Given formula: [tex]\sf A_n= -4(2)^{n-1}[/tex]
simplify substitute the number of term by replacing n
Find first five terms:
[tex]\sf A_1= -4(2)^{1-1}[/tex] ⇒ [tex]\sf A_1= -4[/tex]
[tex]\sf A_2= -4(2)^{2-1}[/tex] ⇒ [tex]\sf A_2= -8[/tex]
[tex]\sf A_3= -4(2)^{3-1}[/tex] ⇒ [tex]\sf A_3= -16[/tex]
[tex]\sf A_4= -4(2)^{4-1}[/tex]⇒ [tex]\sf A_4= -32[/tex]
[tex]\sf A_5= -4(2)^{5-1}[/tex]⇒ [tex]\sf A_5= -64[/tex]
Tenth term:
[tex]\sf A_{10}= -4(2)^{10-1}[/tex] ⇒ [tex]\sf A_{10}= -2048[/tex]
Answer:
[tex]\sf a_1=-4\\a_2=-12\\a_3=-20\\a_4=-28\\a_5=-36\\a_{10}=-76[/tex]
Step-by-step explanation:
[tex]\textsf{Given sequence}: \sf a_n=-4(2n-1)[/tex]
This formula is for the nth term of the sequence.
Therefore, to find any term of the sequence, substitute the position of the term you wish to find as n.
For example, to find the 10th term, substitute n = 10 into the formula:
[tex]\begin{aligned}\sf a_{10} & =-4[2(10)-1)]\\ & = -4(20-1)\\ & = -4(19)\\ & = -76\end{aligned}[/tex]
To find the first 5 terms, substitute n = 1 through n = 5 into the formula:
[tex]\sf a_1=-4[2(1)-1]=-4(2-1)=-4(1)=-4[/tex]
[tex]\sf a_2=-4[2(2)-1]=-4(4-1)=-4(3)=-12[/tex]
[tex]\sf a_3=-4[2(3)-1]=-4(6-1)=-4(5)=-20[/tex]
[tex]\sf a_4=-4[2(4)-1]=-4(8-1)=-4(7)=-28[/tex]
[tex]\sf a_5=-4[2(5)-1]=-4(10-1)=-4(9)=-36[/tex]
how would i find the volume ?
Answer:
4900
Step-by-step explanation:
You multiply lengthxwidthxheight, all the given dimensions to get (25x14x14) 4900
helloooo can someone help meeeeeeeee
Answer:
Option B, [tex](48x^{8}y^{5})[/tex]
Step-by-step explanation:
Step 1: Simplify the exponent
[tex](12x^{2}y^{3})(2x^{3}y)^{2}[/tex]
[tex](12x^{2}y^{3})(2^{2}x^{3*2}y^{1*2})[/tex]
[tex](12x^{2}y^{3})(4x^{6}y^{2})[/tex]
Step 2: Simply the expression
[tex](12x^{2}y^{3}*4x^{6}y^{2})[/tex]
[tex](48x^{2+6}y^{3+2})[/tex]
[tex](48x^{8}y^{5})[/tex]
Answer: Option B, [tex](48x^{8}y^{5})[/tex]
Bags A and B contain some counters.
The number of counters on each bag is the same.
Work out the value of y
Answer: y=3
Step-by-step explanation:
It is a linear equation6y+1=4y+76y-4y=7-12y=6y=6/2y=3You want to take a trip to the beach, which costs $450. You
have $900 in your bank account but must withdraw $60
each week to pay for groceries. What is the maximum
number of weeks you can withdraw money and still have
enough to take your trip to the beach?
I need the inequality, inequality answer, final answer
Answer:
900 - 60n ≥ 450
n ≤ 7.5
Answer: 7 weeks
Step-by-step explanation:
Let n = numberof weeks.
In n weeks, you withdraw 60n from the account.
After withdrawing $60 for n weeks, teh amount must be at least $450. At least $450 means greater than or equal to $450.
900 - 60n ≥ 450
-60n ≥ -450
n ≤ 7.5
Answer: 7 weeks
I need help quick with sampling methods
Leroy's total job benefits were $50,150 last year. his total job expenses for traveling and for professional development for the year were $3,500. which of the following represents his total employment compensation? a. $46,650 b. $47,650 c. $50,150 d. $53,650
An expression has numbers, variables, and mathematical operations. The representation of Leroy's total employment compensation is $46,650.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
As it is given that Leroy's total job benefits were $50,150. while his total job expenses for traveling and for professional development for the year were $3,500. As the total employment compensation is the amount that is the difference between job benefits and job expenses. Therefore,
[tex]\rm Total\ employment\ compensation= Job\ benefits + Job\ expenses[/tex]
[tex]= \$50,150 - \$3,500\\\\= \$46,650[/tex]
Hence, the representation of Leroy's total employment compensation is $46,650.
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Answer:
the representation of Leroy's total employment compensation is $46,650.
Step-by-step explanation:
Subtract these polynomials.
(x^2 + 5x + 2) - (5x^2 - x - 2)
Answer:
-4x^2 + 6x +4
Step-by-step explanation:
Answer:
=x^2+5x+2+−1(5x^2−x−2)
=x^2+5x+2+−1(5x^2)+−1(−x)+(−1)(−2)
=x^2+5x+2+−5x^2+x+2
=x^2+5x+2+−5x^2+x+2
=(x^2+−5x^2)+(5x+x)+(2+2)
=−4x^2+6x+4
Phoebe is concerned that it the error is not fixed, her pay increase wll be less in future
years than it is supposed to be. If Phoebe continues
to work al the company and receives.
an increase of $0.75 per hour instead of a 5% increase. what will be the difference in her
hourly pay in 5 years? Show vour work.
The difference in the pay rate of Phoebe in 5 years will be $11850
How to calculate the pay?Your information is incomplete. Therefore, an overview will be given. Let's assume that the pay rate is $20000. When there is a 5% increase, the new pay rate will be:
= $20000 + (5% × $20000)
= $20000 + $1000
= $21000
When there is $0.75 increase per hour, the new pay rate on 5 years will be:
= (0.75 × 43800)
= $32850
The difference will be:
= $32850 - $21000
= $11850
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pizzzzzzzzzzzzzzzzzzzzzzz help pizzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help
Answer:
1. The sum of the score is 667
2. ???
3. for her to have 95 on her last score the sum would be 762
4. ???
Step-by-step explanation:
1 = add all eight scores to get the sum
3 = add 95 to the sum of the eight scores
PLS HELP PLS I WILL GIVE BRAINLIST
Which punctuation mark goes in the space?
My sister stole a bunch of my things ______ my pants, shoes, and jackets.
Group of answer choices
None
Comma ,
Dash -
Colon :
Semi-Colon ;
Period.
Which punctuation mark goes in the space?
My sister stole a bunch of my things ______ except my favorite blanket.
Group of answer choices
None
Comma ,
Dash -
Colon :
Semi-Colon ;
Period.
Which punctuation mark goes in the space?
My sister stole a bunch of my things ______ because she's rude to me.
Group of answer choices
None
Comma ,
Dash -
Colon :
Semicolon ;
Which punctuation mark goes in the space?
My sister ____ who is rude to me, stole a bunch of my things.
Group of answer choices
None
Comma ,
Dash -
Colon :
Semicolon ;
Which punctuation mark goes in the space?
My sister stole my favorite thing ______ my jacket.
Group of answer choices
None
Comma ,
Dash -
Colon :
Semicolon ;
Period.
Which punctuation mark goes in the space?
If my sister steals one more of my things ______ I'm going to never talk to her again.
Group of answer choices
None
Comma ,
Dash -
Colon :
Semicolon ;
Which punctuation mark goes in the space?
I'm going to tell my dad ______ my mom - if my sister steals more of my things.
Group of answer choices
None
Comma ,
Dash -
Colon :
Semicolon
Which punctuation mark goes in the space?
My sister stole a bunch of my things ______ I'm going to tell my dad.
Group of answer choices
None
Comma ,
Dash -
Colon :
Period.
Which punctuation mark goes in the space?
My sister stole a bunch of my things ______ my dad will punish her for me.
Group of answer choices
None
Comma ,
Dash -
Colon :
Semicolon ;
Which punctuation mark goes in the space?
My sister stole a bunch of my things like ______ my pants, shoes, and jackets.
Group of answer choices
None
Comma ,
Dash -
Colon :
Semicolon ;
Answer:
1.colon
2. semicoln
3. comma
4. none
5. dash
6. comma
7. i am not sure but i think is a colon
8.comma
9. semicoln
10. dash
Step-by-step explanation:
You use colon when listing out something.
Sorry, I am not sure about this answer
Which solution can be simplified to determine when the object will hit the ground? t = t = t = t =
The solution can be simplified to determine when the object will hit the ground is; h(t) = -9.8t² + 20t + 60
What is projectile motion?Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory
Projectile motion
We are told that the projectile motion of an object can be modeled using;
h(t) = gt² + v0*t + h0
Where;
g is the acceleration due to gravity
t is the time since launch
h(t) is the height of the projectile after time t
v0 is the initial velocity
h0 is the initial height.
Now, we are given;
The acceleration due to gravity; g = –9.8 m/s²
Initial velocity; v0 = 20 m/s
Initial height; h0 = 60 m
Hence solution can be simplified to determine when the object will hit the ground is; h(t) = -9.8t² + 20t + 60 h(t) = -9.8t² + 20t + 60
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Answer:
it's c on edge :] have a nice day
Please help me anyone?
Answer:
1/26
Step-by-step explanation:
There are 52 cards....four are 9's 4/52
six possible rolls three are even 3/6
4/52 * 3/6 = 1/26
An airline gathers data on late departures and early arrivals over a month. it finds that the probability of a late departure is 12 percent, the probability of an early arrival is 27 percent, and the probability of both a late departure and an early arrival is 4 percent. which equation shows how to correctly calculate the probability of a late departure or an early arrival? p(late departure or early arrival) = 0.12 0.04 p(late departure or early arrival) = 0.12 0.27 p(late departure or early arrival) = 0.12 0.27 – 0.04 p(late departure or early arrival) = 0.27 0.04 – 0.12
The probability of a late departure or an early arrival P(late departure or early arrival) = 0.12 + 0.27 – 0.04
What is probability?
The probability is defined as the chances of occurence of any event from the sample.
Given: The probability of a late departure is 12 %t, the probability of early arrival is 27%.
i.e. P(late departure)=0.12
P(an early arrival)=0.27
The probability of both a late departure and an early arrival is 4 percent.
P(late departure and early arrival) =0.04
Now, using the formula the probability of the union of two dependent events A and B:-
[tex]\rm P(AUB)=P(A)+P(B)-P(A \cap B)[/tex]
i.e. P(late departure or early arrival) = P(late departure)+P(an early arrival)-P(late departure and early arrival)
=0.12+0.27-0.0.04
Hence, the required equation : P(late departure or early arrival) = 0.12 + 0.27 – 0.04
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The equation that shows how to correctly calculate the probability of a late departure or an early arrival is P(L∪E)=0.12+0.27-0.04.
Probability of late departure P(L) = 0.12
Probability of early arrival P(E) = 0.27
Probability of both a late departure and an early arrival P(L∩E)= 0.04
What is probability?Probability is the measurement of the likelihood of an event.
P(L∪E)=P(L)+P(E)- P(L∩E)
Where P(L∪E) is the probability of a late departure or an early arrival.
So, P(L∪E)=0.12+0.27-0.04
Hence, the equation that shows how to correctly calculate the probability of a late departure or an early arrival is P(L∪E)=0.12+0.27-0.04.
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pls help me with this!
Answer:
0.69
Step-by-step explanation:
In a right triangle, the cosine of one of the acute angles is the ratio of the adjacent ("next to") side to the hypotenuse.
In this triangle, the side adjacent to angle T has length [tex]\sqrt{38}[/tex]. Now you need the length of the hypotenuse, ST. Use the Pythagorean Theorem:
[tex]ST^2=(\sqrt{38})^2+(\sqrt{41})^2 \\\\ST^2=38+41\\\\ST=\sqrt{79}[/tex]
Build the ratio (adjacent) / (hypotenuse) and approximate it with a decimal.
[tex]\cos{T}=\frac{\sqrt{38}}{\sqrt{79}} \approx 0.69[/tex]
[tex]{\large{\red{\mapsto{\maltese{\underline{\green{\boxed{\blue{\underbrace{\overbrace{\pink{\pmb{\bf{Answer:}}}}}}}}}}}}}}[/tex]
To find :-
Cos T = ?
