Answer:
Here are some basic tips that experts suggest.
Discuss math class at home.
Model good math behavior.
Talk through math problems.
Highlight real-life math problems.
Highlight real-life examples of fractions.
Play math games.
Use money to practice math.
Explore math with sports.
Step-by-step explanation:
solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!
Answer:
[0.25, 2]
Step-by-step explanation:
We have
4t² ≤ 9t-2
subtract 9t-2 from both sides to make this a quadratic
4t²-9t+2 ≤ 0
To solve this, we can solve for 4t²-9t+2=0 and do some guess and check to find which values result in the function being less than 0.
4t²-9t+2=0
We can see that -8 and -1 add up to -9, the coefficient of t, and 4 (the coefficient of t²) and 2 multiply to 8, which is also equal to -8 * -1. Therefore, we can write this as
4t²-8t-t+2=0
4t(t-2)-1(t-2)=0
(4t-1)(t-2)=0
Our zeros are thus t=2 and t = 1/4. Using these zeros, we can set up three zones: t < 1/4, 1/4<t<2, and t>2. We can take one random value from each of these zones and see if it fits the criteria of
4t²-9t+2 ≤ 0
For t<1/4, we can plug in 0. 4(0)²-9(0) + 2 = 2 >0 , so this is not correct
For 1/4<t<2, we can plug 1 in. 4(1)²-9(1) +2 = -3 <0, so this is correct
For t > 2, we can plug 5 in. 4(5)²-9(5) + 2 = 57 > 0, so this is not correct.
Therefore, for 4t^2 ≤ 9t-2 , which can also be written as 4t²-9t+2 ≤ 0, when t is between 1/4 and 2, the inequality is correct. Furthermore, as the sides are equal when t= 1/4 and t=2, this can be written as [0.25, 2]
Suppose y varies inversely with X, and y = 36 when x = 1/12. What inverse variation equation relates x and y?
NO LINKS OR ANSWERING YOU DON'T KNOW!!!
a. y= 3x
b. y= 3/x
c. x/3
d. y= x
Answer:
B
Step-by-step explanation:
We are given that y varies inversely with x. Recall that inverse variation has the form:
[tex]\displaystyle y=\frac{k}{x}[/tex]
Where k is the constant of variation.
We are given that y = 36 when x = 1/12. Thus:
[tex]\displaystyle (36)=\frac{k}{\left({}^{1}\!/\!{}_{12}\right)}[/tex]
Solve for k. Multiply both sides by 1/12:
[tex]\displaystyle k=\frac{1}{12}(36)=3[/tex]
Hence, our equation is:
[tex]\displaystyle y=\frac{3}{x}[/tex]
Our answer is B.
The following data were collected from a simple random sample from an infinite population.
13 15 14 16 12
The point estimate of the population standard deviation is _____.
a. 1.581
b. 2.500
c. 2.000
d. 1.414
Answer:
1.581
Step-by-step explanation:
Given the data:
13 15 14 16 12
The point estimate of the standard deviation will be :
√Σ(x - mean)²/n-1
Mean = Σx / n = 70 / 5 = 14
√[(13 - 14)² + (15 - 14)² + (14 - 14)² + (16 - 14)² + (12 - 14)² / (5 - 1)]
The point estimate of standard deviation is :
1.581
Symposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 129 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use ???? = 0.01.
Complete Question
ymposium is part of a larger work referred to as Plato's Dialogues. Wishart and Leach† found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato's Dialogues. A random sample of 498 five-syllable sequences from this manuscript showed that 129 were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato's Symposium? Use = 0.01.
a. What is the value of the sample test statistic? (Round your answer to two decimal places.)
b. Find the P-value of the test statistic. (Round your answer to four decimal places.)
Answer:
a) [tex]Z=2.45[/tex]
b) [tex]P Value=0.0073[/tex]
Step-by-step explanation:
From the question we are told that:
Probability of Wishart and Leach [tex]P=21.4=>0.214[/tex]
Population Size [tex]N=498[/tex]
Sample size [tex]n=12[/tex]
Therefore
[tex]P'=\frac{129}{498}[/tex]
[tex]P'=0.2590[/tex]
Generally the Null and Alternative Hypothesis is mathematically given by
[tex]H_0:P=0.214[/tex]
[tex]H_a:=P>0.214[/tex]
Test Statistics
[tex]Z=\frac{P'-P}{\sqrt{\frac{P(1-P)}{n}}}[/tex]
[tex]Z=\frac{0.2590-0.214}{\sqrt{\frac{0.214(1-0.214)}{498}}}[/tex]
[tex]Z=2.45[/tex]
Therefore P Value is given as
[tex]P Value =P(Z\geq 2.45)[/tex]
[tex]P Value =1-P(Z\leq 2.45)[/tex]
[tex]P Value =1-0.99268525[/tex]
[tex]P Value=0.0073[/tex]
pls help will give brainliest, 5* and thanks
trolls will get reports
Answer:
1.
M = 20 degrees
n =28.74
p = 20.12
2.
B = 73.65 degrees
C = 43.35 degrees
c = 30.05
3.
F = 21 degrees
G = 124 degrees
g = 23.13
Step-by-step explanation:
the law of sines is for a triangle ABC
a/sin(A) = b/sin(B) = c/sin(C)
1.
the sum of all angles in a triangle is always 180 degrees.
so, M = 180 - 125 - 35 = 20 degrees
m/sin(M) = n/sin(N)
12/sin(20) = n/sin(125)
sin(125) = sin(180-125) = sin(55)
n = 12×sin(55)/sin(20) = 28.74
p/sin(P) = m/sin(M)
p/sin(35) = m/sin(20)
p = m×sin(35)/sin(20) = 12×sin(35)/sin(20) = 20.12
2.
a/sin(A) = b/sin(B)
39/sin(63) = 42/sin(B)
sin(B) = 42×sin(63)/39 = 14×sin(63)/13
B = 73.65 degrees
therefore,
C = 180 - 63 - 73.65 = 43.35 degrees
c/sin(43.35) = 39/sin(63)
c = 39×sin(43.35)/sin(63) = 30.05
3.
e/sin(E) = f/sin(F)
16/sin(35) = 10/sin(F)
sin(F) = 10×sin(35)/16 = 5×sin(35)/8
F = 21 degrees
therefore,
G = 180 - 35 - 21 = 124 degrees
g/sin(124) = 16/sin(35)
sin(124) = sin(180-124) = sin(56)
g/sin(56) = 16/sin(35)
g = 16×sin(56)/sin(35) = 23.13
tr(n)*2 I NEE HELP ASAP
Answer:
2TRN
Let me know if this is wrong!
233115555532224444432
Emily drove to town with an average speed of 32 miles per hour, and then back home with an average speed of 38 miles per hour. If her total traveling time was 42 minutes, how far is it from home to town?
Answer:
12.16 milesStep-by-step explanation:
Speed - s, Distance - d, Time - t
Equation of time is:
t = d/sGiven,
s1 = 32 m/h, s2 = 38 m/h, t1 + t2 = 42 min = 42/60 h = 7/10 hTotal time is the sum of time values to and from the town:
d/32 + d/38 = 7/10d/16 + d/19 = 7/5d(1/16 + 1/19) = 7/5d(16 + 19) = 7(16*19)/535d = 425.6d = 425.6/35d = 12.16It is given that,
→ s1= 32 miles/h
→ s2 = 38 miles/h
Now t1 + t2 is,
→ 42 min
→ 42/60 hours
→ 7/10 hours
The formula we use,
→ Time = Distance/Speed
→ t = d/s
Then the total time is the,
Sum of time values to and from the town.
