One sample has ss = 60 and a second sample has ss = 48.if n = 7 for both samples, find each of the sample variances, and calculate the pooled variance. because the samples are the same size, you should find that the pooled variance is exactly halfway between the two sample variances

The formula for d in terms of t is d = 5t2.

The distance that a ball falls in t seconds when dropped vertically is given by the formula d = 0.5 gt2, where g is the acceleration due to gravity and is equal to 9.8 m/s2.

To find a formula for d in terms of t if D is directly proportional to the square of t, we can write:

d = kt2 where k is a constant.

To find the value of k, we use the given information that the ball falls 20 metres in 2 seconds.

Substituting this into the formula, we get:

20 = k(2)220

= 4kk

= 20/4k

= 5

Substituting this value of k into the formula, we get:

d = 5t2

Therefore, the formula for d in terms of t is d = 5t2.

This means that for any value of t, we can use this formula to find the distance that a ball falls when dropped vertically in t seconds. The formula gives us a quick and easy way to calculate the distance without having to use the more complex formula involving acceleration due to gravity.

Learn more about distance -

brainly.com/question/30395212

#SPJ11

The null hypothesis suggests that there is no dissimilarity in escape time among lizards from habitats that have been invaded and those from uninvaded habitats.

The alternative hypotheses is that lizards residing in environments that have been invaded will have a greater tendency to escape quickly as compared to those dwelling in uninvaded habitats.

The consequent p-value will demonstrate the level of statistical significance of the results.

The likelihood of obtaining the observed data, or a more extreme version of it, is denoted by the p-value when considering the null hypothesis.

When the p-value is below 0. 05, it signifies compelling evidence against the null hypothesis, implying that the variation in flee times observed is unlikely to be a random occurrence.

Learn more about hypotheses at: https://brainly.com/question/25263462

#SPJ4

The coefficient of determination is approximately 0.67. It is calculated as the ratio of the regression sum of squares (SSR) to the total sum of squares (SST).

In the given ANOVA table, the regression sum of squares (SSR) is 1,700 and the total sum of squares (SST) is 2,550. To determine the coefficient of determination, we divide SSR by SST:

Coefficient of determination = SSR / SST

Coefficient of determination = 1,700 / 2,550

Coefficient of determination = 0.6667 (rounded to 2 decimal places)

Therefore, the coefficient of determination is approximately 0.67. This means that approximately 67% of the total variation in the dependent variable can be explained by the regression model. The remaining 33% represents the unexplained variation or the variation that is attributed to the error term in the model.

Learn more about coefficient here:

https://brainly.com/question/13431100

#SPJ11

In statistical inference, when testing hypotheses

d. the null and alternative hypotheses are both statements about the unknown value of a population parameter.

Hypothesis testing is a statistical method used to make inferences or draw conclusions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H₀) and the alternative hypothesis (Hₐ).

The null hypothesis (H₀) is a statement about the value of a population parameter that is assumed to be true before any evidence or data is collected. It represents the status quo or the default position that there is no significant difference or effect.

The alternative hypothesis (Hₐ) is a statement that contradicts or opposes the null hypothesis. It represents the researcher's claim or belief that there is a significant difference or effect in the population.

Both the null and alternative hypotheses are statements about the unknown value of a population parameter. The null hypothesis assumes a specific value for the parameter (usually no effect or no difference), while the alternative hypothesis proposes a different value or range of values for the parameter (indicating an effect or difference).

During hypothesis testing, statistical techniques are used to analyze the sample data and evaluate the evidence against the null hypothesis. Based on the results, the researcher either rejects the null hypothesis in favor of the alternative hypothesis or fails to reject the null hypothesis.

To know more about  testing hypotheses click here :

https://brainly.com/question/28331914

#SPJ4

The probability that the average age of a simple random sample of 100 people from the country is less than or equal to 32 years is approximately 0.9938 or 99.38%. This calculation is based on the central limit theorem and the population's average age of 31 years with a standard deviation of 4 years.

By applying the central limit theorem, we know that the distribution of sample means approaches a normal distribution as the sample size increases. In this case, the sample size is 100, which is considered sufficiently large.

To find the probability, we need to calculate the z-score corresponding to the desired average age of 32 years. The z-score formula is given by z = (x - μ) / (σ / √n), where x is the desired average age, μ is the population mean (31 years), σ is the population standard deviation (4 years), and n is the sample size (100).

Substituting the values into the formula, we have z = (32 - 31) / (4 / √100) = 1 / 0.4 = 2.5.

We can then consult the standard normal distribution table or use a calculator to find the probability associated with a z-score of 2.5. The probability is the area under the normal curve to the left of the z-score.

Based on the standard normal distribution table, the probability is approximately 0.9938. Therefore, there is a 99.38% probability that the average age of the simple random sample of 100 people will be less than or equal to 32 years.

To learn more about Standard deviation, visit:

https://brainly.com/question/475676

#SPJ11

The maximum percent error is 6.44%.

Given that the dimensions of a cylindrical can are measured, the height is 100 cm and radius 10 cm. If the radius has a 2% error and the height measured has a 5 % error, then we need to determine the maximum percent error.

Calculation of actual volume of cylindrical can

The volume of the cylinder is given as;

V = πr²h

Where r = radius and h = height

V = π × (10 cm)² × (100 cm)

V = 31,416.00 cm³

Calculation of volume with radius 2% error

The new radius = 10 + 2% of 10 cm= 10 + 0.2 cm= 10.2 cm

The new volume V₂= πr₂²h= π(10.2)²(100)= 32711.62 cm³

Calculation of volume with height 5% error

The new height = 100 + 5% of 100 cm= 100 + 5 cm= 105 cm

The new volume V₃ = πr²h₃= π × (10)² × (105)≈ 32941.45 cm³

Calculation of maximum percent error

The actual volume = 31,416.00 cm³

The maximum volume = 32941.45 cm³

So, the maximum percent error will be given by;

Maximum percent error = |(32941.45 - 31,416.00)/31,416.00| × 100%= 6.44%

Therefore, the maximum percent error is 6.44%.

To learn more about cylinder: https://brainly.com/question/27440983

#SPJ11

The number of different standard license plates possible in Arizona, without any restrictions, is 26^6 or 308,915,776.

Now let's explain the calculation. In Arizona, a standard license plate consists of 6 letters, each of which can be any letter from a through z. Since there are 26 letters in the English alphabet, we have 26 options for each position in the license plate.

To determine the total number of different license plates possible, we multiply the number of options for each position together. In this case, we multiply 26 by itself six times (26^6) to account for all possible combinations of six letters.

By raising 26 to the power of 6, we find that there are 308,915,776 different standard license plates possible in Arizona without any restrictions. Each plate can have a unique arrangement of letters, allowing for a vast number of combinations and possibilities.

Learn more about combinations here:

https://brainly.com/question/29595163

#SPJ11

Using fractions, if year boys built 3/14 of an igloo and year 3 girl have built 3/7 of the same igloo. The total amount of igloo built is 18/28.

Given that, Year 2 boys built 3/14 of an igloo, Year 3 girls have built 3/7 of the same igloo.

To find the total amount of the igloo built, we need to find the common denominator of 14 and 7 which is 14.

Let us convert 3/14 into 6/28 and 3/7 into 12/28.

So, total igloo built,

= 6/28 + 12/28= 18/28

Therefore, the total amount of the igloo built is 18/28.

Learn more about fractions visit:

brainly.com/question/10354322

#SPJ11

The probability that the coin landed heads given that a white ball is selected is 0.3957.

Conditional probability is the probability of one event occurring with some relationship to one or more other events.

Given:

Balls in Urn A = 4 white and 7 red = 11 balls.

Balls in Urn B = 10 white and 14 red = 24 balls.

When coin is tossed the we get either head or tail.

If the coin turns up Heads urn A is selected and if it turns up Tails urn B is selected.

P (A) = P(B) = 0.50

Firstly, we have compute the probability that a white ball is selected as follows

P (W) = P (W ∩ A) + P(W ∩ B)

         = P (White from A) × P (A) + P (White from B) × P (B)

         [tex]=\frac{4}{11} (0.50) + \frac{11}{24} (0.50)[/tex]

         = [tex]0.3164+0.2083[/tex]

         [tex]=0.3447[/tex]

The probability of selecting a white ball is P (W) = 0.3447.

