A scuba diver descended to an elevation of 250 feet, examined some coral, and then ascended 14 feet to observe a school of clownfish. At what elevation was the school of clownfish

Answer: Nany watched 62.5% of the movies

Step-by-step explanation:

5/8 as a percentage is 62.5%

Answer:

type of fish sold

Answer: type of fish gold

Step-by-step explanation: i took the test

The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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(a)R_(4) = (4.7553 + 3.5355 + 2.092 + 0) × (π/8) ≈ 2.6734. Therefore, R_(4) ≈ 2.6734. (b) The graph and the rectangles can be sketched.(c) The estimate R_(4) is an overestimate. (e) L_(4) = (5 + 4.7553 + 3.5355 + 2.092) × (π/8) ≈ 3.9855. Therefore, L_(4) ≈ 3.9855. The estimate L_(4) is an underestimate.

(a) To estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints, we divide the interval [0, π/2] into four equal subintervals.

The width of each rectangle, Δx, is given by:

Δx = (π/2 - 0) / 4 = π/8

To find the height of each rectangle, we evaluate the function at the right endpoint of each subinterval:

f(π/8) = 5 cos(π/8)

f(π/4) = 5 cos(π/4)

f(3π/8) = 5 cos(3π/8)

f(π/2) = 5 cos(π/2)

Now we can calculate the area of each rectangle and sum them up:

Area of rectangle 1 = f(π/8) × Δx

Area of rectangle 2 = f(π/4) × Δx

Area of rectangle 3 = f(3π/8) × Δx

Area of rectangle 4 = f(π/2) × Δx

R_(4) = (f(π/8) + f(π/4) + f(3π/8) + f(π/2)) × Δx

Let's calculate the values:

f(π/8) ≈ 5 × cos(π/8) ≈ 4.7553

f(π/4) ≈ 5 × cos(π/4) ≈ 3.5355

f(3π/8) ≈ 5 × cos(3π/8) ≈ 2.092

f(π/2) ≈ 5 × cos(π/2) ≈ 0

Δx = π/8

R_(4) = (4.7553 + 3.5355 + 2.092 + 0) × (π/8) ≈ 2.6734

Therefore, R_(4) ≈ 2.6734.

(b) The graph and the rectangles can be sketched as follows:

WebAssign Plot:

 0    π/8    π/4   3π/8   π/2

(c) Since the rectangles are constructed using right endpoints, the estimate R_(4) is an overestimate.

(d) To estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and left endpoints, we use the same process as before, but this time we evaluate the function at the left endpoint of each subinterval.

The width of each rectangle, Δx, is still π/8.

Now we evaluate the function at the left endpoints:

f(0) = 5 cos(0)

f(π/8) = 5 cos(π/8)

f(π/4) = 5 cos(π/4)

f(3π/8) = 5 cos(3π/8)

Area of rectangle 1 = f(0) × Δx

Area of rectangle 2 = f(π/8) × Δx

Area of rectangle 3 = f(π/4) × Δx

Area of rectangle 4 = f(3π/8) × Δx

L_(4) = (f(0) + f(π/8) + f(π/4) + f(3π/8)) × Δx

Let's calculate the values:

f(0) ≈ 5 × cos(0) ≈ 5

f(π/8) ≈ 5 × cos(π/8) ≈ 4.7553

f(π/4) ≈ 5 × cos(π/4) ≈ 3.5355

f(3π/8) ≈ 5 × cos(3π/8) ≈ 2.092

Δx = π/8

L_(4) = (5 + 4.7553 + 3.5355 + 2.092) × (π/8) ≈ 3.9855

Therefore, L_(4) ≈ 3.9855.

(e) Since the rectangles are constructed using left endpoints, the estimate L_(4) is an underestimate.

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Given that the cost is $1.10 per pound, we can calculate the cost per servable pound by dividing the total cost ($1.10 * 4 pounds) by the servable weight (2 pounds). Therefore, the correct option is c. $2.20.

The original weight of the food item is 4 pounds, and the cost per pound is $1.10. Therefore, the total cost of the food item is 4 pounds * $1.10 = $4.40.

The servable weight of the food item is 2 pounds. To find the cost per servable pound, we divide the total cost ($4.40) by the servable weight (2 pounds):

Cost per servable pound = Total cost / Servable weight = $4.40 / 2 pounds = $2.20.

Hence, the cost per servable pound for this food item is $2.20. Therefore, the correct option is c. $2.20.

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If the radius to the inside of the shell is 4 millimeters and the radius to the outside of the shell is 4.3 millimeters. the volume of the shell is 19π mm³.

v = 4 / 3πr³

dv =4 / 3π (3r²) dr

Where:

r= radius = 4 cm

dr = 4.3 -4 = 0.3

Hence,

dv = 4 / 3π (16) 3/10

dv =4 / 3π(16) 0.3

dv = 19.2π mm³

dv = 19π mm³ (Approximately)

Therefore the volume of the shell is 19π mm³.

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The required volume of the given solid is (√16 - r²) -(-√16 - r²).

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

Volume and the notion of length are connected.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.

The cubic meter (m3), a derived unit, is the SI unit of volume.

So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.

We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.

The solid's volume is (√16 - r²) -(-√16 - r²).

Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).

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Correct question:

Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

Answer:

10-35-45 and 5-17.5-22.5

Step-by-step explanation:

Answer: The area of a polygon is defined as the area that is enclosed by the boundary of the polygon. In other words, we say that the region that is occupied by any polygon gives its area.

Step-by-step explanation:

The tree's deviation from the vertical due to wind is 2°. At a distance of 42 meters from the tree's base, the angle of elevation to the top of the tree is 35°. To find the tree's height, we use trigonometry. By setting up and solving the appropriate equation, we can determine that the tree's height is obtained by multiplying the tangent of 88° by 42.

Angle of deviation from the vertical due to prevailing winds: 2°

Distance from the base of the tree: d = 42 meters

Angle of elevation to the top of the tree: a = 35°

To find the height of the tree, we can use trigonometry. Let's denote the height of the tree as h.

Drawing a diagram

Draw a diagram with a vertical line representing the tree, inclined at an angle of 2° from the true vertical. Mark a point 42 meters away from the base of the tree, and draw a line from that point to the top of the tree, forming an angle of 35° with the horizontal.

Setting up the trigonometric equation

In the right-angled triangle formed, the angle between the vertical line and the line connecting the point 42 meters away to the top of the tree is (90° - 2°) = 88°. Using trigonometric ratios, we can set up the following equation:

tan(88°) = h / 42

Solving for the height of the tree

Rearrange the equation to solve for h:

h = tan(88°) * 42

Using a scientific calculator or trigonometric table, find the value of tan(88°) and multiply it by 42 to calculate the height of the tree.

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Answer:

£95

Step-by-step explanation:

Given that:

Whitney's initial amount = £265

Nancy's initial amount = £180

Let amount each spent = x (amount is the same)

After spending Whitney has twice as much money as Nancy.

Amount spent by each?

(Whitney's initial amount - x) = 2(Nancy's initial amount - x)

265 - x = 2(180 - x)

265 - x = 360 - 2x

-x + 2x = 360 - 265

x = £95

Hence, they both spent £95

Answer: 45:18 & 35:10, B & C

Step-by-step explanation:

In the question, it says a student-to-teacher ratio so that would eliminate A. Then you would divide each answer by 5 and 2 and see if it is divisible.

For Example:

45/5 and 18/2 you would get 9 and 9

35/5 and 10/2 you would get 7 and 5

10/5 and 7/2 you would get 2 and a decimal/fraction meaning it is not equivalent

So your answers would be B & C

At the end of the code, max contains the value of the larger of x and y.

The correct fragment of code that assigns the larger of x and y to another integer variable max is:int max;

if (x > y) {

   max = x;

} else {

   max = y;

}

In this code fragment, we first declare the integer variable max without assigning it a value. We then use an if statement to compare x and y. If x is greater than y, we assign x to max, otherwise, we assign y to max. At the end of the code, max contains the value of the larger of x and y.

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Answer:

24 ft

Step-by-step explanation:

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

26^2 = 10^2 + length^2

676 - 100 = length^2

length = 576

find the square root

= 24

Answer:

Step-by-step explanation:

Let's break down the problem:

Quotient =  result obtained by dividing one quantity by another

So its division of x (a number implying variable) by 6

Then it says equal to 2 so we can piece together an equation like this

x/6 = 2

Then we use algebra to solve it

6(x/6)= (2)6

x = 12

So 12 is the unknown number

Step-by-step explanation:

2(3x-7)=4

6x - 14 = 4

add 14 to both sides

6x = 18

divide by 6

x = 3

The expression -2.2f + 0.8f - 11 - 8 when simplified is -1.4f - 19

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

-2.2f+0.8f-11-8=

Express properly

So, we have

-2.2f + 0.8f - 11 - 8

When the like terms are collected, we have

-2.2f + 0.8f - 11 - 8 = -2.2f + 0.8f - 11 - 8

When the like terms are evaluated, we have

-2.2f + 0.8f - 11 - 8 = -1.4f - 19

Hence, the expression when simplified is -1.4f - 19

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Answer:

x = 4 units

Step-by-step explanation:

By geometric mean theorem:

Length of perpendicular

\( =\sqrt{2\times 6}\)

\( =\sqrt{12}\)

Next, by Pythagoras theorem:

\( x^2 = 2^2 + (\sqrt {12})^2 \)

\( \therefore x^2 = 4 + 12 \)

\( \therefore x^2 = 16 \)

\( \therefore x =\sqrt{ 16 }\)

\( \therefore x =4\: units\)

Answer:

h = 440.94 feet

Step-by-step explanation:

It is given that,

An architect is standing 370 feet from the base of a building, x = 370 feet

The angle of elevation is 50°.

We need to find the approximate height of the building. let it is h. It can be calculated using trigonometry as follows :

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=370\times \tan50\\\\h=440.94\ \text{feet}\)

So, the approximate height of the building is 440.94 feet

The probability of getting at least 2 defective chips out of 8 is 0.0061, or about 0.61%

To solve this problem, we need to use the binomial distribution formula, which is:

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

Where:
- P(X = k) is the probability of getting k successes
- n is the total number of trials (in this case, n = 8)
- k is the number of successes we're interested in (at least 2, so we need to calculate P(X = 2) + P(X = 3) + ... + P(X = 8))
- p is the probability of getting success on one trial (in this case, p = 0.01)

So let's calculate each term:

P(X = 2) = 8C2 * 0.01^2 * (1-0.01)^(8-2) = 0.0059
P(X = 3) = 8C3 * 0.01^3 * (1-0.01)^(8-3) = 0.0002
P(X = 4) = 8C4 * 0.01^4 * (1-0.01)^(8-4) = 0.0000
P(X = 5) = 8C5 * 0.01^5 * (1-0.01)^(8-5) = 0.0000
P(X = 6) = 8C6 * 0.01^6 * (1-0.01)^(8-6) = 0.0000
P(X = 7) = 8C7 * 0.01^7 * (1-0.01)^(8-7) = 0.0000
P(X = 8) = 8C8 * 0.01^8 * (1-0.01)^(8-8) = 0.0000

Now we can add up all the probabilities:

P(at least 2 defective chips) = P(X = 2) + P(X = 3) + ... + P(X = 8) = 0.0061

So the probability of getting at least 2 defective chips out of 8 is 0.0061, or about 0.61%. This is a relatively small probability, but it's not impossible, so the manufacturer should still take measures to minimize the number of defective chips produced.

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Given

Large necklace sells for a $4.30

Small necklace sells for $4.10

4 large

1 small

Procedure

Total

The answer would be $21.30

Side PW is congruent to side XG because corresponding parts of congruent triangles are congruent.

Generally speaking, the base angles of an isosceles trapezoid are congruent and equal. This ultimately implies that, an isosceles trapezoid has base angles that are always equal in magnitude.

By critically observing the image of this isosceles trapezoid, we can write a two column table proof to prove that PW ≅ XG as follows;

Statements                                                                         Reasons

1. TRGP is an isosceles trapezoid                                     Given

TW ≅ RX                      2. Altitudes of an isosceles trapezoid are congruent.

TW ⊥ PG and RX ⊥ PG                                                 Altitudes form a 90°

∠TWP and ∠RXG are right angles    Perpendicular lines form right angles.

3. ∠TWP ≅ ∠RXG                                        All right angles are congruent.

4. ∠TPW ≅ ∠RGX            5. Angles opposite to congruent sides are congruent.

6. ∠TWP ≅ ∠RXG                                       AAS Congruence Theorem.

PW ≅ XG                    Corresponding parts of congruent triangles are congruent.

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A 95% confidence interval estimate for the variance of service times for all their new automobiles is (9.29, 31.95).

The 95% confidence interval estimate for the variance of service times for all their new automobiles is calculated as follows:

Lower limit of the confidence interval = (n - 1)S² / χ²₀.₀₂₅

Upper limit of the confidence interval = (n - 1)S² / χ²₀.₉₇₅

Where, n is the sample size, S is the sample standard deviation, and χ² is the chi-square distribution value with degrees of freedom (df) = n - 1. Here, n = 15 and df = n - 1 = 15 - 1 = 14.

So, the chi-square distribution values with df = 14 and α/2 = 0.025 and 1 - α/2 = 0.975 are χ²₀.₀₂₅ and χ²₀.₉₇₅, respectively.

From the chi-square distribution table, we get:

χ²₀.₀₂₅ = 5.632 and χ²₀.₉₇₅ = 25.996.

Now, substituting the given values in the above formula, we have:

Lower limit of the confidence interval = (15 - 1)(4²) / 5.632 = 31.95

Upper limit of the confidence interval = (15 - 1)(4²) / 25.996 = 9.29

Hence, the 95% confidence interval estimate for the variance of service times for all their new automobiles is (9.29, 31.95). Therefore, the answer is  (9.29, 31.95).

