Answers
Area of a circle is
[tex] {\pi \times r}^{2} [/tex]
but the area of a sector is the area of the circle multiplied by the angle BEC divided by 360
[tex] \frac{120}{360} \times \pi \times \: r^{2} [/tex]
so the area is
[tex] \frac{1}{3} \times \pi \times 81[/tex]
since r=9
so the area is 81π/3
Ans: 27π
A circle is a curve sketched out by a point moving in a plane. The area of sector BEC when CE = 9 yd is 84.823 yds².
How to find the area of a sector of a circle?The sector of a circle is like a slice of a circular pizza. Its two straight edge's having an angle, and the edge's length(the radius of the circle) are two needed factors for finding the area of that sector.
Since the whole circle with radius 'r' units have 360 degrees angle on the centre of the circle, and its area is
πr² unit², thus, as the angle lessens, this area gets lessened.
360 degree => πr² unit²
[tex]\rm area\ 1 degree = \pi r^2 \: \rm unit^2/360 area\\\\x\ degree = \dfrac{x \times \pi r^2}{360} \: \rm unit^2 area[/tex]
Thus, the area of a sector with edge length 'r' units and interior angle 'x' degrees is given as:
[tex]A = \dfrac{x \times \pi r^2}{360} \: \rm unit^2 area[/tex]Given the length of the radius of the circle, CE is 9 yds. Also, the measure of the ∠BEC at the centre of the circle is 120°. Therefore, the area of sector BEC can be written as,
Area BEC = π × r² × (θ/360°)
= π × 9² × (120° / 360°)
= 84.823 yds²
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Related Questions
HELP ASSAP WILL MARK BRAINIEST!!!!!!!!
Answers
The y-intercept is 1, since the line intersects with the x-axis at (0, 1).
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The function f(x) = −(x + 5)(x + 1) is shown. What is the range of the function? all real numbers less than or equal to 4 all real numbers less than or equal to −3 all real numbers greater than or equal to 4 all real numbers greater than or equal to −3
Answers
all real numbers such that y is less than or equal to 4
ANSWER
all real numbers less than or equal to 4.
EXPLANATION
The given function is
[tex]f(x) = - (x + 5)(x + 1)[/tex]
Expand
[tex]f(x) = - ( {x}^{2} + x + 5x + 5)[/tex]
[tex]f(x) = - ( {x}^{2} + 6x + 5)[/tex]
[tex]f(x) = - {x}^{2} - 6x - 5[/tex]
a=-1,b=-6,c=-5
The x-value of the vertex is given by
a=-1,b=-6,c=-5
[tex]x = \frac{ - b}{2a} [/tex]
[tex]x = - \frac{ - 6}{2( - 1)} = - 3[/tex]
The y-value of the vertex is
[tex]f( - 3) = - ( - 3 + 5)( - 3 + 1)[/tex]
[tex]f( - 3) = - ( 2)( - 2) = 4[/tex]
Since a=-1, the function opens downwards.
The highest value is the y-value of the vertex which is 4.
Therefore the range is all real numbers less than or equal to 4.
The correct choice is A.
If 30 people claimed that they get an average of seven hours of sleep, how many people claimed that they get at least eight hours of sleep each night? [Type your answer as a number.]
Answers
60 people claimed they they got at least eight hours of sleep.
Answer:
78 people claimed that they get at least eight hours of sleep each night.Step-by-step explanation:
We know that 30 people claimed that they get an average of seven hours of sleep. Using the circular diagram, we find that these 30 people represent 25% of the total number of people.
According to the graph, people that get at least eight hours of sleep each night represent 65%, that is, 50% of the people sleep eight hours and 15% sleep nine or more.
Then, we use the rule of three, if 30 people represent 25% of the total, how many people would represents 65%?
[tex]x=65\%\frac{30 \ people}{25 \%} = 78 \ people[/tex]
Therefore, 78 people claimed that they get at least eight hours of sleep each night.
Which factorization can be used to identify the real zeros of the function f(x)=-20x^2+23x-6?
