What are integers and rational numbers?
Answers
Step-by-step explanation:
Integers are a subset of Rational Numbers because all Integers are Rational Numbers.
Step-by-step explanation:
3 is integer but it can be written as \frac{3}{1} \ or \ \frac{6}{2},.. etc.
1
3
or
2
6
,..etc. which is rational form. Hence every integer can be express as Rational Number.
Thus the last option is correct.
Further, Integers can be defined as the whole numbers including zero and positive whole numbers. i.e. ......,-3, -2, -1, 0, 1, 2, 3,.....
Example: -546, 87855889, 0, etc.
Rational Number is the number in the form \frac{p}{q}
q
p
, where q≠0.
Example: \frac{2}{9}, \frac{-1}{267}, \frac{875}{2}, 3, etc.
9
2
,
267
−1
,
2
875
,3,etc.
Related Questions
If the equation below is solved by graphing, which statement is true? log (6 x + 10) = log 1/2 x
Answers
The solution to the given expression is x = -20/11
What are logarithmic functions?
Logarithmic function are inverse of exponential functions. Given the equation below;
log (6 x + 10) = log 1/2 x
In order to determine the solution to the given logarithmic equation, we will first have to cancel the logarithm on both sides to have
6x + 10 = 1/2x
Collect the like terms
6x - 1/2x = 0 - 10
Find the LCD
12x-x/2 = -10
11x/2 = -10
Cross multiply
11x = -2 * 10
11x = -20
Divide both sides by 11
11x/11 = -20/11
x = -20/11
Hence the solution to the given expression is x = -20/11
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Neo leaves home at 6:45 to drive to work. Neo drives a distance of 45 miles.Neo thinks he drives of an average speed of 30 miles per hour.
Neo is correct what time would he arrive at work ?
Answers
The time at which Neo reaches the work destination is A = 8 : 15 AM
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the time at which Neo reaches the work destination be A
Now , the time at which Neo leaves home = 6 : 45 AM
And , the distance between Neo and work = 45 miles
where the speed of Neo is S = 30 miles per hour
So , the distance traveled by Neo in 1 hour = 30 miles
The distance traveled by Neo in 1.5 hours = 45 miles
Therefore , the time required by Neo to reach office is 1.5 hours
And , the time at which Neo reaches the work destination A = 6 : 45 AM + 1.5 hours
On simplifying the equation , we get
The time at which Neo reaches the work destination A = 8 : 15 AM
Hence , the equation is A = 8 : 15 AM
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The serving size for the granola that Tom likes to eat for breakfast is
3
cup. How many servings are there in a box that holds 7 cups?
Answers
Jane is studying the rate at which the sale of a particular brand of chocolate has increased over the years. The graph below shows the number of bars sold, y, in thousands, after x years since the year 2000:
graph of y equals 15 multiplied by 1.1 to the power of x
What does the y-intercept of the graph represent?
a Price of a bar of chocolate
b Number of bars sold in 2000
c Number of bars sold before 2000
d Rate of increase in the sale of chocolates
Answers
y=15(1.1)^0
y=15(1)
y=15
And y is in thousands so this represents the sale of 15000 bars in the year 2000.
Answer:
B. number of bars sold in chocolate
Step-by-step explanation:
i took the test
Which expression represents (12x - 6x + 2)/2 in simplest form? B 3x + 2 C 6x + 1 D. 3x + 1
Answers
3x + 1
Explanations:The given expression is:
\(\frac{12x\text{ - 6x + 2}}{2}\)Since 12x - 6x = 6x, the expression then becomes:
\(\frac{6x\text{ + 2}}{2}\)Factor out 2 from the numerator
\(\frac{2(3x\text{ + 1)}}{2}\)2 cancels out at both the numerator and denominator
The final expression becomes 3x + 1
A family plans to water ski at a local lake. If the temperature outside is 30 degrees C, what is the temperature in degrees F? Use the formula F = 9/5 C + 32 ?
Help
Answers
Answer:
30°C = 86°F
Step-by-step Explanation:
Temperature outside in degree celsius = 30°C
Formula to convert degree celsius to degree fahrenheit:
\( \boxed{ \bf{\degree F = \dfrac{9}{5}\degree C + 32}}\)
By substituting value in the formula, we get:
\( \rm \implies \degree F = \dfrac{9}{5} \times 30 + 32 \\ \\ \rm \implies \degree F = 9 \times 6 + 32 \\ \\ \rm \implies \degree F = 54 + 32 \\ \\ \rm \implies \degree F = 86\)
\( \therefore \) Temperature outside in degree fahrenheit = 86°F
A wire is first bent into the shape of a rectangle with width 4 cm and length 5 cm. Then the wire is unbent and reshaped into a triangle. If each side of the triangle has equal length, what is this length?
Answers
Answer: 6
Step-by-step explanation:
The perimeter of the rectangle is \(2(4+5)=18\).
Thus, each side of the triangle is \(18/3=6\).
the results of a poll indicate that between 33% and 37% of the population of a town visit the library at least once a year. what is the polls margin of error?
Answers
The margin of error is ±2%
What is Margin error?A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.
Let x be margin of error and y be the percentages of the population.
So,
y-x =33%
y +x = 37%
Solving above equations
2y= 70
y= 35%
and x= 2%
Hence, the margin of error is ±2%.
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someone please help.
Answers
Answer: 3,19 which is larger than the original
Step-by-step explanation: if you consider that the original average is 3 you can say that all 25 students have 3 siblings so the average is 3, if you add another students with 8 siblings and do some math (25*3+8)/26 its 3,19
PLEASE HELP ME!!! ASAP SHOW YOUR WORK!!! Given cos x =√15/4 and 90°< x 180°, find the exact value for cos 2x
Answers
Answer:
x=34 because you simplify it and then take 45 and at it to it
Sean arrives at quater to 7 dinner starts at 6:30 is sean early or late for dinner
Answers
Answer:
Sean is late for dinner.
Step-by-step explanation:
A quarter to 7 is 6:45 so he is 15 minutes late to the dinner.
If Sean arrives at quarter to 7 (which means 6:45), he is 15 minutes late for dinner, as dinner started at 6:30.
What is time estimation?When we say that Sean arrived at quarter to 7, it means that he arrived at 6:45, because a quarter of an hour is equivalent to 15 minutes. We can then compare this time to the time that dinner started, which is 6:30.
If Sean arrived at or before 6:30, he would be considered early for dinner. However, since he arrived at 6:45, he is 15 minutes late for dinner. This means that dinner has already started and he has missed the beginning of the meal.
In general, it is considered polite and respectful to arrive on time for a dinner invitation or any other social event. If you are going to be late, it's always a good idea to let your host know so they can adjust their plans accordingly.
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David has a bank account which pays interest at the rate of 1.5% per year, compounded annually. Determine what amount David
must have in the bank, given that he would like to draw an annual salary of $32,635.15 from his account at the end of each year
for 30 years. Round to the nearest cent.
Answers
Answer: the amount that David must have in the bank is $783243.6
Step-by-step explanation:
We would apply the formula for determining present annuity. It is expressed as
PV = R[1 - (1 + r)^- n]r
Where
PV represents the present value of the investment.
R represents the regular payments made(could be weekly, monthly)
r = represents interest rate/number of interval payments.
n represents the total number of payments made.
From the information given,
r = 1.5/100 = 0.015
n = 30 years
R = $32,635.15
Therefore,
PV = 32635.15[1 - (1 + 0.015)^- 30]/0.015
PV = 32635.15[1 - (1.015)^- 30]/0.015
PV = 32635.15[1 - 0.64]/0.015
PV = 32635.15[0.36]/0.015
PV = 32635.15 × 24
PV = $783243.6
a. $783,760.48
on edgen
name the quadrilateral with 2 pairs of consecutive congruent sides with diagonals that meet at a right angle
Answers
The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.
a mountain bike has a cash price of $770. Eric purchases the bike by making a down payment of $23.10 and 24 payments of $43.27. find the finance charge
Answers
The finance charge is $291.58
Here, we want to calculate the finance charge
Firstly, we need to calculate the amount the bike will cost if it was an installmental payment
We have this as;
\(23.1\text{ + 24(43.27) = \$1,061.58}\)The finance charge is simply the difference between what the hire purchase offerred and the cash price
Mathematically, we have this as;
\(1,061.58-770\text{ = \$291.58}\)The sum of two numbers is 61, the difference is 31. What are the numbers?
Answers
Answer:
2x = 92
x = 46
For the next number:
y = 61 - 46
y = 15
Have a great day!
Answer:
Step-by-step explanation:
For the First Number you would:
1. 2x = 92
2. x = 46
For the second number you would :
1. y = 61 - 46
2. y = 15
David and Peter had $90 and $200 respectively. They were each given an equal amount of money. Then Peter had twice as much money as David. How much money did each boy receive?
Answers
find the volume of a prism length = 9 feet, width 2 yards, height = 36 inches
Answers
Answer:
v= 648
Step-by-step explanation:
All you have to do is multiply every single number
9x2x36=648 :)
If f(x)=6x2-4, what is f(1)?
Answers
Answer:
f−1(x)=√6(x+4)6,−√6(x+4)6
Plz let me know if im wrong!!!
Answer:
are u sure this is written correctly?
given that general term 7n+4
evaluate sum of 5th term and 5th term
Answers
\(\boxed{\sf t_n=7n+4}\)
We have to find 5th term\(\\ \sf\longmapsto t_5=7(5)+4\)
\(\\ \sf\longmapsto t_5=35+4\)
\(\\ \sf\longmapsto t_5=39\)
a. compute the sample mean and sample standard deviation for private and public colleges. round your answers to two decimal places.
Answers
The sample mean is = 6.98, the standard deviation is = 4.53 (2) The pint estimate difference is = 20.2 (3) The confidence interval limits are $ 15943.6 and $24456.4
a)
Private Universities
Sample median: 42,500 dollars
Mean = (Σx)/N
where N = Sample size
Σx = sum of all variables
Private colleges
Σx = (52.8+43.2+45.0+33.3+44.0+30.6+45.8+37.8+50.5+42.0) = 425
N = 10
Mean = 425/10 = 42.5 thousand dollars
Standard deviation = S1 = √[Σ(x - xbar)²/N]
Σ(x - xbar)² = (52.8-42.5)² + (43.2-42.5)²
+ (45.0-42.5)² + (33.3-42.5)²
+ (44.0-42.5)² + (30.6-42.5)² + (45.8-42.5)² + (37.8-42.5)² + (50.5-42.5)² + (42.0-42.5)² = 438.56
N = 10
Standard deviation = √[Σ(x - xbar)²/N]
Standard deviation = √(438.56/10) = 6.62 thousand dollars
S1 or the standard deviation equals $6.62k.
b)
The sample means the difference in both circumstances is 42.5 minus 22.3, or 20.2 thousand dollars.
Going to a private college often costs 20.2 thousand dollars more than going to a public institution on average.
c)
A sample distribution's 95% confidence interval for the price difference between private and public colleges is provided as
(15.0, 25.4) dollars in thousands.
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2 QUESTIONS!
When a number is decreased by 10% of itself, the result is 27. What is the number?
Write an equation to model the problem. Use a to represent the number.
Answer:
Solve the equation to find the number:
Answer:
Answers
Answer:
30
Step-by-step explanation:
The equation will be:
x - (10% of x) = 27
x - 0.1x = 30
0.9x = 30
Divide by 0.9
x = 30
The number is 30
Second question:
Length = 2x - 3
Width = x
Perimeter = 72
Perimeter = 2(l + w)
= 2(2x - 3 + x) = 72
4x - 6 + 2x = 72
6x = 72 + 6
6x = 78
w = 78/6 = 13
The width is 13 meters
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 6 rows of the same length, he has 11 chairs left over. If he arranges the chairs in 4 rows of that same length, he has 13 left over. How many chairs does Liam have?
Liam has
chairs.
Answers
Answer:
he has 37 chairs.
steps:
4 x 6 = 24
24 + 13 = 37
In total Liam has 37 chairs.
?
6.2
Divided by 1/2
Answers
Answer:
The answer is 3.1
\(6.2 \div \frac{1}{2} = 3.1\)
If we were to convert it into a **FRACTION** the answer would be : 31/10.
And that i an improper fraction, but as a **MIXED NUMBER** : \(3 \frac{1}{10}\)
All answers would be : 3.1 , 31/10 and 3 1/10
Answer:
0.5167
Step-by-step explanation:
6.2/12 first rewrite 6.2 as an improper fraction or 36/5 then multiply by 1/12 to get the solution of 0.5167.
What is the measure of ZL?
Enter your answer in the box. Round only your final answer to
the nearest hundredth.
m/L=
18 in.
М'
60 in.
N
Answers
Angle L's in the triangle LMN is,
⇒ L = 72.54°
We have to given that;
A triangle LMN is shown in figure.
And, The sides are,
Since, We know that;
A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.
Since, We know that;
⇒ sin L = Opposite / Hypotenuse
And, cos L = Base / Hypotenuse
Two rays after combined into an angle have a single terminal. And, latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms.
Now, We can use trigonometry formula to find the value of angle l we get;
⇒ sin L = Opposite / Hypotenuse
⇒ sin L = LM / LN
⇒ sin L = 18/60
Taking arc sin both side, we get;
⇒ L = 72.54°
Therefore, The value of measure of angle L is triangle LMN is,
⇒ L = 72.54°
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What is 1 1/2 as a percent
Answers
Answer is 550%
Step-by-step explanation:
the easiest way is divide 11 with 2 =5.5
then mutiply 5.5 with 100
the final answer is 550%
1/12 ÷ 8 plz help i dont know the answer
Answers
Answer:
1/12 × 1/8
= 1/ 96 this is the answer
Write this fraction in lowest terms or simplest terms 9/12= Branliest
Answers
Answer:
3/4 = 75%Step-by-step explanation:
The fraction can be simplified by 3.
So 9/3 = 3.
12/3 = 4.
So the fraction becomes 3/4.
3/4 is equal to 3 quarters or 75/100.
75/100 is equal to 75%.
Answer:
3/4
Step-by-step explanation:
The greatest common factor of 9 and 12 is 3.
9÷3/12÷3
3/4
Find the next four terms in the sequence.
1,-4, 16, -64, ...
Answers
Answer:
256, -1024, 4096, -16384
i think that's it
it's being multiplied by -4 (geometric)
Peter had 208 Canadian stamps and 186 Mexican stamps for sale. The stamps were mixed up and sold in packets of 6. How many packets of stamps were there? How many stamps were left over?
Answers
Answer:
65 packets and 4 stamps
Step-by-step explanation:
The first thing we see is that the stamps are mixed... which means they must be added.
208 + 186 = 394 stamps total
Now we see that each packet has 6 stamps. So we divide the number of stamps in total by 6.
394/6= 65.66667
Now we see from that number that the stamps can't quite make 66 packets, so there are 65 packets.
Now we find the number of stamps left over by multiplying the number of packets by 6.
65 x 6= 390
Now we take the total number of stamps minus the number of stamps in packets.
394 - 390 = 4
Therefore, there are four stamps left over.
Hope this helps!
A basketball team has home games on Thursday and Saturday. The two games together earn $4807.50 for the team. Thursday's game generates $152.50 less than Saturday's game. How much money was taken in an each game? How much money did Thursday's game generate?
Answers
Answer:
Thursday's game generated $2327.5
Saturday's game generated $2480
explanation:
Let Saturday's games generates x
Then Thursday's game will generate [ x - $152.50 ]
Saturday's + Thursday's = total earnings
x + x - $152.50 = $4807.50
2x = $4807.50 + $152.50
2x = $4960
x = $(4960)/2
x = $2480
According to statement, Saturday's games earned $2480
Thursdays game earned = $2480 - $152.50 = $2327.5