A group consists of four men and six women. Five people are selected to attend a conference.
a. In how many ways can five people be selected from this group of ten​?
b. In how many ways can five women be selected from the six ​women?
c. Find the probability that the selected group will consist of all women.

Answer: d 6000 bytes

Step-by-step explanation: The web server will acknowledge 6000 bytes of information after receiving 4 packets of data from the PC. This is because 1 packet of data has a size of 1500 bytes. In a situation where the web server receives 4 of these, it is 1500 multiplied by 4 which is 6000 bytes. The window size of 6000 is there to try distract you from calculating the answer correctly, it serves as a misguidance.

The byte of information that the web server acknowledge is 6000 bytes.

From the information given, were told that the web server is utilizing a window size of 6,000 bytes when sending data and a packet size of 1,500 bytes.

The byte of information that'll be received will be:

= 1500 × 4

= 6000 bytes

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Could not do the 2nd one, but will update if I figure it out

To analyze each graph and determine the scenario it models, first, understand the variables on the axes. Label the x- and y-axis with the appropriate quantity and unit of measure. Finally, label each tick mark with the correct intervals based on the scale of the graph.

In order to analyze each graph and determine the scenario it models, we need to understand the information represented on the axes. The x-axis typically represents the independent variable, while the y-axis represents the dependent variable. For example, in a graph showing time on the x-axis and distance on the y-axis, we can determine if the scenario is representing a moving object and measure the time intervals along the x-axis and the distance intervals along the y-axis.

Once we understand the variables represented on the axes, we can label them accordingly. For instance, if the x-axis represents time, we would label it as 'Time (seconds)' or 'Time (minutes)', depending on the unit of measure. Similarly, if the y-axis represents distance, we would label it as 'Distance (meters)' or 'Distance (kilometers)', again depending on the unit of measure.

We would then label each tick mark with the correct intervals based on the scale of the graph. For example, if the x-axis represents time and each tick mark represents 1 second, we would label each tick mark as '1s', '2s', '3s', etc. The same applies to the y-axis based on the unit of measure.

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Answer:

25 seconds

Step-by-step explanation:

Hi there!

In order to answer this question, first we need to know how many bolts per second are produced by each machine, this can be known by dividing the number of bolts by the time it takes.

For machine A:

[tex]A = \frac{120 bolts}{40 s}= 3 \frac{bolts}{s}[/tex]

For machine B:

[tex]B = \frac{100 bolts}{20 s}= 5 \frac{bolts}{s}[/tex]

So, if the two machines run simultaneously, we will have a rate of prodcution of bolts equal to the sum of both:

[tex]A+B=(3+5)\frac{bolts}{s}=8\frac{bolts}{s}[/tex]

Now, we need to know how much time it will take to producee 200 bolts, to find this out we need to divide the amount of bolts by the production rate:

[tex]t = \frac{bolts}{ProductionRate}= \frac{200 bolts}{8 \frac{bolts}{s} }[/tex]

The bolts unit cancell each other and we are left with seconds

[tex]t = \frac{200}{8} s = 25 s[/tex]

So it will take 25 seconds to produce 200 bolts with machine A and B running simultaneously.

Greetings!

Answer:

25 seconds.

Step-by-step explanation:

We have been given that Machine A produces bolts at a uniform rate of 120 every 40 seconds.

Bolts made by Machine A in one second would be [tex]\frac{120}{40}=3[/tex] bolts.

Machine B produces bolts at a uniform rate of 100 every 20 seconds.

Bolts made by Machine B in one second would be [tex]\frac{100}{20}=5[/tex] bolts.

The speed of making bolts in one second of both machines running simultaneously would be [tex]3+5=8[/tex] bolts per second.

[tex]\text{Time taken by both Machines to make 200 bolts}=\frac{200\text{ bolts}}{8\frac{\text{bolts}}{\text{Sec}}}[/tex]

[tex]\text{Time taken by both Machines to make 200 bolts}=\frac{200\text{ bolts}}{8}*\frac{\text{Sec}}{\text{bolts}}[/tex]

[tex]\text{Time taken by both Machines to make 200 bolts}=25\text{ Sec}[/tex]

Therefore, the both machines will take 25 seconds to make 200 bolts.

Answer:

Step-by-step explanation:

72/6=13

Answer:

Each person picked 12 bananas.

Step-by-step explanation:

Given,

Total numbers of banana = 72,

The number of persons = 6,

If each person picks equal number of bananas,

Then,

[tex]\text{Total bananas picked by each person}=\frac{\text{Total bananas}}{\text{Total persons}}[/tex]

[tex]=\frac{72}{6}[/tex]

= 12

The question revolves around basic algebra and setting up an equality equation based on the given information. In this case, from the facts given, we can state Mai's earnings (x) in terms of Noah's earnings plus an additional amount (y), resulting in the equation x = w + y.

The subject of this problem is algebra, specifically involving variables and the concept of equality. In this problem, Noah earned an amount we will denote as w dollars over the summer. Mai, on the other hand, earned x dollars, and it's said that this is an amount of y dollars more than Noah did.

We can express Mai's earnings in terms of Noah's earnings by adding the extra amount to what Noah earned, which gives us the following equality equation:

x = w + y

This equation means that Mai's earnings (x) are equal to the sum of Noah's earnings (w) and the additional amount (y).

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The component of A that is parallel to B can be found using the equation A_parallel to B = (A.B)/|B|. Therefore, the component of A parallel to B is A_parallel to B = Scalar product / |B|

The component of A that is parallel to B can be found using the equation:

Aparallel to B = (A.B)/|B|

where A.B is the dot product of vectors A and B and |B| is the magnitude of vector B.

Since the scalar product is equal to the magnitude of B times the component of A parallel to B, we can rewrite the equation as:

Scalar product = |B| * Aparallel to B

Therefore, the component of A parallel to B is:

Aparallel to B = Scalar product / |B|

Answer:

  8

Step-by-step explanation:

The coordinates of Preston's house are ...

  2J -E = P = 2(-5, 3) -(3, -2) = (-13, 8)

The y-coordinate of P is 8.

Relatively prime means there are no number greater than 1 that divides them both.

Find the GCF for each set:

A. 68 and 119

68: 1 , 2, 4, 17, 34,68

119: 1, 7, 17

Both numbers can be divided by 1 or 17 so are not relative.

B.

40 and 395

are both divisible by 1 and 5 so are not relative.

C. 119 and 715

Are both only divisible by 1, so are relative.

D. 63 and 56

Are divisible by both 1 and 7 so are not relative.

The answer is C. 119 and 715

Answer:

Step-by-step explanation:

y - 1 = 2(x + 8)

y - 1 = 2x + 16

y = 2x + 17

An equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1) is: B. y - 1 = 2(x + 8).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (-8, 1) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 2(x - (-8))

y - 1 = 2(x + 8)

In slope-intercept form, the equation of the line is given by;

y - 1 = 2x + 16

y = 2x + 16 + 1

y = 2x + 17

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Complete Question:

Which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1)?

A. y - 1 = 2(x - 8)

B. y - 1 = 2(x + 8)

C. y - 8 = 2(x + 1)

D. y - 8 = 2(x - 1)

Answer:  d. This study is best described as an experiment.

e. The explanatory variable is whether or not fertilizer X was used.

f. The response variable is the average height for each group of 10 plots.

Step-by-step explanation:

Given : A crop scientist is conducting research with a drought resistant corn hybrid.

She is interested in determining if using fertilizer X will increase plant height.

She prepares 20 single acre plots and randomly assigns 10 to have normal soil while the other 10 are planted with fertilizer X.

This study is best describe as an experiment because the scientist is experimenting about the increase in plant height with an generation of  20 single acre plots not like an observational study where the observer just observe the study without any influence.

Here the fertilizer is used to see the change in the plant height.

So, the explanatory variable is whether or not fertilizer X was used and the response variable is the average height for each group of 10 plots.

A square has all 4 sides equal, so divide the amount of fence available by 4 to get the length of one side of the square

600/4 = 150

Now since the creek is being used for one side, add one side of the square to the other side to get a rectagle 150 by 300 feet.

Area = 150 x 300 = 45,000 square feet.

The maximum possible area of the pasture is;

A_max = 45000 ft²

Available fencing; Perimeter = 600 feet

Number of sides to fence; 3 sides of rectangle

Perimeter of rectangle; P = 2L + 2W

But we are told one of the edges is the creek.

Thus, New perimeter = L + 2W

thus, we have;  L + 2W = 600

L = 600 - 2W

Let's put 600 - 2W for L in the area equation to get;

A = (600 - 2W)W

A = 600W - 2W²

Thus;

dA/dW = 600 - 4W

At dA/dW = 0, we have;

600 - 4W = 0

4W = 600

W = 600/4

W = 150 ft

Let's put 150 for W in L = 600 - 2W

L = 600 - 2(150)

L = 600 - 300

L = 300 ft

 Therefore, Maximum possible area of pasture = 300 × 150 = 45000 ft²

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Answer: True.

Step-by-step explanation:

Let [tex]\mu[/tex] be the population mean.

Given : Null hypothesis = [tex]H_0:\mu=160[/tex]

Alternative hypothesis =[tex]H_1:\mu<160[/tex]

Since , the alternative hypothesis is left-tailed, then the test is a left-tailed test.

The sample mean ([tex]\overlien{x}[/tex]) of the 80 students who were weighed was found to be 142 pounds and the p-value was 0.03.

We know that p-value gives that probability that if the null hypothesis is true, than the sample mean ([tex]\overlien{x}[/tex]) will be at least as small as the actual mean ([tex]\mu[/tex]).

It means that if the mean of all students’ weight is 160 lbs, then there would be only a 3% chance that a randomly selected group of 80 students would have a mean weight of less than 142 lbs.

Hence, the answer is "True".

Final answer:

The statement is true; a p-value of 0.03 indicates a 3% chance of observing a sample mean weight of 142 lbs or less if the true mean weight of all college students is 160 lbs, suggesting strong evidence against the null hypothesis.

Explanation:

The statement provided is true: if the null hypothesis is true (that college students' average weight is 160 lbs), there would only be a 3% chance that a random sample of 80 students would have a mean weight of 142 lbs or less. This small p-value (0.03) typically indicates strong evidence against the null hypothesis, suggesting that the average weight of college students is indeed less than the average American.

In other words, a p-value is the probability that we observe a sample statistic as extreme as the one measured (or more extreme) given that the null hypothesis is true. Taking another example to illustrate the concept: if the null hypothesis assumes no difference in the average height between male and female students, and we observe a sample where the difference is 4 inches with a p-value of 0.04, this means there's a 4% chance we would see at least this large a difference if in reality there was no difference at all.

Answer:

The answer to your question is: 165 in

Step-by-step explanation:

Data

1 cm --------------- 60 inches

If 1 side of the courtyard measures 2.75, what is the actual size of that side?

We can solve this problem with a rule of three

                     1 cm --------------------  60 inches

                    2.75 ---------------------    x

          [tex]\frac{2.75(60)}{1}[/tex]

= 165 inches

Answer:

x=8

Step-by-step explanation:

6. an odd-degree polynomial function.

   f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

Step by step explanation;

6. The graph represent an odd-degree polynomial function.

The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;

f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

Answer:

End behavior: [tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex]  and [tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]

The function has odd-degree.

The number of real zeros in 5.

Step-by-step explanation:

From the given graph it is clear that the graph approaches towards negative infinite as x approaches towards negative infinite.

[tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex]

The graph approaches towards positive infinite as x approaches towards positive infinite.

[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]

For even-degree the polynomial has same end behavior.

For odd-degree the polynomial has different end behavior.

Since the given functions has different end behavior, therefore the graph represents an odd-degree polynomial function.  

If the graph of a function intersects the x-axis at a point then it is a zero of the function.

If the graph of a function touch the x-axis at a point and return then it is a zero of the function with multiplicity 2. It means, the function has 2 equal zeros.

The graph intersect the x -axis at 3 points and it touch the x-axis at origin. So, the number of zeros is

[tex]N=3+2=5[/tex]

The number of real zeros is 5.

Hey!

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Question #1:

= 6n^2 - 2n - 3 + 5n^2 - 9n - 6

= 6n^2 + (-2n) + (-3) + 5n^2 + (-9n) + (-6)

= (6n^2 + 5n^2) + (-2n + -9n) + (-3 + -6)

= (11n^2) + (-11n) + (-9)

Answer: 11n² + (-11n) + (-9)

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Question #2:

= 8c^2 - c + 3 + 2c^2 - c + 2

= 8c^2 + (-c) + 3 + 2c^2 + (-c) + 2

= (8c^2 + 2c^2) + (-c + -c) + (3 + 2)

= (10c^2) + (-2c) + (5)

Answer: 10c² + (-2c) + 5

---------------------------------------------------------

Hope This Helped! Good Luck!

Answer:

1. 11n^2-11n-9

2. 10c^2-2c+5

Step-by-step explanation:

1. 6n^2+5n^2 = 11n^2

-2n-9n = -11n

-3-6=-9

2. 8c^2+2c^2 = 10c^2

-c-c= -2c

3+2=5

Answer:

Option C is the answer.

Step-by-step explanation:

Given diameter is = 2 miles

So, radius will be = 1  mile

Let t represents the number of hours it took Johanna to walk completely around the lake.

Now, the circumference is given as: [tex]2\pi r[/tex]

So, circumference = [tex]2(3.14)(1)[/tex] = 6.28 miles

Johanna's speed = 3 miles/ hour

We know the formula [tex]Time=Distance / Speed[/tex]

t = [tex]6.28/3[/tex]

t = 2.09 hours

This is greater than 2, but less than 2.5, therefore, 2.0 < t < 2.5 is the answer.

Answer:

Asset B generate most benefit.

Step-by-step explanation:

Correlation shows the strength of relation between two variables.

Greater the correlation coefficient greater the strength between two variables.

Since here It is given that Correlation Coefficient between risk reduction and Asset B is higher (i.e. 60%) than the Correlation Coefficient between risk reduction and Asset A (i.e. 40%).

Thus, Asset B generate most benefit.

For risk reduction in a 2-asset portfolio, a lower correlation coefficient would be most beneficial, specifically one closer to -1. This is due to the fact that negative correlation allows for diversification, where one asset rises as the other falls, reducing overall volatility and risk.

In terms of reducing risk for a 2-asset portfolio, a lower correlation coefficient would generate the most benefit. This means two assets that tend not to move in the same direction at the same time. In other words, a negative correlation between Asset A and Asset B would be most beneficial for risk diversification. If Asset A goes up when Asset B goes down, and vice versa, these movements could cancel out and reduce the overall volatility of the portfolio.

Correlation coefficients range from -1 to +1. A coefficient of +1 indicates that the two assets move perfectly together, i.e., they have a perfect positive correlation. A coefficient of -1 means that the two assets move perfectly oppositely, i.e., they have a perfect negative correlation. A coefficient near zero indicates little or no correlation between the assets.

Therefore, the most useful correlation coefficient for risk reduction would be the one closer to -1. This is because the negative correlation coefficients allow for diversification – one asset zigging while the other is zagging – and this helps to provide a safety net against significant loss in the portfolio.

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Answer:

  20 1/4 ft

Step-by-step explanation:

Subtracting the four given lengths from 75 feet will tell you how much is left.

  75 - (12 1/3 +16 1/6 +11 3/4 +14 1/2) = 75 -54 3/4 = 20 1/4

Gabriel has 20 1/4 ft of material left for his 5th banner.

After adding the lengths of the first four banners, we subtract that number from the total material Gabriel originally had. Gabriel has 20 13/24 feet of material left for the fifth banner.

To determine the amount of material left for the fifth banner, we first have to add the lengths of the four banners that Gabriel has already made. These lengths are 12 1/3 ft., 16 1/6 ft., 11 3/4 ft., and 14 1/2 ft. We add these four values together:

12 1/3 + 16 1/6 + 11 3/4 + 14 1/2 = 54 11/24 ft.

Gabriel originally had 75 feet of material, so to find out how much is left for the fifth banner, we subtract the total length of the first four banners from the original amount:

75 - 54 11/24 = 20 13/24 ft.

So, Gabriel has 20 13/24 ft. of material left for the fifth banner.

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Answer:

y - 1 = -4(x - 7).

Step-by-step explanation:

Point-slope equation is:

y - y1 = m(x - x1)  where m = the slope and (x1, y1) is a point on the line.

Here m = -4 , x1 = 7 and y2 = 1, so:

y - 1 = -4(x - 7).

An equation of the line in point-slope form is: D. y - 1 = -4(x - 7).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

x and y represent the data points.

m represent the slope.

At data point (7, 1) and a slope of -4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -4(x - 7)  

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let's bear in mind that B is the midpoint and thus it cuts a segment into two equal halves.

[tex]\bf \underset{\leftarrow \qquad \textit{\large 10x-6}\qquad \to }{\boxed{A}\stackrel{4x+2}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\underline{4x+2}}{\rule[0.35em]{10em}{0.25pt}\boxed{C}}} \\\\\\ AC=AB+BC\implies 10x-6=(4x+2)+(4x+2)\implies 10x-6=8x+4 \\\\\\ 2x-6=4\implies 2x=10\implies x=\cfrac{10}{2}\implies x= 5 \\\\[-0.35em] ~\dotfill\\\\ AC=(4x+2)+(4x+2)\implies AC=[4(5)+2]+[4(5)+2] \\\\\\ AC=22+22\implies AC=44[/tex]

This is a geometry problem, specifically involving the calculation of lengths using the properties of midpoints. A midpoint divides a line into two equal lengths. The problem is solved by equating the length of AB to half of AC to determine the value of x, which is then substituted back into the equation for AC to find its length.

The solution to your problem involves understanding that Point B is the midpoint of AC. A midpoint essentially divides a line into two equal lengths. Therefore, AB is equal to BC which can also be referred to as (AC/2). If AB = 4x+2 and AC = 10x-6, then to solve for the value of x, you would need to equate (4x+2) to (10x-6)/2. After solving this equation, the value of x can then be substituted back into the equation of AC to get the length of AC.

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Answer:

  42 minutes

Step-by-step explanation:

time = distance / speed

time = (7/8 mi)/((1 1/4 mi)/(60 min)) = 60×(4/5)(7/8) min = 42 min

Answer:

For 2 months

Step-by-step explanation:

Let after x months the cost of each health club is same,

Now, In club A,

Membership fees = $ 19,

Monthly fees = $ 21,

So, the total fees for x months = membership fees + total monthly fees for x months

= 19 + 21x

In Club B,

Membership fees = $ 23,

Monthly fees = $ 20,

So, the total fees for x months = membership fees + total monthly fees for x months

= 23 + 20x

Thus, we can write,

19 + 21x = 23 + 20x

21x - 20x = 23 - 21

x = 2

Hence, for 2 months the total cost of each health club would be same.

Answer:

The answer to your question is: lost 70 games; played 154 games

Step-by-step explanation:

Data

Won 84 games

Won 14 more games than it lost

There was no toes.

# of games did the team lose?

# of games did it play?

Process

             games lost = games won - 14

             games lost = 84 - 14

             games lost = 70

# of games played = games won + games lost

# games played = 84 + 70

                           = 154

Answer:

Whittingham's time through the 200 m was 5.55 seconds.

Step-by-step explanation:

Huber's peed = 200m / 6.509s = 30.72m/s

1 meter per second = 3.6 km per hour

30.72 m/s =  [tex]30.72\times36.=110.6[/tex] km/hr

Sam's speed is 110.6 + 19 = 129.6 km/hr

1 km per hour = 0.2778 meter per second.

So, 129.6 km/hr = [tex]129.6\times0.2778[/tex]= 36m/s

So, Sam Whittingham's time through the 200 m was =

[tex]\frac{200}{36}= 5.55[/tex] seconds.

Final answer:

Chris Huber's average speed was 30.73 m/s. Sam Whittingham beat this by 19.0 km/h, or 5.28 m/s, totaling to an average speed of 35.01 m/s. Whittingham's time for the 200m stretch was thus approximately 5.71 seconds.

Explanation:

To calculate Sam Whittingham's time through the 200 m stretch, we first need to find Chris Huber's average speed during his record-setting ride. Huber's time was 6.509 seconds for a 200 meter stretch, giving us an average speed of 200 m / 6.509 s ≈ 30.73 m/s. Whittingham beat Huber's record by 19.0 km/h. Since 1 km/h is approximately 0.27778 m/s, a 19.0 km/h increase translates to 19.0 km/h * 0.27778 m/s/km/h ≈ 5.28 m/s. Therefore, Whittingham's average speed was 30.73 m/s + 5.28 m/s = 35.01 m/s.

To find Whittingham's time for the 200 m stretch, we divide the distance by his average speed.
Time = Distance / Speed
Time = 200 m / 35.01 m/s ≈ 5.71 seconds.

Therefore, Sam Whittingham's record-breaking time through the 200-meter distance was approximately 5.71 seconds.

Answer: There are 241 red candies in the bowl. 482 Green candies in bowl.

Step-by-step explanation:

241 (is the answer) x2= 482. There's TWICE as many green as there is red, since there is 241 red candies, we multply that by two (482). Now let's add to check if it is correct. 241+482= is indeed 723.

Answer:

red = 241

green = 482

Step-by-step explanation:

The total = 723

red candies = x

green candies = y

⇒ x + y =723

There are twice as many green candies as red candies.

this means: y = 2x

x + y = 723

x +2x = 723

3x = 723

x = 241

y = 723 - 241 = 482

To control this y = 2x ⇒ 482 = 2 * 241

This means that there 241 red candies and 482 green candies.

Answer:

Tension in each half of the clothesline is 25 kg

Step-by-step explanation:

When the middle of the line is pulled down  a right triangle is formed in each half of the rope whose legs measure 0.1 m and 5 m respectively.

Since the rope has an insignificant sag, the measure of the hypotenuse of the triangle is approximately equal to that of the longer leg.

The value of the rope tension is equal to the value of the force applied divided by the sine value of the angle of the rope with the horizontal.

So,

[tex]Sin (a)=\frac{0.1}{5} = 0.02[/tex]

T=[tex]\frac{0.5 kg}{0.02}=25kg[/tex]

Answer:

The answer to your question is letter: c) √106 units

Step-by-step explanation:

data

B (5, 3)

D (-4 , -2)

Formula

d = √((x2-x1)² + (y2-y1)²)

dBD = √(-4-5)² + (-2-3)²)

dBD = √(-9)² + (-5)²

dBD = √81 +25

dBD = √106 units

Answer:

D

Step-by-step explanation:

[tex]4=r cos \theta\\-4=r sin \theta\\square ~and~add\\16+16=r^2(cos^2 \theta+sin^2\theta)\\r^2=32\\ r=4\sqrt{2} \\divide \\tan \theta=-1\\as x is positive ,y is negative ,so \theta lies in 4th quadrant.\\tan \theta=-1=-tan 45=tan(360-45)=tan 315\\\theta=315°\\\\co-ordinates~ are~(r,theta) ~or~(-r,\theta+ -180°)\\hence ~co-ordinates~are(4\sqrt{2} ,315°),(-4\sqrt{2} ,135°)[/tex]

Answer:

  D)  26 miles per gallon

Step-by-step explanation:

To find miles per gallon, divide miles by gallons:

  Lily's miles/gallon = (52 miles)/(2 gallon) = 26 miles/gallon

_____

Comment on the answer choices

Unless Lily's car manufactures gas, her mileage will not be negative miles per gallon.