The volume of a cube is 125 cubic inches. What is the length of one side of the cube?

The appropriate test statistic for the hypothesis being tested and to compare the test statistic to a critical value from a distribution table.

An index that is calculated from sample data and whose value determines whether to accept or reject a null hypothesis is a test statistic.

A test statistic is used to determine the probability of obtaining the observed data under the null hypothesis.

If the test statistic falls within a specified range, the null hypothesis is accepted.

If the test statistic falls outside of the specified range, the null hypothesis is rejected.

The test statistic is calculated from the sample data and is based on the distribution of the sample data.

There are many different types of test statistics, each of which is used to test a different hypothesis.

Some common test statistics include the t-statistic, the F-statistic, and the chi-square statistic.
The t-statistic is used to test the difference between the means of two populations.

The F-statistic is used to test the equality of variances between two populations.

The chi-square statistic is used to test the independence of two categorical variables.
In order to calculate a test statistic, one must first formulate a null hypothesis and an alternative hypothesis.

The null hypothesis is the hypothesis that is assumed to be true, and the alternative hypothesis is the hypothesis that is being tested. The test statistic is then calculated from the sample data, and its value is compared to a critical value from a distribution table.

If the test statistic is greater than or equal to the critical value, the null hypothesis is rejected. If the test statistic is less than the critical value, the null hypothesis is accepted.
In conclusion, a test statistic is an index that is calculated from sample data and is used to determine whether to accept or reject a null hypothesis.

It is important to use the appropriate test statistic for the hypothesis being tested and to compare the test statistic to a critical value from a distribution table.

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Answer:

A) x = 13

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the opposite. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& roots)

Multiplications

Divisions

Additions

Subtractions

~

First, root both sides of the equation to eliminate the power:

\((x -7)^2 = (36)\\\sqrt{(x-7)^2} = \sqrt{36} \\x - 7 = 6\)

Next, isolate the variable, x, by adding 7 to both sides of the equation:

\(x - 7 = 6\\x - 7 (+7) = 6 (+7)\\x = 6 + 7\\x = 13\)

x = 13, or A) is your answer.

~

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Z- test statistics should be used when computing a confidence interval given only the number in a sample, the population standard deviation and the sample mean.

A z-test can be used to assess whether or not the means of two populations differ if the data has a normal distribution. For this reason, it is essential to set up the null hypothesis, and the alternative hypothesis, and determine the z-test statistic's value. The choice criterion is founded on the z critical value.

The z-test formula compares the z statistic with the z critical value to see if there is a difference between the means of the two populations. In hypothesis testing, the z critical value delineates the acceptance and rejection regions of the distribution graph. If the test statistic falls within the rejection region, the null hypothesis can be rejected; otherwise, it cannot.

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Answer:

1:24pm

Step-by-step explanation:

Couple of ways to solve this. Here is one method
Convert all times to minutes and find the total number of minutes they spent on all 3 activities. Then convert to hours and minutes and subtract from the end time of 5;28 to get the start time of all activities which is also the start time of watching the movie (first activity)

So time spent:

Movie: 2 hours 18 minutes = 2 * 60 + 18 = 120 + 18 = 138 minutes
Card game: 34 minutes
Soccer: 1 hour 12 minutes = 1 * 60 + 12 = 72 minutes

Total time spent = 138 + 34 + 72 = 244 minutes = 4 hours and 04 minutes

Subtract 4:04 from 5:28 to get 1:24pm

Check
Movie watch starts at 4:04, ends at 1:24 + 2:18 or 3:42pm
Card game starts at 3:42pm ends at 3:42+0:34 ==> 4:16pm
Soccer starts at 4:16pm ends at 4:16pm + 1:12 ==> 5;28pm

Given statement solution is :- To construct a grouped frequency distribution for the given test scores data, we will use the provided classes: 30-40, 40-50, and so on. Here's the grouped frequency distribution:

Classes Frequency

30-40 2

40-50 3

50-60 4

60-70 8

70-80 9

80-90 7

90-100 7

To construct a grouped frequency distribution for the given test scores data, we will use the provided classes: 30-40, 40-50, and so on. Here's the grouped frequency distribution:

Classes Frequency

30-40 2

40-50 3

50-60 4

60-70 8

70-80 9

80-90 7

90-100 7

To create this distribution, we count the number of scores that fall within each class range. For example, the class 30-40 has 2 scores falling within that range (35 and 39), and the class 40-50 has 3 scores (45, 48, and 48).

Note: It seems there is an inconsistency in the data provided. The class range 70-80 has 9 scores, but the frequencies given for the other classes do not match the actual number of scores falling within those ranges. Therefore, I have used the actual counts from the data to construct the grouped frequency distribution.

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The value of the cosine ratio cos(L) is 5/13

The complete question is added as an attachment

Start by calculating the hypotenuse (h) using

h^2 = 5^2 + 12^2

Evaluate the exponent

h^2 = 25 + 144

Evaluate the sum

h^2 = 169

Evaluate the exponent of both sides

h = 13

The cosine ratio is then calculated as:

cos(L) = KL/h

This gives

cos(L) =5/13

Hence, the value of the cosine ratio cos(L) is 5/13

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The parallax problem is a phenomenon that arises when measuring the distance to a celestial object by observing its apparent shift in position relative to background objects due to the motion of the observer.

The parallax effect is based on the principle of triangulation. By observing an object from two different positions, such as opposite sides of Earth's orbit around the Sun, astronomers can measure the change in its apparent position. The greater the shift observed, the closer the object is to Earth.

However, the parallax problem introduces challenges in accurate measurement. Firstly, the shift in position is extremely small, especially for objects that are very far away. The angular shift can be as small as a fraction of an arcsecond, requiring precise instruments and careful measurements.

Secondly, atmospheric conditions, instrumental limitations, and other factors can introduce errors in the measurements. These errors need to be accounted for and minimized to obtain accurate distance calculations.

To overcome these challenges, astronomers employ advanced techniques and technologies. High-precision telescopes, adaptive optics, and sophisticated data analysis methods are used to improve measurement accuracy. Statistical analysis and error propagation techniques help estimate uncertainties associated with parallax measurements.

Despite the difficulties, the parallax method has been instrumental in determining the distances to many stars and has contributed to our understanding of the scale and structure of the universe. It provides a fundamental tool in astronomy and has paved the way for further investigations into the cosmos.

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The recorded time that is most precise among the four different clocks used to time an event is 55.254 seconds. This is because the recording of this time has the highest decimal precision compared to the other three options.

Precision refers to the degree of accuracy of a measurement, calculation, or specification. It's related to the number of digits used to record or express a quantity, and it's a reflection of uncertainty associated with a measurement or calculation. The greater the precision, the more significant digits are recorded. For example, the result of a calculation could be stated as 1.23 or 1.234, or 1.2345 depending on the degree of precision necessary or desired.

To determine which one is the most precise, you can look at the number of decimal places or digits after the decimal point. The option with the most number of decimal places is 55.254 s, which has three decimal places, while the other options have either one or two decimal places. The general rule for determining precision is to look at the smallest division on the scale of the measuring instrument. In this case, it is not given what type of clocks were used, so we cannot determine the smallest division of each clock. However, since 55.254 s has the most decimal places, it is the most precise recording among the four options.

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Bob tardó 55 minutos en limpiar el garaje, por lo que debemos convertir ese tiempo a segundos para saber cuánto tiempo tardó exactamente.

Sabemos que 1 minuto tiene 60 segundos, por lo que podemos utilizar esta información para convertir los 55 minutos a segundos. La fórmula para realizar esta conversión es:

Segundos = Minutos * 60

Aplicando esta fórmula a los 55 minutos que Bob tardó en limpiar el garaje, obtenemos:

Segundos = 55 * 60

Segundos = 3300

Por lo tanto, Bob tardó 3300 segundos, o aproximadamente 55 minutos, en limpiar el garaje.

Es importante destacar que la conversión de tiempo de minutos a segundos es una operación común en matemáticas y cálculo, y es útil para resolver problemas en los que es necesario trabajar con diferentes unidades de tiempo. Además, entender la relación entre diferentes unidades de tiempo es esencial para realizar cálculos precisos y resolver problemas de manera efectiva.

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The excel statement to estimate the test average of these 4 grades is -

An average is the sum of many numbers divided by the total of numbers. It is also known as the arithmetic mean.

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A point estimate is the value of a statistic that estimates the value of a parameter. Question 2 is false and question 3 is true.

Question 1: A point estimate is the value of a statistic that estimates the value of a parameter.A point estimate is a single number that is used to estimate the value of an unknown parameter of a population, such as a population mean or proportion

Question 2: False

Mu (μ) is not used to estimate X. Mu represents the population mean, while X represents the sample mean. The sample mean, X, is used as an estimate of the population mean, μ.

Question 3: True

Beta (β) is indeed used to estimate the population proportion (p) when conducting hypothesis testing on a sample. Beta represents the probability of making a Type II error, which occurs when we fail to reject a null hypothesis that is actually false. By calculating the probability of a Type II error, we indirectly estimate the population proportion, p, under certain conditions and assumptions.

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Answer:

£528.3

Step-by-step explanation:

If €1 = £0.90 then €587 = 587 * £0.90

587 * £0.90 = £528.3

Answer:

The slope is -5x

Step-by-step explanation:

To find the slope, you do rise/run. So to get from one point to the other, you would move 5 units down, and 1 unit to the right.

It can be written as -5/1 or -5.

Hope this helps!

Answer:

up

Step-by-step explanation:

a is positive

The vertex angle of an isosceles triangle is not equal to the base angles of the isosceles triangle.

Given, an isosceles triangle

and we are asked that is vertex angle congruent to the base angles,

Let suppose ABC is an isosceles triangle with AB = AC

as we know that the angles opposite to the equal sides are also equal.

so, ∠ABC = ∠ACB

now, if ∠ABC = ∠ACB = x

then, on using angle sum property, we get

∠ABC + ∠ACB + ∠BAC = 180°

x + x + ∠BAC = 180°

∠BAC = 180° - 2x

as, x ≠ 180° - 2x

therefore, ∠BAC ≠ ∠ABC

So, the vertex angle of an isosceles triangle is not equal to the base angles of the isosceles triangle.

Hence, the vertex angle of an isosceles triangle is not equal to the base angles of the isosceles triangle.

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Answer:

52

Step-by-step explanation:

Order of Operations says to do Parenthesis first, then exponents.

8 x 3²- (14+ 6)

= 8 x 3²- (20)

= 8 × 9 - 20

Then multiply before subtracting in this question.

= 72 - 20

= 52

Answer:

1.74x10^7

Step-by-step explanation:

you count how many times you moved the decimal to the right

can i have brainliest? i only need 2 more

Answer:

1.74x10^7

Step-by-step explanation:

Answer:

x < 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

20 - 2x > -2(x + 2) + 4x

Step 2: Solve for x

Here we see that any value x less than 6 would work as a solution to the inequality.

Answer:

x<6

Step-by-step explanation:

expand

subtract 20 from both sides

simplify

subtract 2x from both sides

simplify

multiply both sides by -1(reverse the inequality)

simplify

divide both sides by 4

simplify

Answer:

b) 20

Step-by-step explanation:

In supplementary angles, the sum of two angles add up to 180°

  3x + 40 + 80 = 180

          3x + 120 = 180

Subtract 120 from both sides,

                    3x = 180 - 120

                   3x = 60

Divide both sides by 3

                     x = 60 ÷ 3

                      \(\boxed{\bf x = 20^\circ}\)

Answer:

132 sq units

Step-by-step explanation:

Using the .01 level of significance means that, in the long run, a Type I error occurs 1 time in 100. This means that if we perform a statistical test 100 times, and we set the level of significance at .01, then we can expect to observe one false positive result due to chance alone. So, the correct option is 1).

A Type I error occurs when we reject a true null hypothesis, or when we conclude that there is a significant difference or relationship between two variables when in fact there is not.

By setting the level of significance at .01, we are minimizing the risk of making a Type I error while increasing the risk of making a Type II error, which occurs when we fail to reject a false null hypothesis. So, the correct answer is 1).

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Answer:The student plotted the y in place of the x corridinte

Step-by-step explanation:hope that helps

Answer: 250 years

Step-by-step explanation:

12/3=4

4 x $1 = $4 per year

$1000/4=250

250 years

Answer:

...?

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

Here A = 16, b = AB = 8 and h = MN , then

\(\frac{1}{2}\) × 8 × MN = 16

4 × MN = 16 ( divide both sides by 4 )

MN = 4 cm → A

Answer:179 cm3

there you go :)

Step-by-step explanation:

Answer:

The value of P(AUB) = 0.438

Step-by-step explanation:

Given:

P(A) = 0.36

P(B) = 0.2

P(A∩B) = 0.122

Find:

The value of P(AUB)

Computation:

P(AUB) = P(A) + P(B) - P(A∩B)

The value of P(AUB) = 0.36 + 0.2 - 0.122

The value of P(AUB) = 0.56 - 0.122

The value of P(AUB) = 0.438

The amplitude of vibrations after a very long time can be approximated by the absolute value of the maximum value of \(cos^2(t),\)which is 1. The amplitude of vibrations after a very long time is 1.

To find the position of the mass when t = π, we need to solve the equation of motion for the given system. The equation of motion for a mass-spring system without damping is given by:

m * x''(t) + k * x(t) = f(t)

where m is the mass, x(t) is the position of the mass as a function of time, k is the spring constant, and f(t) is the applied force.

In this case, m = 5 kg and k = 80 N/m. The applied force is given by \(f(t) = 30e^{-7t}cos^2(t).\)

(a) To find the position of the mass when t = π, we can substitute t = π into the equation of motion and solve for x(π):

\(5 * x''(\pi ) + 80 * x(\pi ) = 30e^{-7\pi }cos^2{\pi }\)

Simplifying this equation gives:

5 * x''(π) + 80 * x(π) = 30\(e^{-7\pi}\)

To solve this second-order linear homogeneous differential equation, we can assume a solution of the form x(π) = A * \(e^{rt}\), where A is a constant and r is the root of the characteristic equation.

The characteristic equation is obtained by substituting x(t) = \(e^{rt}\) into the differential equation:

\(5 * (r^2 * e^{rt}) + 80 * e^{rt} = 0\)

Simplifying this equation gives:

\(r^2 + 16 = 0\)

The roots of this quadratic equation are imaginary: r = ±4i.

Therefore, the general solution of the homogeneous equation is:

\(x(t) = A_1 * cos(4t) + A_2 * sin(4t)\)

To find the particular solution, we can assume a solution of the form \(x(t) = C * e^{-7t}cos^2(t).\) Substituting this into the differential equation gives:

\(5 * (-14e^{-7t}cos^2(t) - 2e^{-7t}sin(2t)cos(t)) + 80 * (e^{-7t}cos^2(t)) = 30e^{-7t}cos^2(t)\)

Simplifying this equation gives:

\(-70e^{-7t}cos^2(t) - 10e^{-7t}sin(2t)cos(t) + 80e^{-7t}cos^2(t) = 30e^{-7t}cos^2(t)\)

Combining like terms gives:

\(10e^{-7t}sin(2t)cos(t) = -40e^{-7t}cos^2(t)\\\\Dividing both sides by 10e^{-7t}cos(t) gives:\)

sin(2t) = -4cos(t)

Dividing both sides by cos(t) gives:

tan(2t) = -4

Solving this equation for 2t gives:

\(2t = tan^{-1}(-4)\\t = (1/2) * tan^{-1}(-4)\)

Substituting t = π gives:

\(x(\pi ) = C * e^{-7\pi }cos^2(\pi )\)

Since cos(π) = -1, this simplifies to:

\(x(\pi ) = -C * e^{-7\pi }\)

Now, to find the value of C, we can use the initial condition that the mass comes to rest in the equilibrium position when t = 0. This means that x(0) = 0. Substituting t = 0 into the equation gives:

\(x(0) = C * e^{-7 * 0}cos^2(0) = C\)

Since x(0) = 0, we have:

0 = C

Therefore, the position of the mass when t = π is:

\(x(\pi ) = -C * e^{-7\pi } = 0\)

So, when t = π, the position of the mass is 0.

(b) To find the amplitude of vibrations after a very long time, we can analyze the behavior of the solution \(x(t) = C * e^{7t}cos^2(t)\) as t approaches infinity.

As t approaches infinity, the term \(e^{-7t}\) becomes negligible compared to \(cos^2(t).\)

Hence, the amplitude of vibrations after a very long time is 1.

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Answer:

6:40pm

Step-by-step explanation:

60-41 = 19

46-19=27 ---> finished playing basketball at 3:27pm

60-27=33

54-33=21 ----> finished swimming at 5:21pm

21+19=40 ----> finished dinner at 6:40pm

Answer:

6:40

Step-by-step explanation:

You need to add the minutes each time separately, starting at the result of the last addition problem.