If the coin lands Heads it implies that urn A was selected.

Then compute the probability that urn A is selected given that a white ball we use the formula for conditional probability

P(A/W)=P(W∩A)/P(W)

          [tex]=\frac{\frac{3}{11}\times0.50 }{0.3447} = 0.3957[/tex]

Therefore, the probability that the coin landed heads given that a white ball is selected is 0.3957.

Learn more about the probability here:

brainly.com/question/24756209

#SPJ4

,,,,,,,,,,,,,,,,,,,,,,

Each pile of plantain fruit would contain 9 fruits. To find the number of fruits in each pile, we need to add up the total number of fruits and divide it by the number of piles.

In this scenario, there were 63 equal piles of plantain fruit and 7 single fruits, resulting in a total of 63 + 7 = 70 fruits. These 70 fruits were divided evenly among 23 travelers. Dividing 70 by 23 gives us the answer of approximately 3.043, but since we are dealing with whole fruits, we round down to 3. Therefore, each pile of plantain fruit would contain 3 fruits.

Learn more about  add up here ; brainly.com/question/27979560

#SPJ11

Answer:

Each bar is labeled with a letter from A to F, and a scale with numbers from 0 to 10 is shown on the left side of the graph. The height of each bar corresponds to a value on the scale, with bar F being the highest and bar A being the lowest.

Step-by-step explanation:

The area of the figure which consists of two congruent triangles and a rectangle is calculated as: 52 cm².

In the diagram given above, we see a composite figure consisting of two triangles that are congruent, and a rectangle, therefore:

Area of the figure = area of the two triangles + area of rectangle.

The Area of the two triangles:

base = 8 cm²

height = 4.5 cm²

Area of the two triangles = 2(1/2 * base * height) = base * height

Area = 8 * 4.5 = 36 cm²

Area of rectangle = length * width = 4 * 4

= 16 cm²

Total area = 36 + 16 = 52 cm²

Learn more about area of figure on:

https://brainly.com/question/30721292

#SPJ1

Area of the shaded part of ⊙K in terms of π is:2/3 * πr².

To find the expression that represents the area of the shaded part of ⊙K in terms of π, we first need to find the area of the entire circle. We can then subtract the area of the unshaded part of the circle to find the area of the shaded part of the circle.

Let's call the radius of the circle r. Then, the area of the entire circle can be found using the

formula for the area of a circle:πr²

The area of the unshaded part of the circle is a sector with a central angle of 120°, which is 1/3 of the entire circle.

Thus, the area of the unshaded sector can be found by taking 1/3 of the area of the entire circle:1/3 * πr²

The area of the shaded part of the circle,

we need to subtract the area of the unshaded sector from the area of the entire circle:

πr² - 1/3 * πr²

Simplifying the expression:2/3 * πr²

Thus, the expression that represents the area of the shaded part of ⊙K in terms of π is:2/3 * πr².

To learn more about circles refer to:

https://brainly.com/question/17357009

#SPJ11

a. The proportion of entrepreneurs whose first startup was at 29 years of age or less is given as 0.95. Therefore, the proportion of entrepreneurs whose first startup was at 30 years of age or more is 0.05. The sample size is 200. The sampling distribution of p where p is the sample proportion of entrepreneurs whose first startup was at 29 years of age or less is given by N(p, σp) where
p = 0.95, q = 0.05, n = 200
σp = √(pq/n) = √(0.95 * 0.05 / 200) = 0.022
Therefore, the sampling distribution of p is N(0.95, 0.022).

b. The proportion of entrepreneurs whose first startup was at 30 years of age or more is given as 0.05. Therefore, the proportion of entrepreneurs whose first startup was at 29 years of age or less is 0.95. The sample size is 200. The sampling distribution of p where p is the sample proportion of entrepreneurs whose first startup was at 30 years of age or more is given by N(p, σp) where

p = 0.05, q = 0.95, n = 200
and
σp = √(pq/n) = √(0.05 * 0.95 / 200) = 0.022

Therefore, the sampling distribution of p is N(0.05, 0.022).

Let's learn more about proportion:

https://brainly.com/question/1496357

#SPJ11

The length of line segment AC is 34 units.

To find the length of line segment AC, we can use the information given about the lengths of line segments AD, BC, and BD. We can apply the segment addition postulate, which states that the length of a whole segment is equal to the sum of the lengths of its parts.

Given:

AD = 54

BC = 20

BD = 36

To find AC, we need to determine the length of segment CD first. We can do this by subtracting the length of segment BD from the length of segment BC.

CD = BC - BD

CD = 20 - 36

CD = -16 (Note: The negative value indicates that CD is shorter than BC, so we need to consider the absolute value.)

Now, to find the length of line segment AC, we can add the lengths of segments AD and CD.

AC = AD + CD

AC = 54 + (-16) (using the absolute value of CD)

AC = 54 - 16

AC = 38 (Note: The negative sign from CD cancels out when we add it to AD.)

However, we need to be careful because we were given the length of line segment AC, not its absolute value. Therefore, we take the absolute value of AC.

|AC| = |38| = 38

Therefore, the length of line segment AC is 38 units.

The length of line segment AC is 38 units. This is determined by subtracting the length of segment BD from the length of segment BC and then adding the resulting length to the length of segment AD.

To know more about length , visit :

https://brainly.com/question/32060888

#SPJ11

The expression "V V2 V3" does not make sense in standard vector notation. In vector notation, vectors are typically combined using operations such as addition, subtraction, scalar multiplication, or the dot product. Simply placing vectors next to each other without an operation between them does not have a defined meaning.

Similarly, the expression "V, X V2 X V3" also does not make sense in standard vector notation. The comma (",") does not represent a valid vector operation. It is unclear what the intention is behind separating the vectors with a comma and an "X".

On the other hand, the expression "V1 • (V2 X V3)" does make sense in standard vector notation. Here, "V2 X V3" represents the cross product of vectors V2 and V3, which results in a new vector. The dot product "•" between V1 and the cross product yields a scalar quantity. This expression represents the projection of V1 onto the plane spanned by V2 and V3, and it can be used to calculate the signed magnitude of V1's component in the direction perpendicular to that plane.

In summary, the expression "V V2 V3" and "V, X V2 X V3" do not make sense in standard vector notation. However, "V1 • (V2 X V3)" is a valid expression representing the projection of V1 onto the plane spanned by V2 and V3.

Learn more about plane here: https://brainly.com/question/32163454

#SPJ11

The rate of change of the angle of elevation of the balloon from the observer when the balloon is 30 meters above the ground is 0.05 radians per second.

To find the rate of change of the angle of elevation of the balloon from the observer, we can use trigonometry. Let's denote the distance between the observer and the point directly below the balloon as 'x', the height of the balloon above the ground as 'h', and the angle of elevation as 'θ'.

Given:

Rate of change of the height of the balloon (h) = 3 meters/sec

Distance between the observer and the point directly below the balloon (x) = 30 meters

Height of the balloon above the ground (h) = 30 meters

To find the rate of change of the angle of elevation (dθ/dt), we need to determine the relationship between the variables x, h, and θ.

From the right triangle formed by the observer, the point below the balloon, and the balloon itself, we can write the following trigonometric relationship:

tan(θ) = h / x

To find the rate of change of the angle of elevation, we need to differentiate this equation with respect to time (t):

d/dt(tan(θ)) = d/dt(h / x)

Using the quotient rule, the left side becomes:

(sec^2(θ)) * (dθ/dt) = (1/x) * (dh/dt)

Now, let's substitute the given values:

sec^2(θ) = (h^2 + x^2) / x^2

dh/dt = 3 meters/sec

h = 30 meters

x = 30 meters

Plugging in these values and rearranging the equation, we can solve for dθ/dt:

(sec^2(θ)) * (dθ/dt) = (1/x) * (dh/dt)

(sec^2(θ)) * (dθ/dt) = (1/30) * (3)

(sec^2(θ)) * (dθ/dt) = 0.1

Since sec^2(θ) is always positive, we can divide both sides of the equation by sec^2(θ):

dθ/dt = 0.1 / sec^2(θ)

Now, we need to find the value of sec^2(θ) when the balloon is 30 meters above the ground. Let's denote this value as sec^2(θ_0).

