Money received in tenth month: $104, as found by the formula of arithmetic progression.
The formula used here is recursive.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given: Money received in first four months: $50, $52, $55, %59.
To find: Money received in tenth month.
Finding:
As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.
That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.
Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+d[/tex], n ≥ 1.
For a₁ = 50, a₂ = a₁ + 2
=> a₂ = 50 + 2
This way, a₅ = a₄ + 5
=> a₅ = 59 + 5 = 64
a₆ = a₅ + 6
=> a₆ = 64 + 6 = 70
a₇ = a₆ + 7
=> a₇ = 70 + 7 = 77
a₈ = a₇ + 8
=> a₈ = 77 + 8 = 85
a₉ = a₈ + 9
=> a₉ = 85 + 9 = 94
a₁₀ = a₉ + 10
=> a₁₀ = 94 + 10 = 104
Thus, the payment received in tenth month will be $104.
The formula so used is recursive, as the consequent values of the given arithmetic sequence are obtained from the preceding values.
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The table shows the amount of money raised by each region. The four regions raised a total of $ ( 5 . 38 × 10 4 ) . Region Amount Raised ($) East 1 . 46 × 10 4 North 2 . 38 × 10 4 South 6 . 75 × 10 3 West ? How much did the West raise? Express the result in scientific notation. $__
The amount raised in the west in scientific notation is 8.650 × 10³.
How to find the amount the west will raise in scientific notation?The four region raised 5.38 × 10⁴ dollars(53800)
According to the table,
Amount east raised = 1.46 × 10⁴ = 14600
Amount North raised = 2.38 × 10⁴ = 23800
Amount South raised = 6.75 × 10³ = 6750
Therefore, the amount raised in the west can be calculated as follows;
amount raised in the west = 53800 - 14600 - 23800 - 6750
amount raised in the west = 8650
amount raised in the west = 8.650 × 10³
Therefore, the amount raised in the west in scientific notation is 8.650 × 10³.
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Function f, graphed below, is NOT an invertible function.
To which intervals could we restrict the domain of f to make it an invertible function?
Choose all answers that apply:
A. 1 ≤ x ≤ 6
B. 0 ≤ x ≤ 8
C. -8< x < -4
-10+5x=7x-4 what is the answer
Answer:
x = -3
Step-by-step explanation:
-10 + 5x = 7x - 4
-7x -7x
-10 - 2x = -4
+10 +10
- 2x = 6
÷-2 ÷-2
x = -3
What two numbers add to (-6) and multiply to (-9)?
Answer: not possible
Step-by-step explanation:
I think you're doing quadratics and if that's the case probably go and rework the problem because that doesn't work.
Question 7 of 10
Which of the following lists of ordered pairs is a function?
OA. (-1, 2), (2, 3), (3, 1), (2, 5)
B. (2, 5), (3, 6), (2,1)
O C. (2, 5), (3, 6), (6,9)
O D. (1, 2), (4, 0), (3, 5), (4, 3)
SUBMIT
The option (B) (2, 5), (3, 6), (6, 9) is a function.
Function:Function, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
"f(x) = ... " is the classic way of writing a function.
For the given situation,
The list of ordered pairs are given in option.
A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate.
According to the definition, the ordered pair should not have same x value.
Thus in option B (2, 5), (3, 6), (6, 9), each input is related to exactly one output.
Hence we can conclude that the list of ordered pairs of option (B) (2, 5), (3, 6), (6, 9) is a function.
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Use the substitution method (show your work and good luck!)
x+y=2
x-y=-10
Write an explicit formula for each arithmetic sequence. 62,59,56,53, . . .
The explicit formula of arthmetic sequence is [tex]a_{n}[/tex] = a + (n-1)d
Here is an explicit formula of the sequences 62, 59, 56, and 53...
[tex]a_{n}[/tex] = 62 + (n-1)(-3)
In the formula, n is any term number and [tex]a_{n}[/tex] is the nth term.
This formula allows us to simply plug on the number of the term we are interested in, and we will get the value of that term.
In order to find the fifth term, for example, we need to plug n = 6
[tex]a_{6}[/tex] = 62 + (6-1)(-3) = 62 + 5× -3
= 62- 15
= 47
In this way, we can find any term by using the explicit formula of an arithmetic sequence.
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Write an equation in slope-intercept form for the line.
(-3,12) and (15,0)
The equation in slope-intercept form for the line given (-3,12) and (15,0) is
[tex]y=-\frac{2}{3}x+ 10[/tex]
Given,
The points = (-3,12) and (15,0)
We know,
Slope of the equation m= [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Substitute the values and find the value of m
m= [tex]\frac{0-12}{15--3}[/tex]
m=[tex]-\frac{12}{18}=-\frac{2}{3}[/tex]
Slope intercept form of the equation is y= mx + b
where b is y intercept form.
Consider one point and substitute the values.
[tex]0=-\frac{2}{3}(15)+b \\0=-10+b\\b=10[/tex]
Then the slope intercept form is
[tex]y=-\frac{2}{3}x+ 10[/tex]
Hence, The equation in slope-intercept form for the line given (-3,12) and (15,0) is [tex]y=-\frac{2}{3}x+ 10[/tex]
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Please resolve it and list the steps the simplest way possible, thanks
Using the graph of g we get (a) value of function g at x=0 is 5
(b) [tex]\lim_{x \to \00} g(x)[/tex] or limit of g(x) at x=0 does not exist
(c) value of function g at x=1 is 4
(d) [tex]\lim_{x \to \11} g(x)[/tex] or limit of g(x) at x=1 is 4
What is limit of a function how can limit be interpreted using graph of that function?
Limit : Limit is the value that a function output approaches as the input approaches to a certain value.
For any function g(x) ,[tex]\lim_{x \to \22} g(x)[/tex] means that the value g(x) approaches as the x approaches to 2 .
From any graph we can easily see that to what value g(x)=y on the curve is approaching when the x is approaching to some value on x axis and if the graph is breaking on the value where x is approaching then the limit does not exist for that value of x.
For given graph
We can see value of value of function g at x=0 is 5 and value of function g at x=1 is 4
As the graph is breaking on x=0 into two functions then [tex]\lim_{x \to \00} g(x)[/tex] or limit of g(x) at x=0 does not exist
As the graph is not breaking at x=1 or we can say that graph of g(x)is approaching to 4 as x approaches to 1 then [tex]\lim_{x \to \11} g(x)[/tex] or limit of g(x) at x=1 is equal to g(1) that is 4
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HELP ASAP What should you substitute for y in the second equation (bottom equation) in order to solve the system by the substitution method?
4x+2y=10
3x+5y = 11
y=____
Answer:
y = 1
if you need answer of x
x = 2
Step-by-step explanation:
Let's solve your system by substitution.
4x+2y=10;3x+5y=11
Step: Solve4x+2y=10for x:
4x+2y=10
4x+2y+−2y=10+−2y(Add -2y to both sides)
4x=−2y+10
4x/4 = −2y+10/4
(Divide both sides by 4)
x= −1/2y+5/2
Step: Substitute −1/2y+5\2 for x in3x+5y=11:
3x+5y=11
3(−1/2y+5/2)+5y=11
7/2y+15/2=11(Simplify both sides of the equation)
7/2y+15/2+−15/2=11+/−152
(Add (-15)/2 to both sides)
7/2y=7/2
7/2y/7/2 = 7/2/7/2
(Divide both sides by 7/2)
y=1
Step: Substitute1for y in x= −1/2y+5/2:
x=−1/2y+5/2
x=−1/2(1)+5/2
x=2(Simplify both sides of the equation)
It is important to check your credit card bill each month. In the next section, you will carefully examine a credit card statement and learn how to look for errors. Most people would notice a major, expensive purchase that they did not make. A smaller, incorrect charge of $6, for example, might go unnoticed unless the entire statement was checked with a calculator. If one million credit card holders were each overcharged $6 each month for five years, what would be the total amount that debtors were overcharged, not including the extra
finance charges? million
The total amount that debtors are overcharged is 360 million dollars.
The unitary method is a technique to find the necessary value by multiplying the single unit value by finding the value of single unit value. We will use the same technique to solve this problem
According to question, $6 is charged per month for 5 years period from 1 million credit card holders
so, the total amount will be
1000000 × $6 × 12 × 5 = $360000000
Final answer: amount will be 360 million dollars
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Draw and label two triangles that could be proved congruent by ASA.
Two diagrams have been drawn that could be proved congruent by the ASA condition.
What exactly seems to be "triangle congruency?"Two triangles are said to be congruent when their three corresponding sides and angles are the same size.To appear identical, these triangles can be moved, rotated, flipped, and turned.They will align if they are moved.Congruence exists when two triangles meet the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
Two diagrams have been drawn that could be proved congruent by the ASA condition.(Refer to the diagram below)Therefore, two diagrams have been drawn that could be proved congruent by the ASA condition.
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A dragonflies wings beat 41 times per second. How many times do they beat in a minute
Is the following relation a function? Justify your answer. Two circles are shown, one labeled x and the other labeled y. The x circle contains the numbers 6, negative 1, and 4. The y circle contains the numbers 2, negative 1, and 3. Arrows map numbers from x to numbers from y. There are arrows going from 6 to 3, from negative 1 to 2, from negative 1 to negative 1, and from 4 to 3. No, because there is an input value with more than one output value No, because there is an output value with more than one input value Yes, because each input value has only one output value Yes, because each output value has only one input value
each input is mapped into only one output, then this relation is a function.
