Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below

Answer:

In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg. So AC = 80√3.

In a 45°-45°-90° triangle, both legs are congruent. So BC = 80.

AB = AC - BC = (80√3 - 80) meters

= 80(√3 - 1) meters

= about 58.56 meters

The distance between points A and B is approximately 138.6 meters.

To find the distance between points A and B, we can use the concept of trigonometry and the given information.

Let's denote the distance between points A and B as x.

From point A, the angle of elevation to the top of the cliff at point D is 30°. This means that in the right triangle formed by points A, D, and the top of the cliff, the opposite side is the height of the cliff (80.0 m) and the adjacent side is x. We can use the tangent function to calculate the length of the adjacent side:

tan(30°) = opposite/adjacent

tan(30°) = 80.0/x

Simplifying the equation, we have:

x = 80.0 / tan(30°)

Using a calculator, we can find the value of tan(30°) ≈ 0.5774.

Substituting the value, we get:

x = 80.0 / 0.5774

Calculating the value, we find:

x ≈ 138.6 meters

In light of this, the separation between positions A and B is roughly 138.6 metres.

for such more question on distance

https://brainly.com/question/12356021

#SPJ8

The equation of the normal line to the curve x^2y^2 = 4 at the point (-1,-2) is y = x - 1.

To find the tangent line and normal line to the curve x^2y^2 = 4 at the point (-1,-2), we need to determine the derivative of the curve equation with respect to x and evaluate it at the given point.

First, let's differentiate the equation x^2y^2 = 4 implicitly with respect to x using the chain rule:

2x * (y^2) + 2y * (2xy * dy/dx) = 0

Simplifying the equation, we have:

2xy^2 + 4xy(dy/dx) = 0

Now, let's find the value of dy/dx at the point (-1,-2). Substitute x = -1 and y = -2 into the equation:

2*(-1)(-2)^2 + 4(-1)*(-2)(dy/dx) = 0

Simplifying further:

8 + 8(dy/dx) = 0

8(dy/dx) = -8

dy/dx = -1

We have found the derivative dy/dx at the point (-1,-2), which is -1. This represents the slope of the tangent line to the curve at that point.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - y₁ = m(x - x₁)

Substituting the values of (-1,-2) and dy/dx = -1 into the equation, we have:

y - (-2) = -1(x - (-1))

y + 2 = -1(x + 1)

y + 2 = -x - 1

y = -x - 3

Therefore, the equation of the tangent line to the curve x^2y^2 = 4 at the point (-1,-2) is y = -x - 3.

To find the normal line, we know that the slope of the normal line is the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is 1.

Using the point-slope form of a line again, we can write the equation of the normal line as:

y - y₁ = m'(x - x₁)

Substituting the values of (-1,-2) and m' = 1 into the equation, we have:

y - (-2) = 1(x - (-1))

y + 2 = x + 1

y = x - 1

for such more question on normal line

https://brainly.com/question/27877215

#SPJ8

Answer:    -8 ≥ x

Step-by-step explanation:

Let x be the number, we set up an inequality:

-183 ≥ 9 + 24x    [we use ≥ to present "at least"]

-192 ≥ 24x

  -8 ≥ x

Answer:

Step-by-step explanation:

Bisector means breaking the segment in half.

answer is A. to have a length exactly half the segment

Answer:

-9(x+1) < 12x+9

if you need me to solve it here it is:

-9x - 9 < 12x + 9

     + 9           +9

-9x      < 12x + 18

-12x       -12x

-18x     <          18

(divide by -18 on both sides)

x < - 1

Therefore, any number is that is greater than -1 will work for this inequality.

Hope this helps!

The opposite of -5 can be represented by situations such as a temperature increase of 5 degrees and a financial gain of $5. Additionally, it can also represent a distance traveled of 5 miles and a weight gain of 5 pounds.

The opposite of -5 is 5. The opposite of a number represents the number with the opposite sign. Here are three situations that can be represented by the opposite of -5:

Situation 1: Temperature Change

If the temperature is currently -5 degrees Celsius and it undergoes a change in the opposite direction, it means it increases by 5 degrees. Therefore, the opposite of -5 represents a temperature increase of 5 degrees.

Situation 2: Financial Gain

Suppose you owe someone $5, and you receive the opposite of that amount. The opposite of owing $5 would be gaining $5. So, the opposite of -5 represents a financial gain of $5.

Additional situations that can be represented by the opposite of -5:

Situation 3: Distance Traveled

If a car has traveled -5 miles, indicating it has moved in the opposite direction, the opposite of that distance would be 5 miles. So, the opposite of -5 represents a distance traveled of 5 miles.

Situation 4: Weight Gain

Imagine someone loses 5 pounds (which can be represented as -5). The opposite of losing 5 pounds would be gaining 5 pounds. Thus, the opposite of -5 represents a weight gain of 5 pounds.

In each of these situations, the opposite of -5 denotes a change in the opposite direction or the reverse of the initial value.

for such more question on situations

https://brainly.com/question/7890421

#SPJ8

Answer:

B. Lenghts of the diagonals

Step-by-step explanation:

Answer:

The 3rd answer is correct.

Step-by-step explanation:

The question involves a mathematical understanding of graphs and data interpretation, specifically ratios. To answer a question like this, typically, you would need to analyze both the graph and table for consistent ratio values. Though the question specifics are unclear, the broader concept involves understanding how ratios can be graphically represented.

Given that the question involves ratios and cards, it appears to fall under a mathematical scope, specifically the interpretation of graphs and data. However, the information provided doesn't give specific details about Chad's data, the ratios of his sports game cards, or the graph he created that shows the possible ratios for Pitchers cards to Infield cards.

Typically, to validate any findings, you would need to look at the graph and the table. Comparing the values of the ratios in the table to the characteristics of the graph would help substantiate any claims. For instance, if Chad's graph shows that there's a 1:2 ratio of pitcher cards to Infield cards, this should be reflected in the table of his sports game cards.

Despite the ambiguous details in the question, you can still grasp the concept of ratios and how they can be represented graphically. For example, if you have a 3:5 ratio of oranges to apples, this can be depicted on a graph where one unit on the Y-axis represents 3 oranges and the corresponding unit on the X-axis signifies 5 apples.

https://brainly.com/question/33676187

#SPJ2

Answer:

Step-by-step explanation:

To find the values of the given expressions using the function g(x) = 2x^2 - 2x + 9, we substitute the given values into the function and simplify the expression. Let's calculate each of the following:

a) g(0)

To find g(0), substitute x = 0 into the function:

g(0) = 2(0)^2 - 2(0) + 9

g(0) = 0 - 0 + 9

g(0) = 9

b) g(-1)

To find g(-1), substitute x = -1 into the function:

g(-1) = 2(-1)^2 - 2(-1) + 9

g(-1) = 2(1) + 2 + 9

g(-1) = 2 + 2 + 9

g(-1) = 13

c) g(2)

To find g(2), substitute x = 2 into the function:

g(2) = 2(2)^2 - 2(2) + 9

g(2) = 2(4) - 4 + 9

g(2) = 8 - 4 + 9

g(2) = 13

d) g(-x)

To find g(-x), substitute x = -x into the function:

g(-x) = 2(-x)^2 - 2(-x) + 9

g(-x) = 2x^2 + 2x + 9

e) g(1 - t)

To find g(1 - t), substitute x = 1 - t into the function:

g(1 - t) = 2(1 - t)^2 - 2(1 - t) + 9

g(1 - t) = 2(1 - 2t + t^2) - 2 + 2t + 9

g(1 - t) = 2 - 4t + 2t^2 - 2 + 2t + 9

g(1 - t) = 2t^2 - 2t + 9

Therefore:

a) g(0) = 9

b) g(-1) = 13

c) g(2) = 13

d) g(-x) = 2x^2 + 2x + 9

e) g(1 - t) = 2t^2 - 2t + 9

Answer:

Step-by-step explanation:

A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres

20 * 10 * 10 = 2000cm^3

1000 cm^3 = 1 Litres

​2000 cm^3 = 2 Litres

Answer:

Jana is likely trying to solve option B:

"A person can afford a $290-per-month loan payment. If he is being offered a 4-year loan with an APR of 0.6%, compounded monthly, what is the most money that he can borrow?"

Step-by-step explanation:

Option B is the correct choice because it aligns with the values entered by Jana into the TVM Solver. Jana set the loan term (N) to 48, which represents 48 months (4 years). The APR value of 0.6% also matches what Jana inputted.

By selecting option B, Jana is attempting to find out the maximum amount of money she can borrow given that she can afford a $290-per-month loan payment and is offered a 4-year loan with an APR of 0.6%, compounded monthly.

This calculation will help Jana determine the loan amount that corresponds to her desired monthly payment and the given loan terms.

The regression line is y = -0.1471x + 2.2386.

To determine the regression line using the LinReg(ax+b) function, we input the given data into the calculator and obtain the values for a and b in the regression equation.

Using the LinReg(ax+b) function with the given data, we have:

X: {14.56, 13.58, 12.69, 14.87, 15.68, 14.28}

Y: {0.25, 0.84, 0.71, 0.65, 0.35, 0.61}

After performing the regression analysis, we obtain the regression equation as follows:

y = -0.2012x + 3.4986

Therefore, the regression line is y = -0.2012x + 3.4986.

Please note that the numerical values provided for a and b are rounded to four decimal places for simplicity.

To check the regression line, we can substitute the given x-values into the equation and compare the calculated y-values with the actual y-values to verify the accuracy of the regression line.

For similar question on regression line.

https://brainly.com/question/17004137

#SPJ8

Answer:

x = 40

you can guess and check.

Answer:

5⁴

Step-by-step explanation:

625= 5×5×5×5

Answer:

The smallest number is 40.

Step-by-step explanation:

Let the number be x. Then the next 4 number will be x+2, x+4, x+6, x+8

.°. x+x+2+x+4+x+6+x+8 = 220

5x + 20 = 220

5x = 200

x = 40

Therefore the smallest of the five consecutive numbers is 40

Mark me as brainliest if you find my answer''Mark-worthy'' :)

The values of L and M in the triangle displayed are 55 and 60 respectively.

The value of angle L can be obtained thus :

125 + L = 180 (sum of angles in a triangle)

L = 180 - 125 = 55°

B.

The value of L can be calculated thus:

55 + (2x - 10) + 65 = 180 (sum of internal angles of a triangle)

120 + 2x - 10 = 180

110+2x = 180

2x = 180-110

x = 35

M = 2(35) -10 = 60°

Therefore, L = 55 and M = 60.

Learn more on Angles:https://brainly.com/question/25770607

#SPJ1

Answer:

First, the graph is overall decreasing with two local maximums and two local minimums.

Second, it has 5 zeros, since there is one intersection and two touching points with the x-axis.

Considering the above observations we can state that:

Third option is correct.The midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b) is (0, b/2).

To find the midpoint of segment WZ, we need to average the x-coordinates and the y-coordinates of the endpoints.

The coordinates of point W are (0, 0), and the coordinates of point Z are (0, b).

To find the x-coordinate of the midpoint, we average the x-coordinates of W and Z:

(x-coordinate of W + x-coordinate of Z) / 2 = (0 + 0) / 2 = 0 / 2 = 0

To find the y-coordinate of the midpoint, we average the y-coordinates of W and Z:

(y-coordinate of W + y-coordinate of Z) / 2 = (0 + b) / 2 = b / 2

Therefore, the midpoint of segment WZ is (0, b/2).

So, the correct answer is (0, b/2).

For more such questions on midpoint

https://brainly.com/question/5566419

#SPJ8

Answer:

Given that sin(θ) = 8/17 and tan(θ) < 0, we can use the trigonometric identity to find cos(θ).

Since sin(θ) = opposite/hypotenuse, we can assign a value of 8 to the opposite side and a value of 17 to the hypotenuse.

Let's assume that θ is an angle in the second quadrant, where sin(θ) is positive and tan(θ) is negative.

In the second quadrant, the x-coordinate (adjacent side) is negative, and the y-coordinate (opposite side) is positive.

Using the Pythagorean theorem, we can find the length of the adjacent side:

adjacent^2 = hypotenuse^2 - opposite^2

adjacent^2 = 17^2 - 8^2

adjacent^2 = 289 - 64

adjacent^2 = 225

adjacent = √225

adjacent = 15

Therefore, the length of the adjacent side is 15.

Now we can calculate cos(θ) using the ratio of adjacent/hypotenuse:

cos(θ) = adjacent/hypotenuse

cos(θ) = 15/17

So, cos(θ) = 15/17.

Answer:

$7000

Step-by-step explanation:

700,000 dollars is equal to 70,000,000 pennies.

To convert 700,000 to pennies.

We need to multiply the number by 100, since there are 100 pennies in a dollar.

1 dollar = 100 pennies.

So,  700,000 × 100

= 70,000,000

Therefore, 700,000 is equal to 70,000,000 pennies.

To learn more on Conversion factor click:

https://brainly.com/question/30567263

#SPJ2

Answer:

I can't understand the language but try people who can

From the Table display of scores and students on a recent exam, The mean of the scores to the nearest 10th is  83.7.

To find the mean of the scores, we need to calculate the sum of the products of each score and its corresponding number of students, and then divide it by the total number of students.

Here's the calculation:

(70 * 6) + (75 * 3) + (80 * 9) + (85 * 5) + (90 * 7) + (95 * 8) = 420 + 225 + 720 + 425 + 630 + 760 = 3180

Total number of students = 6 + 3 + 9 + 5 + 7 + 8 = 38

Mean = Sum of products / Total number of students = 3180 / 38 ≈ 83.7 (rounded to the nearest tenth)

Therefore, the mean of the scores is approximately 83.7.

Know more about mean here:
https://brainly.com/question/1136789

#SPJ8

The slope of 0.75 corresponds to option 3. So, the correct answer is 3) 0.75.

To find the slope, we can use the formula for the slope of a line:

slope (m) = (change in y) / (change in x)

In this case, x represents the number of miles to the destination and y represents the total cost of the load.

Given that the charge to deliver a load 40 miles is $280 and the charge to deliver a load 56 miles is $292, we can set up two points on the line: (40, 280) and (56, 292).

Now let's calculate the change in y and change in x:

Change in y = 292 - 280 = 12

Change in x = 56 - 40 = 16

Plugging these values into the slope formula:

slope (m) = (change in y) / (change in x) = 12 / 16 = 0.75

Therefore, the slope of the line representing the relationship between the number of miles (x) and the total cost of the load (y) is 0.75.

Option 3 is correct.

For more such questions on slope visit:

https://brainly.com/question/16949303

#SPJ8

The discriminant value associated with this equation include the following: A. -5.

In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

In this scenario, we would determine the number of zeros by using the discriminant formula as follows;

Discriminant, D = b² - 4ac

This ultimately implies that, the discriminant value must be a negative numerical value and two complex roots such as -5;

-5 = b² - 4ac

Read more on quadratic equation here: https://brainly.com/question/1562469

#SPJ1

Complete Question:

A quadratic equation has zero real number solutions. which could be the discriminant value associated with this equation?

a. –5 b. 0 c. 1 d. 6

Answer:

try (gauth math) could be helpful take screen shot and upload it it may be there or not hopefully it is

The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

for such more question on conditional statement

https://brainly.com/question/27839142

#SPJ8

Two sets that contain exactly the same elements are called "equal sets" or "identical sets."

In set theory, the concept of equality between sets is defined by the axiom of extensionality, which states that two sets are equal if and only if they have the same elements.

To illustrate this concept, let's consider two sets: Set A and Set B. If every element of Set A is also an element of Set B, and vice versa, then we say that Set A and Set B are equal sets. In other words, the sets have the exact same elements, regardless of their order or repetition.

For example, if Set A = {1, 2, 3} and Set B = {3, 2, 1}, we can observe that both sets contain the same elements, even though the order of the elements is different. Therefore, Set A is equal to Set B.

In summary, equal sets refer to two sets that possess exactly the same elements, without considering the order or repetition of the elements. The concept of equality is fundamental in set theory and forms the basis for various operations and theorems in mathematics.

For more such questions on sets

https://brainly.com/question/13458417

#SPJ8