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1 year ago

The scale on a map is 2 in. =250 miles. If Toledo and Kansas City are 2.25 in. How far are they apart in real life?

Mathematics

1 answer:

yanalaym [24]1 year ago

4 0

Answer:

281.25 miles

Step-by-step explanation:

2=250

1=125

0.5=62.5

0.25=31.25

250+31.25=281.25

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Sav [38]

Answer:

x=17

Step-by-step explanation:

ok so since lines PR and RQ are congruent (we know because of the lines on them), that means angles P and Q are also equal.

now we can set up the equation to find x like this:

29+29+(8x-14)=180 (180 because the three angles of a triangle always equal 180)

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2 years ago

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scZoUnD [109]

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3 years ago

What is the midpoint of the segment show below? can anybody answer it fast

galben [10]

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3 years ago

In ΔOPQ, the measure of ∠Q=90°, the measure of ∠O=26°, and QO = 4.9 feet. Find the length of PQ to the nearest tenth of a foot.

Step2247 [10]

Given:

In ΔOPQ, m∠Q=90°, m∠O=26°, and QO = 4.9 feet.

To find:

The measure of side PQ.

Solution:

In ΔOPQ,

$m\angle O+m\angle P+m\angle Q=180^\circ$ [Angle sum property]

$26^\circ+m\angle P+90^\circ=180^\circ$

$m\angle P+116^\circ=180^\circ$

$m\angle P=180^\circ -116^\circ$

$m\angle P=64^\circ$

According to Law of Sines, we get

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

Using the Law of Sines, we get

$\dfrac{p}{\sin P}=\dfrac{o}{\sin O}$

$\dfrac{QO}{\sin P}=\dfrac{PQ}{\sin O}$

Substituting the given values, we get

$\dfrac{4.9}{\sin (64^\circ)}=\dfrac{PQ}{\sin (26^\circ)}$

$\dfrac{4.9}{0.89879}=\dfrac{PQ}{0.43837}$

$\dfrac{4.9}{0.89879}\times 0.43837=PQ$

$2.38989=PQ$

Approximate the value to the nearest tenth of a foot.

$PQ\approx 2.4$

Therefore, the length of PQ is 2.4 ft.

4 0

2 years ago

A deck of 52 cards contains 12 picture cards. If the 52 cards are distributed in a random manner among four players in such a wa

Mkey [24]

Answer:

The probability that each player will receive three picture cards = 0.0324

Step-by-step explanation:

As given,

A deck of 52 cards contains 12 picture cards

Remaining card = 52 - 12 = 40

So,

Total number of ways in which 12 picture card is distributed = $\frac{12!}{3! 3! 3! 3!}$

Now,

The Total number of ways in which Remaining cards are distributed = $\frac{40!}{10! 10! 10! 10!}$

So,

Total number of ways of getting 3 picture card and remaining card = $\frac{12!}{3! 3! 3! 3!}$ × $\frac{40!}{10! 10! 10! 10!}$

= $\frac{12! 40!}{(3!)^{4} (10!)^{4} }$

Now,

Total number of ways to distribute 52 cards so that each people get 13 card = $\frac{52!}{13! 13! 13! 13!} = \frac{52!}{ (13!)^{4} }$

∴ The probability = $\frac{\frac{12! 40!}{(3!)^{4} (10!)^{4} }}{\frac{52!}{(13!)^{4} }}$

= $\frac{12! 40!}{(3!)^{4} (10!)^{4} }$ × $\frac{(13!)^{4} }{ 52! }$

= $\frac{12! 40!}{(3!)^{4} (10!)^{4} }$ × $\frac{(13.12.11.10!)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41.40! }$

= $\frac{12!}{(3!)^{4} }$ × $\frac{(13.12.11)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}$

= $\frac{479,001,600}{(6)^{4} }$ × $\frac{(1716)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}$

= 0.0324

∴ we get

The probability that each player will receive three picture cards = 0.0324

6 0

2 years ago