Y=21,000(1.20)*. D=anan1 d = a n a n 1 is the formula for figuring out the common difference of an arithmetic series, where d is the common difference and an a n is the nth term. A common difference in an arithmetic series is one between any term and its predecessor, and it is typically denoted by the letter "d".
A Commen difference is defined.A common difference in an arithmetic series is one between any term and its predecessor, and it is typically denoted by the letter "d". So, subtract the first term from the second term, the second term from the third term, etc. to find the common difference of an arithmetic sequence.Every two numbers in an arithmetic sequence that differ from one another constitute the common difference.Take any two consecutive terms as your first step.Step 2: Determine their difference, d = a(n) - a(n-1); a(n-1) is the phrase that comes before a(n) (n).The formula to determine an arithmetic sequence's common difference is: d = a(n) - a(n - 1), where a(n) is a term its succeeding phrase in the series is a(n - 1), and vice versa.To learn more about Commen difference refer to:
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Aniyah arranges 378 seashells into 18 equal rows for a science display how many seashells are in each rows ‘
Answer:
21
Step-by-step explanation:
Do long division of 378 and 18.
The result of the division will be 21.
There will be 21 seashells on reach row for the science display.
Leanne sells magazine subscriptions over the telephone. She earns $14 for every subscription she sells,
How much will Leanne earn if she sells 15 subscriptions?
Leanne earned $224 last month, how many subscriptions did she sell?
Answer:
Amount of money Leanne will earn
= $14 × 15 subscriptions
= $210
Number of subscriptions Leanna sold last month
= $224 ÷ $14
= 16 subscriptions
+
Complete the conversion.
11,880 yd =
mi
Click the icon to view the customary units.
11,880 yd = mi
(Type an integer, fraction, or mixed number.)
The icon to view the customary units in 11880 yields is 6.75 mi
What is meant conversion?
Unit conversion is a multi-step procedure that involves adding, subtracting, multiplying, or dividing by a conversion factor.
Additionally, rounding and choosing the appropriate number of significant digits may be necessary during the process.
To measure various parameters, various units of conversion are utilized.
Counting Length
Weighing Things
Evaluation of Capacity
Temperature Measurement
To better understand, we convert measurement units in mathematics.
For ease of understanding, the length of a table is measured in inches, whereas the length of a garden is measured in yards.
A finger's length cannot be expressed in kilometers.
Units of measurements are necessary to measure various quantities.
divide 11,880 yards length value by 1760 to get 6.75 miles
Therefore the icon to view the customary units in 11880 yields is 6.75 mi
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Find the measure of the marked angles
The measure of the angles is=
The measure of the angles are (4x + 24)° = 52° and (6x - 10)° = 32°; The value of x =7°.
What is vertically opposite angles?
The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal.Vertically opposite angles, or ical angles. A pair of angles that are vertically opposed to one another are always equal. Additionally, a vertical angle and the angle to which it is adjacent are supplementary angles, meaning their sum is 180 degrees.Two lines are said to intersect when they cross at a certain location in a plane. The lines are referred to as parallel when they do not intersect at any point in the plane.So, (4x + 24)° = (6x - 10)°
24° - 10° = 6x - 4x
2x = 14°
x = 14°/2
x = 7°
Substitute x in those values:
(4x + 24) = (4(7) + 24)°
= 28+24
= 52°
(6x - 10)° = (6(7) -10)
= 42° - 10°
= 32°
Hence, the measure of the angles are (4x + 24)° = 52° and (6x - 10)° = 32°; The value of x =7°.
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Answer:
x = 7
Step-by-step explanation:
The measure of the angles are (4x + 24)° = 52° and (6x - 10)° = 32°; The value of x = 7°.
write the equation of a line whose slope is 10 and the y intercept is -15
Answer:
y=10x-15
Step-by-step explanation:
Use slope-intercept form: y=mx+b
M is your slope and B is your Y intercept
since your Y-intercept is negative, and adding a negative is just subtracting, you can just put -15 instead of +-15
If a sample consists of 1900 scores blank of them would be above the first quartile
If a sample consists of 1900 scores from sample no. 476th will be above the first quartile.
What are mean, median, and mode?The three main methods for identifying the average value of a set of integers are mean, median, and mode.
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.
The middle value in a list that is arranged from smallest to greatest is called the median.
The value that appears the most frequently on the list is the mode.
Given a sample consisting of 1900 scores.
∴ The no. of samples that would be above quartile is the next sample from (1/4)th of 1900 which is,
= (1/4)×1900 + 1.
= 475 + 1.
= 476.
So from sample no. 476th will be above the first quartile.
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Rosalyn owns a few vending machines. last night she collected $82.50 in dimes and quarters. If Rosalyn collected 50 more quarters then dimes, how many dimes did she collect?
Answer:
200
Step-by-step explanation:
The cost of x pencils is 150. Write the algebraic expression for the cost of cach pencil.
Answer:
cost of each pencil [tex]= \frac{150}{x}[/tex]
f(x) = x² + 7x +9
Find f(-7)
find the 10th term 10,11,12,13
The 10th term of the series is 19.
Given series is an Arithmetic Progression (AP).
First term = a = 10
Difference = d = 11 -10
= 1
nth term = [tex]a_{n}[/tex] = a + (n-1)d
10th term = [tex]a_{10}[/tex] = 10 + (10 - 1)1
= 10 + 9*1
= 10 + 9
= 19
Hence, 10th term is 19.
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Renuka Jain's Car Wash takes a constant time of 4.5 minutes in its automated car wash cycle. Autos arrive following a
Poisson distribution at the rate of 9 per hour. Renuka wants to know:
a) The average wait time in the line = ______ minutes (round your response to two decimal places).
b) The average number of customers waiting on line = ______ cars (round your response to two decimal places)
a) The average wait time in the line = 13.33 minutes.
b) The average number of customer waiting on line = 4.67 minutes
What do you mean by average?
The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
a) Values:
Arrival rate = 9 per hour
Service rate [tex]= \frac{60}{Service\ time}[/tex]
Service rate [tex]= \frac{60}{4.5} = 13.33[/tex] minutes
b) Queue:
units in queue(LQ) = Arrival Time^2 / (Service rate* (Service rate - Arrival rate))
unit in queue(LQ) [tex]= \frac{ 9^2}{(13.33\times (13.33 - 9))}[/tex]
unit in queue(LQ) = 0.70
Time in Queue(WQ) = Arrival rate / (Service rate * (Service rate - Arrival rate))
time in queue (WQ) [tex]= \frac{9}{ (13.33 \times (13.33 - 9)}[/tex]
time in queue (WQ) = 4.67 minutes
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you are debating about two different computers. if you are paid $10.00/hour and your deductions are fica 7.65%,federal tax witholding 12% and state tax witholding 8%, how many hours do you have to work to pay for the new computer?
To work to pay for the refurbished computer exists 89 hours.
What is meant by tax?Tax compliance refers to policy actions and individual behavior aimed at ensuring that taxpayers are paying the right amount of tax at the right time and securing the correct tax allowances and tax reliefs.
Tax is defined as a mandatory financial charge or some other type of levy imposed on a taxpayer (an individual or legal entity) by a governmental organization in order to fund government spending and various public expenditures (regional, local, or national).
First estimate all the deduction
FICA = $10 per hour × 0.0765 = $0.77 per hr
Fed tax = $10 per hr × 0.12 = $1.2 per hr
State tax = $10 per hr × 0.08 = $0.8 per hr
Remaining pay = 10 – 0.77 – 1.2 – 0.8 = $7.23 per hour
Time required = $640 / $7.23 per hr
Time required = 89 hours
Therefore, the correct answer is option c) 89 hours.
The complete question is:
You are debating about whether to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00. If you are paid $10.00/hour and your deductions are FICA (7.65%), federal tax withholding (12%), and state tax withholding (8%), how many hours do you have to work to pay for the refurbished computer?
a) 111 hours
b) 98 hours
c) 89 hours
d) 87 hours
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the scale on a hiker's map states that 1 in.=3000ft. Anna wants to know how far it is to her next campsite. On the map, the next campsite is 8 in. from her present location. What is the actual distance in feet between Anna's present location and her next campsite?
Answer: 24,000 ft.
Step-by-step explanation:
1in.(8)= 8 in.
SO: 3000ft.(8)= 24,000ft.
the equation of line1 y=5x+1 the equation of line2 2y-10x+3=0
state these two lines are parallel
Line 1 and Line 2 are parallel because they have the same slope.
How to know if lines are parallel?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
m = slopeb = y-interceptTwo lines are parallel if the slopes are the same.
The equation of line 1 is y = 5x + 1
The slope of Line 1 is 5.
Let's find the slope of Line 2 using the equation.
2y - 10x + 3 = 0
Let's represent the equation in slope intercept form to locate the slope easily.
