The 10 forms 1/8 can be written is as follows;
1/81 ÷ 81/2³1/√64[tex]{8}^{ - 1} [/tex][tex]{√64}^{ - 1} [/tex]1 : 8[tex]{2}^{ - 3} [/tex]2/164 : 32How to write 1/8 in different forms?A fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper value of a fraction.
A denominator is the lower value of a fraction.
1 over 8 can be written in the following ways;
1/8
1 ÷ 8
1/2³
= 1 / 2×2×2
= 1/8
1/√64
= 1/8
[tex]{8}^{ - 1} [/tex]
= 1/8
1 : 8
= 1/8
[tex]{√64}^{ - 1} [/tex]
= 1/√64
= 1/8
[tex]{2}^{ - 3} [/tex]
= 1/2³
= 1/8
2/16
= 1/8
4 : 32
= 4/32
= 1/8
In conclusion, 1/8 can be written in different forms including using square root and ratios.
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Solve the following facts. (Round to the nearest hundredth.) A. Current ratio _______________ B. Acid test __________________ C. Average day's collection ___________ D. Asset turnover _____________ E. Profit margin on sales _____________ Current Assets $ 18,000 Accounts Receivable 3,000 Current Liabilities 16,000 Inventory 2,000 Net Sales 41,000 Total Assets 29,000 Net Income 6,000
The solutions to the financial ratio requirements based on the supplied facts are:
A. Current ratio is 1.125.
B. Acid test is 1.
C. Average days' collection is 26.7 days.
D. Asset turnover is 1.4x.
E. Profit margin on sales is 14.63%.
What are financial ratios?Financial ratios are ratios that show the relative magnitude of one financial account to another.
Financial ratios are used to compare or represent an entity's financial performance or position in relative terms.
Current Ratio = Current Assets ÷ Current Liabilities
= $18,000 ÷ $16,000
= 1.125
Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities
= ($18,000 - 2,000) ÷ $16,000
= $16,000 ÷ $16,000
= 1
Average Days' Collection = Accounts Receivable ÷ Net Sales x 365 days
= $3,000 ÷ $41,000 x 365
= 26.7 days
Asset Turnover = Net Sales ÷ Total Assets
= $41,000 ÷ $29,000
= 1.4x
Profit Margin on Sales = Net Income ÷ Net Sales x 100
= $6,000 ÷ $41,000 x 100
= 14.63%
Current Assets = $18,000
Accounts Receivable = $3,000
Current Liabilities = $16,000
Inventory = $2,000
Net Sales = $41,000
Total Assets = $29,000
Net Income = $6,000
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Use PMT=
nearest dollar.
-nt
to determine the regular payment amount, rounded to the
The price of a home is $210,000. The bank requires a 15% down payment and one
point at the time of closing. The cost of the home is financed with a 30-year fixed-
rate mortgage at 6.5%.
a. Find the required down payment.
b. Find the amount of the mortgage.
c. How much must be paid for the one point at closing?
d. Find the total cost of interest over 30 years, to the nearest dollar.
B)
OA) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $2100
d. total cost of interest over 30 years: $196,167
a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $1785
d. total cost of interest ver 30 years: $227,667
Oc) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $2100
d. total cost of interest over 30 years: $227,667
OD) a. down payment: $31,500
b. amount of mortgage: $178,500
c. points paid at closing: $1785
d. total cost of interest over 30 years: $406,167
Answer:
B
a. down payment: $31,500b. amount of mortgage: $178,500c. points paid at closing: $1785d. total cost of interest over 30 years: $227,667Step-by-step explanation:
You want to know the 15% down payment, the mortgage amount, the value of 1 point, and the total interest cost for a 6.5% 30 year loan on a $210,000 home.
Look at the Answer ChoicesThe answer choices all have the down payment as $31,500 and the loan value as $178,500. A "point" is one percent of the loan value (not the home value), so ...
1 point = 0.01 × $178,500 = $1785 . . . . . . eliminates choices A and C
The difference between choices B and D is in the value of the interest paid. Your experience with 30-year loans in this interest rate range tells you that the interest paid is between 1 and 2 times the loan value. That is, the chice $227,667 is more likely correct than the choice $406,167.
Comparing these two numbers, we see they differ by 178,500, which is the value of the loan. That is, we can guess that 406,167 is the total amount repaid, not just the interest.
Answer choice B is the only one that makes sense.
Work the problemIf you like, you can work the problem.
down payment = 15% × $210,000 = $31,500
loan amount = $210,000 -31,500 = $178,500
one point = 0.01 × $178,500 = $1785
The monthly payment is found using the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12t))
A = 178500(0.065/12)/(1 -(1 +0.065/12)^(-12·30)) ≈ 1128.24
The monthly payment amount is about $1128.