Answers
Answer:
see explanation
Step-by-step explanation:
Given f(x) = - 20x² + 23x - 6
To find the zeros set f(x) = 0, that is
- 20x² + 23x - 6 = 0 ( multiply through by - 1 )
20x² - 23x + 6 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 20 × 6 = 120 and sum = - 23
The factors are - 15 and - 8
Use these factors to split the x- term
20x² - 15x - 8x + 6 = 0 ( factor the first/second and third/fourth terms )
5x(4x - 3) - 2(4x - 3) = 0 ← factor out (4x - 3)
(4x - 3)(5x - 2) = 0
Equate each factor to zero and solve for x
4x - 3 = 0 ⇒ 4x = 3 ⇒ x = [tex]\frac{3}{4}[/tex]
5x - 2 = 0 ⇒ 5x = 2 ⇒ x = [tex]\frac{2}{5}[/tex]
Answer:
-(4x - 3)(5x - 2) = 0
Step-by-step explanation:
Find the equation of a circle with a center at (7,2) and a point on the circle at (-2,-5).
( x - 7 )^2 + ( y - 2 )^2 = sqrt 130
( x + 7 )^2 - ( y + 2 )^2 = sqrt 130
( x - 7 )^2 + ( y - 2 )^2 = 130
( x + 7 )^2 - ( y + 2 )^2 = 130
Answers
Answer:
(x - 7)² + (y - 2)² = 130
Step-by-step explanation:
The first step is finding the length of the radius.
r² = (2 - -5)² + (7 - -2)²
= 7² + 9²
= 49 + 81
= 130
The general equation of a circle is:
(x - a)² + (y - b)² = r²
Where (a, b) is the coordinate of the center and r is the radius.
∴ The equation of the required circle is;
(x - 7)² + (y - 2)² = 130
You and a friend join a gym The registration fee is $30 and the monthly Membership is $20 if the total bill for you and your friend is $420 how many months did you pay for?
Answers
First, divide by two, so you are only working with one person’s money. 420 / 2 = 210
Now subtract the $30 registration fee. 210 - 30 = 180
Finally, divide by $20 to find the number of months. 180/20 = 9
So, you and your friend each paid for 9 months.
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Find last years salary if after 3% pay raise, this years salary is $34505
Answers
Answer:
$34,505
s = --------------- = $33,500
1.03
Step-by-step explanation:
Last year's salary was 1.00 s.
A 3% pay raise would thus amount to 0.03s.
This would equal this year's salary: $34,505.
Thus, 1.03s = $34,505; find s, which was last year's salary.
Dividing both sides by 1.03, we get:
$34,505
s = --------------- = $33,500
1.03
Darlene spent 20 minutes jogging and 10 minutes cycling and burned 400 calories . The next day she did 10 minutes of jogging and 20 minutes of cycling and burned 350 calories . How many calories were burned for each minute of jogging and how many for each minute of cycling
Answers
This is very spread out just to show properly but you could get it smaller haha
In this algebra problem, we created two equations from the problem and solved them simultaneously, finding that Darlene burns 15 calories per minute jogging and 10 calories per minute cycling.
Explanation:This question is about working out two equations using two variables, a classic application in
algebra
. Let's call the calories burned per minute jogging as
J
, and the calories burned per minute cycling as
C
. From the information given in the question, we know that:
20J + 10C = 40010J + 20C = 350These equations can be solved simultaneously. To make things easier, let's multiply the second equation by 2, which gives us:
20J + 40C = 700By subtracting equation 1 from this, we get:
30C = 300
, simplifying this, we find that
C = 10 calories per minute for cycling
. Substitute C=10 into the first equation, we get:
20J + 100 = 400
, which simplifies to
J = 15 calories per minute for jogging
. Thus, Darlene burns 15 calories for each minute of jogging and 10 calories for each minute of cycling.
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How do I find the volume
Answers
Answer:
[tex]\large\boxed{V=\dfrac{256\sqrt3}{3}\ cm^3}[/tex]
Step-by-step explanation:
The formula of a volume of a square pyramid:
[tex]V=\dfrac{1}{3}(b^2)(H)[/tex]
b - edge of a base
H - height
We have b = 8cm and the triangle 90 - 60 - 30. The sides of that triangle are in ptoportion 1 : √3 : 2 (look at the picture).
From the picture we have
[tex]a=\dfrac{b}{2}\to a=\dfrac{8}{2}\ cm=4\ cm[/tex]
Therefore
[tex]H=a\sqrt3\to H=4\sqrt3\ cm[/tex]
Substitute:
[tex]V=\dfrac{1}{3}(8^2)(4\sqrt3)=\dfrac{1}{3}(64)(4\sqrt3)=\dfrac{256\sqrt3}{3}\ cm^3[/tex]
To find the volume of any cube you need to know the length, width and height. The formula to find the volume multiplies the length by the width by the height. The good news for a cube is that the measure of each of these dimensions is exactly the same. Therefore, you can multiply the length of any side three times.
Tina had $145 she spent $40 on fruit at the farmers market how to Slovenia the equation 40 + c = 145 to find the amount Tina has left
Answers
To help u out
Change equation to 145-40=
Subtract.
Replace c with 105 so; 40+105=145
you stop for lunch at a local pizza ahop where each pizza is cut into 8 sices. would your hunger be better satisifued with one slice from a 10 inch pizza or 2 slices from a 8 inch pizza and explain why?
Answers
Answer:
Hello there! How are you doing? I am doing fine! I'll answer the question now.
So basically, your hunger would be satisfied with the 2 slices of 8 inches, because although one slice of 8 inches is two inches less than the 10 inch slice. But then you could add another 8 inch slice and it would make it greater and bigger than the one 10 inch slice itself. So in conclusion, the 2, 8 inch slices would be better than the 1, 10 inch slice because 16 inches is greater than 10 inches.
Hope this helped! Your welcome! I can help with other history stuff too! And byee! :)
Step-by-step explanation:
Two slices from an 8-inch pizza provide more pizza than one slice from a 10-inch pizza based on the calculation of the areas of the pizza slices. Therefore, your hunger would be better satisfied with the two pieces from the 8-inch pizza.
Explanation:The subject here is a mathematical comparison of the area of different pizza sizes and the number of slices eaten. The location of a pizza can be calculated using the formula for the circle size, which is πr², where r is the radius of the pizza.
In the case of a 10-inch pizza, the radius is 5 inches (half of the diameter). So the area is π(5)² = 78.5 square inches. One slice of this pizza would be 1/8th of the total area, approximately 9.81 square inches.
For an 8-inch pizza, the radius is 4 inches. So the area is π(4)² = 50.24 square inches. Two slices of this pizza would amount to 1/4th of the total area, approximately 12.56 square inches.
So, when it comes to fulfilling your hunger at lunch, two slices of an 8-inch pizza would be more satisfying as it offers more pizza than one slice of a 10-inch pizza.
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What is the value of x?
x =
(Secants, Tangents, and Angles)
Answers
Answer:
The value of x is [tex]58\°[/tex]
Step-by-step explanation:
we know that
The measurement of the external angle is the semi-difference of the arcs which comprises
so
In this problem
[tex]51\°=\frac{1}{2}(160\°-x\°)[/tex]
solve for x
[tex]102\°=(160\°-x\°)[/tex]
[tex]x=160\°-102\°=58\°[/tex]
Plz help!!!!!!!!!!!!
Answers
Answer:
rational
Step-by-step explanation:
any number that can be written as a fraction is rational, it is also a termintating decimal.
Answer: rational
Step-by-step explanation:
[tex]\dfrac{1}{4}=0.25\\\\\text{Since the decimal terminates (ends), it is a rational number.}[/tex]
ASAP!!!!!
The sanitation department calculated that last year each city resident produced approximately 1.643 × 10^3 pounds of garbage. There are 2.61 × 10^5 people living in the city. How much garbage did the city sanitation department collect last year?
4.2882 pounds
428.820 pounds
428,820 pounds
428,820,000 pounds
Answers
Answer:
428,820,000 pounds
Step-by-step explanation:
The amount of garbage is number of person times the amount produced by each person. Thus, we have:
Amount of Garbage (in pounds) = 2.61 × 10^5 * 1.643 × 10^3
Note: We multiply 2.61 and 1.643, which is 4.28823 & multiplying 10^5 and 10^3 is 10^(5+3) = 10^8
Thus, we have 4.28823 * 10^8 = 428,823,000 pounds
This is approximately 428,820,000 pounds, last answer choice.
Answer:
Other answer is correct, confirmed on E2020
Step-by-step explanation:
Blake ate 2/6 of a pumpkin pie and give 3/6 of the pie to his sister. What fraction of the pumpkin pie was left?
Answers
Final answer:
After Blake ate 2/6 of a pumpkin pie and gave another 3/6 to his sister, the fraction of the pie that was left is calculated by subtracting the total part taken away (5/6) from the whole pie (1), resulting in 1/6 of the pie remaining.
Explanation:
The question asks about determining the fraction of a pumpkin pie left after Blake ate 2/6 of it and gave another 3/6 to his sister. To calculate the remaining portion of the pie, we add the fractions that were eaten and given away, and subtract that sum from the whole pie, which is represented as 1 (or 6/6, since we are working with sixths).
2/6 (eaten by Blake) + 3/6 (given to his sister) = 5/6. This means 5/6 of the pie was either eaten or given away.
To find the fraction of the pie that was left, we subtract the portion that is gone from the whole. Since 5/6 of the pie was no longer available, subtracting this from 1 (the whole pie) gives us 1 - (5/6) = 1/6. Therefore, 1/6 of the pumpkin pie was left.
Simplify the expression 43 + 2(3 − 2).
Answers
Answer:
45
Step-by-step explanation:
Simplify the following:
43 + 2 (3 - 2)
3 - 2 = 1:
43 + 2×1
2×1 = 2:
43 + 2
43 + 2 = 45:
Answer: 45
Answer:
STOP SAYING ITS 45 BECAUSE ITS NOT THE 43 IS SUPPOSED TO BE 4 TO THE POWER OF 3
Step-by-step explanation:
okay?
Rewrite in polar form x^2 + y^2 - 6y - 8 = 0
Answers
Answer:
The correct answer option is [tex]r^2-6rsin(\theta)=8[/tex].
Step-by-step explanation:
We are given the following equation and we are to rewrite it in polar form:
[tex]x^2 + y^2 - 6y - 8 = 0[/tex]
[tex]\left \{ {{x^2+y^2=r^2} \atop {y=rsin \theta}} \right.[/tex]
Here, we need to make a perfect square trinomial:
[tex][r^2-6rsin(\theta)+[/tex] ___[tex]^2]=8[/tex]
[tex]6rsin(\theta)[/tex] ---> [tex]2 .r.3.sin \theta[/tex]
Completing the square to get:
[tex]r^2-6rsin(\theta)+[3sin(\theta)]^2-[3sin(\theta)]^2=8[/tex]
[tex][r-3sin(\theta)]^2=8+[3sin(\theta)]^2[/tex] --> [tex][r-3sin(\theta)]^2=8+9sin^2(\theta)[/tex]
[tex]r-3sin(\theta)=\sqrt{8+9sin^2(\theta)}[/tex] --> [tex]r=\sqrt{8+9sin^2(\theta)} +3sin(\theta)[/tex]
the correct answer is B. r^2=6r sin 0+8
What is the m∠ABC? m∠ABC = 15° m∠ABC = 45° m∠ABC = 60° m∠ABC = 75
Answers
Answer:
60 is c not d
Step-by-step explanation:
Answer:
c. m∠ABC = 60°
Step-by-step explanation:
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On Thursday night, Betsy received $34.50 in tips working as a coat checker. This is $1.75 more than the amount in tips she received on Wednesday night. How much did she receive on Wednesday night?
Answers
she received 32.75 dollars on wednesday night
How do show 4/6 and 5/7 on a number line
Answers
Answer:
|-----|-----|-----|-----0-----|-----| |------|------|------|------|------0------|-----|
0 1/6 2/6 3/6 4/6 5/6 1 0 1/7 2/7 3/7 4/7 5/7 6/7 1
Step-by-step explanation:
since 4/6 means the fourth one of the 6 spots, we can just make a number line that is split into 6 parts and find the fourth line. we do the same thing with seven to get the answers above
Final answer:
To show 4/6 and 5/7 on a number line, mark 42 equal sections between 0 and 1, and place 4/6 at the 28th mark and 5/7 at the 30th mark, as they equate to 28/42 and 30/42 respectively.
Explanation:
To show 4/6 and 5/7 on a number line, you would follow these steps:
Determine a number line with a section that includes both fractions. This might typically be between 0 and 1 if you are only dealing with fractions less than a whole.Divide this section into parts that can accommodate both denominators. For example, a common denominator for 6 and 7 is 42, since 6 * 7 = 42.Mark off 42 equal sections between 0 and 1 on your number line.Count and mark the position that corresponds to 4/6 and 5/7. To find the position of 4/6, you would count 28 sections from 0 (since 4/6 = 28/42). For 5/7, you would count 30 sections from 0 (since 5/7 = 30/42).Place a point or tick mark at these positions and label them accordingly.Both 4/6 and 5/7 will be placed between 0 and 1 on the number line, with 4/6 slightly to the left of 5/7.
-4(j+k+g) plz help using box method
Answers
Answer:
-4j-4k-4g
Step-by-step explanation:
Mai biked 6 3/4 miles today, and Noah biked 4 1/2 miles. How many times the length of Noah’s bike ride was Mai’s bike ride ?
Answers
Answer:
1.5 times.Step-by-step explanation:
Givens:
Mai biked [tex]6\frac{3}{4} \ mi[/tex]Noah biked [tex]4\frac{1}{2} \ mi[/tex]So, to know how many times the length of Noah's bike ride was Mai's bike ride, we can use the following equation:
[tex]6\frac{3}{4} \ mi=x(4\frac{1}{2} \ mi)\\\frac{27}{4}=\frac{9}{2}x\\ x=\frac{54}{36}=\frac{3}{2}=1.5[/tex]
Therefore, Mai biked 1.5 times more miles than Noah.
1.5 times the length of Noah’s bike ride was Mai’s bike ride.
Step-by-step explanation:
Given :
Mai Biked -
[tex]\rm 6\dfrac{3}{4} \; miles = \dfrac {27}{4} \; miles[/tex]
Noah Biked -
[tex]\rm 4\dfrac {1}{2} \; miles = \dfrac {9}{2} \; miles[/tex]
Calculation :
To find how many times the length of Noah’s bike ride was Mai’s bike ride, use below equation
[tex]\dfrac{27}{4}=x\dfrac{9}{2}[/tex]
[tex]\rm x = 1.5 \; times[/tex]
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The ball game begins at 2:00 p.m it takes ying 30 minutes to get to the ball park . At what time should ying leave home to get to the game before 30 minutes before it starts
Answers
Answer:
30 Mintues to get there + 30 Mintues early = 1 hour
2:00 PM - 1 hour = 1 PM
Step-by-step explanation:
A fisherman travels 8 miles downstream with the current in the same time that he travels 3 miles upstream against the current. If the speed of the current was 5 mph what is the speed at which the fisherman travels in still water?
Answers
I also need help with this too so I'm just here to wait and see the answer
The speed is the distance covered by an object at a particular time. The speed at which the fisherman travels in still water is 11 mph.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Let the speed of the boat be represented by x mph.
A fisherman travels 8 miles downstream with the current at the same time that he travels 3 miles upstream against the current. Also, the speed of the current was 5 mph. Therefore,
8 miles/ (x + 5)mph = 3 miles/(x - 5) mph
8x - 40 = 3x + 15
5x = 55
x = 11 mph
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Select the figure obtained when rotating the figure about an axis along its largest side, and find the exact surface area of the resulting figure.
A rectangle with length 22 and width 18.
The figure obtained is a (square/cylinder/sphere)
The exact surface area is ______π.
Answers
Answer:
The figure obtained is a cylinder
The exact surface area is 1440π.
