A scuba diver descends 63 feet in 18 seconds.
What integer represents the change in the
diver’s position in feet per second

Answer:

look at the photo i have sent

In trigonometry, cos B represents the ratio of the adjacent side to the hypotenuse of a right-angled triangle where angle B is one of the acute angles.

The formula for cos B is given as:cos B = adjacent/hypotenuse Now, let's say we have a right-angled triangle ABC where angle B is the acute angle. The side opposite angle B is BC, the side adjacent to angle B is AB and the hypotenuse is AC. To find the value of cos B, we need to know the values of AB and AC. Once we have these values, we can substitute them in the formula for cos B and calculate the value.

To calculate the value of cos B in degrees, we use a calculator or a trigonometric table. If we have the value of cos B in decimal form, we can use the inverse cos function to find the value of B in degrees. For example, if cos B = 0.6, then B = cos-1 (0.6) = 53.13 degrees.To summarize, to find the value of cos B, we need to know the adjacent and hypotenuse sides of a right-angled triangle where angle B is one of the acute angles.

We can then substitute these values in the formula for cos B and calculate the value. If we have the value of cos B in decimal form, we can use a calculator or the inverse cos function to find the value of B in degrees.

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1:24 since this was asked a min ago

The page is in landscape mode with a width : height is 3: 2

Given that,

The printable area is should be 42 square inches on a rectangular page. The margins at the top and bottom of the page are each one inch, while the margins on one side are one inch and two inches, respectively.

x = length of the horizontal side of the printable area

y = length of the vertical side of the printable area

XY = 42 inch²

y = 42/x

page height = y + 1 + 1

page width = x + 1 + 2

A = area of an entire sheet of paper

  = (x+3)(y+2)

  = (x+3)(42/x+2)

  = x(42/x+2)+3(42/x+2)

  = 42+2x+126/x+6

A = 2x+126/x+48

Extremes occur when A' = 0:

A' = 0 = 2 – 126/x²

1 = 63/x²

x² = 9*7

x = 3√(7), x has to be positive

y = 42/x = 42/(3√(7)) = 14√(7)/7 = 2√(7)

What should the dimensions of the page be so that the least amount of paper is used?

page width = x + 3 = 3√(7) + 3 = 3(√(7) + 1)

page height = y + 2 = 2√(7) + 2 = 2(√(7) + 1)

So, the page is in landscape mode with width: height is 3: 2.

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Answer:

The Answer is 850$

Answer:

The square root of 39 is approximately 6.245 so it lies between 6 and 7

Answer:

\(\sqrt{39}\) is located between 6 and 7

Step-by-step explanation:

the square root of 39 is about 6.245. This number is located between the whole numbers 6 and 7.

6 x 6 = 38

39 is in the between

7 x 7 = 49

ANSWER :

139 feet

EXPLANATION :

The surveyor is 150 feet away from the base of the pole.

The transit is 4 feet tall and the angle of elevation to the top of the pole is 42 degrees.

The illustration will be :

We have a right triangle with an angle of 42 degrees.

The side opposite to the angle is x and the side adjacent to the angle is 150

Using Tangent function :

The height of the pole is x + 4

That will be 135 + 4 = 139 ft

Hi!

I can help you with joy!

How to Find the Reciprocal of a Number?

\(\star\bigstar\) Simply flop the number over.

Example: Suppose we need to find the reciprocal of 2.

We flop it over and get

\(\displaystyle\frac{1}{2}\)

Thus, the reciprocal of -3 is

\(\displaystyle-\frac{1}{3}\)

Hope it helps!

Enjoy your day! :)

\(\bf{-MistySparkles^**^*\)

The probability that exactly 17 people out of 100 will have a tree allergy if the prevalence of the allergy in the general population is 0.17 is 0.1056.

The probability of a single person having the allergy is 0.17. The probability of 17 people out of 100 having the allergy can be calculated using the binomial distribution. The binomial distribution is a probability distribution that describes the number of successes in a fixed number of trials, where each trial has a known probability of success.

In this case, the number of trials is 100 and the probability of success is 0.17. The probability of exactly 17 successes is given by the following formula:

P(X=k) = n! / (k!(n-k)!) * p^k * (1-p)^(n-k)

where:

* X is the number of successes

* n is the number of trials

* k is the number of successes we want to calculate the probability of

* p is the probability of success

* (n!) is the factorial of n

* (k!) is the factorial of k

* (n-k)! is the factorial of n-k

Plugging in the values for n, k, and p, we get the following probability:

P(X=17) = 100! / (17!(100-17)!) * 0.17^17 * (1-0.17)^(100-17)

≈ 0.1056

This means that there is a 10.56% chance that exactly 17 people out of 100 will have a tree allergy if the prevalence of the allergy in the general population is 0.17.

It is important to note that this is just a probability. It is possible that more or fewer than 17 people will have the allergy, but the probability of this happening is very low.

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The probability that exactly 17 people out of 100 will have a tree allergy if the prevalence of the allergy in the general population is 0.17 is 0.1056.

