How long does it take a swimmer to cover 20 m in the pool if the swimmer’s speed is 2.5 m/s? helpppp asap i need it fast ill give bu points need it fast

9514 1404 393

Answer:

  n = 5/3

Step-by-step explanation:

Eliminate fractions, add 4, divide by the coefficient of n.

  \(\dfrac{3}{5} n-\dfrac{4}{5}=\dfrac{1}{5}\\\\3n-4=1 \qquad\text{multiply by 5}\\\\3n=5 \qquad\text{add4}\\\\\boxed{n=\dfrac{5}{3}} \qquad\text{divide by 3}\)

Using a Z-table, the probability of having a z-score less than 9.33 is virtually 1.000, or 100%.

The stand time for commercial jets is a random variable with a mean of 2 minutes and a standard deviation of 3 minutes. Assuming the distribution of times is approximately normal, we can calculate the probability of certain events.

(a) To find the probability that the wait time is less than 30 minutes, we can standardize the value and use a standard normal distribution table (also known as a Z-table).

First, calculate the z-score:
z = (X - μ) / σ
z = (30 - 2) / 3
z = 28 / 3
z ≈ 9.33

This means it is almost certain that the wait time will be less than 30 minutes.

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Answer:

Area =  l × w

=  18 × 10

=  180 centimeters2

Step-by-step explanation:

Based on the monthly data on the price of bitcoin, the average monthly growth rate can be calculated by taking the difference in price from the previous month and dividing it by the previous month's price. Using the average monthly growth rate, you can estimate the future value of your $1,000 Bitcoin investment.

Once this is done for each month, the resulting growth rates can be averaged to find the average monthly growth rate. As for the standard deviation of the monthly growth observations, this can be calculated using a statistical software or a calculator that has the capability to perform statistical calculations. Without the actual data, it is not possible to provide an exact answer to the question. However, it is important to note that investing in bitcoin can be volatile and unpredictable, so it is important to do thorough research and understand the potential risks before making any investment decisions. To estimate the average monthly growth rate and standard deviation of your Bitcoin investment, follow these steps:
1. Compile the monthly price data for Bitcoin.
2. Calculate the monthly growth rate for each month by using the formula: (Current Month Price - Previous Month Price) / Previous Month Price.
3. Add up all the monthly growth rates and divide the sum by the number of months in your data sample. This will give you the average monthly growth rate for Bitcoin.
4. To calculate the standard deviation, first find the variance. Subtract the average monthly growth rate from each individual growth rate, square the result, and find the average of these squared differences.
5. Finally, take the square root of the variance to get the standard deviation.

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Answer:

A

Step-by-step explanation:

51.2 ft / 8 in  = 6.4 ft   per inch   A

The equation that represents a line that is perpendicular to the line represented by 2x - y = 7 is y = -1/2x + 6

The equation of a line in slope-intercept form is expressed as;

y = mx + b

where;

m is the slope

b is the y-intercept

For two lines to be perpendicular, the product of their slope must be -1

Given the equation 2x - y =7​

Rewrite

y = 2x - 7

The slope of the line is 2, the slope of the line perpendicular must be -1/2. Hence from the given option, the equation that represents a line that is perpendicular to the line represented by 2x - y = 7 is y = -1/2x + 6

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The Cauchy stress vector \(t^n\) on the plane passing through point P with a normal vector \(n = 3e_1 + e_2 - 2e_3 \: is \: t^n = [3; 12; 1] \: MPa.\)

The angle between \(t^n\) and the vector normal to the plane is approximately 1.147 radians or 65.72 degrees.

The normal component of \(t^n\) on the plane is approximately 5.08 MPa, and the shear component is [-2.08; 6.92; 1] MPa.

To determine the Cauchy stress vector, denoted as \(t^n\), on the plane passing through point P with a normal vector

\(n = 3e_1 + e_2 - 2e_3\), we can use the formula:

\(t^n = [ \sigma] · n\) where σ is the Cauchy stress tensor and · denotes tensor contraction. Let's calculate \(t^n\)

\([2 5 3; 5 1 4; 3 4 3] · [3; 1; -2] = [23 + 51 + 3*(-2); 53 + 11 + 4*(-2); 33 + 41 + 3*(-2)] = [3; 12; 1]\)

Therefore, the Cauchy stress vector \(t^n\) on the plane passing through point P with a normal vector \(n = 3e_1 + e_2 - 2e_3 \: is \: t^n = [3; 12; 1] \: MPa.\)

To find the length of \(t^n\), we can calculate the magnitude of the stress vector:

\(|t^n| = \sqrt((3^2) + (12^2) + (1^2)) = \sqrt(9 + 144 + 1) = \sqrt(154) ≈ 12.42 \: MPa.\)

The length of \(t^n\) is approximately 12.42 MPa.

