an object is traveling on a circle with a radius of 5 cm. if in 20 seconds a central angle of 1/3 radian is swept out, what is the angular speed of the object? what is the linear speed?

The p-value (0.0208) is less than the significance level (0.05), we reject the null hypothesis. This indicates that there is sufficient evidence to suggest the case.

Null hypothesis (H0): The population means are equal, μ1 = μ2.

Alternative hypothesis (Ha): The population means are different, μ1 ≠ μ2.

Select the significance level (α): In this case, α = 0.05.

Now, The test statistic for a two-sample t-test is given by:

  t = (sample mean 1 - sample mean 2) / √((s1² / n1) + (s2² / n2))

  where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Here X₁ = 10, X₂ = 14, s= 3, n₁ =12, n₂ = 18

So, t= (10-14) / √(3²/12) + (3²/18) et:

t= (-4)/ √(3/4 + 1/2)

t= -4 / (5/4)

t= -2.7931

Now, degrees of freedom (df):

= (9/12 + 9/18)² / (((9/12)² / 11) + ((9/18)² / 17))

= 25.164

So, the p value will be 0.0208.

As, p-value is less than α (0.0208 < 0.05), we reject the null hypothesis.

Since the p-value (0.0208) is less than the significance level (0.05), we reject the null hypothesis. This indicates that there is sufficient evidence to suggest the case.

Learn more about Hypothesis test here:

https://brainly.com/question/17099835

#SPJ4

Answer:

1047.12in³

Step-by-step explanation:

The volume of the sphere is:

V= 4/3 πr³

Where r is radius

Therefore the volume of each pinata is:

V= 4/3 x π x 5³

V= 523.6in³

The total:

V = 523.6 + 523.6 = 1047.12in³

The particular solution that satisfies the given condition is s = (16/3)t³ + (9/2)t² - 6t + 120

To find the particular solution of the differential equation ds/dt = 16t² + 9t - 6 with the condition s = 120 when t = 0, we need to integrate the right-hand side of the equation with respect to t and then solve for the constant of integration using the given condition.

First, let's integrate the right-hand side of the equation:

∫(ds/dt) dt = ∫(16t² + 9t - 6) dt

Integrating term by term, we get:

s = (16/3)t³ + (9/2)t² - 6t + C

Now, we can use the given condition s = 120 when t = 0 to determine the value of the constant of integration C:

120 = (16/3)(0)³ + (9/2)(0)² - 6(0) + C

120 = C

Therefore, the particular solution that satisfies the given condition is:

s = (16/3)t³ + (9/2)t² - 6t + 120

To learn more about differential equation click on,

https://brainly.com/question/14507838

#SPJ4

T-value is not always greater than Z-value. Therefore, the statement is false

False. The relationship between a T critical value and a Z critical value is not that a T value is always greater than a Z value. The choice between using a T critical value or a Z critical value depends on the specific context and assumptions of the statistical analysis.

In general, when the sample size is small (typically below 30) and the population standard deviation is unknown, a T critical value is used. The T distribution accounts for the additional uncertainty introduced by the smaller sample size, resulting in wider confidence intervals and more conservative hypothesis tests compared to the Z distribution.

On the other hand, when the sample size is large (typically above 30) or the population standard deviation is known, a Z critical value is used. The Z distribution assumes a large sample size, and it is based on the known population standard deviation or the approximation of the sample standard deviation to the population standard deviation.

Therefore, it is incorrect to state that a T-value is always greater than a Z-value. The choice between T and Z critical values depends on the specific conditions and assumptions of the statistical analysis being performed.

To learn more about “confidence interval” refer to the https://brainly.com/question/15712887

#SPJ11

Answer:

heres the answer I think

Step-by-step explanation:

-3 < x < 1/2

Answer:

Angle EHG

Step-by-step explanation:

If you want explanation tell me in comments

Answer:

the correct answer is angle EHB

The absolute maximum and minimum of the function z = f(x, y) = 3x² - 12x + 3y² - 12y on the domain x² + y² < 4 are not provided.

To find the absolute maximum and minimum of the function z = f(x, y) = 3x² - 12x + 3y² - 12y on the domain D: x² + y² < 4, we need to locate the critical points and examine the boundaries of the domain.

Since the absolute maximum and minimum values are not provided, further calculations are needed to determine these values for the given function on the given domain.

