An athlete runs 1/3 of a mile every 1/20 hour. At this rate, how far does the athlete run per hour?

Answer:

3.5

Step-by-step explanation:

The parenthesis means you multiply the inside number by the outside number.

the negatives cancel each other out so the answer would be positive 3.5.

The quadratic equation with the easiest method that could be used to find the solutions:

5x² + 24x + 21 = 0 :: Factoring

x² + 4x + 27 = 0 :: Completing the Square

x² + 8x + 15 = 0 :: Factoring

-3x² = -5x + 8 :: Dividing by x and simplifying gives Quadratic Formula

An equation is a mathematical statement that uses an equal sign to show that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of an equation is to solve for the variable(s) that make the equation true.

Here,

The easiest method to find the solutions of a quadratic equation depends on the form of the equation and the tools available. Here are some common methods and when they are typically used:

Zero Product Property/Factoring: This method is used when the quadratic equation can be factored into two linear factors, each of which equals zero.

Square Root Property: This method is used when the quadratic equation is in the form of x² = a, where a is a positive number. For example, the equation x² = 9 can be solved using the Square Root Property: take the square root of both sides and remember to include both the positive and negative roots, giving x = ±3.

Completing the Square: This method is used when the quadratic equation is in the form of x² + bx + c = 0, where b and c are constants. Completing the square involves adding and subtracting a constant term to both sides of the equation to create a perfect square trinomial, which can then be factored and solved using the Square Root Property.

Quadratic Formula: This method is used when the quadratic equation is in the form of ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. The Quadratic Formula is x = (-b ± √(b² - 4ac)) / 2a.

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The perimeter of the given triangle are as follow,

perimeter of triangle GHJ = 34 inches.

perimeter of triangle KLM = 17inches.

Perimeter of triangle GHJ is twice of perimeter of triangle KLM.

In triangle GHJ,

K,L,M are the midpoints of GH, HJ, and JG .

GH = 12 inches

KL = 7inches

LJ = 4 inches

'L' is the midpoint of HJ.

HJ = 2(LJ)

    = 2(4inches )

    = 8 inches

Using midpoint theorem we have,

KL = (1/2) GJ

⇒ GJ = 2(KL)

⇒GJ = 2(7)

⇒GJ = 14inches

LM = (1/2)GH

⇒LM = (1/2) ×12 inches

LM = 6 inches

KM= (1/2)HJ

⇒KM = (1/2) ×8

⇒ KM = 4 inches

Perimeter of triangle GHJ

= GH + HJ + JG

Substitute the value we have,

⇒ Perimeter of triangle GHJ = 12 + 14 + 8

Perimeter of triangle GHJ = 34 inches

Perimeter of the triangle KLM = KL + LM + MK

Substitute the value we have,

⇒ Perimeter of the triangle KLM = 7 + 6 + 4

Perimeter of the triangle KLM = 17 inches

Relation between perimeter of triangle GHJ and KLM

34 = 2 (17)

Perimeter of triangle GHJ = 2(Perimeter of triangle KLM)

Therefore, the required perimeters are,

Perimeter of ΔGHJ = 34inches

perimeter of ΔKLM = 17inches

Perimeter of ΔGHJ =2(Perimeter of ΔKLM).

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The above question is incomplete , the complete question is:

In triangle GHJ,

K,L,M are the midpoints of GH, HJ, and JG respectively.

Given GH is 12 inches, KL is 7 inches, and LJ is 4 inches

1. What is the perimeter of triangle GHJ?

2. What is the perimeter of triangle KLM?

3. What is the relationship between the perimeter of triangle GHJ and the perimeter of triangle KLM?

Diagram is attached.

After the triangle is dilated by a scale factor of 1/4, the coordinates of point C' are (10, -14).

We can use the following formula to find the coordinates of point C' after the triangle has been dilated by a scale factor of 1/4:

C' = (1/4)(C - center) + center

where C denotes the original coordinate of point C and centre denotes the dilation center (which is not specified in the problem).

However, because this is the most common choice and is not explicitly stated, we can assume that the center of dilation is the midpoint of line segment AB. Line segment AB's midpoint is:

((8+8)/2, (-24-8)/2) = (8, -16)

So, in the formula, we can substitute this value for Centre:

C' = (1/4)(C - (8, -16)) + (8, -16)

All that remains is to plug in the coordinates of point C and simplify:

C' = (1/4)((16, -8) - (8, -16)) + (8, -16)

= (1/4)(8, 8) + (8, -16)

= (2, 2) + (8, -16)

= (10, -14)

As a result, the coordinates of point C' after the triangle has been dilated by a factor of 1/4 are (10, -14).

