The flywheel on a steam engine rotates 60 revolutions every 15 seconds what is the flywheel rate of revolution per second

To interpolate a cubic spline between the points (0, 1), (2, 2), and (4, 0), we can use the concept of spline interpolation. A cubic spline is a piecewise-defined function consisting of cubic polynomials, which smoothly connects the given points.

In order to construct a cubic spline, we need to determine the coefficients of the cubic polynomials for each interval between the given points. The spline should satisfy three conditions: it must pass through each of the given points, it should have continuous first and second derivatives at the interior points, and it should have zero second derivatives at the endpoints to ensure a smooth connection.

We start by dividing the interval into three subintervals: [0, 2], [2, 4]. For each subinterval, we construct a cubic polynomial that satisfies the interpolation conditions. By imposing the continuity and smoothness conditions at the interior point (2, 2), we can obtain a system of equations. Solving this system gives us the coefficients of the cubic polynomials.

Once we have the coefficients, we can express the cubic spline as a piecewise function. The resulting cubic spline will smoothly connect the given points (0, 1), (2, 2), and (4, 0) and provide an interpolation function between them. This interpolation technique ensures a smooth and continuous curve, which can be useful for approximating values between the given data points.

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Answer:

square root is 13

Step-by-step explanation:

Answer:

13!

Step-by-step explanation:

i used my calculator and did the test k-12! its right!

The chi-square goodness-of-fit test requires that all anticipated counts be at least five and observations be drawn from random sample in order to be valid. The correct statements are I and III only. Correct option is C.

I. The chi-square goodness-of-fit test requires that all anticipated counts be at least five and that observations be drawn from a random sample in order to be valid. This statement is correct. The chi-square goodness-of-fit test is based on the chi-square distribution, which approximates the sampling distribution of the test statistic.

To ensure the validity of the test, it is generally recommended that all expected counts in the cells of the contingency table have a minimum expected count of five. This guideline helps to ensure that the chi-square test statistic follows the chi-square distribution, which is approximately valid under this condition.

II. The chi-square goodness-of-fit test uses 1 − n degrees of freedom. This statement is incorrect. The number of categories being assessed determines the degrees of freedom for the chi-square goodness-of-fit test. It is equal to the total categories less one. So, if there are n categories, the degrees of freedom for the test would be n - 1, not 1 - n.

III. A condition for using the chi-square goodness-of-fit test is that the observations are based on a random sample. This statement is correct. The chi-square goodness-of-fit test assumes that the observations are obtained from a random sample or represent a random selection from a population.

This assumption is important to ensure that the test results are generalizable to the population from which the sample is drawn. If the observations are not based on a random sample, the test results may not be valid or may be biased. Therefore, random sampling is a condition for using the chi-square goodness-of-fit test.

The correct statements are I and III only. Correct option is C.

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Complete question is:

Which of the statements are correct?

I. A condition for using the chi-square goodness-of-fit test is that all expected counts must be at least five.

II. The chi-square goodness-of-fit test uses 1 − n degrees of freedom.

III. A condition for using the chi-square goodness-of-fit test is the observations are based on a random sample.

a) I only

b) II only

c) I and III only

d) II and III only

e) I, II, and III

Answer:

−1+1.732051i

Step-by-step explanation:

Answer:  = 42/12 Or simply = 7/2  

Step-by-step explanation:

2(5/3 + 3/4 ) − 4/3

= 2(5/3) + 2(3/4) − 4/3

= 10/3 + 6/4 - 4/3

= 6/3 + 6/4

= 24/12 + 18/12

= 42/12

Or simply = 7/2      

Answer:

V=301.44ft^3

Step-by-step explanation:

l^2°r^2r^2+h^2

10^2=6^2+h^2

100=36+h^2

100-36=h^3

h^2=64

h=8

Volume of cone:

1/3πr^2h

1/3(π)(6)^2(8)

301.44ft^3

Hope it helps....

Answer: nice

Step-by-step explanation:

Sounds like a Scam though ngl

Answer:

B 2208cm squared

you follow this formula

A=2(wl+hl+hw)

w means width

l means length

h means height

input the numbers and you got your answer.

Hope this helped ;)

Answer:5760 cm2

Step-by-step explanation:length times width times height 12 times 12 is 144 and 144 times 40 is 5770 cm2

Answer:

(a) 25

(b) 9.27

Step-by-step explanation:

Step 1

We have to rearrange the given days set from least to highest

35, 40, 45, 55, 60

(a) the range

Range = The highest number - The least number

= 60 - 35

= 25

(b) the standard deviation of the data set

35, 40, 45, 55, 60.

We find the Mean

Mean = Sum of values/Number of values

= 35+40+45+55+60/5

= 235/5

= 47

We can find the standard deviation now.

The formula =

√(x - Mean)²/n

= √(35 - 47)²+ (40 + 47)² + (45 - 47)² + (55 - 47)² + (60 - 47)²/5

= √144 + 49 + 4 + 64 +169/5

= √430/5

= √86

= 9.273618495

Approximately = 9.27

Given a swimming pool that is 2.50 m deep, we need to determine how far below ground level the bottom of the pool appears to be located.

The apparent depth of an object submerged in a medium, such as water, can be calculated using the concept of refraction. Refraction occurs when light travels from one medium to another, and its speed changes. According to Snell's law, the apparent depth (d') of an object in a medium is related to its actual depth (d) and the refractive index (n) of the medium.

The formula for calculating the apparent depth is:

d' = d / n.

In this case, the actual depth of the pool is 2.50 m, and the pool is filled with water, which has a refractive index of approximately 1.33.

Substituting the values into the formula, we have:

d' = 2.50 m / 1.33 ≈ 1.88 m.

Therefore, the bottom of the pool appears to be located approximately 1.88 meters below ground level. This means that when observing the pool from above, it would appear as if the bottom of the pool is situated 1.88 meters below the surface of the ground.

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Answer:hi there!that same guy did that w my question too :( i’m reporting his answers. i will help u out tho ahah. the answer is 470(32-n). i hope this helps :). have a good dayyy

Step-by-step explanation:

Answer:

(2,6)

Step-by-step explanation:

Answer:

Each smoothie was $4

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

your welcome :)

The time spent by Noah exercising is 130 minutes

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

using the above as a guide, we have the following:

Vera = 60% * Noah

So, we have

60% * Noah = 78

Divide both sides by 60%

Noah = 130

Hence, Noah exercised for 130 minutes

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Answer:

Median is the middle line of the box, Lower quartile is the number of the lower end of the box, Upper quartile is the line at the larger end of the box, Maximum is the largest number in the box plot (end of right whisker), Minimum is the lowest number (end of left whisker).

Step-by-step explanation:

32.

Median: 88

Maximum (largest number): 102

Minimum (lowest number): 38

Interquartile range:

96 - 72 = 24

b.

25 % higher

75 % lower?

c.

You can see the range is more towards the right of the box meaning they have higher scores, and that the median or middle is a higher number so it means that most of the students understood and did well on the test.

???.

First quartile: 16

Second: 19

Third: 20

Range: 4

34.  Since they are already in least to greatest order, all we have to do is graph it!

85 - 99 is 2

100 - 114 is 1

115 - 129 is 5

130 - 144 is 6

Answer:

1.25/4 = 5/16

1.75/5 = 7/20

Determine which one of these fractions is bigger.

Both milkshakes have the same thickness.

Given that,
A mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream. A strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream. Which milkshake is thicker is to be determined.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
According to the question,
A mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream.
Ratio of the milk = 1.25 / 4 = 0.35
A strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream.
Ratio of the milke = 1.75 / 5 = 0.35
comparing the ratio both are equal,

Thus, Both milkshakes have the same thickness.

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The inverse of 177 in mod 901 is indeed 56, as determined through the Extended Euclidean Algorithm by hand calculations.

Given that the inverse of 177 in mod 901 is 56.

To find the inverse of 177 modulo 901 using the Extended Euclidean Algorithm, perform the calculations step by step.

Step 1: Initialize the algorithm with the given values:

a = 901 (modulus)

b = 177 (number for which to find the inverse)

Introduce two variables:

[tex]x_0 = 1, y_0 = 0[/tex]

[tex]x_1 = 0, y_1 = 1[/tex]

Step 2: Perform the iterations of the Extended Euclidean Algorithm:

While b is not zero, repeat the following steps:

Calculate the quotient and remainder of a divided by b:

q = a / b

r = a % b (modulus operator)

Update the values of a and b:

[tex]a = b[/tex]

[tex]b = r[/tex]

Update the values of x and y:

[tex]x = x_0 - q * x_1[/tex]

[tex]y = y_0 - q * y_1[/tex]

Update the values of [tex]x_0, y_0, x_1, y_1[/tex]:

[tex]x_0 = x_1[/tex]

[tex]y_0 = y_1[/tex]

[tex]x_1 = x[/tex]

[tex]y_1 = y[/tex]

Step 3: Once the loop ends and b becomes zero, and obtain the      [tex]gcd(a, b) = gcd(901, 177) = 1[/tex], indicating that 177 has an inverse modulo 901.

Step 4: The inverse of 177 modulo 901 is given by [tex]y_0[/tex], which is 56.

Therefore, the inverse of 177 in mod 901 is indeed 56, as determined through the Extended Euclidean Algorithm by hand calculations.

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Answer:

160

Step-by-step explanation:

101+119+104+115+109+x=548+x

there are 6 terms including x so divide the sum by 6

(548+x)/6=118

multiply both sides by 6

548+x=708

subtract 548

x=160

hope that helps :)

Answer:

160

Step-by-step explanation:

There are 6 numbers in the set

101 + 119 + 104 + 115 + 109 + x = 6(118)

101 + 119 + 104 + 115 + 109 + x = 708

548 + x = 708

-548       -548

x = 160

Interest earned in the first year was $75. If the total interest for the next 10 years is $750, then the investment must be receiving simple interest. False.

If the total interest for the next 10 years is $750, it indicates that the investment is receiving compound interest, not simple interest. In compound interest, the interest earned in each period is added to the principal, resulting in an increasing base for calculating subsequent interest. Simple interest, on the other hand, is calculated solely based on the initial principal amount and does not incorporate any interest earned over time.

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Answer:

73 degrees

Step-by-step explanation:

The total number of all of the angles in a triangle added together should be 180 degrees. You know that one of the angles is 17. The other angle is 90 because it is a right triangle.

90 + 17 = 107

180 - 107 = 73

So, the other angle is 73 degrees. If this is wrong I am so sorry. Hope this helps you, let me know if it is right!

Answer:

73°

Step-by-step explanation:

A right triangle has one right angle and two acute angles.

A right angle is 90° and the question says that one of the angle are 17°.

We need to add both angles together which = 107°.

A triangle internal total angles will always add up to 180°.

So we need to do 180° - 107° to find the missing angle which = 73°.

Also, the question said that the missing angles was acute and 73° is acute.

hope this helps :)

Answer:  27

Step-by-step explanation:

[tex]a_{1}=6\\a_{2}=a_{n-1}+7=a_{2-1} +7=a_{1} +7=6+7=13\\a_{3}=a_{n-1}+7=a_{3-1} +7=a_{2} +7=13+7=20\\a_{4}=a_{n-1}+7=a_{4-1} +7=a_{3} +7=20+7=27[/tex]

Answer:

41.4 in

Step-by-step explanation:

(sin 80) opposite      =    x

          hypotenuse        42

x = 42 * sin (80)  = 41.4 in

Answer:

$20.60

Step-by-step explanation:

You find how much it costs for the total amount of basketballs (10.40×20=208), then you subtract that number from the total cost of everything to get the cost of all the uniforms (620-208=412), then you divide the total costs for all uniforms by 20 to find the cost for a single uniform (412÷20=20.6). Always make sure that the decimals go until the hundredths place for USD.

Hope this helps!

Answer:

[tex]62^{o}[/tex]

Step-by-step explanation:

All the angles in a triangle add up to [tex]180^{o}[/tex]

Every right angle triangle has a right angle in it which is [tex]90^{o}[/tex]

So to find the remaining angle, you do [tex]180^{o}[/tex] - [tex]90^{o}[/tex] - [tex]28^{o}[/tex] = [tex]62^{o}[/tex]

Answer:

£1.95

Step-by-step explanation:

£41.01 + £49.54 + £12.50 = £103.05

£105 - £103.05 = £1.95

Answer:

203 ft²

Step-by-step explanation:

We need to use multiplication for the answer of this.

29 × 7 = 203

so that means that the answer in feet is 203 ft²

good luck hope this helped

-cheesetoasty

Answer:

90 toys

Step-by-step explanation:

We should use the same unit for time.  Rewrite 20 minutes as 1/3 hour.

The unit rate is then:

    3 toys         9 toys

----------------- = -----------

 1/3 hour          hour

Multiply this unit rate by 10 hours, obtaining 90 toys

Answer:

I don't know what you mean by disc but the answer is 80 degrees.

Step by Step explanation:

A triangle is made up of 180 deg

65+35=100

180-100=80

Answer:

F. 80°

Step-by-step explanation:

Because a triangle measues 180°

35+65= 100

180-100=80

So the remaining angle must measure an exact 80°