I need X please and thank you

How many solutions exist for the given equation?

irakobra [83]

Answer:

Its infinite solutions

Step-by-step explanation:

7 0

2 years ago

If a cyclist increases his speed by 3 miles per hour, he can reduce the time required for a 6 mile trip by 10 minutes. What is t

raketka [301]

Answer:

Slower speed = 9 mph

Step-by-step explanation:

Let the initial speed (slower speed) = s mph

Speed 's' = $\frac{\text{Distance}}{\text{Time}}$

s = $\frac{6}{t}$ -------(1)

If the cyclist increases the speed by 3 mph then the final speed = (s + 3) mph

He can reduce the time 't' by 10 minutes ( $\frac{1}{6}$ hours)

Now, (s + 3) = $\frac{6}{t-\frac{1}{6}}$

s + 3 = $\frac{36}{6t-1}$ --------(2)

Substitute the value of 's' from equation (1) to the equation (2).

$\frac{6}{t}+3=\frac{36}{6t-1}$

$\frac{2}{t}+1=\frac{12}{6t-1}$

$\frac{2}{t}-\frac{12}{6t-1}=-1$

$\frac{2(6t-1)-12t}{t(6t-1)}=-1$

$\frac{12t-2-12t}{t(6t-1)}=-1$

$-\frac{2}{t(6t-1)}=-1$

6t² - t = 2

6t² - t - 2 = 0

6t² - 4t + 3t - 2 = 0

2t(3t - 2) + 1(3t - 2) = 0

(2t + 1)(3t - 2) = 0

t = $-\frac{1}{2},\frac{2}{3}$ hours

But the time can't be negative.

Therefore, t = $\frac{2}{3}$ hours is the answer.

From equation (1),

s = $\frac{6}{\frac{2}{3}}$

s = 9 miles per hour.

Slower speed = 9 mph is the answer.

6 0

2 years ago

Billy left home at 9 a.M. And rode his bicycle to the park at an average speed of 10 miles per hour here I got the park at 9:30

tamaranim1 [39]

Answer:

Park is 5 miles from Billy's home.

Step-by-step explanation:

Given:

Billy left home at 9 a.m. And rode his bicycle to the park at an average speed of 10 miles per hour here and got the park at 9:30 a.m.

Now, to find the distance from park to Billy,s home.

Time it took Billy to rode his bicycle from park to home is from 9.30 a.m to 9.30 p.m.

So, the time = (9.30 - 9.00) = 30 minutes

$=\frac{30}{60}$ $=0.5\ hour.$

Speed = 10 miles per hour.

Now, to get the distance from park to Billy's home we put formula:

$Distance=Speed\times Time.$

$Distance=10\times 0.5$

$Distance=5\ miles.$

Therefore, park is 5 miles from Billy's home.

3 0

2 years ago

More comparing decimals

Lisa [10]

When comparing, think of the signs as a crocodile. A crocodile will want to eat greater (bigger) numbers than smaller numbers. So, you can think of it as that way.

2. 0.5 < 0.8 ... 0.8 is greater than 0.5

5. 0.7 = 0.70 ... This is same. 0.70 just has an extra 0 which you don't need.

8. 2.9 > 2.8 ... 2.9 is greater since 9 is bigger than 8.

11. 0.65 > 0.36 ... 65 is greater than 36. Therefore, 0.65 is greater.

14. 4.50 > 4.05 ... 4.50 has a five in the tenth place. 4.05 has five in the hundredth place.

17. 6.01 < 6.1 ... 6.1 has a one in the tenth place. 6.01 has a one in the hundredth place.

5 0

3 years ago

What is the value of the correlation coefficient r of the data set?

enyata [817]

The correct option will be: C) 0.84

Explanation

Formula for Correlation coefficient :

$r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}$

First, for each point(x, y), we need to calculate x², y² and xy .

Then, we will find sum all x, y, x², y² and xy, which gives us Σx, Σy, Σx², ∑y² and Σxy

(Please refer to the attached image for the table )

Here we got, ∑x = 44 , ∑y = 183 , ∑x² = 362 , ∑y² = 6575 and ∑xy = 1480

'n' is the total number of data set, which is 7 here.

So, plugging those values into the above formula..........

$r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}\\ \\ r=\frac{7(1480)-(44)(183)}{\sqrt{[7(362)-(44)^2][7(6575)-(183)^2]}}\\ \\ r=\frac{10360-8052}{\sqrt{(598)(12536)}}\\ \\ r=\frac{2308}{\sqrt{7496528}}\\ \\ r=0.84$

So, the value of the correlation coefficient is 0.84

4 0

2 years ago

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