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
dmitriy555 [2]
3 years ago
12

Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, ha

ve the following properties:
(a) are divisible by 5 and by 7.
(b) are divisible by 7.
(c) are even.
(d) are divisible by 5 but not by 7.
Mathematics
1 answer:
zmey [24]3 years ago
8 0

Answer:

(a) There are 257 numbers which are divisible by 5 and by 7

(b) There are 1286 numbers which are divisible by 7

(c) There are 4500 even numbers

(d) There are 514 numbers which are divisible by 5 but not by 7

Step-by-step explanation:

(a) Since, LCM(5, 7) = 35,

Thus, the numbers divisible by 5 and by 7 between 1000 and 9999,

1015, 1050, 1085............, 9975

Which is an AP,

Having first term, a = 1015,

Common difference, d = 35,

Last term, l = 9975

If n be the number of terms,

\because l = a + (n-1)d

9975 = 1015 + (n-1)35

9975 - 1015 = (n-1)35

8960 = (n-1)35

256 = n-1

\implies n = 256 + 1 = 257

(b) Similarly,  number divisible by 7,

1001, 1008, 1015............, 9996

Here, a = 1001, d = 7, l = 9996

9996 = 1001 + (n-1)7

9996 - 1001 = (n-1)7

8995 = (n-1)7

1285 = n-1

\implies n = 1285 + 1 = 1286

(c) Even numbers between 1000 and 9999 inclusive

1000, 1002, 1004, 1006,........9998

Here, a = 1000, d = 2, l = 9998

9998 = 1000 + (n-1)2

9998 - 1000 = (n-1)2

8998 = (n-1)2

4499 = n-1

\implies n = 4499 + 1 = 4500

(d) Number divisible by 5,

1000, 1005, 1010............, 9995

Here, a = 1000, d = 5, l = 9995

9995 = 1000 + (n-1)5

9995 - 1000 = (n-1)5

8995 = (n-1)5

1799 = n-1

\implies n = 1799 + 1 = 1800

Hence, the number divisible by 5 but not by 7 = numbers divisible by 5 - number divisible by 7

= 1800 - 1286

= 514

You might be interested in
PLZ HELP!!
ludmilkaskok [199]

9514 1404 393

Answer:

  y = -3x^2 -9x +30

Step-by-step explanation:

When a polynomial has a zero at x=p, it has a factor of (x -p). The factors of your quadratic are ...

  f(x) = (x +5)(x -2)

At the point x=3, the value of this product is ...

  f(3) = (3 +5)(3 -2) = (8)(1) = 8

In order for that value to be -24, it needs to be multiplied by a scale factor of -3. The quadratic you want is ...

  y = -3(x +5)(x -2)

  y = -3x^2 -9x +30 . . . . . standard form

3 0
3 years ago
The sum of two consecutive numbers is 73. what are the numbers?
brilliants [131]
Hey there!

2x+1=73.
2x=72.
x=36<span>.
</span>
So the 2 consecutive numbers are 72 and 36!


Hope this helps! :)
6 0
3 years ago
Read 2 more answers
Find the line through
Kaylis [27]

Answer:

(\frac{1}{2},\frac{-1}{2},\frac{1}{2})

Step-by-step explanation:

We have been given the intersection coordinates:

(7,1,-6) and perpendicular to the line x=-1+t ,y=-2+t and z=-1+t

From the condition of perpendicularity we know:  

(7,1,-6)(x,y,z)

\Rightarrow 7x+y-6z=0

Now, we have given x=-1+t , y=-2+t and  z= -1+t

7(-1+t)+(-2+t)-6(-1+t)=0

-7+7t-2+t+6-6t=0

\Rightarrow -3+2t=0

2t=3

t=\frac{3}{2}

Now, substituting t in the given coordinates x,y and z we get:

x=-1+\frac{3}{2}=\frac{1}{2}

y=-2+\frac{3}{2}=\frac{-1}{2}

And z=-1+\frac{3}{2}=\frac{1}{2}



3 0
3 years ago
Read 2 more answers
Find the volume of each sphere. Be sure to include appropriate units.<br> (Show your work)
babunello [35]

Answer:

2145.5m^3

679.2yard

Step-by-step explanation:

v

volume \: of \: a \: sphere =  \frac{4}{3}\pi \: r {}^{3}  \\ when \: r = 8 \\ volume =  \frac{4}{3}  \times  \frac{22}{7}  \times 8 {}^{3}  \\ volume =  \frac{4}{3}  \times  \frac{22}{7} \times 8 \times 8 \times 8 \\ volume =  \frac{4 \times 22 \times 512}{3 \times 7}   \\ volume =  \frac{45056}{21}  \\ volume = 2145.5m {}^{3}  \\  \\ for \: the \: second \: shape \\ volume =  \frac{4}{3}  \times  \frac{22}{7}  \times 5.5 {}^{3}  \\  =  \frac{4}{3}  \times  \frac{22}{7}  \times 166.373 \\  =  \frac{14641}{21}  \\  = 697.2yard

6 0
2 years ago
A sports team is holding a banquet.
Amanda [17]

Answer:

$10

Step-by-step explanation:

1000 divided by 100 = 10

so $10  is the answer

then 100 tickets = $1000

PLEASE MARK BRAINLIEST AND GIVE 5 STARS.

6 0
2 years ago
Other questions:
  • (x2 − 8x + 5) − (−3x2 + 5x − 9)
    12·1 answer
  • The quotient of three times a number and 4 is at least -16
    14·1 answer
  • The graph below shows a system of equations: Draw a line labeled y equals minus x plus 5 by joining the ordered pairs 0, 5 and 5
    12·1 answer
  • How do I convert a number into a percentage ?
    8·1 answer
  • The length of a rectangle is 8.more than the width. the area is 84 square feet. find the length and width of the rectangle.
    15·1 answer
  • Which shows a correct order to solve this story problem? Each morning Mike bikes 3.5 miles. Each afternoon he bikes 2.3 miles. H
    7·2 answers
  • Which inequality represents the situation? The cost of the ticket is no more than $50.
    5·1 answer
  • circle A has a center of (2,3) and a radius of 5 and circle B has a center of (1,4) and a radius of 10. What steps will help sho
    12·1 answer
  • I need help fast.........
    14·1 answer
  • Jessie recently drove to visit her parents who live 756 miles away. On her way there her average speed was 21 miles per hour fas
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!