Answer:
No. If a collegue hire 7 math Ph.D.s, at least 2 will be from the same university.
The only way to have a job for all of them is that all colleges hire 6 math Ph.D.s, one from each university.
Step-by-step explanation:
If the condition is that no college will hire more than one Ph.D. from any given university, no college can hire more than 6 math Ph.D.s, as there are only 6 universities to choose from. If they hire seven, they have to repeat some university, violating the condition.
Then, the only way to have a job for all of them is that all colleges hire 6 math Ph.D.s, one from each university.
Consider the set of sequences of seven letters chosen from W and L. We may think of these sequences as representing the outcomes of a match of seven games, where W means the first team wins the game and L means the second team wins the game. The match is won by the first team to win four games (thus, some games may never get played, but we need to include their hypothetical outcomes in the points in order that we have a probability space of equally likely points).A. What is the probability that a team will win the match, given that it has won the first game?B. What is the probability that a team will win the match, given that it has won the first two games? C. What is the probability that a team will win the match, given that it has won two out of the first three games?
Answer:
a) Probability that a team will win the match given that it has won the first game = 0.66
b) Probability that a team will win the match given that it has won the first two games= 0.81
c) Probability that a team will win the match, given that it has won two out of the first three games = 0.69
Step-by-step explanation:
There are a total of seven games to be played. Therefore, W and L consists of 2⁷ equi-probable sample points
a) Since one game has already been won by the team, there are 2⁶ = 64 sample points left. If the team wins three or more matches, it has won.
Number of ways of winning the three or more matches left = [tex]6C3 + 6C4 + 6C5 + 6C6[/tex]
= 20 + 15 + 6 + 1 = 42
P( a team will win the match given that it has won the first game) = 42/64 = 0.66
b) Since two games have already been won by the team, there are 2⁵ = 32 sample points left. If the team wins two or more matches, it has won.
Number of ways of winning the three or more matches left = [tex]5C2 + 5C3 + 5C4 + 5C5[/tex] = 10 + 10 + 5 +1 = 26
P( a team will win the match given that it has won the first two games) = 26/32 = 0.81
c) Probability that a team will win the match, given that it has won two out of the first three games
They have played 3 games out of 7, this means that there are 4 more games to play. The sample points remain 2⁴ = 16
They have won 2 games already, it means they have two or more games to win.
Number of ways of winning the three or more matches left = [tex]4C2 + 4C3 + 4C4[/tex] = 6 + 4 + 1 = 11
Probability that a team will win the match, given that it has won two out of the first three games = 11/16
Probability that a team will win the match, given that it has won two out of the first three games = 0.69
Which decimal is closest in value to the fraction below?
1/7
O A. 0.8
O B. .33333
O c. 0.143
Answer:
0.143
Step-by-step explanation:
1/7 means 1 divided by 7. 1 divided by 7 is approximately 0.143.
Hope this helps!
List the complete list of numbers that make up pi.
Answer:
Sry, i dont know all of the numbers. Hope this helps!
Here are the first:
Step-by-step explanation:
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601476990902640136394437455305068203496252451749399651431429809190659250937221696461515709858387410597885959772975498930161753928468138268683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456028506016842739452267467678895252138522549954666727823986456596116354886230577456498035593634568174324112515076069479451096596094025228879710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821682998948722658804857564014270477555132379641451523746234364542858444795265867821051141354735739523113427166102135969536231442952484937187110145765403590279934403742007310578539062198387447808478489683321445713868751943506430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675142691239748940907186494231961567945208095146550225231603881930142093762137855956638937787083039069792077346722182562599661501421503068038447734549202605414665925201497442850732518666002132434088190710486331734649651453905796268561005508106658796998163574736384052571459102897064140110971206280439039759515677157700420337869936007230558763176359421873125147120532928191826186125867321579198414848829164470609575270695722091756711672291098169091528017350671274858322287183520935396572512108357915136988209144421006751033467110314126711136990865851639831501970165151168517143765761835155650884909989859982387345528331635507647918535893226185489632132933089857064204675259070915481416549859461637180270981994309924488957571282890592323326097299712084433573265489382
Pls mark Brainliest
If the two angles are complementary, find the measure of each of angle. I am having trouble decoding this problem in it it says 7f and 2f what is the formula for this problem
Answer:
f=10
Step-by-step explanation:
I don't know a formula for this but I can see that <CRE is a 90° angle so 7f+2f=90 and if f=10 7f=70 and 2f=20 which fits
The measure of angle of each is 70° and 20°.
