The common difference and the first four terms are - 12 and 3, -9, -21 , -33 respectively
How to determine the valueGiven that the sum of an arithmetic sequence is 6n-3n²
Let the first term of the sequence be a1The second term of the sequence be a2The third term of the sequence be a3The fourth term be a4d denotes common difference of the sequenceS1 = a1 = 6(1) - 3(1)² = 6 - 3 = 3
S4 = a1 + a2 + a3 + a4 = 6(4) - 3(4)² = -24
a1 + a2+ a3 + a4 + d = -24
4(a1) + d = -24
4(3) + d = -24
12 + d = -24
d = -24 + 12
d = -12
The first four terms are;
T2 = 3 + (2-1) -12
T2 = 3 -12
T2 = -9
T3 = 3 + 2(-12)
T3 = 3 - 24
T3 = -21
T4 = 3 + 3(-12)
T4 = 3 - 36
T4 = -33
Thus, the common difference and the first four terms are - 12 and 3, -9, -21 , -33 respectively
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Random means by chance.
O True
O False
Answer:
True
Step-by-step explanation:
Because you never expect when something may show up once your doing something and forget about what you lost a while back. Sometimes it just pops up and we're like, "Oh that's where it was".
Can't say true or false because both can be answers in different cases, mathematically speaking you can select one thing from a set of similar things having similar chance to be selected. and again you can also select one thing at random from a set of things having different chance of being selected. in my perspective:)
and maybe the question has more chance to be false because if a statement is false at least in one case it is false.
Which fraction is greater, 35/109 or 36/104?? To explain your answer, use our definition of fraction along with reasoning other than finding common denominators, common numerators, cross-multiplying, or converting to decimals.
The fraction that is greater is 36/104 since 34.62% is greater than 32.11%
Percentages and ratioFractions are written as the ratio of two integers. For instance a/b is a fraction.
In order to determine which of the fractions is greater, we will express them as percentage as shown:
35/109 * 100
3500/109
32.11%
Similarly;
36/104 * 100
3600/104
34.62%
Hence the fraction that is greater is 36/104 since 34.62% is greater than 32.11%
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Find the ending
balance:
$2,500 for 25 years at
2.75% annual simple
interest
Show work
Answer:
$4,218.75
Step-by-step explanation:
The formula for computing simple interest I on a principal amount P for t years at an interest rate of R% is given by
I = Prt
The ending balance amount is found by adding the principal to the interest computed
Ending balance = P + I
Here r is the interest rate in % converted to a decimal. This is done by dividing by 100
r = R/100 = 2.75%/100 = 0.0275 per year
I = 2500 x 0.0275 x 25 = 1718.75
So interest I = $1718.75
Ending balance = $2,500 + $1718.75 = $4,218.75
China generated 237.188 billion kilowatt-hours (kWh) of wind energy in 2018. The population in China in 2018 was 1.379 billion. What was the wind energy generated per capita? Give your answer to the nearest hundredth.
Answer:
172 kilowatts.
Step-by-step explanation:
Energy : 237.188 billion = 237,188,000,000 = 2.37188 × 10¹¹
People : 1.379 billion = 1,379,000,000 = 1.379 × 10⁹
Divide both values : 2.37188 ÷ 1.379 = 1.72; 10¹¹ ÷ 10⁹ = 10² ⇒ 1.72 × 10² or 172 kilowatts.
6) Convert the following equivalent scales to ratios.
(i) 1cm=20m
Answer:
[tex]1cm = 20 \times 100 \\ = 2000cm \\ 1cm = 2000cm[/tex]
Express 60 of its prime factors in assessing order and answer in index form
Answer:
2^2×3×5
Step-by-step explanation:
hope this works :)
Construct a frequency distribution for the data using five classes. Describe the shape of the distribution.
