Yesenia swims laps at a pool. For every 10 laps she swims the backstroke, she swims 15 laps of freestyle. Which ratio shows the number of laps Yesenia swims the backstroke to the number of laps she swims freestyle?

The total number of undergraduates attending the college is approximately 4,818. The 2,650 women undergraduates at the college comprise 55% of all undergraduates. We are supposed to calculate the total number of undergraduates that attend the college.

In this case, we can use the concept of percentage to find the total number of undergraduates attending the college. We know that 2,650 women undergraduates are 55% of all undergraduates.Let's assume the total number of undergraduates be x.

Number of women undergraduates = 55% of x = (55/100) * x = (11/20) * xAccording to the question, number of women undergraduates = 2,650.(11/20) * x = 2,650

Multiplying both sides by 20/11 we get,x = 20/11 * 2,650 = 4,818.18Approximately, the number of undergraduates attending the college is 4,818.

The given problem is the total number of undergraduates attending the college is approximately 4,818.

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The total number of combinations of 5 cards that give a full house is 3,744.

What is the combination?

Combinations are a way to count the number of ways to choose a subset of objects from a larger set, where the order of the objects does not matter.

To get a straight, we need to select five cards that are in a sequence and not all in the same suit.

There are 10 possible sequences of five cards (A-2-3-4-5, 2-3-4-5-6, ..., 10-J-Q-K-A), and for each sequence, there are four suits to choose from for each card.

However, we have to subtract the 10 combinations that include all five cards of the same suit (since we want the cards to be not all in the same suit).

Therefore, the total number of combinations of 5 cards that give a straight is:

4 x (10 - 1) - 10 = 36.

To get a flush, we need to select five cards that are all of the same suit and not in sequential order. There are four suits to choose from, and once we choose the suit, we need to select any five cards from that suit. The number of ways to select 5 cards from a set of 13 cards is given by the combination formula:

C(13, 5) = 1,287.

Therefore, the total number of combinations of 5 cards that give a flush is:

4 x 1,287 = 5,148.

To get a full house, we need to select three cards of the same rank and two cards of another common rank.

There are C(13, 1) ways to choose the rank for the three cards, and C(4, 3) ways to choose the suits for those three cards.

For the remaining two cards, we need to choose a different rank, so there are C(12, 1) ways to choose the rank for those cards, and C(4, 2) ways to choose the suits for those cards.

Therefore, the total number of combinations of 5 cards that give a full house is:

C(13, 1) x C(4, 3) x C(12, 1) x C(4, 2) = 3,744.

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Answer: 51

Step-by-step explanation:

We will use the Order of Operations, sometimes known as PEMDAS.

    Given:

5x² - x + 9

    Plug in the value of 3:

5(3)² - (3) + 9

    To the power of 2:

5(9) - 3 + 9

    Multiply:

45 - 3 + 9

   Subtract:

42 + 9

    Add:

51

Answer:

An inequality is a relation which makes a non equal comparison between two of more numbers or other mathematic equations. > I'd greater than < is less than = equal to. ≥ is greater than or equal ≤ less than or equal to. = equal to ≠ not equal

Step-by-step explanation:

Inequality- is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

The Balmer series, the second line would have ni = 4, indicating that the electron transitions from the fourth energy level to the second energy level.

The Balmer series is a series of spectral lines in the emission spectrum of hydrogen. It corresponds to transitions of electrons in hydrogen atoms from higher energy levels (initial states) to the second energy level (final state) with nf = 2.

In the Balmer series, the first line is associated with an initial energy level ni = 3. This means that the electron starts in the third energy level and transitions to the second energy level (nf = 2). Each line in the series corresponds to a different transition between energy levels.

Based on this information, the second line in the Balmer series would correspond to a transition where the electron starts from the fourth energy level (ni = 4) and ends up in the second energy level (nf = 2). This transition represents a higher energy change compared to the first line in the series.

Therefore, for the Balmer series, the second line would have ni = 4, indicating that the electron transitions from the fourth energy level to the second energy level.

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If G is the incenter of triangle ABC the values of the unknown sides are

a) GD = 12

b) BG = 13.42

c) FC = 35

d) BF = 6

Considering that G is the incenter of triangle ABC, we have that

Using the right triangle CDG and applying Pythagoras theorem given by  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

GC² = GD² + DC²

37² = GD² + 35²

GD² = 37² - 35²

GD² = 144

take square root of both sides

GD = √144

GD = 12

Using the right triangle BEG to solve for BG

BG² = EB² + GE²

BG² = 6² + 12²

BG² = 180

take square root of both sides

BG = √180

BG = 13.42

Using the right triangle CFG to solve for FC

GC² = GF² + FC²

rearranging the equation

FC² = GC² - GF²

FC² = 37² - 12²

FC² = 1225

take square root of both sides

FC = √1225

FC = 35

Using the right triangle BFG to solve for BF

BG² = GF² + BF²

rearranging the equation

BF² = BG² - GF²

BF² = 13.42² - 12²

BF² = 36.0964

take square root of both sides

BF = √36.0964

BF = 6

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The required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.

Arithmetic progression is the series of numbers that have common differences between adjacent values.

here,
The Sequences 8, 11, 14,...

first term a = 8
common difference = 11 - 8 = 3

Now,
The explicit formula is given as,
nth terms = a + (n - 1)d
nth term = 8 + (n - 1)3

Thus, the required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.

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The constant C=±eB varies over all possible values of ±ke, where k is any real number, as B varies over all real numbers.

The statement "the constant C=±eB can be any real value as B varies over all real numbers" is not entirely accurate.

The constant C is given by C=±eB, where e is the mathematical constant approximately equal to 2.71828, and B is a fixed real number. When B varies over all real numbers, the constant C will also vary over all real numbers. However, the value of C cannot be any real value; it is restricted by the value of e.

Since e is a fixed constant, the possible values of C are limited to those that can be obtained by multiplying e by a real number and then taking the positive or negative value of the result. Therefore, the possible values of C are of the form ±ke, where k is any real number.

In summary, the constant C=±eB varies over all possible values of ±ke, where k is any real number, as B varies over all real numbers.

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Answer:

C.

Step-by-step explanation:

A concave polygon must have atleast an internal angle which is greater than other angles.

\({ \underline{ \blue{ \sf{christ \: † \: alone}}}}\)

Step-by-step explanation:

I don't see any numbers, so I just give you an example :

11

every position in a number is worth 10 times the value of the position to its very right.

so, in e.g. 11

the left 1 is worth 10 times the value of the right 1.

Answer: Since triangle QRS and triangle TUV are both triangles, we can use the fact that the sum of the interior angles in a triangle is 180 degrees.

In triangle QRS, the measure of angle Q is 117 degrees and the measure of angle R is 180 - 117 = 63 degrees. The measure of angle S is 180 - 63 = 117 degrees, since the angles in a triangle add up to 180 degrees.

In triangle TUV, the measure of angle T is 180 - 30 = 150 degrees and the measure of angle U is 30 degrees. The measure of angle V is 180 - 150 = 30 degrees, since the angles in a triangle add up to 180 degrees.

The measures of LQ and LS can be found using the fact that the exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

The measure of LQ is equal to the sum of the measures of angles R and T:

LQ = 63 + 150 = 213 degrees

The measure of LS is equal to the sum of the measures of angles Q and U:

LS = 117 + 30 = 147 degrees

So the measure of LQ is 213 degrees and the measure of LS is 147 degrees.

Step-by-step explanation:

Answer:

To find the domain and range, we simply solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain. To calculate the range of the function, we simply express x as x=g(y) and then find the domain of g(y)

Step-by-step explanation:

Thats basically it I think

When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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7 lawns / 4 hours = 1.75 hours per lawn.

1.75 hours per lawn x 21 lawns = 36.75 hours total ( 36 hours and 45 minutes)

The equation which can be used to find the amount of time Hiroshi spends on his math homework is 1/4(x + 30 + 60) = x

According to the question,

Let total time Hiroshi spent on his homework be "y"

Total time spent on history homework = 30 minutes

Total time spent on English homework = 60 minutes

It is given that the time spent on math homework is x

and Also that One fourth of his total homework time is spent on math

=> x = 1/4y

=> 4x = y ----------(1)

Also , Sum of time taken in different homework will be equal total time y

=> 30 + 60 + x = y --------(2)

Substituting the values of x from equation (1) in equation (2)

=> 30 + 60 + x = 4x

divide by 4

=> 1/4(x + 30 + 60) = x is equation

=> x + 30 + 60 = 4x

=> 3x = 90

=> x = 90/3

=> x = 30 minutes

Total time taken in doing homework is 120 minutes

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Answer:

7x³y - 35x² + 35y² + 48x²y² - 240xy - 7xy³

Step-by-step explanation:

Dimensions of the cube = (x+7y),(7x-y) and (xy-5)

Volume of the cube = (x+7y) (7x-y) (xy-5)

= (7x² - xy + 49xy - 7y²)(xy - 5)

= 7x³y - 35x² - x²y² + 5xy + 49x²y² - 245xy - 7xy³ + 35y²

= 7x³y - 35x² + 35y² + 49x²y² - x²y² + 5xy - 245xy - 7xy³

= 7x³y - 35x² + 35y² + 48x²y² - 240xy - 7xy³

Volume of the cube = 7x³y - 35x² + 35y² + 48x²y² - 240xy - 7xy³

Answer:  4/9

Step-by-step explanation:

Let x represent the denominator. Then the fraction is: (x - 5)/x

Add 1 to the numerator and denominator   →     (x - 5 + 1)/(x + 1) = 1/2

Cross Multiply:                   1(x + 1) = 2(x - 4)

Distribute:                             x + 1 = 2x - 8

Subtract x from both sides:       1 = x - 8

Add 9 to both sides:                  9 = x

Numerator:  x - 5    →     9 - 5 = 4

Denominator:  x     →     9

So the fraction is: 4/9

Answer:

y = -x+3

Step-by-step explanation:

First find the slope

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

    = ( 2 - -3)/( 1 - 6)

   ( 2+3)/( 1-6)

   5/ -5

   -1

The slope is -1

We can use slope intercept form

y = mx+b  where m is the slope and b is the y intercept

y = -x+b

Substitute a point into the equation

2 = -1 +b

Add 1 to each side

2+1 = -1+1+b

3 = b

y = -x+3

y = -x + 3

\(m = \frac{y_{1} - y_{2} }{x_{1} - x_{2}}\)

\(m = \frac{6 - 1 }{-3 - 2}\)

\(m = \frac{5 }{-5}\)

\(m=-1\)

y = mx + b

substitute

2 = -1(1) + b

2 = -1 + b

3 = b

The value of the triple integral is -16.

Triple integral is a mathematical concept used in calculus to calculate the volume of three-dimensional objects. It extends the concept of a single integral to functions of three variables and integrates over a region in three-dimensional space.

The triple integral of a function f(x, y, z) over a region E in three-dimensional space is denoted by:

∭E f(x, y, z) dV

We can set up the triple integral as follows:

∫∫∫ 16y dV

Where the limits of integration are:

0 ≤ x ≤ 2

0 ≤ y ≤ (2- \(x^2\)z)/(2y)

0 ≤ z ≤ 2/\(x^{2y\)

Note that the upper bound of integration for y is not a constant, but depends on both x and z.

Integrating with respect to y first, we get:

∫∫∫ 16y dV = ∫0^2 ∫\(0^(2-x^2z)/(2x)\)∫\(0^(2/x^2y) 16y dz dy dx\)

= ∫\(0^2\) ∫\(0^(2-x^2z)/(2x) 32/x dx dz\)

= ∫\(0^2\) [16(\(2-x^2z)/x^2\)] dz

= ∫\(0^2 (32/x^2 - 16z)\) dz

= 32∫\(0^2 x^-2 dx - 16\)∫\(0^2\)z dz

= 16 - 16(2)

= -16

Therefore, the value of the triple integral is -16.

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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Answer:

on    e d g e n u i t y 2020, the answer is Set B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

L = W+2A = 63 = W × (W+2)W^2 + 2W = 63W^2 + 2W — 63 =0(W+9)(W-7) = 0W = 7….. L = W+2 = 9Dimenions are 9′ × 7′

The author is comparing this stride rate to that of Olympic Runner Usain Bolt, who has a reported stride rate of 3.5 strides per second.

The number of steps a runner takes in a specific length of time is referred to as stride rate and is commonly expressed in steps per second. You can figure it out by dividing the total number of steps you took during a certain amount of time by how long that time period lasted. Stride rate, which is frequently used as a gauge of running effectiveness, is impacted by a variety of variables, including running speed, terrain, and personal running form.

Hence, in the given section, the author is comparing this stride rate to that of Olympic Runner Usain Bolt, who has a reported stride rate of 3.5 strides per second.

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Answer:

1 out of 3

Step-by-step explanation:

Two desired outcomes and six total outcomes which is 2/6 simplified is 1/3

This post is about the author's experience at an alternative school, which they have been attending since freshman year. They have had the opportunity to explore their interests and develop their own unique learning style with the support of teachers. The atmosphere of the school is friendly and encouraging and the author is very grateful for the experience they have had. They recommend the school to anyone looking for an alternative learning experience.

My name is _________, and I'm a senior at an alternative school. I've been attending this school since my freshman year, and it has been an amazing experience.

At this school, I've been able to explore my interests and develop my own unique learning style. The teachers are supportive and caring, and they encourage students to actively participate in their education. I've had the opportunity to take classes that I'm passionate about and have even been able to design my own coursework.

The atmosphere of the school is also a great one. Everyone is friendly and willing to help each other out. There's no judgement or pressure. We all come from different backgrounds, but that doesn't stop us from working together and having a great time.

I'm so grateful for the experience I've had at this school. It has been an incredible journey, and I am so proud of what I have accomplished. I have grown so much as a person and have had so many opportunities to explore my interests.

I would highly recommend this school to anyone looking for an alternative learning experience. It has been a great place to learn, and I will miss it when I graduate.

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He is  2√19 miles far way from starting point.

Suppose Billy starts at point A, turns at point B, and ends at point D, as shown below.

If Billy turns 60◦ northward and walks six miles, then we can draw a 30 − 60 − 90 triangle whose hypotenuse is 6 miles

It follows that Billy traveled 6/2 = 3 miles eastward during these 6 miles, and that he traveled 3√3 miles northward during these 6 miles. In total, Billy traveled 4 + 3 = 7 miles  eastward and 3√ 3 miles northward.

By the Pythagorean Theorem, the distance from his starting point is q:

(7)2 + (3√3)2

=√49 + 27

= √76

= 2√19 .

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The height of a rider on the London Eye Ferris wheel in London can be modeled by the function h(t) = A * cos(B * t), where t represents time in minutes. The Ferris wheel stands 135 meters tall with a diameter of 120 meters. It takes half an hour (30 minutes) to complete one revolution.

1. At t = 0 minutes, the rider is not at the bottom of the wheel but at the midpoint of the wheel's diameter, so the rider's height is equal to the radius of the wheel, which is half of its diameter. Therefore, the rider's height at t = 0 minutes is 120/2 = 60 meters.

2. To determine the time it takes for the rider to reach the top, we need to find the period of the cosine function. The period (T) is the time it takes for one complete cycle of the function. In this case, the period is equal to the time it takes for the Ferris wheel to make a full revolution, which is 30 minutes. So, the rider reaches the top after half of the period, which is T/2 = 30/2 = 15 minutes. At that time, the rider's height is equal to the sum of the radius of the wheel and its height, which is 60 + 135 = 195 meters.

3. The period of the cosine function is T = 30 minutes.

4. The vertical shift of the function represents the average height of the rider throughout one complete cycle. In this case, the average height is the sum of the radius and the height of the Ferris wheel divided by 2, which is (60 + 135)/2 = 97.5 meters. Therefore, the vertical shift of the function is 97.5 meters. The amplitude of the function is half of the vertical distance between the maximum and minimum values, which is (135 - 60)/2 = 37.5 meters.

5. The equation of the cosine function is h(t) = 97.5 + 37.5 * cos((2π/30) * t). To find the rider's height at t = 21 minutes, we substitute t = 21 into the equation: h(21) = 97.5 + 37.5 * cos((2π/30) * 21) ≈ 185.11 meters.

In summary, the rider's height at t = 0 minutes is 60 meters. It takes 15 minutes for the rider to reach the top, at which point their height is 195 meters. The period of the function is 30 minutes. The vertical shift is 97.5 meters, and the amplitude is 37.5 meters. Using the cosine function, the rider's height at t = 21 minutes is approximately 185.11 meters.

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The number of significant digits in a measurement is determined by following a specific rule. According to the rule, all non-zero digits in a measurement are considered significant. For example, in the measurement 25.4 cm, there are three significant digits (2, 5, and 4) because they are non-zero.

In addition to non-zero digits, there are two more rules to consider. The first rule states that all zeros between non-zero digits are also significant. For instance, in the measurement 1003 g, there are four significant digits (1, 0, 0, and 3) because the zero between the non-zero digits is significant.

The second rule states that trailing zeros at the end of a number are significant only if they are after the decimal point. For example, in the measurement 2.000 s, there are four significant digits (2, 0, 0, and 0) because the trailing zeros after the decimal point are significant. However, in the measurement 2000 m, there are only one significant digit (2) because the trailing zeros are not after the decimal point.

In summary, the number of significant digits in a measurement is determined by considering all non-zero digits, zeros between non-zero digits, and trailing zeros after the decimal point. These rules help in properly representing the precision and accuracy of a measurement.

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