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sleet_krkn [62]
3 years ago
12

How many positive 4-digit integers have only odd digits?

Mathematics
2 answers:
Sav [38]3 years ago
7 0
2,4,6,8 multiply by 3

12345 [234]3 years ago
6 0

Answer:

5^4 = 625

Step-by-step explanation:

There are 5 possible odd digits to choose from:  1,3,5,7,9.

When we chose our first digit, we have 5 choices (the possible odd digits). For every one of those 5 choices, we can chose our second digit in 5 different ways again, then we have 5*5 = 25 ways for choosing our first two digits. We can do the same again, as for every one of the 25 first two digits, we can chose our third digit in 5 different ways (again, the odd numbers). So we multiply it by 5 again. Repeating this one more time, because we have 5 different ways to chose our fourth digit. At the end we will have

5*5*5*5 = 5^4 = 625

This is a commun counting technique.

You might be interested in
Julie and Eric row their boat (at a constant speed) 55 miles downstream for 5 hours, helped by the
Archy [21]

Answer: C = 3 mph is the rate of the current.

Step-by-step explanation:

Hey there!

<u />

<u>You can use the distance formula (d = rt) to solve this problem.  </u>

Downstream trip: d = 55 miles, t = 5 hours, and r = R + C  

R + C is their rowing speed (R) plus the rate of the current (C).  

Upstream trip: d = 55 miles, t = 11 hours, and r = R - C

R - C is their rowing speed (R) minus the rate of the current (C).  

Downstream: 55 mi. = (R + C)5 hrs. Divide both sides by 5: R + C = 11

Upstream: 55 mi. = (R - C)11 hrs. Divide both sides by 11: R - C = 5

<u>Calculations</u>

R + C = 11 Subtract C from both sides.

R = 11 - C Substitute this into: R - C = 5

(11 - C) - C = 5 Simplify and solve for C

11 - 2C = 5 Add 2C to both sides.

11 = 2C + 5 Subtract 5 from both sides.

6 = 2C Divide both sides by 2

C = 3 mph is the rate of the current.

~I hope I helped you! :)~

5 0
3 years ago
What is the angles mSRW?
Scilla [17]

Answer:

126°

Step-by-step explanation:

(2x +18)° = (3x)°

2x + 18 = 3x

18 = 3x - 2x

18 = x

therefore, (3x)° = (3*18)°= (54)°

m\angle SRW + (3x)\degree = 180\degree \\m\angle SRW + 54\degree  = 180\degree \\m\angle SRW = 180\degree  - 54\degree  \\\huge\red{\boxed{m\angle SRW = 126\degree}}

5 0
3 years ago
Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha
Pavel [41]

Answer:

(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14.

(Expand to obtain an equivalent expression for the sphere: x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0)

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}.

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}.

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between \left(x_1, \, y_1, \, z_1\right) and \left(x_2, \, y_2, \, z_2\right) would be:

\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right).

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}.

The equation for a sphere of radius r and center \left(x_0,\, y_0,\, z_0\right) would be:

\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2.

In this case, the equation would be:

\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2.

Simplify to obtain:

\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56.

Expand the squares and simplify to obtain:

x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0.

8 0
3 years ago
Which number is greater . 60 or 7.5
myrzilka [38]

Answer:

60 is greater than 7.5.

step by step

5 0
3 years ago
Find the length of the missing side in the figure below. a = _______ cm.
WITCHER [35]

Answer:

\frac{2 \sqrt{177} }{5}

or

5.32cm correct to 2 decimal places

Step-by-step explanation:

This is a right angled triangle from what I know so we have to apply pythagoras theorem.

{7.1}^{2}  =  {a}^{2}  +  {4.7}^{2}

we need to rearrange this to find a²

{a}^{2}  =  {7.1}^{2}  -  {4.7}^{2}

a =  \sqrt{ \frac{708}{25} }

This can either be written as a fraction or decimal.

a =  \frac{2 \sqrt{177} }{5}

OR

a = 5.32

correct to 2 decimal places

5 0
2 years ago
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