The correct option is "Yes, because each input value has only one output value"
Is the relation a function?
A relation maps elements from a set (called the domain, which is the set of the inputs) into elements from another set (called the range, which is the set of the outputs). Such that these mappings generate coordinate pairs (x, y) or (input, output)
A relation is a function only if all the elements in the domain are mapped into only one value in the range.
On the given relation, we have the coordinate pairs:
(6, 3)
(1, 2)
(-1, -1)
(4, 3)
So we can see that each input is mapped into only one output, then this relation is a function.
The correct option is "Yes, because each input value has only one output value"
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Answer:
C. Yes, because each input value has only one output value
Step-by-step explanation:
Let g be a reflection in the x-axis and a vertical stretch by a factor of 3, followed by a translation 4 units down and 1 unit right of the graph of f(x)=|x|
Please Help me with number 13 IF LM=3,MH=k/9 and LH=5,find K
According to the question, the given parameters with different numbers for the line LH is as follows:
LM =3, MH = k/9 and LH =5
To calculate the distance of the line LH, the expression can be written as:
LH = LM+MH
Substitute the given parameters in the above expression:
5 = 3 + (k/9)
Now, solving above expression, we get the calculated value for the variable 'k':
k = 18 units
Hence, the calculated value for the variable k = 18 units.
How to define distance for the line?
Distance defines the length segment of the line in the coordinate geometry. It is respective length between the two points. In this, the line segment is divided into two parts.
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Of young workers aged 18 to 25,71 % all paid by the hour. If two people are randomly chosen out of a group of 100 young workers, what is the probability that exactly one is paid by the hour?
42% is the probability that exactly one is paid by the hour.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Four perspectives on probability are commonly used: Classical, Empirical, Subjective, and AxiomaticP( exactly one paid by hour ) =
[tex]\frac{71}{100} . \frac{29}{100} + \frac{29}{100} . \frac{71}{100} = \frac{2059 + 2059}{10000}[/tex]
[tex]\frac{4118}{10000} = 42%[/tex]%
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During a clearance sale at a sporting goods store,skateboards were marked down 30%.on saturday,additiobal 25% was taken off already reduced prices of skateborads originally cost 119.50,what was the final price ater all dicounts had been taken?round to the nearest cent
The final price after all discounts is $62.74.
What is the final price?A discount is when the price of an item is decreased. An item becomes cheaper when a discount is applied.
Percentage is the fraction of an amount expressed as an amount out of 100. Percentage is a measure of frequency. The sign used to represent percentage is %.
Price of the skateboard after the first discount = (1 - discount) x initial price
(1 - 0.30) x 119.50
0.70 x 119.50 = $83.65
Price of the skateboard after the second discount = (1 - discount) x discounted price
(1 - 0.25) x $83.65
0.75 x $83.65 = $62.74.
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There are 24 baseball teams in a league each team plays two matches against each of the other teams
work out the total number of matches played
PLSSSSSSSSSSSSSSSSSSSS URGENT
The total number of matches played will be 46. matches.
How to calculate the value?From the information, there are 24 baseball teams in a league each team plays two matches against each of the other teams.
The total number of matches that will be played will be:
= (24 - 1) × 2
= 23 × 2
= 46 matches.
Therefore, the total number of matches played will be 46. matches.
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help needed please!!!
P is directly proportional to the square of Q
Given that when Q = 2, P = 24 find P when Q = 10
Given that when Q = 2, P = 24 the value of P when Q = 10 is 120.
How to calculate the proportion?It should be noted that given that when Q = 2, P = 24, the constant will be;
= 24/2 = 12
Therefore, the value of P when Q is 10 will be:
= 12 × 10
= 120
The value of P is 120.
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connie is ordering new carpet for a room 2.6m 3.8m 8.3m what is the area of the floor
The area of the floor on which Connie is laying the carpet is 9.88 m²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Area is the amount of space occupied by a two dimensional shape or object.
Connie is ordering new carpet for a room 2.6m*3.8m*8.3m. Hence:
Area of the floor = 2.6 m * 3.8 m = 9.88 m²
The area of the floor on which Connie is laying the carpet is 9.88 m²
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What is the acceleration in this graph
2 m/s^2 is the acceleration in the given graph .
WHAT IS ACCELERATION?Acceleration is the general term for any process where the velocity changes. There are only two ways to gain speed: by changing your speed or direction, or by doing both. This is thus because speed and direction both affect velocity.
CALCULATIONSince we formula for acceleration is =
(v - u) / t
where u represents initial velocity , v represents final velocity
so acceleration from graph will be = (7 - 0)/3.5
= 7/3.5
= 2 m/s^2
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Mr. White drove 15 miles in July. He drove 8 times as many miles in September as he did in July. He drove 3 times as many miles in August as he did in September. How many miles did Mr. White drive in August?
The answer is 360 miles
so you do
15 times 8 and that equals 120
so then you also o 120 times 3 and the answer is 360 :>
you are so welcome
Lavania is studying the growth of a population of fruit flies in her laboratory. After 6 days, she had nine more than five times as many fruit flies as when she began the study. If she observes 20 fruit flies on the first day of the study, write and evaluate an expression to find the population of fruit flies Lavania observed after 6 days. Write an expression for the population of fruit flies Lavania observed after 6 days.
The expression to find the population of fruit flies Lavania observed after 6 days is 9 + 5 * 20 and the value is 109
How to write and evaluate an expression to find the population of fruit flies Lavania observed after 6 days?The given parameters are
Day 1 = 20 fruit flies
Day 6 = 9 more than 5 times as many fruit flies on day 1
The above expression can be rewritten as
Day 6 = 9 + 5 * Day 1
This gives
Day 6 = 9 + 5 * 20
Evaluate the product
Day 6 = 9 + 100
Evaluate the sum
Day 6 = 109
Hence, the expression to find the population of fruit flies Lavania observed after 6 days is 9 + 5 * 20 and the value is 109
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Point A is (2,-1) and Point B is (4,3)
(2,-1),(4.3) find the distance
The distance of AB is 2√5.
Given that the point A is (2,-1) and point B is (4,3).
The distance formula gives us the shortest distance between the given two points in a plane of two dimensional.
The given points is point A(x₁,y₁)=(2,-1) and point B (x₂,y₂)=(4,3).
Now, we will use the distance formula to calculate the distance that is D=√(x₂-x₁)²+(y₂-y₁)².
Further, we will substitute the given values in the above formula, we get
D=√(4-2)²+(3-(-1))²
D=√2²+(3+1)²
D=√2²+4²
D=√4+16
D=√20
D=2√5
Hence, the distance of AB from the given points point A is (2,-1) and point B is (4,3) is 2√5.
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Susan travels at a rate of 60 miles per hour for 3 hours. her car uses on average one gallon of gas per 30 miles. how many gallons of gas does she use on her trip?
The average is calculated by adding up all the data sets, then dividing that total by the total number of data points. She used 6 gallons of gas on her trip.
What is meant by average?In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
The two unit rates of (30 miles per gallon) and can be used to convert three hours to gallons of gas (60 miles per hour).
30 miles = 1 gallon of gas used
For (30 × 2) 60 miles = 2 gallons of gas used
2 gallons of gas she used per hour.
Susan goes 180 miles in 3 hours (60 miles per hour).
Therefore,
For 3 hrs = 3 × 2 = 6 gallons of gas used.
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What is the probability of 8
Refer to ®R .
Name the center of the circle.
The center of a circle is the point at which the tip of our compass is placed when drawing a circle. It is the center of the circle's diameter.
What is the Center of the Circle?A circle is a two-dimensional closed figure in which the set of all points in the plane is equidistant from a given point known as the "centre."
The center of a circle is the point at which the tip of our compass is placed when drawing a circle. It is the center of the circle's diameter. The radius of a circle is the distance from the center to any point on its circumference that is always the same.
The center of the circle that is internally tangent to all three triangle sides; the orthocenter, the intersection of the triangle's three altitudes; and the nine-point center, the center of the circle that passes through nine key triangle points.
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WILL GIVE BRAINLIEST X THANKS !
REALLY URGENT
Write each subtraction equation as an addition equation.
a - 9 = 6
p - 20 = -30
z - (-12) = 15
x - (-7 = -10
The subtraction equations written as addition equations are
a + (-9) = 6
p + (-20) = -30
z + 12 = 15
x + 7 = -10
Writing an EquationFrom the question, we are to write each of the given subtraction equation as an addition equation
a - 9 = 6This equation written as an addition equation is
a + (-9) = 6
p - 20 = -30This equation written as an addition equation is
p + (-20) = -30
z - (-12) = 15This equation written as an addition equation is
z + 12 = 15
x - (-7) = - 10This equation written as an addition equation is
x + 7 = -10
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Solve for x.
3x - 8 ≤ 23 AND
- 4x + 26 ≥ 6
Answer:
1) x≤10.33
2) x≤5
Step-by-step explanation:
Question: 3x−8≤23
1) 3x≤31
2) x≤10.33
Question: -4x + 26≥6
1) -4x ≥-20
2) x ≤5
1) 3x < 23 + 8
3x < 31
x < 31/3
x < 10.33
x value will be more than equal to 10.33
2) -4x > 6 - 26
x > -20/-4
x < 5
x value will be less than and equal to 5
