The number of different groups of 7 people who can drive will be 31,824.
A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
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.
Then the number of different groups of 7 people can you drive will be
Different ways = ¹⁸C₇
Different ways = 18! / [(18 - 7)! x 7!]
Different ways = 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11! / (11! x 7 x 6 x 5 x 4 x 3 x 2 x 1)
Different ways = 31824
The number of different groups of 7 people who can drive will be 31,824.
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Then the number of different groups of 7 people can you drive will be
Different ways = ¹⁸C₇
Different ways = 18! / [(18 - 7)! x 7!]
Different ways = 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11! / (11! x 7 x 6 x 5 x 4 x 3 x 2 x 1)
Different ways = 31824
The number of different groups of 7 people who can drive will be 31,824.
Given y1(t) = t^2 is a solution to: t^2y'' - 4ty' + 6y = 0, t > 0 find another solution using the method of reduction of order.
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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the national average family size was reported as 3.18. a random sample of 24 families in one school district had a mean of 3.83 and a standard deviation of 1.43. at the 5% level of significance, does the average family size in this school district differ from the national average? assume the distribution is approximately normal.
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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Ms. Powell’s class voted on where to go for a field trip. The museum received 11 votes, and the aquarium received 16 votes. What is the ratio of votes for the aquarium to votes for the museum? Suppose 3 students who voted to go to the aquarium changed their votes to the museum. How would the ratio change?
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
What are the roots of the quadratic X² 5x =- 6?
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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What is multiplicative formula?
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.
What will come in place of X of the Series 2 5 10 x 2637?
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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What is the nature of roots x2 5 0?
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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There are 120 Calories in a 34
3
4
-cup serving of cereal. How many Calories are there in 6 cups of cereal? Enter your answer in the box.
Calories
Answer:
there are 960 calories in 6 cups of cereal.
Step-by-step explanation:
please give a step by step explanation
∡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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A square church hall had an area of 289m². What is half the perimeter?
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
Determine if triangle KLM and triangle NOP are or are not similar, and, if they
are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
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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Schedule A can be filed with any tax form to itemize deductions for items such as property taxes and charitable contributions paid. True or false
What are the factors of x³ 4x² 11x 30?
The factors of the given expression would be = (x + 2), (x – 3) and (x + 5).
What is factorisation of equations?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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Please help! not very hard, easy points! My test is timed and im having trouble
Solve the following problem. It may be helpful to use draw a chart on scrap paper to organize the information and write the equation. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit.
A grocer wants to make a 10-pound mixture of cashews and peanuts that he can sell for $3.64 per pound. If cashews cost $5.80 per pound and peanuts cost $2.20 per pound, how many pounds of each must he mix?
FL
Intro
2
2
y
E
What is the y-coordinate of point D after a translation of
(x, y) - (x+6, y - 4)?
D'(3.5,
Done
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).
PLEASE HELP Identify the factorization of 36 + 25x^2.
!!WILL HAVE IMAGINARY NUMBERS!!
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
What is the meaning of commutative property?
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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What is root formula?
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:
How many pyramids can fit inside a rectangular prism if both figures have the same measure of bases?
3 pyramids can fit inside a rectangular prism if both figures have the same measures of bases.
what is pyramid?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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I need HUUUGGGE help
The weight of an object on Mars varies directly with its weight on Earth. An object that weighs 50 pounds on Mars weighs 150 pounds on Earth. Determine a direct variation equation to represent this situation. If an object weighs 120 pounds on Earth, determine how much an object would weigh on Mars. Enter this amount, in pounds, into the space provided (enter numerical number only, not the units).
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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Is SSS disability pension lifetime?
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:
Monthly disability pension - For those who made at least 36 SSS contributions every month prior to the semester of impairmentLump-sum payment - For members whose approved disability time is due for less than a year and those whose prior semester of disability was paid for by fewer than 36 monthly paymentsTo learn more about disability here:
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determine whether the following statement is true or not. the center of a confidence interval is always the point estimate for the population parameter. group of answer choices true false
The given statement "the value in the middle of a confidence interval is always the point estimate for the population parameter" is TRUE.
What is a confidence interval?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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What is the nature of roots of 2x² 3x 5 0?
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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The Brown’s family paid a total of $19.00 to bowl 3 games and rent shoes. Each game cost $4.00. Write an equation to represent the total cost y to rent shoes and bowl x games. How much is the shoe rental? How is this represented in the equation?
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:)
please can you solve this question
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
helpp, please!
Andre wanted to measure the width of a creek by his camp but cannot get to the other side of the creek. Andre decided to construct two triangles to determine the width of the creek indirectly. Sighting the position of a tree on the opposite bank of the creek and placing 4 wooden pegs at point N, O, P, and Qas shown in the figure such that MN is perpendicular to NP, NP is perpendicular to PQ, and O is the midpoint of NP. Andre claims that AMNO and AQPO are congruent.
Part A: Provide a valid argument, using geometry theorems or postulates, to validate Andre's claim that AMNO and APQO are congruent.
Part B: Which segment should Andre measure to determine the width of the creek? Explain why.
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
What is congruent triangles?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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A florist ordered a shipment of red, blue, and white carnations to use for table decorations at a banquet. The ratio of red : blue : white carnations in the shipment is 3:1:2. There are 60 white carnations in the shipment. What is the total number of carnations in the shipment? 120 carnations 180 carnations 240 carnations 360 carnations.
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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Calls to the Help Desk: The phone call to a computer software helpdesk occure at the rate of 2.1 per minute between 3.00p.m. and 4:00p.m. Compute the probability that the number of calls to the help desk between 3:10 p.m. and 3:15 p.m. (a) exactly eight. Interpret the result. (6) fewer than eight. Interpret the result. ( at least eight. Interpret the result. You Explain It! Height of 10-Year-Old Males The heights of 10-year-old males are normally distributed with mean = 55.9 inches and o = 5.7 inches. (a) Draw a normal curve with the parameters labeled. (6) Shade the region that represents the proportion of 10-year-old males who are less than 46.5 inches tall. (C) Suppose that the area under the normal curve to the left of x = 46.5 is 0.0496. Provide two interpretations of this result
The probabilities for exact 8 and less than 8 calls can be obtained as 0.1009 and 0.1785 respectively.
What is Poisson distribution?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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In a group trivia game, a team earns 5 points for a correct answer, and -2 points for a
wrong answer. There are 15 questions in the game. Let a represent the number of
correct answers
Which expression represents the total number of points a team earns for
their correct answers?
A.-2x
B.5x
C.x
D.15
Answer: 5a (B)
Step-by-step explanation: