A marine biologist was interested in seeing the relationship between a manatee's weight and food consumption. She gathered data and wanted to construct a graph to display the data in order to observe this relationship.

Is a scatter plot or a line graph more appropriate to construct for the data, given the context of the problem? Explain.

A line graph, because it would show the association or relationship between two variables
A line graph, because it would show how a variable changes over time between each data point given
A scatter plot, because it would show the association or relationship between two variables
A scatter plot, because it would show how a variable changes over time between each data point given

Answer:

Its value is approximately:

G = 6.6743 x 10^-11 m^3 kg^-1 s^-2

Step-by-step explanation:

The value of G is the gravitational constant, which is a physical constant that appears in the law of universal gravitation. Its value is approximately:

G = 6.6743 x 10^-11 m^3 kg^-1 s^-2

This value is used to calculate the force of gravitational attraction between two objects, given their masses and the distance between them. The gravitational constant is a fundamental constant of nature and is important in many areas of physics, including astrophysics, cosmology, and mechanics.

The work required to lift the entire chain to the top of the building is 1,662.9 ft-lbs.

The work required to lift the chain to the top of the building is equal to the potential energy gained by the chain, which is given by

potential energy = mass × gravity × height

where mass is the mass of the chain, gravity is the acceleration due to gravity (32.2 ft/s^2), and height is the length of the chain (18 feet) since it is being lifted vertically.

First, we need to find the mass of the chain. We can use the fact that the weight of the chain is 93 pounds to find the mass using the formula

weight = mass × gravity

Rearranging this formula to solve for mass, we get

mass = weight / gravity

Substituting the given values, we get

mass = 93 pounds / 32.2 ft/s^2 = 2.89 slugs

Now we can calculate the potential energy of the chain using the formula

potential energy = mass × gravity × height

Substituting the values we have calculated, we get

potential energy = 2.89 slugs × 32.2 ft/s^2 × 18 feet = 1,662.9 ft-lbs

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To find the volume of a cone, we use the formula V = (1/3)πr²h or V = (1/3)π(d/2)²h, where r is the radius, d is the diameter, and h is the height of the cone.

Example 1: A cone with a height of 8 cm and a radius of 3 cm.

V = (1/3)π(3²)(8)
V = 24π
V ≈ 75.4 cm³

Example 2: A cone with a height of 12 cm and a diameter of 6 cm.

V = (1/3)π(6/2)²(12)
V = (1/3)π(3²)(12)
V = 36π
V ≈ 113.1 cm³

Example 3: A cone with a height of 5 cm and a diameter of 10 cm.

V = (1/3)π(10/2)²(5)
V = (1/3)π(5²)(5)
V = (1/3)π(25)(5)
V = 125/3π
V ≈ 130.9 cm³

Example 4: A cone with a height of 15 cm and a radius of 2.5 cm.

V = (1/3)π(2.5²)(15)
V = (1/3)π(6.25)(15)
V = (1/3)π(93.75)
V ≈ 98.2 cm³

Puzzle grid:

| 75.4 | 113.1 | 130.9 | 98.2 |
|  -   |   -   |   -   |   -   |
|  -   |   -   |   -   |   -   |
|  -   |   -   |   -   |   -   |

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The measure of exterior angle in the following triangle is A, 125°.

Because the given triangle is a right-angled triangle, ΔABC.

Considering the angles

m∠A = 35°

m∠C = 90°

A triangle's angles add up to 180°.

So,

180° = mA + mB + mC

mA = 35° and mC = 90° are substituted in the equation

35° + m∠B + 90° = 180°

125 + m∠B = 180°

Take 125 off both sides.

125 + m∠B - 125 = 180° - 125

m∠B = 55°

As a result, the angle B is measured as follows:

m∠B = 55°

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it. In a triangle with a 90° angle, the sum of the other two angles is:

180° - 90° = 90°. So, the measure of the exterior angle is 90° + 35° = 125°.

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Complete question:

find the measure of exterior angle in the following triangle 35°

Answer: To solve these problems, we need to use the simple interest formula:

Simple Interest = (Principal x Rate x Time)

Where:

Principal: the amount of money lent or borrowed

Rate: the interest rate

Time: the length of time the money is borrowed for

Q. 1 - How much money in interest will Riley earn?

Using the simple interest formula, we can calculate the interest earned by Riley:

Interest = (Principal x Rate x Time)

Interest = ($12,750 x 5.5% x 4.75 years)

Interest = $3,442.81

Therefore, Riley will earn $3,442.81 in interest.

Q. 2 - When Riley’s friend pays him back, how much money will he have gotten back in all?

To find out how much money Riley's friend will pay him back in all, we need to add the principal and interest together:

Total amount to be paid back = Principal + Interest

Total amount to be paid back = $12,750 + $3,442.81

Total amount to be paid back = $16,192.81

Therefore, when Riley's friend pays him back in full, he will have gotten back $16,192.81 in all.

Step-by-step explanation:

The required perimeter of the square with given measure of the one side length x inches is equals to 4x inches.

The perimeter of a square is the sum of the lengths of all its sides.

If one side of the square is x inches,

Then all sides are also x inches.

This implies, the perimeter of the square is equals to,

Substitute the side length of the square x inches we have,

Perimeter of the square = x + x + x + x

⇒Perimeter of the square = 4x inches

Therefore , the perimeter of the square with one side of x inches is equals to 4x inches.

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Answer:

[tex]2x+5y=20[/tex]

Step-by-step explanation:

Rearranging the equation of the given line into intercept form,

[tex]5y+2x=10 \\ \\ \frac{x}{5}+\frac{y}{2}=1[/tex]

This means the intercepts are [tex](5,0)[/tex] and [tex](0,2)[/tex].

We need to find the equation of the line with intercepts [tex](0,4)[/tex] and [tex](10,0)[/tex]. This equation is [tex]\frac{x}{10}+\frac{y}{4}=1[/tex], which rearranges to give [tex]2x+5y=20[/tex].

Answer:

[tex] \sqrt{ {(0 - ( - 7))}^{2} + {( - 1 - ( - 2))}^{2} } [/tex]

[tex] \sqrt{ {7}^{2} + {1}^{2} } [/tex]

[tex] \sqrt{49 + 1} = \sqrt{50} = 5 \sqrt{2} [/tex]

5√2 units is about 7.07 units.

A one-tailed test of significance could be used whenever the researcher is interested in predicting a direction for the difference.What is a one-tailed test?A one-tailed test is a statistical hypothesis test in which the critical region of a parameter's distribution is only one-sided, indicating that it is either higher or lower than the values obtained from sample data.

A one-tailed test is also known as a one-sided test or a directional hypothesis test.It is used when the research hypothesis states a direction for the population parameter (i.e., greater than or less than a specific value).

For example, if we want to test whether a new drug reduces blood pressure, we could conduct a one-tailed test with the null hypothesis stating that the drug has no effect on blood pressure, and the alternative hypothesis indicating that the drug lowers blood pressure. In this scenario, a one-tailed test will be suitable.

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The fraction of the check and tip did John pay is 5/24.

What are rational numbers?

It is possible to express rational numbers in the form pq, where p and q are integers and q0. The distinction between fractions and rational numbers is that the numerator or denominator of a fraction cannot be negative. As a result, the numerator and denominator of a fraction are whole numbers (denominator 0), as opposed to integers in the case of rational numbers.

Here, we have

Given: A group of three friends ate dinner at a restaurant. When they settled the check and tip, Peter paid 4/5 as much as John paid, and John paid 1/3 as much as Ralph paid.

we have to find a fraction of the check and tip did John pay.

p, j, r, the fractions that each paid.

p + j + r = 1....(1)

p = (4/5)j and j = (1/3)r

From equation(1), we get

(4/5)j + j + 3j = 1

j(4/5 + 1 + 3) = 1

(24/5)j = 1

j = 5/24

We have

r = 3j

r = 3(5/24)

r = 5/8

Hence, the fraction of the check and tip did John pay is 5/24.

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Answer:

The cost of 4 dozen eggs is 4 * $1.25 = $5.

The cost of half a gallon of milk is $2.97.

The total cost of the eggs and milk is $5 + $2.97 = $7.97.

Since Chase has only $10, the minimum price for a dozen eggs is $10 - $7.97 = $2.03.

So the answer is 2.03

Step-by-step explanation:

A given function or graph is needed to find the average rate of change between an interval

The word phrase "negative one fifth is bigger than or equal to the product of negative two thirds" is represented by the inequality "1/5 ≥ (-2/3) x," and its solution is x ≥ 3/10.

