Answer:
Step-by-step explanation:
[tex]F=Ir^t,\text{ where F=final amount, I=initial amount, r=rate of change, t=time}\\ \\ F=58350(1.02)^4\\ \\ F=\$ 63159.92[/tex]
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]
The advantage of crop rotation was which of the following?
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:
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
WILL GIVE BRAINLEST, What is the height of the trapezoid if the Area = 77 ft²?
Answer:
h = 7.333
Step-by-step explanation:
Answer: 7
Step-by-step explanation: I'm not sure about the actual mathematical explanation but I just took the quiz and I'm in the review right now :D
I need help on this, please!
Answer:
(5,9) and (5,3)
Step-by-step explanation:
Because the point is (5,6), and the question tells you to plot two points that are three units away from (5,6) but share the same X coordinate.
The X coordinate is 5. And 6 is the Y coordinate, if we do 6-3=2. 6+3=9.
Use the GCF and the Distributive Property to
rewrite the following expression:
24 +30
Answer:
B = 6(4 + 5)
Step-by-step explanation:
GCF = The greatest common factor, example: GCF of 12 and 16 = 12 is divisible by all of these numbers. The factors for 16 are 1, 2, 4, 8, 16. The two numbers (12 and 16) share common factors (1, 2, 4). The greatest of these is 4 and that is the greatest common factor.
Distributive property = allows us to multiply the number by a group of numbers, which are added together. The distributive property is given by: a(b+c) = ab + ac
The Greatest Common Factor of 24 and 30 is 6 because it is the largest number they have together (24 = 6*4 and 30 = 6*5)
24 divided by 6 = 4
30 divided by 6 = 5
This fits B the most: 6(4 + 5)
The answer is B, I hope this helps!
. The function is shown belo [tex]y=2^x[/tex] If the function is translated 4 units up, which of the following will represent the y-intercept and the equation of the horizontal asymptote of the translated function?
Answer: (0,5); y= 4
Step-by-step explanation:
10x – 3>-23
Please helpppp
Answer:
-2 i think i am not sure though
Step-by-step explanation:
Answer:
x = -2
Step-by-step explanation:
First, add 3 to both sides to get 10x > -20. Then, divide both sides by 10 to get x = -2. I hope this helps :)
50 points! Mhanifa please answer I will mark brainliest
Answer:
C. OBTUSE
Step-by-step explanation:
2. Paris was the son of the king and queen of Troy. When he was born, his mother dreamed that she was giving birth to a flaming torch. Fearful that this was a bad omen, King Priam ordered that the child be left on a hillside to die.
the answer is a. There is 1 as a right angle.
- There are 130 people in a sport centre,
76 people use the gym,
60 people use the swimming pool,
32 people use the track,
23 people use the gym and the pool.
8 people use the pool and the track
20 people use the gym and the track,
6 people use all three facilities,
A person is selected at random
What is the probability that the person uses exactly one of the facilities?
Answer:
0.6462 = 64.62% probability that the person uses exactly one of the facilities
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
20 people use the gym and the track and 6 people use all three facilities
So 20-6 = 14 use exactly the gym and the track and 6 use all three.
8 people use the pool and the track
So 8 - 6 = 2 use exactly the pool and the track.
23 people use the gym and the pool.
So 23 - 6 = 17 use exactly the gym and the pool.
32 people use the track
So 32 - (6 + 14 + 2) = 10 use only the track.
60 people use the swimming pool
So 60 - (6 + 2 + 17) = 35 use only the pool.
76 people use the gym
So 76 - (6 + 14 + 17) = 39 use only the gym
What is the probability that the person uses exactly one of the facilities?
Out of 130, 39 + 35 + 10 = 84 use exactly one of the facilities.
84/130 = 0.6462
0.6462 = 64.62% probability that the person uses exactly one of the facilities
perimeters of similar figures
What is another way to write a2 b3 c2 d?
Answer:
A+A+B+B+B+C+C+D
Step-by-step explanation:
it's just the letter wrote the amount of times the number says
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
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
Grace took one of her friends out to lunch. The lunches cost $100 and she paid 9% sales tax. If Grace left a 15% tip on the $100, how much in total did she pay?
Answer:
124
Step-by-step explanation:
100 x .09=9
100 x ,15=15
9 + 15=24
100+24=124
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
de-13m+5n-8p sustraer 7p-8m+3n
Answer:
its 300
Step-by-step explanation:
Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars.
Estimated Sales Volume =46.63+0.47(Advertising Expenditures)
If the company has a target sales volume of $275,000, how much should the sales manager allocate for advertising in the budget?
Answer:
$485890
Step-by-step explanation:
Given
Estimated Sales Volume =46.63+0.47(Advertising Expenditures)
Required
Find the allocated amount for advertising expenditure when target sales is $275000
Represent the sales volume with V and The advertising expenditure with a.
So, the expression is:
[tex]V = 46.63 + 0.47A[/tex]
Since the expression is in thousands, substitute 275 for V
[tex]275 = 46.63 + 0.47A[/tex]
Collect Like Terms
[tex]275 - 46.63 = 0.47A[/tex]
[tex]228.37= 0.47A[/tex]
Make A the subject
[tex]A = \frac{228.37}{0.47}[/tex]
[tex]A = 485.89[/tex]
Hence, $485890 should be allocated for advertising
please help PLEASE help
Answer:
Your answer would be 4
Step-by-step explanation:
Convert the 4 3/4 into a decimal, 4.75.
First, you must multiply 5 and -3.5 together. Then you add everything on top together.
Divide the fraction
Answer:
F. 4
Explanation:
(5(-3.5)+4(3/4)-3.25) / -4 = 4
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
Mr.Fuller wants to put fencing around his rectuangular-shaped yard. The width of the yard is 55 feet and the length is 75 feet. How many feet of fencing does Mr.fuller need
Answer: 22% fencing
Step-by-step explanation:
Mr. Fuller needs 260 feet of fencing to put around his rectangular yard.
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here,
To find the perimeter of the rectangular yard, we need to add up the lengths of all four sides.
The two sides that are 55 feet long are the width of the yard, and the two sides that are 75 feet long are the length of the yard.
So, the perimeter of the yard is:
Perimeter = 2 × (length + width)
Perimeter = 2 × (75 feet + 55 feet)
Perimeter = 2 × 130 feet
Perimeter = 260 feet
Therefore, Mr. Fuller needs 260 feet of fencing to put around his rectangular yard.
Learn more about perimeter here:
brainly.com/question/6465134
#SPJ3
URGENT!!! Find the value of x using the similar trapezoids below.
Answer:
x= 30
Step-by-step explanation:
find the corresponding ratio AD:EH
20:12=5:3
is it constant? yes because 15:9 is also 5:3
if we're trying to find x on the larger side, we do x:18
what divides into 18 to equal 3? 6
we take 6 times 5 =30 so the ratio is now 30:18=5:3 so we know its correct
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.
Ten friends share 2 pumpkins pies equally. What fraction of a pumpkin pie does each friend get?
Answer:
1/5
Step-by-step explanation:
1/5
Answer:
Each friend would get 1/5 of pumpkin pie I believe
Step-by-step explanation:
student book grade 5 page 87
Answer:
Brainly isn't for answer keys... It's to help you understand how to do something better or just how to do it in general.
Step-by-step explanation:
Which of the following statements is true for a point in the first quadrant of the coordinate plane?
Answer:
The point will have both a positive x value and a positive y value.
Step-by-step explanation:
Since the question leads me to believe this is multiple choice but there are no choices provided, I will do my best to guess what it is wanting.
Which ratio expresses the scale used to create this drawing? The camping site has dimensions of 15 meters by 60 meters.
Answer:
Answer is d on edge 2021
Step-by-step explanation:
Answer:
it is d :)
Step-by-step explanation:
Determine which car gets the better gas mileage. *
Car
honda
toyota
distance
125
120
gallons
5
6
Answer:
honda
Step-by-step explanation:
Pls help I need a good grade
Answer:
f= -14
Step-by-step explanation:
Answer:
f= -14
Step-by-step explanation: