Answer:
The sum of the first 12 terms of the sequence is 2703.673096
Step-by-step explanation:
The nth term of a geometric progression is a(n) = [tex]ar^{n-1}[/tex], where
a is the first termr is the common ratio between each two consecutive termsThe sum of n terms of the geometric progression is s(n) = [tex]\frac{a(r^{n}-1)}{r-1}[/tex]
∵ The third term of a geometric progression is [tex]\frac{63}{4}[/tex]
∴ a(3) = [tex]\frac{63}{4}[/tex]
∵ a(3) = ar²
→ Equate its two right sides
∴ ar² = [tex]\frac{63}{4}[/tex] ⇒ (1)
∵ The sixth term is [tex]\frac{1701}{32}[/tex]
∴ a(6) = [tex]\frac{1701}{32}[/tex]
∵ a(6) = a[tex]r^{5}[/tex]
→ Equate its two right sides
∴ a[tex]r^{5}[/tex] = [tex]\frac{1701}{32}[/tex] ⇒ (2)
→ Divide (2) by (1)
∴ r³ = [tex]\frac{27}{8}[/tex]
→ Take ∛ for both sides
∴ r = [tex]\frac{3}{2}[/tex] = 1.5
→ Substitute the value of r in (1) to find a
∵ a(1.5) = [tex]\frac{63}{4}[/tex]
∴ 1.5a = 15.75
→ Divide both sides by 1.5
∴ a = 10.5
→ Let us find the sum of the first 12 terms
∵ n = 12, a = 10.5, and r = 1.5
→ Substitute them in the rule of the sum above
∵ s(12) = [tex]\frac{10.5(1.5^{12}-1)}{1.5-1}[/tex]
∴ s(12) = 2703.673096
∴ The sum of the first 12 terms of the sequence is 2703.673096
use distributive property to rewrite 3×546
Answer:
1638
Step-by-step explanation:
3(500)+3(40)+3(6)=1500+120+18=1638
Find the value of k so that the line going through the points A(2,7) and B(k, 5)
is parallel to the line y=12x-1
Answer:
Step-by-step explanation:
parallel line y=12x+c
put this point A(2,7)
7=12*2+c
c=-17
so the equation is y=12x-17
now put the point B
k=12*5-17
k=43
X^2-5x+6=0 quadratic form
Answer:
x = 3,2
Step-by-step explanation:
solve for x by finding a,b,c and then apply the quadratic formula.
Answer:x
=
−
3
x
=
−
2
Explanation:
The quadratic formula is:
⇒
x
=
−
b
±
√
b
2
−
4
a
c
2
a
for a quadratic of the form
a
x
2
+
b
x
+
c
.
We have
a
=
1
,
b
=
5
, and
c
=
6
.
x
=
−
5
±
√
5
2
−
4
(
1
)
(
6
)
2
(
1
)
x
=
−
5
±
√
25
−
24
2
x
=
−
5
±
√
1
2
x
=
−
5
±
1
2
Hence,
x
=
−
6
2
=
−
3
and
x
=
−
4
2
=
−
2
I'm not sure why you wanted to use the quadratic formula, but you could just factor the quadratic:
x
2
+
5
x
+
6
=
(
x
+
3
)
(
x
+
2
)
=
0
x
+
3
=
0
→
x
=
−
3
and
x
+
2
=
0
→
x
=
−
2
Step-by-step explanation:
Ellon has 10 cups of flour. A special cake she make to sell in her bakery requires 2 1/3 cups of flour
Irina’s basketball team has a 1 in 6 chance of winning the first-place trophy. She rolled a six-sided number cube repeatedly, assigning her team a number from 1 to 6 to demonstrate the probability that her team would win. Which method did she use to collect her data? survey simulation experiment observational study
Answer:
b is right (simulation)
Step-by-step explanation:
edg
The method of data collection used is the simulation method
What is a number cube?A number cube (also known as a die) is a device that is used in simulating probabilities
Below is how to determine the method she used.
From the question, we have the following highlights:
Chance of winning = 1/6She rolls a number cubeThe outcome is assigned to the team that would winThe highlight 3 above implies that the method of data collection used in this question is the simulation method
This is so because the winning team is determined by rolling a number cube
Read more about random sampling at:
https://brainly.com/question/14470673
Ella is selling baked goods to raise money for charity. She spent $25.00 on baking
supplies. If each baked good sells for $0.75, what is the minimum number of baked
goods Ella needs to sell in order to raise $125.00 after the cost of supplies?
HELP
Answer:
I think the answer might be 141 baked goods. but I dont know don't trust me.
Step-by-step explanation:
Answer:
200.
Step-by-step explanation:
I know math. But if you want an explanation, here it is.
First, you have to add 25 to 125 because you're trying to gain 25 more dollars than 125 dollars to make up for the money you already spent. Next, you need to dive 150, the result of 125 plus 25, by .75 because you're trying to figure out how many goods you need to sell for .75 cents, to get 150 dollars. So, you do the division, and the answer is 200 dollars.
Which of the following is a prime number between 40 and 50? A. 41 B. 45 C. 44 D. 49
Answer:
A.41
Step-by-step explanation:
what is the missing number in the pattern?
Answer:
where's the pattern?
Step-by-step explanation:
you didn't post the pattern
Tank a holds 678500 gallons of water tank b holds 905867 gallons of water how much less water does tank a hold
Answer:
227367 gallon difference
Step-by-step explanation:
You take the Gallons in tank A and the gallons in tank B and you subtract them to find the difference
A mountain road rises 10 feet over a 206-foot run. What is its slope?
It's slope is 5/103 , by using simple calculation for slope.
What is slope?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively. The ratio of the "vertical change" to the "horizontal change" among (any) two distinct points along a line is used to calculate slope. The ratio can also be written as a quotient (also known as "rise over run"), which gives the same number for each and every two distinct points on same line.
Mathematically, it's calculated as "rise over run".
Here,
Rise is given i.e. 10feet.
and foot-run=206.
So, slope = Rise/foot-run
= 10/206
= 5/103 .
Hence, slope = 5/103.
Learn more about slope from given link:
https://brainly.com/question/25722412
#SPJ1
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 2, 3) and (0, negative 1). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (1, 0). Everything to the right of the line is shaded.
Which inequality pairs with y≤−2x−1 to complete the system of linear inequalities represented by the graph?
y −2x+2
y 2x−2
Answer:B i think......
Step-by-step explanation:
Answer: It's y>-2x+2
maria spent 4/7 of money on books,1/5 of it on a pen and 1/14 of it on a newspaper. She has left 220 naira. How much did she originally have?
which multiplication expression is equal to 5/6 ÷1/2
Answer:
enjoy that's the answer
Step-by-step explanation:
the answer is 5/3
Answer:
it would be 5/3 or 1 2/3
Step-by-step explanation:
Determine the range of the following graph:
Answer:
The range of the graph is [tex]Ran\{f\} = [-4, 11)[/tex].
Step-by-step explanation:
From Function Theory we identify the range of the function as the set of values on vertical axis (y-axis). According to the graphic, we find that the range of the following graph, which represents a bounded function, is:
[tex]Ran\{f\} = [-4, 11)[/tex]
The range of the graph is [tex]Ran\{f\} = [-4, 11)[/tex].
De’Shaun is 5 years younger than Nemo. Adela is twice as old as Nemo. Jefferson is 3 times as old as De’Shaun. Altogether their ages total 50. Find each person’s age
Answer:
Nemo: 10
De'Shaun: 5
Adela: 20
Jefferson: 15
Step-by-step explanation:
Let Nemo's age be x
De'Shaun's age= x-5
Adela's age= 2x
Jefferson's age= 3(x-5)
= 3x-15
x+x-5+2x+3x-15= 50
7x-20= 50
7x= 50+20
7x= 70
x= 10
Nemo's age= 10
De'Shaun's age= 10-5
= 5
Adela's age= 2(10)
= 20
Jefferson's age= 3(10)-15
= 30-15
= 15
Answer:
Age of Nemo = 10 years
De'shaun's age = 5 years
Adela's age = 20 years
Jefferson's age = 15 years
Step-by-step explanation:
Age of Nemo = x years
So, De'shaun's age = x - 5
Adela's age = 2*x = 2x
Jefferson's age = 3* (x -5) = 3*x - 3*5 = 3x -15
Total age = 50
x + x - 5 + 2x + 3x - 15 = 50 {Combine like terms}
x + x + 2x + 3x - 5 - 15 = 50
7x - 20 = 50
7x = 50 + 20
7x = 70
x = 70/7 = 10
Age of Nemo = 10 years
De'shaun's age = 10 - 5 = 5 years
Adela's age = 2* 10 = 20 years
Jefferson's age = 3*10 -15 = 30 - 15 = 15 years
Jane has saved 600 dollars in a college fund. She added money to the account over the next year and at the end of the year the account had 890 dollars. Write an equation to represent the amount she saved over the year.
Answer:
$290.00
Step-by-step explanation:
The equation would be 890-600=290 because if you subtract the base amount from the final savings it would give you how much she saved altogether.
Sunday by 11:59pm
Points
me di
Hal 0
Question
Laura's sporting goods store purchased a bicycle at the wholesale price of $400. Laura marked up the price 22%. What is
the amount of markup?
Provide your answer below:
B FEEDBACK
MORE INSTRUCTION
SUBMIT
Content attribution
Answer:
The amount of markup is 88 dollars.
Step-by-step explanation:
Given that the whole sale price of bicycle is: $400
[tex]P = \$400[/tex]
Mark up is the profit that the seller of the product makes after selling the product more in price more than its cost or buying price.
Given that mark up percentage is 22%
It can be written mathematically as:
[tex]Mark\ up = 22\%\ of\ Price\\Mark\ up = 0.22 * P\\Mark\ up = 0.22 * 400\\= \$88[/tex]
Hence,
The amount of markup is 88 dollars.
Write Word form for 6 (16+27)
Answer:
two hundred and fifty eight
Step-by-step explanation:
cause 6 (16+27) is equal to 258.
Or the equations is said six multiplied by 16 plus 27
What is the image point of (1, 4) after a translation left 5 units and down 5
units?
Answer:
(-4,-1)
All you have to do to find it is subtract x by 5 and subtract y by 5. :)
The car travelled at the constant speed of 50.5 mph for 3 hours.
How far did the car travelled?
151.5 miles
Step-by-step explanation:
50.5 × 3 = 151.5
Answer:
151.5 Miles
Step-by-step explanation:
A constant speed means the speed was the same throughout the whole trip, also meaning there were no stops. So the answer is as simple as 50.5x3
Hope this helps :)
Write the equation of the line that passes through the points (-8,-5) (5,−8)
Answer:
y=-3/13x-89/13
Step-by-step explanation:
m=y²-y¹/x²-x¹
m=(-8)-(-5)/5-(-8)
m=-3/13
y-y=m(x-x1)
y-(-8)=-3/13(x-5)
y+8= -3/13x+15/13
-8 -8
y=-3/13x-89/13
PLEASE IS DUE IN A FEW MINUTES..
An rock is thrown upward from a platform that is 214 feet above ground at 80 feet per second. Use the projectile formula to determine when the rock hit the ground.
WILL GIVE BRAINLIEST
Consider the line that passes through each pair of given points, and decide what type of slope the line has.
(2, 4) and (5, 1)
(-7, 8) and (-7,0)
(6,-3) and (-4,-3)
(3,5) and (-1,2)
Answer:
2.) undefined slope 3.) zero slope (i'm not sure what 1 and 4 are, sorry!)
Step-by-step explanation:
undefined slope has the same x-coordinate and the denominator becomes 0. it also is a vertical line. for a zero slope, it has the same y-coordinate and the numerator is 0. this is a horizontal line. *this is my first response so if i am wrong, that is embarrassing*
when was the bill of rights ratified
Answer:
Step-by-step explanation:
December 15, 1791
Answer:
December 15, 1791
Step-by-step explanation:
Translate the phrase into an algebraic expression.
2 more than y
Answer:
2 + Y
Step-by-step explanation:
Two more than Y would be adding 2 to y, therefore adding 2 to y.
2 + Y
This table shows the times it took four students to complete a 40-meter race.
Race Times
Student
Time
(in seconds)
Joe
13.07
Justin
13.6
Maria
13.06
Melinda
13.7
Which statement about these times is true?
A: 13.7 > 13.07
B: 13.07 > 13.6
C: 13.6 > 13.7
D: 13.06 > 13.07
If f(x) = x - 4 and g(x) = 3x + 5, find (f + g)(x).
a) 4x + 9
b) 2x + 9
c) 2x - 1
d) 4x + 1
Answer:
4x+9
Step-by-step explanation:
x-4 +3x+5
x+3x+5+4=4x+9
-100x - 100 = 0
-100x = ?
x = ?
Answer:
x = 100
Step-by-step explanation:
-100x - 100 = -100x
+100= +100
-100x= -100x + 100
x=100
Answer:
x = 100
Step-by-step explanation:
The total area of the polygon is 176 square feet. Find the value of x. x= ft
Answer:
x = 6 ft
Step-by-step explanation:
Area of the polygon = area of the square + 2(area of the triangle)
Area of the polygon = 176 ft²
Area of the square = length × width = 16 × 8 = 128
Area of the two triangles = 2(½*base*height) 2(½*x*8) = 8x
Plug in the above values into the equation for area of the polygon. Thus:
176 = 128 + 8x
Subtract 128 from each side
176 - 128 = 8x
48 = 8x
Divide both sides by 8
6 = x
x = 6 ft
Answer:
x=6ft
Step-by-step explanation:
Is this a function please help I’m failing
Answer:
Yes
Step-by-step explanation:
The relation is a function. For a relation to be a function there must be a unique x value for each y value. So this means x's can not repeat, and in this relation, the x-values never repeat. Therefore this is a function.