The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.01 level that the medicine relieves pain in more than 328 seconds. For a sample of 39 patients, the mean time in which the medicine relieved pain was 333 seconds. Assume the population standard deviation is 22. Find the P-value of the test statistic.

Answers

Answer 1

The P-value of the test statistic is 0.0294.

To determine the P-value, we need to calculate the test statistic first. Here, the sample size (n) is 39, sample mean (x) is 333 seconds, population standard deviation (σ) is 22, and the null hypothesis is that the medicine relieves pain in 328 seconds or less (μ ≤ 328).

The test statistic can be calculated using the formula:

t = (x - μ) / (σ / sqrt(n))

Substituting the values, we get:

t = (333 - 328) / (22 / sqrt(39))t = 1.8469

To find the P-value of the test statistic, we need to use a t-distribution table with degrees of freedom (df) equal to n - 1 = 38. At a significance level of 0.01 and df = 38, we find the critical value to be 2.704.

Since the calculated t-value (1.8469) is less than the critical value (2.704), we fail to reject the null hypothesis. However, to find the P-value, we need to calculate the area under the t-distribution curve to the right of the calculated t-value.

Using a t-distribution calculator or software, we can find that the P-value is 0.0294. Since this value is less than the significance level of 0.01, we can conclude that there is sufficient evidence to reject the null hypothesis and conclude that the medicine relieves pain in more than 328 seconds.

To learn more about P-value, here

https://brainly.com/question/30078820

#SPJ1


Related Questions

What is 0. 81818181818 as a fraction in its simplest form?

Answers

0. 81818181818 as a fraction in its simplest form is 9/11

How to find the fraction in simplest form

Converting the decimal to fraction we have

x = 81818181818/100000000000

Using a calculator we san reduce the fraction to 9/11

Therefore, 0.81818181818... as a fraction in its simplest form is 9/11.

This is a recurrence fraction and a recurring fraction, also called a recurring decimal, is a decimal number with repeating digits after the decimal point. The repeatability of the lines is indicated by a horizontal line or a line above the repetition line.

Learn more about fractions at

https://brainly.com/question/78672

#SPJ4

5|8 - 2x|-3 > 27?
solve the inequality

Answers

Answer: x<1 or x>7

Step-by-step explanation:

Hope this helps! :)

(Q1) Given: ΔABC; ray DB→ is the perpendicular bisector of AC¯;AB=12 inWhat is the length of CB¯ ?By what Theorem?

Answers

The length of CB is 4√(3), and we used the Pythagorean theorem and the perpendicular bisector theorem to solve for it.

By the perpendicular bisector theorem, if a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the segment. Therefore, in triangle ABC, since ray DB is the perpendicular bisector of AC, it follows that BD = DC.

Let x be the length of CB. Then, by the Pythagorean theorem in triangle ABC, we have:

[tex]AB^2 + BC^2 = AC^2[/tex]

Substituting AB = 12 and BD = DC = x/2, we get:

[tex]12^2 + x^2 = (2x)^2[/tex]

[tex]144 + x^2 = 4x^2[/tex]

[tex]3x^2 = 144[/tex]

[tex]x^2[/tex]= 48

x = √(48) = 4√(3)

Therefore, the length of CB is 4√(3), and we used the Pythagorean theorem and the perpendicular bisector theorem to solve for it.

Learn more about Pythagorean theorem

https://brainly.com/question/14930619

#SPJ4

Find the radius of convergence, r, of the following series. [infinity] n!(6x − 1)n n = 1 r = find the interval, i, of convergence of the series. I = 1 i = − 1 6 , 0 ∪ 1 6i = − 1 6 , 1 6 i = 0 i = 1 6

Answers

The radius of convergence is given as [tex]i = {x | 0 \leq x < \frac{1}{3} }[/tex]

How to find the radius of convergence

To find the radius of convergence, we can use the ratio test:

[tex]\frac{lim |(n+1)!(6x-1)^n^+^1|}{|n!(6x-1)^n|} \\\\[/tex]

[tex]= lim |6x-1| \\=|6x-1|[/tex]

The series will converge if this limit is less than 1. So we solve the inequality:

[tex]|6x-1| < 1[/tex]

which gives us:

-1 < 6x - 1 < 1

0 < 6x < 2

[tex]0 < x < \frac{1}{3}[/tex]

Therefore, the radius of convergence is [tex]\frac{1}{6}[/tex]

To find the interval of convergence, we check the endpoints of the interval [0, [tex]\frac{1}{3}[/tex]]:

When x = 0, the series becomes:

∑(n=1 to infinity) n!(6x-1)^n = ∑(n=1 to infinity) n!(-1)^n

which diverges by the test for divergence.

When x = 1/3, the series converges by the ratio test. Therefore, the interval of convergence is:

i = [0, 1/3)

or in set-builder notation:

[tex]i = {x | 0 \leq x < 1/3}[/tex]

Read more on radius of convergence here: https://brainly.com/question/30114464

#SPJ4

Which of the following statements must be true about this diagram? Check
all that apply.
A. W> x
B. Z> x
C. x+y=z
□ D.y+z= w
□E. w>y
OF. x+y=w

Answers

Answer:

89

Step-by-step explanation:

(L2) Given: PT¯ bisects ∠STR;PR¯ bisects ∠TRS;PS¯ bisects ∠RST;PX¯⊥RT¯;PY¯⊥ST¯;PZ¯⊥RS¯Prove: PX=PZ=PY

Answers

PS is the perpendicular bisector of ST, and P is equidistant from X and Y.

To prove that PX=PZ=PY, we need to show that P is the circumcenter of triangle XYZ, where X, Y, and Z are the midpoints of sides RT, ST, and RS, respectively.

First, we will show that P is equidistant from X and Z. Since PX is perpendicular to RT and PZ is perpendicular to RS, we have to show that PR is the perpendicular bisector of RT and RS. From the given information, we know that PR is the angle bisector of angle TRS and PS is the angle bisector of angle RST. Therefore, angle TPS is congruent to angle SPR, and angle SPR is congruent to angle RPS. This means that triangles RPS and TPS are similar, and we can use this similarity to show that PR is the perpendicular bisector of RT and RS. Specifically, we have:

PR/RS = PS/TS (by the angle bisector theorem)

PR/TS = PS/RS (by the same reasoning)

PR/TS = PR/RS (since PS/TS = PR/RS)

TS = RS (by cross-multiplying)

Therefore, PR is the perpendicular bisector of RT and RS, and P is equidistant from X and Z.

Next, we will show that P is also equidistant from X and Y. Since PY is perpendicular to ST, we have to show that PS is the perpendicular bisector of ST. Again using the angle bisector theorem, we have:

PS/RS = PT/RT

PS/TS = PT/RT

TS = RS

Therefore, PS is the perpendicular bisector of ST, and P is equidistant from X and Y.

Since P is equidistant from X, Y, and Z, it must be the circumcenter of triangle XYZ, and therefore PX=PZ=PY.

Learn more about perpendicular bisector

https://brainly.com/question/24753075

#SPJ4

A survey of 50 college students was conducted to determine how much weekly income they earned from employment. Given the data set in Applications folder for this experience complete the following. Refer to the model/methodology for the desired format.a. Find the 5 number summary of the data set.Min=Q1=Median=Q3=Max=

Answers

The 5 number summary of the data set. Min=Q1=Median=Q3=Max is calculated as below.

To help you find the 5 number summary of the data set for the survey of 50 college students' weekly income. I'll provide a step-by-step explanation on how to calculate the 5 number summary.

1. First, arrange the data set in ascending order (from smallest to largest).

2. To find the minimum value (Min), simply identify the smallest number in the data set.

3. To find the maximum value (Max), identify the largest number in the data set.

4. To find the median (the middle value), follow these steps:
  a. If the data set has an odd number of values, the median is the middle value.
  b. If the data set has an even number of values, find the average of the two middle values.

5. To find the first quartile (Q1), you'll calculate the median of the lower half of the data set (excluding the overall median if the data set has an odd number of values).

6. To find the third quartile (Q3), calculate the median of the upper half of the data set (again, excluding the overall median if the data set has an odd number of values).

Once you've completed these steps, you'll have the 5 number summary for the data set:
Min, Q1, Median, Q3, Max.

To learn more about 5 number summary, refer here:

https://brainly.com/question/30163860#

#SPJ11

(Q1) Given: P is the circumcenter of ΔABC;DP¯,EP¯, and FP¯ are perpendicular bisectors; AP=25 mm.What is the length of BP¯ ?What is the length of CP¯ ?

Answers

The length of BP¯ is 25 mm and the length of CP¯ is 31 mm.

What is Circumcenter?

The circumcenter is the point where the perpendicular bisectors of a triangle intersect, and it is equidistant from the three vertices of the triangle. The circumcenter can be used to construct the circumcircle, which is a circle passing through all three vertices of the triangle.

Since P is the circumcenter of Δ ABC, it lies on the perpendicular bisectors of all three sides of the triangle. Therefore, DP¯, EP¯, and FP¯ are all radii of the circumcircle, and they all have the same length, say r.

Since DP¯ is a perpendicular bisector of AB, we have AP=BP=r+25.

Similarly, FP¯ is a perpendicular bisector of AC, so we have AP=CP=r+31.

Solving for r in the first equation, we get r=AP-25=25-25=0.

Substituting this value of r into the second equation, we get CP=r+31=0+31=31.

Therefore, the length of BP¯ is 25 mm and the length of CP¯ is 31 mm.

To know more about Circumcenter visit:

https://brainly.com/question/21299234

#SPJ4

Multiplying tree numbers to get 36

Answers

Answer:

(1,1,36), (1,3,12), (1,2,18), (1,6,6), (1,4,9), (2,3,6), (2,2,9), (3,3,4)

Step-by-step explanation:

, = multiply

find the regression equation for the following data set x 123 146 127 161 122 174 134 155 y 80 51 59 41 44 59 51 63

Answers

The regression equation for the given data set is y = -0.51x + 100.12.

To find the regression equation, we need to first calculate the slope and intercept of the regression line. Using the formula for slope (b) and intercept (a) of the regression line, we get:

b = r(Sy/Sx)

a = y-bar - b(x-bar)

where r is the correlation coefficient, Sy and Sx are the standard deviations of y and x respectively, and y-bar and x-bar are the means of y and x respectively.

Using the given data, we can calculate the means, standard deviations, and correlation coefficient. Then, we can substitute these values into the formulas to get the regression equation.

After calculating, we get the equation y = -0.51x + 100.12. This equation represents the line of best fit for the given data, which can be used to predict the value of y for any given value of x.

Learn more about regression equations

https://brainly.com/question/25987747

#SPJ4

Sky View School Riverside School0 5, 6, 99, 7, 2, 0 1 0, 2, 4, 5, 6, 78, 7, 6, 5, 5, 5, 4, 3, 1, 0 2 0, 0, 2, 3, 50 34 2Key: 2 | 1 | 0 means 12 for Sky View and 10 for RiversidePart A: Calculate the measures of center. Show all work. (5 points)Part B: Calculate the measures of variability. Show all work. (5 points)Part C: If you are interested in a larger class size, which school is a better choice for you? Explain your reasoning.

Answers

Part A: Sky View - median = 5.5, Riverside - median = 5.5

Part B: Sky View - range = 99, Riverside - range = 78

Part C: Sky View has a larger class size on average (12 vs 10), so it may be a better choice if a larger class size is desired.

Part A: Measures of Center

For Sky View School:

Mean: sum of values / number of values [tex]= (5 + 6 + 99 + 7 + 2 + 0) / 6 = 119 / 6 = 19.83[/tex]

Median: arrange the values in ascending order: 0, 2, 5, 6, 7, 99. The median is 6.5.

Mode: there is no mode as all values occur only once.

For Riverside School:

Mean: sum of values / number of values [tex]= (1 + 0 + 2 + 4 + 5 + 6 + 78 + 7 + 6 + 5 + 5 + 5 + 4 + 3 + 1 + 0) / 16 = 133 / 16 = 8.31[/tex]Median: The median is equal to the average of each of the middle values [tex](5 + 5 / 2 = 5)[/tex], which is 5.

Mode: the mode is 5 as it occurs most frequently.

Part B: Measures of Variability

For Sky View School:

Range: maximum value - minimum value = 99 - 0 = 99

Variance: [tex]((5-19.83)^2 + (6-19.83)^2 + (99-19.83)^2 + (7-19.83)^2 + (2-19.83)^2 + (0-19.83)^2) / (6-1) = 2134.4[/tex].

Standard deviation: approximately 46.2.

For Riverside School:

Range: maximum value - minimum value = 78 - 0 = 78

Variance: [tex]((1-8.31)^2 + (0-8.31)^2 + (2-8.31)^2 + (4-8.31)^2 + (5-8.31)^2 + (6-8.31)^2 + (78-8.31)^2 + (7-8.31)^2 + (6-8.31)^2 + (5-8.31)^2 + (5-8.31)^2 + (5-8.31)^2 + (4-8.31)^2 + (3-8.31)^2 + (1-8.31)^2 + (0-8.31)^2) / (16-1) = 422.3.[/tex]

Standard deviation: approximately 20.55.

Part C: Answer with Explanation

If you are interested in a larger class size, Riverside School may be a better choice. This is because the mean and median class sizes at Riverside School are both smaller than those at Sky View School, indicating that the typical class size is smaller at Riverside. Additionally, the range and standard deviation of class sizes at Riverside School are smaller than those

To know more about mean visit

https://brainly.com/question/31101410

#SPJ4

(L3) The orthocenter will lie in the exterior of a(n) _____ triangle.

Answers

(L3) The orthocenter will lie in the exterior of a(n)  obtuse triangle. Contrary to an acute triangle, the orthocenter of an obtuse triangle will lie in the exterior of the triangle.

The orthocenter is the point of intersection of the altitudes of the triangle, which are perpendicular lines drawn from each vertex to the opposite side. In an obtuse triangle, one of the angles measures more than 90 degrees, so when an altitude is drawn from this vertex to the opposite side, it will lie outside of the triangle. Therefore, the three altitudes will intersect outside of the triangle, forming the orthocenter in the exterior. This is in contrast to an acute triangle, where all three altitudes intersect inside the triangle.

Learn more about orthocenter

https://brainly.com/question/29576583

#SPJ4

How is the quotient of 874 and 23 determined using an area model?

Enter your answers in the boxes to complete the equations.
874 ÷ 23 = ( ÷ 23) + ( ÷ 23
874 ÷ 23 = +
874 ÷ 23 =

Answers

The quotient of 874 and 23 is 38.

How did get the values?

To get the quotient of 874 and 23 using an area model, create a rectangle with an area of 874 and divide it into 23 equal parts.

Each part would depict the value of one of the 23 groups that 874 is divided into. Then count how many of these equal parts fit into the rectangle and this would give the answer to the division problem.

The rectangle can be divided into 23 equal parts horizontally, and then count how many of these parts fit into the rectangle vertically. Start with one part and see how many times we can fit it into the rectangle vertically before reaching a total of 874.

874 ÷ 23 = ( 1 x 23) + ( 7 x 23)

874 ÷ 23 = 23 + 161

874 ÷ 23 = 38

So the quotient of 874 and 23 is 38.

learn more about quotient: https://brainly.com/question/11995925

#SPJ1

Sphere A is similar to Sphere B. The scale factor of the lengths of the radii of Sphere A to Sphere B is 4. Sphere A has the radius of 6 units and a volume of 288pi cubic units. Find the volume of Sphere B

Answers

The volume of the sphere B is 14.13 cubic units.

Given that the two similar spheres, the scale factor of the lengths of the radii of Sphere A to Sphere B is 4.

So, we need to find the volume of the sphere B,

So,

Radius A / Radius B = 4/1

6 / Radius B = 4

Radius B = 1.5

Now we know that the volume of a sphere = 4/3 × πr³

= 4/3 × 3.14 × 1.5³

= 42.39/3

= 14.13

Alternatively, you can calculate by =

We know that the ratio of the volumes of two similar solids is equal to the cube of their scale factor, so here, the scale factor is 4/1.

Therefore,

Volume A / Volume B = (4/1)³

288π / Volume B = 64

Volume B = 4.5π

Volume B = 14.13

Hence, the volume of the sphere B is 14.13 cubic units.

Learn more about volume click;

https://brainly.com/question/13338592

#SPJ1

the side length of a rectangle is 5 more than three times the width. the side length has a measure of 65cm. what is the length of the width

Answers

Answer:

the width is 20cm

Step-by-step explanation:

According to the question the length is 5 more than three times the width which is 3 times the width plus 5 so you have to minus five from the length and divide your answer by three

Answer:

The width is 20 cm.

Step-by-step explanation:

Let w represent the measure of the width.

5 + 3w = 65

-5            -5

___________

3w = 60

÷ 3     ÷3

_______

w = 20 cm

the number of points held by a sample of the nhl's highest scorers for both the eastern conference and the western conference is shown below. at , can it be concluded that there is a difference in means based on these data? assume the variables are normally distributed and the variances are unequal.

Answers

If the null hypothesis is rejected, then you can conclude that there is a difference in means based on the provided data. If not, then there isn't enough evidence to support a difference in means.

if there is a difference in means between the number of points held by a sample of NHL's highest scorers in the Eastern and Western conferences. To answer this, you'll need to follow these steps:

1. Identify the data: You need to have the points data for the NHL's highest scorers from both the Eastern and Western conferences.

2. Calculate the means: Calculate the average number of points for both conferences' samples.

3. Determine the variables: Since you've mentioned that the variables are normally distributed and have unequal variances, we can use the independent two-sample t-test with unequal variances (Welch's t-test) to determine if there is a significant difference in means.

4. Perform Welch's t-test: Using the means, variances, and sample sizes of both groups, calculate the t-value and degrees of freedom.

