By the ratio test, the series converges if
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(x-2)^{n+1}}{(n+1)!2^{n+1}}}{\frac{(x-2)^n}{n!2^n}}\right|=|x-2|\lim_{n\to\infty}\frac{n!2^n}{(n+1)!2^{n+1}}[/tex]
[tex]=\displaystyle\frac{|x-2|}2\lim_{n\to\infty}\frac1{n+1}[/tex]
is less than 1. The limit itself is 0 < 1, so the series converges everywhere, i.e. on the entire real line [tex](-\infty,\infty)[/tex].
20
Select the correct answer.
What is the purpose of a FICA tax?
A. It provides health insurance for people who are retired or disabled.
B. It helps the state government finance education projects.
C. It helps local councils finance development projects.
Reset
Next
Answer:
A. It provides health insurance for people who are retired or disabled.
Step-by-step explanation:
FICA stands for Federal Insurance Contributions Act, which is a law. It is a compulsory tax from the payroll of all employees in the United State to provide health insurance for retired as well as disabled people. It has a definite percentage with no conditional or exemption deductions to assist the government to fund social security and medicare.
This make it possible for the government to cater for the two sects of people in the society that are registered easily.
Find f(-3) if f(x) = x•x
Answer:
9
Step-by-step explanation:
f(x) = x•x
f(-3) = -3*-3
f(-3)= 9
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
7 nickels, 12 dimes
Step-by-step explanation:
n+d= 19
5n+10d= 155 ⇒ n+2d= 31
comparing the 2 equations we get
d=12, then n= 7
2. If I paid $1.45 for an apple and an orange, and the apple cost 15 cents more than the orange, how much did the orange cost?
Answer:
0.80 + 0.65 = 1.45
Step-by-step explanation:
apple: 0.80
orange: 0.65
find the length of the line segment whose endpoints are ( 3, -2 ) and ( 5, 4 ) in simplest radical form
Answer:
2√10
Step-by-step explanation:
The length of this line segment lies along the hypotenuse of a right triangle. As we go from (3, -2) to (5, 4), the horizontal change is 2, and the vertical change 6. Apply the Pythagorean Theorem to find the length of the hypotenuse, which is also the line segment in question:
length = √[ 2^2 + 6^2 ] = √[4 + 36] = √40 = √4·√10 = 2√10
What is the value of x in the equation 3X minus 4Y equals 65, when Y equals four
Answer:
Step-by-step explanation:
3x-4y=65
3x=65+4y
x=(65+4y)/3, when y=4
x=(65+4*4)/3
x=(65+16)/3
x=81/3
x=27
What is the vertex of the graph of y=-x^2
Answer:
(0,0)
Step-by-step explanation:
The Graph shows that 0,0 is the first x-y value which is vertex
Answer:c
Step-by-step explanation:
9(x-4) = 9x-33
how many solutions does this have?
Answer:
No solution
Step-by-step explanation:
Because x = 0
How many two-digit primes have both their digits non-prime?
Answer:
{ 11 , 19 , 41 , 61 , 89 } is only the two digits number having both their non-prime.
Step-by-step explanation:
What is the definition of an obtuse angle?
Answer:
an obtuse angle is an angle more than 90 degrees but less than 180 degrees
Step-by-step explanation:
:)
what are possible rational roots of f(x)= 3x^4-x^3+x^2_x+5
Answer:
x=0
so the roots are (0,0)
Omar's credit card has an APR of 26% calculated on the previous monthly
balance. His credit card record for the last 7 months is shown in the table
below.
End of
Month
1
2.
3
4
5
6
7
Previous
Balance
$0.00
$301.23
$254.41
$169.46
$191.45
$121.58
$195.55
New
Charges
$301.23
$266.65
$89.54
$198.32
$165.98
$211.34
$397.54
Payment
Received
$0.00
$320.00
$180.00
$180.00
$240.00
$140.00
$340.00
Finance
Charges
$0.00
$6.53
$5.51
$3.67
$4.15
$263
$4.24
Princip
Paid
$0.00
$313.47
$174.49
$176.33
$235.85
$137.37
$335.76
lew
Balance
$301.23
$254.41
$169.46
$191.45
$121.58
$195.55
$257 33
On what amount of money will Omar be charged interest for month 8?
A. $195.55
B. $257.33
C. $397.54
D. $340.00
Answer:
B. $257.33
Step-by-step explanation:
Interest will be charged on the New Balance after the Month 7 payment, $257.33.
What is the equation of a line that has a slope of 2 and passes through the point (4,6) ?
Answer:
[tex]y-6=2\,(x-4)[/tex]
or in slope y-intercept form :
[tex]y=2x-2[/tex]
Step-by-step explanation:
The easiest way of find the answer for this is to use what is called the "point-slope" form of a line, because you are in fact given the value of the slope (m) and also a point [tex](x_0,y_0)[/tex] it goes through:
[tex]y-y_0=m\,(x-x_0)[/tex]
In our case the equation becomes:
[tex]y-y_0=m\,(x-x_0)\\y-6=2\,(x-4)\\[/tex]
This can also be written in the slope-intercept form by solving for "y" and operating to remove the parenthesis:
[tex]y-6=2\,(x-4)\\y=2x-8+6\\y=2x-2[/tex]
60 POINTS PLEASE HELP!!!What is the transformation of A(6, 4) when dilated by a scale factor of ½, using the origin as the center of dilation?
Answer:
see below
Step-by-step explanation:
Multiply each of the coordinates by the dilation factor:
A' = (1/2)A = 1/2(6, 4) = (3, 2)
Point A gets transformed to point A'(3, 2), matching choice B.
I need Help can someone help me with this answer
Answer:
Hi there!
The distance L between two points (x1, y1) and (x2, y2) in two-dimensional plane could be calculated by:
L = sqrt((y2 - y1)^2 + (x2 - x1)^2)
The distance between two points (-5, 4) and (3, -2) can therefore be calculated by:
L = sqrt( (-2 - 4)^2 + (3 - -5)^2) = sqrt( 6^2 + 8^2) = sqrt(36 + 64) = sqrt(100 ) = 10
=> Option C is correct.
Hope this helps!
:)
f(n+1)=f(n)-5. If f(1)=100, what is f(6)
Answer:
75
Step-by-step explanation:
Given:
f(1) = 100
f(n+1) = f(n) - 5
Solve for:
f(6)
Solution:
f(1) = 100
f(2) = f(1) - 5 = 100 - 5 = 100 - 1 x 5 = f(1) - 1 x 5
f(3) = f(2) - 5 = 100 - 5 - 5 = 100 - 2 x 5 = f(1) - 2 x 5
...
f(n) = f(n - 1) - 5 = 100 - (n-1) x 5 = f(1) - (n-1) x 5
=> f(6) = f(1) - (6-1) x 5 = 100 - 5 x 5 = 100 - 25 = 75
Hope this helps!
What is the surface area of the cube below?
A. 12 units2
B. 20 units2
C. 8 units2
D. 24 units2
Answer:
24 units squared or D
Step-by-step explanation:
The Surface Area of a cube is 6(x²) x is the side length.
x=2
6(4)=24
The value of surface area of cube is,
⇒ SA = 24 units²
What is mean by Cuboid?A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.
Given that;
Side of cube = 2 units
Now, We know that;
the surface area of the cube with side 'a' is,
⇒ SA = 6a²
Hence, We get;
the surface area of the cube is,
⇒ SA = 6 × 2²
⇒ SA = 24 units²
Learn more about the cuboid visit:
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What’s the correct answer for this? Solve for x
Answer:
x = 40
Step-by-step explanation:
Given 2 secants to a circle from an external point, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is
8(8 + x) = 12(12 + 20) ← distribute parenthesis on both sides
64 + 8x = 12 × 32 = 384 ( subtract 64 from both sides )
8x = 320 ( divide both sides by 8 )
x = 40
Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 7%. If the rate of decay is proportional to the amount of the substance present at time t, find the amount remaining after 24 hours. (Round your answer to one decimal place.)
Answer:
The amount remaining after 24 hours is 17.5 milligrams.
Step-by-step explanation:
The rate of decay is proportional to the amount of the substance present at a time
The equation is
Rate=k*amount remaining at(time)
Where k = constant of proportionality.
So we don't know the value of k, let's find it.
7= k(70)(6)
K= 1/60
Amount remaining after 24 hours
7= 1/60 * x* (24)
(60*7)/24= x
17.5 = x
The amount remaining after 24 hours is 17.5 milligrams.
What is the value of 4p − 2, when p = 8? 16 24 30 34
Answer:
4p - 2
4(8) - 2
32 - 2 = 30
The answer is 30.This is because you have to substitute the value of the number they give into the equation. This will give you the number of 4 to be multiplied by 8. This is because the x is the number 8.
Hope this helped!
Answer:
What is the value of 4p − 2 when P 8?
the answer is 30.
Step-by-step explanation:
There are 10 clean individual socks in your sock drawer. There is only one matching pair among them. In the dark, you reach into the drawer and randomly pick 2 socks. What is the probability that you choose the matching pair
The required probability of choosing the matching pair of socks is approximately 0.0222 or 2.22%.
To find the probability of choosing the matching pair of socks, we need to consider the total number of possible outcomes and the number of favorable outcomes.
In this case, there are 10 individual socks in the drawer, and only one matching pair. When you randomly pick 2 socks, there are C(10, 2) = 45 possible outcomes, as you are choosing 2 socks out of 10.
The favorable outcome is when you choose the matching pair, which can occur in only one way.
Therefore, the probability of choosing the matching pair of socks is:
P(matching pair) = favorable outcomes / total outcomes
= 1 / 45 ≈ 0.0222
So, the probability of choosing the matching pair of socks is approximately 0.0222 or 2.22%.
Learn more about probability here:
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The population of a small town in central Florida has shown a linear decline in the years 1992-2000. In 1992 the population was 48000 people. In 2000 it was 44880 people.
A) Write a linear equation expressing the population of the town P
P
in terms of t
t
, the number of years since 1992.
Answer: c
B) If the town is still experiencing a linear decline, what will the population be in 2003?
Answer:
P = -390t +48,000P = 43,710 in 2003Step-by-step explanation:
A) We are given two pairs of (t, P): (0, 48000), (8, 44880). We can use these with the 2-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
P = (44880 -48000)/(8 -0)(t -0) +48000
P = -3120/8t +48000
P = -390t +48000
__
B) In 2003, t = 11, so we have ...
P = -390(11) +48000 = 43710
The population in 2003 is predicted to be 43,710.
What number is 144% of 5.19
Answer:
7.4736
Step-by-step explanation:
A = 144% of 5.19 means: A = (144/100) x 5.19 = 7.4736
Hope this helps!
Select the correct answer.
What is the sum of this arithmetic series?
586 +564 + 542 + ... +212
Answer:
sum of the series = 7182
Step-by-step explanation:
This is an arithmetic series. The first term is known as 586 and the last term is known as 212. We are ask to find the sum of the series. The common difference of this sequence is -22 . The difference between the next term and the previous term is -22. Let us find the number of terms.
common difference = 564 - 586 = -22
number of terms = n
nth term = a + (n - 1)d
212 = 586 + (n - 1)-22
212 = 586 - 22n + 22
212 - 586 - 22 = -22n
-396 = -22n
divide both sides by -22
n = -396/-22
n = 18
Using the formula for sum
sum of nth term = n/2(a + l)
where
l = last term
a = first term
n = number of term
sum of nth term = n/2(a + l)
sum of nth term = 18/2(586 + 212)
sum of nth term = 9(798 )
sum of the series = 7182
can the value of y be the same for all X values in a function
Answer:
yes
Step-by-step explanation:
One such function is ...
f(x) = 0
No matter what the value of x is, the value of y is 0. The graph of it is a horizontal line.
The Great Pyramid is an example of a___ a0_____ a1.
Answer:
Triangular Pyramid
Step-by-step explanation:
A triangular pyramid has 4 triangular sides and a rectangular base
mine was Square, Pyramid
that is what my answer was.
Hope you have a Blessed Day
God is with you.
Can someone help this is really difficult for me
Answer:
D.strong
Step-by-step explanation:
Answer:
strong
Step-by-step explanation:
definitely not parabolic
pretty positive (not negative)
pretty strong (not weak)
I guess strong
(don't be angry if it is wrong, I'm not a regression and best fit expert)
The height of an object above the ground in feet can be modeled as a function of time, t, in seconds using the equation: h(t)= -16(t-3)^2 + 288 for t grater than or equal to 0. a)Find the time in seconds when the object reaches the ground (h=0). Round your answer to the nearest second. Hint- Solve by taking the square root. b) Find all times when the object is at a height of 150 feet. Round your answer to the nearest second. Hint-Solve by taking the square root.)
Answer:
(a) t = 7 sec approximately; (b) t = 6 sec
Step-by-step explanation:
(a) Set h(t)= -16(t-3)^2 + 288 = 0 and solve for t:
16(t-3)^2 = 288
After simplification, this becomes (t - 3)^2 = 18, or t - 3 = ±3√2.
Because t can be only zero or positive, t = 3 + 3√2 = 7 seconds
(b) Solve h(t)= -16(t-3)^2 + 288 = 150:
-16(t-3)^2 = - 162
or (t - 3)^2 = 10.125, or
t - 3 = ±3.18, or, finally, t = 6.18 sec (discard t = -0.18 sec)
Line p is parallel to line q. Parallel lines p and q are crossed by lines a and b to form 2 triangles. At parallel line p, angle 4 is formed by line b and angle 5 is formed by line a. Angle 6 is the third angle. At parallel line q, angle 3 is formed by line 3 and angle 2 is formed by line b. Angle 1 is the third angle. Which set of statements about the angles is true? Angle 1 is congruent to angle 6, angle 5 is congruent to angle 4, angle 3 is congruent to angle 2 Angle 2 is congruent to angle 4, angle 3 is congruent to angle 6, angle 1 is congruent to angle 5 Angle 3 is congruent to angle 6, angle 1 is congruent to angle 2, angle 5 is congruent to angle 4 Angle 6 is congruent to angle 1, angle 5 is congruent to angle 3, angle 4 is congruent to angle 2
Answer:
add all angles
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
John and Trey both leave the coffee shop at the same time, but in opposite directions. If Trey travels 7 mph faster than John and after 5 hours they are 85 miles apart, how fast is each traveling?
John is traveling __________ mph
Trey is traveling __________ mph
Answer:
John is traveling 5 mph
Trey is traveling 12 mph
Step-by-step explanation:
we will concept of speed distance and time where
distance = speed * time
Let the speed of john be x miles per hour
if, Trey travels 7 mph faster than John
then speed of trey = (x+7) miles per hour
Time of travel for both of them = 5 hours
distance traveled by john in 5 hours = x* 5 = 5x miles
distance traveled by john in 5 hours = (x+7) * 5 = (5x + 35)miles
total distance covered by them = 5x miles + (5x + 35)miles = (10x+35) miles
it is given that after 5 hours they were 85 miles apart, thus the distance above calculated should be equal to 85 miles
10x+35 = 85
=>10x = 85 -35
=> 10x = 50
=> x = 50/10
=> x = 5
Thus, speed of john is 5 miles per hour
speed of Trey is: x+7= 5 + 7 = 12 miles per hour