in how many ways can a president, vice-president, and treasurer be chosen from a group of 4 freshmen and 4 sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions? on person cannot serve in more than one position

Answer:

B

Step-by-step explanation:

We start by trying out option A

2(1) + 3(3) = 9

1 + 5(3) = 15

9 and 15 are not equal to one another.

This means it has to be the other option, B.

Answer:

Step-by-step explanation:

Answer:

Area A, is x times y

Step-by-step explanation:

To find the area you must multiply the light x width of a rectangle or square

um.... kauser is this u

Answer:its hard to say

The number of fluids remaining after x weeks is given by the following equation:

y = 100 - 9x.

Hence the number of fluids remaining after week x is found replacing x by the week at the above equation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For this problem, the parameters are given as follows:

Hence the function is given as follows:

y = 100 - 9x.

The problem is incomplete, hence the function used to obtain the amounts is presented.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-8}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{(-4)}}} \implies \cfrac{-11}{-6 +4} \implies \cfrac{ -11 }{ -2 } \implies \cfrac{11 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-7}-\underset{x_1}{(-7)}}} \implies \cfrac{2 +1}{-7 +7} \implies \cfrac{ 3 }{ 0 } \implies \stackrel{\textit{vertical line}}{{\Large \begin{array}{llll} unde fined \end{array}}} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{9}}} \implies \cfrac{ 0 }{ -15 } \implies \stackrel{\textit{horizontal line}}{\text{\LARGE 0}}[/tex]

keep in mind that whenever you notice the x-coordinates are the same, it's a vertical line, and whenever the y-coordinates are the same, is a horizontal line.

For the given table -

The equation for line of best fit is Y = -1.000 · X + 11.25.

The correlation coefficient is -0.443533.

x and y have negative and strong correlation.

What is correlation coefficient?

A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.

The table of data is given.

The formula for equation of the line of best fit is -

Y = b·X + a

On adding the values in a graphing calculator the equation is -

Y = -1.000 · X + 11.25

Here, the slope is -1 and y-intercept is 11.25.

The formula for correlation coefficient is -

r = [n(∑xy) - (∑x)(∑y)] / [n∑x² - (∑x²)][n∑y² - (∑y²)]

n = Number of values or elements

∑x = Sum of 1st values list

∑y = Sum of 2nd values list

∑xy = Sum of the product of 1st and 2nd values

∑x² = Sum of squares of 1st values

∑y² = Sum of squares of 2nd values

For the given table the values are -

n = 8, ∑x = 68, ∑y = 22, ∑xy = 145, ∑x² = 620, ∑y² = 274

Plug in all the values in the equation -

r = [8(145) - (68)(22)] / [8(620) - (620)][8(274) - (274)]

r = -0.443533

When the values of two variables grow while one variable's values fall. The correlation coefficient would be negative in that situation.

The weak and adverse association is indicated by the coefficient's negative value. And if "r" keeps moving in the direction of -1, the relationship is moving in the negative direction.

Therefore, the equation is Y = -1.000 · X + 11.25 and r value is -0.443533.

To learn more about correlation coefficient from the given link

https://brainly.com/question/27842223

#SPJ1

The ratio of hours spent at soccer practice to hours spent at a birthday party are 2 for every 3.

What is a ratio?

A ratio is produced by comparing or condensing two related pieces of data. Looking at the reciprocity of the relationship allows us to calculate the number of times one quantity is equal to another. To put it simply, a ratio is a number that can be used to represent one thing as a proportion of another.

We are given that for soccer practice, Sara spends 2 hours and for birthday party, she spends 3 hours.

So, the ratio of hours spent at soccer practice to hours spent at a birthday party is  2 for every 3.

Hence, the ratio is  2 for every 3.

Learn more about ratio from the given link

https://brainly.com/question/12024093

#SPJ1

Question: The table shows how many hours Sara spent at several activities one Saturday.

Activity "Hours

Soccer practice 2

Birthday party 3

Science project 1

What is the ratio of hours spent at soccer practice to hours spent at a birthday party?

