The first term of a geometric sequence is 4 and grows exponentially by a factor of 3. Murphy writes out the terms and says that the sum of the 4th and 5th terms is 1,296. Explain Murphy's error and correct it. (Fill in the blanks)
Murphy added terms
____
together. The correct sum of the 4th and 5th terms is ___
(Simplify your answer.)
The geometric sequence can increase or decrease exponentially
The correct sum of the 4th and the 5th terms is 432
How to determine the correct sum?The given parameters are:
Initial value (a) = 4
Growth factor (r) = 3
The nth term of a geometric sequence is calculated as:
[tex]T_n = ar^{n-1}[/tex]
This gives
[tex]T_n = 4 * 3^{n-1}[/tex]
For the 4th term; we have:
[tex]T_4 = 4 * 3^{4-1}[/tex]
[tex]T_4 = 108[/tex]
For the 5th term, we have:
[tex]T_5 = 4 * 3^{5-1}[/tex]
[tex]T_5 = 324[/tex]
Add the 4th and the 5th terms
Sum = 108 + 324
Sum = 432
Hence, the correct sum of the 4th and the 5th terms is 432
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Volt Electronics sells a Y-Box game console for $207. The store markup on thr Y-Box is 38%. What was the wholesale price that the store paid for it?
The wholesale price that the store paid for the Y-Box game is $150.
What is the wholesale price?When the price of an item is marked up, it means that the price of the item was increased by a certain percentage. The good then becomes more expensive.
Wholesale price = selling price / ( 1 + percentage mark up)
$207 / (1+ 38)
$207 / (1.38) = $150
To learn more about profit, please check: https://brainly.com/question/26181966
can you pls help me i need it?
Answer:
$114.75
Step-by-step explanation:
You have to multiply the hours by the wage. Looking at the time that the worker was in during the morning, it was a total of 4 hours. Since the wage is $13.50/hr, we would multiply 13.50 by 4.
13.50 * 4 = 54.00
So, now we have to add together the total hours in the afternoon. If we count the time, we get 4 1/2 hours. So, now we multiply 13.50 by 4.5.
13.50 * 4.5 = 60.75
Now, to find the total pay for that day, we add both the morning and the afternoon pay together.
54.00 + 60.75 = 114.75
Therefore, the pay for this day is $114.75.
Given the equation of a circle. X^2+ y^2 - 6x + 2y +1 = 0, find the coordinates of the center and the length of the radius.
Coordinates for the center=
Length of the radius =
Answer:
I know the answer but you may select me as Brainliest
Find the volume of combined solid from the given figure.
Answer:
1944 cubic cm
Step-by-step explanation:
Find the answer by figuring out the volumes independently for each figure. After doing that, add both volumes together to get the full volume.
Bottom figure: 1440 cubic cm
Top figure: 504 cubic cm
Add those together: 1944 cubic cm
Solve for A
ASAP ANSWER
Step-by-step explanation:
A = B
7x + 40° = 3x + 112°
7x - 3x = 112° - 40°
4x = 72°
x = 18°
A = 7x + 40°
= 7(18°) + 40°
= 126° + 40°
= 166°
hope it help
can you help to answer my question? my math is better ,but my english is bad ,can you help me,please
A cylinder has a volume of 320 pi cubic inches and a height of 5 inches what is the radius
Answer:
As Per Provided Information
A cylinder has a volume of 320 pi cubic inches and a height of 5 inches.
We have been asked to determine the radius of the cylinder .
Using Formulae
[tex] \purple{\boxed {\bf\: Volume_{(Cylinder)} = \pi {r}^{2}h}}[/tex]
Substituting the value and let's solve for radius .
[tex] \sf \qquad \longrightarrow \: 320 \pi \: = \pi \: \times r {}^{2} \: \times 5 \\ \\ \\ \sf \qquad \longrightarrow \:320 \cancel{\pi} = \cancel{ \pi} \times r {}^{2} \: \times 5 \\ \\ \\ \sf \qquad \longrightarrow \:320 = r {}^{2} \: \times 5 \\ \\ \\ \sf \qquad \longrightarrow \:r {}^{2} \: = \cfrac{320}{5} \\ \\ \\ \sf \qquad \longrightarrow \: {r}^{2} = \cancel\cfrac{320}{5} \\ \\ \\ \sf \qquad \longrightarrow \: {r}^{2} = 64 \\ \\ \\ \sf \qquad \longrightarrow \:r \: = \sqrt{64} \\ \\ \\ \sf \qquad \longrightarrow \:r \: = 8 \: inch[/tex]
Therefore,
Radius of cylinder is 8 Inches .What can you tell about the numbers?
Equations can be for example like: -1 ≤ x < 4
Answer:
Step-by-step explanation:
The numbers lies between 80 and 140
80 < x <140
Hollow dot at point 80 and 140 indicates that 80 and 140 are not included
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 1 yard long, and the height of the equilateral triangle is 0.9 yards. The pyramid's slant height is 1 yard. What is its surface area?
Answer:
base: 1/4 * 12^2 * √3 = 36√3
each face: 1/2 * 12 * 8 = 48
Now finish it off
Step-by-step explanations:
In the figure below, triangle ABC undergoes a reflection and a translation to become triangle PQR. In triangle ABC, m
The angle measures of triangle PQR are: m
Answer:
Step-by-step explanation:
A corresponds to angle P, so angle P measues 70 degrees.
Similarly, angle Q measures 60 degrees and angle R measures 50 degrees.
Use the dot plot to answer the question.
A dot plot that has 3 dots at 1, 4 dots at 2, 3 dots at 3, 4 dots at 4, 5 dots at 5, & 3 dots at 6.
What is the mean of the data set in the dot plot?
Enter your answer as a number rounded to the nearest tenth, like this: 42.5
which inequality does the graph represent?
Answer: x ≥ -1
Step-by-step explanation:
First, we see the filled in dot, so we know x can be equal to -1. Since this is a ray, all valid values of x must be greater or equal to -1. Therefore, our answer is x ≥ -1
How is the graph of g(x) = -x2-2 related to the graph of f(x)=x2?
The graph of gx) = -x2-2 is reflected across the y-axis and translated up 2 units.
The graph of g(x) = -x2–2 is reflected across the x-axis and translated up 2 units.
The graph of g(x) = -x2-2 is reflected across the y-axis and translated down 2 units.
The graph of g(x) = -x2-2 is reflected across the x-axis and translated down 2 units.
Answer:
The graph of g(x) = -[tex]x^{2}[/tex]-2 is reflected across the x-axis and translated down 2 units.
Step-by-step explanation:
- f(x) reflects the graph over the x-axis; f(-x) would reflect the graph over the y-axis
f(x) + k translates the graph up k units; f(x) - k translates the graph down k units
if there are 15 plane 2 crash 1 breakdown how many planes are left
Answer:
15 planes
Step-by-step explanation:
none disappear, just change shape/ability. its a riddle.
Answer:
15-2-1 = 15-3 = 12.
there are 12 planes left.
Step-by-step explanation:
hope this helped have a nice day
please help i am confused.
Can someone help me on this question? I’ll give brainliest if you answer soon!!!
Answer:
∠ 5
Step-by-step explanation:
Given;
Which angle number represents ∠ WYU
picture
Solve;
First, we have to find the letters WYU in the picture.
Knowing that, WY is an edge, YU is an edge.
And these two sides intersect at Y.
So you get ∠ WYU. As shown in the figure in the picture, 5 represents
∠ WYU
~Learn with Lenvy~
I am thinking of a number. The sum of its digits is divisible by 2. My number is a multiple of 11. My number is greater than 4 x 5 but less than 7 x 8+ 23. The number is a multiple of 3. What is my number? Is it possible to have more than one answer?
Answer:
66
Step-by-step explanation:
Number:xy
20<xy<79
Multiples of 2,3,11
The least common multiple of this number is 66.
What is the center and radius of the circle given by x2 + y2 - 10x - 12y + 24 = 0?
Answer:
centre (5, 6 ) , r = [tex]\sqrt{37}[/tex]
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r the radius
given
x² + y² - 10x - 12y + 24 = 0 ( collect x and y terms together and subtract 24 from both sides )
x² - 10x + y² - 12y = - 24
using the method of completing the square
add ( half the coefficient of the x / y terms)² to both sides
x² + 2(- 5)x + 25 + y² + 2(- 6)y + 36 = - 24 + 25 + 36
(x - 5)² + (y - 6)² = 37 ← in standard form
with centre (h, k ) = (5, 6 ) and r = [tex]\sqrt{37}[/tex]
Four eighths of kelly’s beads are red, 18 are white, and the rest are blue.
what fraction of kelly’s beads are blue?
Solve for x.
8.7 + X = 7
1.1
---
x = [?]
X = 62.4
:)
to get X, i would subtract, 71.1 - 8.7, and the answer would be X, not %100 sure though sorry.
20 people reported enjoying dancing and 11 of them were under 40. What percentage of people who enjoy dancing are under 40 years old?
Step-by-step explanation:
11 ÷ 20 = 0.55
0.55 × 100 = 55
so 55%
What shape am i 3equal side each 4cm not right angles
Answer:
Triangle
Step-by-step explanation:
A regular triangle has equal sides and no right angles. Hope this helps. ^^
Fifteen less than the square of a number is the same
as twice the number. Find the number.
Call the number : a
We have : [tex]a^{2} - 15 = 2a[/tex]
[tex]- > a^{2} - 2a = 15 - > a(a-2) = 15[/tex]
Now, we list all the numbers that can be multiplied to get 15 :
1 x 15 (and reverse)
3 x 5 (and reverse)
-1 x (-15) (reverse)
-3 x (-5) (a l s o r e v e r s e)
We substitute in :
If a = 1 -> a(a-2) = 1 x (-1) = -1 (not equal 15)
If a = 3 -> a(a-2) = 3 x 1 = 3 (not equal 15)
If a = -1 -> a(a-2) = -1 x (-3) = -3 (also not equal 15)
And if a = -3 -> a(a-2) = -3 x (-5) = 15 (satisfied)
So, the number is -3
Recheck : -3(squared) - 15 = 9 - 15 = -6
Twice of -3 = -6
[tex]========================================[/tex]
First of all, let the unknown number be z.
Then, "the square of z" means "z squared" which is the same as "z times z" or just z².
Now, "fifteen less than the square of z" means we subtract 15 from z²:
z²-15
Then, this equals twice the number, or 2 times z:
z²-15=2z
[tex]========================================[/tex]
Notes:-Hope everything is clear.Let me know if you have any questions!Always remember: [tex]\boxed{Knowledge~is~power!}[/tex]Enjoy your day!Answered by[tex]\boxed{An~Emotional~Helper}[/tex]:-)
Find the GCF of 78 and 93.
Answer:
3
Step-by-step explanation:
Prism M is a dilation of Prism N. The height of Prism M is 4 3/4 ft, and the volume of Prism M is 68 2/5 ft³. The height of Prism N is 2 3/8 ft. What is the volume of Prism N?Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
8 11/20 ft³
Step-by-step explanation:
For dilated figures, the ratio of volumes is the cube of the ratio of corresponding linear dimensions.
Vn/Vm = (Hn/Hm)³
Vn = Vm(Hn/Hm)³ = (68 2/5 ft³)((2 3/8 ft)/(4 3/4 ft))³
Vn = (342/5 ft³)((19/8)/(19/4))³ = (342/5 ft³)(1/2)³ = 342/40 ft³
Vn = 8 11/20 ft³
The volume of Prism N is 8 11/20 ft³.
Answer:
The answer is 8 11/20.
PLSS help this is important
(will give brainliest)
Answer:
A (first one)
Step-by-step explanation:
From T to T' you add 2 to the x and subtract 3 from the y
Then you do that to the x and y on O and Y
So for O, -4+2 is -2 and 1-3=-2
then you just do that for Y and you get (0,0) when applied
Use your TI-83 to determine the necessary t* value for a 90% confidence interval
based on a sample size of 55 and a sample standard deviation of 7.42.
2.005
1.669
1.96
1.645
2.67
Answer:
Step-by-step explanation:
It is 1.645. My calculator is a little off though; see attached picture.
A rectangular prism has a length of 3 inches, a width of 5 inches, and a height of 7 inches.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
in.³
Answer:
105³
Step-by-step explanation:
3x5=15
15x7=105
105 is your answer.
name 2 semi circles
Answer:
Arc CDE and arc EAC.
Step-by-step explanation:
Semicircles are exactly one-half of a circle and are always equal to 180 degrees. Since line CE is a horizontal line, measuring 180 degrees, 2 semicircles can be arcs CDE and EAC because they equal half of the circle.
I hope this helps!
If the scale factor here is 3 (k=3), and if the distance from A to B is 8 units, then what would be the distance from A’ to B’?
8
8/3
24
3
Distance between A'B':-
8k8(3)24Option C