What is the image of the point (5, -3) after a rotation of 90°
counterclockwise
about the origin?

Answer:

Area = 10.85 square centimeters

Step-by-step explanation:

The formula for area of triangle is

A = 1/2bh, where

We see from the diagram that the base is 6.2 cm and the height is 3.5 cm.  Thus, we can plug these numbers in for b and h in the base formula to find the area, A:

A = 1/2(6.2)(3.5)

A = 1/2(21.70)

A = 10.85 square centimeters

To write 45 + 3/10 + 8/1000 as a decimal, we need to convert the fractions 3/10 and 8/1000 to their equivalent decimal form and then add all three numbers. The result is 45.308, which can be simplified to 45.31 by rounding to the nearest hundredth.

Explanation:

To convert 3/10 to a decimal, we divide 3 by 10, which gives 0.3. To convert 8/1000 to a decimal, we divide 8 by 1000, which gives 0.008. We can then add 45, 0.3, and 0.008 to get:

45 + 0.3 + 0.008 = 45.308

To simplify this result to the nearest hundredth, we look at the digit in the third decimal place (8) and round the digit in the second decimal place (0) up to 1 if the third decimal place is 5 or greater. In this case, the third decimal place is 8, which is greater than 5, so we round up to get:

45.31

Therefore, 45 + 3/10 + 8/1000 is equal to 45.31 when written as a decimal.

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The total number of dolls they had in the beginning was 35, and after Jacky gave Peter 15 dolls, they each had 25 dolls. So, they had a total of 50 dolls in all.

Let the initial number of dolls Jacky had be 5x, and the initial number of dolls Peter had be 2x. So, the total number of dolls they had in the beginning was 5x + 2x = 7x.

After Jacky gave Peter 15 dolls, Peter had (2x + 15) dolls, and Jacky had (5x - 15) dolls. As they had an equal number of dolls after this, we get the equation:

5x - 15 = 2x + 15

Simplifying this, we get:

3x = 30

x = 10

So, the initial number of dolls Jacky had was 5x = 50, and the initial number of dolls Peter had was 2x = 20. Therefore, the total number of dolls they had in the beginning was 50 + 20 = 70.

After Jacky gave Peter 15 dolls, they each had 25 dolls, and the total number of dolls they had in all was 25 + 25 = 50.

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An equation that represents the amount of cheddar, c, needed per cup of broccoli, b is: D. c = 1/3(b).

In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

c = kb

Where:

Next, we would determine the constant of proportionality (k) based on the data points provided as follows:

Constant of proportionality, k = c/b

Constant of proportionality, k = 3/4/(9/4)

Constant of proportionality, k = 3/4 × 4/9.

Constant of proportionality, k = 1/3

Therefore, the required equation is given by;

c = kb

c = 1/3(b)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The probability of getting TTH or THH is (1/2) * (1/2) * (1/2) = 1/8, as each toss is independent and has a probability of 1/2.

To find the probability that a fair coin is flipped a multiple of three times before coming up heads, we can consider the possible outcomes. Let's denote H as heads and T as tails.

The first toss can either be T or H with equal probabilities of 1/2 each. If it's H, the experiment ends. If it's T, we move to the second toss.

For the second toss, the possibilities are TH or TT. If it's TH, the experiment ends. If it's TT, we move to the third toss.

For the third toss, the possibilities are TTH, TTT, or THH. If it's TTH or THH, the experiment ends. If it's TTT, we move to the fourth toss.

Following this pattern, we can see that the experiment ends when we get TTH, THH, TTTTH, TTTTTTH, or any sequence of T's followed by H. These are the outcomes where the coin is flipped a multiple of three times before coming up heads.

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By Simplifying the expression, [tex](π(0.175)^2 - π(0.125)^2)/π(0.175)^2 * 100.[/tex] we find the percentage reduction in the area of the sample due to the test.

To find the percentage reduction in area of the sample, we need to calculate the difference in cross-sectional areas before and after the tensile test.

The cross-sectional area of a rod can be calculated using the formula: [tex]A = πr^2[/tex], where r is the radius of the rod.

Given that the initial diameter of the rod is 0.350 inches, the initial radius (r1) is 0.350/2 = 0.175 inches. Therefore, the initial cross-sectional area (A1) is[tex]π(0.175)^2.[/tex]

Similarly, the final diameter of the rod is 0.250 inches, and the final radius (r2) is 0.250/2 = 0.125 inches. The final cross-sectional area (A2) is [tex]π(0.125)^2[/tex].

Now, we can calculate the percentage reduction in area using the formula: (A1 - A2)/A1 * 100.

Substituting the values, we have: [tex](π(0.175)^2 - π(0.125)^2)/π(0.175)^2 * 100.[/tex]

Therefore, by Simplifying the expression, we find the percentage reduction in the area of the sample due to the test.