Given :-
Perpendicular(P) = RS = √41
Base(B) = RT = √38
Formula to be used :-
We will use here a trignometry formula to find hypotenuse (H) which is ST.
(hypotenuse)² = (perpendicular)² + (base)²
[tex] \cos(A) = \frac{base}{hypotenuse} [/tex]
Solution:-
H² = P² + B²
H² = (√41)² + (√38)²
H² = 41 + 38
H² = 79
H = √79
[tex] \cos(T) = \frac{B}{H} \\ \cos(T) = \frac{ \sqrt{38} }{ \sqrt{79} } \\ \cos(T) = \frac{6.17}{8.89} \\ \cos(T) = 0.69[/tex]
Result :-
The value of cos(T) is 0.69.
[tex] - 5 = a - 3[/tex]
I need help with this problem
[tex]~~-5=a-3\\\\\implies a =-5+3\\\\\implies a = -2[/tex]
I don't know what to do with this help I think it's right but
Answer:
Nice handwriting!
Step-by-step explanation:
I have no idea im only in 8th grade.
I NEED HELP WITH THIS
Answer:
Step-by-step explanation:
a) 147
b)147
c) 152
d)65
Answer:
a) mean = 147
b) median = 147
c) mode = 152
d) range = 65
Step-by-step explanation:
firsly let’s arrange the numbers of the set in ascending order:
117 , 119 , 138 , 142 , 152 , 152 , 174 , 182
a)
[tex]Mean = \frac{117+119+138+142+152+152+174+182}{8} =\frac{1176}{8} =147[/tex]
b) the median is the average of the two middle numbers :
[tex]117,119,138, \frac{142,152}{} , 152,174,182[/tex]
[tex]median=\frac{142+152}{2}= 147[/tex]
c) the modal height is 152 because 152 is the value that appears most frequently (2 times) in our set
d) the range of a set is the difference between the highest and lowest numbers :
Then
the range = 182-117 = 65
Hoy Many times as great as 10% is 100% answer
Answer: 100% is 10 times as great as 10%
Step-by-step explanation: 10 * 10 = 100 or 100 divided by 10 equals 10. Have a nice day~
Answer:
um.....10
Step-by-step explanation:
100% (1) ÷ 10% (0.10) = 10
[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex] [tex]Have[/tex] [tex]a[/tex] [tex]great[/tex] [tex]day![/tex] [tex]:)[/tex]
What is the line of the slope shown below
Answer:
3
Step-by-step explanation:
[tex]\frac{-3-6}{2--1}=\frac{-9}{3}=3[/tex]HELP ME PLEASEEEEE, DUE IN A FEW MINUTES!
Step-by-step explanation: 130
[tex]g(n) = 3n + 1[/tex]
[tex]h(n) = 4n + 3[/tex]
[tex](goh) (n)= g(h(n))[/tex]
[tex] = g(4n + 3) = 3(4n + 3) + 1[/tex]
[tex] = 12n + 9 + 1 = 12n + 10[/tex]
Therfore
[tex](gof)(n) = 12n + 10[/tex]
Now
[tex](gof)(10) = 12(10) + 10 = 120 + 10 = 130[/tex]
[tex](gof)(10) = 130[/tex]
I hope it helped you
Step-by-step explanation:
g(n) × h(n)
=(3n+1)(4n+3)
= 12n² +9n +4n +3
= 12n² +13n + 3
then sub 10 in place of n
12n² +13n + 3
= 12(10)²+13(10)+3
=1200+130+3
=1333
9) 78% of what is 159 tons?
Answer:
78:159*100 =
(78*100):159 =
7800:159 = 49.06
Figure ABcD is a parallelogram. If point C lies on the line x=2, what is the y-value of point C?
The value of y in point C is 0. So, C is located at (2, 0) in the Cartesian plane.
Given that a parallelogram ABCD is shown in the Cartesian plane.
The points are:
A = (-1, 2)
B = (2, 3)
C = (2, y)
D = (-1, -1)
We are asked to find the value of y in the point C.
To find the value of y in point C, we can use the fact that the slope of line AB is equal to the slope of line DC, and the slope of line BC is equal to the slope of line DA.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:
slope = (y₂ - y₁) / (x₂ - x₁)
Let's calculate the slope of line AB and DC:
Slope of AB = (3 - 2) / (2 - (-1))
= 1 / 3
∴ Slope of DC = 1 / 3.
