We know that the line integral of the curve C is equal to the difference between the anti-derivative at the final point B and the antiderivative at the initial point A. Therefore, Vg⋅dr= F(B) - F(A)⇒ Vg⋅dr= [2(5)²(5) + 3(5)² + C] - [90 + C]⇒ Vg⋅dr= 184
The question states that the function g(x,y) = 2x² + 3y² and the curve C is the arc of a curve from point A(4,3) to point B(5,5). The task is to find the value of the line integral along curve C.
Therefore, we need to use the fundamental theorem for line integrals to evaluate the line integral. To use the fundamental theorem for line integrals, we must first evaluate the gradient vector field of the function. Then we need to find the antiderivative of the gradient vector field of the function. We can obtain the antiderivative by integrating the gradient vector field along the curve C using the initial and final points of the curve. The value of the line integral of the curve C is equal to the difference between the antiderivative at the initial point A and the antiderivative at the final point B, i.e., Vg⋅dr= F(B) - F(A).
Step-by-step solution: Given, the function g(x,y) = 2x² + 3y²Let us calculate the gradient vector of the function g(x,y).∇g(x,y) = [∂g/∂x, ∂g/∂y]⇒ ∇g(x,y) = [4x, 6y]Therefore, the gradient vector field of g(x,y) is V = [4x, 6y].
Now, we need to find the antiderivative of the gradient vector field of the function. Let us integrate V along the curve C from A(4,3) to B(5,5). The curve C is given by y = x + 1.We know that the line integral along curve C is given by the formula, Vg⋅dr= ∫C V . dr = F(B) - F(A)
Therefore, we need to find the antiderivative F of V.F(x,y) = ∫V dx⇒ F(x,y) = 2x²y + 3y² + C. Since we have two variables, we need to find the value of C using the initial point A(4,3).F(4, 3) = 2(4)²(3) + 3(3)² + C⇒ F(4, 3) = 90 + C
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Given that the function is G(x, y) = 2x² + 3y² and Arc of a curve C from point A(4, 3) to point B(5, 5). The value of the line integral [tex]\int _C[/tex] (2x² + 3y²) ds is 106.67.
Solution: In the given question, we have a function G(x, y) = 2x² + 3y² and an arc of a curve C from point A(4, 3) to point B(5, 5).
We are to use the fundamental theorem for line integrals to find the value of [tex]\int _C[/tex] (2x² + 3y²) ds.
Step 1: First, we will find the parametric equations of the given curve.
The points A(4, 3) and B(5, 5) are given.
We can write the parametric equations of the curve C as: x = f(t) and y = g(t), where a ≤ t ≤ b, and f(a) = 4, g(a) = 3, f(b) = 5, g(b) = 5.
Here, the curve C is the straight line from A(4, 3) to B(5, 5), so we can choose any convenient parameterization.
A possible one is: t → r(t) = (4 + t, 3 + t), 0 ≤ t ≤ 1.
Step 2: Next, we will find dr/dt and ds/dt.
We have: r(t) = (4 + t)i + (3 + t)j
⇒ dr/dt = i + j.
Square of the magnitude of the tangent vector: |dr/dt|² = (1)² + (1)²
= 2.
Magnitude of the normal vector:
|n| = √(ds/dt)²
= √(2)
= √2.
Magnitude of the velocity vector:
|v| = √(dr/dt)²
= √2.
Step 3: Now, we will find the limits of integration and substitute the required values in the integral.
Given: [tex]\int _C[/tex] (2x² + 3y²) ds.
We have: r(t) = (4 + t)i + (3 + t)j
⇒ r'(t) = i + j
⇒ |r'(t)| = √2.
We know that the length of the curve C from A to B is given by:
Length of the curve = [tex]\int _C[/tex] ds
= [tex]\int_a^b[/tex] |r'(t)| dt
= [tex]\int_0^1[/tex] √2 dt
= √2.
Now, we have the value of ds: ds = √2 dt.
Then, we can write the integral as follows:
[tex]\int _C[/tex] (2x² + 3y²) ds = [tex]\int_0^1[/tex] (2(4 + t)² + 3(3 + t)²) √2 dt
= [tex]\int_0^1[/tex] (32 + 32t + 10t²) √2 dt
= [32t + 16t² + (10/3)t³[tex]]_0^1[/tex]
= 32 + 16 + (10/3)
= 106.67.
