As per the travelling distance, if they meet in hours, then the rate of each cyclist is r₂ miles per hour.
Let's assume that the two towns are A and B, and the distance between them is d miles. Let the first cyclist start from town A and travel towards town B, and the second cyclist start from town B and travel towards town A. Let's also assume that the first cyclist travels at a rate of r₁ miles per hour, and the second cyclist travels at a rate of r₂ miles per hour.
Now, let's consider the time it takes for the two cyclists to meet. Since they are traveling towards each other, their combined speed is (r₁ + r₂) miles per hour. We can use the formula:
distance = speed × time
to find the time it takes for them to meet. Let t be the time taken for them to meet, then we can write:
d = (r₁ + r₂) × t
where d is the distance between the two towns.
Now, we need to solve for r₁ and r₂. We can use the fact that the two cyclists meet in hours to write:
t = d / (r₁ + r₂)
Substituting this expression for t in the equation we got earlier, we get:
d = (r₁ + r₂) × (d / (r₁ + r₂))
Simplifying this equation, we get:
r₁ + r₂ = d / t
Substituting the value of t, we get:
r₁ + r₂ = d / (d / (r₁ + r₂))
r₁ + r₂ = (r₁ + r₂)
This equation tells us that the sum of the rates of the two cyclists is equal to the distance between the two towns divided by the time it takes for them to meet.
We can now use algebra to solve for r₁ and r₂. Let's assume that r₁ is the faster cyclist, then we have:
r₁ = (d / t) - r₂
Substituting the value of t, we get:
r₁ = (d / (d / (r₁ + r₂))) - r₂
Simplifying this equation, we get:
r₁ = (r₁ + r₂) - r₂
r₁ = r₁
This equation tells us that the rate of the faster cyclist is equal to itself, which is obvious.
Now, we can find the rate of the slower cyclist by using the fact that:
r₂ = (d / t) - r₁
Substituting the value of t, we get:
r₂ = (d / (d / (r₁ + r₂))) - r₁
Simplifying this equation, we get:
r₂ = (r₁ + r₂) - r₁
r₂ = r₂
This equation tells us that the rate of the slower cyclist is also equal to itself, which is obvious.
Therefore, we can conclude that the rate of the faster cyclist is r₁ miles per hour, and the rate of the slower cyclist is r₂ miles per hour, where:
r₁ = (d / t) - r₂
r₂ = (d / t) - r₁
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traffic accidents at a particular intersection in campustown follow a poisson distribution with an average rate of 1.4 per week. (a) find the exact calculation using the poisson distribution for the probability that there would be exactly 70 accidents at this intersection in one year (i.e., 52 weeks). (b) find an approximation using the normal distribution for the probability that there would be exactly 70 accidents at this intersection in one year (i.e., 52 weeks).
The exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.
What is Prοbability ?Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.
(a) Tο find the exact prοbability that there wοuld be exactly 70 accidents at the intersectiοn in οne year, we can use the Pοissοn distributiοn fοrmula:
P(X = k) =( [tex]e^{(-λ)[/tex] * [tex]λ^k[/tex]) / k!
where X is the number of accidents, λ is the average rate of accidents per week (1.4), and k is the number of accidents we're interested in (70).
To find the probability of 70 accidents in one year, we need to adjust the value of λ to reflect the rate over a full year instead of just one week. Since there are 52 weeks in a year, the rate of accidents over a year would be 52 * λ = 72.8.
So, we have:
P(X = 70) = ([tex]e^{(-72.8)[/tex]* [tex]72.8^(70)[/tex]) / 70!
Using a calculatοr οr sοftware, we can evaluate this expressiοn and find that:
P(X = 70) ≈ 0.00382
Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.
