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3 years ago

6

The product of two numbers is 48. The first number is positive, and the second number is four more than twice the first number.

Find the two numbers.

1 answer:

Katena32 [7]3 years ago

3 0

The answer is 12 and 4 because 4 times 2 is 8 and if you add that by four more that would equal 12 the same amount as the first nubmer

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A small combination lock on a suitcase has 4 wheels, each labeled with the 10 digits 0 to 9. how many 4 digit combinations are

tamaranim1 [39]

This is the easiest way to solve this problem:

Imagine this represents how many combinations you can have for each of the 4 wheels (each blank spot for one wheel): __ __ __ __

For the first situation it says how many combos can we make if no digits are repeated.
We have 10 digits to use for the first wheel so put a 10 in the first slot
10 __ __ __
Since no digit can be repeated we only have 9 options for the second slot
10 9_ __ __
Same for the third slot, so only 8 options
<u>10</u> <u> 9 </u> <u> 8 </u> __
4th can't be repeated so only 7 options left
<u>10</u> <u> 9 </u> <u> 8 </u> <u> 7
</u><u>
</u>Multiply the four numbers together: 10*9*8*7 = 5040 combinations

For the next two do the same process as the one above.

If digits can be repeated? You have ten options for every wheel so it would look like this: <u>10</u> <u>10</u> <u>10</u> <u>10
</u>
10*10*10*10 = 10,000 combinations

If successive digits bust be different?
We have 10 for the first wheel, but second wheel only has 9 options because 2nd number can't be same as first. The third and fourth wheels also has 9 options for the same reason.

<u>10</u> <u> 9</u><u> </u> <u> 9 </u> <u> 9 </u>

10*9*9*9 = 7290 combinations

8 0

3 years ago

A sleep time of 15.9 hours per day for a newborn baby is at the 10h percentile of the distribution of sleep times for all newbor

Nuetrik [128]

Answer:

option (D) 16.5

Step-by-step explanation:

Data provided:

Sleep time of , X = 15.9 is at the 10th percentile

Standard deviation, σ = 0.5 hour

also,

10th percentile of normal distribution is

Z = F⁻¹(0.10)

or

Z = - 1.28 (Using Standard Normal distribution)

Now,

$\\Z=\frac{X-\mu}{\sigma}$

or

X = μ + ( σ × Z )

or

μ = X - ( σ × Z )

on substituting the respective values, we get

μ = 15.9 - 0.5 × (-1.28)

or

μ = 16.5

Hence, the correct answer is option (D) 16.5

8 0

3 years ago

What does the fundamental theorem of algebra illustrate?

UNO [17]

Answer:

The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.

Step-by-step explanation:

The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.

We have to find the roots of this given equation.

If a quadratic equation is of the form $ax^{2}+bx +c=0$

Its roots are $\frac{-b+\sqrt{b^{2}-4ac } }{2a}$ and $\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

Here the given equation is $2x^{2}-4x-1$ = 0

a = 2

b = -4

c = -1

If the roots are $x_{1} and x_{2}$ , then

$x_{1}$ = $\frac{-2+\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}$

= $\frac{4 +\sqrt{24}}{4}$

= $\frac{2+\sqrt{6} }{2}$

$x_{2}$ = $\frac{-2-\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}$

= $\frac{4 +\sqrt{8}}{4}$

= $\frac{2-\sqrt{6} }{2}$

These are the two roots of the equation.

6 0

3 years ago

Is 5 in the solution of x+3>8?

Ivan

Answer: D) No; If x is 5, the expression on the left simplifies to 8, making the inequality false.

In other words, if x = 5, then x+3 becomes 5+3 which ultimately becomes 8, but this is not greater than 8 on the right side.

Your steps could look like this

x+3 > 8

5+3 > 8 ... replace x with 5

8 > 8 ... this is a false inequality

8 0

3 years ago

What is the maximum length of a rod that can fit into a box with dimensions 4 x 3 x 12in?

Stella [2.4K]

Should just be your largest dimension which is 12, right?

5 0

3 years ago