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jenyasd209 [6]
2 years ago
8

How many positive integers less than 10,000 are such that the product of their digits is 210?A. 24

Mathematics
1 answer:
Nataly [62]2 years ago
5 0

Answer:

correct option is D. 54

Step-by-step explanation:

given data

product of digits = 210

integers = 10000

to find out

How many positive integers less than 10,000

solution

we know product of digits 210 are = 1 × 2× 3×5×7

210 = 1 × 6 × 5 × 7

here 2 × 3 = 6 ( only single digit )

here 4 digit numbers with combinations of the digits are = {1,6,5,7} and {2,3,5,7}

3 digit numbers with combinations of digits are = {6,5,7}

and product of their digits =  210

so combination will be

combinations of {1,6,5,7} is  4! = 4 × 3 × 2 × 1 =   24

combinations of {2,3,5,7}  is 4! =  4 × 3 × 2 × 1 = 24

combinations of {6,5,7} is 3! = 3 × 2 × 1 =  6

so total is = 24 + 24 + 6

total is = 54

so correct option is D. 54

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Step-by-step explanation:

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3 years ago
The length of a rectangle 8 more than the width .the area is 513 square inches .find the length and width of the rectangle
Pani-rosa [81]

Answer:

width =19 inches

length= 27 inches

Step-by-step explanation:

Let width be w inches so according to given scenario as length is 8 more than width so the equation becomes

l=8+w inches (Equation 1)

Area of Rectangle= L*w

Area= 513

L*w=513    (Equation 2)

Putting l's value from equation 1 in equation 2

(8+w)w=513

w^2+8w-513=0

Making Factors

w^2+27w-19w-513=0

w(w+27)-19(w+27)=0

(w-19)(w+27)=0

w=19, w=-27

as width cannot be negative so if we only consider w=19 then

l=8+19

l=27

3 0
3 years ago
Question 5
baherus [9]

9514 1404 393

Answer:

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Step-by-step explanation:

The solution is found where the lines meet. Parallel lines never meet, so there is no solution.

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2 years ago
Find the commission on a sale of $8,432 at 12 % commission.
UkoKoshka [18]

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Step-by-step explanation:

5 0
2 years ago
Given the vectors, a=3i+4j, b=-2i+5j, c=10i-j, d=-1/3i+5/2j, find -0.4a-0.3b+0.2d=?
sveta [45]

Answer:

-\frac{2}{3}i - \frac{13}{5}j

Step-by-step explanation:

-0.4(3i + 4i) - 0.3(-2i + 5j) + 0.2(-\frac{1}{3}i + \frac{5}{2}j)

-1.2i - 1.6j + 0.6i - 1.5j - \frac{0.2}{3}i + 0.5j

Converting to fraction form;

-\frac{6}{5}i + \frac{3}{5}i - \frac{1}{15}i - \frac{8}{5}j - \frac{3}{2}j + \frac{1}{2} j

<u>Solving the i part;</u>

\frac{-18i + 9i - i}{15} = -\frac{2}{3}i

<u>Solving the j part;</u>

\frac{-16j-15j+5j}{10} = -\frac{13}{5}j

So -0.4a - o.3b + 0.2d =  -\frac{2}{3}i - \frac{13}{5}j

6 0
3 years ago
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