For an acute angle θ, the equation sin(θ)=cos(6) is true. What is the value of θ? Show or explain your answer

Answer:

16428 oranges

Explanation:

Total yield = number of trees × number of oranges in each tree

Initial yield = 600×24= 14400 oranges

To find the equation needed, let x = additional trees and y= total yield

Number of trees = 24 +x

Number of oranges in each tree = 600-12x

Equation of total yield y= (24+x)(600-12x)

y= 14400-288x+600x-12x²

y= -12x²+312x+14400

Using a graphing calculator, from the graph drawn for this quadratic equation, we notice that it is a parabola. Therefore to find the maximum value, we should find the maximum point which is at the vertex of the parabola, we use the formula x= -b/2a

A quadratic equation is such: ax²+bx+c

Therefore x =-312/2×-12

x= -312/-24

x= 13

So we can conclude that in order to maximise oranges from the trees, the person needs to plant an additional 13 trees. Substituting from the above:

24+x=24+13= 37 trees in total

y= -12x²+312x+14400= -12×13²+312×13+14400= -2028+4056+14400

=16428 oranges in total yield

The number of trees that gives the most yield is 37

The given parameters are:

Represent the additional number of trees with x.

So, we have:

The equation that represents the total yield (y) becomes

[tex]y = (24 + x) \times (600 - 12x)[/tex]

Expand

[tex]y= 14400-288x+600x-12x\²[/tex]

Evaluate the like terms

[tex]y= 14400+312x-12x\²[/tex]

Rewrite as:

[tex]y= -12x\²+312x+14400[/tex]

Differentiate

[tex]y'= -24x+312[/tex]

Set to 0

[tex]-24x+312 = 0[/tex]

Solve for x

[tex]-24x=-312[/tex]

[tex]x=13[/tex]

Recall that:

Trees per acre = 24 + x

This gives

[tex]Trees = 24 + 13[/tex]

[tex]Trees = 37[/tex]

Hence, the number of trees that gives the most yield is 37

Read more about quadratic functions at:

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Answer:

y=4 and x=0

Step-by-step explanation:

4(5y-20)+3y=12

20y-80+3y=12

23y-80=12

23y=92

y=4

Substitute y as 4 to get x.

Answer:

y=4

x=0

Step-by-step explanation:

4x + 3y = 12

X - 5y =-20

Multiply second equation by 4

4x + 3y = 12

4x - 20y = - 80

Subtract

23y = 92

y = 92/23

y =4

Put the value in first equation

4x + 12 =12

So 4x = 0

Therefore x= 0

Answer:

Ethan sold more

Step-by-step explanation:

2/3 and 1/4

Simplify to 8/12 and 4/12

8/12 is more

Answer:

 Standard error (S.E) =  0.048  ≅ 0.05

Step-by-step explanation:

Explanation:-

Given  sample size 'n'=76

Given the dean who randomly selects 76 students and finds that 58 out of 76 are receiving financial aid.

Sample proportion

                         [tex]p = \frac{x}{n} = \frac{58}{76} = 0.7631[/tex]

The standard error is determined by

                     [tex]S.E = \sqrt{\frac{p(1-p)}{n} }[/tex]

                     [tex]S.E = \sqrt{\frac{0.763(0.2369}{76} }[/tex]

  Standard error is 0.048  ≅ 0.05

Answer: x = -2/3

[tex]\frac{x}{x+2}- \frac{4}{x-2}=1\\\\<=>\frac{x(x-2)}{(x+2)(x-2)}-\frac{4(x+2)}{(x+2)(x-2)}=1\\\\\\<=>\frac{x(x-2)-4(x+2)}{(x-2)(x+2)}=1\\\\\\=>x(x-2)-4(x+2)=(x-2)(x+2)\\\\\\<=> x^{2} -2x-4x-8=x^{2} -4\\\\\\<=>-6x-8=-4\\\\\\<=>-6x=8-4\\\\\\<=>-6x=4\\\\\\<=>x=-4/6=-2/3[/tex]

Step-by-step explanation:

Step-by-step explanation

2.5 cups = 5servings

x cups = 8servings

2.5*8 = 5*x

20 = 5x

divide both sides by the coefficient of x

20/5 = 5x/5

4 = x

i.e x = 4

Answer:

3,510

Step-by-step explanation:

3,511.1 is closer to 3,510 than it is to 3,520

Answer:

[tex]\displaystyle \frac{118}{125}[/tex]

Step-by-step explanation:

Trigonometry

Calculate

[tex]\sin (3\sin^{-1}(2/5))[/tex]

We use the formula for the sine of triple angle:

[tex]\sin 3x=3\sin x-4\sin^3 x[/tex]

And recall:

