Answer:
sin(20) sin(40) cos(40) cos(20) [sin(20)*cos(20)]*[sin(40)*cos(40)][sin(2*20)/2]*[sin(2*40)/2][sin(40)*sin(80)]/2Suppose a random variable X is best described by a uniform probability distribution with range 1 to 5. Find the value of that makes the following probability statements true.
a) P(X <-a)= 0.95
b) P(X
c) P(X
d) P(X ->a)= 0.89
e) P(X >a)= 0.31
Answer:
a) 4.8
b) 2.96
c) 4.4
d) 1.44
e) 3.76
Step-by-step explanation:
What we will do is solve point by point, knowing the following:
Fx (x) = P (X <= x) = (x - 1) / 4
a) P (X <-a) = 0.95
Fx (a) = 0.95
(a -1) / 4 = 0.95
a = 1 + 0.95 * 4
a = 4.8
b) P (X <a) = 0.49
Fx (a) = 0.49
(a -1) / 4 = 0.49
a = 1 + 0.49 * 4
a = 2.96
c) P (X <a) = 0.85
Fx (a) = 0.85
(a -1) / 4 = 0.55
a = 1 + 0.85 * 4
a = 4.4
d) P (X> a) = 0.89
P (X <a) = 1 - 0.89 = 0.11
Fx (a) = 0.11
(a -1) / 4 = 0.11
a = 1 + 0.11 * 4
a = 1.44
e) P (X> a) = 0.31
P (X <a) = 1 - 0.31 = 0.69
Fx (a) = 0.69
(a -1) / 4 = 0.69
a = 1 + 0.69 * 4
a = 3.76
What is the greatest common factor of 48 and 32?
Answer:
GCF - 16
Step-by-step explanation:
48 - 1, 2, 3, 4, 6, 8, 12, 16
32 - 1, 2, 4, 8, 16
Hope this helps! :)
Answer:
16
Step-by-step explanation:
48=3*16
32=2*16
Please help! Need Geometry help!!!!!
Answer:
938 feet
Step-by-step explanation:
b/c every angle of a rectangle is 90° u can u Pythagorean theroem to solve the question
a*a+ b*b=c*c
900*900+264*264=c*c
c=√879,696
c=938feet
Answer:
938 feet
Step-by-step explanation:
Well to solve this we need to use the Pythagorean Theorem,
[tex]a^2 + b^2 = c^2[/tex].
So we have a and b which are 900 and 264,
and we need to find c or the walking distance.
So we plug in 900 and 264 for a and b.
[tex](900)^2 + (264)^2 = c^2[/tex]
So, 900*900 = 810,000
264 * 264 = 69696
810000 + 69696 = 879696
So now we have,
879696 = c^2
To get the c by itself we do,
[tex]\sqrt{879696} = \sqrt{c}[/tex]
= c = 937.921105424
c = 938 rounded to the nearest foot
Thus,
the solution is 938.
Hope this helps :)
I flip a fair coin 17 times. Answer the following questions:
a. What is the probability of getting 9 heads?
b. What is the probability of getting 2 heads?
c.. What is the probability of getting 1 tail?
d. What is the probability of getting 14 or more heads?
e. What is the probability of getting 17 tails?
Answer:
A) 0.1855
B) 0.0010376
C) 0.0001297
D) 0.006363
E) 0.000007629
Step-by-step explanation:
In calculation of a probability, we normally take the ratio of the number of ways to meet a certain condition (i.e. the numerator) divided by the number of ways to pick from a pool (i.e. the denominator).
So what are the number of ways the flip of a coin 17 times can come out?
A coin has a head and tail, so each toss will have two possible results. If we toss once, we have 2 possible results. If we toss, twice we have 2² = 4 possible results.
If we toss thrice, we have 2³ = 8 possible results, etc.
Thus, for 17 tosses, we will have 2^(17) = 131072 possible results.
A) To achieve the probability of getting 9 heads, we will use combination formula;
C(n, k) = n! / (k!(n - k)!)
In this case, n = 17 and k = 9
So,
P(9 heads) = 17! / (9!(17 - 9)!) = 24310
Thus,
P(9 heads in 17 tosses of a fair coin) = 24310/131072 = 0.1855
B) Similar to A above;
P(2 heads) = 17! / (2!(17 - 2)!) = 136
Thus,
P(2 heads in 17 tosses of a fair coin) = 136/131072 = 0.0010376
C) Similar to A above;
P(1 tail) = 17! / (1!(17 - 1)!) = 17
Thus,
P(1 tail in 17 tosses of a fair coin) = 17/131072 = 0.0001297
D) probability of getting 14 or more heads?
Since, there are 17 tosses, this will be;
P(14 or more heads in 17 tosses) = P(14 heads in 17 tosses) + P(15 heads in 17 tosses) + P(16 heads in 17 tosses) + P(17 heads in 17 tosses)
P(14 heads) = 17! / (14!(17 - 14)!) = 680
P(15 heads) = 17! / (15!(17 - 15)!) = 136
P(16 heads) = 17! / (16!(17 - 16)!) = 17
P(17 heads) = 17! / (1!(17 - 17)!) = 1
Thus;
P(14 heads in 17 tosses) = 680/131072 = 0.005188
P(15 heads in 17 tosses) = 136/131072 = 0.0010376
P(16 heads in 17 tosses) = 17/131072 = 0.0001297
P(1 head in 17 tosses) = 1/131072 = 0.00000763
P(14 or more heads in 17 tosses) = 0.005188 + 0.0010376 + 0.0001297 + 0.00000763 = 0.006363
E) Similar to A above;
P(17 tails) = 17! / (17!(17 - 17)!) = 1
Thus,
P(17 tails in 17 tosses of a fair coin) = 1/131072 = 0.000007629
Is (0,-2) a solution of 3x - y = 2?
Answer:
yes, (0,-2) is the answer when graphing this equation.
Step-by-step explanation:
Answer:
yes.
Step-by-step explanation:
the twelve inch square tiles are shipped in boxes of sixteen pieces per box. each of the boxes weighs twenty four pounds. approximately how many ounces does each tile weigh?
Answer:
1.411764706
Step-by-step explanation:
24/17=1.411764706
I NEED HELP ASAP,THANKS! :)
Roland’s Boat Tours sells deluxe and economy seats for each tour it conducts. In order to complete a tour, at least 1 economy seats must be sold and at least 6 deluxe seats must be sold. The maximum number of passengers allowed on each boat is 30 Roland’s Boat Tours makes $40 profit for each economy seat sold and $35 profit for each deluxe seat sold. What is the maximum profit from one tour? Show work.
Answer:
$1170
Step-by-step explanation:
Let x and y represent the numbers of economy and deluxe seats sold. The constraints are ...
x ≥ 1y ≥ 6x +y ≤ 30And the objective function we want to maximize is ...
p = 40x +35y
__
I find it convenient to graph the equations and locate the objective function line as far from the origin as possible. The graph is shown, along with the solution.
Here, it's even simpler than that. The profit per seat is the greatest for economy seats, so Roland's should sell as many of those as they can. The only limit is that 6 seats must be deluxe. The remaining 30-6=24 can be economy. So, the profit will be maximized for ...
24 economy seats and 6 deluxe seats
The corresponding profit will be ...
24(40) +6(35) = 1170
The maximum profit from one tour is $1170.
whats 1/2 + 2/4 - 5/8?
Answer:
3/8
Step-by-step explanation:
Step 1: Find common denominators
1/2 = 4/8
2/4 = 4/8
Step 2: Evaluate
4/8 + 4/8 - 5/8
8/8 - 5/8
3/8
Alternatively, you can just plug this into a calc to evaluate and get your answer.
Answer:
3/8
Step-by-step explanation:
Look at the denominator:
2, 4, 8. The LCM (Lowest Common Multiple) is 8.
So this equation becomes
4/8+4/8-5/8=3/8
Given a joint PDF, f subscript X Y end subscript (x comma y )equals c x y comma space 0 less than y less than x less than 4, (1) (5 pts) Determine the constant c value such that the above joint PDF is valid. (2) (6 pts) Find P (X greater than 2 comma space Y less than 1 )(3) (9 pts) Determine the marginal PDF of X given Y
(1) Looks like the joint density is
[tex]f_{X,Y}(x,y)=\begin{cases}cxy&\text{for }0<y<x<4\\0&\text{otherwise}\end{cases}[/tex]
In order for this to be a proper density function, integrating it over its support should evaluate to 1. The support is a triangle with vertices at (0, 0), (4, 0), and (4, 4) (see attached shaded region), so the integral is
[tex]\displaystyle\int_0^4\int_y^4 cxy\,\mathrm dx\,\mathrm dy=\int_0^4\frac{cy}2(4^2-y^2)=32c=1[/tex]
[tex]\implies\boxed{c=\dfrac1{32}}[/tex]
(2) The region in which X > 2 and Y < 1 corresponds to a 2x1 rectangle (see second attached shaded region), so the desired probability is
[tex]P(X>2,Y<1)=\displaystyle\int_2^4\int_0^1\frac{xy}{32}\,\mathrm dy\,\mathrm dx=\boxed{\dfrac3{32}}[/tex]
(3) Are you supposed to find the marginal density of X, or the conditional density of X given Y?
In the first case, you simply integrate the joint density with respect to y:
[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^x\frac{xy}{32}\,\mathrm dy=\begin{cases}\frac{x^3}{64}&\text{for }0<x<4\\0&\text{otherwise}\end{cases}[/tex]
In the second case, we instead first find the marginal density of Y:
[tex]f_Y(y)=\displaystyle\int_y^4\frac{xy}{32}\,\mathrm dx=\begin{cases}\frac{16y-y^3}{64}&\text{for }0<y<4\\0&\text{otherwise}\end{cases}[/tex]
Then use the marginal density to compute the conditional density of X given Y:
[tex]f_{X\mid Y}(x\mid y)=\dfrac{f_{X,Y}(x,y)}{f_Y(y)}=\begin{cases}\frac{2xy}{16y-y^3}&\text{for }y<x<4\text{ where }0<y<4\\0&\text{otherwise}\end{cases}[/tex]
Box A contains 5green and 7 red balls. Box B contains 3green, 3 red and 6 yellow balls. A box is sleeted at random and a ball is drawn at random from it. What is the probability that the drawn ball is green?
Answer:
5/48Step-by-step explanation:
Given
the sample space for box A
green balls = 5
red balls= 7
sample size= 5+7= 12
the sample space for box B
green balls = 3
red balls= 3
yellow balls= 6
sample size= 3+3+6= 12
The probability of drawing a green ball from box A= 5/12
The probability of drawing a green ball from box B= 3/12= 1/4
Therefore the probability of picking a green ball from either of the boxes at random is =[tex]=\frac{5}{12} *\frac{1}{4}[/tex][tex]=\frac{5}{48}[/tex]
The figure shows a person estimating the height of a tree by looking at the
top of the tree with a mirror. Assuming that both the person and the tree form
right angles with the ground, which of the following proportions can be used
to estimate the height of the tree
Answer:
[tex]\frac{6}{5} =\frac{x}{12}[/tex]
Step-by-step explanation:
Write a proportion in the form:
Height/side= height/side
The side lengths are 5 and 12.
The height (of the 5 side) is 6.
The proportion can be written as:
[tex]\frac{6}{5} =\frac{x}{12}[/tex]
The shape on the left is transformed to the shape on the right. Figure A B C D is rotated to form figure A prime B prime C prime D prime. Which of the following statements describes the transformation? A B C D right-arrow A prime B prime C prime D prime A prime B prime C prime D prime right-arrow A B C D A B C D right-arrow D prime A prime C prime B prime D prime B prime C prime A prime right-arrow C A D B
Answer:
A
Step-by-step explanation:
I did the test and it is the only one that makes sense
Answer:
a
Step-by-step explanation:
Find the volume V of the described solid S. The base of S is a circular disk with radius 4r. Parallel cross-sections perpendicular to the base are squares.
Answer:
(1024/3)r^3.
Step-by-step explanation:
Step one: So, we have that x^2 + y^2 = 4^2 × r^2(when z component = 0) . Hence, there is the need to make y^2 the subject of the formula.
Step two: 4y^2 = 16r^2 - x^2. Where 4 ×(16r^2 - x^2) is the the cross sectional area.
Step three: the next thing to do here is to integrate the cross sectional area making 4r and -4r the upper limit and lower limit for the integration.
Step four: the integration will then give a product (16 × 64)/3 A = (1024/3)r^3.
