if there are five people in a car and 1 person is the driver, how many unique seating arrangements are there
Answer:
none
Step-by-step explanation: if the person driving is one of the five people than none
If (a + b + c)‐¹= a‐¹+ b‐¹ + c‐¹, show that (a + b + c)³ = a³ + b³ + c³.
Step-by-step explanation
:We have to prove that (a + b + c)³ - a³ - b³ - c³ = 3(a + b ) (b + c) (c + a).
Considering LHS,
LHS : (a + b + c)³ - a³ - b³ - c³
= [(a + b + c)³ - a³] - (b³ + c³)
Using the algebraic identity,
a³ - b³ = (a - b)(a² + b² + ab)
(a + b + c)³ - a³ = ((a + b + c) - a)((a + b + c)² + a² + (a + b + c)a)
Using the algebraic identity,
(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)
= (b + c)(a² + b² + c² + 2(ab + bc + ca) + a² + a² + ab + ac)
= (b + c)(3a² + b² + c² + 3ab + 2bc + 3ac)
Using the algebraic identity,
a³ + b³ = (a + b)(a² + b² - ab)
b³ + c³ = (b + c)(b² + c² - bc)
So, [(a + b + c)³ - a³] - (b³ + c³) = (b + c)(3a² + b² + c² + 3ab + 2bc + 3ac) - [(b + c)(b² + c² - bc)]
= (b + c)[3a² + b² + c² + 3ab + 2bc + 3ac - (b² + c² - bc)]
= (b + c)[3a² + b² + c² + 3ab + 2bc + 3ac - b² - c² + bc]
= (b + c)[3a² + 3ab + 3bc + 3ac]
= (b + c)[3(a² + ab + bc + ac)]
= (b + c)[3(a(a + b) + c(b + a)]
= (b + c)[3(a + c)(a + b)]
= 3(a + b)(b + c)(a + c)
= RHS
(Get 30 points for answer, please answer truthfully)
Carter and his children went into a movie theater and he bought $33 worth of drinks and candies. Each drink costs $4.50 and each candy costs $3. He bought 3 times as many drinks as candies. Determine the number of drinks and the number of candies that Carter bought.
Answer:
6 drinks
2 boxes of candy
==================================================
Explanation:
x = number of drinks
y = number of boxes of candy
These two variables represent positive integers.
"He bought 3 times as many drinks as candies" which means we can set up the equation x = 3y
-------------
1 drink costs $4.50
x drinks cost 4.50x dollars
1 box of candy costs $3
y boxes of candy cost 3y dollars.
4.50x + 3y = total cost = 33 dollars
Therefore, we arrive at the second equation of 4.50x+3y = 33
-------------
We have this system of equations
[tex]\begin{cases}x = 3y\\4.50x+3y = 33\end{cases}[/tex]
I'll use substitution to solve. Replace x with 3y in the second equation, then isolate y.
[tex]4.50x+3y = 33\\\\4.50(3y)+3y = 33\\\\13.50y+3y = 33\\\\16.50y = 33\\\\y = 33/16.50\\\\y = 2\\\\[/tex]
This tells us he bought 2 boxes of candy.
Use that value to find x.
[tex]x = 3y\\\\x = 3*2\\\\x = 6\\\\[/tex]
Carter also bought 6 drinks.
-------------------------------
Check:
6 drinks = 6*4.50 = 27 dollars2 boxes of candy = 2*3 = 6 dollarsTotal cost = 27+6 = 33 dollarsThe answers are confirmed.
Another way to confirm the answers is to plug (x,y) = (6,2) into each equation of the system I mentioned earlier. After simplifying, you should get the same thing on both sides.
A visual way to confirm the answers is to graph each equation on the same xy grid. The two lines intersect at (6,2). You can use a graphing tool such as Desmos or GeoGebra.
Write 0.000000836 in scientific notation.
The decimal 0.000000836 in scientific notation is 8. 36 × 10^-7
What is scientific notation?Scientific notation can be defined as a way of expressing numbers too small or too large to be conveniently written in decimal form.
It is also referred to as standard index form, standard form and scientific form.
It is commonly used for complex calculations with lengthy numbers.
It is also described as a method of expressing numbers in the terms of a decimal number that is between 1 and 10, and not 10 itself multiplied by a power of 10.
Given the decimal;
0.000000836
In scientific notation, it is written as;
8. 36 × 10^-7
The power is negative because the zeros are counted towards the right side.
Hence, the value is 8. 36 × 10^-7
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A year hence a father will be 5 times as old as his son. Two years ago, he was three times as old as his his son will be four years hence. Find their present age.
A group of friends went to a hamburger bar 2/5 of them bought a hamburger, 1/3 of them bought just chips, and the rest bought cola, what fraction of the group bought food? what fraction just bought drinks
By adding the given fractions, we can see that 11/15 of the friends bought food, and 4/15 bought drinks.
What fraction of the group bought food?
We know that 2/5 of the group bought a hamburger, and 1/3 of them bought chips.
Then the total fraction of friends who bought food is given by the addition of the two fractions above.
2/5 + 1/3
finding a common denominator we will get:
(3/3)*(2/5) + (5/5)*(1/3)
6/15 + 5/15
11/15
So 11/15 of the friends bought food, and the rest:
4/15 bought drinks.
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David catches 75 camels, tags them, and releases them. A few weeks later, a helicopter pilot takes an aerial photograph of 310 camels, 25 of which are tagged. To the nearest whole number, what is the best estimate for the camel population?
Answer:
103
Step-by-step explanation:
[tex]\frac{75}{310} = \frac{25}{p}\\ 25 X \frac{310}{75} = 103[/tex]
Tell how you can ue mental math to find 45. 8 X 10 to the 3rd power and 45. 8 X 0. 1
The result of 45.8*10^3 is going to be 45800. Using mental math, 45.8*0.1 will be 4.58.
What is mental math?A set of abilities known as mental math enable people to perform calculations "in their heads" without the aid of paper and pencil or a calculator. Recalling math information, such as 8 x 5 = 40, is one of these abilities. Rounding numbers and estimating calculations are additional abilities. Mathematical calculations made solely with the human brain, without the aid of any materials or tools like a calculator, are referred to as mental calculations. When computing tools are not available, when mental calculation is quicker than other methods, or even in a competitive setting, people may use it.
Here,
45.8*10³=45800
45.8*0.1=4.58
The value of 45.8*10³ will be 45800. The value of 45.8*0.1 will be 4.58 using mental math.
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Do you know the answer~?
then please help me!!!!!!!!!!!!!!
The amount of Chemical B needed is 1.6 g.
what is graph?This refers to a diagram that shows a series of one or more points, lines, line segments, curves, or areas that represents the variation of a variable when compared with that of one or more other variables.
The quantity of Chemical B is plotted against the quantity of Chemical A.
Chemical B is plotted on the vertical axis using the scale of 1 cm to represent 2 units. Chemical A is plotted on the horizontal axis using the scale of 1 cm to represent 1 unit.
Therefore, on the graph, the line passing through the origin of the graph shows that when 1.4 g of Chemical A is used 1.6 g of Chemical B is needed.
Calculations:Chemical B is plotted on the vertical axis using the scale of 1 cm to represent 2 units.
To get the amount of Chemical B is on vertical axis = 2 grams
5 boxes
=0.4 g
Tracing the mass of Chemical A used 1.4 g it meets the line passing through the center at 4th line (4th box).
To get the amount of Chemical B is on vertical axis = amount of Chemical B per box * the number of line (boxes).
To get the amount of Chemical B is on vertical axis = 0.4 g * 4 lines (boxes)
= 1.6 g
Hence The amount of Chemical B needed is 1.6 g.
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Look at picture !!!!
Slope=
Y-intercept=
Equation=
Answer:
y = -5x -2
Step-by-step explanation:
Equation y=mx+b
Slope m=(y2-y1)/(x2-x1)
Slope m=(-7- -2)/(1 - 0)
Slope m=(-7 + 2)/(1 - 0)
Slope m=(-5)/(1)
Slope m= -5
Point-slope form = y − y 1 = m ( x − x 1 )
Point-slope form = y − -2 = -5 ( x − 0 )
Point-slope form = y + 2 = -5x − 0
Point-slope form = y = -5x -2
byuiedu
brightstormcom
In an arithmetic sequence, each term after the first is found by multiplying the previous term by a constant.
True false question.
True
False
Answer: False
Step-by-step explanation:
The statement you are giving is for the Geometric Sequence, not the arithmetic sequence. So this is false!
#6: Clayton is flying a model helicopter. The helicopter starts
on the roof of a building that is 85 feet above the ground.
Clayton makes the helicopter climb at a constant rate. After
10 seconds, the helicopter is 120 feet above the ground. How
many feet above the ground will the helicopter be after 20
seconds?
A. 130 B. 155 C. 205 D. 240
Answer:
155 feet
Step-by-step explanation:
the building is 85 feet high that's where drone starts
the drone flies to 120 feet in 10 seconds from 85 feet so the rate equals 35 feet per 10 second
in 20 seconds the drone would be 70 feet higher.
so the final height would be 85 feet plus 70 feet which equals 155 feet.
hope that helps
First try was incorrect
Hercules ate 6 hot dogs every 16 minutes. At that rate, how long,
minutes, will it take to eat 18 hot dogs?
Answer:
48 minutes
Step-by-step explanation:
6 : 16 = 18 : x
x = 16 * 18 / 6
x = 16 * 3
x = 48
what effect does increasing the sample size have on the probability? provide an explanation for this result.
Increasing the given sample size will decreases the probability because σx will decreases as n value increases.
In Statistitics whenever we test a hypothesis for testing a statistic, we use confidence interval. Confidence interval is on either side of an assumed value a margin of error. Margin of error is calculated as critical value * sigma/sqrt of n. Thus we find that whenever n increases, margin of error decreases.
Thus making confidence interval narrower and thus making probability for accepting null hypothesis a less value. As the pattern sizes increase, the range of every sampling distribution decreases so they emerge as more and more leptokurtic. The variety of the sampling distribution is smaller than the variety of the authentic populace. Therefore, as a pattern length increases, the pattern imply and general deviation might be nearer in fee to the populace imply μ and general deviation σ.
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In canada, 63% of households speak english as their primary language, and 23% speak french as their primary language. if two canadian households are selected at random, what is the probability that the first household speaks french, but the second household speaks english? (0.23)(0.63) = 0.1449 0.23 0.63 = 0.86 0.23 0.63 – (0.23)(0.63) = 0.7451 startfraction 0.23 over 0.63 endfraction = 0.3650
The probability that the first household speaks French, but the second household speaks English, is 0.1449. The correct option is a.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
In Canada, 63% of households speak English as their primary language, and 23% speak French as their primary language.
Let A be the event that the household speaks French and B be the event that the household speaks English.
Converting percentage to decimals,
63% = 0.63
and 23% = 0.23
According to the question,
P (A) = 0.23 and P (B) = 0.63.
Then, the probability that the first household speaks French, but the second household speaks English is,
Probability =(0.23) x (0.63)
=0.1449
Therefore, the probability that the first household speaks French, but the second household speaks English is 0.1449.
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56% of what number is 21
Answer:
The answer is 37.5.
Step-by-step explanation:
finding an irrational number between which given pair of numbers supports the idea that irrational numbers are dense in real numbers? math 3
If there is another element of the same set between any two members of a set, we can say that the set is dense.
We'll show that the first choice—3.14 and pi—is the right one.
To prove that the set of irrational numbers contains a lot of real numbers, we must first discover an irrational number that lies between two specified real numbers.
In order to extend this to the real set, which is the union of irrational numbers and rational numbers, we should be able to find an irrational number between a rational number and an irrational number (or between an irrational number and a rational number). This is because we know that irrational numbers are dense (between two irrational numbers we can find another irrational number).
The first option, which has one of each, will then be the right choice.
Pi is irrational, while 3.14 is rational.
Finding an irrational number between these two indicates that the real set contains many irrational numbers.
(Note that the third option likewise has an irrational and a rational number, but the first one, [tex]e^{2}[/tex], is larger than the second one[tex]\sqrt{54}[/tex], thus it is written wrongly; for this reason, we did not choose it.)
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What is the address of the element 0 ?
Please por favor someone help me out (;
The answers are 1) Distributive property 2) Combining like terms 3) Subtraction property of equality 4) Subtraction property of equality 5) Subtraction property of equality
What is mathematical identities?An identity is an equality that holds true regardless of the values chosen for its variables. They are used in simplifying or rearranging algebra expressions.
Given; 4x-2(3+2x) = 2x+11
1) 4x-6-4x = 2x+11 = Distributive property
2) 4x-4x-6 = 2x-11 = Combining like terms
3) -6 = 2x-11 = Subtraction property of equality
4) -17 = 2x = Subtraction property of equality
5) -8.5 = 2 = Subtraction property of equality
Hence, the answers are 1) Distributive property 2) Combining like terms 3) Subtraction property of equality 4) Subtraction property of equality 5) Subtraction property of equality
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Giving Brainly to whoever helps! Thanks.
Answer:
140 hamburgers
Step-by-step explanation:
to find the answer we must first use a let statement and write an equation
let x = hamburgers
hamburgers * 2 is cheeseburgers and added together that is 420
so
x + 2x = 420
now solve
3x = 420
x = 140
140 hamburgers were sold
Answer:
Step-by-step explanation:
240 divided by 3= 80
80+80=160
160 hamburgers sold altogether on Wednesday.
Cynthia is a real estate agent. In one of her properties, a large square
room has an area of 405 square feet. To find the length of one side of
the room, Cynthia writes V405 feet. Simplify this expression, using the
first rule of radicals.
The expression after simplifying with the first rule of radicals is 9√5.
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is side²
We have,
Area of a square = side² _______(1)
Area = 405 square feet _______(2)
From (1) and (2) we get,
405 square feet = Side²
Side = √405 feet
[ 405 = 81 x 5 ]
Side = √(81 x 5)
[ 9² = 81 ]
Side = 9√5
Thus,
The side length is 9√5 feet.
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(1 point) how many different ways can a race with 6 runners be completed? (assume there is no tie.) your answer is : 36
There are 720 different ways can a race with 6 runners be completed.
What is a combination?
The process of combining or the condition of combining. a combination of things; an amalgamation of concepts. a grouping of notes: A chord is a grouping of notes. a grouping of people or entities acting together to impede commerce.
Here, we have
The winner can be chosen from all 6 runners, the second person can be chosen from 5 people, the third - from 4, and so on.
So the total number of possible results can be calculated as:
n = 6×5×4×3×2×1= 6!
= 720
Hence, there are 720 different ways can a race with 6 runners be completed.
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In order to walk to school from your house, you walk 0. 8 mi north and 0. 5 miles east. What is the direct distance from your house to school
The direct distance from your house to school as calculated from the given data is 0.9434 miles.
Let
the distance walked North = A = 0.8 miles
the distance walked East= B = 0.5 miles
the direct distance between house and school be C
On using pythagoras theorem,
C² = A² + B²
= 0.8 ²+ 0.5 ²
= 0.89
C =0.9434 miles
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem.
According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c , C² = A² + B².
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Please help me, I need this for tomorrow’s test
Answer:
12
Step-by-step explanation:
14 + 7 = 21
14 / 21 = ⅔
AE = 18
x / 18 = ⅔
x = 18 x ⅔
x = 12
Three times the sum of x and 7 is 27. What is x?
Answer:
2
Step-by-step explanation:
it says 3 times the sum of x and 7 equals 27 so 1st divide 27 by 3 which gives you 9 and then subtract 7 which is given and that gives you 2 for your answer
The winner of a 1000 mile race drove his car to victory at a
rate of 131.3009 mph. What was his time (to the nearest
thousandth of an hour)?
He took 7.616 hours for victory at the speed of 131.3009 and cover 1000 miles.
What is distance?
The distance between two sites is the length of the route. The metre is the SI unit for distance.
What is speed?
The speed at which an object’s location changes in any direction. The distance travelled divided by the time it took to travel that distance is how fast something is moving.
What is time?
The amount of time that something happens, goes through a process, or remains the same.
Speed= 131.3009 mph
Total distance= 1000 miles
Speed = distance/ time
time= distance/ speed
time= 1000/131.3009
(nearest thousandth means round off upto 3 decimal places)
time= 7.616 hours
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The product of two consecutive numbers is 3306. What are the numbers?
a) about what percentage of scores were between between 68 and 82? 68 % b) about what percentage of scores were between 61 and 75?
Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%
What is percentage?One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.
Here,
Given: Total number of freshman =500
mean =75 and standard deviation =7
a) the percentage of scores that fell between 68 and 82
340 is the number of freshman whose scores that fell between 68 and 82
thus,
percentage = 340 /500 * 100
=> percentage = 68%
b)the percentage of scores that fell between 61 and 75
237 is the number of freshman whose scores that fell between 61 and 75
thus,
percentage = 237/500 * 100
=> percentage = 47.4%
Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%
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when there are three treatment groups and 300 participants, what is the degrees of freedom in the denominator of the f-statistic calculation?
The degrees of freedom in the denominator of the f-statistic calculation is 2.
Explain the term degrees of freedom?The number of distinct bits of information required to construct a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df.
It is determined by subtracting the number of constraints from the sample size.Normal reporting of the results of a statistical test includes the test statistic and the degrees of freedom in brackets.Its degrees of freedom refers to the quantity of independent data points utilized to generate the statistic.For the stated question-
degrees of freedom df = n - 1
n = 3 groups
df = 3 - 1
df = 2
Thus, the degrees of freedom in the denominator of the f-statistic calculation is 2.
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What is the domain of the function of x graphed below?
(-6.-5)
A {xx>-1}
(-1.3)
Cx-5
B {x-6
D {xx<3}
Answer:
Step-by-step explanation:
B is the answer
Create a line from-6,-5 to the x axis to -6 and draw a line from -1,3 down to x axis because that is your domain. Make sure to look at your open circles or closed circles at end of the line, if closed there are block brackets, If open then it is parenthesis. If it is a coordinate it is curly brackets. So therefore the answer is B