The probability of a single person having the allergy is 0.17. The probability of 17 people out of 100 having the allergy can be calculated using the binomial distribution. The binomial distribution is a probability distribution that describes the number of successes in a fixed number of trials, where each trial has a known probability of success.

In this case, the number of trials is 100 and the probability of success is 0.17. The probability of exactly 17 successes is given by the following formula:

P(X=k) = n! / (k!(n-k)!) * p^k * (1-p)^(n-k)

where:

* X is the number of successes

* n is the number of trials

* k is the number of successes we want to calculate the probability of

* p is the probability of success

* (n!) is the factorial of n

* (k!) is the factorial of k

* (n-k)! is the factorial of n-k

Plugging in the values for n, k, and p, we get the following probability:

P(X=17) = 100! / (17!(100-17)!) * 0.17^17 * (1-0.17)^(100-17)

≈ 0.1056

This means that there is a 10.56% chance that exactly 17 people out of 100 will have a tree allergy if the prevalence of the allergy in the general population is 0.17.

This means that there is a 10.56% chance that exactly 17 people out of 100 will have a tree allergy if the prevalence of the allergy in the general population is 0.17.

It is important to note that this is just a probability. It is possible that more or fewer than 17 people will have the allergy, but the probability of this happening is very low.

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The probability of spinning two greens on the spinner is equal to 1/16.

We need to find the probability of spinning a green on the first spin and then the probability of spinning another green on the second spin.

Since 4 equal sections on the spinner and one of them is green, the probability of spinning a green on the first spin is 1/4.

Therefore, the probability of spinning a green on the second spin is; 1/4.

P(spinning two greens) = P(green on first spin) x P(green on second spin)

= (1/4) * (1/4)

= 1/16

Therefore, the probability of spinning two greens on the spinner = 1/16.

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Answer:

16

Step-by-step explanation:

since one pie goes for quater cup then four cups makes 16quaters

Answer:

\((x^2 -4y^2)^2\)

Step-by-step explanation:

\(x^4 -8x^2 y^2 +16y^4 \\ x^4 -4x^2 y^2 -4x^2 y^2 +16y^4 \\ (x^4 -4x^2 y^2) +(-4x^2 y^2 +16y^4) \\ x^2(x^2 -4y^2) -4y^2(x^2 -4y^2) \\ (x^2 -4y^2)(x^2 -4y^2) \\ (x^2 -4y^2)^2\)

The number of plastic tubing needed to fit around the edge of the pool is 423.3 ft².

The number of plastic tubing needed to fit around the area is calculated from the difference between the area of the rectangle and area of the circular pool.

Area of the circular pool is calculated as;

A = πr²

where;

A = π (15 ft / 2)²

A = 176.7 ft²

The area of the rectangle is calculated as follows;

A = length x breadth

A = 20 ft x 30 ft

A = 600 ft²

The number of plastic tubing needed to fit around the edge of the pool is calculated as;

The difference in the area = 600 ft² - 176.7 ft² = 423.3 ft²

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Answer:

Step-by-step explanation:

Essentially, we can use the pythagorean rule that:

a^2+b^2=c^2

c^2 resembles the hypotenuse, which is almost always the largest number. therefore, we simply have to find two which equal the largest side:

9^2+40^2=41^2

81+1600=1681

1681=1681

Based on this math, A is our right angle!

Hope this helps!

A new form of the triple integral \(\int\limits^1_0\int\limits^x_0\int\limits^y_0 {f(x,y,z)} \, dzdydx\) as a = 0, b = 1, g2(z) = 1, h2(y,z) = 1.

In other words, we want the integration order to be totally reversed for

\(\int\limits^1_0\int\limits^x_0\int\limits^y_0 {f(x,y,z)} \, dzdydx\)

Keep in mind that this area is quite simple to define. The planes z = y and y = x, as well as the coordinate planes x=y=z=0 , define our boundaries. We essentially have upper bounds z = y = x = 1 because x ∈[ 0, 1 ]. Therefore, we can alternatively express the region as:-

0 ≤ x ≤ y

0 ≤ y ≤ z

z∈ I0,1I. So

\(\int\limits^1_0\int\limits^x_0\int\limits^y_0 {f(x,y,z)} \, dzdydx = \int\limits^1_0\int\limits^z_0\int\limits^y_0 {f(x,y,z)} \, dxdydz\)

Remember that a double integral could be set up in two different ways. Our number of alternative orders of integration increases from two to six when we include that third integral. We will rewrite the supplied integral in one of the other five possible orders in this exercise.

hence,

\(\int\limits^1_0\int\limits^x_0\int\limits^y_0 {f(x,y,z)} \, dzdydx = \int\limits^1_0\int\limits^z_0\int\limits^y_0 {f(x,y,z)} \, dxdydz\)

Therefore, the new form of the triple integral \(\int\limits^1_0\int\limits^x_0\int\limits^y_0 {f(x,y,z)} \, dzdydx\) as a = 0, b = 1, g2(z) = 1, h2(y,z) = 1.