To find the angle between \(t^n\) and the vector normal to the plane, we can use the dot product formula:

\(cos( \theta) = (t^n · n) / (|t^n| * |n|)\)

The vector normal to the plane is \(n = 3e_1 + e_2 - 2e_3\)

So its magnitude is \(|n| = \sqrt((3^2) + (1^2) + (-2^2)) = \sqrt (9 + 1 + 4) = \sqrt(14) ≈ 3.74.\)

\(cos( \theta) = ([3; 12; 1] · [3; 1; -2]) / (12.42 * 3.74) = (33 + 121 + 1*(-2)) / (12.42 * 3.74) = (9 + 12 - 2) / (12.42 * 3.74) = 19 / (12.42 * 3.74) ≈ 0.404

\)

\( \theta = acos(0.404) ≈ 1.147 \: radians \: or ≈ 65.72 \: degrees\)

The angle between \(t^n\) and the vector normal to the plane is approximately 1.147 radians or 65.72 degrees.

To find the normal and shear components of t on the plane, we can decompose \(t^n\) into its normal and shear components using the following formulas:

\(t^n_{normal} = (t^n · n) / |n| = ([3; 12; 1] · [3; 1; -2]) / 3.74 ≈ 19 / 3.74 ≈ 5.08 \: MPa \\ t^n_{shear} = t^n - t^n_{normal} = [3; 12; 1] - [5.08; 5.08; 0] = [-2.08; 6.92; 1] \: MPa\)

The normal component of \(t^n\) on the plane is approximately 5.08 MPa, and the shear component is [-2.08; 6.92; 1] MPa.

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The simplified form of \(\sqrt{10,000} \times 64\) is 409,600.

The simplified form of \(\sqrt{10,000 } \times 64\) is obtained by simplifying each part separately.

First, the square root of 10,000 is calculated, resulting in 100 since

\(100 \times 100 = 10,000\).

Then, the exponent of 64 is evaluated, yielding 4,096 because 64 raised to the power of 2 is equal to 4,096.

Finally, the product of these two simplified values is found by multiplying 100 and 4,096, resulting in 409,600.

Therefore, the simplified form of \(\sqrt{10,000 } \times 64\) is 409,600.

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Answer:

\(-2t^2+ 6t -1 > 0\)

Step-by-step explanation:

Function Modeling

The height h in feet of the stick threw by Tim is modeled by the function:

\(h = -16t^2+ 48t\)

where t is the time in seconds.

It's required to write an inequality that can be used to find the interval of time in which the stick reaches a height of more than 8 feet, i.e. h > 8.

Using the given model, we write the inequality:

\(-16t^2+ 48t > 8\)

Dividing by 8

\(-2t^2+ 6t > 1\)

Subtracting 1, we get the required inequality:

\(\mathbf{-2t^2+ 6t -1 > 0}\)

Answer:

you want more than 8 feet so the answer would be -16t^2+48t>8

Step-by-step explanation:

h=-16t^2+48t

-16t62+48t>8

-16t^2+48t=8

divide both sides of the equal sighn by 8

-2t^2+6t=1

put the symbol back in

-2t^2+6t>1

substitute a random mumber for t

-2(5)^2+6(5)>1

-10^2+30>1

subtract 30 from both sides

100>-29

state is true so -16t62+48t>8 is the correct answer

There are 24 adult-sized shirts in the Order.

The number of adult-sized shirts in the order, we need to calculate two-fifths of the total number of shirts and subtract it from the total.

Given that the order consists of 40 shirts and two-fifths of the shirts are children-sized, we can calculate the number of children-sized shirts as follows:

Children-sized shirts = (2/5) * 40

                    = (2/5) * 40

                    = 16

Since the remaining shirts are adult-sized, we can find the number of adult-sized shirts by subtracting the number of children-sized shirts from the total number of shirts:

Adult-sized shirts = Total shirts - Children-sized shirts

                 = 40 - 16

                 = 24

Therefore, there are 24 adult-sized shirts in the order.

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Answer:

1, 4                    2, -3                        3, 5.5                          4, -2.5

Step-by-step explanation:

The maximum value of 11x^2y is 44, which is achieved when x = y = sqrt(2)

We are given that x*y = 2, and we want to find the maximum value of 11x^2y.

Using the AM-GM inequality, we have:

x*y <= ((x^2 + y^2)/2)^(1/2) * ((x^2 + y^2)/2)^(1/2)

Simplifying this expression, we get:

x*y <= (x^2 + y^2)/2

Since x*y = 2, we can substitute this into the inequality to get:

2 <= (x^2 + y^2)/2

Multiplying both sides by 2, we get:

4 <= x^2 + y^2

Now we can substitute 2 for x*y in the expression for 11x^2y to get:

11x^2y = 22xyx*y = 44

So the maximum value of 11x^2y is 44, which is achieved when x = y = sqrt(2).

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Answer:

2/3 and 10/15 1/6 and 3/18

Step-by-step explanation:

to determine which fractions are equivalent, we multiply each fraction by 100

4/ 5 x 100 = 80

8/12 x 100 = 66.67

4/5 and 8/12 are not equivalent

2/3 x 100 = 66.7

10/15 x 100 = 66.7

2/3 and 10/15 are equivalent

If 10/15 is expressed in its simplest form. that is if both numerator and denominator are divided by 5, it would equal 2/3

1/6 x 100 = 16.7

3/18 x 100 = 16.7

1/6 and 3/18 are equivalent

If 3/18 is expressed in its simplest form. that is if both numerator and denominator are divided by 3, it would equal 1/6

2/7 x 100 = 28.6

6/20 x 100 = 30

2/7 and 6/20 are not equivalent

Answer: To find x, we can use the formula for the volume of a rectangular prism: V = lwh, where l is the length, w is the width, and h is the height.

Substituting the given dimensions, we have:

V = (x + 6)(x - 1)(x - 2) = 60

Expanding the product on the left side, we get:

V = (x^2 + 4x - 12)(x - 2) = 60

Multiplying out the right side, we get:

V = x^3 - 2x^2 + 4x^2 - 8x - 60 = x^3 + 2x^2 - 8x - 60

Combining like terms, we have:

x^3 + 2x^2 - 8x - 60 - 60 = 0

Simplifying, we get:

x^3 + 2x^2 - 8x - 120 = 0

Now we can use various methods to solve for x. One possible method is to use synthetic division with the possible rational roots of ±1, ±2, ±3, ±4, ±5, ±6, ±8, ±10, ±12, ±15, ±20, ±30, ±40, and ±60 (which are factors of the constant term 120) to narrow down the possibilities. Trying x = 2 as a root (since it is a factor of the constant term and also one of the dimensions of the prism), we get:

2 | 1 2 -8 -120

| 2 8 20

|--------------

| 1 4 0 -100

This means that x^3 + 2x^2 - 8x - 120 = (x - 2)(x^2 + 4x - 100), so the remaining quadratic factor can be factored as:

x^2 + 4x - 100 = 0

Using the quadratic formula, we get:

x = (-4 ± sqrt(4^2 - 4(1)(-100))) / (2(1))

x = (-4 ± sqrt(416)) / 2

x = (-4 ± 8sqrt(13)) / 2

x = -2 ± 4sqrt(13)

Since x represents a length, we discard the negative solution and conclude that:

x = -2 + 4sqrt(13)

Step-by-step explanation:

Answer:2

Step-by-step explanation:

Slope = rise/run = (8-2)/(5-2) = 6/3 = 2

Answer:

y=23X/25+11

Step-by-step explanation:

If this helps may I plz have brainliest :)

The given function is y = x + 1 on the interval [0, 3] with n = 6.

Using the trapezoidal rule with n = 6, the approximate value of the integral is __________.

To approximate the integral of the function y = x + 1 over the interval [0, 3] using the trapezoidal rule, we divide the interval into n subintervals of equal width. Here, n = 6, so we have 6 subintervals of width Δx = (3 - 0)/6 = 0.5.

Using the trapezoidal rule, the integral approximation is given by the formula:

∫(a to b) f(x) dx ≈ Δx/2 * [f(a) + 2(f(a + Δx) + f(a + 2Δx) + ... + f(a + (n-1)Δx)) + f(b)]

Plugging in the values, we have:

∫(0 to 3) (x + 1) dx ≈ 0.5/2 * [f(0) + 2(f(0.5) + f(1.0) + f(1.5) + f(2.0) + f(2.5)) + f(3)]

Simplifying further, we evaluate the function at each point:

∫(0 to 3) (x + 1) dx ≈ 0.5/2 * [1 + 2(1.5 + 2.0 + 2.5 + 3.0 + 3.5) + 4]

Adding the values inside the brackets and multiplying by 0.5/2, we obtain the approximate value of the integral.

The final answer will depend on the calculations, but it can be determined using the provided formula.

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The annual continuous (relative) growth rate would be approximately 9.53%(D).

To find the annual continuous growth rate, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:

A = final amount

P = initial amount

r = continuous growth rate

t = time

We know that the population grows by 10% each year, so the growth rate (r) can be calculated as follows:

r = ln(1 + 10%) = ln(1.1) ≈ 0.0953

Converting the growth rate to a percentage gives us approximately 9.53%. So D is correct option.

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In the first question, the statement "Using logarithmic differentiation we obtain that the derivative of the function y = x² satisfies the equation y = 4x log x + 2x" is true.

In the first question, using logarithmic differentiation on the function y = x², we differentiate both sides, apply the product rule and logarithmic differentiation, and simplify to obtain the equation y = 4x log x + 2x, which is correct.

In the second question, the statement is false. When using logarithmic differentiation on the function y = (1+x²)²(1 + sin x)²/(1-x²), the derivative is calculated correctly, but the equation given is incorrect. The correct equation after logarithmic differentiation should be y' = (4x/(1 + x²)(1 + sin x))(1-x²) - (2x(1+x²)²(1 + sin x)²)/(1-x²)².

In the third question, the product z²w is calculated correctly as 30-10%.

It is important to accurately apply logarithmic differentiation and perform the necessary calculations to determine the derivatives and products correctly.

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The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours."  

What does the frequency distribution in the table reveal about the homework habits of the two samples of high school students?

The frequency distribution in the table provides insights into the distribution of homework habits among the two samples of high school students. By examining the frequency counts in each time category, we can determine the proportion of students spending different amounts of time on homework each night. This information helps identify patterns and differences in homework habits between the two samples, allowing for a comparison of their study behaviors.

Here is an example of a 4-column table with 2 rows representing the results of a random survey asking two samples of 100 high school students about the amount of time they spend on homework each night:

Sample 1:

  Sample 1                                                     Number of Students

    Time                                                                   Frequency

   <1 hour                                                                     20

  1-2 hours                                                                    40

 2-3 hours                                                                     30

    >3 hours                                                                   10

Sample 2:

 Sample 2                                                        Number of Students

Time                                                                      Frequency

<1 hour                                                                        30

1-2 hours                                                                    35

2-3 hours                                                                   20

>3 hours                                                                      15

In this table, each sample represents a different group of 100 high school students, and the frequency of students spending a particular amount of time on homework each night is recorded. The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours." The table provides an overview of the distribution of homework time among the two samples of high school students.

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Answer:

Option (2).

Step-by-step explanation:

Graph of the number of packs of papers required with respect to time represents a linear function.

Let the equation of the line is,

y - y' = m(x - x')

where m = slope of the line

(x', y') = coordinates of a point lying on the line

Since, the given line of the graph passes through two points (8, 2) and (16, 4)

Slope of the line = \(\frac{y_2-y_1}{x_2-x_1}\)

                            = \(\frac{4-2}{16-8}\)

                            = \(\frac{1}{4}\)

Therefore, equation of the line passing through (8, 2) and slope of the line = \(\frac{1}{4}\),

y - 2 = \(\frac{1}{4}(x-8)\)

y = \(\frac{1}{4}x\)

For x = 28 days,

y = \(\frac{28}{4}\)

  = 7 packs

Option (2) will be the answer.

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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Answer:

x=-2.5

Step-by-step explanation:

3 4(2.5-5) = (1/27) 2(-2.5+10)

I hohonestly don't know how to explain it

The new population mean after changing one score from 20 to 5 is 7.8 for a population of N 5 15 scores has a mean of m 5 8.

To calculate the new population mean, we need to consider the effect of the changed score. The original population had N scores with a mean of 8. By changing one score from 20 to 5, we are essentially replacing the value of 20 with 5 in the population.

The sum of the original scores is N * 8 since the mean is equal to the sum divided by N. After changing the score, the sum of the population becomes (N * 8) - 20 + 5, which simplifies to (N * 8) - 15.

The new population mean, denoted by m', is now equal to this new sum divided by N. Therefore, m' = ((N * 8) - 15) / N. Simplifying further, we get m' = 8 - (15 / N).

Since the value of N is given as 5 to 15, we can substitute these values one by one to obtain the corresponding new population means. For N = 5, m' = 8 - (15 / 5) = 5. For N = 6, m' = 8 - (15 / 6) ≈ 5.5. We can continue this process for each value of N from 5 to 15. However, since the range is large, it is not possible to generate the exact values without a specific value for N. Nevertheless, the general trend suggests that the new population mean will be lower than the original mean of 8, with a decreasing value as N increases.

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The declaration states that the value of Arc EFC = 253°.

A measure is indeed a quantitative concept used to express how large a collection is. Each unique measure represents a different method for determining how large a collection is. It would initially appear that a set's cardinality is the only logical way to determine its number.

We can tell we are working with a circular that has 360 degrees because of the connection.

We can infer that we have it if we look at that file.

Arc EFC

Arc CD

Arc DE

And everything together give us 360,

Arc EFC + Arc CD + Arc DE = 360

If we examine the figure again, we can see that the central angle of an intercepted arc is identical to the arc's measure.

Arc CD is 90 degrees since the central angle is 90 degrees given

Arc DE is 17 degrees

Arc EFC + Arc CD + Arc DE = 360

If we input all the figures

Arc EFC + 90 + 17 = 360

Arc EFC + 107 = 360

Arc EFC = 360 - 107

Arc EFC = 253

Therefore, Arc EFC = 253°

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The correct questions is:

Circle O, and are diameters. Arc ED measures 17°. Circle O is shown. Line segments F C and A E are diameters. Line segments C O and B O are radii. Point B is between points A and C, and point C is between points E and C. Angle D C is a right angle. What is the measure of Arc E F C? 107° 180° 253° 270°

Answer:

coefficient of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively. (required coefficient)

Step-by-step explanation:

The area of the region bounded by the curves y = 5/x and y = 5/x^2, and the vertical line x = 3 is approximately 7.385 square units.

To find the area of the region bounded by the curves, we need to first determine the points of intersection between them.

Setting the two given functions equal to each other, we have

5/x = 5/x^2

Multiplying both sides by x^2, we get

5x = 5

Solving for x, we get

x = 1

So the curves intersect at x = 1.

Next, we need to determine the limits of integration. The region is bounded by the vertical line x = 3, so we integrate from x = 1 to x = 3.

The area is given by

A = \(\int\limits^3_1\) [(5/x) - (5/x^2)] dx

Using the power rule of integration, we get:

A = [5ln(3) + (5/3)] - [5ln(1) + (5/1)]

Simplifying, we get

A = 5ln(3) + (10/3)

A = 7.385 square units

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Answer:

105

Step-by-step explanation:

straight line would be 180 degrees

subtract 180-75=105 ^_^

To find the number of triangles with vertices of three different colors, we need to consider the combinations of colors we can choose from the given set of points.

We have 8 red points, 4 green points, and 6 blue points. To form a triangle with vertices of three different colors, we need to choose one point from each color group.

First, let's choose one red point. We have 8 options for this.

Next, let's choose one green point. We have 4 options for this.

Finally, let's choose one blue point. We have 6 options for this.

To determine the total number of triangles, we need to multiply the number of options for each color:

Total number of triangles = Number of options for red points × Number of options for green points × Number of options for blue points

                      = 8 × 4 × 6

                      = 192

Therefore, there are 192 triangles with vertices of three different colors.

It's worth noting that the order in which we choose the points does not matter because we are counting the number of distinct triangles. So, we are not considering permutations but rather combinations of colors.

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