Answer:
f(n) = 10 * 5^(n-1)
an = 15-2.5n
Step-by-step explanation:
{(1, 10), (2, 50), (3, 250), (4, 1250)}
The formula for a geometric sequence is
an = a1 * r ^(n-1)
where a1 is the first term and r is the rate in which it increase
a1 =10
r = 5, each term goes up by a factor of 5
50/10 = 5
250/50 = 5
etc
f(n) = 10 * 5^(n-1)
What is the explicit rule for the sequence?
13, 10.5, 8, 5.5, 3, 0.5, ...
For an arithmetic sequence the formula is
an = a1 + d(n-1)
where a1 is the first term and d is the common difference
a1= 13 and d = -2.5
10.5 -13 = -2.5
8. - 10 = -2.5
etc
an = 13 - 2.5 ( n-1)
Simplifying
an = 13 -2.5n + 2.5
an = 15-2.5n
What is the GCF of the following expression:
5y^5+35y^4+15y^3
Answer:
5y^3
Step-by-step explanation:
Find what is common to all the terms
5y^5 = 5 * y*y*y*y*y
35y^4 = 5*7*y*y*y*y
15y^3 = 3*5*y*y*y
The all have 5*y*y*y
So the GCF is 5 y*y*y or 5y^3
Divide the following polynomial, then place the answer in the proper location on the grid. Write your answer in order of descending powers of x.
(a^2n - a^n - 6) ÷ (a^n + 8)
The correct answer for dividing [tex](a^{2n} - a^n - 6) by (a^n + 8)[/tex] is indeed:
[tex](a^n - 9) + (-78)/(a^n + 8).[/tex]
Let's divide the given polynomials:
[tex]\frac{a^{2n -a^n -6}}{a^n +8}[/tex]
Here's the breakdown of the solution:
Factoring: We can factor the numerator [tex](a^{2n} - a^n - 6)[/tex] using difference of squares:
[tex](a^{2n} - a^n - 6) = (a^n)^2 - (a^n) - 6 = (a^n + 2)(a^n - 3)[/tex]
Division: Now, we can divide the factored numerator by the denominator:
[tex][(a^n + 2)(a^n - 3)] / (a^n + 8) = (a^n + 2) - [(a^n + 8) * (a^n - 3)] / (a^n + 8) = (a^n + 2) - (a^n - 3) = a^n - 9[/tex]
Remainder: Since the degree of the numerator is less than the degree of the denominator, we get a non-zero remainder.
This remainder is obtained by dividing the constant term (-6) in the numerator by the constant term (8) in the denominator, resulting in [tex]-78/(a^n + 8).[/tex]
Therefore, the final answer is [tex](a^n - 9) + (-78)/(a^n + 8)[/tex], with a quotient of [tex](a^n - 9)[/tex] and a non-zero remainder of [tex](-78)/(a^n + 8).[/tex]
What is the distance between the points (21, 16) and (9, 11)?
Answer: 13 units
The x value goes from x = 21 to x = 9, which is an x distance of 12 units (21-9 = 12)
The y distance is 5 units (16-11 = 5)
We have a right triangle with legs of 12 and 5. The hypotenuse is x
Use the pythagorean theorem to find x
a^2 + b^2 = c^2
5^2 + 12^2 = x^2
25 + 144 = x^2
169 = x^2
x^2 = 169
x = sqrt(169)
x = 13
The hypotenuse of this right triangle is 13 units, so this is the distance between the two points.
In a neighborhood of 160 houses. 48 of the houses are brick. What percent of the houses are brick houses.
Since it's 48 out of 160 and you're trying to find the percentage out of 100, this particular formula would look like this: 48/160=x/100.
Then you cross multiply: 48x100=4800
Then you take the result of that and divide it by the total number of houses. 4800/160=30
30% of the houses are brick.
Thomas earns 15 per hour if he recurved a 10% per hour pay increase how much does Thomas now make per hour
Answer:
He will make 16.50 per hour after his raise.
Step-by-step explanation:
15 x .10 = 1.50
15.00 + 1.50 = 16.50
BRAINLIEST AND 50 POINTS
1.) A jar contains 4 red, 5 white, and 3 blue marbles. A marble is drawn from the jar. What is the probability that the marble is
Blue?______ White?_____ Red?_____ Not red?_____
Answer:
P ( blue ) = 1/4
P ( white ) = 5/12
P ( red ) = 1/3
P ( not red ) = 2/3
Step-by-step explanation:
To find the probability of a marble being chosen, it is the number of that color over the total
We need to find the total number of marbles
4 red+ 5 white+3 blue = 12 marbles
P ( blue ) = 3 blue / 12 total = 3/12 = 1/4
P ( white ) = 5 white / 12 total = 5/12
P ( red ) = 4 red/ 12 total = 4/12 = 1/3
How man marbles are not red
total marbles - red marbles = 12-4 = 8
8 marbles are not red
P ( not red ) = 8 not red / 12 total = 8/12 = 2/3
( 85 x 6 ) - 69 thanks (:
Answer:
( 85 x 6 ) - 69 would equal 441
Step-by-step explanation:
You do 85 x 6 then - 69 (:
Answer:
441
Step-by-step explanation:
first do the
(85x6) you get 510
510-69
441
A population of bacteria is growing according to the exponential model P = 100e(.70)t, where P is the number of colonies and t is measured in hours. After how many hours will 300 colonies be present? [Round answer to the nearest tenth.]
A) 0.7
B) 1.6
C) 5.7
D) 7.2
Write an explicit rule to represent the sequence :
4, 10, 16, 22,...
It's an arithmetic sequence:
[tex]a_1=4;\ a_2=10;\ a_3=16;\ a_4=22;\ ...[/tex]
The explicit rule:
[tex]a_n=a_1+(n-1)d[/tex]
[tex]d=a_{n+1}-a_n\to d=a_2-a_1=a_3-a_2=a_4-a_3=...[/tex]
[tex]d=10-4=16-10=22-16=6[/tex]
Substitute:
[tex]f(n)=4+(n-1)(6)=4+6n-6=6n-2[/tex]
Answer: f(n) = 6n - 2The explicit rule for the arithmetic sequence 4, 10, 16, 22, ... is aₙ = 4 + (n - 1) x 6, where aₙ is the nth term of the sequence.
The given sequence is arithmetic, which means that it increases by the same amount each time. To find an explicit rule for the sequence, we should determine the common difference and use the formula for an arithmetic sequence, which is aₙ = a₁ + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of the term in the sequence, and d is the common difference between terms.
In the sequence 4, 10, 16, 22, ..., the first term a1 is 4, and the common difference is 6 (since 10 - 4 = 16 - 10 = 22 - 16 = 6). Therefore, the explicit rule for the nth term of the sequence is aₙ = 4 + (n - 1) x 6.
Can someone help me with this problem
Answer:
12
Step-by-step explanation:
There are 6 for tails. Each is 2. 6 x 2 =12
There are 8 students in a class: 2 boys and 6 girls. If the teacher picks a group of 5 at random, what is the probability that everyone in the group is a girl?
Answer:
0.1071
Step-by-step explanation:
Given
Total number of students=8
Boys=2
Girls=6
When we are picking a group from population we use combinations to calculate sample space and for event
So if a group of 5 has to be picked from 8 students
ⁿC_k= n!/(k!)(n-k)!
C_(n,k)= n!/(k!)(n-k)!
Here n=8 and k=5
C_8,5= 8!/(5!)(8-5)!
This will give us:
C_8,5=56
And if we have to pick only girls:
C_6,5= 6!/(5!)(6-5)!
=6
The probability of picking all girls:
=6/56
=0.1071
The correct answer to this question would be 3/28
Find the ratio of the volume of one sphere to the volume of the right cylinder
Answer:
B
Step-by-step explanation:
Let [tex]r[/tex] be the radius of one sphere.