So,
1/3 = (y+1) / (2+1)
1/3 = (y + 1) / 3
y + 1 = 1
y = 0
Hence, we get the value of y in point C is 0.
[Note:- you can simply look at the graph and can determine the location of the point C]
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What is the value of y in this system of equations?
Negative 6 x + 2 y = negative 18. Negative 3 x minus 2 y = 54.
Answer:
y = - 21
Step-by-step explanation:
System of equations:
- 6x + 2y = - 18
- 3x - 2y = 54
To find y will look to eliminate x:
- 6x + 2y = - 18
- 3x - 2y = 54 (multiply both sides by -2)
- 6x + 2y = - 18
6x + 4y = - 108
---------------------------- (add those two equations)
6y = - 126 (divide both sides by 6)
y = - 126/6 (simplify by 6)
y = - 21
Answer: -21
Step-by-step explanation:
What is the Volume of the square pyramid? (Round to the nearest tenth as needed)
Answer:
5229 mm³
Step-by-step explanation:
Volume of square pyramid
[tex]\sf \boxed{Volume \ of \ the \ square \ pyramid = \dfrac{1}{3}*b^2*H}[/tex]
b = base length = 25 mm
H = height
We have to find 'H' using Pythagorean theorem,
slant height (hypotenuse) = 28 mm
leg₁ = base length ÷ 2 = 25÷2 = 12.5
leg₂ = H
H² + (12.5)² = 28²
H² = 784 - 156.25
= 627.75
[tex]\sf H = \sqrt{627.75}[/tex]
H = 25.01 mm
[tex]\sf \text{Volume of square pyramid =$\dfrac{1}{3}*25*25*25.1$ }[/tex]
= 5229 mm³
[tex]\sf \boxed{\text{Volume of square pyramid = \dfrac{1}{3}*25*25*28}}[/tex]
ASAP worth 50 points
Answer:
32.5 square feet
Step-by-step explanation:
Area of a trapezoid
1/2 x (a + b) x ha and b = length of parallel sidesh = heightSolving
Here : a = 5, b = 8, and h = 5Area = 1/2 x (5 + 8) x 5Area = 1/2 x 13 x 5Area = 65/2Area = 32.5 square feetAnswer:
32.5 square feet
Step-by-step explanation:
here we just find the area of both shapes within the trapezoid and add them, let's start with the triangle,
formula for the area of a triangle is 0.5 × base × height
therefore,
the area of the triangle is 7.5
the area of a square is equal to the length of the side squared.
5^2 = 25
the sum of 25 + 7.5 = 32.5
final answer is 32.5 square feet
if you need any further guidance make sure to ask:)
A farmer is planting a circular garden with a radius of 32 feet and needs to know the area to determine how many plants to purchase.
What is the area of the garden?
Use 3.14 for π.
Enter your answer, as a decimal, in the box.
Answer:
3215.36 ft^2.
Step-by-step explanation:
Area = 3.14 * r^2
= 3.14 * 32^2
= 3215.36 ft^2.
Pls help! This is due soon!
Answer:
A. 30°, 70° and 80°
B. 10cm
Step-by-step explanation:
A. the two triangle have same angles
so the angles of triangle 2 are 30°, 70° and 80°
B. the perimeter of triangle, is twice as long as the perimeter of
triangle 2
so the perimeter of triangle 2 is 20÷2 = 10 cm
If the sum of a number and six is doubled, the result is two less than the number. Find the number.
X =
Answer:
-14
Step-by-step explanation:
let the number= X
from the statement,
(X+6)×2 = X - 2
open bracket
2X +12 = X- 2
2X-X = -2-12
X = -14
is 1/2 x + 6 > 11 equal to x=-3
Answer:
Rewrite the whole as an equivalent fraction 2.1 Subtracting a whole from a fraction. Rewrite the whole as a fraction using 2 as the denominator.
A penquin dives at 18 feet per minute how many minutes does it take to
dive to -54 feet?
3 Minutes
30 Seconds
5 Minutes
4 Minutes
Answer:
The answer would be (D) 4 minutes.
Step-by-step explanation:
18 x 4= 54
I have had this question before have an amazing day!!!!