Answer:
x<3
Step-by-step explanation:
5x+12+3x<36
First subtract 12 from both sides.
5x+3x<24
Next combine like terms on the left side (5x and 3x)
8x<24
Next divide 8 from both sides
x<3
Two athletes practice for a marathon by running back and forth on an 11-mile course. They start running simultaneously, one at a speed 2 mph faster than the other's speed. How fast does each run if they meet 1 hour 6 minutes after starting? (The faster runner is already returning at this point.) How far from the starting point do the runners meet?
Answer:
Faster runner speed: 11 mph
Slower runner speed: 9 mph
Distance from starting point: 9.9 miles
Step-by-step explanation:
Let the slower runner speed be: x
Faster runner speed: x+2
1 hour 6 minutes = 1.1 hours
Slower: 1.1(x) = 1.1x miles
Faster: 1.1(x+2) = 1.1x+2.2 miles
This means that the faster runner had gone 2.2 miles more than the slower runner.
1.1x + 2.2 > 11 miles (This is true as we know the faster runner is coming back from the 11 mile run)
1.1x > 11 - 2.2 miles
1.1x > 8.8 miles
x > 8.8 / 2.2 miles
x > 8 mph
1.1x < 11 miles (we know this is true as the slower runner has to have gone less than 11 miles as the faster runner met him on his way back)
x < 11 / 1.1 miles
x < 10 miles
8 < x < 10
Although x could be any number including decimal between 8 and 10, the obvious first answer would be 9. However we need to check if this answer is correct.
Slower runner distance to the end:
1.1(9) = 9.9 miles
11 - 9.9 = 1.1 miles
Faster runners distance from the end (when coming back)
1.1(9+2) = 1.1(11) = 12.1 miles
12.1 - 11 = 1.1 miles
The speeds 9 mph and 11 mph are now proven to be the right speeds. Using our equation before, we can figure out the distance from the starting point that they meet at. This is just how far the slower runner has gotten. So, 1.1(9) = 9.9 miles from the starting point
Solve For X. Please add an explanation.
Answer:
Your answer is 2.5
Hope that this is helpful. Vote and like it
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.
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:
Is a coin flip random? Why or why not, in your opinion?
Choose the correct answer below.
A.
Yes. You will get heads on every other flip.
B.
Yes. You cannot predict the outcome beforehand.
C.
No. You must run numerous trials before you can tell.
D.
No. You can predict the outcome beforehand.
Answer:
B
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Which fraction is equivalent to (7-3)*3/10^4-10^2
A. 16/25
B. 1/25
C. 8/1125
D. 16/2475
Answer:
C.8/1125 is the answer......
F(t)=212-6t
what is the value of t when F (t) = 140?
Answer: -628
Step-by-step explanation:
F(140) = 212 - 6(140)
F(140) = 212 - 840
F(140) = -628
What does the enlargement look like and what are the coordinates?
Answer:
(-6, -3) (-3,-3) (-3,-6)
Step-by-step explanation:
Multiple all of the vertices by 1.5.
(-6, -3) (-3,-3) (-3,-6)
Hope I helped!
[enlargment will still be a triangle]
Hello Brainly pleas help
Answer:
can you take a better pick
Step-by-step explanation:
6. Find the ICM of 60 and 400
Answer: it's 1200
Step-by-step explanation: please give me brainliest
400x3=1200
60x20=1200
Pls help I need a good grade
Answer:
f= -14
Step-by-step explanation:
Answer:
f= -14
Step-by-step explanation:
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!!
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!
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.
help please (will mark brainliest or however you spell it)
If a1 = 4 and an = -3an-1 then find the value of a4.
