A farmer plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital. The farmer has at most 800 hours of labor and $2400 of capital available. If the profit from an acre of wheat is $80 and from an acre of corn is $100, how many acres of each crop should she plant to maximize her profit?

Answer:

1/6

Step-by-step explanation:

1/2 multiplied by 1/3

Answer: To find the product of two matrices A and B, we must use the matrix multiplication rules.

Matrix A is a 2x2 matrix with values [2 3; 4 5] and matrix B is a 2x2 matrix with values [1 2; 3 4].

The result of matrix multiplication, AB, will also be a 2x2 matrix.

To find each element in the resulting matrix, we take the dot product of the corresponding row in matrix A and column in matrix B.

The first element in the resulting matrix AB, is found by taking the dot product of the first row in matrix A and the first column in matrix B:

(21) + (33) = 2+9 = 11

The second element in the resulting matrix AB, is found by taking the dot product of the first row in matrix A and the second column in matrix B:

(22) + (34) = 4+12 = 16

The third element in the resulting matrix AB, is found by taking the dot product of the second row in matrix A and the first column in matrix B:

(41) + (53) = 4+15 = 19

The forth element in the resulting matrix AB, is found by taking the dot product of the second row in matrix A and the second column in matrix B:

(4*2)

Step-by-step explanation:

Answer:

17 miles, it took her, altogether.

Step-by-step explanation:

Answer:

Step-by-step explanation:

10

Ws

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer:

The new size of the diagram would be 28 cm by 16.8 cm. This is calculated by multiplying the original dimensions of 16 cm and 12 cm by the ratio of 7:4. Therefore, the new width of the diagram would be 16 cm x 7 = 112 cm and the new height would be 12 cm x 4 = 48 cm. The new size of the diagram is therefore 112 cm by 48 cm, which can be simplified to 28 cm by 16.8 cm

Step-by-step explanation:

A photocopier that enlarges in the ratio 7:4 will increase the size of the diagram by a factor of 7/4. To find the new size of the diagram, we can multiply the original measurements by the factor of enlargement.

The new width of the diagram will be:
16 cm × 7/4 = 28 cm

The new height of the diagram will be:
12 cm × 7/4 = 21 cm

Therefore, the new size of the diagram will be 28 cm by 21 cm.

Answer: The new size of the diagram will be 28 cm by 21 cm.

(A) Triangle ABC, and triangle QPR are similar based on side-side-side (SSS) similarity.

(B) Triangle ABC and triangle DEF are similar based on side-side-side (SSS) similarity.

(C) ) Triangle STU and triangle JPM are similar based on side-angle-side (SAS) similarity.

(D) ) Triangle SMK and triangle QTR are similar based on angle-angle (AA) similarity.

Similar triangles have the same corresponding angle measures and proportional side lengths.

The triangle similarity criteria are:

(A) Triangle ABC, and triangle QPR are similar based on side-side-side similarity.

12/8 = 9/6

1.5 = 1.5

(B) Triangle ABC and triangle DEF are similar base on side-side-side similarity as shown in the side lengths.

(C) ) Triangle STU and triangle JPM are similar base on side-angle-side similarity.

14/10 = 21/15

1.4 =

(D) ) Triangle SMK and triangle QTR are similar base on angle-angle similarity.

SMK = 90⁰, 60⁰, 30⁰

QTR =  90⁰, 30⁰, 60⁰

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The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

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The points to be graphed are (6, 0) and (0, 3). The graph of the equation is shown in the attached image

y = - 1/2x + 3

In order to graph the equation of the line:

First, find the value of x when y = 0:

y = - 1/2x + 3 , when y = 0:

0 = - 1/2x + 3

1/2x = 3

x = 3 × 2

x = 6

Also, find the value of y when x = 0:

y = - 1/2x + 3, when x = 0:

y = - 1/2(0) + 3

y = 3

Therefore,  the values to be plotted on our graph are (6, 0) and (0, 3). The image of the graph is attached

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The calculated value of x at g(x) = 2 is x = 2.5

from the question, we have the following parameters that can be used in our computation:

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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The two prime numbers that add up to 100005, based on the properties of prime numbers would be 2 and 100003.

To find the two prime numbers, the relevant relationship would be  the Goldbach's Conjecture. This posits that every even number greater than 2 can be expressed as the sum of two prime numbers.

So, to write an odd number as the sum of two prime numbers, one of the prime numbers has to be 2 because we know that 2 is the only even prime number.

The other number would therefore be:

= 100005 - 2

= 100003

100003 is a prime number so the two prime numbers are 2 and 100003.

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Answer:

She Jen djzksndhdi

Step-by-step explanation:

Answer:

Thank you so much!! let me know if you need any help on anything!

Step-by-step explanation:

Answer:

(i) False. Let A = 30° and B = 60°, then sin (A + B) = sin (30° + 60°) = sin 90° = 1 and, sin A + sin B = sin 30° + sin 60° = 1/2 + √3/2 = 1+√3/2(ii) True. sin 0° = 0 sin 30° = 1/2 sin 45° = 1/√2 sin 60° = √3/2 sin  90° = 1 Thus the value of sin θ increases as θ increases.(iii) False. cos 0° = 1 cos 30° = √3/2 cos 45° = 1/√2 cos 60° = 1/2 cos 90° = 0 Thus the value of cos θ decreases as θ increases.(iv) True. cot A = cos A/sin A cot 0° = cos 0°/sin 0° = 1/0 = undefined.

Step-by-step explanation:

Answer: 24

Step-by-step explanation:

Basically you just need to add them simply breaking them up then adding them

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

The amount John have left after purchase is $10.8.

John  earned $45.90 during the summer break.

He used 1 / 6 of the money to buy trading card. Then he used the following amount to buy the trading card.

Then, he used 3/5 of the remaining amount to buy a sketchbook, and also spends $4.50. Therefore, the total he spends can be computed as follows:

So, He spent

The amount he has left = 45.90 - 7.65 - 22.95 - 4.50 = $10.8

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The simplified equation is (π2 / 2) * ∫[0, ∞] (x(2x-1) * e(-x) / (Γ(x) * Γ(1 - x)) DX

a. To prove B(x+1, y) = x * B(x, y), proceed as follows.

Start with B(x+1, y) = [(x+1)! * y!] / ((x+y+2)!) (using the definition of B(x, y)).

Rewrite 1 / (x+1) to (x+y+2 - (y+1)) / (x+y+2) .

Using the formula above, express B(x+1, y) as (x+y+2) / (x+y+2) * [(x+1)! to rewrite. * y!] / ((x+y+2)!) - (y+1) / (x+y+2) * [(x+1)! * y!] / ((x+y+2) !).

Simplify the formula to (x+y+2) / (x+y+2) * B(x, y) - (y+1) / (x+y+2) * B(x, y) increase.

Simplify further to B(x, y) - (y+1) / (x+y+2) * B(x, y).

Note that B(x, y) can be expressed as (x / (x+y+1)) * B(x, y) .

Substitute this formula in the previous step to get,

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y).

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y)

= x * B(x, y)

You have now proved B(x+1, y) = x * B(x, y).

b. We wish to prove the identity Γ(2x) = ((2sin(πx))) * Γ(x) * Γ(x + 1/2).

Integrate ∫[0, ∞] (x(2x-1) * Start with dx.

Evaluating this integral using the permutation u = du is obtained.

Simplify the integral to (1/2) * Γ(x + 1/2).

Express sin(πx) as π / (Γ(x) * Γ(1 - x)).

Let the original integral be π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) * e(-x) * (1/sin( πx) Rewrite.)) DX.

Substituting the equations,

The integral, π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) *

We get * (π / (Γ(x) * Γ(1 - x)))) dx.

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Answer:

a) 0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) 0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) 0.064 = 6.4% probability that 7 of them are discovered.

Step-by-step explanation:

For itens a and b, we use conditional probability.

For item c, we use the binomial distribution along with the conditional probability.

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

a) If it has an emergency locator, what is the probability that it will not be discovered?

Event A: Has an emergency locator

Event B: Not located.

Probability of having an emergency locator:

66% of 72%(Are discovered).

20% of 100 - 72 = 28%(not discovered). So

\(P(A) = 0.66*0.72 + 0.2*0.28 = 0.5312\)

Probability of having an emergency locator and not being discovered:

20% of 28%. So

\(P(A cap B) = 0.2*0.28 = 0.056\)

Probability:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.056}{0.5312} = 0.105\)

0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) If it does not have an emergency locator, what is the probability that it will be discovered?

Probability of not having an emergency locator:

0.5312 of having. So

\(P(A) = 1 - 0.5312 = 0.4688\)

Probability of not having an emergency locator and being discovered:

34% of 72%. So

\(P(A \cap B) = 0.34*0.72 = 0.2448\)

Probability:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2448}{0.4688} = 0.522\)

0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?

p is the probability of being discovered with the emergency recorder:

0.5312 probability of having the emergency recorder.

Probability of having the emergency recorder and being located:

66% of 72%. So

\(P(A \cap B) = 0.66*0.72 = 0.4752\)

Probability of being discovered, given that it has the emergency recorder:

\(p = P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4752}{0.5312} = 0.8946\)

This question asks for P(X = 7) when \(n = 10\). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 7) = C_{10,7}.(0.8946)^{7}.(0.1054)^{3} = 0.064\)

0.064 = 6.4% probability that 7 of them are discovered.

Answer:

171 > 117

Step-by-step explanation:

171 is greater than 117 meaning the alligator is eating the bigger number, 171.

