Malcolm trains on his kayak every weekend. He paddles upstream (against current) for 3 ½ hours and then returns downstream (with current) in 2hrs 6 minutes. If the river flows at 3km/ h, find:
* The paddling speed in still water
* The distance he paddles upstream.

The value of a + b + c is 42.

Let's set the arrival time of one of the mathematicians, let's say the first mathematician, to be t minutes after 9 a.m.

The likelihood that a second mathematician will show up while the first one is in the cafeteria is [tex]$ \frac{m}{60}[/tex], since the second mathematician has a [tex]\frac{m}{60} $-hour[/tex] window to arrive while the first is there.

⇒The probability that they arrive during some overlapping time is then [tex]$2\left(\frac{m}{60}\right)\left(1 - \frac{m}{60}\right)$[/tex]. This probability must be equal to 0.4.

⇒So we have the equation [tex]$2\left(\frac{m}{60}\right)\left(1 - \frac{m}{60}\right) = 0.4$[/tex].

⇒Solving for m yields [tex]$m = 24 - 4\sqrt{14}[/tex].

Therefore, the a + b + c = 24 + 4 + 14 =42.

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The polynomial in standard form is:

F(x) = 2x³ - x² + 5x - 3

Option B is the correct answer.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The standard form of a polynomial is ax³ + bx² + cx + d.

A.

F(x) = -3 - x² + 2x³ + 5x

This is not in standard form.

B.

F(x) = 2x³ - x² + 5x - 3

This is in standard form.

C.

F(x) = -3 + 5x - x² + 2x³

This is not in standard form.

D.

F(x) = 5x + 2x³ - x² - 3

This is not in standard form.

Thus,

F(x) = 2x³ - x² + 5x - 3 is in the standard form.

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The part overlapped is showing the acute scalene triangles.

An acute scalene triangle can be defined as a triangle whose angles are less than 90 degrees and all three sides and angles are different in measurement.

Given that, in a graphic organizer, the left circle represents scalene triangles. The right circle represents acute triangles.

Here, we are asked to find that which figure belongs in the part of the organizer where the circles overlap,

In graphic organizers, the overlapped portion shows the common part between other portions.

Therefore, the common in both the triangles will be an acute scalene triangle,

Hence, the part overlapped is showing the acute scalene triangles.

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The expression to represent the given scenario is 3x²-7. Therefore, option D is the correct answer.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, the sum of three times the square of a number and -7.

Let the unknown number be x.

Now, the expression is 3x²+(-7)

= 3x²-7

Therefore, option D is the correct answer.

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The change in the position of the minute hand should be matched with the angle made by the change as follows;

The minute hand moves from 2 to 9 = 7π/6 radians

The minute hand moves from 5 to 10 = 5π/6 radians.

The minute hand moves from 3 to 7 = 2π/3 radians.

The minute hand moves from 4 to 6 = π/3 radians.

The minute hand moves from 1 to 4 = π/2 radians.

In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Generally speaking, the angle between numbers that represents the hands on an analog clock is equal to π/6 radians.

When the minute hand moves from 2 to 9, we have:

Difference = 9 - 2 = 7

Angle = 7 × π/6 = 7π/6 radians.

When the minute hand moves from 5 to 10, we have:

Difference = 10 - 5 = 5

Angle = 5 × π/6 = 7π/6 radians.

When the minute hand moves from 3 to 7, we have:

Difference = 7 - 3 = 4

Angle = 4 × π/6 = 4π/6 = 2π/3 radians.

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The required scale factor used to dilate Figure A to make Figure B is 5/4.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges.

The ratio of the volumes of two similar pyramids is equal to the cube of the ratio of their corresponding side lengths. Therefore, the scale factor used to dilate Figure A to make Figure B is equal to the cube root of the ratio of their volumes:

scale factor = cube root of (volume of Figure B / volume of Figure A)

scale factor = cube root of (375 / 192)

scale factor = cube root of (125 / 64)

scale factor = 5/4

Therefore, the scale factor used to dilate Figure A to make Figure B is 5/4.

