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Free_Kalibri [48]
3 years ago
12

Lazare is dividing 52.8 ounces of cereal equally into 9 bags. Which is the best way to estimate the amount of cereal in each bag

?
Mathematics
1 answer:
satela [25.4K]3 years ago
5 0

If I'm not mistaken it's 5.9

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Prove that sin3a-cos3a/sina+cosa=2sin2a-1
Sloan [31]

Answer:

\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1

Step-by-step explanation:

we are given

\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1

we can simplify left side and make it equal to right side

we can use trig identity

sin(3a)=3sin(a)-4sin^3(a)

cos(3a)=4cos^3(a)-3cos(a)

now, we can plug values

\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)}

now, we can simplify

\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)}

\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)}

\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)}

now, we can factor it

\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)}

\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)}

we can use trig identity

sin^2(a)+cos^2(a)=1

\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)}

we can cancel terms

=3-4(1-sin(a)cos(a))

now, we can simplify it further

=3-4+4sin(a)cos(a))

=-1+4sin(a)cos(a))

=4sin(a)cos(a)-1

=2\times 2sin(a)cos(a)-1

now, we can use trig identity

2sin(a)cos(a)=sin(2a)

we can replace it

=2sin(2a)-1

so,

\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1


7 0
3 years ago
Read 2 more answers
Last year, 31 2 acres of strawberry fields produced approximately 14,700 pounds of strawberries. This year the number of acres p
USPshnik [31]

So in 5 acres of land produces 21,000 pounds of strawberries.

Step-by-step explanation:

Step 1:

Last year, 3\frac{1}{2} acres i.e 3.5 acres produced 14,700 pounds of strawberries. So we need to determine how many strawberries were produced per acre.

To do this we divide the total number of strawberries produced by the number of acres it was produced in.

The number of strawberries produced per acre= \frac{14,700}{3.5} = 4,200 pounds.

Step 2:

To determine the number of strawberries in 5 acres of land, we multiply the number of strawberries per acre by the number of acres.

The number of strawberries produced in 5 acres= 5(4,200) = 21,000 pounds.

So in 5 acres of land produces 21,000 pounds of strawberries.

5 0
3 years ago
at silver gym membrship is 25$ per month and personal training sessions are thirty dollars each.At fit factor membership is 65$
NARA [144]
25+30x=65+20x
30x=40+20x
10x=40
x=40/10
x=4

x is for the number of sessions

ANSWER: 4 sessions
It will cost 145$ for both gyms after 4 sessions.
3 0
3 years ago
Read 2 more answers
If you roll a 6-sided die what is the probability of rolling a one?
Ainat [17]

Answer:

the probablity of rolling a one is 1/6

Step-by-step explanation:

4 0
2 years ago
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Simone saved $65.35 more than her brother Dan and $37.50 less than her sister Carly. Carly saved $127.75. Write and solve equati
elena55 [62]
Siamone has $65.32 + DAN 
Dan has CARLY - $37.50
CARLY = $127.75 
Plug Carly into Dan's equation... 
$127.75 - $37.50 = $90.20
DAN = $90.20
Plug Dan into Siamone's equation
$65.32 + $90.20 = $155.57
5 0
3 years ago
Read 2 more answers
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