Answer:
For this case we want to find the probability that a senior is chosen at random not planning to attend college after graduation so then we can use the complement rule given by:
[tex] P(A') = 1-P(A)[/tex]
Where A is the vent of interest and replacing we got:
[tex] P(A') = 1-0.85= 0.15[/tex]
So then the probability that a senior is chosen at random not planning to attend college after graduation is 0.15 or 15%
Step-by-step explanation:
For this case we know that the sample size if n =240 and we also know that the probability that in the Evan's class the any student are planeed to attend collge after graduation is:
[tex] P(A) =0.85[/tex]
For this case we want to find the probability that a senior is chosen at random not planning to attend college after graduation so then we can use the complement rule given by:
[tex] P(A') = 1-P(A)[/tex]
Where A is the vent of interest and replacing we got:
[tex] P(A') = 1-0.85= 0.15[/tex]
So then the probability that a senior is chosen at random not planning to attend college after graduation is 0.15 or 15%
How do i solve 3/4 x 4 7/12 =
Answer:
2.9375
Step-by-step explanation:
3/4×47/12
3×47/4×12
141/48
2.9375
Answer:
4x12=48
48+7=55
4 7/12 as an improper fraction is 55/12
multiply the numerator with numerator and denominator with denominator
3x55=165
4x12=48
165/48 can be divided by 3
165/3=55__48/3=16
55/16 is simplified
55/16=3 r 7 so the fraction is 3 7/16
Hope this helps
Step-by-step explanation:
Courtney sold 48 cantaloupes at the farmers' market and had 25 left. Which equation could be used to find x, the number of cantaloupes Courtney had originally?
Answer:
48+25=x
Step-by-step explanation:
Answer:
The answer is D :)
Thank me later.
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Circle with centre (0,2) will have the equation
(x)²+(y-2)² = r²
Finding r² by distance formula using P(-7,2)
r² = (-7-0)²+(2-2)²
r² = (-7)²
r² = 49
So substituting in the equation
x²+(y-2)² = 49
If 25 new born babies are randomly selected, what is the probability that the 25 babies are born that their mean weigh less than 3100g?
Answer:
Step-by-step explanation:
Given that
n = 25
mean = 3100
standard deviation = 500
[tex]\bar x = \frac{500}{\sqrt{25} }[/tex]
= 500 / 5
= 100
N ( μ = 3500, (500)² / 25)
N = (3500,(100)² )
b) P ( x < 3100)
c) Z score
[tex]z = \frac{x - u _{\bar x}}{\sigma \_ {\bar x}}[/tex]
[tex]u_{\bar x}= 3500[/tex]
[tex]\sigma _{\bar x}= 100[/tex]
[tex]z = \frac{3100-3500}{100} \\\\= -4[/tex]
d)
probability=
P ( x < 3100) = P < -4 = 0
Answer:
a) The parameters for the sampling distribution include
Mean = μₓ = 3500 g
Standard deviation = σₓ = 100 g
Required probability = P(x < 3100)
b) The image of the probability density curve is presented in the attached image.
c) The z-score for 3100 g in the sampling distribution = -4.00
d) The probability that the 25 babies that are born that their mean weigh less than 3100 g = 0.00003
Step-by-step explanation:
Complete Question
Suppose we know the birth weights of babies is normally distributed, with mean of 3500 g and standard deviation 500g.
If 25 new born babies are randomly selected, what is the probability that the 25 babies are born that their mean weigh less than 3100g?
a) What are the parameters?
b) Draw a probability density curve for the problem.
c) What is the z-score of the weight?
d) What is the required probability?
Solution
The Central limit theorem explains that for a random sample of adequate size obtained from a normal distribution with independent variables, the mean of the sampling distribution is approximately equal to the population mean and the sampling distribution is approximately of the nature of the population distribution (normal) with the standard deviation of the sampling distribution given as
Standard deviation of the sampling distribution = [(Population Standard deviation)/√n]
σₓ = (σ/√n)
Mean of Sampling distribution = Population mean
μₓ = μ = 3500 g
σₓ = (σ/√n) = (500/√25) = 100 g
a) The parameters for the sampling distribution include
Mean = μₓ = 3500 g
Standard deviation = σₓ = 100 g
Required probability = P(x < 3100)
b) The image of the probability density curve is presented in the attached image.
c and d) To obtain the required probability, we need the z-score for 3100 g, so we standardize 3100g
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (3100 - 3500)/100 = - 4.00
To determine the required probability 45mg/L, P(x < 3100) = P(z < -4.00)
We'll use data from the normal probability table for these probabilities
P(x < 3100) = P(z < -4.00) = 0.00003
Hence, the probability that the 25 babies that are born that their mean weigh less than 3100 g = 0.00003
Hope this Helps!!!!
Suppose that you are holding your toy submarine under the water. You release it and it begins to ascend. The graph models the depth of the submarine as a function of time. What is the domain and range of the function in the graph?
Answer:
Domain : 0 ≤ t ≤ 3
Range : -4 ≤ d ≤ 0
Step-by-step explanation:
The graph attached models the depth of submarine as a function of time.
Points on x-axis represent the time and points on y-axis represent increase in height of the submarine.
Domain of a function is represented by the points on x-axis.
Therefore, Domain : 0 ≤ t ≤ 3
Range of function is represented by te points on y-axis.
Therefore, Range : -4 ≤ d ≤ 0
PLEASE HELP AS QUICKLY AS POSSIBLE THANK YOU :)
Answer:
C.
Step-by-step explanation:
Some rectangles can be squares, since they fit the criteria for both if it is a square, but not ALL rectangles can be squares, since squares have ALL 4 sides congruent, whereas rectangles only have 2 sets of sides congruent.
5x + 6y = 32
5x – 6y = 8
Which variable or variables will be eliminated when you add the system of equations?
Answer:
The variable y is eliminated.
Step-by-step explanation:
To add a system of equations, we add the common terms. x with x, y with y and values with values.
In this question:
5x + 6y = 32
5x – 6y = 8
Adding:
5x + 5x + 6y - 6y = 32 + 8
10x = 40
So the variable y is eliminated.
Answer:
10x 40
Step-by-step explanation:
A force of 8 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching it from its natural length to 14 in. beyond its natural length? W = ft-lb
Answer:
The work done in stretching it from its natural length to 14 in. beyond its natural length is W=8.17 ft-lb.
Step-by-step explanation:
We know that a force of 8 lb is required to hold a spring stretched 8 in. beyond its natural length.
This let us calculate the spring constant k as:
[tex]F=kx\\\\k=F/x=(8 \;lb)/(8\;in)=1\;lb/in[/tex]
We know that work is, in an scalar form, the product of force and distance.
The force F is equal to the spring constant multiplied by the distance from the natural length.
Then, as the force changes with the distance from the natural length, we have to calculate integrating:
[tex]W=\int_0^{14}F\,dx=\int_0^{14}kx\,dx\\\\\\W=\dfrac{1}{2}kx^2\left|^{14}_0=\dfrac{1}{2}(1\,lb/in)(14 \,in)^2-\dfrac{1}{2}(1\,lb/in)(0 \,in)^2[/tex]
[tex]W=98lb\cdot in-0lb-in\\\\W=98(lb\cdot in)\cdot \dfrac{1 \,ft}{12\,in}=8.17\;lb\cdot ft[/tex]
OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT
Answer:
290
Step-by-step explanation:
(11*8)*2=176, (11*3)*2=66, (3*8)*2=48, 48+176+66= 290
given:f(x)=x-7 and h(x)=2x+3 write the rule for f(h(x))
Answer:
Step-by-step explanation:
h(x) = 2x + 3
f(2x+3)
2x+3 - 7
2x - 4
Trey is estimating the length of a room in his house. The actual length of the room is 17 m. Trey's estimate is 15 m.
Find the absolute error and the percent error of Trey's estimate. If necessary, round your answers to the nearest tenth.
Answer:
Absolute error = 2m
Step-by-step explanation:
Absolute Error = Measured Value - Actual Value
17m - 15m = 2m
Answer:
2m and 11.8%
Step-by-step explanation:
Absolute error is defined mathematically as;
Error/original value
[Original value - estimated value]
[17-15 ] = 2m
The percentage error would be
[Original value - estimated value]/ original value
[17-15 ] /17 × 100%
0.1176 × 100% = 11.76%
11.8%[ to the nearest tenth]
Find the largest prime factor of 309^2 - 147^2.
Answer: 2^4*3^5*19
Step-by-step explanation:
You also need to divided by 2 four times, then divided by 3 five times, then the final one is divided by 19.
The largest prime factor of 309² - 147² is, 19.
What is Greatest common factors?The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The expression is,
⇒ 309² - 147²
Now, We can simplify as;
⇒ 309² - 147²
⇒ (309 - 147) (309 + 147)
⇒ 162 × 456
⇒ 2 × 3 × 3 × 3 × 3 × 2 × 2 × 2 × 3 × 19
Thus, The largest prime factor of 309² - 147² is,
⇒ 19
Learn more about the Greatest common factors visit:
https://brainly.com/question/219464
#SPJ2
Lines sand tare perpendicular. If the slope of line sis 5, what is the slope of
line t?
Answer:
-1/5
Step-by-step explanation:
Perpendicular lines have slopes that are the opposite reciprocal of one another.
The slope of line t is the opposite reciprocal of the slope of line s:
slope of t = -1/(slope of s)
slope of t = -1/5
What is the length of the line?
square root of 119
square root of 60
13
square root of 17
Answer:
13
Step-by-step explanation:
The line is the hypotenuse of a right triangle that is 5 units high and 12 units wide. The Pythagorean theorem, or the distance formula, tells you the length is ...
length = √(5² +12²) = √(25+144) = √169
length = 13
A cellular phone network uses towers to transit calls. Each tower transmits a circular area. on a grid of a city, the equations given represent the transmission boundaries of the towers. Tell which towers, is any, transmit to a phone located at M(3.5, 4.5).
Tower A: x^2 + y^2 = 9
Tower B: (x - 5)^2 + (y - 3)^2 = 6.25
Tower C: (x - 2)^2 + (y - 5)^2 = 4
Answer:
B
Step-by-step explanation:
Notice that
[tex](3.5-5)^2 + (4.5-3)^2 = 4.5[/tex]
Since 4.5 is less than 6.25, tower B transmits to that phone
Answer:
Towers B and C transmit to the phone.
Step-by-step explanation:
First, let see the location of the center for each tower:
Tower A
[tex]A (x,y) = (0,0)[/tex]
Tower B
[tex]B (x,y) = (5,3)[/tex]
Tower C
[tex]C(x,y) = (2,5)[/tex]
Now, the distance between the location of the phone and any of the towers by means of the Pythagorean equation. The phone is under the influence of a tower only if distance is less than transmission boundaries. Then:
Tower A
[tex]d_{A} = \sqrt{(3.5-0)^{2}+(4.5-0)^{2}}[/tex]
[tex]d_{A} \approx 5.701[/tex]
[tex]d_{A} > 3[/tex]
Tower B
[tex]d_{B} = \sqrt{(3.5-5)^{2}+(4.5-3)^{2}}[/tex]
[tex]d_{B} \approx 2.121[/tex]
[tex]d_{B} < 2.5[/tex]
Tower C
[tex]d_{C} = \sqrt{(3.5-2)^{2}+(4.5-5)^{2}}[/tex]
[tex]d_{C} \approx 1.581[/tex]
[tex]d_{C} < 2[/tex]
Towers B and C transmit to the phone.
