[tex]cos\frac{\pi }{30}cos\frac{\pi }{5} + sin\frac{\pi }{30} sin\frac{\pi }{5}[/tex]

Answer:

The time duration of the ocra whale spends under water is 4 seconds

Step-by-step explanation:

The equation that model the path of the ocra whale is presented as follows;

k(x) = x² - 2·x - 8

Where;

x = The time elapsed in seconds under water

k(x) = The height in feet below water

Therefore, the point where the ocra whale enters the water, k(x) = 0

At the point of submerging below the water surface, we have;

k(x) = 0 = x² - 2·x - 8

Factorizing the quadratic equation gives;

0 = x² - 2·x - 8 = (x - 4)·(x + 2)

Therefore, when k(x) = 0, either;

(x - 4) = 0, which gives, x = 4

(x + 2) = 0, which gives, x = -2

Given that 'x' represent the time, the time elapsed while the whale is under water, x = 4 seconds

Part (A)

We have 6 red and 4 blue marbles, so 6+4 = 10 total.

The probability of getting red is 6/10 since we have 6 red out of 10 total.

The probability of getting another red is 5/9 because we don't put the first marble back.

The probability of getting two reds in a row is (6/10)*(5/9) = 30/90 = 1/3

========================================================

Part (B)

4/10 represents the probability of getting blue on the first try

3/9 represents the probability of getting a blue marble on the second try

We don't put the marble back.

(4/10)*(3/9) = 12/90 = 4/30 is the probability of getting two blues in a row.

========================================================

Part (C)

Add up the results of parts (A) and (B)

1/3 + 4/30

10/30 + 4/30

(10+4)/30

14/30

7/15

The result 7/15 is the probability of either getting two reds OR getting two blues (pick one case only). This tells us that 7 out of 15 times we'll have this happen. This must mean the remaining 8 times will have two marbles of different colors.

So 8/15 is the probability of picking one marble of each color.

------

As an alternative, we could also consider it like this

(6/10)*(4/9) = 24/90 = 4/15

This represents the probability of picking red first, then blue next.

Similarly,

(4/10)*(6/9) = 24/90 = 4/15

represents the probability of picking blue first, then red next.

Therefore, 4/15+4/15 = 8/15 is the probability of getting one of each color.

-----

Answer:

527.52cm^2

Step-by-step explanation:

First we need to find the eqauation of this which is:

2 pi*r^2 + 2 pi*r*h

The raduis is half of the diameter so 3

Now just plug in the values and solve

2*3.14*3^2 + 2*3.14*3*25

The answer is 527.52

If you were to round it you would get

527.5 or 528

hope this helps have a good day/night <3

Answer:

x < 10

Step-by-step explanation:

2x-8 <12

Add 8 to each side

2x-8+8 <12+8

2x< 20

Divide by 2

2x/2 < 20/2

x < 10

Answer:

The third one is the answer.

Answer:

[D] [tex]\displaystyle \lim_{h \to 0} \frac{[5(x + h)^2 - 2(x + h)] - (5x^2 - 2x)}{h}[/tex]

General Formulas and Concepts:

Calculus

Limits

Derivatives

Definition of a Derivative: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = 5x^2 - 2x[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

Step-by-step explanation:

x-axis:(2,-3)

y-axis:(-2,3)

Answer:

y = (-3/4)x + 7

Step-by-step explanation:

Answer:

y = -3/4x - 7

Step-by-step explanation:

Slope Intercept form: y=mx + b where m = slope and b = intercept.

Isolate y.

9x + 12y = -84

-9x             -9x (subtract 9x from both sides)

12y = -9x - 84

(divide by 12)

y = -9/12x - 7

(simplify fraction)

y = -3/4x - 7

Answer:

3/5

Step-by-step explanation:

There are 12 window seats and 8 aisle seats giving us a total of 20 seats.

12/20 = 3/5

Therefore, the probably the next person will be assigned a window seat is 3/5.

Answer:

a² + 16a - 612 = 0

Step-by-step explanation:

Here is the complete question :

The width of an extra large rectangle poster is 8 inches more than half its length. The area of this poster is 306 square inches

Write an equation in one variable that could be used to find the number of inches in the dimensions of this poster.

Area of a rectangle = length x width

Let length = a

width = 8 + 1/2a

Area =  (8 + 1/2a) x a

306 =  (8 + 1/2a) x a

multiply both sides of the equation by 2

612 = 16a + a²

a² + 16a - 612 = 0

the dimensions of the poster can be determined using quadratic formula

Answer:

0.1

Step-by-step explanation:

Answer:

√2 = 1.41

√5 = 2.23

SO IF YOU MULTIPLY SEE

3.1622776601683793319988935444327

Step-by-step explanation:

Answer:

C) 80

Step-by-step explanation:

triangles always add up to 180 degrees, so 80+20=100 the missing angle is 80 degrees

Answer:

-6 < x < -5

Step-by-step explanation:

(x+7)^5 = 20

Raise both sides to the (1/5) power

x + 7 = 1.820564203

Subtract 7 from both sides

x = -5.179435797

-6 < x < -5

CP hens remianing = 5000

A. cone

D. triangular pyramid

E. square pyramid

(Look at the photo at the bottom.)

First, know what a cross section is. A cross section is the exposed shape or surface when a straight cut is made through a 3D figure. For example, if I make a cross section, or cut, through a sphere, the cross section will be a circle. The newly exposed surface is in the shape of a circle.

We want to know which 3D figures can make 2 different cross sections, parallel to the base, that are congruent. Congruent means same shape but different size. Parallel to the base means the cut is completely horizontal.

Here's a photo of Edge incase you're doubtful.

Answer: A, D, E

Step-by-step explanation:

Answer:

option 4

Step-by-step explanation:

Given

f(x) = x² - 5x - 6

To find the zeros let f(x) = 0 , that is

x² - 5x - 6 = 0

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)

The factors are - 6 and+ 1, since

- 6 × 1 = - 6 and - 6 + 1 = - 5 , then

(x - 6)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 6 = 0 ⇒ x = 6

Answer:

11

Step-by-step explanation:

Drum stick = 11 grams of protein.

Cheese sticks (x) = 7grams.

Let Y represents the range of function.

y = 11 + 7x

Let the domain is x > = 0

range is y > = 11

Answer:

4

Step-by-step explanation:

3*5*4*3*2*1

3x-x+2=4

Answer:

C.   107°

Step-by-step explanation:

Angles 4 and 8 measures the same since they're congruent.

A straight line measures 180°

180° - 73° = 107°

Answer:

1 is the answer have a good day

Answer:

Mean = 10

Variance = 30.89

Standard Deviation = 5.56

Step-by-step explanation:

Find the Mean, Variance and Standard deviation

6, 14, 8, 2, 11, 7, 12, 4, 18, 18

Step 1

We rearrange the data and find the Mean

2, 4, 6, 7, 8, 11, 12, 14, 18, 18

Mean = Sum of values/Number of values

= 2 + 4+ 6+ 7+ 8 + 11 + 12 + 14 + 18 +18/10

= 100/10

= 10

Step 2

We find the variance of this sample days ma

Variance = (x - Mean)²/n - 1

n = 10

Hence,

=( (2 - 10)² +(4 - 10)²+ (6 - 10)²+ (7 - 10)² + (8 - 10)² + (11 - 10)² + (12 - 10)² + (14 - 10)² + (18 - 10)² +(18 - 10)²) /10 -1

= ( 64 + 36 + 16 + 9 + 4 + 1 + 4 + 16 + 64 +64)/9

= 278/9

= 30.88888889

Approximately = 30.89

Step 3

Standard Deviation = √Variance

= √30.89

= 5.5578772926

Approximately = 5.56

Answer

A.x=8

1/3x-2/3x=2

x-2=6

x=6x2

x=8

Answer: 190

Step-by-step explanation:

Answer:

C. 137

Step-by-step explanation:

Answer:

2.0936 * [tex]10^{2}[/tex]

Hope that this helps!

Answer:

675in

Step-by-step explanation:

not it

Answer:

s+18=120

s=102

Step-by-step explanation:

Basically, she had 120 after everything was done, so we know 120 is on the right side of the equal sign. We know she had an unknown number of songs and after she added 18 it was 120. That means the equation is s+18=120

Now to solve it is simple, just isolate s by subtracting 18 on both sides.

s+18=120

-18       -18

s=102

Answer:

Answer:

Correlation coefficient for the data in the table was found to be 0.93

Step-by-step explanation:

The correlation coefficient for the data in the table is 0.93.

The correlation coefficient is used to measure the relationship that exists between two or more variables. If two variables have a positive correlation, as one of the variable increases, the other variable increases. If one of the variable decreases, the other variable decreases.

When calculated on a financial calculator, the correlation coefficient is 0.93.

To learn more about correlation, please check: https://brainly.com/question/27246345

#SPJ2

Answer:

The value of w is -9.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-9-7)/(w-(-5))

m=-16/(w+5)

-16/(w+5)=4

w+5=-16/4

w+5=-4

w=-4-5

w=-9

Step-by-step explanation:

x²+x²= 10

2x²=10

x²=10/2=5

x =√5 or 2.24

Answer:

16 square units

Step-by-step explanation:

hope that helps

Answer:

A

Step-by-step explanation:

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