Find the value of [tex]\frac{1^2+1*2+2^2}{1^3*2^3} + \frac{2^2+2*3+3^2}{2^3*3^3} +...+\frac{9^2+9*10*10^2}{9^3*10^3}
Observe that the [tex]n[/tex]-th term in the sum is
[tex]\dfrac{n^2 + n(n+1) + (n+1)^2}{n^3(n+1)^3} = \dfrac{3n^2 + 3n + 1}{n^3 (n+1)^3} \\\\ ~~~~~~~~ = \dfrac{(n+1)^3 - n^3}{n^3(n+1)^3} \\\\ ~~~~~~~~ = \dfrac1{n^3} - \dfrac1{(n+1)^3}[/tex]
Then the sum telescopes, and we have
[tex]\displaystyle \sum_{n=1}^{9} \frac{n^2 + n(n+1) + (n+1)^2}{n^3 (n+1)^3} = \sum_{n=1}^{9} \left(\frac1{n^3} - \frac1{(n+1)^3}\right) \\\\ ~~~~~~~~ = \left(\frac1{1^3} - \frac1{2^3}\right) + \left(\frac1{2^3} - \frac1{3^3}\right) + \cdots + \left(\frac1{8^3} - \frac1{9^3}\right) + \left(\frac1{9^3} - \frac1{10^3}\right) \\\\ ~~~~~~~~ = \frac1{1^3} - \frac1{10^3} \\\\ ~~~~~~~~ = 1 - \frac1{1000} = \boxed{\frac{999}{1000}}[/tex]
The sum of the series is 999/1000 .
What is a Series ?A series is a sequence of expression in a certain pattern.
The series of n terms is given
[tex]\rm \frac{1^2+1*2+2^2}{1^3*2^3} + \frac{2^2+2*3+3^2}{2^3*3^3} +...+\frac{9^2+9*10*10^2}{9^3*10^3}[/tex]
nth term of the series is given by
[tex]\rm T_n = \rm \dfrac{n^2 + n(n+1)+ (n+1)^2}{n^3*(n+1)^3}[/tex]
On simplification it can be written as
[tex]\rm T_n = \rm \dfrac{3n^2 + 3n+1}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{3n(n +1)+1}{n^3*(n+1)^3}\\\\\\T_n = \rm \dfrac{ (n +1)^3 - n^3}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{ 1}{n^3} - \dfrac{1}{(n+1)^3}[/tex]
The sum of terms from 1 to 9 is given by
∑ ( [tex]\rm \frac{ 1}{n^3} - \frac{1}{(n+1)^3}[/tex])
= [tex]\rm \dfrac{1}{1^3} - \dfrac{1}{2^3} + \dfrac{1}{2^3} - \dfrac{1}{3^3}+ .......... + \dfrac{1}{9^3} - \dfrac{1}{10^3}[/tex]
= (1/1³) - (1/10³)
= 999/1000
Therefore the sum of the series given is 999/1000
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keiko david and tony have a total of 106$ in their wallets. david has $6 less than keiko tony has 2 times what david has. how much do they have in their wallets? Please help
Keiko have $31 in her wallet.
David have $25 in his wallet.
Tony have $50 in his wallet.
Step-by-step explanation:Keiko
Let x = the amount in Keiko’s wallet.
David
David has $6 less than Keiko .
x - 6
Tony
Tony has has two times what David has.
2(x - 6)
The total sum of their money = 106
Keiko
x + x - 6 + 2(x - 6) = 106
2x - 6 + 2x - 12 = 106
4x - 18 = 106
4x = 106 + 18
4x /4 = 124/4
x = 31
Therefore Keiko have $31 in her wallet.
David
x - 6
31 - 6 = 25
Therefore David have $25 in his wallet.
Tony
2(x - 6)
2(31 - 6)
2(25) = 50
Therefore Tony have $50 in his wallet.
To check your work out
31 + 25 + 50 = 106
Which system of equations has a solution of (0,1,2),
A.) 3x - y = -1
2y - z = 4
X- y + z = -1
B.) 2x + 4y = 4
y - 5z = 9
x+y+z=2
C.) -2x + 2y = 2
y + 7z = 13
1-y-z=0
D.) I + 3y - z = 1
4x + 2y = 2
5y - 2z = 1
Answer:
D
Step-by-step explanation:
well, you can simply put the arguments where belong and if you check choice D
5(1)–2(2)=1
so that will be the answer
how do you solve this?
B. The standard deviation is he square root of variance. The larger the standard deviation the more variation
Answer:
this is quite an easy problem.
Step-by-step explanation:
The problem appears to be asking for the class with the greatest variability of test 1, which merely means that you are looking for the graph that has the most distributed test scores. The graph that shows the largest difference in each test score will be your answer.
Question 11
Points 2
Mary has four T-shirts-T₁, T2, T3, and T4, and
three pairs of jeans-J1, J2, and J3. The number
of possible ways she can choose her outfit is:
O 12
The computation shows that the number of possible ways will be 12.
How to calculate the value?From the information given, Mary has four t-shirts-T₁, T2, T3, and T4, and three pairs of jeans-J1, J2, and J3.
Therefore, the number of possible ways that she can choose her outfit will be:
= 4 × 3 = 12
In conclusion, the correct option is 12.
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Write the equation of the line that is parallel to the line y=−74x−2 through the point (4,-2).
Parallel lines have the same slope, so since the slope of the given line is -74, the slope of the line we want to find is also -74.
Substituting into point-slope form,
[tex]y+2=-74(x-4)\\\\y+2=-74x+296\\\\\boxed{y=-74x+294}[/tex]
Cedrick is going to meet his mother for dinner at a restaurant halfway between his house and hers. On a coordinate grip map, Cedrick’s house is at (–51, –26) and his mom lives at (2, –4).
Where is the best restaurant for them to meet?
Greek restaurant at (–25, –15)
French restaurant at (–27, –11)
Mediterranean restaurant at (–28, –12)
Thai restaurant at (–38, –1)
Using the mid-point concept, the best restaurant for them to meet is given by:
Greek restaurant at (–25, –15).
What is the midpoint concept?The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
For the midpoint between his house and his mom's, the coordinates are given as follows:
x = (-51 + 2)/2 = -49/2 = -24.5.y = (-26 - 4)/2 = -30/2 = -15.Hence the Greek restaurant is the best option, as it is closest.
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Use clustering estimation to find the approximate total in the following question.
What is the estimated total of 674, 692, 724, and 739?
ill make you brainliest
The estimated total of 674, 692, 724, and 739 is: 2800.
Clustering estimation techniqueTo find the sum using clustering estimation technique first step is to round each number to the nearest 10s.
674 into 670
692 into 690
724 into 720
739 into 740
Second step is to add
Addition=670+690+720+740
Addition=2820
2820 to the nearest 100s is 2800.
Therefore the estimated total of 674, 692, 724, and 739 is: 2800.
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Here's the work I've done. Is it right?
V=πr^2h
π(0.375)^2(0.80)
=0.4m^3 (smallest cylinder)
π(0.625)^2(0.80)
=1.0m^3 (middle cylinder)
0.70+0.80
=1.5m (height for big cylinder)
π(1.5)^2(1.5)
=10.6m^3
10.6m^3+0.4m^3+1.0m^3
=12.0m^3
The spa will fit 12.0m^3 of water
Answer: [tex]6.67m^3[/tex]
Step-by-step explanation:
For hemisphere...
diameter (d1) = 3m
radius (r1) = (3/2)m
The total volume of the hemisphere
[tex]v1=\frac{2}{3} \pi (r1)^3[/tex]
[tex]=\frac{2}{3} \pi (\frac{3}{2} )^3[/tex]
[tex]=\frac{9}{4} \pi[/tex]
-----------------------------------------------------------------------
For smaller cylinder
diameter (d2) = 0.75
radius (r2) = 0.75/2m
height (h2) = 0.80m
Volume of smaller cylinder
(V2) = [tex]\frac{1}{3} \pi (r2)^2h2[/tex]
[tex]=\frac{1}{3} \pi (\frac{0.75}{2} )^2*0.80[/tex]
[tex]=\frac{3}{80} \pi[/tex]
------------------------------------------------------------------------
For bigger cylinder
Volume of bigger cylinder =
[tex]V3=\frac{1}{3} \pi (\frac{1.25}{2} )^2*0.70[/tex]
[tex]=\frac{35}{384} \pi[/tex]
-----------------------------------------------------------------------
Volume of water = [tex](v1 - v2 - v3) =\frac{9}{4} \pi -\frac{3}{80} \pi -\frac{35}{384} \pi = 6.67 m^3[/tex]
6. Construct the Truth Table and Determine whether each of the following compound
proposition is a Tautology, Contradiction or Contingency.
The first expression is Contingency.
The second expression is Tautology.
The third expression is Contingency.
What is Truth table?A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra.
What is Contingency?A sentence is called a contingency if its truth table contains at least one 'T' and at least one 'F. '
What is Contradiction?A statement is called a contradiction if the final column in its truth table contains only 0's.
What is Tautology?A tautology is a statement that is always true.
The first expression is Contingency.
The second expression is Tautology.
The third expression is Contingency.
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What is the angle of rotation for the following figure?
Answer:
Angle rotation 120 ,90,60,45
What is the slope of a line parallel to the line whose equation is3x−4y=8?
−43
−34
34
43
Answer:
The parallel slope for this equation is going to be [tex]\frac{3}{4}[/tex] hope that helps and can you mark me as brainlist please.
Dr. Silas studies a culture of bacteria under a microscope. The function b_1(t)=1200(1.8)^t represents the number of bacteria t hours after Dr. Silas begins her study.
The number of bacteria in a second study is modeled by the function b_2(t)=1000(1.8^t.
What does the value of 1000 represent in this situation?
What does the difference of 1200 and 1000 mean between the two studies?
The _ means the 1&2 is under the b
The value of 1000 represent the initial population of bacteria in the study and the difference of 1200 and 1000 mean difference between the initial populations in the studies.
What are exponential Function ?Exponential functions are are written as y(x) = abˣ
Here
a is the initial population
b is the rate of growth or decrease
x is the time taken
The Given exponential function is
[tex]\rm b_1(t) = 1200( 1.8 )^t\\\\b_2(t) = 1000 (1.8)^t[/tex]
From the standard equation of Exponential function
(a) a = 1200 and 1000 is the initial population of the bacteria
(b)The difference of 1200 and 1000 means the difference between the initial populations in the studies
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Find the value(s) of x in the function f(x) = |-2x – 3| when f(x) = 5. (Separate multiple answers with a comma.)
Answer:
x = -4, 1
Step-by-step explanation:
Since we have a absolute value function here, we can tell there is goning to be multiple values.
First we will find x with the original function since we know |5| = 5.
Given f(x) = 5 = -2x-3,
[tex]2x-3 = 5 \\
-2x-3+3 = 5 + 3 \\
-2x = 8 \\
x = \frac{8}{ - 2} \\ = - 4[/tex]
Now we also know that |-5| = 5 as well (absolute value)
Given |-2x-3| = |-5|,
[tex] - 2x - 3 = - 5 \\ - 2x - 3 + 3 = - 5 + 3\\ - 2x = - 2 \\ x = \frac{ - 2}{ - 2} \\ = 1[/tex]
You can verifiy these 2 values by substituting them into the equation.
f(-4) = |-2(-4)-3|
= |8-3|
= |5|
= 5
f(1) = |-2(1)-3|
= |-2-3|
= |-5|
= 5
A modulus function is defined as a function that gives positive value for either a negative or positive argument. The values of x for given condition are -4 and 1.
What is a Modulus function?A function in the form of f(x) = |x| is known as a modulus function. The graph of a modulus function is symmetric about y-axis.
The function is given as,
f(x) = |-2x-3|
which implies that f(x) = -2x - 3 for x > 0 and f(x) = -(-2x - 3 )for x < 0
As per the question ,
Substitute the value of f(x) = 5, for both the cases to get the value of x as,
-2x - 3 = 5 and -(-2x - 3 ) = 5
=> x = -4 and x = 1.
Hence, the values of x obtained for the given condition are x =-4 and x = 1.
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Which is not a method for solving a system of equations?
A. Graphing
B. Substitution
C. Fundamental Theorem of Arithmetic
D. Linear combination
Fundamental Theorem of Arithmetic is not a method for solving a system of equations.
What are system of equation?A system of equations is a collection of two or more equations with a same set of unknowns.
The system of equation can be solved using the following method.
Graphing methodSubstitution methodLinear combinationThe graphing involves using graph to find the intersection of the system of equation.
Substitution method involves substituting one variable to another.
Therefore, Fundamental Theorem of Arithmetic is not a method for solving a system of equations
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If f(x) = 3x + 2, what is f(5)?
Answer:
17
Step-by-step explanation:
f(5) means replacing any x in the equation with 5, so that would give you 3*5 + 2
in order of operations, 3*5 = 15 + 2 = 17
hope this helped! :)
Brad bought an MP3 player on sale at a 20%
discount from its regular price of $120. If there
is a 5% sales tax that is calculated on the sale
price, how much did Brad pay?
Answer:
$100.8
Step-by-step explanation:
Discount=20% of 120 =24
Before tax: BP=120-24=96
After Tax BP=105% of 96=$100.8
Write −1.2 as a ratio of two integers.
Answer: (-6:5)
Step-by-step explanation:
6/5 = 1.2
-1 * 6 = -6
-6/5 = -1.2
thus...
Ratio = (-6:5)
Solve the equation on the
interval [0, 2π).
