The weights of running shoes are normally distributed with a population standard deviation of 3 ounces and an unknown population mean. if a random sample of 23 running shoes is taken and results in a sample mean of 18 ounces, find a 90% confidence interval for the population mean.

Step-by-step explanation:

Given : Level of significance :

Then , significance level :

Since , sample size : , which is small sample (n<30) so the test applied here is a t-test.

Sample mean :

Standard deviation:

Degree of freedom=

Using t-distribution table , Critical value :

The confidence interval for population mean is given by :-

Hence,  a 90% confidence interval for the population mean=

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.