The data set: ages of dishwashers (in years) in 20 randomly selected households
table ( (12 6 4 9 11 1 7 8 9 8)(9 13 5 15 7 6 8 8 2 1) )
The shape of the distribution of the given data set is : Bell shaped
What is Frequency distribution ?
Frequency distribution, in statistics, a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times. Simple examples are election returns and test scores listed by percentile. A frequency distribution can be graphed as a histogram or pie chart.
Data: 12 6 4 9 11 1 7 8 9 8 9 13 5 15 7 6 8 8 2 1
Classes = 5
Class Frequency
1-3 →3
4-6 →4
7-9 →9
10-12 →2
13-15 →2
The shape of the distribution is peak at the center and down at both the ends,
Therefore, we can say that the shape of the distribution is bell shaped.
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1. Suppose we have two consecutive odd integers. If the smaller one is “x” ; what would we call the large one?
2. We are told there are two consecutive odd integers and the smaller one is 12 more than one third the large one. Use the answer to problem 1 to write a clean equation then find the integers
Main Answer:1) (x + 2)
2) The numbers are 19 and 21.
Concept and definitions should be there:
An odd integer n is an integer which is not a multiple of 2 (or equivalently one more than a multiple of 2). The odd integers are ..., -5, -3, -1, 1, 3, 5, ... Every odd integer can be written in the form 2k + 1 for some unique integer k.
The product of any two odd integers is odd and the result of a division where both the dividend and the divisor are odd is odd. But the sum and difference of any two odd integers are even.
The sum and difference of an even integer and odd integer are odd. Besides 2, all prime numbers are odd. Also, odd integers are really cool
This article is a stub. Help us out by expanding it.
Given data:
1) We have two consecutive odd integers.
Solving part:
Remember that the distance between any two consecutive odd numbers is 2.
5 - 3 = 2
7 - 5 = 2
13 - 11 = 2
etc.
So if the smaller of the two odd numbers is x, then the larger one will be (x + 2).
Given that:
2) We have two consecutive odd numbers, let's write them as:
Solving part:
(2*n + 1) and (2*n + 3)
Where n is an integer number.
We know that the smaller one is 12 more than one third of the larger one, so we have:
(2*n + 1) = 12 + (2*n + 3)/3
Now we can solve this for n
2*n + 1 = 12 + (2/3)*n + 1
2*n - (2/3)*n = 12 + 1 - 1
(4/3)*n = 12
n = (3/4)*12 = 9
n = 9
Then the two consecutive odd integers are:
(2*n + 1) = (2*9 + 1) = 19
(2*n + 3) = (2*9 + 3) = 21
Final Answer:1) (x + 2)
2) The numbers are 19 and 21.
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Which shows (3^2)^-2 in standard form
Answer:
1/81
Step-by-step explanation:
[tex](3^2)^{-2}=3^{-4}=\frac{1}{3^4}=\frac{1}{81}[/tex]
NEEEEED HELP ASAP!!!
Answer this question please
Solve for X: 4x+3x-x=-5+6x
Since the values on both sides of the expression are different, hence the equation has no solution.
Solving linear equationsLinear equation are equations that has a linear degree of 1. The standard linear equation is y = mx + b
Given the expression 4x+3x-x=-5+6x
Collect the like terms
4x+3x-x = -5+6x
4x+3x-x-6x = -5
7x - 7x = -5
Simplify
-0x = -5
0x = 5
x = 5/0
Since the values on both sides of the expression are different, hence the equation has no solution.
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The value of x is -5
What are algebraic expressions?Algebraic expressions are expressions that comprised of;
variablestermsfactorscoefficientsconstantsThey are also made of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc
Given the equation;
4x + 3x = -5 + 6x
Let's solve for x
We have;
collect like terms
4x + 3x - 6x = -5
Add or subtract like terms
7x - 6x = - 5
x = -5
Thus, the value of x is -5
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18x - 3
6 + 25x
does anyone know?
GIVING BRAINIEST IF CORRECT!!!!
