1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gemiola [76]
3 years ago
10

Let x and y be any numbers at all with x ≤ y. Show that the number of integers between x and y is [y] - [x] +1.That is show that

the number of integers between x and y is = (the floor of y) - (the ceiling of x) +1
Mathematics
1 answer:
ddd [48]3 years ago
5 0

Answer:

the explanation is given below.

Step-by-step explanation:

  • Here what is applied is assumption of range of values of number from say 1 - 100
  • In total, i stopped at 100 on the dot.

from this, the lowest number is 1 and the highest number is 100

  • hence the range of the numbers = Difference between Highest and Lowest
  • range = 100 - 1 = 99, the 99 gotten as the range is indicative that a number has been missing.

  • In order to make up the 100, an integer is added to the difference = 99, i.e 99 is added to 1 to make up the 100.

  • Furthermore, if 0 is exclusively out when numbers are counted up 100 with 0 inclusive, in such case, the first and last number are excluded from the counting. as such the integers will be {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20.........., 99} since both 0 and 100 are not included.

  • Here, if we try to get the range = highest - lowest = 99 - 1 = 98, it implies that to make up the 99, an integer is added to the result of the difference = 98+1 = 99

  • As such, the number of integers between two numbers is the difference between the highest and the lowest number plus 1 i.e highest - lowest + 1 = y - x +1 = (the floor of y) - ( the ceiling of x) + 1
You might be interested in
Mason has a collection of 49¢ stamps, 20¢ stamps, and 34 stamps worth $23.55. He has 56 total 49¢ and 20+ stamps and the number
tatuchka [14]

Answer:

Mason has

  • 16 20¢ stamps;
  • 25 3¢ stamps;
  • 40 49¢ stamps.

Step-by-step explanation:

Let x be the number of 20¢ stamps, then the number of 3¢ stamps is  x + 9.

Mason has 56 total 49¢ and 20¢ stamps, then the number of 49¢ stamps is 56 - x.

Amounts:

  • in 49¢: 49(56-x) cents;
  • in 20¢: 20x cents;
  • in 3¢: 3(x+9) cents.

Total amount:

  • 49(56-x)+20x+3(x+9);
  • $23.55.

Hence,

49(56-x)+20x+3(x+9)=2,355\\ \\2,744-49x+20x+3x+27=2,355\\ \\-49x+3x+20x=2,355-2,744-27\\ \\-26x=-416\\ \\26x=416\\ \\x=16

Mason has

  • 16 20¢ stamps;
  • 25 3¢ stamps;
  • 40 49¢ stamps.
5 0
3 years ago
Marco states that 7.696696669…… is a rational number because it is a repeating decimal. Is he correct? Justify your answer.
Allisa [31]

Answer:

no because at the end it is 669 not 696 so it is not repeating decimal

3 0
3 years ago
Read 2 more answers
What is the equation of the line that goes through the point (6,-1) and is parallel to the line represented by the equation belo
stepladder [879]

\huge{\boxed{y=-\frac{5}{6} x+4}}

Parallel lines share the same slope, so the slope of the parallel line in this case must be -\frac{5}{6}.

Point-slope form is y-y_1=m(x-x_1), where m is the slope and (x_1, y_1) is any known point on the line.

Plug in the values. y-(-1)=-\frac{5}{6} (x-6)

Simplify and distribute. y+1=-\frac{5}{6} x+5

Subtract 1 from both sides. \boxed{y=-\frac{5}{6} x+4}

6 0
3 years ago
Read 2 more answers
Need help! will award brainiest
coldgirl [10]

Answer:

\sf slope: \boxed{\bf \frac{1}{3} }

Explanation:

\sf slope :\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{rise}{run} \  \ \  \  where  \ (x_1, \ y_1) ,(x_2, \ y_2)  \ are \ points

Find slope:

\rightarrow \sf \dfrac{x_2-x_1}{y_2-y_1}

<em>insert values</em>

\rightarrow \sf \dfrac{3-5}{-4-2}

<em>simplify</em>

\rightarrow \sf \dfrac{1}{3}

4 0
2 years ago
Read 2 more answers
3/4 divided by n = 24
Sophie [7]
The answer is n= 1/32

4 0
3 years ago
Read 2 more answers
Other questions:
  • A map has a scale of 1 inch to 15 miles . If 2 cities are 3.4 inches apart on the map , what is the actual distance between the
    6·2 answers
  • Please help thank you
    11·1 answer
  • Which has more people a car that is 3/4 full or a car that is 1/4 full
    5·2 answers
  • Mr Brown has a family Railcard
    11·2 answers
  • "A quadrilateral is a trapezoid if and only if it has exactly one pair of parallel sides."
    15·2 answers
  • Simon used 3 pears and 9 apples to make a fruit salad. What was the ratio of the number of pears to the number of apples in the
    8·1 answer
  • How many 45. angles would it take to turn in a complete circle
    12·2 answers
  • The odds that it will snow tomorrow are 9 to 6. What is the probability that it will not snow tomorrow?a) 0.1818
    10·1 answer
  • Determine the x-intercept and the y-intercept for the graph of this equation:<br> 2x - 3y + 36 = 0
    9·1 answer
  • Find g(x), where g(x) is the translation 7 units down of f(x)=x.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!