Thus, the value of the line integral [tex]\int _C[/tex] (2x² + 3y²) ds is 106.67.
The required answer is: 106.67.
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what are the next three terms of the following sequence
1,4,6,11,21,38
The next three terms of the sequence 1, 4, 6, 11, 21, 38 are 70, 123, 216.
To find the next term in the sequence, we need to identify the pattern or rule governing the sequence. Looking at the given terms, we can observe that each term is obtained by adding the previous term and a specific number.
From the given sequence:
4 = 1 + 3
6 = 4 + 2
11 = 6 + 5
21 = 11 + 10
38 = 21 + 17
The difference between the consecutive terms appears to be increasing by 1 each time. So, we can infer that the next difference would be 17 + 1 = 18.
Now, to find the next term:
38 + 18 = 56
56 + 19 = 75
75 + 20 = 95
Therefore, the next three terms of the sequence are 70, 123, 216.
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Find m∠MON..........
is the equation y = x ^2 + 3 a function?
Answer: Yes it is
Step-by-step explanation:
Answer:
Yes it is. Succese to The homework
The ages (in years) of nine men and their systolic blood pressures (in millimeters of mercury) are given below. Age 16 25 39 49 22 57 22 64 70 118 175 118 185 199 Systolic blood pressure 109 122 143 199 a) Name the dependent and independent variables [2 marks] b) Calculate the correlation coefficient and interpret your results. [12+2 marks] c) Find the coefficient of determination and interpret your results. [2 marks] d) Develop the regression equation for the data set. e) Predict the blood pressure of a 50-year-old man
a) Dependent variable: Systolic blood pressure
Independent variable: Age
b) Calculations: xi (age) yi (Systolic blood pressure)xiyi (age × systolic blood pressure)xi^2 (age²)yi^2 (systolic blood pressure²)16 109 1,744 256 11,88125 122 3,050 625 14,88439 143 5,577 1,521 20,44949 199 9,751 2,401 39,60122 118 2,596 484 13,92457 175 9,975 3,249 30,62522 118 2,596 484 13,92464 185 11,840 4,096 34,22570 199 13,930 4,900 39,601∑x = 561∑y = 1,450∑xy = 61,059∑x² = 19,200∑y² = 249,141r = [9 (∑xy) - (∑x)(∑y)] / sqrt([9∑x² - (∑x)²][9∑y² - (∑y)²]) = 0.664- The correlation is moderate positive. As age increases, systolic blood pressure also increases.
c) R² = r² = 0.4416- 44.16% of the variability in systolic blood pressure is explained by age.
d) Regression Equation: y = a + bx where a = (y mean) - b (x mean) Using the means x mean = 62.3 and y mean = 161.1a = (161.1) - b (62.3)a = 33.62y = 33.62 + 1.083x
The regression equation is y = 33.62 + 1.083x.
e) Predicting the blood pressure of a 50-year-old man:y = 33.62 + 1.083xy = 33.62 + 1.083(50)y = 33.62 + 54.15y = 87.77
The predicted blood pressure is 87.77.
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pleaaaaseeeeeee help!!!!!!!!!!!!!!!!!!!!!
brainliest and 20 points
Answer:
x=0
Step-by-step explanation:
Answer:
Short answer: Empty set ∅
if x is less than -1 then it can't be greater than 1
anyone know the answers to 3, 4, 5 and six
is 700 yards bigger then 2000 feet?
Answer:
Yes, 700 yards bigger than 2000 feet because 700 yards = 2100 feet
Step-by-step explanation:
There are 3 feet in a yard, so that means we need to multiply 700 yards by 3 to get the number of feet there are in 700 yards.
700 yards × 3 feet = 2100 feet
700 yards = 2100 feet
2100 feet > 2000 feet
Answer:
Yes!
Step-by-step explanation:
700 yards is equal to 2100 feet, making it 100 feet longer.
I really need help please and thank you
Answer:
x = 8
Step-by-step explanation:
You can set up the equation 6/4 = 12/x and then cross multiply to solve for x
What is the simplified form of the following expression? Assume y does not equal 0. 3 square root 12x^2 over 16y
Answer:
Ok y does not = 0 (They say this because is y=0 it would be undefined anything divided by 0 is undefined)
[tex](3\sqrt{12x^2})/16y\\[/tex]
Answer: [tex](3x\sqrt{3})/8y[/tex]
what is the diameter of a circle with a circumference of 56 inches?
Answer:
17.83in
Step-by-step explanation:
Diameter of circle with circumference 56 inches 17.81 inches .
Given,
Circumference = 56 inches
Now,
Circumference of circle = 2πr
r = radius of circle.
Substitute the values to get the value of radius,
56 = 2 × π × r
56 = 2× 22/7× r
r = 56 × 7/44
r = 8.909 inches.
Next,
Diameter = 2 (Radius)
Diameter = 2 * 8.909
Diameter = 17.81 inches .
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Qn) Consider an IQ test for which the scores of adult Americans are known to have a normal distribution with expected value 100 and Variance 324, and a second IQ test for which the scores of adult Americans are known to have a normal distribution with expected value 50 and Variance 100. Under the assumption that both tests measure the same phenomenon ("Intelligence"), what score on the Is cond test is comparable to a score of 127 on the first test? I plain your answer
The score on the second test that is comparable to a score of 127 on the first test is 131.
Given that: IQ test for which the scores of adult Americans are known to have a normal distribution with an expected value of 100 and Variance of 324 and another IQ test for which the scores of adult Americans are known to have a normal distribution with an expected value of 50 and Variance 100.
Let x denote the first test score that is comparable to a second test score of 127. Then, we have; (127 − 100) / 18 = (x − 50) / 10 (the z-scores corresponding to the scores)
Simplifying the above equation gives;
(127 − 100) × 10 = (x − 50) × 18
Solve for x as follows;
(127 − 100) × 10 + 50 = (x) × 18
Hence, x = 131
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The score on the second test which is equivalent to a score of 127 on the first test is 4.332, or approximately 4.33 (rounded to two decimal places).
If X1, X2 are the IQ scores of the first and second tests respectively, we are given that X1 and X2 are both normally distributed. This means that their expected values and variances are known.
E(X1) = 100, Var(X1) = σ1² = 324E(X2) = 50, Var(X2) = σ2² = 100
We need to find the score, x on the second test which is equivalent to a score of 127 on the first test.
Therefore, we need to find
P(X1 ≤ 127) and then solve for x so that
P(X2 ≤ x) = P(X1 ≤ 127).
We know that
Z1 = (X1 - μ1) / σ1 and
Z2 = (X2 - μ2) / σ2 where μ1, μ2 are the respective expected values.
For a given probability P(Z ≤ z), we can find z using a standard normal table. Therefore, we can rewrite P(X1 ≤ 127) in terms of Z1 as follows;
P(X1 ≤ 127) = P((X1 - μ1) / σ1 ≤ (127 - μ1) / σ1) = P(Z1 ≤ (127 - μ1) / σ1) = P(Z1 ≤ (127 - 100) / 18) = P(Z1 ≤ 1.5)
The corresponding score on the second test, X2 can be found using;
Z2 = (X2 - μ2) / σ2 ⇒ X2 = σ2 Z2 + μ2
From the given values, μ2 = 50 and σ2 = 10.
Therefore,
X2 = σ2 Z2 + μ2 = 10 Z2 + 50
We need to find the value of x such that
P(Z2 ≤ x) = P(Z1 ≤ 1.5).
From a standard normal table,
we have P(Z ≤ 1.5) = 0.9332 and therefore,
P(Z2 ≤ x) = 0.9332 implies that
x = (0.9332 - 0.5) / 0.1 = 4.332.
Therefore, the score on the second test which is equivalent to a score of 127 on the first test is 4.332, or approximately 4.33 (rounded to two decimal places).
We are given
E(X1) = 100, Var(X1) = σ1² = 324E(X2) = 50, Var(X2) = σ2² = 100
We need to find x such that P(X1 ≤ 127) = P(X2 ≤ x).
Therefore, we find P(X1 ≤ 127) in terms of Z1 as follows;
P(X1 ≤ 127) = P(Z1 ≤ (127 - 100) / 18) = P(Z1 ≤ 1.5) = 0.9332
The corresponding value of X2, denoted by x can be found from
P(Z2 ≤ x) = P(Z1 ≤ 1.5).
From a standard normal table, we have
P(Z ≤ 1.5) = 0.9332 and therefore,
P(Z2 ≤ x) = 0.9332 implies that
x = (0.9332 - 0.5) / 0.1 = 4.332.
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Suppose that you used technology to find the least-squares regression line from a table of values for two variables and the results were displayed as follows.
m = -0.03576 b = 42.17093 r^2 = 0.8914 r = -0.9438
What can we say about the relationship between the two variables?
Since the r-value is quite close to -1 (only 0.0562 away), we can conclude that the two variables are strongly negatively associated. This implies that when one variable increases, the other variable decreases.
In statistics, the correlation coefficient is used to quantify the linear relationship between two variables. The r-value ranges from -1 to 1, indicating the degree to which the variables are positively or negatively associated.
The r-value measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1.
The closer the r-value is to -1, the stronger and more negative the correlation is.
The closer the r-value is to 1, the stronger and more positive the correlation is.
A value of 0 indicates that there is no linear relationship between the variables.In this case, the r-value is -0.9438.
Because the r-value is negative, the two variables are negatively associated. The closer the r-value is to -1, the stronger the negative association is.
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Use the given conditions to write an equation for the line Passing through ( - 3,8) and parallel to the line whose equation is 3x - By - 7 = 0 The equation of the line is (Simplify your answer. Type an equation using x and y as the variables.
The equation of the line parallel to 3x - By - 7 = 0 and passing through (-3, 8) is B*y - 8B = -3x - 9.
To find the equation of a line parallel to the given line, we need to determine the slope of the given line. The equation of the given line is 3x - By - 7 = 0.
We can rewrite this equation in the slope-intercept form (y = mx + b), where m represents the slope and b is the y-intercept. By rearranging the equation, we have:
By - 7 = -3x
By = -3x + 7
Dividing both sides by B (assuming B ≠ 0):
y = (-3/B)x + 7/B
From the equation y = (-3/B)x + 7/B, we can see that the slope of the given line is -3/B.
Since the line we're looking for is parallel to the given line, it will have the same slope. Therefore, the slope of the line we seek is also -3/B.
We are given that the line passes through the point (-3, 8). We can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Substituting the values (-3, 8) for (x1, y1) and -3/B for m:
y - 8 = (-3/B)(x - (-3))
y - 8 = (-3/B)(x + 3)
Multiplying through by B:
By - 8B = -3(x + 3)
Simplifying:
B*y - 8B = -3x - 9
The equation of the line parallel to 3x - By - 7 = 0 and passing through (-3, 8) is B*y - 8B = -3x - 9.
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heLp pls sOmeBoDy and tyy
Answer :
AB = 48.88
Step-by-step explanation:
We will use the sin fulmera
[tex] \frac{ \sin(134°) }{ab} = \frac{ \sin(18°) }{21} \\ \\ ab = 48.88[/tex]
I hope that is useful for you :)
Answer:
48.9
Step-by-step explanation:
[tex]\frac{A}{sinA}=\frac{B}{sinB} =\frac{C}{sinC}[/tex] (you can flip the equation around)
[tex]\frac{21}{sin18} = \frac{AB}{sin134}[/tex]
[tex]AB=\frac{21*134}{sin18}= 48.88448235[/tex]
Sorry for the late answer I was distracted
(450) + (28.75x) = 967.50
solve for x
Answer:
18
Step-by-step explanation:
Hello,
In order to solve for x, we need to isolate the variable on one side of the equation.
To do this, we subtract 450 from both sides of the equation, and this will give you:
28.75x = 517.5
As mentioned, we need to isolate x, so we divide both sides by 28.75. This will give the following.
x = 18
Hope this helps!
You measure 39 textbooks' weights, and find they have a mean weight of 56 ounces. Assume the population standard deviation is 9 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.
Give your answers as decimals, to two places
_____ < μ < _______
The 95% confidence interval for the true population mean is 53.18 < μ < 58.82
What is the 95% confidence interval?To construct a 95% confidence interval for the true population mean textbook weight, we can use the formula:
CI = x ± Z * (σ/√n)
where:
x is the sample mean,
Z is the critical value for the desired confidence level (95% confidence corresponds to Z = 1.96),
σ is the population standard deviation, and
n is the sample size.
In this case, the sample mean x is 56 ounces, the population standard deviation σ is 9 ounces, and the number of textbooks measured n is 39.
Plugging these values into the formula, we have:
CI = 56 ± 1.96 * (9/√39)
Calculating the values:
CI = 56 ± 1.96 * (9/√39)
CI = 56 ± 1.96 * (9/6.24)
CI = 56 ± 1.96 * 1.44
CI = 56 ± 2.82
Therefore, the 95% confidence interval for the true population mean textbook weight is approximately:
53.18 < μ < 58.82
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What is the monthly payment for an $8,720 loan at 12.5 percent for 15 years?
$107.43
$10,617.40
$16,088.40
$19,337.40
The monthly payment for an $8,720 loan at 12.5 percent for 15 years is $312.84
How to calculate the compound interestThe formula for calculating the compound interest is expressed as:
A = P(1+r/n)^nt
Given
P = $8720
r = 12.5% = 0.125
n = 12
t = 15
Substitute
A = 8720(1+0.125/12)^180
A = 1.8622 * 8720
A = $56,312.74
Monthly payment = 56,312.74/180
Monthly payment = 312.84
Hence the monthly payment for an $8,720 loan at 12.5 percent for 15 years is $312.84
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2x + y = 2
x – 2y = -4
what is x and y?
Answer:
x = 0
y = 2
Step-by-step explanation:
2x + y = 2 (Multiply by 2)
x – 2y = -4
4x + 2y = 4
x – 2y = -4
5x = 0
x = 0
2x + y = 2
2(0) + y = 2
0 + y = 2
y = 2
Which is more, 8 yards or 24 feet?
Answer:
They are the same thing!
Step-by-step explanation:
8*3=24 (Because 1 yard is 3 feet)
24 = 24!
Answer:
8yd 24ft= 48ft 0.000000in
Step-by-step explanation:
A horse 64 feet from the center of a merry-go-round makes 27 revolutions. In order to travel the same distance, how many revolutions would a horse 16 feet from the center have to make?
carol is making baby blankets for her daughters twins. If one blanket needs 43/4 yd of fabric, how much fabric does carol need for two blankets?
Answer:
21 1/2 yd
Step-by-step explanation:
43/4 + 43/4 = 21 1/2 yd
Question is in picture
Answer:
the answer will be 14,3 ok but check it
Three coffees and two muffins cost a total of $7. Two
coffees and four muffins cost $8.
Let x = cost of coffees
Let y = cost of muffins
how do i write this in a system of linear equations?
Step-by-step explanation:
3 coffees + 2 muffins = $7
therefore,
[tex]3x + 2y = 7[/tex]
2 coffees + 4 muffins = $8
therefore,
[tex]2x + 4y = 8[/tex]
Answer:
i think in every coast we're adding two shillings in the first sentence the total was 5 and we paid $7 and in the second sentence the total was 8 dollars meaning we added to shillings.
Step-by-step explanation:
in my school we are taughtthat we shouldn't mix goats with sheeps so we this the same way we can't mix x and y so in my opinion I guess you can say x + y =to that amount of money at the end you paid if it's 8 dollars or 7 dollars. we can say x represents the coffees and y represents the muffins that's how I get it I hope you want to be angry with me. for example 3 + 2 equals to 7 .3 + 2 is 5 so we'll carry five to the other side of equals where we will make it be minus so we'll say 7 - 5 where will get 2
Pleaseee answer these two questions helppppp ill give you brainliest answer if you knowwww help pleaseeee
Answer:
The theoretical probabilty of the coin landing on tails is 50/50 so their is a 50% chance of it landing on tails so theoretically it would land on tails 15 out of 30 times
Step-by-step explanation:
Let f(x) = 2x–8 and g(x) = x + 2. Find f(g(x)) and g(f(x)).
Answer:
g(f(x)) = 2x - 6
f(g(x)) = 2x - 4
Step-by-step explanation:
g(f(x)) = 2x - 8 + 2
g(f(x)) = 2x - 6
f(g(x)) = 2(x + 2) - 8
f(g(x)) = 2x - 4
Answer: g ( 2 x − 8 ) = 2 x− 6
Step-by-step explanation: MAKE ME BRAINLIEST!!!!!