2y - 10x + 3 = 0
2y = 10x - 3
y = 10 / 2 x - 3 / 2
y = 5x - 3 / 2
The slope of line 2 is 5
Therefore, Line 1 and Line 2 are parallel.
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PLEASE!!!! In the linear equation shown, which variable would represent the output (range) values?
y = mx + b
B
X
M
y
The variable y represents the range or output values of the function.
What is the Range of a function?The range of a function is the set of output values of the function.
The given equation is y = mx + b.
Note that x is an independent variable, therefore, we substitute the values for x and calculate the value of y to that value of x.
Therefore, y denotes the range or output values of the function.
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The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam. Passed exam Did not pass exam Row Totals Completed exam review 55% 10% 65% Did not complete exam review 20% 15% 35% Column Totals 75% 25% 100% Part A: What is the percentage of students who failed the exam, given that they completed the exam review? Round to the nearest percentage. (2 points) Part B: What is the percentage of students who failed the exam, given that they did not complete the exam review? Round to the nearest percentage. (2 points) Part C: Is there an association between failing the exam and completing the exam review? Justify your answer. (2 points)
The percentages are given as follows:
a) Failed, given that they completed the review: 15.38%.
b) Failed, given that they did not complete the review: 42.86%.
Considering these percentages, for item c, there is an inverse association between failing the exam and completing the exam review, as the percentage of those who failed completing the review is way less than the percentage of those who failed without completing the review.
What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction, which is used along basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.
A percentage is one example of application of proportions, as it is the division of the number of desired outcomes by the number of total outcomes and multiplied by 100%.
For item a, we have that:
Total outcomes: 65% completed the review.Desired outcomes: 10% failed the exam.Hence the percentage is:
p = 10/65 x 100% = 15.38%.
For item b, we have that:
Total outcomes: 35% did not complete the review.Desired outcomes: 15% failed the exam.Hence the percentage is:
p = 15/35 x 100% = 42.86%.
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Jenna earns $7.75 per hour working at the mall. If Jenna worked 26 2/5 hours last week, how much did she earn before taxes were taken out?
Answer:
The correct answer is: 204.6
Step-by-step explanation:
(26 * 7.75) + (2/5 * 7.75) = 204.6
Fill in the table.
X(input) Y(output)
1 0
3 4
4 6
7
20
The values of p and q are 12 and 38 when for the missing outputs y when the table is given with input and output.
Given that,
The table is
Input Output
X Y
1 0
3 4
4 6
7 p
20 q
We have to find the p and q values.
Take the points as
(x,y)=(1,0),(3,4),(4,6),(7,p) and (20,q)
Take the points (1,0) and (3,4)
Equation of the line is
y=mx+b
Where
The slope of the line is m, and the intercept is b.
Slope of the line is rise/run
m=4-0/3-1
m=4/2
m=2
Now,
y=mx+b
0=2(1)+b
2+b=0
b=-2
The equation of the line is y=2x-2.
Take the point(7,p)
p=2(7)-2
p=14-2
p=12
Take the point (20,q)
q=2(20)-2
q=40-2
q=38
Therefore, The values of p and q are 12 and 38 when for the missing outputs y when the table is given with input and output.
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Find the length of the segment of the line with equation y = 5x – 2 between x = 3 and x = 4. Give your answer to 1 dp.
Answer:
5.1 units
Step-by-step explanation:
[tex]f(x)=5x-2\\f(3)=5(3)-2=13\\f(4)=5(4)-2=18[/tex]
[tex]\Delta x=1 unit=a\\\Delta y=5 units=b\\a^2+b^2=c^2\\(1)^2+(5)^2=c^2\\\sqrt26=c\\c=5.1 units[/tex]
Which number on this nutrition label appears high? Which nutrient does the number represent? How might the quantity of this
nutrient affect your health?
In the information provided, cholesterol is high and accounts for 39% of the total. It may have a negative impact on heart health as well.
Cholesterol;-
Any member of the lipid class of chemical compounds is referred to as cholesterol. Sterols are a subclass of lipids.
All animal cells produce cholesterol, which is a structural component of animal cell membranes.
It may result in a number of issues, including obesity, heart disease, and stones. As its level is 39% in the amount provided, this is high.
Therefore, cholesterol looks to be a high-nutrient food.
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use implicit differentiation to find y" in terms of y and y.
The value of y' by implicit differentiation, the value of y is [tex]y = \sqrt{5x +c}[/tex]
What is implicit differentiation?We differentiate each side of an equation with two variables by taking one as a variable and the rest are constant.
