The 10th, 4th and 1st term of an A.P are three consecutive find the common ratio of the G.P and the sum of the 6th term, taking the 1st term to be 4
Answer:
S_6 = 252
Step-by-step explanation:
We are told that the 10th, 4th and 1st term of an A.P are three consecutive terms of a G.P.
Now,formula for nth term of an AP is;
a_n = a + (n - 1)d
Thus;
a_10 = a + (10 - 1)d
a_10 = a + 9d
Also;
a_4 = a + (4 - 1)d
a_4 = a + 3d
First term is a.
Thus, since they are consecutive terms of a G.P, it means that;
(a + 9d)/(a + 3d) = (a + 3d)/a
Cross multiply to get;
a(a + 9d) = (a + 3d)(a + 3d)
a² + 9ad = a² + 6ad + 9d²
a² will cancel out to give;
9ad - 6ad = 9d²
3ad = 9d²
Divide both sides by 3d to get;
a = 3d
We are told that the first term is 4.
Thus, 4 = 3d
d = 4/3
We saw earlier that ratio of the GP is (a + 3d)/a
Thus; r = (4 + 3(4/3))/4 = 8/4 = 2
Sum of n terms of a G.P is given by;
S_n = a(rⁿ - 1)/(r - 1)
S_6 = 4(2^(6) - 1)/(2 - 1)
S_6 = 252
Both Kendra and maria tutor students after school. The table below shows the amount of money Kendra earned tutoring after school based on the number of hours tutored. maria calculates her earnings based on the number of hours she does using the equation P=9.1h. They each tutored 22 hours last week. who made the most money
Answer:
Maria made more money
20 points, help. I have this due in like 20 minutes.
Answer:
in sequence, -7, 3, 43, -27
Step-by-step explanation:
IF YOU KNOW MATH PLS HELP ME
Answer:
x ≈ 2.55
Step-by-step explanation:
Since the triangles are congruent then DE ≡ AB , that is
DE = AB
76x - 7 = x + 184 ( subtract x from both sides )
75x - 7 = 184 ( add 7 to both sides )
75x = 191 ( divide both sides by 75 )
x ≈ 2.55 ( to the nearest hundredth )
Graph the equation.
y + 2 = 3(x + 1)
Answer:
it is a
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
Slope: 3
y-intercept: (0,1)
can someone help? i need help ♀️
Answer:
Mean: 29.6
MAD: 10
Step-by-step explanation:
Answer:
Mean = 29.6
MAD = 10
Step-by-step explanation:
For the mean, just add all of the points together and divide it by 10 since there are 10 games.
For the MAD, use the mean and subtract is from each of the games. As an example, just do 23-29.6 and ignore if it is a negative sign. Do it for all and then add up the leftovers. Then divide it by the 10 games.
(6.6+1.4+1.6+8.4+10.6+8.4+15.4+4.6+26.6+16.4)/10
Check out a khan academy video about it if you're having trouble
Chocolate Cravings sells 6 chocolate covered pretzels for $1.80 and 5 chocolate covered strawberries for $6.00. At this rate, what is the total cost of buying 2 pretzels and 2 strawberries? WHO EVER ANSWERS THIS FIRST WILL GET 45 POINTS AND WILL BE RATED BRAINIEST
Answer:
60 for chocolate pretzels and 1.50 for strawberry for the total cost will be 2.10$
Step-by-step explanation:
Answer:
the total would be 1.50
Step-by-step explanation:
Devon has been saving $5 & $10 for the past four years. Over spring break he wanted to see how much money he has saved up. After counting the money he calculated that he has a total of $395 & had 49 bills. Based on this information, how many $5 & $10 bills does he have?
Answer:
19 five dollar bills
30 ten dollar bills
Step-by-step explanation:
x=number of $5 bills
y=number of $10 bills
x+y=49
x=49-y
5x+10y=395
substitute for x
5(49-y)+10y=395
245-5y+10y=395
245+5y-245=395-245
5y=150
5y/5=150/5
y=30
x=49-30=19
Lainey bought a set of 20 markers for $6
What is the cost of 111 marker?
Answer:
370
Step-by-step explanation:
First find the unit rate aka price per pencil: 20 divided by 6 equals 3.333
Then find amount for all pencils
3.333 by 111 is 369.963
Then we round up to have a realistic amount of pencils to 370
In EFG, L is the centroid. If LJ=9 find EL.
Answer:
LG=LE=LF since it is the centroid. So I think it would also be 9.
PLZ PLZ PLZ help 50 points
Answer:
i think im to late sorry
Step-by-step explanation:
$1111 at 11% for 11 years
Answer:
$1344.31
Step-by-step explanation:
1111*0.11*11=1344.31
PLEASE HELP :))
3
Solve for x.
6
12
5
r-1
Answer:
12 is the answer
Step-by-step explanation:
12 is the answer
Work out the perimeter of a regular octagon with side length 2.6mm
Answer:
20.8mm
Step-by-step explanation:
We know that an octagon has 8 sides, and since this is a regular octagon we can safely say that all sides are equal.
This means all sides are 2.6mm.
So if we run the calculation:
2.6mm × 8 = 20.8mm (Side Length × Number of Sides = Perimeter)
We have our final answer!
I = Prt (solve for P)
Answer:
Step-by-step explanation:
Divide both sides by rt
[tex]P=\frac{I}{rt}[/tex]
Answer:
[tex]p=\frac{i}{rt}[/tex]
Step-by-step explanation:
What is an equation of the line that passes through the points (4, -5) and (2, 0)?
Answer:
y = - [tex]\frac{5}{2}[/tex] x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, - 5) and (x₂, y₂ ) = (2, 0)
m = [tex]\frac{0+5}{2-4}[/tex] = [tex]\frac{5}{-2}[/tex] = - [tex]\frac{5}{2}[/tex] , then
y = - [tex]\frac{5}{2}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (2, 0 )
0 = - 5 + c ⇒ c = 0 + 5 = 5
y = - [tex]\frac{5}{2}[/tex] x + 5 ← equation of line
Burger = 8.00
Fries = 2.00
Drink = 1.00
Tax = 7%
Tip = 20%
Total = _______
Answer:
$13.79
Step-by-step explanation:
$8.00+$2.00+$1.00=$11.00
7%=$0.77
$11.00+$0.77=$11.77
20%=$2.02
$11.77+42.02=$13.79
What is the area of the squares? The problems are in the picture below. 15 points!!!
Answer:
Top Left= 40yd²
Top Right= 441yd²
Bottom Left= 21ft²
Bottom Right= 105ft²
Step-by-step explanation:
Top left- 10×4= 40
Top right- 21×21= 441
Bottom right- 7×3= 21
Bottom left- 15×7=105
Akira and Hideo are twins with different jobs. Akira earns five-eighths of what Hideo earns, but Akira’s expenses are half of Hideo’s. Akira ends up saving 40% of his income. What percentage of his income does Hideo save?
9514 1404 393
Answer:
25%
Step-by-step explanation:
Apparently, we're to assume that anything not spent is saved.
Let Hideo's income be 1. Then Akira's income is 5/8. Akira's expenses are 60% = 3/5 of that value, so ...
Akira's expenses = (3/5)(5/8) = 3/8 . . . . . of Hideo's income
Hideo's expenses are twice this amount, so ...
Hideo's expenses = (2)(3/8) = 3/4 . . . . . of Hideo's income
That means Hideo saves 1 -3/4 = 1/4 = 25/100 = 25% of his income.
Hideo saves 25% of his income.
8.) The cross country team ran 1.428 hours yesterday and 1.24 hours today. Each member of the team ran 3.3 miles every hour. How many miles did each member run yesterday?
9514 1404 393
Answer:
4.7124 mi
Step-by-step explanation:
(3.3 mi/h) · (1.428 h) = 4.7124 mi
Each team member ran 4.7124 miles yesterday.
Angle 3 is equal to angle
A local movie theater has an offer that for every seven movies you pay to go see, they will give you free passes for two other movies. If you paid to see 42 movies last year, how many free passes did you receive?
_free passes
A local movie theater has an offer that for every seven movies you pay to go see, they will give you free passes for two other movies. If you paid to see 42 movies last year, how many free passes did you receive?
Answer: 12
Step-by-step explanation: 42/7 = 6 and you get 2 free passes so 6 x 2 = 12
A polling firm wants to use a one-sample z interval to estimate what proportion of voters in a country plan on
voting for a certain candidate. They want the margin of error to be no more than £3% at 99% confidence.
What is the smallest sample size required to obtain the desired margin of error?
Answer:
1844
Step-by-step explanation:
For polling firm survey on voters, the smallest sample size which is required to obtain the desired margin of error, is 1850.
What is margin of error?The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.
[tex]MOE=z\times\dfrac{\sigma}{\sqrt{n}}[/tex]
Here, z is the critical value and n is the sample size.