(b) Tο use the nοrmal distributiοn as an apprοximatiοn, we need tο assume that the Pοissοn distributiοn can be apprοximated by a nοrmal distributiοn with the same mean and variance. Fοr a Pοissοn distributiοn, the mean and variance are bοth equal tο λ, sο we have:
mean = λ = 1.4
variance = λ = 1.4
Tο use the nοrmal apprοximatiοn, we need tο standardize the Pοissοn randοm variable X by subtracting the mean and dividing by the square rοοt οf the variance:
[tex]Z = (X - mean) / \sqrt{(variance)[/tex]
Fοr X = 70, we have:
Z = (70 - 1.4) / [tex]\sqrt{(1.4)[/tex] ≈ 57.09
We can then use a standard nοrmal table οr calculatοr tο find the prοbability that a standard nοrmal randοm variable is greater than οr equal tο 57.09. This prοbability is extremely small and practically 0, indicating that the nοrmal apprοximatiοn is nοt very accurate fοr this particular case.
Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.
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The approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
(a) Using the Poisson distribution, the probability of exactly 70 accidents at this intersection in one year (i.e., 52 weeks) is:
P(X = 70) = (e^(-λ) * λ^x) / x!
where λ = average rate of accidents per week = 1.4
and x = number of accidents in 52 weeks = 70
Therefore, P(X = 70) = (e^(-1.4) * 1.4^70) / 70! ≈ 3.33 x 10^-23
(b) We can use the normal approximation to the Poisson distribution to approximate the probability that there would be exactly 70 accidents at this intersection in one year. The mean of the Poisson distribution is λ = 1.4 accidents per week, and the variance is also λ, so the standard deviation is √λ.
To use the normal distribution approximation, we need to standardize the Poisson distribution by subtracting the mean and dividing by the standard deviation:
z = (x - μ) / σ
where x = 70, μ = 1.452 = 72.8, σ = √(1.452) ≈ 6.37
Now we can use the standard normal distribution table to find the probability that z is less than or equal to a certain value, which corresponds to the probability that there would be exactly 70 accidents at this intersection in one year:
P(X = 70) ≈ P((X-μ)/σ ≤ (70-72.8)/6.37)
≈ P(Z ≤ -0.44)
≈ 0.3300
Therefore, the approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.
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can you please answer this for me
Answer:
x = 8
Step-by-step explanation:
the angle between the tangent and the radius at the point of contact A is 90°
then Δ ABP is right at A
using Pythagoras' identity in the right triangle
BP² = AP² + AB² , that is
(x + 9)² = x² + 15² ← expand parenthesis on left side using FOIL
x² + 18x + 81 = x² + 225 ( subtract x² from both sides )
18x + 81 = 225 ( subtract 81 from both sides )
18x = 144 ( divide both sides by 18 )
x = 8
Create multiple A line with a slope of 4 and y-intercept -6. a. representations of each line described below. b. A line with a slope of that passes through the point (5,7). 2 C. Any line parallel to the line in part (b). d. A line perpendicular to the line in part (b), passing through the origin.
After following all the listed steps, you can determine that it will be a graph with lines going through the y-int of -6.
Anyone know how to do this?
The value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.
Explain about the angle bisector theorem?Angles are measurements created by joining two lines, also known as the vertex. Geometric forms such as triangles but also rectangles contain internal angles produced by their sides.
The sum of the internal angles of each geometric figure gives it a general size. We can do operations like bisecting an angle geometrically.Every angle that is bisected is split into two equal-sized angles. Starting at the vertex that makes up the primary angle, the bisector is drawn.Using the angle bisector theorem in the given triangles:
The ratios of the sides will be equal.
AB / BC = AD / DC
AB = 9 ; BC = 11.7 AD = 3.6
Put the values.
9/11.7 = 3.6 / AD
AD = 3.6*11.7 / 9
AD = 4.68
Thus, the value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.
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i need help with work attached
The equation of the polynomial using finite difference is y = 18x^3 - 126x^2 + 269x - 163 and other solutions are shown below
Finding the equation of the polynomialTo find the equation of the polynomial table using finite difference, we need to calculate the differences.
The differences are obtained by subtracting each value of y from the next value of y and this is repeated for the differences
So, we have
x 1 2 3 4 5
y -2 15 -4 49 282
1st 17 -19 53 233
2nd -36 72 180
3rd 108 108
Since the third differences are all the same, this indicates that the original data can be represented by a cubic polynomial.
We can use the formula for a cubic polynomial:
y = ax^3 + bx^2 + cx + d
Using the table of values, we have:
a + b + c + d = -2
8a + 4b + 2c + d = 15
27a + 9b + 3c + d = -4
64a + 16b + 4c + d = 49
Using a graphing calculator, we have
a = 18, b = -126, c = 269 and d = -163
So, we have
y = 18x^3 - 126x^2 + 269x - 163
Equations of the cubic polynomialWe can use the formula for a cubic polynomial:
y = a(x - x1)(x - x2)(x - x3)
Using the ordered pairs, we have:
y = a(x + 3)(x + 1)(x - 2)
At (0, -12), we have
a(0 + 3)(0 + 1)(0 - 2) = -12
a = 2
So, we have
y = 2(x + 3)(x + 1)(x - 2)
Expand
y = 2x^3 + 4x^2 - 10x - 12
Equations of the cubic polynomialWe can use the formula for a cubic polynomial:
y = a(x - x1)(x - x2)(x - x3)
Using the ordered pairs, we have:
y = a(x + 10)(x + 5)(x - 4)
At (-8, -2), we have
a(-8 + 10)(-8 + 5)(-8 - 4) = -2
a = -1/36
So, we have
y = -1/36(x + 10)(x + 5)(x - 4)
Expand
[tex]y = -\frac{x^3}{36}-\frac{11x^2}{36}+\frac{10x}{36}+\frac{200}{36}[/tex]
The number of solutions in g(x)We have
g(x) = -9x^5 + 3x^4 + x^2 - 7
g(x) is a polynomial function of odd degree (5), so it will have at least one real root.
Also, the leading coefficient is negative;
So, g(x) has at least one root in the interval (-∞, ∞).
Since g(0) = -7 < 0 and g(1) = -12 < 0, and g(x) is continuous, there exists a root of g(x) in the interval (0, 1).
Similarly, since g(-1) = 6 > 0 and g(-2) = 333 > 0, there exists a root of g(x) in the interval (-2, -1).
Since g(x) is a polynomial of odd degree, it cannot have an even number of real roots.
Therefore, g(x) has exactly one real root.
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Which statement is true about the local minimum of the graphed function?
Answer:
Step-by-step explanation:
The local minimum value of a graph is the point where the graph changes from a decreasing function to an increasing function.
Maya is cutting strips of fabric to use when she makes a basket. She cuts a strip of fabric that is 9 1/3 yards long into pieces that are 2/3 yards long.
How many 2/3-yard long pieces can she cut from the strip of fabric?
A. 9 2/3
B. 9 1/3
C. 14
D. 6 2/9
Answer:
Step-by-step explanation:
Cathy had 6 different softball uniforms: 2 red short sleeve, a black long sleeve, 2 gold short sleeve, and a gold long sleeve. What is the probability of Carrie randomly selecting a gold short sleeve top on Monday, not replacing it, and then randomly selecting a red short sleeve tank on Tuesday?
The probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday is 2/15.
To find the probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday, we need to multiply the probabilities of these two events occurring.
The probability of selecting a gold short sleeve top on Monday is 2/6, or 1/3. There are 2 gold short sleeve tops out of a total of 6 uniforms.
After selecting a gold short sleeve top on Monday and not replacing it, there are 5 uniforms left, of which 2 are red short sleeve tanks. Therefore, the probability of selecting a red short sleeve tank on Tuesday is 2/5.
To find the probability of both events occurring, we multiply the probabilities together:
(1/3) * (2/5) = 2/15
Therefore, the probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday is 2/15.
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stion 6 of 10
A circular fence is being used to surround a goldfish pond as shown.
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7.25 m
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I'm sorry, but I don't see a question or any context for your statement. Could you please provide more information or clarify your request?
then what is the value of
M-N?
The value of M - N is [tex]8x^2[/tex] + 11x - 9 by subtracting the value of N from the value of M.
To find the value of M - N, we first need to subtract the second polynomial N from the first polynomial M.