Choose 1 answer:

1 for every 2

2 for every 1

2 for every 3

3 for every 2

Answer:

The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where r is the radius and h is the height. In this case, the volume is 500 ml, or 0.5 liters. To convert liters to cm, we can use the conversion factor 1 liter = 10 cm^3. Therefore, the height of the jug can be calculated as follows:

0.5 liters = 0.5 x 10 cm^3 = 500 cm^3

V = πr^2h

500 = π x (3 cm)^2 x h

h = 500 / (π x (3 cm)^2)

Approximating π as 3.14, we get:

h = 500 / (3.14 x (3 cm)^2)

h = 500 / (3.14 x 9 cm^2)

h = 500 / 28.26 cm^2

h = 17.67 cm

So the height of the cylindrical measuring jug is approximately 17.67 cm. Therefore, the distance between each marking, which represents 100 ml of volume, is 17.67 cm / 5 = 3.534 cm.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

To determine the distance between each of the markings, we need to determine the height of the jug for each 100 ml increment.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. We know the volume of the jug is 500 ml, or 0.5 liters, and the radius is 3 cm, so we can solve for the height:

0.5 liters = π * (3 cm)^2 * h

h = 0.5 liters / π * (3 cm)^2

h = 0.5 liters / 9π cm^2

Now that we have the height of the jug per 100 ml, we can divide it by 5 to determine the height between each marking:

Marking height = h / 5

= 0.5 liters / 9π cm^2 / 5

= 0.1 liters / 9π cm^2

So the distance between each of the markings is the height of the jug for each 100 ml increment divided by 5.

Let's call the width of the rectangle "w".

According to the problem, the length of the rectangle is 12 meters more than 5 times the width, so we can write that as:

L = 5w + 12

And the area is given as 32 square meters, so we can write that as:

A = L * w = 32

Now we have two equations:

5w + 12 = L

L * w = 32

We can use the first equation to substitute the value of L in the second equation:

L = 5w + 12

32 = (5w + 12) * w = 5w^2 + 12w

Expanding the right side of the equation, we get:

32 = 5w^2 + 12w

Now we have a quadratic equation that we can solve for w. To do this, we can use the quadratic formula:

w = (-b ± √(b^2 - 4ac)) / 2a

where a = 5, b = 12, and c = -32. Plugging in these values, we get:

w = (-12 ± √(12^2 - 4 * 5 * -32)) / (2 * 5)

w = (-12 ± √(144 + 640)) / 10

w = (-12 ± √(784)) / 10

w = (-12 ± 28) / 10

w = (16 / 10) or ( -40 / 10)

w = 1.6 or -4

Since the width cannot be negative, the width must be 1.6 meters.

In a case whereby the  total mass of a box and some oranges was 25 kg. The total mass of the same box and some apples was 11 kg. The mass of the oranges was 3 times the mass of the apples, the mass of the oranges is 21kg.

The concept that will be used here is simplificatiopn.

We can set up as:

let a represent the box

let b represent the orange

lect c represent the apple

Then a + b = 25

a+ c = 11 ....................................................(2)

b = 3c.......................................(3)

substract equation 2 from 1

b-c = 11 ....................................(4)

substitute eqn 3 into 4

b-c = 14

3c - c =14

2c= 14

c= 7

from eqn 3

b = 3c

b = 3*7 =21

Then mass of orange = 21 kg

from  eqn 2

a+ c = 11

a= 11-7= 4

mass of empty box = 4kg

Learn more about mass at:

https://brainly.com/question/25959744

#SPJ1

The vertex form equivalent to the given expression; 2x² + 8x as required to be determined in the task content is; 2 (x + 2)² + 8.

The vertex form equivalent of the given expression can be determined as follows;

2x² + 8x

2 (x² + 4x)

2 ( (x + 2)² + 4)

= 2 (x + 2)² + 8.

Ultimately, the vertex form equivalent of the given expression as required is; 2 (x + 2)² + 8.

Read more on vertex form;

https://brainly.com/question/24850937

#SPJ1

Answer:

5024

Step-by-step explanation:

3903+2804= 6707

6707-1683=5024

Answer:

Graph C.

The question asks for the graph that consists of:

Non-negative values

Values that are, at most, 80

This means that any graphs where a value goes below 0 or above 80 do not work. C is the only graph that does not go below 0 or above 80.

Answer:

3/4 > 1/4

Step-by-step explanation:

3/4 is 75%, and 1/4 is 25 percent. 3/4 is greater than 1/4!

Service a has 75% of all the scheduled deliveries, and service b has the remaining 25%, their on-time rates are 80% and 60% respectively, the probability that a package is delivered on time is 0.75 or 75%.

To calculate the probability that a package is delivered on time, we need to use the law of total probability and the probabilities of on-time delivery for each messenger service.

Let A denote the event that a package is delivered by Service A, and B denote the event that a package is delivered by Service B. Then, we have:

P(on-time delivery) = P(on-time delivery | A) * P(A) + P(on-time delivery | B) * P(B)

where P(on-time delivery | A) is the probability that a package is delivered on time given that it was sent through Service A, and P(A) is the probability that a package is sent through Service A.

Similarly, P(on-time delivery | B) is the probability that a package is delivered on time given that it was sent through Service B, and P(B) is the probability that a package is sent through Service B.

From the information given in the question, we know that P(A) = 0.75, P(B) = 0.25, P(on-time delivery | A) = 0.8, and P(on-time delivery | B) = 0.6. Substituting these values into the above formula, we get:

P(on-time delivery) = 0.8 * 0.75 + 0.6 * 0.25

= 0.6 + 0.15

= 0.75

Intuitively, this result makes sense because Service A, which has a higher on-time rate and delivers 75% of the packages, dominates the total probability of on-time delivery. However, the contribution of Service B cannot be ignored completely and reduces the overall on-time rate slightly.

To learn more about probability click on,

https://brainly.com/question/17483505

#SPJ4

a. The probability of getting exactly 451 girls in 887 births is 0.0578.

b. The probability of getting 451 or more girls in 887 births is 0.0478. To determine if 451 girls in 887 births is unusually high, we compare this probability to a significance level (alpha) of choice and then either reject or accept the null hypothesis.

c. The probability from part (b) is more relevant for trying to determine whether the technique is effective because it considers a range of outcomes that are consistent with the hypothesis that boys and girls are equally likely.

d. Based on the​ results, we can reject the hypothesis that boys and girls are equally likely and conclude that the gender-selection technique is effective in increasing the likelihood of having a girl.

Probability is the likelihood of an event occurring or not occurring.

Mathematically;

a. To find the probability of getting exactly 451 girls in 887 births, we can use the binomial distribution with n = 887 and p = 0.5 (since boys and girls are equally likely).

The probability of getting k girls is given by the formula:

P(k girls) = (n choose k) * p^k * (1-p)^(n-k)

Plugging in the values, we get:

P(451 girls) = (887 choose 451) * 0.5^451 * 0.5^436

P(451 girls) = 0.0578 (rounded to four decimal places)

b. To find the probability of getting 451 or more girls in 887 births, we can add up the probabilities of getting 451, 452, 453, ..., up to 887 girls. The cumulative binomial distribution is used to determine the probability of getting k or fewer girls:

P(k or fewer girls) = sum((n choose i) * p^i * (1-p)^(n-i), i = 0 to k)

Since we want the probability of getting 451 or more girls, we can subtract the probability of getting 450 or fewer girls from 1:

P(451 or more girls) = 1 - P(450 or fewer girls)

= 1 - sum((887 choose i) * 0.5^i * 0.5^(887-i), i = 0 to 450)

= 0.0478

d. To determine if the gender-selection technique is effective, we need to compare the probability of getting 451 or more girls (from part (b)) to a significance level (alpha) of our choice.

Using an alpha set to 0.05, the probability of getting 451 or more girls in 887 births is 0.0478, it is less than 0.05. Therefore, we reject the hypothesis that boys and girls are equally likely and conclude that the gender-selection technique is effective in increasing the likelihood of having a girl.

Learn more about probability and binomial distribution at: https://brainly.com/question/9325204

#SPJ1

Answer:

The figure is made up of a rectangle and two triangles. The dimensions of the rectangle are 10 cm by 5 cm, so the area of the rectangle is 10 * 5 = 50 cm^2.

Each of the two triangles has a base of 4 cm and a height of 3 cm, so the area of each triangle is (1/2) * 4 * 3 = 6 cm^2. The total area of the two triangles is 2 * 6 = 12 cm^2.

The total area of the figure is the sum of the areas of the rectangle and the triangles: 50 + 12 = 62 cm^2.

Step-by-step explanation:

70 cm or 0.7 m

3.5 x 100 = 350

350 / 5 = 70

Answer:

the sum of 2rude 5 is 4.47-(answer)and the sum of 3 rude 7 is 7.79-(answer).

Hi there, here's your answer:

Given the question [tex]2\sqrt{5} + 3\sqrt{7}[/tex]

Since these two roots have no common factors, we can either leave the expression as it is, or simplify using the values of the roots.

In which case, [tex]\sqrt{5} = 2.236[/tex] and [tex]\sqrt{7} = 2.645[/tex]

On simplifying, we get

[tex]2\sqrt{5}[/tex] = 2 × 2.236 = 4.472

And

[tex]3\sqrt{7}[/tex] = 3 × 2.645 = 7.935

Thus, the sum will be 4.472 + 7.935 = 12.407

Hope it helps! Please mark as Brainliest!

Answer:

ED = 4 cm

Step-by-step explanation:

given 2 secants from an external point to the circle, then the product of one secant's external part and the entire secant is equal to the product of the other secant's external part and that entire secant, that is

CD × CE = CB × CA

8(8 + x) = 6(6 + 10) = 6 × 16 = 96 ( divide both sides by 8 )

8 + x = 12 ( subtract 8 from both sides )

x = ED = 4 cm

Answer:

SAS

Step-by-step explanation:

There are two pairs of congruent sides, and the pair of angles between the congruent sides is also congruent.

Number of cubes with edge length 1/2cm that fit in the prism is 11160 and the volume of the prism is 1395 cubic centimeter

Dimensions of the rectangular prism = [tex]7\frac{1}{2}[/tex] cm × 12 cm × [tex]15\frac{1}{2}[/tex] cm

Convert the mixed fraction to the simple fraction

The dimensions of the rectangular prism = 15/2 cm × 12 cm × 31/2 cm

The volume of the rectangular prism = w × l × h

Where

w is the width

l is the length

h is the height

The volume of the rectangular prim = 15/2 × 12 × 31/2

= 1395 cubic centimeter

The side off the cube = 1/2 cm

Volume of the cube = a^3

= (1/2)^3

= 0.125 cubic centimeter

Number of cubes will fit in rectangular prism = Volume of rectangular prism /  Volume of the cube

= 1395 / 0.125

Divide the terms

= 11160 cubes

Therefore, 11160 cubes will fit in the rectangular prism and the volume of the prism is 1395 cubic centimeter

Learn more about rectangular prism here

brainly.com/question/21308574

#SPJ4

The theater sold 30 adult tickets and 20 children tickets.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Let, The number of adult tickets be 'x' and the number of children tickets be 'y'.

Therefore, 10x + 5y = 400...(i) and x + y = 50...(ii)×10 ⇒ 10x + 10y = 500...(iii)

Now, Subtracting equation (i) from equation (iii) we have,

5y = 100.

y = 20, and hence x = 30.

So, They have sold 30 adult tickets and 20 children tickets.

learn more about linear equations here :

https://brainly.com/question/29739212

#SPJ1

Answer:

Step-by-step explanation:

We can start by finding the amount of water the leaky faucet loses in one hour:

5 gallons / 20 hours = 0.25 gallons per hour

This means that the leaky faucet loses 0.25 gallons of water every hour.

To find how many gallons of water the faucet will leak in 48 hours, we can multiply the rate of leakage per hour by the number of hours:

0.25 gallons/hour x 48 hours = 12 gallons

Therefore, the leaky faucet will lose 12 gallons of water in 48 hours.

Answer:

  x = 11

Step-by-step explanation:

You want to know the measure of x in a square marked with one portion of the bisected corner angle as being (6x -21)°.

We presume quadrilateral PQRS is a square, so each of the corner angles is 90°, and each of the diagonals bisects the corner angles. That mean ...

  (6x -21)° = 90°/2

  6x = 66 . . . . . . . . . . divide by °, add 21

  x = 11 . . . . . . . . . . . divide by 6

A right isosceles triangle is a triangle with a right angle (90 degrees) and two sides that are equal in length. This means that the triangle is also a special case of an isosceles triangle where the two equal sides are adjacent to the right angle.

To identify a right isosceles triangle among a group of shapes, you should look for the shape that has a right angle and two sides of equal length. One way to check for the right angle is to look for a corner that forms a square angle (i.e., 90 degrees), and one way to check for the equal sides is to compare the length of each side.

For such more question on triangle:

https://brainly.com/question/17335144

#SPJ4

The following question may be like this:

What is a right isosceles triangle?

From the following, a panel data set consists of data on the same cross-sectional units over a given period of time while a pooled data set consists of data on different cross-sectional units over a given period of time is the difference between panel and pooled cross-sectional data.

Panel data refers to samples of the same cross-sectional units observed at multiple points in time.

For example we will follow the same set of households X, Y and Z, for each time period we collect data i.e. in 1990 and we will also interview the same households in 1995.

Pooled data occur when we have a “time series of cross sections,” but the observations in each cross section do not necessarily refer to the same unit.

For example we will take household income data on households X, Y and Z, in 1990. And then we will take the same income data on households G, F and A in 1995. Although we are interested in the same data, we are taking different samples (using different households) in different time periods.

To know more about panel data

https://brainly.com/question/30657393

#SPJ4