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2 years ago

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200 cans of food were distributed to 3 charity homes. 2/5 of the cans were given to the first home, 1/3 of the remainder to the

second home and the rest to the third home. How many cans did the third home receive?

1 answer:

Mrrafil [7]2 years ago

8 0

I believe 80 cans were given

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The table shows the results of a poll of 200 randomly selected juniors and seniors who were asked if they attended prom. Find th

Zielflug [23.3K]

Answer:

(a) $\frac{7}{25}$

(b) $\frac{19}{116}$

(c) $\frac{28}{125}$

Step-by-step explanation:

Number of juniors who attended prom,n(J)=28

Number of seniors who attended prom,n(S)=97

Total of those who attended prom=125

Number of juniors who did not attend prom,n(J')=56

Number of seniors who did not attend prom,n(S')=19

Total of those who attended prom=75
Total Number of students=200

(a) P (a junior who did not attend prom)

$P(J')=\frac{56}{200}= \frac{7}{25}$

(b)

$P(Senior)=\frac{116}{200}$

$P ($did not attend prom$ | senior)=\frac{\text{P(seniors who did not attend prom)}}{P(Senior)} \\=\frac{19/200}{116/200} \\=\frac{19}{116}$

(c)P (junior | attended prom)

$P(Senior)=\frac{84}{200}$

$P (Junior|$ attended prom$)=\frac{\text{P(juniors who attended prom)}}{P(\text{those who attended prom)}} \\=\frac{28/200}{125/200} \\=\frac{28}{125}$

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2 years ago

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These questions are really important for me to answer please guys help me

marysya [2.9K]

Answer:

$\cos(41 = adj \div hyp$

$\cos(41) = \frac{y}{30cm}$

$y = \cos(41) \times 30$

y=29.62017

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2 years ago

Help fast ASAP for 10 points

Zina [86]

Answer:

PQRS → P'Q'R'S'

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Determine the angles made by the vector v = (67)i + (-15)j with the positive x- and y-axes. write the unit vector n in the direc

vivado [14]

Consider the picture attached.

From right triangle trigonometry:

tan(α)=(opposite side)/(adjacent side)=15/67=0.2239

using a scientific calculator we find that arctan(0.2239)=12.62°

thus α=12.62°, is the angle that the vector makes with the positive x-axis.

The angle made with the + y-axis is 12.62°+90°=102.62°.

The length of the vector v can be determined using the Pythagorean theorem:

$|v|= \sqrt{ 67^{2} + 15^{2} }= \sqrt{4489+225}= \sqrt{4714}=68.8$

Thus, to make v a unit vector, without changing its direction, we need to divide v by |v|=68.8.

This means that the x and y components will also be divided by 68.8, by proportionality.

So, the unit vector in the direction of v is:

<span>(67/68.8)i + (-15/68.8)j=0.97 i + (- 0.22)j
</span>

Answer: 12.62°; 102.62°; 0.97 i + (- 0.22)j

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2 years ago

I need the whole solution

ddd [48]

Confused what the question is. Are you looking for the product or the zeroes?

If you are looking for the product, then:

Use foil to get: sec²(1) - sec²(-csc²) -1(1) -1(-csc²)

= sec² + sec²csc² - 1 + csc²

= sec²csc² + sec² + csc² - 1

= sec²csc² + 1 - 1 (NOTE: sec² + csc² = 1 is an identity)

= sec²csc²

Answer: sec²csc²

***************************************************

If you are looking for the zeroes, then:

Using the zero product property, set each factor equal to zero and solve.

<u>First factor:</u>

sec²Θ - 1 = 0

sec²Θ = 1

secΘ = 1, -1

remember that secΘ is $\frac{1}{cos}$

$\frac{1}{cos}$ = 1 $\frac{1}{cos}$ = -1

cross multiply to get:

cosΘ = 1 cosΘ = -1

use the unit circle (or a calculator) to find that Θ = 0 and π

<u>Second factor:</u>

1 - csc²Θ = 0

1 = csc²Θ

1, -1 = cscΘ

remember that cscΘ is $\frac{1}{sin}$

$\frac{1}{sin}$ = 1 $\frac{1}{sin}$ = -1

cross multiply to get:

sinΘ = 1 sinΘ = -1

use the unit circle (or a calculator) to find that Θ = $\frac{\pi}{2}$ and $\frac{3\pi}{2}$

Answer: 0, π, $\frac{\pi}{2}$ , $\frac{3\pi}{2}$

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3 years ago