What is the solution to the initial value problem J²u(x, t) D.E.: J²u(x, t) Ət² = dx² I.C.: [u(x,0) = e-x² ut (x,0) = 0 Ans. u(x,t) = [e−(z−¹)² + e¯(x+t)²]. [infinity] < x
The solution to the given initial value problem is u(x,t) = [e−(z−¹)² + e¯(x+t)²]. [infinity] < x
Given Differential equation is J²u(x, t) Ət² = dx²I.
C is u(x,0) = e-x² and ut (x,0) = 0
We need to find the solution to the given initial value problem. The general solution to the given Differential equation is
u(x,t) = f1(x − t) + f2(x + t)
where f1 and f2 are arbitrary functions. We need to find the particular solution that satisfies the given initial conditions. Given intial condition,
u(x,0) = e-x² …………(1)
ut (x,0) = 0…………(2)
Let us find the value of f1(x) and f2(x) using the given intial condition,
From equation (1)u(x,0) = f1(x) + f2(x) = e-x²
Now, Differentiating f1(x) + f2(x) = e-x² w.r.t x, we getf1'(x) + f2'(x) = -2x ………..(3)
From equation (2)
ut (x,0) = f1'(x) + f2'(x) = 0
On solving the above two equations, we get
f1'(x) = x, f1(x) = ½x² + C1
and
f2'(x) = -x, f2(x) = ½x² + C2
Now, the particular solution is
u(x,t) = ½(x − t)² + C1 + ½(x + t)² + C2
u(x,t) = (x² + t² + C1 + C2)………….(4)
Using the initial condition u(x,0) = e-x² in equation (4)
e-x² = x² + C1 + C2
Now, we know that for large value of x, the term e-x² becomes negligible. So, C1 + C2 = 0 ⇒ C2 = -C1
Substituting C2 = -C1 in equation (4), we get
u(x,t) = [e−(z−¹)² + e¯(x+t)²]. [infinity] < x
The solution to the given initial value problem is u(x,t) = [e−(z−¹)² + e¯(x+t)²]. [infinity] < x.
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Find the value of x, then find each angle measure.
Answer:
x = 9
m<J = 57
m<K = 44
m<L = 79
Step-by-step explanation:
Theorem:
The sum of the measures of the angles of a triangle is 180°.
We add the measures of the angles, and set the sum equal to 180. Then we solve for x, and use the value of x to find the measure of each angle.
7x - 6 + 3x + 17 + 9x - 2 = 180
Combine like terms on the left side: 7x + 3x + 9x = 19x and -6 + 17 - 2 = 9
19x + 9 = 180
Subtract 9 from both sides.
19x = 171
Divide both sides by 19.
x = 9
Now we find the measure of each angle.
m<J = 7x - 6 = 7(9) - 6 = 63 - 6 = 57
m<K = 2x + 17 = 3(9) + 17 = 27 + 17 = 44
m<L = 9x - 2 = 9(9) - 2 = 81 - 2 = 79
Please help me!!! I will try to mark brainliest if the answer is correct!
Answer:
I think the first is answer bcz 35+55=90 ..... 180-90=90
7 2/3 +-5 1/2+8 3/4 solve.
Answer:
big shaq
Step-by-step explanation:
. Find the area under the standard normal curve. from z = 0 to z = 1.46 from z = -0.32 to z = 0.98 from z = 0.07 to z = 2.51 to the right of z = 2.13 to the left of z = 1.04|
The areas under the standard normal curve are:
From z = 0 to z = 1.46: approximately 0.4306From z = -0.32 to z = 0.98: approximately 0.6126From z = 0.07 to z = 2.51: approximately 0.4959To the right of z = 2.13: approximately 0.0161To the left of z = 1.04: approximately 0.8508What is the area under the standard normal curve?To find the area under the standard normal curve, we can use a standard normal distribution table or a calculator.
Area from z = 0 to z = 1.46:
Using a calculator, the area under the curve from z = 0 to z = 1.46 is 0.4306.
Area from z = -0.32 to z = 0.98:
Using a calculator, the area under the curve from z = -0.32 to z = 0.98 is 0.6126.
Area from z = 0.07 to z = 2.51:
Using a calculator, the area under the curve from z = 0.07 to z = 2.51 is 0.4959.
Area to the right of z = 2.13:
Using a calculator, the area to the right of z = 2.13 is 0.0161.
Area to the left of z = 1.04:
Using a calculator, the area to the left of z = 1.04 is 0.8508.
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