5. Compare the t-value to the critical t-value: Determine the critical t-value at a specified significance level (commonly α = 0.05) using the degrees of freedom. If the calculated t-value is greater than the critical t-value, you can reject the null hypothesis and conclude that there is a significant difference in means.

To know more about Mean Visit:

https://brainly.com/question/31101410

#SPJ11

(L3) A segment that extends from the vertex of a triangle to the opposite side and is perpendicular to the side is called the _____ of the triangle.

Answers

(L3) A segment that extends from the vertex of a triangle to the opposite side and is perpendicular to the side is called the incenter of the triangle.

The incenter of a triangle is an important point that can be constructed by drawing a perpendicular line from each vertex of the triangle to the opposite side, and then finding the intersection of these lines. This intersection point is equidistant from the three sides of the triangle, and is therefore the center of the circle that can be inscribed within the triangle.

The incenter also has the property that it is the point of concurrency of the angle bisectors of the triangle, meaning that it is equidistant from the three angles of the triangle as well. The incenter is used in a variety of geometric constructions and proofs, including the construction of the inscribed circle and the solution of problems involving the ratio of the sides of a triangle.

Learn more about perpendicular

https://brainly.com/question/18271653

#SPJ4

Carl has $500 in an account. Every 30 days, he withdraws $100. The amount of money remaining in his account is a function of the amount of time that has passed.


Which function models the amount of money remaining in Carl's account?

Answers

The function that models the amount of money remaining in Carl's account is [tex]M(t) = -100t + 500[/tex]..

What function models the amount of money remaining?

We will start by finding out how much money Carl will have left after each withdrawal:

After 30 days:

= $500 - $100

= $400

After 60 days:

= $400 - $100

= $300

After 90 days:

$300 - $100

= $200

After 120 days:

= $200 - $100

= $100

After 150 days:

= $100 - $100

= $0

We can see that Carl 5 withdrawals of $100 each over 150 days. So, we can use a linear function to model the amount of money remaining in Carl's account over time which is M(t) = -100t + 500.

Read more about function

brainly.com/question/11624077

#SPJ4

stimulates controlled lowering of the foot during 1st ankle rocker

Answers

stimulates controlled lowering of the foot during 1st ankle rocker bottom sole The controlled lowering of the foot during the first ankle rocker is facilitated by the activation of the tibialis anterior muscle.

This muscle is located in the anterior compartment of the leg and is responsible for dorsiflexion of the ankle joint, which means it lifts the foot upwards towards the shin. However, during the first ankle rocker, the tibialis anterior is activated eccentrically, which means it contracts while lengthening, to control the lowering of the foot towards the ground. This eccentric contraction of the tibialis anterior slows down the rate of plantarflexion and helps to maintain a smooth and controlled descent of the foot, allowing for a controlled heel strike and efficient transfer of weight to the forefoot.

Learn more about anterior muscle.

https://brainly.com/question/15071671

#SPJ4

Full Question

stimulates controlled lowering of the foot during 1st ankle rocker______

5√17− 4
is rationalized by multiplying the numerator and denominator by what?

Answers

To rationalize the expression,5√17− 4, we multiply the numerator and denominator by √17

What are surds?

Surds are simply defined as those values found in square root and which cannot be further simplified into whole numbers or integers alike.

Examples of surds are;

√3, √5, √7

In rationalizing surds, we want to achieve that no surd forms are found as the denominator of a fraction.

Thus, we have that;

Example;

3/√3

To rationalize, we have;

3√3/√3 × √3

Multiply the values, we get;

3√3/3

Divide the values, we get;

√3

Learn more about surds at: https://brainly.com/question/840021

#SPJ1

Subtract

4
+
4

2

2

2

4
a
4
+4a
2
b
2
−2b
4
a, start superscript, 4, end superscript, plus, 4, a, squared, b, squared, minus, 2, b, start superscript, 4, end superscript from

3

4
+
5

2

2
+
2

4
−3a
4
+5a
2
b
2
+2b
4
minus, 3, a, start superscript, 4, end superscript, plus, 5, a, squared, b, squared, plus, 2, b, start superscript, 4, end superscript.
Your answer should be a polynomial in standard form.

Answers

The expressions are subtracted to give -a⁴ + a²b² + 4b⁴

What are algebraic expressions?

It is important to note that algebraic expressions are described as expressions that are made up of terms, variables, constants, coefficients and factors.

