What is the product of -3 1/3 and -8 7/10

Write equation for the line with a slope "undefined" and has the same x-intercept as x−y−1=0

Mariana [72]

Answer:

Step-by-step explanation:

Lines with undefined slopes are perfectly vertical, of the form "x = ". A line with "the same x-intercept" as the given line that has an undefined slope will be the line that we want. I know that sounds confusing; we'll work through it then I'll explain it better. In order to find the x-intercep of the given line, solving it for y will make it a bit easier to "see". Therefore,

-y = -x + 1 and

y = x - 1. The x-intercept exists when y = 0, so setting y equal to 0 and solving for x:

0 = x - 1 and

1 = x. That's the x-intercept. It's also the line that we want that has an undefined slope, because "x = " lines are lines vertical lines and vertical lines have undefined slopes.

x = 1 is the line you want.

8 0

3 years ago

Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms

miv72 [106K]

Hint :-

Break the given sequence into two parts .
Notice the terms at gap of one term beginning from the first term .They are like $\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ . Next term is obtained by multiplying half to the previous term .
Notice the terms beginning from 2nd term , $4,7,10,13$ . Next term is obtained by adding 3 to the previous term .

Solution :- 

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

$\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ .

We can see that this is in Geometric Progression where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

$\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]$

Notice the term $\dfrac{1}{2^{25}}$ will be too small , so we can neglect it and take its approximation as 0 .

$\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]$

$\\\implies \boxed{ S_1 \approx 1 }$

$\rule{200}2$

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

$\implies S_2=\dfrac{n}{2}[2a + (n-1)d]$

Substitute ,

$\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}$

Hence sum = 908 + 1 = 909

7 0

3 years ago

Starting at home, Luis traveled uphill to the gift store for 50 minutes at just 6 mph. He then traveled back home along the same

Georgia [21]

Answer:

Therefore his average speed for the entire trip is 8 mph.

Step-by-step explanation:

Given, In 50 minutes Luis traveled uphill to gift store at 6 mph.

6 mph means in 1 h= 60 minutes Luis can covered 6 mile.

In 1 minutes Luis can covered $\frac{6}{60}$ mile.

In 50 minutes Luis can covered $\frac{6\times 50}{60}$ mile

= 5 mile

Again when he come back at home, the speed was 12 mph.

12 mph means in 1 h= 60 minutes Luis can covered 12 mile.

Therefore he traveled 12 mile in 60 minutes

He traveled 1 mile in $\frac{60}{12}$ minutes.

He traveled 5 mile in $\frac{60\times 5}{12}$ minutes

= 25 minutes.

Total distance for the entire trip is =(5+5) mile=10 mile

Total time for the entire trip is = (50+25) minutes = 75 minutes

$\textrm{Average speed}=\frac{\textrm{Total distance}}{\Textrm {total time}}$

$=\frac{10}{75}$ m/min

$=\frac{10\times 60}{75}$ mph

= 8 mph

Therefore his average speed for the entire trip is 8 mph.

4 0

3 years ago

Find the rate and unit rate of these please!

Sunny_sXe [5.5K]

You already have the rates, what you need to find out now is the unit rates. To do this, you simply take first number (eg.420) to divide by the second number (eg. 7).
a.60 miles per hour
b. 12 customers per day
c. 2.5 meters in 1 pound
d. $1.592 for 1 ound

8 0

3 years ago

Read 2 more answers

We have seen that the standard deviation σ measures the spread of a data set about the mean μ. Chebyshev’s inequality gives an e

Salsk061 [2.6K]

Answer:

100

Step-by-step explanation:

First we find the mean of this set of data. We find the mean by finding the sum of data values and dividing it by the number of data values:

5+10+10+10+10+10+10+15 = 80

There are 8 data values; 80/8 = 10. The mean is 10.

To find the standard deviation, subtract the mean from each value; square the difference; add the squares; divide by the number of data values; and take the square root:

5-10 = -5; 10-10 = 0; 10-10 = 0; 10-10 = 0; 10-10 = 0; 10-10 = 0; 10-10 = 0; 15-10 = 5

(-5)^2 = 25; 0^2 = 0; 0^2 = 0; 0^2 = 0; 0^2 = 0; 0^2 = 0; 0^2 = 0; 5^2 = 25

25+0+0+0+0+0+0+25 = 50

50/8 = 6.25

√6.25 = 2.5

The standard deviation is 2.5.

This means two standard deviations, or 2σ, is 2(2.5) = 5.

This gives us μ-2σ = 10-5 = 5 and μ+2σ = 10+5 = 15.

Since all of our data is between 5 and 15, 100% is within two standard deviations of the mean.

5 0

3 years ago