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3 years ago

^^picture attached :)

Mathematics

2 answers:

AysviL [449]3 years ago

8 0

25 percent. you get this answer by dividing 15 by 60 so......15/60

Phantasy [73]3 years ago

5 0

#1 is 25% 15/60= 4=0.25=25%

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All digits in a dropdown number are different, and one of its digits is the average of all its digits. It has at least two digit

Svetradugi [14.3K]

1. Start the search among 2-digit numbers. A dropdown number (DDN) with 2 digits is a number $ab$ such that

$\dfrac{a+b}2 = a \implies a + b = 2a \implies b = a$

$\dfrac{a+b}2 = b \implies a+b = 2b \implies a=b$

but both of these solutions violate the requirement that the digits are distinct, so there are no 2-digit DDNs.

A 3-digit DDN $abc$ is such that

$\dfrac{a+b+c}3 = a \implies a+b+c = 3a \implies b+c = 2a$

or $a+c=2b$ if the average is $b$ , or $a+b=2c$ if the average is $c$ . The smallest possible value for $a$ is 1 since we require 3 digits. Then $b+c=2$ , and we can pick $b=0$ and $c=2$ to get the smallest DDN, 102.

2. In a 4-digit DDN $abcd$ , we have

$\dfrac{a+b+c+d}4 = a \implies a + b + c + d = 4a \implies b+c+d=3a$

or $a+c+d=3b$ or $a+b+d=3c$ or $a+b+c=3d$ .

We're free to fix $a=1$ and $b=0$ to try to get the smallest DDN. This leaves us with $c+d=3$ or $c+d=-1$ or $1+d=3c$ or $c=3d$ .

The first two cases are impossible - the only choices for $c,d$ such that $c+d=3$ are 1 and 2, and the sum of two positive integers must be positive. The smallest possible value of $c$ is 2; this leaves us with $1+d=6$ or $2=3d$ , but the latter case is impossible because 3 does not divide 2. So $d=5$ , and the smallest 4-digit DDN is 1025.

To find the largest DDN, start with the largest possible values for $a$ and $b$ . Let $a=9$ and $b=8$ . Then $c+d=19$ or $c+d=15$ or $17+d=3c$ or $17+c=3d$ . At most, we can have $c+d=13$ with 7 and 6, so the first two cases are impossible. If we maximize $c=7$ , then either $17+d=21\implies d=4$ or $24=3d\implies d=8$ (which we don't want). So the largest 3-digit DDN is 9874.

3. I don't have an analytical solution to this, but using brute force (program) the total count is 112.

4. It is possible; consider 1249 and 1250, with digital averages

$\dfrac{1+2+4+9}4=4 \text{ and } \dfrac{1+2+5+0}4=2$

which happens to be the smallest pair. (Also found with brute force.)

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2 years ago

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Convert [−1,∞) to inequality notation use the variable x.

Trava [24]

Answer:

$-1\leq x$

Step-by-step explanation:

We want to convert the interval [-1, ∞) to inequality notation using x as the variable.

The interval [-1, ∞) reads: "All real numbers between -1 and positive infinity."

In other words, it is all numbers greater than or equal to -1 and less than positive infinity.

Therefore:

$-1\leq x$

Note that we do not use "or equal to" for the infinity as we can never really "equal" infinity.

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3 years ago

What is the mode of this data set? 4, 69, 84, 69, 90, 75, 94, 90, 90, 1, 5

nika2105 [10]

Answer:

Step-by-step explanation:

90 because it occurs most in the data set.

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3 years ago

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Help me please I don’t know what to do

den301095 [7]

To find an inverse function first replace f(x) with y

f(x) = 8*sqrt(x)
y = 8*sqrt(x)

Then, simply switch the places of the x and y.

x = 8sqrt(y)

Now solve for the new y by squaring both sides (to get rid of the root)

x^2 = 64y

divide to get

y = x^2/64. This is the inverse function or option C.

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3 years ago

Which set of sides would make a right angle?

Lynna [10]

The answer is 5,12,13 as when you plug these into the Pythagorean theorem :
5^2 + 12^2 = 13^2
25 + 144 = 169
13^2 = 169
Hope this helps :)

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3 years ago

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