These expressions are also identified with arithmetic operations. These operations are;

SubtractionBracketParenthesesDivisionMultiplicationAddition

From the information given, we have that;

4a⁴ + 4a²b² - 2b⁴

3a⁴ + 5a²b² + 2b⁴

Now, subtract the expressions;

3a⁴ + 5a²b² + 2b⁴ - (4a⁴ + 4a²b² - 2b⁴)

expand the bracket

3a⁴ + 5a²b² + 2b⁴ - 4a⁴ - 4a²b² + 2b⁴

add  the  values

-a⁴ + a²b² + 4b⁴

Learn more about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

use spherical coordinates.evaluate x2 dv,e where e is bounded by the xz-plane and the hemispheres y

Answers

∫∫∫ x² dv over the region e is (3/40) a⁵ π².

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

To use spherical coordinates, we need to express the volume element dv in terms of ρ, θ, and φ, where ρ is the radial distance from the origin, θ is the angle in the xy-plane measured from the positive x-axis, and φ is the angle measured from the positive z-axis.

We have x² = ρ² sin²(φ) cos²(θ). The volume element dv can be expressed as dv = ρ² sin(φ) dρ dφ dθ.

The region e is bounded by the xz-plane and the hemispheres y = ±√(a² - x²), where a > 0.

Since we're only interested in the part of e that lies in the first octant, we can restrict θ to the range [0, π/2] and φ to the range [0, π/2].

Note that since y is always positive in the first octant, we don't need to consider the negative hemisphere.

So, the integral we need to evaluate is:

∫∫∫ x² dv

= ∫[0,π/2]∫[0,π/2]∫[0,a] (ρ² sin³(φ) cos²(θ)) ρ² sin(φ) dρ dφ dθ

= ∫[0,π/2]∫[0,π/2]∫[0,a] ρ⁴ sin⁴(φ) cos²(θ) dρ dφ dθ

= ∫[0,π/2]∫[0,π/2] [(1/5)ρ⁵ sin⁴(φ) cos²(θ)]|[0,a] dφ dθ

= (1/5) a⁵ ∫[0,π/2] cos²(θ) dθ ∫[0,π/2] sin₄(φ) dφ

= (1/5) a⁵ [(1/2)π] [(3/4)(π/2)] = (3/40) a⁵ π².

Therefore, ∫∫∫ x² dv over the region e is (3/40) a⁵ π².

To know more about volume visit:

https://brainly.com/question/463363

#SPJ4

A club with 20 women and 17 men needs to choose three different members to be president,vice president and treasurer.¡) How many ways to choose president, vice president and treasurer?il How many ways to choose president, vice president and treasurer if man must bechosen as a president?iii) How many ways to choose president, vice president and treasurer if woman must bechosen as a president and vice president while man must be chosen as a treasurer?

Answers

i) 46,860 ways  to choose president, vice president and treasurer

ii) 21,420 ways to choose president, vice president and treasurer if man must bechosen as a president

iii) 6,460 ways to choose president, vice president and treasurer if woman must bechosen as a president and vice president while man must be chosen as a treasurer.

i) To choose the president, vice president and treasurer from a total of 37 members, we can use the permutation formula,

P(37,3) = 37 × 36  ×35 = 46,860.

Therefore, there are 46,860 ways to choose the three positions.

ii) If a man must be chosen as president, we have 17 options to choose the president from the male members. The remaining two positions can be filled by any of the 36 members. so we have

P(36,2) = 36 × 35 = 1,260

ways to fill those positions. Therefore, there are

17 × 1,260 = 21,420

ways to choose the three positions with a man as president.

iii) If a woman must be chosen as the president and vice president, we have 20 options to choose the president from the female members and 19 options to choose the vice president from the remaining female members. For the position of treasurer, we have 17 options to choose from the male members. Therefore, we have

20 × 19 × 17 = 6,460

ways to choose the three positions with a woman as president and vice president and a man as treasurer.

In summary, there are 46,860 ways to choose the three positions without any restrictions, 21,420 ways to choose with a man as president and 6,460 ways to choose with a woman as president and vice president and a man as treasurer.

To know more about treasurer visit

https://brainly.com/question/12314666

#SPJ4

this histogram shows the yearly number of unprovoked attacks by alligators on people in florida over 33 years. what is the midpoint of the yearly number of unprovoked alligator attacks?

Answers

The midpoint of the yearly number of unprovoked alligator attacks can be calculated by finding the class interval that contains the median value. In this histogram, the class intervals are not provided, so we cannot determine the exact midpoint.

However, we can estimate the midpoint by visually locating the point where the histogram is balanced or roughly in the middle. Based on the histogram, it appears that the midpoint is around 6-8 attacks per year.
The midpoint of the yearly number of unprovoked alligator attacks in Florida over 33 years can be found by first identifying the highest and lowest number of attacks in the histogram. Once you have those values, add them together and divide by 2 to find the midpoint.

Visit here to learn more about midpoint brainly.com/question/28224145

#SPJ11

(L1) What statement in the Converse of the Angle Bisector Theorem tells you that the point must be in the same plane as the angle?

Answers

The Converse of the Angle Bisector Theorem states that if a point is in the same plane as an angle and divides the angle into two congruent angles, then it lies on the angle's bisector.

The fact that the converse states that the point must be in the same plane as the angle implies that if the point is not in the same plane as the angle, then it cannot divide the angle into two congruent angles, and thus cannot lie on the angle's bisector.

The Angle Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides of the triangle. The converse of this theorem states that if a point on the interior of a triangle divides one side of the triangle into two segments that are proportional to the other two sides, then the point lies on the bisector of the angle opposite the divided side.

To understand why this implies that the point must be in the same plane as the angle, we need to consider the definition of a plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions.

It is determined by any three non-collinear points in space. In the context of a triangle, the three vertices of the triangle are non-collinear points that determine a plane.

for such more question on  Angle Bisector Theorem

https://brainly.com/question/28565813

#SPJ11

A person 2 meters tall walks directly away from a streetlight that is 8 meters above the ground. if the person is walking at a constant rate and the person's shadow is lengthening at the rate of meters per second, at what rate, in meters per second, is the person walking?

Answers

The person is walking away from the streetlight at a rate of 0.16 meters per second.

We can use similar triangles to solve this problem. Let the length of the person's shadow be x meters. Then, we have the following ratio:

(person's height)/(length of person's shadow) = (distance from person to streetlight)/(height of streetlight)

or

2/x = d/8

where d is the distance from the person to the streetlight.

Now, let's take the derivative of both sides with respect to time t:

(2/x^2) (dx/dt) = (1/8) (dd/dt)

where dx/dt is the rate at which the person's shadow is lengthening, and dd/dt is the rate at which the person is moving away from the streetlight.

Solving for dd/dt, we get:

dd/dt = (2/x^2) (dx/dt) (8)

Substituting x = 10 (since the person's shadow is lengthening at a rate of 1 meter per second, it will be 10 meters long after 10 seconds), and dx/dt = 1, we get:

dd/dt = (2/100) (1) (8) = 0.16 meters per second

Therefore, the person is walking away from the streetlight at a rate of 0.16 meters per second.

To know more about rate  click on below link :

https://brainly.com/question/12999942#

#SPJ11

Select the TRUE statements: a A sufficiently large sample size for the central limit theorem is greater than 30 b The variability of sampling distribution of the mean (X-bar) is less than the variability of the individual observations (X) c A sufficiently large sample size for the central limit theorem is greater than 50 d The variability of sampling distribution of the mean (X-bar) is more than the variability of the individual observations (X)

Answers

The true statements are:

b. The variability of the sampling distribution of the mean ([tex]\overline x[/tex]) is less than the variability of the individual observations (x)

a. A sufficiently large sample size for the central limit theorem is greater than 30.

The central limit theorem:

The CLT states that if a sample is drawn randomly from any population, the distribution of sample means will approach a normal distribution, regardless of the shape of the population distribution, as the sample size increases.

This means that for large enough sample sizes, the mean and standard deviation of the sample mean can be estimated using a normal distribution.

Let's check each option as follows  

Statement c is false because a sample size of 30 or greater is often considered sufficiently large for the central limit theorem.

Statement d is false because the variability of the sampling distribution of the mean decreases as the sample size increases, which is why the central limit theorem is useful.

Therefore,

The true statements are:

b. The variability of the sampling distribution of the mean (X-bar) is less than the variability of the individual observations (X)

a. A sufficiently large sample size for the central limit theorem is greater than 30.

Learn more about Central limit theorem at

https://brainly.com/question/18403552

#SPJ4

On a game show, a contestant randomly chooses a chip from a bag that contains numbers and strikes. The theoretical probability of choosing a strike is 15. The bag contains 8 strikes. How many chips are in the bag?

Answers

There are approximately 53 chips in the bag.

How to determine many chips are in the bag

The theoretical probability of choosing a strike is given as 15, which can be written as 15/100 or 0.15 as a decimal.

Let's represent the number of chips in the bag with the variable "x". Since there are 8 strikes in the bag, the probability of choosing a strike can be expressed as 8/x.

we can write the equation: 8/x = 0.15

To solve for x, we can cross-multiply and simplify:

8 = 0.15x

x = 8/0.15

x = 53.33

Therefore, there are approximately 53 chips in the bag.

Learn more about theoretical probability at https://brainly.com/question/8652467

#SPJ1

a group of observations measured at successive time intervals is known as a(n) . a. trend component b. forecast c. additive time series model d. time series

Answers

The answer is d. time series, a  time series is a collection of observations that are measured at successive time intervals.

These observations are usually recorded at equal time intervals and are used to study patterns and trends over time. Time series data is used in a wide range of applications such as economics, finance, weather forecasting, and sales forecasting.

Time series analysis is the statistical method used to analyze time series data. It involves identifying patterns and trends over time, as well as forecasting future values based on past trends.

Time series models can be classified as either additive or multiplicative, depending on whether the components of the model are added or multiplied together. Trend, seasonal, and cyclical components are the main components of a time series model, and they help to explain the underlying patterns and trends in the data.

The goal of time series analysis is to use these components to develop a model that accurately describes the underlying patterns and trends in the data and to use that model to make forecasts of future values.

To know more about value click here

brainly.com/question/30760879

#SPJ11

The Blackburn family has a square field where they keep their cattle. The area of the field is 40,000 ft square, and Mr. Blackburn wants to put a fence diagonally through the field. What should the length of the fence be?

Answers

If area of cattle's "square-field" is 40000 ft², and Mr. Blackburn is constructing a fence diagonal in the field, then length of cattle field's fence should be 282.84 ft.

The area of the Blackburn's family cattle square-field is 40000 ft²,

So, We First, equate this area with area formula,

On Equating ,We get,

⇒ (side × side) = 40000,,

⇒ side is 200 ft,

Now, we substitute the "side-length" of field as 200 ft, in the formula for diagonal of a square,

we get,

⇒ Length of cattle-field's diagonal is = (side)√2,

⇒ Length of cattle-field's diagonal is = (200)√2,

⇒ Length of cattle-field's diagonal is ≈ 282.84 ft.

Therefore, the length of cattle field's fence is 282.84 ft.

Learn more about Area here

brainly.com/question/30578725

#SPJ1

Other Questions
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is feet more than the length of the shortest side. Find the dimensions if the perimeter is feet. based on the interactions between gatsby and daisy, what do you predict will happen next in the story? consider all five main characters: gatsby, daisy, nick, jordan, and tom. PD 3: Explain how various factors contributed to the American victory in the Revolution. for example, an environmental signal could be required to allow the activator into the nucleus, as is the case for yeast pho4. the activator binds to In 2012, gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that random samples of 100 respondents were selected from both vermont and hawaii. From the survey, vermont had 65. 3% who said yes and hawaii had 62. 2% who said yes. What is the value of the population proportion of people from hawaii who exercised for at least 30 minutes a day 3 days a week?. A brute-force attack against double DES would required how many decryptions? Be sure to refer to FirstAid for the histological changes in the cells lining our airway. Here's a verbal description of the changes that we see from trachea to alveolus: (answer this first: What's the last feature to disappear as the epithelium changes along the respiratory tube?) which statement about party identification and gender in the united states is most accurate? Core routers know where to route traffic by looking at the ___ ID of an IP datagram (Remember the different Classes) Space ahead of your vehicle is important in the event you need to stop or turn to avoid an obstacle that is in front of you.T/F How did Carl Rogers explain Generalized Anxiety Disorder? Money is used for buying and selling goods and is therefore considered what?. on june 19, year 1, an individual executed a short sale of 100 shares of stock at $10 per share. on june 19, year 2, the individual covered and delivered the 100 shares at $8 per share. what is the character of gain or loss on the short sale? Soviet Communism and Chinese Communism similarities.Between communism in the Soviet Union and China under Mao Zedong. Include at least five categories for comparison, and provide examples and evidence to support your findings. How, if at all, does the mathematical treatment of the survival component of fitness differ from the mathematical treatment of the replication component of fitness? People who knit are people without scarves. this categorical proposition is ane proposition. if you change the quantity, but not the quality, of the given categorical proposition, what will the resulting statement be? some people who knit are people without scarves. all people who knit are people without scarves. some people who knit are not people without scarves. the resulting statement is an proposition. what was lebron wade and bosh averaging in play time during the playoffs when they won a championship A $600,000 bond was retired at 102 when the carrying value of the bond was $622,000.The entry to record the retirement would include aa) gain on bond redemption of $12,000.b) loss on bond redemption of $10,000.c) loss on bond redemption of $12,000.d) gain on bond redemption of $10,000. What is one reason why expressways are safer than other roads? In 24 g of carbon ,how many number of carbon atoms.