The inequality that symbolises the word phrase as supplied in the task content must be determined, as is evident from the assignment's content.

Negative one fifth is more than or equal to the product of negative two thirds and a number, which is how the disparity is expressed.

Therefore,

Let the number = y

- 1 / 5 ≥ - 2 / 3 × y

- 1 / 5 ≥ - 2 / 3 y

Now, multiply both sides of the inequality by - 3 / 2

Therefore,

- 1 / 5 (- 3 / 2) ≤ y

3 / 10 ≤ y

y ≥ 3 / 10

Therefore, y is greater than or equal to three tenths.

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Yes, Lucia will be able to form a triangular-shaped sandbox using the railroad ties without cutting them.

To determine if a triangle can be formed, you can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side.

In this case, the sides are 10 feet, 12 feet, and 8 feet. Let's check if the Triangle Inequality Theorem holds true for each combination:

1. 10 feet + 12 feet = 22 feet > 8 feet (Yes)
2. 10 feet + 8 feet = 18 feet > 12 feet (Yes)
3. 12 feet + 8 feet = 20 feet > 10 feet (Yes)

Since all three combinations satisfy the Triangle Inequality Theorem, Lucia can create a triangular-shaped sandbox with the given railroad ties.

The Triangle Inequality Theorem is a mathematical principle that states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, if a, b, and c are the lengths of the sides of a triangle, then:

a + b > c

b + c > a

a + c > b

If any of these inequalities is not true, then the given lengths do not form a valid triangle.

This theorem is important in geometry and other fields that involve measurements of distance or length. It is also used in many practical applications, such as designing bridges, buildings, and other structures, where the strength and stability of the structure depend on the lengths and angles of the sides of the triangles involved.

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a)Since the height of the basketball is only 6.3 feet when it reaches a height of 17 feet at t = 0.23 seconds, the teenager will not make the basket.

b) To find the height of the teenager, we need more information, such as their arm span or jumping ability.

what is  height ?

Height is the measurement of how tall someone or something is, typically referring to the distance from the bottom to the top of an object or person. It can be measured in different units, such as feet, meters, or centimeters

In the given question,

a. To determine if the teenager will make the basket, we need to see if the height of the basketball when it reaches the hoop, which is at a height of 17 feet, is greater than or equal to 17 feet. So, we set h(t) = 17 and solve for t:

-16t² + 20t + 5.5 = 17

-16t² + 20t - 11.5 = 0

Using the quadratic formula, we get:

t = (-20 ± sqrt(20² - 4(-16)(-11.5))) / (2(-16))

t ≈ 1.79 or t ≈ 0.23

Since the basketball will reach a height of 17 feet at two different times, we need to determine the height of the basketball at each of these times and see if it is greater than or equal to 17 feet.

When t = 0.23 seconds:

h(0.23) = -16(0.23)² + 20(0.23) + 5.5 ≈ 6.3 feet

When t = 1.79 seconds:

h(1.79) = -16(1.79)² + 20(1.79) + 5.5 ≈ 17.1 feet

Since the height of the basketball is only 6.3 feet when it reaches a height of 17 feet at t = 0.23 seconds, the teenager will not make the basket.

b. To find the height of the teenager, we need more information, such as their arm span or jumping ability. The function h(t) represents the height of the basketball, not the height of the teenager.

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The higher the value of Cronbach's alpha, the higher the internal consistency reliability of the assessment.

A measurement of internal consistency that allows researchers to determine how well the different items/questions within a test measure different aspects of the same topic is known as reliability.

Reliability refers to the consistency of the results of an assessment. In other words, it refers to the extent to which an assessment yields stable and consistent results. Researchers use various methods to assess the reliability of an assessment.

These include test-retest reliability, inter-rater reliability, and internal consistency reliability.

In this case,

The internal consistency reliability is the method that allows researchers to determine how well the different items/questions within a test measure different aspects of the same topic.

Internal consistency reliability is a method that measures the consistency of the results of an assessment by examining the relationships among the different items/questions within the assessment. It looks at the degree to which the items/questions within an assessment measure the same thing or construct.

If the different items/questions within an assessment are measuring the same thing, then the assessment is said to have high internal consistency reliability. If the items/questions are measuring different things, then the assessment is said to have low internal consistency reliability.

Researchers use various statistical methods to assess internal consistency reliability. One of the most common methods is Cronbach's alpha, which measures the degree to which the items/questions within an assessment are correlated with each other.