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The area of the bedroom in the terms of p and q is (6p7q)² square units.

What is the area of square?

The amount of square units required to fill a square is referred to as the area of a square. In general, the region contained within a flat object's or 2D figure's boundary is referred to as the area. The unit of measurement is square, with square metres serving as the default.

We are given that a bedroom is in the shape of a square with the length as 6p7q.

We know that area of a square is the square of the side.

So, from this we get

⇒ Area = (6p7q)² square units

Hence, the area of the bedroom in the terms of p and q is (6p7q)² square units.

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The probability that 5 or less students will withdraw from a math course if 30 students are enrolled is 0.6826.

This can be calculated using the binomial probability formula, which states that the probability of a certain number of successes in a certain number of trials is equal to the number of combinations of successes times the probability of each success. In this case, the probability of success (withdrawing) is 0.10 and the number of trials (students enrolled) is 30.

For this example, the probability of 5 or less successes (withdrawals) is calculated by adding together the probabilities of 0 successes, 1 success, 2 successes, 3 successes, 4 successes, and 5 successes. That gives us a probability of 0.6826.

This is equivalent to saying that 68.26% of students enrolled in a math course will not withdraw. It is also equivalent to saying that 31.74% of students enrolled in a math course will withdraw.

To illustrate this, if we assume that 30 students are enrolled in a math course, we would expect that approximately 19 students will not withdraw (68.26%) and approximately 11 students will withdraw (31.74%).

In conclusion, the probability that 5 or less students will withdraw from a math course if 30 students are enrolled is 0.6826.

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Answer:

Step-by-step explanation:

8

Answer:

  no

Step-by-step explanation:

You want to know if a triangle with sides 54, 66, and 87 is a right triangle.

The side lengths of a right triangle will satisfy the relation given by the Pythagorean theorem. Here, that would require ...

  54² +66² = 87²

  2916 +4356 = 7569

  7272 = 7569 . . . . . . . . . false — not a right triangle

Triangle WXY is not a right triangle, so XY is not tangent to circle W.

__

Additional comments

The parity of the integer side lengths of a right triangle is always even. That is, there can be two odd side lengths, but never just one odd side length.

Side lengths 54 and 66 are even, while length 87 is odd. There is only one odd side length, so this triangle cannot be a right triangle.

A tangent always meets a radius at right angles, so XY is a tangent if and only if angle X is a right angle.

90 mm Hg is Zigg's mean arterial pressure.

Here's the formula for calculating MAP: MAP = (CO x SVR) + CVPR

where:

CO stands for cardiac output (measured in liters per minute).

SVR stands for systemic vascular resistance (measured in mm Hg/L/min).

CVPR stands for central venous pressure (measured in mm Hg).

Now, let's get started with the calculation of MAP.

First, let's calculate CO (cardiac output): CO = HR x SV

where:

HR is heart rate (measured in beats per minute).

SV is stroke volume (measured in milliliters per beat).

CO = 140 bpm x 95 mlCO = 13300 ml/minCO = 13.3 L/min

Next, we need to calculate SVR (systemic vascular resistance).

The formula for calculating SVR is: SVR = (MAP - CVP) / CO

where:

MAP is mean arterial pressure (measured in mm Hg).

CVP is central venous pressure (measured in mm Hg).

CO is cardiac output (measured in liters per minute).

Since we don't have CVP in this question, let's assume it to be zero.

SVR = (MAP - 0) / 13.3 L/minSVR = MAP / 13.3 L/min

Now, we can rearrange the above equation to calculate

MAP:

MAP = SVR x 13.3 L/minMAP = 60 mm Hg (diastolic pressure) + 1/3 (systolic pressure - diastolic pressure)MAP = 60 mm Hg + 1/3 (150 mm Hg - 60 mm Hg)MAP = 60 mm Hg + 30 mm HgMAP = 90 mm Hg

Therefore, Ziggy's mean arterial pressure (MAP) is 90 mm Hg.

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The type of transformation that occurred in each object are:

1) Rotation

2) Translation

3) Reflection

4) Translation

There are different types of transformations of objects such as:

Translation: Translation is said to occur when we slide a figure in any direction.

Reflection: Reflection is said to occur when we flip a figure over a line.

Rotation: Rotation is said to occur when we rotate a figure a certain degree around a point.

Dilation: Dilation is said to occur when we enlarge or reduce a figure.

1) The given transformation is rotation because the original object was clearly rotated.

2) The given transformation is said to be translation because the object just changed position.

3) The transformation that occurred is said to be a reflection because it is a mirror image.

