A list of rational numbers is given.


one and five eighths, negative three halves, seventeen percent, negative 1.7


Part A: Rewrite all the values into an equivalent form as fractions. (3 points)


Part B: Rewrite all the values into an equivalent form as decimal numbers. (3 points)


Part C: List the given rational numbers from greatest to least. (3 points)


Part D: How did you determine their order? Please explain your answer. (3 point)

Answer:

Option D

13

Step-by-step explanation:

|–5 – 8|

= l-13l

= 13 (Ans)

Once mona returns to her starting point, swam a total of 132 yards.

It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

We can use the Pythagorean theorem to find the distance that Mona has swum. Let's call the diagonal distance between the northwest and southeast corners of the swimming pool "d".

Using the Pythagorean theorem, we have:

d² = 44² + 33²

d² = 1936 + 1089

d² = 3025

d = 55

Therefore, the diagonal distance that Mona has swum is 55 yards. However, since she swam along the width and length of the pool as well, we need to add those distances to the diagonal distance to get the total distance she swam.

Mona swam 44 yards along the width and 33 yards along the length, so her total distance swum is:

55 + 44 + 33 = 132 yards

Therefore, Mona swam a total of 132 yards.

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Answer:

A) 60%

Step-by-step explanation:

24/40

= 0.6

0.6*100

= 60%

I really hope this is right and it helps.

As stated in the assertion The ladder will be able to climb up the building around 34.64 feet.

We can use the Pythagorean theorem to address this issue by referring to "height" and taking into account the 40-foot ladder that is situated 20 feet from the building's base. According to the theorem, the square root of the length of the hypotenuse, or side opposite the side with the right angle, in a right-angled triangle, is equal to the sum of each square of the lengths of each of the other two sides.

In this instance, the height of the ladder on the building serves as the hypotenuse, with the distance to the building's base serving as one of its sides. These sides should be labelled as follows:

The Ladder's hypotenuse measures 40 feet

- Side 1 is 20 feet away from the base.

Side 2 (height attained) equals h

The Pythagorean theorem yields the following result: 402 = 202 + h2.

1600 = 400 + h2 h2 = 1200 h 34.64 feet when h is solved for.

The ladder may therefore climb the building to a height of about 34.64 feet.

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Answer:

\(\boxed{y=|\frac{1}{2}x - \frac{3}{2}|+3}\)

Step-by-step explanation:

The translation is a horizontal translation.

The graph is translated 1 unit to the left. So the value of x is added by 1.

\(f(x+1)\)

\(y=|\frac{1}{2} (x+1)-2|+3\)

\(y=|\frac{1}{2}x + \frac{1}{2} -2|+3\)

\(y=|\frac{1}{2}x + - \frac{3}{2}|+3\)

Answer:

There is a negative correlation in the data set

Step-by-step explanation:

B

The correlation between the variables as shown is a negative correlation.

A scatter plot is a plot or graph that shows the association between two variables. It can be used to ascertain the correlation between variables at a glance.

Hence, we can see from the scatter plot as shown in the image attached to the question that the correlation between the variables as shown is a negative correlation.

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a. The standard error of the mean can be determined using the formula:

Standard error of the mean = population standard deviation / square root of sample size

Plugging in the given values, we get:

Standard error of the mean = 25 / square root of 250
Standard error of the mean = 25 / 15.8114
Standard error of the mean = 1.579 (rounded to 3 decimal places)


The standard error of the mean measures the amount of variability or error that is expected in the sample mean when compared to the true population mean. It is calculated by dividing the population

by the square root of the sample size. In this case, the standard error of the mean is 1.579, indicating that the sample mean of 20 is expected to be off by around 1.579 units from the true population mean.

c. To determine the 95% confidence interval for the population mean, we can use the formula:

Confidence interval = sample mean +/- (critical value) x (standard error of the mean)

The critical value can be obtained from a t-distribution table with n-1 degrees of freedom, where n is the sample size. For a 95% confidence interval and 249 degrees of freedom, the critical value is 1.96.

Plugging in the given values, we get:

Confidence interval = 20 +/- (1.96) x (1.579)
Confidence interval = 20 +/- 3.095
Confidence interval = (16.905, 23.095) (rounded to 3 decimal places)


The confidence interval is a range of values that is expected to contain the true population mean with a certain degree of confidence. In this case, we are 95% confident that the true population mean falls within the range of 16.905 to 23.095. This means that if we were to repeat this sampling process many times, 95% of the resulting confidence intervals would contain the true population mean.

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The values of x when f(z) = 3 are x = -2 and x = -8.

The two points on the graph  are (-2, 3) and (-8, 3).

The function f(x) = x^2 + 10x + 19 is given.

Let's find when f(a) = 3.

To find the value of x when f(a) = 3, we substitute f(x) = 3 into the equation:

3 = a^2 + 10a + 19

Rearranging the equation:

a^2 + 10a + 16 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula.

However, upon inspection, we can see that the equation cannot be factored easily.

Hence, we will use the quadratic formula:

a = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 10, and c = 16.

Substituting these values into the formula:

a = (-10 ± √(10^2 - 4(1)(16))) / (2(1))

Simplifying:

a = (-10 ± √(100 - 64)) / 2

a = (-10 ± √36) / 2

a = (-10 ± 6) / 2

So, we have two possible values for a: a = (-10 + 6) / 2 = -2 and a = (-10 - 6) / 2 = -8.

Therefore, the values of x when f(z) = 3 are x = -2 and x = -8.

Now, let's find two points that lie on the graph of f(x) using the values we found.

Substituting x = -2 into f(x), we get:

f(-2) = (-2)^2 + 10(-2) + 19 = 4 - 20 + 19 = 3

So, one point on the graph is (-2, 3).

Substituting x = -8 into f(x), we get:

f(-8) = (-8)^2 + 10(-8) + 19

f(-8) = 64 - 80 + 19 = 3

So, another point on the graph is (-8, 3).

Hence, the two points on the graph of f(x) are (-2, 3) and (-8, 3).

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Answer:

An algebraic equation is an equation used in algebra which uses numbers and letters. The letters are representing unknown numbers and are called variables.

Answer:

An algebraic equation is "a mathematical statement in which two expressions are set equal to each toher."

If that is too complicated to understand, look at it like this. An algebraic equation usually has two things: an equal sign, and letters. For example, this is an algebraic equation: x + 3 = 7.

Step-by-step explanation:

Answer:

9-8=1 times 2 =2

Step-by-step explanation:

it is times mutple 2

The Lissajous figure associated with the equations X = 2cos(nt) and y = cos(nt + n/4) is a four-leafed clover with cusps at the vertices of a square.

A Lissajous figure is a type of graph that illustrates the relationship between two oscillating variables that are perpendicular to one another. It is created by plotting one variable on the x-axis and the other variable on the y-axis. In order to construct a Lissajous figure associated with the equations X = 2cos(nt) and y = cos(nt + n/4), we need to first perpendicularly superimpose the two equations.

To do this, we will plot the two equations on the same graph using different colors. Then, we will rotate the y-axis by a quarter turn, so that it is perpendicular to the x-axis. Finally, we will draw the Lissajous figure by tracing the path of the point (X, Y) as t increases from 0 to 2π.Let's start by plotting the two equations on the same graph. The equation X = 2cos(nt) is a cosine function with amplitude 2 and period 2π/n.

The equation y = cos(nt + n/4) is also a cosine function, but it has been shifted by n/4 radians to the left. Its amplitude is 1 and its period is 2π/n. We can plot both functions on the same graph as follows:Now we need to rotate the y-axis by a quarter turn. This means that we need to swap the roles of x and y. The new x-axis will be the old y-axis, and the new y-axis will be the old x-axis. We can do this by plotting the same graph again, but swapping the x and y values:

Finally, we can draw the Lissajous figure by tracing the path of the point (X, Y) as t increases from 0 to 2π. The Lissajous figure associated with the equations X = 2cos(nt) and y = cos(nt + n/4) is shown below:Answer:Therefore, the Lissajous figure associated with the equations X = 2cos(nt) and y = cos(nt + n/4) is a four-leafed clover with cusps at the vertices of a square.

