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2 years ago

Compute P7,2. (Enter an exact number.)

Mathematics

2 answers:

Katarina [22]2 years ago

8 0

Answer:

Step-by-step explanation:

The permutation formula is P(n, r) = n! / (n - r)!. We know that n = 7 and r = 2 so we can write:

7! / (7 - 2)!

= 7! / 5!

= 7 * 6 * 5 * 4 * 3 * 2 * 1 / 5 * 4 * 3 * 2 * 1

= 7 * 6 (5 * 4 * 3 * 2 * 1 cancels out)

= 42

Simora [160]2 years ago

3 0

Answer:

$\boxed{42}$

Step-by-step explanation:

Apply the permutation formula.

$P(n,r)=\frac{n!}{ (n-r)!}$

$P=number \: of \: permutations\\n=total \: number \: of \: objects \: in \: the \: set\\r=number \: of \: choosing \: objects \: from \: the \: set\\$

$n=7\\r=2$

Plug in the values and evaluate.

$P(7,2)=\frac{7!}{ (7-2)!}$

$P(7,2)=\frac{7!}{ (5)!}$

$P(7,2)=\frac{5040}{120}$

$P(7,2)=42$

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Step-by-step explanation:

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2 years ago

A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored

pickupchik [31]

Answer:

We conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.

Step-by-step explanation:

The complete question is: A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were:

Number sampled: 1,000 (republican) , 800 (democrats)

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$p_2$ = proportion of Democrats in favor of lowering the standards.

SO, Null Hypothesis, $H_0$ : $p_1 \geq p_2$ {means that there is an equal or larger proportion of Republicans in favor of lowering the standards}

Alternate Hypothesis, $H_A$ : $p_1 < p_2$ {means that there is a larger proportion of Democrats in favor of lowering the standards}

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where, $\hat p_1$ = sample proportion of Republicans in favor of lowering the standards = $\frac{200}{1000}$ = 0.20

$\hat p_2$ = sample proportion of Democrats in favor of lowering the standards = $\frac{168}{800}$ = 0.21

$n_1$ = sample of Republicans = 1000

$n_2$ = sample of Democrats = 800

So, the test statistics = $\frac{(0.20-0.21)-(0)}{\sqrt{\frac{0.20(1-0.20)}{1000}+\frac{0.21(1-0.21)}{800} } }$

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The value of z test statistics is -0.52.

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P-value = P(Z < -0.52) = 1 - P(Z $\leq$ 0.52)

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Answer:

1) c ║ d by consecutive interior angles theorem

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3) ∠2 ≅ ∠5 by definition of congruency

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6) ∠8 and ∠9 are supplementary ${}$ Consecutive interior angles theorem

Step-by-step explanation:

1) Statement ${}$ Reason

m∠4 + m∠7 = 180° ${}$ Given

m∠4 ≅ m∠6 ${}$ Vertically opposite angles

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2) Statement ${}$ Reason

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∴ m∠3 + m∠6 = 180° ${}$ Transitive property

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∠2 = ∠1 ${}$ Definition of congruency

∠2 = ∠5 ${}$ Transitive property

∠2 ≅ ∠5 ${}$ Definition of congruency.

4) Statement ${}$ Reason

∠1 ≅ ∠5 ${}$ Given

∠3 ≅ ∠4 ${}$ Given

∠1 = ∠5 ${}$ Definition of congruency

∠3 = ∠4 ${}$ Definition of congruency

∠5 ≅ ∠4 ${}$ Vertically opposite angles

∠5 = ∠4 ${}$ Definition of congruency

∠5 = ∠3 ${}$ Transitive property

∠1 = ∠3 ${}$ Transitive property

∠1 ≅ ∠3 ${}$ Definition of congruency.

t ║ v ${}$ Corresponding angle theorem

5) Statement ${}$ Reason

∠5 ≅ ∠16 ${}$ Given

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∠2 = ∠4 ${}$ Definition of congruency

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∠5 + ∠11 = 180° ${}$ Sum of angles on a straight line

∠14 + ∠11 = 180° ${}$ Transitive property

∠14 and ∠11 are supplementary ${}$ Definition of supplementary angles

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∠2 = ∠4 ${}$ Transitive property

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∠2 and ∠4 are corresponding angles ${}$ Definition

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∠8 and ∠9 are supplementary ${}$ Consecutive interior angles theorem.

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2 years ago

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Pavel [41]

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( $\partial E$ denotes the boundary of $E$ ), we want to find $M(x,y)$ and $L(x,y)$ such that

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The line integral is then

$\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy$

We parameterize the boundary by

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with $0\le t\le2\pi$ . Then the integral is

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###

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