→ d/32 + d/38 = 7/10
→ d/16 + d/19 = 7/5
→ d{(1/16) + (1/19)} = 7/5
→ d(16 + 19) = (7/5) × (16 × 19)
→ 35d = 425.6
→ d = 425.6/35
→ d = 12.16
Hence, the distance is 12.16 miles.
A home gardener estimates that 24 apple trees will have an average yield of 104 apples per tree. But because of the size of the garden, for each additional tree planted the yield will decrease by two apples per tree. (a) How many additional trees should be planted to maximize the total yield of apples
Answer:
The farmer should plant 14 additional trees, for maximum yield.
Step-by-step explanation:
Given
[tex]Trees = 24[/tex]
[tex]Yield = 104[/tex]
[tex]x \to additional\ trees[/tex]
So, we have:
[tex]Trees = 24 + x[/tex]
[tex]Yield = 104 - 2x[/tex]
Required
The additional trees to be planted for maximum yield
The function is:
[tex]f(x) = Trees * Yield[/tex]
[tex]f(x) = (24 + x) * (104 - 2x)[/tex]
Open bracket
[tex]f(x) = 24 * 104 + 104x - 24 * 2x - x * 2x[/tex]
[tex]f(x) = 2796 + 104x - 48x - 2x^2[/tex]
[tex]f(x) = 2796 + 56x - 2x^2[/tex]
Rewrite as:
[tex]f(x) = - 2x^2 + 56x + 2796[/tex]
Differentiate
[tex]f'(x) = -4x + 56[/tex]
Equate [tex]f'(x) = -4x + 56[/tex] to 0 and solve for x to get the maximum of x
[tex]-4x + 56 = 0[/tex]
[tex]-4x =- 56[/tex]
Divide by -4
[tex]x =14[/tex]
The farmer should plant 14 additional trees, for maximum yield.
in the past year bill watch 64 movies that he thought were very good he watched 80 movies over the whole year of the movies he watched what percentage did he rate as very good
Answer:
he rate it 16%
Step-by-step explanation:
64-80\100=16
Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places
Answer:
0.33
Step-by-step explanation:
See comment for complete question
Given
[tex]H = 60\%[/tex]
[tex]W=25\%[/tex]
[tex]HW = 20\%[/tex] --- at-home wins
Required
The proportion of at-home games that were wins
This proportion is represented as:
[tex]Pr = HW : H[/tex]
Substitute values for HW and H
[tex]Pr = 20\% : 60\%[/tex]
Divide by 20%
[tex]Pr = 1 : 3[/tex]
Express as fraction
[tex]Pr = 1 /3[/tex]
[tex]Pr = 0.33[/tex]
Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = e−3x
Answer:
The equation of [tex]f(x) = e^{-3\cdot x}[/tex] by Maclaurin series is [tex]f(x) = \Sigma\limits_{i=0}^{\infty} \frac{(-3\cdot x)^{i}}{i!}[/tex].
Step-by-step explanation:
The Maclaurin series for [tex]f(x)[/tex] is defined by the following formula:
[tex]f(x) = \Sigma\limits_{i = 0}^{\infty} \frac{f^{(i)}(0)}{i!} \cdot x^{i}[/tex] (1)
Where [tex]f^{(i)}[/tex] is the i-th derivative of the function.
If [tex]f(x) = e^{-3\cdot x}[/tex], then the formula of the i-th derivative of the function is:
[tex]f^{(i)} = (-3)^{i}\cdot e^{-3\cdot x}[/tex] (2)
Then,
[tex]f^{(i)}(0) = (-3)^{i}[/tex] (2b)
Lastly, the equation of the trascendental function by Maclaurin series is:
[tex]f(x) = \Sigma\limits_{i=0}^{\infty} \frac{(-3)^{i}\cdot x^{i}}{i!}[/tex]
[tex]f(x) = \Sigma\limits_{i=0}^{\infty} \frac{(-3\cdot x)^{i}}{i!}[/tex] (3)
I NEED HELP ILL MARK!!!
Answer:
c) tan
Step-by-step explanation:
For the 63-deg angle, YZ is the opposite leg. The unknown side, AY, is the adjacent leg. The trigonometric ratio that relates the opposite and adjacent legs is the tangent.
Answer: c) tan
What's more to do? Task 1 Directions: Solve for the volume of the following: A. Rectangular Prism 1.1-9 m w 4 m h = 3 m 2.1 = 10 cm w=7 cm h = 15 cm 3.1 = 14 m w= 10 m h=9 m B. Cube 4. s = 12 cm 5. s= 6m
Answer:
Step-by-step explanation:
A). Volume of a rectangular prism = Length × Width × Height
= lwh
1). Volume of a rectangular prism if the measures of the sides are,
Length (l) = 9 cm
Width (w) = 4 cm
Height (h) = 3 cm
Therefore, volume = lwh
= 9 × 4 × 3
= 108 cm³
2). Length = 10 cm
Width = 7 cm
Height = 15 cm
Volume = lwh
= 10 × 7 × 15
= 1050 cm³
3). Length = 14 cm
Width = 10 cm
Height = 9 cm
Volume = 14 × 10 × 9
= 1260 cm³
B. Volume of a cube = (Side)³
4). If the measure of one side = 12 cm
Volume of the cube = (12)³
= 1728 cm³
5). If the measure of one side = 6 cm
Volume of the cube = (6)³
= 216 cm³
Lia can rent a van for either $90 per day with unlimited mileage or $50 per day with 250 free miles and an extra 25¢ for each mile over 250. For what number of miles traveled in one day would the unlimited mileage plan save Lia money? (Show work)
Answer:
ok so 90 is 40 more dollars then 50 and there is 4 25 cents in each dollars so
4*40=160
so she would have to drive 161 miles to save money
Hope This Helps!!!
What is the level of measurement for "year of birth"?
Answer:
interval?
Step-by-step explanation:
I'm not sure. I think so....hope its correct :)
Identify the dependent and independent variable in y = 12x - 30.
Step-by-step explanation:
guess
Dependent variable: y and Independent variable: x
gauthammath dot com
Yalll ya gurl is struggling I need help SOS
Answer:
22 mi
Step-by-step explanation:
From the question given above, the distance from E to F is 6 in.
Thus, we can obtain the distance from E to F (i.e mi) by using the scale provided in the question. This is illustrated below:
3 in = 11 mi
Therefore,
6 in = 6 in × 11 mi / 3 in
6 in = 22 mi
Therefore, the distance from E to F is 22 mi
A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.)
Answer:
1100 ft³
Step-by-step explanation:
Use the formula for the volume of a cylinder. For height, use the average of the minimum and maximum depths.
V = πr²h
r = d/2 = 20 ft/2 = 10 ft
h = (1 ft + 6 ft)/2 = 3.5 ft
V = π(10 ft)²(3.5 ft)
V = 1100 ft³
Please help it’s a test and I can’t get logged out
Answer:
the anwer is B ( i mean second option)
And you can try it
you will find ;
[tex]y = \frac{x}{3} - 1[/tex]
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ツ
Tell whether ΔABC and ΔDCB can be proven congruent.
A. Yes, ΔABC and ΔDCB can be proven congruent by SSS.
B. Yes, ΔABC and ΔDCB can be proven congruent by HL.
C. No, ΔABC and ΔDCB aren’t congruent because they share a side.
D. No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
Answer:
D. No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
Cách tính chu vi hình vuông?
Answer:
Xin hãy đánh dấu cho tôi là một người tồi tệ nhất
Để tìm chu vi hình vuông, bạn phải nhân 2 cạnh với 4..
Sử dụng công thức
chu vi = 4 * (một mặt)
Solve the quadratic equation 12x^2 - 288 = 0 using the square root method.
Answer:
C) x = ± 4
Step-by-step explanation:
12x² - 288 = 0
Add 288 on both sides. Anything plus zero gives itself.12x ² = 288
Divide both side by 12[tex] \small \sf \: x {}^{2} = \frac{288}{12} \\ [/tex]
Divide 288 by 12 to get 24[tex]\small \sf x {}^{2} = \frac{ \cancel{288 }}{ \cancel{12}} \\ [/tex]
x² = 24
Taking square root of each side and remember to use positive and negative roots[tex] \small \sf \: \sqrt{x {}^{2} } = ± \sqrt{ 24} [/tex]
[tex] \small \sf \: x_1, _2 = ± \sqrt{ 24} [/tex]
[tex] \small \sf \: x_1, _2 = ± 4.899 [/tex]
Which one of the following fractions is the largest? 3 /10 , 3 /2 , 1 /10 ,4/5, 10 /3 2 /3 , 10 /1 ,5 /4
Answer:
10/1 is the largest because 10÷1 = 10
Answer:
10/1 = 10 and is by far the biggest value in the list
Step-by-step explanation:
b) The cost of 1 kg of sweets is Rs 750. Find the cost of 1 kg sweet. 2
Hi Friends!
please help me with these questions !
Answer/Step-by-step explanation:
2. a. 5y - 3 = -18
Add 3 to both sides
5y - 3 + 3 = -18 + 3
5y = -15
Divide both sides by 5
5y/5 = -15/5
y = -3
b. -3x - 9 = 0
Add 9 to both sides
-3x - 9 + 9 = 0 + 9
-3x = 9
Divide both sides by -3
-3x/-3 = 9/-3
x = -3
c. 4 + 3(z - 8) = -23
Apply the distributive property to open the bracket
4 + 3z - 24 = -23
Add like terms
3z - 20 = -23
Add 20 to both sides
3z - 20 + 20 = - 23 + 20
3z = -3
Divide both sides by 3
3z/3 = -3/3
z = -1
d. 1 - 2(y - 4) = 5
1 - 2y + 8 = 5
-2y + 9 = 5
-2y + 9 - 9 = 5 - 9
-2y = -4
-2y/-2 = -4/-2
y = 2
3. First, find the sum of 3pq + 5p²q² + p³ and p³ - pq
(3pq + 5p²q² + p³) + (p³ - pq)
3pq + 5p²q² + p³ + p³ - pq
Add like terms
= 3pq - pq + 5p²q² + p³ + p³
= 2pq + 5p²q² + 2p³
Next, subtract 2pq + 5p²q² + 2p³ from 3p³ - 2p²q² + 4pq
(3p³ - 2p²q² + 4pq) - (2pq + 5p²q² + 2p³)
Apply distributive property to open the bracket
3p³ - 2p²q² + 4pq - 2pq - 5p²q² - 2p³
Add like terms
3p³ - 2p³ - 2p²q² - 5p²q² + 4pq - 2pq
= p³ - 7p²q² + 2pq
4. Perimeter of the rectangle = sum of all its sides
Perimeter = 2(L + B)
L = (5x - y)
B = 2(x + y)
Perimeter = 2[(5x - y) + 2(x + y)]
Perimeter = 2[5x - y + 2x + 2y]
Add like terms
Perimeter = 2(7x + y)
Substitute x = 1 and y = 2 into the equation
Perimeter = 2(7(1) + 2)
Perimeter = 2(7 + 2)
Perimeter = 2(9)
Perimeter = 18 units
5. First let's find the quotient to justify if the value we get is greater than or less than 2.25
7⅙ ÷ 3⅛
Convert to improper fraction
43/6 ÷ 25/8
Change the operation sign to multiplication and turn the fraction by the left upside down.
43/6 × 8/25
= (43 × 8)/(6 × 25)
= (43 × 4)/(3 × 25)
= 172/75
≈ 2.29
Therefore, the quotient of 7⅙ ÷ 3⅛ is greater than 2.25
Simplify the following expression.
3^{0}
Answer:
Anything to the power of zero (with the exception of zero itself) is equal to one.
So 3⁰ = 1
g A two-factor study with 3 levels of factor A and 3 levels of factor B uses a separate sample of 10 participants in each treatment condition. How many participants are needed for the entire study
Answer:
the total number of participants required is 90
Step-by-step explanation:
Given the data in the question;
Factor A has three levels
Factor B has three levels
sample size n; ten participants
we have two Way ANOVA involving Factor A and Factor B.
Now,
{ Total # Participants Required } = { #Levels factor A } × { #Levels factor B } × { Sample size of each level }
we substitute
{ Total # Participants Required } = 3 × 3 × 10
{ Total # Participants Required } = 9 × 10
{ Total # Participants Required } = 90
Therefore, the total number of participants required is 90
If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week.
Answer:
0.9898 = 98.98% probability that there will not be more than one failure during a particular week.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
3 failures every twenty weeks
This means that for 1 week, [tex]\mu = \frac{3}{20} = 0.15[/tex]
Calculate the probability that there will not be more than one failure during a particular week.
Probability of at most one failure, so:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.15}*0.15^{0}}{(0)!} = 0.8607[/tex]
[tex]P(X = 1) = \frac{e^{-0.15}*0.15^{1}}{(1)!} = 0.1291[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.8607 + 0.1291 = 0.9898[/tex]
0.9898 = 98.98% probability that there will not be more than one failure during a particular week.
2.6.67
Two cylindrical cans of soup sell for the same price. One can has a diameter of 6 inches and a height of 7 inches. The other has a diameter of 7 inches and a height
of 6 inches. Which can contains more soup and, therefore, is the better buy?
Which can contains more soup and therefore, is the better buy?
Please help :)
Answer:
second can
Step-by-step explanation:
The radius is half of the diameter.
The radius is squared in the formula for the volume of the cylinder.
A diameter of 7 and height of 6 will make a larger can than a diameter of 6 and height of 7.
The Statistical Abstract of the United States published by the U.S. Census Bureau reports that the average annual consumption of fresh fruit per person is 99.9 pounds. The standard deviation of fresh fruit consumption is about 30 pounds. Suppose a researcher took a random sample of 38 people and had them keep a record of the fresh fruit they ate for one year.
Appendix A Statistical Tables
(Round all z values to 2 decimal places. Round your answers to 4 decimal places.)
a. What is the probability that the sample average would be less than 90 pounds?
p =
b. What is the probability that the sample average would be between 98 and 105 pounds?
p =
c. What is the probability that the sample average would be less than 112 pounds?
p =
d. What is the probability that the sample average would be between 93 and 96 pounds?
p =
Answer:
Hence,
a) The probability that the sample average would be less than 90 pounds is 0.0210.
b) The probability that the sample average would be between 98 and 105 pounds is 0.5045.
c) The probability that the sample average would be less than 112 pounds is 0.9935.
d) The probability that the sample average would be between 93 and 96 pounds is 0.1341.
Step-by-step explanation:
a) [tex]P(X < 90) = P(Z < (90 - 99.9) / (30\sqrt(38)))[/tex]
= P(Z < -2.03) = 0.0210
b )[tex]P(98 < x <105) = P((98 -99.9) / (30 \sqrt(38)) < Z < (105 -99.9) / (30 \sqrt(38)))[/tex]
= P(-0.39 < Z < 1.05) = 0.5045
c ) [tex]P(X < 112) = P(Z < (112 - 99.9) / (30\sqrt(38)))[/tex]
= P(Z < 2.49) = 0.9935
d )[tex]P(93 < x < 96) = P((93 -99.9) / (30 \sqrt(38)) < Z < (96 -99.9) / (30 \sqrt(38)))[/tex]
= P( -1.42 < Z < -0.8 )
= 0.2119 - 0.0778 = 0.1341