A train 182m long takes 14sec to cross a signal post .calculate speed in km/hr

Cerrena [4.2K]

37 because theres 32 plus 5 which makes it 37

5 0

3 years ago

In a random sample of 5 residents of the state of Texas, the mean waste recycled per person per day was 1.9 pounds with a standa

sammy [17]

<h2>Answer with explanation:</h2><h2 />

The confidence interval for population mean is given by :-

$\overline{x} \pm\ t_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : n= 5, since n<30 , so the test we use here is t-test.

Sample mean : $\overline{x}=1.9\text{ pounds}$

Standard deviation: $\sigma=0.89\text{ pounds}$

Significance level : $1-\alpha:1-0.99=0.01$

By using the standard normal distribution table , the critical value corresponds to the given significance level will be :-

$t_{n-1,\alpha/2}=t_{5-1,0.01/2}=t_{4,0.005}=4.604$

Now, the 99% confidence interval for the mean waste recycled per person per day for the population of Texas will be :-

$1.9\pm\ (4.604)\dfrac{0.89}{\sqrt{5}}\\\\\approx1.9\pm1.832\\\\=(1.9-1.832,1.9+1.832)=(0.068,\ 3.732)$

Hence, the 99% confidence interval for the mean waste recycled per person per day for the population of Texas = (0.068, 3.732)

5 0

3 years ago

Please help with the question in the picture!

Stella [2.4K]

Answer:

Tan C = 3/4

Step-by-step explanation:

Given-

∠ A = 90°, sin C = 3 / 5

METHOD - I

Sin² C + Cos² C = 1

Cos² C = 1 - Sin² C

Cos² C = $1 - \frac{9}{25}$

Cos² C = $\frac{25 - 9}{25}$

Cos² C = $\frac{16}{25}$

Cos C = $\sqrt{\frac{16}{25} }$

Cos C = $\frac{4}{5}$

As we know that

Tan C = $\frac{Sin C}{Cos C }$

Tan C = $\frac{\frac{3}{5} }{\frac{4}{5} }$

Tan C = $\frac{3}{4}$ 

METHOD - II

Given Sin C = $\frac{3}{5} = \frac{Height}{Hypotenuse}$

therefore,

AB ( Height ) = 3; BC ( Hypotenuse) = 5

∵ ΔABC is Right triangle.

∴ By Pythagorean Theorem-

AB² + AC² = BC²

AC² = BC² - AB²

AC² = 5² - 3²

AC² = 25 - 9

AC² = 16

AC ( Base) = 4

Since,

Tan C = $\frac{Height}{Base}$ 

Tan C = $\frac{AB}{AC}$

Hence Tan C = $\frac{3}{4}$ 

4 0

3 years ago

What is the slope of -2x + 4y = 12 ?

Daniel [21]

Answer:

Slope: 1/4

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Write the series using summation notation. Then find the sum of the series.

ivolga24 [154]

Hello, please consider the following.

$\displaystyle 1+2+3+...+12=\sum_{k=1}^{k=12} {k}=\dfrac{12*13}{2}=6*13=78$

For the second we will need to put on the same denominator.

$\displaystyle \dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{14}=\sum_{k=1}^{k=7} {\dfrac{1}{2k}}\\\\=\dfrac{1}{2}\dfrac{420+210+140+105+84+70+60}{5*7*3*2*2}\\\\=\dfrac{1}{2}\dfrac{1089}{420}\\\\=\dfrac{1089}{840}=1.296429...$

Thank you.

3 0

3 years ago