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Answer:

15

Step-by-step explanation:

from the first then it is 0+7=7

and from the last it is 0+8=8

then the number of cars available in the station is 8+7=15

The given equation is

To solve for x, the logarithm to indices relationship will be applied

That is

Hence

This is simplified to get

Therefore, the value of x = 4

HEIGHT = 15cm

Step-by-step explanation:

2 * 22/7 * 7 (7+h )= 968

2 * 22 (7+h)=968

(7+h) = 968/44

7 + h = 22

h = 22 - 7

= 15 cm

Answer:

The height of cylinder is 15 cm.

Step-by-step explanation:

Given :

To Find :

Using Formula :

\({\star{\small{ \underline{ \boxed{\sf{\red{TSA_{(Cylinder)} = 2\pi r(r + h)}}}}}}}\)

Solution :

Substituting all the given values in the formula to find height of cylinder :

\({\longrightarrow{\small{\sf{ \: TSA_{(Cylinder)} = 2\pi r(r + h)}}}}\)

\({\longrightarrow{\small{\sf{ \: 968= 2 \times \dfrac{22}{7} \times 7(7 + h)}}}}\)

\({\longrightarrow{\small{\sf{ \: 968= 2 \times \dfrac{22}{\cancel{7}} \times \cancel{7}(7 + h)}}}}\)

\({\longrightarrow{\small{\sf{ \: 968= 2 \times 22(7 + h)}}}}\)

\({\longrightarrow{\small{\sf{ \: 968= 44(7 + h)}}}}\)

\({\longrightarrow{\small{\sf{ \: (7 + h) = \dfrac{968}{44}}}}}\)

\({\longrightarrow{\small{\sf{ \: (7 + h) = \cancel{\dfrac{968}{44}}}}}}\)

\({\longrightarrow{\small{\sf{ \: (7 + h) = 22}}}}\)

\({\longrightarrow{\small{\sf{ \: 7 + h = 22}}}}\)

\({\longrightarrow{\small{\sf{ \: h = 22 - 7}}}}\)

\({\longrightarrow{\small{\sf{ \: h = 15 \: cm}}}}\)

\({\star{\small{ \underline{ \boxed{\sf{\red{Height = 15cm}}}}}}}\)

Hence, the height of cylinder is 15 cm.

\(\underline{\rule{220pt}{3pt}}\)

Step-by-step explanation:

To find the cost of painting the blackboard, we first need to calculate its area.

Length of the blackboard = 5m 20cm = 5.20m

Breadth of the blackboard = 3m 40cm = 3.40m

Area of the blackboard = Length x Breadth

Area = 5.20m x 3.40m

Area = 17.68 square meters

The cost of painting 1 square meter at the rate of Rs. 10 is Rs. 10. Therefore, the cost of painting 17.68 square meters is:

Cost = Area x Rate

Cost = 17.68 square meters x Rs. 10 per square meter

Cost = Rs. 176.80

Therefore, the cost of painting the blackboard at the rate of Rs. 10 per square meter would be Rs. 176.80.

The value of x is 120° .

Given,

In triangle HGF,

HF and FG and are equal in length and ∠G is 60° .

Now,

If the sides are equal there angles will be equal.

So,

FG and FH are equal thus angle ∠H will be equal to 60° .

Sum of all the interior angles of triangle is 180° . Thus ∠F will be equal to 60° .

Now,

∠H and x° will form linear pair.

∠H + x°  = 180°

x = 120° .

Hence all the angles of the triangle are obtained.

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Answer:

0.5%

Step-by-step explanation:

The prevalence rate shows the proportion of people that have a disease in a population and to be able to calculate it, you have to divide the number of people that have a disease by the population:

Prevalence rate=(5/1,000)*100

Prevalence rate=0.005*100

Prevalence rate=0.5%

According to this, the answer is that if there are five cases of H1N1 in the community of 1,000 people, the prevalence rate is 0.5%.

If a data set measured over time goes up and down multiple times, but remains around the same mean, it is more likely the result of negative feedback loops.

Negative feedback loops work to stabilize a system and keep it around a set point, which is reflected in the consistent mean of the data set.

Positive feedback loops, on the other hand, amplify deviations from the set point, resulting in a data set with larger fluctuations and a less stable mean.

