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Ostrovityanka [42]
3 years ago
5

Suppose PR = 54, solve for QR 4x-1 3x-1 P R

Mathematics
1 answer:
Svet_ta [14]3 years ago
5 0

Answer:

QR = 23

Step-by-step explanation:

P, A, and R are collinear.

PR = 54

PQ = 4x - 1

QR = 3x - 1

To solve for the numerical length of PR, let's generate an equation to find the value of x.

According to the segment addition postulate:

PQ + QR = PR

(4x - 1) + (3x - 1) = 54 (substitution)

Solve for x

4x - 1 + 3x - 1 = 54

Combine like terms

4x + 3x - 1 - 1 = 54

7x - 2 = 54

Add 2 to both sides

7x - 2 + 2 = 54 + 2

7x = 56

Divide both sides by 7

\frac{7x}{7} = \frac{56}{7}

x = 8

QR = 3x - 1

Plug in the value of x into the equation

QR = 3(8) - 1 = 24 - 1

QR = 23

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A dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population of cows. She randomly as
mina [271]

Answer:

Step-by-step explanation:

Given that a dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population of cows. She randomly assigns nold = 8 to get the old diet, and nnew = 5 to get the new diet including the additive.

From the data given we get the following

           N       Mean      StDev     SE Mean

Sample   1    8           43       5.1824 1.832

Sample   2   5           73     21.0832 9.429

df = 11

Std dev for difference = 13.3689

a) Yes the two are independent.  The two sets of cows randomly chosen are definitely independent. Paired means equal number should be there and homogeneous conditions should be maintained.

b) Enclosed

c) Comparison of two means is the test recommended here.  Because independent samples are used.\

d) Test statistic= -3.1233

(because of unequal variances we use that method)

95% confidence interval =  ( -56.6676 , -3.3324 )

p value <0.05 our alpha

So reject null hypothesis.

The two means are statistically significantly different.

3 0
3 years ago
If the coefficient of determination for a data set is 0.75 and the SSE for the data set is 13, what is the SST for the data set?
nadya68 [22]
Answer : SSE = 9
r^2 = 0.75
r^2 = 1 - (SSE/SST)
SSE/SST = 1 - r^2 = 1 - 0.75 = 0.25
<span>SST = 9/0.25 = 36</span>
8 0
3 years ago
Read 2 more answers
Write 0.216 as a rational number in lowest terms
lozanna [386]

Answer:

=\frac{27}{125}

Step-by-step explanation:

0.216

\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}

\mathrm{There\:are\:}3\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\:therefore\:multiply\:and\:divide\:by\:}1000

=\frac{0.216\cdot \:1000}{1000}

=\frac{216}{1000}

216,\:1000

\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}

2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}

=2\cdot \:2\cdot \:2\cdot \:3\cdot \:3\cdot \:3

2,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}

=2\cdot \:2\cdot \:2\cdot \:5\cdot \:5\cdot \:5

\mathrm{The\:prime\:factors\:common\:to\:}216,\:1000\mathrm{\:are\:}

=2\cdot \:2\cdot \:2

\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2=8

=8

=\frac{8\cdot \:27}{8\cdot \:125}

\mathrm{Cancel\:the\:common\:factor:}\:8

=\frac{27}{125}

Hence, the correct answer is =\frac{27}{125}

6 0
2 years ago
You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 5 d
Salsk061 [2.6K]

Answer:

1/15

Step-by-step explanation:

You have a 1/3 chance of being an elf.

You have a 1/5 change of having the magic tool.

1/3 × 1/5 = 1×1/3×5 = 1/15

5 0
3 years ago
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Find the range of possible lengths of the third side using the given side lengths <br> 10, 7
Tomtit [17]

Answer:

3 < x < 17

Step-by-step explanation:

Given 2 sides then the possible range of the third side x is

difference of 2 sides < x < sum of 2 sides , that is

10 - 7 < x < 10 + 7

3 < x < 17

8 0
3 years ago
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