Solve the inequality a−32<1 and write the solution in interval notation, using improper fractions if necessary.
Answer:
( -∞ , 33 )
Step-by-step explanation:
To solve the inequation a-32 < 1, we need to sum on both sides 32, as:
a - 32 + 32 < 1 + 32
a < 33
It means that the solutions are all the number that are smaller than 33 or in interval notation it would be:
( -∞ , 33 )
Where 33 is not included in the interval.
Select the expression that is equivalent to (x - 1)2.
O A. x2 - 2x + 2
O B. x2 - x + 2
O C. x2 - x + 1
O D. x2 – 2x + 1
Answer:
D
Step-by-step explanation:
(x - 1)² = (x - 1)(x - 1)
x² - x- x + 1 = x² - 2x + 1
Beginning three months from now, you want to be able to withdraw $2,300 each quarter from your back account to cover college expenses over the next four years. If the account pays .45 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next four years?
Answer:
$36,450.46
Step-by-step explanation:
The amortization formula can be used to figure this. For quarterly payment A, the principal invested must be P for interest rate r and compounding n times per year for t years.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
2300 = P(0.0045/4)/(1 -(1 +0.0045/4)^(-4·4))
2300 = P·0.06309934
P = 2300/0.06309934 = 36450.46
You need $36,450.46 in your account today so that you can withdraw $2300 quarterly for 4 years.
Write your answer using only positive exponents
Answer:
Step-by-step explanation:
Hello
[tex](-4b^5c^{-6})^3\\\\=(-1)^34^3b^{15}v^{-18}\\=-64b^{15}c^{-18}\\\\=\dfrac{-64b^{15}}{c^{18}}\\[/tex]
hope this helps
The simplified form of the given exponential expression is -64b¹⁵/c¹⁸.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given exponential expression is (-4b⁵c⁻⁶)³.
Here, the given expression can be written as -4³(b⁵)³(c⁻⁶)³
= -64b¹⁵c⁻¹⁸
= -64b¹⁵/c¹⁸
Therefore, the simplified form of the given exponential expression is -64b¹⁵/c¹⁸.
To learn more about an exponents visit:
https://brainly.com/question/15993626.
#SPJ2
URGENT!! Solve the triangle for all missing sides and angles. Part 2: Use the law of sines to find the length of side a. Part 3: Use any method to find the length of side c.
Answer:
B = 55°
a ≈ 143
c ≈ 212
Step-by-step explanation:
From the triangle above we are given a triangle with two known angles and a known side. The sum of angles in a triangle is 180°. Since we are given two angles, the last angle can be gotten when you subtract the two known angles from 180°. Therefore,
angle B = 180° - 42° - 83°
angle B = 55°
To find side a we can use law of sine
a/sin A = b/sin B
a/sin 42° = 175/sin 55°
a/0.66913060635 = 175/0.81915204428
cross multiply
0.81915204428 a = 117.097856113
divide both sides by 0.81915204428
a = 117.097856113 /0.81915204428
a = 142.950087143
a ≈ 143
To find side c
b/sin B = c/sin C
175/sin 55 = c/sin 83°
cross multiply
c sin 55° = 175 sin 83°
divide both sides by sin 55°
c = (175 × 0.99254615164)/0.81915204428
c = 173.695576537 / 0.81915204428
c = 212.043146019
c ≈ 212
solve for n n/5+0.6=2
Answer:
N=7
Step-by-step explanation:
It is correct on Khan
Consider the following function. f(x) = 2x + 5. Place the steps for finding f-1 (x) in the correct order. A. x-2/5= y B. y = 2x + 5 C. y-5 = 2x D. X-5/2=y E. f-1(x) = x-5/2 F.x= 2y+ 5 G. x-5= 2y H. f-1(x) = x-2/5
Answer:
[tex]\boxed{\sf \ \ f^{-1}(x)=\dfrac{x-5}{2} \ \ }[/tex]
Step-by-step explanation:
hello,
the easiest way to understand what we have to do is the following in my opinion
we can write
[tex](fof^{-1})(x)=x\\<=>f(f^{-1}(x))=x\\<=>2f^{-1}(x)+5=x\\<=>2f^{-1}(x)+5-5=x-5 \ \ \ subtract \ \ 5\\<=> 2f^{-1}(x)=x-5 \\<=> f^{-1}(x)=\dfrac{x-5}{2} \ \ \ divide \ by \ 2\\[/tex]
so to follow the pattern of your question
y = 2x + 5
we need to find x as a function of y, so let's swap x and y
x = 2y + 5
then subtract 5
x - 5 = 2y
then divide by 2
[tex]\dfrac{x-5}{2}=y[/tex]
finally
[tex]f^{-1}(x)=\dfrac{x-5}{2} \\[/tex]
hope this helps
Answer:
1. y= 2x + 5
2. x = 2y + 5
3. x - 5 = 2y
4. (x-5)/2 =u
5. f^-1(x) = (x-5)/2
Step-by-step explanation:
:)
Easy geometry just find area shade boxes thank you plz help
Answer:
45 square units
Step-by-step explanation:
To figure out the area of a trapezoid, the formula is. A= (b1 + b2)h ÷2 . b1 is the top side which is 7 units and b2 is the bottom side which is 11 units. The height (h) is a vertical line going from the top to the bottom which is 5 units. All you need to do now is plug in those numbers and solve the equation.
