In a hexagonal-close-pack (HCP) unit cell, the ratio of lattice points to octahedral holes to tetrahedral holes = 1 : 1 : 2 is AB3
let the :
Number of lattice point = 1x.
Number of octahedral points = 1x
Number of tetrahedral points = 2x
If anions occupy the HCP lattice points and cations occupy half of the octahedral holes.
Number of anions occupying the HCP lattice points, A= 1x
Number of cations occupying the octahedral points, B = 1x
The formula of the compound will be =
If anions occupy the HCP lattice points and cations occupy all of the octahedral and the tetrahedral holes.
Number of anions occupying the HCP lattice points, A= 1x
Number of cations occupying the octahedral points, B = x
Number of cations occupying the tetrahedral points, B = 2x
total number of cations = x + 2x = 3x
The formula of the compound will be = AB3
learn more about of compound here
https://brainly.com/question/14250657
#SPJ4
for all negative semidefinite matrix, the first principal determinant has to be either 0 or negative. A. True B.False
A is negative semidefinite if and only if all the kth order principal minors of A are ≤ 0 if k is odd and ≥ 0 if k is even. The given statement is true.
What is a negative semidefinite matrix?
A Hermitian matrix with all of its eigenvalues being nonpositive is known as a negative semidefinite matrix. Using the Wolfram Language's NegativeSemidefiniteMatrixQ[m], a matrix may be checked to see if it is negative semidefinite.
The direction of space is inverted when the determinant is negative. If you give your fingers dimensions before transformation and they remain true after, it indicates that the orientation of space has not changed and the determinant is positive.
To learn more about negative semidefinite matrix visit:https://brainly.com/question/16969351
#SPJ4
Which of the following represents the series? (2 points)
–12 + (–5) + 2 + 9 + 16
sum from k equals 0 to 4 of negative 19 plus 7 times k
sum from k equals 1 to 5 of negative 19 minus 7 times k
sum from k equals 0 to 4 of negative 12 plus 7 times k
sum from k equals 1 to 5 of negative 12 minus 7 times k
The option that represents the arithmetic series is;
Option C: sum from k equals 0 to 4 of negative 12 plus 7 times k
What is the formula for the arithmetic sequence?
An arithmetic series is defined as an arithmetic sequence, whereby each term of the series is gotten from the previous term by the addition or subtraction of a common term.
The series is given as;
-12 + (-5) + 2 + 9 + 16
By careful observation, we see that each term in the series is gotten from the previous term by the addition of 7.
The series here is therefore an example of arithmetic sequence.
The equation of the series when the first term is -12 can therefore be written as; -12 + 7·k
Where;
-12 is the first term
7 is the common difference
n is the number of terms
k = n - 1
When k = 0, we have;
-12 + 7·k
= -12 + 7 × 0
= -12
When k = 1, we have;
-12 + 7·k
= -12 + 7 × 1
= -5
When k = 2, we have;
-12 + 7·k
= -12 + 7 × 2
= 2
When k = 3, we have;
-12 + 7·k
= -12 + 7 × 3
= 9
When k = 4, we have;
-12 + 7·k
= -12 + 7 × 4
= 16
Therefore, we conclude that using values of k that range from k = 0 to k = 4, the expression that represents the series is therefore the option C
Read more about Arithmetic Sequence at; https://brainly.com/question/6561461
#SPJ1
Compute the directional derivatives of the following functions along unit vectors at the indicated points in directions parallel to the given vector. (a) rx, y) = x^y, (Xo, yo) = (e, e), d = 8i + 15j (b) f(x, y, z) = e^x + yz, (Xo, yo, Zo) = (1, 1, 1), d = (1,-4, 4) (c) f(x, y, z) = xyz, (xo, yo, Zo) = (1, 0, 1), d = (1, 0,-1)
The derivative of given function is D(yz+e^x)d(1,1,1) = (3*((59)^1/2)*e)/59≈1.06167045295814
We have to find the directional derivative of the given function
f(x,y,z) = yz+e^x at (x0,y0,z0)=(1,1,1) in the direction of the vector
d⃗ =(3,−5,5)
Find the gradient of the function and evaluate it at the given point:
To find the gradient of a function (which is a vector), differentiate the function with respect to each variable.
∇f= (∂f/∂x,∂f/∂y,∂f/∂z)
∂f/∂x = ∂( yz+e^x )/∂x
The derivative of a sum/difference is the sum/difference of derivatives:
∂f/∂x = ∂( yz)/∂x +∂(e^x )/∂x since the derivative of y and z with respect of x is zero.
∂f/∂x = e^x The derivative of exponential is d(e^x)/dx=e^x.
Similarly
d(yz+e^x)/dy = z and d(yz+e^x)/dz = y
∇(yz+e^x)(x0,y0,z0)=(e^x,z,y)
Finally plug in the point we get the result
∇(yz+e^x)|(x0,y0,z0)=(1,1,1)=(e,1,1)
∇(yz+ex)|(x0,y0,z0)=(1,1,1)=(e,1,1)
Now we Find the length of the vector: |d⃗ |=((3)^2+(−5)^2+(5)^2)^1/2 =(59)^1/2
To normalize the vector, divide each component by length:
d = ((3*((59)^1/2))/59 ,(−5*(59)^1/2)/59,(5*(59)^1/2)/59)
Finally, the directional derivative is the dot product of the gradient and the normalized vector:
D(yz+e^x)d(1,1,1) = (e,1,1). ((3*((59)^1/2))/59 ,(−5*(59)^1/2)/59,(5*(59)^1/2)/59)
D(yz+e^x)d(1,1,1) = (3*((59)^1/2)*e)/59≈1.06167045295814
learn more about of derivative here
https://brainly.com/question/14860134
#SPJ4
use exponential fitting to find a closed formula for the sequence: 4, 5, 7, 11, 19, 35, 67, ...
The exponential form of the given sequence is - [tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex] where x is a set of whole numbers and n is a set of natural numbers.
The given sequence is - 4, 5, 7, 11, 19, 35, 67, ...
the first term - [tex]t_1[/tex] is 4
Hence, we can write the sequence as follows-
4 + [tex]2^0[/tex] = 5
5+[tex](2)^1[/tex]=7
7+[tex](2)^2[/tex]=11
11+[tex](2)^3[/tex]=19
and so on.
Here, we are adding the previous term with the exponential form of 2.
thus, we can conclude that -
[tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex]
where, x is a set of whole numbers, and n is a set of natural numbers.
Read more about Sequences:
brainly.com/question/28417178
#SPJ4
Mr. Martinez has a 16-ounce Starbucks drink. He drinks 10 ounces. What is the percent of ounces Mr. Martinez has left of his drink?
well, he has left only 6 oz.
now, if we take the 16(origin amount) to be the 100%, what is 6 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 16 & 100\\ 6& x \end{array} \implies \cfrac{16}{6}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 8 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 8x=300\implies x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5[/tex]
10. Which of the following sets of ordered pairs does not describe a function?
A
((7,-2), (5, 0), (3, 3), (1, -2)}
B
((7, 2), (5, 4), (3, 6), (1, 8))
C ((7, 2), (7, 0), (3,-2), (1,4)}
D ((7, 7),(5, 5), (3, 3), (1, 1))
Answer:
C {(7, 2), (7, 0), (3,-2), (1,4)}
Step-by-step explanation:
In a function, x = 7 can't be at both 2 and 0 because it would not pass the vertical line test.
The playing time X of classical CDs has the normal distribution with a mean of 54 and a standard deviation of 5; the N(54, 5) distribution. What is the relative frequency of classical CDs with a playing time X between 44 and 54 minutes? (2 points)
a)47.5%
b)52.5%
c)50%
d)81.5%
Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 44 and 54 minutes is 0.8150= 81.5%.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
The z-score measures how many standard deviations the measure is above or below the mean.
Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
The relative frequency of classical CDs with playing time X between 44 and 54 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 44, hence:
X = 54:
Z = 3
Z = 3 has a p-value of 0.9987.
X = 54:
Z = -1
Z = -1 has a p-value of 0.1584.
0.9987 - 0.1584 = 0.8150
More can be learned about the normal distribution at brainly.com/question/4079902
#SPJ4
Solve the equation.12d-14=-2
Show Hint
Hint: Be sure to use inverse operations.
Solve the equation. 10 s -9=32
Show Hint
Hint: Be sure to use inverse operations.
Solve the equation. {c}/{-10}-5=9
Show Hint
Hint: Be sure to use inverse operations.
Answer: The answer is -2.34
Step-by-step explanation: Get Good
A card is drawn randomly from a standard 52-card deck. Find the following: Write all answers as simplified fractions (not mixed numbers). Probability the card drawn is a face card _____
Probability the card drawn is not a face card. ____
Odds in favor of drawing a face card ______
Odds against drawing a face card _____
The probability the card drawn is a face card is 3/13. The probability the card drawn is not a face card is 10/13. The odds in favor of drawing a face card is 3/10. The odds against drawing a face card are 10/3.
There are 52 cards in a standard deck, and 12 of them are face cards (jack, queen, and king). Therefore, the probability of drawing a face card is 12/52, or 3/13.
The probability of not drawing a face card is 1 minus the probability of drawing a face card. Since the probability of drawing a face card is 3/13, the probability of not drawing a face card is 1 - 3/13, which is 10/13.
The odds in favor of drawing a face card are 3:10, or 3/10. The odds against drawing a face card are 10:3, or 10/3.
In summary:
The probability the card drawn is a face card: 3/13
The probability the card drawn is not a face card: 10/13
Odds in favor of drawing a face card: 3/10
Odds against drawing a face card: 10/3
To know more about probability visit :
brainly.com/question/11234923?referrer=searchResults
#SPJ4
Mark pays out his debt at regular intervals every 6 months. He pays $500 each time. If the interest on the loan is 2% compounded semi-annually and he still has 8 years left to pay off the debt, how much does he still owe?
To find out how much Mark still owes on his debt, we need to calculate the amount of interest that has accrued on the loan over the time that he has been paying it off. The interest on the loan is compounded semi-annually, so the amount of interest that accrues on the loan will be added to the principal every six months. Since Mark has been paying off his debt for 8 years and the interest is compounded semi-annually, he will have made 16 payments of $500.
To calculate the total amount of interest that has accrued on the loan, we need to know the original principal amount of the loan. Since we don't have that information, we won't be able to calculate the exact amount that Mark still owes on his debt. However, we can use the information that we have to make an educated guess.
If Mark has been making payments of $500 every six months for eight years, then he has paid a total of $500 x 16 = $<<50016=8000>>8000 in principal and interest payments. If the interest on the loan is 2% compounded semi-annually, then the total amount of interest that has accrued on the loan over the past eight years is $8000 x 2% = $<<80002*.01=160>>160. This means that the original principal amount of the loan was $8000 - $160 = $<<8000-160=7840>>7840.
Since Mark still has 8 years left to pay off the debt, and he is making payments of $500 every six months, he will need to make a total of 8 years x 2 payments per year = <<82=16>>16 more payments of $500 to pay off the debt. This means that he will have to pay a total of $500 x 16 = $<<50016=8000>>8000 in principal and interest over the next eight years.
Since the total amount of interest that has accrued on the loan over the past eight years was $160, the total amount of interest that will accrue on the loan over the next eight years is also $160. This means that the total amount of interest that Mark will have to pay over the next eight years is $160 x 2 = $<<160*2=320>>320.