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The congruence equation ax ≡ b (mod n) has a solution if and only if gcd(a, n) | b, where n ∈ N and a, b ∈ Z.

To prove this, we will use Bezout's theorem, which states that for any integers a and b, there exist integers x and y such that ax + by = gcd(a, b).

First, let's assume that the congruence equation ax ≡ b (mod n) has a solution. This implies that there exists an integer x such that ax - b = kn for some integer k. Rearranging this equation, we have ax - kn = b. Now, let's consider the greatest common divisor of a and n, denoted as d = gcd(a, n).

Since d divides both a and n, it also divides ax and kn. Therefore, it must divide their difference as well, which gives us d | (ax - kn). Substituting ax - kn = b, we have d | b, which proves that gcd(a, n) | b.

Conversely, let's assume that gcd(a, n) | b. This means that there exists an integer k such that b = kd where d = gcd(a, n). Now, let's consider the equation ax + ny = d, where x and y are integers obtained from Bezout's theorem.

Multiplying both sides of the equation by k, we have akx + kny = kd. Since b = kd, we can rewrite this as akx + kny = b. This equation shows that x is a valid solution for ax ≡ b (mod n) since it satisfies the congruence relation.

Therefore, we have shown that the congruence equation ax ≡ b (mod n) has a solution if and only if gcd(a, n) | b.

In conclusion, the congruence equation ax ≡ b (mod n) has a solution if and only if gcd(a, n) | b, where n ∈ N and a, b ∈ Z.

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The probability  is 0.0808 or 8.08%

To answer this question, we need to use the normal distribution formula:

Z = (X - μ) / σ

where:

Z = the standard score or z-score

X = the value we want to find the probability for (in this case, X = 173)

μ = the mean (μ = 180)

σ = the standard deviation (σ = 5)

Substituting the values, we get:

Z = (173 - 180) / 5 = -1.4

Using a calculator or a standard normal distribution table, we can now determine the likelihood of getting a value below -1.4.

We can determine the probability that corresponds to a z-score of -1.4 by using a standard normal distribution table, which is approximately 0.0808.

Therefore, the probability of getting less than 173 calls during a given hour of the day is 0.0808 or 8.08% (rounded to the nearest thousandth).

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The length and the width are 12 yards and 16 yards

The formula for calculating the perimeter of a rectangle is expressed as;

Perimeter =2( l + w)

Given that the parameter are;

Length = 4 + w

Substitute the values into the formula

52 = 2( 4 + w + w)

collect like terms

52 = 2(4 + 2w)

expand the bracket

52 = 8 + 4w

collect like terms

4w = 52 - 8

subtract the values

4w = 48

Make 'x' the subject of formula

w = 12 yards

L = 16 yards

Hence, the values are 12 yards and 16 yards

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Answer:

60

Step-by-step explanation:

80/100 times 75 and you will get 60

Step-by-step explanation:

Add the equations to eliminate q

5p-3q<0

3p+3q<24

8p<24

p< 3

Plug in value of p to an equation

3(3)+3q<24

3q<24-9

q< 5

Answer:

$600 per month

Step-by-step explanation:

You are looking for 1/6 of 3,600. An easy way to finding it is just by dividing 3600 by 6, which gives you 600.

Using the Well-Ordering Principle (WOP), it can be proven that in every tournament with n players (where n is a natural number), there is at least one top player, defined as someone who either beats every other player or beats someone who beats the other player.

We will prove this statement by contradiction. Assume that there exists a tournament with n players where there is no top player. This means that for each player, there exists either another player who beats them or a chain of players such that each player beats the next one. Now, consider the set S of all players in this tournament. Since S is a non-empty set of natural numbers, it has a least element, let's say k.

Now, player k either beats every other player in the tournament, making them a top player, or there exists a player, let's say player m, who beats player k. In the latter case, we have a chain of players: k, m, p_1, p_2, ..., p_t, where p_1 beats p_2, p_2 beats p_3, and so on until p_t.

However, this contradicts the assumption that there is no top player, as either player k beats every other player (if m does not exist), or player m beats someone who beats the other player (if m exists). Hence, by contradiction, we have shown that in every tournament with n players, there is at least one top player.

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Answer:

25. Yes, it is a function, because none of the x outputs are repeating

Step-by-step explanation:

Hey there!

25). Ans;

It is a function. [ many to one function].

26).Ans; Put all values of "x" in (2x^2+7).

a. f(x) = -2

\( f( - 2)= 2 \times { (- 2)}^{2} + 7\)

So, f(-2)= 15

b. f(x)= -1.

\(f( - 1) = 2 \times ( { - 1)}^{2} + 7\)

So, f(-1)= 9

c. f(x)= 0

\(f(0) = 2 \times ( {0)}^{2} + 7\)

So, f(0)= 7

d. f(x)= 1

\(f(1) = 2 \times {(1)}^{2} + 7\)

So, f(1)= 9

e. f(x)= 2

\(f(2) = 2 \times {(2)}^{2} + 7\)

So, f(2)= 15

f. f(x)= 3.

\(f(3) = 2 \times {(3)}^{2} + 7\)

So, f(3)= 25.

Hope it helps...

Should there be a global effort to sharply reduce the cutting and burning of old-growth forests?

Yes, there should be a global effort to sharply reduce the cutting and burning of old-growth forests. Old-growth forests are vital ecosystems that provide numerous environmental, social, and economic benefits. They are home to diverse species, including endangered ones, and play a crucial role in carbon sequestration, mitigating climate change, and preserving biodiversity.

Cutting and burning old-growth forests contribute to deforestation, habitat loss, and greenhouse gas emissions. It disrupts ecosystems, threatens species survival, and exacerbates climate change. Protecting old-growth forests is essential for maintaining ecological balance and promoting sustainable development.

Numerous references and scientific studies support the importance of preserving old-growth forests. Some relevant sources include:

"The Importance of Old-Growth Forests" by the World Wildlife Fund (WWF): https://www.worldwildlife.org/initiatives/old-growth-forests

"Old-growth forest protection: A key tool in fighting climate change" by The Nature Conservancy: https://www.nature.org/en-us/what-we-do/our-insights/perspectives/old-growth-forest-protection-fighting-climate-change/

"Old-Growth Forests: Function, Fate and Value" by the United Nations Environment Programme (UNEP): https://www.unep-wcmc.org/resources-and-data/old-growth-forests-function-fate-and-value

These resources provide comprehensive information on the importance of old-growth forest conservation and the need for global efforts to reduce cutting and burning practices.

The question provided seems incomplete and unclear. It mentions a relationship between letters of the alphabet and percentages but does not provide any context or options to choose from. Please provide more information or clarify the question, and I'll be glad to assist you further.

Answer:

Answer:

A) y ≥ -3x + 4

Step-by-step explanation:

Given the graph of an inequality, where it shows that the y-intercept is (0, 4), and the line has a negative slope (as it declines from left to right). To figure out the value of the slope, choose two points from the graph, and substitute its values into the slope equation,

m = (y2 - y1)/(x2 - x1)

Let (x1, y1) = (0, 4)

(x2, y2) = (2, -2)

m = (-2 - 4)/(2 - 0)

m = -6/2

m = -3

Now that we have the value of the slope, m = -3, and the y-intercept, b = 4:

We need to determine which part of the region is shaded. Choose a test point that is not on the graph.  Let's use the point of origin, (0, 0) to see whether it is included as a solution:

Option A: y ≥ -3x + 4

Substitute values of (0, 0) into the inequality statement:

0 ≥ -3(0) + 4

0 ≥ 0 + 4

0 ≥ 4 (False statement). The shaded region must not contain the given test point, (0, 0), which is actually the case in your given graph. The right-half plane is the shaded region.  Hence, y ≥ -3x + 4 is the correct inequality statement that represents the graph.

The answer cannot be y ≤ -3x + 4 because if you plug in the test point into y ≤ -3x + 4, it will provide a true statement.

y ≤ -3x + 4

0 ≤ -3(0) + 4

0 ≤ 0 + 4

0 ≤  4 (True statement, which means that the region where the test point is located should be shaded).

Therefore, the correct answer is Option A) y ≥ -3x + 4

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Answer:

principal is the correct answer

Step-by-step explanation:

principal is the correct answer

Answer:

Its b

Step-by-step explanation:

I took the test on edge 2020