Is the dynamic organisation within the individual that determine his unique adjustment to the environment

Answer:

Step-by-step explanation:

Given the expression sin(9z − 1) = cos(6z + 1), for 0 < z ≤ 90, we are to find z

Note that sin theta = cos(90-thetsa)

sin(9z − 1) = cos(6z + 1)

cos (90 - (9z-1)) = cos(6z + 1)

cos (90 - 9z+1)) = cos(6z + 1)

cos (91-9z) = cos(6z + 1)

Cos will cancel out to have;

91-9z = 6z+1

-9z - 6z = 1-91

-15z = -90

z = 90/15

z = 6

Hence the value of z is 6

Answer:

x = 78

Step-by-step explanation:

(x-8) + 20 = 90

x - 8 = 90 - 20

x - 8 = 70

x = 70 + 8

x = 78

Check:

(78-8) + 20 = 90

70 + 20 = 90

Answer:

the 2 arrow

-sorry I don't really know what I meant by notation

Step-by-step explanation:

--------->->---------- (line a)

--------->->---------- (line b)

line is parallel to line b which is shown with the arrows this means that they cannot intercept no matter how long the line goes. it also means they have the same slope.

Answ

What formation is that

Step-by-step explanation:

Answer:

hmmmmmmmmm

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

10x4= 40 5x4=20 so 40+20=15x4

Answer:

a

Step-by-step explanation:

Answer:

x=9 im pretty sure

Step-by-step explanation:

Answer:

Your answer is <, Hope it helps.

Answer:

6, 9, 12

Step-by-step explanation:

sum of two sides must be greater than third side

Answer:

a. -1

b. -3

Explanation:

To solve negative and positive numbers on the number line, we make a simple analogy. If we wanted to -3+2 for instance:

Imagine a customer placed an order for 3 bags of apples from your store but you are out of stock and only have 2 bags left. You then come to an agreement with the customer to send 2 bags now and send the remaining one later in the week when your stock arrives from your supplier. In this way, you are only able to send two bags which you have,+2, and then be owing the customer one bag left(-1) to deliver out of the three, -3.

To solve -2+1 on the number line, with -2 on the left side of 0(negative) on the number line and +1 on the right side of 0(positive), we use same analogy above.

-2+1= -1

Also using same analogy, -2+(-1)= -3

Note: +1×-1=-1

Answer:

10 hours

Step-by-step explanation:

Because if u divide the speed t= 4320miles/432mph=10h

Using compound interest formula, the the amount after 5 years is  $15,095.39

The total amount a college student has in a saving account if 13000 dollars was invested and earned 3% compounded quarterly for 5 years can be calculated as follows:

Therefore,

\(A = p(1 +\frac{r}{n} )^{nt}\)

where

Therefore,

p = 13000 dollars

t = 5 years

n = 4

r = 3% = 0.03

Therefore,

\(A = p(1 +\frac{r}{n} )^{nt}\)

\(A = 13000(1+ \frac{0.03}{4} )^{(4)(5)}\)

A = 13,000.00(1 + 0.0075)²⁰

A = $15,095.39

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The minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

In the question, we are asked to use Lagrange multipliers to find the minimum distance between the origin and the plans 3x + y + 2z = 28.

Lagrange multipliers state that if we want to minimize a function, f(x, y, z), subject to a constraint g(x, y, z) = constant, then ∇f = λ∇g.

We want to minimize the distance, and the distance formula says that the distance from the origin to a point (x, y, z), is given as:

D = √(x² + y² + z²), which can also be shown as:

D² = x² + y² + z².

The gradient of this function is: (2x + 2y + 2z), which needs to be equal to the gradient of the constraint equation multiplied by the constant, λ, that is, λ(3, 1, 2), which gives:

2x = 3λ, or, x = (3/2)λ,

2y = λ, or, y = λ/2, and,

2z = 2λ, or, z = λ.

Substituting these in the equation of the plane, 3x + y + 2z = 28, we get:

3(3/2)λ + λ/2 + λ = 28,

or, 6λ = 28,

or, λ = 28/6 = 14/3.

Thus, we get:

x = (3/2)λ = 7,

y = λ/2 = 7/3, and,

z = λ = 14/3.

Substituting these in the distance formula, we get:

D = √(7² + (7/3)² + (14/3)²) = √(49 + 49/9 + 196/9) = √(686/9) = 8.73.

Thus, the minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

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Hence, the equation has no solution. The correct option is option C.

Answer:

first is positive

second is also positive

third id negative

forth is also negative

Step-by-step explanation:

1) and 2) It is because there is no sign before the solution.

for 3) and 4) there is a - (minus) sign before the product so the solution is negative.

Answer:

$750

Step-by-step explanation:

Larger share = $450

Smaller share : Larger share :: 2 : 3

Smaller share = (larger share x 2) / 3

= (450x2)/3

= 300

Sum= larger share + smaller share

= $450 + $300 = $750

Answer:

The first one.

Step-by-step explanation:

You need to add those two meters together.

As per the statements given in the question, the equations are N(t) = 930 + (t/4)32, N(t) = 930 - (t/2)64, N(t)= 930 + (2t)36.

In mathematics, a fraction is represented by a specific number that designates a portion of an entire. A fraction is a piece or section of a whole, whereby a can have been any number, a particular value, or an object.

As per the given information in the question,

Total number of students enrolled in new charter = 930

1.

Increases by 32 students every 4 years, the equation will be,

N(t) = 930 + (t/4)32

Here, t is the number of years.

2.

Decreases by 64 students every 2 years, the equation will be,

N(t) = 930 - (t/2)64

One more

3.

Increases by 36 students every semester (twice each year), the equation will be,

N(t)= 930 + (2t)36

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The simplified expression in exponential form would be 23^(a + b).

To simplify the numerical expression 23a x 23b, we can combine the like terms.

Step 1: Simplify 23a and 23b individually.

The expression 23a means multiplying 23 by a, and 23b means multiplying 23 by b. We cannot simplify them further because we do not have specific values for a and b.

Step 2: Combine the simplified terms.

When we multiply 23a by 23b, we multiply the coefficients (23 x 23) and the variables (a x b). Therefore, the simplified expression is:
(23 x 23) x (a x b)

Step 3: Calculate the coefficient and write the answer in exponential form.

The coefficient (23 x 23) is equal to 529. In exponential form, we can write it as 23^2. So the final simplified expression is:
23^2 x (a x b)

In summary, the simplified numerical expression 23a x 23b can be written as 23^2 x (a x b) in exponential form.

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The area of one triangle is 48 square feet when θ = 60°

The area of one triangle is 27.7 square feet when θ = 60°.

To find the area of the triangle, we can use the formula for the area of an isosceles triangle: A = (1/2) * base * height. In this case, the base of the triangle is given as 8 ft.

Given that the height is represented by y = 4 tan θ, we need to find the value of y when θ = 60°. Substituting θ = 60° into the equation, we have y = 4 tan 60°. Using the tangent of 60°, which is √3, the height is y = 4 * √3.

Now we can calculate the area of the triangle. Plugging in the values into the formula, we get A = (1/2) * 8 ft * (4 * √3) ft = 16√3 ft².

Rationalizing the denominator (√3) by multiplying both the numerator and denominator by √3, we have A = 16 * √3 * √3 ft² = 16 * 3 ft² = 48 ft².

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Answer:

5

Step-by-step explanation:

2x + x = 15

3x = 15

x = 15/3

x = 5

SC = x = 5

Answer: quantifies the economic devastation of natural and man-made disasters

Answer:

75x^2+12x-14

Step-by-step explanation:

75x^2+12x-14

There are 9 possible schedules to play basketball such that dave can play on monday or wednesday or both which is union of two set .

so this question seems like we have to take union of ways of palying on monday or wednesday

let n(m) be number of ways of playing on monday

n(w) be number of ways of playing on wednesday

we have to find n(m∪w)

n(mUw) = n(m) +n (w) - n(m∩ w)

so n(m) = \(4_C__2\) as one day is now fixed which is monday so we have 4 available days and 2 days to play.

n(m) = \(4_C__2\)  = 6

similary n(m) = n(w) = 6

now  n(m∩w) = \(3_C__1\) as now we have  2 fixed day and we have 3 day remaining and only one day to play.

n(m∩w) = \(3_C__1\) =3

now n(mUw) = n(m) +n (w) - n(m∩ w)

=> 6 + 6 -3

=> 12 - 3

so n(mUw) = 9

so we have 9 schedules to paly keeping condition given in the question.

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Answer:

1 is >

2 is >

I think this is right, you may need to confirm this

The apprοpriate οptiοns fοr the questiοn are:

b) Nο. The trials dο nοt have the same success.

c) Nο. The number οf trials is nοt fixed.

d) Yes. The trials are independent, identical, have οnly twο οutcοmes, have the same success, and the number οf trials is fixed.

Prοbability is a branch οf mathematics cοncerned with numerical descriptiοns οf hοw likely an event is tο οccur οr hοw likely a statement is tο be true. The prοbability οf an event is a number between 0 and 1, where, rοughly speaking, 0 indicates the impοssibility οf the event and 1 indicates a certainty.

a) Trials are nοt independent: In this carnival game, the trials are interdependent, as cοntestants' guesses can be influenced by previοus guesses and infοrmatiοn they gather.

b) Attempts dο nοt have the same success rate: The prοbability οf success (cοrrectly guessing the field) may vary depending οn the skill οr luck οf the cοntestant. Therefοre, the tests dο nοt have the same success.

c) The number οf attempts is nοt fixed: The questiοn mentiοns that the cοntestant plays the game several times, which means that the number οf attempts may vary. The number οf attempts is therefοre nοt fixed.

d) The trials are independent, identical, have οnly twο οutcοmes, have the same success rate, and the number οf trials is fixed: Althοugh οptiοns a, b, and c are incοrrect, οptiοn d cοrrectly describes the characteristics οf the binοmial prοbability distributiοn. Trials are independent (each guess dοes nοt affect the οthers), identical (the bοxes are identical), have οnly twο οutcοmes (success οr failure), have the same prοbability οf success, and the number οf trials is fixed.

e) Trials have mοre than twο οutcοmes: The carnival game invοlves οnly twο οutcοmes: tο guess cοrrectly οr nοt. Sο exams have nο mοre than twο οutcοmes.

f) Trials are nοt identical: The bοxes in the carnival game are identical and the rules οf the game remain the same fοr each trial. Therefοre, the exams are identical.

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Answer:

72

if you need help with ratios then you can divide the smaller number by the bigger number