To learn more about “Lagrange multipliers” refer to the https://brainly.com/question/4609414

#SPJ11

3.14 x 11 = 34.54

Pi = 3.14 so times by 11 = 34.54

Answer:

Top:(4r⁹+3r³-5)

Bottom: r⁵

Step-by-step explanation:

Answer:

384

Step-by-step explanation:

v= L x W x H

v= 4 x 2 x 1.2

v= 9.6

9.6 x 40 = 384

lmk if you have any questions  :)

Answer:

A

Step-By-Step Explanation:

Step One: The first step is to figure out the volume of one. The volume formula is length times width times height. We have all the dimensions so: 4 times 2 times 1.2= 9.6.

Step Two: Now, we just mutiply the number by 40 since there are 40 slabs: 384.

The equation is separable. The solution to the initial value problem is y(t) = y(0) = -3.

A. The equation is separable. The solution to the initial value problem is y(t) = ___

To determine whether the given differential equation is separable, we need to check if it can be written in the form dy/dt = g(t) * h(y), where g(t) is a function of t only and h(y) is a function of y only.

In this case, the equation is dy/dt = 2ty + 1. We can rearrange it as:

dy = (2ty + 1) dt

Now, we can see that we have both y and t terms on the right-hand side, indicating that the equation is not yet separable.

Therefore, the correct choice is B. The equation is not separable.

Unfortunately, no solution can be provided for the initial value problem y(0) = -3 since the equation is not separable.

Learn more about initial value here

https://brainly.com/question/514233

#SPJ11

Answer:

25 tickets

Step-by-step explanation:

If the answer is wrong, I don't know what to say because the answer I got is 25

The would be 25 more gift card raffle ticket than shopping spree raffle tickets if there are 500 total raffle tickets

An equation is an expression that shows the relationship between two or more numbers and variables.

The shopping spree raffle tickets is 35% while the gift card tickets is 40%. Hence for 500 tickets:

Difference = (40% - 35%) * 500 = 25 tickets

The would be 25 more gift card raffle ticket than shopping spree raffle tickets if there are 500 total raffle tickets

Find out more on equation at: https://brainly.com/question/2972832

Answer:

40

Step-by-step explanation:

2 cups = 1 pt

therefore

1/2 is the equation

...

80/2 = 40

Answer:

$5934

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² = 4² + ([tex]\sqrt{5}[/tex] )² = 16 + 5 = 21 ( take the square root of both sides )

x = [tex]\sqrt{21}[/tex] → B

Answer:

The answer to this question is $14,916

Step-by-step explanation:

18,469 - 3,553 = 14916

As he already has money for the car.

A bar model is shown in the linked picture.

a. Probability of losing the second thumb war is also 0.38.

b. Probability of losing the third thumb war is also 0.38.

Given that Nate loses 38% of all thumb wars.

We can use the probability of losing the thumb war as

p=0.38.

The probability of winning is

1-0.38=0.62.

a) Probability of losing two thumb wars in a row is:

P(loses two in a row) = P(loses first) × P(loses second)

The probability of losing the first thumb war is 0.38.

The probability of losing the second thumb war is also 0.38

So,

P(loses two in a row) = (0.38) × (0.38)

= 0.1444

b) Probability of losing three thumb wars in a row is:

P(loses three in a row) = P(loses first) × P(loses second) × P(loses third)

The probability of losing the first thumb war is 0.38.

The probability of losing the second thumb war is also 0.38

The probability of losing the third thumb war is also 0.38.

So,

P(loses three in a row) = (0.38) × (0.38) × (0.38)

= 0.054872

c) When events are independent, their complements are independent as well.

If the probability of winning the thumb war is p, then the probability of losing the thumb war is 1-p.

The complement of "losing three in a row" is "not losing three in a row".

P(not loses three in a row) = 1 - P(loses three in a row)P(not loses three in a row)

= 1 - 0.054872

= 0.945128

The probability that Nate loses three thumb wars in a row, but does not lose four in a row is the probability of losing three minus the probability of losing four in a row.

P(loses three but not four in a row) = P(loses three in a row) - P(loses four in a row)

P(loses four in a row) = P(loses three in a row) × P(does not lose the next)

P(loses four in a row) = (0.38) × (0.38) × (0.38) × (0.62)

= 0.02081416

P(loses three but not four in a row) = 0.054872 - 0.02081416

= 0.03405784

The probability that Nate loses two thumb wars in a row is 0.1444

The probability that Nate loses three thumb wars in a row is 0.054872.

To know more about probability visit:

https://brainly.com/question/13604758

#SPJ11

y = -2/5 x + 22/5 is the required equation of the line passing the coordinates

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

Given the coordinate points (-4, 6) and (6, 2), the slope of the line is expressed as:

Slope = 2-6/6+4

Slope = -4/10
Slope = -2/5

For the y-intercept

2 = -2/5(6) + b

2 + 12/5 = b
b = 22/5

Hence the equation of the line passing the coordinate is y = -2/5 x + 22/5

Learn more on equation of a line here: https://brainly.com/question/18831322

#SPJ1

Answer:

x = 1/2

y = 3

Step-by-step explanation:

Remark

The diagonals of a parallelogram cut each other in half. That means that x lengths are equal and the y lengths are equal

Equations

3y = y + 6

10x = 6x + 2

Solution for x

10x = 6x + 2                     Subtract 6x from both sides

10x - 6x = 6x - 6x + 2

4x = 2                              Divide by 4

4x/4 = 2/4

x = 1/2

Solution for y

3y = y + 6

3y - y = y- y + 6

2y = 6

y = 3

Answer:

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Answer:

pi, and square root of 2

I don't think you're ACTUALLY going to give me brainliest

Answer: i think its 10

Step-by-step explanation:

Answer:

yes and no....It depends if u got the answer correct then u got ur mark but if the teacher expects your answer a certain way then u might lose maybe just 1 mark but dont stress it looks good and u should get full marks

Answer:

5.86

Step-by-step explanation: its right on delta math

Step-by-step explanation:

I think that is your answer because in the Himalayas it lies between latitudes 26.

Answer:

x = 138

Step-by-step explanation:

Exterior angle thm:

68 + 70 = x

x = 138

The 90% confidence interval is approximately 2,400 and 3,400.

The 90% confidence interval of the true population mean can be calculated using the formula: sample mean ± (critical value * standard error). Since the sample size is small (n=27), we need to use the t-distribution and its corresponding critical value. For a 90% confidence level with 26 degrees of freedom (n-1), the critical value is approximately 1.706.

Using the given values, the standard error is calculated as the sample standard deviation divided by the square root of the sample size: 900 / sqrt(27) ≈ 171.97.

Substituting the values into the formula, the 90% confidence interval is approximately 3,000 ± (1.706 * 171.97), which yields a range of approximately 2,424.5 to 3,575.5.

Therefore, the closest option to the 90% confidence interval is 2,400 and 3,400.

To learn more about “sample” refer to the https://brainly.com/question/24466382

#SPJ11

The statement |A ∪ B ∪ C| = |A| + |B| + |C| is true, which means the statement is proven.

Let A, B, and C be sets with finite cardinalities that satisfy A ∩ B ∩ C = ∅.

We have to prove that |A ∪ B ∪ C| = |A| + |B| + |C|.

The addition law of sets states that the cardinality of a union of two finite sets is equal to the sum of the cardinalities of the sets minus the cardinality of their intersection.

Thus, we get: |A ∪ B ∪ C| = |A ∪ B| + |C| − |(A ∩ B) ∪ C| = (|A| + |B| − |A ∩ B|) + |C| − |(A ∩ B) ∩ C| = |A| + |B| + |C| − |A ∩ B ∩ C|.Since A ∩ B ∩ C = ∅, we get |A ∪ B ∪ C| = |A| + |B| + |C|.

Thus, the statement is proven.

To learn more about sets

https://brainly.com/question/30096176

#SPJ11

The concentration of sugar in the solution in the tank after 33 minutes is approximately 0.00734 kg/L or 7.34 g/L.

(a) Initially, the tank contains pure water, so there is no sugar in the tank. Therefore, the amount of sugar in the tank initially is 0 kg.

(b) The amount of sugar in the tank after t minutes can be calculated using the formula:

amount = 166.6(1 - [tex]e^{-t/340}[/tex])

Here, t is the time in minutes. This formula is derived from the exponential decay model, where the rate of sugar leaving the tank is proportional to the amount of sugar present. The constant 166.6 represents the equilibrium amount of sugar in the tank.

As time passes, the term [tex]e^{-t/340}[/tex] approaches 1, and the amount of sugar in the tank approaches the equilibrium amount of 166.6 kg.

(c) To find the concentration of sugar in the solution in the tank after 33 minutes, we need to divide the amount of sugar by the volume of the tank. The volume of the tank is given as 2380 L.

First, let's calculate the amount of sugar in the tank after 33 minutes using the formula from part (b):

amount = 166.6(1 - [tex]e^{-33/340}[/tex])

amount ≈ 166.6(1 - 0.895)

amount ≈ 166.6(0.105)

amount ≈ 17.493 kg

Now, we can calculate the concentration:

concentration = amount / volume

concentration = 17.493 kg / 2380 L

concentration ≈ 0.00734 kg/L

Therefore, the concentration of sugar in the solution in the tank after 33 minutes is approximately 0.00734 kg/L or 7.34 g/L.

Learn more about exponential decay model here:

https://brainly.com/question/30165205

#SPJ11