4(sin x)² - 2 = 0
The solutions to the equation on the given interval are;
x = π/4, 3π/4, 5π/4, 7π/4.
What is the solution to the equation on the interval?Given that;
4(sin x)² - 2 = 0Interval = [ 0, 2π )4(sin x)² - 2 = 0
Add 2 to both sides and divide both sides 4
4(sin x)² - 2 + 2 = 0 + 2
4(sin x)² = 2
(4(sin x)²)/4 = 2/4
(sin x)² = 1/2
Square both sides
√((sin x)²) = ±√(1/2)
sin x = ±√(1/2)
sin x = ±(√2)/2
Next, we solve for x
Not that 180° = π
x = sin⁻¹ ( (√2)/2 ) = 45° = 180°/4 = π/4
x = π/4
Since the sine function is positive in the first and second quadrant, we subtract the reference angle from π to find the solution in the second quadrant.
x = π - π/4
x = 3π/4
Now, we find the period of sin x
2π / |b|
We know that, the distance between a number and zero is 1
2π / 1
2π
Hence, period of sin x function is 2π, values will repeat every 2π radians in both direction.
Since sine function is negative in third and fourth quadrant,
x = 2π + π/4 + π
x = 5π/4
Now, add 2π to every negative angle to get a positive angle
x = 2π + ( - π/4 )
x = 2π×4/4 - π/4
x = ((2π × 8) - π ))/4
x = (8π - π)/4
x = 7π/4
Therefore, the solutions to the equation on the given interval are;
x = π/4, 3π/4, 5π/4, 7π/4.
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Please help!
P(A) = 1/3
P(B) = 2/9
P(A U B) = 4/9
Find P(A ∩ B).
A. 1
B. 1/3
C. 1/9
D. 20/18
Answer:
[tex]\sf C. \quad \dfrac{1}{9}[/tex]
Step-by-step explanation:
Addition Law for Probability
[tex]\sf P(A \cup B)=P(A)+P(B)-P(A \cap B)[/tex]
Given:
[tex]\sf P(A)=\dfrac{1}{3}=\dfrac{3}{9}[/tex]
[tex]\sf P(B)=\dfrac{2}{9}[/tex]
[tex]\sf P(A \cup B)=\dfrac{4}{9}[/tex]
Substitute the given values into the formula and solve for P(A ∩ B):
[tex]\implies \sf P(A \cup B) = P(A)+P(B)-P(A \cap B)[/tex]
[tex]\implies \sf \dfrac{4}{9} = \sf \dfrac{3}{9}+\dfrac{2}{9}-P(A \cap B)[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{3}{9}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{3+2-4}{9}[/tex]
[tex]\implies \sf P(A \cap B) = \sf \dfrac{1}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{3}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{3+2-4}{9}[/tex]
[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{9}[/tex]
The product of w and 6
Answer:
w x 6
Because W is a variable and we don't know what W so it the equation is gonna be a open sentance
HELP ME PLEASE I WILL GIVE POINTS THANK YOU SO MUCH
The angle of X is 108°
Given,
XW ≅ YZ
∠Z = 72°
then ∠X = ?
Properties of trapezoid are:
The base sides are the only pair of sides that are parallel. Other than the base, the remaining sides are all non-parallel and equal in length. The length of the diagonals is constant. the same for the base angles.We know that from the figure that ∠Z = ∠V & ∠W = ∠U
∵ Isosceles trapezoid rule
And sum of all the angles in a trapezoid = 360°
Now, 2 × 72 = 144
∴ 360 ₋ 144 = 216°
Now sum of other two angles = 216°
one angle = 216/2
= 108°
Therefore the angle of ∠X is 108°
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he Golfing Emporium had a set of 10 golf clubs that were marked on sale for $780. This was a discount of 30% off the original selling price.
Step 2 of 4 : If the golf clubs cost The Golfing Emporium $620, what was their profit? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
The profit for the Golfing Emporium is $160.
How to get the profit?
We know that profit is defined as the difference between the revenue and the cost.
Here, we know that on the sale, the Golfing Emporium sells the set of clubs at $780 (this is the already discounted price).
While when they buy the set, the pay $620 for it.
Then the profit is given by:
P = $780 - $620 = $160
The profit for the Golfing Emporium is $160.
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use venn diagram to find the elements in each set A'
Based on the Venn diagram, the elements in set A can be found to be 2, 3 ,5, 7,and 9.
What are the elements in set A?The elements in set A would be those which are in A alone and in set B as well.
The numbers in set A alone are:
7, 3, 5, 9
The number in set B and A is 2.
