Taking into account the rule of three, 1110,4275 Mexican pesos was 81.35 dollars worth and 6.67 dollars was 91.03 Mexican pesos worth.
Rule of threeThe rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following expression must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
Amount of Mexican pesos in this casesOn October 23, 2011, one U.S. dollar was worth 13.65 Mexican pesos. So, you can apply the following rules of three:
If 1 dollar is equal to 13.65 Mexican pesos, 81.35 dollars is equal to how many Mexican pesos?1 dollar ⇒ 13.65 Mexican pesos
81.35 dollars ⇒ x
So: [tex]x=\frac{81.35 dollarsx13.65 Mexican pesos}{1 dollar}[/tex]
Solving:
x= 1110,4275 Mexican pesos
f 13.65 Mexican pesos is equal to 1 dollar, 91.03 Mexican pesos is equal to how many dollars?13.65 Mexican pesos ⇒ 1 dollar
91.03 Mexican pesos ⇒ x
So: [tex]x=\frac{91.03 Mexican pesosx 1 dollar}{13.65 Mexican pesos}[/tex]
Solving:
x= 6.67 dollars
In summary, 1110,4275 Mexican pesos was 81.35 dollars worth and 6.67 dollars was 91.03 Mexican pesos worth.
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Two children had 110 marbles between them. After one child had lost half her marbles
and the other had lost 20 they had an equal number. How many marbles did each child
start with and how many did they finish with?
Answer:
1 child - 60 another child - 50
Step-by-step explanation:
we start from the end. they had a equal number.
child A lost half therefore we give them another half having 2 units as shown in the diagram. child B had 1 unit plus 20 because he lost 20 which total adds up to 110. from there you have
3 units + 20 = 110
3 units = 90
1 unit = 30
since A has 2 units,
30 × 2 = 60
child A has 60.
since B has 1 unit plus 20
30 + 20 = 50
[tex](4 * 3^x)'[/tex]
Evaluate
Answer:
[tex]\approx 4.39 \cdot 3^x[/tex]
Step-by-step explanation:
Recall a property:
[tex](c\cdot f(x))'=c\cdot f(x)'[/tex], where [tex]c[/tex] is a constant.
Apply the property to the task:
[tex](4\cdot 3^{x})'=4\cdot (3^x)'[/tex]
Recall a property of the derivative of an exponential function:
[tex](a^x)'=a^x \cdot \ln{a}[/tex]
Apply the property to the task:
[tex]4\cdot 3^x \cdot \ln 3[/tex]
Since [tex]\ln 3\approx 1.0986[/tex], it follows:
[tex]4\cdot 3^x \cdot \ln 3 \approx 4\cdot 1.0986 \cdot \ln3[/tex]
Multiply the numbers.
The answer is about [tex]4.39\cdot 3^x[/tex].
Help me with this please!!
The cost that will be charged based on the information is $10.00.
How to calculate the amount?From the information given, the estimate is 4% and the replacement cost is given as $250.
The amount that will be charged will be:
= 4% × $250
= 0.04 × $250
= 10.00
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Which choice is equivalent to the quotient below?
-/100/-/25
the answer to this equation is 4
graph absolute value of x-1
It gives magnitude of the number or variables.
It is also known as an absolute value the function.
The result of this modulus function is always positive.
Draw the graph:
f(x) = |x-1|
f(x) = -(x-1) when x-1 is negative
f(x) = (x-1) when x-1 is positive
when x = -2, f(x) = 3
when x = -1, f(x) = 2
when x = 0, f(x) = 1
when x = 1, f(x) = 0
when x = 2, f(x) = 1
Using this values, draw the graph of f(x) = |x-1|
Hence, the required modulus of x-1 graph.
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Write 0,0234234... in the form m/n where m and n are relatively prime.
Answer:
m=26, n=111
Step-by-step explanation:
Let 0,0234234... be x
Then 100x = 23,4234234...
100x-x=23,4234234...-0.0234234...
99x=23,4
999x=234
111x=26
x=26/111
m=26, n=111
Find the solution, if possible, to the following system of equations using any method.
Give your answer in fraction form if necessary. Show all work. If you use matrices, you MUST write out the augmented matrix you inputted into the calculator.
3 − 4 + = −4
4 − 8 + 7 = 2
−2 + 4 − 3 = 5
simplify the expression -2v+15d
Answer:
isn't this already fully simplified?
Step-by-step explanation:
Circle properties can be used to prove that various shapes are polygons.
The question is incomplete. Below you will get the missing part of the question.
Find whether the given statement is true or false ?
True. Circle properties can be used to prove that various shapes are polygons.
With a centre of the circles, sides of an angle with vertex outside the circle, and arcs inside the circle, various shapes can be polygon.
