The number 12/3 belongs to the sets of Whole Numbers, Integers, and Rational Numbers.
Explanation:The number 12/3 belongs to the following sets: Whole Numbers, Integers, and Rational Numbers.
A whole number is an integer that is greater than or equal to zero. Since 12/3 = 4, which is a positive integer, it belongs to the set of Whole Numbers.
An integer is any positive or negative whole number, including zero. Since 12/3 = 4, it is a positive integer and belongs to the set of Integers.
A rational number is any number that can be expressed as a fraction. Since 12/3 can be simplified to 4, it is a rational number.
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Find the perimeter of a triangle with sides 11 inches, 5 inches, and 13 inches. Show your work.
how to convert 8.6 into mixed numbers
One month,ruby worked 6 hours more than Isaac, and Svetlana worked 4 times as many hours as ruby. Together they worked 138 hours find the number of hours each person worked
A rectangular floor is 24 feet long and 9 feet wide. What is the area of the floor in square yards?
Which of the following ordered pairs represents the solution to the system of equations below?
-3x+2y=2
7x-3y=7
A. (2, 4)
B. (4, 7)
C. (7, 14)
D. (8, 13)
F(x, y) = y3/x, p(1, 3), u = 1 3 2i + 5 j (a) find the gradient of f.
Mr. Smith wishes to retire in 16 years. When he retires he would like to have $500,000 in his bank account. Mr. Smith's bank pays 10% per year compounded annually. How much should he deposit now to attain his goal?
Final answer:
Mr. Smith should deposit $119,631.97 now to have $500,000 in his bank account after 16 years, assuming a 10% annual compound interest rate.
Explanation:
To calculate how much Mr. Smith should deposit now to attain his retirement goal of $500,000 in 16 years with an annual compound interest rate of 10%, we use the formula for the present value of a future sum, which is:
PV = FV / (1 + r)^n
Where:
PV is the present value (the amount to deposit now)
FV is the future value (the desired amount in the account)
r is the annual interest rate (as a decimal)
n is the number of years
Plugging in Mr. Smith's values, we have:
PV = $500,000 / (1 + 0.10)^16
Calculating the denominator first:
(1 + 0.10)^16 = 1.10^16 = 4.1772
Now, divide the future value by this amount:
PV = $500,000 / 4.1772
= $119,631.97
Therefore, Mr. Smith should deposit $119,631.97 now to reach his goal of $500,000 in 16 years with a 10% annual compound interest rate.
x+29=−11
what does X equal
you have a credit card with a balance of $1256.34 and a 9.5% APR. A late payment fee of $29.00 is added to the principal if you pay after 5/28. You make a payment for $200.00 on 5/28. How much interest did you pay?
Answer:
The interest paid will be $9.946 ≈ $9.95.
Step-by-step explanation:
p = 1256.34
r = [tex]9.5/12/100=0.007917[/tex] (monthly)
Now, given is :
A late payment fee of $29.00 is added to the principal if you pay after 5/28. You make a payment for $200.00 on 5/28.
As the payment is made on the last date, so no extra charge will be paid. So, it is simple interest of [tex]1256.34\times0.007917=9.946[/tex]
Hence, the interest paid will be $9.946 ≈ $9.95.
Three years ago, Marry was three times as old as his brother. Five years from now he will be twice as old as his brother. How is Marry now?
How many orders of magnitude is $1000 than a nickel?
six turns of a wire are wrapped around a pipe with a length of 24 inches in length and a circumference of 4 inches. What is the length of the wire?
find the rectangular coordinates of the point (-4, pi/3)
Answer:
[tex]\texttt{The rectangular coordinates of the point (-4, pi/3)}=(-2,-2\sqrt{3})[/tex]
Step-by-step explanation:
Conversion of parametric form of ( r , θ ) to rectangular coordinate can be done by using the formula ( rcosθ , rsinθ ).
Here we need to convert (-4, pi/3) in to rectangular coordinate form.
Which can be converted to rectangular coordinate form as
[tex]\left ( -4cos\left ( \frac{\pi}{3} \right),-4sin\left ( \frac{\pi}{3} \right)\right )=\left ( -4\times \left ( \frac{1}{2} \right),-4\times \left ( \frac{\sqrt{3}}{2} \right)\right )=(-2,-2\sqrt{3})[/tex]
[tex]\texttt{The rectangular coordinates of the point (-4, pi/3)}=(-2,-2\sqrt{3})[/tex]
The rectangular coordinates of the point (-4, pi/3) is:
(-4, pi/3)= (-2, -2[tex]\sqrt{3}[/tex])What is a Coordinate?This refers to the system which is used to find out the position of points in a geometric element.
First of all, we have to convert to parametric form
( r , θ ) to rectangular coordinate with the use of the formula ( rcosθ , rsinθ ).Next, we have to convert (-4, pi/3) in to rectangular coordinate form.
(-4 x (1/2), -4 x ([tex]\sqrt{3}[/tex]/2)) = n(-2, -2 [tex]\sqrt{3}[/tex])
After the conversion,
This would bring the rectangular coordinate form to:
(-4, pi/3)= (-2, -2[tex]\sqrt{3}[/tex])Read more about rectangular coordinates here:
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Two students, Jennifer and Jamal, factored the trinomial 6x2 − 3x − 9. Jamal factored it as 3(2x − 3)(x + 1) and Jennifer factored it as (2x − 3)(3x + 3). Indicate which student factored the trinomial completely and which student did not, and explain why. (10 points)
How to find the derivative of functions: y=(5x+7)(x+5)^3
A cafe only sells two types of sandwiches, turkey, and steak. The cafe charges $4 for turkey sandwiches and $6 for steak sandwiches. Last month, the cafe sold $4524 worth of sandwiches. The cafe sold a total of 925 sandwiches.
How many turkey sandwiches did they sell?
Answer:
They sold 513 turkey sandwiches.
Step-by-step explanation:
Let t be the number of turkey sandwiches and s be the number of steak sandwiches.
With these variables, we can create equations for the totals they've given us:
Total sandwiches = [tex]t+s=925[/tex]
Total income = [tex]4t+6s=4524[/tex]
Now we can solve the system for the number of turkey sandwiches and steak sandwiches
Isolate t for [tex]t+s=925[/tex] => [tex]t=925-s[/tex]Substitute [tex]t=925-s[/tex] into [tex]4t+6s=4524[/tex][tex]4\left(925-s\right)+6s=4524[/tex]
Solve for s[tex]3700-4s+6s=4524\\3700+2s=4524\\3700+2s-3700=4524-3700\\2s=824\\\frac{2s}{2}=\frac{824}{2}\\s=412[/tex]
For [tex]t=925-s[/tex] substitute s = 412[tex]t=925-412\\t=513[/tex]
They sold 513 turkey sandwiches and 412 steak sandwiches.
What is the product of 4.5 ⋅ 105 and 1.6 ⋅ 102?
An interior angle and an exterior angle are adjacent. The interior angle measures 84°. What is the measure of the exterior angle?
The measure of the exterior angle is
What is Exterior Angle?External angles are those that run parallel to a polygon's inner angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle.
We have,
The interior angle measures 84°.
We know that
Exterior angle + interior angle = 180
Exterior angle = 180 - Interior angle
Exterior angle = 180 - 84
Exterior angle = 96
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Suppose a parabola has a vertex (5,-3) and also passes through (6,1). Write the equation of the parabola in vertex form
The equation of the parabola with vertex (5, -3) and passing through (6, 1) in vertex form is y = [tex]4(x - 5)^2 - 3.[/tex]
To write the equation of a parabola in vertex form, we use the formula:
y = [tex]a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola. Given the vertex (5, -3) and a point (6, 1) the parabola passes through, we can plug these values into the equation to find a.