Answer: 45 square units
Step-by-step explanation:
This shape can be broken down into two diffrent peices
The first peice is the rectangle
The second peice is the triangle
And both of these peices area's added together will yeild the total area
The rectangle is 7 units long and 5 units high, so it has an area of (7X5) = 35
The triangle is a little bit more complicated, it's formula is (BaseXHeight)/4
So all we need to do is plug in The base of the triangle = 4
And the Height of the trianlge = 5
So the triangles area is... (4X5)/2= 10
35+10=45 square units
Which equation, when solved, gives 8 for the value of x?
A: 5/2x+7/2x=3/4x+14
B: 5/4x-9=3/2x-12
C: 5/4x-2=3/2x-4
D: 5/2x-7=3/4x+14
Answer:
Step-by-step explanation:
C. 5x/4-2=3x/2-4
5x/4 -2=6x/4-4
+4 +4
5x/4+2=6x/4
-5x/4
2=x/4
*4
x=8
Answer:
your answer is C
Step-by-step explanation:
Construct a confidence interval of the population proportion at the given level of confidence.
x equals =860
n equals =1200
94% confidence
The lower bound of the confidence interval is __?
Answer:
The lower bound of the confidence interval is 0.6922.
Step-by-step explanation:
We have to calculate a 94% confidence interval for the proportion.
The sample proportion is p=0.7167.
[tex]p=X/n=860/1200=0.7167[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.7167*0.2833}{1200}}\\\\\\ \sigma_p=\sqrt{0.000169}=0.013[/tex]
The critical z-value for a 94% confidence interval is z=1.8808.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.8808 \cdot 0.013=0.0245[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.7167-0.0245=0.6922\\\\UL=p+z \cdot \sigma_p = 0.7167+0.0245=0.7412[/tex]
The 94% confidence interval for the population proportion is (0.6922, 0.7412).
What is coefficient of the term of degree of degree 5 in the polynomial below 3x^6+5-x^2+4x^5-9 which one is the right answer A. 3 B. 4 C. 6 D. 5
Answer:
B. 4
Step-by-step explanation:
We are looking for the coefficient of the term x⁵. When we see it in the polynomial as 4x⁵, our coefficient and answer would then be 4.
Please Help! Select the correct answer. Simon used these steps to solve an equation:
Answer:
A.
Step-by-step explanation:
From Step 3 to Step 4, Simon added -42 to both sides.
This is the addition property of equality: as long as you add the same thing to both sides, the equation remains equal.
A.
Find the values of x and y in these equations. (x + yi) + (4 + 6i) = 7 − 2i (equation A) (x + yi) − (-8 + 11i) = 5 + 9i (equation B)
Answer:
Step-by-step explanation:
(x+yi)+4+6i=7-2i
x+yi=7-2i-4-6i
x+yi=3-8i
equating real and imaginary parts
x=3,y=-8
B.
x+yi=5+9i+(-8+11i)
x+yi=5+9i-8-11i
x+yi=-3-2i
equating real ,and imaginary parts
x=-3
y=-2
The value of x and y for equation A is
[tex]x=3, y=-8[/tex]
The value of x and y for equation B is
[tex]x=-3 , y=20[/tex]
Given :
[tex](x + yi) + (4 + 6i) = 7 - 2i[/tex]
find the value of x and y in the given equation
Lets open the parenthesis and combine like terms
Equate the real and imaginary part to solve for x and y
[tex]\left(x+4\right)+\left(y+6\right)i=7-2i\\x+4=7\\x=3\\\\y+6=-2\\y=-2-6\\y=-8[/tex]
The value of x=3 and y=-8
Now we do the same with second equation
[tex](x + yi) - (-8 + 11i) = 5 + 9i\\\\x+8+yi-11i=5+9i\\\left(x+8\right)+\left(y-11\right)i=5+9i\\x+8=5\\x=-3\\\\y-11=9\\y=9+11\\y=20[/tex]
The value of x and y is x=-3 and y=20
Learn more : brainly.com/question/18552411
Jimmy will be selling hot dogs at the football game. He bought hot dogs, buns, and condiments for a total of \$8$8dollar sign, 8 and now wants to calculate how many hot dogs he has to sell to make a profit. He graphs the profit he will make, (P)(P)left parenthesis, P, right parenthesis, as a function of the number
Answer:
the photo shows the answer ^D^ hope this helps~
Step-by-step explanation:
+also included the correct sign for confirmation xD
Answer:
up answer is correct :)
Step-by-step explanation:
Arrange in ascending order. 8/13, 2/9,28/29
Step-by-step explanation:
he operation of sorting fractions in ascending order: 18/46, 28/41, 29/38, 29/44, 32/30 ... terms equivalents: 18/46=(2×3^2)/(2×23)=((2×3^2)÷2)/((2×23)÷2)=9/23; 28/41 already reduced to ... by the largest exponents: LCM (9, 28, 29)=2^2×3^2× 7×29=7308 Calculate LCM, the least ... /10 </13 </19
An airplane descends during the last hour of it's flight to prepare for landing. It's altitude changes at an average of -0.15 km per minute for those 60 minutes. Write an expression to represent the total change in the airplane's elevation. ( plz answer, will give brainliest )
Answer:
-.15 km/ minute * 60 minutes
-9 km
Step-by-step explanation:
The rate is -.15 km per minute
We have 60 minutes
distance = rate times time
change in elevation is the same as the distance change
change in elevation = -.15 km/ minute * 60
change in elevation =-9 km
Answer:
(0.15 km/min) * (60 min)
Step-by-step explanation:
We see that the plane descends 0.15 kilometres every minute over the span of 60 minutes.
Use the distance-rate-time formula: d = rt, where d is the distance, r is the rate, and t is the time.
Here, our rate is r = 0.15 km/min and our time is t = 60 minutes. Then the total change in elevation is:
d = rt
d = 0.15 * 60 = 9 km
Note that we disregard the negative sign from -0.15 km/min because the question is asking for the change in elevation. Change is never a negative value.
Hence, the expression will be: 0.15 * 60, which simplifies to 9 km.
~ an aesthetics lover
(09.06 HC)
The function H(t) = -16t2 + 90t + 75 shows the height H(t), in feet, of a projectile after t seconds. A
second object moves in the air along a path represented by g(t) = 31 + 32.2t, where g(t) is the height, in
feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 2 through 5 for the 2 functions. Between what 2 seconds is the
solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem.(4 points)
Answer: h(t) = g(t) between 4 and 5 seconds
Step-by-step explanation:
h(t) = -16t² + 90t + 75
g(t) = 31 + 32.2t
[tex]\begin{array}{c|c|c|c|c}\qquad&\underline{\quad t=2\quad }&\underline{\quad t=3\quad}&\underline{\quad t=4\quad }&\underline{\quad t=5\quad }\\h(t)&191&201&179&125\\g(t)&95.4&127.6&159.8&192\end{array}\right][/tex]
Notice that g(t) is increasing from t=2 to t=5, while h(t) is increasing from t=2 to t=3 and then decreasing.
At t=4, h(t) > g(t)
At t = 5, g(t) > h(t)
therefore, the two lines must intersect at a point between t=4 and t=5.
You can graph this to verify the answer.