Here, a polling firm wants to use a one-sample z interval to estimate, the number of proportion of voters in a country plan on voting for a certain candidate.
The margin of error for this test is 3% or 0.03 and the confidence interval is 99 percent.
The z value on the confidence interval of 99 percent is 2.576. Here, the standard deviation for this survey is 50 percent, or 0.50.
Put the value in the above formula as,
[tex]0.03=(2.576)\times\dfrac{0.5}{\sqrt{n}}\\n\approx1850[/tex]
Hence, for polling firm survey on voters, the smallest sample size which is required to obtain the desired margin of error, is 1850.
Learn more about the margin of error here;
https://brainly.com/question/10218601
guys plz help im not good at this
Answer:
Radius is 3.5 cm
Diameter is 7 cm
Step-by-step explanation:
Radius is half the diameter
They give you the diameter at 7 cm
Then you have to half that to get 3.5 cm as the radius
Answer:
The answers are the diameter is 7 because whatever the line across is it's the diameter and the radios is half of what the diameter is so whatever is half of 7 is your radios.
Step-by-step explanation:
Diameter: 7
Radios: 3.5 or 3 1/2
How many times bigger is a group of 21 marbles than a group of 7 marbles?
Answer:
21/7=3
3 times bigger.
Step-by-step explanation:
I need this questions done for my class, we went over this but I forgot. Can you guys say the answer and explain so I don’t forget again? Thank you so much!
1) 2/5 x 3 =?
Since we cannot possibly cancel the denominators, let us multiply 2 and 3.
Answer will become, 6/5.
2) 2/3x3 =?
We can cut 3 and 3.
Answer will become, 2.
3) 2/5 x 3=?
This is a repeated question and the answer remains the same as the 1st question's answer, 6/5.
4) 3/2 x 3=?
We cannot cancel the denominators, let us multiply 2 and 3.
Answer is, 9/2.
Write 14/square root of 2 + square root of 50 in the form b square root of 2 where b is an integer
Step-by-step explanation:
[tex] \frac{14}{ \sqrt{2} } + \sqrt{50} \\ \frac{ \sqrt{2} \times \sqrt{2} \times 7}{ \sqrt{2} } + \sqrt{25 \times 2} \\ \\ 7 \sqrt{2} + 5 \sqrt{2} = 12 \sqrt{2} [/tex]
The given expression can be written in the form of b√2 as 12√2 where b = 12.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given expression is [tex]14/\sqrt{2}+\sqrt{50}[/tex].
It can be rewritten as,
[tex]14/\sqrt{2}+\sqrt{50}[/tex]
Multiply √2 to both numerator and denominator of 14/√2 as,
14√2/2 + √50
⇒ 7√2 + √(5 × 5 × 2)
⇒ 7√2 + 5√2 = 12√2
On comparing 12√2 with b√2, it is obtained as,
b = 12
Hence, the given expression can be written as 12√2.
To know more about algebraic expression click on,
brainly.com/question/953809
#SPJ2
if the length of the longest side of the rectangle is 20cm find the shaded area to the nearest hundredth PLEASE HELPP !
Answer:
150pi
Step-by-step explanation:
lets just say the two circles are 10 and 10 in diameter. so, one square is 5 radius. The square is 25pi area. so two are 50pi area. the area of the rectangle is 200, so 150pi
Please tell me if I'm wrong D:
helpppppppp i'm literally starting to think i need a tutor
Answer:
x = 55
Step-by-step explanation:
Here, we want to get the value of x
From the diagram , we can see that we have a right- triangle
and thus,
x + 35 = 90
x = 90-35
x = 55
write the equation of this line in y= mx + b form:
Answer:
y = 2.5x + 3
Step-by-step explanation:
y = mx + b
y = 2.5x + 3
As you can see, each unit is not 1, its 0.5. We need to go up 5 times, and so 0.5 times 5 gives us 2.5, and thats how i got my slope.
I got 3 as my y-intercept because it's were the line intersects the y axis.
Hope this helped!
Have a supercalifragilisticexpialidocious day!
Answer:
y=5x+3
Step-by-step explanation:
Slope: y2-y1 over x2-x1 so it will be 3-(-2) over 0-(-1) and the answer will be 5.
Y intercept: In order to find the y intercept it is necessary to replace the y an x coordinate in the equation: y= mx+b and replace 3=5(0)+b... simplifying would be 3=b
so the final answer would be y=5x+3