In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo and Mary both completed the Hermosa Beach Triathlon, where Leo competed in the Men, Ages 30 - 34 group while Mary competed in the Women, Ages 25 - 29 group. Leo completed the race in 1:22:28 (4948 seconds), while Mary completed the race in 1:31:53 (5513 seconds). Obviously Leo finished faster, but they are curious about how they did within their respective groups. Can you help them? Here is some information on the performance of their groups:The finishing times of the Men, Ages 30 - 34 group has a mean of 4313 seconds with a standard deviation of 583 seconds.The finishing times of the Women, Ages 25 - 29 group has a mean of 5261 seconds with a standard deviation of 807 seconds.The distributions of finishing times for both groups are approximately Normal.if the distributions of finishing times are not nearly normal, would the values of the standard score in part a change? explain your reasoning.

No, milliliters (mL) and centiliters (cl) are not the same units of measurement. They are both units of volume, but with different scales.

A milliliter (mL) is a unit of volume in the metric system, equal to one-thousandth of a liter (1 mL = 0.001 L). Milliliters are commonly used to measure the volume of liquids, such as medicine or cooking ingredients.

A centiliter (cl) is also a unit of volume, and it is equal to one hundredth of a liter (1 cl = 0.01 L). Centiliters are less commonly used than milliliters and are generally used in the same contexts where milliliters are used.

In conclusion, mL and cl are different units of volume and cannot be used interchangeably. Milliliters are smaller units than centiliters, so when converting between the two, a conversion factor of 10 must be used. For example, 1 cl = 10 mL.

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Answer:    

Step-by-step explanation:

Answer: 4

Step-by-step explanation: the median is 39, the median of the upper is 36 and the median of the lower is 40. 36-40=4

Answer:

∠ 2 = 40°

Step-by-step explanation:

complementary angles sum to 90° , that is

∠ 1 + ∠ 2 = 90°

50° + ∠ 2 = 90° ( subtract 50° from both sides )

∠ 2 = 40°

Answer:

Step-by-step explanation:

A Turing machine (TM) is considered undecidable if there is no algorithm that can decide, in a finite amount of time, whether a given input string is accepted by the machine or not.

One common way to prove that a TM is undecidable is by using Rice's Theorem. Rice's Theorem states that, for a large class of computational problems, if a problem is nontrivial (i.e., there exist both positive and negative instances of the problem), it is undecidable.

Another way to prove the undecidability of a TM is by reducing the halting problem to it. The halting problem is the problem of determining, given a TM and an input string, whether the TM halts on the input or not. It has been proven that the halting problem is undecidable, so if you can show that the problem you are considering is equivalent to the halting problem, then you have proven that the problem is also undecidable.

These are just two of many ways to prove that a TM is undecidable. The exact proof will depend on the specific TM and problem in question.

Answer:

10.32

Step-by-step explanation:1.29 x 8 = 10.32 hope this helps

Answer:

They are not equivalent expressions

Step-by-step explanation:

Let's expand each expression and see if they are the same
6(-b + 8) = 6 x (-b) + 6 x 8 = -6b + 48

2(-3b + 4) = 2 x (-3b) + 2 x 4 = -6b + 8

So while the terms -b are the same, the constants are different

Hence the two expressions are not equivalent

Answer:

Step-by-step explanation:

3(x−3)=6

Divide both sides by 3.

x−3=

3

6

​

Divide 6 by 3 to get 2.

x−3=2

Add 3 to both sides.

x=2+3

Add 2 and 3 to get 5.

x=5

Answer:

a What does it mean for a manufacturer’s warranty and an extended warranty to overlap? both warranties cover the same period.

Step-by-step explanation:

Answer:

ABBBB

Step-by-step explanation:

Answer:

A. 24 math problems

B. 20 tests

Step-by-step explanation:

A.

We know

1 hour = 60 minutes

Jaxon completed 12 math problems in 30 minutes

30 mins = 12 math problems

60 mins = 12 x 2 = 24 math problems

So, he finishes 24 math problems in an hour.

B.

We know

1 hour = 60 minutes

Mrs. Maven corrected 5 tests every 15 minutes.

