A math teacher is investigating the problem of students losing their graphing calculators because their names aren’t written on them. In a random sample of 50 students, only 32 had their names written on their graphing calculators. The teacher constructs a 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators and obtains (0.465, 0.815). What is the correct interpretation of this confidence interval? The teacher can be 99% confident that a majority of students at this school write their names on their graphing calculators.

The teacher can be 99% confident that the interval from 46.5% to 81.5% captures the true proportion of students who write their names on their graphing calculators.

In 99% of samples taken, between 46.5% and 81.5% of the sampled students would write their names on their graphing calculators.

There is a 1% probability that the proportion of all students who write their names on their graphing calculators is either below 0.465 or above 0.815.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

Why you be expecting me to do your math u stupid butt? i ain't gonna but ima get points so you know what i'm sayin boii