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3 years ago

If LR = 12 and LP = 7, find PR. Explain.

Mathematics

2 answers:

sergiy2304 [10]3 years ago

5 0

Answer:

PR = 5 because LP + PR = LR according to the Segment Addition Postulate, and 7 + 5 = 12 using substitution

Step-by-step explanation:

The naming of the segments suggests that point P is between L and R, so that ...

LP + PR = LR

This corresponds to the last choice.

_____

Comments on the alternate interpretation

On the other hand, if point L is between P and R, then the segments are PL and LR. The Segment Addition Postulate would tell you that ...

PL + LR = PR

The Reflexive Property of Congruence would tell you that PL = LP. The Substitution Property would tell you LP can be substituted into this equation, making it ...

LP + LR = PR

and by the commutative property, ...

LR + LP = PR.

Multiple properties of addition and congruence are involved with this interpretation, which more or less matches the third choice. That is, the simple explanation of answer choice 3, by itself, is insufficient to explain why the length of PR should be considered to be 19, not 5.

inysia [295]3 years ago

3 0

Answer:

PR = 5 because LP + PR = LR according to the Segment Addition Postulate, and 7 + 5 = 12 using substitution.

Step-by-step explanation:

I am pretty sure i am right

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Find the? inverse, if it? exists, for the given matrix. [4 3] [3 6]

True [87]

Answer:

Therefore, the inverse of given matrix is

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

Step-by-step explanation:

The inverse of a square matrix $A$ is $A^{-1}$ such that

$A A^{-1}=I$ where I is the identity matrix.

Consider, $A = \left[\begin{array}{ccc}4&3\\3&6\end{array}\right]$

$\mathrm{Matrix\:can\:only\:be\:inverted\:if\:it\:is\:non-singular,\:that\:is:}$

$\det \begin{pmatrix}4&3 \\3&6\end{pmatrix}\ne 0$

$\mathrm{Find\:2x2\:matrix\:inverse\:according\:to\:the\:formula}:\quad \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}$

$=\frac{1}{\det \begin{pmatrix}4&3\\ 3&6\end{pmatrix}}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}$

$\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc$

$4\cdot \:6-3\cdot \:3=15$

$=\frac{1}{15}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}$

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

Therefore, the inverse of given matrix is

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

4 0

3 years ago

The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of m

UkoKoshka [18]

Answer:

Let X the random variable that represent the delivery times of a population, and for this case we know the distribution for X is given by:

$X \sim N(14.7,3.7)$

Where $\mu=14.7$ and $\sigma=3.7$

Since the distribution of X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we have;

$\mu_{\bar X}= 14.70$

$\sigma_{\bar X} =\frac{3.7}{\sqrt{40}}= 0.59$

Step-by-step explanation:

Assuming this question: The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of 14.7 minutes and a standard deviation of 3.7 minutes. Let R be the mean delivery time for a random sample of 40 orders at this restaurant. Calculate the mean and standard deviation of $\bar X$ Round your answers to two decimal places.

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the delivery times of a population, and for this case we know the distribution for X is given by:

$X \sim N(14.7,3.7)$

Where $\mu=14.7$ and $\sigma=3.7$

Since the distribution of X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we have;

$\mu_{\bar X}= 14.70$

$\sigma_{\bar X} =\frac{3.7}{\sqrt{40}}= 0.59$

4 0

3 years ago

Which expressions are equivalent to − 56 z + 28 −56z+28minus, 56, z, plus, 28? Choose 2 answers: Choose 2 answers: (Choice A) A

Dmitrij [34]

Answer:

$(D)-2(28z-14) \: and\:\\(E) -7(8z-4)$

Step-by-step explanation:

We are to determine which of these expressions are equivalent to: $-56 z + 28$

$(A)\frac{1}{2}\cdot(-28z+14) \\(B)(-1.4z+0.7)40\\(C)(14-7z)\cdot(-4)\\(D)(8z-4)(-7)\\(E)-2(-28z-14)$

$-56 z + 28$

If we factor out -2

$-56 z + 28=-2(\frac{ -56 z}{-2} + \frac{28}{-2})=-2(28z-14)$

If we factor out -7

$-56 z + 28=-7(\frac{ -56 z}{-7} + \frac{28}{-7})=-7(8z-4)$

Therefore, the two equivalent expressions are:

$-2(28z-14) \: and\: -7(8z-4)$

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2 years ago

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nika2105 [10]

Answer:

Step-by-step explanation:

3 0

3 years ago

Jones has a 100-acre farm. he sells it to a developer who is going to build houses. the developer will use 10% of the land for s

Sholpan [36]

The first thing we must do is find the amount of land that will be used for the 120 lots.
We must remember that 10% of the land will not be used for the lots.
We have then:
$100 - (0.10) * (100) = 100 - 10 = 90 acres.
$
Then, we must consider the following conversion of units:
$1 acre = 43560 ft ^ 2
$
Applying the conversion we have:
$(90) * (43560) = 3920400 ft ^ 2
$
Then, the amount of square feet for each lot is given by:
$3920400/120 = 32670 ft ^ 2
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Answer:
There will be 32670 square feet in each lot.

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3 years ago