The measures of the arithmetic sequence are given as follows:
a. [tex]S_{10} = 350[/tex]
b. [tex]A_{n + 1} = 17 + 4n[/tex]
c. [tex]S_n = \frac{n(30 + 4n)}{2}[/tex]
d. [tex]A_n = 17 + 4(n - 1)[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the rule shown below:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
The sum of the first n terms is given by the rule shown below:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
The equation given for this problem is:
[tex]a_{n + 4} = 4n + 17[/tex]
Hence the sequence can be written as follows:
17, 21, 25, 29, 33.
Then the first term and the common ratio are given as follows:
[tex]a_1 = 17, d = 4[/tex]
Then the nth term is of:
[tex]A_n = 17 + 4(n - 1)[/tex]
The (n + 1)th term is of:
[tex]A_{n + 1} = 17 + 4(n + 1 - 1)[/tex]
[tex]A_{n + 1} = 17 + 4n[/tex]
The sum of the first n terms is of:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
[tex]S_n = \frac{n(17 + 17 + 4(n - 1))}{2}[/tex]
[tex]S_n = \frac{n(30 + 4n)}{2}[/tex]
The sum of the first ten terms is of:
[tex]S_{10} = \frac{10(30 + 4(10))}{2} = 350[/tex]
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The sum of two numbers is
36. Three times the smaller plus
twice the larger is 87. Find the
two numbers.
Answer:
2 and 43.5
Step-by-step explanation:
Last year, Amy deposited $1000 into an account that paid 2% interest per year and $3000 into an account that paid 7% interest per year. No withdrawals were made from the accounts.
Answer the questions below. Do not do any rounding.
(a) What was the total interest earned at the end of 1 year?
(b) What was the percent interest for the total deposited?
If no withdrawals were made from the accounts. The total interest earned at the end of 1 year is $230 and the percent interest for the total deposited is 5.75%.
How to find the total interest earned?a. Total interest earned :
Total interest earned = (0.02)($1000)+(0.07)($3000)
Total interest earned =$20+$210
Total interest earned =$230
b. Percent interest amount deposited
Percent interest amount deposited = Total interest earned / Total amount deposited
Percent interest amount deposited = $230 /( $1,000 + $3,000)
Percent interest amount deposited = $230 / $4000
Percent interest amount deposited = 0.0575 × 100
Percent interest amount deposited =5.75%
Therefore $230 is the interest earned and 5.75 is the percent interest.
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Question 4 of 10
If f(x) = 2(x)² +5√(x+2), complete the following statement (round your
answer to the nearest hundredth):
f(0) =
The function of f(0) =7.0710.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
f(x) = 2(x)² +5√(x+2)
f(0) = 2*0 +5√2
f(0) = 7.0710
Hence the value will be 7.0710.
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-2.5f+0.8f-16-9=
(Simplify your answer. Use integers or c
Answer:
[tex]-1.7f+-25[/tex]
Step-by-step explanation:
1 ) To simplify combine like terms...
[tex]=-2.5f+0.8f+-16+-9[/tex]
[tex]=(-2.5f+0.8f)+(-16+-9)[/tex]
[tex]=-1.7f+-25[/tex]
Hope this helps! :)
A food company stores grain in a hopper. The hopper is 12 feet in diameter and holds 2024.5 cubic feet of grain. When turned on, the hopper empties grain at a constant rate of 42 cubic feet per second. About how long does it take for the hopper to empty all the grain?
The hopper will empty all of the grain in approximately 48.2 seconds .
Total amount of grain in the hopper = 2024.5 cubic feet
Rate at which the grain is emptied = 42 cubic feet /second.
Time taken to empty the grain
= 2024.5 / 42
= 48.202...
≈ 48.2 seconds
The ratio of two related quantities represented in several units is known as a rate. The numerator of something like the ratio expresses the rate of change for the other dependent variable if the denominator of both ratios is expressed as a single unit of each of these quantities and it is assumed that even this quantity can also be changed in a predictable way.