In the right triangle, when the balloon is 30 meters above the ground, we have:

sec^2(θ_0) = (h^2 + x^2) / x^2

sec^2(θ_0) = (30^2 + 30^2) / 30^2

sec^2(θ_0) = (900 + 900) / 900

sec^2(θ_0) = 2

Now, we can substitute this value back into the equation for dθ/dt:

dθ/dt = 0.1 / sec^2(θ_0)

dθ/dt = 0.1 / 2

dθ/dt = 0.05

Therefore, the rate of change of the angle of elevation of the balloon from the observer when the balloon is 30 meters above the ground is 0.05 radians per second.

for such more question on angle of elevation

https://brainly.com/question/19594654

#SPJ11

The smaller number is 7 and the larger number is 14.

Let's represent the smaller number as x and the larger number as y.

According to the given information, we have two equations:

Equation 1: x + y = 21 (the sum of the two numbers is 21)

Equation 2: y = x + 7 (one number is 7 more than the other)

We can solve this system of equations to find the values of x and y.

Substituting Equation 2 into Equation 1, we have:

x + (x + 7) = 21

Combining like terms, we get:

2x + 7 = 21

Subtracting 7 from both sides:

2x = 14

Dividing both sides by 2:

x = 7

Now, we can substitute the value of x back into Equation 2 to find y:

y = 7 + 7

y = 14

Therefore, the smaller number is 7 and the larger number is 14.

Learn more about Smaller Number at

brainly.com/question/4241533

#SPJ4

The volume of the prism is approximately 55.72 x 150 = 8358 cubic cm.

To find out the volume of the triangular prism, you need to take two steps.Step 1: Determine the volume of the cylinderTo determine the volume of the cylinder, use the formulaVcylinder = πr²hwhere V is the volume of the cylinder, r is the radius of the cylinder and h is the height of the cylinder.    

In this question, we are given that the cylinder has a diameter of 2 cm, which means the radius is 1 cm and the height of the cylinder is not given.Therefore, we cannot directly calculate the volume of the cylinder. However, we are given that the cylinder has drilled through the triangular prism, so we can calculate the volume of the material removed from the prism by the cylinder. This volume will be equal to the volume of the cylinder.Vcylinder = πr²h= π(1 cm)²h= πh cubic cm.Step 2: Determine the volume of the triangular prismWe are given that the triangular prism has a base of 5 cm and a height of 5 cm. The height of the prism is 14 cm.Using the formula for the volume of a triangular prism,Vtriangular prism = 1/2 × base × height × height of prism= 1/2 × 5 cm × 5 cm × 14 cm= 175 cubic cmNow, we know that the volume of the cylinder is equal to the volume of the material removed from the prism by the cylinder.

Therefore,V cylinder = V triangular prism πh = 175 cubic cm π(1 cm)h = 175 cubic cmh = 175/π cmh ≈ 55.72 cubic cm. Therefore, the volume of the prism is approximately 55.72 x 150 = 8358 cubic cm. Answer: 8358.  

Learn more on traingle here:

brainly.com/question/2773823

#SPJ11

To calculate the volume of the region bounded by the equations x² + y² + z² = 25 and x² + y² = 9, we can set up triple integrals for the projections onto the x-axis, y-axis, and z-axis.



To find the volume using the given equations, we can set up a triple integral. The limits of integration depend on the projection axis.

i) For the projection onto the x-axis, the limits of integration for x will be from -3 to 3 (from the equation x² + y² = 9). The limits of integration for y will be from -√(9 - x²) to √(9 - x²) (from the equation x² + y² + z² = 25), and the limits of integration for z will be from -√(25 - x² - y²) to √(25 - x² - y²). Integrating 1 with respect to x, y, and z over these limits will give the volume.

ii) For the projection onto the y-axis, the limits of integration for y will be from -3 to 3. The limits of integration for x will be from -√(9 - y²) to √(9 - y²), and the limits of integration for z will be from -√(25 - x² - y²) to √(25 - x² - y²). Integrating 1 with respect to y, x, and z over these limits will give the volume.

iii) For the projection onto the z-axis, the limits of integration for z will be from -√(25 - x² - y²) to √(25 - x² - y²). The limits of integration for x will be from -3 to 3, and the limits of integration for y will be from -√(9 - x²) to √(9 - x²). Integrating 1 with respect to z, x, and y over these limits will give the volume.

To learn more about integral click here

brainly.com/question/14502499

#SPJ11

To approximate the probability that the average salary of 100 major league players exceeded $1.1 million, we can use the properties of the sampling distribution of the sample mean.

The distribution of salaries for professional sports players is assumed to be approximately normal. Therefore, the distribution of sample means will also be approximately normal, regardless of the sample size.

To calculate the z-score, we use the formula z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, the sample mean is $1.1 million, the population mean is $1.6 million, the population standard deviation is $0.7 million, and the sample size is 100. Substituting these values into the formula, we find the z-score to be z ≈ -7.14.

Using the standard normal distribution table or a statistical software, we can find the probability that the z-score is less than -7.14. This probability is very close to 0, which means the approximate probability that the average salary of the 100 players exceeded $1.1 million is option b: approximately 0.

Learn more about mean here:

https://brainly.com/question/31101410

#SPJ11

The price of the shoes before the discount is $15.10

Let the cost of shoes be x.

The total cost before discount will be $22 + x.

After a discount of 50%, the discount on entire purchase = (50/100) * ($22 + x)

                                                                                                = 11 + 0.5x

We know that total discount is $18.55

According to the question,

Total discount = 11 + 0.5x = $18.55

Subtracting 11 from both sides of the equation, we get:

0.5x = 18.55 - 11

       = 7.55

Simplifying the above equation, we get:

x = (7.55/0.5)

  = 15.10

Learn more about Discount from :

https://brainly.com/question/1548141

#SPJ11

The total number of cannonballs required to build a pyramid 15 layers high is 120.

To determine the number of cannonballs required to build a pyramid 15 layers high, we need to calculate the total number of cannonballs in each layer and then sum them up for all 15 layers.

A pyramid is formed by stacking layers of cannonballs, with each layer having one less cannonball than the layer below it.

The number of cannonballs in each layer can be determined by using the formula for the sum of an arithmetic series.

The formula for the sum of an arithmetic series is:

Sum = (n/2)(first term + last term)

In this case, the first term is 1 (the top layer of the pyramid) and the last term is 15 (the bottom layer of the pyramid).

The number of terms, n, is equal to the number of layers, which is 15.

Using the formula, we can calculate the number of cannonballs in each layer and then sum them up for all 15 layers:

Sum = (15/2)(1 + 15) = 7.5 [tex]\times[/tex] 16 = 120

Therefore, the total number of cannonballs required to build a pyramid 15 layers high is 120.

In summary, the pirates would need a total of 120 cannonballs to build a pyramid that is 15 layers high and break the world cannonball stacking record.

For similar question on pyramid.  

https://brainly.com/question/30517561  

#SPJ11

The steps to construct an equilateral triangle inscribed in a circle are as shown above.

A polygon is a plane figure that is bound by three or more line segments that join at the vertices. Polygons can be constructed through a series of steps using various tools such as a compass, a straight edge, and a protector. Given the problem in step 2 to construct regular polygons inscribed in a circle, let us construct an equilateral triangle inscribed in a circle as follows:Step-by-step construction of an equilateral triangle inscribed in a circle by hand using a compass and straightedge:Step 1: Draw a circle of radius r and label the center O. Step 2: Construct a line segment that passes through the center O of the circle, and let the line segment be labeled AB. Step 3: Place the compass on point A and draw an arc that intersects circle O at point C. Without adjusting the compass, place the compass on point B and draw another arc that intersects circle O at point D. Step 4: With the same radius from Step 3, place the compass on point C and draw an arc that intersects line AB at point E. Step 5: Place the compass on point D and draw another arc with the same radius from Step 3 that intersects line AB at point F. Step 6: Draw a line segment from point C to point F and another line segment from point D to point E. The line segments CF and DE should intersect at point G.Step 7: Draw a line segment from point G to point O.

Finally, triangle CEF is the desired equilateral triangle inscribed in the circle O.A screenshot of the construction is as follows:Answer: The steps to construct an equilateral triangle inscribed in a circle are as shown above.

To know more about equilateral triangle :

https://brainly.com/question/23846997

#SPJ11

The probability that the average of the 25 measurements exceeds 185 mg/dl is approximately 0.1056, or 10.56%.

To calculate the probability that the average of the 25 measurements exceeds 185 mg/dl, we can use the Central Limit Theorem, which states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

Given that the population mean is 180 mg/dl and the population standard deviation is 20 mg/dl, we can calculate the standard error of the mean (SE) using the formula:

SE = population standard deviation / √(sample size)

SE = 20 / √(25) = 20 / 5 = 4 mg/dl

Now, we need to convert the average of 185 mg/dl into a z-score using the formula:

z = (sample mean - population mean) / SE

z = (185 - 180) / 4 = 5 / 4 = 1.25

To find the probability that the average exceeds 185 mg/dl, we need to calculate the area under the normal distribution curve to the right of the z-score of 1.25.

We can use a standard normal distribution table to find this probability.

Using a standard normal distribution table, we find that the cumulative probability to the left of z = 1.25 is approximately 0.8944. Therefore, the probability to the right of z = 1.25 is:

1 - 0.8944 = 0.1056

So, the probability that the average of the 25 measurements exceeds 185 mg/dl is approximately 0.1056, or 10.56%.

Learn more about probability click;

https://brainly.com/question/31828911

#SPJ4

The five sets given in the problem were analyzed to determine if they are subspaces of c[−1, 1]. It was found that the first, second, and fourth sets are subspaces of c[−1, 1], while the third and fifth sets are not subspaces of c[−1, 1].

Subspaces of c[−1, 1] can be determined by checking if they satisfy the following three conditions:

The following are the subspaces of c[−1, 1]:

(a) The set of functions f in c[−1, 1] such that f(−1) = f(1).

This is a subspace of c[−1, 1].

Let f and g be two functions in the set. Then, (f+g)(−1) = f(−1) + g(−1) = f(1) + g(1) = (f+g)(1).

Thus, the set is closed under addition. Also, if k is a scalar and f is a function in the set, then

(kf)(−1) = kf(−1) = kf(1) = (kf)(1).

Thus, the set is closed under scalar multiplication.

Finally, the zero function in c[−1, 1] satisfies f(−1) = f(1) and hence belongs to the set.

Therefore, the set is a subspace of c[−1, 1].

(b) The set of odd functions in c[−1, 1]. This is a subspace of c[−1, 1].

Let f and g be two odd functions in the set. Then, (f+g)(−x) = f(−x) + g(−x) = −f(x) − g(x) = −(f+g)(x).

Thus, the set is closed under addition.

Also, if k is a scalar and f is an odd function in the set, then,

(kf)(−x) = kf(−x) = −kf(x) = (kf)(x).

Thus, the set is closed under scalar multiplication.

Finally, the zero function in c[−1, 1] is odd and hence belongs to the set.

Therefore, the set is a subspace of c[−1, 1].

(c) The set of continuous nondecreasing functions on [−1, 1]. This is not a subspace of c[−1, 1].

For example, the functions f(x) = x and g(x) = 2x − 1 are both continuous and non-decreasing on [−1, 1], but their sum f+g is not nondecreasing on [−1, 1].

(d) The set of functions f in c[−1, 1] such that f(−1) = 0 and f(1) = 0. This is a subspace of c[−1, 1].

Let f and g be two functions in the set. Then,

(f+g)(−1) = f(−1) + g(−1) = 0 + 0 = (f+g)(1).

Thus, the set is closed under addition.

Also, if k is a scalar and f is a function in the set, then,

(kf)(−1) = k(f(−1)) = 0 = (kf)(1).

Thus, the set is closed under scalar multiplication.

Finally, the zero function in c[−1, 1] satisfies f(−1) = 0 and f(1) = 0 and hence belongs to the set.

Therefore, the set is a subspace of c[−1, 1].

(e) The set of functions f in c[−1, 1] such that f(−1) = 0 or f(1) = 0. This is not a subspace of c[−1, 1].

For example, the functions f(x) = x and g(x) = −x are both in the set, but their sum f+g is not in the set because

(f+g)(−1) = 0 and (f+g)(1) = 0, but

(f+g)(0) = 0 + 0 = 0,

which means that f+g is not in the set.

Therefore, out of the five sets given in the problem, only the first, second, and fourth sets are subspaces of c[−1, 1].

Learn more about subspaces visit:

brainly.com/question/28384717

#SPJ11

The high-low method is a cost estimation technique that involves analyzing the two most extreme periods of activity to estimate fixed and variable cost behavior. It is commonly used in managerial accounting to determine the fixed and variable components of a mixed cost.

Here are the characteristics of the high-low method:

Based on the two most extreme periods of activity: The method compares the cost incurred during the period of highest activity (high point) and the cost incurred during the period of lowest activity (low point). By examining the differences in costs between these two points, it attempts to separate the fixed and variable elements of the cost.

Provides a good estimate of true fixed and variable cost behavior: The high-low method assumes that the variable cost component varies proportionally with the level of activity, while the fixed cost component remains constant. By using the high and low points, it calculates the slope of the cost line and the y-intercept, which represent the variable and fixed costs, respectively.

Difficult to apply and requires a statistical software package: While the high-low method is a relatively simple technique, it can be challenging to apply in practice. Determining the high and low points requires careful analysis of the available data. Additionally, the method may not capture all the nuances of cost behavior, especially if the relationship between cost and activity is not linear. To perform the calculations accurately, statistical software packages or spreadsheets are often utilized.

Uses only two data points: One of the limitations of the high-low method is that it relies on only two data points. This can lead to potential inaccuracies if the data points chosen are not representative of the entire range of activity. The method assumes that the cost behavior between the high and low points is linear, which may not always be the case.

In summary, the high-low method is a cost estimation technique that provides an estimate of fixed and variable cost behavior by analyzing the two most extreme periods of activity. It can be a useful tool, but it has limitations and requires careful consideration of data selection and interpretation.

for such more question on high-low method

https://brainly.com/question/28138570

#SPJ11

The sampling technique being used is a combination of stratified sampling and cluster sampling.

In this scenario, the sampling process involves multiple stages. Let's break it down:

By combining stratified sampling at the state level and cluster sampling at the college/university level, this approach allows for efficient sampling while still maintaining some level of representation and variation. It helps ensure that undergraduates from different states and colleges/universities are included in the final sample.

The sampling technique used in this scenario is a combination of stratified sampling and cluster sampling. This multi-stage approach helps select a representative sample of undergraduate students from different states and colleges/universities in the United States.

To know more about combination visit:

https://brainly.com/question/28065038

#SPJ11

The recipe can be made 25 times with a 10kg bag of potatoes.

To determine how many times the recipe can be made with a 10kg bag of potatoes, we need to know the amount of potatoes required for one recipe. Let's assume that one recipe requires 400 grams (0.4kg) of potatoes.

To calculate the number of times the recipe can be made, we divide the weight of the bag of potatoes (10kg) by the weight of potatoes required for one recipe (0.4kg):

10kg / 0.4kg = 25

Therefore, the recipe can be made 25 times with a 10kg bag of potatoes.

Based on the assumption that each recipe requires 0.4kg of potatoes, a 10kg bag of potatoes would be sufficient to make the recipe 25 times. It's important to note that the actual potato quantity required may vary depending on the specific recipe.

To know more about recipe visit:

https://brainly.com/question/28000963

#SPJ11

The required probabilities for the events in question are:

Based on the parameters given :

Number of red slots = 18

Number of black slots = 18

Number of green slots = 2

Total number of slots = 18+18+2 = 38

A.)

Probability of green slots 2 or more times :

(2/38)² × (36/38)²³ = 0.00080

B.)

Probability of ball not entering the green slots

1 - P(green slots)

P(not entering green slot ) = 1 - 0.0008 = 0.9992

C.)

probability that ball falls into black slot 15 or more times :

(18/38)¹⁵ * (20/38)¹⁰ = [tex]2.21\times10^{-8}[/tex]

D.)

Probability that ball falls into red slot 10 or less times :

(10/38)¹⁰ * (28/38)¹⁵ = [tex]1.63\times10^{-8}[/tex]

Therefore, the required probabilities are :

Learn more on probability:https://brainly.com/question/15246027

#SPJ4