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The measure of the angles are

1. 14°

2. 141°

3. 39°

4. 39°

The 4-letter code is DCAA

From the question, we ae to determine the measure of the angles and then the 4-letter code

From the diagram,

m ∠B + m ∠C = 180° (Sum of angles on a straight line)

Then,

1.

9x + 15° + 3x - 3° = 180°

12x + 12° = 180°

12x = 180° - 12°

12x = 168°

x = 168°/12

x = 14°

Thus, D

2.

m ∠B = 9x + 15°

m ∠B = 9(14) + 15°

m ∠B = 126° + 15°

m ∠B = 141°

Thus, C

3.

m ∠C = 180° - m ∠B

m ∠C = 180° - 141°

m ∠C = 39°

Thus, A

4.

m ∠A = m ∠C (Vertically opposite angle)

m ∠A = 39°

Thus, A

Hence, the code is DCAA

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at t = 5, the speed of the bungee jumper is decreasing at a rate of 200 ft/s^2.It is clear that the bungee jumper is rising most rapidly at t = 5, as this is when their velocity (h') is decreasing most rapidly.

h(t)  h'(t)

0   0

2.5   -200

4   -400

5   -600

h'(4.5) = -400 ft/s

h'(5) = -600 ft/s

h'(5.5) = -800 ft/s

The bungee jumper is rising most rapidly at t = 5.

h"(5) = -200 ft/s^2

The bungee jumper's height at time t (in seconds) is given in the table. Using the given data, we can estimate h'(4.5), h'(5), and h'(5.5) to be -400 ft/s, -600 ft/s, and -800 ft/s respectively. It is clear that the bungee jumper is rising most rapidly at t = 5, as this is when their velocity (h') is decreasing most rapidly. We can also estimate h"(5) to be -200 ft/s^2, which is the rate of change of the velocity of the bungee jumper. This means that at t = 5, the speed of the bungee jumper is decreasing at a rate of 200 ft/s^2.

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Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\tt 12x=2y+7 \\ y=6-2[/tex]

Substitute y = 6x-2

[tex]\tt 12x=2\left(6x-2\right)+7[/tex]

[tex]\tt 12x=12x+3[/tex]

Cancel 12x from both sides:-

[tex]\tt {0=3}[/tex]

Since the sides are not equal, there's no solution.

___________________

Hope this helps!

Exact:  1436.75504cm3

About: 1436.8cm3

pls mark brainliest if correct

Answer:

To simplify the given expressions, we can use the property of exponents that states:

x^m * x^n = x^(m+n)

Using this property, we can simplify (x^4) (x^2) as:

(x^4) (x^2) = x^(4+2) = x^6

Similarly, we can simplify (x^3) (x^5) as:

(x^3) (x^5) = x^(3+5) = x^8

Therefore, (x^4) (x^2) and (x^3) (x^5) simplify to x^6 and x^8 respectively.

Answer:

Step-by-step explanation:

It is possible to use the exponents' property, which states:

x(m+n) = x^xm * xn)

This property allows us to simplify (x4) (x2) as follows:

(x^4) (x^2) = x^(4+2) = x^6

Similar to this, we can express (x3) (x5) as:

(x^3) (x^5) = x^(3+5) = x^8

As a result, (x4) (x2) and (x3) (x5) become x6 and x8, respectively.

The proportion of resistors with resistances less than 90 Ω is 0.125, the mean resistance is 85 Ω, the standard deviation of the resistances is 8.66 Ω, and the cumulative distribution function of the resistances is 1/800x2−80x.

(a) The proportion of resistors with resistances less than 90 Ω is given by the integral of the probability density function f(x) from 80 to 90, which is 0.125.

(b) The mean resistance is given by the following formula:

Mean Resistance = [tex]∫x·f(x)dx[/tex]

Substituting the given equation for f(x) into this formula and integrating, we get the mean resistance to be 85 Ω.

(c) The standard deviation of the resistances is given by the following formula:

Standard Deviation = [tex]√∫(x−Mean Resistance)2·f(x)dx[/tex]

Substituting the given equation for f(x) and the mean resistance into this formula and integrating, we get the standard deviation of the resistances to be 8.66 Ω.

