PLEASE HELP LAST DAY:
Pat's soccer team has 15 players. 2/3
of the players went out for frozen yogurt after their last win. How many players went out for yogurt?

how many players went out to get frozen yougurt

The given statement: n(n+1)(2n+1) is divisible by 6 for all positive integers n.

Step-by-step explanation: We need to prove that n(n+1)(2n+1) is divisible by 6 for all positive integers n using mathematical induction.

Step 1: First, lets prove the statement for the smallest possible value of n. The smallest value of n is 1. So, let's check whether the given statement is true for n = 1 or not.

\(LHS = 1(1+1)(2*1+1) = 6\)

It is divisible by 6. Hence, the statement is true for n=1.

Step 2: Let's assume that the statement is true for n=k. So, we can say that n(n+1)(2n+1) is divisible by 6 for n=k. i.e., n(n+1)(2n+1) = 6a (for some integer a).

Step 3: We need to prove the statement is true for n=k+1.

So, we need to prove that (k+1){(k+1)+1}[2(k+1)+1] is divisible by 6

Using the assumption we made in step 2.

\(LHS = (k+1){(k+2)}[2k+3] = (k+1)(k+2)(2k+3)LHS = (2k+3)k(k+1)(k+2)LHS = 2[k(k+1)(k+2)] + 3[k(k+1)]\)

Now, k(k+1)(k+2) is divisible by 6 using the assumption made in step 2.

So, LHS = 2[k(k+1)(k+2)] + 3[k(k+1)] is also divisible by 6.

Hence, the statement is true for n=k+1.

Step 4: Using steps 1 to 3, we can say that the given statement is true for n=1 and if it is true for n=k, then it is also true for n=k+1.

Hence, by mathematical induction, we can say that the statement is true for all positive integers n.

Hence, it is proved that n(n+1)(2n+1) is divisible by 6 for all positive integers n.

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Answer:

A, C, E, F

Step-by-step explanation:

since nothing else was said, it is a general triangle. nothing special about it.

so, the only rules are that the sum of any pair of sides must be longer than the 3rd side (otherwise, if the 3rd side is longer, the sides could not connect).

A. 10.

so, we have

6 + 9 > 10 true

6 + 10 > 9 true

9 + 10 > 6 true

therefore this is a possible 3rd side.

B. 2.

so, we have

6 + 9 > 2 true

6 + 2 > 9 false

9 + 2 > 6 true

therefore this is NOT a possible 3rd side.

C. 4.

so, we have

6 + 9 > 4 true

6 + 4 > 9 true

9 + 4 > 6 true

therefore this is a possible 3rd side.

D. 15.

so, we have

6 + 9 > 15 false

6 + 15 > 9 true

9 + 15 > 6 true

therefore this is NOT a possible 3rd side (this triangle is a special case as 6+9 = 15 : it can only exist as a completely flat line and is therefore not a triangle).

E. 12.

so, we have

6 + 9 > 12 true

6 + 12 > 9 true

9 + 12 > 6 true

therefore this is a possible 3rd side.

F. 7.

so, we have

6 + 9 > 7 true

6 + 7 > 9 true

9 + 7 > 6 true

therefore this is a possible 3rd side.

Answer: The answer is F.

Step-by-step explanation: It’s F because the number would be multiplied equally because all of the number are multiplied by 2. The rest of them either have variables or variables with numbers in them, which looks kind of funky, so F is the answer. I hope you get it right :). Sorry, if I was late for the reply and if you already figured it out… :(.

Answer:

x=8 and y=17

Step-by-step explanation:

hope this helps

Since the percent grade in period 1 was 92% and in period 2 was 96%, then the percent change from period 1 to 2 was 4%.

Since the percent grade in period 2 was 96% and in period 3 was 99%, then the percent change from period 2 to 3 was 3%.

Since 4% is 1% greater than 3%, then the percent change from grading period 1 to 2 was 1% greater than the percent change from grading period 2 to 3.

Therefore, the answer is: 1.0%.

Answer: No you can not make any triangles with 2 inches, 2 inches and 4 inches. hoped this helped!

Step-by-step explanation:

Answer:

-33

Step-by-step explanation:

-17and den u add &16 together soon u have to additional into get -33

There were 204 participants from the three schools

The given parameters are:

X = 12 + Y

X = Z - 18

Girls = Boys + 50

The ratios of the number of boys to girls in the schools are:

1 : 2

1 : 5

2 : 1

This means that:

So, we have:

Boys = 1/3X + 1/6Y + 2/3Z

Girls = 2/3X + 5/6Y + 1/3Z

Substitute the above equations in Girls = Boys + 50

2/3X + 5/6Y + 1/3Z = 1/3X + 1/6Y + 2/3Z + 50

Evaluate the like terms

1/3X + 2/3Y - 1/3Z = 50

Multiply through by 3

X + 2Y - Z = 150

So, we have:

X = 12 + Y

X = Z - 18

X + 2Y - Z = 150

Substitute X = 12 + Y in X = Z - 18 and X + 2Y - Z = 150

12 + Y = Z - 18 ⇒ Y - Z = 30

12 + Y + 2Y - Z = 150 ⇒ 3Y - Z = 138

Subtract Y - Z = 30 from the equation 3Y - Z = 138 to eliminate Z

2Y = 108

Divide by 2

Y = 54

Substitute Y = 54 in X = 12 + Y

X = 12 + 54

X = 66

Substitute X = 66 in X = Z - 18

66 = Z - 18

Solve for Z

Z = 66 + 18

Z = 84

So, the total number of participants from the 3 schools is

Total = X + Y + Z

This gives

Total = 66 + 54 + 84

Evaluate the sum

Total = 204

Hence, there were 204 participants from the three schools

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Answer:

-3 > x

Step-by-step explanation:

Answer: (2, 6)

Step-by-step explanation:

We know that \(\overrightarrow{UM}=\overrightarrow{MT}\). From the given coordinates, \(\overrightarrow{UM}=(-1, -2)\). Therefore, the coordinates of \(T\) are \((3,8)+(-1,-2)=(2,6)\).

Answer:

See below

Step-by-step explanation:

Quarters= 25(x)

Nickels =5(x+16)

25x+5(x+16)=590 (no decimal)

If you solve for x, you’ll get the number of quarters.

The family members were 3 adults and 2 children.

We have given that the,

A family of 10 purchased tickets to the county fair.

Tickets for adults cost $6 and tickets for children cost $3

Total cost is $42.

We have to determine how many family members were adults and children

(3 x 10) + (2 x 6)

30+12=42

Therefore we get 3 adults and 2 children.

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The value of the radius that minimizes the amount of Aluminium is 4.64 cm and it gives the local minimum of the function

From the question, the volume of the aluminium is given as

Volume = 200pi cm^3

Rewrite this volume properly using the correct symbols and units

So, we have the following representation

Volume = 200π cm³

Solving further, we make use of the volume of a cylinder (i.e. a can)

The volume of a sphere is represented as

V = πr²h

Substitute Volume = 200π cm³ in

πr²h = 200π

Make h the subject in the above equation

This gives

h = 200π/πr²

Cancel the common factors

h = 200/r²

The surface area of a can is

A = 2πr(h + r)

So, we have

A = 2πr(200/r² + r)

This gives

A = 400π/r + 2πr²

Differentiate the function

This gives

A' = -400π/r² + 4πr

Set the differentiated function to 0

-400π/r² + 4πr = 0

So, we have

-400π/r² = -4πr

Cross multiply

-400π = -4πr³

Divide through by -4π

r³ = 100

Take the cube roots

r = 4.64

Hence, the radius that given minimum material is 4.64 cm

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The recursive formula for an of the sequence 4,-20,100,-500 is an = an-1 * -5

The recursive formula for a sequence is a formula that requires the computation of all previous terms in order to find the value of an. In this case, the sequence is 4, -20, 100, -500.

To find the recursive formula for this sequence, we need to first determine the common ratio between the terms. The common ratio can be found by dividing any term by the term before it.

For example,

-20/4 = -5 and

100/-20 = -5.

The common ratio for this sequence is -5.

The recursive formula for this sequence can be written as:
an = an-1 * -5
This means that to find the nth term of the sequence, we need to multiply the term before it by -5.

For example, to find the 5th term of the sequence, we would use the formula:
a5 = a4 * -5 = -500 * -5 = 2500

Therefore, the recursive formula for the sequence 4, -20, 100, -500 is an = an-1 * -5.

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The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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Answer:

C(-3,3)

Step-by-step explanation:

Given

A = (7,-1)

B = (2,1)

AB:AC = 1:2

Required

Determine the coordinates of C

Since, B is between A and C; we need to determine ratio BC as follows;

\(AB:AC = 1:2\)

Convert to division

\(\frac{AB}{AC} = \frac{1}{2}\)

AC = AB + BC;

\(\frac{AB}{AB + BC} = \frac{1}{2}\)

Cross Multiply

\(2 * AB = 1 * (AB + BC)\)

\(2 AB = AB + BC\)

\(2AB - AB = BC\)

\(AB = BC\)

Divide both sides by BC

\(\frac{AB}{BC} = 1\)

Rewrite as

\(\frac{AB}{BC} = \frac{1}{1}\)

Write as ratio

\(AB:BC = 1:1\)

Next is to determine the coordinates of C as follows;

Because B is between both points. we have:

\(B(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})\)

Where

\(m:n = AB:BC = 1:1\)

\(B(x,y) = B(2,1)\)

\(A(x_1,y_1) = A(7,-1)\)

So; we're solving for x2 and y2

\(B(2,1) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})\)

Where

Solving for x2;

\(x = \frac{mx_2 + nx_1}{m+n}\)

\(2 = \frac{1 * x_2 + 1 * 7}{1+1}\)

\(2 = \frac{x_2 + 7}{2}\)

Cross Multiply

\(2 * 2 = x_2 + 7\)

\(4 = x_2 + 7\)

\(x_2 = 4 - 7\)

\(x_2 = -3\)

Solving for y2;

\(y = \frac{my_2 + ny_1}{m+n}\)

\(1 = \frac{1 * y_2 + 1 * -1}{1+1}\)

\(1 = \frac{y_2- 1}{2}\)

Cross Multiply

\(2 * 1 = y_2 - 1\)

\(2 = y_2 - 1\)

\(y_2 = 2 + 1\)

\(y_2 = 3\)

Hence, the coordinates of C are: C(-3,3)

Answer:

\(\huge\boxed{\sf 6(x + 2)}\)

Step-by-step explanation:

= 2(5x + 3) - 2(2x - 3)

Expand

= 10x + 6 - 4x + 6

Combine like terms

= 10x - 4x + 6 + 6

Add or subtract as indicated

= 6x + 12

Take 6 common

= 6(x + 2)

\(\rule[225]{225}{2}\)

Hope this helped!

Question 13.

The estimated monthly cost of an energy-efficient refrigerator is $57, meaning the yearly cost is

Question 14.

The least energy-efficient refrigerator costs $72 per month, meaning the annual cost is

Therefore, the amount you will save on an energy-efficient refrigerator be

Hence, the amount saved on an energy-efficient refrigerator will be $180.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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Answer:

4/5

Step-by-step explanation:

Convert 4y+5x=16 to slope intercept form

4y=-5x+16

y=-5/4+4

Perpendicular line has slope of 4/5

The answers to each part of the question are mentioned above.

        y = a(x – h)² + k    or     x = a(y – k)² +h.

        where - (h, k) denotes the vertex.

Given is the equation of a parabola as -

(x - 1)² = y + 2​

We can write the equation as -

y = (x - 1)² - 2

        \($y=\frac{1}{4 \left(f - k\right)} \left(x - h\right)^{2} + k\)

        \($y=\frac{1}{4 \left(\frac{-7}{4} - (-2)\right)} \left(x - h\right)^{2} + k\)

        - 2 - (- 7/4) = d - (- 2)

        d = - 9/4

        y = d

        y = -9/4

Therefore, the answers to each part of the question are mentioned above.

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Answer:

Step-by-step explanation:

Answer is 30

Answer:

Rm14 500

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Answer:

tan A = ± 1/√3 or ± 0.58

Step-by-step explanation:

2 ways to solve this question.

1. cos 2A = 1/2       2A = 60° or 300° or 420° or ....

   A = 30° or 150° or 210° ....

  tan A = tan 30° or tan 150° or ... = ± 1/√3

2. cos 2A = 2 cos²A - 1        1/2 = 2 cos²A - 1     cos²A = 3/4

   cos 2A = 1 - 2 sin²A         1/2 = 1 - 2 sin²A       sin²A = 1/4

   tan²A = sin²a/cos²A = (1/4) / (3/4) = 1/3

   tan A = ± 1/√3 or ± 0.58

Using difference quotient, the simplification of f(2+h)−f(2)/h is 2h + 8

To simplify using the difference quotient, we need to evaluate the expression:

f(2+h) - f(2)/h

where f(x) = 2x^2 - 5.

First, let's find f(2+h):

f(2+h) = 2(2+h)^2 - 5

      = 2(4 + 4h + h^2) - 5

      = 8 + 8h + 2h^2 - 5

      = 2h^2 + 8h + 3

Now, let's find f(2):

f(2) = 2(2)^2 - 5

    = 2(4) - 5

    = 8 - 5

    = 3

We can now substitute these values into the difference quotient expression:

f(2+h) - f(2)

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

     h

= (2h^2 + 8h + 3 - 3) / h  

(Substitute f(2+h) and f(2))

= (2h^2 + 8h) / h        

(Simplify)

= 2h + 8                

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Answer:

I'm pretty sure it's B -2 -3 :))))

The slopes of GH, HI, IJ, and JG include the following:

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope GH = (-3 + 9)/(-4 + 7)

Slope GH = 6/3

Slope GH = 2.

Slope HI = (5 + 3)/(-6 + 4)

Slope HI = -8/2

Slope HI = -4.

Slope IJ = (-1 - 5)/(-9 + 6)

Slope IJ = -6/-3

Slope IJ = 2.

Slope JG = (-9 + 1)/(-7 + 9)

Slope JG = -8/2

Slope JG = -4.

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Answer:

APPALACHIAN MOUNTAINS

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PLEASE MARK THIS ANSWER AS THE BRAINLIEST

Answer:

We know that the plant grows by 3 inches each week (7 inches - 4 inches = 3 inches, and 10 inches - 7 inches = 3 inches). Therefore, after 5 weeks, the plant will be 4 inches + (3 inches × 5) = 19 inches tall.

Step-by-step explanation:

- The plant is 4 inches tall when Dana buys it.

- After one week, the plant grows by 3 inches to reach a height of 7 inches.

- After a second week, the plant grows by another 3 inches to reach a height of 10 inches.

- So, the plant grows by 3 inches each week.

- After 3 weeks, the plant will be 10 inches + 3 inches = 13 inches tall.

- After 4 weeks, the plant will be 13 inches + 3 inches = 16 inches tall.

- After 5 weeks, the plant will be 16 inches + 3 inches = 19 inches tall.

Therefore, the correct answer is d) 19 inches tall.