Hence the hopper will empty all the grain in about 48.2 seconds.
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Order these numbers from least to greatest. 7.209, 7.23, 7.3, 7.1032
Answer:
7.1032,7.209,7.23,7.3.
so we can not put the dot and imagine like 71032 72090 we not put the 0 but it's can not be with no 0 72300 and we not put 0 73000 it most greatest so
i write answer on the top!
What is the equation of the line shown in the graph?
The equation of the given line is y = 2x + 4
What is the equation of a line?The equation y = mx + c is the general equation of any straight line, where m is the slope of the line and c is the y -intercept.
Given a line passing through points (-1, 2) and (-3, -2)
We know (y - y1) = [(y2−y1)/(x2−x1)](x - x1).
Therefore, y - 2 = [(-2-2)/(-3+1)](x+1)
y-2 = 2x + 2
y = 2x + 4
Hence, The equation of the given line is y = 2x + 4
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On his trip to meet Clare, Kiran brought his dog with him. At the same time Kiran
and Clare started walking, the dog started running 6 miles per hour. When it got to
Clare it turned around and ran back to Kiran. When it got to Kiran, it turned around
and ran back to Clare, and continued running in this fashion until Kiran and Clare
met. How far did the dog run?
According to the given distance, the dog can run on 22.5 miles
Distance:
Distance refers the the length of the line joining the two points. Here the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.
Given,
On his trip to meet Clare, Kiran brought his dog with him.
Here at the same time Kiran and Clare started walking, the dog started running 6 miles per hour.
When they got to Clare it turned around and ran back to Kiran. And when it got to Kiran, it turned around and ran back to Clare, and continued running in this fashion until Kiran and Clare met.
Here we know that they meet after 3.75 hours.
And we know that the dog was running 6 miles per hour
So, for 3.75 hours, it can be calculated as,
=> 3.75 x 6
=> 22.5
Therefore, then the dog can ran 22.5 miles.
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Is 3 4/9 greater than 3 4/5?
Samantha invested $660 into a account that paid 3.5% interest compounded annually. Samantha did not make any addition deposits or withdrawals
What is the total amount of interest paid by the investment at the the of 5 years ?
$115.50
$783.87
$123.87
$2,755.50
115.5 is the total amount of interest paid by this investment at the end of 5 years
What is the Percentage?
percentage, a relative value indicating the hundredth parts of any quantity.
Given,
Samantha invested $660 into an account that paid 3.5% interest compounded annually.
We need to find the total amount of interest paid by this investment at the end of 5 years
A=P(1+rt)
A is the final amount
P is the principal amount
r is the rate of interest
t is time
A=?,P=660,r=3.5%=0.035, t=5
A=660(1+0.035(5))
=660(1+0.175)
=660(1.175)
A=775.5
To check the total amount of interest paid by this investment at the end of 5 years
We need to find the difference between the initial amount and the final amount
775.5-660 =115.5
Hence 115.5 is the total amount of interest paid by this investment at the end of 5 years
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Periodic Inventory Using FIFO, LIFO, and Weighted Average Cost Methods The units of an item available for sale during the year were as follows: Jan. 1 Inventory 16 units at $31 $496 Aug. 13 Purchase 14 units at $33 462 Nov. 30 Purchase 13 units at $35 455 Available for sale 43 units $1,413 There are 21 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the inventory cost using the (a) first-in, first-out (FIFO) method; (b) last-in, first-out (LIFO) method; and (c) weighted average cost method (round per-unit cost to two decimal places and your final answer to the nearest whole dollar). a. First-in, first-out (FIFO) $fill in the blank 1 b. Last-in, first-out (LIFO) $fill in the blank 2 c. Weighted average cost
The ending inventory cost on December 31 for 21 units, under the three inventory methods, is as follows:
a) first-in, first-out (FIFO) method: $719
b) last-in, first-out (LIFO) method: $661
c) weighted average cost method: $690
What does the ending inventory cost?The ending inventory cost is the difference between the cost of goods available for sale and the cost of goods sold determined by the various inventory methods.
Some of the inventory methods include:
First-in, First-outLast-in, First-outWeighted AverageSpecific Identification.Date Activities Units Unit Cost Total
Jan. 1 Inventory 16 $31 $496
Aug. 13 Purchase 14 $33 462
Nov. 30 Purchase 13 $35 455
Available for sale 43 $1,413
Average cost = $32.86 ($1,413 ÷ 43)
Ending inventory 21
Units sold = 22 (43 - 21)
a) FIFO:
Ending inventory = $719 (13 x $35 + 8 x $33)
Cost of goods sold = $694 ($1,413 - $719)
b) LIFO:
Ending inventory = $661 (16 x $31 + 5 x $33)
Cost of goods sold = $752 ($1,413 - $661)
c) Weighted Average:
Ending inventory = $690 (21 x $32.86)
Cost of goods sold = $723 (22 x $32.86)
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somebody answer, please?
The table displays data collected, in meters, from a track meet.
one fourth 6 2 4
3 two thirds one third nine halves
What is the median of the data collected?
2.5
4.5
2
3
The median of the data collected from a track meet is 2 meters.
What is median?The median is the middle number in a sorted, ascending or descending list of numbers.
To calculate the median of the given date, we folloe the steps below.
Collected date: 1, 4, 6, 2, 4, 3, 2/3, 1/3, 1/2
Step 1: Rearreange the date in accending order.
1/3, 1/2, 2/3, 1, 2, 3, 4, 4, 6Step 2: Pick the middle of the number in the arranged data
Median = 2 meters.Hence, the median of the data collected is 2 meters.
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Answer:
2.5
Step-by-step explanation:
Princess can sel an average of
21 muffins per day She needs to earn
$30 per day to meet her fundraising goal.
How much does she need to charge for
each muffin to reach her goal? Round to the
hearest cent.
Step-by-step explanation:
x = price per muffin
21 × x = 30
x = 30/21 = 10/7 = $1.428571429... ≈
≈ $1.43
she needs to charge $1.43 per muffin.
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. the premium antifreeze solution contains 60% pure antifreeze. the company want to obtain 180 gallon of a mixture that contain 35% pure antifreeze. how many gallon of water and how many gallon of the premium antifreeze solution must be mixed
The gallons of water and gallons of the premium antifreeze solution that must be mixed are 60 gallons and 120 gallons respectively.
How to determine the gallons of water and premium antifreeze solution?In order to solve this word problem, we would assign a variable to the gallons of water and premium 60% antifreeze that is required, and then translate the word problem into algebraic equation as follows:
Let the variable w represent the gallons of water.Let the variable p represent the premium 60% antifreeze.Since the premium antifreeze solution contains 60% premium antifreeze, we have the following mathematical expression:
w + p = 180 ....equation 1.
0.60p = 0.40(180) ....equation 2.
From equation 2, we have:
0.60p = 0.40(180)
0.60p = 72
Premium antifreeze, p = 72/0.60
Premium antifreeze, p = 120 gallons.
For the gallons of water, we have:
w + p = 180
Water, w = 180 - p
Water, w = 180 - 120
Water, w = 60 gallons.
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1. Which function below is an exponential function?
Answer:
D
Step-by-step explanation:
A customer at the store wanted to buy a different watch that was listed at $88 but had a 15% discount. Then the customer had to pay a sales tax of 5% on the dis...
The customer have to pay $87.9 for the watch.
A customer at the store wanted to buy a different watch that was listed at $88 but had a 15% discount.
Given the information is
Watch is listed at $88 and had a discount of 15%
The customer had to pay a sales tax of 5%
Than, by reducing the discount from the price listed
= $88 - 15%
= 88 - [tex]\frac{15}{100}[/tex]
= 87.85
Now we have to add 5% tax to the discounted price
= 87.85+5%
= $87.9
Hence the answer is the customer have to pay $87.9 for the watch.
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As a member of the hiking club, you have paid
a total of $51 after 4 months and a total of $105
after 10 months. What is the linear equation in
slope-intercept form that models this situation.
The linear equation in the slope intercept form that models this situation is y = 9x + 15 .
In the question ,
it is given that ,
a member of hiking club paid $51 for 4 months ,
let the number of months be represented on x coordinate , and
the amount paid be represented on y coordinate .
So , the point becomes (4 , 51).
also given that you pay a total of $105 after 10 months ,
the second point becomes (10 , 105).
to find the equation in slope intercept form , we need slope ,
So , Slope = (105-51)/(10-4)
= 54/6
= 9
So , the equation having the point (4,51) and slope as 9 , in slope intercept form is
(y - 51) = 9(x - 4)
y - 51 = 9x - 36
y = 9x - 36 + 51
y = 9x + 15
Therefore , The linear equation in the slope intercept form that models this situation is y = 9x + 15 .
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7,17,27,37,47,57 whath other observations you can make about the pattern
The observation I can make of the pattern is that the sequence always increase by 10.
How to solve an arithmetic pattern?The sequence above shows an arithmetic pattern. Therefore, the arithmetic formula can be used to solve the next sequence.
7, 17, 27, 37, 47, 57..
Therefore,
aₙ = a + (n - 1)d
where
a = first termd = common differencen = number of termsTherefore,
a = 7
d = 17 - 7 = 10
Hence, the arithmetic formula is as follows:
aₙ = 7 + (n - 1)10
aₙ = 7 + 10n - 10
aₙ = 10n - 3
The sequence always increase by 10.
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10% of your grade is participation, 30% is class work/homework, 60% is test /projects. a student had an average of 100 for participation, 95 for class work/homework and 75 for test/projects. What the is the grade in the class?
The overall weighted average grade for this student in the class is 83.5%.
How is the weighted average grade computed?The weighted average grade is a function of the multiplication of each rate by the average score for each grading category.
The class grades are added to obtain the total grade that the student received for the different categories, involving class participation, classwork/homework, and tests/projects.
Grade Average Class Grade
Participation 10% 100 10% (10% x 100%)
Classwork/Homework 30% 95 28.5% (30% x 95%)
Test/projects 60% 75 45% (60% x 75%)
Total grade in class 83.5%
Thus, from the student's participation, classwork/homework, and tests/projects, we can summarize that they scored an average weighted grade of 83.5%.
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We want to construct a box whose base length is 2 times the base width. The material used to build the top and bottom cost $ 11 per square feet and the material used to build the sides cost $ 3 per square feet. If the box must have a volume of 40 cubic feet determine the dimensions that will minimize the cost to build the box.
The dimensions that will minimize the cost, obtained from the cost function are;
Width = [tex]\sqrt[3]{\frac{45}{11} }[/tex] feet
Length = [tex]2\cdot \sqrt[3]{\frac{45}{11} }[/tex] feet
Height = [tex]\dfrac{20}{\left(\sqrt[3]{\frac{45}{11} }\right)^2 }[/tex]
What is a function?A function is a rule, or law or expression that provides the definition between an input variable and an output variable.
Base length of the box = 2 × The base width of the box
Cost of the material used to build the top and the bottom = $11 per square feet
Cost of the material used to build the sides = $3 per square feet
Volume of the box = 40 cubic feet
Let x represent the width of the base of the box, and let y represent the height of the box
The information from the question indicates;
The length of the base of the box = 2·x
The volume of the box, V = x × 2·x × y = 2·x²·y = 40
V = 2·x²·y = 40
[tex]y = \dfrac{40}{2\cdot x^2} = \dfrac{20}{x^2}[/tex]
The cost of the box which can be obtained from the surface area of the box can be found as follows;
Cost of the top and the bottom = 2 × x × 2·x × 11 = 44·x²
Cost of the material for the sides = (2 × x × y + 2 × 2·x × y) × 3 = 18·x·y
Cost of the box, C = 44·x² + 18·x·y
[tex]C = 44\cdot x^2 + 18\cdot x \times \dfrac{20}{x^2} = \dfrac{44\cdot x^2+360}{x}[/tex]
To minimize the cost of the box, we get;
[tex]C' =\dfrac{d}{dx}\left( \dfrac{44\cdot x^2+360}{x}\right) = 0[/tex]
[tex]\dfrac{d}{dx}\left( \dfrac{44\cdot x^3+360}{x}\right) = \dfrac{x\times 44\times 3 \times x^2 - \left(44\times x^3+360\right)}{x^2} = \dfrac{88\cdot x^3-360}{x^2} =0[/tex]
At the minimum cost, [tex]\dfrac{88\cdot x^3-360}{x^2} =0[/tex]
Therefore; 88·x³ - 360 = 0
88·x³ = 360
[tex]x = \sqrt[3]{\dfrac{360}{88} } =\sqrt[3]{\dfrac{45}{11} }[/tex]
The width of the base of the box that minimizes the cost is; [tex]x =\sqrt[3]{\dfrac{45}{11}}[/tex]
The length of the base of the box that minimizes the cost is; [tex]2\cdot x =2\times \sqrt[3]{\dfrac{45}{11}}[/tex]
The height of the box that minimizes the cost is; [tex]\dfrac{20}{x^2} = \dfrac{20}{\sqrt[3]{\dfrac{45}{11} } }[/tex]
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Compare the following functions:
Function A: y = 4x −5
Function B: _______.
What is the slope/rate of change of Function A? ______.
What is the slope/rate of change of Function B between f(0) and f(1)? ______.
What is the slope/rate of change of Function B between f(1) and f(2)? ______.
What is the slope/rate of change of Function B between f(2) and f(3)? _____.
The slope of Function A is _______.
The slope of Function B is _______.
The slope of the function A which is presented as an equation and the slope of function B presented as a table are presented as follows;
The slope of function A is 4
The slope of function B are;
Between f(0) and f(1), the slope is 1
Between f(1) and f(2), the slope is 3
Between f(2) and f(3), the slope is 5
What is the slope of a graph of a function?The slope is found by the ratio of the rise to the run of the graph.
The function A is; y = 4·x - 5
Function A is of the form y = m·x + c
Where;
m = The slope of the function = 4
Therefore;
The slope of function A is 4
The first difference of the values of function B is not a constant.
The value of f(0) in function B is 0
The value of f(1) in function B is 1
The slope between f(0) and f(1) is m = (f(1) - f(0))/(1 - 0)
Which indicates that m = (1 - 0)/(1 - 0) = 1
The slope of function B between f(1) and f(2) is found as follows;
f(2) = 4, f(1) = 1, from which we get;
m = (4 - 1)/(2 - 1) = 3
The slope between f(2) and f(1) is 3
The slope of the function B between f(2) and f(3) is found as follows;
f(2) = 4, f(3) = 9, from which we get;
m = (9 - 4)/(3 - 2) = 5
The slope of the function B between f(2) and f(3) is 5
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Write (-4x^2ya^3)^2 as a monomial in standard form.
Answer:
[tex]16a^6x^4y^2[/tex]
Step-by-step explanation:
To simplify this expression, use the exponent rule stating that when an exponent is put to an exponent, the exponent values are multiplied (e.g., [tex](x^2)^2 = x^{2 \cdot 2} = x^4[/tex])
Using that rule, we get:
[tex](-4x^2ya^3)^2 = (-4)^2 \cdot x^{(2 \, \cdot \, 2)} \cdot y^2 \cdot a^{(3 \, \cdot \, 2)}[/tex].
This can be simplified to
[tex]16 \cdot x^4 \cdot y^2 \cdot a^6[/tex],
which can be written as:
[tex]16a^6x^4y^2[/tex]
using the commutative property of multiplication.
A monkey gathered 4 coconuts per minute. Is it a rate or unit rate?
Answer: unit rate
Step-by-step explanation:
its obvious
Answer:
I believe it is a unit rate
An interest survey was taken at a summer camp to plan leisure activities. The results are given in the tree diagram.
The tree diagram shows campers branching off into two categories, prefer outdoor activities, which is labeled 80%, and prefer indoor activities, which is labeled 20%. Prefer outdoor activities branches off into two sub-categories, prefer hiking, which is labeled 70%, and prefer reading, which is labeled 30%. Prefer indoor activities branches off into two subcategories, prefer hiking, which is labeled 20%, and prefer reading, which is labeled 80%.
What percentage of the campers prefer outdoor activities and reading?
24%
30%
56%
80%
The percentage of the campers prefer outdoor activities and reading is A. 24%.
What is the percentage?From the information, the tree diagram shows campers branching off into two categories, prefer outdoor activities is labeled 80%, and those who prefer reading, which is labeled 30%.
Therefore, percentage of the campers prefer outdoor activities and reading will be:
= Percentage for outdoor × Percentage of reading
= 80% × 30%
= 24%
In conclusion, the correct option is A.
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Answer: 56% i did the test
Step-by-step explanation:
If 1300 square centimeters of material is available to make a box with a square base and an open top, find the largest possible
volume of the box.(include units)
You are on vacation in New York City, and you need to get around town to different locations. Below are the rates for 2 different cab companies, locally dubbed "The Red Cabs" and "The Green Cabs".
How many miles would you travel for the cost to be the same for both cabs and how much will that cost you?
What is the difference in cost between the two companies if you need to travel 8 miles?
After seeing all your vacation photos on S n a p b o o k, your cousin decided they wanted to visit New York City also. They asked for some general advice on traveling around the city. What advice would you give them about which cab company they should use when they travel around the city?
Answer:
The costs are equal at 3 miles. It coest $8 for either company
At 8 miles the green cost 13 and the red cost 18.
My advice would be to use the Red compnay if traveling less than 3 miles and the green company is traveling more than 3 miels. At 3 miles the costs are the same.
Step-by-step explanation:
Which ordered pair in the form (x, y) is a solution of this equation?
x + 7y= 10
Answer: (3, 1)
Step-by-step explanation:
Plug in each coordinate and see if the equation holds true:
[tex](13, 2)\\13+2(7)=13+14=27\neq 10[/tex]
[tex](2, 1)\\2+7(1)=2+7=9\neq 10[/tex]
[tex](4, 1)\\4+7(1)=4+7=11\neq 10[/tex]
[tex]3+7(1)=3+7=10[/tex]
If you want easy access to your money for paying bills, eating out, etc, it is best to use a ____________ account.
If you want easy access to your money for paying bills, eating out, etc, it is best to use a checking account.
What is checking account?A checking account is a sort of bank account that enables simple deposits and withdrawals of cash for everyday use.
For instance, you may use your debit card to withdraw cash, deposit a check you receive, or set up direct deposit to get your paychecks.
It is advisable to utilize a checking account if you want quick access to your money for things like paying bills and dining out.
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Raina's penny bank is 1/10 full. After she adds 480 pennies, it is 1/2 full. How many pennies can Raina's bank hold?
Answer:
1,200 pennies
Step-by-step explanation:
a property map is drawn at a scale of 1:1000. Calculate the corresponding actual distance for each distance between 2 points on the map.
10 cm
= __ cm
If two points on the map measures 10 cm, with a scale of 1 : 1000 the actual distance is 10 000 cm
How to find the actual distance on a scale of 1 :1000information gotten from the question
a scale of 1:1000
2 points on the map 10 cm = ?
Scale factors refer to the amount or the factor the image on a map was increased or reduced in comparison with the actual dimension of the image
A map has a scale of 1 : 1000
the scale factor is 1/1000 then 10/?
1/1000 = 10/?
cross multiplying gives
? = 10 000 cm
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