Answer:
i think it's C sorry if it's wrong
Step-by-step explanation:
i took the test and got it right so
Answer:
The third option
Step-by-step explanation:
1. To determine whether a relation is a function given a graph, use the
following criterion:
if every vertical line you can draw goes though only 1 point, then the relation is a function If you can draw a vertical line that goes though 2 or more points, y is not a function of x. This is called the vertical line test.2. As you can see, if you draw a vertical line at a specific place in the third graph, it will go through 2 or more points.
Therefore, the correct answer is the third option/graph.
Is the area of the base of a shape different from the area of the whole shape?
Answer:
Yes, its going to be different because the base is only a piece of the whole shape, not the entire thing. Hope this helps! plz mark brainliest if possible :)
Step-by-step explanation:
can someone tell me the answer to this
Answer: W=12m
Step-by-step explanation:
If f(x) = 3x² -1 and g(x) = x+2, find (f + g)(x).
Answer:
(f+g)(x) = 3x^2+x+1
Step-by-step explanation:
It may look hard at first, but all the question is asking you to do is add both of the equations together.
(f+g)(x) = (3x^2-1) + (x+2)
(f+g)(x) = 3x^2+x+1
What values of x
and y
satisfy the system of equations {8x+9y=−36x+7y=1} If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475),
enter it like this: (42/53, 64/75) If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf. "
The solution to the system of equations is (x, y) = (-3/11, -1/11).To find the values of x and y that satisfy the system of equations:
8x + 9y = -3 ...(Equation 1)
-6x + 7y = 1 ...(Equation 2)
We can solve this system of equations using various methods such as substitution or elimination. Let's use the elimination method:
To eliminate the x terms, we can multiply Equation 1 by 6 and Equation 2 by 8:
48x + 54y = -18 ...(Equation 3)
-48x + 56y = 8 ...(Equation 4)
Now, we can add Equation 3 and Equation 4:
(48x - 48x) + (54y + 56y) = -18 + 8
110y = -10
y = -10/110
y = -1/11
Substituting the value of y = -1/11 into Equation 1:
8x + 9(-1/11) = -3
8x - 9/11 = -3
8x = -3 + 9/11
8x = (-33 + 9)/11
8x = -24/11
x = -3/11
Therefore, the solution to the system of equations is (x, y) = (-3/11, -1/11).
So, the values of x and y that satisfy the system of equations are x = -3/11 and y = -1/11.
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Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled i procedures satisfied. Independent random samples of released prisoners in the fraud and firearms offense categories yielded the following information on time served in months. Obtain a 90% confidence interval for the difference between the mean times served by prisoners in the fraud and firearms offense categories
(Note X_1=8.94. s-1= 3.87 x_2 = 17.62 and s_2 = 4.12)
The 90% contidence interval is from ____ to ______
(Round to three decimal places as needed)
The 90% confidence interval is from −11.447 to −5.913.
Given that: Sample size of fraud, n1 = 26
Sample size of firearms, n2 = 35
Sample mean of fraud, x1 = 8.94 months
Sample mean of firearms, x2 = 17.62 months
Sample standard deviation of fraud, s1 = 3.87 months
Sample standard deviation of firearms, s2 = 4.12 months T
he two samples are independent
We need to find the 90% confidence interval for the difference between the mean times served by prisoners in the fraud and firearms offense categories. Now, the point estimate of the difference in means of two populations is:
x1 − x2 = 8.94 − 17.62 = −8.68
Using the pooled t-interval formula, we get:
[8.68 − tα/2 × Sp(1/n1 + 1/n2), 8.68 + tα/2 × Sp(1/n1 + 1/n2)]
Here, the degrees of freedom is df = n1 + n2 - 2 = 59 at the 0.10 level of significance. tα/2 = t0.05 = 1.671,
from t-distribution table Pooled variance Sp
= [(n1 - 1) × s1² + (n2 - 1) × s2²] / (n1 + n2 - 2)= [(26 - 1) × 3.87² + (35 - 1) × 4.12²] / (26 + 35 - 2)≈ 17.07
Therefore, the 90% confidence interval is given as follows:
[8.68 - 1.671 × (sqrt(17.07) × sqrt(1/26 + 1/35)), 8.68 + 1.671 × (sqrt(17.07) × sqrt(1/26 + 1/35))]=[−11.447, −5.913] (rounded to three decimal places)
Hence, the required confidence interval is from −11.447 to −5.913.
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1. Determine whether the stress function = 50x² - 60xy - 70y² satisfies the conditions of compatibility for a two-dimensional problem. Obtain the stress distribution in the matrix plate. Also draw a sketch showing the boundary stresses on (tensor) form. [4+4+2 points]
The stress function satisfies the conditions of compatibility for a two-dimensional problem.
Given stress function is 50x² - 60xy - 70y²
To determine whether the stress function satisfies the conditions of compatibility for a two-dimensional problem, it is required to find the strains and then check for compatibility equations.
Strain components are given as,
εx = ∂υ/∂x + (du/dx)
εy = ∂υ/∂y + (du/dy)
γxy = ∂υ/∂y + (du/dx)
Here,
υ = 50x² - 60xy - 70y²
du/dx = 100x - 60
ydu/dy = -60x - 140y
∂υ/∂x = 100x - 60y
∂υ/∂y = -60x - 140y
∂²υ/∂y² = -140
∂²υ/∂x² = 100
Now,εx = 100x - 60
yεy = -140y - 60
xγxy = -60y - 60x
Taking derivative of εy w.r.t x,
∂(εy)/∂x = -60
Similarly, taking derivative of εx w.r.t y,
∂(εx)/∂y = -60
∴ The stress function satisfies the conditions of compatibility for a two-dimensional problem.
Stress components are given as,
σx = (C11εx + C12εy)
σy = (C21εx + C22εy)
τxy = (C44γxy)
Here,C11 = C22 = 100, C12 = C21 = -60 and C44 = 0
Therefore,
σx = 100(100x - 60y) - 60(-140y - 60x)
= 19600x - 8800
yσy = -60(100x - 60y) + 100(-140y - 60x)
= -19600y + 8800x
τxy = 0
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Polly Petunia is Chief Horticulturalist for the Southwest region, encompassing Arizona, New Mexico, and Texas. She wants to survey amateur gardeners in her region to determine what, if any, water conservation practices they employ in their home gardening. Polly sends her survey to 150 randomly selected gardeners in each state. Polly is using:
Polly Petunia, the Chief Horticulturalist for the Southwest region, is using a method called stratified random sampling to survey amateur gardeners in her region.
Stratified random sampling involves dividing the population into distinct groups or strata based on certain characteristics that are relevant to the research objective.
In this case, Polly is dividing the population of amateur gardeners in the Southwest region into three strata based on the states: Arizona, New Mexico, and Texas.
Once the population is divided into strata, Polly selects a random sample from each stratum. She sends her survey to 150 randomly selected gardeners from each state, resulting in a total sample size of 450 gardeners (150 from each state).
By using stratified random sampling, Polly ensures that her sample is representative of the population in terms of the geographic distribution across the three states.
This method allows her to obtain insights specific to each state while still maintaining a random selection within each stratum.
Using stratified random sampling helps increase the precision and accuracy of the survey results.
It allows Polly to make more accurate inferences and draw conclusions about the water conservation practices of amateur gardeners in each state, as well as the overall Southwest region.
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The left and right ends of the normal probability distribution extend indefinitely, never quite touching the horizontal axis. True False
It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.
The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.
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68 pages read in 40 minutes
Answer:
1.7 pages per minute
Step-by-step explanation:
divide 68 by 40 and you get 1.7
Mia is making smoothies. Each smoothie uses 1/2 cup of yogurt. How much yogurt
does she need to make 7 smoothies?
To solve, we'll need to _______
because we know the SIZE of the groups and the _______
but we don't know the ______
Answer: 3.5 cups
To solve, we'll need to multiply because we know the SIZE of the groups and the amount of groups but we don't know the total amount.
Write an equation of the circle with center \( (5,9) \) and radius \( 11 . \)
Give the equation of the circle centered at the origin and passing through the point \( (0,4) \).
The equation of the circle centered at the origin and passing through the point (0, 4) is \($x^2+y^2=16$\).
Let the center of the circle be represented as (h,k) and the radius of the circle be represented as r.
The general equation of a circle is given by \($$(x-h)^2+(y-k)^2=r^2$$\)
where the center of the circle is (h, k), and the radius is r
The equation of the circle with center (5, 9) and radius 11 is \($$(x-5)^2+(y-9)^2=11^2$$\)
To get the equation of the circle centered at the origin and passing through the point (0, 4), the center of the circle is the origin, which means (h, k) = (0, 0), and the radius r is given as the distance from the origin to (0, 4).
That distance is 4 units.
Therefore, the equation of the circle can be given by \($$(x-0)^2+(y-0)^2=4^2$$\)
Simplifying the equation gives:\($$x^2+y^2=16$$\)
Therefore, the equation of the circle centered at the origin and passing through the point (0, 4) is \($x^2+y^2=16$\).
