The value of c that satisfies the condition is -6. To find the values of c such that the area of the region bounded by the parabolas y = 16x^2 - c^2 and y = c^2 - 16x^2 is 18.
We can set up an integral to calculate the area between the two curves.
The area between the curves can be found by integrating the difference between the upper and lower curves with respect to x over the interval where the curves integral
Let's set up the integral:
A = ∫[a,b] (upper curve - lower curve) dx
In this case, the upper curve is y = 16x^2 - c^2 and the lower curve is y = c^2 - 16x^2.
To find the values of a and b, we need to set the two curves equal to each other and solve for x.
16x^2 - c^2 = c^2 - 16x^2
Adding 16x^2 to both sides:
32x^2 = 2c^2
Dividing both sides by 2:
16x^2 = c^2
Taking the square root of both sides:
4x = ±c
Solving for x:
x = ±(c/4)
Now, we need to find the values of c that satisfy the condition where the area is 18. We set up the integral and solve for c:
18 = ∫[c/4, -c/4] [(16x^2 - c^2) - (c^2 - 16x^2)] dx
Simplifying:
18 = ∫[c/4, -c/4] (32x^2 - 2c^2) dx
Evaluating the integral:
18 = [32/3 * x^3 - 2c^2 * x] evaluated from c/4 to -c/4
Simplifying further:
18 = (32/3 * (-c/4)^3 - 2c^2 * (-c/4)) - (32/3 * (c/4)^3 - 2c^2 * (c/4))
Simplifying and solving for c:
18 = (c^3/24 - c^3/8) - (c^3/24 + c^3/8)
18 = -c^3/12 - c^3/12
36 = -c^3/6
c^3 = -216
Taking the cube root:
c = -6
Therefore, the value of c that satisfies the condition is -6.
So the answer is -6.
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What is the one shape of cross-section we could create by slicing the cylinder perpendicular to its base
Answer:
rectangle
Step-by-step explanation:
A rectangle represents a figure with four sides having equal opposite sides and the inside angle between the two adjacent sides is ninety degree.
When any plane is made to pass through the cylinder creating a cross section which is perpendicular to its base, it results a two-dimensional cross sectional shape of a rectangle.
Find the distance between the points (–8,10) and (4,10).
Answer:
12
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√[4 - (-8)]² + (10 - 10)²
√(12)² + (0)²
√144 + 0
√144
=12
Bacteria triples every 3 hours. If there are 450 bacteria at t=0
min how many after 200 min
Therefore, the number of bacteria after 200 minutes can be found by multiplying the initial number of bacteria (450) by the tripling factor (3) raised to the power of 2 (for the full cycles) and multiplying by the remaining fraction of the tripling factor for the partial cycle.
Since the bacteria triples every 3 hours, we can calculate the number of tripling cycles that have occurred in 200 minutes. Since 3 hours is equivalent to 180 minutes, there are 2 full cycles in 200 minutes. To calculate the remaining fraction of the tripling cycle, we divide the remaining time (20 minutes) by the length of a single cycle (180 minutes). The fraction is 20/180, which simplifies to 1/9.
Now, we can calculate the number of bacteria after 200 minutes. We start with the initial number of bacteria, which is 450, and multiply it by the tripling factor (3) raised to the power of the number of full cycles (2). This accounts for the full cycles. Then, we multiply this result by the remaining fraction of the tripling factor (1/9) to account for the partial cycle.
Therefore, the number of bacteria after 200 minutes can be calculated as follows:
Number of bacteria = 450 * (3^2) * (1/9) = 450 * 9 * (1/9) = 450
Hence, after 200 minutes, there will still be 450 bacteria.
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The odds against a certain football team winning the championship are 70 : 1. a) Determine the probability that the team wins the championship. b) Determine the probability that the team does not win the championship.
a) The probability that the team wins the championship is approximately 0.0141 or 1.41%. b) The probability that the team does not win the championship is approximately 0.9859 or 98.59%.
a) To determine the probability that the team wins the championship, we need to convert the odds against winning into a probability.
The odds against winning are given as 70:1. This means that for every 70 unfavorable outcomes (losing), there is 1 favorable outcome (winning).
To calculate the probability of winning, we divide 1 by the sum of the favorable and unfavorable outcomes:
Probability of winning = 1 / (70 + 1) = 1 / 71 ≈ 0.0141 (or 1.41%)
Therefore, the probability that the team wins the championship is approximately 0.0141 or 1.41%.
b) The probability of not winning the championship is equal to 1 minus the probability of winning:
Probability of not winning = 1 - 0.0141 = 0.9859 (or 98.59%)
Therefore, the probability that the team does not win the championship is approximately 0.9859 or 98.59%.
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Function f is a quadratic function passing through the points (-4,0),(0,–12) and (3,0). Function g is modeled by the graph. Over which interval are both functions negative?
Answer:
Open points on 1 and 3 with ray connecting them
Step-by-step explanation:
Because it's right.
Answer:
Step-by-step explanation:
Let A and B be disjoint compact subspaces of a Hausdorff space X. Show that there exist disjoint open sets U and V, with ACU and BCV.
In Hausdorff-space "X", if A and B are disjoint "compact-subspaces", then there is disjoint "open-sets" U and V such that A is contained in U and B is contained in V, this is because by Hausdorff-Property, the existence of disjoint open neighborhoods for any two "distinct-points".
To prove the existence of disjoint "open-sets" U and V with A⊂U and B⊂V, where A and B are "compact-subspaces" of "Hausdorff-space" X,
Step (1) : A and B are disjoint compact-subspaces, we use Hausdorff property to find "open-sets" Uₐ and [tex]U_{b}[/tex] such that "A⊂Uₐ" and "B⊂[tex]U_{b}[/tex]", and "Uₐ∩[tex]U_{b}[/tex] = ∅". This can be done for every pair of points in A and B, respectively, because X is Hausdorff.
Step (2) : We consider, set U = ⋃ Uₐ, where "union" is taken over all of Uₐ for each-point in A. U is = union of "open-sets", hence open.
Step (3) : We consider set V = ⋃ [tex]U_{b}[/tex], where union is taken over for all [tex]U_{b}[/tex] for "every-point" in B. V is also a union of open-sets and so, open.
Step (4) : We claim that U and V are disjoint. Suppose there exists a point x in U∩V. Then x must be in Uₐ for some point a in A and also in [tex]U_{b}[/tex] for some point b in B. Since A and B are disjoint, a and b are different points. However, this contradicts the fact that Uₐ and [tex]U_{b}[/tex] are disjoint open sets.
Therefore, U and V are disjoint open sets with A⊂U and B⊂V.
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The given question is incomplete, the complete question is
Let A and B be disjoint compact subspaces of a Hausdorff space X. Show that there exist disjoint open sets U and V, with A⊂U and B⊂V.
solve for x to the nearest
Answer:
in right angled triangleBCD
BC=√{DC²-BC²)=√{10²-6²)=8
again in right angled triangle ABC
AB=√(BC²-AC²)
x=√(8²-7²)=3.87
sales tax: 68% shirts: $35 pants: $27 shoes: $44 what is the total cost
Help with question 3 please I’ll give brainlest
Answer: b
Step-by-step explanation: When you rotate it around the axis (think of it as a pole) it will become a cylinder with radius 5
what is 4836 divided by 9735829 plus 28369 times 284383?
Answer:
2.28871.0005^14
Step-by-step explanation:
Answer:
i got 8067661468.26
Step-by-step explanation:
What is the area of a rectangle with side lengths 2/5 feet and 4/6 feet?
Answer:
[tex]\frac{4}{15}[/tex] (4/15)
Step-by-step explanation:
[tex]\frac{4}{6}=\frac{2}{3}[/tex]
[tex]\frac{2}{5}*\frac{2}{3};[/tex]
1- Multiply the numerators:
[tex]2*2=4[/tex]
2- Multiply the denominators:
[tex]5*3=15[/tex]
3- Thus:
[tex]\frac{2}{5}*\frac{2}{3}= \frac{4}{15}[/tex]
Hope this helps ;)
Consider the derivation of the quadratic formula below. What is the missing radicand
in Step 6?
Answer:
[tex]\frac{b^2 - 4ac}{4a^2}[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required:
Complete step 6
At step 5, we have:
[tex](x + \frac{b}{2a})^2 = \frac{b^2}{4a^2} - \frac{4ac}{4a^2}[/tex]
Take LCM
[tex](x + \frac{b}{2a})^2 = \frac{b^2 - 4ac}{4a^2}[/tex]
Take square roots of both sides to get step 6
[tex]x + \frac{b}{2a} = \±\sqrt{\frac{b^2 - 4ac}{4a^2}}[/tex]
Hence, the missing radicand is: [tex]\frac{b^2 - 4ac}{4a^2}[/tex]
2/6, 5/12, 3/7, and 4/10. List least to most
If Y is inversely proportional to x and y=4 when x= 100, what is the value of y when x=250
Answer:
y=10
Step-by-step explanation:
[tex]\frac{4}{100}[/tex]=[tex]\frac{y}{250}[/tex]
cross-multiply, 4*250=100y
isolate the variable and solve for y, 1000=100y
divide 100 on both sides, 10=y
A fresh food distributor receives orders from 100 customers daily. Assume that the quantities ordered by customers, in kg, are independent continuous random variables uniformly distributed over the interval (0, 9). Assuming that the distributor only has the capacity to ship 477 kg of products daily, calculate the probability that all orders are fulfilled on a day chosen at random. Indicate the result to at least four decimal places.
The probability that all orders are fulfilled on a day chosen at random is approximately 1. Answer: 1.0000 (rounded off to at least four decimal places).
The quantities ordered by customers are independent continuous random variables, and they are uniformly distributed over the interval (0, 9).
The fresh food distributor only has the capacity to ship 477 kg of products daily, and the distributor receives orders from 100 customers daily.
The probability that all orders are fulfilled on a day chosen at random is given by;P(all orders fulfilled) = P(X1 + X2 + ... + X100 < 477)
where X is the quantity ordered by each customer. Since X is a continuous random variable, we can use the probability density function of a uniform distribution to calculate the probability density function of X as;f(x) = 1/9, 0 < x < 9
Hence, the probability that all orders are fulfilled on a day chosen at random is given by;
P(all orders fulfilled) = P(X1 + X2 + ... + X100 < 477)= P[(X1/9) + (X2/9) + ... + (X100/9) < (477/9)]= P[U < (53 + 1/3)], where U ~ Uniform(0, 1)
Now, using the central limit theorem, we can approximate the distribution of U by a normal distribution with mean μ = 1/2 and variance σ^2 = 1/12 such that;Z = (U - μ) / σ ~ N(0, 1)
Hence, P[U < (53 + 1/3)] = P[Z < (53 + 1/3 - μ) / σ]= P[Z < (53 + 1/3 - 1/2) / sqrt(1/12)]≈ P[Z < 9.6067]≈ 1
Thus, the probability that all orders are fulfilled on a day chosen at random is approximately 1. Answer: 1.0000 (rounded off to at least four decimal places).
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43 - u = 69
how much is u?
Answer:
69-43= 26
therefore "U" is worth 26 U=26
Step-by-step explanation:
Answer:
its 26, because whaen u subtract 43 from 69 u will get 26
the acceleration of an oscillator undergoing simple harmonic motion is described by the equation ax(t)=−(18m/s2)cos(33t) , where the time t is measured in seconds.
The equation [tex]ax(t) = -(18 m/s^2)cos(33t)[/tex] describes the acceleration of an oscillator. The acceleration varies sinusoidally with time, following a cosine function, and has a maximum value of [tex]-18 m/s^2[/tex].
The given equation [tex]ax(t) = -(18 m/s^2)cos(33t)[/tex] represents the acceleration of an oscillator undergoing simple harmonic motion. In this equation, t represents time measured in seconds.
The term cos(33t) indicates that acceleration varies sinusoidally with time. The cosine function has a period of 2π, meaning it completes one full cycle over the interval [0, 2π]. The coefficient 33 in front of t determines the frequency of oscillation. In this case, the oscillator completes approximately 33 cycles per second.
The negative sign indicates that the acceleration is directed opposite to the displacement of the oscillator. As the oscillator moves in one direction, the acceleration pulls it back in the opposite direction, causing it to oscillate around a stable equilibrium position.
The maximum acceleration is given by [tex]-18 m/s^2[/tex], which represents the amplitude of the oscillation. The acceleration varies between [tex]-18 m/s^2[/tex] and [tex]18 m/s^2[/tex], with the maximum magnitude occurring when the cosine function is at its peak value of 1 or -1.
Overall, the equation describes the acceleration of an oscillator undergoing simple harmonic motion, providing information about its amplitude, frequency, and direction of motion.
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You are making freshly squeezed orange juice for a brunch you are catering. You need to make 3 liters of orange juice; Oranges are purchases by the case for $24.Each case contains 100 oranges. Each orange weighs 6 ounces and has a yield percent, for juicing, of 50%. what is the edible portion cost for the orange juice for this brunch?
Answer : The edible portion cost for the orange juice for this brunch is $9.6.
Explanation :
GivenData: Cost of each case = $24 Number of oranges in each case = 100 Weight of each orange = 6 ounces Yield percentage of each orange = 50% Amount of orange juice required = 3 liters Formula used:To find the edible portion cost of orange juice, we need to find the cost per liter of orange juice and then multiply it by the required amount of orange juice.
Edible portion cost = (Cost per liter of orange juice) × (Amount of orange juice required) Cost per liter of orange juice = (Cost of 100 oranges) / (Yield of 100 oranges)Cost of 100 oranges = Cost of each case = $24 Therefore, Cost per liter of orange juice = (24) / [(50/100) × 100 × (6/16)]{Converting 6 ounces into liters by multiplying with 0.0166667}Cost per liter of orange juice = $3.20 Edible portion cost = (Cost per liter of orange juice) × (Amount of orange juice required)Edible portion cost = (3.2) × (3) = $9.6 Therefore, the edible portion cost for the orange juice for this brunch is $9.6.
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A guy wire supporting a radio tower is attached to the tower 128 feet above the ground. The wire makes a 45 degree angle with the ground. How long is the guy wire
Answer:
181 feet
Step-by-step explanation:
From the the diagram attached ,
Sinθ = a/b..................... Equation 1
Where θ = angle to the horizontal, a = Height of the tower, b = length of the wire.
make b the subject of the equation
b = a/sinθ................. Equation 2
Given: a = 128 feet, θ = 45°
Substitute these values into equation 2
b = 128/sin45°
b = 128/0.7071
b = 181 feet
b = 181 feet
a) The difference of the age of two sisters is 5 years and the product of their age is
24. Find the age of the two sisters.
Answer:
3 years old and 8 years old
Step-by-step explanation:
8-3=5
3x8=24
plz mark me as brainliest
Express (–1+iV3) and (-1 – iV3) in the exponential form to show that:
2nnt (-1+iV3)n +(-1 – iV3)n = 2n+1cos 3
The proof of 2ⁿ (-1 + i√3)ⁿ + (-1 - i√3)ⁿ can be expressed as 2ⁿ⁺¹cos(πn/3) is proved below.
To express (-1 + i√3) and (-1 - i√3) in exponential form, we can use Euler's formula, which states that [tex]e^{(i\theta)[/tex] = cos(θ) + isin(θ).
Let's start with (-1 + i√3):
(-1 + i√3) = 2 x (cos(π) + i x sin(π/3))
Now, let's simplify (-1 - i√3):
(-1 - i√3) = 2 (cos(π) - isin(π/3))
Therefore, we have:
(-1 + i√3) = 2 e^(iπ/3)
(-1 - i√3) = 2 e^(-iπ/3)
Now, let's substitute these exponential forms into the expression:
2ⁿ (-1 + i√3)^n + (-1 - i√3)^n
= 2ⁿ(2 e^(iπ/3))^n + (2 e^(-iπ/3))^n
= 2ⁿ⁺¹ e^(iπn/3) + 2^(n+1) e^(-iπn/3)
Using Euler's formula again, we know that [tex]e^{(i\theta)} + e^{(-i\theta)[/tex] = 2cos(θ).
Therefore, we can rewrite the expression as:
2ⁿ⁺¹ (cos(πn/3) + cos(-πn/3))
= 2ⁿ⁺¹(cos(πn/3) + cos(πn/3))
= 2ⁿ⁺¹ 2 cos(πn/3)
= 2ⁿ⁺¹cos(πn/3)
So, we have shown that 2ⁿ (-1 + i√3)ⁿ + (-1 - i√3)ⁿ can be expressed as 2ⁿ⁺¹cos(πn/3).