M - N = ([tex]5x^2[/tex] + 7x - 4) - ([tex]-3x^2[/tex] - 4x + 5)
To subtract the polynomials, we need to add the opposite of the second polynomial (i.e., add the negative of N) to the first polynomial M:
M - N = [tex]5x^2[/tex] + 7x - 4 + [tex]3x^2[/tex] + 4x - 5
Now we can combine like terms:
M - N = ([tex]5x^2 + 3x^2[/tex]) + (7x + 4x) + (-4 - 5)
M - N = [tex]8x^2[/tex] + 11x - 9
Therefore, the value of M - N is [tex]8x^2[/tex] + 11x - 9.
In summary, we found the value of M - N by subtracting the polynomial N from the polynomial M and then combining like terms. The resulting polynomial is [tex]8x^2[/tex] + 11x - 9.
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Assume these triangles are similar. What is the value of x? :))))
The value of x in the given similar triangles is 30.8.
What are similar triangles?If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.
Similar figures are described as items with the same shape but varying sizes, such as two or more figures. A hula hoop and the wheel of a bicycle are two examples of things whose forms are similar to one another.
Given that the triangles are similar, thus the ratio of their sides are equal.
Here, 28/10 = x / 11
Using cross multiplication we have:
x = 28 / 10 (11)
x = 30.8
Hence, the value of x in the given similar triangles is 30.8.
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(X+3)(X-8) = -30 solve using the quadratic formula
Answer:
X = 3,2
Step-by-step explanation:
1)Expand.
[tex]x^{2}[/tex] - 8X+3X - 24 = -30
2)Simplify [tex]x^{2}[/tex]-8X+3X-24 to [tex]x^{2}[/tex]-5X - 24.
[tex]x^{2}[/tex] – 5X – 24 = –30
3)Move all terms to one side.
[tex]x^{2}[/tex] - 5X - 24+ 30 = 0
4)Simplify [tex]x^{2}[/tex]–5X-24+30 to [tex]x^{2}[/tex] - 5X + 6.
[tex]x^{2}[/tex] - 5X + 6 = 0
5)Factor [tex]x^{2}[/tex]–5X+6.
(X-3)(X-2) = 0
6)Solve for X.
X = 3,2
Question 17 A grain silo has a cylindrical shape. Its radius is 3.5 ft, and its height is 35 ft. Answer the parts below. Make sure that you use the correct units in your answers. X Progress: 0/2 Part 1 of 2 3.5 ft Next Question 35 ft (a) Find the exact volume of the silo. Write your answer in terms of it.
Answer:
428.75π ft³
Step-by-step explanation:
You want the exact volume of a cylinder 35 ft high with a radius of 3.5 ft.
VolumeThe volume is given by the formula ...
V = πr²h
V = π(3.5 ft)²(35 ft) = 428.75π ft³ . . . . . use the given values
The exact volume of the cylinder is 428.75π ft³.
during the 2020 census, jerome was given a geographical area that he was in charge of surveying. on one particular street with 10 homes, he was instructed to interview the residents at 3 of the homes. how could jerome choose a simple random sample of these houses to interview? he plans to visit the homes at 10:00 am. if someone is not home, what should he do?
To choose a simple random sample assign different numbers to the house and visit by choosing randomly.
To choose a simple random sample of the 3 homes to survey,
Jerome could assign each home a number from 1 to 10,
And then use a random number generator or a table of random numbers to select three numbers.
He would then visit the homes corresponding to those numbers for the survey.
For example,
if he assigned the following numbers to each home,
1, 2, 3, 4, 5, 6, 7, 8, 9 ,10
He could use a random number generator or table of random numbers to select three numbers, such as 2, 5, and 9.
He would then visit the homes at 2, 5, 9 for the survey.
If someone is not home when Jerome visits,
He should make a note of it and try to arrange a time to come back and conduct the survey.
If it is not possible to arrange another time,
He should make a note that the household was not surveyed and move on to the next household in the sample.
It is important to keep track of which households were surveyed and which were not.
And to try to minimize any biases that may arise from nonresponse.
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The measures of the angles of a triangle are shown in the figure below. Solve for x. (2x+10) 36
please help with solving find the value of k and the two roots of x
The approximate value of K of the given quadratic equation is: 16.842
How to solve Quadratic equations?The general expression of a quadratic function is:
ax² + bx + c = 0
The quadratic formula to find the roots is expressed as:
x = [-b ± √(b² - 4ac)]/2a
The product of the 2 roots of the quadratic equation is equal to the constant term.
Let a and b be used to denote the roots of a given quadratic equation.
But according to given condition, one root is equal to the square of the other root. Thus: b = a²
Thus:
a + a² = k
a * a² = 48
a³ = 48
a = 2∛6
Thus:
2∛6 + (2∛6)² = k
k = 16.842
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please please help me super quickkk
Answer:
C
Step-by-step explanation:
What is the domain of the function y = 2x²? To answer the question, ask yourself if there
are any restrictions on the values you may substitute for x.
Answer:
Step-by-step explanation:
Any value of x may be substituted into this function. So the domain is:
[tex]D=(-\infty , \infty)[/tex] or D=all real [tex]x[/tex]
I am not sure the format how you have been taught to write the answer.
[Questions in the image]
Answer:
a) 675
b) 12
c) y = 12x + 675
d) y = 12 (500) + 675 = $6,675
how does a snak moove with no legs
Answer: it slithers
Step-by-step explanation:
To further explain it They move by dragging their body throughout in the form of loops. Hence, snakes have a crawling or slithering type of movement
Answer:
Overlapping belly scales provide friction with the ground that gives snakes a preferred direction of motion, like the motion of wheels or ice skates.
Step-by-step explanation:
Hope this helps! =D
Mark me brinaliest!=D
Choose ALL answers that describe the polygon ABCD if measure A is congruent to measure B, and measure C is congruent to measure D.
and segment Ab is parallel to segment CD
Parallelogram
Quadrilateral
Rectangle
Rhombus
Square
Trapezoid
The answers that describe the polygon ABCD if measure A is congruent to measure B, and measure C is congruent to measure D, and segment AB is parallel to segment CD are;
A. Parallelogram
B. Quadrilateral
C. Rectangle
D. Rhombus
E. Square
What is a parallelogram?In Mathematics, a parallelogram simply refers to a four-sided geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that is composed of two (2) equal and parallel opposite sides.
What is a rhombus?In Mathematics and Geometry, a rhombus is a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal).
In conclusion, a square, parallelogram, rectangle, rhombus, and quadrilateral satisfies the given conditions.
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Patricia has a savings account with $89 in it that earns 4.7% simple interest per year. How much money, to the nearest penny, will Patricia have in 5 years?
Answer:simpler interest is 109.92. Annual compounded interest is 111.98
Step-by-step explanation:
Answer: $209.2
Step-by-step explanation:
hey! i'm gonna try to make this as simple as possible;
with simple interest, the formula to this is I = PRT (Interest = Principle x Rate x Time).
we're going to take the $89 , 4.7% simple interest and the 5 years together into the same sentence like the formula.
89 (Principle, the money) x 4.7% (Interest rate) x 5 (Time). we'll narrow down the decimal by moving the decimal forward once so we get a decimal of .47 / 0.47.
back to the equation, it is now 89 x .47 x 5. multiply all those and you'll get a sum of 209.15! by the end of the five years, patricia will have $209.15. to the nearest penny, she will have $209.2. (5 or more, it goes to the next number. 4 or less, it stays in the same place.)
hope this helped :)
The sum of interior angles of a regular polygon is
1800⁰. Calculate the size of one exterior angle of
the polygon.
Answer:
36
Step-by-step explanation:
Anyone know how to do this
The missing value that completes the frequency table is 100.
How to find the missing value that completes the frequency table?A frequency table is a statistical tool that summarizes data by displaying the frequency (or count) of each category or interval in a data set. It is commonly used in data analysis to organize and understand categorical or numerical data.
The missing value is the frequency for the value range between 28 and 30 (i.e 28 ≤ x ≤30). Looking at the histogram, you will notice that the frequency for the value between 28 and 30 is 100 (Check the attached image).
Therefore, the missing value is 100.
