Answers
The Arithmetic sequences are-
-5, 5, -5, 5, - 5, 5.... Not Arithmetic sequences96, 48, 24, 12, 6... Not Arithmetic sequences18, 5.5, -7, -19.5, -32... Arithmetic sequences-1, -3, -9, -27, -81.... Not Arithmetic sequences16, 32, 48, 64..... Arithmetic sequencesWhat is defined as the arithmetic series?Arithmetic sequences are those in which the difference d among successive terms remains constant. An arithmetic sequence's general term can be written as: an = a₁ + (n)d in terms of first term a₁, common difference d, and index n.The common difference must be same for the sequence to be arithmetic;
d₁ = a₂- a₁
d₂ = a₃ - a₂
Thus, d₁ = d₂
Check the common differences for given sequences are-
A. -5, 5, -5, 5, - 5, 5....
d₁ = 5 - (-5) = 10
d₂ = -5 - 5 = -10
d₁ ≠ d₂, not a Arithmetic sequences
B. 96, 48, 24, 12, 6...
d₁ = 48 - 96 = -48
d₂ = 24 - 48 = -24
d₁ ≠ d₂, not a Arithmetic sequences
C. 18, 5.5, -7, -19.5, -32...
d₁ = 5.5 - 18 = -12.5
d₂ = -7 - 5.5 = - 12.5
d₁ = d₂, Arithmetic sequences
D. -1, -3, -9, -27, -81....
d₁ = -3 -(-1) = -2
d₂ = -9 - (-3) = -6
d₁ ≠ d₂, not a Arithmetic sequences
E. 16, 32, 48, 64.....
d₁ = 32 - 16 = 16
d₂ = 48 - 32 = 16
d₁ = d₂, Arithmetic sequences
Thus, the common difference must be equal for Arithmetic sequences.
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Related Questions
It is important to understand how probability works in statistics because ______.
Answers
Probability are important information when applying descriptive statistics. Probability is the branch of mathematics concerning numerical descriptions. the correct option is (B).
What is probability?Descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.
here, we have,
A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,
Probability formula:
P(A) = Probability(Event) = Favorable Outcomes/Total Outcomes
P(A) = x/n
where,
P(B) is the probability of an event 'B'.
n(B) is the number of favorable outcomes of an event 'B'.
n(S) is the total number of events occurring in a sample space
Descriptive statistics are brief informational coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread). Measures of central tendency include the mean, median, and mode, while measures of variability include standard deviation, variance, minimum and maximum variables, kurtosis, and skewness.
The main purpose of descriptive statistics is to provide information about a data set. In the example above, there are hundreds of baseballs players that engage in thousands of games. Descriptive statistics summarizes the large amount of data into several useful bits of information.
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Mr.chong has some money to buy tins of paint. if he buys 18 tins of paint. he will need another $80. if he buys 10 tins of paint, he will have $32 left.
Answers
Amount of one tin of paint is $14 and the total amount Mr. Chong have is $172.
Let amount of one tin of paint = x
Let the total amount Mr. Chong having = y
On buying 18 tins of paint, he will need another $80. This can we mathematically represented as,
18x = y + 80
On rearranging this equation can be written as,
18x - y = 80 equation 1
On buying 10 tins of paint, he will will have $32 left. This can we mathematically represented as,
10x = y - 32
On rearranging this equation can be written as,
-10x + y = 32 equation 2
On adding equation 1 and equation 2, we get
18x - y -10x + y = 80 + 32
8x = 112
x = (112/8) = 14
On substituting x = 14 in equation 2 , we get
-140 + y = 32
y = 172
So, amount of one tin of paint is $14 and the total amount Mr. Chong have is $172.
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If a quadratic function has the rule f(x)=(x-h)^2+k, what will cause a vertical translation?
Option 1: Changing the value of h
Option 2: Changing the value of k
Please help me as soon as possible, thanks.
Answers
to apply a vertical translation we changed the value of k, which is the y-value of the vertex of the quadratic equation.
Then the correct option is the second one.
What will cause a vertical translation?
First, remember that for a general function f(x) we define a vertical translation of N units as:
g(x) = f(x) + N
If N > 0, the translation is upwards.If N < 0, the translation is downwards.In this case, we have the function:
f(x) = (x - h)^2 + k
If we apply a vertical translation of N units, then we get the new function:
f'(x) = (x - h)^2 + k + N
Now we have two constants, we can define:
k ' = k + N
Then the new quadratic function is:
f'(x) = (x - h)^2 + k'
So, as you can see, to apply a vertical translation we changed the value of k, which is the y-value of the vertex of the quadratic equation.