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The slope of the given graph is determined as 1/3.

The slope of a line is a measure of its steepness of the graph. Mathematically, slope is calculated as rise over run or  change in y divided by change in x.

The formula is given as;

slope = Δy / Δx

where;

The slope of the given graph is calculated as follows;

choose the following coordinate points;

( x₁, y₁) = (-6, 0 )

( x₂, y₂) = ( 6 , 4 )

The slope = ( y₂ - y₁ ) / ( x₂ - x₁)

slope = ( 4 - 0 ) / ( 6 - - 6)

slope = ( 4 ) / ( 12)

slope = 1 / 3

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Answer: Use a point-slope equation to find the amount he will raise if he completes the walk.

Step-by-step explanation:

We can start by using the point-slope equation:

y - y1 = m(x - x1)

where y is the amount James raises, x is the number of miles he walks, m is the rate at which he raises money per mile, and (x1, y1) is a point on the line.

We know that James raises $15 extra for every mile he walks, so m = 15. We also know that he has received $600 in fixed pledges, which is the amount he would raise if he walked 0 miles. So (0, 600) is a point on the line.

Using this information, we can write the point-slope equation:

y - 600 = 15(x - 0)

Simplifying, we get:

y = 15x + 600

This equation tells us the amount James will raise, y, for any number of miles he walks, x. For example, if he completes the 6-mile walk, we can plug in x = 6 to find:

y = 15(6) + 600 = 690

Therefore, if James completes the walk, he will raise $690.

{Hope This Helps! :)}

The correct answer is c.A(n)  use case diagram shows the object classes and relationships involved in a use case.

A use case diagram is a visual representation that shows the object classes and relationships involved in a use case. It provides a high-level view of the system and illustrates how different actors interact with the system through various use cases. Use case diagrams depict the functionalities and interactions between actors and the system, helping to understand the system's behavior and requirements. They are widely used in software development and system analysis to capture and communicate the system's functionality in a clear and organized manner.

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The area and circumference of the circles are solved

Given data ,

Let the area and circumference be represented as A and C

Now , the circles are

Circumference of circle = 2πr

Area of the circle = πr²

a)

Radius = 7 m

C = 2 ( π ) ( 7 )

C = 43.98 m

A = π ( 7 )²

C = 153.938 m²

b)

Diameter = 30 feet

C = 2 ( π ) ( 15 )

C = 94.24 feet

A = π ( 15 )²

C = 706.858 feet²

c)

Radius = 10.2 inches

C = 2 ( π ) ( 10.2 )

C = 64.088 inches

A = π ( 10.2 )²

C = 326.85 inches²

d)

Diameter = 9 mm

C = 2 ( π ) ( 4.5 )

C = 28.274 mm

A = π ( 4.5 )²

C = 63.617 mm²

Hence , the circles are solved

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Answer:

Length = 6.49 cm

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Since we're already given the area and width and want to find the length, we can first rewrite the area formula in terms of l:

A/w = l

Now, we can plug in 25.311 for A and 3.9 for w to solve for l, the length:

25.311 / 3.9 = l

6.49 cm = l

We can check that 6.49 is the correct length by plugging everything into the regular area formula and checking that we get 25.311:

25.311 = 6.49 * 3.9

25.311 = 25.311

The volume of the cylinder is 36.8 cm³

We have,

The diameter of the cylinder = 2.5 cm

The radius of the cylinder = 2.5 / 2 = 1.25 cm

The height of the cylinder.

= 2.5 + 2.5 + 2.5

= 7.5 cm

Now,

The volume of the cylinder.

= πr²h

= 3.14 x 1.25 x 1.25 x 7.5

= 36.8 cm³

Thus,

The volume of the cylinder is 36.8 cm³

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Answer:

1 : 125

Step-by-step explanation:

We know that,

1m → 100cm

Accordingly, first, let us convert 5m into centimeters by multiplying it by 100.

5m × 100 = 500cm

So,

4cm : 5m

4cm : 500cm

4 : 500

To write the ratio in its simplest form divide it by 4.

1 : 125

The fraction that satisfies the given conditions is 2/5.

We are looking for a fraction that meets the following criteria:

1. Less than 1/2

2. Not equal to 3/10

3. Greater than 0

4. Not equal to 1/5

Let's analyze the options:

1. 0.3: This decimal is less than 1/2 and greater than 0, but it is equal to 3/10, so it does not satisfy the second condition.

2. 7/10: This fraction is greater than 1/2, so it does not satisfy the first condition.

3. 1/2: This fraction is equal to 1/2, so it does not satisfy the first condition.

4. 0.8: This decimal is greater than 1/2, so it does not satisfy the first condition.

5. 6: This whole number is greater than 1/2, so it does not satisfy the first condition.

6. 2/5: This fraction is less than 1/2, greater than 0, and it is different from both 3/10 and 1/5. Hence, it satisfies all the given conditions.

Therefore, the fraction 2/5 is the correct answer that meets all the specified criteria.

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The distance between Ibadan and Onitsha is 450km

The distance between Ibadan and Kafanchan is 636. 4km

To determine the distance, we have that;

The distance of Onitsha from Kafanchan is 450km

The distance between Ibadan and Onitsha is x

The distance between Ibadan and Kafanchan is y

Note that the third quadrant is 270 degrees

Then, the value of the angle = 270 - 225 = 45 degrees

Then, using the tangent identity, we have that;

tan 45 = x/450

cross multiply the values

x = 450km

Also, using the sine identity

sin 45 = 450/y

cross multiply the values

y = 636. 4 km

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The coordinates of the quadrilateral after a reflection over the line with equation y = x are:

Ordered pair (1, -3).

Ordered pair (2, -4).

Ordered pair (5, -5).

Ordered pair (5, -3).

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.

Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is given by this transformation rule:

(x, y)                                    →              (y, x)

Ordered pair (-3, 1)    →        Ordered pair (1, -3).

Ordered pair (-4, 2)    →        Ordered pair (2, -4).

Ordered pair (-5, 5)    →        Ordered pair (5, -5).

Ordered pair (-3, 5)    →        Ordered pair (5, -3).

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Main Answer:The best interpretation of the slope of 0.031.

Supporting Question and Answer:

What does the slope of 0.031 represent in the context of the scatterplot and regression line?

The slope of 0.031 represents the average increase in income, in dollars, for every unit increase in the rent for a 222 -bedroom apartment in the major American cities.

Body of the Solution:The best interpretation of the slope of 0.031 in this context would be as follows:

For every increase of 1 unit in the rent for a 222- bedroom apartment in the major American cities, the average income in dollars increases by approximately $0.031.

In other words, there is a positive correlation between the rent for a 222-bedroom apartment and the average income in these cities. As the rent increases, the average income tends to increase as well, although the relationship is not necessarily causative. The slope of 0.031 indicates the magnitude and direction of this relationship.

Final Answer:Therefore,the best interpretation of the slope of the fitted line, which is 0.031.

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The best interpretation of the slope of 0.031.

The slope of 0.031 represents the average increase in income, in dollars, for every unit increase in the rent for a 222 -bedroom apartment in the major American cities.

The best interpretation of the slope of 0.031 in this context would be as follows:

For every increase of 1 unit in the rent for a 222- bedroom apartment in the major American cities, the average income in dollars increases by approximately $0.031.

In other words, there is a positive correlation between the rent for a 222-bedroom apartment and the average income in these cities. As the rent increases, the average income tends to increase as well, although the relationship is not necessarily causative. The slope of 0.031 indicates the magnitude and direction of this relationship.

Therefore, the best interpretation of the slope of the fitted line, which is 0.031.

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Jose will get something other than a 2.  If Jose uses the random number generator 500 times, we can predict that he will get a result other than a 2 approximately 375 times (75% of 500).

It is highly likely that Jose will get something other than a 2 at least once during the 500500 times he uses the random number generator. This is because the generator produces 1, 2, 3, 1, comma, 2, comma, 3, comma, or 4 with equal probability, and there are 4 possible outcomes. Therefore, the probability of getting a 2 is only 1/4 or 25%. This means that there is a 75% chance of getting something other than a 2.

To further support this prediction, we can use the law of large numbers, which states that as the number of trials increases, the experimental probability of an event will converge to the theoretical probability. In this case, as Jose uses the random number generator more and more times, the percentage of times he gets a 2 should get closer and closer to 25%. Therefore, it is highly likely that Jose will get something other than a 2 at least once during the 500500 times he uses the generator.

In order to provide you with an accurate answer, let's rephrase the question with the relevant information:

Jose is going to use a random number generator 500 times. Each time he uses it, he will get a 1, 2, 3, or 4. Complete the following statement with the best prediction: Jose will get something other than a 2.

Since the random number generator can produce four possible outcomes (1, 2, 3, and 4), each outcome has a 25% chance of occurring.

Therefore, the probability of getting something other than a 2 is 75% (25% for each of the other three outcomes). If Jose uses the random number generator 500 times, we can predict that he will get a result other than a 2 approximately 375 times (75% of 500).

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The formula for the perimeter of an oval is given as

P = 2π√((a² + b²)/2)

Oval is a shape that is not entirely circle but spherical. It is usually called or also known as an ellipse.

The formula for finding the perimeter (circumference) of an ellipse is:

P = 2π√((a² + b²)/2)

where:

P is the perimeter (or circumference) of the oval

π is a mathematical constant approximately equal to 3.14159

a is the distance from the center of the ellipse to its furthest point in the horizontal direction (semi-major axis)

b is the distance from the center of the ellipse to its furthest point in the vertical direction (semi-minor axis).

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Answer:

Its the perimeter of an oval ö

Nah, im just joking, it's 2 times pie times the square root of((a² + b²)/2)

Step-by-step explanation:

Sorry I don't have some of the symbols

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Given Pauls age is three times barts age in 14 years pauls age will be twice as barts age, therefore, Bart is currently 14 years old, and Paul is currently 42 years old.

Let's assume that Bart's current age is x. Then, Paul's current age is 3x. In 14 years, Bart's age will be x + 14, and Paul's age will be 3x + 14. We know that Paul's age in 14 years will be twice Bart's age in 14 years. We can set up an equation to solve for x:

3x + 14 = 2(x + 14)

Simplifying this equation, we get:

3x + 14 = 2x + 28

x = 14

Therefore, Bart's current age is x = 14, and Paul's current age is 3x = 42.

To check our answer, we can verify that in 14 years, Paul's age will be twice Bart's age:

Paul's age in 14 years = 42 + 14 = 56

Bart's age in 14 years = 14 + 14 = 28

56 = 2(28)

Thus, our solution is correct. Bart is currently 14 years old, and Paul is currently 42 years old.

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The value of Tan( A) = 53.1°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

sin(tetha) = opp/hyp

cos( tetha) = adj/hyp

tan ( tetha) = opp/adj

The opposite to the angle A is a which is 8, the adjacent is 6 and hypotenuse 10

Tan(A) = 8/6

Tan(A) = 1.33

A = tan^-1 ( 1.33)

A = 53.1°

therefore the value of tan A is 53.1°

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The order from utmost precise to least precise is

8.431 grams, 15.46 seconds, 980 meters, 900 miles.

Ranking the following in order from utmost precise to least precise

8.431 grams ( utmost precise) This dimension has the loftiest position of perfection as it includes three decimal places.

15.46 seconds - This dimension has two decimal places, indicating a advanced position of perfection compared to whole figures.

980 meters  measures This dimension is a whole number and lacks decimal places, making it less precise than measures with decimal values.

900 long hauls( Least precise) This dimension is also a whole number and lacks decimal places, making it the least precise among the given options.

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Answer:

0.8

Step-by-step explanation:

In order to find its decimal form, we first need to divide the fraction.

[tex]4\div 5=0.8[/tex]

In decimal form, 4/5 = 0.8. The number is already rounded to the nearest tenth.

A common formula/theorem when working with right triangles is called the Pythagorean Theorem.

Pythagorean Theorem: a^2 + b^2 = c^2

---a and b are legs of the triangle

---c is the hypotenuse

8^2 + 6^2 = c^2

64 + 36 = c^2

100 = c^2

c = 10

Answer: The length of the hypotenuse of the triangle is 10cm.

Hope this helps!

The volume of Cylinder #2 is about 157 cm³ greater than the volume of Cylinder.#1 The correct answer is D. 157 cm³.

To compare the volumes of the two cylinders, we will use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.
Cylinder #1:
Radius (r1) = 5 cm
Height (h1) = 18 cm
Volume of Cylinder #1 (V1) = π × r1² × h1 = π × 5² × 18 = π × 25 × 18 = 450π cm³
Cylinder #2:
Radius (r2) = 5 cm (same as Cylinder #1)
Height (h2) = 20 cm
Volume of Cylinder #2 (V2) = π × r2² × h2 = π × 5² × 20 = π × 25 × 20 = 500π cm³
Now, we will find the difference in volumes:
Difference = V2 - V1 = 500π cm³ - 450π cm³ = 50π cm³ ≈ 157 cm³
So, the volume of Cylinder #2 is about 157 cm³ greater than the volume of Cylinder #1. The correct answer is D. 157 cm³.

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Answer:

The area of the right triangle is approximately 77.5 square yards.

Answer:

77.5 yards

Step-by-step explanation:

area of right-angled triangle = 0.5 x 7.75 X 20

= 10 X 7.75

=77.5 yards

Answer:

The answer cannot be given as exact prices are not listed. How to do it could be explained as below:

Step-by-step explanation:

The first thing you have to do is find the price of the shoes. Then you take $250 (the amount of money in the gift card) and subtract it from the price of the shoes.

Then, we take the number we got from above and divide it by how much 1 pair of socks costs. You could get a decimal, and if you do, pretend that the numbers after the decimal don't exist. This number is the number of possible socks you could order only using the gift card.

Message:
Hope this helped! <3

Answer:

-16r^2 - 10r

Step-by-step explanation:

all you got to do is distribute