15 mins = 5 tests corrected

60 mins = 5 x 4 = 20 tests corrected

So, she grades 20 tests every hour.

The value of the composition function g ( f ( 0 ) ) = 2

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the first function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = 4x + 1

Let the second function be represented as g ( x )

Now , the value of g ( x ) is

g ( x ) = 5x - 3

Now , the composition function is g ( f ( 0 ) )

where the value of f ( 0 ) is

f ( 0 ) = 4 ( 0 ) + 1

f ( 0 ) = 1

Now , the value of g ( 1 ) is

g ( 1 ) = 5 ( 1 ) - 3

g ( 1 ) = 2

Therefore , the value of g ( 1 ) is 2

Hence , the composition function is solved and the value is 2

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The angle 2π/7 in its standard position is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Angle = 2π/7

The coordinates of this point can be found by using the formula for converting from polar to rectangular coordinates:

x = cos(2π/7)

y = sin(2π/7)

So, we have

x = 0.62

y = 0.78

As an ordered pair, we have

(0.62, 0.78)

This means that we plot (0.62, 0.78)

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[tex]\pi \int\limits^6_0 {\frac{26}{3} } \, x^{2} -\frac{1}{9} x^{4} dx[/tex] is the integral that uses the method of disks/washers to find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified lines.

A method for determining the volume of a solid of revolution of a solid-state material while integrating along an axis "parallel" to the axis of revolution is known as disc integration, also known as the disc method in integral calculus.

This technique stacks an endless number of discs with varied radii and minuscule thickness to produce the final three-dimensional form. To create hollow solids of revolutions, the same ideas may also be applied when using rings in place of discs (this is known as the "washer technique").

As opposed to this, shell integration integrates along an axis that is parallel to the axis of revolution. The solution can be seen in the attached images below.

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Now we have the values of h0 and v, so we can write the quadratic function that represents the situation: h(t) = -16t^2 - 0.1125t + 18

What is Quadratic function ?

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants, and x is the variable. The term "quadratic" comes from the fact that the highest degree of the variable x in the function is 2, making it a second-degree polynomial.

Let's use the equation of motion for a free-falling object to model the acorn's motion:

h(t) = -16t^2 + vt + h0

where:

h(t) is the height of the acorn at time t

t is the time in seconds

v is the initial vertical velocity (upwards or downwards)

h0 is the initial height of the acorn

We know that the acorn is thrown from the top of an 18-foot tree, so its initial height is h0 = 18 feet. We also know that after 0.2 seconds, the acorn reaches a height of 18.36 feet above the ground, so:

h(0.2) = 18.36

-16(0.2)^2 + v(0.2) + 18 = 18.36

Simplifying the equation, we get:

-3.2v + 18 = 18.36

-3.2v = 0.36

v = -0.1125

Therefore, the initial vertical velocity of the acorn is v = -0.1125 feet/second (negative because it is moving downwards).

Now we need to find the height of the acorn after 1 second. Using the same equation of motion:

h(1) = -16(1)^2 + v(1) + 18

We know that the height of the acorn after 1 second is 7 feet above the ground, so:

-16 + v + 18 = 7

v = -5

the initial vertical velocity of the acorn is v = -5 feet/second (negative because it is moving downwards).

This is the quadratic function that models the height of the acorn at any time t in seconds, where h(t) is in feet.

Therefore, Now we have the values of h0 and v, so we can write the quadratic function that represents the situation h(t) = -16t^2 - 0.1125t + 18

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The four levels of measurement in statistics are nominal, ordinal, interval, and ratio. They differ in terms of the properties of the data and the types of statistical analyses that can be performed on the data.

Nominal level involves data that can be placed into categories or groups with no inherent order or ranking. Examples of nominal data include gender, race, and occupation.

Ordinal level involves data that can be ranked or ordered, but the differences between the data points are not necessarily equal. Examples of ordinal data include educational levels (e.g., high school, college, graduate), or rankings of movies on a scale of 1-5.

Interval level involves data where the differences between the data points are equal, but there is no true zero point. Examples of interval data include temperature (measured in Celsius or Fahrenheit) and calendar years.

Ratio level involves data that has a true zero point and the differences between data points are equal. Examples of ratio data include height, weight, and time.

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These are some of the main sources of error that can contribute to the margin of error in a survey or study.

The margin of error in a statistical survey or study is a measure of the uncertainty or variability in the results.

Here,
The margin of error reflects the potential difference between the sample estimate and the true population value. The margin of error is calculated by taking into account various sources of errors, including,

Sampling error: Sampling error arises from the fact that the sample is only a subset of the population and thus may not perfectly represent the population. The larger the sample size, the smaller the sampling error.

Other various sources are non-response error, Coverage error, Measurement error, Response bias, Weighting error, and  Model error.

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Han's strategy is correct, as V = πr²h is the exact formula for the volume of a cylinder of radius r and height h.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

This is the exact formula used by Han, hence the strategy is correct.

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The solution of the system of equations is 5 comma negative one half is

Two or more expressions with an Equal sign is called as Equation.

The given system of equations are

y equals negative one half times x plus 2

y=-1/2x+2

y equals one half times x minus 3

y=1/2x-3

Now substitute equation 2 in equation 1

1/2x-3=-1/2x+2

1/2x+1/2x=2+3

x=5

Now y=-1/2(5)+2

y=-5/2+2=-1/2

Hence, 5 comma negative one half is the solution of the system of equations.

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The standard deviation is the positive square root of the sample variance.

Standard deviation is a measure of the spread or dispersion of a set of data from its mean (average) value. It tells us how much the individual values in a dataset deviate from the average value. In other words, it indicates the extent to which the data points are spread out or clustered around the mean.

The formula for standard deviation is the square root of the variance, which is calculated by finding the average of the squared differences between each data point and the mean. The standard deviation is expressed in the same units as the original data and is denoted by the symbol "σ" for the population standard deviation or "s" for the sample standard deviation.

A small standard deviation indicates that the data points are clustered around the mean, while a large standard deviation indicates that the data points are spread out over a wider range. The standard deviation can be used to determine the range of values within which the majority of the data points lie. For example, if the standard deviation is 2, then about 68% of the data points will be within 2 standard deviations of the mean.

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The surface areas of the given cylinders are 94.5 in²,150.72 in², 100.48 in², 200.96 in² and 314 in²

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.

Given are cylinders, we need to find the surface area of them,

The surface area of a cylinder  = 2πr(h+r), where r and h are radius and height of the cylinder,

1) Height = 2 in and radius = 3 in

Surface area = 2·3.14·3·(3+2) = 94.5 in²

2) Height = 5 in and radius = 3 in

Surface area = 2·3.14·3(5+3) = 150.72 in²

3) Height = 6 in and radius = 2 in

Surface area = 2·3.14·2(6+2) = 100.48 in²

4) Height = 4 in and radius = 4 in

Surface area = 2·3.14·4(4+4) = 200.96 in²

5) Height = 4 in and radius = 4 in

Surface area = 2·3.14·5(5+5) = 314 in²

Hence, the surface areas of the given cylinders are 94.5 in²,150.72 in², 100.48 in², 200.96 in² and 314 in²

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The required algebraic expression for the verbal expression is 3w.

From the question, we have the following parameters that can be used in our computation:

3 times as many wins as last season

If we let "w" be the number of wins last season, then "3 times as many wins as last season" can be expressed as:

3w

Hence, the algebraic expression for "3 times as many wins as last season" is 3w.

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Step-by-step explanation:

I am not able to complete your geometry similar triangles project but I can guide you on how to complete the project.

To create a picture of an object with 12 triangles (similar triangles), you need to follow the steps mentioned in the project description. First, create a triangle and measure and label the sides in centimeters. Then, choose three different scale factors and multiply each side of the triangle by the scale factor. This will give you the new triangle. Repeat this process for five more sets of triangles, making sure that the side lengths are different each time.

Next, fill in the ratios, angle measures, and repeat for your 5 other sets of triangles. To help with the accuracy of your triangles, it might be helpful to measure one angle from your original triangle and use the same angle measurements on the corresponding angle of your new triangle.