Then the correct option is the second one.
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Jasmine is 20 years old. Her brother Zac is 6 years more than half her age. Which of the following is the correct expression for Zac's age?
(20 ÷ 2) + 6
(20 ÷ 2) − 6
10 x 2 + 4
10 − (2 x 4)
Answers
Zac would be 16 years old.
what is the slope of the line that passes through the points (-9,0) and (-17,4)? write your answer in simplest form
Answers
Answer: -1/2
Step-by-step explanation:
Check out the attached photo
A group of friends enjoys playing miniature golf together. here are a set of final scores from a recent outing: 39, 41, 44, 50, 54, 56, 56, 56, 61 what is the mode?
Answers
Answer:
56
Step-by-step explanation:
The mode of a data set is the number that appears the most, which in this situation would be 56
:D
if an expression is x+4=10 could x=6
Answers
Answer:
Yep,
Step-by-step explanation:
First the expression is in this way:
x+4=10
Now shift the 4 ro RHS, then it will become as follows:
x=10-4
Now 10-4 is 6
Therefore, x=6
For each chore Faith does, her mom gives her $5.50. The equation y=5.5x can be used to represnt this situation. What is the constant of proportioality? What does the constant of proportianality represent in the context of the probelm?
Answers
The constant of proportionality for y = 5.5x will be 5.5.
What is defined as the constant of proportionality?The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, rate constant, unit rate, continuous of variation, and even the rate of change.A directly proportional relationship relation is shown below.
y ∝ x
where
∝ = the proportionality symbol
The variables that are related are y and x. Therefore,
y = kx
where
k is the proportionality constant.
For each chore Faith does, her mom gives her $5.50, which is shown by;
Using y = kx, the equations y = 5.5x can be designed as a directly proportional relationship.
As a result, k = 5.5 has been the proportionality constant.
The proportionality constant for y = 5.5x is 5.5.
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the width of a rectangular garden is x-meter and it's length is & more than it's width
Find the (a)areas, (b)perimeter.
pa help po need po now
Answers
Answer:
A. width = x - 4.5
B. 111 = 2(x + (x -4.5))
Step-by-step explanation:
A. The width is 4.5 meters shorter than x, so is x -4.5.
__
B. The perimeter is twice the sum of length and width. It is 111 meters, so an equation for it could be ...
111 = 2(x + (x -4.5))
Two hundred liters of a punch that contains 35% fruit juice is mixed with300 liters of another punch. the resulting fruit punch is 20% fruit juice. find the percent of fruit juice in the 300liters of punch
Answers
If two hundred liters of a punch that contains 35% fruit juice is mixed with 300 liters of another punch and the resulting fruit punch is 20% fruit juice, then the percent of fruit juice in 300 liters of punch is calculated to be 10%.
The percentage of fruit juice in 300 liters of punch can be calculated by forming a linear equation.
A linear equation also termed a first-degree equation is an equation with one or more variables that have the highest power of one.
A linear equation for this problem can be given as:
the volume of the first punch × percentage of fruit juice in the first punch + the volume of the second punch × percentage of fruit juice in the second punch = total volume × total percentage of fruit juice
Consider x = percentage of unknown fruit juice
Now add the given values in the equation:
200 × 35 + 300(x) = 500 × 20
7000 + 300(x) = 10000
300(x) = 10000 - 7000
300(x) = 3000
x = 3000 / 300
x = 10%
Hence, the percentage of fruit juice in 300 liters of punch is calculated to be 10%.
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A three-centimeter cube has been painted red on all sides. it is cut into one centimeter cubes. how many cubes will be there with only one side painted red?
Answers
There will be only 6 cubes with only one side painted red.
Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.
According to the question
A 3 cm cube is divided into one centimeter cube.
Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.
Since there are 6 faces,
cubes painted one side red = 6x1=6.
Therefore , There will be only 6 cubes with only one side painted red.
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helpppppppppppppppp!!!
Answers
Answer:
I think it would be 71ft
Step-by-step explanation:
Since the cliff was 85ft and she dove 6 ft underwater, the total distance she traveled was 71ft
Answer:
91 feet
Step-by-step explanation:
Theyre asking for how far he leaped.
The cliff jump above ocean level is 85 ft.
But he went an additional 6 ft underwater.
