consider reordering the letters in the word tennessee. use the technique shown in example 9.5.11 to answer the following questions. (a) if the n's are placed first, how many ways are there to choose positions for them? if the e's are placed second, how many ways are there to choose positions for them? if the s's are placed third, how many ways are there to choose positions for them? if the t is placed fourth, how many ways are there to choose a position for it? so, the total number of ways to reorder the letters in the word tennessee is . (b) imagine placing the letters into positions in a different order. if the e's are placed first, how many ways are there to choose positions for them? if the t is placed second, how many ways are there to choose a position for it? if the s's are placed third, how many ways are there to choose positions for them? if the n's are placed fourth, how many ways are there to choose positions for them? (c) when the method suggested in part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is ---select--- when the method of part (a) is used.
Answer:
Step-by-step explanation:
(a) If the n's are placed first, 36 ways are there to choose positions for them. If the e's are placed second, 35 ways are there to choose positions for them. If the s's are placed third, 3 ways are there to choose positions for them. If the t is placed fourth, 1 way is there to choose a position for it.
(b) If the e's are placed first, 126 ways are there to choose positions for them. If the t is placed second, 5 ways are there to choose a position for it. If the s's are placed third, 6 ways are there to choose positions for them. If the n's are placed fourth, 1 way is there to choose position for it.
(c) Part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 36*35*3*1=3780. Part (a) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 126*5*6*1 =3780.
What is permutation of rearranging letters?
A permutation is a (possible) rearrangement of objects. For example, there are 6 permutation of rearranging letters a, b, c: abc, acb, bac, bca, cab, cba. a b c , a c b , b a c , b c a , c a b , c b a .
The total number of ways to reorder the letters in the word "tennessee" is calculated by considering the different ways the letters can be placed first, second, third, and fourth. The number of ways to place the n's first is 9!/(7!2!), the number of ways to place the e's second is 7!/(4!3!), the number of ways to place the s's third is 3!/2!1!, and the number of ways to place the t fourth is 1. When these values are multiplied together, the total number of ways to reorder the letters is 36*35*3*1=3780.
Again placing the letters into positions in a different order. The number of ways to place the e's first is 9!/(4!*5!), the number of ways to place the t second is 5!/(4!*1!), the number of ways to place the s's third is 4!/(2!*2!) and the number of ways to place the n's fourth is 2!/(2!*0!). When these values are multiplied together, the total number of ways to reorder the letters is 126*5*6*1 =3780.
Therefore, the total number of ways to reorder the letters in the word "tennessee" is 3780 in both orders.
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a) 36, 35, 3, 1 ways; b) 126, 5, 6, 1 ways; c) total number of ways to reorder the letters in the word tennessee is 3780 for both a) and b).
(a) If the n's are placed first, 36 ways are there to choose positions for them. If the e's are placed second, 35 ways are there to choose positions for them. If the s's are placed third, 3 ways are there to choose positions for them. If the t is placed fourth, 1 way is there to choose a position for it.
(b) If the e's are placed first, 126 ways are there to choose positions for them. If the t is placed second, 5 ways are there to choose a position for it. If the s's are placed third, 6 ways are there to choose positions for them. If the n's are placed fourth, 1 way is there to choose position for it.
(c) Part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 36*35*3*1=3780. Part (a) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 126*5*6*1 =3780.
What is permutation of rearranging letters?
A permutation is a (possible) rearrangement of objects. For example, there are 6 permutation of rearranging letters a, b, c: abc, acb, bac, bca, cab, cba. a b c , a c b , b a c , b c a , c a b , c b a .
The total number of ways to reorder the letters in the word "tennessee" is calculated by considering the different ways the letters can be placed first, second, third, and fourth. The number of ways to place the n's first is 9!/(7!2!), the number of ways to place the e's second is 7!/(4!3!), the number of ways to place the s's third is 3!/2!1!, and the number of ways to place the t fourth is 1. When these values are multiplied together, the total number of ways to reorder the letters is 36*35*3*1=3780.
Again placing the letters into positions in a different order. The number of ways to place the e's first is 9!/(4!*5!), the number of ways to place the t second is 5!/(4!*1!), the number of ways to place the s's third is 4!/(2!*2!) and the number of ways to place the n's fourth is 2!/(2!*0!). When these values are multiplied together, the total number of ways to reorder the letters is 126*5*6*1 =3780.
Therefore, the total number of ways to reorder the letters in the word "tennessee" is 3780 in both orders.
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A local plumber makes house calls. She charges $30 to come out to the house and $40 per hour for
her services. For example, a 4-hour service call costs $30 + $40(4) = $190.
A. Statistic Hours of Service Call Cost of Service Call
Mean 4.5 30+40(4.5) = 210
Median 3.5 30+40(3.5) = 170
SD 1.2 40(1.2) = 48
IQR 2.0 40(2.0) = 80
Minimum 0.5 30+40(0.5) = 50
Do these summary statistics indicate that a Normal model is appropriate here? Explain.
The mean and the median of the given data are 210 and 170.
What are Mean and Median?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
The four-hour service call costs
$30 + $40(4) = $90
(a) The given table summary details and finds the cost of the service cells
Statics Hour of service call cost of service call
Mean 4.5 30 + 40(4.5) = 210
Median 3.5 30 + 40 (3.5 = 170
SD 1.2 30 + 40 (1.2) = 78
TQR 2.0 30 + 40 (2.0) = 110
Minimum 0.5 30 + 40 (0.5) = 50
(b) The service call corresponding score is 1.50
z score = 138-4.5/1.2 = 113.75
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Judy and Cassie each opened a savings account on the same day. Judy started by putting $300 in her account, and she will deposit an additional $12 each week. Cassie made an initial deposit of $100, and she will add $20 more each week. Eventually, Judy and Cassie will each have the same amount saved. How many weeks will that take?
Write a system of equations, graph them, and type the solution.
Answer: 25 weeks
Step-by-step explanation:
Let W represent the number of weeks
Judy equation is
12W + 300
Cassie equation is
20W + 100
Now let's solve it! Our system of equation is
12W + 300 = 20W + 100
Subtract 300 from both sides
12W = 20W -200
Subtract 20W from both sides
-8W = -200
W = 25 weeks
So, it takes 25 weeks for Judy and Cassie to have the same amount saved.
Answer:
let judy = 300 + 12W
cassie = 100 + 20W
300 + 12W = 100 + 20W
300 - 100 = 20W - 12W
200 = 8W
W = 25
CHECKING:
300 + 12(25) = 100 + 20(25)
300 + 300 = 100 + 500
600 = 600
Therefore, it will take 25 days for Judy and Cassie so that they have the same amount saved.
THE GRAPH IS IN THE PICTURE,line graph
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-The dot plots show rainfall totals for several spring storms in highland areas and lowland areas.
The dot plots show that the lowland areas experienced significantly more rainfall than the highland area during spring storms, with a larger range and maximum rainfall.
The dot plots show the rainfall totals for several spring storms in both highland and lowland areas. The dots representing the lowland areas are more spread out and have a larger range compared to the dots representing the highland areas. This indicates that the lowland areas experienced more rainfall than the highland areas during these storms. Additionally, the maximum rainfall for the lowland areas is greater than the maximum rainfall for the highland areas, further emphasizing the difference in rainfall between the two areas. This could be due to a number of factors, such as the higher elevation of the highland areas resulting in less moisture being able to accumulate, or the lower temperature of the highland areas resulting in less evaporation and thus less rainfall. Additionally, the lower elevation of the lowland areas could result in more moisture being able to accumulate, and the higher temperature of the lowland areas could result in more evaporation, leading to increased rainfall. Regardless of the cause, the data from the dot plots clearly show that the lowland areas experienced more rainfall than the highland areas during these spring storms.
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Find the 87th term of the arithmetic sequence -19, -13, -7…
Answer:
497
Step-by-step explanation:
a(87) = -19+(87-1)6
a(87)=-19+(86)6
a(87)=-19+516
a(87)=497
I used the arithmetic formula which is an=a1+(n-1)d.....
Which numbers for the numerator
and denominator make the equation.
true? Complete the equation. Fill in
the bubble before the number that is
correct.
Answer:
Step-by-step explanation
So in the fraction 3/8 the numerator is 3. In the fraction 1/9 the numerator is 1.
I need help with this
The value of the function (f o g )(11) is -1
How to find the value of the given function?Applying composite function formula,
(f o g )(x) = f [g (x)]
Here ,f(x) = [tex]\sqrt{x} - 3[/tex]
g (x ) = x - 7
(f o g )(x) =f [x - 7 ]
=[tex]\sqrt{x-7} -3[/tex] --(1)
Substitute x = 11 in the given function in (1)
[tex](f o g )(11) =\sqrt{11-7} -3\\(f o g )(11) =\sqrt{4} - 3\\(f o g )(11) = 2 -3 = -1[/tex]
The value of the function (f o g )(11) is -1
What is a composite function?A composite function is a function whose values are obtained by applying one function to an independent variable.Then using the result to apply the second function, and the domain of which is made up of the independent variable values for which the output of the first function falls within the domain of the second. The composition of functions is a particular instance of the composition of relations, and it is sometimes also indicated by °.Therefore, all characteristics of composition of relations, including associativity, are also characteristics of composition of functions. However, composition of functions differs from multiplication of functions ,if it is defined at all and has a number of distinct characteristics, most notably that it is non-commutative.So, option 2 is correct .To learn more about composite function, refer:
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You want to put $2,500 in a simple interest account. It has a 4% annual interest rate. How long must you invest that money to earn $500 in interest?
A) 1.25 years
B) 2.5 years
C) 5 years
D) 20 years
Answer:c
Step-by-step explanation:
Answer: C) 5 years
Step-by-step explanation:
Formula for the simple interest is: I = P * r * t, where: I = $500, P = $2,500, r = 0.04 and t stays for the number of the years. 500 = 2,500 * 0.04 * t; 500 = 100 * t; t = 500 : 100; t = 5.
How do you complete the proof?
From the proof below, we have been able to prove that IK bisects ∠HIJ by CPCT postulate
How to complete the proof of congruent angles?Congruent angles are defined as angles that have equal measure.
Now, we are given that;
IK bisects ∠HKJ
HK ≅ JK
Thus, since IK bisects ∠HKJ, then it means that by definition of angle bisector that;
∠HKI = ∠JKI
Now, we are also told that HK ≅ JK.
Now, by reflexive property of congruence, we can say that IK is congruent to itself.
Thus, we now have 2 congruent sides and an include angle and as such both triangles are congruent by SAS Congruency postulate.
Thus, we can conclude that ∠HIK = ∠JIK by CPCT which states that Corresponding parts of Congruent Triangles are congruent.
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Select the correct answer.
What is the zero of the function represented by this graph?
The graph shows the cube root function with no start or end point. Some major points on the graph are (minus 4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).
A.
B.
C.
D.
The zero of the graph is x = -4
How to determine the zero of the graph?From the question, we have the following parameters that can be used in our computation:
Major points on the graph are (minus 4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).
Express the points, properly
So, we have the following representation
Major points on the graph are (-4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).
Write out the points
(-4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).
The zeros of the graph are the point where y = 0
In this case, the points are
(-4, 0)
So, we have
x = -4
Hence, the zero is x = -4
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What is 3 5 equivalent to as a fraction?
The fractions equivalent to 3/5 are 6/10, 9/15, 12/20, etc.
Now, According to the question:
Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. This is the reason why these fractions get reduced to the same number when they are simplified.
Let us understand the two ways in which we can make equivalent fractions:
Multiply the numerator and the denominator by the same number, or,Divide the numerator and the denominator by the same number.Hence, the equivalent fractions for 3/5 are:
(3/5) × (2/2) = (3 × 2) / (5 × 2) = 6/10
(3/5) × (3/3) = (3 × 3) / (5× 3) = 9/15
(3/5) × (4/4) = (3 × 4) / (5 × 4) = 12/20
Thus, 6/10, 9/15, 12/20 are equal to 3/5,
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Rosie ran directly toward her home at a constant velocity for 78 seconds. In one-third of that time, she ran 52 meters. What was Rosie's velocity?
The velocity of Rosie when running is 2 meters per second
How to determine the velocity of Rosie?From the question, we have the following parameters that can be used in our computation:
Time = 1/3 of 78 seconds
Distance covered = 52 meters
The velocity can be calculated using the following equation
Velocity = Distance covered/Time
Substitute the known values in the above equation, so, we have the following representation
Velocity = 52/(1/3 * 78)
Evaluate the quotient
Velocity = 2
Hence, the velocity is 2 meters per second
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What does associative property look like?
The associative property looks like a + (b + c) = (a + b) + c.
According to the associative property, if 3 numbers are added or multiplied then the grouping of numbers does not change the final result.
The associative property is applicable in addition as well as in multiplication.
According to the associative property in addition - when 3 numbers, say a, b, and c are being added then their sum will not change even if the grouping of numbers is changed. It can be presented as:
(a + b) + c = a + (b + c)
According to the associative property in multiplication - when 3 numbers, say a, b, and c are being multiplied then their product will not change even if the grouping of numbers is changed. It can be presented as:
(a × b) × c = a × (b × c)
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Is algebra a hard math?
Linear algebra is too hard because it is not very intuitive, it places a powerful emphasis on rigorous proofs, and its concepts are very different and difficult to visualize.
Linear algebra is difficult because it is naturally different from most high school and college courses you have taken until now.
Linear algebra is a branch of mathematics that deals with mathematical structures closed under the operations of addition and scalar multiplication and that comprises the theory of systems of linear equations, matrices, determinants, vector spaces, and linear transformations.
Linear algebra is hard to study. Linear algebra is one of the most difficult courses that most STEM majors will study in university.
Linear algebra is not a simple class because it is a very abstract course, and it requires strong analytical and logical skills.
Linear algebra is considered a demanding course by STEM majors since it gets exponentially complex and perplexing as the term progresses.
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a cone with a radius of 4.96 and a volume of 102
The volume of a cone is given by the formula:
V = (1/3) * π * r² * h
Where V is the volume, r is the radius, and h is the height.
In this case, we know the radius (4.96) and the volume (102), so we can use the formula to solve for the height.
Substituting the known values into the formula, we get:
102 = (1/3) * π * (4.96)² * h
Dividing both sides by (1/3) * π * (4.96)², we get:
h = 102 / [(1/3) * π * (4.96)²]
Substituting in the value for π, we get:
h = 102 / [(1/3) * 3.14 * (4.96)²]
Which simplifies to:
h = 102 / [(1/3) * 3.14 * 24.1952]
Which simplifies to:
h = 102 / (0.7853 * 24.1952)
Which simplifies to:
h = 102 / 19.1268
Which is approximately 5.33.
Therefore, the estimated height of the cone is approximately 5.33.
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Answer:
Step-by-step explanation:
The volume of a clone = 1/3 × π × r^2 × h
Volume, v = 102
Radius r = 4.96
r^2 = 4.96^2 = 24.6016
Approximately = 24.6
π = 3.142
v = 1/3 x π x r^2 x h
Cross multiply
3v = π x r^2 x h
h = (3 x 102) / 24.6 x 3.142
h = 3.959 cm
I hope this was helpful
What additional information is needed to show that △ ABC ≅ △ DEF by SSS?
SSS congruence of triangles is proved when all three sides of considered two triangles are congruent(that is, of equal measures).
What is SSS congruence of triangles?If two considered triangles have corresponding side pairs congruent(for all three sides), then both the triangles are congruent. This proof of congruence is triangle is done by SSS congruence of triangles (Side Side Side congruence)
Since it is given that the sides CB and FE are congruent, and since it is given that sides AB and DE are congruent too.
Thus, for SSS congruence of both considered triangles, we need the third side pair of the given triangles to be congruent too.
Thus, we need the line segment DF congruent to the line segment AC.
We can write it symbolically as:
[tex]$\overline{D F} \cong \overline{A C}$[/tex] (remember that order doesn't matter here. This can be written as [tex]$\overline{A C} \cong \overline{D F}$[/tex] .)
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question 6 do these data provide convincing evidence that age and body fat percentage are significantly positively associated? why or why not? use quantitative information based on the model output to support your answer, and make sure to note the p-value you use to make this decision. 0 / 1 point yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.000. since the p-value is small we reject the null hypothesis of no relationship. yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039. since the p-value is small we reject the null hypothesis of no relationship. yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039 / 2
The correct answer is b). Yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039. Since the p-value is small we reject the null hypothesis of no relationship.
In statistics, the p-value is used to determine the likelihood that the observed relationship between two variables occurred by chance. If the p-value is small, it means that the relationship is statistically significant and unlikely to have occurred by chance. In this case, the p-value of 0.039 indicates that there is a statistically significant positive relationship between age and body fat percentage.
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Match each value of r to its scatterplot: Data 100 09 09 GRAPHA OP 8 3 40 8 0 100 Det 001 OH 0 GRAPH B OP 30 100 Duta 00 GRAPH C 爱 arch Data 100 80 60 OOO GRAPHD 20 0 0 20 40 80 100 Data 100 80 09 OOOOOOOOOOOOOOOO GRAPHE ON OZ 0 0 20 40 50 09 100 A [Choose B [ Choose -1 0.373 -0.908 0.881 -0.732 [ Choose C > D [ Choose E [Choose ]
Graphs and the correlation coefficients are mentioned below-
Graph{A} : 0.373Graph{B} : - 0.908Graph{C} : - 0.732Graph{D} : 0.881Graph{E} : - 1What is Scatter plot?
A scatter plot uses dots to represent values for two different numeric variables. There are three types of scatter plots or charts -
U-shapedlinear exponential.There are the three most important correlations as -
positive correlationnegative correlationno correlationGiven are the scatter plots and the associated correlation coefficient.
Correlation coefficient : it is a measure of linear correlation between two sets of data. Mathematically, we can write -[tex]$r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]
r = correlation coefficient
[tex]$x_{i}[/tex] = values of the x-variable in a sample
[tex]$\bar x[/tex] = mean of the values of the x-variable
[tex]$y_{i}[/tex] = values of the y-variable in a sample
[tex]\bar y[/tex] = mean of the values of the y-variable
The graph and their corresponding values of [r] are mentioned below -
Graph{A} : 0.373Graph{B} : - 0.908Graph{C} : - 0.732Graph{D} : 0.881Graph{E} : - 1Therefore, graphs and the correlation coefficients are mentioned below-
Graph{A} : 0.373Graph{B} : - 0.908Graph{C} : - 0.732Graph{D} : 0.881Graph{E} : - 1To solve more questions on scatter plots, visit the link below-
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Mavis is interested in whether military dependency is related to gender in american samoa. Here is data she collected about the population of american samoa in 201020102010:.
Mavis is interested in whether military dependency is related to gender in american samoa. then Male = 0.4193 and Female = 0.5087
What does distribution mean in work?
Distribution is the activity of both selling and delivering products and services from manufacturer to customer. This can also be called product distribution. As businesses become more global it becomes important to improve distribution to ensure that customers and all members of the distribution channel are happy.
To obtain the marginal distribution of gender :
Total number of civilians (male + female)
(26393 + 27330) = 53,723
Male :
P(male) = number of male / total
P(male) = 26393 / 53,723 = 0.4912793
P(Female) = number of Female / total
P(Female) = 27330 / 53,723 = 0.5087206
Complete question :
Mavis is interested in whether military dependency is related to gender in American Samoa. Here is data she collected about the population of American Samoa in 2010.
Millitary status _________ female ____ Male
In armed forces _________ 28 _______ 59
Millitary dependent ______ 928 ______ 781
Civilian _______________ 26393 ___27330
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A certain math test has a mean of 50 and a standard deviation of 12. the teacher wants to convert the scores to a new scale using the transformation x*=65+0.6x. what are the new mean and standard deviation?
a) mean=50, standard deviation=7.2
b) mean=95, standard deviation=7.2
c) mean=95, standard deviation=12
d) mean=95, standard deviation=72.2
e) mean=77, standard deviation=12
Answer:
(b) mean=95, standard deviation=7.2.
Step-by-step explanation:
To find the new mean and standard deviation, we first need to apply the transformation to the original mean and standard deviation.
The new mean is given by: x*=65+0.6x
Substituting in the original mean of 50, we get: x*=65+0.6(50) = 95
The new standard deviation is given by: s*=0.6s
Substituting in the original standard deviation of 12, we get: s*=0.6(12) = 7.2
Therefore, the new mean and standard deviation are (b) mean=95, standard deviation=7.2.
Your couing ay 5,953 round to 5,053 when rounded to the nearet hundred. If your couin correct ? Explain
No , cousin is not correct because when 5,953 is rounded to the nearet hundred the value should be 6000 .
Given :
What is rounding to the nearest hundred ?
Rounding a number to the nearest hundred means to write down the multiple of 100 that is nearest to the number .
if the hundred value number is less than 5 then we must round to the lowest value .if the hundred value number is greater than 5 then we must round to the highest near value .so here given number = 5,953
so here the number 53 is greater than 50 .
We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
so the number after rounded = 6000
so his cousin is incorrect .
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For each set of numbers find the mean (average).
6, 12, 10, 8
Answer:
9
Step-by-step explanation:
add all the numbers: 6+12+10+8=36
then divide by the amount of numbers there are: 36/4=9
A cuboid has a lateral surface of 260 cm and a height of 10 cm. The dimensions of the base are: one is 3 cm smaller than the other. Instruction: First, we find the perimeter of the base of the cuboid as a ratio of the side surface to the height. (260cm2: 10cm=26 cm.) Then we write the equation x+x-3+x+x-3=26cm, where with x we marked one of the sides, we find the sides
Answer:
A cuboid is a 3-dimensional shape with six rectangular faces, four of which are the sides or lateral faces, and the other two are the base and the top. To solve the problem, we can first find the perimeter of the base of the cuboid by dividing the lateral surface area by the height. In this case, the perimeter of the base is 26 cm.
To find the dimensions of the base, we can set up an equation using the given information. Let x be one of the sides of the base, and let y be the other side. Since one of the sides is 3 cm smaller than the other, we can write the equation as:
x + x - 3 + x + x - 3 = 26 cm
We can simplify the equation by combining like terms:
4x - 6 = 26 cm
Next, we can solve the equation by adding 6 to both sides and then dividing by 4:
4x = 32 cm
x = 8 cm
Therefore, the dimensions of the base of the cuboid are 8 cm x 11 cm (since one side is 3 cm smaller than the other). The perimeter of the base is 26 cm, and the height of the cuboid is 10 cm.
Step-by-step explanation:
Is for the next 2 min please help
Answer:
Step-by-step explanation: 44/59 = 0.74576271186 so that means the answer is around 74.5% or 74.6%
how do you solve this ?
Step-by-step explanation:
first of all, remember for life :
the sum of all angles in a triangle is always 180°.
so, in this right-angled triangle we have therefore
180 = b + 90 + 71
b = 180 - 90 - 71 = 19°
and then regarding a and b :
the sum of all angles around a single point on one side of a line is also always 180°.
why ? because the line can be seen as the extended diameter of a circle, with that point being the center of the circle. and one side of the line is representing half of that circle. and a half-circle is 180°.
so,
a + b = 180
a + 19 = 180
a = 180 - 19 = 161°
FYI, the reason for the first principle (all angles in a triangle are together 180°) is also based on a half-circle concept : any right-angled triangle can be seen as inscribed into a half-circle, with the Hypotenuse (the baseline opposite of the 90° angle) being the diameter of the circle, and the center of the circle being the midpoint of the Hypotenuse.
Simplify.
-7+8i / 10i
A) 2i+4 / 5
B) - i / 5
C) 7i+8 / 10
D) 4i+4 / 5
The outcome of the complex number given is 7i+8/10 in its most basic form. Option C
Simplifying complex expressionsComplex numbers are referred to as the square root of negative numbers. For instance √-1 = i.
In this expression 'i" is a complex number.
Given the expression below;
-7+8i / 10i
Rationalise
-7+8i / 10i * 10i/10i
= 10i(-7+8i)/10(i²)
= -70i+18(-1)/10(-1)
= -70i - 18/-10
= 7i+1.8
Hence the result of the given complex number in its simplest form is 7i+8/10
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What makes similar shapes similar?
The property scale factor make the similar shapes similar one.
The term shape in math refers the outline or the boundary of an object.
Here we need to find the property that makes the similar shape similar.
As per the definition of shape we have identified that the shape has the following property, they are listed as,
=> Length
=> Breadth
=> height.
All these are collectively called scaling factor,
Based on these values we have take the two similar shapes such as similar triangles, similar rectangles, similar square, are the shapes whose dimensions are in equal or common ratio but the size or length of their sides vary.
Therefore the common ratio is called the scale factor.
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Astronauts for nasa must measure between 62 and 75 inches tall. Which equation best represents the minimum and maximum heights accepted for nasa astronauts?.
The minimum and maximum heights accepted for NASA astronauts are 62 inches and 75 inches, respectively. These values can be represented by the following equation: 62 <= height <= 75
This equation can be read as "the height must be greater than or equal to 62 inches and less than or equal to 75 inches."
Alternatively, you can represent the minimum and maximum heights using the following inequality:
62 < height < 75
This inequality can be read as "the height must be greater than 62 inches and less than 75 inches."
Either of these equations can be used to represent the minimum and maximum heights accepted for NASA astronauts.
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f(x) = x^8e^x f'(x) = f"(x) = Find an equation of the tangent line to y= e^x/x, (1, e).
As per the given function, the equation of tangent line is y - e = e(x -1)
The term tangent line in math referred as a function y=f(x) can be calculate the slope by taking derivative m=f′(x) then at a given point (x1,y1) equation of tangent line is given by the formula y−y1=m(x−x1)
Here we have given the expression y = eˣ/x
Now, we have to calculate the tangent line for the given function,
Let us consider, Slope of the tangent line is written as,
=> m = dy/dx
Now, we have written it as,
=> dy/dx = eˣ/x
then the equation is equate with the slope, then we get,
=> m = eˣ/x
When we put the value of x as 1, then we get
=> m = e
Here we know that the point value is (1, e)
Therefore, the equation of the tangent line is written as,
=> y - e = e(x -1)
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What type of set is X?
A set X is a subset of set Y (Written as X ⊆ Y) if every element of X is an element of set Y.
What is a set ?A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.
A set has many types, such as;
Empty Set or Null set: It has no element present in it.Example: A = {} is a null set.
Finite Set: It has a limited number of elements.Example: A = {1,2,3,4}
Infinite Set: It has an infinite number of elements.Example: A = {x: x is the set of all whole numbers}
Equal Set: Two sets which have the same members.Example: A = {1,2,5} and B={2,5,1}: Set A = Set B
Subsets: A set ‘A’ is said to be a subset of B if each element of A is also an element of B.Example: A={1,2}, B={1,2,3,4}, then A ⊆ B
Universal Set: A set which consists of all elements of other sets present in a Venn diagram.Example: A={1,2}, B={2,3}, The universal set here will be, U = {1, 2,3}
A set X is a subset of set Y (Written as X ⊆ Y) if every element of X is an element of set Y.
Example : − Let, X = { 1, 2, 3, 4, 5, 6 } and Y = { 1, 2 }. Here set Y is a subset of set X as all the elements of set Y is in set X. Hence, we can write Y ⊆ X.
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