Ice cream vs temperature

Find the number of positive integers less than 100,000 whose digits are among 1, 2, 3, and 4. Hint consider the

Verdich [7]

Answer:

1364 is the number of possibilities for positive integers less than 1,00,000.

Step-by-step explanation:

1. 5 digit numbers:

We have 5 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 5 digit numbers:

$4 \times 4 \times 4 \times 4 \times 4\\ \Rightarrow 1024$

2. 4 digit numbers:

We have 4 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 4 digit numbers:

$4 \times 4 \times 4 \times 4 \\ \Rightarrow 256$

3. 3 digit numbers:

We have 3 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 3 digit numbers:

$4 \times 4 \times 4 \\ \Rightarrow 64$

4. 2 digit numbers:

We have 2 places here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 2 digit numbers:

$4 \times 4 \\ \Rightarrow 16$

5. 1 digit numbers:

We have 1 place here, and each place can have 4 options because repetition is allowed.

So, total number of possibilities for 1 digit numbers:

$4$

We can add all the above possibilities to find the total.

So, number of positive integers less than 100,000 whose digits are among 1, 2, 3, and 4 = 1024 + 256 + 64 + 16 + 4 = 1364

3 0

3 years ago

In the figure, x:y = 2:3 and y:z = 3:5. If x = 10, find the value of z. 15 20 25 30

Solnce55 [7]

x:y =x: y

10: y =2:3

2y=30

y=15

y:z=y:z

15:z=3:5

3z=75

z=25

7 0

3 years ago

Factor 9x2 + 6x + 12x + 8

Vesnalui [34]

Step-by-step explanation:

9x2= 3 • 3 • x2

6x= 3 • 2 • x

12x= 2 • 2 • 3 • x

8= 2 • 2 • 2

4 0

4 years ago

Daniel went to the baseball game with $35 to spend after he bout his ticket. He bought 4 hot dogs for $1.75,2$5 .he spends the r

seraphim [82]

Answer:

9.3

Step-by-step explanation:

35-7=28

28 divided by 3 = 9.3

Or $9 and 3 cents

4 0

3 years ago

The animal shelter had a special on adoption rates for their dogs and cats. Each dog adoption fee was $75 and each cat adoption

lidiya [134]

Answer:

3 dogs and 5 cats were adopted out on Christmas eve.

Step-by-step explanation:

Let the number of dogs adopted out on Christmas eve be x and the number of cats be y.

From the question,

On Christmas Eve, the animal adopted out 8 total animals

That is, x + y = 8 ...... (1)

and brought in $400 in total adoption fees.

Also from the question,

Each dog adoption fee was $75 and each cat adoption fee was $35.

∴ On Christmas Eve,

75x + 35y = 400 ...... (2)

Now, to determine how many dogs and how many cats were adopted out on Christmas Eve, we will solve the two equations simultaneously.

From equation (1)

x + y = 8

Make x the subject of the relation.

∴ x = 8 - y ...... (3)

Substitute the value of x into equation (2)

75(8 - y) + 35y = 400

600 - 75y + 35y = 400

600 -40y = 400

600 - 400 = 40y

200 = 40y

∴ 40y = 200

y = 200/40

y = 5

Substitute the value of y into equation (3)

x = 8 - y

x = 8 - 5

x = 3

∴ x = 3 and y = 5

Hence, 3 dogs and 5 cats were adopted out on Christmas eve.

4 0

3 years ago