85+6=91 feet
A small town has two local high schools. High School A currently has 850 students and is projected to grow by 75 students each year. High School B currently has 1000 students and is projected to grow by 65 students each year. Let AA represent the number of students in High School A in tt years, and let BB represent the number of students in High School B after tt years. Write an equation for each situation, in terms of t,t, and determine which high school is projected to have more students in 11 years.
Answers
Answer:
For High School A, let denote the number of students after years. Define analogously.
Then and .
After 6 years the number of students in both high schools would be the same.
Step-by-step explanation:
For High School A, let denote the number of students after years. Define analogously.
Since we start out at 850 students at High School A and it is growing by 35 students every year, we must have that .
Since we start out at 700 students at High School B and it is growing by 60 students every year, we must have that .
Setting the two equations equal to each other, we see that
So after 6 years the number of students in both high schools would be the same.
after finishing the prep work, gilberta and maría start removing wallpaper at the same time. gilberta removes the paper at a constant rate of 4.3\,\text{m}^24.3m 2 4, point, 3, start text, m, end text, squared per hour, while maría removes 3.4\,\text{m}^23.4m 2 3, point, 4, start text, m, end text, squared of paper per hour. gilberta's room starts with 35\,\text{m}^235m 2 35, start text, m, end text, squared of paper, and maría's room starts with 30.5\,\text{m}^230.5m 2 30, point, 5, start text, m, end text, squared of paper.
Answers
The inequality that depicts when Gilberta has much more wallpaper left throughout her room than Mara does in hers using linear functions is:
t< 5.
A linear function is :A linear function has a straight line as its graph. The following is the form of a linear function. a + bx = y = f(x). One independent variable but one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
According to the given information:Following t hours, the quantities Gilberta and Maria have remaining are determined by:
G(t) = 35 - 4.3t.
M(t) = 30.5 - 3.4t.
Gilberta has more papers when:
G(t) > M(t).
So,
35 - 4.3t > 30.5 - 3.4t
-0.9t < -4.5
Multiplying by -1:
0.9t < 4.5
t < 4.5/0.9
t < 5.
The inequality is:
t < 5.
The inequality that depicts when Gilberta has much more wallpaper left throughout her room than Mara does in hers using linear functions is:
t< 5.
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Which graph is the result of reflecting f(x) = (8)* across the y-axis and then across the x-axis?
--8-7-6-5-4-3
8
7-
6-
th
7
8
co t
7
6
10
5
4-
3
NW
2-
4-
1₁
2
Answers
Which graph results when f(x) = (8)* is first reflected across the y-axis and then across the x-axis?
Option 1 for Question 1
Option 1 for Question 2
Option 3 for Question 3
Option 1 for Question 4
Option 1 to Question 5
1) We subtract from any sequence to find the common difference d. For instance, =(-4) - (-15) = -4+15 = 11. Hence, choice 1. The answer for the sequence is (11).
2) In case a sequence is
The sequence's eighth term, then, will be = 25-24 = 1. Therefore, choice 1 is right.
Question #3: Any arithmetic series has the following explicit rule
As a result, choice three is right.
4. Reggie started off with 195 cards, and each week, 16 more cards are added.
In light of this query
There are 16 common differences in the sequence.
The order is going to be
the amount of cards will be after the 12th week.
Therefore, choice 1 is right.
5th query: If the sequence is
Then
and
The usual difference is 7-3 = 4.
Therefore
Choice 1. is the right response.
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If cot 0=7/8 evaluate : (i) (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) (ii) cot¹0
Answers
Answer: The value of (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) =0.2086
and [tex]cot^{1}[/tex]θ=7/8
Step-by-step explanation:
Let base and height of a triangle be 7k and 8k
By applying Pythagoras theorem in Δ ABC, we get
[tex]AC^{2} = AB^{2} +BC^{2}[/tex]
= (7k)2 + (8k)2
= 49k2 + 64k2
= 113k2
AC = √113k2
= √113k
so hypotenuse =[tex]\sqrt{133}k[/tex];
now ;
=(1 + sin θ) (1 - sin θ)(1 + cos θ) (1 - cos θ)[since : (a + b)(a - b) = (a2 - b2)]
=(1 - [tex]sin^{2}[/tex]θ)(1 - [tex]cos^{2}[/tex]θ)
=[1 - (8/√113)2] [1 - (7/√113)2]
= (1 - 64/113) (1 - 49/113)
= (49/113) (64/113)
= 0.2086
hence;
The value of (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) =0.2086
and [tex]cot^{1}[/tex]θ=7/8
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Answer:
Step-by-step explanation:We will use the basic concepts of trigonometric ratios to solve the problem.