(d) The cumulative distribution function of the resistances is given by the following formula:

[tex]CDF(x) = ∫f(x)dx[/tex]

Substituting the given equation for f(x) into this formula and integrating, we get the cumulative distribution function to be [tex]1/800x2−80x[/tex] (where x is the resistance).

The proportion of resistors with resistances less than 90 Ω is 0.125, the mean resistance is 85 Ω, the standard deviation of the resistances is 8.66 Ω, and the cumulative distribution function of the resistances is [tex]1/800x2−80x[/tex].

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a) A U B = A: Accordingly, the union of sets A and B equals set A. In other words, set A includes every component that may be found in either set A or set B. This indicates that set B is a subset of set A. (i.e., all the elements in set B are also in set A).

b) A ∩ B = A: As a result, set A is equal to the intersection of sets A and B. In other words, set A includes all of the components found in both sets A and B. We can infer that set A is a subset of set B from this (i.e., all the elements in set A are also in set B).

c) A - B = A:  Thus, the set of items in set A that are not present in set B is the same as set A. In other words, set B contains nothing that isn't also present in set A. This indicates that set B is a subset of set A. (i.e., all the elements in set B are also in set A).

d) A ∩ B = A U B: This implies that the union of sets A and B is equal to the intersection of those two sets. Only if one of the sets is a subset of the other can this be true. In particular, if set A is a subset of set B, then set B is equal to the union of sets A and B, and set A is equal to the intersection of sets A and B. If set B is a subset of set A, then set B is equal to the intersection of sets A and B and set A is equal to the union of sets A and B.

e) A - B = B - A: The set of elements in set A but not in set B are therefore equivalent to the set of elements in set B but not in set A. In other words, every element in both sets is identical. This is only possible if both sets are identical or both sets are empty (i.e., neither set has any elements). As a result, from this assertion alone, we are unable to infer any particular link between sets A and B.

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Answer:

Step-by-step explanation:

To find the product of the factors 3.78 and 9.2, we simply multiply them together:

3.78 × 9.2 = 34.776

Therefore, the product of the factors 3.78 and 9.2 is 34.776.

Option B. 2 K is the correct graph (check the attached image) of parent function after transformation.

In mathematics, a transformation is a function that, typically with some geometrical foundation, maps a set X to itself, i. e. f: X → X. Vector space linear transformations are one example.

A point, line, or geometric figure can be changed in four different ways that are all collectively referred to as transformations. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.

A graph can be altered in three basic ways: by shifting, or compressing, and by flipping. According to the definition of transformation, we can rotate around any point, reflect our image over any line, and translate any vector. These are rigid transformations in which the image is consistent with its pre-image.

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Answer: 4.

Step-by-step explanation:

1/3 of 12?

12 divided by 3 = 4.

a) The 95% confidence interval for the mean length of the skulls of this species of bird is (5.35, 6.01) cm.

b) The 95% confidence interval for the true standard deviation of the skull length of the given species of bird is (0.18, 0.40) cm.

(a) To find a 95% confidence interval for the mean length of the skulls of this species of bird, we can use the following formula:

mean ± (t-score * standard deviation / square root of sample size)

Where mean is the sample mean (5.68 cm), standard deviation is the sample standard deviation (0.29 cm), and sample size is the number of skeletons (10).

To find the t-score, we can use the t-distribution table for 9 degrees of freedom (sample size - 1). For a 95% confidence interval, the t-score with 9 degrees of freedom is 1.833.

Plugging in the values, we get:

5.68 ± (1.833 * 0.29 / √(10))

= 5.68 ± 0.33

So the 95% confidence interval for the mean length of the skulls of this species of bird is (5.35, 6.01) cm.

(b) To find a 95% confidence interval for the true standard deviation of the skull length of the given species of bird, we can use the following formula:

standard deviation / √(sample size) * t-score

Where standard deviation is the sample standard deviation (0.29 cm), and sample size is the number of skeletons (10).

To find the t-score, we can use the t-distribution table for 9 degrees of freedom (sample size - 1). For a 95% confidence interval, the t-score with 9 degrees of freedom is 2.306.

Plugging in the values, we get:

0.29 / √(10) * 2.306

= 0.11

So the 95% confidence interval for the true standard deviation of the skull length of the given species of bird is (0.29 - 0.11, 0.29 + 0.11) = (0.18, 0.40) cm.

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Answer: 3 < c < 13   (choice C or third answer choice)

======================================================

Explanation:

Consider a triangle with sides: a,b,c

Furthermore, we'll have a = 5 and b = 8 as the two known sides.

Due to a modification of the Triangle Inequality Theorem, the third side will have the condition that:

b-a < c < b+a

where b ≥ a must be the case.

----------

Let's plug in those a & b values to determine the range for c.

b-a < c < b+a

8-5 < c < 8+5

3 < c < 13

This points us to Choice C as the final answer.

Answer: 9.43398113206

Step-by-step explanation:

A^2 + B^2 = C^2

5^2 + 8^2 = √89

= 9.43398113206

Answer: the third option

Step-by-step explanation:

If the area to the right of a standard normal random variable z is 0.9803, the value of z is approximately -2.05.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. A normal distribution is a continuous probability distribution that is symmetric and bell-shaped, and it is often used to model many real-world phenomena.

A standard normal random variable, denoted by Z, is a random variable that follows a standard normal distribution. This means that the probability density function of Z is given by:

f(z) = (1/√(2*pi)) * e^(-z^2/2)

where pi is the mathematical constant pi (approximately 3.14159), e is the mathematical constant e (approximately 2.71828), and sqrt() represents the square root function.

The cumulative distribution function (CDF) of Z is given by:

F(z) = P(Z <= z) = integral from -infinity to z of f(x) dx

The CDF gives the probability that a standard normal random variable Z is less than or equal to a given value z.

To find the value of z for a given area under the curve, we use the inverse of the CDF. That is, we find the value of z that corresponds to a given probability or area under the curve. In this case, we were given an area to the right of z, so we first found the area to the left of z by subtracting the given area from 1.

Then, we used a standard normal distribution table or calculator to find the z-value that corresponds to this area. This is often denoted as the "z-score" for the given probability or area.

The z-score is a standardized value that tells us how many standard deviations a given value is from the mean of the standard normal distribution. In this case, a z-score of approximately -2.05 means that the value is 2.05 standard deviations below the mean of the standard normal distribution.

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Answer:

congruent

Step-by-step explanation:

The opposite sides of a parallelogram are congruent.

We can also determine this from the markings in the diagram.

The equation of line k is y = x + 1.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ 1 = 1

At data point (-4, -3), a linear equation of this line can be calculated in point-slope form as follows:

y - (-3) = 1(x - (-4))

y + 3 = x + 4

y = x + 1

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Answer:

28/35 and 25/35

Step-by-step explanation:

To find the equivalent fraction of 4/5 and 5/7 with a common denominator, we can find the least common multiple (LCM) of the two denominators. The LCM of 5 and 7 is 35. So, to get the equivalent fractions with a common denominator of 35, we can multiply both the numerator and denominator of each fraction by the same number so that the denominators become 35:

4/5 becomes 4 x 7/5 x 7 = 28/35

5/7 becomes 5 x 5/7 x 5 = 25/35

So, the equivalent fractions of 4/5 and 5/7 with a common denominator of 35 are 28/35 and 25/35, respectively.

Answer:

y = -1/4x + 2

Step-by-step explanation:

First you have to pick 2 points on the line, then you find the slope of the line from those 2 points. The slope formula is m = (y2-y1) / (x2-x1), and filling the variables in with the points (0,2) and (4,1) gives you m = (1-2) / (4-0), which gives you m = -1/4.

Once you have found the slope, you look for the y-intercept which is the point where the x-value is 0, and that is 2 in this graph.

You can then put this information into slope-intercept form, y= mx + b. m represents the slope and b represents the y-intercept. The answer is y = -1/4x + 2

The expression for the number of episodes taped in 6 seasons is 6x.

Every mathematical statement that comprises of numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

If x represents the number of television show episodes that are taped in a season, then the number of episodes taped in 6 seasons would be:

6x

This is because the number of episodes taped in one season is x, so to find the total number of episodes taped in 6 seasons, we simply multiply x by 6. Therefore, the expression for the number of episodes taped in 6 seasons is 6x.

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Profitability ratios is a type of financial ratio shows the combined effects of liquidity, asset management and debt management of a business. So the statement is true.

Financial ratios are calculations used to assess various data to evaluate the company's performance. It is calculated using quantitative data from financial statements. There are mainly four financial ratios

So the statement given is true.

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Answer: a) The set W contains the zero vector, since (0,0,0) = (3s,-2s,s) for s = 0.

The set W is closed under addition and scalar multiplication:

If (3s1, -2s1, s1) and (3s2, -2s2, s2) are in W, then their sum, (3(s1 + s2), -2(s1 + s2), (s1 + s2)), is also in W.

If (3s, -2s, s) is in W and c is any scalar, then (3cs, -2cs, cs) is also in W.

The set W has a basis of {(3, -2, 1)}. To see this, we can write any vector in W as a scalar multiple of (3, -2, 1). For example, (3s, -2s, s) = s(3, -2, 1). The dimension of the set W is 1.

b) The set W contains the zero vector, since (t-2,0,6-3t) = (t-2,0,6-3t) for t = 2.

The set W is closed under addition and scalar multiplication:

If (t1 - 2, 0, 6 - 3t1) and (t2 - 2, 0, 6 - 3t2) are in W, then their sum, ((t1 + t2) - 2, 0, 6 - 3(t1 + t2)), is also in W.

If (t - 2, 0, 6 - 3t) is in W and c is any scalar, then (ct - 2c, 0, 6c - 3ct) is also in W.

The set W has a basis of {(1, 0, -3)}. To see this, we can write any vector in W as a scalar multiple of (1, 0, -3). For example, (t - 2, 0, 6 - 3t) = t(1, 0, -3) - 2(1, 0, -3). The dimension of the set W is 1.

c) The set H contains the zero vector, since (2b, a, 3b) = (0,0,0) for b = 0 and a = 0.

The set H is closed under addition and scalar multiplication:

If (2b1, a1, 3b1) and (2b2, a2, 3b2) are in H, then their sum, (2(b1 + b2), a1 + a2, 3(b1 + b2)), is also in H.

If (2b, a, 3b) is in H and c is any scalar, then (2cb, ca, 3cb) is also in H.

The set H has a basis of {(2,1,3)}. To see this, we can write any vector in H as a scalar multiple of (2,1,3). For example, (2b, a, 3b) = b(2,1,3) + a(0,1,0). The dimension of the set H is 2.

d) The set H contains the zero vector, since (−b + 2c, b, 4c) = (0,0,0) for b = 2c.

Step-by-step explanation:

The midpoint of a line segment is the point located halfway between two endpoints.

Therefore, if the points and have the coordinates (x1, y1) and (x2, y2), respectively, then the coordinates of the midpoint, , are defined as:

[tex]M = (x1 + x2)/2, (y1 + y2)/2[/tex].

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Since we know the coordinates of the two points, we can calculate the slope of the line using the formula:

[tex]m = (y2 - y1)/(x2 - x1).[/tex]

Using the values of x1, y1, x2, and y2, we can calculate the slope of the line. We can then use the coordinates of and to calculate the y-intercept of the line, b.

Once we have determined the slope and y-intercept of the line, we can substitute these values into the equation of a line, y = mx + b, to determine the equation of the line.

The length of the line is equal to the distance between the two points and, for two points with coordinates (x1, y1) and (x2, y2), we can use the distance formula to calculate the length:

[tex]L = √((x2 - x1)^2 + (y2 - y1)^2)[/tex].

Substituting the values of x1, y1, x2, and y2 into this equation will give us the length of the line, which is equal to .

Therefore, the equation of the line and the length of the line are and , respectively.

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