Step-by-step explanation:
since it is geometric sequence we will use the formula
[tex]tn = {ar}^{n - 1} [/tex]
a = 6
r = 4
The first term
T1(a) = 6
The second term
[tex]t2 = {a \times r}^{2 - 1} [/tex]
[tex]t2 = {6 \times 4}^{1 } = 24[/tex]
The Third Term
[tex]t3 = {a \times r}^{3 - 1} = {a \times r}^{2} [/tex]
[tex]t3 = {6 \times 4}^{2} = 6 \times 16 = 96[/tex]
The fourth term
[tex]t4 = {a \times r}^{4 - 1} = {a \times r}^{3} [/tex]
[tex]t4 = {6 \times 4}^{3} = 6 \times 64 = 384[/tex]
The fifth term
[tex]t5 = {a \times r}^{5 - 1} = {a \times r}^{4} [/tex]
[tex]t5 = {6 \times 4}^{4} = 6 \times 256 = 1,536[/tex]
i hope these helped
Answer:
6, 24, 96, 384, 1536, ...
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
a = 6r = 4Substitute the given values of a and r into the formula to create an equation for the nth term:
[tex]a_n=6(4)^{n-1}[/tex]
To find the first 5 terms of the geometric sequence, substitute n = 1 through 5 into the equation.
[tex]\begin{aligned}\implies a_1&=6(4)^{1-1}\\&=6(4)^{0}\\&=6(1)\\&=6\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_2&=6(4)^{2-1}\\&=6(4)^{1}\\&=6(4)\\&=24\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_3&=6(4)^{3-1}\\&=6(4)^{2}\\&=6(16)\\&=96\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_4&=6(4)^{4-1}\\&=6(4)^{3}\\&=6(64)\\&=384\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_5&=6(4)^{5-1}\\&=6(4)^{4}\\&=6(256)\\&=1536\end{aligned}[/tex]
Therefore, the first 5 terms of the given geometric sequence are:
6, 24, 96, 384, 1536, ...Keenan scored 80 points on an exam that had a mean score of 77 points and a standard deviation of 4.9 points. Rachel scored 78 points on an exam that had a mean score of 75 points and a standard deviation of 3.7 points. Find Keenan's and Rachel’s z-scores, to the nearest hundredth.
Answer:
Keenan's z-score was of 0.61.
Rachel's z-score was of 0.81.
Step-by-step explanation:
Z-score:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Keenan scored 80 points on an exam that had a mean score of 77 points and a standard deviation of 4.9 points.
This means that [tex]X = 80, \mu = 77, \sigma = 4.9[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 77}{4.9}[/tex]
[tex]Z = 0.61[/tex]
Keenan's z-score was of 0.61.
Rachel scored 78 points on an exam that had a mean score of 75 points and a standard deviation of 3.7 points.
This means that [tex]X = 78, \mu = 75, \sigma = 3.7[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75 - 78}{3.7}[/tex]
[tex]Z = 0.81[/tex]
Rachel's z-score was of 0.81.
Colin invests £1500 into a savings account. The bank gives 4% compound interest for the first 3 years and 5% thereafter. How much will Colin have after 4 years to the nearest pound?
1500(1+0.04)^3 = 1687.30
1687.30(1+0.05) = 1771.67 to the nearest pound: 1772
Evaluate the expression.
-2.035 – 1.008 - 3.04 + 0.008
Answer:
-6.075
Step-by-step explanation:
simple addition/subtraction
we multiply all the terms by "-1"
we add the first three terms then subtract the last from it
This data is an example of
A. a linear function
B. a nonlinear function
C. neither a linear nor nonlinear function - it is not a
function at all
Answer:
a nonlinear function I think because it's a quadratic one?? kinda
Find the area of the shape shown in the diagram below (dimensions are in ft):
Answer:
where is the picture???????????
Piper is going to invest $74,000 and leave it in an account for 11 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest hundredth of
a percent, would be required in order for Piper to end up with $108,000?
For the length given below draw a line segment to match. Express the measurement as a equivalent mixed number. 4.8 cm
Answer:
there's nothing there
Step-by-step explanation:
The solution is, The length of line segment AB is 3.4cm.
What is Line segment?Line segment is the part of line which have two endpoint and bounded by two distinct end points and it contain every point on the line which is between its endpoint.
here, we have,
The area of octagon is given as 2a^2(1+sqrt{2})
Where a is the side of octagaon.
All lengths of sides of octagon are same.
now, we get,
As, 2a^2(1+sqrt{2}) = 54cm
so, we have,
Then, a^2 = 54/2(1+sqrt{2})
a^2 = 54/4.828
a^2 = 11.19
a = 3.4 cm
Hence, The solution is, The length of line segment AB is 3.4cm.
Learn more about the line segment visit:
brainly.com/question/280216
#SPJ2
complete question;
What is the length of line segment AB, rounded to the
nearest tenth?
3.4 cm
O 4.8 cm
24 cm
0 27 cm
find the slope based on the date below
x: -4, 0, 4 8
y: 3, 8 13 18
HELPPP QUICKK PLZZ
Answer:
The slope is [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Slope of a dataset:
The slope of a dataset, having two points, is given by the change in y values divided by the change in x values
In this question:
Two points:
x = 0, y = 8
X = 4, y = 13
The slope is:
[tex]m = \frac{13 - 8}{4 - 0} = \frac{5}{4}[/tex]
The slope is [tex]\frac{5}{4}[/tex]
SRRY BUT PLEASE HELP What percent is equivalent to 1/25?
4%
5%
20%
25%
Answer:
4%
Step-by-step explanation:
1/25 is equal to 0.04
To convert a decimal to a percent... move the decimal 2 spots to the right
This will give you 4%
Hope this helps!
HOW TO CONVERT 1/25 TO A PERCENTAGE?
To write 1/25 to a percentage, you must remember that 1 equals 100% and that what you must do is multiply the number by 100 and add the symbol% at the end.
[tex] \bold{1 /25 * 100 = 0.04 * 100 = 4\%}[/tex]
And finally we have:
[tex] \bold{1/25 \: a \: percentage equals 4\%}[/tex]
A triangle has vertices at B(-3,0), C(2, -1), D(-1,2). Which series of transformations would produce an image with vertices B"(4,1), C"(-1,0), D"(2, 3)?
O(x, y) - (X. -y). (x, y) (x + 1. y + 1)
O(x, y) - (-x, y). (X. y) (x + 1, y + 1)
O(x, y) - (x, -y), (x, y) (X + 2, Y + 2)
O(x, y) - (-x, y), (x, y) + (x + 2, Y + 2)
Answer:
(b) (x, y) ⇒ (-x, y); (x, y) ⇒ (x + 1, y + 1)
Step-by-step explanation:
A graph shows the image is consistent with reflection over the y-axis
(x, y) ⇒ (-x, y)
and translation right 1, up 1
(x, y) ⇒ (x +1, y +1)
These transformations are listed in the second choice.
__
In the attachment, the original image is blue, the reflected image is purple, and the final translated image is red.
Hector puts together two tables to make a long table for a class picnic.
One table is 7 feet 7 inches long. The other table is 6 feet 9 inches long.
What is the total length of the two tables?
Answer: 14 feet 4 inches
Step-by-step explanation:
Given: The length of the first table = 7 feet 7 inches
The length of the second table = 6 feet 9 inches
The total length of two tables = 7 feet 7 inches + 6 feet 9 inches
= (7+6) feet (7+9) inches
=13 feet 16 inches
Since 1 feet = 12 inches
The total length of two tables = 13 feet+ (12 inches +4 inches)
=13 feet +( 1 feet +4 inches)
= 14 feet 4 inches
Hence, the total length of the two tables = 14 feet 4 inches
I’m dead for not knowing this
The correct answer is A: -2 + 2 = 0
Janice and Emily are selling raffle tickets. So far they have sold 42 tickets, which is 12% of what they're trying to sell. How many tickets total are they trying to sell?
Answer:
350 tickets
Step-by-step explanation:
if you do 42/350, it would equal 12%, so 350 is the total
How many gallons are in of a 7-gallon container of milk?
Answer:
7
Step-by-step explanation:
Uhh 7 divided by 1 is 7?
Answer:
7
Step-by-step explanation:
There are 7 gallons in a 7-gallon container of milk.
Tricia made a 55% on her science test. If she got 11 problems correct, how many questions were on the test?
Answer:
20 questions
Step-by-step explanation:
20 · 0.55 = 11
Giving BRAINLYIST to whoever gets it right! PLEASE HELP!
Answer:
area = 117 cm²
Step-by-step explanation:
area = 1/2(b1 + b2)h
area = 1/2(17 + 9)(9)
area = 117 cm²
Answer:
A=117
Step-by-step explanation:
:))
A building in a city has a rectangular base. The length of the base measures 70 ft less than twice the width. The perimeter of this base is 820 ft. What are the dimensions of the base?
Answer:
160 ft, 250ft
Step-by-step explanation:
Rectangular base:
Width = w
length =2w - 70
Perimeter = 820 ft
2*(length + width) = 820
2*(2w - 70 + w ) = 820
2 *(2w + w - 70) = 820 {Combine like terms}
2* (3w - 70) = 820
3w*2 - 70*2 = 820
6w - 140 = 820
6w = 820 + 140 {Add 140 to both side}
6w = 960 {Divide both sides by 6}
w = 960/6
w = 160 ft
length = 2*160 - 70
= 320 - 70
= 250 ft
A recipe calls for one egg to serve every four people. It also requires two tbsp of salt for every five eggs used. If you are cooking a
banquet for 300 people, how many tbsp of salt will you need?
a. 7.5 tsp
b. 30 tsp
c. 15 tsp
d. 60 tsp
I
No calculator is allowed on this question.
