Answer:
A. 1,162.5
Step-by-step explanation:
Write the next two terms and add them up:
S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A
================================================
Explanation:
{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5
Sn = a*(1-r^n)/(1-r)
S5 = 600*(1-0.5^5)/(1-0.5)
S5 = 1,162.5
-----------
Check:
first five terms = {600, 300, 150, 75, 37.5}
S5 = sum of the first five terms
S5 = 600+300+150+75+37.5
S5 = 1,162.5
Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = 1/sqrt(n)
This sequence converges to 0.
Proof: Recall that
[tex]\displaystyle\lim_{n\to\infty}\frac1{\sqrt n}=0[/tex]
is to say that for any given [tex]\varepsilon>0[/tex], there is some [tex]N[/tex] for which [tex]\left|\frac1{\sqrt n}-0\right|=\frac1{\sqrt n}<\varepsilon[/tex] for all [tex]n>N[/tex].
Let [tex]N=\left\lceil\frac1{\varepsilon^2}\right\rceil[/tex]. Then
[tex]n>\left\lceil\dfrac1{\varepsilon^2}\right\rceil\ge\dfrac1{\varepsilon^2}[/tex]
[tex]\implies\dfrac1n<\varepsilon^2[/tex]
[tex]\implies\dfrac1{\sqrt n}<\varepsilon[/tex]
as required.
Question 2 Rewrite in simplest radical form 1 x −3 6 . Show each step of your process.
Answer:
√(x)
Step-by-step explanation:
(1)/(x^-(1/2)) that's 3 goes into -3 leaving 1 and goes into 6 leaving 2
1/2 is same as 2^-1
so therefore we can simplify the above as
x^-(-1/2)
x^(1/2)
and 4^(1/2)
is same as √(4)
so we conclude as
√(x)
Jaclyn is one-fourth of a foot taller than John. John is 31/6 feet tall. How many feet tall is Jaclyn
Answer:
5 5/12
Step-by-step explanation:
31/6 feet + 1/4 foot
= 31/6 + 1/4
= [(31 * 4) / 6 * 4] + [(1 * 6) / 4 * 6]
= [ 124/24 ] + [ 6/24 ]
= (124 + 6) / 24
= 130 / 24
= 5 10/24
= 5 5/12
Hope this helps! Tell me if I'm wrong!
One way to calculate the target heart rate of a physically fit adult during exercise is given by the formula h=0.8( 220−x ), where h is the number of heartbeats per minute and x is the age of the person in years. Which formula is equivalent and gives the age of the person in terms of the number of heartbeats per minute?
Answer:
The answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
Step-by-step explanation:
Given:
[tex]h=0.8( 220-x )[/tex]
Where [tex]h[/tex] is the heartbeats per minute and
[tex]x[/tex] is the age of person
To find:
Age of person in terms of heartbeats per minute = ?
To choose form the options:
[tex]A.\ x=176-h\\B.\ x=176-0.8h\\C.\ x=-1.25h+220\\D.\ x=h-0.8220[/tex]
Solution:
First of all, let us have a look at the given equation:
[tex]h=0.8( 220-x )[/tex]
It is value of [tex]h[/tex] in terms of [tex]x[/tex].
We have to find the value of [tex]x[/tex] in terms of [tex]h[/tex].
Let us divide the equation by 0.8 on both sides:
[tex]\dfrac{h}{0.8}=\dfrac{0.8( 220-x )}{0.8}\\\Rightarrow \dfrac{1}{0.8}h=220-x\\\Rightarrow 1.25h=220-x[/tex]
Now, subtracting 220 from both sides:
[tex]\Rightarrow 1.25h-220=220-x-220\\\Rightarrow 1.25h-220=-x[/tex]
Now, multiplying with -1 on both sides:
[tex]-1.25h+220=x\\OR\\\bold{x = -1.25h+220}[/tex]
So, the answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
tan inverse 1/4 +tan inverse 2/7 = 1/2 cos inverse 3/5
Answer:
The equation is always false
Step-by-step explanation:
arctan1/4+arctan2/7=1/2arccos3/5
0.24497866+0.27829965=1/2(0.92729521)
0.52327832 =0.46364760
not equivalent and will never be.
Find the doubling time of an investment earning 8% interest if interest is compounded continuously. The doubling time of an investment earning 8% interest if interest is compounded continuously is ____ years.
Answer:
Step-by-step explanation:
Using FV = PV(1 + r)^n where FV = future value, PV = present value, r = interest rate per period, and n = # of periods
1/PV (FV) = (PV(1 + r^n)1/PV divide by PV
ln(FV/PV) = ln(1 + r^n) convert to natural log function
ln(FV/PV) = n[ln(1 + r)] by simplifying
n = ln(FV/PV) / ln(1 + r) solve for n
n = ln(2/1) / ln(1 + .08) solve for n, letting FV + 2, PV = 1 and rate = 8% or .08 compound annually
n = 9
n = ln(2/1) / ln(1 + .08/12) solve for n, letting FV + 2, PV = 1 and rate = .08/12 compound monthly
n = 104 months or 8.69 years
n = ln(2/1) / ln(1 + .08/365) solve for n, letting FV + 2, PV = 1 & rate = .08/365 compound daily
n = 3163 days or 8.67 years
Alternatively
A = P e ^(rt)
Given that r = 8%
= 8/100
= 0.08
2 = e^(0.08t)
ln(2)/0.08 = t
0.6931/0.08 = t
t= 8.664yrs
t = 8.67yrs
Which ever approach you choose to use,you will still arrive at the same answer.
Which geometric sequence has a first term equal to 55 and a common ratio of -5? {-55, 11, -2.2, 0.44, …} {55; 275; 1,375; 6,875; …} {55, 11, 2.2, 0.44, …} {55; -275; 1,375; -6,875; …}
Answer:
The answer is 55, -275, 1375, -6875......
Step-by-step explanation:
Find the derivative of the function f(x) = (x3 - 2x + 1)(x – 3) using the product rule.
then by distributing and make sure they are the same answer
Answer:
Step-by-step explanation:
Hello, first, let's use the product rule.
Derivative of uv is u'v + u v', so it gives:
[tex]f(x)=(x^3-2x+1)(x-3)=u(x) \cdot v(x)\\\\f'(x)=u'(x)v(x)+u(x)v'(x)\\\\ \text{ **** } u(x)=x^3-2x+1 \ \ \ so \ \ \ u'(x)=3x^2-2\\\\\text{ **** } v(x)=x-3 \ \ \ so \ \ \ v'(x)=1\\\\f'(x)=(3x^2-2)(x-3)+(x^3-2x+1)(1)\\\\f'(x)=3x^3-9x^2-2x+6 + x^3-2x+1\\\\\boxed{f'(x)=4x^3-9x^2-4x+7}[/tex]
Now, we distribute the expression of f(x) and find the derivative afterwards.
[tex]f(x)=(x^3-2x+1)(x-3)\\\\=x^4-2x^2+x-3x^3+6x-4\\\\=x^4-3x^3-2x^2+7x-4 \ \ \ so\\ \\\boxed{f'(x)=4x^3-9x^2-4x+7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
For some postive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770. The value of Z is
Answer:
1.16
Step-by-step explanation:
Given that;
For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770.
This implies that:
P(0<Z<z) = 0.3770
P(Z < z)-P(Z < 0) = 0.3770
P(Z < z) = 0.3770 + P(Z < 0)
From the standard normal tables , P(Z < 0) =0.5
P(Z < z) = 0.3770 + 0.5
P(Z < z) = 0.877
SO to determine the value of z for which it is equal to 0.877, we look at the
table of standard normal distribution and locate the probability value of 0.8770. we advance to the left until the first column is reached, we see that the value was 1.1. similarly, we did the same in the upward direction until the top row is reached, the value was 0.06. The intersection of the row and column values gives the area to the two tail of z. (i.e 1.1 + 0.06 =1.16)
therefore, P(Z ≤ 1.16 ) = 0.877
PLEASE HELPPPPP!!!!!!!!!!!!!!!Which relationships have the same constant of proportionality between y and x as the following graph?Choose two answers!!
Answer:
B, E
Step-by-step explanation:
You can use these strategies to compare the given graph and the other representations.
A & B) See if the point (x, y) = (8, 6) marked on the first graph works in the given equation.
A -- 6y = 8x ⇒ 6(6) = 8(8) . . . FALSE
B -- y = (3/4)x ⇒ 6 = (3/4)8 . . . True
__
C) Compare this graph to the given graph. They don't match.
__
D & E) Plot a point from the table on the given graph and see where it falls.
D -- The point (x, y) = (3, 4) lies above the line on the given graph.
E -- The point (x, y) = (4, 3) lies on the given graph.
_____
Choices B and E have the same constant of proportionality as shown in the given graph.
Answer:
B and E
Step-by-step explanation:
For lunch, Kile can eat a sandwich with either ham or a bologna and with or without cheese. Kile also has the choice of drinking water or juice with his sandwich. The total number of lunches Kile can choose is
Answer:
8
Step-by-step explanation:
Ham with or without cheese-2 choices
Bologna with or without cheese-2 choices
Bologna with cheese with water or juice-2 choices
Bologna without cheese with juice or water-2 choices
Ham with cheese with juice or water -2 choices
Ham without cheese with juice or water -2 choices
2+2+2+2=8
Kile has 8 choices for lunch
Find the vector and parametric equations for the line through the point P(0, 0, 5) and orthogonal to the plane −1x+3y−3z=1. Vector Form: r
Answer:
Note that orthogonal to the plane means perpendicular to the plane.
Step-by-step explanation:
-1x+3y-3z=1 can also be written as -1x+3y-3z=0
The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).
Let us find a point on this line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively
Therefore, the vector equation is given as:
-1(x-0) + 3(y-0) + -3(z-5) = 0
-x + 3y + (-3z+15) = 0
-x + 3y -3z + 15 = 0
Multiply through by - to get a positive x coordinate to give
x - 3y + 3z - 15 = 0
which expression have a value of 2/3
A: 8+(24 divided by 12) X 4
B:8+24 divided by (12X4)
C: 8+24 divided 12X4
D: (8+24) divided (12X4)
A low-noise transistor for use in computing products is being developed. It is claimed that the mean noise level will be below the 2.5-dB level of products currently in use. It is believed that the noise level is approximately normal with a standard deviation of .8. find 95% CI
Answer:
The 95% CI is [tex]2.108 < \mu < 2.892[/tex]
Step-by-step explanation:
From the question we are told that
The population mean [tex]\mu = 2.5[/tex]
The standard deviation is [tex]\sigma = 0.8[/tex]
Given that the confidence level is 95% then the level of confidence is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
=> [tex]\alpha = 5\%[/tex]
=> [tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the values is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
here we would assume that the sample size is n = 16 since the person that posted the question did not include the sample size
So
[tex]E = 1.96* \frac{0.8}{\sqrt{16} }[/tex]
[tex]E = 0.392[/tex]
The 95% CI is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
substituting values
[tex]2.5 - 0.392 < \mu < 2.5 + 0.392[/tex]
substituting values
[tex]2.108 < \mu < 2.892[/tex]
A diameter that is perpendicular to a chord bisects the chord. True False
Answer:
[tex]\Large \boxed{\sf True}[/tex]
Step-by-step explanation:
[tex]\sf A \ diameter \ that \ is \ perpendicular \ to \ a \ chord \ bisects \ the \ chord.[/tex]
Answer:
True!!
I just did the assignment and got it right
Factor.
x2 – 5x - 36
(x - 9)(x + 4)
(x - 12)(x + 3)
(x + 9)(x - 4)
(x + 12)(x - 3)
Answer:
The answer is option AStep-by-step explanation:
x² - 5x - 36
To factor the expression rewrite -5x as a difference
That's
x² + 4x - 9x - 36
Factor out x from the expression
x( x + 4) - 9x - 36
Factor out -9 from the expression
x( x + 4) - 9( x+ 4)
Factor out x + 4 from the expression
The final answer is
( x - 9)( x + 4)Hope this helps you
Answer:
[tex] \boxed{(x - 9) \: (x + 4) }[/tex]
Option A is the correct option.-
Step-by-step explanation:
( See the attached picture )
Hope I helped!
Best regards!
8. When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the _______.
A. remainder
B. dividend
C. quotient
D. divisor
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.
A. remainder
B. dividend
C. quotient
D. divisor
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Answer:
a. remainder
Step-by-step explanation:
took the test
dont leave your house without a vest
or you will get hit in the vital organs in your chest
A population of bacteria P is changing at a rate of dP/dt = 3000/1+0.25t where t is the time in days. The initial population (when t=0) is 1000. Write an equation that gives the population at any time t. Then find the population when t = 3 days.
Answer:
- At any time t, the population is:
P = 375t² + 3000t + 1000
- At time t = 3 days, the population is:
P = 13,375
Step-by-step explanation:
Given the rate of change of the population of bacteria as:
dP/dt = 3000/(1 + 0.25t)
we need to rewrite the given differential equation, and solve.
Rewriting, we have:
dP/3000 = (1 + 0.25t)dt
Integrating both sides, we have
P/3000 = t + (0.25/2)t² + C
P/3000 = t + 0.125t² + C
When t = 0, P = 1000
So,
1000/3000 = C
C = 1/3
Therefore, at any time t, the population is:
P/3000 = 0.125t² + t + 1/3
P = 375t² + 3000t + 1000
At time t = 3 days, the population is :
P = 375(3²) + 3000(3) + 1000
= 3375 + 9000 + 1000
P = 13,375
Use the order of operations to simplify this expression 1.2x3.5x4.1= What
[tex] 1.2\times3.5\times4.1=[(1+0.2)(3+0.5)](4+0.1)[/tex]
$=[1\times3+1\times0.5+0.2\times3+0.2\times0.5](4+0.1)$
$=(3+0.5+0.6+0.1)(4+0.1)$
$=(4.2)(4+0.1)=(4+0.2)(4+0.1)$
$=4\times4+4\times0.1+0.2\times4+0.2\times0.1$
$=16+0.4+0.8+0.02=17.22$
Each leg of a 45°-45°-90° triangle measures 12 cm.
What is the length of the hypotenuse?
Z
х
45°
45°
O 6 cm
12 cm
12 cm
O 672 cm
O 12 cm
O 122 cm
Answer:
The legs are 12 cm each, so the hypotenuse is
√(144+144)=12√2
Step-by-step explanation:
Applying the Pythagorean Theorem, the length of the hypotenuse is: 12√2 cm.
The Pythagorean TheoremWhere, a and b are two legs of a right triangle, and c is the hypotenuse, the Pythagorean Theorem states that, c² = a² + b².Given the two legs of the right triangle to be 12 cm
Therefore:c² = 12² + 12².
c² = 288
c = √288
c = 12√2 cm
Therefore, applying the Pythagorean Theorem, the length of the hypotenuse is: 12√2 cm.
Learn more about, the Pythagorean Theorem on:
https://brainly.com/question/654982
In a stable matching problem, if every man has a different highest-ranking woman on his preference list, and given that women propose, then it is possible that, for some set of women's preference lists, all men end up with their respective highest-ranking woman.a. Trueb. False
Answer:
True
Step-by-step explanation:
The statement given above in the question is correct. It is mentioned that men are free to create a list of women's according to their preferences. There will be order sequence of women and men places them in queue of their preference. The men proposes the women with highest ranking in the list then it is possible that all men gets their preferred choice.
What are the solution(s) of the quadratic equation 98 - x2 = 0?
x = +27
Ox= +63
x = +7/2
no real solution
Answer:
±7 sqrt(2) = x
Step-by-step explanation:
98 - x^2 = 0
Add x^2 to each side
98 =x^2
Take the square root of each side
±sqrt(98) = sqrt(x^2)
±sqrt(49*2) = x
±7 sqrt(2) = x
Answer:
[tex]\huge \boxed{{x = \pm 7\sqrt{2} }}[/tex]
Step-by-step explanation:
[tex]98-x^2 =0[/tex]
[tex]\sf Add \ x^2 \ to \ both \ sides.[/tex]
[tex]98=x^2[/tex]
[tex]\sf Take \ the \ square \ root \ of \ both \ sides.[/tex]
[tex]\pm \sqrt{98} =x[/tex]
[tex]\sf Simplify \ radical.[/tex]
[tex]\pm \sqrt{49} \sqrt{2} =x[/tex]
[tex]\pm 7\sqrt{2} =x[/tex]
[tex]\sf Switch \ sides.[/tex]
[tex]x= \pm 7\sqrt{2}[/tex]
Chapter: Simple linear equations Answer in steps
Answer:
6x-3=21
6x=24
x=4
........
6x+27=39
6x=39-27
6x=12
x=2
........
8x-10=14
8x=24
x=3
.........
6+6x=22
6x=22-6
x=3
......
12x-2=28
12x=26
x=3
.....
8-4x=16
-4x=8
x=-2
.....
4x-24=3x-3
4x-3x=24-3
x=21
....
9x+6=6x+12
9x-6x=12-6
3x=6
x=2
Answer:
Step-by-step explanation:
1. 3(2x - 1) = 21
= 6x - 3 = 21
= 6x = 24
= x = 24/6 = 4
------------------------------
2. 3(2x+9) = 39
= 6x + 27 = 39
= 6x = 39 - 27
= 6x = 12
= x = 12/6 = 2
--------------------------------
3. 2(4x - 5) = 14
= 8x - 10 = 14
= 8x = 14+10
= x = 3
-------------------------------
Please help with this
Answer:
B) x=80°
Step-by-step explanation:
This is a hexagon, so it has interior angles equaling 720°. (N-2)*180
So the equation would be
78+134+136+132+2x+x=720
480+3x=720
3x=720-480
3x=240
x=80°
A rotating light is located 16 feet from a wall. The light completes one rotation every 2 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 20 degrees from perpendicular to the wall.
Answer:
a
Step-by-step explanation:
answer is a on edg
Write the equation of the line that passes through (−2, 6) and (2, 14) in slope-intercept form. (2 points)
Answer:
[tex]y = 4x + 14[/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation we must first find the slope of the line
Slope of the line using points (−2, 6) and (2, 14) is
[tex]m = \frac{14 - 6}{2 + 2} = \frac{8}{2} = 4[/tex]
Now we use the slope and any of the points to find the equation of the line.
Equation of the line using point ( - 2, 6) and slope 4 is
[tex]y - 6 = 4(x + 2) \\ y - 6 = 4x + 8 \\ y = 4x + 8 + 6[/tex]
We have the final answer as
[tex]y = 4x + 14[/tex]
Hope this helps you
A sequence of 1 million iid symbols(+1 and +2), Xi, are transmitted through a channel and summed to produce a new random variable W. Assume that the probability of transmitting a +1 is 0.4. Show your work
a) Determine the expected value for W
b) Determine the variance of W
Answer:
E(w) = 1600000
v(w) = 240000
Step-by-step explanation:
given data
sequence = 1 million iid (+1 and +2)
probability of transmitting a +1 = 0.4
solution
sequence will be here as
P{Xi = k } = 0.4 for k = +1
0.6 for k = +2
and define is
x1 + x2 + ................ + X1000000
so for expected value for W
E(w) = E( x1 + x2 + ................ + X1000000 ) ......................1
as per the linear probability of expectation
E(w) = 1000000 ( 0.4 × 1 + 0.6 × 2)
E(w) = 1600000
and
for variance of W
v(w) = V ( x1 + x2 + ................ + X1000000 ) ..........................2
v(w) = V x1 + V x2 + ................ + V X1000000
here also same as that xi are i.e d so cov(xi, xj ) = 0 and i ≠ j
so
v(w) = 1000000 ( v(x) )
v(w) = 1000000 ( 0.24)
v(w) = 240000
A table has five bowls. None of the quantities in the bowls are prime, though the last two bowls are empty. Two of the quantities are squares, and when added to the remaining number, the sum is 21. What are the amounts in the first three bowls?
Since two of the quantities are squares and the sum of all of three is equal 21, then the possible values of those two quantities are: 1,4,9,16
Let's consider each possibility
1 and 4
21-1-4=16, but 16 is also square and there can be only two square so NO
1 and 9
21-1-9=11, but 11 is prime, so NO
1 and 16
21-1-16=4... 4 is a square ,so NO
4 and 9
21-4-9=8 , 8 is not prime and not a square, so YES
4 and 16
21-4-16=1, but 1 is a square ,so NO
9 and 16
9+16=25>21 so.. NO
Therefore, the amounts in the first three bowls are 4,8,9.
I will rate brainly if you answer this The number of weekly social media posts varies directly with the square root of the poster’s age and inversely with the cube root of the poster’s income. If a 16-year-old person who earns $8,000 makes 64 posts in a week, what is the value of k?
Answer:
[tex]\large \boxed{\sf \bf \ \ k=320 \ \ }[/tex]
Step-by-step explanation:
Hello,
The number of weekly social media posts varies directly with the square root of the poster’s age and inversely with the cube root of the poster’s income.
If a 16-year-old person who earns $8,000 makes 64 posts in a week, what is the value of k?
[tex]64=\dfrac{\sqrt{16}}{\sqrt[3]{8000}}\cdot k=\dfrac{4}{20}\cdot k=\dfrac{1}{5}\cdot k=0.2\cdot k\\\\k=64*5=320[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What is 1/3 of 675 is left