[tex]\sin \sin^{-1}x=x[/tex]

For this problem, we set:

[tex]x=\sin^{-1}(2/5)[/tex]

Thus:

[tex]\sin 3x=3\sin (\sin^{-1}(2/5))-4\sin^3 (\sin^{-1}(2/5))[/tex]

[tex]\displaystyle \sin 3x=3*\frac{2}{5}-4\left(\frac{2}{5}\right)^3[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-4*\frac{8}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6*25}{125}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{150-32}{125}[/tex]

[tex]\mathbf{\displaystyle \sin 3x=\frac{118}{125}}[/tex]

Answer:

2. unlikely

Step-by-step explanation:

The probability of rolling a 2 is 1/6, 0r 0.1666...  .

Probabilities and their meanings:

0   -   impossible

between 0 and 0.5   -   from unlikely to almost as likely as not

0.5   -   as likely as not

between 0.5 and 1   -   from as likely as not to almost certain

1   -   certain

This probability is 0.1666... which is in the category from 0 to 0.5. It is closer to 0 than to 0.5, so although it is not impossible, it is unlikely.

Answer: 2. unlikely

Step-by-step explanation:

x+y=17 (First equation)

x-y=3 (Second equation)

Solving Equation (i)

x+y=17

x=17-y(First equation)

Putting value of x in equation (ii)

x-y=3

x=3+y

17-y=3+y

17=3+y+y

17=3+2y

2y=17-3

y=14/2

y=7

Putting value of y in equation(i)

x=17-y

x=17-7

x=10

Answer:

6/7

Step-by-step explanation:

you already have a common denominator, so 4/7 plus 2/7 is 6/7

Answer:

[tex]\boxed{\frac{6}{7} }[/tex]

Step-by-step explanation:

[tex]\frac{4}{7} + \frac{2}{7}[/tex]

[tex]= \frac{4 + 2}{7}[/tex]

[tex]= \frac{6}{7}[/tex]

9514 1404 393

Answer:

  f(x) = x³ -5x² +2x +8

Step-by-step explanation:

If the function has a zero of p, then it has a factor of (x-p). The polynomial of least degree will only have factors corresponding to the given zeros:

  f(x) = (x -(-1))(x -2)(x -4)

  = (x +1)(x -2)(x -4)

  = (x² -x -2)(x -4)

  f(x) = x³ -5x² +2x +8

Answer:

132

Step-by-step explanation:

132

Step-by-step explanation:

First, find how many beats are in a minute by creating a proportion:

\frac{11}{5} = \frac{x}{60}

Cross multiply and solve for x:

5x = 660

x = 132

So, there are 132 beats in one minute.

This means the constant of proportionality is 132.

Answer:

132

Step-by-step explanation:

Step-by-step explanation:

f(x) = x

g(x) =3x

point if intersection

f(x) =g(x)

x = 3x

It's like walking but faster, so you go faster like sonic lol.

Answer:

32000 grams

Step-by-step explanation:

The weight of a 32 kg child in pounds is 70.56 pounds.

What is Measurement unit?

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

The weight of baby = 32 kg

Now,

Since, 1 kg = 2.205 pounds

So, We convert the weight of baby from kg to pounds as;

1 kg = 2.205 pounds

32 kg = 32 x 2.205 pounds

         = 70.56 pounds.

Thus, The weight of a 32 kg child in pounds is 70.56 pounds.

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Answer:

“A systematic arrangement” of data in rows and columns is called Table.

Explanation: A table is used to arrange data in rows and columns

Answer:

yellow 9/25

yellow and green is 14/25

Using it's concept, it is found that the probabilities are given as follows:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 9 out of 25 are yellow, then 5 out of 24 will be green, hence:

P(yellow, then green) = 9/25 x 5/24 = 45/(25 x 24) = 0.075 = 7.5%.

For both blue, we have that they are, respectively, 6 out of 25 and 5 out of 24, hence:

P(both blue) = 6/25 x 5/24 = 30/(25 x 24) = 0.05 = 5%.

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Answer:

The secret number is 93.

Answer:

C

Step-by-step explanation:

Answer:

40+2+0.1

Step-by-step explanation:

Answer:

2 books

Step-by-step explanation:

8 x 6 = 48

Answer:

4 x [tex]\frac{3}{2}[/tex] = 6

Step-by-step explanation:

The division equation would be 4 divided by 2/3, but that is equal to 4 x 3/2 = 6.

Hope it helps! (I'm so sorry if it's wrong).

Answer:

2.66

Step-by-step explanation:

2/3 of 4 is the same as:

2/3 * 4 = (2/3) * (4/1)

By the rules for multiplying fractions, this is (2*4) / (3*1) = 8/3

8/3 is 2.66