Adding the amount of interest that Mark will have to pay over the next eight years to the amount of principal that he will have to pay, we find that the total amount that Mark will owe on the loan over the next eight years is $8000 + $320 = $<<8000+320=8320>>8320.
Therefore, if Mark has been paying off his debt for eight years and still has eight years left to pay, he still owes a total of $8320 on the loan.
the probability of heads of a coin is , and this bias is itself the realization of a random variable which is uniformly distributed on the interval . to estimate the bias of this coin. we flip it times, and define the (observed) random variable as the number of heads in this experiment. throughout this problem, you may find the following formula useful: for every positive integers , given the observation , calculate the posterior distribution of the bias . that is, find the conditional distribution of , given . for ,
The resulting conditional mean squared error of the LMS estimator, given N=3 is 0.0383746
What is conditional distribution formula?In general, the conditional distribution of X given Y does not equal the conditional distribution of Y given X, i.e., pX|Y(x|y)≠pY|X(y|x). If X and Y are independent, discrete random variables, then the following are true: pX|Y(x|y)=pX(x)pY|X(y|x)=pY(y)
What is full conditional distribution?The full conditional for a given node (parameter) is simply the product of the probability model (likelihood or prior) for that node and its parent node (at least up to a constant of proportionality).
1) fY|N(y∣N=3)=84 y^6 (1-y)^3
2)0.0636363
To learn more about conditional distribution visit
https://brainly.com/question/14310262
#SPJ4
Please help!!!!!!!!!!
Answer:
[tex]6^{\frac{1}{12}}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt[3]{6} }{\sqrt[4]{6} } =\frac{6^{\frac{1}{3} } }{6^\frac{1}{4} }[/tex]
[tex]= 6^{\frac{1}{3}[/tex] ÷ [tex]6^{\frac{1}{4}}[/tex]
= [tex]6^{\frac{1}{3}-\frac{1}{4}}[/tex]
=[tex]6^{\frac{4}{12}-\frac{3}{12}}[/tex]
[tex]= 6^\frac{1}{12}[/tex]
PLEASE ANSWER! I WILL GIVE BRAINEST!
A student is building a squirrel feeder for a family member. The figure is a model of the feeder.
(A rectangular prism with dimensions 2 and three fourths inches by 16 and one half inches by 4 inches.)
How much feed can the container hold?
The weight of meteorite A is 8times the weight of meteorite B. If the sum of their weights is 189 tons, find the weight of each.
The weight of meteorite A and B are 21 and 168 tons respectively.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, The weight of meteorite A is 8 times the weight of meteorite B. And the sum of their weights is 189 tons,
To find their weights we need to establish an equation, relating their weights,
Let weight of meteoroid B be x, then weight of meteoroid A will be 8x,
Establishing the equation,
8x+x = 189
9x = 189
x = 21
8x = 21x8 = 168
Hence, The weight of meteorite A and B are 21 and 168 tons respectively.
For more references on equations, click;
https://brainly.com/question/29657992
#SPJ1
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7
The volume of the cone is approximately 134 ft cube.
The cone would fit in 4 times in the red beach ball.
How to find the volume of a sphere and cone?The diameter of the red beach ball is 8 inches, then the cone has the same radius and a height of 8 inches .
Therefore, to know the number of times the beach ball will fit into the cone, we have to find the volume of each solid shape.
Therefore,
volume of the beach ball(sphere) = 4πr³
where
r = radiusr = 8 /2 = 4 inches
volume of the beach ball(sphere) = 4 × π × 4³
volume of the beach ball(sphere) = 256π ft³
Therefore,
volume of the cone = 1 / 3 πr²h
where
r = radiush = heightvolume of the cone = 1 / 3 × π × 4² × 8
volume of the cone = 128π / 3
volume of the cone = 42.7π
volume of the cone = 134.078
volume of the cone ≈ 134 ft³
Therefore,
volume of beach ball / volume of cone = 256π / 42.7π = 5.99531615925
Therefore, the cone will fit 4 times into the red beach ball.
learn more on volume here: https://brainly.com/question/9994313
#SPJ1
Help!!!
A spinner is divided into five equal sections labeled 1, 2, 3, 4, and 5. Another spinner
is divided into two equal sections labeled A and B. Nigel will spin each spinner one
time.
How many of the possible outcomes have a number less than 3 or an A?
Hint: first write out the sample space (you should have 10)
Which samples have a number less than 3 or an A?
Answer:
There are 5 possible outcomes when the first spinner is spun, and 2 possible outcomes when the second spinner is spun. Therefore, the sample space of possible outcomes when both spinners are spun is 5 x 2 = <<5*2=10>>10.
The possible outcomes are:
1A
1B
2A
2B
3A
3B
4A
4B
5A
5B
Of these, 3A, 2A, 1A, and 4B have a number less than 3 or an A. Therefore, there are 4 possible outcomes that have a number less than 3 or an A.
Step-by-step explanation:
13,140 divided by 12
Answer:
1095
Step-by-step explanation:
Donnelle has already saved $350.00
Donnelle can save $45 per week from her
part-time job. How many weeks will it take her to
save at least $2150 to pay cash for a used car?
Which inequality matches the graph?
Answer:
2n + 5 ≤ 7 The first choice
Step-by-step explanation:
2n + 5 ≤ 7 Subtract 5 from both sides.
2n + 5 - 5 ≤ 7 - 5
2n ≤ 2 Divide both sides by 2
[tex]\frac{2n}{2}[/tex] ≤ [tex]\frac{2}{2}[/tex]
n [tex]\leq[/tex] 1
Answer:
2x +5 ≤ 7
I hope my answer helps you.
Use the diagram to solve for x.
Which polynomial is the product of (4x−3)(x2+2x−6)?
The polynomial that is the product of (4x−3)(x²+2x−6) is 4x³ + 5x² - 30x + 18
Which polynomial is the product of (4x − 3)(x² + 2x − 6)?A polynomial simply refers to the expression that is composed of constant, variables, and exponents that are combined by mathematical operations.
The product of the polynomial will be:
= (4x −3)(x² + 2x − 6)
= 4x³ + 8x² - 24x - 3x² - 6x + 18
= 4x³ + 5x² - 30x + 18
The product is 4x³ + 5x² - 30x + 18.
Learn more about polynomial on:
brainly.com/question/2833285
#SPJ1
the table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. which statements about the function described by the table are true? check all that apply. the independent variable is the number of people. the initial value (initial fee) for the picnic is $40. the rate of change is $8.67 per person. as the number of people increases, the total cost of the picnic increases. if 4 people attended the picnic, the total cost would be $46.
The correct statements are:
a) The independent variable is the number of people.
b) The initial value (initial fee) for the picnic is $40.
d) As the number of people increases, the total cost of the picnic increases.
A general linear equation is given by:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is given by the formula:
m = (y - y')/x - x'
Now let's analyze the table:
The x-values are the ones in the left and the y-values are the ones on the right, now from the table we can use two points, let's use the first two:
(6, 52) and (9, 58).
Then the slope is:
a = (58 - 52)/9 -6 = 2
Then the line is something like:
y = 2*x + b
To find the value of b, we use the point (6, 52). This means that when x = 6, y must be equal to 52.
We will get:
52 = 2*6 + b
52 = 12 + b
52 - 12 = b = 40
Then the linear equation is:
y = 2*x + 40
Now let's see which statements are correct.
a) The independent variable is the number of people.
True, the "x" represents the number of people.
b) The initial value (initial fee) for the picnic is $40.
True, the y-intercept does not depend on the value of x, so we can say that you need to pay that indifferent of the number of people that goes.
c)The rate of change is $8.67 per person.
False, the rate of change is equal to the slope, in this case is $2 per person.
d) As the number of people increases, the total cost of the picnic increases.
True.
e) If 4 people attended the picnic, the total cost would be $46.
To see if this is true or not, we just need to evaluate the function that we got in x = 4.
y = 2*4 + 40 = 48
So we can see that this is false.
Therefore, the correct statements are A, B, D
To learn more about linear equation refer here
brainly.com/question/11897796
#SPJ4
A group of 2342 students were surveyed about the courses they were taking at their college with the
following results:
1031 students said they were taking Dance.
1058 students said they were taking Science.
1059 students said they were taking English.
449 students said they were taking Science and Dance.
459 students said they were taking Science and English.
456 students said they were taking Dance and English.
218 students said they were taking all three courses.
Fill in the following Venn Diagram with the cardinality of each region then answer the questions
below.
Science
IV.
11.
VII.
V.
English
VI.
How many students took Science, Dance, or English?
How many students took Dance and English, but not Science?
How many students took Science or didn't take Dance?
How many students took none of the courses?
Dance
III.
How many students took Science or English, but not Dance?
VIII.
The missing features of the Venn diagram include the following:
I=472, II=449 ,IV=459 ,V=218 , VI=456,
What is a Venn diagram?A Venn diagram is a circular illustration of how variables are interrelated to each other.
To solve for I;
Total number of students taking dance = 1031
Total number of students taking science and dance= 449
Total number of students taking all three courses= 218
Total number of students taking science and English = 459
Therefore, the number of students taking only science;
I =( II-V)+ (IV-V)
I= (449-218)+(459-218)
I = 231+241
I= 472
The number of students that took Science, Dance, or English =V= 218
The number of students took Dance and English, but not Science = VI = 456
The number of students took Science or didn't take Dance = IV = 459
The number of students took none of the courses = VIII = U
The number of students took Science or English, but not Dance = 459 students.
Learn more about Venn diagram here:
https://brainly.com/question/24713052
#SPJ1
State the null and alternative hypotheses you would use to test the following situation.An annual report showed that Florida topped the nation with 24% of its motorist uninsured. After implementing several new programs during the last two years, the state reevaluated its percentage of uninsured motorists. Determine the null and alternative hypotheses for a test to determine whether the proportion of uninsured motorists has decreased over the last two years.H_{0} / p = 0.24H_{1} / p > 0.24H_{0} / p = 0.24H_{1} :p ne0.24H_{0} / p > 0.24 H_{1} / p < 0.24H_{0} / p = 0.24 H_{1} / p < 0.24
Answer: Im sorry I cant help im just doing this for points
Step-by-step explanation:
The correct answer is [tex]H_0: p = 0.24 and H_1: p < 0.24[/tex].
How to write this in maths notationIn mathematical notation, the null hypothesis can be written as:
H_0: p = 0.24
where p is the proportion of uninsured motorists in Florida.
The alternative hypothesis can be written as:
H_1: p < 0.24
This means that we are testing the hypothesis that the proportion of uninsured motorists has decreased to a level that is less than 24%.
The null hypothesis is the default assumption, and we will only reject it if we have enough evidence to support the alternative hypothesis. In this case, we would need to collect data that suggests that the proportion of uninsured motorists has decreased to a level that is significantly less than 24%.
The correct answer is [tex]H_0: p = 0.24 and H_1: p < 0.24[/tex].
The other options are incorrect because they either do not specify the direction of the hypothesis test (i.e., whether we are testing whether the proportion of uninsured motorists has increased or decreased) or they are not supported by the given information.
Read more about Null hypothesis here:
https://brainly.com/question/30535681
#SPJ2
5. El lado canadiense de las Cataratas del Niagara tiene un caudal de 600,000 litros por segundo. ¿Cuántos
galones de agua fluyen por las cataratas en 1 minuto?
Answer:
9,510,223.49 galones!
Step-by-step explanation:
Primero, tienes que saber la cauntidad de los litros en un galon.
Hay 3.7854 litres en un galon
ahora, hacemos un ratio
1 galon = 3.7854 litres
? galones = 600,000 litres
Para encontrar la respuesta, divide 600,000 por 3.7854 para obtener la cauntidad de los galones
600,000 ÷ 3.7854 = 158,503.725 galones
158,503. 725 litres fluyen por segundo.
Hay 60 segundos en un minuto asi que, tenemos que multiplica nuestra respuesta por 60 para calcular nuestra respuesta final.
158,503. 725 × 60 = 9,510,223.49 galones!
Help me pls asappp……
Answer:
a. (0,1)
b. slope is -2
y-1=-2x
Step-by-step explanation:
Simplify the expression to a polynomial in standard form:
(x + 3)(2x" + 3x + 7)
Answer:
2x³ + 9x² + 16x + 21-------------------------------------
Given expression:
(x + 3)(2x² + 3x + 7)Distribute and simplify:
(x + 3)(2x² + 3x + 7) = Givenx(2x²) + x(3x) + 7x + 3(2x²) + 3(3x) + 21 = Distribute2x³ + 3x² + 7x + 6x² + 9x + 21 = Collect like terms2x³ + 9x² + 16x + 21 AnswerDetermine whether the graph represents a function. Explain.
Answer:
No.
Step-by-step explanation:
A function have only one output (y) for each x. This is not true with this graph. For example: the point (6,1) and ( 6,5) are both on the graph. The input 6 has more than 1 output. It has the output of 1 and 5. Since it has more than one output, it is not a function.
Derek boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed. Let h represent John's height above the center of the Ferris wheel (in feet) and let t represent the number of mintues since the ride started. a. Suppose the radius of the Ferris wheel is 20 feet and the Ferris wheel rotates at 1 radian per minute. Plot the relationship between h and t for this scenario. 20- 1o -10 -20 ear All Draw: b. Now, suppose the radius of the Ferris wheel is 20 feet and the Ferris wheel rotates at 2 radians per minute. Plot the relationship between h and t for this scenario. 30 20- 10 10 20 ear All Draw c. Now, suppose the radius of the Ferris wheel is 25 feet and the Ferris wheel rotates at 2 radians per minute. Plot the relationship between h and t for this scenario. 30 20 10 20 r All Draw:
The result for all expressions are
a) r(t) = 6.5t radians
b) C(t) = 20cos(6.5*t) feet
c) H(t) = 36 - C(t)
The situation is depicted in the picture attached considering the center of the wheel as the center of the coordinates system.
Since the angular speed is constant, to find an expression for the angle r(t) in radians we just cross-multiply:
6.5 radians __________ 1 minute
r(t) radians ____________ t minutes
and obviously, r(t) = 6.5t radians
The height C(t) above the center after t minutes is given by
C(t) = 20cos(r(t)) ===> C(t) = 20cos(6.5*t) feet
When C(t) < 0 means that derek wheel is below the center of the wheel.
Since the center of the Ferris wheel is 36 feet above the ground, the height H(t) above the ground after t minutes is given by
H(t) = 36 - C(t)
To learn more about coordinate system visit:
brainly.com/question/29762404
#SPJ4
Financial analysts forecast Safeco Corp.’s (SAF) growth rate for the future to be 12 percent. Safeco’s recent dividend was $1.60.
What is the value of Safeco stock when the required return is 14 percent? (Round your answer to 2 decimal places.)
The value of Safeco stock given the required return growth rate and the dividend of the stock is $89.60.
What is the value of Safeco stock?The value of the stock can be determined using the constant growth dividend model. According to the model, the value of the stock is a function of the growth rate, dividend and the required return of the stock.
Value of the stock = [dividend x (1 + g)] / (r - g)
where
r = required return
g = growth rate
Value of the stock = [1.60 x (1.12) / (0.14 - 0.12)
Value of the stock = 1.792 / 0.02
Value of the stock = $89.60
Learn more about stock on:
https://brainly.com/question/14742629
#SPJ1