The higher the value of Cronbach's alpha, the higher the internal consistency reliability of the assessment.

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Answer:

B

Step-by-step explanation:

The independent variable is t (time) because no matter what happens the weeks will still pass. The dependent variable is b (balance) because it depends on the amount of time passed. You can see that after every week the balance decreases by 50. So when the independent variable increases by 1, the dependent variable decreases by 50.

Based on the lengths of the sides, we can see that the triangle is scalene. Based on the slopes of the sides, we can see that the triangle is acute since all the slopes are negative or less than 1.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

To find the desired slopes and lengths of the triangle formed by the points M(-7, 8), N(-1, 9), and O(0, 3), we can use the distance formula and the slope formula.

Distance formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Using this formula, we can find the lengths of the sides of the triangle:

Length of MO:

d(MO) = √((0 - (-7))² + (3 - 8)²) = √(7² + 5²) = √(74)

Length of NO:

d(NO) = √((-1 - (-7))² + (9 - 8)²) = √(6² + 1²) = √(37)

Length of MN:

d(MN) = √((-1 - (-7))² + (9 - 8)²) = √(6² + 1²) = √(37)

Slope formula:

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Using this formula, we can find the slopes of the sides of the triangle:

Slope of MO:

m(MO) = (3 - 8) / (0 - (-7)) = -5/7

Slope of NO:

m(NO) = (9 - 8) / (-1 - (-7)) = 1/6

Slope of MN:

m(MN) = (9 - 8) / (-1 - (-7)) = 1/6

Characterization of the triangle:

Based on the lengths of the sides, we can see that the triangle is scalene (no two sides have the same length). Based on the slopes of the sides, we can see that the triangle is acute (all angles are less than 90 degrees) since all the slopes are negative or less than 1. Additionally, we can see that the side MO is the longest side of the triangle, and since the slope of MO is negative, we can conclude that the angle opposite side MO is the largest angle in the triangle.

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if x = 25, quadrilateral ABCD will be a trapezoid with AB || CD.thus, the answer is (C) 25.

What is trapezoid?

For quadrilateral ABCD to be a trapezoid, it must have a pair of parallel sides. In other words, either AB || CD or AD || BC. We can use the angle measures to determine which condition must be satisfied.

Trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The height of a trapezoid is the perpendicular distance between the bases. The area of a trapezoid can be calculated by taking the average of the lengths of the two bases and multiplying by the height. The formula for the area of a trapezoid is: Area = (base1 + base2) / 2 * height

If AB || CD, then opposite angles must be supplementary, which means that:

A + D = 180°

Substituting the given angle measures, we get:

3x + (5x-20) = 180

Simplifying, we get:

8x - 20 = 180

Adding 20 to both sides, we get:

8x = 200

Dividing both sides by 8, we get:

x = 25

Therefore, if x = 25, quadrilateral ABCD will be a trapezoid with AB || CD.

Thus, the answer is (C) 25.

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B) 0.18

To convert 2/11 into decimal form, divide 2 by 11 using a calculator or long division.

The result is 0.18181818... (the pattern of 18s repeats indefinitely).

Therefore, 2/11 as a decimal is approximately 0.1818 (rounded to four decimal places).

Answer:

B. [tex]0.\overline{18}[/tex]

Step-by-step explanation:

2/11 in decimal form is a set of repeating 18's:

0.181818181818...

This can be represented using bar notation, where digits under the bar repeat infinitely:

[tex]0.\overline{18}[/tex]

__

Extra note:

A trick for fractions with 99 in the denominator is that, when the fraction is converted into a decimal, the numerator of the fraction is the repeating two digits.

In this problem, when we convert 2/11 to 99ths:

[tex]\dfrac{2}{11} \cdot \dfrac{9}{9} = \dfrac{18}{99}[/tex],

we can see that 18 is in the numerator, so that is the repeating part of the decimal [tex]0.\overline{18}[/tex].

