I’ve been stuck on this someone please help me solve this question

There are 56 different combinations of 5 friends that can be selected from the group of 8 friends (option C)

To determine the number of different combinations of 5 friends that can be selected from a group of 8 friends, we use the concept of combinations in combinatorial mathematics.

The number of ways to choose [tex]\( k \)[/tex] elements from a set of [tex]\( n \)[/tex] elements is given by the binomial coefficient [tex]\(\binom{n}{k}\)[/tex], which is calculated as:

[tex]\[\binom{n}{k} = \frac{n!}{k!(n-k)!}\][/tex]

In this scenario:

[tex]\( n = 8 \)[/tex] (total number of friends)

[tex]\( k = 5 \)[/tex] (number of tickets available, hence number of friends to be chosen)

We need to calculate [tex]\(\binom{8}{5}\)[/tex]:

[tex]\[\binom{8}{5} = \frac{8!}{5!(8-5)!} = \frac{8!}{5! \cdot 3!}\][/tex]

First, we calculate the factorials involved:

[tex]\( 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320 \)[/tex]

[tex]\( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \)[/tex]

[tex]\( 3! = 3 \times 2 \times 1 = 6 \)[/tex]

Now, substitute these values into the binomial coefficient formula:

[tex]\[\binom{8}{5} = \frac{40320}{120 \times 6} = \frac{40320}{720} = 56\][/tex]

Therefore, there are [tex]\( 56 \)[/tex] different combinations of 5 friends that can be selected from the group of 8 friends.

Answer:

its A :)

Step-by-step explanation:

Answer:

128 yards

Step-by-step explanation:

Final answer:

By applying the Pythagorean theorem to the right-angled triangle sail, with the longest edge being the hypotenuse (16 yards) and the bottom edge as one side (8 yards), the height of the sail is calculated to be approximately 13.856 yards.

Explanation:

To determine how tall the sail is, we can use the Pythagorean theorem if we assume that the sail is a right-angled triangle, which is common in sailboat sails. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If we let the longest edge (16 yards) be the hypotenuse (c) and the bottom edge (8 yards) be one of the other sides (a), we can find the height (b) of the sail using the equation:

c² = a² + b²

So,

16² = 8² + b²

256 = 64 + b²

b² = 256 - 64

b² = 192

b = √192

b ≈ 13.856 yards (rounding to three decimal places)

Therefore, the sail is approximately 13.856 yards tall.

Answer:

          [tex]\large\boxed{\large\boxed{5ft}}[/tex]

Explanation:

A ramp is modeled by a right triangle with hypotenuse equal to the length of the ramp, horizontal leg equal to the ground length(horizontal run), and vertical leg equal to the rise.

Hence, you can use Pythagora's theorem:

            [tex](13ft)^2=(12ft)^2+y^2[/tex]

Solve of the y, which represents the rise:

              [tex]y^2=(13ft)^2-(12ft)^2=169ft^2-144ft^2=25ft^2\\\\y=5ft[/tex]

Final answer:

Using the Pythagorean theorem with the length of the ramp as the hypotenuse (13 feet) and the horizontal distance covered (12 feet), it is determined that the ramp rises 5 feet high.

Explanation:

To determine how high the ramp rises, we can use the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (adjacent and opposite).

Let's denote:

Using the Pythagorean theorem:

a² + b² = c²

Substituting the known values:

12² + b² = 13²

144 + b² = 169

To find b, we subtract 144 from both sides of the equation:

b² = 169 - 144

b² = 25

Taking the square root of both sides gives us the height:

b = √25 = 5 feet

Therefore, the ramp rises 5 feet high.

Volume of the cylinder is 3696 m²

Step-by-step explanation:

⇒ V = 22/7 × 14² × 6 = 3696 m²

The height of the tree is 60 meters.

Explanation:

Let the height of the tree be x. The tree casts a shadow of [tex]x-49[/tex] meters and the distance from the top of the tree to the end of the shadow is [tex]x+1[/tex] meters.

The sides of the triangle are attached in the image below:

Using pythagoras theorem,

[tex]x^{2}+(x-49)^{2}=(x+1)^{2}[/tex]

Expanding, we get,

[tex]2 x^{2}-98 x+2401=x^{2}+2 x+1[/tex]

[tex]2 x^{2}-98 x+2400=x^{2}+2 x[/tex]

[tex]2 x^{2}-100 x+2400=x^{2}[/tex]

[tex]x^{2}-100 x+2400=0[/tex]

Solving the equation using the quadratic formula [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex], we get,

[tex]x=\frac{-(-100)\pm\sqrt{(-100)^{2}-4 \cdot 1 \cdot 2400}}{2 \cdot 1}[/tex]

Simplifying, we have,

[tex]x=\frac{100\pm\sqrt{10000-9600}}{2}[/tex]

[tex]x=\frac{100\pm\sqrt{400}}{2}[/tex]

[tex]x=\frac{100\pm{20}}{2}[/tex]

Thus,

[tex]x=\frac{100+20}{2} \\x=\frac{120}{2} \\x=60[/tex]  and  [tex]x=\frac{100-20}{2} \\x=\frac{80}{2} \\x=40[/tex]

where the value [tex]x=40[/tex] is not possible because substituting the value [tex]x=40[/tex] in [tex]x-49[/tex] results in negative solution. Which is not possible.

Hence, the value of x is 60.

Thus, The height of the tree is 60 meters.

Answer:

=50x+116

Step-by-step explanation:

5+5x(10)−88+200−1

=5+50x+−88+200+−1

Combine Like Terms:

=5+50x+−88+200+−1

=(50x)+(5+−88+200+−1)

=50x+116

Answer:

166

Step-by-step explanation:

remember order of operations

PEMDAS

parentheses ( )

exponents x^2

multiply or divide (from left to right) * /

add or subtract (from left to right) + -

first step multiply 5*10=50

5+50-88+200-1

next 5+50=55

55-88+200-1

next 55-88= -33

-33+200-1

next -33+200= 167

167-1= 166

The estimated value of 19% of 44 is 8 as per the percentage rule and rounding decimals rule.

The correct option is 8.

To estimate 19% of 44, we can start by finding 10% of 44, which is simply moving the decimal point one place to the left. So, 10% of 44 is 4.4.

Next, we can estimate 5% of 44 by dividing 10% by 2. This gives us 2.2.

Now, to estimate 19% of 44, we can add the estimates for 10% and 5%. So, 4.4 + 2.2 equals 6.6.

Given the options of 8, 9, 9.5, and 10, we can see that the estimate of 19% of 44 is closest to 9.

Therefore, the estimated value of 19% of 44 is 8.

It's important to note that this is an estimation, and the actual value of 19% of 44 is 8.36. The estimation technique used here is a quick approximation that can be useful in situations where an exact calculation is not required or when a rough estimate is sufficient.

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The complete question:

Estimate 19% of 44.
The available options are:

8, 9, 9.5, and 10.

Answer:

Step-by-step explanation:

y−intercept=  

−7

1

​  

=−0.14286

Answer:

A and B

Step-by-step explanation:

A.

The points are (1,2) and (4,8)

(4,8)=4(1,2)

(4,8)∝(1,2)

B.

The points are(1,6)and (3,4)

We don't established any relation between them.

So , there is no relation between them.

C.

The points are (1,6) and (3,4)

We don't established any relation between them.

So , there is no relation between them.

D.

The points are (2,1) and (4,2)

(4,2) = 2(2,1)

(4,2)∝(2,1)

Answer:

5.175

Step-by-step explanation:

Answer:

5.175

Step-by-step explanation:

Answer:50%

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Answer:

Step-by-step explanation:

programs can be written in multiply languages. for this solution I'll be writing in C++.

#include<iostream> // this is called the preprocessor definition

using namespace std;

int main()                      //the main function

{

   int num, product;      //declaration of the variables

    cout << "enter the whole number";  

    cin >> num;

    product = num * 12;

     cout << product; // displaying the final results

     return 0;

}

Answer:32

Step-by-step explanation:

The pattern seems to double each time there is a new week. By the fourth week he saved $8, and it asks how much he saved by the sixth week. We know $8 x 2 = 16 and 16 x 2 = 32, SO, by the sixth week Mikhail saved $32!

Answer: 135cm

Step-by-step explanation

Volume of a cylinder = πr²h

Volume of a cone. = 1/3πr²h

The two shapes are both solid shapes.

Since the have same volume, we can then equate the two together and solve for the height of the cone.

Now make H the height and R the radius of the cylinder and h the height and r the radius of the cylinder.

Now equating the two

πR²H = 1/3πr²h

Now substitute for the values now

Multiply through by 3

3πR²H = πr²h

But π is common so it could be obliterated from the equation

3R²H = r²h

3 x 12² x 20 = 8² x h

3 x 144 x 20 = 64 x h

60 x 144 = 64h

8640. = 64h

Therefore

h = 8640/64

= 135cm

Answer:

5 (for c only)

Step-by-step explanation:

for c:

1st cleaning company: [tex]y=17x+15[/tex]

2nd cleaning company: [tex]y=20x[/tex]

set up as a system of equations. for them to cancle out make the y of one equation negative. I'll be making the second one negative ( it doesn't matter though)

it will look like:

[tex]y=17x+15[/tex]

[tex]-y=-20x[/tex]

make the two equations on top of eachother and line the terms up. Then combine them. The variable "y" will cancle out and you'll be left with

[tex]0=-3x+15[/tex]

then you will add 3x to both sides to get [tex]3x=15[/tex] then divide both sides by 3 to get [tex]x=5[/tex]

if you plug in 5 for x into both of the original equations you will see that they will both make $100 in five hours. So you answer is 5

let's say the original number is "a".

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of "a"}}{\left( \cfrac{5}{100} \right)a}\implies \cfrac{5a}{100} \\\\\\ \stackrel{\textit{"a" increased by 5\%}}{a + \cfrac{5a}{100}\implies \cfrac{105a}{100}}~\hfill \stackrel{\textit{5\% of }\frac{105a}{100}}{\left( \cfrac{5}{100} \right)\cfrac{105a}{100}}\implies \cfrac{525a}{10000}\implies \cfrac{21a}{400}[/tex]

[tex]\bf \stackrel{\frac{105a}{100}\textit{ increased by 5\%}}{\cfrac{105a}{100}+\cfrac{21a}{400}}\implies \cfrac{21a}{20}+\cfrac{21a}{400}\implies \cfrac{420a+21a}{400}\implies \cfrac{441a}{400} \\\\\\ 1.1025a\implies 1a+0.1025a\implies \stackrel{\textit{original}}{a} + \stackrel{\textit{10.25\% added}}{\cfrac{10.25}{100}a}[/tex]

Answer:

isnt it n 24

Step-by-step explanation:

80

The question implies that you're counting by tens & the number comes after 70 and before 90. This is the only number that fits this description.

Using logical concept, the value of the number in question will be 80.

Let the number be n ;

Hence, we have ;

70, n, 90

n - 70 = 10 - - (1)

90 - n = 10 - - - (2)

Using either of the two expressions, we can obtain the value of n :

n - 70 = 10

n = 10 + 70

n = 80

Hence, the number is 80

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Answer:

c. 43*

Step-by-step explanation:

1) 180-133= 47

2) 80-90= 90

3) 90+47= 137

4) 180-137= 42*

The correct answer is y=3/2x+4

[tex](14x+21y)(6ab-3a) = 3a(2b - 1)(14x + 21y)[/tex]

Solution:

Given that,

[tex](14x+21y)(6ab-3a)[/tex]

We have to factor out terms and write as a product of 2 binomials and monomial

A monomial is a mathematical expression with only one term, while a binomial is a mathematical expression with two terms.

From given expression,

[tex](14x+21y)(6ab-3a) = (14x + 21y)(3 \times 2ab -3a)[/tex]

3 and a are common factors in second bracket

[tex](14x+21y)(6ab-3a) = 3a(2b - 1)(14x + 21y)[/tex]

Hence, the product of two binomial is written in two binomial and a monomial

Answer:

392 students

Step-by-step explanation:

Given: 3/8 of the seventh grade students were taking advanced math at the beginning of the year.

          Seven dropped out by the end of the year.

          There are 140 students taking advanced math at the end of the year.

Lets assume total number of students of seventh grade be "x".

As given, 3/8 of the seventh grade students were taking advanced math at the beginning of the year.

∴ Number of student took advanced maths at the beginning= [tex]\frac{3}{8} \times x= \frac{3x}{8}[/tex]

We know, 7 student dropped out of advanced math by the end of the year.

Now, forming an equation to determine number of students taking advanced math at the end of the year.

⇒ [tex]\frac{3x}{8} -7= 140[/tex]

Solving the equation  to find number of student in seventh grade.

⇒ [tex]\frac{3x}{8} -7= 140[/tex]

Adding both side by 7

⇒ [tex]\frac{3x}{8} = 140+7[/tex]

Multiplying both side by 8

⇒[tex]3x= 147\times 8[/tex]

Dividing both side by 3

⇒[tex]x= \frac{147\times 8}{3}[/tex]

∴ [tex]x= 392[/tex]

Hence, there are 392 students in seventh grade.

Marlie's federal unsubsidized student loan will accrue $3,627.34 in interest over a 4.5-year non-payment period, given a 4.29% annual interest rate.

The subject of this problem is calculating interest accrued on an unsubsidized student loan. First, we need to understand that the 4.29% interest is an annual rate. So, for 4.5 years, the rate would become: 4.29% * 4.5 = 19.305%.

To calculate the amount of interest that will accrue during this period, we simply multiply this by the principal loan amount ($18,800). So, $18,800 * 19.305% = $3,627.34. Therefore, Marlie will accrue $3,627.34 in interest over this 4.5-year period.

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Marlie, who took a Federal Unsubsidized student loan that accumulates interest over time, will accrue $3,628.83 in interest during her 4.5 years of non-payment.

The subject of this question is about interest calculation on a Federal Unsubsidized student loan. Interest on an unsubsidized loan like Marlie's accumulates from the time the loan is disbursed until it's paid in full, including during the non-payment period. The interest that will accrue can be calculated using the formula I = PRT, where 'I' is the interest, 'P' is the principal amount (the initial amount of loan), 'R' is the annual interest rate in decimal, and 'T' is the time the money is borrowed for in years.

In Marlie's case, P = $18,800, R = 4.29/100 = 0.0429, and T = 4.5. Therefore, the interest accrued will be I = 18800 * 0.0429 * 4.5. After performing the calculation, the total interest that Marlie will accrue over the non-payment period is $3,628.83.

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Answer:

$120

Step-by-step explanation:

2/3 of Mary's money + 1/2 of Mary's money is equal to 7/6 of Mary's money

7/6 of Mary's money = $210

Mary's money = m

210 = 7/6*x

180 = x

Mary's money = $180

Suzy's original money = 2/3 of 180

2/3 * 180 = 120

Answer:

996 in²

Step-by-step explanation:

The figure is composed of a square and a triangle.

Using Pythagoras' identity on one of the right triangles within the triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides

let the base of the right triangle be x, then

x² + 35² = 37², that is

x² + 1225 = 1369 ( subtract 1225 from both sides )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12

Thus the base of the upper triangle = 2x = 2 × 12 = 24

Area of upper triangle = 0.5 bh ( b is the base and h the height )

Area = 0.5 × 24 × 35 = 12 × 35 = 420 in²

The length of the side of the square is therefore 24 in

Area = 24 × 24 = 576

Total area = 576 + 420 = 996 in²

Answer:

Always write it except if distributing 1. This does NOT apply for -1!

Step-by-step explanation:

The monthly rate is $45 for this cellphone plan.

Step-by-step explanation:

Given,

Amount charged for cell phone = $60

Amount paid by Regina for 24 month plan = $1140

Number of months = 24

Let,

m be the monthly rate for cellphone plan

Number of months * Monthly rate + cellphone charges = Amount paid

[tex]24m+60=1140\\24m=1140-60\\24m=1080[/tex]

Dividing both sides by 24

[tex]\frac{24m}{24}=\frac{1080}{24}\\m=45[/tex]

The monthly rate is $45 for this cellphone plan.

Keywords: subtraction, division

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