Find the function value sin120°

Step-by-step explanation:

See image.....as these are definitions, it is self-explanatory:

Answer:

(-3b) (10a -3b)

Step-by-step explanation:

(5a–3b)^2–25a^2

Replace (5a–3b) with x

x^2 - (5a) ^2

We have the difference of squares

( x-5a) (x+5a)

Now replace x with (5a -3b)

(5a -3b -5a) ( 5a -3b +5a)

Combine like terms

(-3b) (10a -3b)

Answer:

(5a-3b)²-25a²

= 25a²+9b²-2×5a×3b-25a { (a-b)²= a²+b²-2ab}

=9b²-30ab

=3b(3b-10a)

= -3b(10a-3b)

Ans

Hope, it helped!

Answer:

It will be 1:50

Step-by-step explanation:

Answer:

11:50 + 2 hr. = 1:50 or 13:50 Military/European time

Step-by-step explanation:

The eigenvalues of A are the complex numbers +2i and -2i.The diagonalized form of the matrix B is [1 0 0; 0 1 0; 0 0 -1]

A. A matrix A can be written in the form of

A = [a b; c d]

The eigenvalues λ of A can be calculated using the following formula:

λ = (a+d ± √(a+d)^2 -4(ad-bc))/2

Substituting the values of A gives

λ = (0 + 0 ± √(0)^2 - 4(-2))/2

λ = 2i and -2i

Since the eigenvalues are complex, the matrix cannot be diagonalized over C.

B. The eigenvalues of B can be calculated using the same formula as above

λ = (a+d ± √(a+d)^2 -4(ad-bc))/2

Substituting the values of B gives

λ = (0 + 1 ± √(1)^2 - 4(0))/2

λ = 1, 0, -1

To diagonalize the matrix, we must find the eigenvectors associated with each eigenvalue. The eigenvectors of B can be calculated using the following formula:

v = (a - λI)x

Substituting the values of B and the eigenvalues gives:

v1 = (0 - 1I)x

v2 = (0 - 0I)x

v3 = (0 - (-1I))x

The eigenvectors are

v1 = [1 0 0]

v2 = [1 0 0]

v3 = [0 1 0]

The diagonalized form of the matrix B is

[1 0 0; 0 1 0; 0 0 -1]

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The missing value 'x' in the two-way relative frequency table is 0.36.

To convert the two-way table to a two-way relative frequency table, we need to calculate the relative frequencies for each category. Relative frequency is calculated by dividing the frequency of a particular category by the total count in that row or column.

Let's denote the missing value as 'x'. To find the value of 'x', we need to ensure that the sum of the relative frequencies in each row and each column adds up to 1.

First, let's calculate the relative frequencies for each category:

Likes hockey: The total count in this row is 12 + 18 = 30.

Relative frequency of "Likes hockey" = 12/30 = 0.4

Relative frequency of "Doesn't like hockey" = 18/30 = 0.6

Likes baseball: The total count in this column is 12 + 14 = 26.

Relative frequency of "Likes baseball" = 12/26 ≈ 0.4615

Relative frequency of "Doesn't like baseball" = 14/26 ≈ 0.5385

To ensure that the relative frequencies add up to 1, we can set up the following equations:

0.4 + x = 1 (sum of relative frequencies in the "Likes hockey" row)

0.4615 + 0.5385 + x = 1 (sum of relative frequencies in the "Likes baseball" column)

Simplifying the equations, we have:

x = 0.6 (1 - 0.4) = 0.6 * 0.6 = 0.36

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Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8

Answer:

32

Step-by-step explanation:

2x+6=5x-9

3x=15,

x=5

2(5)+6=10+6=16

5(5)-9=25-9=16

16+16=32

The model for S(t) is given as:

S(t) = (-0.03t^2 + 1.6t - 13.65)^(-1)

This model predicts the searching period length in days. It is an inverse function of the quadratic equation (-0.03t^2 + 1.6t - 13.65). As the temperature increases, the searching period decreases, indicating that the larvae are more efficient at finding the host tree at higher temperatures.

To calculate S(25), we substitute t = 25 into the equation:

S(25) = (-0.03(25)^2 + 1.6(25) - 13.65)^(-1)

= (-0.03(625) + 40 - 13.65)^(-1)

= (-18.75 + 26.35)^(-1)

= 7.6^(-1)

= 0.1316 days

Therefore, when the air temperature is 25 degrees Celsius, the predicted length of the searching period is approximately 0.1316 days.

The model for N(t) is given as:

N(t) = -0.85t^2 + 45.4t - 547

This model predicts the percentage of larvae surviving the searching period. It is a quadratic function (-0.85t^2 + 45.4t - 547). As the temperature increases, the percentage of larvae surviving the searching period may increase or decrease depending on the behavior of the quadratic function.

To calculate N(25), we substitute t = 25 into the equation:

N(25) = -0.85(25)^2 + 45.4(25) - 547

= -0.85(625) + 1135 - 547

= -531.25 + 1135 - 547

= 56.75%

Therefore, when the air temperature is 25 degrees Celsius, the predicted percentage of larvae surviving the searching period is 56.75%.

2. The rate of change of the searching period S(t) with respect to temperature t can be found by taking the derivative of the function S(t) with respect to t, which is denoted as ds/dt.

ds/dt = d/dt [(-0.03t^2 + 1.6t - 13.65)^(-1)]

To find when ds/dt = 0, we set the derivative equal to zero and solve for t:

ds/dt = 0

However, without the specific equation of S(t) in its original form, it is not possible to provide an exact value of t when ds/dt equals zero.

Regarding the behavior when t = 0, we cannot determine this without further information or the specific form of the function S(t). The behavior at t = 0 depends on the equation itself and how it is defined.

3. The rate of change of the percentage of larvae surviving the searching period N(t) with respect to the length of the searching period S(t) can be found by taking the derivative of the function N(t) with respect to S(t), denoted as dN/dS.

dN/dS = d/dS [(-0.85t^2 + 45.4t - 547)]

This rate of change provides information about how the percentage of larvae surviving the searching period changes with respect to the length of the searching period. It gives insight into the sensitivity

Answer: 5/6 of the yard mowed

Step-by-step explanation:

    We will add 1/3 to 3/6 to find the total amount of yard mowed so far.

1/3 + 3/6 = 2/6 + 3/6 = 5/6 of the yard mowed

Answer:

It would equal 25/38.29

Step-by-step explanation:Hope this helps!

Answer:

1728 yds

Step-by-step explanation:

Answer:

4 1/10 when u have a inproper fraction like that every 10 is one whole number

Answer:

To find the probability that the randomly selected point will lie inside the square, we need to find the area of the square and the area of the figure, and then divide the area of the square by the area of the figure.

The area of the square is 7 mm x 7 mm = 49 mm^2.

To find the area of the figure, we can divide it into a rectangle and two right triangles. The rectangle has dimensions of 8 mm x 14 mm, so its area is 8 mm x 14 mm = 112 mm^2. Each right triangle has base 8 mm and height 6 mm, so each triangle has an area of (1/2) x 8 mm x 6 mm = 24 mm^2. The total area of the figure is therefore 112 mm^2 + 24 mm^2 + 24 mm^2 = 160 mm^2.

The probability of selecting a point inside the square is then 49 mm^2 / 160 mm^2, which is approximately 0.3063 or 30.63%.

Therefore, the answer is closest to 26.1%, which is the third option.

Step-by-step explanation:

The distance that Mr. Stein drove can be represented by the expression: \(140 - x\)

A mathematical phrase made up of one or more variables, constants, and arithmetic operations like addition, subtraction, multiplication, and division is known as an algebraic expression. Exponentiation and other mathematical operators could also be present.

Let's assume that Mr. Smith drove "x" miles before Mr. Stein took over the driving.

Then, the total distance they traveled is 140 miles.

So, the distance that Mr. Stein drove can be represented by the expression:

140 - x

Therefore, This is because if Mr. Smith drove "x" miles, then the remaining distance that needed to be covered by Mr. Stein would be the difference between the total distance of 140 miles and the distance already driven by Mr. Smith.

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The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.

We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.

(1/2) * Base * Height = Area

We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.

Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters

Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).

Using these values as a substitute in the formula, we obtain:

Area =\((1/2) * 54 * 56 = 1512\) square centimeters

centimetres square

It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.

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The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

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Answer:

hope it helps

incase you don't understand feel free to ask.

The answers are 1) 360,000, 2) 217,060, 3) 37,140 and 4) 180,080.

1) To calculate the amount of premium paid by the employee and the employer =

Consider employee medical insurance payable, and employee life insurance payable.

The journal entries for accrual payroll, including employee deductions, consider sales salaries expense office salaries expense, social sec taxes payable Medicare tax payable, employee income taxes, life insurance payable, union dues, salaries payable.

2) Journal entry for cash payment of net payroll for month of July consider salaries payable and cash.

3) Calculate the unemployment tax amount, consider state unemployment taxes and federal unemployment taxes,

Journey Entries for accrued employer payroll taxes,

Payroll taxes expenses, social taxes, Medicare taxes, state unemployment taxes, federal unemployment taxes, employee medical and life insurance.

4) Journal entries for cash payment of all libraries, consider, social medical taxes, employee fed, medical, life and state income taxes payable.  

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Answer:

  11

Step-by-step explanation:

The first 12 terms of the sequence are ...

  1 1 2 3  5 8 13 21  34 55 89 144

The first term that is greater than 60 is the 11th term, 89.

  n = 11

The volume of cone is 175 m³

Firstly,

Volume of Pyramid.

The volume (V) of a pyramid is  

V = ⅓Ah

Data:

V = 175m³

Calculation:

175 = ⅓× A× h

Ah = 175*3

Ah = 525m³

Secondly,

The volume (V) of a cone is

V = ⅓Ah

Data:

Ah = 525 m³

Calculation:

V = ⅓ A× h

V = 175 m³

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Any two consecutive terms in an arithmetic sequence have the same difference.

We can find this common difference by subtracting any two consecutive terms.

common difference = -1/4 - 1 = -5/4

Then the missing number is just -3/2 + (-5/4) = -13/4

Answer:

X=6

Step-by-step explanation:

3 times 6 is 18 so x is 18

Answer:

\( \huge{ \fbox{ \sf{x = 6}}}\)

Step-by-step explanation:

\( \star{ \sf \: \: 3x = 18}\)

\( \text{ Step \: 1 \: : divide \: both \: sides \: by \: 3}\)

\( \mapsto{ \sf{ \frac{3x}{3} = \frac{18}{3} }}\)

\( \text{Step \: 2 : calculate}\)

\( \mapsto{ \sf{ x = 6}}\)

Hope I helped!

Best regards! :D

~\( \text{theanimegirl}\)

Answer:

£9.60

Step-by-step explanation:

20% of £8 = £1.60

1.60 + 8 = £9.60

Answer:

5 21/40

Step-by-step explanation:

easy maths

The equation of the mathematical statement is: y= 1.75x.

Based on the information given, we can assume that the growth per year for Amy's tree is given by:

y = 1.75x

where x is the number of years after planting the seed.

However, this is not in the form of y = mx + b.

To write it in that form, we need to isolate y on one side of the equation:

y = 1.75x + 0

where m = 1.75 and b = 0.

Therefore, the equation of the mathematical statement is:

y = 1.75x + 0 or simply y = 1.75x.

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Answer:

The question doesn’t state what T represents, so I will assume T is one of two points:

1. The midpoint of R and S, or

2. S is the midpoint of RT.

1. T((-9+2)/2,(4-1)/2)=T(-7/2,3/2)

2. T(x,y): S(2,-1)=((-9+x)/2,(4+y)/2); 2=(-9+x)/2, 4=-9+x, x=13; (4+y)/2=-1, 4+y=-2, y=-6. T(13,-6)

Step-by-step explanation:

This should do it. I hope it is clear.

9514 1404 393

Answer:

  (x^(1/2))(x^(1/2)) = x^(1/2 +1/2) = x^1 = x

Step-by-step explanation:

The rule of exponents is ...

  (x^a)(x^b) = x^(a+b)

From which ...

  (x^a)(x^a) = x^(a+a) = x^(2a)

So, if we want two identical factors that have a product of x = x^1, then the exponents of those factors will be such that ...

  x^(2a) = x^1

  2a = 1

  a = 1/2

The square root is defined as one of two identical factors that have a product equal to the specified value. That is ...

  (√x)(√x) = x

Above, we have shown that ...

  (x^(1/2))(x^(1/2)) = x

so, we can conclude ...

  √x = x^(1/2)

_____

Additional comment

In like fashion, we can show that the n-th root of a number is the same as that number to the 1/n power. It's really a matter of definition. Since the square of x^(1/2) is x, we call x^(1/2) the square root. It is used commonly enough that it has its own symbol: √x.

Answer:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:

Answer:

Step-by-step explanation:

use an ASA triangle  with law of sine

since we know that 180 = 20 +45 + C   .. solve for C = 115°

now use  law of sines    c/ sin(C) = b/sin(B) .. and solve for b

Sin(20)*100/sin(115) = b

b = 37.73774 ft

that's the hypotenuse of the 45 triangle

SOH CAH TOA   to remember how trig functions fit

use b*Cos(45) = adj

26.6846 = adj

The bird is 26.7 ft. from the ground