Answer:
aₙ = 5*(1/5)^(n - 1)
Step-by-step explanation:
The recursive relation for a geometric sequence is:
aₙ = aₙ₋₁*R
where R is the common ratio.
We could write this in a general form as:
aₙ = a₁*(R)^(n - 1)
where a₁ is the first term of the sequence.
In this case we know that:
R = 1/5
And that:
a₆ = 1/625
Then we can replace these values in the above relation to get:
a₆ = (1/625) = a₁*(1/5)^(6 - 1) = a₁*(1/5^5) = a₁*(1/3125)
1/625 = a1*(1/3125)
(3125/625) = a1 = 5
Then the formula will be:
aₙ = 5*(1/5)^(n - 1)
How many natural numbers are between 34 and 72? and, how many whole numbers between -2 and 25?
Answer:
There are 37 natural numbers between 34 and 72.
There are 25 whole numbers between -2 and 25.
Step-by-step explanation:
1. Natural numbers between 34 and 72
2. Whole numbers between -2 and 25
1.35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71.
2.0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24.
A salesperson at a jewelry store earns 5% commission each week. Last week, Heidi sold 640 worth of jewelry. How much did Heidi make in commission? How much did the jewelry store make from sales?
Answer:
12,800 Dollars USD
Step-by-step explanation:
Helppp pleaseeee xxxxx
Answer:
[tex] h = 3\sqrt{3} [/tex]
[tex] c = 4\sqrt{2} [/tex]
Step-by-step explanation:
✔️Finding h using trigonometric ratio:
Reference angle = 60°
Opposite = h
Adjacent = 3
Thus:
[tex] tan(60) = \frac{h}{3} [/tex]
[tex] \sqrt{3} = \frac{h}{3} [/tex] (tan 60 = √3)
Multiply both sides by 3
[tex] 3\sqrt{3} = h [/tex]
[tex] h = 3\sqrt{3} [/tex]
✔️Finding c using trigonometric ratio:
Reference angle = 45°
Hypotenuse = 8
Adjacent = c
Thus:
[tex] cos(45) = \frac{c}{8} [/tex]
[tex] \frac{\sqrt{2}}{2} = \frac{c}{8} [/tex] (cos 45 = √2/2)
Multiply both sides by 8
[tex] \frac{\sqrt{2}}{2} \times 8 = c [/tex]
[tex] \sqrt{2} \times 4 = c [/tex]
[tex] c = 4\sqrt{2} [/tex]
At Barlow school, 4/9 of the 873 students are boys. At Willow school, 2/3 of the 630 students are girls
Which school has a greater of boys and how many?
Answer:
I have attached the answer
Mr.Farrar spent a total of $43.87 after tax on new clothes at a clothing store. He brought 1 pair of sandals for $8.02 t-shirts fo $9.49 each and 1 pair of jeans. The tax on the purchase was $2.87 how much did Mr.Farrar pay for the pair of jeans?
Answer:
43.87 - 8 = 35.87 (sandals)
9.49 + 9.49 = 18.98 ( for two t-shirts)
35.87 - 18.98 = 16.89 (t-shirts)
16.89 - 2.87 = 14.02 (taxes)
Andrea payed $14.02 for a pair of jeans
Hopes this helps you!
Step-by-step explanation:
What’s the value of x? :/
Answer:
[tex] x = 27 [/tex]
Step-by-step explanation:
According to congruent chords and arcs theorem, if [tex] \overline{XY} \cong \overline{ZY} [/tex] then [tex] \arc{XY} \cong \arc{ZY} [/tex].
This means that [tex] \arc{XY} = \arc{ZY} = (6x - 20) degrees [/tex]
Thus:
[tex] \arc{XY} + \arc{ZY} + \arc{ZX} = 360 [/tex] (full circle = 360°)
[tex] \arc{XY} = (6x - 20) [/tex]
[tex] \arc{ZY} = (6x - 20) [/tex]
[tex] \arc{ZX} = 76 [/tex]
Plug in the values into the equation
[tex] (6x - 20) + (6x - 20) + 76 = 360 [/tex]
[tex] 6x - 20 + 6x - 20 + 76 = 360 [/tex]
Add like terms
[tex] 12x + 36 = 360 [/tex]
Subtract 36 on both sides
[tex] 12x = 360 - 36 [/tex]
[tex] 12x = 324 [/tex]
Divide both sides by 12
[tex] x = 27 [/tex]
Thee questionn is beloww
Given:
[tex]m\angle ABC=60[/tex]
To find:
The [tex]m\angle ADC[/tex].
Solution:
In circle B, [tex]\angle ABC[/tex] is central angle and [tex]\angle ADC[/tex] is inscribed angle from two points A and C.
According to central angle theorem, central angle is always twice of inscribed angle.
[tex]m\angle ABC=2(m\angle ADC)[/tex] [Central angle theorem]
[tex]60=2(m\angle ADC)[/tex]
Divide both sides by 2.
[tex]\dfrac{60}{2}=m\angle ADC[/tex]
[tex]30=m\angle ADC[/tex]
Therefore, [tex]m\angle ADC=30[/tex].
Nate has $50 to spend at the grocery store. he fills his shopping cart with items totaling $46 at checkout he willhave to pay 6% sales tax on all items in the cart. Does he have enough money to buy everything in his cart?
Answer:
Yes
Step-by-step explanation:
This is becuase 46 x 1.06= 48.76, thats less than $50.
Answer:
yes
Step-by-step explanation:
tax will be $2.76 therefore it will come up to $48.76
A pipe is leaking in the school bathroom . it leaked 3 gallons of water in 6 hours.
Find the constant of proportionality
Answer:
0.5 gallons per hour
Step-by-step explanation:
Please help I'll give brainlest
Which of the following is 1,215 divisible by? Select all that apply.
A.3
B.2
C.9
D.10
E.5
F.8
G.4
H.6
Answer: A,C,E
Step-by-step explanation:
All of the other answers give you a decimal.
Answer:
ACEStep-by-step explanation:
A
1215 divided by 3 = 405
B
1215 divided by 9 = 135
C
1215 divided by 5 = 243
*The other answers can give a decimal answer.
A large rectangle is made by joining three identical small rectangles as shown.
The perimeter of one small rectangle is 21cm. The width of one small rectangle is x cm.
Work out the perimeter of the large rectangle. The final line of your answer should be the form, perimeter of large rectangle is ...cm
Answer: 35 cm
Step-by-step explanation:
As shown in the image attached, the A large rectangle is made by joining three identical small rectangles,
The width of one small rectangle is x cm and the length of one small rectangle is 2x cm. Therefore the perimeter of the small rectangle is given as:
2(length + width) = Perimeter
2(2x + x) = 21
2(3x) = 21
6x = 21
x = 21/6 = 3.5 cm
x = 3.5 cm
From the image attached, the width of the large rectangle is 2x (x + x) and the length is 3x (2x + x). Therefore, the perimeter of the large rectangle is:
2(length + width) = Perimeter
2(3x + 2x) = Perimeter
Perimeter = 2(5x)
Perimeter = 10x
Perimeter = 10(3.5)
Perimeter = 35 cm
Step-by-step explanation:
Perform the following operation
and express the answer in
scientific notation.
6.300x10^-5 – 7.200x10^-3
[?]*10
Answer:
Step-by-step explanation:
6.3 x10^-5 -7.200 x10^-3= - 0.007137=7.137x10-3
Answer:-7.137 x 10^-3
Step-by-step explanation:
Lucy $154 made for 11 hours of work. At the same rate, how much would she make for 8 hours of work?
Answer:
19.25
Step-by-step explanation:
3/5+(-7/5)= can someone help me with this please
Answer:
[tex]-\frac{4}{5}[/tex]
Step-by-step explanation:
Because both of the fractions have a common denominator they can be subracted without any other work.
Find the indicated probability.
If P(A or B) = 0.8, P(A) = 0.4, and P(A and B)= 0.15, find P(B).
P(B)=
(Simplify your answer. Type an integer or a decimal.)
Answer:
[tex]P(B) = 0.55[/tex]
Step-by-step explanation:
Given
[tex]P(A\ or\ B) = 0.8[/tex]
[tex]P(A) = 0.4[/tex]
[tex]P(A\ and\ B) = 0.15[/tex]
Required
Find P(B)
In probability, we have:
[tex]P(A\ or\ B) = P(A) + P(B) - P(A\ sd B)[/tex]
Substitute values
[tex]0.8 = 0.4 + P(B) - 0.15[/tex]
Collect Like Terms
[tex]P(B) = 0.8 - 0.4 + 0.15[/tex]
[tex]P(B) = 0.55[/tex]
A company that makes hair care products had 9,000 people try a new shampoo. Of the 9,000 people,
18 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
Answer:
0.2%
Step-by-step explanation:
18/9000×100%
now use calculator
Answer: 0.2 percent
Step-by-step explanation:
This is the number of people who were allergic to the shampoo/ total people
18/9000
Simplify!
