Answer:
A
Step-by-step explanation:
The sum to infinity of a geometric series is
S (∞ ) = [tex]\frac{a}{1-r}[/tex] ( - 1 < r < 1 )
where a is the first term 8 and r is the common ratio, hence
S(∞ ) = [tex]\frac{8}{1-\frac{1}{2} }[/tex] = [tex]\frac{8}{\frac{1}{2} }[/tex] = 16
This sum of the infinite geometric series is 16 since the correct option is (A) 16.
Definition of infinite geometric series:The sum of infinite geometric sequences is called an infinite geometric series. There would be no final term in this series. The infinite geometric series has the general form a1+a1r+a1r2+a1r3+..., where a1 is the first term and r is the common ratio. The sum of all finite geometric series can be found.
How to find the sum of the series?In terms of the first term a1 and the common ratio r, the sum is...[tex]S =\frac {a_1}{(1-r)}[/tex]
We discover... by substituting the given numbers and performing the arithmetic...[tex]S = 8/(1 -1/2) = 16[/tex]
The total number of items in the series is 16.
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HELPP ASSAP WILL MARK BRAINIEST
Answer:
Step-by-step explanation:
H=7+30t-16t²
20=-16t²+30t+7
0=-16t²+30t-13
T=(-30±√(900-4(16)13))/-32
T=0.68 s or T=1.2 s
Answer:
Step-by-step explanation:
f(x)=-11x-2 and g(x) =7x-4 find (f°g)(x)
Answer:
- 77x + 42
Step-by-step explanation:
note that (f ○ g)(x) = f(g(x)
Substitute x = g(x) into f(x)
f(g(x))
= f(7x - 4)
= - 11(7x - 4) - 2
= - 77x + 44 - 2
= - 77x + 42
Mark's soup recipe makes 6 servings and uses 4 carrots and 2 potaoes. How many potaoes and carrots does mark need for 15 servings?
Answer:
10 carrots and 5 potatoes
Step-by-step explanation:
1) 15÷6=2.5
2)4 x 2.5=10
3)2 x 2.5=5
oc is perpendicular to ab
Since OC is perpendicular to AB, the line AB gets split evenly. So
[tex]ab = 2ac[/tex]
So AB=2*6.7=13.4
Ans: Option B, 13.4 units
Length of ab is B. 13.4 units
What is a circle?A closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre" is called a circle.In a circle the length of the chord is bisected by the perpendicular joining the center.How to find the length of ab?According to the problem,
ab is the chord.oc is perpendicular to ab∴ OC should bisect AB
Length of AC = Length of BC = 6.7 units∴ Length of AB = 13.4 units.
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Simplify the expressions. Show your work.
(X-2) (3x-4)
Please don’t guess
Answer: 3x^2-10x+8
Step-by-step explanation:
x*3x+x(-4)+(-2)*3x+(-2)(-4) Foil Method
3x^2-4x-6x+8 Add and subtract like factors
Answer:
3x² - 10x + 8Step-by-step explanation:
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex](x-2)(3x-4)=(x)(3x)+(x)(-4)+(-2)(3x)+(-2)(-4)[/tex]
[tex]=3x^2-4x-6x+8[/tex] combine like terms
[tex]=3x^2+(-4x-6x)+8=3x^2-10x+8[/tex]
PLEASE HELP
City A and city B each have 10 parks. The table shows the number of acres for each park in the two cities.
City A : 6 9 10 7 10 10 2 5 8 8
City B : 5 10 8 11 7 12 6 5 4 5
Select from the drop-down menus to correctly complete each statement.
The mean number of acres for each park for the two cities is:
A. About the same
B. Much greater for City A than for City B
C. Much greater for City B than for City A
The range for the number of acres for parks for the two cities is:
A. The same
B. Greater for City A than for City B
C. Much greater for City B than for City A
The mean number of acres for each park for the two cities is:
City A: 7.5
City B: 7.3
Hence, It is Much greater for City A than for City B.
And, The range for the number of acres for parks for the two cities is : 8
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
The table shows the number of acres for each park in the two cities.
City A: 6 9 10 7 10 10 2 5 8 8
City B : 5 10 8 11 7 12 6 5 4 5
For City A:
Minimum acre of park = 2
Maximum acre of park = 10
Hence, Range = Maximum-Minimum
Range = 10-2
Range = 8
Now mean is calculated as:
Mean = 6 + 9 + 10 + 7 + 10 + 10 + 2 + 5 + 8 + 8 / 10
= 75/10
= 7.5
For City B:
Minimum acre of park = 4
Maximum acre of park = 12
Hence, Range = Maximum-Minimum
Range = 12-4
Range = 8
Now mean is calculated as:
Mean = 5 + 10 + 8 + 11 + 7 + 12+ 6 + 5+ 4 + 5 / 10
= 73/10
= 7.3
Hence, The mean number of acres for each park for the two cities is:
City A: 7.5
City B: 7.3
Hence, It is Much greater for City A than for City B.
