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marishachu [46]

2 years ago

14

If line WP is a median and an angle bisector, AP = 3y+11, PH = 7y - 5, angle HWP = x +12, angle PAW = 3x - 2, and angle HWA = 4x

- 16, find x and y. Is WP also an altitude? Explain.

1 answer:

zmey [24]2 years ago

8 0

∠ HWA / 2 = ∠HWP
( 4 x - 16 ) / 2 = x + 12
4 x - 16 = 2 x + 24
2 x = 40
x = 20
AP = PH
3 y + 11 = 7 y - 5
16 = 4 y
y = 4
∠PAW = 60 - 2 = 58°
∠PWA = 32°, ∠PWH = 32°
∠AWH = 64°
∠WHA = 58°
Therefore Δ AWH is isosceles. Line WP is an altitude because it bisects the base of an isosceles triangle.

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mamaluj [8]

Answer:

The maximum volume of space that 1,000 BTUs will cool is 400 cubic foot.

Step-by-step explanation:

Given : A total of 1,000 BTUs are needed to cool a space. If 2.5 BTUs are needed to cool 1 cubic foot of space.

To find : What is the maximum volume of space that 1,000 BTUs will cool?

Solution :

Applying unitary method,

2.5 BTU are needed to cool 1 cubic foot of space.

So, 1 BTU are needed to cool $\frac{1}{2.5}$ cubic foot of space.

Then,1000 BTU are needed to cool $\frac{1}{2.5}\times 1000$ cubic foot of space.

i.e. 1000 BTU are needed to cool 400 cubic foot of space.

Therefore, the maximum volume of space that 1,000 BTUs will cool is 400 cubic foot.

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2 years ago

Consider two independent tosses of a fair coin. Let A be the event that the first toss results in heads, let B be the event that

aliina [53]

Answer with Step-by-step explanation:

We are given that two independent tosses of a fair coin.

Sample space={HH,HT,TH,TT}

We have to find that A, B and C are pairwise independent.

According to question

A={HH,HT}

B={HH,TH}

C={TT,HH}

$A\cap B=$ {HH}

$B\cap C$ ={HH}

$A\cap C$ ={HH}

P(E)= $\frac{number\;of\;favorable\;cases}{total\;number\;of\;cases}$

Using the formula

Then, we get

Total number of cases=4

Number of favorable cases to event A=2

$P(A)=\frac{2}{4}=\frac{1}{2}$

Number of favorable cases to event B=2

Number of favorable cases to event C=2

$P(B)=\frac{2}{4}=\frac{1}{2}$

$P(C)=\frac{2}{4}=\frac{1}{2}$

If the two events A and B are independent then

$P(A)\cdot P(B)=P(A\cap B)$

$P(A\cap)=\frac{1}{4}$

$P(B\cap C)=\frac{1}{4}$

$P(A\cap C)=\frac{1}{4}$

$P(A)\cdot P(B)=\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}$

$P(B)\cdot P(C)=\frac{1}{4}$

$P(A)\cdot P(C)=\frac{1}{4}$

$P(A)\cdot P(B)=P(A\cap B)$

Therefore, A and B are independent

$P(B)\cdot P(C)=P(B\cap C)$

Therefore, B and C are independent

$P(A\cap C)=P(A)\cdot P(C)$

Therefore, A and C are independent.

Hence, A, B and C are pairwise independent.

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2 years ago

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alexgriva [62]

Answer:

x = 1.5

Step-by-step explanation:

Given

$\frac{x}{2} \geq 0.75$

$\frac{x}{2} < 2.5$

Required

Find the value of x.

First, the inequalities need to be rewritten and merged;

if $\frac{x}{2} \geq 0.75$ , then

$0.75 \leq \frac{x}{2}$

Multiply both sides by 2

$2 * 0.75 \leq \frac{x}{2} * 2$

$1.5 \leq x$

Similarly;

$\frac{x}{2} < 2.5$

Multiply both sides by 2

$2 * \frac{x}{2} < 2.5 * 2$

$x < 5$

Merging these results together; to give

$1.5 \leq x < 5$

This means that the range of values of x is from 1.5 to 4.9999....

From the question, x is the smallest rational number; from the range above ( $1.5 \leq x < 5$ ), the minimum value of x is 1.5 and 1.5 is a rational number;

Hence, x = 1.5

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Answer:

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Step-by-step explanation:

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