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Please Help! 60 points for a rapid reply- please look at the question below= The Figure of circle A shown has a diameter of PR which intersects with QS at point B and the measurements shown, Calculate the following measures-
The measures in the circle given in the image above are calculated as:
1. m<PSQ = 130°; 2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.
How to Find the Measures in the Circle?In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.
1. m<PSQ = m<PAQ
Substitute:
m<PSQ = 130°
2. Find m<PBQ:
m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]
Substitute:
m<PBQ = 1/2(130 + 2(35))
m<PBQ = 100°
m<AQS = 180 - [m<BAQ + m<PBQ]
Substitute:
m<AQS = 180 - [(180 - 130) + 100]
m<AQS = 30°
3. m(QR) = m<QAR
Substitute:
m(QR) = 100°
4. m(PS) = 180 - m(RS)
Substitute:
m(PS) = 180 - 2(35)
m(PS) = 110°
5. m(RS) = 2(35)
m(RS) = 70°
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A boutique owner sells a salt scrub that is made of a tropical oil blend costing $7.95 per ounce and sea salt costing $1.45 per ounce. The salt scrub ultimately costs $3.40 per ounce. In order to make a new batch of the salt scrub, she just ordered 6 ounces of the tropical oil blend. How many ounces of sea salt will she need to make the salt scrub with the correct proportions?
Answer:
14
Step-by-step explanation:
7.95\cdot 6+1.45\cdot \:x=\left(6+x\right)3.4
x=14
`2` pizzas bake at `800`°F.
What should the oven temperature be for `4` pizzas?
Answer:
I Do Not know but I think 200
HELP ASAP
Classic Cars paid €9000 for a vintage Ferrari and sold for €11,250. What percentage profit did they make?
Answer:770000
Step-by-step explanation:
That how much they made
Answer:
€8988.75
Step-by-step My bad that's not the answer
help me pls
me has tried
The natural polymers are matched with their uses as;
Natural rubber; Option 2
Starch; Option 4
Silk; Option 5
DNA; Option 3
Cellulose; Option 1
What are natural polymers?Natural polymers are simply defined as materials that are wide spread in nature or are also extracted from plants or animals.
Different natural polymers like silk, DNA, cellulose, starch, natural rubber have their distinct uses.
Cellulose is mostly used in veterinary foods, wood, paper, clothes, cosmetic and also in pharmaceutical industries for drug production. Silk is used for clothing such as shirts, suits, ties, blouses.DNA is used for inheritance, coding for proteins, and also for providing instructions for life.Starch is used in food production.Natural rubber is mostly used for rubber production.Learn about natural polymers at: https://brainly.com/question/13939101
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Help with this question
The image below showcases a right triangle .
My questions:
What is a c, what does that represent
What is this problem asking for me
How do I solve this problem? Are there any formulas in place?
The perimeter of triangle is 66.24 units.
What is triangle?
In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane
Main body:
according to question :
c = 28
let the vertices be A,B,C
∠A= 30°
by using trigonometric ratios,
BC/ AB = sin30°
AB = C = 28
BC/28 = sin30°
BC = 28*sin30°
BC= 28*(1/2)
BC = 14
similarly
AB /CA = cos 30°
28/CA = √3/2
CA = 28*√3/2
CA = 14/√3
CA = 24.24
Hence , perimeter = AB +BC +CA = 28+14+24.24
=66.24 units
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Determine the sum of the solutions to: 5x^2-16x+3=0
A. 3/5
B. 16
C. 8
D. 16/5
The sum of the two solutions is equal to 17/5.
How to find the solutions of the quadratic equation?Here we want to solve the quadratic equation:
5x^2 - 16x + 3 = 0
Using the quadratric formula, we will get the solutions:
\(x = \frac{16 \pm \sqrt{(-16)^2 - 4*3*5} }{2*5} \\\\x = \frac{16 \pm14 }{10}\)
Then the two solutions of the quadratic equation are:
x = (16 + 14)/10 = 30/10 = 3
x = (16 - 14)/10 = 2/10 = 2/5
The sum is: 3 + 2/5 = 3 + 2/5 = 15/5 + 2/5 = 17/5
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Which of the following expressions represents the value, in dollars, of a certain number of nickels, n, and dimes, d? 0. 15nd 0. 15n d 0. 10n 0. 05d 0. 05n 0. 10d.
Answer: the ansner is d
Step-by-step explanation:
The expression representing the total value of the coins specified is given by: Option D : 0.05n + 0.10d
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For the given case, we've got to find the value of the amount those coins make up together.
The price (in dollars) of specific coins are:
Nickle= $0.05Dime = $0.10Since, it is given that there are n nickels and d dimes, thus, total amount is
Total amount = $(0.05 + 0.05+ ... + 0.05 (n times)) +
$(0.10 + 0.10 + ... + 0.10 (d times) )
Total amount = $ (0.05 × n + 0.10 × d) = 0.05n + 0.10d in dollars)
(we don't write symbols like of currency generally, and understand it from context. Also, sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together)
Hence, The expression representing the total value of the coins specified is given by: Option D : 0.05n + 0.10d
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I’m pretty sure the answer is c but I need further help to understand if I am right or not
Answer:
you are correct'v'
Step-by-step explanation:
in the first column it adds the next odd number, 1, 3, 5,7
and in the 2nd it mutiplies by 2 so it would be faster by a whole lot
Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. What was the total cost before sales tax? Round your answer to the nearest cen
The total cost before the sales tax was 19.828 pounds.
For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.
We have to determine the total cost before sales tax.
As per the question, we have prices as:
cost of turkey = 3.95 per pound
cost of egg cheese = 1.3 per pound
cost of egg salad = 0.89 per pound
The total cost of turkey = 3.8 × 3.95 = 15.01 pounds
The total cost of cheese = 2.2 × 1.3 = 2.86 pounds
The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds
The total cost before sales tax = 15.01 + 1.958 +2.86
Apply the addition operation, and we get
The total cost before sales tax = 19.828 pounds
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The question seems to be incomplete the correct question would be:
Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?
Which expression is equivalent to 30(1/2x-2)+40(3/4y-4)?
Answer:
15x+30y-220
Step-by-step explanation:
Took the test!
Answer:
The person above is correct I got it right on edge quiz 2021
Step-by-step explanation:
!!!!!!!hope I helped lol
What is the area of the trapezoid?
A) 176 cm^2
B)192 cm^2
C)208 cm^2
D)224 cm^2
Answer:
a
Step-by-step explanation:
.
For the following data points a) finds the linear interpolation spline b) find the quadratic interpolation spline?
X= -2,-1,0,1,2
Y=2,1,2,3,2
a) Linear Interpolation Spline for the data points are -
-2 <= x < -1: y = -x + 0
-1 <= x < 0: y = x + 2
0 <= x < 1: y = x + 2
1 <= x <= 2: y = -x + 4
b) Quadratic Interpolation Spline for the data points are -
-2 <= x <= -1: y = -x² - 2x + 2
-1 <= x <= 0: y = 2x² + 2
0 <= x <= 1: y = x² + 2x + 2
1 <= x <= 2: y = x² + 2x + 2
a) Linear Interpolation Spline:
To find the linear interpolation spline, we need to determine the line segments that connect adjacent data points.
Given data points:
X = [-2, -1, 0, 1, 2]
Y = [2, 1, 2, 3, 2]
Step 1: Determine the slopes between adjacent points
m1 = (Y[1] - Y[0]) / (X[1] - X[0]) = (1 - 2) / (-1 - (-2)) = -1 / 1 = -1
m2 = (Y[2] - Y[1]) / (X[2] - X[1]) = (2 - 1) / (0 - (-1)) = 1 / 1 = 1
m3 = (Y[3] - Y[2]) / (X[3] - X[2]) = (3 - 2) / (1 - 0) = 1 / 1 = 1
m4 = (Y[4] - Y[3]) / (X[4] - X[3]) = (2 - 3) / (2 - 1) = -1 / 1 = -1
Step 2: Determine the y-intercepts of the line segments
b1 = Y[0] - m1 × X[0] = 2 - (-1) × (-2) = 2 - 2 = 0
b2 = Y[1] - m2 × X[1] = 1 - 1 × (-1) = 1 + 1 = 2
b3 = Y[2] - m3 × X[2] = 2 - 1 × 0 = 2
b4 = Y[3] - m4 × X[3] = 3 - (-1) × 1 = 3 + 1 = 4
Step 3: Define the linear interpolation spline for each segment
For the first segment (-2 <= x < -1):
y = m1 × x + b1 = -1 × x + 0
For the second segment (-1 <= x < 0):
y = m2 × x + b2 = x + 2
For the third segment (0 <= x < 1):
y = m3 × x + b3 = x + 2
For the fourth segment (1 <= x <= 2):
y = m4 × x + b4 = -x + 4
b) To find the quadratic interpolation spline, we will use quadratic polynomial equations to interpolate between the given data points.
Given data points:
X = [-2, -1, 0, 1, 2]
Y = [2, 1, 2, 3, 2]
Step 1: Determine the coefficients of the quadratic polynomials
We will find three quadratic polynomials, each interpolating between three consecutive data points.
For the first quadratic polynomial (interpolating points -2, -1, and 0):
Using the formula y = ax² + bx + c, we substitute the given data points to form a system of equations:
4a - 2b + c = 2
a - b + c = 1
c = 2
Solving the system of equations, we find a = -1, b = -2, and c = 2.
Thus, the first quadratic polynomial is y = -x² - 2x + 2.
For the second quadratic polynomial (interpolating points -1, 0, and 1):
Using the same process, we find a = 0, b = 2, and c = 2.
Thus, the second quadratic polynomial is y = 2x² + 2.
For the third quadratic polynomial (interpolating points 0, 1, and 2):
Using the same process, we find a = 1, b = 2, and c = 2.
Thus, the third quadratic polynomial is y = x² + 2x + 2.
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A survey was given to a random sample of 1350 residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. Of those surveyed, 64% of the people said they were in favor of the plan. At the 95% confidence level, what is the margin of error for this survey expressed as a percentage to the nearest tenth?
The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.
To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.
The formula for calculating the standard error is:
Standard Error = sqrt((p * (1 - p)) / n)
where p is the sample proportion and n is the sample size.
In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.
Plugging in the values:
Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)
\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)
≈ 0.0131
Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.
Margin of Error = z * Standard Error
= 1.96 * 0.0131
≈ 0.0257
Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:
Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100
= (0.0257 / 0.64) * 100
≈ 4.0%
Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.
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Let F(x) = integral from 0 to x sin(3t^2) dt. Find the MacLaurin polynomial of degree 7 for F(x)
Answer:
\(\displaystyle \int^x_0\sin(3t^2)\,dt\approx x^3-\frac{27}{42}x^7\)
Step-by-step explanation:
Recall the MacLaurin series for sin(x)
\(\displaystyle \sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-...\)
Substitute 3t²
\(\displaystyle \displaystyle \sin(3t^2)=3t^2-\frac{(3t^2)^3}{3!}+\frac{(3t^2)^5}{5!}-...=3t^2-\frac{3^3t^6}{3!}+\frac{3^5t^{10}}{5!}-...\)
Use FTC Part 1 to find degree 7 for F(x)
\(\displaystyle \int^x_0\sin(3t^2)\,dt\approx\frac{3x^3}{3}-\frac{3^3x^7}{7\cdot3!}\\\\\int^x_0\sin(3t^2)\,dt\approx x^3-\frac{27}{42}x^7\)
Hopefully you remember to integrate each term and see how you get the solution!
Both the z and t distributions have the following properties: Multiple select question. bimodal skewed symmetric around 0 with asymptotic tails bell-shaped
False.
The statement is incorrect because neither the z nor the t distribution is necessarily skewed symmetric. While they are both bell-shaped and have asymptotic tails, the shape of the distribution depends on the degrees of freedom for the t distribution and the mean and standard deviation for the z distribution.
The z and t distributions share several properties, which include:
1. Skewed: Both distributions are not skewed, as they are symmetric around 0.
2. Symmetric around 0: Both the z (standard normal) and t distributions are symmetric around 0, which means that they have equal probability on both sides of 0.
3. Asymptotic tails: Both distributions have asymptotic tails, which means that the tails of the distributions approach but never touch the horizontal axis.
4. Bell-shaped: Both the z and t distributions are bell-shaped, with a peak at the center (0) and tails extending to the left and right.
So, the correct properties for both z and t distributions are: symmetric around 0, asymptotic tails, and bell-shaped.
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A score that is 2.5 standard deviations below the mean would have a z score of ______ . a. 0 b. 2.5 c. 25 d. -2.5
A z-score represents the number of standard deviations a data point is away from the mean. A score that is 2.5 standard deviations below the mean would have a z-score of -2.5 that is option D.
A z-score is a statistical measure that indicates how many standard deviations a particular data point is away from the mean of a distribution. It is calculated using the formula:
z = (x - μ) / σ
Where:
z is the z-score,
x is the value of the data point,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.
If a score is 2.5 standard deviations below the mean, it means that the value of x is 2.5 times the value of σ below the mean. In other words, it is located in the left tail of the distribution.
Since the z-score represents the number of standard deviations away from the mean, a score that is 2.5 standard deviations below the mean would have a z-score of -2.5. The negative sign indicates that the score is below the mean.
So, if we substitute the values into the z-score formula:
z = (x - μ) / σ
-2.5 = (x - μ) / σ
This equation represents the z-score being -2.5, indicating that the score is 2.5 standard deviations below the mean.
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