The elements in set A is therefore:
2, 3 , 5, 7,and 9
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Consider a population that grows according to the recursive rule
P
n
=
P
n
−
1
+
25
, with initial population
P
0
=
30
.
Then:
P
1
=
P
2
=
Find an explicit formula for the population. Your formula should involve
n
(use lowercase n)
P
n
=
Use your explicit formula to find
P
100
P
100
=
The explicit formula for the arithmetic sequence is: [tex]P_n = 30 + 25n[/tex]
Using the formula, we have that [tex]P_{100} = 2530[/tex].
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
From the recursive formula, we have that:
[tex]a_1 = 30 + 25 = 55, d = 25[/tex]
Hence the explicit formula is:
[tex]P_n = 55 + 25(n-1)[/tex]
[tex]P_n = 30 + 25n[/tex]
Then, when n = 100:
[tex]P_{100} = 30 + 25(100) = 2530[/tex]
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5. Ellie's street address is a prime number greater than 10 and less than 19. Which of the following could be Ellie's street address?
We want to find a prime number greater than 10 and less than 19.
* What is a prime number?
Prime number is a number that cannot be divided by any number other than 1 and itself
There are so many possibilities:
Ellie's street address could be 11, 13 or 17
Hope it helps!
Please help with this question if you can
Line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional
Parallel lines theoremIn the given diagram,
If
[tex]\frac{|AB|}{|ED|} =\frac{|AC|}{|EC|}[/tex]
Then,
Line AE is parallel to line BD
From the given information,
|AB| = x = 9
|ED| = 5
|AC| = 9 + 11 = 20
|EC| =5 + 7 = 12
Thus,
[tex]\frac{9}{20}=\frac{5}{12}[/tex]
20 × 5 = 9 × 12
100 ≠ 108
∴ The lines are not parallel
Hence, line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional
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In major league baseball, a no-hitter is a game in which a pitcher, or pitchers, doesn't give up any hits throughout the game. No-hitters occur at a rate of about three per season. Assume that the duration of time between no-hitters is exponential. What is the probability that an entire season elapses with a single no-hitter? If an entire season elapses without any no-hitters, what is the probability that there are no no-hitters in the following season? What is the probability that there are more than 3 no-hitters in a single season?
Using the Poisson distribution, it is found that:
There is a 0.0498 = 4.98% probability that an entire season elapses with a single no-hitter.If an entire season elapses without any no-hitters, there is a 0.0498 = 4.98% probability that there are no no-hitters in the following season.There is a 0.3528 = 35.28% probability that there are more than 3 no-hitters in a single season.What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.The average rate is of 3 no-hitters per season, hence:
[tex]\mu = 3[/tex].
The probability that an entire season elapses with a single no-hitter is P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}3^{0}}{(0)!} = 0.0498[/tex]
There is a 0.0498 = 4.98% probability that an entire season elapses with a single no-hitter.
Seasons are independent, hence:
If an entire season elapses without any no-hitters, there is a 0.0498 = 4.98% probability that there are no no-hitters in the following season.
The probability that there are more than 3 no-hitters in a single season is P(X > 3) given as follows:
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}3^{3}}{(3)!} = 0.2240[/tex]
Then:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0498 + 0.1494 + 0.2240 + 0.2240 = 0.6472[/tex]
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.6472 = 0.3528[/tex]
There is a 0.3528 = 35.28% probability that there are more than 3 no-hitters in a single season.
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#280 at the
Nader plans to buy a car. He can afford to pay
end of each month for 3 years. The best interest rate
he can find is 9.8% la, compounded monthly.
for this interest rate, the most he could spend on a car
is $8702.85,
Determine the amount he could spend on the
purchase of the car if the interest rate is 9.8%.la,
Compounded annually.
Based on the amount that Nader can pay per month, and the interest rate as well as the period, the amount he could spend if the rate was annual is $8,385.33.
How much could Nader spend on the car?If Nader can pay $280 per month, the amount he can pay per year i:
= 280 x 12
= $3,360
The amount that he can spend on the car is the present value of these yearly payments:
= 3,360 x (1 - (1 + 9.8%)⁻³) / 9.8%
= 3,360 x 2.49563439768461
= $8,385.33
Find out more on the present value of periodic payments at https://brainly.com/question/17244776.
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The height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t^2 + 88t where "t" is the time it is in the air. For how many seconds the ball is in the air before it hits the ground?
Answer:
t=5.5
Step-by-step explanation:
The ball hits the ground when h = 0.
[tex]-16t^2 + 88t = 0 \\ \\ 2t^2 - 11t =0 \\ \\ t(2t-11)=0 \\ \\ t=0, 5.5[/tex]
However, as the answer must be positive, t=5.5