A population has mean 555 and standard deviation 40. Find the mean and standard deviation of sample means for samples of size 50. Find the probability that the mean of a sample of size 50 will be more than 570.
Answers
The probability that the mean of a sample of size 50 will be more than 570 is approximately 0.0047, or 0.47%.
What the probability that the mean of a sample of size 50 will be more than 570?To find the mean and standard deviation of sample means for samples of size 50, we can use the properties of the sampling distribution.
The mean of the sample means (μₘ) is equal to the population mean (μ), which is 555 in this case. Therefore, the mean of the sample means is also 555.
The standard deviation of the sample means (σₘ) can be calculated using the formula:
σₘ = σ / √(n)
where σ is the population standard deviation and n is the sample size. In this case, σ = 40 and n = 50. Plugging in these values, we get:
σₘ = 40 / √(50) ≈ 5.657
So, the standard deviation of the sample means is approximately 5.657.
Now, to find the probability that the mean of a sample of size 50 will be more than 570, we can use the properties of the sampling distribution and the standard deviation of the sample means.
First, we need to calculate the z-score for the given value of 570:
z = (x - μₘ) / σₘ
where x is the value we want to find the probability for. Plugging in the values, we get:
z = (570 - 555) / 5.657 ≈ 2.65
Using a standard normal distribution table or calculator, we can find the probability associated with this z-score:
P(Z > 2.65) ≈ 1 - P(Z < 2.65)
Looking up the value for 2.65 in the standard normal distribution table, we find that P(Z < 2.65) ≈ 0.9953.
Therefore,
P(Z > 2.65) ≈ 1 - 0.9953 ≈ 0.0047
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Related Questions
if x=5, y=-3, and z=-7 z=-7, evaluate 3x^2-9y/yz
Answers
I just need to know if the answer is B or D
Answers
Step 1. The two functions we have are:
\(\begin{gathered} f(x)=2x^2 \\ g(x)=\sqrt[]{x-2} \end{gathered}\)And we are asked to find the composite function f(g(x)) and the domain.
Step 2. The function that we need to find is:
\(f(g(x))\)To find this, we substitute g(x) into the x value of f(x):
\(f(g(x))=2(\sqrt[]{x-2})^2-1\)Step 3. Simplifying:
The square root and the power of two cancel each other
\(f(g(x))=2(x-2)^{}-1\)Distributing the multiplication by 2:
\(f(g(x))=2x-4-1\)Combining the like terms:
\(f(g(x))=\boxed{2x-5}\)Step 4. Find the domain. The domain is the set of possible values that the x variable can take.
Remember the two original functions:
\(\begin{gathered} f(x)=2x^2 \\ g(x)=\sqrt[]{x-2} \end{gathered}\)for f(x) x can take any value. But for g(x) the square root cannot be a negative number, therefore, x-2 has to be equal to or greater than 0:
\(\begin{gathered} \text{Domain:} \\ x-2\ge0 \end{gathered}\)Solving for x:
\(\begin{gathered} \text{Domain:} \\ x\ge2 \end{gathered}\)This domain also applies to the composite function f(g(x)), and it can be written as follows:
\(D\colon\mleft\lbrace x|x\ge2\mright\rbrace\)Answer: Option four
\(\begin{gathered} f(g(x))=2x-5 \\ D\colon\lbrace x|x\ge2\rbrace \end{gathered}\)Write each equation in function notation. y=12+3/4x
Answers
Step-by-step explanation:
y = f(x)
this has the same meaning. y is just the variable for the functional result value. while x is usually used as variable for the input value.
so (I recommend to use the brackets to make sure that people understand it is meant that x gets multilevel by 3 in the numerator, and not by 4 in the denominator),
y = 12 + (3/4)x
is the same as
f(x) = 12 + (3/4)x
you could also write it as
f(x) = 12 + 3x/4
don't skip things, always think about the rules of the sequence of the operations in an expression, and how a reader could understand it. always be as precise, complete and consistent as possible.
Someone me help plz!!!
Answers
Answer:
(D) \(3 \pm i\sqrt{3}\)
Step-by-step explanation:
We can solve this using the quadratic formula, where a is 1, b is -6, and c is 12.
\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\frac{-(-6)\pm\sqrt{6^2-4\cdot1\cdot12}}{2\cdot1}\\\\\frac{6\pm\sqrt{36-48}}{2}\\\\\frac{6\pm\sqrt{-12}}{2}\\\\\frac{6\pm i\sqrt{12}}{2}\\\\3\pm i\sqrt{3}\\\\\)
Hope this helped!
A computer store compiled data about the accessories that 500 purchasers of new tablets bought at the same time they bought the tablet. Here are the results: 411 bought cases 82 bought an extended warranty 100 bought a dock 57 bought both a dock and a warranty 65 both a case and a warranty 77 bought a case and a dock 48 bought all three accessories 58 bought none of the accessories A. What is the probability that a randomly selected customer bought exactly 1 of the accessories?
Answers
The probability that a randomly selected customer bought exactly 1 of the accessories is 0.664, or 66.4%.
To find the probability that a randomly selected customer bought exactly 1 of the accessories, we need to determine the number of customers who bought exactly 1 accessory and divide it by the total number of customers.
Let's denote the events:
A = customer bought a case
B = customer bought an extended warranty
C = customer bought a dock
We are given the following information:
411 customers bought cases (A)
82 customers bought extended warranties (B)
100 customers bought docks (C)
57 customers bought both a dock and a warranty (B ∩ C)
65 customers bought both a case and a warranty (A ∩ B)
77 customers bought both a case and a dock (A ∩ C)
48 customers bought all three accessories (A ∩ B ∩ C)
58 customers bought none of the accessories
To find the number of customers who bought exactly 1 accessory, we can sum the following quantities:
(A - (A ∩ B) - (A ∩ C)) + (B - (A ∩ B) - (B ∩ C)) + (C - (A ∩ C) - (B ∩ C))
(A - (A ∩ B) - (A ∩ C)) represents the number of customers who bought only a case.
(B - (A ∩ B) - (B ∩ C)) represents the number of customers who bought only an extended warranty.
(C - (A ∩ C) - (B ∩ C)) represents the number of customers who bought only a dock.
Calculating the above expression, we get:
(411 - 65 - 77) + (82 - 65 - 57) + (100 - 77 - 57) = 332
Therefore, there are 332 customers who bought exactly 1 of the accessories. To find the probability, we divide this number by the total number of customers, which is 500:
Probability = 332/500 = 0.664
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(2- 7/18: 1/4) : x = x: (4/9:16)
Answers
HOPE THIS HELPS YOU
Evaluate −30 ÷ −6.
A. 5
B. −5
C. 6
D.−6
Answers
Answer:
5
Step-by-step explanation:
First, you can take out -5 and -6 because when dividing a negative by another negative, the quotient will be positive. And 30/6 is equal to 5
Explanation:
Here is an Integer Rule Cheat Sheet for you to use (I had to use the same one too).
Ma Amati’s bought x number of shirts for the new members of the dance team. The total amount paid for x shirts, including $2.99 shipping, was $118.99. Each shirt cost $14.50. There was no sales tax on this purchase. Which equation could be used to find x, the number of shirts bought
Answers
Answer: y = 14.50x + 2.99
Step-by-step explanation:
The equation is y = mx + b
y is the total cost and x is the number of shirt
We know each shirt is $14.50, and she bought x shirts, so 14.50 is the slope
The 2.99 shipping fee is the y-intercept
So our equation is
y = 14.50x + 2.99
ABCD is a rectangle and ∠BOC=56
Find ∠ADO,
Answers
The value of angle ADO in the rectangle is 62°.
How to calculate the angle?From the information, angle BOC = 56°
In a rectangle, there are two congruent diagonals.
Therefore DO = AO
angle ADO = angle DAO
angle DOA = 56° (vertical opposite angles)
sum of all three interior angles in a triangle = 180°
angle ADO + angle DAO + angle DOA = 180°
angle ADO + angle ADO + 56° = 180°
2angleADO = 180° - 56°
2angleADO = 124°
Divide
angle ADO = 124/2
angle ADO = 62°
Hence, the measure of angle ADO = 62°
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A company manufactures small refrigerators. The total cost to manufacture 43 refrigerators is $5075. The total costs to manufacture 118 refrigerators is $10700. Assume that total cost, C, is linearly related to the number of refrigerators, x, the company manufactures and includes a fixed cost and a cost per refrigerator.
Answers
A) Let C(x) the cost of manufacturing x refrigerators, since C is linearly related to x, then we can set the following equation:
\(C(x)=mx+b\text{.}\)To determine the values of m and b we will use the fact that:
\(\begin{gathered} C(43)=5075, \\ C(118)=10700. \end{gathered}\)Therefore we can set the following system of equations:
\(\begin{gathered} m\cdot43+b=5075, \\ m\cdot118+b=10700. \end{gathered}\)Subtracting the second equation from the first one we get:
\(\begin{gathered} m\cdot118+b-m\cdot43-b=10700-5075, \\ 75m=5625. \end{gathered}\)Dividing the above equation by 75 we get:
\(\begin{gathered} \frac{75m}{75}=\frac{5625}{75}, \\ m=75. \end{gathered}\)Substituting m=75 in 43m+b=5075, and solving for b we get:
\(\begin{gathered} 43\cdot75+b=5075, \\ b=5075-43\cdot75, \\ b=1850. \end{gathered}\)Therefore:
\(C(x)=75x+1850.\)B) Evaluating C(x) at x=123 we get:
\(\begin{gathered} C(123)=75\cdot123+1850, \\ C(123)=11075. \end{gathered}\)C) From the equation we get that the fixed cost is $1850.
D) The cost to produce each additional refrigerator is $75.
Answer:
(a)
\(C(x)=75x+1850.\)(b) $11075.
(c) $1850.
(d) $75.
a finite sequence of three-digit integers has the property that the tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term. for example, such a sequence might begin with the terms 247, 475, and 756 and end with the term 824. let be the sum of all the terms in the sequence. what is the largest prime factor that always divides ?
Answers
The largest prime factor that always divides the sum of the terms in the sequence is 37.
The sequence is finite and consists of three-digit integers.
The tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term.
From the above property of the sequence, we can see that each digit at the units, tens as well as hundreds place will appear the same number of times in the sequence.
Let "x" be the sum of the digits at unit place in all the terms.
The sum of all the terms is "S".
S = 111*x
S = 3*37*x
We can clearly see that the sum "S" is divisible by 37.
Hence, the largest prime factor that always divides the sum of the terms in the sequence is 37.
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I will mark you brainiest!!!
A passenger train left the station and traveled toward Las Vegas at an average speed of 55mph. A cattle train left at the same time and traveled in the opposite direction with an average speed of 65mph. Which equation best represents this situation when the trains are 960 mi apart?
A - 65x - 55(2) = 960
B - 65x - 55x = 960
C - 65x + 55(2) = 960
D - 65x + 55x = 960
E - 65(2) + 55x = 960
Answers
Answer:
The answer is b
Step-by-step explanation:
The distance traveled by the passenger train and the cattle train is equal to the total distance between them, which is 960 miles. Let x be the time (in hours) traveled by the passenger train and cattle train. Then, the equation that represents this situation is:
55x + 65x = 960
Simplifying the left-hand side of the equation, we get:
120x = 960
Dividing both sides by 120, we get:
x = 8
Therefore, the correct equation is:
B - 65x - 55x = 960
solve these simultaneous equations 2x+3y=13 4x-y=-2
Answers
Answer:
x = \(\frac{1}{2}\), y = 4
Step-by-step explanation:
2x + 3y = 13
4x - y = -2
Lets get the equation of the y value;
4x - y = -2
Subtract 4x to both sides;
-y = -4x - 2
Divide both sides by -1
y = 4x + 2
Substitute y in the second equation;
2x + 3y = 13
2x + 3(4x + 2) = 13
Distribute;
2x + 12x + 6 = 13
14x + 6 = 13
Subtract 6 from both sides;
14x = 7
Divide both sides by 14;
x = \(\frac{1}{2}\)
Lets calculate the value of x;
\((4)\frac{1}{2} - y= -2\\\frac{4}{2} - y =-2\\ 2 - y=-2\\\)
Subtract 2 from both sides;
-y = -4
Divide both sides by -1
y = 4
ANSWER FAST, WILL GIVE BRAINLIEST
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
The heights of the girls in an advanced swimming course are 55, 60, 59, 52, 65, 66, 62, and 65 inches. Match the measures of this data with their values.
65
61
8
14
60.5
median
arrowRight
mean
arrowRight
interquartile range
arrowRight
range
arrowRight
Answers
60.5 is mean
61 is median
65 is interquartile range
14 is range
Answer:
60.5 is mean.
_________________
61 is median.
_________________
65 is interquartile range.
_________________
14 is range.
Question 12 of 17
Which of the following pairs of functions are inverses of each other?
A. f(x)=3(3)-10 and g(x)=+10
-8
B. f(x)= x=8+9 and g(x) = 4(x+8)-9
C. f(x) = 4(x-12)+2 and g(x)=x+12-2
4
OD. f(x)-3-4 and g(x) = 2(x+4)
3
Answers
Answer:
Step-by-step explanation:
To determine if two functions are inverses of each other, we need to check if their compositions result in the identity function.
Let's examine each pair of functions:
A. f(x) = 3(3) - 10 and g(x) = -8
To find the composition, we substitute g(x) into f(x):
f(g(x)) = 3(-8) - 10 = -34
Since f(g(x)) ≠ x, these functions are not inverses of each other.
B. f(x) = x + 8 + 9 and g(x) = 4(x + 8) - 9
To find the composition, we substitute g(x) into f(x):
f(g(x)) = 4(x + 8) - 9 + 8 + 9 = 4x + 32
Since f(g(x)) ≠ x, these functions are not inverses of each other.
C. f(x) = 4(x - 12) + 2 and g(x) = x + 12 - 2
To find the composition, we substitute g(x) into f(x):
f(g(x)) = 4((x + 12) - 2) + 2 = 4x + 44
Since f(g(x)) ≠ x, these functions are not inverses of each other.
D. f(x) = 3 - 4 and g(x) = 2(x + 4)
To find the composition, we substitute g(x) into f(x):
f(g(x)) = 3 - 4 = -1
Since f(g(x)) = x, these functions are inverses of each other.
Therefore, the pair of functions f(x) = 3 - 4 and g(x) = 2(x + 4) are inverses of each other.
What is the volume of the rectangular prism?
Answers
Answer: 24
Step-by-step explanation:
Volume = L x W x H
Volume = 4 x 2 x 3
Volume = 24
A blue die and a red die are thrown. B is the event that the blue comes up an odd number. E is the event that both dice come up odd.
Enter the sizes of the sets |E ∩ B| and |B|
Answers
The size of the set |E ∩ B| is 2, and the size of the set |B| is 3.
There are six possible outcomes when two dice are thrown:
{(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (6,1), (6,2), (6,3)}.
Out of these 18 outcomes, the following three satisfy the event E (both dice are odd): (1,3), (3,1), and (3,3).
The following outcomes satisfy event B (the blue die is odd): (1,1), (1,3), (2,1), (2,3), (3,1), and (3,3).
Therefore, the size of the set |E ∩ B| is 2 (the two outcomes that satisfy both events are (1,3) and (3,1)), and the size of the set |B| is 3 (three outcomes satisfy the event B).
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If the rise and run on one section are, respectively, 3.0 m and 6.3 m, what is the run on the other section if its rise is 4.3 m
Answers
The the run on the other section if its rise is 4.3 m = 9.03m
How top solve for the runTo get the run on the other section we have to use the cross multiplication formula, using m1 = m2
Such that we would have
3.0/6.3 = 4.3/x
6.3 * 4.3 = 3.0 * x
= 27.09 = 3x
divide through by 3
x = 9.03
Hence we conclude that the the run on the other section if its rise is 4.3 m = 9.03m
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Anna has saved $525 for a new flat-screen television. She plans to save an additional $50 per month. An equation that represents her total
savings as a function of the number of months she will save, m, is s(m) = 525 + 50m. Anna wishes to buy a flat-screen television that
costs $1,225, including tax. Which of these statements is true?
s(3) = 1725, so it will take Anna 3 months to save enough to buy the television.
s(14) = 1225, so it will take Anna 14 months to save enough to buy the television.
s(1225) = 61250, so it will take Anna 61,250 months to save enough to buy the
television
There is not enough information to answer the question.
Answers
Answer:
2nd one (14)
Step-by-step explanation:
525+50m=1225 take 525 from both sides
50m=700 divide 50 from both sides
m=14
If will take 14 months to save up the money.
Solve for x - 11 = 28x−11=28
Answers
Answer:
x = 39
Step-by-step explanation:
To solve the equation x - 11 = 28, you can add 11 to both sides of the equation:
x - 11 + 11 = 28 + 11
x = 39
So the solution to the equation is x = 39.
(Please give brainlist)
\(x - 11 = 28\)
Add 11 to both sides:
\(x-11+11=28+11\)
\(\boxed{x = 39}\)
a fair die is tossed, and the up face is noted. if the number is even, the die is tossed again; if the number is odd, a fair coin is tossed. consider the following events: a: 5a head appears on the coin.6 b: 5the die is tossed only one time.6 a. list the sample points in the sample space. b. give the probability for each of the sample points. c. find p ( a ) and p ( b ). d. identify the sample points in ac , bc , a b, and a b. e. find p1ac 2, p1bc 2, p1a b2, p1a b2, p1ab2 , and p1b a2 . f. are a and b mutually exclusive events? independent events? why?
Answers
a) Sample space: {1,2,3,4,5,6} for the first toss of the die. If the result is even, then another toss is made, resulting in the sample space {2,4,6} for the second toss. If the first toss is odd, a coin is tossed, resulting in the sample space {H, T} for the coin toss.
b) Each outcome in the sample space has an equal probability of 1/6, except for the outcomes in {2,4,6}, which have a probability of 1/18 for the second toss.
c) P(a) = P(H) = 1/6, P(b) = 1/2.
d) ac: {5H}, bc: {1,3,5}, ab: { }, a∪b: {1,3,5,H}.
e) P(ac) = 1/6, P(bc) = 3/6 = 1/2, P(a∩b) = 0, P(a∪b) = 4/6 = 2/3, P(a|b) = P(ab)/P(b) = 0/1/2 = 0, P(b|a) = P(a∩b)/P(a) = 0/1/6 = 0.
f) a and b are not mutually exclusive events because there is a possibility that both events can occur together. They are not independent because the outcome of the first toss affects the likelihood of the second toss or coin toss.
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There were 80 runners to start a race. In the first half of the race, 1/5 of them dropped out. In the second half of the race, 5/8 of the remaining runners dropped out. How many runners finished the race
Answers
Answer:
24
Step-by-step explanation:
Initially, there were 80 runners in the race. After the first half, 1/5 of them dropped out (given). Therefore, 4/5*80=64 runners remain. In the second half, 5/8 of these 64 runners drop out, meaning 3/8*64=24 runners finished the race.
Which algebraic expression represents this word description?
The quotient of six and the sum of a number and eight
O
2+8
d
O
A. **8
B. + 8
o
o
O
c. 78
6
D. Ő +8
SUBMIT
h
Answers
A diagonal of a rectangle splits the rectangle into two 300-60 •-90° triangles. If the diagonal of the rectangle is 21 in, what is the length and width of the rectangle. Find the area
Answers
When the diagonal of a rectangle splits the rectangle into two producing angles 30 - 60 - 90 the sides of the rectangle is
Area of a rectangle is solved to get 191 square in
How to find the lengths of the rectangleThe problem is solved using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The shape describes a right triangle of
opposite = width
adjacent = length
hypotenuse = diagonal
The dimensions are calculated using SOH and CAH
sin 30 = opposite / hypotenuse
sin 30 = width / 21
width = 21 * sin 30
width = 10.5
For the length
cos 30 = adjacent / hypotenuse
cos 30 = length / 21
length = 21 * sin 30
length = 18.19
Area of a rectangle = length * width
Area of a rectangle = 18.19 * 10.5
Area of a rectangle = 190. 995
Area of a rectangle = 191 square in
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Can someone please help me. Thanks
Answers
Answer:
\(c= \sqrt{288}\)
Step-by-step explanation:
Use the Pythagorean Theorem
\(a^2 + b^2 = c^2\)
\(12^2 + 12^2 = c^2\)
\(144+144=c^2\)
\(288 =c^2\)
\(\sqrt{288} =\sqrt{c^2}\)
\(\sqrt{288} = c\)
Find the product of (x − 5)2.
x2 + 10x + 25
x2 − 10x + 25
x2 − 25
x2 + 25
Answers
Answer:
\({x}^{2} - 10x + 25\)
Step-by-step explanation:
How can we solve this?For this problem, we can break the equation into (x - 5) use FOIL. First, Outer, Inner, Last.
(x - 5) (x - 5)
First, multiply the two Xs together.
X * X =
\( {x}^{2} \)
Now, the outer numbers and values.
X * -5 =
\( - 5x\)
Then, it's the inner numbers and values.
-5 * x =
\( - 5x\)
Finally, multiply the last numbers.
-5 * -5 =
\( 25\)
Now that we have multiplied all of the values, we can put the answers from FOIL together.
\( {x}^{2} - 5x - 5x + 25\)
Now, add any like terms.
\( - 5x - 5x = - 10x\)
The answer is
\( {x}^{2} - 10x + 25\)
Find the value of x, (x-7)°(2x+1) °
Pleas help!!!!
Answers
Answer:
x = 32
Step-by-step explanation:
2x+1 + x-7 = 90
3x - 6 = 90
3x = 96
x = 32
Write an inequality describing the given quantity. Example: An MP3 player can hold up to 120 songs. Solution: The number of songs is n where 0≤n≤120,n an integer. Minimum class size at a certain school is 12 students, and state law requires fewer than 18 students per class. The class size is n, where
Answers
The inequality 12 ≤ n < 18 describes the class size requirements, where the class size "n" must be equal to or greater than 12 students and less than 18 students.
The inequality describing the given quantity, where the minimum class size at a certain school is 12 students and state law requires fewer than 18 students per class, is:
12 ≤ n < 18
In this inequality, "n" represents the class size, and the symbol "≤" indicates "less than or equal to," while the symbol "<" indicates "less than."
The lower bound of the inequality, 12, represents the minimum class size required by the school. It states that the class size must be equal to or greater than 12 students. In other words, a class size of 12 or more students is allowed.
The upper bound of the inequality, 18, represents the maximum class size permitted by state law. However, since the law requires fewer than 18 students per class, the strict inequality symbol "<" is used instead of "≤." This means that the class size must be less than 18 students.
Combining both bounds in the inequality, we have 12 ≤ n < 18. This indicates that the class size, represented by "n," must be equal to or greater than 12, but strictly less than 18.
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The equation of a function is given.
f(x)=(2x-3)(3x+4)
What is one of the zeros of the function?
Answers
Answer:
3/2 or -4/3
Step-by-step explanation:
2x-3=0, 3x+4=0
x=3/2 or-4/3
a box is at rest and a force of a 837 N is applied to it. IF frictional force 400 N,determine the net force?
Answers
Answer:
FNet = 437N
Step-by-step explanation:
The equation for net force is
FNet = Fa + Fg + Ff + FN. where FNet is the net force, Fa is the applied force and Fg is the force due to gravity, Ff is the frictional force and FN is the normal force
We do not have a normal force or a force due to gravity
FNet = Fa + Ff
Applied force Fa = 837 N
The frictional force works opposite the applied force
Frictional force Ff = -400 N
FNet = 837 - 400
FNet = 437N