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3 years ago

Part A: Divide (8x4y3 + 4x3y2 - 2x2y - 12x2y4) by -2x2y. Show your work, and justify each step.

1 answer:

5 0

Let's simplify step-by-step.8x4y3+4x3y2−2x2y−12x2y4=8x4y3+4x3y2+−2x2y+−12x2y4Answer:=8x4y3−12x2y4+4x3y2−2x2y

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The coordinates of a point on a coordinate grid are (−2, 6). The point is reflected across the x-axis to obtain a new point. The

Juliette [100K]

The reflected coordinate will be (-2,-6)

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3 years ago

Read 2 more answers

Conduct the appropriate hypothesis test and compute the test statistic. A company that produces fishing line undergoes random te

andre [41]

Answer:

Option D) Yes, because the test statistic is -2.01

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 30 pound

Sample mean, $\bar{x}$ = 29.1 pounds

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, s = 2 pounds

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 30\text{ pounds}\\H_A: \mu < 30\text{ pounds}$

We use one-tailed(left) t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{29.1 - 30}{\frac{2}{\sqrt{20}} } = -2.012$

Now,

$t_{critical} \text{ at 0.05 level of significance, 19 degree of freedom } = -1.729$

Since,

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis. Thus, there were enough evidence to conclude that the fishing line breaks with an average force of less than 30 pounds.

Option D) Yes, because the test statistic is -2.01

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3 years ago

Kevin counts 75 chicks in the hen house. He also sees more chicks outside the hen house. How can Kevin count to find how many ch

stellarik [79]

What we know:

we know that there are 75 chicks in the hen house, we also know that in all there are 108 chicks

What we need to find:

we need to find out how many chicks were outside

Answer equation:

108 - 75 = 33

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3 years ago

What is 78,400,000 expressed in scientific notation?

Virty [35]

Answer:

7.84 × 10 ^7

Step-by-step explanation:

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2 years ago

Let M be the set of all nxn matrices. Define a relation on won M by A B there exists an invertible matrix P such that A = P BP S

Sophie [7]

Answer:

Recall that a relation is an equivalence relation if and only if is symmetric, reflexive and transitive. In order to simplify the notation we will use A↔B when A is in relation with B.

Reflexive: We need to prove that A↔A. Let us write J for the identity matrix and recall that J is invertible. Notice that $A=J^{-1}AJ$ . Thus, A↔A.

Symmetric: We need to prove that A↔B implies B↔A. As A↔B there exists an invertible matrix P such that $A=P^{-1}BP$ . In this equality we can perform a right multiplication by $P^{-1}$ and obtain $AP^{-1} =P^{-1}B$ . Then, in the obtained equality we perform a left multiplication by P and get $PAP^{-1} =B$ . If we write $Q=P^{-1}$ and $Q^{-1} = P$ we have $B = Q^{-1}AQ$ . Thus, B↔A.

Transitive: We need to prove that A↔B and B↔C implies A↔C. From the fact A↔B we have $A=P^{-1}BP$ and from B↔C we have $B=Q^{-1}CQ$ . Now, if we substitute the last equality into the first one we get

$A=P^{-1}Q^{-1}CQP = (P^{-1}Q^{-1})C(QP)$ .

Recall that if P and Q are invertible, then QP is invertible and $(QP)^{-1}=P^{-1}Q^{-1}$ . So, if we denote R=QP we obtained that

$A=R^{-1}CR$ . Hence, A↔C.

Therefore, the relation is an equivalence relation.

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3 years ago