A lumber company is making boards that are 2599.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 23 is made, and it is found that they have a mean of 2600.3 millimeters with a standard deviation of 13.0. A level of significance of 0.05 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the boards are either too long or too short?

There is no sufficient evidence to support  the claim that the boards are either too long or too short

Step-by-step explanation:

From the question we are told that

   The  population mean is

    The sample size is  

     The  sample mean is  

    The  standard deviation is  

     The  level of significance is  

The  null hypothesis  is  

  The  alternative  hypothesis is

Generally the test statistics is mathematically represented as

=>          

=>            

Now from the normal distribution table  the critical value  of   is  

Hence from the evaluated and obtained value we see that

Hence we fail to reject the null hypothesis  

  Thus we can conclude that there is no sufficient evidence to support  the claim that the boards are either too long or too short

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.