Consider ΔABC as shown below where angle B is a right angle.
If cot θ = 7/8, evaluate: (i) (1 + sin θ)(1 - sin θ) / (1 + cos θ)(1- cos θ), (ii) cot²θ
cot θ = side adjacent to θ / side opposite to θ = AB/BC = 7/8
Let AB = 7k and BC = 8k, where k is a positive integer.
By applying Pythagoras theorem in Δ ABC, we get
AC2 = AB2 + BC2
= (7k)2 + (8k)2
= 49k2 + 64k2
= 113k2
AC = √113k2
= √113k
Therefore, sin θ = side opposite to θ / hypotenuse = BC/AC = 8k/√113k = 8/√113
cos θ = side adjacent to θ / hypotenuse = AB/AC = 7k/√113k = 7/√113
(i) (1 + sin θ) (1 - sin θ) / (1 + cos θ) (1 - cos θ) = 1 - sin2θ / 1 - cos2θ [Since, (a + b)(a - b) = (a2 - b2)]
= [1 - (8/√113)2] / [1 - (7/√113)2]
= (1 - 64/113) / (1 - 49/113)
= (49/113) / (64/113)
(ii) cotФ≈
= 49/64
The cost per unit of an item is called the
Answers
Answer:
breakeven point,
Step-by-step explanation:
Simplify completely:
(4x^3)^2
Answers
Answer:
16^6
Step-by-step explanation:
please help g(x) = f(x + 4) - 10 = 9^(x + 4) - 10
Answers
The expression for g(x) is 9x + 26
What is a function?A function can be defined as an expression, law or rule explaining the relationship between an independent and dependent variable.
Given the function;
g(x) = f(x + 4) - 10
Where f = 9
Substitute into the function;
g(x) = 9( x + 4) -10
expand the bracket
g(x) = 9x + 36 - 10
collect like terms
g(x) = 9x + 26
Thus, the expression for g(x) is 9x + 26
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Are 12,16,20 pythagorean triplets. Explain why.
Answers
Answer:
The numbers that make up today's date—12, 16, and 20—form a Pythagorean triple. That is, 12² + 16² = 20².
Step-by-step explanation:
Answer:Yes, these are pythagorean triplets because they are multiples of 4. 4 times 3 is twelve.4 times 4 is 4.And 4 times 5 is 20.
7. What is the simple interest on a housing loan of $350,000, over 30 years with *
a rate of 4.5%?
A : $35,000
B -$350,000
C-$47,250
D-$472,500
Answers
Answer:$472,500
Step-by-step explanation: I did $350,000 multiplied by 4.5% and got 15750 and then multiplied 15750 by 30 and then got $472,500
Jasmin babysits for the Smith family with 2 children. They pay her $10 an hour. She babysat 12 hours for the Smiths this week. Jasmin babysits for the Johnson family with 5 kids. They pay her $15 an hour. She babysat 6 hours for the Johnson's this weekend.
How much was she paid altogether?
Answers
The amount Jasmin was paid altogether was $210
From the question, we are to determine how much Jasmin was paid altogether
From the given information,
The Smith family pay her $10 an hour.
and
She babysat for the Smith family for 12 hours
Thus,
The amount she was paid by the Smith family is 12 × $10 = $120
Also,
The Johnson family pay her $15 an hour
and
She babysat for the Johnson family for 6 hours
Thus,
The amount she was paid by the Johnson family is 6 × $15 = $90
Therefore,
The amount she was paid altogether = $120 + $90
The amount she was paid altogether = $210
Hence, the amount Jasmin was paid altogether was $210
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Which exponential function bests models the graph below?
A.
B.
C.
D.
D.
Answers
Option A. [tex]Y = 3(2)^{X}[/tex]
Here, looking at the graph we can see that when x = 0, the value of y will be 3. Thus, (0, 3) is a solution to the given function.
Putting x = 0 in the given options, we see that
A. y = 3(1) = 3 (as anything raised to the power is 1)
B. y = 2(1) = 2
C. y = 4(1) = 4
D. y = 3(1) = 3
Thus, we can eliminate option B and C as (0, 3) does not satisfy these equations.
Now, if we take x = 1, from the graph we can see that the value of y will be 6.
Substituting x = 1 in the remaining two options, we get
A. y = 3(2) = 6
D. y = 3(4) = 12
Thus, D is also eliminated.
Option A, y = 3(2)^x is the correct answer.
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A company invests $12,000 to produce a product that will sell for $49.60. Each unit costs $7:45 to produce. (a) How many units must the company sell to break even? units (b) How many units must the company sell to make a profit of $115,0002 units
Answers
Answer:
Step-by-step explanation:
a=number of products
product profit=49,60-7,45=42,15
115000+1200=42,15xa
127000=42,15xa
a=3013
What is the gradient of the graph shown?
Give your answer in its simplest form.
Answers
Answer:
1/3
Step-by-step explanation:
Gradient or slope can be found using the point-slope formula:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
We can rearrange the equation to find slope (m) like so:
[tex]m=\frac{y-y_{1} }{x-x_{1} }[/tex]
To use this formula we need to find two well-defined points and use their coordinates.
Let's use (0,2) and (3,3) because they are clear points on the graph.
(0,2) will represent [tex]x[/tex] and [tex]y[/tex] in the equation respectively, and (3,3) our other point will represent [tex]x_{1}[/tex] and [tex]y_{1}[/tex].
Now we just need to plug the numbers into the equation:
[tex]m=\frac{2-3}{0-3} \\\\m=\frac{-1}{-3} \\m=\frac{1}{3}[/tex]
The gradient of the graph is 1/3.
Hope this helped!
Which graph shows the solution of the inequality −|x − 2| + 9 > 6?
Answers
answer is -1 < x < 5
-|x - 2|+ 9 > 6
Rearrange the terms
-|x - 2| > 6 - 9
-|x - 2| > - 3
then divide both sides of the inequality by the co- efficient of variable
|x - 2| < 3
convert the absolute inequality to standard inequality
-3 <x - 2 < 3
separate compound inequalities into system of inequality
{x - 2}> -3
{x - 2 < 3}
Rearrange variable to the left side of the equation
x > -3 + 2
calculate the sum or difference
x > -1
x -2 < 3
Rearrange variable to the left side of the equation
x < 3 + 2
calculate the sum or difference
x < 5
x > -1 and x < 5
Find intersection
-1 < x < 5
Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
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The shaded region displayed in the graph does not include the dashed line. Which of the following best represents all the shaded points?
Answers
help me i rlly need help this is do in few mins
Answers
Answer:
Step-by-step explanation:
first we can turn these mixed fractions into normal numbers so
1.42<.336 FALSE
.54>1.357 false
.615>.96 false
1.16>1.83 TRUE
Find the circumference
and the area of a circle with radius 9 m.
Use the value 3.14 for and do not round your answers. Be sure to include the correct units in your answers.
Answers
Answer:
56.52m is the circumference. The area is 254.34[tex]m^{2}[/tex]
Step-by-step explanation:
The equation for the circumference of a circle is c=2πr with r being the radius. So 2(3.14)(9)=56.52m. The area equation for a circle is A=π[tex]r^{2}[/tex] so it would be (3.14)(9)^2 or (3.14)(81) which equals 254.34[tex]m^{2}[/tex]
Please help will give brainiest if right
Answers
Answer:
Equation: 2x + x + 72 = 180m∠1 = 72°m∠2 = 108°Step-by-step explanation:
The angles lie on a straight line summing to total 180 degrees.
Form an equation:
m∠1 + m∠2 = 180
2x + x + 72 = 180
and solve:
3x + 72 = 180
3x = 180 - 72
3x = 108
x = 36
Find m∠1: 2(x) = 2(36) = 72°Find m∠2: x + 72 = 36 + 72 = 108°Answer:
see below
Step-by-step explanation:
We are here given a straight line which is splitted into two parts by a line , such that it makes two angles.
Also we know that the angle measure of a straight line is 180° . Therefore; here the sum of angles 1 and 2 will be 180° .
So that,
==> angle 1 + angle 2 = 180°
==> 2x + x + 72° = 180°
==> 3x = 180° - 72°
==> 3x = 108°
==> x = 108°/3
==> x = 36° .
The equation which we used to solve the problem is ,
==> Equation = 2x + x + 72° = 180°
For finding the individual angels substitute the value of x into their expressions , as ;
==> angle 1 = 2x = 2(36°) = 72°
==> angle 3 = x + 72° = 36° + 72° = 108° .
And we are done!