And, The range for the number of acres for parks for the two cities is : 8
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Translate the sentence into an equation. Twice the difference of a number and 4 equals 5 . Use the variable x for the unknown number.
Answer:
2(x-4) = 5
Step-by-step explanation:
2(x-4) = 5 since the difference of a number and 4 translates to x-4 and twice the difference translates to 2(x-4).
The required equation is, 2(x-4) = 5
What is equation ?
It is a mathematical statement which contains two algebraic expressions on both sides of an ' = ' sign.
Equation shows the equality between the expressions in left hand and right hand side.
What is the required equation ?According to the problem, the variable for the unknown number = x
Now we have to establish the equation.
Difference between x & 4 = (x-4)
Twice the difference between x & 4 = 2(x-4)
Twice the difference between x & 4 is equals to 5.
∴ The equation is, 2(x-4) = 5
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Can you please help me asp because I am really confuse !. Plus you get 14 points!!
Answer:
1. B
2. 2 and 1/8 cups
Step-by-step explanation:
You just had to make common denominators and then your would subtract
Answer:
1) B
2) 2 1/8 cups
Step-by-step explanation:
1) make the denominator the same so it is 5 4/12 minus 2 9/12. You get 2 7/12 which is greater than 2 1/2 (2 6/12) and smaller th an 3
2) 8 7/8 minus 6 3/4 is equivalent to 8 7/8 minus 6 6/8 which is 2 1/8
All done mentally.
Answer this for 20 pts and brainliest!!!!! (Please hurry up! "I am in a hurry!)
When there was no snow fall, the line would be flat ( horizontal).
There was no snow Between 3:30 pm and 2:00 pm.
Answer:
12:30 pm to 1:00 pm.
Step-by-step explanation:
Hope this helps you.
solve the system of equations using subsitutions. x-4y=111 and 2y-x=-7
Answer:
[tex]\frac{x}{4}-\frac{111}{4}\\x=2y+7[/tex]
I'm pretty sure this is correct!
Answer:
(- 97, - 52)
Step-by-step explanation:
given the 2 equations
x - 4y = 111 → (1)
2y - x = - 7 → (2)
Rearrange (1) expressing x in terms of y by adding 4y to both sides
x = 111 + 4y → (3)
Substitute x = 111 + 4y into (2)
2y - (111 + 4y ) = - 7 ← distribute and simplify left side
2y - 111 - 4y = - 7
- 2y - 111 = - 7 ( add 111 to both sides )
- 2y = 104 ( divide both sides by - 2 )
y = - 52
Substitute y = - 52 into (3) for corresponding value of x
x = 111 + 4(- 52) = 111 - 208 = -97
Solution is ( - 97, - 52 )
Which equation represents the same proportional relationship as the graph
The slope of the given linear line is 3/5 thus the equation is y = 3/5 x so option (A) is correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
The slope of the line is 3/5
Since, the equation is y = mx + c where m is the slope and c is the y-intercept.
In the given line c = 0 and m = 3/5
y = 3/5 x
Hence "The slope of the given linear line is 3/5 thus the equation is y = 3/5 x".
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Maria earns a 15% commission on her car sales. How much commission would Mariabearn on a sale of $23,000?
Answer:
$3,450
Step-by-step explanation:
As Maria earns 15% commission, a car sale of $23,000 would lead to a $3,450 commission. This can be achieved by multiplying .15 (15% translated into a decimal) to the total car sale of $23,000.
x = commission
x = 23,000 * (.15) = 3,450
Final answer:
Maria would earn a commission of $3,450 on a sale of a car priced at $23,000, calculated by multiplying the sale amount by her 15% commission rate.
Explanation:
Maria earns a 15% commission on her car sales. If she sells a car for $23,000, her commission is calculated by multiplying the total sale amount by the commission rate. To find the commission, use the following formula:
Commission = Sale Amount × Commission Rate
Commission = $23,000 × 0.15
Commission = $3,450
Therefore, Maria would earn a commission of $3,450 on a sale of $23,000.
a tree 3 feet tall grows 8% each year . how tall will the tree be at the end of 14 years ? round the answer to the nearest hundredth
Answer:
33.61 ft
Step-by-step explanation:
First you find the product of 3ft and 8%
3.0(0.8)=2.4
Then you find the product of 2.4 and 14years
2.4(14)=33.61
Using the formula for exponential growth, a tree that is initially 3 feet tall and grows at a rate of 8% per year would be approximately 5.23 feet tall at the end of 14 years.
Explanation:
To solve this problem, we can use the formula for exponential growth: Final amount = Initial amount * (1 + Growth rate) ^ Number of periods.
The initial height of the tree is given as 3 feet. This is our initial amount. The growth rate is 8% per year, so we represent this as 0.08 in our formula. The number of periods is 14 years.
So, we have:
Final height = 3 * (1 + 0.08) ^ 14
To find the final height, we multiply 3 by 1.08 raised to the power of 14. Doing the math, the tree would be approximately 5.23 feet tall at the end of 14 years, rounded to the nearest hundredth.
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Li rolls a pair of number cubes twice. On both rolls, the sum is 7. Are the rolls dependent or independent events?
Answer:
these are independent
Step-by-step explanation:
Please help ASAP! Which answer is the correct one?
a survey asked 60 students if they play an instrument and if they are in band
1.- 35 students play and instrument
2.- 30 students are in band
3.- 30 students are not in band.
which table shows these dates correctly entered in a two way frequency table?
Answer:
A
Step-by-step explanation:
B doesn't work because you can have people who are in a band and not in a band at the same time, which is showing in the first spot
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
Number of students asked in a survey = 60
Number of students who play an instrument = 35
Number of students who are in band = 30
Number of students who are not in band = 30
So, the two way frequency table would be :
Play instrument Not play instrument Total
In band 30 0 30
Not in band 5 25 30
Total 35 25 60
Hence, option 'a' is correct.
URGENT!!! WILL AWARD ALL POINTS Which expression is equivalent to sin(2β)sinβ for all values of β for which sin(2β)sinβ is defined?
Select the correct answer below:
2sin2β−tan2β
cot2β−2cos2β
1−tan2β
csc2β−2
2cosβ
Answer:
sin2b sin b
2 sin b cos b sin b
2 cos b sin^2 b
1−cos2b cos b
1- (2cos^2 b−1) cosb
2 cos beta
Answer:2sin =bahsyg=a=78sinb-7823sin= 1-tan2b
The probability of giving birth to a boy is 1/2. What is the probability that a family with 5 children will have at least 2 boys?
a)about 81.3%
b)about 76.9%
c)about 62.5%
d)about 90.3%
Answer:
0.78
Step-by-step explanation:
"The probability that a family with 5 children will have at least 2 boys" is equivalent to the complement 1 - P(family will have 1 or 0 boys).
We can use a calculator with statistical functions built in to calculate this probability. The function needed is for binomial probability: binom(n, p, x).
P(family will have 1 or 0 boys) = binomcdf(5, 0.5, {0, 1} ) produces two results: one the probab. of having 0 boys and one the probab. of having 1 boy: 0.03125 and 0.1875. We add these together, obtaining 0.21875.
Then we subtract this result from 1 to obtain The probability that a family with 5 children will have at least 2 boys: 1 - 0.21875 = 0.78125, which may be reasonably rounded off to 0.78.
Answer:
81.3%.
Step-by-step explanation:
This is Binomial probability.
Prob( Getting 1 boy) = 5C1 (1/2)^5
= 0.156
Prob ( Getting all girls = 5C5 (1/2)^5
= .031.
So Prob( at least 2 boys = 1 - (0.156 + 0.031)
= 0.813
= 81.3%.
2x^2 -19x + 35 =0
Factor
Answer:
(-x+7) (-2x+5) are the factor of 2x²-19x+35=0
20 points! Write the expression in simplest form.
(-11/2 x + 3) - 2(-11/4 x - 5/2) =
Answer: 11x+ 8
Step-by-step explanation:
9...................
For this case we must evaluate the following expression:
[tex]\sqrt [4] {16}[/tex]
We have by definition of properties of powers and roots that:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
On the other hand, we can rewrite the 16 as:
[tex]16 = 2 * 2 * 2 * 2 = 2 ^ 4[/tex]
So:
[tex]\sqrt [4] {16} = \sqrt [4] {2 ^ 4} = 2 ^ {\frac {4} {4}} = 2 ^ 1 = 2[/tex]
ANswer:
Option D
I have another one!
(6m−7)⋅4
Thanks!!
4*6m=24m
-7*4=-28
24m -28
Answer:
24m-28
Step-by-step explanation:
which quadratic equation is equivalent to (x^2-1)^2 -11(x^2-1)+24=0
A)u^2-11u+24=0 where u=(x^2-1)
B) (u^2)^2 -11(u^2) +24 where u = (x^2-1)
C)u^2+1-11u+24 =0 where u =(x^2-1)
D)(u^2-1)^2 -11(u^2-1) +24 where u =(x^2-1)
Answer:
[tex]\large\boxed{A)\ u^2-11u+24=0}[/tex]
Step-by-step explanation:
[tex](x^2-1)^2 -11(x^2-1)+24=0\\\\\text{Substitute}\ (x^2-1)=u\\\\\underbrace{(x^2-1)}_{u}\ ^2 -11\underbrace{(x^2-1)}_{u}+24=0\to u^2-11u+24=0[/tex]
Answer: The correct option is
(A) [tex]u^2-11u+24=0,~~\textup{where }u=(x^2-1).[/tex]
Step-by-step explanation: We are given to select the correct quadratic equation that is equivalent to the following equation :
[tex](x^2-1)^2-11(x^2-1)+24=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Let us consider that
[tex]u=x^2-1.[/tex]
Substituting the value of u in equation (i), we get
[tex](x^2-1)^2-11(x^2-1)+24=0\\\\\Rightarrow u^2-11u+24=0.[/tex]
Thus, the required equivalent quadratic equation is
[tex]u^2-11u+24=0,~~\textup{where }u=(x^2-1).[/tex]
Option (A) is CORRECT.
Choose the inequality in that represents the following graph
The inequality is determined by examining the graph, identifying the lines, their slopes and determining if they are increasing or decreasing. Positive slopes are for increasing lines and negative slopes are for decreasing lines. Inequalities should represent the identified lines and their slopes.
Explanation:From your question, it seems that there's a graph involved depicting certain lines and you're supposed to choose an inequality that represents the graph. As per the given information that line A is decreasing and line B is increasing, it sounds like these lines may represent an inequality on the coordinate plane. Consider the slope of line A and line B. If one is steeper than the other, the steeper slope has a larger absolute value. An increasing line indicates a positive slope, while a decreasing line indicates a negative slope. For example, if line A is y < -2x + 3 (negative slope, line decreasing) and line B is [tex]y > 5x + 1[/tex](positive slope, line increasing), the inequality would be [tex]y > 5x + 1 - y < -2x + 3.[/tex]For a precise and correct answer, you need to analyze the graph, identify lines, intercepts, slopes, and shading to form the correct inequality.
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What is the distance from A to B?
A) 7
B) 8
C) 15
D) 17
I’m not too sure
Answer:
A. 7
Step-by-step explanation:
count the squares
Answer:
The answer is A
Step-by-step explanation:
Each square on the grid is 1 unit, and the distance from A to B is 7 squares which is 7 units
pleasssssssss heeeelllllpppppp!!!! Bethany attached two cubes side by side.
What is the volume of the entire figure?
36 in 3
74 in 3
468 in 3
720 in 3
Answer:
468
Step-by-step explanation:
The volume of a cube is V = s³. Fin the volume of each cube separately and add together for the volume all together.
The small cube has side length 5 so V = 5³ = 125.
The large cube has side length 7 since 12 - 5 = 7. So V = 7³ = 343.
Together the volume is 125 + 343 = 468
Answer:
468
Step-by-step explanation:
24 students is _% of 43
Answer:
(24 / 43) * 100 = 55.81395349 %
which equals roughly 55.81 %
Step-by-step explanation:
The car owned by a person is part of his or her ____.
a.
investment assets
b.
liquid assets
c.
long term assets
d.
use assets
Please select the best answer from the choices provided
Answer:
The correct answer would be A
Step-by-step explanation:
Solve.
y = 2x + 3
x + y = 6
Please show work so I can understand how to solve this equation.
Answer:
x=1
Step-by-step explanation:
you would substitute the first equation in for the y in the second equation
x + 2x+3 =6
then you would combine the x's
3x +3 = 6
Then you would move the 3 to the other side with the six
3x =6-3 3x = 3
Then finally you would divide the three
3x/3 = 3/3 x=1
Identify the sequence 3,888, 216, 12, 2/3... as arithmetic, geometric, neither, or both.
A: arithmetic
B: geometric
C: neither
D: both
It is a geometric sequence but not an arithmetic sequence. So the answer is B
Mr. price drives 123 miles each day on his bus route he gets reimbursed .56 per every mile he drives. How much will mr. price reimbursed for 2 days of his bus route
he will be reimbursed 137.26 dollars for two days