So, from this description, we can say that, circle properties can be used to prove that various shapes are polygons.
Hence, the given statement is true.
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Write the range of each function for the given domain:
f(x) = 3 + 2x; Domain = {-8, 4)
Answer:
the range of each function for the given domain are the step of 3+2x are equal the -8,4
Need the answer please anyone!!!
The correct expression is the one in option B.
[tex]P(x) = (x - \sqrt{4} )*(x - 2)*(x + 2)[/tex]
Which is the correct expression?If we know that a polynomial has the known zeros:
{x₁, x₂, ..., xₙ}
Then the factored form is:
[tex]p(x) = a*(x - x_1)*...*(x - x_n)[/tex]
Where a is the leading coefficient, in this case we take a = 1.
Here we also know that the zeros are:
√4, 2, -2.
Then the factored form is just:
[tex]P(x) = (x - \sqrt{4} )*(x - 2)*(x - (-2))\\\\P(x) = (x - \sqrt{4} )*(x - 2)*(x + 2)[/tex]
Then we conclude that the correct option is B.
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Find K such that the number 23K10 is
divisible by 2, 3, and 5
2021
The values of K that will make 23K10 to be divisible by 2, 3 and 5 are; 0, 3, 6 and 9
How to use divisibility rules?We want to find the number K in 23K10 that will make it divisible by 2, 3 and 5.
Now, for the number to be divisible by 2, 3 and 5, then it means it must be divisible by the LCM which is; 2 * 3 * 5 = 30
Now, the divisibility rule for 30 is that it must be divisible by 3 and 10.
If 23K10 is divisible by 3, sum of digits will be multiple of 3.
Thus;
2 + 3 + K + 1 + 0 = K + 6 must be equal to 0, 3, 6, 9, 12, 15, 18....
Thus, K could either be 0, 3, 6 or 9
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Mary borrows $1250 from the bank. The loan terms is 18 months with 5% annual interest. How much interest will she pay? How much will she pay back in all?
Answer: 3375
Step-by-step explanation: The formula for simple interest is P( Principal, or initial amount) x R ( Rate or the percentage) x T ( Time) all out of 100( because of the percentage)
P x R x T/100
1. 1250 x 18 x 15/ 100
If you can simplify, or divide or cancel out, please do, it’ll make it easier; the 0 at the end of 1250, takes out one 0 from 100. 5 could cancel out 15 and 10, leaving them at 3 and 5 respectively, and lastly the two ( the hundred broken down) dividing 18, leaving us with 9.
2. 125 x 27
With all the breaking down we just did, we just have to multiply the two, leaving us with your answer: 3375.
Hope this was helpful
What is the simplified form of this expression √-150
Answer: [tex]\boldsymbol{5i\sqrt{6}}[/tex]
where [tex]i = \sqrt{-1}[/tex]
=============================================
Work Shown:
[tex]\sqrt{-150}\\\\\sqrt{-1*25*6}\\\\\sqrt{-1}*\sqrt{25}*\sqrt{6}\\\\i*5*\sqrt{6}\\\\\boldsymbol{5i\sqrt{6}}\\\\[/tex]
The trick with these type of problems is to factor the number into pieces such that we pull out the largest perfect square factor. In this case, that factor is 25. We also pull out the -1.
The rule used is [tex]\sqrt{A*B} = \sqrt{A}*\sqrt{B}[/tex] that lets us break up the root.
Using a crankshaft, a carpenter drills a 1 cm radius hole through a ball of wood along a diameter. If the radius of the ball is 4 cm, determine the volume of wood remaining.
Answer:263.89cm cubed
Step-by-step explanation:
Volume of A Sphere: 4/3 pi radius cubed
4cubed= 64
64 times pi=201.061
201.061 multiply 4/3= 268.08
1cubed= 1
1 times pi=3.14
3.14 times 4/3= 4.19
268.08-4.19= 263.89cm cubed
Which equation represents a line that is perpendicular to the line passing through (-4,7) and (1,3)?
The equation perpendicular to the line passing through the points (-4,7) and (1,3) is[tex]y=\frac{5}{4}x-2[/tex]
Equation perpendicular to a lineThe slope of the given line is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{3-7}{1-(-4)} \\\\m=\frac{-4}{5}[/tex]
The equation perpendicular to the given line will be of the form
[tex]y-y_1=\frac{-1}{m} (x-x_1)[/tex]
Substitute [tex]x_1=-4, y_1=7, and m=\frac{-4}{5}[/tex]
[tex]y-7=\frac{5}{4}(x+4)\\\\ y=\frac{5}{4}x+5-7\\\\ y=\frac{5}{4}x-2[/tex]
Therefore, the equation perpendicular to the line passing through the points (-4,7) and (1,3) is [tex]y=\frac{5}{4}x-2[/tex]
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Answer: [tex]y = -\frac{5}{4} x - 2[/tex]
Step-by-step explanation:
What is the solution to the equation
1/4x-1/8=7/8+1/2x?
Answer:
x=-1/4
Step-by-step explanation:
1 / 4x-1/8 = 7/8 + 1 / 2x <=> 1/4x - 1/2x = 7/8+1/8 <=> 1/4x-2/4x = 1 <=> -1/4x = 1
<=> x= -1/4
Answer:
2.7 + 8x/8.2
Step-by-step explanation:
1/4x - 1/8 = 7/8 + 1/2x x/4 - 1/8 = 7/8 + x/2
8x + 4 (-1)/4.8 = 2.7 + 8x/8.2
Calculate the unit cost per Kg if it costs $16.99 for 454 g package of cooked shrimp.
Answer:
$37.42 / kg
Step-by-step explanation:
Divide 16.99 by 454 to get the unit cost per gram. This equals 0.037422907…
Take this number and multiply it by 1000, while rounding it to the nearest hundredth after.
This equals about $37.42 / kg.
Harpreet, Sukhpreet and Komalpreet are three sisters. Sukhpreet is x years old. Harpreet is 3 years older than Sukhpreet. Komalpreet is twice the age of Harpreet. If the average age of the three sisters is 15, how old is Harpreet?
Answer:
12
Step-by-step explanation:
Givens
Harpreet = x + 3
Sukhpreet = x
Komalpreet = 2*(x + 3)
Average Age = 15
Equation
[(x + 3) + x + 2*(x + 3) ] / 3 = 15 Multiply both sides by 3
Solution
3 [(x + 3) + x + 2*(x + 3) ] / 3 = 15 * 3 Combine
[(x + 3) + x + 2*(x + 3) ] = 45 Remove the brackets
x + 3 + x + 2x + 6 = 45 Combine like terms
4x + 9 = 45 Subtract 9 from both sides
4x + 9 - 9 = 45 - 9 Combine
4x = 36 Divide by 4
4x/4 = 36/4
x = 9
Answer
Harpreet is x+ 3 = 9 + 3 = 12
Write the sentence as a proportion.
1(1)/(2) cups of milk is to 10 bagels as (3)/(4) cups of milk is to 5 bagels
PLEASE HELP!!!!!
Below, the two-way table is given for a class of
students.
Freshmen Sophomore Juniors Seniors Total
2
2
6
3
Male
4
Female 3
Total
6
4
If a student is selected at random, find the
probability the student is a male given that it's a
senior.
P (Male | Senior) = [?]
Round to the nearest whole percent.
Enter
Answer:
7%
Step-by-step explanation:
homework! This is a stats problem I’ve been struggling with and need help thanks!!!
Price of article = $315.50
Down payment = $31.55
Monthly payment amount = $16.50
Duration of payments = 20 months
Interest
(
I
)
=
2
y
c
m
(
n
+
1
)
True annual interest rate to the nearest tenth=
The true annual interest rate to the nearest tenth is 16.7%.
How is interest determined?The interest amount for this scenario can be determined by computing the total mortgage payment and subtracting the mortgage amount from the earlier figure.
Since payment was made for 20 months, the interest rate can be annualized using 24 months as below.
Data and Calculations:Price of article = $315.50
Down payment = $31.55
Mortgage amount = $283.95
Monthly payment amount = $16.50
Duration of payments = 20 months
Total payment (mortgage and interest) = $330 (20 x $16.50)
Interest = $46.05 ($330 - $283.95)
Annualized interest rate = 16.7% ($46.05/$330 x 24/20)
Thus, the true annual interest rate to the nearest tenth is 16.7%.
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Which is the equation in slope-intercept form for the line that passes through (−2, 15) and is perpendicular to 2x + 3y = 4?
y=−32x+18
y=32x−12
y=23x+18
y=32x+18
The linear equation that respects the given conditions is:
[tex]y = \frac{3}{2}x + [/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.When two lines are perpendicular, the multiplication of their slopes is of -1. Hence, considering it is perpendicular to 2x + 3y = 4.
[tex]2x + 3y = 4[/tex]
[tex]3y = -2x + 4[/tex]
[tex]y = -\frac{2x}{3} + \frac{4}{3}[/tex]
Then:
[tex]-\frac{2}{3}m = -1[/tex]
[tex]m = \frac{3}{2}[/tex]
Hence:
[tex]y = \frac{3}{2}x + b[/tex]
It passes through (−2, 15), that is, when x = -2, y = 15, hence:
[tex]y = \frac{3}{2}x + b[/tex]
[tex]15 = \frac{3}{2}(-2) + b[/tex]
15 = -3 + b
b = 18.
So the equation is:
[tex]y = \frac{3}{2}x + [/tex]
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What’s the formula for the geometric mean of three numbers?
Answer:
Geometric mean is most commonly represented as:
[tex]\sqrt{abc}[/tex]
Geometric mean formula is represented by [tex]\sqrt[n]{\sf x_1 \cdot x_2 \cdot x_3 \cdot ... x_n}[/tex] where n resembles term position and x₁, x₂, x₃ are numbers and they continue.
The formula for geometric mean of three numbers [n = 3]:
Solution: [tex]\sqrt[3]{\sf x_1 \cdot x_2 \cdot x_3 }[/tex]
Example's:
Geometric mean of 5 numbers [n = 5] : [tex]\sqrt[5]{\sf x_1 \cdot x_2 \cdot x_3 \cdot x_4 \cdot x_5 }[/tex]
Geometric mean of 2 numbers [n = 2] : [tex]\sqrt[2]{\sf x_1 \cdot x_2 }[/tex]
A bus covers a certain distanc in 45 minutes if it runs at a Speed of 60km/hr. What must be the speed of the bus in order to reduce the time by 20 minutes .
2.66 is the speed
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You are a loan officer at the West Elm Savings and Loan. Mr. and Mrs. Brady are in your office to apply for a mortgage loan on a house they want to buy. The house has a market value of $160,000. Your bank requires 1/5 of the market value as a down payment.
(a)
What is the amount (in $) of the down payment? $
(b)
What is the amount (in $) of the mortgage for which the Bradys are applying? $
(c)
Your bank offers the Bradys a 30-year mortgage with a rate of 5%. At that rate, the monthly payments for principal and interest on the loan will be $5.37 for every $1,000 financed. What is the amount (in $) of the principal and interest portion of the Bradys' monthly payment? $
(d)
What is the total amount (in $) of interest that will be paid over the life of the loan? $
(e)
Your bank also requires that the monthly mortgage payments include property tax and homeowners insurance payments. If the property tax is $1,710 per year and the property insurance is $1,458 per year, what is the total monthly payment (in $) for PITI (principal, interest, taxes, and insurance)? $
(f)
To qualify for the loan, bank rules state that mortgage payments cannot exceed 14 of the combined monthly income of the family. If the Bradys earn $3,750 per month, will they qualify for this loan?
Yes, they will http://qualify.
No, they will not qualify.
(g)
What monthly income (in $) would be required to qualify for this size mortgage payment? $
a) The amount (in $) of the down payment is $32,000.
b) The amount (in $) of the mortgage for which the Bradys are applying is $128,000.
c) The amount (in $) of the principal and interest portion of the Bradys' monthly payment, at $5.37 for every $1,000 financed, is $687.36.
d) The total amount (in $) of interest that will be paid over the life of the loan is $$119,449.60.
e) The total monthly payment (in $) for PITI (principal, interest, taxes, and insurance) is $951.36.
f) Based on the bank rules that state that mortgage payments cannot exceed 14% of the combined monthly income of $3,750, B. No, they will not qualify.
(g) The monthly income (in $) that would be required to qualify for this size mortgage payment is $4,909.71 ($687.36/0.14).
Data and Calculations:Down payment = 1/5 or 20%
Home Price = $160,000
Down Payment = 20%
Loan Term = 30 years
Interest Rate = 5%
Annual property tax = $1,710 per year
Annual property insurance = $1,458 per year
Monthly taxes and insurance = $264 ($3,168/12)
Monthly PITI (principal, interest, taxes, and insurance) = $951.36 ($264 + $687.36)
14% of $3,750 = $525
Results:
Monthly Pay: $687.36 ($5.37 x $128,000/$1,000)
Loan Amount $128,000 ($160,000 - $32,000)
Down Payment = $32,000 ($160,000 x 20%)
Total of 360 Mortgage Payments = $247,449.60 ($687.36 x 360)
Total Interest = $119,449.60 ($247,449.60 - $128,000)
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A jar contains 2 red marbles numbered 1 to 2 and 10 blue marbles numbered 1 to 10. A marble is drawn at random from the jar. Find the probability of the given event.
The probability that the randomly chosen marble will be red is 1/6 or 0.1667.
What is the probability of an event?The probability of an event is the possibility, chance, or likelihood for an event to take place or occur.
From the given information:
Let us find the probability that if marble is drawn at random from the jar, the given marble will be red:
The total number of marble = 10 + 2 = 12 marbles.
There are 2 red marbles and 10 blue marblesThe probability that the randomly chosen marble will be red is:
P(red) = 2/12
P(red) = 1/6
P(red) = 0.1667
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britt estimated 8.8-6.2 by subtractions 9-6=3.it is overestimate or underestimate?
How many sides does a nonagon have