Answer:the answer is 15 units
Step-by-step explanation:
just took the test
If two opposite sides of a square are increased by 13 meters and the other sides are decreased by 7 meters, the area of the rectangle that is formed is 69 square meters. Find the area of the original square.
Answer:
(x + 13)(x - 7) = 69
x² + 6x - 91 = 69
x² + 6x - 160 = 0
(x + 16)(x - 10) = 0
x = 10, so the area of the original square is 100 m².
The area of the figure is square units.
3 units, 8 units, 3 units, 9 units, 3 units, 21 units
The area of the figure is 114 square units.
To determine the area of the figure, we need to identify its shape.
From the given dimensions, it appears that we have three rectangular sections.
The first section has a length of 3 units and a width of 8 units, giving us an area of 3 [tex]\times[/tex] 8 = 24 square units.
The second section has a length of 3 units and a width of 9 units, resulting in an area of 3 [tex]\times[/tex] 9 = 27 square units
The third section has a length of 3 units and a width of 21 units, yielding an area of 3 [tex]\times[/tex] 21 = 63 square units.
To find the total area of the figure, we need to sum up the areas of the individual sections:
Total area = 24 + 27 + 63 = 114 square units.
Therefore, the area of the figure is 114 square units.
It's important to note that without a clear description or diagram of the figure, it's challenging to provide an accurate interpretation.
The given dimensions could represent various arrangements, and the resulting area would vary accordingly.
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4
Number of Years
m
N
1
16
18
18°
19°
22°
30°
20
Mark this and return
28
22
24
26
Average Daily Temperature
30
The mean of the temperatures in the chart is 24° with a standard deviation of 4°. Which temperature is within one
standard deviation of the mean?
32
Save and Exit
Next
Submit
The temperature of 30° is within one standard deviation of the mean.
To determine which temperature is within one standard deviation of the mean, we need to consider the range that falls within one standard deviation above and below the mean.
Given that the mean temperature is 24° with a standard deviation of 4°, one standard deviation above the mean would be 24° + 4° = 28°, and one standard deviation below the mean would be 24° - 4° = 20°.
Looking at the temperatures in the chart, we can see that the temperature of 30° is within one standard deviation of the mean. It falls within the range of 28° (one standard deviation above the mean) and 20° (one standard deviation below the mean).
Therefore, the temperature of 30° is within one standard deviation of the mean.
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i need help!!!! does anyone know this..!!???
The period of the frequency factor b that is given in the diagram above would be = 0.2 sec.
How to determine the period of the frequency factor b given above?The frequency of a water wave is defined as the number of times the wave completes a cycle within a given period of time. While the period is the time it takes for the completion of a cycle.
The dot the represents the frequency factor b is the green dot on the wave table. Therefore the period as traced from the graph= 0.2 sec.
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. Initially 100 milligrams of a radioactive substance was present.
After 6 hours the mass had decreased by 3%. If the rate of
decay is proportional to the amount of the substance present at
time t, nd the amount remaining after 24 hours.
Answer:
Incomplete Question
What is the probability that you will be in district 12 with Katniss & Peeta?
Answer:
0
Step-by-step explanation:
theres only 2 people each district
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
The mapping shown does not represents a function
Determining if the mapping is a functionFrom the question, we have the following parameters that can be used in our computation:
The mapping
From the mapping, we have
(1, 7), (8, 3), (8, -1) and (3, 0)
The above ordered pair is not a function
This is so because the input value 8 have different output values 3 and -1
i.e. it would not pass the vertical line test when represented on a graph
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Question 1 (1 point)
Caroline wants to create a helix shape by using the screw modifier. Unfortunately,
when she tries the screw modifier, it keeps spinning her model around an axis
without any vertical movement. What does she need to change to get the vertical
movement that will give it a helix-like shape?
Screw option needs to be set to something greater than 0.
Screw option needs to be set to 0.
Screw option needs to be set to something less than 0.
Screw option needs to be turned off.
Question ? (1 point) ✓ Saved
The correct answer is Screw option needs to be set to something greater than 0.
To get the vertical movement and create a helix-like shape using the screw modifier, Caroline needs to change the screw option to something greater than 0.
The screw option determines the amount of vertical displacement or height of the helix shape.
By setting the screw option to a value greater than 0, Caroline can control the vertical movement of the model as it spirals along the axis, resulting in a helix-like shape.
Therefore, the correct answer is:
Screw option needs to be set to something greater than 0.
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Hi I could use some help with this question, thank you in advance.
apologies for mislabeling this as college
Using the property of vertical angles, the value of x is 24 degrees
What are vertical angles?Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines. They are opposite each other and share a common vertex, but they are not adjacent angles.
When two lines intersect, they form four angles at the point of intersection. The vertical angles are the angles that are directly across from each other and are formed by opposite pairs of intersecting lines. In other words, if you draw a line segment connecting the vertices of the vertical angles, it will divide the intersection into two pairs of congruent angles.
The property of vertical angles is that they have equal measures. This means that if one vertical angle measures a certain number of degrees, the other vertical angle will also measure the same number of degrees.
In this problem, to find the value of x, we have to use the property of vertical angles which states that vertical angles are equal to one another.
This implies that ∠ABC = DBE
3x - 14 = 2x + 10
Collect like terms
3x - 2x = 10 + 14
x = 24°
The answer is option D.
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Pls help I need this answer
Answer:
B , D , A
Step-by-step explanation:
(4x³ - 4 + 7x) - (2x³ - x - 8)
distribute the first parenthesis by 1 and the second by - 1
= 4x³ - 4 + 7x - 2x³ + x + 8 ← collect like terms
= 2x³ + 8x + 4 ← equivalent to expression B
---------------------------------------------------------------
(- 3x² + [tex]x^{4}[/tex] + x) + (2[tex]x^{4}[/tex] - 7 + 4x) ← remove parenthesis
= - 3x² + [tex]x^{4}[/tex] + x + 2[tex]x^{4}[/tex] - 7 + 4x ← collect like terms
= 3[tex]x^{4}[/tex] - 3x² + 5x - 7 ← equivalent to expression D
------------------------------------------------------------------
(x² - 2x)(2x + 3)
each term in the second factor is multiplied by each term in the first factor, that is
x²(2x + 3) - 2x(2x + 3) ← distribute parenthesis
= 2x³ + 3x² - 4x² - 6x ← collect like terms
= 2x³ - x² - 6x ← equivalent to expression A
write the first five multiples of 17
Step-by-step explanation:
write the first five multiples of 17
17 x 1 = 1717 x 2 = 3417 x 3 = 5117 x 4 = 6817 x 5 = 85
Therefore, the first five multiples of 17 are 17 , 34 , 51 , 68 and 85 .
a
35°
8
X
8
12
35⁰
For the two right triangles
above, explain why
X
12. What
trigonometric ratio is equal to
the two given ratios.
X = 4√6 because the tangent of 35 degrees is equal to X/8 in the first right triangle and 12/X in the second right triangle.
We have two right triangles with an angle of 35 degrees and side lengths of 8 units and 12 units.
To explain why X = 12, we can use the trigonometric ratio of tangent (tan). In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
In the first right triangle, the side opposite to the angle of 35 degrees is X, and the adjacent side is 8 units. So, we have:
tan(35 degrees) = X / 8
Similarly, in the second right triangle, the side opposite to the angle of 35 degrees is 12 units, and the adjacent side is X. So, we have:
tan(35 degrees) = 12 / X
Since the tangent of an angle is the same regardless of the orientation of the triangle, we can equate the two ratios:
X / 8 = 12 / X
To solve for X, we can cross-multiply:
X^2 = 8 * 12
X^2 = 96
Taking the square root of both sides, we get:
X = √96
Simplifying, we have:
X = 4√6
Therefore, X is equal to 4 times the square root of 6.
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write the standard form of the equation of a circle with radius 2 and )-14,-13).
Answer:
11? I'm so sorry if it's incorrect. I apologize.
The parallel gram shown below has an area of 72 units^2
Answer:
h = 12 units
Step-by-step explanation:
The formula for the area of a parallelogram is given by:
A = bh, where
b is the base of the parallelogram,and h is an altitude (i.e., a perpendicular line that connects the two bases of a parallelogram).Thus, the base is 6 units. We can find the height by dividing the area by 6:
A = bh
72 = 6h
72/6 = h
12 = h
Thus, the height of the parallelogram is 12 units.
Scores on the Wechsler Adult Intelligence Scale for the 20 to 34 age group are approximately Normally distributed with mean 110 and standard deviation 15. How high must a person score to be in the top 4% of all scores? (Round your answer to the nearest whole number, if necessary.)
Answer:
The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
Step-by-step explanation:
What is defined as the normal distribution?
A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder taper off symmetrically toward any extreme.
A histogram inside a normal distribution curve is sometimes used to design the curve.
The formula for the normal distribution is;
z = (x - μ)/σ
where,
z = z- score, taken fro table
Mean μ = 110
Standard deviation σ = 15
Sample mean x.
If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.
In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.
z = 1.7
Put the value in formula ad find x.
1. 7 = (x - 110)/15
x = 25.5 + 110
x = 135.5
x = 136 (whole number)
Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.
Solve 4563÷257 using long division method show the steps
2 5 7 ÷ 4 5 6 3
- 2 5 7
1993
- 1 7 9 9
Answer:
194
Select the correct answer. What is the solution to this equation? 9^x - 1 = 2 O A. - 1/1/20 OB. 2 O C. OD. 1/1/20 1 23 Edmentum. All rights reserved. Reset Next
Answer:
D. 1/2
Step-by-step explanation:
9^x - 1 = 2
9^x = 3
x = log{sub}9 (3)
x = 1/2 (9^(1/2)=3)
If the expenditure of a person is 75% of his income and his income tax which is 13% of his income is $585. What is his expenditure?
The person's expenditure is $1,755. (30 words)
To find the expenditure, we need to determine the person's income first. Since the income tax is 13% of the income and is given as $585, we can calculate the income. Dividing the income tax by the tax rate gives us the income. So, $585 divided by 0.13 equals $4,500, which is the person's income.
Now, we can calculate the expenditure. Given that the expenditure is 75% of the income, we can multiply the income by 0.75 to find the expenditure. So, $4,500 multiplied by 0.75 equals $3,375. Therefore, the person's expenditure is $3,375. (120 words)
In summary, the person's expenditure is $3,375. To find this, we first determined the person's income by dividing the given income tax of $585 by the tax rate of 13%, resulting in an income of $4,500.
Then, we calculated the expenditure by multiplying the income by 0.75 since the expenditure is stated to be 75% of the income. Thus, the person's expenditure is $3,375.
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What's the lateral area of the cylinder?
A. 251 yd.²
B. 314 yd.²
C. 503 yd.²
D. 13 yd.²
Answer:
2π(5)(10) = 100π yd² = about 314 yd²
B is the correct answer.
Si 3,390 kg de plomo ocupan un volumen de 0.3m3. Encuentra la densidad del plomo.
The density of lead is 11,300 kg/[tex]m^3[/tex], which means that lead is a dense material with a significant mass per unit volume.
To find the density of lead, we can use the formula:
Density = Mass / Volume
Given that the mass of lead is 3,390 kg and the volume is 0.3 [tex]m^3[/tex], we can substitute these values into the formula:
Density = 3,390 kg / 0.3[tex]m^3[/tex]
To simplify the calculation, we divide the mass by the volume:
Density = 11,300 kg/[tex]m^3[/tex]
Therefore, the density of lead is 11,300 kg/[tex]m^3[/tex].
Density is a physical property of a substance that describes how much mass is packed into a given volume. In this case, the density of lead tells us that for every cubic meter of lead, there are 11,300 kilograms of mass.
It is important to note that the density of lead is a characteristic property and remains constant regardless of the size or shape of the sample. It is a useful parameter in various scientific and industrial applications.
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The question probable may be:
If 3,390 kg of lead occupy a volume of 0.3 m^3, find the density of lead.
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Ship A receives a distress signal from the northeast, and ship B receives a distress
signal from the same vessel from the west. At what location is the vessel in distress
located? Describe how you arrived at your conclusion using complete sentences. You
must show all work in order to receive credit. (10 points)
3
2
A
NE
12pt
13
W
B
Edit View Insert Format Tools
Paragraph
B T
Table
U
D
The vessel in distress is located at (-x, y), with the exact coordinates depending on the specific distances and positions of ships A and B.
To determine the location of the vessel in distress, we can analyze the information given about the distress signals received by ships A and B.
Ship A received a distress signal from the northeast, while Ship B received a distress signal from the west.
Let's consider the compass directions:
Northeast (NE) is a direction that lies between north and east.
West (W) is a direction perpendicular to both north and south.
From this information, we can deduce that the vessel in distress must be located at the intersection of the northeast and west directions.
To find this intersection point, we can draw a diagram or use a coordinate system. Let's assume the origin (0,0) represents the starting point of both ships A and B.
Based on the given information, we know that ship A received a distress signal from the northeast. This means that the vessel in distress must be located in the direction of the positive x-axis (east) and the positive y-axis (north) from the origin.
On the other hand, ship B received a distress signal from the west. This indicates that the vessel in distress must be located in the direction of the negative x-axis (west) from the origin.
Combining these two pieces of information, we can conclude that the vessel in distress is located at the point where the positive y-axis (north) intersects with the negative x-axis (west). In coordinate notation, this point can be represented as (-x, y), where x and y are positive values.
Therefore, the vessel in distress is located at (-x, y), with the exact coordinates depending on the specific distances and positions of ships A and B.
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HELP DUE IN 3 DAYS!!!!! Which symbol should go in the box to make the equation true, and why? (1 point) the fraction two fourths followed by a box followed by the fraction four eighths a >, because the fraction two fourths is equal to the fraction eight eighths. b >, because the fraction two fourths is equal to the fraction six eighths. c =, because the fraction four eighths is equal to the fraction two fourths. d =, because the fraction four eighths is equal to the fraction two halves.
The correct answer is c) =, because the fraction four eighths is equal to the fraction two fourths.
To determine which symbol should go in the box to make the equation true, let's analyze the fractions given and compare their values.
The fraction "two fourths" can be simplified to "one-half" since both the numerator and denominator can be divided by 2. Therefore, "two fourths" is equal to "one-half."
Now, let's look at the fraction "four eighths." We can simplify this fraction by dividing both the numerator and denominator by 4, which gives us "one-half" as well. So, "four eighths" is also equal to "one-half."
Now, based on the given fractions, we have the equation:
(one-half) [BOX] (one-half)
We need to determine the correct symbol to fill in the box.
Looking at the values of the fractions, we see that both "two fourths" and "four eighths" are equivalent to "one-half." Therefore, the correct symbol to make the equation true is the equality symbol (=).
Hence, the correct answer is:
c) =, because the fraction four eighths is equal to the fraction two fourths.
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Let X_1,…,X_n be a random sample. For S(X_1,…,X_n )=1/(1/n ∑_(i=1)^n▒〖(x_i-c)〗^2 ) , find its asymptotic distribution where EX^k=α_k.
The asymptotic distribution of the estimator S(X₁, ..., Xₙ) is a standard normal distribution, denoted as N(0, 1).
To find the asymptotic distribution of the estimator S(X₁, ..., Xₙ), we can use the Central Limit Theorem (CLT). However, we need some additional assumptions to apply the CLT, such as the finite variance of the random variables.
Given that E(Xᵢ^k) = αₖ for all k, we can assume that the random variables Xᵢ have a finite variance. Let's denote the variance of Xᵢ as Var(Xᵢ) = σ².
First, let's simplify the estimator S(X₁, ..., Xₙ):
S(X₁, ..., Xₙ) = 1 / (1/n ∑ᵢ (Xᵢ - c)²)
Notice that the numerator is a constant and doesn't affect the asymptotic distribution. So, we can focus on analyzing the denominator.
Let's calculate the expected value and variance of the denominator:
E[1/n ∑ᵢ (Xᵢ - c)²] = 1/n ∑ᵢ E[(Xᵢ - c)²] = 1/n ∑ᵢ (Var(Xᵢ) + E[Xᵢ]² - 2cE[Xᵢ] + c²)
= 1/n (nσ² + α₁ - 2cα₁ + c²) (using the fact that E[Xᵢ] = α₁ for all i)
Var[1/n ∑ᵢ (Xᵢ - c)²] = 1/n² ∑ᵢ Var[(Xᵢ - c)²] = 1/n² ∑ᵢ (Var(Xᵢ - c)²) = 1/n² ∑ᵢ (Var(Xᵢ))
= 1/n² (nσ²) = σ²/n
Now, let's apply the CLT. According to the CLT, if we have a sequence of independent and identically distributed random variables with a finite mean (μ) and a finite variance (σ²), the sample mean (in this case, our denominator) converges in distribution to a standard normal distribution as the sample size approaches infinity.
Therefore, as n approaches infinity, the asymptotic distribution of S(X₁, ..., Xₙ) will follow a standard normal distribution.
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prove that the lim x→−3 (10 − 2x) = 16
Answer:
Proving that the limit of the equation 10 - 2x as x approaches -3 is 16 involves using the definition of a limit.
Here's how you would approach it:
Let epsilon be a small positive number. We want to find a value of delta such that if x is within a distance of delta from -3, then 10 - 2x is within a distance of epsilon from 16.
So, we start with:
|10 - 2x - 16| < epsilon
Simplifying,
|-2x - 6| < epsilon
And using the reverse triangle inequality,
|2x + 6| > ||2x| - |6||
Now, we can choose a value for delta such that if x is within delta of -3, then |2x + 6| is within delta + 6 of |-6| = 6.
So,
||2x| - |6|| < epsilon
and therefore:
|2x - 6| < epsilon
Choosing delta = epsilon/2, we can prove that:
0 < |x + 3| < delta -> |2x - 6| < epsilon
Therefore, we have proved that the limit of 10 - 2x as x approaches -3 is 16 using the definition of a limit.
Step-by-step explanation:
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Two models R1 and R2 are given for revenue (in millions of dollars) for a corporation. Both models are estimates of revenues from 2030 through 2035, with t = 0 corresponding to 2030.
R1 = 7.23 + 0.25t + 0.03t^2
R2 = 7.23 + 0.1t + 0.01t^2
How much more total revenue (in millions of dollars) does that model project over the six-year period ending at t = 5? (Round your answer to three decimal places.)
Step-by-step explanation:
To find the difference in total revenue projected by the two models over the six-year period ending at t = 5, we need to calculate the revenue for each model from t = 0 to t = 5 and subtract the results.
For R1:
R1 = 7.23 + 0.25t + 0.03t^2
Substituting t = 5:
R1(5) = 7.23 + 0.25(5) + 0.03(5^2)
R1(5) = 7.23 + 1.25 + 0.75
R1(5) = 9.23 + 0.75
R1(5) = 9.98 million dollars
For R2:
R2 = 7.23 + 0.1t + 0.01t^2
Substituting t = 5:
R2(5) = 7.23 + 0.1(5) + 0.01(5^2)
R2(5) = 7.23 + 0.5 + 0.25
R2(5) = 7.73 + 0.25
R2(5) = 7.98 million dollars
To find the difference, we subtract R2(5) from R1(5):
Difference = R1(5) - R2(5)
Difference = 9.98 - 7.98
Difference = 2 million dollars
Therefore, the model R1 projects 2 million dollars more in total revenue than R2 over the six-year period ending at t = 5.
Find the area to the right of the z-score 0.41 under the standard normal curve.
z0.20.30.40.50.000.57930.61790.65540.69150.010.58320.62170.65910.69500.020.58710.62550.66280.69850.030.59100.62930.66640.70190.040.59480.63310.67000.70540.050.59870.63680.67360.70880.060.60260.64060.67720.71230.070.60640.64430.68080.71570.080.61030.64800.68440.71900.090.61410.65170.68790.7224
The area to the right of the z-score 0.41 under the standard normal curve is approximately 0.3409.
To find the area to the right of the z-score 0.41 under the standard normal curve, we need to calculate the cumulative probability or area under the curve from 0.41 to positive infinity.
Since the standard normal distribution is symmetric around the mean (z = 0), we can use the property that the area to the right of a z-score is equal to 1 minus the area to the left of that z-score.
From the given z-table, we can look up the area to the left of 0.41, which is 0.6591.
The area to the right of 0.41 is then:
Area = 1 - 0.6591
Area = 0.3409
Therefore, the area to the right of the z-score 0.41 under the standard normal curve is approximately 0.3409.
This means that approximately 34.09% of the data falls to the right of the z-score 0.41 in a standard normal distribution.
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Write the equation of this conic section in conic form: 100pts pls
The equation of the conic section in conic form is (x - 1) = (y + 6)²/4.
To write the equation of the conic section in conic form, we can complete the square to transform the equation into its standard form. Let's start with the given equation:
y² - 4x + 12y + 32 = 0
Rearranging the terms, we have:
y² + 12y - 4x + 32 = 0
To complete the square for the y-terms, we add and subtract the square of half the coefficient of y (which is 6 in this case):
y² + 12y + 36 - 36 - 4x + 32 = 0
Simplifying this, we get:
(y + 6)² - 4x + 4 = 0
Now, rearranging the terms, we have:
(y + 6)² = 4x - 4
Dividing both sides of the equation by 4, we get:
(y + 6)²/4 = x - 1
Finally, we can write the equation in conic form:
(x - 1) = (y + 6)²/4
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The Probable question may be:
Which type of conic section is defined by the equation y²-4x+12y + 32 = 0?
This is an equation of a parabola
Write the equation of this conic section in conic form:
Describe the given translation: T(0, 7)
Answer:
ok t means some thing but zero and seven should be solved
A sample consists of the following N = 7 scores: 5, 0, 4, 5, 1, 2 and 4.
a. Compute the mean and standard deviation for the sample
Mean =
Standard deviation=
b. Find the z-score for each score in the sample
X= 5, z=
X= 0, z=
X= 4, z=
X= 5, z=
X= 1, z=
X= 2, z=
X= 4, z=
a. Mean = 3
Standard deviation = 2
b. The z-scores for each score in the sample are: 1, -1.5, 0.5, 1, -1, -0.5, 0.5.
a. To compute the mean and standard deviation for the sample, we follow these steps:
Calculate the mean (average)
Mean = (sum of all scores) / (number of scores)
Mean = (5 + 0 + 4 + 5 + 1 + 2 + 4) / 7
Mean = 21 / 7
Mean = 3
The mean of the sample is 3.
Calculate the standard deviation
The formula for standard deviation for a sample is given by:
Standard deviation = sqrt((sum of squared differences from the mean) / (number of scores - 1))
First, calculate the squared differences from the mean for each score:
(5 - 3)^2 = 4
(0 - 3)^2 = 9
(4 - 3)^2 = 1
(5 - 3)^2 = 4
(1 - 3)^2 = 4
(2 - 3)^2 = 1
(4 - 3)^2 = 1
Next, sum up these squared differences:
4 + 9 + 1 + 4 + 4 + 1 + 1 = 24
Now, divide this sum by (number of scores - 1):
24 / (7 - 1) = 24 / 6 = 4
Finally, take the square root of this result:
Standard deviation = sqrt(4) = 2
The standard deviation of the sample is 2.
b. To find the z-score for each score in the sample, we use the formula:
z = (X - Mean) / Standard deviation
For each score, we substitute the values into the formula:
X = 5, z = (5 - 3) / 2 = 2 / 2 = 1
X = 0, z = (0 - 3) / 2 = -3 / 2 = -1.5
X = 4, z = (4 - 3) / 2 = 1 / 2 = 0.5
X = 5, z = (5 - 3) / 2 = 2 / 2 = 1
X = 1, z = (1 - 3) / 2 = -2 / 2 = -1
X = 2, z = (2 - 3) / 2 = -1 / 2 = -0.5
X = 4, z = (4 - 3) / 2 = 1 / 2 = 0.5
The z-scores for each score in the sample are:
z = 1, z = -1.5, z = 0.5, z = 1, z = -1, z = -0.5, z = 0.5
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