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An 800 investment that earns 3% annual interest compound yearly for 4 years
The final amount earned on the investment after 4 years is $900.40.
An investment of $800 is made at an annual interest rate of 3% compounded yearly for 4 years. To calculate the final amount earned on the investment after 4 years, we can use the formula for compound interest:
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
where:
A = the final amount
P = the principal investment, which is $800 in this case
r = the annual interest rate, which is 3% or 0.03 as a decimal
n = the number of times the interest is compounded per year, which is once per year in this case
t = the number of years, which is 4 in this case
Plugging in the values, we get:
A = 800(1 + 0.03/1)¹ˣ⁴
A = 800(1.03)⁴
A = 800(1.1255)
A = $900.40
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1. Solve 8^2x=32^(x+3)
(a)Rewrite the equation using the same base.
(b)Solve for x. Remember to show all work
PLEASE SHOW ALL WORK FOR BRAINLIEST
(a) We can rewrite 32 as 2^5, so we have:
8^(2x) = (2^5)^(x+3)
Simplifying the right side, we get:
8^(2x) = 2^(5x+15)
(b) Now we can use the fact that 8 is 2^3, so we can rewrite the left side as (2^3)^(2x) = 2^(6x), giving us:
2^(6x) = 2^(5x+15)
Since the bases are equal, we can equate the exponents and solve for x:
6x = 5x + 15
x = 15
Therefore, the solution is x = 15.
Show that if AB = AC and A is nonsingular, then the cancellation law holds; is, B = C.
When AB = AC and A is nonsingular, then the cancellation law holds; is, B = C. The statement is true.
In matrix algebra, the cancellation law is a crucial property to know. It states that if AB = AC, then B = C when A is a nonsingular matrix.
The given statement is true, which means that if AB = AC and A are nonsingular, then B = C. The cancellation law in matrix algebra is a property that helps in solving linear equations involving matrices. It states that if AB = AC and A is a nonsingular matrix, then B = C.
Therefore, we can say that if AB = AC and A is nonsingular, then B = C is true.
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How does g(x)=3x change over the interval from x=8 to x=10?
The function g(x)=3^x change over the interval from x=8 to x=10 by a factor of 9
Changes in g(x)=3^x from x=8 to x=10The function g(x)=3^x is an exponential function. As x increases, the value of g(x) increases at an increasing rate.
Therefore, over the interval from x=8 to x=10, g(x) will increase at an increasing rate.
To see this, we can calculate g(8) and g(10) and observe the difference between the two values.
g(8) = 3^8 = 6561
g(10) = 3^10 = 59049
So, the rate is
Rate = 59049/6561
Rate = 9
This means that the rate is by a factor of 9
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distribute and simplify the following: (v+8)•(v+9)
Answer:
(v+8) x (v+9)
We can multiply v into the other two terms in the second bracket, then we can do the same with 8.
(v*v + v*9) + (8*v + 8*9)
v² + 9v + 8v + 72
v² + 17v + 72.
a random digit dialing sample of 2092 adults found that 1318 used the internet. of the users, 1041 said that they expect businesses to have web sites that give product information. in your business economics class at school, your teacher said that 80% of all internet users believe this. what is the appropriate z-value to use in this situation?
The appropriate z-value to use in the situation given in the question is 1.28.
Given,Total number of adults in the sample = 2092
Number of adults using the internet = 1318
Number of internet users who expect businesses to have websites that give product information = 1041
Probability of internet users who expect businesses to have websites that give product information as per the teacher's statement = 80% = 0.8
To find the appropriate z-value to use in this situation, we need to calculate the standard error of proportion, which is given by:
SEp = √[p(1-p)/n]
where p is the proportion of internet users who expect businesses to have websites that give product information and n is the sample size.
Substituting the given values in the formula,
SEp = √[(1041/1318)(1-1041/1318)/1318]SEp = 0.019
z-value is given by:
z = (p - P)/SEp
where P is the proportion of internet users who expect businesses to have websites that give product information as per the teacher's statement.
Substituting the given values in the formula,
z = (0.8 - 1041/1318)/0.019
z = - 1.28
The appropriate z-value to use in this situation is -1.28.
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