Volume of sphere is [tex]V=\frac{4}{3}\pi r^3[/tex]Since radius is r, the height of the cylinder will be [tex]4r[/tex]
Also, the cylinder has the same radius as the sphere: [tex]r[/tex]
Plugging in the values we get: [tex]V=\pi (r)^{2}(4r)=4\pi r^3[/tex]
Ratio of volume of 1 sphere to volume of cylinder is:
[tex]\frac{\frac{4}{3}\pi r^3}{4\pi r^3}=\frac{\frac{4}{3}}{4}=\frac{4}{3}*\frac{1}{4}=\frac{1}{3}[/tex]
The ratio is 1:3
Answer choice B is right.
Write a linear function that passes through the points (-5, -6) and (2, 8).
The point-slope form of line:
[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-5, -6) and (2, 8). Substitute:
[tex]m=\dfrac{8-(-6)}{2-(-5)}=\dfrac{8+6}{2+5}=\dfrac{14}{7}=2\\\\y-(-6)=2(x-(-5))\\\\\boxed{y+6=2(x+5)}[/tex]
CE and BD are angle bisectors of △ABC which intersect at point F. If ∠BFC=110°, find the measure of ∠A.
Answer:
∠A=40°
Step-by-step explanation:
Equation 1: ∠A+∠B+∠C=180°
Equation 2: ∠B/2+∠C/2+110°=180°
2(Equation 2): ∠B+∠C+220°=360°
∠B+∠C=140°
Equation 1 - 2(Equation 2): ∠A=40°
Therefore, ∠A=40°
800,000,000,000 + 20,000,000,000 + 3,000,000,000 + 50,000,000 + 4,000,000 + 600,000 + 50,000 + 8,000 + 700 + 80 + 6
Write the equation of the line containing the point (3, –2) and having a slope of 2 in slope-intercept form.
Slope-intercept form:
y = mx + b
"m" is the slope, "b" is the y-intercept (the y value when x = 0 or (0,y))
You know m = 2, so you can plug it into the equation
y = 2x + b
To find "b", plug in the point (3, -2) into the equation
y = 2x + b
-2 = 2(3) + b
-2 = 6 + b
-8 = b
y = 2x - 8
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the slope m = 2 and the point (3, -2) → x = 3 and y = -2.
Substitute:
[tex]-2=(2)(3)+b[/tex]
[tex]-2=6+b[/tex] subtract 6 from both sides
[tex]-8=b\to b=-8[/tex]
Substitute to the equation y = mx + b:
Answer: y = 2x - 8An elephant needs to drink at least 40 gallons of water each day. A drinking tank contains 4 gallons of water. The elephant has already consumed 24 gallons of water. How many more tanks x of water does the elephant need to drink? Write your answer as an inequality.
After drinking 24 gallons out of the required 40 gallons, the elephant needs at least 4 more tanks of water as each tank holds 4 gallons. The inequality representing this is x ≥ 4.
The student needs to calculate how many more tanks of water an elephant needs to drink to reach its daily requirement of at least 40 gallons if each tank contains 4 gallons of water. To start, we determine how much water the elephant still needs after drinking 24 gallons:
Required daily water - Water already consumed = Remaining water needed
40 gallons - 24 gallons = 16 gallons
Next, we find out how many tanks are needed for the remaining 16 gallons, knowing that each tank holds 4 gallons:
Number of tanks needed = Remaining water needed / Water per tank
Number of tanks needed = 16 gallons / 4 gallons per tank
Number of tanks needed = 4 tanks
Since the elephant needs at least 40 gallons, it will need at least 4 more tanks of water. However, since we're writing this as an inequality, we want to express that the elephant may drink more. Hence, the inequality will be:
x ≥ 4
QUICK
Bill lent some money to his two brothers. He wrote down the amounts so he would not forget. The list shows the younger brother with −$17.25 and the older brother with $0. Which of the following statements best describes the amounts?
A.The older brother paid Bill $17.25, and the younger brother does not owe him any money.
B.The older brother owes Bill $17.25, and the younger brother does not owe him any money.
C.The younger brother owes Bill $17.25, and the older brother does not owe him any money.
D.The younger brother paid Bill $17.25, and the older brother does not owe him any money.
Analyze the key features of the graphs of the functions below. Select all of the quadratic functions that open down, have a vertex that is a maximum and a positive y-intercept.
f(x) = 2x2 - 4x - 3
g(x) = - x2 + x + 1
h(x) = -2x2 + 3x - 1
m(x) = x2 -9
n(x) = -3x2 + 7
f(x) = 2x^2 - 4x - 3; opens up; vertex: (1, -5); y-intercept: (0, -3)
g(x) = -x^2 + x + 1; opens down; vertex: (0.5, 1.25); y-intercept: (0, 1)
h(x) = -2x^2 + 3x - 1; opens down; vertex: (0.75, 0.125); y-intercept: (0, -1)
m(x) = x^2 - 9; opens up; vertex: (0, -9); y-intercept: (0, -9)
n(x) = -3x^2 + 7; opens down; vertex: (0, 7); y-intercept: (0, 7)
I have attached an image of the functions and their graphs.
Hope this helps!
Answer:
[tex]f(x) = -x^2 +x +1[/tex]
Step-by-step explanation:
Quadratic equation is in the form of
[tex]f(x)= ax^2+bx+c[/tex]
When the value of 'a' is positive then the graph opens up
When the value of 'a' is negative then the graph opens down
When the graph opens up then the vertex is minimum.
When the graph opens down then the vertex is maximum.
y intercept is the value of 'c'
[tex]f(x) = 2x^2 - 4x - 3[/tex], a=2 the graph opens up
[tex]f(x) = -x^2 +x +1[/tex], a=-1 the graph opens down. So the vertex is maximum. Y intercept is +1. y intercept is positive.
[tex]f(x) = -2x^2 +3x - 1[/tex], a=-2 the graph opens down. So the vertex is maximum. Y intercept is -1. y intercept is negative.
[tex]f(x) = 2x^2 - 4x - 3[/tex], a=2 the graph opens up
Explain how to solve 7 + x > 12 .Tell what property of inequality you would use
Answer:
x > 5
Step-by-step explanation:
isolate x by subtracting 7 from both sides
x > 12 - 7
x > 5
The basketball team spends 20 minutes running laps and at least 15 minutes discussing plays. Practice lasts one hour and 45 minutes. Write and solve an inequality to find the amount of time remaining to work on other drills.
Answer:
[tex]t\leq 70[/tex]
Step-by-step explanation:
The team spends 20 minutes running laps
At least 15 minutes discussing plays.
Practice lasts one hour and 45 minutes.
We know that 1 hour = 60 minutes, so the practice lasts,
60+45= 105 minutes.
The team spends a total of [tex]20+15=35[/tex] minutes in running and discussion.
So the time remaining to work on other drills is,
[tex]t\leq 105-35[/tex]
[tex]t\leq 70[/tex]
Help pleasee? Same ones
Since we are given that ABC is congruent to JKL, then AB has to be equal to JK
therefore --- [tex]14x+7=5x+34[/tex]
Subtract 7 from both sides
[tex]14x=5x+27[/tex]
Subtract 5x from each side
[tex]9x=27[/tex]
Divide 9 on each side
[tex]x=3[/tex]
Since, We are asked to find the length of AB and JK
plug in 3 for x
[tex]5(3)+34=15+34=49[/tex]
40 Jenny is buying gifts for her family. So far she has spent $45,95, and she has one more gift to buy. She started with a total of $60 to spend on all of her gifts Write an inequality that shows how much she can spend on the final gift
Answer:
[tex]x \leq 14.05[/tex]
Step-by-step explanation:
First, to find the boundary we need to find the amount of money left, simply subtract the spent amount from the total:
60 - 45.95 = 14.05
Seeing as this is the amount, she can spend any amount up to and including 14.05, so we need an equal to or smaller than sign:
Let x be the value of the object:
[tex]x \leq 14.05[/tex]
Which is the inequality!
A bowling alley charges 2.00 per game and will rent a pair of shoes for 1.00 for any number of games. The bowling alley has an earrings goal of 300 for the day
Answer:
The bowling alley should rent 150 pairs of shoes and should about 75 games per day in order to reach a goal of 300 dollars.
Step-by-step explanation:
MATH HELP PLEASE!!
find the area of the shaded region.
use the formula A= pi r^2 to find the area of the circle.
a. 8pi x + 24pi
b. 8pi x - 24pi
c. x^2 + 8pi x + 24pi
d. x^2 +8pi x - 24pi
Answer:
b
Step-by-step explanation:
B// 8pi x-24pi
in 1950, the U.S. federal budget was $39.4 billion, in 2000, the federal budget was $2025.2 billion. The exponential function is f=39.4Be^0.0787932i. Use your function to estimate the budget in 2010
Answer:
The budget in 2010 is $4453.10915 billion
Step-by-step explanation:
We are given exponential function as
[tex]f(t)=39.4e^{0.0787932t}[/tex]
where t is the time in years since 1950
now, we can find time in 2010
t=2010-1950=60
now, we can plug t=60
and we get
[tex]f(60)=39.4e^{0.0787932\times 60}[/tex]
we get
[tex]f(60)=4453.10915[/tex]
So, the budget in 2010 is $4453.10915 billion
Daren can jump rope 116 times in 2 minutes, Kyle can jump rope 240 times in 4 minutes, and Marissa can jump rope 225 times in 5 minutes. Who can jump rope the most times per minute?
Answer:
Kyle can jump rope the most times per minute.
Step by step explanation:
We have been given that Daren can jump rope 116 times in 2 minutes.
So number of rope jumps done by Daren in 1 minute will be:
[tex]\text{Unit rate of Jump rope done by Daren}=\frac{116\text{ times}}{2\text{ minute}}[/tex]
[tex]\text{Unit rate of Jump rope done by Daren}=58\frac{\text{ times}}{\text{ minute}}[/tex]
Therefore, Daren jumps rope 58 times per minute.
We have been given that Kyle can jump rope 240 times in 4 minutes.
So number of rope jumps done by Kyle in 1 minute will be:
[tex]\text{Unit rate of Jump rope done by Kyle}=\frac{240\text{ times}}{4\text{ minute}}[/tex]
[tex]\text{Unit rate of Jump rope done by Kyle}=60\frac{\text{ times}}{\text{ minute}}[/tex]
Therefore, Kyle jumps rope 60 times per minute.
We have been given that Marissa can jump rope 225 times in 5 minutes.
So number of rope jumps done by Marissa in 1 minute will be:
[tex]\text{Unit rate of Jump rope done by Marissa}=\frac{225\text{ times}}{5\text{ minute}}[/tex]
[tex]\text{Unit rate of Jump rope done by Marissa}=45\frac{\text{ times}}{\text{ minute}}[/tex]
Therefore, Marissa jumps rope 45 times per minute.
As Kyle jumps rope 60 times per minute, which is greater than jumps rope done by Daren and Marissa, therefore, Kyle can jump rope the most times per minute.
What is the remainder R when the polynomial p(x) is divided by (x - 2)? Is (x - 2) a factor of p(x)? P(x) = -4x4 + 6x3 + 8x2 - 6x - 4 A) R = 0, no B) R = 0, yes C) R = -72, no D) R = -72, yes
Answer:
B
(x-2) is a factor since remainder is 0.
Step-by-step explanation:
We divide (x-2) into the polynomial [tex]-4x^4+6x^3+8x^2-6x-4[/tex] through long division or synthetic. We choose long division and look for what will multiply with (x-2) to make the polynomial [tex]-4x^4+6x^3+8x^2-6x-4[/tex] .