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Answer:

18 square centimeters

Step-by-step explanation:

YW :)

Answer:

Ariana is correct.

Step-by-step explanation:

56 - 11 min to warm up = 45 mins of running

9 min per mile*5 miles = 45 mins of running

Ariana is correct because of the work shown above.

Hope this helps!

Answer:

A & C

Step-by-step explanation:

Factors of 18 : 1, 2, 3, 6, 9, 18

18

/\

2 9

/\

3 3

Prime factorization : 18 = 2x3x3

18

/\

3 6

/\

2 3

Prime factorization : 18 = 3x2x3

The correct option for the area of the figure formed by a triangle and a parallelogram is 32 square millimeters.

To get the area of the figure, we solve for the area of the triangle and that of the parallelogram, and then add our results together.

area of a triangle is half the product of its base and height

area of parallelogram is the base multiplied by its height

the triangle has base = 8mm and height = 3mm

so

area of the triangle = (8mm × 3mm)/2

area of the triangle = 24mm²/2

area of the triangle = 12mm²

the parallelogram has base = 5mm and height = 4mm

so

area of the parallelogram = 5mm × 4mm

area of the parallelogram = 20mm²

Therefore, the area of the figure which is the sum of the area of the triangle and the area of the parallelogram is;

12mm + 20mm² = 32mm² or 32 square millimeters

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Answer: 2x, x^3, 3x^4, 4x^5, 34

Step-by-step explanation:

Standard form starts with the lowest degree to the highest, then ends with any naked numbers

Trigonometric functions  ,The value of the given expression, cos² 60° + sin 30° * (tan 45° - 2), is -1/4.

Given expression,

1. Start by evaluating the trigonometric functions:

  - cos² 60° = (1/2)² = 1/4

  - sin 30° = 1/2

  - tan 45° = 1

2. Substitute the values into the expression:

  cos² 60° + sin 30° * (tan 45° - 2)

  = (1/4) + (1/2) * (1 - 2)

3. Simplify the expression further:

  = 1/4 + 1/2 * (-1)

  = 1/4 - 1/2

  = 1/4 - 2/4

  = -1/4

Therefore, the value of the given expression, cos² 60° + sin 30° * (tan 45° - 2), is -1/4.

Trigonometric functions such as cosine (cos), sine (sin), and tangent (tan) represent the ratios between the sides of a right triangle. By substituting the corresponding angle values, we can evaluate these functions. In this case, we evaluated the functions for 60°, 30°, and 45°, and then substituted them into the given expression. Finally, we simplified the expression to obtain the result of -1/4.

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comparing value

3x+2=-3x-2

6x=-4

x=-4/6Have solution.

y=-2x+10

y=-2x+10

both are equal So no solution.

3rd

y=-x+4

y=-x+4

both are equal So no solution

4th

3x+y=8

3x+y=9

both are equal So no solution

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

|           | Popcorn | No Popcorn |

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

| Drink     |    74   |     15     |

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

| No Drink  |    10   |     6      |

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

The completed two-way table is as shown above.

We construct a two-way table summarizing the results. Let's use the information provided:

1. 105 people entered the theatre
2. 84 people had popcorn
3. 10 out of 84 people with popcorn did not have a drink
4. 6 people walked in without popcorn or a drink

Now let's construct the two-way table:

---------------------------
|           | Popcorn | No Popcorn |
---------------------------
| Drink     |    A    |     B      |
---------------------------
| No Drink  |    C    |     D      |
---------------------------

We need to fill in the values for A, B, C, and D:

1. A = People with popcorn and a drink = Total with popcorn - those without a drink = 84 - 10 = 74
2. C = People with popcorn but no drink = 10 (given in the question)
3. D = People with neither popcorn nor a drink = 6 (given in the question)
4. To find B, we need to find the total number of people with a drink. We know 105 people entered, and 6 had neither popcorn nor a drink, so there were 105 - 6 = 99 people with either popcorn or a drink. Since 84 people had popcorn, this means there were 99 - 84 = 15 people with only a drink.
5. B = People with a drink but no popcorn = 15

Now let's fill in the table:

---------------------------
|           | Popcorn | No Popcorn |
---------------------------
| Drink     |    74   |     15     |
---------------------------
| No Drink  |    10   |     6      |
---------------------------

So, the completed two-way table is as shown above.

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The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y-4=1/4(x-8). The slope-intercept form of the equation for this line is y = x/4 + 2.

The equation of the line in the point-slope form :

y - b = m(x - a)

where m is the slope and (a,b) are the points on the line.

y - 4 = (x - 8)/4

Here, m = 1/4 and (a,b) = (8,4)

The equation of the line in slope-intercept form:

y = mx +c

y = x/4 + c

To find c, putting (8,4) into the above equation,

4 = 2 + c

c = 2

Therefore, y = x/4 + 2 is the slope-intercept form.

What is the intercept?

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The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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