Step-by-step explanation:
* Lets study the rotation of a rectangle around one of its sides
- If the dimensions of the rectangle are length (L) and width (W)
- If we rotate the rectangle around its length (L), we will construct
a cylinder with radius = W and height = L
- If we rotate the rectangle around its width (w), we will construct
a cylinder with radius = L and height = W
∵ The surface area of any cylinder =
perimeter of base × height + 2 base area
∵ The base is a circle
∴ perimeter base = 2πr and base area = πr²
∴ The surface area = 2πrh + 2πr²
* In first case:
- Surface area = 2π(W)L + 2π(w)² = 2πWL + 2πW²
* In second case:
- Surface area = 2π(L)W + 2π(L)² = 2πLW + 2πL²
* Now lats check our question:
∵ L = 22 and W = 18
- It will rotate around the largest side
∴ It will rotate around L
∴ The figure obtained is a cylinder
* From the explanation above this is the first case
∵ L = 22 and W = 18
∵ The surface area = 2πWL + 2πW²
∴ The surface area = 2 × 18 × 22 × π + 2 × (18)² × π
= 792π + 648π = 1440π
* The exact surface area is 1440π.
Choose the solution to this inequality. 7/2≥b+9/5
Answers
The solution to the given inequality is [tex]b\leq 1.7[/tex]
InequalitiesFrom the question, we to determine the solution to the inequality.
To determine the solution of the inequality, we will determine the value of the variable. The variable in the given question is b.
The inequality can be solved as shown below.
[tex]\frac{7}{2} \geq b + \frac{9}{5}[/tex]
Multiply through by 10
That is,
[tex]10 \times \frac{7}{2} \geq 10\times b + 10\times \frac{9}{5}[/tex]
This becomes
[tex]5 \times 7 \geq 10b + 2 \times 9[/tex]
[tex]35 \geq 10b + 18[/tex]
Now, subtract 18 from both sides
[tex]35 - 18\geq 10b + 18-18[/tex]
[tex]17 \geq 10b[/tex]
This becomes,
[tex]10b \leq 17[/tex]
Divide both sides by 10
[tex]\frac{10b}{10} \leq \frac{17}{10}[/tex]
[tex]b\leq 1\frac{7}{10}[/tex]
OR
[tex]b\leq 1.7[/tex]
Hence, the solution to the given inequality is [tex]b\leq 1.7[/tex]
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need help asap!!! plzz
Use mental math to find 31% of $200.
(A)$52.00
(B)$42.00
(C)$62.00
(D)$72.00
Answers
Answer:
(C)$62.00
Step-by-step explanation:
$200 x .31 = $62.00
the answer is C it is $62.00
What is the value of n? Enter your Answer in the box. N=
Answers
n can be whatever number u want it to be or whatever number given because it is a variable
A number is chosen at random from the positive, even integers from 2 to 50. Find the probability that the number chosen is divisible by 3 or 8
Answers
Answer:
2/5
Step-by-step explanation:
it is 2/5
Probability = 12/25 or 48%.
To find the probability that a number chosen at random from the positive, even integers from 2 to 50 is divisible by 3 or 8, we need to count the number of even integers within this range that are divisible by 3 or 8, and then divide this count by the total number of even integers in the range.
First, let's find how many even integers between 2 and 50 are divisible by 3.
The even integers divisible by 3 in this range are: 6, 12, 18, 24, 30, 36, 42, 48.
Count: 8
Now, let's find how many even integers between 2 and 50 are divisible by 8.
The even integers divisible by 8 in this range are: 8, 16, 24, 32, 40, 48.
Count: 6
Notice that 24 and 48 are counted twice because they are divisible by both 3 and 8. We only want to count them once.
So, the total count of even integers between 2 and 50 that are divisible by 3 or 8 is 8 (from being divisible by 3) + 6 (from being divisible by 8) - 2 (counting 24 and 48 once) = 12.
Now, we calculate the total number of even integers between 2 and 50:
Total even integers between 2 and 50 = (50 - 2) / 2 + 1 = 25
Now, we can calculate the probability:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
= 12 / 25
= 0.48
So, the probability that a number chosen at random from the positive, even integers from 2 to 50 is divisible by 3 or 8 is 0.48.
!!!! MUCH HELP NEEDED I RAISED THE POINTS TO 22 AND WILL GIVE BRAINLIEST !!!!!
what is the 16th term in the sequence 2, 6, 18, 54, 162. . . . . . . ?
Answers
Answer:
The 16 term will be 28,697,814
Step-by-step explanation:
The pattern here is that Each number is being Multiplied by 3
Example= (2x3=6) (6x3=18) (18x3=54) (54x3=162) keep doing that until you get the 16th term.
Took me a while....
Hopes this helps you!