Answer:
30
Step-by-step explanation:
300/4=75
75/5=15
15*2=30
Please help will give brainliest
Answer:
angle a+angle b+angle c=180°
90°+38°+angle c=180°
128°+angle c=180°
angle c=180°-128°
angle c =52°
52°+n°=180°
n=180°-52
n=128°
Without solving, identify whether each of the following equations has a unique solution, no solution, or infinitely many solutions.
3.2 + 6 = -8
0 1 solution
O No Solution
O Infinite solutions
Answer:
No solution
Step-by-step explanation:
please help meeeeeeeeeeeeeeeee
Answer:
hi
Step-by-step explanation:
i think so...
[tex]\pi \times {r}^{2} \times \frac{h}{3} \\ 3.14 \times 3.5 \times \frac{9}{3} \\ = 32.97[/tex]
hope it helps
bye
What is the volume of the figure?
HELP
Answer:
the anser is 88 i think
Step-by-step explanation:
beacuse 5.8=40
5.8=40
1.8=8
or it could be
264
Step-by-step explanation:
Figure on the left: 5x5x8 = 200
Figure on the right: 8x1x8 = 64
200+64=264
Answer:
264
Step-by-step explanation:
Figure on the left: 5x5x8 = 200
Figure on the right: 8x1x8 = 64
200+64=264
what are 3 different equations that have x=5 as a solution
Answer:
1) x+y=50
2) 5x+2y=200
3)2x+4y=200
Hope this helps!
Answer:
x+3=8, 2x-8=2, and 4x-4=16
Step-by-step explanation:
Victor wants to buy fertilizer for his yard. The yard measure 55 feet by 60 feet the direction on the bag
of fertilizer say that one bag will cover 1,230 sq ft.
How many bags of fertilizer should Victor buy to be sure that he covers the entire yard?
Victor should buy
bags of fertilizer.
Answer:
3 bags
Step-by-step explanation:
55 x 60 = 3300 ft²
3300/1230 = 2.68 bags
what is 3/7 divided by 2/5?
Answer:
1 1/14
you have to multiply by the reciprocal of the second fraction
Find the mode, median, mean, lower quartile (Q1), upper quartile (Q3), minimum, maximum, range, interquartile range, and standard deviation for the data set. Then create a box and whisker plot. Be sure to show work for finding the lower and upper fence and then plot any possible outliers appropriately. Round answers to the nearest hundredth.
1) The following data is the points that
Melody scored in her first 13 games of her
basketball season.
16, 12, 14, 9, 8, 12, 14, 28, 15, 18, 7, 14, 6
Answer is in a photo. I can only upload it to a file hosting service. link below!
bit.[tex]^{}[/tex]ly/3a8Nt8n
Diane scored 356.789 points Jeff scored 190.499 points how many more points did Diane score than Jeff
Answer: 166.29
Step-by-step explanation:
Answer:
It's 166.29
Diane score 166.29 more than jeff
Step-by-step explanation:
356.789
- 190.499
= 166.29
A quart and a liter of the same kind of drink are on a shelf and are the same price. Which one should you pick if you are really thirsty?
quart
doesn't matter - they are the same amount
liter
User averysmartperson is helping with this question.
Answer:
[tex]x^2 + (y-60)^2 = 30,625[/tex]
Step-by-step explanation:
There are 42 carts, so there is 42 spaces in between them; if one of those spaces are 25pi/3 feet long, then 42 of them would be 25*42*pi/3 = 350pi (Perfect! no fractions)
350pi is the circumference. Now if we plug that into the circumference equation we get:
C = 2pi*r
350pi = 2pi*r
Divide both sides by pi to get rid of it
350 = 2r
Divide both sides by 2
r = 175 feet
So the new equation to graph it is:
x^2+y^2 = 175^2 = 30,625
We also know that the center of the Ferris wheel has to be at least 60 feet from the ground. Since the radius is more than that, a good bit of the Ferris wheel has to be underground OR we can make it higher (keyword: at least) if we want it to be above ground. I'll do the equation for underground since it more closely represents the question.
subtracting a number from y, shifts the graph up that much so:
[tex]x^2 + (y-60)^2 = 30,625[/tex]
I can't really draw it electronically but I can graph it:
Select all ratios equivalent to 3:2.
2:1
7:16
21:14
Answer:
Step-by-step explanation:
21 : 14
Both have 7 in common
3 : 2
So Option C 21 : 14 is the correct answer