Multiply and express in simplest radical form.
50 POINTS The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h.
A=h(a+b)/2
Solve for b.
Answer:
[tex]\mathrm{b = 2\frac{A}{h} - a}[/tex]
Translation:
Option C.
based on the equation 5×x+860=2×x+380, you can say
The value of x is -160.
An equation in which the power of any variable is not more than one is called a linear equation.
Here, we are given a linear equation as follows-
5 × x + 860 = 2 × x + 380
⇒ 5x + 860 = 2x + 380
Let us solve the given equation-
Subtracting 2x from both sides, we get
5x - 2x + 860 = 2x - 2x + 380
3x + 860 = 380
Subtracting 860 from both sides-
3x + 860 - 860 = 380 - 860
3x = -480
dividing both sides by 3,
3x/3 = -480/3
x = -160
Thus, the value of x comes out to be -160.
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what is the value of x?
help would be so appreciated
Answer:
x = 23
Step-by-step explanation:
The two angles are supplementary angles.
Supplementary angles sum 180°
(6x+4) + 38 = 180
6x + 42 = 180
6x = 180 - 42
6x = 138
x = 138/6
x = 23
Check:
6*23 + 4 + 38 = 180
138 + 42 = 180
Answer:
x = 23Step-by-step explanation:
We know that the sum of angles of a linear pair is always equal to 180°. These angles are also known as supplementary angles.
[tex]\bf 6x+4+38^o=180^o[/tex] (Add numbers)
[tex]\bf 6x+42=180[/tex] (Simplify)
[tex]\bf 6x+42-42=180-42[/tex](Subtract both sides by 42)
[tex]\bf 6x=138[/tex] (Simplify)
[tex]\bf \cfrac{6x}{6}=\cfrac{138}{6}[/tex] (Divide both sides by 6)
[tex]\bf x=23[/tex]
Therefore, x = 23.
_____________________
Hope this helps!
Have a great day!
Please help I will give you brainliest
Answer:
$7.4
each bag of milk cost $7.4
Answer: $7.4
Step-by-step explanation: i did this and i remember it!
Which table represents y as a function of x?
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
An equation represents a represents only when there is a unique value of x for every value of y. when it represents u as a function of x.
i.e if we draw lines parallel to y axis and it cuts the curve two or more than two times at a particular value of x then it doesn't represent a function at all.
And as we can see in the given tables,
1.) 12.23 is the value of x for both 5.4 and 6.4
2.) 0.31 is the value of x for both 55 and 59
4.) 20 is the value of x for both 245 and 255
So, the only table representing y as a function of x is table 3.
Answer:
table 3 is correct i took the test
Step-by-step explanation:
Find an equation for the line which passes through (-2,8) and is perpendicular to the line containing (0,1) and (4,5).
The equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .
Let the equation of line passes through the point (-2, 8) be y = mx + b.
Where m is the slope of the line and b is the y intercept of the line.
According to the given question.
A line passes through the points (-2, 8).
And it is also perpendicular to the line containing (0, 1) and (4, 5).
Since, the line is perpendicualr to the line conatining (0, 1) and (4, 5).
So, the slope of the line whose equation is to be find is given by
m = -1/(5 - 1/4-0)
⇒ m = -1/4/4 = -1
Thereofre, the equation of line with slope -1 is
y = -1x + b
Also, it passes through (-2, 8)
So,
8 = -1(-2) + b
⇒ 8 - 2 = b
⇒ b = 6
Thereofore, the equation of line which passes through (-2, 8) and perpendicular to the line conatining (0, 1) and (4, 5) is y = -x + 6 .
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Graph the function. Identify the domain and range.
Factor as the product of two binomials. x 2 + 3 x − 4
Answer:
[tex](x-1)(x+4)[/tex]
Step-by-step explanation:
Given:
[tex]x^2+3x-4[/tex]
The best way to write a polynomial with three terms as a product of binomials is to FACTOR!
The middle number is 3 and the last number is -4.
Factoring means we want something like
[tex](x+?)(x+?)[/tex]
We need two numbers that...
ADD together to get 3 and
MULTIPLY together to get -4
Test the numbers -1 and 4:
[tex]-1+4=3\\(-1)4=-4[/tex]
These are the right numbers! Now, I can write them as factored binomials!
[tex](x-1)(x+4)[/tex]
3. Log(x) +2= log(y) Which is larger x or y and by how much?
Answer:
y is 100 times larger than x===========================
Use identities[tex]log (a) + log (b) = log (ab)[/tex],[tex]a = log (10^a)[/tex],If [tex]log (a) = log (b)[/tex], then a = b.Rewrite and comparelog (x) + 2 = log (y)log (x) + log (10²) = log (y)log (x) + log (100) = log (y)log (100x) = log (y)100x = yy = 100xy is greater by 100 times
Two consecutive positive integers such that the square of the second integer added to 4 times the first is equal to 41
Answer:
4 and 5
Step-by-step explanation:
We need 2 positive numbers that are right beside each other, like 1 and 2. When the problem is translates into number format we get:
y^2+4x=41
x = 1st # and y = 2nd #
so if we do 4 (x) and 5 (y)
5^2+4(4)=41
the statement is true.
1 2/3 + 3 3/4 as a fraction
Answer:
5/3 + 15/4 are the fractions
can someone please explain this
Answer: x=-3-[tex]\sqrt{7}[/tex] or x=-3+[tex]\sqrt{7}[/tex]
Step-by-step explanation:
f(x)=x+1. g(x)=x+5
(f * g)(x)=
f(x)*g(x)=
(x+1)(x+5)=
x^2+5x+x+5=x^2+6x+5
x^2+6x+5=3
x^2+6x+9=7 ==> Add 4 on both sides of the equation
(x+3)^2=7
x+3=[tex]\sqrt{7}[/tex]
x=-3+[tex]\sqrt{7}[/tex]
x+3=-[tex]\sqrt{7}[/tex]
x=-3-[tex]\sqrt{7}[/tex]
I`m trying to figure this out. Please see question with multiple choices.
The equivalent expression of (10⁻² . 4⁵)⁻² is 10⁴ / 4¹⁰
How to find equivalent expression?We have to find the expression that is equivalent to the expression below:
(10⁻² . 4⁵)⁻².
Therefore, using the law of indices,
[tex](x^{a} )^{b} = x^{ab}[/tex]
Hence, let's find the equivalent expression by applying the laws of indices.
(10⁻² . 4⁵)⁻² = 10⁴ . 4⁻¹⁰
Also, applying the law of indices,
[tex]x^{-b} = \frac{1}{x^{b} }[/tex]
Therefore,
10⁴ . 4⁻¹⁰ = 10⁴ / 4¹⁰
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I just need the answer for C. Please answer quick this is due tmr morning!! worth 20 points and brainliest
Answer:
The answer is 7 for C.
Step-by-step explanation:
7+7=14 and 7x7=49
The diamond just asks for numbers that make up a pattern for the two given numbers.
Carlos is paid $17.90 per hour regularly. If he worked 45 hours last week, what was his gross pay? Carlos is paid at time-and-a-half for overtime.
Answer:
$ 850.25
Step-by-step explanation:
I will assume anything over 40 hours is 'overtime'
total pay will be
regular pay + overtime pay
17.90 * 40 hr + (17.90 * 1.5)(5hr) = $ 850.25
One-stray Problem Solving
POSSIBLE POINTS: 5.88
A rectangular playground is to be fenced in using a wall on one side and 210 meters of fencing for the other three sides. The area A(z) in square meters
of the playground is a function of the length z in meters of the side parallel to the wall.
What is the area of the playground when z = 50?
square meters