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3 years ago

How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed?

1 answer:

6 0

There are 6 digits. Each digit can take ten different numbers except for the first digit since it cannot be zero.

So:

9 x 10 x 10 x 10 x 10 x 10

900000 numbers.

Another way of thinking about this is to just count up to 999,999. Obviously there are 999,999 different numbers here. But since our number has to have 6 digits in them, we have to delete 99,999 numbers. Thus there are 900,000 different numbers.

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Why the slope of a horizontal line is always zero.

nlexa [21]

Yes the slope of a horizontal line is always zero because it does not have a vertical incline or decline

5 0

3 years ago

Walter invests $12,000, part at 7% annual interest and part at 8.5% annual interest. How much is invested at each rate if Reggie

MAXImum [283]

Answer:

for 7% , $8,000

for 8.5%, $4,000

Step-by-step explanation:

Key amount at 7% be x and amount at 8.5% be y

Mathematically;

x + y = 12,000 ••••••(i)

Let’s now work

with the interest;

7% of x + 8.5% of y = 900 ••••••(ii)

0.07x + 0.085y = 900

So we have two equations to solve simultaneously

From 1, x = 12,000-y

Substitute this into ii

0.07(12000-y) + 0.085y = 900

840-0.07y + 0.085y = 900

0.015y = 900-840

0.015y = 60

y = 60/0.015

y = 4000

x = 12000-4000

x = $8,000

7 0

3 years ago

To make green paint, students mixed yellow paint with blue paint. The table below shows how many yellow and blue drops from a dr

meriva

The answer is 7 because the question is asking tje several student tje paint had

3 0

3 years ago

A rectangular parking lot has an area of 15,000 feet squared, the length is 20 feet more than the width. Find the dimensions

faust18 [17]

Dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet

<h3>Solution:</h3>

Given that

Area of rectangular parking lot = 15000 square feet

Length is 20 feet more than the width.

Need to find the dimensions of rectangular parking lot.

Let assume width of the rectangular parking lot in feet be represented by variable "x"

As Length is 20 feet more than the width,

so length of rectangular parking plot = 20 + width of the rectangular parking plot

=> length of rectangular parking plot = 20 + x = x + 20

The area of rectangle is given as:

$\text {Area of rectangle }=length \times width$

Area of rectangular parking lot = length of rectangular parking plot $\times$ width of the rectangular parking

$\begin{array}{l}{=(x+20) \times (x)} \\\\ {\Rightarrow \text { Area of rectangular parking lot }=x^{2}+20 x}\end{array}$

But it is given that Area of rectangular parking lot = 15000 square feet

$\begin{array}{l}{=>x^{2}+20 x=15000} \\\\ {=>x^{2}+20 x-15000=0}\end{array}$

Solving the above quadratic equation using quadratic formula

General form of quadratic equation is

${ax^{2}+\mathrm{b} x+\mathrm{c}=0$

And quadratic formula for getting roots of quadratic equation is

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

In our case b = 20, a = 1 and c = -15000

Calculating roots of the equation we get

$\begin{array}{l}{x=\frac{-(20) \pm \sqrt{(20)^{2}-4(1)(-15000)}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{400+60000}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{60400}}{2}} \\\\ {x=\frac{-(20) \pm 245.764}{2 \times 1}}\end{array}$

$\begin{array}{l}{=>x=\frac{-(20)+245.764}{2 \times 1} \text { or } x=\frac{-(20)-245.764}{2 \times 1}} \\\\ {=>x=\frac{225.764}{2} \text { or } x=\frac{-265.764}{2}} \\\\ {=>x=112.882 \text { or } x=-132.882}\end{array}$

As variable x represents width of the rectangular parking lot, it cannot be negative.

=> Width of the rectangular parking lot "x" = 112.882 feet

=> Length of the rectangular parking lot = x + 20 = 112.882 + 20 = 132.882

Hence can conclude that dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet.

3 0

3 years ago

PLSSSS HELP ME!!!

Phoenix [80]

Amount of juice hold by Cup B which is in the shape of a cylinder having width 2 inches that is radius 1 inches and height 7 inches

= cubic inches

Amount of juice hold by cup A which is in the shape of a cone having width 2 inches that is radius 1 inches and height 3 inches

= cubic inches

Amount of juice that cup B will hold than cup A when both are completely full = cubic inches

= 6 × 3.14

= 18.84 cubic inches

Option A: 18.8 cubic inches

7 0

3 years ago