The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses: 4.6 12.1 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1 11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5 7.5 6.2 5.8 2.7 3.4 10.4 9.8 6.6 3.7 6.4 8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.2 6.2 5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3 7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.1 7.2 5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2 8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7 5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6 10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6 7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3 9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2 8.3 3.1 4.9 5.0 6.0 8.2 6.3 3.8 6.0 (a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)
Answer:
Step-by-step explanation:
For n=129 and with leaf unit = 0.1, the stem and leaf chart of the given data on Shower-flow rate (L/min) is as follows:
2 28
Stem leaves
3----------1344567789
4----------01356889
5----------00001114455666789
6----------0000122223344456667789999
7----------00012233455555668
8----------02233448
9----------012233335666788
10----------2344455688
11--------- 2335999
12---------- 17
13-------- 9
14--------36
15---------- 0035
16---------None
17---------None
18 ----------3
* From steam and leaf chart we note that minimum Shower flow rate is 2.2 whereas maximum is 18.3 L/mim. Further typical or representative rate is 7.0 L/min.
* The display of data on steam and leaf chart shows that data is positively skewed means concentration of data on left side or lower value side is high as compared to other side.
* Distribution is not symmetric rather very clear positive skew ness is observed through steam and leaf chart. Even distribution is Unimodal.
* From steam and leaf chart is indicative to conclude that the highest observation 18.3 is outlier.
A section of an exam contains two multiple-choice questions, each with three answer choices (listed "A", "B", and "C"). Assuming the outcomes to be equally likely, find the probability (as a reduced fraction) that neither of the answers is "B". [Hint: List all the outcomes of the sample space first.]
Answer:
[tex]p = \frac{4}{9}[/tex]
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Sample space:
All posible outcomes.
First answer - Second answer:
A - A
A - B
A - C
B - A
B - B
B - C
C - A
C - B
C - C
9 possible outcomes.
Probability that neither is B.
A - A
A - C
C - A
C - C
4 possible outcomes.
So
[tex]p = \frac{4}{9}[/tex]
What’s the correct answer for this?
Answer:
36
Step-by-step explanation:
Diameter AB bisects the chord
MO = NO
5x+3=6x
3 = 6x-5x
x = 3
Now
MN = 5x+3+6x
MN = 5(3)+3+6(3)
MN = 15+3+18
MN = 36
Two models R1 and R2 are given for revenue (in billions of dollars per year) for a large corporation. The model R1 gives projected annual revenues from 2008 through 2015, with t = 8 corresponding to 2008, and R2 gives projected revenues if there is a decrease in the rate of growth of corporate sales over the period. Approximate the total reduction in revenue if corporate sales are actually closer to the model R2. (Round your answer to three decimal places.) R1 = 7.21 + 0.55t R2 = 7.21 + 0.44t
Answer:
7.0422 is the correct answer to the given question .
Step-by-step explanation:
Given
R1 = 7.21 + 0.55t
R2 = 7.21 + 0.44t
Decrease in the revenue can be determined by the formula
[tex]= Reduction\ in\ R1\ -\ Reduction\ in\ R2[/tex]
[tex]= (7.21 + 0.55t ) - (7.21 + 0.44t)[/tex]
=0.11 t
Now overall Reduction can be determined by the interval from t=8 to t=15
Consider c=0.11 t
[tex]\frac{dc}{dt}[/tex]=0.11
Now integrated the equation from t=8 to t=15 to determine total reduction in revenue
[tex]=\int_{8}^{15}\sqrt{1+0.11^2}\ dL[/tex]
[tex]=7.0422[/tex]
81. Restaurants. About 12% of the restaurants in the US are pizzerias, and there are about 70,000 pizzerias in the US. Estimate the total number of restaurants in the United States.
Answer:
For this case we know that 12% of the restaurants in the Us are pizzerias and there are about 70000 pizzerias in Us. So then we can apply a proportion rule given by:
[tex]\frac{70000}{12} = \frac{x}{100}[/tex]
Where x represent the total of restaurants representing the 100% and if we solve for x we got:
[tex] x = 100 \frac{70000}{12}= 583333.33[/tex]
So then there is approximately between 58333 and 58334 restaurants in US with the result obtained.
Step-by-step explanation:
For this case we know that 12% of the restaurants in the Us are pizzerias and there are about 70000 pizzerias in Us. So then we can apply a proportion rule given by:
[tex]\frac{70000}{12} = \frac{x}{100}[/tex]
Where x represent the total of restaurants representing the 100% and if we solve for x we got:
[tex] x = 100 \frac{70000}{12}= 583333.33[/tex]
So then there is approximately between 58333 and 58334 restaurants in US with the result obtained.
what’s the correct answer for this?
Answer:
A.
Step-by-step explanation:
98%
The probability of not winning the raffle is 100% - 2% = 98%
f(x)=2x-6 g(x)=3x+9, find (f+g)
Answer:
(f+g)(x) = 5x +3
Step-by-step explanation:
(f+g)(x) = f(x) +g(x)
= (2x -6) +(3x +9)
= 2x +3x -6 +9
(f+g)(x) = 5x +3
Penni Precisely buys 100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower. After one year, AA was up 20%, BB was down 25%, and CC was unchanged. For the second year, AA was down 20% from the previous year, BB was up 25% from the previous year, and CC was unchanged. If A, B, and C are the final values of the stock, then:______A) A = B = CB) A = B < CC) C < B = AD) A < B < CE) B < A < C
Answer:
E) B < A < C
Step-by-step explanation:
Penni Precisely buys 100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower.
Initial Values are: A, B and C
After one year, A was up 20%, B was down 25%, and C was unchanged.
Values after one year:
A=(100%+20%) of $100=$120 worth of stock.B=(100-25%) of $100=$75 worth of stock.C=100% of $100=$100 worth of stock.For the second year, A was down 20% from the previous year, B was up 25% from the previous year, and C was unchanged.
Values after the second year
A=(100%-20%) of $120 =80% of $120=$96 worth of stock.B=(100%+25%) of $75 =125% of $75=$93.75 worth of stock.C=100% of $100 =$100 worth of stock.Therefore, from the final values of the stock, we have that:
B<A<C
The correct option is E.
An old saying in golf is "You drive for show and you putt for dough." The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour's world money list are examined. The average number of putts per hole and the player's total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software. the p-value for the test in question 3 is 0.0087. p-value for the test in question 3 is 0.0087. a correct interpretation of this result is that:____________
Answer:
With this P-value, we have statistical evidence to support the claim that there is a relationship between the average number of putts per hole and the player's total winnings.
Step-by-step explanation:
In this case, the hypothesis test has the following hypothesis:
Null hypothesis: there is no relationship between the average number of putts per hole and the player's total winnings.
Alternative hypothesis: there is relationship between the average number of putts per hole and the player's total winnings.
Then, a P-value of 0.0087 is, without doubt, a strong evidence that the null hypothesis is false.
With this P-value, we have statistical evidence to support the claim that there is a relationship between the average number of putts per hole and the player's total winnings.
You deposit $5000 each year into an account earning 4% interest compounded annually. How much will you have in the account in 35 years?
Answer:
$ 402,722.01
Step-by-step explanation:
It costs Neil $2.88 to make two dozen muffins. He sold the muffins for $.80 each. If Neil sold six dozen muffins how much profit did he make from the sale?
Hi!