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Answer:

51.33

Step-by-step explanation:

Step-by-step explanation

From the boat's standpoint, which is what we want anyway, there is a right triangle, with the distance from the lighthouse the adjacent side, the opposite is 200,' and the boat the point desired. The tangent is needed.

From the boat's standpoint, which is what we want anyway, there is a right triangle, with the distance from the lighthouse the adjacent side, the opposite is 200,' and the boat the point desired. The tangent is needed.tangent 18.33 degrees (33 minutes is 33/60 of a degree)=200x

Answer:

113,046

Step-by-step explanation:

Add inside of parentheses first to get

(498)x(227)

Multiply to get

113,046

Conclusion of the given statement is  a party with a large number of customers is associated with a longer time for the party to leave the restaurant.

What do you mean by correlation?

Correlation is a statistical measure of how linearly two variables are related (that is, do they change at a constant rate). This is a general tool for describing simple relationships without stating cause and effect.

The strength of the linear link between two variables is measured by correlation. A positive correlation suggests a direct relationship between the two variables, whereas a negative correlation shows an inverse relationship.

Additionally, a correlation is deemed to be very weak if its magnitude is less than 0.2. The magnitude is regarded as weak if it is between 0.2 and 0.4. It is regarded as a moderate correlation if it is between 0.4 and 0.6. The magnitude between 0.6 and 0.8 is thus seen as being strong, and any magnitude between 0.8 and 1 is regarded as being extremely strong.

We can draw the following conclusion regarding each of the given statements because there is a correlation coefficient of 0.78 between "The number of clients in a party at the restaurant" and "Time till the party left the restaurant":

Since the order of magnitude is between 0.6 and 0.8, we can say that a party with a large number of customers is associated with a longer time for the party to leave the restaurant.

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Find the slope of the parallel line

(7, 2) and is parallel to y= -2x+1?

When two lines are parallel, they have the same slope.  

                ⇒  if the slope of the given line is = - 2      

                     then the slope of the parallel line (m) = - 2

Determine the equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:  

                              ⇒  y - 2  =  - 2 (x - 7)                                  

We can therefore write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:  

                     since   y - 2  = - 2 (x - 7)  

y = 220/ ((10/3) * √22)

It is given that area is 200 square feet. Cost is 3 dollar per foot. Fourth side costs 12 dollars per foot.

This f(x,y) needs to represent the cost of the fence so we can look at each side's price. We can choose the fourth side to be along the x axis and be represented by 13x. The other sides therefore must be represented by 5y, 5y, and 5x.

So, our cost, f(x,y) = 13x + 5x + 5y + 5y = 18x + 10y

Our constraint is xy = 220 as defined by the area of a rectangle.

We can then take our constraint to be put in terms of exclusively x, giving us y = 220/x

Plugging this into our cost, the thing we are minimizing, we get f(x) = 18x + 2200/x

In order to find the minimum we use the first derivative test, taking f'(x) and finding the critical points.

f'(x) = 18 - 2200/x2

Setting this equation to be equal to 0 we find that x = ±√2200/18 . But the negative answer doesn't make sense because distance cannot be negative so we throw it out.

x = (10/3) * √22

We must verify that this is a minimum by confirming the following:

If x < (10/3) * √22, f'(x) < 0. So, f(x) is decreasing when x < (10/3) * √22.

If x > (10/3) * √22, f'(x) > 0. So, f(x) is increasing when x > (10/3) * √22.

Thus, we have guaranteed that (10/3) * √22 is the x dimension. Now we plug in this value in our original equation to find y and that is our y dimension. So, y = 220/ ((10/3) * √22)

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The correct option, for the sum of the series is

d. its sum is 1/10

To find the sum of the series Σ 1 / (n+9)(n+10), we can rewrite it as follows:

Σ 1 / (n+9)(n+10) * 1(n + 9) = Σ (1 / (n+9)) - (1 / (n+10))  * 1(n + 9)

Now, let's evaluate the terms of the series:

When n = 0:

Term 1: 1 / (0+9) = 1/9

Term 2: 1 / (0+10) = 1/10

Term 3:  1(0 + 9) = 9

Therefore, the sum of the series when n = 0 is:

(1/9 - 1/10) * 9 = 1/90 * 9

So, the sum of the series when n = 0 is 1/10.

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Answer:

5

Step-by-step explanation:

EF = 47 - 7x = 1/2 BC = 1/2 * (14+4x)

solve for x

x=6

so EF = 47-7*6 =  5