Finally, color your object poster and make sure to include the title of your object on the top of your poster board and your name on the back. Also, make sure that the handouts are fully filled out with scale factors, proportions, and angles and that the cutouts match those drawn on the grid paper.

With these steps, you should be able to complete your geometry similar triangles project successfully!

The solution is,

The average of the data set is 275

The range is given as 300.

The range can be described as the distance that lies between the maximum and the minimum value in a data set.

here, we have,

to solve for the average distance of electric cars:

The average would be a summation of the data under the electric vehicle divided by the total number of data in the table

given that,

We have ,

250 + 250 + 250 + 400 + 300 + 300 + 350 + 100 / 8

= 2200 / 8

= 275

now,

we get,

= 400 - 100

= 300

Hence, The solution is,

The average of the data set is 275

The range is given as 300.

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The constant c that satisfies the condition of probability mass function of the random variable are 1/55, 1/30, 1/56

(a) For f(x) to be a probability mass function, it must satisfy the following conditions:

1. f(x) ≥ 0 for all x

2. Σf(x) = 1, where the sum is taken over all possible values of X

Here, x can take values 1, 2, 3, 4

So, Σf(x) = f(1) + f(2) + f(3) + f(4) = c + 4c + 9c + 16c = 30c

For Σf(x) = 1, we need 30c = 1. So, c = 1/30.

(b) Here, x can take values 1, 2, 3,...,10

For Σf(x) = 1, we need c(1+2+3+...+10) = c(55) = 1. So, c = 1/55.

(c) Here, x can take values 1, 2, 3,...

For Σf(x) = 1, we need c(14+142+143+...) = c(14)(1+2+3+...) = c(14)∞ = 1. So, c = 1/(14∞).

(d) Here, x can take values 0, 1, 2, 3

For Σf(x) = 1, we need c(12+22+32+42) = c(1+4+9+16) = c(30) = 1. So, c = 1/30.

(e) Here, x can take values 1, 2, 3,...,n

For Σf(x) = 1, we need c(1+2+3+...+n) = c(n(n+1)/2) = 1. So, c = 2/(n(n+1)).

(f) Here, x can take values 0, 1, 2, 3

For Σf(x) = 1, we need c(12×3+22×4+32×5+42×6) = c(56) = 1. So, c = 1/56.

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There was $36 amount of money has Amy saved.

In mathematics, the Multiplication model performs Multiplying values on either side of the operator.

For example 4×2 = 8

The amount of money saved by Henry = $12

Since Amy has three times as much money as Henry.

The amount of money saved by Amy = $12 × 3

Apply the multiplication operation, and we get

The amount of money saved by Amy = $36

Hence, there was $36 amount of money has Amy saved.

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44 °F was found out to be equivalent to approximately 6.67 °C using conversion formula of Fahrenheit to Celsius.

To convert a temperature from Fahrenheit to Celsius, you can use the following formula:

°C = (°F - 32) x 5/9

where °C is the temperature in Celsius, and °F is the temperature in Fahrenheit.

Using this formula, we can convert 44 °F to Celsius as follows:

°C = (44 - 32) x 5/9

= 12 x 5/9

= 6.67 °C (rounded to two decimal places)

Therefore, 44 °F is equivalent to approximately 6.67 °C.

On the Fahrenheit scale, water freezes at 32 degrees Fahrenheit (°F) and boils at 212 °F, at standard atmospheric pressure.

On the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C), and the boiling point of water is defined as 100 °C, at standard atmospheric pressure.

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Answer:

Let's say the number of sweets that Amol has is A.

According to the problem, the number of sweets that Gemma has is 6 times the number of sweets that Amol has. Therefore, Gemma has 6A sweets.

The number of sweets that Harry has is half the number of sweets that Gemma has. Therefore, Harry has 1/2 * 6A = 3A sweets.

So the ratio of the number of sweets that Amol, Gemma, and Harry have respectively is:

A : 6A : 3A

Simplifying this ratio by dividing each term by A, we get:

1 : 6 : 3

Therefore, the ratio of the number of sweets that Amol has to the number of sweets that Gemma has to the number of sweets that Harry has is 1:6:3

Answer:

so subtract the area of the circle from the area of the square.

81-63.585=17.415

Step-by-step explanation: