A sequence is defined by a₁ = 4, an = a(n-1) + 4. What is the 6th term of the
sequence?
Hence , the 6th term of the sequence is 24
Arithmetic Progression (AP) could be a sequence of numbers so as, during which the distinction between any 2 consecutive numbers could be a constant worth. it's conjointly known as Arithmetic Sequence. as an example, the series of natural numbers: one, 2, 3, 4, 5, 6,… is associate degree patterned advance, that includes a common distinction between 2 serial terms (say one and 2) adequate to one (2 -1).
It is given that first term is 4 and nth term is a(n) = a(n-1) + 4 ......(1)
Putting n = 6 in equation (2) , we get sixth term
a(6) = 4(6-1) +4
a(6) = 4(5) + 4
a(6) = 20 + 4
a(6) = 24
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Read the problem. Identify what you need to know. Then organize the data to solve the problem.
Find the probability that a point chosen at random lies in the shaded region.
A. 0.22
B. 0.25
C. 0.28
D. 0.32
The probability that a point is chosen at random will lie in the shaded area will be 0.32.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Here favorable outcomes will be the shaded portion and the total outcome will be the total circular portion.
Favorable Outcome = Area of shaded portion = 1/2 x 18 x 18/2
= 81 inch sq.
Total Outcome = Total area = 81 π inch sq.
Probability, P(E) = 81/ 81 π = 1/32
Hence, the probability that a point chosen at random will lie in the shaded area is 0.32.
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Solve.
please and thank you!
Answer:
Step-by-step explanation:
2(x+3)/3 + 3(x-6)/2=1-x
2x+6/3 + 3x-18/2=1-x
2(2x+6)/3 + 3(3x-18)=6-6x
4x+12+9x-54=6-6x
13x-49=6-6x
13x+6x=6+42
19x/19=48/19
x=49/19
Write an algebraic expression that models each situation.
Jenny had 130 , but she is spending 10 per week.
The algebraic expression of the situation "Jenny had $130, but she is spending $10 per week is 130-10x
Given,
The total amount she had = $130
Amount she spend per week = $10
Consider the number of weeks as x
Then the algebraic expression = 130-10x
Hence, the algebraic expression of the situation "Jenny had $130, but she is spending $10 per week" is 130-10x.
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Natalie works as a playground supervisor for 8 weeks during the summer at a rate of
$15.27/h. She works a 40-hour week but averages 3 hours of overtime each week,
paid at time and a half. How much will she earn each week, and for the whole
summer?
Natalie will receive a weekly salary of $656.61 and a summer salary of $10505.76.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Natalie earns $15.27 per hour while working as a playground supervisor for 8 weeks throughout the summer. Although she works a 40-hour week, she typically puts in 3 hours of overtime.
For a week = ( 40 + 3 ) x 15.27 = $656.61
For a summer = 4 x 4 = 16 weeks
For a summer = 16 x $656.61 = $10505.76
Therefore, Natalie will be paid $656.61 for a week and for summer $10505.76.
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Helpp, practice problems.
By comparing the intercepts of the linear equation with the ones in the graph, we conclude that the given graph corresponds with the linear equation.
How to know if the graph represents the given equation?
Here we have the linear equation:
1.5*s + 3.5*c = 21
And we have a graph, which we want to see if it is the graph of the linear equation.
To check this, we just need to look at the intercepts, the variable "c" is on the vertical axis and the variable "s" is on the horizontal axis.
The "s" intercept is what we get when we take c = 0, replacing that we will get:
1.5*s + 3.5*0 = 21
1.5*s = 21
s = 21/1.5 = 14
This means that the line should pass through the point (14, 0), and we can see that this happens.
The other intercept is what we get when we take s = 0.
1.5*0 + 3.5*c = 21
c = 21/3.5 = 6
The other intercept is at (0, 6), which we also can see on the graph.
With that is enough to conclude that the given graph represents the given linear equation.
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the difference of six and two divided by 4 in numerical expression
Answer: 1 thank you
Step-by-step explanation:
Solve the inequality 4-2x>7-3x
Hello,
[tex]4 - 2x > 7 -3x[/tex]
[tex]3x - 2x > 7 - 4[/tex]
[tex]x > 3[/tex]
S = ] 3 ; +∞ [
find the volume of the given shape
Answer:
[tex]{ \tt{volume = base \: area \times height \times length}} \\ \\ { \tt{v = \frac{1}{2} (a + b) \times h \times l }} \\ \\ { \tt{v = \frac{1}{2} (1.7 + 2.3) \times 1.3 \times 1.5}} \\ \\ { \tt{v = 2 \times 1.3 \times 1.5}} \\ \\{ \tt{v = 3.9 \: {m}^{3} }}[/tex]
Answer:
3.9 m³
Step-by-step explanation:
To find the volume of a right prism, multiply its base area by its height.
For the given shape:
Base = trapezoid ABCDHeight = 1.5 mArea of a trapezoid
[tex]\boxed{A = \dfrac{1}{2}(a+b)h}[/tex]
Where a and b are the bases and h is the height.
From inspection of the given diagram:
a = BC = 1.7 mb = AD = 2.3 mh = CD = 1.3 mSubstitute the given values into the formula to find the area of the trapezoid base (ABCD):
[tex]\begin{aligned}A & = \dfrac{1}{2}(a+b)h\\\implies ABCD & = \dfrac{1}{2}(BC+AD)CD\\ &=\dfrac{1}{2}(1.7+2.3)(1.3)\\&=\dfrac{1}{2}(4)(1.3)\\&=(2)(1.3)\\&=2.6\; \sf m^2\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Volume of prism} & = \textsf{Area of base} \times \sf height\\\implies V & = ABCD \times 1.5\\V & = 2.6 \times 1.5\\V & = 3.9\;\sf m^3\end{aligned}[/tex]
Which equation does NOT represent a direct variation?
a. y=x
b. 2 x-y=5
c. 2 x-y=0
d. 2 x-5 y=0
The graph of 2x - y = 5 does not represent a direct variation.
Direct variation is variation in which the quotient of the two variables is constant. A constant ratio of two quantities means that one quantity varies directly with the other or that the two quantities vary directly. In symbols, the direct variation formula is y=k*x or k=y/x.
k is known as the constant of variation or the constant of proportionality.
This means that as x increases, y increases, and as x decreases, y decreases, and their ratio is always the same.
The graph of the direct variation equation is a straight line through the origin.
The graph of 2x-y =5 does not pass through the origin, so it does not represent a direct variation. (consult the images attached below).
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Find the tenth term of each arithmetic sequence. 15,23,31, ...........
The 10th term of an Arithmetic Progression (AP) is (a₁₀ = 87.)
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between the two mathematical orders is a constant value (AP). Arithmetic Sequence is another name for it.
We'd come across a few important words in AP that were denoted as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP also can be described in aspects of common differences.
The following is the formula for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the given sequence is; 15,23,31, ...........
Consider the first term is'a₁' = 15
Consider 'a₂' = 23 is the second term.
Consider the third term is 'a₃' = 31
Calculate the common difference;
d = a₂ - a₁
Put the values in the above obtained equation;
d = 23 - 15 = 8
Now, to estimate the value of the 10th term using the formula of nth term.
an = a + (n − 1) × d , n = total number of terms = 10.
Put all the values;
a₁₀ = 15 + (10 - 1) × 8
a₁₀ = 15 + 9 × 8
a₁₀ = 15 + 72
a₁₀ = 87
Therefore, the value of the 10th term is calculated as a₁₀ = 87.
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Simplify each sum or difference. State any restrictions on the variables.
-5 y / 2y-1 - y + 3 / 2y - 1
The simplification of each sum or difference of given expression [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex] is equal to (-3)(2y+1)/ (2y-1). Restriction on the variables is given by y ≠1/2.
As given in the question,
Given expression is [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex]
Simplify the expression by taking the least common multiple
[tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}\\\\= \frac{-5y-y-3}{2y-1}\\ \\= \frac{-6y-3}{2y-1}\\ \\= \frac{-3(2y+1)}{2y-1}[/tex]
Restriction on the variables is given by y ≠1/2.
Therefore, the simplification of each sum or difference of given expression [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex] is equal to (-3)(2y+1)/ (2y-1). Restriction on the variables is given by y ≠1/2.