Answer:
[tex]a_4 = -108[/tex]
Step-by-step explanation:
Given
[tex]a_n = -3a_{n-1}[/tex]
[tex]a_1 = 4[/tex]
Required
Find [tex]a_4[/tex]
[tex]a_4 = -3a_{4-1}[/tex]
[tex]a_4 = -3a_3[/tex]
We calculate for a3
[tex]a_3 = -3a_{3-1}[/tex]
[tex]a_3 = -3a_2[/tex]
Calculate for a2
[tex]a_2 = -3a_{2-1[/tex]
[tex]a_2 = -3a_1[/tex]
Substitute 4 for a1
[tex]a_2 = -3*4[/tex]
[tex]a_2 = -12[/tex]
Substitute -12 for a2 in [tex]a_3 = -3a_2[/tex]
[tex]a_3 = -3 * -12[/tex]
[tex]a_3 = 36[/tex]
Substitute 36 for a3 in [tex]a_4 = -3a_3[/tex]
[tex]a_4 = -3*36[/tex]
[tex]a_4 = -108[/tex]
A study showed that 25% of the students drive themselves to school. Based on the suggested probability, in a class of 18 students, what would be the probability that at least 6 students drive themselves to school? (CDF)
A) 0.139
B) 0.283
C) 0.717
D) 0.861
Answer:
B) 0.283
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
25% of the students drive themselves to school.
This means that [tex]p = 0.25[/tex]
Class of 18 students
This means that [tex]n = 18[/tex]
What would be the probability that at least 6 students drive themselves to school?
This is
[tex]P(X \geq 6) = 1 - P(X < 6)[/tex]
In which
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{18} = 0.006[/tex]
[tex]P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{17} = 0.034[/tex]
[tex]P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{16} = 0.096[/tex]
[tex]P(X = 3) = C_{15,3}.(0.25)^{3}.(0.75)^{15} = 0.17[/tex]
[tex]P(X = 4) = C_{15,4}.(0.25)^{4}.(0.75)^{14} = 0.213[/tex]
[tex]P(X = 5) = C_{15,5}.(0.25)^{5}.(0.75)^{13} = 0.199[/tex]
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.006 + 0.034 + 0.096 + 0.17 + 0.213 + 0.199 = 0.718[/tex]
[tex]P(X \geq 6) = 1 - P(X < 6) = 1 - 0.718 = 0.282[/tex]
Closest option is B, just a small rounding difference.
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:
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:
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
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
The following expression represents the profit made by John as he mows lawns: P = 20L
- 100
Which description correctly interprets each part of the expression?
its c because i already did that and got it right
What is the diameter of a sphere with a volume of 78006 in?
Answer: 53.0
Step-by-step explanation:
Then the diameter equals 53.0122774
The diameter of the sphere is 53.01 inch
What is a Sphere?
A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the diameter of the sphere be = d
The radius of the sphere be = r
The volume of the sphere is V = 78006 inch³
The Volume of a Sphere = ( 4/3 ) πr³
Substituting the values in the equation ,we get
( 4/3 ) πr³ = 78006 inch³
Now , Multiply by ( 3 / 4 ) on both sides , we get
πr³ = ( 78006 x 3 ) / 4
= 58504.5 inch³
Divide by π on both sides , we get
r³ = 58504.5 / π
= 18622.56 inch³
Taking cube roots on both sides , we get
r = 26.506 inch
So , the radius of the sphere is r = 26.506 inch
Now , the diameter of the sphere is d = 2 x r
= 2 x 26.506
= 53.01 inch
Hence , The diameter of the sphere is 53.01 inch
To learn more about sphere click :
https://brainly.com/question/27933834
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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:
What is the quotient of 33.288 and 7.6?
Answer:
219/50 or 4.38
Step-by-step explanation:
divide
A coordinate plane.
Which statements are true? Check all that apply.
The line that goes through the points (3,7) and (–2,7) is a horizontal line.
The equation x = –8 is a vertical line that goes through the point (–8,3).
The line that goes through the points (0,5) and (0,–7) is a vertical line.
The points on a horizontal line have the same x-coordinate.
Answer:
A , B, and C
Step-by-step explanation:
i just did it
Find the equation of a line parallel to the equation y = 5x + 7 through the point (2,7).
Answer:
y = 5x + 7
Step-by-step explanation:
1. Substitue the numbers into their spots.
7 = 5(2)+b
2. Find b by simplifying
7 = 10 + b
-3 = b
3. Substitute it back in since parallel lines have the same slope.
How much is 20% off of $90.75?
solving the systems of linear equations by substitution.
x+2y=6
5x+2y=18
3/8x5/4 Helpppppp pls
Answer:
9/25 or .36
Step-by-step explanation: