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2 years ago

Find the coordinates of the midpoint of a segment with the given endpoints W(-12, -7), T(-8, -4)

2 answers:

4 0

Finding the midpoint coordinates of any segment really boils down to finding the midpoints of each individual coordinate.

The x-coordinates of the two points are -12 and -8 - the number halfway between those two is -10, so that'll be the midpoint's x-coordinate. The y-coordinates are -7 and -4 - -5.5 is halfway between these two, so the y-coordinate will be 5.5.

Putting the two together, the midpoint of the segment WT has the coordinates (-10, -5.5).

Ludmilka [50]2 years ago

3 0

You can find the midpoint with the following formula:

$\frac{x1+x2}{2}$ , $\frac{y1+y2}{2}$

Substitute the corresponding values into the formula.

$\frac{(-12)+(-8)}{2}$ , $\frac{(-7)+(-4)}{2}$

$\frac{-20}{2}$ , $\frac{-11}{2}$

-10, -5.5

The coordinates of the midpoint are (-10, -5.5).

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Triangle QRS is a right triangle with the right angle at vertex R. The sum of m∠Q and m∠S must be equal to 45°. greater than 45°

S_A_V [24]

According to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. If we know one angle is already 90, we do 180-90=90. The other 2 angles must add up to 90, exactly.

8 0

2 years ago

Read 2 more answers

A human body while sleeping generates about 300 BTUs of body heat per hour. If two people are sleeping in a bedroom that is 15 f

Katarina [22]

Given:
one person can produce:
E = 300 BTUs of body heat per hour
dimensions of the bedroom is:
V = 15 ft × 12 ft × 10 ft

required: is the energy per volume if 2 persons sleeps in 7 hours
let T be the total energy produce per volume

T = (300 BTU per hour per person) ( 7 hours) ( 2 person) / ( 15 ft × 12 ft × 10 ft)

T = 2.3 BTU / ft^3

4 0

1 year ago

A player of a video game is confronted with a series of four opponents and an 80% probability of defeating each opponent. Assume

mixer [17]

Answer:

(a) 0.4096

(b) 0.64

Step-by-step explanation:

The probability that the player wins is,

$P(W)=0.80$

Then the probability that the player losses is,

$P(L)=1-P(W)=1-0.80=0.20$

The player is playing the video game with 4 different opponents.

It is provided that when the player is defeated by an opponent the game ends.

All the possible ways the player can win is: {L, WL, WWL, WWWL and WWWW)

(a)

The results from all the 4 opponents are independent, i.e. the result of a game played with one opponent is unaffected by the result of the game played with another opponent.

The probability that the player defeats all four opponents in a game is,

P (Player defeats all 4 opponents) = $P(W)\times P(W)\times P(W)\times P(W)=[P(W)]^{4} =(0.80)^{4}=0.4096$

Thus, the probability that the player defeats all four opponents in a game is 0.4096.

(b)

The probability that the player defeats at least two opponents in a game is,

P (Player defeats at least 2) = 1 - P (Player losses the 1st game) - P (Player losses the 2nd game) = $1-P(L)-P(WL)$

$=1-(0.20)-(0.80\times0.20)\\=1-0.20-0.16\\=0.64$

Thus, the probability that the player defeats at least two opponents in a game is 0.64.

(c)

Let X = number of times the player defeats all 4 opponents.

The probability that the player defeats all four opponents in a game is,

P(WWWW) = 0.4096.

Then the random variable $X\sim Bin(n=3, p=0.4096)$

The probability distribution of binomial is:

$P(X=x)={n\choose x}p^{x} (1-p)^{n-x}$

The probability that the player defeats all the 4 opponents at least once is,

P (X ≥ 1) = 1 - P (X < 1)

= 1 - P (X = 0)

$=1-[{3\choose 0}(0.4096)^{0} (1-0.4096)^{3-0}]\\=1-[1\times1\times (0.5904)^{3}\\=1-0.2058\\=0.7942$

Thus, the probability that the player defeats all the 4 opponents at least once is 0.7942.

3 0

1 year ago

A home’s value increases at an average rate of 5.5% each year. The current value is $120,000. What function can be used to find

Wewaii [24]

Answer:

$y=120,000(1.055)^x$

Step-by-step explanation:

we know that

The equation of a exponential growth function is given by

$y=a(1+r)^x$

where

y is the value of the home

x is the number of years

a is the initial value

r is the rate of change

we have

$a=\$120,000\\r=5.5\%=5.5/100=0.055$

substitute

$y=120,000(1+0.055)^x$

$y=120,000(1.055)^x$

7 0

2 years ago

How many ounces of pure nickel must be added to 150 ounces of alloy 70% pure to make an alloy which is 85% pure?

galben [10]

Answer:

150 oz.

Step-by-step explanation:

There are already 150 ounces of alloy of nickel.

Of this 150 oz, 70% is pure i.e. nickel content = 150(0.7) = 105 oz

Now available is

Nickel Other metals

105 45

Let x oz of pure nickel is added.

Then new alloy will have 105+x oz nickel in total of 150+x oz.

Percentage pure = $\frac{105+x}{150+x} =85%$

Simplify to get

$\frac{105+x}{150+x} =\frac{85}{100} \\\\Cross multiply:\\85(150+x) =100(105+x)\\12750+85x =10500+100x\\100x-85x = 12750-10500\\15x = 2250\\x = 150$

Hence answer is 150 oz should be added.

6 0

1 year ago