Let a,b,c,d be real numbers such that 1/a+Ï + 1/b+Ï + 1/c+Ï = 2/Ï
where Ï is non real cube root of unity choose the correct answer. abc+bcd+acd+abd is equal to
First, we can rewrite the given equation as:
1/a+Ï + 1/b+Ï + 1/c+Ï = (1/Ï)(1/a + 1/b + 1/c)where Ï is the non real cube root of unity.
We can then multiply both sides of the equation by Ï to get:
1/a + 1/b + 1/c = 2(1/a + 1/b + 1/c)This simplifies to:
1/a + 1/b + 1/c = 0Since a, b, and c are all real numbers, we know that 1/a, 1/b, and 1/c are also real numbers. Therefore, the sum of these three real numbers must also be a real number. The only way that 1/a + 1/b + 1/c can equal 0 is if all three of these terms are equal to 0.
Thus, we can conclude that a = b = c = 0.
Since a, b, and c are all equal to 0, we know that abc + bcd + acd + abd must also equal 0. Therefore, the answer is 0.
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The cash register receipts each day last week at a coffee shop were $1,846, $1,521, $1,439, $1,439, $1,851, $2,722, and $2,540. (a) Find the mean. (Round your answer to to the nearest cent.)
9. Mai rode on a train at a rate of speed of 70 miles per hour for 3 hours. Then she rode in a car at a rate
of speed of 50 miles per hour for 2 hours. What is the difference between the number of miles Mai
rode on the train and the number of miles she rode in the car?
a. 20
b.
60
c.
100
d. 110
The difference between the number of miles travelled on train and car is 110 miles
How to determine the difference between the number of milesFrom the question, we have the following parameters that can be used in our computation:
Distance 1 (train): 70 miles per hour for 3 hoursDistance 2 (car): 50 miles per hour for 2 hoursThe difference between the distance covered can be calculated as
Distance difference = The difference of the product of speed and time
Substitute the known values in the above equation, so, we have the following representation
Distance difference = 70 * 3 - 50 * 2
Evaluate the products
Distance difference = 210 - 100
Evaluate the difference
Distance difference = 110 miles
Hence, the distance difference is 110 miles
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A shoe store uses a 60% markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of $55?
Answer:The selling price of shoes after a markup of 60% of the price will be equal to $81.60
Step-by-step explanation:
i don't think this is right
Find (f - g)(x), if f(x) = 2x2 + 2 and g(x) = 6x2 + 6.
To find (f - g)(x), you can subtract g(x) from f(x):
(f - g)(x) = f(x) - g(x)
= (2x2 + 2) - (6x2 + 6)
= -4x2 + (-4)
= -4(x2 - 1)
Therefore, the result of (f - g)(x) is -4(x2 - 1).
Evaluate the following 14/2+4*4-4
Answer:
14/2+4x4-4= 19
Step-by-step explanation:
calculate
7+19-4
which is 19
(BODMAS rule is used here)
14/2 + 4 × 4 - 4
7 + 4 × 4 - 4
7 + 16 - 4
7 + 12
19
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the height of a triangle is 2 more than twice the base. the area is 20 square feet. find the quadratic equation that represents this situation if the formula for the area of a triangle is A = 1/2 bh.Select one a. 2b^2 - b - 20 = 0b. b^2 + 2b= 0с. b^2 + b - 20 = 0d. b^2 + 2b + 20 = 0
On solving the provided question we can say - area = 1/2 x b x (2b+2), area = [tex]b^2 + b -20 {[/tex]
What is Triangle?A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees. A three-sided form is a triangle. Triangles are known by a variety of names. Triangle kinds are determined by the size of the angles and the length of the sides (angles). Depending on how long their sides are, triangles fall into one of three categories. Isosceles, equilateral, and uneven
Let 'b' be the base of the triangle, then
then height is - 2b + 2
area = 1/2 bxh
area = 1/2 x b x (2b+2)
area =
[tex]b^2 + b -20 {[/tex]
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Im stuck on finding G im wondering if someone can help me
Answer:
G=15-1.25×t
or,G=1.25(12-t)
Answer:
G= 15-t1.25
Step-by-step explanation:
What is 1.8 rounded to the nearest tenth
Answer: 1.8 rounded to the nearest tenth will remain as 1.8 because 0.8 is 8 tenths
Answer:
Step-by-step explanation:
11.3
3. (8.4B) The graph below shows the relationship
between the number of dollars a worker earns,
and the number of hours worked. What does the slope of the graph represent? HELP PLEASE
The slope of the graph represent d)The number of hours worked to earned dollors
What is Slope of the graph?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, although it may be found in O'Brien's (1844)and Todhunter'sformulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which provides the same valueTo learn more about Slope of the Graph refer to:
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H(x) = -4x - 3, find h (2)
Answer:
h(2) = (-11)
Step-by-step explanation:
h(x) = (-4x - 3), if h(2)
h(2) = (-4(2) - 3)
h(2) = -8 - 3
h(2) = (-11)
Thus, The answer is (-11) if h(2)
A company has found that the demand for its product varies inversely as the price of the product. When the price x is 4.75 dollars, the
demand y is 500 units.
