7. Test the relationship between the mass of an object and how far that object slides off the end of the ramp. a. Write a testable hypothesis in the form "If the mass of an object (blank), then the distance it slides from the end of a ramp will (blank) because...."

Using the similar triangles theorem, the value of x is 21

From the question, we are to determine the value of x in the given diagram.

From the given information,

We have a diagram that shows two similar triangles.

From the similar triangles theorem, we can write that

14 / (14 + 6) = x / (x + 9)

Solving for x in the equation

14 / (14 + 6) = x / (x + 9)

This can be written as

14 / 20 = x / (x + 9)

7 / 10 = x / (x + 9)

10(x) = 7(x + 9)

10x = 7x + 63

10x - 7x = 63

3x = 63

Divide both sides of the equation by 3

3x / 3 = 63 / 3

x = 21

Hence, the value of x is 21

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If angle mFCD = (2x + 5)° and m∠FED = (3x − 10)°, the value of x is 1. Option A is the correct answer.

Since FCD and FED are adjacent angles, their sum must be equal to the measure of angle FCE:

m∠FCD + m∠FED = m∠FCE

Substituting the given measures, we get:

(2x+5) + (3x-10) = m∠FCE

Simplifying the left side, we get:

5x-5 = m∠FCE

We know that the sum of the angles in triangle FCE is 180 degrees, so we can use that information to solve for x:

m∠FCE + m∠FEC + m∠CEF = 180

Substituting in the value we found for m∠FCE, and noting that m∠FEC and m∠CEF are each 90 degrees since triangle FCE is a right triangle, we get:

5x-5 + 90 + 90 = 180

Simplifying and solving for x, we get:

5x + 175 = 180

5x = 5

x = 1

Therefore, the value of x is 1.

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If m∠FCD = (2x + 5)° and m∠FED = (3x − 10)°, what is the value of x?

a. 1

b. 3

c. 7

d. 4

Answer:

37

Step-by-step explanation:

5(37)=185

185-5=180

Answer:

1270 students

Step-by-step explanation:

3020×42/100=1268.4

so approximately 1270

Answer:

We can start by drawing a diagram of the triangle ABC:

      A

     / \

    /   \

   /     \

  /       \

 /         \

B ----------- C

We know that angle A is 30 degrees and angle C is 120 degrees, so angle B must be:

angle B = 180 - angle A - angle C

= 180 - 30 - 120

= 30 degrees

Now we can use the sine function to find the length of the perpendicular from B to AC produced. Let's call this length x:

sin(angle B) = perpendicular / hypotenuse

sin(30) = x / 20

We can solve for x by multiplying both sides by 20 and taking the sine of 30:

x = 20 sin(30)

x = 20 (1/2)

x = 10

Therefore, the length of the perpendicular from B upon AC produced is 10 feet.

Step-by-step explanation:

The height of the original skyscraper is 350 meters.

To find the height of the original skyscraper, we need to use the scale factor of 250.

First, we need to figure out how many times bigger the original skyscraper is compared to the model. We can do this by dividing 1 by 250:

1 / 250 = 0.004

This means that the original skyscraper is 0.004 times bigger than the model.

To find the height of the original skyscraper, we need to multiply the height of the model (1.4 meters) by the scale factor (250):

1.4 x 250 = 350 meters

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Answers: Angle ABE = 117 And DBE = 27

Answer:

Step-by-step explanation:

Step 1: Recall the formula for the volume of a right rectangular prism: Volume = length x width x height.

Step 2: Note that we are given the height of the water tank (11 feet), but we need to find the length and width.

Step 3: Use the formula for the area of a rectangle to find the length and width of the top of the water tank. The area is given as 220 ft², so:Area = length x width

220 ft² = length x width.

Step 4: Find two numbers that multiply to 220 and also have a sum of 2 times the height (22 feet). One way to do this is to list the factor pairs of 220 and check the sums:1 x 220 = 220 (not a factor pair)2 x 110 = 220 (not a factor pair)4 x 55 = 220 (not a factor pair)5 x 44 = 220 (not a factor pair)10 x 22 = 220 (sum is 32)11 x 20 = 220 (sum is 31)20 x 11 = 220 (sum is 31)22 x 10 = 220 (sum is 32)Therefore, the length and width of the top of the water tank are 11 feet and 20 feet (or 20 feet and 11 feet).

Step 5: Plug in the values for the length, width, and height into the volume formula and solve:Volume = length x width x height

Volume = 11 ft x 20 ft x 11 ft

Volume = 2,420 ft³

the final answer: The volume of the water tank is 2,420 cubic feet.

Recursive function calls can be less efficient than loops in certain cases because they create additional function calls and memory overhead. However, recursive functions can also be more efficient in some scenarios, particularly when dealing with complex data structures or problems that naturally lend themselves to a recursive approach. Ultimately, the efficiency of a recursive function versus a loop depends on the specific problem and how it is implemented.

Recursive function calls are generally less efficient than loops. This is because recursion can consume more memory and processing power due to the overhead of maintaining a separate function call stack for each recursive call. Loops, on the other hand, often have lower memory usage and can be more efficient in terms of processing time, especially for simple tasks or iterations. However, there are cases where recursion can provide a more elegant solution, but it's important to consider the trade-offs between readability and efficiency.

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- Air pollution in Mexico City has been declining over the last several decades. (True)
- The decline in air pollution has had positive impacts on human health and mortality. (True)
- The graph shows the relationship between ozone concentration and the number of infant deaths per 100,000 births. (True)
- The vertical axis on the left is labeled deaths per 100,000 births. (False)
- The line for ambient ozone concentration shows a decrease over time. (True)
- The line for infant mortality shows an increase over time. (False)
- The data for both lines are approximated. (True)

Based on the provided data and graph, here are the statements and their truth values:

1. Air pollution, specifically ambient ozone (O3) concentration, in Mexico City has been declining from 1997 to 2005.
- True
2. Infant deaths per 100,000 births have also been decreasing from 1997 to 2005.
- True
3. There is a correlation between decreasing O3 concentration and the decrease in infant deaths per 100,000 births.
- True
4. The vertical axis on the left is labeled deaths per 100,000 births.

-False
5. The line for ambient ozone concentration shows a decrease over time.

-True
6. The line for infant mortality shows an increase over time.

-False
7. The data for both lines are approximated.

-True

Remember that correlation does not imply causation, but the data does show a relationship between the decrease in air pollution and the decrease in infant mortality in Mexico City during the given time period.

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The area under the standard normal curve between z=0.5 and z=1.4 is given by P(0.5 < z < 1.4) = 0.2277 approximately. The answer is (iv).

To find the area under the standard normal curve between z = 0.5 and z = 1.4, we need to use a calculator to find the probabilities associated with different z-scores.

We can begin by finding the value of the cumulative distribution function (CDF) for z = 0.5 and z = 1.4. The CDF gives us the probability of getting a z-score less than or equal to a given value. We can then subtract the CDF value for z = 0.5 from the CDF value for z = 1.4 to get the probability of getting a z-score between 0.5 and 1.4.

Using a calculator, we can find that the CDF value for z = 0.5 is 0.6915 and the CDF value for z = 1.4 is 0.9192.

Therefore, the probability of getting a z-score between 0.5 and 1.4 is:

P(0.5 < z < 1.4) = 0.9192 - 0.6915 = 0.2277

Therefore, the correct answer is (iv) 0.2277.

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For the given conjecture, which is "the average weight loss for a sample of people who exercise 30 minutes per day for 6 weeks is greater than 8.2 pounds", the null and alternative hypotheses can be stated as follows:

Null Hypothesis (H0): The average weight loss for the sample is equal to or less than 8.2 pounds (≤ 8.2 lbs).
Alternative Hypothesis (H1): The average weight loss for the sample is greater than 8.2 pounds (> 8.2 lbs).

These hypotheses are formed to test whether there is significant evidence to support the conjecture that exercising 30 minutes per day for 6 weeks leads to an average weight loss of more than 8.2 pounds.

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If p > 5 is prime and p is divided by 10, then the remainders are 1, 3, 7, or 9

The given information, we know that p is a prime number greater than 5, and that p is divided by 10. This means that p must end in either 0 or 5. since those are the only digits that allow for a number to be divisible by 10.

However, we also know that p is prime, which means it cannot be divisible by any number other than 1 and itself. This rules out the possibility of p ending in 0. since any number ending in 0 is divisible by 10 (and therefore not prime).

Therefore, p must end in 5. This means that p can be written in the form:

p = 10n + 5

where n is some integer. Now, let's consider what happens when we divide p by 10:

p/10 = (10n + 5)/10 = n + 0.5

Since p/10 is not an integer (it has a decimal component of 0.5), we know that p cannot be evenly divided by 10. Therefore, when p is divided by 10, there must be a remainder.

To determine what possible remainders there could be, we can look at the possible values for the last digit of p. Since p ends in 5, the last digit can only be 1, 3, 7, or 9 (since these are the only digits that, when multiplied by 5 and added to 10n, result in a number ending in 5).

Therefore, if p > 5 is prime and p is divided by 10, the remainder must be either 1, 3, 7, or 9.

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The correct option to represent the sample data is: option (A) . Since the data is categorical and discrete, a bar graph is the most appropriate way to display the data

A bar graph, also known as a bar chart, is a graphical representation of data in which the data is presented using rectangular bars. The length or height of each bar is proportional to the value that it represents.

The correct answer is: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44.

Since the data is categorical and discrete, a bar graph is the most appropriate way to display the data. The bars should be labeled with the sports and their corresponding heights should be the number of students who chose that sport.

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The dimensions of the rectangle with the greatest possible area are 2[tex]\sqrt{(2)}[/tex] by 4.

Let's denote the dimensions of the rectangle as length (L) and width (W). Since the base of the rectangle is on the x-axis, the width of the rectangle is equal to the x-coordinate of the upper corners of the rectangle.

Let's assume that the x-coordinate of the upper corners of the rectangle is x. Then, the width of the rectangle is W = 2x, and the length of the rectangle is L = 6 -[tex]x^2[/tex].

The area of the rectangle is A = LW = [tex]2x(6 - x^2) = 12x - 2x^3.[/tex]

To find the maximum area, we need to take the derivative of A with respect to x and set it equal to zero:

[tex]dA/dx = 12 - 6x^2 = 0[/tex]

Solving for x, we get:

x = ±sqrt(2)

Since we are interested in the dimensions of the rectangle on the parabola, we take the positive value of x.

Therefore, the width of the rectangle is:

W = 2x = 2sqrt(2)

And the length of the rectangle is:

L = 6 - [tex]x^2[/tex]= 6 - 2 = 4

So the dimensions of the rectangle with the greatest possible area are 2sqrt(2) by 4.

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a) P(X=k) is equal to the probability that Y falls within the range [k-1, k).

b) The probability that X takes on a particular value k is equal to the difference between the CDF of Y evaluated at k and the CDF of Y evaluated at k-1.

a) This can be calculated using the cumulative distribution function (CDF) of the exponential distribution. P(X=1) = F_Y(1), P(X=2) = F_Y(2) - F_Y(1), P(X=3) = F_Y(3) - F_Y(2), and so on, where F_Y(k) is the CDF of Y evaluated at k.

b) This is because P(k-1 ≤ Y < k) = F_Y(k) - F_Y(k-1). Therefore, P(X=k) = F_Y(k) - F_Y(k-1) for all k = 1, 2, ... . This formula can be used to calculate the probabilities associated with each value of X.

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The probability that the archer takes at least 5 attempts to hit the bullseye is 0.4096.


To find this probability, we need to calculate the complementary probability, i.e., the probability of the archer hitting the bullseye within the first 4 attempts.

Suppose the probability of hitting the bullseye in a single attempt is p, then the probability of missing it is (1-p). We can now calculate the probability of hitting the bullseye within the first 4 attempts as:

1 - (Probability of missing the bullseye in all 4 attempts) = 1 - (1-p)⁴.

Now, to find the probability of the archer taking at least 5 attempts, we subtract the complementary probability from 1:

P(at least 5 attempts) = 1 - [1 - (1-p)⁴] = (1-p)⁴.

Assuming p is given or can be determined, you can calculate the probability using the formula provided.

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Since the pmf is not valid, we cannot find the expected value of X using the formula E[X] = Σn f(X = n).

a. To show that the given pmf is a valid pmf, we need to show that it satisfies two conditions:

f(X = n) >= 0 for all n

Σf(X = n) = 1 over all possible values of X

For the first condition, we have:

f(X = n) = n(n+1)(n+2)

Since n, n+1, and n+2 are all positive for any positive integer n, f(X = n) is also positive for all n.

For the second condition, we have:

Σf(X = n) = Σn(n+1)(n+2)

= Σ[n^3 + 3n^2 + 2n]

= Σn^3 + 3Σn^2 + 2Σn

= (1^3 + 2^3 + ... + ∞^3) + 3(1^2 + 2^2 + ... + ∞^2) + 2(1 + 2 + ... + ∞)

= (ζ(3)) + 3(ζ(2)) + 2(ζ(1))

where ζ(k) is the Riemann zeta function evaluated at k.

Since ζ(1) = ∞, this sum diverges, which means that the pmf is not a valid probability mass function.

b. Since the pmf is not valid, we cannot find the expected value of X using the formula E[X] = Σn f(X = n).

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There may be other possible combinations of nickels and pennies that would add up to $0.37 and 37 coins, but we can be sure of the three statements below.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

We can say the following things for sure about the coins in Malika's pocket:

Malika has at least one nickel in her pocket. If she had all pennies, she would have 37 pennies, which would be worth only $0.37.

However, 37 nickels would be worth $1.85, which is a more reasonable amount of money to have in one's pocket.

The total value of the coins in Malika's pocket is $0.37 or less. If Malika had even one dime or quarter, the total value of the coins in her pocket would be greater than $0.37.

The number of pennies in Malika's pocket is at least 12. This is because 25 nickels would be worth $1.25, and the remaining coins would need to make up the remaining $0.12.

Twelve pennies are worth $0.12, so Malika must have at least that many.

Hence, there may be other possible combinations of nickels and pennies that would add up to $0.37 and 37 coins, but we can be sure of the three statements above.

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We can write the equivalence class of m as [m] = {n ∈ Z : m + n is even}.

(a) To show that ∼ is an Equivalence relation, we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.

Reflexivity: For any integer m, we have |m - 3| = |m - 3|, so m ∼ m. Therefore, ∼ is reflexive.

Symmetry: For any integers m and n, if |m - 3| = |n - 3|, then |n - 3| = |m - 3|, so n ∼ m. Therefore, ∼ is symmetric.

Transitivity: For any integers m, n, and p, if |m - 3| = |n - 3| and |n - 3| = |p - 3|, then |m - 3| = |p - 3|, so m ∼ p. Therefore, ∼ is transitive.

To find the equivalence classes of ∼, we need to determine the sets of integers that are related to each other. For any integer m, the equivalence class of m is the set of all integers n such that |m - 3| = |n - 3|. In other words, the equivalence class of m is the set of integers that are the same distance from 3 as m. We can write the equivalence class of m as [m] = {n ∈ Z : |m - 3| = |n - 3|}.

(b) To show that ∼ is an equivalence relation, we need to show that it satisfies three properties: reflexivity, symmetry, and transitivity.

Reflexivity: For any integer m, we have m + m = 2m, which is even. Therefore, m ∼ m. Therefore, ∼ is reflexive.

Symmetry: For any integers m and n, if m + n is even, then n + m is also even, so n ∼ m. Therefore, ∼ is symmetric.

Transitivity: For any integers m, n, and p, if m + n is even and n + p is even, then m + p is even, so m ∼ p. Therefore, ∼ is transitive.

To find the equivalence classes of ∼, we need to determine the sets of integers that are related to each other. For any integer m, the equivalence class of m is the set of all integers n such that m + n is even.

In other words, the equivalence class of m is the set of integers that differ from m by an even amount. We can write the equivalence class of m as [m] = {n ∈ Z : m + n is even}.

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This information portrays an assortment of geometric shapes and structures, including triangles and quadrilaterals.

The following components are featured:

Triangle Inequality: Triangle ABC embodies the triangle inequality principle which conveys that the sum of any two sides in a triangle must be longer than the third side's length.

Congruent Triangles: As demonstrated by their corresponding tick marks, triangles DEF and GHI display exceptional conformity, representing identical size and shape.

Quadrilateral: Quadrilateral JKLM precisely exhibits trapezoid characteristics, with one pair of parallel sides and one couple of non-parallel edges.

Additional Shapes: Additionally, the example also includes diverse other geometrical figures, like circles, rectangles as well as a pentagon.

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The probability of choosing an apple and then an orange is 0.167

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

3 apples, 5 oranges and 2 tangerines

When the apple is selected, we have

P(Apple) = 3/10

The apple is not returned

So, we have

P(Orange) = 5/9

The required probability is

P = 3/10 * 5/9

Evaluate

P = 0.167

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Answer:

Sue paid $98.40 in all.

