Answer:
n = 19
Step-by-step explanation:
[tex](1 + 3x)^{n} = {1}^{n} + {1}^{n - 1} .(3x)^{1}.nC1 + {1}^{n - 2}.(3x)^{2} .nC2 + ...[/tex]
Third term coefficient:
[tex]1^{n - 2}.(3)^{2} .nC2 = 1539 \\ 9.nC2 = 1539 \\ nC2 = 171 \\ [/tex]
nCr = n!/((n - r)!r!)
nC2 = 171
n!/((n - 2)!2!) = 171
n!/2(n - 2)! = 171
n!/(n - 2)! = 342
n.(n - 1).(n -2).../((n - 2).(n - 3).(n - 4)...) = 342
n(n - 1) = 342
n² - n = 342
(n - ½)² - ¼ = 342
(n - ½)² = 1369/4
(n - ½) = ±37/2
n = 1/2 ± 37/2
n = -18 or n = 19
Since we are told n is a positive integer, it is 19
Select the correct answer. What is the solution to this inequality? 3(1/4)^x+1<192
The solution to the exponential inequality is x < -4.
What is the exponential inequality?The exponential inequality given in this problem is:
[tex]3\left(\frac{1}{4}\right)^{x + 1} < 192[/tex]
Then:
[tex]\left(\frac{1}{4}\right)^{x + 1} < \frac{192}{3}[/tex]
[tex]\left(\frac{1}{4}\right)^{x + 1} < 64[/tex]
[tex]\left(\frac{1}{4}\right)^{x + 1} < 4^3[/tex]
Applying the exponent property, we have that:
[tex]4^3 = \left(\frac{1}{4}\right)^{-3}[/tex]
Hence:
[tex]\left(\frac{1}{4}\right)^{x + 1} < \left(\frac{1}{4}\right)^{-3}[/tex]
[tex]x + 1 < -3[/tex]
[tex]x < -4[/tex]
The solution is is x < -4.
You can learn more about inequalities at https://brainly.com/question/18290022
Help me please- Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
Answer:
One booster pack is worth 9 cards and one premade deck is worth 37 cards.Step-by-step explanation:
We know that:
9x + 7y = 340 cards4x + y = 73 cardsy = Cost of premade decks (In cards)x = Cost of booster packs (In cards)Work:
9x + 7y = 340 cards4x + y = 73 cards
4(9x + 7y = 340 cards)9(4x + y = 73 cards)
36x + 28y = 340 x 4 cards36x + 9y = 73 x 9 cards
19y = 1360 - 65719y = 703y = 703/19 = 37This means that 1 premade deck is worth 37 cards. Now, let's substitute the value of y into the first equation to find x.
9x + 7y = 340 cards=> 9x + 7(37) = 340 cards=> 9x + 259 = 340 cards=> 9x = 81 cards=> x = 9 cardsHence, one booster pack is worth 9 cards and one premade deck is worth 37 cards.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
WILL MARK BRAINLIEST! Manny signed up for a cell phone plan to pay for his text messaging. The table shows his monthly bill based on how many text messages he
sends. Answer the question below
Answer:
I believe it's D :)
Step-by-step explanation:
Answer:
The answer is A: The amount he must pay for each text message
Step-by-step explanation:
B is wrong because that would be for the x-value
C is wrong because that would be for the x-value
D is wrong because that is his monthly bill for if he texts
Hope this helps and Mark Brainliest Please!! :)
Find the slope of the line that passes through ( 10, 97) and (-11, 2).
Answer:
95/21
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-97)/(-11-10)
m=-95/-21
m=95/21
HELP ME PLEASE!!!
Using the parallelogram, find each measure.
WZ: _____
XY:______
ANGLE W:_____
ANGLE X:______
ANGLE Y:______
ANGLE Z:_____
This recipe makes enough pastry for 8 pasties.
Tara has 1.4 kg of flour, 600 g butter and plenty of water.
What is the maximum number of pasties she can make?
Recipe: Pastry for 8 pasties
400 g flour
150 g butter
4 tablespoons water
Answer:
I think it's 4 but I could be wrong so really sorry if I am
Two squares have sides 12cm and 4cm respectively. What is the ratio of their sides
Answer:
3 : 1
Step-by-step explanation:
We have to compare the value of two sides.
Ratio of sides = 12 : 4 = [tex]\dfrac{12}{4}=\dfrac{4*3}{4*1}=\dfrac{3}{1}[/tex]
= 3 : 1
The sum of two numbers is -5 What could
the numbers be?
Find as many solutions as you can.
Answer:
For this problem, all-natural numbers are solutions and can be answers to this problem.
Small Examples:
-1 + -4 = -5
-3 + -2 = -5
9 + -14 = -5
3 + -8 = -5
-26 + 21 = -5
Is the following statement true or false?
The intersection of two lines can be a ray.
Answer:
True the intersection of two lines can be a ray.
Giving 50 points!!!!!!!!!
Answer:
Step-by-step explanation:
o.3 I think not sure but wanted to help u
Answer:
o.3 I think not sure but wanted to help u
Step-by-step explanation:
Determine which point is the solution to the given system of inequalities (y≥2x+4 and x<4-y).
Select all that apply.
A (0,0)
B (0,-4)
C (-2,0)
D (-2,6)
E (-4,2)
F (2,-4)
Answer:
C (-2,0), E (-4,2)Step-by-step explanation:
Given system:
y ≥ 2x + 4 and x < 4 - yPlot the system and then verify the given points:
A (0,0) B (0,-4) C (-2,0) D (-2,6) E (-4,2) F (2,-4)Refer to attached
The points within the intersected region are C and E
Graph attached
find the missing angles
Answer:
The new angles are in color
HELP ME PLEASE!
i’ll mark brainliest if you’re correct!
Answer:
36
Step-by-step explanation:
7x+4 = 15x-12
7x = 15x-16
-8x = -16
-8x/-8 = -16/-8
x = 2
BD = 15x-12 + 9x
BD = 15(2)-12 + 9(2)
BD = 30-12 + 18
BD = 18 + 18
BD = 38
The answer is 36 I took the test. :)
The sum of two consecutive even integers is 196. Which expression may be used to solve the
problem?
On + (n + 2) = 196
On + n = 196
(n + 2) + (n + 4) = 196
2n = 196
Answer:
the answer is 98. 196 ÷ 2 = 98
how to use inverse cosin
Answer:
sec
Step-by-step explanation:
1/cosin = sec or cosin^-1
what is the inverses for ⅛
Answer:
The inverse of 1/8 is 8.
A box is 41 cm long, 32 cm wide, and
26 cm high. Is the volume closer to 3,600
or 36,000 cubic cm?
Answer:
Closer to 36,000cm^3
Step-by-step explanation:
To find the volume, we can use the formula [ h * w * l ].
41 * 32 * 26 = 34,944
If we round to the nearest thoudsand, we get 35,000 which is closer to 36,000 than 3,600.
Best of Luck!
Answer:
The volume is closer to 36,000 cubic centimeters.
Step-by-step explanation:
Given the following question where...
[tex]v=w\times l \times h[/tex]
[tex]l=41[/tex]
[tex]w=32[/tex]
[tex]h=26[/tex]
Substitute:
[tex]v=32\times41\times26[/tex]
[tex]32\times41=1312[/tex]
[tex]1312\times26=34112[/tex]
[tex]v=34112cm^2[/tex]
Hope this helps.
what
UX
is the
value
ABC
of L
AX
+
B.
Answer:
72°
Step-by-step explanation:
Angle B is the same as angle C in this isosceles triangle. The sum of the angles is 180°, so you have ...
x + 2x +2x = 180°
x = 180°/5 = 36°
∠ABC = 2x = 2(36°) = 72°
Please answer, This is for a test.
Answer:
less than or subtract
Step-by-step explanation:
PLEASE ANSWER THIS !