Given
The function is [tex]y^2 + 5 = 5x[/tex]
where x and y are variables..
On differentiating the equation, we have;
[tex]2yy' + 0 = 5[/tex]
on simplifying, we have
2yy' = 5
Now solve the equation explicitly for y and differentiate to get y' in terms of x.
2yy' = 5
Separate the variables
[tex]y^2 = 5x + c[/tex]
Taking square root on both the side
[tex]y = \sqrt{5x +c}[/tex]
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Which equation is true regarding the angles formed by the diagonals and sides of the rhombus? x + y = z 2x = y + z z + x = 2y 2x + 2y = 4zWhich equation is true regarding the angles formed by the diagonals and sides of the rhombus? x + y = z 2x = y + z z + x = 2y 2x + 2y = 4z
The equation that shows that angles angles formed by the diagonals and sides of the rhombus is x + y = z
How to show the relation to express the anglesThe diagonals of rhombus intersect each other at 90 degrees
z = angle formed at the diagonal = 90
x and y angle sides of the rhombus
applying the sum of angles of a triangle property
z + x + y = 180
where z = 90
90 + x + y = 180
x + y = 180 - 90
x+ y = 90
therefore x + y = z
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Yadira and her friend are renting a property together. The monthly rent is $1,050.00, and monthly utilities will average $365.00. Yadira will pay three fifths of the rent since her bedroom is larger. Determine how much Yadira's friend will pay each month for rent and utilities. (1 point)
$420.00
$602.50
$707.50
$812.50
Answer:
$602.50
Step-by-step explanation:
The monthly rent is $1,050.00.
If Yadira pays 3/5 ths of the rent, then her friend will pay 2/5 ths of the rent:
[tex]\implies \sf \dfrac{2}{5}\;of\;1050=\dfrac{2}{5} \times 1050=420[/tex]
Therefore, Yadira's friend pays $420 for rent.
If the monthly utilities average is $365, Yadira's friend's portion of the utilities will be half of the total:
[tex]\implies \sf \dfrac{1}{2}\;of\;365=\dfrac{1}{2} \times 365=182.5[/tex]
Therefore, Yadira's friend pays $182.50 for utilities.
So the total amount Yadira's friend will pay each month is:
[tex]\implies \sf Rent + Utilities=420+182.50=602.50[/tex]
The table below gives the cost per person buy tickets to an upcoming concert. Find the rate of change.
1/74
1/222
148/1
74/1
Answer:
222-148=74 (people 3-2=1)
296-222=74 (people 4-3=1)
370-296=74 (people 5-4=1)
so 1/74 is the answer
1) Three runners run 100 yards race. Sara runs the
race in 9.25 seconds. Alex runs the race in 8.625
Seconds and Tonya runs the race in 9.8 seconds. Who
has the winning time?
The person that has the winning time is Alex.
How to know the person with winning time?From the information given, three runners run 100 yards race. Sara runs the race in 9.25 seconds and Alex runs the race in 8.625 seconds and Tonya runs the race in 9.8 seconds.
It should be noted that in a race, the person that has the lowest time wins.
In this situation, the person with 8.625 seconds is the lowest.
Therefore, Alex wins.
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A farmer with 350 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? What are the dimensions of the enclosed area?
The width, labeled x in the figure, is
(Type an integer or decimal rounded to the nearest tenth as needed.)
The length, labeled 350-2x in the figure, is
(Type an integer or decimal rounded to the nearest tenth as needed.)
The largest area that can be enclosed is
The solution to the questions are:
The width, labelled x in the figure is 87.5 metersThe length, labelled 350-2 x in the figure, is 175 metersThe largest area that can be enclosed is 15312.5 square metersHow to determine the width and the length of the rectangle?From the question, we have the following parameters that can be used in our computation:
Length = 350 - 2x
Width = x
The area of a rectangle is the product of its dimensions
So, we have
Area = Length x Width
Substitute the known values in the above equation, so, we have the following representation
A = (350 - 2x) * x
Evaluate
A = 350x - 2x²
Differentiate and set to 0
350 - 4x = 0
So, we have
4x = 350
Divide by 4
x = 87.5
Recall that
Length = 350 - 2x
So, we have
Length = 350 - 2 x 87.5
Evaluate
Length = 175
The area is then calculated as
Area = Length x Width
So, we have
Area = 175 x 87.5
Evaluate
Area = 15312.5 square meters
Hence, the area is 15312.5 square meters
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One plane can travel 10 miles per hour faster than another. One of them goes 510 miles in the same time it takes the other to go 495 miles. What are their speeds?
The planes' speeds would be ____ miles per hour.
This is a proportion math problem.
If one plane can travel 10 miles per hour faster than another. The planes' speeds would be 435 miles per hour.
How to find the speed?let s = speed of the slower plane
then
(s+10) = speed of the faster
time = distance /speed
495/s =510 /(s+10)
495s = 510s + 5100
Combine like terms
495 - 510s = 5100
15s = 5100
Divide both side by 15s
s = 5100/15
s = 425 mph ( speed of the slower plane)
Speed of the fastest plane
(s+10)
425 +10
= 435 mph
Therefore the speed of the fastest is 435 mph.
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1) Solve the exponential equation 7^g = 14
2) Solve the exponential equation 6^u = 22
3) Solve the exponential equation 7^x-2 = 7
4) Solve the exponential equation (0.66)^k = 9
5) Solve the exponential equation 8^a = 16
6) Solve the exponential equation 12^z = 25
7) Solve the exponential equation 4^x-5 = 8
8) Solve the exponential equation (0.28)^v = 7
9) Solve the exponential equation 2^y = 18
10) Solve the exponential equation 17^b = 36
The solutions to each of the given exponential functions are;
1) g = 1.356
2) u = 1.725
3) x = 3
4) k = -5.288
5) a = 4/3
6) z = 1.295
7) x = 13/2
8) v = -1.5286
9) y = 4.17
10) b = 1.2648
How to solve exponential equations?Exponential equations are usually in the form a^(x) = b^(y) . To solve exponential equations with same base, we normally make use of the property of equality of exponential functions .
1) 7^(g) = 14
gIn 7 = In 14
g = In 14/In 7
g = 1.356
2) 6^(u) = 22
u In 6 = In 22
u = In 22/In 6
u = 1.725
3) 7^(x - 2) = 7
7^(x - 2) = 7¹
Equating the exponents gives;
x - 2 = 1
x = 3
4) (0.66)^k = 9
k In 0.66 = In 9
k = In 9/In 0.66
k = -5.288
5) Exponential equation 8^a = 16
2^(3a) = 2⁴
Equating the exponents gives;
3a = 4
a = 4/3
6) The exponential equation 12^z = 25;
z In 12 = In 25
z = In 25/In 12
z = 1.295
7) The exponential equation 4^(x-5) = 8
2^(2(x - 5)) = 2^(3)
2x - 10 = 3
2x = 13
x = 13/2
8) (0.28)^v = 7
vIn 0.28 = In 7
v = In 7/In 0.28
v = -1.5286
9) 2^y = 18
y In 2 = In 18
y = In 18/In 2
y = 4.17
10) 17^b = 36
b In 17 = In 36
b = In 36/In 17
b = 1.2648
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What is an equation of the line that passes through the points (-5,0) and (-2,-3)
x + y + 5 = 0 is the equation of the line that passes through the points (-5,0) and (-2,-3).
Given, two points (-5,0) and (-2,-3).
We are asked to find an equation of the line that passes through the given points.
As, we know
the equation of a line is
(y - y1)/(x - x1) = (y1 - y2)/(x1 - x2)
(y - 0)/(x - (-5)) = (0 - (-3))/(-5 - (-2))
y/(x + 5) = 3/-3
y/(x + 5) = -1
y = -(x + 5)
y = -x - 5
x + y + 5 = 0
Hence, x + y + 5 = 0 is the equation of the line that passes through the points (-5,0) and (-2,-3).
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Your original purchase price was $825.00 plus 7% sales tax. You enter into an agreement where the interest (12.5% APR) is waived for the first 12 months provided you make the required monthly payments; otherwise the interest is accrued from the date of purchase. You miss the first payment due date. The late fee is $35.00. How much is the interest?
If your original purchase price was $825.00 plus 7% sales tax and the interest is accrued from the date of purchase. The interest is $9.20.
How to find the interest?First step is to find the monthly interest rate
Monthly interest rate =12.5% / 12
Monthly interest rate = 1.0417%
Second step is to find the total amount applied for credit
Total amount applied for credit= $825+ ($825 × 7%)
Total amount applied for credit =$882.75
Now let find the interest
Interest = $882.75 x 1.0417%
Interest =$9.19
Interest = $9.20 (Approximately)
Therefore the interest is $9.20.
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Answer:
1. a late payment/missed fee
2. accrued interest
3. $9.20
4. $9.66
Hope This Helps!