1/500=0.02=0.2 percent of people
Which substitution method should be the best used to solve which system of equations
Answer: 6x+2y=1
Step-by-step explanation:
because it just is
Find the size of the angle 2 x
Answer:
Given - Angles measure 2x , X and 3x
To find - Measures of 2x
Solution -
2x + X = 180° ( forming linear pair )
3x = 180°
x = 180/3
x = 60°
2x = 2 × 60 = 120°
Answer:
120°
plz give brainlist
Step-by-step explanation:
since 2x and x form a straight angle you get the equation
2x + x = 180
combine like terms
3x = 180
devide by 3
x = 60
evaluate 2x
2(60) = 120
What is the inverse of the function f(x) = x +3?
1- First, replace f(x) with y
f(x) = x +3 ⇒ y = x + 3
2. Replace every x with a y and replace every y with an x .
y = x + 3 ⇒ x = y + 3
3. Solve the equation from Step 2 for y.
x = y + 3 ⇒ y = x-3
4 - Replace y with f⁻¹(x).
f⁻¹(x) = x-3
The inverse is f⁻¹(x) = x-3
9 × ( 6+ 11 ) = (9 6) (9 11)
assuming the 9 6 and 9 11 are fractions, we get:
9 x ( 6 + 11 ) = (9/6) (9/11) =
153 = 27/22
Answer:
9(17) = (9 x 6)+(9 x 11)
153 = 54 + 99
153 = 153
Hope this helped! If it did, please give me brainliest! It would help a lot! Thanks! :D
Helpppp pleaseeeeeeee
Answer:
x= 6.85 or 89/13
Step-by-step explanation:
perimeter is sum of all sides added, so add them all and set them equal to 84
4(x-3) + 3x - 1 + 6x + 8 = 84
distribute
4x + 12 + 3x - 1 + 6x + 8 = 84
combine like terms
13x - 5 = 84
solve for x
x = 89/13 = 6.85
I need help with this
Answer:
A.
Step-by-step explanation:
I gotchu fam. The first thing that you would want to do is find the slope. The slope is the change in y divided by the change in x. Based on the points on the line, the change in y is 2 because it goes up two, and the change in x is one because it goes over 1. This would make your slope 2/1, or just 2! Now we have our slope, so we want to find our y-intercept. There are two ways that we can do this. The first way is just eyeballing it, but sometimes that's not always accurate. We're just going to do that because its faster (lol). It looks around -2. With this information, we have our entire equation! y=mx+b. we can plug in our information. y=2x-2. And that's how your answer's A! Hope this helps.
The graph shows the number of hours that Tammy spends typing for work, x, and the amount of pay that she earns, y.
What is the slope of the line?
- 1 / 4
- 8 / 17
- 4
- 6
Answer: The slope of the line = 4.
Step-by-step explanation:
We know that ,
Slope of a line passes through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Here , the line passes through points (2,18) and (8,42).
Then the slope of the given line = [tex]\dfrac{42-18}{8-2}[/tex]
[tex]=\dfrac{24}{6}=4[/tex]
Hence, the slope of the line = 4.
Answer:
4
Step-by-step explanation:
i took the test and got it right
Solve for n.
below
.....................
Answer:
n = 12
I hope this helps!
unit rate of 122 and 10 please
I need help right now brain listed if somone helps me!
Answer:
6/5
Step-by-step explanation:
Remember: to divide a number by a fraction, invert the fraction and multiply.
Here "the number" is 4/5 and you want to divide it by 2/3. Invert the '2/3', obtaining 3/2, and then multiply the '4/5" by '3/2":
12/10 = 6/5 (answer)
Find the LCM of the denominators in these fractions
5/6 and 1/14
Answer:
35/42 and 3/42
Step-by-step explanation:
Multiply by 3.
HOPE THIS HELPS :)
The LCM of the denominators in the fractions 5/6 and 1/14 is 42.
What is Least Common Multiple(LCM)?The least common multiple is defined as the least positive integer that is dividable by both given numbers.
A group's Least Common Multiple (LCM) is the smallest number that is a multiple of all the numbers.
To find the least common multiple (LCM) of two numbers, you can list the multiples of each number and find the smallest number that is a multiple of both.
The multiples of 6 are 6, 12, 18, 24, 30, and so on. The multiples of 14 are 14, 28, 42, 56, and so on. The smallest number that is a multiple of both 6 and 14 is 42, so the LCM of 6 and 14 is 42.
Therefore, the denominators in the fractions 5/6 and 1/14 have an LCM of 42.
To learn more about the Least Common Multiple(LCM) here :
https://brainly.com/question/17256135
#SPJ2
What is the only number that is a factor of every number?
A.5
B.2
C.1
D. 3.54
Answer:
the answer of the question is c.1
Express as a fraction or a mixed number
1 1/2%
Answer:
5 and 1/2
Step-by-step explanation:
Is 5/12 closer to 0, 1, 1/2
Answer:
1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
1/2 is 6/12. 6/12 is close to 5/12 than the others.