Step-by-step explanation:

Let the original price of the dress be $x.

The amount of tax Sue paid is $6.40, which is 8% of the original price, so:

0.08x = $6.40

Solving for x:

x = $6.40 / 0.08 = $80

Sue was charged 15% duty on the original price, which is:

0.15($80) = $12

So the total cost of the dress, including tax and duty, is:

$80 + $6.40 + $12 = $98.40

The equation 4x + 3y = -18 is parallel to the given line since they have the same slope.

The equation of a line in slope-intercept form is expressed as y = mx + b

where

m is the slope

b is the y-intercept

Given the equation below

y =-4/3x-7

The slope of the line is -4/3.

In order to determine the equation that represents a line which is parallel to the line, we need to determine the line that has a slope of -4/3

For the equation 4x + 3y = -18:

3y = -4x - 18

Divide through by 3 to have:

3y/3 = -4x/3 - 18/3

y = -4/3 x - 6

Since the slope of the line is -4/3, hence the equation 4x + 3y = -18 is parallel to the given line.

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The area of quadrilateral EDFG is approximately 21 cm²

We are given that 3DE = 3FC = AB.

Thus:

The area of ΔFCB = ¹/₆ * the area of ABCD

Area of ΔFCB = ¹/₆ * 140 = 23.33 cm²

Area of ΔCFG/Area of ΔCED = (CF/CE)²

Side length of ABCD is: CD = √140 = 11.83 cm

FC = 1/3 * CD

FC = 3.944 cm

CE = √(DE² + CD²)

CE = √(3.944² + 11.83²)

CE = 12.47 cm

Area of ΔCFG/Area of ΔCED = (3.944/12.47)² = 1/10

Area of ΔCFG = 1/10 * 140/6 = 2.33 cm²

Area of EDFG = (140/6) - (140/60) = 21 cm²

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Answer: By plotting the functions f(x) = x-4 and g(x) = 3x - 12 on a coordinate plane, we can see that the transformation from f(x) to g(x) was a vertical stretch by a factor of three with no translation. This transformation has a "k" value of 3. We can see that the slope of g(x) is three times steeper than that of f(x), and that the y-intercept of g(x) is similarly three times lower than that of f(x), representing the vertical stretch by a factor of three.

Step-by-step explanation:

Answer: When a spring is compressed or stretched, it will try to restore its equilibrium position by exerting a force equal and opposite to the external force. So the external work done by us in compression as well as stretching will store in the spring as potential energy

Answer: Energy of the spring is equal when compressed as when stretched.

Step-by-step explanation: Potential Energy (PE) of the spring is highest at both compression and when stretched. During this time, the Kinetic Energy (KE) is zero. When the spring is at rest, KE is highest and PE is zero.

Volume of solid is 8000 cubic yards.

We know that,

Volume is defined as the amount of space occupied by an object within the boundaries in the three dimensional space.

A base of a solid whose height is 20 yards is shown.

Let us consider the solid as cube.

Volume of cube = a^3 cubic units.

Here side, a =20 yards.

Volume ,V= 20^3

                 = 8000 cubic yards.

Hence, Volume of solid is 8000 cubic yards.

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Each outcome has a probability of 1/6, since the die is fair and each face is equally likely to appear.

a discrete random variable is a type of random variable where the possible values it can take on are countable and finite (like rolling a die and getting a specific number).

In this case, X represents the value shown on a single roll of a fair die, which can take on the values 1, 2, 3, 4, 5, or 6. Therefore, X is a discrete random variable with six possible outcomes.
X represents a discrete random variable in this scenario, which is the value shown on a single roll of a fair die. A discrete random variable has a finite or countable number of possible outcomes. In the case of a fair die, the possible outcomes for X are the integers 1 through 6, as there are six distinct faces on the die. Each outcome has a probability of 1/6, since the die is fair and each face is equally likely to appear.

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Answer:

It's 25

Step-by-step explanation:

I took the quiz.

Answer: scalene.

Step-by-step explanation: Based on the given measurements of the sides and angles of the triangle, we can classify each triangle by its sides as follows:

9.8, 4.8, and 6.8: These three sides have different lengths, so the triangle is scalene.

Therefore, the triangle is scalene.

Note that the angles given in the problem are not necessary to classify the triangle by its sides, as the sides uniquely determine the type of triangle.