You volunteer to help drive people home from an event. There are 18 people who need rides, but you can only fit 7 of them in your vehicle. How many different groups of 7 people can you drive? 5,040 31,824 22,913,280 160,392,960.

For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

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Answer:

Shoes rental cost: $7

The equation to find the cost is 19 = 4x + y

Step-by-step explanation:

Each game = $4

There are 3 games

They paid a total of $19.00

We have the equation to find the cost is

19 = 4x + y

Now let's put 3 in for x to solve for the cost of renting shoes!

19 = 4(3) + y

19 = 12 + y

y = $7

So, the equation to find shoe rental cost is 19 = 4x + y, and the cost to rent shoes is $7

Answer:

Step-by-step explanation:

19=4x+y is the equation .------1

here x is number of games.

y is cost to rent shoes.

it is given that x=3

so equation 1 becomes

19-12=y

so y=7

which is shoe rental cost

simple:)

since we have our two medians, we need to add them up 1st then divide the sum by two;

50+60

    2

= 110

    2

= 55

55 is the median

The given statement "the value in the middle of a confidence interval is always the point estimate for the population parameter" is TRUE.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

The point estimate for the population parameter is always the value at the center of a confidence range.

You have a 5% probability of being incorrect with a 95% confidence interval.

We have a 10% probability of being incorrect with a 90% confidence interval.

A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

Therefore, the given statement "the value in the middle of a confidence interval is always the point estimate for the population parameter" is TRUE.

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As pert the t-test there is sufficient evidence that the average family size in this school district differ from the national average.

Let us assume null and alternate hypothesis.

H₀ = Average family size is 3.18

Hₐ = Average family size is not 3.18

The value of t = (Sample Mean - 3.18) / s/√n

where,

Sample Mean = 3.83

n = 24

s = 1.43

So, t = (3.83 - 3.18) / (1.43 / √24)

t = 2.2268

Degree of freedom = n - 1 = 23

The p-value = 0.0360

As the p-value <0.05, so the null hypothesis will be rejected.

Therefore, there is enough proof to conclude that this school district's average family size is different from the national average.

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Answer:

there are 960 calories in 6 cups of cereal.

Step-by-step explanation:

The triangle KLM and triangle NOP are similar.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The length of side KLM are KL = 18, LM = 19, MK = 20.

The length of side NOP are NO = 54, OP = 57, NP = 60.

The ratio length of sides is

54/18 = 57/19 = 60/20 = 3

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

According to SSS rule triangle KLM and triangle NOP are similar.

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Answer:

x = (6 i)/5 or x = -(6 i)/5

Step-by-step explanation:

Solve for x:

25 x^2 + 36 = 0

Subtract 36 from both sides:

25 x^2 = -36

Divide both sides by 25:

x^2 = -36/25

Take the square root of both sides:

Answer:  x = (6 i)/5 or x = -(6 i)/5

∡ABD and ∡BAD = ∡55°

As we can see Δ ABD is isosceles

so,

∡ABD = ∡BAD (let us assume them to be ∡F)

Therefore

∡ABD+∡BAD+∡ADB = 180°

2∡F+∡ADB = 180°

2∡F + 70° = 180°

∡F = 55°

∡ABD = ∡BAD = 55°

Now

∡ABD + ∡CBD = 180° (Supplementary Angles)

55° + ∡CBD = 180°

∡CBD = 125°

As the sum of all the angles in a triangle is 180°

∡BDC +∡DCB +∡CBD = 180°

∡BDC + 29° +125° = 180°

Hence

∡BDC = 26°

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The nature of the roots of the equation 2x^2 - 3x + 5 = 0 is imaginary or unreal.

We know that the general form of a quadratic equation is:

ax^2 + bx + c =0

The equation we have is:

2x^2 - 3x + 5 = 0

Comparing the given equation with the general form of a quadratic equation, we get that:

a = 2, b= -3, and c = 5

We know that if D = b^2 - 4ac < 0, then the roots of the quadratic equation are imaginary or unreal.

Therefore, b^2 - 4ac = (-3)^2 - 4x2x5 = -31 < 0.

Hence, we conclude that the nature of the roots of the give equation is imaginary or unreal.

The question is incomplete, the complete question is:

What is the nature of roots of  2x^2 - 3x + 5 = 0 ?

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On solving the provided question, we can say that 50 will therefore be the missing number in the series 2 5 10 x 2637.

What are odd numbers?

A number that is odd is one that can't be partitioned flawlessly into matches. One remains after dividing an odd number by two. The numbers 1, 3, 5, 7, 9, 11, 13, and 15 are consecutively odd. While odd numbers cannot be divided in half, even numbers can. 3, 5, 7, 9, 11, 13, and 15 are unusual cases. Even numbers include 2, 4, 6, 8, 10, 12, and 14.

According to the given question:

Following the numbers 3, 5, 7, 9, 11, and 13, which are all odd numbers, the provided series moves on to 13.

Therefore,

After 37, there will be a break before 50.

50 will therefore be the missing number.

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Answer:

like a ratio

Step-by-step explanation:

A multiplicative comparison involves comparing two quantities such that when one is multiplied by a specified number, the other is produced. For example, Sam has twice as many balloons as Sid. Sid has 3 balloons.

The nature of the roots of the equation x^2 - 5 = 0 is real and unequal.

We know that the general form of a quadratic equation is:

ax^2 + bx + c =0

The equation we have is:

x^2 - 5 = 0

Comparing the given equation with the general form of a quadratic equation, we get that:

a = 1, b= 0, and c = -5

If D = b^2 - 4ac > 0, then we say that the roots of the quadratic equation are real and unequal.

Here, (0)^2 - 4x1x(-5) = 20 >0,

hence we conclude that nature of the roots of the equation x^2 - 5 = 0 is real and unequal.

The question is incomplete, the complete question is:

x^2 - 5 = 0.

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Commutative property states that the product or sum of two numbers do not change even if the places of numbers are changed or if the numbers move from one place to another.

The Commutative Property is derived from the word commute, which means to move. It states that the product or sum of two numbers do not change even if the places of numbers are changed or if the numbers move from one place to another.

The commutative property of addition states that a + b = b + a

The commutative property of multiplication states that a × b = b ×  a.

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3 pyramids can fit inside a rectangular prism if both figures have the same measures of bases.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges.

The ratio of volume of pyramid and a prism is 1:3 when they have the same base and height.

A cylinder with the same radius and height is precisely filled with the contents of three conical cups. A prism with the same base and height as three rectangular-base pyramids is exactly filled with their contents.

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The roots of the given quadratic equation "x² -5x = -6"  is x = 2 and x = 3   .

The Roots of the Quadratic Equation are defined as the number , which satisfies the equation .

The equation is given as x² -5x = -6 ;

rewriting the given equation ,

we get ; x² -5x +6 = 0 .

= x² -3x -2x +6 = 0    ,...By using split the middle term .

= x(x - 3) -2(x - 3) [tex]=[/tex] 0 ;

= (x - 2)(x - 3) [tex]=[/tex] 0 .

On equating the factors ,  x - 2 = 0    and   x - 3 = 0 ;

Simplifying further ,

we get ;

x = 2   and x = 3 .

Therefore , the roots of the quadratic are  x = 2 and x = 3 .

The given question is incomplete , the complete question is

What are the roots of the quadratic x² -5x = -6 ?

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Answer:

Step-by-step explanation:

Part A: you can just restate parts of the text to make a vaild argument or you can make you own

Part B: he should measure N, O, P and Qas

Triangles MNO and QPO are congruent. To find the width of the creek, Andre should find the measurement of NP

When two triangles are congruent, their corresponding three sides and their three angles match precisely.

Given that

O is the midpoint of NP,

NP is perpendicular to MN, and

NP is perpendicular to PQ.

When two lines intersect at a specific point, the opposite angles formed in this situation are equal.

a) Then ∠MNP =∠QPO=90°

∠MON=∠QOP

Also, NO = OP (by the definition of midpoints)

Therefore, Triangles MNO and QPO are congruent by ASA rule

And,

b) To find the width of the creek, Andre should find the measurement of NP, because according to the figure the width is represented by NP. He should find NO and OP and then add it.

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Answer:

34 m

Step-by-step explanation:

s=side of square

A=Area of square

P = Perimeter of square

s*s = A

s*s = 289

s^2 = 289

s = [tex]\sqrt{289}[/tex]

s = 17 m

P = s + s + s + s

P = 4s

P = 4(17)

P = 68 m

68/2 = 34 m

Answer: 5a (B)

Step-by-step explanation:

The factors of the given expression would be = (x + 2), (x – 3) and (x + 5).

Factorisation of equations is defined as the expression of a given equation as a product of several other factors.

From the equation given; x³ 4x² 11x 30. it's factorisation would be done by getting the first root by trial and error method∶

Since the sum of the coefficients is not zero, 1 is not a root

Let x = -2

⇒ -8 + 16 + 22 – 30 = 0

∴ -2 is or (x + 2) is a factor

Dividing x3 + 4x2 – 11x – 30 by (x + 2)

Quotient = x2 + 2x – 15

⇒ x2 + 5x – 3x – 15 = 0

⇒ x (x + 5) – 3 (x + 5) = 0

⇒ (x – 3) (x + 5) = 0

Other factors are (x – 3) and (x + 5)

∴ (x + 2), (x – 3) and (x + 5) are the roots of the equation

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Answer:

(3,1)

Step-by-step explanation:

(x+ 6, y -4)

The x tells us the movements are right or left. Right would be a positive movement and left would be a negative movement.

The y tells us the movements are up or down.  Up would be a positive movement and down would be a negative movement.

D is at the point ( -3,5)  

(x + 6, y -4)  Is telling us that from the point of D, move right 6 spaces and down 4 spaces.  You will know be at the point (3,1).

As per the given ratio, the total number of flowers in shipment is 180.

The term Ratio in math basically compares quantities, which means that it shows the value of one quantity with respect to the other quantity.

Here we have given that the florist ordered a shipment of red, blue, and white carnations to use for table decorations at a banquet.

And we need to find  the total number of carnations in the shipment.

While we looking into the given question, we know that the ratio of red : blue : white carnations in the shipment is 3:1:2.

Here we aloo know that there are 60 white carnations in the shipment

Then let us consider if a and b are two values, their ratio will be a:b,

Then the ratio of flowers is written as

=> red: blue: white = 3:1:2

Where red flowers are 3x, and the blue flowers are x, and the white flower are 2x.

So, the total number of flowers = 3x+x+2x = 6x

When we apply the value of whit\te flowers = 60

Then the value of x is calculated as,

=> 2x = 60

=> x = 30

Therefore, the total number of flowers = 6x = 6×30 = 180

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Answer:Square Root Formula

The square root formula of a number, x is given as,

√x = x1/2

Suppose, x is any number such that, x = y × y, the formula to calculate the square root of x will be,

√x = √(y × y) = y

where, y is the square root of any number x. This also means that if the value of y is an integer, then x would be a perfect square.

Step-by-step explanation:

The probabilities for exact 8 and less than 8 calls can be obtained as  0.1009 and 0.1785 respectively.

Poisson distribution is applied for the case where the events occur in a specific period of time with constant rate.

The given case belongs to Poisson distribution,

It can be solved as follows,

(a) The probability of exactly 8 calls can be obtained as,

P(Exact 8 calls) =  [tex]e^{-\lambda} \lambda^{x}/x![/tex]

Where x = 8 and λ = 2.1 × 5 = 10.5.

Then, the probability is  obtained as,

⇒ e⁻⁸ × 10.5⁸/8!

⇒ 0.1009

It implies that if 100 calls are selected randomly for the interval of 5 minute, 10 calls can be expected.

(b)  The probability of less than 8 calls can be obtained as

P(Less than 8) = [tex]\sum_{x =1}^{7}e^{-\lambda}\lambda^{x}/ x![/tex]

⇒ P(Less than 8) = 0.1785

It implies that out of 100 randomly selected 5 minute calls, around 18 have less than 8 calls.

Hence, the required probabilities for the given case are 0.1009 and 0.1785 respectively.

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The weight of the object on Mars would be 40 pounds.

What are ratio and proportion?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

An object that weighs 50 pounds on mars weighs 150 pounds on earth.

Let the object weighing 120 pounds on Earth, weighs x pounds on Mars.

We can solve this equation as :

                50/150 = x/120

                 x = 40 pounds

Hence, the weight of the object on Mars would be 40 pounds.

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2909/2000

Based on the given conditions, formulate: 16 divided by 11

Evaluate the equation/expression: 1.4545

Convert decimal into fraction: 14545/10000

Reduce the fraction: 2909/2000

Answer: 2909/2000

The only SSS members eligible for a monthly disability stipend for life are those who are absolutely and permanently incapacitated.

Members of SSS who have a total or partial permanent disability receive a financial benefit. Depending on the member's number of monthly SSS contribution payments, the reward is either paid as a monthly disability pension or a one-time lump sum benefit.

Cash Benefits for SSS Members with Disabilities:

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