Evaluate the triple integral ∭Tx2dV, where T is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,3,0), and (0,0,3).

We opt to accept the null hypothesis. Given the following details provided: the Sample mean equals 28.8 miles per gallon, Sample size n is 120, and Alpha α is 0.01 with a sample standard deviation of 6.89 miles per gallon. Initially, we set up the null and alternative hypotheses. Utilizing a two-tailed t-test facilitates this hypothesis testing. By substituting the relevant values we calculate, and eventually conclude that we fail to reject the null hypothesis, endorsing that the average MPG for the Toyota Highlander Hybrid vehicles is indeed 28 miles per gallon.

Answer:

  E  None of the above

Step-by-step explanation:

A suitable proportion is...

 

or any other equivalent representation of this proportion. None of the provided options correspond with this, hence it is valid to select...

  None of the above.

Answer:

Given:

In the rhombus QRST, diagonals QS and RT cross at points W and U ∈ QR, while point V ∈ RT is such that UV⊥QR. (as illustrated in the diagram below)

To prove: QW•UR = WT•UV

Proof:

In a rhombus, the diagonals meet at right angles and bisect one another,

Thus, in QRST

QW≅WS, WR ≅ WT, and ∠QWR = ∠QWT = ∠RWS = ∠TWS = 90°.

Considering triangles QWR and UVR,

             (Right angles)

             (Shared angles)

By the AA similarity postulate,

The sides corresponding in similar triangles maintain proportionality,

                (∵ WR ≅ WT )

Thus, it is proved.