Answers
Using substitution method, the solution to the system of linear equations
x = 26667 and y = 533
What is the solution to the system of linear equation?Let's set up the system of equations based on the given information.
Let:
x = number of currency A
y = number of currency B
Equation 1: x + y = 3200 (Total budgeted spending money)
Equation 2: 1.30x + 1.50y = Total cost of purchasing currency (to be determined)
Based on the information provided, Abigail wants to have five times as much currency A as currency B:
Equation 3: x = 5y
Now, let's solve the system of equations using substitution method
Substitute Equation 3 into Equation 1:
5y + y = 3200
6y = 3200
y = 3200 / 6
y = 533.33 (approximately)
Substitute the value of y back into Equation 3 to find x:
x = 5(533.33)
x = 2666.67 (approximately)
Now, let's calculate the total cost of purchasing currency using Equation 2:
Total cost of purchasing currency = 1.30x + 1.50y
Total cost of purchasing currency = 1.30(2666.67) + 1.50(533.33)
Total cost of purchasing currency = 3466.67 + 800
Total cost of purchasing currency = 4266.67 (approximately)
Therefore, the system of equations has a solution where:
x ≈ 2667 (number of currency A)
y ≈ 533 (number of currency B)
This means that Abigail should exchange approximately 2667 units of currency A and 533 units of currency B. The total cost of purchasing the currency would be approximately $4266.67.
In practical terms, this means that Abigail will have a budgeted spending money of $3200, and she plans to allocate it between currency A and currency B based on the given exchange rates and her preference of having five times as much currency A as currency B.
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Related Questions
use the GCF and the distributive property to find the sum of 30 and 78
Answers
Answer:
6(5 +13) = 108
Step-by-step explanation:
The GCF can be found by considering the factoring of the two numbers:
30 = 2·3·5
78 = 2·3·13
The greatest common factor is 2·3 = 6. Then the sum is ...
30 +78 = 6(5 +13) = 6(18) = 108
Henry wrote a total of 12 pages over 4 hours. How many hours will Henry have to spend writing this week in order to have written a total of 15 pages? Assume the relationship is directly proportional.
Answers
Answer:
5 hours.
Step-by-step explanation:
12 ÷ 4 = 3. 3 pages an hour, which would mean 5 hours to write a total of 15 pages.
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
pls help ............ explain
Answers
Answer:
Step-by-step explanation:
50 points Which word best describes the degree of overlap between the
two data sets?
O moderate
O low
O high
none
X
XX
X X XX
XX X
10
X
X
xxx
XX
40
XX
50
60
Answers
The word best describes the degree of overlap between the two data sets
O low
How to determine the degree of over lapThe degree of overlap generally refers to the extent to which two or more sets share common elements.
Specifically the degree of overlap can be defined as the number of elements that are contained in more than one of the sets being considered
In the problem the degree of overlap is low, since the data points shared only points 50 and 55
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What is the value of x?
C 5
C42
(+6)
(3-16)
22
38
Answers
1.What is the equation of a circle with center (-2, 2) and radius 3?
Answers
Answer:
(x + 2)² + (y - 2)² = 3²
Step-by-step explanation:
Equation of a circle is (x - a)² + (y - b)² = r²,
where a is the x-coordinate of the centre of the circle, b is the y-coordinate of the centre of the circle, r is the circle's radius.
So, we have (x - -2)² + (y - 2)² = 3²
subtract a minus means we add.
(x + 2)² + (y - 2)² = 3²
3. In triangle ABC, 4A is a right angle, and m<B = 45°. What is the length of BC? If your answer is not an integer, leave it in simplest radical form.
A. 18 ft.
B. 18√2
C. 18√3
D. 36
what is the answer? thank you
Answers
Find the volume of a pyramid with a square base, where the side length of the base is
10.6
in
10.6 in and the height of the pyramid is
12.3
in
12.3 in. Round your answer to the nearest tenth of a cubic inch.
Answers
Answer:
V = 460.68
Step-by-step explanation:
V=(lwh)/3
Volume = (1/3) * base area * height
In this case, the base of the pyramid is a square with a side length of 10.6 inches, so the base area can be calculated as:
Base area = side length * side length
Let's calculate the base area first:
Base area = 10.6 in * 10.6 in
Next, we'll substitute the values into the volume formula:
Volume = (1/3) * (10.6 in * 10.6 in) * 12.3 in
Calculating this expression will give us the volume of the pyramid. Rounding the answer to the nearest tenth of a cubic inch will provide the final result.
Solve the following equation
3^(2x)-10.3^x+9=0
Answers
Answer:
x≈1.63634604
Step-by-step explanation:
It a lot of work
4.4s + 6.2 = 8.8s - 1.8
please help
Answers
Answer:
s = 1.81
Step-by-step explanation:
4.4(1.81)+6.2=8.8(1.81)-1.8
plug in and multiply if you'd like to clarify :)
Answer:
=Steps
4.4s+6.2=8.8s−1.8
Multiply both sides by 10
4.4s· 10+6.2· 10=8.8s· 10−1.8· 10
Refine
44s+62=88s−18
Subtract 62 from both sides
44s+62−62=88s−18−62
Simplify
44s=88s−80
Subtract 88s from both sides
44s−88s=88s−80−88s
Simplify
−44s=−80
Divide both sides by −44
−44s
−44 =
−80
−44
Show Steps
Simplify
s=
20/11
Step-by-step explanation:
A hot-air balloon is 1550 feet off the ground and its altitude is slowly changing at a constant rate of −712 feet per second.
How many seconds, s, will it take for the balloon to drop to below 465 feet?
Drag and drop a symbol and value to correctly complete the solution to this inequality.
( K12 )
Answers
Building and solving an equation to model the situation, it is found that it will take 1.52 seconds for the balloon to drop to below 465 feet.
The initial height is of 1550 feet.Each second, the height decreases by 712 feet.Hence, the equation that models the height of the balloon after t seconds is:
\(h(t) = 1550 - 712t\)
To find how many seconds, s, will it take for the balloon to drop to below 465 feet, we have to find t for which h(t) < 465, hence:
\(h(t) < 465\)
\(1550 - 712t < 465\)
\(712t > 1085\)
\(t > \frac{1085}{712}\)
\(t > 1.52\)
It will take 1.52 seconds for the balloon to drop to below 465 feet.
A similar problem is given at https://brainly.com/question/25290003
Answer:
s > 144 2/3
Step-by-step explanation:
m ∠ � = ( � + 21 ) ∘ ∠A=(x+21) ∘ and m ∠ � = ( 4 � − 30 ) ∘ ∠B=(4x−30) ∘ , then find the measure of ∠ � ∠B.
Answers
The measure of angle B is given as follows:
m < B = 49.2º.
What are complementary angles?Two angles are said to be complementary angles when the sum of their measures is of 90º.
The measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.As the angles are complementary, the value of x is obtained as follows:
x + 21 + 4x - 30 = 90
5x - 9 = 90
5x = 99
x = 19.8.
Hence the measure of angle B is obtained as follows:
m < B = 4 x 19.8 - 30
m < B = 49.2º.
Missing InformationThe measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.The angles are complementary, and it asks for the measure of angle B.
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Enter the number of tens and ones in the chart for 61+14=75
Answers
Pierre is 3 years older than his brother, Claude. 1. Write an equation that represents how old Pierre is (p) when Claude is c years old.
Answers
The equation which is used to represent the ages of Pierre and Claude is given by p = c + 3.
The question can be formulated in the form of Linear equation in two variables.Linear equation in two variables can be written in the form of ax + by = c where a, b and c are constant terms and x, y are independent and dependent variables respectively. Here in this question the age of Pierre is represented as p and the age of Claude is represented as c. Since, Pierre is 3 years older than Claude then the equation representing their age can be formulated as:
p = c + 3 where p is Pierre's age and c is Claude's age and this represents that Pierre's age will be given when we will add 3 years more in the age of Claude.
Thus, the equation representing the age of Pierre is p = c + 3.
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Answer:
p=c+3
20 years old
Step-by-step explanation:
3 x 2 1/2= ?????????????????/
Welp
Answers
Answer:15/2
Step-by-step explanation:
which property of exponents must you apply to the express p 1/2 to derive p as the result
Answers
The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.
The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.
The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.
For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.
Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.
So we have derived p as the result using the Power of a Power Property.
In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.
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The two top concert tours in 2016 were concert A and concert B. Based on average ticket prices, it cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B. Three tickets for concert B cost a total of $687. How much did an average ticket cost for each tour?
Answers
The average ticket cost for each concert is given as follows:
Concert A: $188.83.Concert B: $95.67.How to obtain the ticket costs?The ticket costs are obtained by a system of equations, for which the variables are given as follows:
Variable a: cost for Concert A.Variable b: cost for Concert B.It cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B, hence:
6a + 6b = 1707
a + b = 284.5.
Three tickets for concert B cost a total of $687, hence the cost for concert B is of:
3b = 687
b = 287/3
b = $95.67.
Replacing into the first equation, the cost for concert A is given as follows;
a = 284.5 - 95.67
a = $188.83.
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If an investment company pays 6% compounded semiannually, how much will you have 5 years from now if you deposit $900?
How much would you earn if it were simple interest instead of compound interest?
Answers
With compound interest of 6% paid semiannually, a deposit of $900 would result in $1,191.02 after 5 years, while simple interest would earn $270, resulting in a total of $1,170.
To calculate the future value of an investment with compound interest, we can use the following formula:
FV =\(PV * (1 + r/n)^{(n*t)}\)
where FV, PV, r, n and t is the future value, present value, annual interest rate, number of compounding periods per year and number of years respectively.
In this case, the present value (PV) is $900, the annual interest rate (r) is 6%, and the interest is compounded semiannually, so there are 2 compounding periods per year (n=2). The period (t) of investment is 5 years.
Using these values, we can calculate the future value (FV) as follows:
FV = \(\$900 * (1 + 0.06/2)^{(2*5)\)
= \(\$900 * (1.03)^{10\)
= $1,191.02
Therefore, the future value of the investment after 5 years with compound interest would be $1,191.02.
If the interest were simple interest instead of compound interest, the calculation would be simpler. Simple interest is calculated as follows:
I = P x r x t
where I is the interest, P is the principal or present value, r is the interest rate, and t is the time period.
In this case, the interest rate is still 6% and the investment period is still 5 years, but the interest is calculated only on the principal amount of $900. Therefore, the interest earned would be:
I = $900 x 0.06 x 5
= $270
Therefore, the total amount after 5 years with simple interest would be the sum of the principal and the interest earned, which is:
Total = $900 + $270
= $1,170
Therefore, if the interest were simple interest instead of compound interest, the total amount after 5 years would be $1,170, and the interest earned would be $270.
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Kyle sold an antique through an online auction website. The website host charges kyle $15, plus 2.5% of the final selling price of the antique. After selling the antique, kyle had to pay the website host $32. What was the selling price?
Answers
The selling price of the antique through an online auction website is $680.
Given that,
Kyle sold an antique through an online auction website.
The website host charges Kyle $15, plus 2.5% of the final selling price of the antique.
After selling the antique, Kyle had to pay the website host $32.
Let x be the selling price of the antique.
We get an equation,
15 + (2.5% × x) = 32
15 + 0.025x = 32
0.025x = 17
x = $680
Hence the selling price is $680.
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Which of the following statement(s) is (are) true?
I. The set of all second-degree polynomials with the standard operations is a vector space. II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space. III. The set of second quadrant vectors with the standard operations is a vector space A) 1 B) II and III C) II and III D) 11
Answers
The true statement is; II. Option D
How to determine the correct statementsFrom the information given, we have that;
I. The set of all second-degree polynomials with the standard operations is a vector space
II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space
III. The set of second quadrant vectors with the standard operations is a vector space
Note that;
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a) Work out the percentage population increase from 2001 to 2011.
Give your answer to 1 decimal place.
Answers
The percentage population increase from 2001 to 2011 is 50%.
To calculate the percentage population increase from 2001 to 2011, you need the population figures for both years. Let's assume the population in 2001 was 100,000 and in 2011 it was 150,000.
The formula to calculate the percentage increase is:
Percentage Increase = ((New Value - Old Value) / Old Value) * 100
Plugging in the values:
Percentage Increase = ((150,000 - 100,000) / 100,000) * 100 = (50,000 / 100,000) * 100 = 0.5 * 100 = 50%
Therefore, the percentage population increase from 2001 to 2011 is 50%.
Please note that the actual population figures for the respective years need to be used in the calculation to obtain an accurate result. The example above is for illustrative purposes.
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Is 21 over the square root of 4 a rational or irrational?
Answers
The algebraic expression ''21 over the square root of 4'' is a Rational number.
What is square root of a number?
The square root of a number is a value that multiplied by itself gives the same number.
Given that;
The algebraic expression is;
⇒ ''21 over the square root of 4''.
Now,
Since, The algebraic expression is;
⇒ ''21 over the square root of 4''.
It can be written as;
⇒ 21 / √4
⇒ 21 / 2
Since, The number 21 / 2 is of the form p / q where, 2 ≠ 0.
Hence, The number 21 / 2 is a Rational number.
Therefore,
The algebraic expression ''21 over the square root of 4'' is a Rational number.
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Give an example of two different sets of data, in which both box plots have the same range and IQR and yet represent completely different data. Explain.
Answers
Answer:
set 1 and 2
Step-by-step explanation:
Set 1 has 10
Set 2 has 13
1.
Look at the expression.
3x + 4
Which of these describes the expression?
A. the sum of 3 and x and 4
B. the product of 3 and x and 4
C. the sum of 4 and the product of 3 and X
D. the product of x and the sum of 3 and 4
Answers
Answer:
C. the sum of 4 and the product of 3 and X
Answer:
I would assume C
Step-by-step explanation:
The equation is the sum of 4 plus the product of 3 and x
What is the value of x?
D
(2x)
E R
(4x + 10)
V
700
Answers
Step-by-step explanation:
180° = 2x + 70 + 4x + 10
180° = 2x + 4x + 70 + 10
180° = 6x+ 80
180 - 80 = 6x
100 = 6x
6x = 100
x = 16.66
x ≈ 17°
Confused PLEZZZZZ HELLLPPPP
Answers
Answer:B
Step-by-step explanation:
Answer:
believe it is the last one because the room is decreasing at 4 per minute so it would be -4x. Then the room is a 300 capacity so you would minus the -4x from the 300 leaving the formula as p(x)=300-4x
Which graph represents the function g(z)=√2-1+1?
Answers
In response to the given question, we can state that Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.
what is function?Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.
Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.
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help me out please!!!!
Answers
Answer:
I believe the Answer is C.
Step-by-step explanation:
Refer to the table summarizing service times (seconds) of dinners at a fast food restaurant. How many individuals are included in the summary? Is it possible to identify the exact values of all of the original service times?
Time (sec) Frequency
60 to 119 7
120 to 179 24
180 to 239 14
240 to 299 1
300 to 359 4
Answers
Answer:
Based on the provided information, the table summarizes service times (in seconds) of dinners at a fast food restaurant. To determine the number of individuals included in the summary, we can sum up the frequencies listed in the table:
7 + 24 + 14 + 1 + 4 = 50
Therefore, there are 50 individuals included in the summary.
Regarding the exact values of all the original service times, it is not possible to determine them precisely based on the given information. The table only provides ranges of service times and their corresponding frequencies. We can determine the range within which each individual's service time falls, but we cannot determine the exact value within that range.
How many solutions does the system have?
5x−y=2
5x−y=−2
Answers
Answer:
10
Step-by-step explanation:
Answer:
khan says no solution
Step-by-step explanation:
khan knows best