So for this you need an equation. It will be 72 • 0.8 - 2.88 • 3
this is bc 12 x 6 is 72 and 3 bc 2 x 3 is 6.
so after you solve it you should get : $48.96..Hope this helped! :))
expand and simplify (4+√2)(6-√2)
Answer:
[tex]22+2\sqrt{2}[/tex]
Step-by-step explanation:
[tex](4+\sqrt{2} )(6-\sqrt{2} )[/tex]
[tex]4(6)-4\sqrt{2} +6\sqrt{2} -2[/tex]
[tex]24+2\sqrt{2} -2[/tex]
[tex]22+2\sqrt{2}[/tex]
A sports-equipment factory produces sports balls. On Monday, they produced 1,080 balls altogether. All of the balls they produced were either volleyballs or soccer balls. They produced 7 times as many volleyballs as soccer balls. How many soccer balls did the factory produce on Monday?
Answer: 135 soccer balls
Step-by-step explanation:
In this equation, let x represent the number of soccer balls, and 7x represent the number of volley balls.
7x + x = 1,080
8x = 1,080
Now divide 1,080 by 8 to get the number of soccer balls.
1,080 / 8 = 135
In case you’re wondering how to find the number of volley balls, just multiply 135 by 7
135 * 7 = 945
The sum of two numbers is 9.9, and the sum of the squares of the numbers is 53.21. What are the numbers?
Answer:
There are two possibilities:
[tex]x_{1} = 3.5[/tex] and [tex]y_{1} = 6.4[/tex]
[tex]x_{2} = 6.4[/tex] and [tex]y_{2} = 3.5[/tex]
Step-by-step explanation:
Mathematically speaking, the statement is equivalent to this 2-variable non-linear system:
[tex]x + y = 9.9[/tex]
[tex]x^{2} + y^{2} = 53.21[/tex]
First, [tex]x[/tex] is cleared in the first equation:
[tex]x = 9.9 - y[/tex]
Now, the variable is substituted in the second one:
[tex](9.9-y)^{2} + y^{2} = 53.21[/tex]
And some algebra is done in order to simplify the expression:
[tex]98.01-19.8\cdot y +2\cdot y^{2} = 53.21[/tex]
[tex]2\cdot y^{2} -19.8\cdot y +44.8 = 0[/tex]
Roots are found by means of the General Equation for Second-Order Polynomials:
[tex]y_{1} \approx \frac{32}{5}[/tex] and [tex]y_{2} \approx \frac{7}{2}[/tex]
There are two different values for [tex]x[/tex]:
[tex]y = y_{1}[/tex]
[tex]x_{1} = 9.9-6.4[/tex]
[tex]x_{1} = 3.5[/tex]
[tex]y = y_{2}[/tex]
[tex]x_{2} = 9.9 - 3.5[/tex]
[tex]x_{2} = 6.4[/tex]
There are two possibilities:
[tex]x_{1} = 3.5[/tex] and [tex]y_{1} = 6.4[/tex]
[tex]x_{2} = 6.4[/tex] and [tex]y_{2} = 3.5[/tex]
Convert the line integral to an ordinary integral with respect to the parameter and evaluate it. ModifyingBelow Integral from nothing to nothing With Upper C (y minus z )ds∫C(y−z)ds; C is the helix left angle 12 cosine t comma 12 sine t comma t right angle12cost,12sint,t, for 0 less than or equals t less than or equals 2 pi0≤t≤2π The value of the ordinary integral is nothing.
C is parameterized by
[tex]\vec r(t)=\langle x(t),y(t),z(t)\rangle=\left\langle12\cos t,12\sin t,t\right\rangle[/tex]
for 0 ≤ t ≤ 2π. In the integral, replace y and z as above, and the line element ds is
[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt=\sqrt{145}\,\mathrm dt[/tex]
So the integral is
[tex]\displaystyle\int_C(y-z)\,\mathrm ds=\sqrt{145}\int_0^{2\pi}(12\sin t-t)\,\mathrm dt[/tex]
sin(t) has period 2π, so that term contributes nothing to the integral, leaving us with
[tex]\displaystyle\int_C(y-z)\,\mathrm ds=-\sqrt{145}\int_0^{2\pi}t\,\mathrm dt=\boxed{-2\pi^2\sqrt{145}}[/tex]