Answer:

445788

Step-by-step explanation:

OMG too difficult man!!

Thanks to my calculator to solve this hard question

9514 1404 393

Answer:

  y = 8√3

Step-by-step explanation:

In the 30°-60°-90° "special" triangle, the ratio of sides lengths is ...

  1 : √3 : 2 = 8 : y : hypotenuse

In order for these ratios to be equal, we must have ...

  y = 8√3

__

If you want to solve this using your trig skills, you recognize that ...

  Tan = Opposite/Adjacent

  tan(30°) = 8/y

  y = 8/tan(30°) . . . . where tan(30°) = 1/√3

  y = 8√3

Answer:

10 hours

Step-by-step explanation:

380 - 80 = 300

30 : 1 = 300 : x

x = 300 / 30

x = 10

Answer: 16.1

Step-by-step explanation:

Answer

approximately 0.0067

Step-by-step explanation:

If you multiply 0.0067 with 16,500 you get about 110.55 and the more you keep going with the 6, the closer it gets to 110$.

Answer:

31

Step-by-step explanation:

the next number is 31 in this series

Answer:

\(\displaystyle \mathbf{\frac{5}{(c+4)}}\)

Step-by-step explanation:

Division of Rational Expressions

When dividing two rational expressions like f(c) / g(c), it's usually easier to multiply the numerator by the reciprocal of the denominator: f(c) * (1/g(c)). The reciprocal is just flipping the numerator and the denominator.

Let's find the following division:

\(\displaystyle \frac{\frac{c^2-64}{3c^2+26c+16}} {\frac{c^2-4c-32}{15c+10}}\)

First, we factor the polynomials where possible.

\(c^2-64 = (c-8)(c+8)\)

\(3c^2+26c+16=(3c+2)(c+8)\)

\(c^2-4c-32=(c-8)(c+4)\)

\(15c+10=5(3c+2)\)

Substituting:

\(\displaystyle \frac{\frac{c^2-64}{3c^2+26c+16}} {\frac{c^2-4c-32}{15c+10}}=\frac{\frac{(c-8)(c+8)}{(3c+2)(c+8)}} {\frac{(c-8)(c+4)}{5(3c+2)}}\)

Multiplying by the reciprocal of the denominator:

\(\displaystyle \frac{\frac{c^2-64}{3c^2+26c+16}} {\frac{c^2-4c-32}{15c+10}}=\frac{(c-8)(c+8)}{(3c+2)(c+8)}\cdot \frac{5(3c+2)}{(c-8)(c+4)}\)

Simplifying by (c+8)(3c+2)(c-8):

\(\displaystyle \frac{\frac{c^2-64}{3c^2+26c+16}} {\frac{c^2-4c-32}{15c+10}}=\frac{5}{(c+4)}\)

Answer:

\(\displaystyle \mathbf{\mathbf{\frac{5}{(c+4)}}}\)

Aw I'm in grade 8, but I could've helped you..

Answer:

mode

Step-by-step explanation:

me too

y=4x-9

y=x-3

-4x + y = -9

-x +y = -3              //-1

-4x + y = -9

x - y = 3

---------------------

-3x = -6

x = 2

y = 2-3

y = -1

Answer:

(2, -1)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

y = 4x - 9

y = x - 3

Step 2: Solve for x

Step 3: Solve for y

By comparism using the given scale ratio, the weight of Ellie at birth is 7.7pounds.

Ratio simply compares values, it shows how much of one thing is related or compared to another thing.

Given the data in the question;

To determine the weight of Ellie, we simply say;

0.75pounds : 0.9pounds = 6.4pounds : X

0.75pounds / 0.9pounds = 6.4pounds / X

Cross multiply

0.75pounds × X = 0.9pounds × 6.4pounds

0.75pounds × X = 5.76pounds²

X = 5.76pounds² / 0.75pounds

X = 7.68pounds

X = 7.7pounds

Therefore, by comparism using the given scale ratio, the weight of Ellie at birth is 7.7pounds.

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9514 1404 393

Answer:

  3^5

Step-by-step explanation:

It can be helpful to remember that an exponent signifies repeated multiplication.

The product in the numerator has 4 factors of 3 multiplied by 5 more factors of 3, for a total of 9 factors of 3.

The product in the denominator has 2 factors of 3 multiplied by 2 more factors of 3, for a total of 4 factors of 3.

The 4 factors of 3 in the denominator cancel 4 of the 9 factors of 3 in the numerator, leaving a value of 5 factors of 3.

The value of the expression is 3^5.

_____

In terms of rules of exponents, the value is ...

  (3^4)(3^5)/((3^2)(3^2))

  = 3^(4+5)/3^(2+2)

  = 3^9/3^4

  = 3^(9-4) = 3^5

__

Those rules are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)/(a^c) = a^(b-c)