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3x - 1 = 4x+8-х what is the answer
Answer:
No Solutions
Step-by-step explanation:
Hello!
Solve for x by isolating the variable.
Solve for x3x - 1 = 4x + 8 - x3x - 1 = 3x + 8 Combine like terms-1 = -8 Subtract 3x from both sidesSince -1 does not equal to -8, there are no solutions for x that makes this equation true.
Answer:
no solution
Step-by-step explanation:
3x-1=4x+8-x
add like terms
3x-1=3x+8
add 1 to both sides
3x=3x+9
subtract 3x from both sides
0=9
no answer!
Evaluate each expression for the given values of the variables.
4(2m - n) - 3(2m - n) ; m=-15 and n=-18
The result of the expression 4(2m - n) - 3(2m - n) for the variables m= -15 and n= -18 is -12
Given,
The algebraic expression = 4(2m - n) - 3(2m - n)
Expand the terms
4(2m - n) - 3(2m - n)= 8m-4n-6m+3n
Combine the like terms
8m-4n-6m+3n = 2m-n
We know,
m= -15
n= -18
Substitute the values in the expression
2m-n= 2(-15)-(-18)
=-30+18
= -12
Hence, the result of the expression 4(2m - n) - 3(2m - n) for the variables m= -15 and n= -18 is -12
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A new cell phone sold for $200, which was 200% of the actual cost. What is the actual price of the cell phone?
Answer:
Step-by-step explanation:
200 / 2 = $100
solve the inequality
Answer:
the inequality solution is -19
A school allots £1500 to spend on a trip to the theatre.
Theatre tickets have a regular cost of £48 each and are on offer for
1/6
off.
A train ticket for the day will cost £15 each.
If 2 teachers and the maximum number of students attend, how many students go on the trip
Answer: 38 pounds
Step-by-step explanation: School allots £1500 to spend on a trip to the theatre.
Theatre tickets have a regular cost of £35 each and are on offer for 1/5 off
therefore 4/5*35 = 28 for the tickets
:
A train ticket for the day will cost £15 each.
therefore total cost for each: 28 + 15 = 43 pounds each
:
If 2 teachers and the maximum number of students attend, how much money will the school have left over?
:
let s = no. of students
43(s+2) =< 1500
43s + 86 =< 1500
43s =< 1500 - 86
43s =< 1414
s =< 1414/43
s =< 32.88, 32 students max
:
find how much left over. plus 2 teachers = 34 people
1500 - 43(34) =
1500 - 1462 = 38 pounds left over
4y+20x-12=0 solve for y, would appreciate some help, in struggling a bit
Answer:
y = 3 - 5x
Step-by-step explanation:
Answer:
Step-by-step explanation:
4y+20x−12=0
4y−12=−20x
4y=−20x+12
4y=12−20x
4/4y = 12−20x / 4
y= 12−20x / 4
y=3−5x
What is the solution of √4 x-23 -3 = 2 ?
The solution of the given equation √(4x-23) - 3 = 2 is (x = 14.25).
What is meant by square numbers?A 'Square Number' is the result of multiplying a number or integer (not really a fraction) by itself.
For instance, 3 multiplied by 3 equals 3 squared, or 3 x 3 = 32. So, in essence, a square number is really the exponential form of multiplying a number or integer by itself. Also, if we multiply the number on its own again, we get the integer's cube, a x a x a = a³.Now, as per the given equation;
√(4x-23) - 3 = 2
This could also be written as;
√(4x-23) = 2 + 3
√(4x-23) = 5
Now, squaring on the both side;
(4x-23) = 25
Open the brackets;
4x - 32 = 25
4x = 25 + 32
4x = 57
x = 14.25
Therefore, the solution of the given equation √(4x-23) - 3 = 2 is calculated as (x = 14.25).
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answer this please (will give brainliest)
Answer:
Step-by-step explanation:
Me personally, thinks that p is 9, and M is one or 4.
Think about it this way; 40-4p = _ SO, 40-4(9) = 4 because its like
40- 4 x 9 (40-36=4).
Next thing; m(p) 1(9) OR 4(9)
I HOPE YOU FIGURE IT OUT GOOD LUCK BYE!
In a telephone poll, 31 people said they like shopping and 6 people said they do not like shopping. What is the ratio of the number of people who do not like shopping to the number of people who like shopping?
Answer:
31 to 6
Step-by-step explanation:
31 to 6,
Find the missing term of each geometric sequence. 2,□ ,0.5, . . . .
The missing term of the given geometric sequence can be 1 or -1
Given a geometric sequence,
2, □ ,0.5, . . . .
Hence, we know that
a(1) = 2
a(3) = 0.5
and the missing term is a(2).
The formula for the nth term of a geometric sequence is:
a(n) = a(1) . rⁿ⁻¹
Substitute a(1) =2 and n = 3
a(3) = 2 . r³⁻¹
0.5 = 2 . r²
r² = 0.5/2 = 0.25
r = 0.5 or r = -0.5
Take r = 0.5, then
a(2) = a(1) . r
= 2 . (0.5) = 1
Take r = -0.5, then
a(2) = a(1) . r
= 2 . (-0.5) = -1
Therefore, the missing term, a(2) can be 1 or -1
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7. Nina has 2/3 cup of shampoo left in the shampoo bottle. She uses 1/8 cup of shampoo to wash her hair. If nina washes her hair every day, how many days can she wait before opening a new bottle of shampoo?
Answer:
5 days
Step-by-step explanation:
Make 1/8 and 2/3 have the same denominator
the Least common multiple is 24
1/8 becomes 3/24 and 2/3 becomes 16/24
she can use it 5 more times with a remainder of 1/24 of a cup of shampoo remaining
Expand each binomial. (3-x)⁵
The expand each binomial. (3-x)⁵ is:
-x⁵ + 15x⁴ -90x³ + 270x² - 243x + 243
We solve first by perfect square trinomial, then we apply the distributive property.
(3 - x)⁵ = (3 - x)²(3 - x)²(3 - x)
(3 - x)²= 9 - 6x + x²
(9 - 6x + x²)(9 - 6x + x²)81 - 54x + 9x² - 54x + 36x² - 6x³ + 9x² - 6x³ + x⁴
x⁴ - 12x³+ 54x² - 108x + 81
(x⁴ - 12x³+ 54x² - 108x + 81)(3 - x)
3x⁴ - 36x³+ 162x² - 324x + 243 - x⁵ + 12x⁴ - 54x³ + 108x² - 81x
-x⁵ + 15x⁴ -90x³ + 270x² - 243x + 243
What is a polynomial?A polynomial is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms.
Depending on the number of terms it can be :
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help, please!!!!!!!!!!
Given that triangle GHI and JKL are similar, the measure of side JK to the nearest tenth is 43.7
What is the measure of side JK?Similar triangles are triangles that have the same shape and are proportional, but their sizes may vary.
Given that;
Triangle GHI is similar triangle JKLSide IH = 13Side GH = 9.8Side LK = 58Side JK = ?Since the triangle are similar;
IH/GH = LK/JK
Plug in the given values and solve for side JK.
13/9.8 = 58/JK
Cross multiply
13 × JK = 58 × 9.8
13 × JK = 568.4
JK = 568.4 / 13
JK = 43.7
Given that triangle GHI and JKL are similar, the measure of side JK to the nearest tenth is 43.7.
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Approximate:
A. √370
B. √71
12 and 5/6x -14x + 1/6
Answer:
-x
Step-by-step explanation:
12 5/6=77/6
77/6x-14x+1/6x
77/6x+1/6x-14x
78/6x-14x
78/6x-84/6x
-6/6x
-x
Answer:
-9750
Step-by-step explanation:
what is 1492949 x 14232416344123432?
Answer:
2.12482717E22
Step-by-step explanation:
question is in the picture
Answer:
18 tables: $143
t tables: $35 + $6t
Step-by-step explanation:
35 + 6t
35 + 6(18) = 35 + 108 = 143
Solve for the value of s (3s-2)°
(4s-6)°
Answer:
(3s-2)°+(4s-6)°=90
3s-2+4s-6=90
7s-8=90
7s=90+8
7s=98
Dividing both sides by 7
S=98/7
S=14