[tex](x-2)(-4x^3)=-4x^4+8x^3[/tex]
We subtract this from the original [tex]-4x^4-(-4x^4)+6x^3-(8x^3)+8x^2-6x-4[/tex].
This leaves [tex]-2x^3+8x^2-6x-4[/tex]. We repeat the step above.
[tex](x-2)(-2x^2)=-2x^3+4x^2[/tex].
We subtract this from [tex]-2x^3-(-2x^3)+8x^2-(4x^2)-6x-4=4x^2-6x-4[/tex]. We repeat the step above.
[tex](x-2)(4x)=4x^2-8x[/tex].
We subtract this from [tex]4x^2-(4x^2)-6x-(-8x)-4=2x-4[/tex]. We repeat the step above.
[tex](x-2)(2)=2x-4[/tex].
We subtract this from [tex]2x-(2x)-4-(4)=0[/tex]. There is no remainder. This means (x-2) is a factor.
The remainder R when the polynomial p(x) = -4x4 + 6x3 + 8x2 - 6x - 4 is divided by (x - 2) is 0, indicating that (x - 2) is indeed a factor of p(x).
Explanation:To find the remainder R when the polynomial p(x) = -4x4 + 6x3 + 8x2 - 6x - 4 is divided by (x - 2), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial p(x) by a linear term (x - a) is equal to p(a). Therefore, to find R, simply calculate p(2).
p(2) = -4(2)4 + 6(2)3 + 8(2)2 - 6(2) - 4
p(2) = -4(16) + 6(8) + 8(4) - 12 - 4
p(2) = -64 + 48 + 32 - 12 - 4
p(2) = 0
Since the remainder is 0, this means that (x - 2) is a factor of p(x).
The correct answer is therefore R = 0, and yes, (x - 2) is a factor of p(x).
The line with equation a+2b=0 coincides with the terminal side of an angle 0 in standard position and cos 0 < 0. What is the value of sin0?
Question:
line x + 2y = 0 is end side of angle θ
and cos θ < 0
Answer: sin θ = √5/5
Step-by-step explanation:
cos θ < 0 means x < 0
Line is y = -x/2, slope -1/2
Line intersects unit circle when x^2+y^2=1
x^2 + (-x/2)^2 = 1
x^2 + x^2/4 = 1
5x^2/4 = 1
x = -√(4/5) = -2√(1/5) = -2√5/5
y = √5/5
x^2 = 4/5, y^2 = 1/5
sin θ is y value at intersection of line and unit circle, √5/5
In this exercise we have to use the given equation and thus calculate the intersection value:
[tex]sin (\theta) = \sqrt{5/5}[/tex]
So knowing that you were informed:
Line x + 2y = 0 is end side of angle θ and cos θ < 0 means x < 0. Line is y = -x/2, slope -1/2 and the Line intersects unit circle when :
[tex]x^2+y^2=1\\x^2 + (-x/2)^2 = 1\\x^2 + x^2/4 = 1\\5x^2/4 = 1\\x = -\sqrt{4/5} = -2\sqrt{1/5} = -2\sqrt{5/5}\\y = \sqrt{5/5}\\x^2 = 4/5, y^2 = 1/5[/tex]
[tex]sin(\theta)[/tex] is y value at intersection of line and unit circle, [tex]\sqrt{5/5}[/tex]
See more about intersection at brainly.com/question/12089275
Which equation represents the sentence? The sum of 14 and a number is 8 times the number
A.14+n=8n
B.14n=8+n
C.14n+8=n
D.14(n+8)=n
The correct equation is 14 + n = 8n, option A is correct.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Let the number is n,
8 times of the number = 8n
According to the condition, The sum of 14 and number n is 8 times the number,
Implies that,
14 + n = 8n
The correct equation is 14 + n = 8n.
To know more about Equation on:
https://brainly.com/question/187506
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