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2 years ago

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The school auditorium has 900 seats. The inequality, with x representing adults and y representing children, can be solved to fi

nd the possible combinations of adults and children attending an event. Which reason describes why the ordered pair (450, 450) must be included in the solution set of the inequality?

1 answer:

Paha777 [63]2 years ago

5 0

Answer:

Step-by-step explanation:

The ordered pair is located on the boundary line of the graph of the inequality, and because the sign is "less than or equal to", the values on the boundary line are also included in the solution set.

Looking at this logically, we also see that it certainly possible for half the seats to be occupied by adults and half by children.

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Bernard solved the equation 5x+(-4)=6x+4 using algebra tiles.Which explains why Bernard added 5 negative x-tiles to both sides i

Volgvan

5x+(-4)-5x=6x+4-5x
-4=x+4
x=-8

To get rid of 5x on the left side.

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2 years ago

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Can someone answer this correctly pls

AleksandrR [38]

Answer:

i = 45% and ii = 47% (Rounded)

Step-by-step explanation:

Simply divide 27 by 60 to get i:

27/60=.45

Convert to a percent chance.

.45=45%

Then divide 395 by 840 to get ii:

395/840=.47

Convert to a percent chance.

.47=47%

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1 year ago

Question 8. PV = nRT, solve for T please?<br><br>Question 10. C= Wtc÷1000, solve for W, please?

sp2606 [1]

Answers:

$\huge \boxed{T= \frac{P V}{n R} } \\ \\ \\ \\ \huge \boxed{W= \displaystyle \frac{1000C }{tc}}$

$\rule[225]{225}{2}$

Step-by-step explanation:

<h2>8.</h2>

$P \cdot V = n \cdot R \cdot T$

Dividing both sides by n · R:

$\displaystyle \frac{P \cdot V}{n \cdot R} =T$

<h2>9.</h2><h2 />

$\displaystyle C=\frac{Wtc }{1000}$

Multiplying both sides by 1000:

$1000C=Wtc$

Dividing both sides by tc:

$\displaystyle \frac{1000C }{tc}=W$

<h2 />

$\rule[225]{225}{2}$

4 0

2 years ago

In a triangle ,Angle B is twice as large as Angle A.Angle C is five more than Angle B. What are the angle measurements of Angles

777dan777 [17]

Answer:

∠ A = 35°, ∠ B = 70°, ∠ C = 75°

Step-by-step explanation:

let ∠ A be x then ∠ B is 2x ( twice as large as A ) and

∠ C is 2x + 5 ( 5 more than B )

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

x + 2x + 2x + 5 = 180, that is

5x + 5 = 180 ( subtract 5 from both sides )

5x = 175 ( divide both sides by 5 )

x = 35

Thus

∠ A = x = 35°

∠ B = 2x = 2 × 35° = 70°

∠ C = 2x + 5 = 70 + 5 = 75°

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2 years ago

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Suppose that X has a discrete uniform distribution on the integers 0 through 9. Determine the mean, variance, and standard devia

Anna35 [415]

With 10 integers available, $X$ has PMF

$\mathbb P(X=x)=\begin{cases}\dfrac1{10}&\text{for }0\le x\le9,x\in\mathbb Z\\\\0&\text{otherwise}\end{cases}$

We're interested in the statistics of the new random variable $Y=5X$ . To do this, we need to know the PMF for $Y$ . This isn't too hard to find.

$\mathbb P(Y=y)=\mathbb P(5X=y)=\mathbb P\left(X=\dfrac y5\right)$

Since the PMF for $X$ gives a value of $\dfrac1{10}$ whenever $x$ is an integer between 0 and 9, it follows that $\dfrac y5$ must also be an integer for the PMF to give the identical value of $\dfrac1{10}$ . This means

$\mathbb P(Y=y)=\begin{cases}\dfrac1{10}&\text{for }y\in\{0,5,\ldots,45\}\\\\0&\text{otherwise}\end{cases}$

Now the mean (expectation) is

$\mathbb E(Y)=\displaystyle\sum_yy\mathbb P(Y=y)=\frac1{10}\sum_{y\in\{0,\ldots,45\}}y$
$\mathbb E(Y)=\dfrac{225}{10}=22.5$

The variance would be

$\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2$
$\mathbb V(X)=\displaystyle\sum_yy^2\mathbb P(Y=y)-\mathbb E(Y)^2$
$\mathbb V(X)=\displaystyle\frac1{10}\sum_{y\in\{0,\ldots,45\}}y^2-\left(\frac{225}{10}\right)^2$
$\mathbb V(X)=\dfrac{7125}{10}-\dfrac{50625}{100}=206.25$

The standard deviation is the square root of the variance, so you have

$\sqrt{\mathbb V(X)}=\sqrt{206.25}\approx14.3614$

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2 years ago