Given this minitab printout, the response variable in this multiple regression equation is a numerical variable. Multiple regression is a statistical method used to examine the relationship between a dependent variable (also known as the response variable) and two or more independent variables (also known as predictors or explanatory variables).The minitab printout typically shows the coefficient estimates of the regression equation, along with various other statistics such as the R-squared value, standard error, etc. However, it doesn't indicate whether the response variable is categorical or numerical.A response variable is categorical if it can only take on a limited number of discrete values or categories. Examples of categorical variables include gender, occupation, marital status, etc. A response variable is numerical if it can take on any value within a certain range. Examples of numerical variables include age, income, height, etc.In the given minitab printout, the response variable is the variable labeled "Cust_Satisfaction." This variable is measured on a scale from 1 to 100, and therefore, it can take on any numerical value within that range. Hence, we can conclude that the response variable in this multiple regression equation is a numerical variable.

The expected value of the number of games played is 5.5 games, and the variance is 1.25.

To find the expected value of the number of games played, we need to consider all the possible ways the match can end. Since the match is a best of 7, one team needs to win at least 4 games. The possible outcomes are:

Team A wins in 4 games: AAAA

Team A wins in 5 games: AABAA or ABAAA

Team A wins in 6 games: ABAABA, ABABAA, or ABBAAA

Team A wins in 7 games: ABABABA, ABABAB, ABBABAA, or ABBABAAA

Similarly, we can list the possible outcomes for Team B winning in 4, 5, 6, or 7 games. However, since both teams are equally likely to win each game, the probability of each outcome is the same. Therefore, the expected value of the number of games played is:

E(X) = (41/8) + (52/8) + (63/8) + (72/8) = 5.5 games

To find the variance, we need to first calculate the squared deviation from the expected value for each outcome. For example, for the outcome AABAA, the deviation is (5-5.5) = -0.5, and the squared deviation is (-0.5)^2 = 0.25. We can then multiply each squared deviation by the probability of that outcome and sum them up,

Var(X) = (1/8)(4-5.5)^2 + (2/8)(5-5.5)^2 + (3/8)(6-5.5)^2 + (2/8)(7-5.5)^2

= 1.25

Therefore, the expected value of the number of games played is 5.5 games, and the variance is 1.25.

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Answer:

Rounding to the nearest centimeter, we get p ≈ 57 cm.

Step-by-step explanation:

We are given a triangle ΔPQR with r = 38 cm, m∠P = 49°, and m∠Q = 127°. We are asked to find the length of side p.

First, let's find m∠R:

m∠R = 180° - (m∠P + m∠Q)

m∠R = 180° - (49° + 127°)

m∠R = 180° - 176°

m∠R = 4°

Now, we have all three angles of the triangle: P = 49°, Q = 127°, and R = 4°. We can use the Law of Sines to find the length of side p:

p/sin(P) = r/sin(R)

Let's plug in the known values:

p/sin(49°) = 38/sin(4°)

Now, solve for p:

p = (sin(49°) * 38) / sin(4°)

p ≈ 56.96 cm

Rounding to the nearest centimeter, we get p ≈ 57 cm.

Area of trapezoid= 1/2 (13.4+5.6)×4

= 1/2 ×19

=76/2

=38yd

Answer: 61.56%

Step-by-step explanation:

To find what percent 39.4 is of 64, we can use the following formula:

(percent / 100) * 64 = 39.4

Solving for percent, we get:

percent = (39.4 / 64) * 100

percent = 0.615625 * 100

percent = 61.56 (rounded to the nearest hundredth)

Therefore, 39.4 is approximately 61.56% of 64 when rounded to the nearest hundredth.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{JK}\\ a=\stackrel{adjacent}{5}\\ o=\stackrel{opposite}{49} \end{cases} \\\\\\ JK=\sqrt{ 5^2 + 4.9^2}\implies JK=\sqrt{ 25 + 24.01 } \implies JK=\sqrt{ 49.01 }\implies JK\approx 7[/tex]

According to the given information, the solutions to the equation 7x²-34=2x²+16 are x = √10 and x = -√10.

What is quadratic equation?

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0 where a, b, and c are constants, and x is the variable.

To solve for x in the equation 7x²-34=2x²+16 using square roots, we can first simplify the equation by moving all the x² terms to one side and all the constant terms to the other side:

7x² - 2x² = 16 + 34

5x² = 50

5x²/5 = 50/5

x² = 10

Finally, we can take the square root of both sides (remembering to include both the positive and negative square root, since x could be positive or negative):

x = ±√10

Therefore, the solutions to the equation 7x²-34=2x²+16 are x = √10 and x = -√10.

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Answer:

The answer to the expression 448m^2−49.81m is 448m^2 - 49.81m. It cannot be simplified further without knowing the value of m.