Find the 6th term of the geometric sequence whose common ratio is 3/2 and whose first term is 6.
Answer:
The 6th term will be:
[tex]a_6=\frac{729}{16}[/tex]
Step-by-step explanation:
Given
a₁ = 6common ratio r = 3/2To determine
a₆ = ?
A geometric sequence has a constant ratio r and is defined by
[tex]a_n=a_1\cdot r^{n-1}[/tex]
substituting a₁ = 6, r = 3/2
[tex]a_n=6\cdot \left(\frac{3}{2}\right)^{n-1}[/tex]
Determining 6th term
substituting n = 6 in the given equation
[tex]a_n=6\cdot \left(\frac{3}{2}\right)^{n-1}[/tex]
[tex]a_6=6\cdot \left(\frac{3}{2}\right)^{6-1}[/tex]
[tex]=6\cdot \frac{3^5}{2^5}[/tex]
[tex]=\frac{3^5\cdot \:6}{2^5}[/tex]
[tex]=\frac{3^5\cdot \:2\cdot \:3}{2^5}[/tex]
Cancel the common term
[tex]=\frac{3^6}{2^4}[/tex]
[tex]=\frac{729}{16}[/tex]
Therefore, the 6th term will be:
[tex]a_6=\frac{729}{16}[/tex]
If $5,000 is invested at 6% interest, how much money must be invested at 8% interest so that the total interest from the two investments is $660 after one year?
Answer:
$4500
Step-by-step explanation:
Simple Interest formula = Principal × Rate × Time
Let the amount of the money invested at 8% Interest = x
Hence:
$5000 × 6% × 1 + x × 8% × 1 = $660
$300 + 0.08x = $660
0.08x = $660 - $300
0.08x = $360
x = $360/0.08
x = $4500
Therefore , the amount that must be invested at 8% interest is $4500
If polygon ABCD is moved right 3 and up 2, what would the new coordinates of vertex D?
a) (0,9)
b) (1,0)
c) (4,2)
d) (-3,5)
the measure of ∠G is 82°. What is the measure of its compliment?
Answer:
First off, complementary angles are when 2 angles add up to 90 degrees. So if one angle is 82 degrees the other is 8 degrees.
Step-by-step explanation:
A basketball player made 44 out of 100 attempted free throws. What percent of free throws was made?
Answer:he has a 44% free throw rate
Step-by-step explanation:
Two dice are rolled in succession. Determine the probability that their sum is 10 or more, given that the first die is a 5 or 6. Show your work.
can someone give me an example of transformation of electrical to mechanical energy
ill mark u as brain list
Answer:
i need this for a challenge
Step-by-step explanation:
what is the value of y in the solution to the system of equations 5x-y=25 and x+4y=-10
Answer:
y=-3.571
Step-by-step explanation:
To get rid of the x's make the other x cancel out the other.
5x-y=25+(-5(x+4y=-10)=-21y=75= -3.571
Answer:
x+4y =10
5x-y =25
Step-by-step explanation:
x=10-4y
5(10-4y)-y =25
50-20y-y =25
50-21y = 25
-21y = 25-50
-21y =-25
y =25/21
Substitute y =25/21 in equation 1
x + 4(25/21) = 10
x +100/84 =10
x=10-100/84
if there are 5 people per 10000 buses how many will there be
Answer:
45 x 5 = 225 so 225 students altogether on 5 buses
Step-by-step explanation:
have a good day
Answer:
50,000 people.
Step-by-step explanation:
5 people on each bus.
10,000 buses total.
5 x 10,000 = 50,000
Find the length of side AB.
Give your answer to 3 significant figures.
C
410
13.5 cm
A
B
ANSWER:
sin41 × 13.5 = 8.85679
rounded to 3 sig fig
= 8.57
Answer:
8.86 cm
Step-by-step explanation:
The sine rule shows the relationship between the sides of a triangle and its opposite sides. Sine rule states that given a triangle with side a and opposite angle A, side b and opposite angle B, side c and opposite angle C then:
[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]
From the image attached, let AB = x, its opposite angle is 41°. BC = 13.5 cm and its opposite angle is 90° (right angle). Therefore using sine rule:
[tex]\frac{x}{sin(41)} =\frac{13.5}{sin(90)} \\\\x=sin(41)*\frac{13.5}{sin(90)}\\\\x=8.8568\\\\ x=8.86\ cm\ to\ 3\ s.f[/tex]
x = AB = 8.86 cm
On a city map 3/4 inch corresponds to 7 1/2 miles bonnie drives from her house to a movie theater and then from a movie theater to a restaurant. On the map the movie theater is 1/2 inch from her house and the restaurant is 3/4 inch from the theater how many miles does Bonnie driven when she gets to the restaurant
A. 1 1/4
B. 9 3/8
C. 10
D. 12 1/2
Answer:
Option D: [tex]12\frac{1}{2}[/tex] is the correct answer.
Step-by-step explanation:
Given that:
3/4 inches on map are equal to [tex]7\frac{1}{2}[/tex] miles
We will find the unit rate in term of inches.
[tex]\frac{3}{4}\ inches = 7\frac{1}{2}\\\\Unit\ rate = \frac{15}{2}*\frac{4}{3}\ miles\\\\Unit\ rate = 10\ miles\ per\ inch[/tex]
Total distance covered by Bonnie according to map;
Total distance = [tex]\frac{1}{2}+\frac{3}{4} = \frac{2+3}{4}[/tex]
Total distance = [tex]\frac{5}{4}\ miles[/tex]
Actual distance = [tex]\frac{5}{4}*10 = \frac{25}{2}\ miles \\[/tex]
Actual distance = [tex]12\frac{1}{2}\ miles[/tex]
Hence,
Option D: [tex]12\frac{1}{2}[/tex] is the correct answer.
I just need to write the standard form for the equation
Answer:
wcsvbth5435y4wte3rwth54u3
Which of the following correctly expresses the number below in scientific
notation?
0.00000628
Answer:
E. 6.28 x 10^-6
Step-by-step explanation:
8.5675859
rational or irrational ?
Answer: irrational
Step-by-step explanation:
Answer:
irrational
Step-by-step explanation:
A gray crayon is made with 5\text{ mL}5 mL5, start text, space, m, L, end text of black wax for every 6\text{ mL}6 mL6, start text, space, m, L, end text of white wax.
Step-by-step explanation:
Given that,
A gray crayon is made with 5 mL of black wax for every 6 mL of white wax.
We need to find the mixture will create the same shade of gray.
For this we need to make the ratio same.
If we multiply 5 mL and 6 mL by 3 to make the ratio same.
5 mL × 3 = 15 mL
6 mL × 3 = 18 mL
Hence, 15 mL of black wax mixed with 18 mL of white wax is mixed so as to make the ratio same.
Answer:
15ml of black wax mixed with 18ml of white wax
35ml of black wax mixed with 42ml of white wax
Step-by-step explanation: Khan Academy
2 3/8 x 3 3/4 divided by 2 2/3
Answer:
57/32
Step-by-step explanation:
171/32 divided by 2 2/3
A tennis camp charges $40 per student for a full-day
camp. The camp runs only if at least 5 students sign
up, and it limits the enrollment to 16 campers a day.
The amount of revenue, in dollars, that the tennis camp
collects is a function of the number of students that
enroll.
The equation R(n)=40n defines this function.
What is the input?
Answer:
40(5)= $200
Step-by-step explanation:
I think thats right but im not sure
What is the value of the function when x = 3?
y =
Answer:
9, plug 3 in for x and multiply 3(3)
What is the area of the real objet that the scale drawing models
A. 300 square cm
B. 60 square cm
C. 25 square cm
D. 12 square cm
Answer:
C. 25 square cm
Step-by-step explanation:
HELP PLZ
What connections can we make between finding the slope of a line connecting two points and the distance between those same two points?
Answer:
Using two of the points on the line, you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run: Slope =riserun Slope = rise run .
Step-by-step explanation:
hope this helps
what is the slope of the graph of the equation 4x - 6y=2?
A.-4
B.-1
C.2/3
D.3/2
2/3 is the slope of the graph of the equation 4x - 6y=2. Option C is correct.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The equation of the graph is 4x - 6y=2
We need to convert this to the slope intercept form y=mx+b
4x - 6y=2
Subtract 4x from both sides
-6y=2-4x
Divide both sides by -6
y=-2/6+4/6x
y=2/3x-2/6
Hence 2/3 is the slope of the graph of the equation 4x - 6y=2
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Select the correct answer.
What is the solution for x in the equation?
-3x+7X-8 = 34 + 9x-2
OA
L =
OB.
L =
COM
OC.
I = 8
OD.
I = -8
Answer:
-8
Step-by-step explanation:
-3x+7x-8=34+9x-2
we move the x's to the left and the numbers to the right
4x-9x=32+8
-5x=40
x=-40/5
x=-8
HELP! SSUUUUUUUUPER EASY! REEEEEEEEEEEALLY QUICK! I'm just du. mb
Answer:
15m^6
Step-by-step explanation:
Multiply 3 times 5
add 4 and 2
Which of the following expressions is equivalent to xy^3?
(options in the pic)
Answer:
A
Step-by-step explanation:
[tex] {xy}^{3} [/tex]
means that xy is being multiplied with itself thrice.
Hence,
[tex]xy \times xy \times xy[/tex]
i WILL give brainiest
Answer:
(9t/4)
Step-by-step explanation:
HERE'S UR ANS...FRND...
T×9
= ————
4
9T
= ———
4
I DONT WANT BRAINLIEST....I ONLY WANTED UR SATISFACTION....
HOPE IT HELPS...
at southeast middle school 16 1/4 % of the students wear braces. what fraction of the students wear braces?
Answer:
4
Step-by-step explanation:
divide them
Hey there!
16 1 / 4% = 16(4) + 1 = 64 + 1 = 65
65 / 4% = 16.25%
• Percentages usually run out of 100
16.25 / 100
• Finding out the ratio of your given number, multiply the numerator and denominator by the number 4
16.25 * 4 / 100 * 4
16.25 * 4 = 65 (numerator)
100 * 4 = 400 (denominator)
• Equation: 65 / 400
• REDUCE the GIVEN FRACTION (65/400)
• Once when you have the fraction reduced you should have came up with: 13/80 (aka your answer)
• Answer: 13/80 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
13 = -2 ( y - 4 ) + 3y
Answer:
5
Step-by-step explanation:
13 = -2y + 8 + 3y
13 = y+8
y = 5
4. A boat shop rents its boats for $20 per hour and charges a flat fee of
$10 dollars for insurance in case of damage. What is the total cost for
renting one boat for 5 hours? Hint: multiply and add the fee. *
O $100
$110
$30
O $70
Answer:
4 hours
Step-by-step explanation:
Let x = # of hours
22x + 10 = 98
-10 -10
____________
22x = 88
22
x = 4
Which is a like radical to 3 sqrt 54 and 3 sqrt 128 when the expression are simplified?
Answer:
A.) [tex]3\sqrt[]{2}[/tex]
Step-by-step explanation:
Edge 2020 assingment
Goodluck everybody!
∛2 is the radical part of both ∛54 and ∛128 when the expression are simplified.
What is Number system?A number system is defined as a system of writing to express numbers.
Let us write the prime factors of 54.
54/2 = 27
When fifty four is divided by 2 we get twenty seven.
27/3=9
Twenty seven divided by three is nine.
9/3=3
So 54 = 2 × 3 × 3 × 3
we know ∛ 3 × 3 × 3 = 3
∛54 = ∛ 3 × 3 × 3×2 = 3∛2
Hence, ∛2 is the radical part of both ∛54 and ∛128 when the expression are simplified.
To learn more on Number system click:
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Which rule applies to the translation of the RED trapezoid to the BLUE trapezoid?
)
(c.y) - (x* 2, y- 3)
B)
(x. y) - (x+ 4, y- 5)
(x, y) - (x + 2, y - 5)
D)
(.Y) - (x- 2, y - 5)
Answer:
b
Step-by-step explanation: