A single serving of hot chocolate requires 0.75 cups of milk. Nina used 7 cups of milk to make hot chocolate for her 9 friends. Did she make enough for each friend to get a serving of hot chocolate?

The number of groups, using the combination formula, for each case, is given as follows:

a) Same number of students from each grade: 1,245,816,000

b) At least two grade nine students: 31,650,886,995.

c) James and Lucy are in it: 2,481,256,778.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

For item a, the groups are taken as follows:

Hence the number of groups is:

[tex]C_{10,3}C_{11,3}C_{12,3}C_{13,3} = \frac{10!}{7!3!} \times \frac{11!}{8!3!} \times \frac{12!}{9!3!} \times \frac{13!}{10!3!} = 120 \times 165 \times 220 \times 286 = 1,245,816,000[/tex]

For item b, the total number of groups, without considering the restriction, is:

[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]

The number of groups with none students from grade 9 is:

[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]

The number of groups with one student from grade 9 is:

[tex]C_{10,1}C_{36,11} = 10 \times \frac{36!}{11!25!} = 6,008,052,960[/tex]

Using complementary events, the number of groups with at least two grade 9 students is:

38,910,617,655 - (1,251,677,700 + 6,008,052,960) = 31,650,886,995.

For item c, considering Jamie and Lucy in it, the remaining 10 students are taken from a set of 44, hence:

[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]

More can be learned about the combination formula at https://brainly.com/question/11732255

#SPJ1

The number of guests at the wedding is 276.

Since 1/3 of the guests choose beef and 5/12 choose chicken, the fraction for vegetarian will be:

= 1 - (1/3 + 5/12)

= 1 - 3/4

= 1/4

Therefore, let the total number of guests be x.

This will be illustrated as:

1/4 × x = 69

0.25x = 69

Divide

x = 69 / 0.25

x = 276

Therefore, there are 276 guests.

Learn more about fractions on:

brainly.com/question/17220365

#SPJ1

If a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual percentage rate of growth is 9.6%

The initial population was 5000

The population in 2015 is 6000

let the rate of growth be r

aₙ = arⁿ-¹

6000 = 5000 r⁵⁻¹

6000/5000 = r⁴

6/5 = r⁴

r = 1.2⁻⁴

r = 0.48

r = 48%

the annual percentage rate of growth 48/5 = 9.6

Therefore, if a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual percentage rate of growth is 9.6%

To learn more about geometric progression refer here

https://brainly.com/question/24643676

#SPJ1

Answer:

==========================

The given function is the combination of three lines:

The values of the function at the given points are:

Answer:

Generally, more selective schools may require or recommend a writing score, while less selective ones may not (though there certainly are exceptions). It's worth noting that most schools no longer require the ACT with Writing, though many schools recommend it.

Step-by-step explanation:

Step-by-step explanation:

if p(A)=0.17, p(B)=0.42 and p(AorB)=0.59, are A and B mutually exclusive

The slope of the line is -3 and the equation of the line formed by the points is y + 3x = 6.

From the table we can see that the line passes through the points:

(-6,6) ,(5,-3) ,(4,0) and (3,3) .

Let us consider any two points on the line (4,0) and (3,3) .

We know that the slope of the line can be found by using the intercept formula

Hence slope = (3-0) / (3-4) = 3/ -1 = -3

Now the equation of the line is :

y - 3 = -3(x-3)

or, y - 3 = -3x +9

or, y + 3x = 6

The letter m is frequently used to represent the slope of an object that resembles a line in the plane that contains the x and y axes. The slope is defined as the difference in two independent locations along the line expressed in y coordinate less by the equivalent difference in x coordinate.

Therefore slope of the line is -3.

To learn more about slope visit:

https://brainly.com/question/11559942

#SPJ1

Answer:

1. Given.

2. Definition of congruent segments.

3. Segment Addition Postulate.

4. Substitution Property of Equality.

5. Transitive Property of Equality.

6. Subtraction Property of Equality.

7. Definition of congruent segments.

Step-by-step explanation:

Statement 1

[tex]\overline{AB} \cong \overline{CD}; \; \overline{CE} \cong \overline{AE}[/tex]

Reason:  Given.

Statement 2

[tex]AB=CD; \;CE=AE[/tex]

Reason:  Definition of congruent segments.

Congruent segments are segments that have the same length.

Statement 3

[tex]AE+EB=AB; \; CE+ED=CD[/tex]

Reason:  Segment Addition Postulate.

A line segment divided into smaller pieces is the sum of the lengths of all those smaller segments.

Statement 4

[tex]CE+EB=CD[/tex]

Reason:  Substitution Property of Equality.

For all numbers a and b, if a=b, then a may be replaced by b in any equation or expression.

Statement 5

[tex]CE+ED=CE+EB[/tex]

Reason:  Transitive Property of Equality.

For all numbers a, b and c, if a=b and b=c, then a=c.

Statement 6

[tex]ED=EB[/tex]

Reason:  Subtraction Property of Equality.

For all numbers a, b and c, if a=b, then a-c=b-c.

Statement 7

[tex]\overline{ED} \cong \overline{EB}[/tex]

Reason:  Definition of congruent segments.

Congruent segments are segments that have the same length.

Answer:

x = 4 ; y = -1

Step-by-step explanation:

y = -2x + 7

x + 2(-2x+7) = 2

x -4x + 14 = 2

-3x = 2 -14

-3x = -12

-3/-3 x = -12/-3

x = 4

y = -2* 4 + 7

y = -8 + 7

y = -1

According to the given depression angle, ship is 4.4 miles apart from ship B.

Depression angle:

Depression angle refer an angle that is formed with the horizontal line if the line of sight is downward from the horizontal line.

Given,

A pilot is flying over the ocean. She determines that the angles of depression to two ships are 74° and 48°, as shown in the figure below. The plane is 5 miles from the ship located at point A.

Here we need to find the distance between the two ships.

Here we know the following,

Distance between plane and Ship A = 5 miles.

And the depression angle = 74°, 48°

Let us consider the following, that they sit on a line,

So under this situations,

=> 80 - 48 - 74 = 58 degrees.

The next thing we have to do is bring this 74 degree angle inside the diagram. Because it is congruent to this interior angle because they are alternate.

Then it can be written as,

=> x = sin 74°/5

=> x = 4.4

Therefore, the two ships are 4.4 miles apart from each other.

To know more about Depression angle here.

https://brainly.com/question/13514202

#SPJ1

Answer:

12 inches

Step-by-step explanation:

Let be "x" the top inches (in the model) of a eighty four foot building.

According to the information provided in the exercise, we be aware of that the top of a two-story establishing is 21 toes and in the scale model its top is 3 inches.

Knowing this, we can set up the following proportion: 3/21=x/84

The final step is to get to the bottom of for "x" in order to calculate its value.

Answer:

Below

Step-by-step explanation:

The equation ( you need to commit to memory) is:

FV = PV ( 1+i)^n      FV = future value    PV = present value(110 000)

                               i = decimal interest per PERIOD = .08 /4 = .02

                                 n = # of periods = 40  (it is a quarterly period by 10 yrs)

FV = 110 000 ( 1 + .02)^40 =  242 884 .36 dollars

Answer: 25 1/3

Step-by-step explanation:

Answer:

124.644

Step-by-step explanation:

28.2*4.42=124.644.

Answer:

28.2 × 4.42= 124.644

and in non-decimal it's 124644 removing 3 decimal places

Step-by-step explanation:

Brainiest, please

thank you

[tex] \bold{1: 3a + 2a \: = 5a}[/tex]

[tex]\bold{2: - 5b - 7b = - 12b}[/tex]

[tex]\bold{3: - a {}^{2} - 9 a{}^{2} = - 10a {}^{2}}[/tex]

[tex]\bold{4: 3a {}^{x - 2} + 5a {}^{x - 2} = 8a {}^{x - 2}}[/tex]

[tex] \bold{5: 18x - 11x = 7x}[/tex]

[tex]\bold{6: 5a - 8a + a - 6a + 21a = 13}[/tex]

The reduction of similar terms is an operation that aims to convert two or more similar terms into a single term.

In these cases you must add or subtract either addition, subtraction or subtraction and addition, using the law of signs.

[tex]\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\bold{Law \: of \: signs: }} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times + = + \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \times + = - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times - = - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \times - = + \end{gathered} [/tex]

Answer:

x = 105

Step-by-step explanation:

To solve for x, we simply need to isolate it:

[tex]\frac{2}{7}x+\frac{1}{5}x=51\\ \frac{17}{35}x=51\\ x=105[/tex]

The simplest radical form of the radicals given are:

1. The simplest radical form of √175 is 5 √7.

2. The simplest radical form of √5 / 12 is √5 / 12.

First, let us understand the radical:

A radical can also be called a surd. A surd is an irrational number. We say that it is irrational because it can not be expressed as a terminating decimal.

1.

We are given:

√175

We need to write in the simplest radical form.

175 can be written as:

175 = 5 * 5 * 7

√175 = √ 5 * 5 * 7

√175 = √ 5 * 5 * √7

√175 = 5 √7

So, the simplest form of √175 is 5 √7.

2.

We are given:

√5 / 12

We need to write in the simplest radical form.

√5 / 12 is already in the simplest form.

So, the simplest form of √5 / 12 is √5 / 12.

Thus, the simplest radical form of the radicals given are:

1. The simplest radical form of √175 is 5 √7.

2. The simplest radical form of √5 / 12 is √5 / 12.

To learn more about radical visit:

https://brainly.com/question/15476889

#SPJ1

Answer:

63 is the answer.

Step-by-step explanation:

9p=9xp, p=7, so 9x7=63. ;)

Answer:

22.3 gm

Step-by-step explanation:

720 is this many half lives :   720 / 1690

   so there will be this much left   30 gm ( 1/2)^(720/1690) = 22.3 gm

The probability of drawing the Blue 4 is an example of .R′f.E′

Red cards = 1,2,3

Blue cards =1,2,3,4,5,6

Pr(R) =  Drawing a red card = 3/9 = 1/3

Pr(B)= Drawing a blue card = 6/9 = 2/3

Pr(E) = Drawing an even card = 4/9

Pr(O) = Drawing an odd number card = 5/9

Probability of drawing the blue 4 ? = Pr(blue, 4) = 1/9

From the options

(A) R or O = Pr(R) + Pr(O)  = 1/3 + 1/9 = 8/9 ........(Not equal to 1/9)

(B) B and O = Pr(B) × Pr(O) =  2/3 × 5/9 = 10/21......(Not equal to 1/9)

(C) R or E = Pr(R) + Pr(E) = 1/3 + 4/9 = 7/9.......(Not equal to 1/9)

(D) R and O = Pr(R) + Pr(O) = 1/3 × 5/9 = 5/27.......(Not equal to 1/9)

(E) R'. E' = 1-Pr(R)-1-Pr(E) =

                1-1/3 =2/3- 1-4/9 =5/9

               2/3-5/9 = 1/9......( equal to 1/9).

Hence, the probability of drawing the Blue 4 is an example of .R′f.E′

To learn more about probability refer here

https://brainly.com/question/24756209

#SPJ1

Disclaimer: the question given by you is incomplete, the solution is done as per a similiar question which is

A deck of cards contains RED cards numbered 1,2,3 and BLUE cards numbered 1,2,3,4,5,6. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.Drawing the Blue 4 is an example of which of the following events? Select all correct answers.Select all that apply:a.R OR Ob.B AND Oc.R OR Ed.R AND Oe.R′f.E′

Answer:

The slope of the line passing through the points [tex](-2, 2)[/tex] and [tex](-5, 5)[/tex] is equal to: [tex]-1[/tex]

Step-by-step explanation:

The slope of a line can be found with the following formula

[tex]m=\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where [tex]x_2 > x_1[/tex]

Then substituting the values ​​with the given ones we have

[tex]m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{2-5}{-2-(-5)}=\frac{-3}{-2+5}=\frac{-3}{3} =-1[/tex]

So the slope of the line passing through the given points is [tex]-1[/tex]

Answer:

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

Answer:

$1580.69

Step-by-step explanation:

Monthly Payment Formula

[tex]\sf PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}[/tex]

where:

Given:

Substitute the values into the formula to calculate the monthly payment:

[tex]\implies \sf PMT=\dfrac{12000(0.00415)\left(1+0.00415\right)^{60}}{\left(1+0.00415\right)^{60}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{49.8\left(1.00415\right)^{60}}{\left(1.00415\right)^{60}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{63.84764727}{0.2820812705}[/tex]

[tex]\implies \sf PMT=226.3448656[/tex]

Therefore, the total payments over the life of the loan is the monthly payment multiplied by the total number of months:

[tex]\implies \sf 226.3448656 \times 60=\$13580.69[/tex]

To calculate how much interest Jessie pays over the life of the loan, subtract the original loan amount from the total payments amount:

[tex]\implies 13580.69-12000=\$1580.69[/tex]

Therefore, the interest Jessie will pay over the life of the loan is $1580.69.

The difference between the cost of one candy per ounce and the other candy is that: Almond bark costs $0.50 more per ounce than peanut brittle.

Mathematically, a direct proportion can be represented the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for each candy as follows:

For Peanut Brittle, we have the following:

Constant of proportionality (k) = 10/10

Constant of proportionality (k) = 1.0

For Almond Bark, we have the following:

Constant of proportionality (k) = 3/2

Constant of proportionality (k) = 1.5

Next, we would determine the difference in cost:

Difference in cost = 1.5 - 1.0

Difference in cost = $0.50.

Read more on proportionality here: brainly.com/question/12866878

#SPJ1

The amounts drained by each pipe, considering a system of equations, are given as follows:

The variables to the system of equations are presented as follows:

A water tank holds a total of 5,600 gallons, hence:

x + y + z = 5600.

Pipe B drains twice as much as pipe A, hence:

y = 2x.

Pipe C drains 65 gallons more than pipe B, hence:

z = 65 + y = 65 + 2x.

Replacing the last two equations into the first, the amount drained by Pipe A is obtained as follows:

x + y + z = 5600.

x + 2x + 65 + 2x = 5600

5x = 5535

x = 5535/5

x = 1107 gallons.

Hence the remaining amounts are given as follows:

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

Answer: c. 1

Step-by-step explanation:

[tex]\displaystyle\\(cot\theta)(sin\theta)(sec\theta)=\\\\\frac{cos\theta}{sin\theta}(sin\theta)\frac{1}{cos\theta} =\\\\\frac{cos\theta (sin\theta)(1)}{sin\theta(cos\theta)}=\\\\1[/tex]

Each individual paid the sum of $23.4 including state tax at the restaurant

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%".

In the problem, their total bill is $50.88 and they gave a 30% tip

We should fid 30% of 50.88

0.3 * 50.88 = $15.264

30% of $50.88 is $15.264

If we add this up and then find the state tax to it.

15.264 + 50.88 = 66.144.

Find 6% of 66.144 to determine the state tax.

0.06 * 66.144 = 3.96864

The total amount spent is 66.144 + 3.96864 = 70.11264

We can divide this equally amongst the three people to get the individual payment = 70.11264/3 = 23.37088

Rounding this to the nearest cent, we have 23.4.

We can say each person paid $23.4 at the end of the day

Learn more on percentage here;

https://brainly.com/question/843074

#SPJ1

Answer:

25

Step-by-step explanation:

2000/4=500

500/20=25

Answer: 125

Step-by-step explanation: you see if you take your 20$ you ern of of selling a shirt then the price you buy it for 4$ then defied it by 2000$ you get 125.

Answer: 4

Step-by-step explanation:  your going to divide -2 by 1 and you get 2 then add 4 and you get 6 pls give me brainliest :)

Answer:$583.93 is the original price