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2. How does the graph of the following function compare to the quadratic parent function? * (1 Point) 8 (x) = x2 + 5 Moves up 5 Moves down 5 Moves to the left 5 Moves to the right 5
Answer:
b
Step-by-step explanation:
oi did the quiz f. 6373737
Simplify 4(3n + 2b + k)
a. 12nbk
b. 12n + 2bk
c. 12n + 8b + 4k
d. 24bkn
Answer:
C
Step-by-step explanation:
4(3n+2b+k)
12n+8b+4k
So it would be C.
---
hope it helps
In a certain chemical, the ratio of zinc to copper is 3 to 14. Ajar of the chemical contains
546 grams of copper. How many grams of zinc does it contain?
It contains grams of zinc
Answer:
Given -
In a certain chemical, the ratio of zinc to copper is 4 to 13.
The chemical contains 546 grams of copper.
Prove -
How many grams of zinc does it chemical contain.
Answer
suppose that scalar multiple of the zinc and copper be y .
As given
In a certain chemical, the ratio of zinc to copper is 4 to 13.
The chemical contains 546 grams of copper.
Than equation is
13y = 546
13y = 546
y = 42
Zinc contain in the certain chemical = 4y
= 4 42
= 168 grams
Therefore 168 grams of zinc contain in a certain chemical .Step-by-step explanation:
A=4 B=7 C=11 D=13 Given this number line, cd=
Answer:
.
Step-by-step explanation:
i dont know this i really hard
Answer: 2
Step-by-step explanation:
Compute in the ancient Egyptian way: (b) 55÷6 (a) 26 ÷ 20 (c) 71 21 ÷ (d) 25 18 (e) 52 ÷ 68 (f) 13 36
Ancient Egyptian way of computation, division was performed using a method called "repeated subtraction." (a) 26 ÷ 20 = 1 remainder 6.
(b) 55 ÷ 6 = 9 remainder 19.
(c) 71 21 ÷ = 50 remainder 29.
(d) 25 18 ÷ = 7.
(e) 52 ÷ 68 = 0 remainder 52.
(f) 13 36 ÷ = 0 remainder -23.
In the ancient Egyptian way of computation, division was performed using a method called "repeated subtraction." Here's how it would be applied to the given divisions:
(a) 26 ÷ 20:
To divide 26 by 20, we repeatedly subtract 20 from 26 until we cannot subtract anymore. The number of times we subtract is the quotient.
26 - 20 = 6
6 - 20 = -14 (cannot subtract anymore)
Therefore, 26 ÷ 20 = 1 remainder 6.
(b) 55 ÷ 6:
Using the same method, we repeatedly subtract 6 from 55 until we cannot subtract anymore.
55 - 6 = 49
49 - 6 = 43
43 - 6 = 37
37 - 6 = 31
31 - 6 = 25
25 - 6 = 19 (cannot subtract anymore)
Therefore, 55 ÷ 6 = 9 remainder 19.
(c) 71 21 ÷:
To divide 71 21 by a number, we first convert it to a whole number by multiplying the fraction part by the denominator.
71 21 = 71 + (21/100) = 71 + 21/100
Now, we can perform division using repeated subtraction.
71 - 21 = 50
50 - 21 = 29 (cannot subtract anymore)
Therefore, 71 21 ÷ = 50 remainder 29.
(d) 25 18 ÷:
Similar to the previous case, we convert 25 18 to a whole number.
25 18 = 25 + (18/100) = 25 + 18/100
Performing division:
25 - 18 = 7
Therefore, 25 18 ÷ = 7.
(e) 52 ÷ 68:
Since 52 is smaller than 68, the quotient is 0.
Therefore, 52 ÷ 68 = 0 remainder 52.
(f) 13 36 ÷:
Converting to a whole number:
13 36 = 13 + (36/100) = 13 + 36/100
Performing division:
13 - 36 = -23 (cannot subtract anymore)
Therefore, 13 36 ÷ = 0 remainder -23.
Please note that the ancient Egyptian method of division is not as efficient as modern division methods and may not produce exact decimal results.
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Identify the like terms in the expression 4x+5-x^3-3x
Look at photo for the question and answer choices... NO LINKS OR BLANK ANSWERS
(also i added a cute/funny question aswell)
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Answer:
Rhombus Square
Step-by-step explanation:
Jim , a meteorologist for local television XYZ, would like to report the rainfall. The following are the rainfall measurements (in inches) for to-day’s date for 14 randomly chosen past years. The data are as follows: 0.47 0.27 0.13 0.54 0.08 1.05 0.34 0.26 0.42 0.17 0.50 0.86 0.01 2.5 NOTE: answers should be given to 2 decimal places REQUIRED 1. Find the RANGE of the data provided and what measure does this show 2. Calculate the sample variance . Why is variance not written in? 3. Calculate the sample standard deviation. What information does this measure give to the users? Why is it necessary to compute standard deviation instead of stopping at the variance calculation? 4. Find the COEFFICIENT OF VARIATION 5. Use Z-score to find if there is any outliers in the series
Where the above is given,
Range -2.49 inchesSample variance - 0.5599Sample standard deviation - 0.7483Coefficient of variation - 7497.32% Z14 = 3.3999, which is greater than 2, suggesting that the data point 2.50 inches may be considered an outlier based on the Z-Score criterion.What is the explanation for the above ?Range
Range = Maximum value - Minimum value
Range = 2.50 - 0.01
= 2.49 inches
Sample Variance
Step 1 - Calculate the mean (average) of the data.
Mean = (0.47 + 0.27 +0.13 + 0.54 + 0.08 + 1.05 + 0.34 + 0.26 + 0.42 + 0.17 + 0.50 + 0.86 + 0.01 + 2.5) / 14
= 1.36 /14
= 0.0971
Step 2 - Calculate the squared deviation from the mean for each data point.
Deviation from mean = Data point - Mean
Squared deviation = (Deviation from mean)²
Sum of squared deviations = (0.3739 + 0.0091 + 0.7307 + 0.1638 + 0.9469 + 0.104 + 0.0145 + 0.0081 + 0.0971 + 0.3037 + 0.0601 + 0.2601 + 1.0679 + 3.1391)
= 7.2799
Sample Variance = Sum of squared deviations / (n - 1)
= 7.2799/ (14 - 1)
= 0.5599
Sample Standard Deviation:
Sample Standard Deviation = √(Sample Variance)
= √0.5599
= 0.7483
Coefficient of Variation:
Coefficient of Variation = (Sample Standard Deviation / Mean) * 100
= (7.2799/ 0.0971) * 100
= 7497.32
Z-Scores for each data point
Z1= (0.47 - 0.0971)/ 0.7212= 0.5318
Z2= (0.27 - 0.0971)/ 0.7212= 0.9983
Z3= (0.13 - 0.0971)/ 0.7212= 0.0456
Z4= (0.54 - 0.0971)/ 0.7212= 0.6189
Z5= (0.08 - 0.0971)/ 0.7212= -0.0251
Z6= (1.05 - 0.0971)/ 0.7212= 1.2914
Z7= (0.34 - 0.0971)/ 0.7212= 0.4574
Z8= (0.26 - 0.0971)/ 0.7212= 0.2251
Z9= (0.42 - 0.0971)/ 0.7212= 0.4969
Z10= (0.17 - 0.0971)/ 0.7212= 0.1002
Z11= (0.50 - 0.0971)/ 0.7212= 0.6506
Z12= (0.86 - 0.0971)/ 0.7212= 1.0242
Z13= (0.01 - 0.0971)/ 0.7212= -0.1208
Z14= (2.50 - 0.0971)/ 0.7212= 3.3999
To determine if there are any outliers, we can compare the absolute values of the Z-Scores to a certain threshold , commonly considered as 2.
If the absolute value of a Z-Score is greater than 2, it indicates that the corresponding data point is an outlier.
In this case, Z14 = 3.3999, which is greater than 2 , suggesting that the data point 2.50 inches may be considered an outlier based on the Z-Score criterion.
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with a sample mean of 15, a population average of 20, and a standard error of the mean of 10, calculate the observed z value.
a. -0.5
b. 0.5
c. 2.0
d. -2.0
The observed z value can be calculated as (sample mean - population mean) / standard error of the mean, which in this case is -0.5. Hence, option a is correct.
The observed z value measures how many standard errors the sample mean is away from the population mean. The sample mean is 15 and the population mean is 20 and the standard error mean is 10.
Subtracting the population mean from the sample mean, we get -5. Dividing -5 by 10, we find that the observed z value is -0.5. Therefore, the observed z value is -0.5, which corresponds to option (a).
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