4)  The given transformation is said to be translation because the object just changed position.

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Answer: You would probably have to play about 10 rounds.

The value οf x = 4√2 in the given right angle triangle.

A clοsed triangle has three vertices, three sides, and three angles.

The symbοl fοr a triangle with the three vertices P, Q, and R is PQR. Sandwiches and signbοards in the shape οf triangles are the mοst prevalent triangle-shaped οbjects.

A triangle is made up οf several cοmpοnents. It has 3 sides, 3 vertices, and 3 angles.

Three vertices, three internal angles, and three sides make up a triangle.

Accοrding tο the triangle's "angle sum prοperty," a triangle's three inner angles can never add up tο mοre than 180 degrees.

Using the Pythagοras theοrem

x² = 4² + 4²  (both sides are equal as opposite angles are equal)

x² = 16 + 16

x² = 32

x = √32

x = [tex]\sqrt{16 \times 2}[/tex]

x = 4√2

Thus, the value of x = 4√2 in the given right angle triangle.

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Answer:

Slope is -2. So, choice D is the best option.

Step-by-step explanation:

Start with one point then use the formula to get to the next point:

Rise
------

Run

Let's start at (0,5) then count down 2 points, which is the "Rise"(seems like an interesting name to pick but it works).
Next, you go to the right once. Which counts as the "Run".

Remember: The slope is like a ratio, and the "y" will always go as the numerator and the "x" as the denominator. Which is why "Rise" is on top and the "Run" is on the bottom.

So your answer would be 2/1. And that simplifies to 2. But since you went down and not up, it would be negative 2.

Hope this helps and if you have any other questions or need clarification please ask!

Answer: 100 cm

Step-by-step explanation:

1. Since the problem tells us that they are similar, we can infer that this larger rectangle is the same rectangle, only bigger.

2. With this information, we can do the equation 49/12.25 because then we will get the amount the rectangle grows by.

3. 49/12.25=4

4. Now, we can multiply the length(25) by 4.

5. 25 x 4=100

6. The length of the larger rectangle is 100.

I hope this helps!

Using the proportionality we know that 24 is the value of C.

Every relationship that has a constant ratio is said to be proportionate.

For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.

An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.

So, the table is as follows:

Part      8    B    D

Part     10   15   45

Whole  A    C    72

Due to the fact that the two parts will be proportional to the whole.

Then,

C /72 = 15/45

C = 72/3

C = 24

Therefore, using the proportionality we know that 24 is the value of C.

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(a) To set up a proof by contradiction for the statement "For each positive real number r, if r^2 = 18, then r is irrational," we will assume the opposite of the given statement. Specifically, we would assume that there exists a positive real number r such that r^2 = 18, and r is rational (not irrational).

(b) To complete the proof by contradiction, follow these steps:

1. Assume that there exists a positive real number r such that r^2 = 18, and r is rational.
2. Since r is rational, we can write it as a fraction a/b, where a and b are integers with no common factors other than 1 (i.e., a and b are coprime) and b ≠ 0.
3. We have r^2 = 18, so (a/b)^2 = 18.
4. Squaring both sides, we get a^2 / b^2 = 18.
5. Rearrange the equation: a^2 = 18b^2.
6. Since 18 is an even number, a^2 is also an even number, which implies that a is an even number (let's say a = 2k, where k is an integer).
7. Substitute a with 2k: (2k)^2 = 18b^2, which simplifies to 4k^2 = 18b^2.
8. Divide both sides by 2: 2k^2 = 9b^2.
9. Now, we see that the left side of the equation is an even number (2k^2), which implies that 9b^2 is also an even number. However, 9 is an odd number, so for 9b^2 to be even, b must be even.
10. Both a and b are even, which contradicts our original assumption that a and b are coprime (having no common factors other than 1).

Therefore, our assumption that there exists a positive real number r such that r^2 = 18 and r is rational leads to a contradiction. Thus, the original statement is true: for each positive real number r, if r^2 = 18, then r is irrational.

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Therefore, the 95% confidence interval for the population standard deviation is approximately (2.6, 12.3).

