Given the equations, which of the following represents z1 * z2? Using the same values in #6, which of the following represents z1/z2 in standard form?
The selected answers are incorrect.
Answers
Answer:
First Attachment : Option A,
Second Attachment : Option C
Step-by-step explanation:
We are given that,
z₁ = [tex]3(\cos ((\pi )/(6))+i\sin ((\pi )/(6)))[/tex] and z₂ = [tex]4(\cos ((\pi )/(3))+i\sin ((\pi )/(3)))[/tex]
Therefore if we want to determine z₁( z₂ ), we would have to find the trigonometric form of the following expression,
[tex]3(\cos ((\pi )/(6))+i\sin ((\pi )/(6)))*4(\cos ((\pi )/(3))+i\sin ((\pi )/(3)))[/tex]
( Combine expressions )
= [tex]12(\cos ( \pi /6+\pi / 3 ) + i\sin (\pi /6 +\pi / 3 )[/tex]
( Let's now add [tex]\pi / 6 + \pi / 3[/tex], further simplifying this expression )
[tex]\frac{\pi }{6}+\frac{\pi }{3} = \frac{\pi }{6}+\frac{\pi 2}{6} = \frac{\pi +\pi 2}{6} = \frac{3\pi }{6} = \pi / 2[/tex]
( Substitute )
[tex]12(\cos ( \pi /2 ) + i\sin ( \pi /2 ) )[/tex]
And therefore the correct solution would be option a, for the first attachment.
______________________________________________
For this second attachment, we would have to solve for the following expression,
[tex]\frac{3\left(\cos \left(\frac{\pi \:}{6}\right)+i\sin \left(\frac{\pi \:}{6}\right)\right)}{4\left(\cos \left(\frac{\pi \:}{3}\right)+i\sin \left(\frac{\pi \:}{3}\right)\right)}[/tex]
From which we know that cos(π/6) = √3 / 2, sin(π/6) = 1 / 2, cos(π/3) = 1 / 2, and sin(π/3) = √3 / 2. Therefore,
[tex]\:\frac{3\left(\cos \left(\frac{\pi }{6}\right)+i\sin \left(\frac{\pi }{6}\right)\right)}{4\left(\cos \left(\frac{\pi }{3}\right)+i\sin \left(\frac{\pi }{3}\right)\right)}:\quad \frac{3\sqrt{3}}{8}-i\frac{3}{8}[/tex]
[tex]\frac{3\sqrt{3}}{8}-i\frac{3}{8} = \frac{3\sqrt{3}}{8}-\frac{3}{8}i[/tex]
Our solution for the second attachment will be option c.
Related Questions
How much would you need to deposit in an account now in order to have $6,000 in the account in 8 years? Assume the account earns 6% interest compounded monthly. (could anyone do this whole problem out?
Answers
Answer:
$3,717
Step-by-step explanation:
Hello, in 1 year there are 12 months.
Let's note I the Initial amount.
So, after 1 month we will get the following, because we compute the interest amount for one month only.
I * ( 1 + 6% * (1/12) )
And the next month, we will have interest of the amount available from previous month so it gives
[tex]I * ( 1+6\% * \dfrac{1}{12} ) * ( 1+6\% * \dfrac{1}{12} ) \\\\=I*(1+\dfrac{6}{12*100})^2\\\\=I*(1+\dfrac{1}{200})^2\\\\=I*(1.005)^2[/tex]
... and after n months ...
[tex]I*(1.005)^n[/tex]
8 years is 8*12 = 96 months. so we are looking for I such that
[tex]I*(1.005)^{96}=6000\\\\<=> I =\dfrac{6000}{1.005^{96}}\\\\=\boxed{3717.14345....}[/tex]
Thank you.
The sides of a rectangle are in ratio 2:5,the longer side is 20 cm. Find the length of the shorter side
Answers
Answer:
8 cm
Step-by-step explanation:
x:y= 2:5
x/y = 2/5
5x = 2y
y is the longer side
5x=2(20)
x=8 cm
The length of the shorter side is 8 cm.
What is rectangle?
A rectangle more generally than any quadrilateral whose axes of symmetry pass through each pair of opposite sides.This definition includes both right-angled rectangles and rectangles. Each has an axis of symmetry that is parallel and equidistant from a pair of opposite sides and a second that is a perpendicular bisector of those sides, but in the case of a crossed rectangle the first axis is not the axis of symmetry of either side. . that it divides.
Quadrilaterals that have two axes of symmetry, each passing through a pair of opposite sides, belong to the larger class of quadrilaterals that have at least one axis of symmetry through a pair of opposite sides. These quadrilaterals consist of isosceles trapezoids and crossed isosceles trapezoids (crossed quadrilaterals with the same arrangement of vertices as an isosceles trapezoid).
Given, sides of a rectangle are in ratio 2:5.
Let length of a rectangle be 5x cm and breadth of a rectangle be 2x cm.
We know length of a rectangle is longer than breadth.
So, length of the rectangle is 20 cm.
According to question,
[tex]5x = 20 \\ x = \frac{20}{5} \\ x = 4[/tex]
So, length of the rectangle (5×4) = 40 cm and breadth of the rectangle (2×4) = 8 cm.
Breath is shorter side of rectangle.
Therefore,The length of the shorter side is 8 cm.
Rectangle related one more question:
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is this correct if not which one?
Answers
Answer:
C.
Step-by-step explanation:
[tex]\frac{7x}{3y}+\frac{12x}{9y}[/tex]
We can reduce the second term:
[tex]\frac{7x}{3y} +\frac{4x}{3y}[/tex]
Since they now have a common denominator, we can add them:
[tex]=\frac{7x+4x}{3y}=11x/3y[/tex]
The answer is C.
So, yes, you're answer was correct!
given point (-6, -3) and a slope of 4, write an equation in point-slope form
Answers
Answer:
y = 4x + 21
Step-by-step explanation:
Hello!
Point-slope form is y - y1 = m(x - x1)
y1 is the y point
x1 is the x point
m is the slope
Put in what you know
y - -3 = 4(x - -6)
Subtracting a negative is the same as adding
y + 3 = 4(x + 6)
Distribute the 4
y + 3 = 4x + 24
Subtract 3 from both sides
y = 4x + 21
The answer is y = 4x + 21
Hope this helps!
Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major: Accounting 83 Management 68 Marketing 85 Economics 64 Total 300 Has there been any significant change in the number of students in each major between the last school year and this school year?
Answers
Answer:
There has been no significant change in the number of students in each major between the last school year and this school year.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: There has been no change in the number of students.
Hₐ: There has been a significant change in the number of students.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
Here,
[tex]O_{i}[/tex] = Observed frequencies
[tex]E_{i}=N\times p_{i}[/tex] = Expected frequency.
The chi-square test statistic value is, 1.662.
The degrees of freedom is:
df = 4 - 1 = 4 - 1 = 3
Compute the p-value as follows:
[tex]p-value=P(\chi^{2}_{k-1} >1.662) =P(\chi^{2}_{3} >1.662) =0.645[/tex]
*Use a Chi-square table.
The p-value is 0.645.
The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.
Thus, it can be concluded that the there has been no significant change in the number of students in each major between the last school year and this school year.
A rectangular city is 3 miles long and 10 miles wide. What is the distance between opposite corners of the city? The exact distance is ______ miles How far is it to the closest tenth of a mile? Answer: The distance is approximately ______ miles.
Answers
Answer:
The exact distance is [tex]\sqrt{109}[/tex] miles.
The distance is approximately 10.4 miles.
Step-by-step explanation:
It is given that a rectangular city is 3 miles long and 10 miles wide. So,
Length = 3 miles
Width = 10 miles
We need to find the distance between opposite corners of the city. It means, we need to find the length of the diagonal of the rectangle.
Using Pythagoras theorem, the length of diagonal is
[tex]d=\sqrt{l^2+w^2}[/tex]
where, l is length and w is width.
Substitute l=3 and w=10.
[tex]d=\sqrt{(3)^2+(10)^2}[/tex]
[tex]d=\sqrt{9+100}[/tex]
[tex]d=\sqrt{109}[/tex]
The exact distance is [tex]\sqrt{109}[/tex] miles.
Now,
[tex]d=\sqrt{109}[/tex]
[tex]d=10.4403065[/tex]
[tex]d\approx 10.4[/tex]
The distance is approximately 10.4 miles.
A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary. The sample information is submitted to Minitab with the following results:
Analysis of Variance
Source df SS MS F P
Factor 3 28.17 9.39 5.37 0.010
Error 15 26.26 1.75
Total 18 54.43
A) Reject H0 if F >
B) For the 0.05 level of significance, is there a difference in the mean difference in the mean number of months before a raise was anted among the four CPA firms?
Answers
Answer:
A) Reject H0 if F > 5.417
B) we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms
Step-by-step explanation:
A) From the table, we can see that we have df1 = 3 and df2 = 15. And we are given a significance level of α = 0.01
We are also given f-value of 1.75
Thus,from the f-distribution table attached at significance level of α = 0.01 and df1 = 3 and df2 = 15, we have;
F-critical = 5.417
Normally, we reject H0 if F > 5.417
But in this case, F is 1.75 < 5.417 and so we conclude that we do not reject H0 at the 0.01 level of significance
B) for 0.05 level of significance, df1 = 3 and df2 = 15, from the 2nd table attached, we have;
F-critical = 3.2874
Again the f-value is less than this critical one.
Thus, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms
Ejercicio 2.-
Se dispone a almorzar en un restoran donde habitualmente deja como propina (tip) el
15% del total a pagar, o sea, del consumo más impuesto (tax).
El impuesto en ese condado es del 7% del consumo.
Se da cuenta de que no trajo sus tarjetas y solamente cuenta con $25
en efectivo (cash). Calcule el
valor máximo de los platos que va a ordenar en su almuerzo teniendo en cuenta tax y
tip.
Answers
Answer:
El valor máximo de los platos a ordenar en el almuerzo es de $ 20.32.
Step-by-step explanation:
Sea [tex]c[/tex] el coste máximo que puede asumir el comensal, medido en pesos, el cual es representada por la siguiente suma:
[tex]c = c_{o} + c_{i} + c_{ii}[/tex]
Donde:
[tex]c_{o}[/tex] - Coste del consumo, medido en pesos.
[tex]c_{i}[/tex] - Coste del impuesto en el condado, medido en pesos.
[tex]c_{ii}[/tex] - Coste de la propina, medido en pesos.
Ahora, los costes por impuesto y por propina se determinan en función del coste de consumo:
Coste del impuesto en el condado
[tex]c_{i} = r_{i}\cdot c_{o}[/tex]
Donde [tex]r_{i}[/tex] es la razón entre el coste del impuesto en el condado y el coste del consumo, adimensional.
Coste de la propina
[tex]c_{ii} = r_{ii}\cdot (c_{o}+c_{i})[/tex]
[tex]c_{ii} = r_{ii}\cdot (c_{o}+r_{i}\cdot c_{o})[/tex]
[tex]c_{ii} = r_{ii}\cdot (1 + r_{i})\cdot c_{o}[/tex]
Donde [tex]r_{ii}[/tex] es la razón entre el coste de la propina y la suma de los costes de consumo y del impuesto del condado, adimensional.
Entonces, la suma completa queda representada por:
[tex]c = c_{o} + r_{i}\cdot c_{o}+r_{ii}\cdot (1+r_{i})\cdot c_{o}[/tex]
[tex]c = [1+r_{i}+r_{ii}\cdot (1+r_{i})]\cdot c_{o}[/tex]
A continuación, se despeja el coste de consumo (valor máximo de los platos):
[tex]c_{o} = \frac{c}{1 +r_{i}+r_{ii}\cdot (1+r_{i})}[/tex]
Si [tex]c = \$\,25[/tex], [tex]r_{i} = 0.07[/tex] y [tex]r_{ii} = 0.15[/tex], entonces:
[tex]c_{o} = \frac{\$\,25}{1+0.07+0.15\cdot (1+0.07)}[/tex]
[tex]c_{o} = \$\,20.32[/tex]
El valor máximo de los platos a ordenar en el almuerzo es de $ 20.32.
Please answer this correctly without making mistakes
Answers
Answer:
1/4 miles
Step-by-step explanation:
Hey there!
Well starting at Campbell and going to Morristown it is 1/4 miles.
Going from Campbell to Clarksville it is 2/4 miles.
So to find the difference we’ll subtract.
2/4 - 1/4
= 1/4 miles
Hope this helps :)
Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste?
A. none of these
B. Let “1,2,3” represent preferring the toothpaste and “0,4,5,6,7,8,9” represent not recommending the toothpaste.
C. Let “1,2,3” represent preferring the toothpaste and “4,5,6,7,8,9” represent not recommending the toothpaste.
D. Let “0,1,2” represent preferring the toothpaste and “3,4,5,6,7,8” represent not recommending the toothpaste.
Reset Selection
Answers
Answer:
b
Step-by-step explanation:
only b has 10 didgets. it could be a since the didgets aren't very random, but then again, i think it's b
Let favorable event“1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.
Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste to determine.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
While going throughout the option in options C and D number so the sample is not equal to 10 so both the statement is false. Option B is the correct option because the sample space is also equal to 10 and the number of the favorable events is also 3 which is mentioned in the question.
Thus, let favorable event “1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.
Learn more about probability here:
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If xy = 1 what is the arithmetic mean of x and y in terms of y? Please show work as detailed as possible
Answers
Answer:
(1+y^2) /2y
Step-by-step explanation:
arithmetic mean is the average of x and y
(x+y)/2
Using the equation
xy = 1
and solving for x
x = 1/y
Replacing x in the first equation
(1/y + y) /2
Multiply by y/y
(1/y + y) /2 * y/y
(1/y + y)*y /2y
(1+y^2) /2y
In a simple regression analysis with age as the only explanatory variable, the effects of other factors, such as faminc, are
Answers
Answer:
In the error term.
Step-by-step explanation:
A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).
Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.
Let $x=5$, $y=\frac{3}{4}$, and $z=-\frac{1}{7}$. What is $$\frac{xz}{y}?$$
Answers
Answer:
-20/21Step-by-step explanation:
Given x = 5, y = 3/4 and z = -1/7, 2=we are to calculate [tex]\frac{xz}{y}[/tex]. Substituting the value of x, y and z into the expression will give;
[tex]= \frac{xz}{y}\\\\ \frac{5(-1/7)}{3/4} \\= \frac{-5/7}{3/4}\\\\= \frac{-5}{7} * \frac{4}{3}\\ \\ = \dfrac{-20}{21}\\[/tex]
Hence the value of the expression is -20/21
Find s. Consider the set of differences between two dependent sets: 84, 85, 83, 63, 61, 100, 98. Round to the nearest tenth.
Answers
Answer:
s is [tex]s =15.3[/tex]
Step-by-step explanation:
From the question we are told that
The data is
Generally the mean is evaluated as
[tex]\= x = \frac{84+ 85+ 83+ 63+ 61+100+ 98}{7}[/tex]
[tex]\= x = 82[/tex]
The standard deviation is mathematically represented as
[tex]s = \frac{\sum (x- \= x)^2}{n-1}[/tex]
[tex]s =\sqrt{ \frac{ (84-82)^2+ (85-82)^2 +( 83-82 )^2 +(63-82) ^2 + ( 61-82)^2,+ (100-82)^2 + (98-82)^2}{7-1}}[/tex]
[tex]s =15.3[/tex]
Solve for x. Question 12 options: A) 8 B) 5 C) 14 D) 10
Answers
Answer:
B) 5
Step-by-step explanation:
Proportions:
8 ⇒ 10
20 ⇒ 5x
5x = 20*10/8
5x = 25
x = 25/5
x = 5
Excel:In cell B13, create a formula using the VLOOKUP function that looks up the value from cell A11 in the range A5:B7, returns the value in column 2, and specifies an exact match.
Answers
Answer:
=Vlookup'B13' A11' 7'false
Press enter.
Step-by-step explanation:
Vlookup is a technique in excel which enables users to search for criterion values. It is vertical lookup function in excel which return a value from a different column. The formula for Vlookup function is:
=Vlookup'select cell you want to look up in' select cell you want to lookup from' select column index number' true/false.
where true is approximate match and false is exact match.
Answer:=VLOOKUP(J2,A2:G23,2,FALSE)
Step-by-step explanation:
a. In cell J3, begin to enter a formula using the VLOOKUP function.
b. Use the Project ID (cell J2) as the lookup value.
c. Use the Projects table (range A2:G23) as the table_array.
d. Use the Project Name column (column 2) as the col_index_num.
e. Specify an exact match (FALSE) for the range_lookup.
88 feet/second = 60 miles/hour. How many feet per second is 1 mile/hour? (Hint: divide both sides of the equation
by the same amount.)
Round to the nearest thousandth.
One mile per hour is equivalent to
ao feet/second
Answers
Explanation:
88 ft/sec = 60 mi/hr
88/88 ft/sec = 60/88 mi/hr (divide both sides by 88)
1 ft/sec = 60/88 mi/hr
1 ft/sec = 15/22 mi/hr
1 ft/sec = 0.681 mi/hr
explain why the APR does not compare loans for different lengths of time
Answers
Answer:
APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.
Step-by-step explanation:
Determine whether the normal sampling distribution can be used. The claim is p < 0.015 and the sample size is n
Answers
Complete Question
Determine whether the normal sampling distribution can be used. The claim is p < 0.015 and the sample size is n=150
Answer:
Normal sampling distribution can not be used
Step-by-step explanation:
From the question we are told that
The null hypothesis is [tex]H_o : p = 0.015[/tex]
The alternative hypothesis is [tex]H_a : p < 0.015[/tex]
The sample size is n= 150
Generally in order to use normal sampling distribution
The value [tex]np \ge 5[/tex]
So
[tex]np = 0.015 * 150[/tex]
[tex]np = 2.25[/tex]
Given that [tex]np < 5[/tex] normal sampling distribution can not be used
Based on the normal sampling assumption, the product of the sample size and the proportion must be greater than or equal to 5. Hence, since, the condition isn't met, then the normal sampling cannot be used.
Given the Parameters :
Proportion, p = 0.015Sample size, n = 150Test if np ≥ 5 :
(150 × 0.015) = 2.252.25 < 5
Hence, np < 5 ;
Hence, the normal sampling distribution cannot be used.
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A student wrote the following equation and solution. Explain the error and correctly solve the equation: √p = 9/16 p = 3/4
Answers
Answer:
see below
Step-by-step explanation:
√p = 9/16
We need to square each side, not take the square root
(√p)^2 =( 9/16)^2
p = 81/256
Lester Hollar is vice president for human resources for a large manufacturing company. In recent years he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months. Below are the results. At the .05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.
Employee Before After
1 6 5
2 6 2
3 7 1
4 7 3
5 4 3
6 3 6
7 5 3
8 6 7
Answers
Answer:
t >± 1.895
t= 0.1705
Step-by-step explanation:
The null and alternative hypotheses are
H0: μd=0 Ha: μd>0
Significance level is set at ∝= 0.05
The critical region for t df=7 t >± 1.895
The test statistic under H0 is
t = d/ sd/ √n
Which has t distribution with n-1 degrees of freedom
Employee After Before d = after - before d²
1 6 5 1 1
2 6 2 4 16
3 7 1 6 36
4 7 3 4 16
5 4 3 1 1
6 3 6 -3 9
7 5 3 2 4
8 6 7 -1 1
∑ 14 84
d`= ∑d/n= 14/8= 1.75
sd²= 1/8( 84- 14²/8) = 1/8 ( 84 - 24.5) = 59.5
sd= 7.7136
t= 3/ 7.7136/ √8
t= 0.1705
Since the calculated value of t= 0.1705 < ± 1.895 therefore reject the null hypothesis at 5 % significance level . On the basis of this we cannot conclude that the number of absences has declined.
This need to be correct plzzzzzzzzzzzz I got this answer wrong so send the new one
Answers
Answer:
$215,892.50
Step-by-step explanation:
This is a problem of compound interest.
In compound interest Amount A for principal p charged at interest r% per annum is given by
A = p(1+r/100)^n
where n is the time period in years.
_____________________________
given
p = $100,000
r = 8%
t = 10 years
A= 100,000( 1+ 8/100)^10
A= 100,000( 1.08)^10
A = $215,892.50
So , you need to pay $215,892.50 in total to debt cleared of debt.
logx - logx-1^2=2log(x-1)
Answers
Answer:
x is approximately 2.220744
Step-by-step explanation:
This can be simplified a little using properties of logarithms, and then solve it by graphing:
[tex]log(x)-log(x-1)^2=2\,log(x-1)\\log(x)-2\,log(x-1)=2\,log(x-1)\\log(x)=4\,log(x-1)[/tex]
So we use a graphing tool to find the intersection point of the graph of [tex]log(x)[/tex], and the graph of [tex]4\,log(x-1)[/tex]
Please see attached image for the graph and solution.
The value of x is approximately 2.220744
Answer:
x = 2.32011574011
Step-by-step explanation:
The problem with your original equation is that it is a long way of saying ...
log(x) -log(x) -1 = 2log(x-1)
0 -1 = 2log(x-1)
which has the solution ...
-1/2 = log(x -1)
1/√10 = x -1
x = 1 + 1/√10 ≈ 1.3162278
__
We have asked for clarification, and what we got was ...
[tex]\log{(x)}-\log{(x-1^2)}=2\log{(x-1)}[/tex]
which, again, is a long way of saying ...
[tex]\log{(x)}-\log{(x-1)}=2\log{(x-1)}[/tex]
The other reasonable interpretation of your 'clarified' equation is ...
[tex]\log{(x)}-\log{((x-1)^2)}=2\log{(x-1)}[/tex]
which you already have an answer to. You have declared that a "misconception."
So, we are left with the interpretation that the equation you want a solution to is ...
[tex]\log{(x)}-\log{(x-1)}=2\log{(x-1)}[/tex]
_____
When solving these graphically, I like to write the equation as a function whose zero(s) we're trying to find. For this, when we subtract the right side, we get ...
[tex]f(x)=\log{(x)}-3\log{(x-1)}[/tex]
A graphing calculator shows that f(x) = 0 when ...
x ≈ 2.32011574011
__
If you don't like my interpretation, check out the second attachment. It has your x-1² as the argument of the middle term. You can see that the calculator interpreted that the same way I did (as required by the order of operations).
Marnie solved the proportion 150/170=x/510 to find the value of X
Answers
Answer:
x = 450
510/170 = 3
x/150 = 3
x = 450
Answer:
X=450 is the answer.
Step-by-step explanation:
Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.
Answers
Answer:
[tex] \sqrt{4 {}^{2} + ( - 4) {}^{2} } [/tex]
[tex] \sqrt{32} [/tex]
and the angle
[tex] \tan( \alpha ) = - 4 \div 4 = - 1[/tex]
and since the sin component is -ve, we have our angle on 4th quadrant, which equals 315 degrees
Options:
Determine two pairs of polar coordinates for the point (-4, 4) with 0° ≤ θ < 360°. (5 points)
Group of answer choices
(4 , 135°), (-4 , 315°)
(4 , 45°), (-4 , 225°)
(4 , 315°), (-4 , 135°)
(4 , 225°), (-4 , 45°)
Step-by-step explanation:
The guy asking forgot to provide the options you can comment the awnswe in the comments just do it before brainly turns off comments to try and prevent people from learning
What is the domain of f(x)=2/5x+6
Answers
Answer:
Look at that picture
Step-by-step explanation:
How to convert 2cm to feet?
Answers
Answer:
Divide by 30.48: It would be 0.0656168 feet.
Step-by-step explanation:
Answer:
0.0656
Step-by-step explanation:
2.54 cm = 1 in
12 in = 1 ft
2.54 * 12 = 30.48
2/30.48 = 0.0656167979
An urn contains 9 red marbles, 6 white marbles, and 8 blue marbles marbles. A child randomly selects three (without replacement) from the urn. Find the probability all three marbles are the same color
Answers
Answer:
P(identical colours) = 160/1771 (0.0903 to four decimals)
Step-by-step explanation:
Given 9R, 6W and 8B marbles (total = 9+6+8 = 23)
Choose three without replacement.
Need probability three identical colours.
Use the multiplication rule.
P(RRR) = 9/23 * 8*22 * 7*21 = 12 / 253
P(WWW) = 6/23 * 5/22 * 4/21 = 20/1771
P(BBB) = 8/23 * 7/22 * 6/21 = 8/153
Probability of getting identical colours
= P(RRR)+P(WWW)+P(BBB)
= 160/1771 (0.0903 to four decimals)
Using the probability concept, it is found that there is a 0.0903 = 9.03% probability all three marbles are the same color.
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A probability is the number of desired outcomes divided by the number of total outcomes.The order in which the marbles are chosen is not important, and they are also chosen without replacement, which means that the combination formula is used to find the number of outcomes.-----------------
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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The desired outcomes can be:
3 from a set of 9(all red).3 from a set of 6(all white).3 from a set of 8(all blue).Thus:
[tex]D = C_{9,3} + C_{6,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{6!}{3!3!} + \frac{8!}{3!5!} = 160[/tex]
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The total outcomes are 3 from a set of 9 + 6 + 8 = 23. Thus:
[tex]T = C_{23,3} = \frac{23!}{3!20!} = 1771[/tex]
The probability is:
[tex]p = \frac{D}{T} = \frac{160}{1771} = 0.0903[/tex]
0.0903 = 9.03% probability all three marbles are the same color.
A similar problem is given at https://brainly.com/question/10896842
An experimental probability is ______ likely to approach the theoretical probability if the number of trials simulated is larger. A. as B. more C. less D. not
Answers
Answer:
B. More
Step-by-step explanation:
This is according to the law of large numbers
An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.
What is an experimental probability and theoretical probability?Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.
An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed
Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.
Learn more about probability here:
https://brainly.com/question/9627169
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When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 4kg, the acceleration of the object is 15/ms2. If the same force acts upon another object whose mass is
10kg, what is this object's acceleration?
Answers
Answer:
[tex]a = 6m/s^2[/tex]
Step-by-step explanation:
Given
When mass = 4kg; Acceleration = 15m/s²
Required
Determine the acceleration when mass = 10kg, provided force is constant;
Represent mass with m and acceleration with a
The question says there's an inverse variation between acceleration and mass; This is represented as thus;
[tex]a\ \alpha\ \frac{1}{m}[/tex]
Convert variation to equality
[tex]a = \frac{F}{m}[/tex]; Where F is the constant of variation (Force)
Make F the subject of formula;
[tex]F = ma[/tex]
When mass = 4kg; Acceleration = 15m/s²
[tex]F = 4 * 15[/tex]
[tex]F = 60N[/tex]
When mass = 10kg; Substitute 60 for Force
[tex]F = ma[/tex]
[tex]60 = 10 * a[/tex]
[tex]60 = 10a[/tex]
Divide both sides by 10
[tex]\frac{60}{10} = \frac{10a}{10}[/tex]
[tex]a = 6m/s^2[/tex]
Hence, the acceleration is [tex]a = 6m/s^2[/tex]