Find a mathematical model that gives the demand y in terms of the price x in dollars.
With the help of algebra mathematical model equation for demand of company's product is given by the equation d = 1800 / p.
What is algebra?
The area of mathematics known as algebra deals with the representation of problems as mathematical expressions. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.
Let demand for company's product d vary inversely with its price p, which means
d ∝ ( 1/p ) or d = k * ( 1/ p) = k / p ----- 1
As when p = 4.5, d = 400
Putting these in (1), we get 400 = k/ 4.5
Hence #k=400 x 4.5=1800 and our model equation is
d = 1800/p
Hence mathematical model equation for demand of company's product is given by the equation d = 1800 / p.
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The above table shows statistics on the ages, in years, of the people who attended a lecture last week. The data are summarized in the boxplot shown.Which of the following statements is supported by the table and boxplot?answer choicesThe range of the distribution is 20 years.There were 43 people who attended the lecture.At least 50% of the people who attended the lecture were 43 years or younger.At least 75% of the people who attended the lecture were age 53 years or younger.At least 25% of the people who attended the lecture were 33 years old.
The boxplot shows that the majority of the people who attended the lecture were age 53 or younger, which means at least 75 percentage of the people were in that range.
The table and boxplot provide information about the ages of the people who attended a lecture last week. The boxplot shows that the majority of the people who attended the lecture were age 53 or younger. This is supported by the table, which shows that the median age is 53 and the interquartile range is between 36 and 53. This indicates that at least 75% of the people who attended the lecture were age 53 years or younger. The range of the distribution is 20 years, with the minimum age being 18 and the maximum age being 38. This suggests that there were at least two people in each age range, from 18 to 38. This also indicates that there were at least 43 people who attended the lecture. The boxplot also shows that at least 25% of the people who attended the lecture were 33 years old. This is supported by the table, which shows the lower quartile is 33.
Interquartile range = Maximum - Minimum
Interquartile range = 53 - 36 = 17
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Consider two securities, a and b. security a and b have a correlation coefficient of 0.65. security a has standard deviation of 12, and security b has standard deviation of 25. calculate the covariance between these two securities.
a. 300
b. 461.54
c. 261.54
d. 195
e. 200
The correct answer is option D. The covariance between securities a and b is 195.
To calculate the covariance between securities a and b, we can use the formula:
covariance = correlation coefficient * standard deviation of security a * standard deviation of security b
Plugging in the given values, we get:
covariance = 0.65 * 12 * 25 = 195
Therefore, the answer is (d) 195.
The covariance between two securities measures the extent to which the two securities tend to move together. A positive covariance indicates that the securities tend to move in the same direction, while a negative covariance indicates that the securities tend to move in opposite directions.
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Select all terms equivalent to √24.
A: the area of a square with side length 24 units
B: the side length of a square with area 24 units
C: the positive number x, where x - x = 24
D: the positive number y, where y = 24-24
E: the edge length of a cube with volume 24 cubic units
F: the volume of a cube with edge length 24 units
Answer:
B, E
Step-by-step explanation:
Determine a series of transformation that would map Figure S onto Figure T.
Answer:
reflection then rotation
Step-by-step explanation:
how do you solve -40 -(-12/5) =
Answer:
Below
Step-by-step explanation:
-40 -(-12/5) = -200/5 + 12/5 = -188/5 = - 37 3/5
A basketball team has 12 players. For the last game of the season the coach will randomly select 5 players to start the game. The first player selected is the center, the second player selected is the power forward, the third player selected is the forward, the fourth player selected is the shooting guard, and the fifth player selected is the point guard. Determine the number of different ways the coach can pick up he line of the game
The number of different ways the coach can pick up the line of the game is 792 ways
Step-by-step explanation:
Let n- number of players, r-selection of players.
We can select them using Combination: nCr = 12C5
Combination formula nCr =[tex]\frac{n!r!}{ (n-r)!}[/tex] = 12C5 = [tex]\frac{12!5!}{(12-5)! }[/tex]
=[tex]\frac{12!5!}{ 7!}[/tex]
= 792ways
The number of different ways the coach can pick up the line of the game is 792 ways.
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Please give me detailed answer
The values of x, y and z are 5, 18 and 12 using the congruent triangles properties and triangles sum properties.
What are the characteristics of a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
In congruent triangles all the sides are equal, with respect to the other triangle.
Calculation:Given that ΔUVW≅ΔTSR.
We can see that in TSR triangle the lengths of TR and TS are given as 50 and 53 now the remaining side RS is 5y-33 as we know that both triangles are similar we compare side RS with side VW
i.e..,
5y-33 = 57
5y = 90
y = 18
So we can now compare vertices vertex V is vertex R , vertex W is vertex S and vertex U is vertex T.
So equating the sides of triangles we get,
12x-7 = 53 and 3z+14 = 50
12x = 60 3z = 36
x= 5 z = 12
The values of x, y and z are 5, 18 and 12 using the similar triangles properties and triangles sum properties.
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11/3 of x is 55 find x
Answer:
16.5
Step-by-step explanation:
11/3 =3 and 1/3 so 55/3 and 1/3 = 16.5 or 16 and 1/2
graph the line y=3/2x
The equation of the line passes the origin. And the inclination of the line with the x-axis is 3/2. And the graph is given below.
What is a linear equation?An association between various factors brings about a straight model when a diagram is shown. The variable will have a level of one.
The straight condition is given as,
y = mx + c
Where m is the incline of the line and c is the y-block of the line.
The equation of the line is given below.
y = (3/2)x
The y-intercept is zero. Then the condition of the line passes the beginning. Furthermore, the tendency of the line with the x-pivot is 3/2.
The graph of the line is drawn below.
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Is DEF = ABC? If so, type the reason, if not type no.
Answer:
Yes
Step-by-step explanation:
All you need to do is figure out the missing angles. We know that the three angles in a triangle add up to 180 degrees.
For angle B in ABC, 180-52-39= 89. So angle B = 89 degrees.
For angle D in DEF, 180-39-89= 52. So angle D = 52 degrees.
Then see if the order of the angles match up.
DEF = 52 degrees, 89 degrees, 39 degrees
ABC = 52 degrees, 89 degrees, 39 degrees
The order of the same angles match, so triangle DEF and triangle ABC are equal.
Answer:
Yes, triangle DEF is similar to triangle ABC because their corresponding angles are the same size.
Step-by-step explanation:
Interior angles of a triangle sum to 180°.
⇒ ∠A + ∠B + ∠C = 180°
⇒ 52° + ∠B + 39° = 180°
⇒ ∠B = 89°
⇒ ∠D + ∠E + ∠F = 180°
⇒ ∠D + 89° + 39° = 180°
⇒ ∠D = 52°
Two triangles are similar if their corresponding angles are the same size.
If ΔDEF ~ ΔABC then:
∠D = ∠A∠E = ∠B∠F = ∠CFrom inspection of the given diagram:
∠D = 52° and ∠A = 52° so ∠D = ∠A∠E = 89° and ∠B = 89° so ∠E = ∠B∠F = 39° and ∠C = 39° so ∠F = ∠CTherefore, the triangles are similar because their corresponding angles are the same size.
part 1: 2 airplanes left the same airport at the same time. One is traveling at 422 mph straight east, the other is traveling 384 mph straight west.
How long will it take before they are 6045 miles apart?
part 2: 2 airplanes left the same airport at the same time. One is traveling at 422 mph straight NORTH, the other is traveling 384 mph straight WEST.
How long will it take before they are 1997 miles apart?
The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
2 planes left a similar air terminal simultaneously. One is going at 422 mph straight east, the other is voyaging 384 mph straight west.
If the distance between them is 6045 miles. Then the time is calculated as,
T = 6045 / (384 + 422)
T = 6045 / 806
T = 7.5 hours
2 planes left a similar air terminal simultaneously. One is going at 422 mph straight NORTH, the other is voyaging 384 mph straight WEST.
If the distance between them is 1997 miles. Then the time is calculated as,
T = 1997 / (384 + 422)
T = 1997 / 806
T = 2.48 hours
The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.
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pls help with both questions
I’ll give BRAINLIEST if correct need asap question is in the photo attached
Graph the line using the slope and y-intercept, or two points.
Slope:
1
y-intercept: (0,3)
x y
0 3
1 4
The ordered pairs model an exponential function, where w is the function name and t is the input variable.
{(1,60),(2,240),(3,960),(4,3840)}
What is the function equation in sequence notation?
wt=
Answer:
The answer is in my screen shot:
Explanation:
It's a geometric sequence with common ratio 3. You can calculate the common ratio by dividing the 240 by 80 or likewise 720 by 240.
Emily loves to go the spa she and her friends go twice a month each visit she gets a 90 minute massage for $125 and a deluxe manicure and pedicure for $65. How much does she spent at the spa each month?
Answer: $380
Step-by-step explanation:
First, we will find the price per visit using addition.
$125 + $65 = $190
Next, we notice it says "twice a month" in the question. We will multiply the value above by two to find the price per month.
$190 * 2 = $380
Answer:
twice a month of 125 + 65
2($125 + $65)
= 2($190)
= $380
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-In an experiment studying the effects of alcohol on social anxiety, alcohol is the ______ variable. A.) independent. B.) confounding. C.) random. D.) dependent.
In an experiment studying the effects of alcohol on social anxiety, alcohol is the dependent variable. So, correct option is option D.
What is Dependent variable ?Variables: The goal of all research is to describe and explain global dispersion. Variance is just the difference. That is, the fluctuations that occur naturally in the world, or the changes that occur as a result of manipulation. A variable is the name given to the variance you want to describe. A variable is the result of a force or is itself a force that changes another variable. There are two types of variables.
DependentIndependentWhen researchers administer an active drug to one group of people and placebo or an inactive drug to another group of people, the independent variable is drug treatment. Each person's response to active drug or placebo is called the dependent variable.
In this case, an experiment examining the effects of alcohol on social anxiety. Alcohol is the dependent variable here.
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100 POINTS!!!!
a) The next event requires each runner to jump 10 hurdles that are spaced 8.5 meters apart. If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line, how long is the race? Show your work. (3 points)
PLEASE QUICK
Answer:
100.72
Step-by-step explanation:
[tex]Given,[/tex]
event requires each runner to jump 10 hurdles that are spaced 8.5 meters apart.
If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,
To Find: how long is the raceSolution:
runner to jump 10 hurdles that are spaced 8.5 meters apart.
Distance between 10 hurdles
=(10-1)* 8.5
=9*8.5
=76.5
If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,
Hence length of race = 13.72+76.5+10.5
=100.72
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Answer:
100.72 meters
Step-by-step explanation:
To find the total length of the race, we need to sum:
The distance from the starting line to the first hurdle.The distances between the hurdles.The distance from the last hurdle to the finish line.The distance from the starting line to the first hurdle is 13.72 meters.
The distance between each of the 10 hurdles is 8.5 meters.
There are 9 spaces between hurdles 1 and 10, so the distance between the hurdles is 9 × 8.5 = 76.5 meters.
The distance from the last hurdle to the finish line is 10.5 meters.
To find the total length of the race, add these distances together:
[tex]\begin{aligned}\textsf{Total length of the race} &=\sf 13.72\; meters + 76.5\; meters + 10.5 \;meters\\\\&=\sf 100.72\; meters\end{aligned}[/tex]
Therefore, the race is 100.72 meters long.
determine the longest wavelength photon (in nm) which can remove an electron from mercury metal if the work function of the metal is 4.475 ev (1 ev
To determine the longest wavelength photon which can remove an electron from mercury metal, we need to use the equation:
wavelength = hc/work function
What are photons?Photons are just light particles. Photons are basic subatomic particles that convey the electromagnetic force (and so much more). The photon is the basic unit of electromagnetic radiation, or the "quantum."
What is wavelength?A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is often defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm).
To determine the longest wavelength photon which can remove an electron from mercury metal, you need to use the equation:
wavelength = hc/work function
where h is the Planck constant (6.626 x 10^-34 Js), c is the speed of light (2.998 x 10^8 m/s), and work function is the minimum energy needed to remove an electron from the metal, in this case 4.475 eV.
Plugging these values into the equation gives:
wavelength = (6.626 x 10^-34 Js)(2.998 x 10^8 m/s)/(4.475 x 1.602 x 10^-19 J/eV)
This simplifies to:
wavelength = 404.4 nm
So, the longest wavelength photon which can remove an electron from mercury metal is 404.4 nm.
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