What are Angles?Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.
Angles are usually measured in degrees or radians.
The given angles are complementary.
That is, ∠CRE is complementary, which means the angle is 90 degrees.
∠CRT + ∠TRE = 90°
(7f)° + (2f)° = 90°
9f = 90°
f = 90 / 9
f = 10
Hence ∠CRT = (7f)° = 70°
∠TRE = (2f)° = 20°
Hence the measure of each of the angle is 70° and 20°.
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Given the following functions f(x) and g(x), solve f[g(6)]. f(x) = 6x + 12 g(x) = x − 8
Answer:
Answer:
Option 2nd is correct.
=0.
Step-by-step explanation:
Given the function:
Solve:
First calculate:
f[g(x)]
Substitute the function g(x)
Replace x with x-8 in the function f(x) we get;
The distributive property says that:
Using distributive property:
⇒
Put x = 6 we get;
Therefore, the value of is 0.
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
f(x) = 6x + 12
g(x) = x − 8
f(g(6))=?
g(6)=6-8= -2
f(-2)= -2*6+12= -12+12=0
f(g(6))= f(-2)=0
Solve the system of equations. \begin{aligned} & -5y-10x = 45 \\\\ &-3y+10x=-5 \end{aligned} −5y−10x=45 −3y+10x=−5
Answer:
x = -2
y = -5
Step-by-step explanation:
We can solve this algebraically (substitution or elimination) or graphically. I will be using elimination:
Step 1: Add the 2 equations together
-8y = 40
y = -5
Step 2: Plug y into an original equation to find x
-3(-5) + 10x = -5
15 + 10x = -5
10x = -20
x = -2
And we have our final answers!
Answer:
[tex]\boxed{\sf \ \ \ x=-2 \ \ \ and \ \ \ y=-5 \ \ \ }[/tex]
Step-by-step explanation:
let s solve the following system
(1) -5y-10x=45
(2) -3y+10x=-5
let s do (1) + (2) it comes
-5y-10x-3y+10x=45-5=40
<=>
-8y=40
<=>
y = -40/8=-20/4=-5
so y = -5
let s replace y in (1)
25-10x=45
<=>
10x=25-45=-20
<=>
x = -20/10=-2
so x = -2
I’ll give out Brainly-ist to the correct one
Use your calculator to estimate the value of
log740.
Click on the correct answer.
1.519
1.896
1.354
Answer:
1.896
Step-by-step explanation:
You can answer this just using your number sense.
[tex]\log_7{(40)}\approx 1.896[/tex]
You know that 49 = 7², so log₇(49) = 2. The log function has a fairly small slope, so log₇(40) will not be far from 2.
_____
If you want to use your calculator, you can use the "change of base formula".
log₇(49) = log(49)/log(7) ≈ 1.602060/0.845098 ≈ 1.896
Pls Help!
Given the polynomial function below, find F(3).
F(x) = 2x3 - 7x + 1
A. 34
B. -8
C. 26
D. -2
Answer:
34
Step-by-step explanation:
F(x) = 2x^3 - 7x + 1
Let x= 3
F(3) = 2* 3^3 - 7*3 + 1
= 2 * 27 -21+1
= 54 -21 + 1
= 34
Answer: 34
Step-by-step explanation:
Please help me with this math problem
Answer:
[tex] 1 \frac{1}{24} [/tex]
Step-by-step explanation:
[tex] \frac{5}{6} + \frac{1}{3} . \frac{5}{8} \\ \\ = \frac{5}{6} + \frac{5}{24} \\ \\ = \frac{5 \times 4}{6 \times 4} + \frac{5 }{24} \\ \\ = \frac{20}{24} + \frac{5 }{24} \\ \\ = \frac{20 + 5}{24} \\ \\ = \frac{25}{24} \\ \\ = 1 \frac{1}{24} \\ [/tex]
Help please if your good at maths ?
Answer:
Year 7 = 75 students
Year 9 = 25 students
Step-by-step explanation:
Year 7 has 3/8 of the total since the circle is divided into 8 sections and has 3 of the 8 sections
3/8 * 200 students = 75
Year 9 has 1/8 of the total since the circle is divided into 8 sections and has 1 of the 8 sections
1/8 * 200 =25
(06.02)A six-sided number cube labeled 1 through 6 is rolled 200 times. An even number is rolled 115 times. Compare the theoretical probability of rolling an even number with the relative frequency of rolling an even number and select one of the statements below that best describes the situation. The theoretical probability and relative frequency are the same. The theoretical probability is larger than the relative frequency. The theoretical probability is smaller than the relative frequency. There is not enough information to determine the relative frequency.
