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
Murrr4er [49]
3 years ago
6

For how many three digit numbers (100 to 999) is the sum of the digits even? (For example, 343 has an even sum of digits: 3 + 4

+ 3 = 10 which is even.) Find the answer and explain why it is correct in at least two different ways.
Mathematics
1 answer:
n200080 [17]3 years ago
4 0

Answer:

there are 425 numbers of three digits whose the sum of the digits is even.

Step-by-step explanation:

Option 1:

It is necessary to accomplish one of the next conditions:

(1) all of the digits are even.

(2) exactly 2 of the digits are odd

Then, for the first condition:

4x5x5 = 100 -> this is because the first digit can not be 0.

for the second condition:

(3C1)*5*5*5-1*5*5 =3*125-25=350

where 3C1 is a combination.  The 3C1 determines which of the three digits is even, and it is necessary to subtract the numbers under 100 with the other 2 digits odd.

So, there are 450 numbers of three digits whose the sum of the digits is even.

Option 2:

there are 900 three digit number and 5*5*5 =125 has 3 odd numbers and 5*5*5+4*5*5+4*5*5=325 has 1 odd number, so there are 450 numbers of three digits whose the sum of the digitis is odd, so 900-450 whose the sum of the digits is even.

You might be interested in
If a triangle is a right triangle then the other two angles must be acute true or false ?
kolezko [41]

Answer:

The sum of the angles in any triangle is 180 degrees. If one of the three angles is 90 degrees (a right angle) the the sum of the other two angles is 90 degrees. Therefore each of the other two angles must be acute.

The statement is TRUE.

Step-by-step explanation:


8 0
3 years ago
Solve the system of equations.<br><br><br> 2x + 3y = 1<br> y = 3x + 15
MrMuchimi
Since y=3x+15
sub 3x+15 for y in other equation

2x+3(3x+15)=1
2x+9x+45=1
minus 45
11x=-44
divide 11
x=-4

sub
y=3x+15
y=3(-4)+15
y=-12+15
y=3

(-4,3)
6 0
3 years ago
URGENT! (Grades close tomorrow and turning this in will boost my grade from a B to an A in College Algebra. I can't figure these
zvonat [6]

Answer:

  24.  see below for a drawing with axis intercepts labeled

  30.  the plane is parallel to the y-z plane. It is "x=4". The only axis intercept is (4, 0, 0).

Step-by-step explanation:

24. The axis intercepts are fairly easily found. You can do it a couple of ways.

<u>first way</u>

  • Set other variables to zero and divide by the coefficient of the variable of interest.

For 3x +5y +15z = 15, the x-intercept can be found by setting y and z to zero. This gives ...

  3x = 15

so, dividing by 3 tells you the x-intercept is ...

  x = 15/3 = 5

Likewise, the y- and z-intercepts are, respectively, ...

  y = 15/5 = 3

  z = 15/15 = 1

So, the points where the plane crosses the axes are ...

  (5, 0, 0), (0, 3, 0), (0, 0, 1) . . . . axes intercepts

__

<u>second way</u>

  • Divide by the constant on the right, and express all coefficients as denominators

Doing that gives ...

\dfrac{3x+5y+15z}{15}=1\\\\\dfrac{x}{5}+\dfrac{y}{3}+\dfrac{z}{1}=1

The denominators are the corresponding intercepts. (This is called the "intercept form" of the equation of the plane.)

From the above equation, we see the axis intercepts are ...

  (5, 0, 0), (0, 3, 0), (0, 0, 1) . . . . same as above

Actually, the math for these two methods is virtually identical. The second way does it "all at once", so can take fewer steps. Effectively, you're doing the math of the "first way" and expressing the result in the denominator.

__

Please note that when a variable is missing, there is no intercept for that axis. That is, the plane is parallel to that axis. (In problem 30, for example, the y- and z-variables are missing. The plane x=4 is parallel to the y- and z-axes (the y-z plane).)

_____

In the first attached drawing, the x-axis is red, the y-axis is green, and the z-axis is blue. The labeling of the points is difficult to see, but the axes are a different (lighter) color behind the plane than in front of it. This plane forms a triangle in the first octant (x, y, z > 0).

In the second attached drawing, the x=0 plane is blue; the y=0 plane is green, and the z=0 plane is red. The plane of the equation is yellow. This figure better shows the triangle in the first octant.

3-D graph paper (isometric graph paper) grids are available with a web search. Such might make it easier to draw the planes you need to draw. (See the third attachment for one example.)

3 0
3 years ago
How would you solve y+1= -4x ? with a step by step solution
polet [3.4K]

Answer:

There are an infinite number of solutions.

Step-by-step explanation:

An equation with 2 unknowns give an infinite amount of solutions, here is just one of the many:

Let y= 3 ( y can be any number)

(3) + 1 = -4x

4 = -4x

x = -4/4

x= -1

(x;y) = (-1;3)

Generally x and y can be any number, just let x or y be any number, then find the other variable based on the value of the number u assumed.

3 0
3 years ago
Please help i dont understand this problem
DaniilM [7]

y=x+5

Step-by-step explanation:

The opposite of y is x axis

7 0
3 years ago
Other questions:
  • If x is equal to 2 minus root 3 find the value of x minus one upon X whole cube
    14·1 answer
  • The next student presents a monologue that is about 0.5 minutes long. What effect will this have on the graph?
    6·2 answers
  • Please give correct answer :(
    7·2 answers
  • Based on the housing data below, which equation can be used to calculate
    8·1 answer
  • Jack plotted the graph below to show the relationship between the temperature of his city and the number of ice cream cones he s
    13·2 answers
  • Dan and Luke are running in a 20 mile charity benefit wrist if Dan runs at 3 miles per hour and Luke runs at 4 miles per hour ho
    7·1 answer
  • For a given population of high school seniors, the Scholastic Aptitude Test (SAT) in mathematics has a mean score of 500 with a
    6·1 answer
  • The answer to this would be highly appreciated
    7·1 answer
  • What 2 numbers multiply to make -30 and combine to make -7? ____and____<br> Help PLEASEE
    6·2 answers
  • The initial and terminal points of a vector are given. Write the vector as a linear combination of the standard unit vectors i a
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!