To construct a 95% confidence interval for the population standard deviation, we will use the chi-square distribution. Here are the steps:

Step 1: Identify the given values.
n = 5 (sample size)
s = 4.4 (sample standard deviation)
c = 0.95 (confidence level)

Step 2: Find the degrees of freedom.
df = n - 1 = 5 - 1 = 4

Step 3: Find the chi-square values.
For a 95% confidence interval, we will use the values corresponding to 2.5% and 97.5% in the chi-square distribution table. For df = 4:
Chi-square (0.025) = 11.143
Chi-square (0.975) = 0.485

Step 4: Calculate the confidence interval for the population variance.
Lower limit:[tex] (n - 1) * s^2 / Chi-square (0.025) = 4 * (4.4)^2 / 11.143 = 6.960[/tex]
Upper limit:[tex] (n - 1) * s^2 / Chi-square (0.975) = 4 * (4.4)^2 / 0.485 = 151.977[/tex]

Step 5: Calculate the confidence interval for the population standard deviation by taking the square root of the variance limits.
Lower limit: [tex]√6.960 = 2.6[/tex]
Upper limit:[tex] √151.977 = 12.3[/tex]

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Answer:

Step-by-step explanation:

minor, semi, minor, major   (in that order)

minor is smaller than a semi-circle while major is larger than a semi-circle.

The unit rate at which the bakery makes donuts is 2 donuts per minute.

The slope of the line would also be 2 since the number of donuts made is directly proportional to the time elapsed. This means that for every minute that passes, 2 donuts are made.

To find the unit rate, we divide the total number of donuts made (30) by the time it takes to make them (15 minutes).

Unit rate = 30 donuts ÷ 15 minutes = 2 donuts per minute

To find the slope of the line, we use the formula:

slope = rise ÷ run

In this case, the "rise" is the number of donuts made and the "run" is the time elapsed. Therefore, the slope is:

slope = 30 donuts ÷ 15 minutes = 2 donuts per minute.

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Answer:

1.6 minutes

Step-by-step explanation:

6.4 meters/4 speed

Answer:

16/36 = 12/27

the percentage of racers who did not complete the marathon is 8.3% when rounded to the nearest tenth of a percent.

To find the percentage of racers who did not complete the marathon, we need to divide the number of racers who did not complete by the total number of racers and then multiply by 100 to get a percentage.

Number of racers who did not complete = 12 + 7 = 19

Total number of racers = 230

Percentage of racers who did not complete = (19/230) x 100% = 8.3%

Therefore, the percentage of racers who did not complete the marathon is 8.3% when rounded to the nearest tenth of a percent.

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Simplifying the expression resulted to x° = x

The expression x° = ½ • (30 + 2x – 30) can be simplified as follows:

The term 30 - 30 simplifies to 0, so we can remove it from the expression:

x° = ½ • (30 + 2x - 30)

x° = ½ • (2x)

We can simplify the fraction ½ by dividing the numerator by the denominator:

x° = x

Therefore, the solution to the equation x° = ½ • (30 + 2x – 30) is x = x°. In other words, any value of x is equal to its corresponding value in degrees.

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Answer:

In this problem, we have a right triangle where the hypotenuse is the 30-foot support cable and one leg is 22 feet (the distance from the base of the pole to where the cable is attached). To find the angle that the cable makes with the ground, we need to use trigonometry. The tangent of an angle in a right triangle is equal to the length of the opposite side divided by the length of the adjacent side. In this case, we want to find tan(θ), where θ is the angle between the cable and the ground. Therefore, tan(θ) = opposite/adjacent = 22/30 = 0.7333. Taking inverse tangent on both sides gives us θ = tan^-1(0.7333) ≈ 36.7 degrees to one decimal place. Therefore, to the nearest tenth, the measure of the angle that the cable makes with the ground is approximately 36.7 degrees.

The given cross product formula is slightly incorrect. The correct cross product of two vectors in R3 is defined by (a1, a2, a3) × (b1, b2, b3) = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1). We are given vector v = (-1, 3, 0) and asked to find the matrix A of the linear transformation [tex]T(x) = v × x.[/tex]
Let x = (x1, x2, x3) be a vector in R3. Then, using the cross product formula, we have:
T(x) =[tex]v × x = (-1, 3, 0) × (x1, x2, x3) = (3x3 - 0x2, 0x1 - (-1)x3, (-1)x2 - 3x1)[/tex]
T(x) =[tex](3x3, x3, -x2 - 3x1)[/tex]
Now, we can express the linear transformation as a matrix A multiplied by the vector x:
[tex]A * (x1, x2, x3) = (3x3, x3, -x2 - 3x1)[/tex]
The matrix A can be found by comparing the components of the vectors:
A = | 0  -3   0 |
     | 0   0   1 |
     |-3  -1   3 |
So, the matrix A of the linear transformation from R3 to R3 given by T(x) = v × x is:
A = | 0  -3   0 |
     | 0   0   1 |
     |-3  -1   3 |

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EXPLANTION:

1. For a browsing time of 17 minutes, the predicted amount spent can be calculated using the equation of the regression line:

Y = 2 + 0.98X, where X is the browsing time in minutes.

Step-by-step:
Y = 2 + 0.98(17)
Y = 2 + 16.66
Y = 18.66 dollars

The observed value (40.3 dollars) is above the regression line, as it is higher than the predicted amount spent (18.66 dollars).

2. For a browsing time of 14 minutes, the predicted amount spent can be calculated using the equation of the regression line:

Y = 2 + 0.98X.

Step-by-step:
Y = 2 + 0.98(14)
Y = 2 + 13.72
Y = 15.72 dollars

The observed value (10.84 dollars) is below the regression line, as it is lower than the predicted amount spent (15.72 dollars).

3. For a browsing time of 28 minutes, the predicted amount spent can be calculated using the equation of the regression line:

Y = 2 + 0.98X.

Step-by-step:
Y = 2 + 0.98(28)
Y = 2 + 27.44
Y = 29.44 dollars

The observed value (27.2 dollars) is below the regression line, as it is lower than the predicted amount spent (29.44 dollars).

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The total number of eggs is 1542.

To find the total number of eggs, we can use the fact that the 540 eggs sold represent 35% of the total eggs. We can start by setting up a proportion:

35/100 = 540/x

where x is the total number of eggs. To solve for x, we can cross-multiply and simplify:

35x = 54000

x = 54000/35

x = 1542.86

Therefore, the total number of eggs is approximately 1542.86. Since we can't have a fraction of an egg, we can assume that the total number of eggs is 1542.

To find the number of eggs that are not sold, we can subtract the number of eggs sold from the total number of eggs:

1542 - 540 = 1002

Find out more about The total number of eggs is 1542.

To find the total number of eggs, we can use the fact that the 540 eggs sold represent 35% of the total eggs. We can start by setting up a proportion:

35/100 = 540/x

where x is the total number of eggs. To solve for x, we can cross-multiply and simplify:

35x = 54000

x = 54000/35

x = 1542.86

Therefore, the total number of eggs is approximately 1542.86. Since we can't have a fraction of an egg, we can assume that the total number of eggs is 1542.

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Answer:

The television tower is 132 feet high.

Step-by-step explanation:

Let h be the height of the television tower. Set up and solve this proportion.

[tex] \frac{3}{5} = \frac{h}{220} [/tex]

[tex]5h = 660[/tex]

[tex]h = 132[/tex]

Answer:

(a) To find the mean value, we sum up all the values and divide by the number of values:

Mean = (17 + 22 + 25 + 27 + 32 + 40 + 45 + 51 + 59 + 62) / 10 = 36.0

So, the mean value is 36.0.

To find the median value, we first need to put the data set in order from smallest to largest:

17, 22, 25, 27, 32, 40, 45, 51, 59, 62

The median is the middle value of the data set, which is 36 in this case.

So, the median value is 36.0.

(b) To find the mean absolute deviation (MAD), we first need to find the deviation of each value from the mean:

|17 - 36.0| = 19.0

|22 - 36.0| = 14.0

|25 - 36.0| = 11.0

|27 - 36.0| = 9.0

|32 - 36.0| = 4.0

|40 - 36.0| = 4.0

|45 - 36.0| = 9.0

|51 - 36.0| = 15.0

|59 - 36.0| = 23.0

|62 - 36.0| = 26.0

Next, we find the mean of these deviations:

MAD = (19.0 + 14.0 + 11.0 + 9.0 + 4.0 + 4.0 + 9.0 + 15.0 + 23.0 + 26.0) / 10

MAD = 13.0

So, the mean absolute deviation for this data set is 13.0.

(c) To find the percentage of the data set that lies closer than the MAD to the mean, we count how many values are within one MAD of the mean. We have:

17, 22, 25, 27, 32, 40, 45, 51, 59, 62

The values within one MAD of the mean (36.0 +/- 13.0) are:

17, 22, 25, 27, 32, 40, 45, 51

So, 8 out of 10 values are within one MAD of the mean.

The percentage of the data set that lies closer than the MAD to the mean is:

8 / 10 * 100% = 80%

(a) To find the mean value, we sum up all the values and divide by the number of values:

Mean = (7 + 7 + 7 + 8 + 8 + 9 + 10 + 32) / 8 = 9.5

So, the mean value is 9.5.

To find the mean absolute deviation (MAD), we first need to find the deviation of each value from the mean:

|7 - 9.5| = 2.5

|7 - 9.5| = 2.5

|7 - 9.5| = 2.5

|8 - 9.5| = 1.5

|8 - 9.5| = 1.5

|9 - 9.5| = 0.5

|10 - 9.5| = 0.5

|32 - 9.5| = 22.