How many different 6-digit PIN codes using only the digits 0-9 are possible?

Pachacha [2.7K]

4x - y = 61
2y = x

substitute x = 2y in first equaation:-

4(2y) - y = 61
7y = 61
y = 61/7

so x = 2 * 61/7 = 122/7

y = 8 5/7 and x = 17 3/7

7 0

3 years ago

A ball is thrown vertically upward. After seconds, its height (in feet) is given by the function 56t - 16t^2 . What is the maxim

mr Goodwill [35]

Answer:

Therefore the maximum height that the reach is 49 feet after 1.75 seconds.

Step-by-step explanation:

Given that,

A ball is thrown vertically upward. After t seconds its height is given by the function

$h=56t-16 t^2$

where h is height in feet.

Maximum value:

Given function f(x)= at²+bt+c.

Find the value $-\frac{b}{2a}$
Putting $x= -\frac{b}{2a}$ in the given function.
The maximum value of the given function is $f(-\frac{b}{2a})$ .

Here a= -16 , b=56 and c=0

The ball attains its maximum height when $t=-\frac{56}{2.(-16)}=1.75$ s.

Putting the value of t in the given function

$h=(56\times 1.75)-16(1.75)^2$

=49 feet

Therefore the maximum height that the reach is 49 feet after 1.75 seconds.

6 0

3 years ago

Alexis washes 10 1/2 windows in 3/4 hours. At this rate, how many windows can she wash in one hour?

Zepler [3.9K]

Alexis can wash a total of 14 windows in 1 hour

<h3><u>Solution:</u></h3>

Given that Alexis washes $10\frac{1}{2}$ windows in $\frac{3}{4}$ hours

<u><em>To find: </em></u>number of windows washed in one hour

To simplify the calculations we will convert the given mixed fraction to improper fraction

$\begin{array}{l}{=10 \frac{1}{2}} \\\\ {=\frac{2 \times 10+1}{2}} \\\\ {=\frac{21}{2}=10.5}\end{array}$

Hence, to wash 10.5 windows, Alexis takes 0.75 hours

Let "n" be the number of windows washed in 1 hour

10.5 windows ⇒ 0.75 hours

"n" windows ⇒ 1 hour

By cross-multiplication we get,

$n \times 0.75 = 10.5 \times 1$

$n = \frac{10.5}{0.75} \\\\n = 14$

Thus Alexis can wash 14 windows in one hour

4 0

4 years ago

2ND TIME REPOST

Mars2501 [29]

Are you trying to figure out what X is? One of the equations equal to 4, and the rest equal to 24.

6 0

3 years ago

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same consta

maksim [4K]

Answer:

Step-by-step explanation:

a) Mean = (17 + 11 + 15 + 14 + 16)/5 = 14.6

Standard deviation = √(summation(x - mean)²/n

n = 5

Summation(x - mean)² = (17 - 14.6)^2 + (11 - 14.6)^2 + (15 - 14.6)^2 + (14 - 14.6)^2 + (16 - 14.6)^2 = 21.2

Standard deviation = √(21.2/5 = 2.06

Approximating to 1 decimal place, s = 2

The new data set is

68, 44, 60, 56, 64

Mean = (68 + 44 + 60 + 56 + 64)/5 = 58.4

Summation(x - mean)² = (68 - 58.4)^2 + (44 - 58.4)^2 + (60 - 58.4)^2 + (56 - 58.4)^2 + (64 - 58.4)^2 = 339.2

Standard deviation = √(339.2/5 = 8.24

c) The standard deviation of the new data is 4 times the standard deviation of the previous data

In general, multiplying each data value by the same constant c results in the standard deviation being |c| times as large.

d) s = 2.1 miles

Since 1 mile = 1.6 kilometers, the constant with which we would multiply the given standard deviation is 1.6. Therefore, converting to kilometers, it becomes

1.6 × 2.1 = 3.36 km

8 0

3 years ago