Answer:
a=4.5
Step-by-step explanation:
6a+42=18a-12
54=12a
4.5=a
Please help it is due today
Simplify (4³)⁵
(I am not asking anyone to solve it, I am only asking for it to be simplified)
A. 12⁵
B. 4⁸
C. (1/4) ¹⁵
D. 4¹⁵
for the problem 1/5g - 1/10 -g+ 1/3/10g -1/10 tyson created an equivalent expression using the folling steps is his final expression equivalent to the initial expression
No, Tyson's final expression is not equivalent to the initial expression.
Fraction addition;According to Tyson's evaluation after collecting like terms; we have;
1/5g +(-1g) + 1(3/10g) + (-1/10) + (-1/10)open parenthesis
1/5g - 1g + 3/10g - 1/10 - 1/10Upon addition of like terms; we have;
(-1/2)g -1/5.Hence, the correct expression is; (-1/2)g -1/5
Read more on fraction addition;
https://brainly.com/question/11562149
Solve the math problem
Answer:
No solutions
Step-by-step explanation:
Solve: Using substitution
We know what y equals. Plug that in for the other equation to solve for x
-8x + 2y = 3-8x + 2(4x + 5) = 3-8x + 8x + 10 = 310 = 3There are no solutions to this problem because 10 cannot equal to 3
-Chetan K
Answer:
The system has no solution
hope it's helpful
can you please help me
Answer:
$147
Step-by-step explanation:
Let's set up two ratios...
273:13
x:7
Simplify the first ratio by dividing both numbers by 13...
21:1
x:7
We know that 1*7 is 7 so we can multiply 21 by 7 to get x
21*7=147
x=$147
I. Simplify each equation. Use a scratch paper for your solution then write your final answer in the blank.
1.) 20 + 4 + 8 ÷ 4 x (5 - 3) = _______________
2.) 3² - 6 = __________________
3.) 19 + 2 – 3 x 7 = _____________________
4.) 2 - 4 ÷ 2 = _______________
5.) (3 + 2) - (5 - 2²) = ____________________
6.) 52 ÷ 5 x 5 – 5 + 5 = ________
7.) 2 x (6 + 2 - 8) = _____________________
8.) (50 – 2 x 3) – 46 = ________
9.) 1000 + 99 = ________________________
10.) 6 + 7 x 3 – 27 = __________
Write the equation of the line that is perpendicular to the line given and through the given point. Do not use spaces in your equation. y=-x-3 (-1, 4) *
Answer:
y=x+5
Step-by-step explanation:
The equation is given in slope-intercept form, so we can read the slope from the equation. It is the x-coefficient, -1.
The slope of the perpendicular line will be the opposite reciprocal of this value:
-1/-1 = 1
The new y-intercept will be ...
b = y -mx = (4) -(1)(-1) = 5
Then the slope-intercept equation of the perpendicular line is ...
y = x +5
1. What value of y satisfies y/3 =<12
Answer:
y[tex]\leq[/tex]36
Step-by-step explanation:
y/3[tex]\leq[/tex]12
y[tex]\leq[/tex]36
Answer:
y<36
Step-by-step explanation:
36/3 = 12
Given that f(x) = 10x + 45, find f(-2)
Answer:
f(-2) is 25
Step-by-step explanation:
[tex]{ \tt{f(x) = 10x + 45}}[/tex]
» f(-2) means that x is -2
[tex]{ \tt{f( - 2) = 10( - 2) + 45}} \\ { \tt{f( - 2) = - 20 + 45}} \\ { \tt{f( - 2) = 25}}[/tex]
A factory makes rugs at a constant rate of 10 rugs every 4 hours. Part B How many rugs does the factory make in 1 hour? 1 4 of a rug 1 4 of a rug 2 5 of a rug
Nadia is a stockbroker. earns 12% commission each week. Last week, she sold $6,800 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she make in commission in 2011?
Answer:
$816
Step-by-step explanation:
816 × 52= $42,432
............