So, the total repaid is 360 payments of $1128.24, or $406,167.
The interest paid is this amount less the principal:
interest paid = $406,167 -178,500 = $227,667
Solve the proportion: 3/x=15/45
Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
1 ) Cross-multiply...
[tex]\frac{3}{x}[/tex] ÷ [tex]\frac{15}{45}[/tex]
[tex]3[/tex] × [tex]45 = 15[/tex] × [tex]x[/tex]
[tex]135=15x[/tex]
2 ) Flip the equation...
[tex]15x=135[/tex]
3 ) Divide both sides by 15...
[tex]\frac{15x}{15}[/tex] = [tex]\frac{135}{15}[/tex]
[tex]x = 9[/tex]
Hope this helps! :)
Which expression is equivalent to 5x - 5x + 3x - 3x?
Answer:
0
Step-by-step explanation:
subtracting same numbers give you zero
A school is arranging a field trip to the zoo. The school spends 862.68 dollars on passes for 40 students and 2 teachers. The school also spends 345.20 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Answer:
0.150985
Step-by-step explanation:
You add the two decimals together which gives you 120788.
Then, you move the decimal 4 places which is 12.0788.
Then you divide 12.0788 by 2 which gives you 6.0394.
Finally, you divide 6.0394 by 40 which gives you 0.150985.
convert the following percents to a decimal. show steps. help fast pls
10%
15%
17.5%
0.125%
113%
202.125%
Answer:
below
Step-by-step explanation:
0.1
0.15
0.175
0.00125
1.13
2.02125
Abigail Henderson has $1360 budgeted for spending money on an upcoming trip to country and country be countries currency is trading $1.30 per Curren$y a and country bees currencies trading at $1.60 per currency be she plans to spend more time In country a so she wants to four times as much of currency a as currency be
Abigail Henderson's budget of $1,360 and the $1.30 and $1.60 trading price of the currency of country A and country B gives;
The equation that represents the total cost is; 1.3·x + 1.4·y = 1,360The number of each currency Abigail plans to buy are;
The number of units of currency of country A, x = 800The number of units of the currency of country B, y = 200What is a budget?A budget provides an estimation of a person, business, or country's income and expenditure over a specified period or duration.
The amount Abigail Henderson budgeted = $1,360
The per currency exchange rate for country A = $1.30
The per currency exchange rate for country B = $1.60
The number of currency A Abigail wants = 4 × The number of currency B
Which gives; x = 4·y
The equation that represents Abigail's total cost of buying currencies is presented as follows;
1.3·x + 1.6·y = 1,360
Plugging in the value of x gives;
1.3 × (4·y) + 1.6·y = 1,360
6.8·y = 1,360
y = 1,360 ÷ 6.8 = 200
The number of currency of country B, Abigail purchases, y = 200
The number of currency of country A Abigail plans to buy, x = 4 × 200 = 800
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How many liters of paint are in a 5 gallon bucket round your answer to the nearest liter
Answer:
19 liters
Step-by-step explanation:
On one campus, 620 undergraduate students work 50 or more weeks. If this student body is average in terms of work habits, about
how many undergrads would you expect there to be on the entire campus?
Answer:
Step-by-step explanation:
A family wants to save $100 each month. They record their progress toward this goal at the end of each month. What would a recording of $0 mean?
A recording of $0 for the family simply means that they have not saved anything or have spent all the savings.
What is savings?Savings simply means keeping of miney for a period of time in order to cater for future expenses. Saving is defined as income that is not spent or deferred consumption. Saving methods include putting money aside in a deposit account, a pension account, an investment fund, or as cash. Saving also entails lowering expenses, such as recurring costs.
Here, the family wants to save $100 each month and they record their progress toward this goal at the end of each month.
A recording of $0 simply means no savings.
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factor and graph the equation -0.01x² +0.5x
The graph and factor to the given equation are x= 50 or x=0.
What is equation?
An equation may be a formula in arithmetic that expresses the equality of 2 expressions by connecting them with the sign =.
Main body:
I am assuming the equation as : -0.01[tex]x^{2}[/tex] + 0.5x =0
Now first removing the decimal from the equation ,
-[tex]x^{2}[/tex]/100 + 5x/10 = 0
-[tex]x^{2}[/tex] + 50 x = 0
switching signs , we get
[tex]x^{2}[/tex] - 50x= 0
taking x as common
x(x-50) =0
so either x = 0
or
x- 50 = 0
x =50
Hence the value of x are 0 or 50.
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Given the polynomial f(x) = 2x3 + 7x2 + x − 10, which of the following is true?
a (x + 2) is a factor since f(2) = 0.
b (x − 2) is a factor since f(2) = 0.
c (x + 2) is a factor since f(−2) = 0.
d (x − 2) is a factor since f(−2) = 0.
Answer:
Step-by-step explanation:
Given:
2[tex]x^{3}[/tex]+7[tex]x^{2}[/tex]+x-10
factor it
I used MatLab roots(x) to find these so I kinda cheated :P
-2.5, -2 , 1
so we know -2 is a factor and, then
x+2=0 is a factor
so the "x+2" answer C)
Help with this precalc question
The principal amount invested at the rate of 6% for 3 years, then the investment results in $717.38.
What is compound interest?Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.
As per the given information in the question,
Principle, P = $600
Rate, r = 6%
Time, t = 3 years.
Compound quarterly, r = 6/4
t = 4 × 3 = 12
Use the formula,
[tex]A = P(1+\frac{r}{100} )^t[/tex]
A = 600(1 + 6/4 × 100)¹²
A = 600 × (203/200)¹²
A = $717.38
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Explain the steps for (-1/5) divided by 3/10 x (-2.4).
Answer: The correct answer is 14/7
Step-by-step explanation: This is the correct answer because it's explaining how to do it
Given m || n, find the value of x and y.
(3y-17) (6x+20)°
(7x+13)
n
Answer:
Value of x = 7° & y = 45°
Step-by-step explanation:
According to the question m || n.
For x:
[tex] \rm \implies (7x + 13) \degree = (6x + 20) \degree \\ \\ \rm \implies 7x - 6x = 20 \degree - 13\degree \\ \\ \rm \implies x = 7 \degree[/tex]
For y:
[tex] \rm \implies (3y - 17)\degree + (6x + 20) \degree = 180\degree \\ \\ \rm \implies (3y - 17)\degree + (6 \times 7 + 20)\degree = 180\degree \\ \\ \rm \implies (3y - 17)\degree + (42 + 20)\degree = 180\degree \\ \\ \rm \implies 3y - 17\degree + 62\degree = 180\degree \\ \\ \rm \implies 3y + 45\degree = 180\degree \\ \\ \rm \implies 3y = 180\degree - 45\degree \\ \\ \rm \implies 3y = 145\degree\\ \\ \rm \implies y = \bigg( \frac{145}{3} \bigg) ^\degree \\ \\ \rm \implies y = 45\degree[/tex]
A bottle maker assumes that 24% of his bottles are defective. If the bottle maker is right, what is the probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4%? Round your answer to four decimal places.
The probability that the proportion of defective bottles in a sample of 546 bottles would differ from the population proportion by greater than 4% is: 10.9069.
What is the probability that the population proportion will be greater than 4%?To obtain the correct value, we need to use the formula for the Z score. This formula requires that we subtract the average or mean value from the data point provided and divide the remaining value by the standard deviation.
Here is the formula:
z = (x-μ)/σ
First population proportion = 0.24
The sample proportion, hat p = 0.04
Z score =
[tex]0.04 - 0.24 / \sqrt 0.24 (1 - 0.24) / 546[/tex]
So, the Z score will
= -10.9469
So, when the z score = - 10.9469, the probability that Z is greater than - 10.9469, is = 10.9069
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tan(tan^-1x)=x where?
Tan of arc tan x is equal to x when the angle x is 0 degrees
What is tan as used in math?Tangent is the ratio of the side opposite the angle we know or want to know over the side adjacent to that angle, and is sometimes abbreviated as tan.
In a right angle triangle, the formula for tan is as below
Tangent (tan) = opposite / adjacent
Arc tan (tan^(-1)) is the inverse of tan = adjacent / opposite
Arc tan is equal to tan when the angel is zero degree
therefore, tan (tan^(-1) x) = x
when x = 0
tan^(-1) 0 = 0
tan 0 = 0
tan (tan^(-1) 0)
tan (0)
0
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complete question
At what point does tan(tan^-1(x))=x
=
4(7x), what is the value of a(-2)
The value of the function f(x) = 4 ( 7x ) for x = -2 is equal to f( -2 ) = -56.
As given in the question,
Given expression is equal to :
f(x) = 4 ( 7x )
Calculate the value of the given function for x = -2 is given by :
Substitute value of x = -2 we get.
f(-2)
= 4 ( 7 ( -2) )
Seven is positive and 2 is negative , multiplication of positive to negative is always negative.
So, 7 ( -2 ) is -14 Substitute in above equation we get,
= 4 ( -14 )
= -56
Therefore, the value of the function f(x) = 4 ( 7x ) for x = -2 is equal to
f( -2 ) = -56.
The complete question is :
If f(x) = 4 (7x) , what is the value of f(-2)?
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Frank raises cattle for livestock. Last year, he sold exactly 30% of his cattle to a local rancher. If Frank has not gained or lost any cattle since last year, which of the following could be the total number of cattle he currently owns?
A) 610
B)520
C)350
D)300
The total number of cattle Frank currently owned could be C)350
How to find the total number of cattle Frank currently ownedThe problem is asking multiples of 7.
Multiples of 7 come into play after working the the percentage as follows
Frank sold 30%, the percentage left is
= 100% - 30%
= 70%
= 0.7
The multiple of 7 that is a number 7 will divide without remainder here is 350 and this is the correct answer.
= 350 / 0.7
= 500
This means Frank had 500 cattle sold
0.3 * 500 = 150
currently having
= 500 * 0.7 = 350
= 500 - 150 = 350
Remember that a cattle will always be in whole number
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What is the sum -10 + (-9) + (-8) + ... + 9 + 10 +11 + 12?
Answer:
23
Step-by-step explanation:
the numbers from -10 to 10 cancel out, so all that is left is 11+12=23
What is the equation of the line in standard form?
A. x-2y=4
B. x+2y=4
C. 2x+y=2
D. 2r-y-2
Answer:
D. 2x -y = 2
Step-by-step explanation:
You want to know the standard-form equation of the line through points (-1, 4) and (2, 2) as shown on the graph.
Intercept formThe graph shows the x-intercept of the line is a=1, and the y-intercept of the line is b=-2. This means the intercept form of the equation is ...
x/a +y/b = 1
x/1 +y/(-2) = 1
Standard formMultiplying this equation by 2 gives ...
2x -y = 2 . . . . the standard form equation for the line
__
Additional comment
The standard form equation can also be developed from the coordinates of points on the line:
(y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1
(2 -(-4))x -(2 -(-1))y = (2 -(-4))(-1) -(2 -(-1))(-4)
6x -3y = -6 +12
Dividing by 3 gives the standard form equation ...
2x -y = 2
What is the image point of (-8, 1) after the transformation D₂ 0 R180 ?
The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).
Given that,
The point is (-8,1)
We must locate the point's picture.
In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).
We have the following for a 2 scale factor dilation:
Point A (-8, 1)
= (-8 × 2, 1 × 2)
= Point A' is (-16, 2)
By applying a rotation of 180° to the given point, the coordinates of its image is given by:
(x, y)→(-x, -y)
Points A' = (-16, 2)
Points A' = (-(-16), -(1)) = (16, -1).
Therefore, The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).
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The equation: -2(x - 5) = 4x is solved in several steps below. For each step, select the reason that best justifies it.
Equations:
2x + 10 = 4x
-2x + 10 + 2x = 4x + 2x
10 = 6x
10/6 = 6x/6
5/3=x
Options:
Simplifying
Subtraction Property of Equality
Multiplication Property of Equality
Addition Property of Equality
Distributive Property
Division Property of Equality
The order of reasons that best justifies each step of the equation's solution is as follows;
-2x + 10 = 4x (Distributive property)-2x + 10 + 2x = 4x + 2x (Addition property of Equality)10 = 6x (Simplifying)10/6 = 6x/6 (Division property of Equality)5/3 = x (Simplifying).What are the reasons that justify the steps of the solution?It follows from the task content that the reasons which best justify each step of the solution be identified.
Therefore; Given the equation; -2(x - 5) = 4x; we have;
-2x + 10 = 4x (Distributive property)-2x + 10 + 2x = 4x + 2x (Addition property of Equality)10 = 6x (Simplifying)10/6 = 6x/6 (Division property of Equality)5/3 = x (Simplifying).Ultimately, the reasons which best justifies each of the steps as required are as provided above.
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Answer: Justification for each step is provided below.
Step-by-step explanation:
Original Equation: -2(x - 5) = 4x
-2x + 10 = 4x --> Distributive property - simplify the left side
-2x + 10 + 2x = 4x + 2x --> Addition property of Equality - add 2x to both sides
10 = 6x --> Simplifying
10/6 = 6x/6 --> Division Property of Equality - divide each side by 6
5/3 = x --> Simplifying
Considering the Matrix: Give the solution in terms of x. Show work.
1 0 -.05 I 2
0 1 2 I 1
0 0 0 I 0
The solution to the system of equations, in terms of x, considering the augmented matrix, is of:
y = -40x + 81.x = 20x - 40.Augmented matrix of system of equationsThe augmented matrix of a system of equations is built as follows:
Each of the columns before the | represents the coefficients of a variable.The column after the | represents the numeric value of the expression.In this problem, there are three columns before the |, the there are three variables given as follows:
x,y and z.
The expression from the first row is:
x -0.05z = 2.
The expression from the second row is:
y + 2z = 1.
The third row is all zero, meaning that there is a free variable, hence the solution to the system is written as a function of x as follows:
x - 0.05z = 2
0.05z = x - 2.
z = (x - 2)/0.05
z = 20x - 40.
Hence the solution for y is:
y = 1 - 2z
y = 1 - 40x + 80
y = -40x + 81.
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simplify tana+cota help asap
Using trigonometric ratios, tan a + cot a = (cos a + sin a) / sin a * cos a
Trigonometric RatioThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trigonometric ratios are evaluated with respect to sides and angles.
In the question given, the trig ratio is
tan a + cot a
We can simplify this as
tan a = sin a / cos a
cot a = 1 / tan a = 1 / sin a / cos a = cos a / sin a
Adding both ratios together
tan a + cot a = (sin a / cos a) + (cos a / sin a)
tan a + cot a = (cos a + sin a) / sin a * cos a
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What’s the answer???
Answer:
2nd
Step-by-step explanation:
A relation contains the points (1,-4), (3, 2), (4, -3), (x, 7), and (-4, 6).
For which value of a will the relation be a function?
O-4
O-3
O 3
O 4%
For x = -3 the relation will be a function.
We know that a relation is a function when for each input there is exactly one output.
In this question, we need to find the value of x for which the relation will be a function.
We need to select the value of x such that x ≠ 1, 3, 4, -4
This means x must be -3
Therefore, For x = -3 the relation will be a function.
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For each chart below, identify the output rule and classify the function as exponential, linear or neither.
The classification and the output rule for each function in this problem is given as follows:
1. Output rule: y = 5x + 11. Classification: Linear.
2. Output rule: y = 2^x. Classification: Exponential.
3. Output rule: y = 3 if |x| is even, y = 1 if |x| is odd. Classification: Neither.
What defines a linear function?A linear function is defined when the increase of 1 in x result in the addition of a constant to y, hence the rule is:
y = mx + b.
In which:
m is the addition to y when x increases by one.b is the value of y when x = 0.Hence, for the first table, as 5 is added to x when x increases by one, the rule is:
y = f(x) = 5x + 16.
What defines an exponential function?An exponential function is defined when the increase of 1 in x result in the multiplication of a constant to y, hence the rule is:
y = a(b)^x.
In which:
b is the addition to y when x increases by one.a is the value of y when x = 0.Hence, for the second table, the rule is:
y = 2^x.
For the third table, none of the definitions for linear and for exponential functions are true, hence the function is neither, as it is a piece-wise function that assumes one value for odd numbers and another for even numbers.
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The equation of line s is y= – 4x– 5/3 . Line t includes the point ( – 3,3) and is parallel to line s. What is the equation of line t?
The equation of the parallel line t is y = -4x - 9
How to determine the line equation?The equation of line s given as
y = -4x - 5/3
Also, from the question
The point on line t is given as
Point = (-3, 3)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = -4
This means that the slope of y = -4x - 5/3 is -4
The slopes of parallel lines are equal
This means that the slope of the line t is -4
The equation of the parallel line is then calculated as
y = m(x - x₁) +y₁
Where
m = -4
(x₁, y₁) = (-3, 3)
Substitute the known values in the above equation
y = -4(x + 3) + 3
Evaluate
y = -4x - 12 + 3
Evaluate the sum
y = -4x - 9
Hence, the parallel line has an equation of y = -4x - 9
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Emi is a veterinarian. In a given week, 50% of the 16 dogs she saw were boxers. Antonio is also a veterinarian. In the same week, 7 of the 35 dogs he saw this week were Boxers. Each wants to record the part, the whole, and the percent.
Emi will need to locate the whole in this case because she already has the part and the percentage.
What is a whole?In mathematics, the total number of items being analyzed, in this case, the total number of dogs, is represented by a whole.
The term "part" refers to a quantity that is typically smaller than the total and describes particular qualities. For instance, 20 of the 30 students in a classroom enjoy playing basketball. The part is 20 then.
The relationship between the part and the whole is represented by the percentage, which is a number followed by the symbol%. In this instance, the proportion of boxers and overall dogs are related.
Emi already knows the percentage (50%), the part (16), and the total number of dogs, which in this case is 32, as a result of this.
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