Answer:
The theoretical probability is smaller than the relative frequency
Step-by-step explanation:
6-sided cube rolled 200 times
Probability of an even number is 1/2= 0.5
200*1/2= 100- theoretical probability
Experimental frequency= 115
Relative frequency= 115/200= 0.575
0.575 > 0.5
The theoretical probability is smaller than the relative frequency
Answer:
The theoretical probability is smaller than the relative frequency.
Step-by-step explanation:
Tamar is measuring the sides and angles of Triangle T U V to determine whether it is congruent to the triangle below. For triangle K L M, side K M is 27 millimeters, side L M is 20 millimeters, and side K L is 12 millimeters. Angle K is 45 degrees, angle M is 25 degrees, angle L is 110 degrees. Which pair of measurements would eliminate the possibility that the triangles are congruent? Measure of angle T = 25 degrees and Measure of angle U = 45 degrees Measure of angle T = 110 degrees and Measure of angle V = 25 degrees Measure of angle T = 25 degrees and TU = 12 Measure of angle T = 110 degrees and UV = 27
Answer: Measure of angle T = 25 degrees and Measure of angle U = 45 degrees
Step-by-step explanation:
Measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.
What are congruent triangles?
" Triangles are said to be congruent if the corresponding sides and angles of the one triangle are equals to the other triangles."
According to the question,
In triangle KLM,
KM =27millimeters
LM = 20millimeters
KL = 12 millimeters
∠K= 45degrees
∠M= 25 degrees
∠L = 110degrees
From the given measurements of the triangle we have,
side with measure 27millimeters is opposite to angle 110° .
side with measure 12millimeters is opposite to angle 25° .
side with measure 20millimeters is opposite to angle 45°.
From the conditions in triangle TUV to be congruent to triangle KLM ,
Measure of angle T = 25 degrees and TU = 12 is against the given condition of congruent triangle.
As angle T and side TU are adjacent to each other, which is against the correspondence of the given triangle.
Hence, measure of angle T = 25 degrees and TU = 12 is the pair of measurements would eliminate the possibility that the triangles are congruent.
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PLEASE answer pic provided
Answer:
50 to 60 seconds is the answer
Please answer this correctly
Answer:
25%
Step-by-step explanation:
less than 30 is from minimum to lower quartile. so, 25%
The profile of the cables on a suspension bridge may be modeled by a parabola. The central span of the bridge is 1210 m long and 128 m high. The parabola y equals 0.00035 x squared gives a good fit to the shape of the cables, where StartAbsoluteValue x EndAbsoluteValue less than or equals 605, and x and y are measured in meters. Approximate the length of the cables that stretch between the tops of the two towers.
Answer:
The approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.
Step-by-step explanation:
The equation of the parabola is:
[tex]y=0.00035x^{2}[/tex]
Compute the first order derivative of y as follows:
[tex]y=0.00035x^{2}[/tex]
[tex]\frac{\text{d}y}{\text{dx}}=\frac{\text{d}}{\text{dx}}[0.00035x^{2}][/tex]
[tex]=2\cdot 0.00035x\\\\=0.0007x[/tex]
Now, it is provided that |x | ≤ 605.
⇒ -605 ≤ x ≤ 605
Compute the arc length as follows:
[tex]\text{Arc Length}=\int\limits^{x}_{-x} {1+(\frac{\text{dy}}{\text{dx}})^{2}} \, dx[/tex]
[tex]=\int\limits^{605}_{-605} {\sqrt{1+(0.0007x)^{2}}} \, dx \\\\={\displaystyle\int\limits^{605}_{-605}}\sqrt{\dfrac{49x^2}{100000000}+1}\,\mathrm{d}x\\\\={\dfrac{1}{10000}}}{\displaystyle\int\limits^{605}_{-605}}\sqrt{49x^2+100000000}\,\mathrm{d}x\\\\[/tex]
Now, let
[tex]x=\dfrac{10000\tan\left(u\right)}{7}\\\\\Rightarrow u=\arctan\left(\dfrac{7x}{10000}\right)\\\\\Rightarrow \mathrm{d}x=\dfrac{10000\sec^2\left(u\right)}{7}\,\mathrm{d}u[/tex]
[tex]\int dx={\displaystyle\int\limits}\dfrac{10000\sec^2\left(u\right)\sqrt{100000000\tan^2\left(u\right)+100000000}}{7}\,\mathrm{d}u[/tex]
[tex]={\dfrac{100000000}{7}}}{\displaystyle\int}\sec^3\left(u\right)\,\mathrm{d}u\\\\=\dfrac{50000000\ln\left(\tan\left(u\right)+\sec\left(u\right)\right)}{7}+\dfrac{50000000\sec\left(u\right)\tan\left(u\right)}{7}\\\\=\dfrac{50000000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+5000x\sqrt{\dfrac{49x^2}{100000000}+1}[/tex]
Plug in the solved integrals in Arc Length and solve as follows:
[tex]\text{Arc Length}=\dfrac{5000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+\dfrac{x\sqrt{\frac{49x^2}{100000000}+1}}{2}|_{limits^{605}_{-605}}\\\\[/tex]
[tex]=1245.253707795227\\\\\approx 1245.25[/tex]
Thus, the approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.
While conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems. The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013. Is this an unusually high number of faulty modems
Answer:
We conclude that this is an unusually high number of faulty modems.
Step-by-step explanation:
We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.
The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.
Let p = population proportion.
So, Null Hypothesis, [tex]H_0[/tex] : p = 0.013 {means that this is an unusually 0.013 proportion of faulty modems}
Alternate Hypothesis, [tex]H_A[/tex] : p > 0.013 {means that this is an unusually high number of faulty modems}
The test statistics that would be used here One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion faulty modems= [tex]\frac{10}{367}[/tex] = 0.027
n = sample of modems = 367
So, the test statistics = [tex]\frac{0.027-0.013}{\sqrt{\frac{0.013(1-0.013)}{367} } }[/tex]
= 2.367
The value of z-test statistics is 2.367.
Since, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that this is an unusually high number of faulty modems.
Please answer this correctly
Answer:
54
Step-by-step explanation:
The pink parts are 9 out of total 11 parts.
9/11
Multiply with 66.
9/11 × 66
= 54
Hey there! :)
Answer:
P(Pink) = 54.
Step-by-step explanation:
Begin by calculating the possibility of the spinner landing on pink:
[tex]P(pink) = \frac{pink}{total}[/tex]
Therefore:
[tex]P(Pink) = \frac{9}{11}[/tex]
In this question, the spinner was spun 66 times. Since we have solved for the probability, we can set up ratios to find the probability of the spinner landing on pink out of 66.
[tex]\frac{9}{11}= \frac{x}{66}[/tex]
Cross multiply:
594 = 11x
Divide both sides by 11:
x = 54.
P(Pink) = 54.
What is the product? (3x-b)(2x^2-7x+1) A. -12x^2+42x-6 B. -12x^2+21x+6 C. 6x^3-33x^2+45x-6 D. 6x^3-27x^2-39x+6
Answer:
C.6x³-33x² + 45x-6
Step-by-step explanation:
(3x-6)(2x^2-7x+1)
= 3x(2x² - 21x +1) -6(2x² - 7x+1)
= (6x³ - 21x² + 3x) - (12x² - 42x+6)
= 6x³ - 21x² + 3x -12x² + 42x -6
= 6x³-33x² + 45x-6
Find an explicit formula for the following sequence, an which starts with a1=−1. −1,1/2,−1/3,1/4,−1/5,…
Answer:
The sequence can be represented by the formula of its nth term:
[tex]a_n=\frac{(-1)^n}{n}[/tex]
Step-by-step explanation:
Notice that we are in the presence of an alternate sequence (the values alternate from negative to positive. Therefore we need to take into account that there should be a factor "-1" raised to the "n" value for the sequence. Also, given that the sequence looks in absolute value like the harmonic sequence, we conclude upon the following general form for the "nth" term of the sequence:
[tex]a_n=\frac{(-1)^n}{n}[/tex]
LA=
Round your answer to the nearest hundredth.
A
5
B
3
Answer:
You didn't state it but you need to find Angle A.
From the Pythagorean Theorem, we calculate side ac
side ac^2 = 5^2 - 3^2 =25 -9 = 16 Side AC = 4
arc tangent angle A = 3 / 4 = .75
angle A = 36.87 Degrees
Step-by-step explanation:
Consider the diagram and the proof below.
Given: In △ABC, AD ⊥ BC
Prove: StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
Triangle A B C is shown. A perpendicular bisector is drawn from point A to point D on side C B forming a right angle. The length of A D is h, the length of C B is a, the length of C A is b, and the length of A B is c.
A 2-column table has 7 rows. The first column is labeled Statement with entries In triangle A B C line segment A D is perpendicular to line segment B C, In triangle A D B sine (uppercase B) = StartFraction h Over c EndFraction, c sine (uppercase B) = h, In triangle A C D, sine (uppercase C) = StartFraction h Over b EndFraction, b sine (uppercase C) = h, question mark, StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction. The second column is labeled Reason with entries given, definition of sine, multiplication property of equality, definition of sine, multiplication property of equality, substitution, and division property of equality.
What is the missing statement in Step 6?
b = c
StartFraction h Over b EndFraction = StartFraction h Over c EndFraction
csin(B) = bsin(C)
bsin(B) = csin(C)
Answer:
c- the right triangle altitude theorem
Step-by-step explanation:
i did it on edge! ; )
The missing statement in Step 6 is ,c- The right triangle altitude theorem.
We have given that,
In △ABC, AD ⊥ BC
Prove: StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction.
Triangle A B C is shown.
What is the right triangle altitude theorem?The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse
Therefore we have,
A perpendicular bisector is drawn from point A to point D on side C B forming a right angle.
The length of A D is h, the length of C B is a, the length of C A is b, and the length of A B is c.
So the missing statement in Step 6
b = c
c=The right triangle altitude theorem.
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Will give BRAINLIEST! Find the set of x values that satisfy this inequality. 2 | 5x − 4 | > 6 Select one:a. x ≤ 7 / 5 and x ≥ 1 / 5b. x > 7 / 5c. x > 7 / 5 or x < 1 / 5d. 1 / 5 ≤ x ≤ 7 / 5
Answer:
c. x > 7 / 5 or x < 1 / 5
Step-by-step explanation:
2 | 5x − 4 | > 6
| 5x - 4 | > 3
5x -4 > 3 ⇒ 5x > 7 ⇒ x > 7/55x -4 < -3 ⇒ 5x < 1 ⇒ x < 1/5So combining the 2 above we get:
x > 7/5 or x < 1/5Correct choice is c.
Answer:
x>7/5 or x <1/5
Step-by-step explanation:
2 | 5x − 4 | > 6
Divide by 2
2/2 | 5x − 4 | > 6/2
| 5x − 4 | > 3
There are two solutions one positive and one negative ( the negative flips the inequality)
5x-4 >3 or 5x-4 < -3
Add 4 to each side
5x-4 +4>3+4 or 5x-4+4 < -3+4
5x >7 or 5x <1
Divide by 5
x>7/5 or x <1/5
The figure shows a square floor plan with a smaller square area that will accommodate a combination fountain and pool.The floor with the fountain pool area removed has an area of 33 Square meters and a perimeter of 36 meters. Find the dimensions of the floor and the dimensions of the square that will accommodate the fountain and pool.
Answer:
(x, y) = (7, 4) meters
Step-by-step explanation:
The area of the floor without the removal is x^2, so with the smaller square removed, it is x^2 -y^2.
The perimeter of the floor is the sum of all side lengths, so is 4x +2y.
The given dimensions tell us ...
x^2 -y^2 = 33
4x +2y = 36
From the latter equation, we can write an expression for y:
y = 18 -2x
Substituting this into the first equation gives ...
x^2 -(18 -2x)^2 = 33
x^2 -(324 -72x +4x^2) = 33
3x^2 -72x + 357 = 0 . . . . write in standard form
3(x -7)(x -17) = 0 . . . . . factor
Solutions to this equation are x=7 and x=17. However, for y > 0, we must have x < 9.
y = 18 -2(7) = 4
The floor dimension x is 7 meters; the inset dimension y is 4 meters.
If the statement shown is rewritten as a conditional statement in if-then form, which best describes the conclusion?
When a number is divisible by 9, the number is divisible by 3.
then the number is divisible by 3
then the number is divisible by 9
O if a number is divisible by 3
O if a number is divisible by 9
Answer:
Correct statement: "the number is divisible by 3".
Step-by-step explanation:
The statement provided is:
When a number is divisible by 9, the number is divisible by 3.
The general form of a conditional statement in if-then form is:
[tex]p\rightarrow q[/tex]
This implies that if p, then q.
The part after the "if" is known as the hypothesis and the part after the "then" is known as the conclusion.
The if-then form of the provided statement is:
If a number is divisible by 9, then the number is divisible by 3.
So, the conclusion is:
"the number is divisible by 3"
Answer:
a
Step-by-step explanation:
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Answer:
(x-1)(x-4)
Step-by-step explanation:
I used long division with polynomials to help me find the other factor to this problem. Divide x cubed -5x squared -6x+8 by x+2 to get x squared -5x+4.
Hope this helps!
Answer: (x + 2) (x - 4) (x - 1)
Step-by-step explanation:
Use synthetic division. If the remainder (last digit) is zero, then it is a factor. The other digits represent the coefficients of the reduced polynomial.
x³ - 3x² - 6 + 8 ; x + 2 = 0 --> x = -2
-2 | 1 -3 -6 8
| ↓ -2 10 -8
1 -5 4 0 → remainder is 0
Reduced polynomial: x² -5x + 4
= (x - 4) (x - 1)
Factored form: (x + 2) (x - 4) (x - 1)
In its first month of operations, Weatherall Company made three purchases of merchandise in the following sequence: (1) 120 units at $5, (2) 460 units at $6, and (3) 100 units at $7. Collapse question part (a1) Calculate the average unit cost. (Round answer to 2 decimal places, e.g. 15.25.) Average unit cost
Answer: 4h4hj4h44 n4
Step-by-step explanation: b4jb4j 4 n4
1) Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation.
2 x − x2 + 1 = 0, x1 = 2
What is x3 =?
2) Use Newton's method to find all solutions of the equation correct to six decimal places.
x + 4 = x^2 - x
What is X =?
3) Use Newton's method to find all solutions of the equation correct to six decimal places.
5 cos(x) = x + 1
What is X =?
4) A graphing calculator is recommended.
Use Newton's method to find all solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.
5A) Use Newton's method to find the critical numbers of the function
f(x) = x6 ? x4 + 3x3 ? 4x
What is X =?
B) Find the absolute minimum value of f correct to four decimal places.
Answer:
Check below, please
Step-by-step explanation:
Hello!
1) In the Newton Method, we'll stop our approximations till the value gets repeated. Like this
[tex]x_{1}=2\\x_{2}=2-\frac{f(2)}{f'(2)}=2.5\\x_{3}=2.5-\frac{f(2.5)}{f'(2.5)}\approx 2.4166\\x_{4}=2.4166-\frac{f(2.4166)}{f'(2.4166)}\approx 2.41421\\x_{5}=2.41421-\frac{f(2.41421)}{f'(2.41421)}\approx \mathbf{2.41421}[/tex]
2) Looking at the graph, let's pick -1.2 and 3.2 as our approximations since it is a quadratic function. Passing through theses points -1.2 and 3.2 there are tangent lines that can be traced, which are the starting point to get to the roots.
We can rewrite it as: [tex]x^2-2x-4=0[/tex]
[tex]x_{1}=-1.1\\x_{2}=-1.1-\frac{f(-1.1)}{f'(-1.1)}=-1.24047\\x_{3}=-1.24047-\frac{f(1.24047)}{f'(1.24047)}\approx -1.23607\\x_{4}=-1.23607-\frac{f(-1.23607)}{f'(-1.23607)}\approx -1.23606\\x_{5}=-1.23606-\frac{f(-1.23606)}{f'(-1.23606)}\approx \mathbf{-1.23606}[/tex]
As for
[tex]x_{1}=3.2\\x_{2}=3.2-\frac{f(3.2)}{f'(3.2)}=3.23636\\x_{3}=3.23636-\frac{f(3.23636)}{f'(3.23636)}\approx 3.23606\\x_{4}=3.23606-\frac{f(3.23606)}{f'(3.23606)}\approx \mathbf{3.23606}\\[/tex]
3) Rewriting and calculating its derivative. Remember to do it, in radians.
[tex]5\cos(x)-x-1=0 \:and f'(x)=-5\sin(x)-1[/tex]
[tex]x_{1}=1\\x_{2}=1-\frac{f(1)}{f'(1)}=1.13471\\x_{3}=1.13471-\frac{f(1.13471)}{f'(1.13471)}\approx 1.13060\\x_{4}=1.13060-\frac{f(1.13060)}{f'(1.13060)}\approx 1.13059\\x_{5}= 1.13059-\frac{f( 1.13059)}{f'( 1.13059)}\approx \mathbf{ 1.13059}[/tex]
For the second root, let's try -1.5
[tex]x_{1}=-1.5\\x_{2}=-1.5-\frac{f(-1.5)}{f'(-1.5)}=-1.71409\\x_{3}=-1.71409-\frac{f(-1.71409)}{f'(-1.71409)}\approx -1.71410\\x_{4}=-1.71410-\frac{f(-1.71410)}{f'(-1.71410)}\approx \mathbf{-1.71410}\\[/tex]
For x=-3.9, last root.
[tex]x_{1}=-3.9\\x_{2}=-3.9-\frac{f(-3.9)}{f'(-3.9)}=-4.06438\\x_{3}=-4.06438-\frac{f(-4.06438)}{f'(-4.06438)}\approx -4.05507\\x_{4}=-4.05507-\frac{f(-4.05507)}{f'(-4.05507)}\approx \mathbf{-4.05507}\\[/tex]
5) In this case, let's make a little adjustment on the Newton formula to find critical numbers. Remember their relation with 1st and 2nd derivatives.
[tex]x_{n+1}=x_{n}-\frac{f'(n)}{f''(n)}[/tex]
[tex]f(x)=x^6-x^4+3x^3-2x[/tex]
[tex]\mathbf{f'(x)=6x^5-4x^3+9x^2-2}[/tex]
[tex]\mathbf{f''(x)=30x^4-12x^2+18x}[/tex]
For -1.2
[tex]x_{1}=-1.2\\x_{2}=-1.2-\frac{f'(-1.2)}{f''(-1.2)}=-1.32611\\x_{3}=-1.32611-\frac{f'(-1.32611)}{f''(-1.32611)}\approx -1.29575\\x_{4}=-1.29575-\frac{f'(-1.29575)}{f''(-4.05507)}\approx -1.29325\\x_{5}= -1.29325-\frac{f'( -1.29325)}{f''( -1.29325)}\approx -1.29322\\x_{6}= -1.29322-\frac{f'( -1.29322)}{f''( -1.29322)}\approx \mathbf{-1.29322}\\[/tex]
For x=0.4
[tex]x_{1}=0.4\\x_{2}=0.4\frac{f'(0.4)}{f''(0.4)}=0.52476\\x_{3}=0.52476-\frac{f'(0.52476)}{f''(0.52476)}\approx 0.50823\\x_{4}=0.50823-\frac{f'(0.50823)}{f''(0.50823)}\approx 0.50785\\x_{5}= 0.50785-\frac{f'(0.50785)}{f''(0.50785)}\approx \mathbf{0.50785}\\[/tex]
and for x=-0.4
[tex]x_{1}=-0.4\\x_{2}=-0.4\frac{f'(-0.4)}{f''(-0.4)}=-0.44375\\x_{3}=-0.44375-\frac{f'(-0.44375)}{f''(-0.44375)}\approx -0.44173\\x_{4}=-0.44173-\frac{f'(-0.44173)}{f''(-0.44173)}\approx \mathbf{-0.44173}\\[/tex]
These roots (in bold) are the critical numbers
A manufacturer knows that their items have a normally distributed length, with a mean of 18.1 inches, and standard deviation of 3.7 inches. If one item is chosen at random, what is the probability that it is less than 28.9 inches long
Answer:
Step-by-step explanation:
z = (X - μ) / σ, where X = date, μ = mean, σ = standard deviation
z = (28.9 - 18.1) / 3.7
z = 18.6
0.06681 is the area for this z.
6.681% shall be shorter than 18.6 inches.
Given that cosθ=817 and sinθ=−1517 . What is the value of tanθ?
Answer:
tan∅ = -1517/817
Step-by-step explanation:
tan∅ = sin∅/cos∅
Answer:
Step-by-step explanation:
The owner of a small machine shop has just lost one of his largest customers. The solution to his problem,he says, is to fire three machinists to balance his workforce with his current level of business. The owner says that it is a simple problem with a simple solution. The three machinists disagree. Why
Answer:
It may look simple to the owner because he is not the one losing a job. For the three machinists it represents a major event with major consequences