Answer:
The work done in stretching the spring is 8 lb.ft
Step-by-step explanation:
Given;
Applied force, F = 192 lb
extension of the spring, x = 3 ft
Determine the spring constant from the applied force and extension;
[tex]k = \frac{F}{x} \\\\k = \frac{192 \ lb}{3 \ ft} \\\\k = 64 \ lb/ft[/tex]
When the spring is stretched 6 inches beyond its natural length, the work done is calculated as follows;
x = 6 inches = 0.5 ft
[tex]W = \frac{1}{2} kx^2\\\\W = \frac{1}{2} (64 \ lb/ft)(0.5 \ ft)^2\\\\W = 8 \ lb.ft[/tex]
Therefore, the work done in stretching the spring is 8 lb.ft
Two students have a bitter disagreement about the answer to a homework question and decide to settle their differences in a duel at the golf cours. The rules of the duel are simple:
Each student takes a single shot from the 18th tee. If only one student's shot lands on the green, that student is declared the victor and the duel is over. If both students' shots land on the green, the result is a draw and the duel is over. If they both miss the green, then they repeat another round (and so on) until the duel ends in a draw or with a victor. The result of each tee shot is independent. Student A has not spent much time at the golf course, resulting in a 0.55 probability that her tee shot will hit the green. Student B golfs regularly, resulting in a 0.76 probability that his tee shot will hit the green.
Required:
a. Whatâs the probability that the duel ends in round 1?
b.Whatâs the probability that the duel ends in the 3rd round?
c. Whatâs the probability that the duel ends in a draw (i.e., that neither student wins)?
Answer:
a.) P(duel end in round 1 ) = 0.892
b.) P(duel ends in the 3rd round) = 0.010
c.) P(duel ends in a draw) = 0.418
Step-by-step explanation:
Let
P(A) - Probability that Student A will hit the green.
P(¬A) - Probability that Student A will miss the green.
P(B) - Probability that Student B will hit the green.
P(¬B) - Probability that Student B will miss the green.
Given,
P(A) = 0.55 , P(B) = 0.76
As we know that,
P(A) + P(¬A) = 1
⇒P(¬A) = 1 - P(A)
= 1 - 0.55
= 0.45
⇒P(¬A) = 0.45
And
P(B) + P(¬B) = 1
⇒P(¬B) = 1 - P(B)
= 1 - 0.76
= 0.24
⇒P(¬B) = 0.24
So, we get
P(A) = 0.55 , P(B) = 0.76
P(¬A) = 0.45, P(¬B) = 0.24
a.)
P(duel end in round 1 ) = P( both hit on green or only one hit on green )
= P(A).P(B) + [ P(A).P(¬B) + P(¬A).P(B) ]
= 0.55(0.76 ) + [ 0.55(0.24) + 0.45(0.76) ]
= 0.418 + [ 0.132 + 0.342 ]
= 0.418 + [ 0.474 ]
= 0.892
⇒P(duel end in round 1 ) = 0.892
b.)
P(duel ends in the 3rd round) = P( duel miss green in 1st round × duel miss green in 2nd round × both hit on green or only one hit on green in 3rd round )
= [ P(¬A).P(¬B) ] × [ P(¬A).P(¬B) ] × { P(A).P(B) + [ P(A).P(¬B) + P(¬A).P(B) ] }
= [ 0.45(0.24) ] × [ 0.45(0.24) ] × { 0.55(0.76 ) + [ 0.55(0.24) + 0.45(0.76) ] }
= [ 0.108 ] × [0.108] × { 0.418 + [ 0.132 + 0.342 ] }
= 0.011664 × 0.892
= 0.010404 ≈ 0.010
⇒P(duel ends in the 3rd round) = 0.010
c.)
P(duel ends in a draw) = P(both students' shots land on the green)
= P(A).P(B)
= 0.55(0.76)
= 0.418
⇒P(duel ends in a draw) = 0.418
Show work
4.87 x 7.23
Answer:
Step-by-step explanation:
Here are your workings
4.87 x 7.23 simplify
Step 2
(4.87)(7.23) Add brackets(Optional)
Then you multiply the two exponents to get 35.2101
Your answer would be 35.2101
At the City Zoo, of the zoo is set aside for the monkeys. There are 4 different monkeys, each
with an equal-sized area. What fraction of the zoo is set aside for one monkey area?
Can someone plz answer me...
A.1/4
B.4/15
C.1/13
D.1/36
i think part of this question is missing between “at the city zoo” and “of the zoo.”
but i think the answer could be a.
because if there are 4 different monkeys, and they all got 1/4 of space, it would be equal.
Choose 5 cards from a full deck of 52 cards with 13values (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A) and 4 kinds(spade, diamond, heart, and club). Count how many possible ways to geta(a)Two-pairs: Two pairs plus another card of a different value, for example:(b)Flush: five cards of the same suitbutdifferent values, for example: (c)Full house: A three of a kind and a pair, for example: (d)Four of a kind: Four cards of the same value, for example:
Answer:
a) 182 possible ways.
b) 5148 possible ways.
c) 1378 possible ways.
d) 2899 possible ways.
Step-by-step explanation:
The order in which the cards are chosen is not important, which means that we use the combinations formula to solve this question.
Combinations 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]
In this question, we have that:
There are 52 total cards, of which:
13 are spades.
13 are diamonds.
13 are hearts.
13 are clubs.
(a)Two-pairs: Two pairs plus another card of a different value, for example:
2 pairs of 2 from sets os 13.
1 other card, from a set of 26(whichever two cards were not chosen above). So
[tex]T = 2C_{13,2} + C_{26,1} = 2*\frac{13!}{2!11!} + \frac{26!}{1!25!} = 182[/tex]
So 182 possible ways.
(b)Flush: five cards of the same suit but different values, for example:
4 combinations of 5 from a set of 13(can be all spades, all diamonds, and hearts or all clubs). So
[tex]T = 4*C_{13,5} = 4*\frac{13!}{5!8!} = 5148[/tex]
So 5148 possible ways.
(c)Full house: A three of a kind and a pair, for example:
4 combinations of 3 from a set of 13(three of a kind ,c an be all possible kinds).
3 combinations of 2 from a set of 13(the pair, cant be the kind chosen for the trio, so 3 combinations). So
[tex]T = 4*C_{13,3} + 3*C_{13.2} = 4*\frac{13!}{3!10!} + 3*\frac{13!}{2!11!} = 1378[/tex]
So 1378 possible ways.
(d)Four of a kind: Four cards of the same value, for example:
4 combinations of 4 from a set of 13(four of a kind, can be all spades, all diamonds, and hearts or all clubs).
1 from the remaining 39(do not involve the kind chosen above). So
[tex]T = 4*C_{13,4} + C_{39,1} = 4*\frac{13!}{4!9!} + \frac{39!}{1!38!} = 2899[/tex]
So 2899 possible ways.
Which inequality is true if p = 2.8?
Complete question :
Which inequality is true if p = 2.8?
3p < 10.2
13.6 ≤ 3.9p
5p > 17.1
8.5 ≥ 2.5p
Answer:
3p < 10.2
8.5 ≥ 2.5p
Step-by-step explanation:
To obtain the true expression, put p = 2.8 in all the options and choose the true inequality expression :
3(2.8) < 10.2
8.4 < 10.2 ( true)
13.6 ≤ 3.9p
13.6 ≤ 3.9(2.8)
13.6 ≤ 10.92 ( False)
5p > 17.1
5(2.8) > 17.1
14 > 17.1 ( False)
8.5 ≥ 2.5p
8.5 ≥ 2.5(2.8)
8.5 ≥ 7 (True)
2+5x+1/2x^3dx
Answer
Answer:
[tex]2x+\frac{5x^2}{2}+\frac{x^4}{8}+C[/tex]
Step-by-step explanation:
I notice you have a dx at the end of the equation, this leads me to believe this is an integral. With no bounds of integration, I will solve for the indefinite integral. I will also interpret your equation as follows:
[tex]\int \:2+5x+\frac{1}{2}x^3dx[/tex]
Sum rule tells us:
[tex]\int \:2dx+\int \:5xdx+\int \frac{1}{2}x^3dx[/tex]
From this we get:
[tex]2x+\frac{5x^2}{2}+\frac{x^4}{8}[/tex]
Don't forget to add the constant!
[tex]2x+\frac{5x^2}{2}+\frac{x^4}{8}+C[/tex]
find b and round to the nearest tenth... (geometry) plz help fast i’m behind
Answer:
5.51 cm
Step-by-step explanation:
Carlos saves aluminum cans to sell to the recycling center. He recently recycled 43 pounds of cans and received $23.65. How many dollars would he get at this rate for recycling 200 pounds of cans?
Answer:
$354
Step-by-step explanation:
first we need to find out how much 1 lb of can is then we can multiply that by 200 to get the answer.
so I divided 43 by 23.65 and got 1.81818181
i'll round that to $1.82 so that equals 1 lb of a can
multiply that by 200
the answer is $354
For recycling 200 pounds of cans, he will get $110.
What is equation modelling? What is a mathematical equation and expression?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that Carlos saves aluminum cans to sell to the recycling center. He recently recycled 43 pounds of cans and received $23.65.
For 43 pounds, he recieved $23.65
For 1 pound, he will receive $(23.65/43)
For 200 pounds, she will receive $(23.65/43) x 200 or $110.
Therefore, for recycling 200 pounds of cans, he will get $110.
To solve more questions on functions, expressions and equation modelling, visit the link below -
brainly.com/question/17421223
#SPJ2
blank tens 15 ones = 6 tens 5 ones
Step-by-step explanation:
_x_tens 5 ones=6tens 5 ones
5x=65
x=65/5
x=13
sorry i donot get answer at 15 ones.
A cone has a base area of 20 m and a volume of 160 m. Find the height of the cone
Given:
Base area of cone =20 m²
Volume of the cone = 160 m³
To find:
The height of the cone.
Solution:
We know that, the volume of a cone is
[tex]V=\dfrac{1}{3}Bh[/tex]
Where, B is the base area and h is the height of the cone.
Putting V=160 and B=20, we get
[tex]160=\dfrac{1}{3}(20)h[/tex]
[tex]480=20h[/tex]
[tex]\dfrac{480}{20}=h[/tex]
[tex]24=h[/tex]
Therefore, the height of the cone is 24 m.
Select three ratios that are equivalent to
8
:
20
8:208, colon, 20.
Choose 3 answers:
Choose 3 answers:
(Choice A)
A
1
:
4
1:41, colon, 4
(Choice B)
B
4
:
10
4:104, colon, 10
(Choice C)
C
24
:
60
24:6024, colon, 60
(Choice D)
D
2
:
5
2:52, colon, 5
(Choice E)
E
10
:
24
10:24
Answer:
Its b,c,d
Step-by-step explanation:
Which of the following is a rational number?
square root of 79, square root of 80, square root of 81, square root of 82
Answer:
square root of 81.
Step-by-step explanation:
I have data with 2 independent variables measuring the effectiveness of 3 different antibiotics at different dosages. I don't know if I should use a bar graph or line graph
The Maryland State Department of Education reports that 12% of the high school students in that state attend private high schools. The University of Maryland wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools. They select a random sample of 450 applications, and find that 46 of those students attend private schools.
The question is incomplete. Here is the complete question.
The Maryland State Department of Education reports that 12% of the high school students in that state attend private high schools. The University of Maryland wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 application on file to estimate the percentage of students applying for admission who attend private schools. They select a random sample of 450 applications, and find that 46 of those students attend private schools. Create and interpret a 95% confidence interval.
Answer and Step-by-step explanation: Th proportion of students that attend private schools in the sample is
[tex]p=\frac{46}{450}[/tex]
p = 0.102
At 95% confidence, z-score is 1.96.
Standard deviation for sample proportion is calculated as
[tex]\sigma = \sqrt{\frac{p(1-p)}{n} }[/tex]
For this sample, it will be
[tex]\sigma = \sqrt{\frac{0.10(1-0.1)}{450} }[/tex]
[tex]\sigma=\sqrt{0.0002}[/tex]
[tex]\sigma=0.01414[/tex]
Interval is calculated as
p ± zσ
Then
0.102 ± 1.96(0.01414)
0.102 ± 0.028
Interval is 0.074 < p < 0.13
What confidence interval means is that with a certainty of 95%, we are confident that the true population proportion of students who attend private schools are between 0.074 and 0.13.
- {(-3, 3), (1, 1), (0, -2), (1,-4), (5, -1)}
Function?
Answer:
Step-by-step explanation:
It is not a function. (1,1) and (1,-4) are both points on the graph.
the mean of four numbers is 9 what is the total of the four numbers?
Answer:
36
Step-by-step explanation:
36/4 = 9 wish this helps!
PLEASE ANSWER FAST I HAVE 30MINS!!!!!! Which graph shows the result of dilating this figure by a factor of 4 about the origin? On a coordinate plane, rectangle A B C D has points (negative 1, 1), (3, 1), (3, negative 1), (negative 1, negative 1). On a coordinate plane, rectangle A prime B prime C prime D prime has points (negative 4, 4), (12, 4), (12, negative 4), (negative 4, negative 4). On a coordinate plane, rectangle A prime B prime C prime D prime has points (negative 2, 2), (6, 2), (6, negative 2), (negative 2, negative 2). On a coordinate plane, rectangle A prime B prime C prime D prime has points (negative 0.25, 0.25), (0.75, 0.25), (0.75, negative 0.25). (negative 0.25, negative 0.25). On a coordinate plane, rectangle A prime B prime C prime D prime has points (negative 0.5, 0.5), (1.5, 0.5), (1.5, negative 0.5), (negative 0.5, negative 0.5).
Answer:
2
Step-by-step explanation:
abshxhdbxbjsbxbsbxnd
Mr. Voelz estimates that he will spend $10 on concessions at the basketball game, He actually spends $15. What is the percent error?
PLEASE ANSWER
Answer:
.........................................................................................................................................................................
Step-by-step explanation:
If R is the midpoint of PS with PR=6x+16 and RS=-26 then find PS
Answer:
PS = 116
Step-by-step explanation:
Given:
PR = 6x + 16
RS = 12x - 26
Required:
Find PS
Solution:
Since R is the midpoint of PS, therefore,
PR = RS
6x + 16 = 12x - 26
Collect like terms
6x - 12x = -16 - 26
-6x = -42
Divide both sides by -6
x = -42/-6
x = 7
✔️PS = PR + RS (segment addition postulate)
PS = 6x + 16 + 12x - 26
Plug in the value of x
PS = 6(7) + 16 + 12(7) - 26
PS = 42 + 16 + 84 - 26
PS = 116
Solve For X. Please add an explanation.
Answer:
Your answer is 2.5
Hope that this is helpful. Vote and like it
if someone could explain this to me :((
Answer:
A) (0,2)
Step-by-step explanation:
The Y-Intercept is where the line on the coordinate plane meets the y axis which in this case is 2
Answer:
A. (0, 2)
Step-by-step explanation:
So first things first, you will want to either put the line on a graph by hand or, in a graphing calculator, I recommend DESMOS
the table is a set of coordinates so
(-4, -18) (-2.5, -10.5) (-.4, 0) (0, 2) (2, 12)
Then you'll put these coordinates into a graph and the point you see touching the y-line is your answer, (0, 2)
hope this helps!!
How much is 20% off of $90.75?
what phrases describes the expression of 16-y
What phrases describes the expression of 16-y
Answer: -9
Hope this helps~
What is 2 1/3 divided by 1/2?
Also, I have the answer but is it 7/6 or 4 2/3?
Answer:
4 2/3
Step-by-step explanation:
hope this helps you in any way
What is the quotient of 33.288 and 7.6?
Answer:
219/50 or 4.38
Step-by-step explanation:
divide
50 points! I only want mhanifa to help me so no one else answer unless you actually know how to do it
Answer:
Bbc
Step-by-step explanation:
What is the x intercept of the graph of the inequality 2x + 3y > 12
Answer: x intercept = 6
This is the location (6,0)
===============================================================
Explanation:
I assume you're talking about the boundary line of the inequality. The boundary line equation is 2x + 3y = 12
To find the x intercept, plug in y = 0 and solve for x
2x + 3y = 12
2x + 3(0) = 12
2x = 12
x = 12/2
x = 6
The boundary line 2x+3y = 12 crosses the x axis at x = 6.
We can say the x intercept is x = 6. This is the location (6,0).
Side note: the y intercept is y = 4, which is found by plugging in x = 0 and solving for y.
Pls help I need a good grade
Answer:
f= -14
Step-by-step explanation:
Answer:
f= -14
Step-by-step explanation:
3/8x5/4 Helpppppp pls
Answer:
9/25 or .36
Step-by-step explanation:
Which numbers are irrational?
Select each correct answer.
15−−√
21−−√
−9√
14√
Answer:
Step-by-step explanation:
square root of 15 is 3.8=irrational
square root of 21 is 4.58=irrational
square root of -9 is doesn't have a real square root
square root of 14 is 3.7 =irrational