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3 years ago

How many whole numbers between 1 and 1000 do not contain the digit 1?

Mathematics

1 answer:

8090 [49]3 years ago

5 0

Answer:

728

Step-by-step explanation:

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6. Complete the two-column proof.

olya-2409 [2.1K]

Answer:

Given: $\frac{x}{6} + 2 = 15$ ......[1]

To prove : x =78

Subtraction property states that you subtract the same number to both sides of an equation.

Subtract 2 from both sides of an equation [1];

$\frac{x}{6} + 2 - 2= 15 -2$

Simplify:

$\frac{x}{6} = 13$ ......[2]

Multiplication property states that you multiply the same number to both sides of an equation.

Multiply 6 to both sides of an equation [2];

$\frac{x}{6} \times 6 = 13 \times 6$

Simplify:

$x = 78$ proved!

Statement Reason

1. $\frac{x}{6} + 2 = 15$ Given

2. $\frac{x}{6} = 13$ Subtraction property of equality

3. $x = 78$ Multiplication property of equality

8 0

3 years ago

Read 2 more answers

Find perimeter in cm of the diagram

boyakko [2]

3 sides of square is 3*12=36 cm

perimeter for the full circle is 2 * pi * radius

which is =2 * 22/7 * 12 =75.43 cm

so 360° =75.43 cm

for 150° = 75.43/360 *150 =31.43

all together =36 +31.43 =67.43 cm

8 0

3 years ago

What is 9.1 less than a number is less than 4.6 equals?

Brilliant_brown [7]

Answer:

n > 13.7

Step-by-step explanation:

Writing a symbolic statement, we get:

n - 9.1 < 4.6

Multiplying all three terms by 10 removes fractions:

10n - 91 > 46

Adding 91 to both sides isolates the 10n term:

10n > 46 + 91, or 10n > 137

Then n > 137/10, or n > 13.7

4 0

2 years ago

Please work out and explain

Mekhanik [1.2K]

Answer:

a = 22

b = 31

c = 13

Step-by-step explanation:

The sum is the same in each row, column, and diagonal.

One of the diagonals is already complete. The sum is:

16 + 25 + 34 = 75

So the first row adds up to 75:

a + 37 + 16 = 75

a = 22

The second row adds up to 75:

19 + 25 + b = 75

b = 31

And the third row adds up to 75:

34 + c + 28 = 75

c = 13

We can check our answer by finding the sum of each column and the other diagonal.

22 + 19 + 34 = 75

37 + 25 + 13 = 75

16 + 31 + 28 = 75

22 + 25 + 28 = 75

3 0

3 years ago

A plane flying horizontally at an altitude of 1 mi and a speed of 470 mi/h passes directly over a radar station. Find the rate a

kiruha [24]

Answer:

407 mi/h

Step-by-step explanation:

Given:

Speed of plane (s) = 470 mi/h

Height of plane above radar station (h) = 1 mi

Let the distance of plane from station be 'D' at any time 't' and let 'x' be the horizontal distance traveled in time 't' by the plane.

Consider a right angled triangle representing the above scenario.

We can see that, the height 'h' remains fixed as the plane is flying horizontally.

Speed of the plane is nothing but the rate of change of horizontal distance of plane. So, $s=\frac{dx}{dt}=470\ mi/h$

Now, applying Pythagoras theorem to the triangle, we have:

$D^2=h^2+x^2\\\\D^2=1+x^2$

Differentiating with respect to time 't', we get:

$2D\frac{dD}{dt}=0+2x\frac{dx}{dt}\\\\\frac{dD}{dt}=\frac{x}{D}(s)$

Now, when the plane is 2 miles away from radar station, then D = 2 mi

Also, the horizontal distance traveled can be calculated using the value of 'D' in equation (1). This gives,

$2^2=1+x^2\\\\x^2=4-1\\\\x=\sqrt3=1.732\ mi$

Now, plug in all the given values and solve for $\frac{dD}{dt}$ . This gives,

$\frac{dD}{dt}=\frac{1.732\times 470}{2}=407.02\approx 407\ mi/h$

Therefore, the distance from the plane to the station is increasing at a rate of 407 mi/h.

6 0

3 years ago