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lianna [129]
3 years ago
11

A teacher took 25 students on a field trip to a museum. Of the 25 students, 16 students had never been to a museum before. What

percent of the students had never been to a museum?
Mathematics
1 answer:
nikdorinn [45]3 years ago
6 0

Answer:

Percentage of the students that have never been to a museum = 64%

Step-by-step explanation:

The teacher took 25 students on a field trip to a museum. This means Total number of students( students that have been to the museum before + students that have not been to the museum before ) = 25 students

Students that have never been to a museum before = 16 students

Percentage of the students that have never been to a museum =(16/25)×100 =0.64×100

=64%

Therefore,

Percentage of students that have been to the museum is 100-64 =36%

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Find sin(a+b) if tan(a)=7/24 where a is in the third quadrant
ludmilkaskok [199]
The complete question in the attached figure

we have that
tan a=7/24    a----> III quadrant
cos b=-12/13   b----> II quadrant
sin (a+b)=?

we know that
sin(a + b) = sin(a)cos(b) + cos(a)sin(b<span>)
</span>
step 1
find sin b
sin²b+cos²b=1------> sin²b=1-cos²b----> 1-(144/169)---> 25/169
sin b=5/13------> is positive because b belong to the II quadrant

step 2
Find sin a and cos a
tan a=7/24
tan a=sin a /cos a-------> sin a=tan a*cos a-----> sin a=(7/24)*cos a
sin a=(7/24)*cos a------> sin²a=(49/576)*cos²a-----> equation 1
sin²a=1-cos²a------> equation 2
equals 1 and 2
(49/576)*cos²a=1-cos²a---> cos²a*[1+(49/576)]=1----> cos²a*[625/576]=1
cos²a=576/625------> cos a=-24/25----> is negative because a belong to III quadrant
cos a=-24/25
sin²a=1-cos²a-----> 1-(576/625)----> sin²a=49/625
sin a=-7/25-----> is negative because a belong to III quadrant

step 3
find sin (a+b)
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin a=-7/25
cos a=-24/25
sin b=5/13
cos b=-12/13
so
sin (a+b)=[-7/25]*[-12/13]+[-24/25]*[5/13]----> [84/325]+[-120/325]
sin (a+b)=-36/325

the answer is
sin (a+b)=-36/325

8 0
3 years ago
Nadia is a stockbroker.She earns 11% commission each week, She sold $7,500 worth stocks.How much did she make last week in commi
Monica [59]

Answer:

a). Nadia made a total of $825 last week in commission sales

b). The total amount Nadia in commission in 2011=$42,900

Step-by-step explanation:

Step 1

Express the amount in commission she earns from her sales as follows;

C=S×r

where;

C=commission earned

S=total value of stock sales

r=commission rate

In our case;

C=unknown

S=$7,500

r=11%=11/100=0.11

replacing;

C=11% of 7,500

C=(11/100)×7,500

C=0.11×7,500=825

Nadia made a total of $825 last week in commission sales

b). To express the total amount she made in 2011, we derive the formula below;

Total amount (2011)=Average weekly commission×number of weeks in 2011

where;

Average weekly commission=$825

number of weeks in 2011=52

replacing;

Total amount (2011)=(825×52)=42,900

The total amount Nadia in commission in 2011=$42,900

4 0
3 years ago
An unfair coin with​ Pr[H] = 0.2 is flipped. If the flip results in a​ head, a marble is selected at random from a urn containin
satela [25.4K]
Normally when dealing with coins the probability of getting heads or tails is 0.5 each. However in this case since its an unfair coin, the probability of getting heads is 0.2. 
H - head 
T - tails
R - red marble
pr (H) = 0.2
urn
6 red and 4 blue
pr (T)   = 0.8
urn
3 red and 5 blue

when heads is obtained 
red - 6/10 -0.6
blue - 4/10 - 0.4
therefore when multiplying with 0.2 probability of getting heads
pr (R ∩ H) red - 0.6*0.2 = 0.12

when tails is obtained 
red - 3/8 - 0.375
blue - 5/8 - 0.625
when multiplying with 0.8 probability of getting tails
pr (R ∩ T) red - 0.375 * 0.8 = 0.3

using bayes rule the answer can be found out, 
the following equation is used;
pr (H | R) = pr (R ∩ H) / {pr (R ∩ H) + pr (R ∩ T)}
               = 0.12 / (0.12 + 0.3)
               = 0.12 / 0.42
               = 0.286
the final answer is 0.286
6 0
3 years ago
Which of the following are ordered pairs for the equation y = 1/3x - 1?
stellarik [79]

Answer:

answer is the 2nd one

Step-by-step explanation:

y = 1/3(3) - 1 = 1 - 1 = 0   (3,0)

y = 1/3(0) - 1 = 0 - 1 = -1   (0, -1)

y= 1/3(6) - 1 = 2 - 1 = 1     (6, 1)

8 0
3 years ago
Abraham is preparing for a race. He plans to run between 24 and 30 miles a week, either 3 or 4 days a week, and the same number
e-lub [12.9K]

Answer: Abraham could run 8 miles each day for 3 days and get 24. He could run 6 miles each day for 4 days and get 24.

Abraham can run 10 miles each day for 3 days and get 30 or he could run 7.5 miles a day for 4 days and get 30.

Not sure if this is the answer it wants or not

3 0
3 years ago
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