For the point (6, 1):
[tex]1 = a(6 - 5)^2 - 3[/tex]
[tex]1 = a(1)^2 - 3[/tex]
4 = a
So, the equation of the parabola in vertex form is:
y = [tex]4(x - 5)^2 - 3[/tex]
find the solution of the system of equations.
-7x-6y=59
-8x-6y=58
The average American consumes about 20 gallons of ice cream in one year. At this rate, how many liters of ice cream will 50 Americans consume in one week? Round to the nearest hundredth.
Given points K'(1, -2) and L'(1, -4), what are the coordinates of the point J' that produces a triangle J'K'L' congruent to JKL resulting from a rotation of 90 degrees clockwise around the point (1, -6)?
Brittany received 8 silver dollars on her eighth birthday. After her next birthday she had 15 and after the next she had 22. After her eleventh birthday she had 29 silver dollars. How many silver dollars will she have after her 16th birthday if her collection increases at the same rate every year?
How many cubic centimeters are there in 2.11 yards^3? express your answer in cubic centimeters to three significant figures?
1 cubic inch=16.39 cubic cm. 1 yard=36 inches. 36 x 2.11=75.96 cubic inches.
75.96 cubic in x 16.39 = 1244.9844 = 1.24 x 10³ cubic cm.
I believe this is correct
Answer:
1,613,219.190 cm^3
Step-by-step explanation:
There is 1 inch per every 2.53 cm, we just need to do the multiplication to the square:
[tex](\frac{2,11yards^3}{x})(\frac{91,44 cm}{1 yard})(\frac{91,44 cm}{1 yard})(\frac{91,44 cm}{1 yard})=\frac{764,558,8579cm^3*2,11yd^3}{1yd^3}\\x=1,613,219.190 cm^3[/tex]
SO now we know that 2,11 yards^3 are equal to 1,613,219.190 cm^3
why did the catholic church feel threatened by the heliocentric theory of the universe
Catholic Church felt threatened by the heliocentric theory of the Universe as Church as church felt that it will reduce its authority over the commons. Authority of the Church was at its highest peak during the era and these inventions were challenging its teaching and beliefs.
Further Explanations:
Chronicles of the Catholic Church began with Christ and his pedagogy, while its continuation of the Christian community was established by disciple of Jesus. It was considered that Bishops were successors to Jesus apostles and the Church leaders are its successor to Saint Peter. They even were practicing the power of regional assembly to resolve the doctrinal and policy issues.
The theory of heliocentric was given by Galileo Galleli for which he was trialed and condemned by the Catholic Church in 1633. His discoveries were opposing the Church as it pronouncedheliocentrism to be precisely heretical. Books on Heliocentrism were banned and Gallelio was even forced to stop his teaching defending Heliocentric theories.
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Answer Details
Grade:High School
Subject: History
Chapter:Catholic Church
Keywords:Catholic Church, Christ, pedagogy, Christian community, Bishops, Saint Peter, Galileo Galleli, Catholic Church, Heliocentrism, doctrinal
the scale on a map is 2 cm=25 miles. Dave measured the distance to the next town at 5cm. Hoiw many miles away is the next town?
Answer:
The next town is 62.5 miles away.
Step-by-step explanation:
Scale problems can be solved by a simple rule of three.
The scale on a map is 2 cm=25 miles
This means that for each 2cm we measure on the map, the real distance is 25 miles.
Dave measured the distance to the next town at 5cm. Hoiw many miles away is the next town?
How many miles are 5 cm. So
2cm - 25 miles
5cm - x miles
[tex]2x = 25*5[/tex]
[tex]x = 62.5[/tex]
The next town is 62.5 miles away.
A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean of 30 thousand miles and a standard deviation of 10 thousand miles. complete parts (a) through (c) below.
a. nbsp what proportion of trucks can be expected to travel between 18 and 30 thousand miles in a year?
To solve this problem, we have to make use of the z statistic. The formula for z score is:
z = (x – u) / s
where x is the sample value = 18,000 to 30,000, u is the sample mean = 30,000, and s is the standard deviation = 10,000
at x = 18,000
z = (18,000 – 30,000) / 10,000 = - 1.2
at x = 30,000
z = (30,000 – 30,000) / 10,000 = 0
So find for the P at values of z = -1,2 and z = 0.
P (z = - 1.2) = 0.1151
P (z = 0) = 0.5000
The proportion in between is the difference:
P (18,000 < x < 30,000) = 0.5000 – 0.1151 = 0.3849
So about 38.49% can be expected to travel 18,000 to 30,000 miles in a year
Using z-scores and the normal distribution, we can calculate that approximately 38.49% of trucks can be expected to travel between 18 and 30 thousand miles in a year.
Explanation:This problem involves the normal distribution in mathematics, particularly statistics. Given that the distance travelled per truck per year is normally distributed, we can calculate the proportion of trucks that may be expected to travel between 18 and 30 thousand miles in a year using z-scores.
The first step is to calculate the z-scores for the two distances we are concerned with. The z-score is a measure of how many standard deviations an element is from the mean. Given a mean of 30 thousand miles and a standard deviation of 10 thousand miles, the z-score for 18 thousand miles is (18 - 30) / 10 = -1.2, and the z-score for 30 thousand miles is (30 - 30) / 10 = 0.
You then need to find the area between these two scores on a standard normal distribution table, which gives you the proportion of trucks likely to travel this distance. Looking up -1.2 and 0 in a standard normal table gives us values of 0.1151 and 0.5000 respectively. The difference between these two areas (0.5000 - 0.1151) is 0.3849, or 38.49% when expressed as a percentage. Thus, we can expect approximately 38.49% of trucks to travel between 18 and 30 thousand miles in a year.
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Larry mixed 15 grams of salt with 210 grams of a 5% salt solution in water. What is the percent of salt in his new solution?
Answer:
11.33%
Step-by-step explanation:
Amount of salt which Larry has to mix= 15 grams
In 210 gm of salt solution, content of salt= 5%
Amount of salt in salt solution= 5 % of 210 grams
Amount of salt in salt solution= [tex]\frac{5}{100}[/tex] of 210 grams
Amount of salt in salt solution= [tex]\frac{21}{2}[/tex]
Amount of salt in salt solution= 10.5 grams
Now the 15 grams of salt have to mix with 5% of salt solution
Total amount of salt= 15+ 10.5
Total amount of salt = 25.5 gram
Total amount of salt solution=15+ 210= 225 grams
Percentage of salt in new solution=[tex]\frac{amount of new salt}{ amount of new solution}[/tex] ×100
Percentage of salt in new solution=[tex]\frac{25.5}{ 225}[/tex] ×100
Percentage of salt in new solution= 0.13333×100
Percentage of salt in new solution= 11.33% (approx)
Hence, the correct answer is 11.33%
a shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50 if you buy 5 bags and spend $17 how many of each size bag did you buy
3 one-pound bags;2 three-pound bags
Answer
Find out the how many of each size bag did you buy .
To proof
Let us assume that the one-pound bags = x
Let us assume that the three-pound bags = y
As given
if you buy 5 bags
than the equation becomes
x + y = 5
As given
a shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50
if you buy 5 bags and spend $17
than the equation becomes
2x + 5.50y = 17
2x + 5.50y = 17
than the two equation are
2x + 5.50y = 17 and x + y = 5
mulitply x + y = 5 by 2 and subtracted from 2x + 5.50y = 17
2x - 2x + 5.50 y - 2y = 17 - 10
3.5y = 7
[tex]y = \frac{7}{3.5}[/tex]
y = 2
put y = 2 in x + y = 5
x = 5 -2
x = 3
Therefore one-pound bags of peanuts bags are 3 and three-pound bags of peanuts bags are 2 .
Hence proved
How many different pairs of numbers with a difference of 12