2 is b = 10.
a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.
2b × 3 = 6
(2b × 3) / 2 = 6 / 2
3b = 3
b = 3/3
b = 1
Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.
c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.
6 + 7b - 6 = 41 - 6
7b = 35
b = 35/7
b = 5
Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.
b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.
32 - 3b - 32 = 2 - 32
-3b = -30
b = (-30)/(-3)
b = 10
Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.
d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.
(100/5b) × 5b = 2 × 5b
100 = 10b
b = 100/10
b = 10.
Therefore, the solution for b in the equation 100/5b = 2 is b = 10.
In summary, the solutions for b in the given equations are:
a) b = 1
c) b = 5
b) b = 10
d) b = 10
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describe the sample space in terms of the condition (functional or defective) of each nozzle after a year. let ""f"" denote a functional nozzle after a year and ""d"" denote a defective one.
The sample space, in terms of the condition (functional or defective) of each nozzle after a year, can be represented using the symbols "f" and "d" to denote a functional and defective nozzle, respectively.
The possible outcomes in the sample space can be described as a combination of these symbols. For example, if we have three nozzles, the sample space could include outcomes such as "fff" (all three nozzles are functional), "dfd" (the first and third nozzles are functional, while the second one is defective), "ffd" (the first two nozzles are functional, while the third one is defective), and so on.
Each outcome in the sample space corresponds to a particular arrangement or configuration of functional and defective nozzles after a year. The sample space encompasses all the possible combinations and provides a comprehensive representation of the different outcomes that can occur.
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A=6(1/2bh)
solve for h
Answer:h=a/3b
Step-by-step explanation: