The probability that a woman is actually pregnant given that the test is positive is 0.974 (or 97.4%).
a) To find the probability that a woman is actually pregnant given that the test is positive, we can use Bayes' theorem:
P(p|+) = P(+|p) P(p) / P (+)
where P(p) is the prior probability of a woman being pregnant (which is 0.82), P (+) is the probability of a positive test result, and P(+|p) is the conditional probability of a positive test result given that the woman is pregnant.
We are given that the test has a false positive rate of 0.02, which means that P(+|~p) = 0.02 (where ~p denotes "not pregnant"). We are also given that the test has a correct positive rate of 0.95, which means that P (+|p) = 0.95. Therefore, we can calculate:
P (+) = P(+|p) P(p) + P(+|~p) P(~p)
= 0.95 * 0.82 + 0.02 * (1 - 0.82)
= 0.802
Substituting into Bayes' theorem, we get:
P(p|+) = 0.95 * 0.82 / 0.802
= 0.974
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Use the Fundamental Counting Principle to find the total number of possible outcomes.
The number of possible outcomes is given as follows:
18 outcomes.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, we have that:
There are 3 options for the location.There are 6 options for the activity.Hence the number of outcomes is given as follows:
3 x 6 = 18 outcomes.
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Given g(x) = x² - 8 and h(x) = -6x + 1, what is the correct way to start to find g(h(x))
The correct way to start finding g(h(x)) is to replace the output of h(x) in
the variables of g(x).
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.
In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Given, g(x) = x² - 8 and h(x) = - 6x + 1,
Now, g(h(x)) is the output of h(x) is the input of g(h(x)).
Therefore, g(h(x)) is g(- 6x + 1) = (- 6x + 1)² - 8.
g(h(x)) = - (6x - 1)² - 8.
g(h(x)) = - (36x² - 12x + 1) - 8.
g(h(x)) = - 36x² + 12x - 1 - 8.
g(h(x)) = - 36x² + 12x - 9.
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Which function is most likely graphed on the coordinate plane below?
f(x) = 3x – 11 f(x) = –4x + 12 f(x) = 4x + 13 f(x) = –5x – 19
The graph given is of the function f(x) = –5x – 19
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given is a graph, we need to determine the graph belongs to which function,
From the figure it is noticed that the f(x) is a straight line, so it must be in the form of,
f(x) = ax+b
Where, a coefficient of x and b are constants.
From the graph it is noticed that as the value of x increases the value f(x) decreases. It means the function have negative slope and the coefficient of x must be negative.
The function intersect the y-axis at below the origin. It means the value of b must be negative.
The sign of both constant and coefficient are negative. According to this statement the correct option is D.
In function f(x) = –5x – 19 both constant and coefficient are negative.
Put x=0, we get f(x)=-19, so the y-intercept is (0,-19).
Put f(x)=0, we get x = -19/5, so the x-intercept is (-19/5, 0).
Since both x and y intercepts are negative,
Therefore, option D is correct.
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What’s 10 more than triple P
The value of mathematical expression is,
⇒ 10 + 3P
What is Mathematical expression?Mathematical expression is defined as the collection or combination of the numbers, variables and functions by using operations like as addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 10 more than triple P.
Now, We can simplify mathematical expression as;
Triple P = 3P
Hence, We get the expression as;
⇒ 10 more than triple P.
⇒ 10 + 3 × P
⇒ 10 + 3P
Therefore, We get;
The value of mathematical expression is,
⇒ 10 + 3P
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Suggest an alternative method we can use to determine the equivalence point if you could not use a colorimetric indicator.
If a colorimetric indicator is not available, an alternative method for determining the equivalence point in a titration is to use a pH meter.
A pH meter is a device that measures the acidity or basicity of a solution and gives a numerical value for the pH.
In an acid-base titration, the pH of the solution changes as the titrant is added to the analyte. Initially, the pH is determined by the analyte, which is usually acidic. As the titrant is added, it reacts with the analyte to form a neutral or basic solution, and the pH increases. At the equivalence point, all of the analyte has reacted with the titrant.
To use a pH meter to determine the equivalence point, the pH of the solution is monitored as the titrant is added. Initially, the pH is low due to the acidity of the analyte. As the titrant is added, the pH increases, and a sharp increase in pH is observed at the equivalence point.
The advantage of using a pH meter to determine the equivalence point is that it provides a more precise and accurate method than visual indicators, which can be affected by factors such as color blindness or variations in lighting conditions. Additionally, a pH meter can be used for both acid-base and redox titrations.
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Re-write the quadratic function below in Standard Form y = 4(x−7)(x+3)
plsssssssss help
The quadratic function y = 4(x−7)(x+3) is re-written in standard form as
4x²- 16x - 84 = 0
How to write the standard formThe general formula for a quadratic function is expressed as;
ax² + bx + c = 0
From the information given, we have;
y = 4(x−7)(x+3)
expand the bracket, we get;
(x−7)(x+3)
x²+ 3x - 7x - 21
add or subtract the like terms
x² - 4x - 21
Multiply by 4, we have;
4(x² - 4x - 21)
4x²- 16x - 84 = 0
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Levels of Measurement!
What type of measure scale is being used? Nominal, Ordinal, interval or Ratio.
1. A satisfaction survey of a social website by number:
1 = very satisfied, 2 = somewhat satisfied, 3 = not satisfied.
2. The colors of crayons in a 24-crayon box.
3. Baking temperatures for various main dishes: 350, 400, 325, 250, 300
4. The distance in miles to the closest grocery store.
5. High school men soccer players classified by their athletic ability:
Superior, Average, Above average.
1) A satisfaction survey of a social website by number is Ordinal.
2) The colors of crayons in a 24-crayon box are nominal.
3) The baking temperatures for various main dishes are interval.
4) The distance in miles to the closest grocery store is Ratio
5) High school men soccer players classified by their athletic ability are Ordinal.
The satisfaction survey scale is ordinal since the numbers are used to indicate the order of satisfaction (i.e., very satisfied is higher than somewhat satisfied, which is higher than not satisfied), but the difference between each level is not known.
The colors of crayons are nominal since they are categorical and do not have an inherent order or numeric value.
The baking temperatures are interval, as the differences between the values are meaningful, but there is no true zero point (i.e., 0 degrees does not indicate the absence of temperature).
The distance to the closest grocery store is ratio, as it has a true zero point (i.e., 0 miles means no distance), and the differences between distances are meaningful and measurable.
The classification of high school soccer players by athletic ability is ordinal since the categories are ordered, but the differences between them are not known.
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A store manager instructs some new trainees that a measuring tape priced at $3 winds up costing a customer $3.24 once the sales tax is included. What is the sales tax percentage?
Answer: To find the sales tax percentage, we can start by subtracting the cost of the item itself from the total cost with tax included.
In this case, the cost of the item is $3, and the total cost with tax included is $3.24, so:
$3.24 - $3 = $0.24
Next, we can divide the amount of sales tax by the cost of the item, and multiply by 100 to find the percentage:
$0.24 ÷ $3 × 100 = 8%
So the sales tax percentage is 8%.
Step-by-step explanation:
Answer:
Step-by-step explanation:
$3 item
h = 100 * 3.24 - 3/ 3 = 24/3 = 8 1 = 8%
Sales tax percentage is = 8%
A rectangle has a perimeter of 74 centimeters.The length of the rectangle is 5 centimeters less than twice the width.What is the area of the rectangle,in square centimeters?
The area of the rectangle is 322 square centimeters.
Given data :- The perimeter of a rectangle P =74 meter. If the length is 5 meter less than twice it's width.
The dimensions of the rectangle =?
Let assume that the length of the rectangle L = (2x -5)m
And the width of the rectangle W = x meter
Now Perimeter P = 2(L+W)
74 = [2{x+(2x-5)}]
3x-5=37
3x= 42 , x = (42/3)= 14 meter
So the required width of the Rectangle W = 14 meter
Similarly , L = (2*14 - 5) = 23
Now , area of the rectangle = 14*23
Therefore, area of the rectangle = 322
Hence , the area of the rectangle is 322 square centimeters.
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Explain how the tiles show that 2s + 3s² is not
equivalent
to 5s.
The size of s² blocks is larger than that of blocks of s and this shows that the expressions 2s+3s² is not equivalent to 5s.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expressions are 2s+3s² and 5s.
Here, 2s+3s²≠5s
Substitute s=-1 in 2s+3s²≠5s, we get
2(-1)+3(-1)²≠5(-1)
1≠-5
Substitute s=2 in 2s+3s²≠5s, we get
2(2)+3(2)²≠5(2)
16≠10
Therefore, the size of s² blocks is larger than that of blocks of s and this shows that the expressions 2s+3s² is not equivalent to 5s.
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"Your question is incomplete, probably the complete question/missing part is:"
Is 2s+3s² equivalent to 5s? Use math tiles to model 2s+3s² and 5s.
s+s s²+s²+s² s+s+s+s+s
2s 3s² 5s
The expression 2s+3s² is not equivalent to 5s. Explain how that tiles show that 2s+3s² is not equivalent to 5s.
for
6. Tami multiplies two fractions. The first fraction is greater than -1 but less than 0. The
notei
second fraction is greater than 0 but less than 1.
Which statement describes the product of the two fractions Tami multiplied?
The product of the two fractions Tami multiplied will be a negative number between 0 and -1.
How to find the product of the multiplicationSince the first fraction is negative greater than -1 but less than 0
and the second fraction is positive, greater than 0 but less than 1, their product will be negative.
This is because when a negative number multiplies a positive number the product is a negative number
Moreover, since both numbers are in fraction and less than whole their multiplication will also be a reduction tending towards zero
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Using the graphing tool, write the exponential function that best modes the number of trees infected
The exponential function that best modes the number of trees infected [tex]y = a * e^{bx}[/tex]
what is exponential function ?
An exponential function is a mathematical function of the form [tex]f(x) = a^x[/tex] where "a" is a constant called the base, and "x" is the exponent. The base "a" is usually a positive number greater than 1, although it can be any positive number, including fractions and decimals.
Given by the question:
Assuming that the number of infected trees follows an exponential growth pattern, we can use the following equation:
[tex]y = a * e^{bx}[/tex]
where y is the number of infected trees at a given time, x is the time elapsed, a is the initial number of infected trees, and b is the rate of growth.
To find the values of a and b that best fit the data, we can use regression analysis techniques. We would need to input the data into a statistical software program, such as R or Excel, and run a regression analysis to estimate the values of a and b.
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Determine which of the following transformations are linear transformations
A. The transformation T1
defined by T1(x1,x2,x3)=(x1,0,x3)
B. The transformation T2
defined by T2(x1,x2)=(2x1−3x2,x1+4,5x2)
.
C. The transformation T3
defined by T3(x1,x2,x3)=(x1,x2,−x3)
D. The transformation T4
defined by T4(x1,x2,x3)=(1,x2,x3)
E. The transformation T5
defined by T5(x1,x2)=(4x1−2x2,3|x2|)
.
The transformation T1 defined by T1(x1,x2,x3)=(x1,0,x3) is linear transformation among the five given questions.
A linear transformation satisfies two properties: additivity and homogeneity. That is, for any vectors u and v, and any scalars a and b:
T(u + v) = T(u) + T(v)
T(au) = aT(u)
Using these properties, we can determine which of the given transformations are linear transformations:
A. The transformation T1 defined by T1(x1,x2,x3)=(x1,0,x3)
T1(u+v) = (u1+v1, 0, u3+v3) = (u1, 0, u3) + (v1, 0, v3) = T1(u) + T1(v)
T1(au) = (au1, 0, au3) = a(u1, 0, u3) = a*T1(u)
Therefore, T1 is a linear transformation.
The transformation T2 defined by T2(x1,x2)=(2x1−3x2,x1+4,5x2)
T2(u+v) = (2(u1+v1)−3(u2+v2), u1+v1+4, 5(u2+v2))
= (2u1−3u2, u1+4, 5u2) + (2v1−3v2, v1+4, 5v2) = T2(u) + T2(v)
However, T2 does not satisfy homogeneity property. Consider a = -1 and u = (1, 1):
T2(-u) = (-2, 5, -5)
-1*T2(u) = (-2, -5, -5)
Therefore, T2 is not a linear transformation.
The transformation T3 defined by T3(x1,x2,x3)=(x1,x2,−x3)
T3(u+v) = (u1+v1, u2+v2, -(u3+v3)) = (u1, u2, -u3) + (v1, v2, -v3) = T3(u) + T3(v)
T3(au) = (au1, au2, -au3) = a*(u1, u2, -u3) = a*T3(u)
Therefore, T3 is a linear transformation.
The transformation T4 defined by T4(x1,x2,x3)=(1,x2,x3)
T4(u+v) = (1, u2+v2, u3+v3) ≠ (1, u2, u3) + (1, v2, v3) = T4(u) + T4(v)
T4(au) = (1, au2, au3) ≠ a(1, u2, u3) = a*T4(u)
Therefore, T4 is not a linear transformation.
The transformation T5 defined by T5(x1,x2)=(4x1−2x2,3|x2|)
T5(u+v) = (4(u1+v1)−2(u2+v2), 3|u2+v2|)
= (4u1−2u2, 3|u2|) + (4v1−2v2, 3|v2|) ≠ T5(u) + T5(v)
T5(au) = (4au1−2au2, 3|au2|) ≠ a*T5(u)
Therefore, T5 is not a linear transformation.
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What's the possible values of z when t = 81
( be it real or complex number )
[tex] {z}^{2} = \sqrt{t} [/tex]
So annoying ~
Answer:
[tex]\boxed{\mathrm{z=\pm 3}}[/tex]Step-by-step explanation:
[tex]\mathrm{z^2=\sqrt{t}, \; when, \; t=81}[/tex]
Substitute t with 81:-
[tex]\mathrm{z^2=\sqrt{81}}[/tex]
Since 9*9 =81, square of 81 is 9:-
[tex]\mathrm{z^2=9}[/tex]
Take the square root of both sides.
[tex]\mathrm{z=\pm \sqrt{9} }[/tex]
and since 3*3 = 9 the square root of 9 will be 3.:-
[tex]\mathrm{z=\pm 3}[/tex]
_____________________
Hope this helps!
Determine whether watch triangle should be solved by law of singes or law or cosines and Solve the triangle
Using the law of cosines, as we have two sides and an angle, the length b is given as follows:
b = 17.92.
What is the law of cosines?The law of cosines states that we can find the side c of a triangle as follows:
c² = a² + b² - 2abcos(C)
In which:
C is the angle opposite to side c.a and b are the lengths of the other sides.For this problem, the length b is opposite to the angle of 47º, hence it is obtained as follows:
b² = 20² + 24² - 2 x 20 x 24 x cosine of 47 degrees
b² = 321.28
b = sqrt(321.28)
b = 17.92.
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Figure order is a rectangle what are the coordinates of point Q
The coordinates of point Q in the rectangle named QRST is (5, 5).
What are Coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given:
We have the Graph having coordinate T(5, 2).
and, length of QT = 3 unit
As, the vertical distance shows the y coordinate then the y coordinate of Q is 3.
and, the x coordinate is same as T.
Then, the Coordinate of Q is (5, 2+3) or (5, 5).
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When conducting a two-sided test of significance, the value of the parameter under the null hypothesis is not plausible and will not be contained in a 95% confidence interval when: A. The p-value is less than or equal to 0.05 B. The p-value is greater than 0.05. C. There is no relationship between the p-value and the con fidence interval.
The value of parameter under null hypothesis which is not plausible , will not be contained in a 95% confidence interval when (a) p value is less than or equal to 0.05 .
The "P Value" is the probability of observing a test statistic as extreme or more extreme than the one computed from the sample data, assuming the null hypothesis is true.
When the p value is less than equal to 0.05 , it indicates that the observed test statistic is statistically significant at the 5% level of significance, means that the null hypothesis will be rejected.
Therefore , the parameter value that is assumed under the null hypothesis is not plausible and is not likely to be in a 95% confidence interval.
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The given question is incomplete , the complete question is
When conducting a two-sided test of significance, the value of the parameter under the null hypothesis is not plausible and will not be contained in a 95% confidence interval when
(a) The p-value is less than or equal to 0.05
(b) The p-value is greater than 0.05.
(c) There is no relationship between the p-value and the confidence interval.
A system of two linear equations in two variables is shown on the coordinate grid.
10
8
6
*
10-8-6-4-2 2 4 6 8 10
-2
-6
A
69
Which system of equations does the graph represent?
The graph of the two linear functions is f(x) = 2x and f(x) = x.
What are the three types of solutions for a system of linear equations?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Let, The first table be,
x = 2 4 6 8.
y = 4 8 12 16.
We can observe that when x = 2, y = 4, and when x = 4 y = 8.
Therefore, The equation is y = 2x.
The second table is,
x = 1 2 3 4.
y = 1 2 3 4.
Here, y is equal to x, Therefore, The equation is y = x.
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Amplitude is ______.
the maximum displacement of a function on a graph
the minimum displacement of a function on a graph
Amplitude is the maximum displacement of a function on a graph.
What is amplitude?
Amplitude is the maximum displacement of a function on a graph. It refers to the maximum height or distance from the baseline of a wave or oscillation.
It is often used in physics and engineering to describe the strength or size of a signal, vibration, or wave. In simple terms, it can be thought of as the "peak-to-peak" distance of a waveform, or the height of the waveform above and below the baseline.
But the minimum displacement of a function on a graph would typically be referred to as the minimum value or the "valley" of the function.
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23
Referring to the Fig. in Question #23, find the cosine of angle R.
Reduce the answer to the lowest terms.
24
Referring to the Fig. in Question #23, find the tangent of angle R.
Reduce the answer to the lowest terms.
The cosine of angle R is 3/5 and tangent of angle R is 4/3.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given right triangle is RTS.
We have to find the cosine of angle R
We know that cos theta = Adjacent side/hypotenuse.
CosR=6/10
=3/5
Now let us find tangent of angle R
Tan theta = opposite side/adjacent side
=8/6
=4/3
Hence, the cosine of angle R is 3/5 and tangent of angle R is 4/3.
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Mr. Adams has a circular flower bed with a
diameter of 2 feet. He wishes to increase the size of this bed so that it will have nine times as much planting area. What must be the diameter of the new bed?
(F) 6 feet
(G) 8 feet
(H) 12 feet
(J) 16 feet
(K) none of these
Please Help!!!
Answer: (F) 6 feet
Step-by-step explanation:
The area of a circle is proportional to the square of its radius. So if we increase the diameter of the flower bed by a factor of x, its area will increase by a factor of x^2. We want to find the diameter of the new bed that will have nine times the planting area of the old bed.
Let d be the diameter of the new bed. Then its radius is r = d/2, and its area is A = πr^2. We want:
9A = π(D/2)^2
where D is the diameter of the old bed. Substituting r = D/2, we get:
9A = π(D/2)^2
= πr^2
So we can solve for d by equating the right-hand sides and taking the square root:
9πr^2 = πd^2
d^2 = 9r^2
d = 3r
Therefore, the diameter of the new bed must be three times the diameter of the old bed. The diameter of the old bed is 2 feet, so the diameter of the new bed is 3 times that, or 6 feet.
determine the volume of a solid formed by revolving the region bounded by the curve , the line , and the line about the line .
The value of V = 2π/3. To find the volume of the solid, we need to use the method of cylindrical shells.
First, we need to solve for the x and y intercepts of the curve. Setting x = 0 gives y = 0, and setting y = 0 gives x = ±1. So the curve intersects the x-axis at (-1, 0) and (1, 0).
Next, we need to find the height of each cylindrical shell. The height is given by the difference between the y-values of the curve and the line x = 1. Solving for y in 2xy = 1 + x^2, we get y = (1 + x^2)/(2x). So the height of the cylindrical shell at x is given by (1 + x^2)/(2x).
Finally, we need to find the radius of each cylindrical shell. The radius is simply x.
So the volume of the solid is given by the integral from x = 0 to x = 1 of 2πx(1 + x^2)/(2x) dx. Simplifying and integrating, we get V = 2π/3.
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Complete Question:
Find the volume of the solid formed by revolving the region bounded by the curve 2x y = the line 1 + x2 y = 0, and the line x = 1 about the y-axis. V=?
Suppose you surveyed 30 people and asked them whether they are white (W) white (N), and how many traumas (serious accidents, rapes, or crimes) they have enced in the past year. You also asked them to tell you whether they perceive theme as being in the upper, middle, working, or lower class. Your survey resulted in the data presented in the table below: a. Identify the level of measurement for each variable. b. Construct raw frequency tables for race. c. What proportion of the 30 individuals is nonwhite? What percentage is white?
a. The level of measurement for each variable are Race: Nominal, trauma: Ratio, Social Class: Ordinal.
b. Raw frequency tables for race:
Race Frequency
W 21
N 9
c. The proportion of the 30 individuals who are nonwhite is: 9/30 = 0.3
So, 30% of the individuals are nonwhite.
The percentage of individuals who are white is: 21/30 x 100% = 70%
So, 70% of the individuals are white.
Race is a nominal variable because it is a categorical variable that does not have any inherent order or ranking. The two categories are "W" for white and "N" for nonwhite.
Trauma is a ratio variable because it is a quantitative variable that has a meaningful zero point. This means that a value of zero indicates the absence of the thing being measured, and values greater than zero indicate a greater quantity of the thing being measured.
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Kendra and Allen Tovsky have a combined income of $142,573. They have 1099 forms which report $650 in dividends. They also have $8,500 in income from rental property. They are able to reduce their income by $12,500. What is their adjusted gross income?
Kendra and Allen Tovsky's adjusted gross income is $139,223.
What is Adjusted Gross Income (AGI)?Adjusted Gross Income (AGI) is defined as an individual's gross income minus various adjustments made to that income, such as trade and business deductions.
To calculate Kendra and Allen Tovsky's adjusted gross income (AGI), we need to start with their total income and subtract any deductions or adjustments they are eligible for.
Their total income is:
Combined income: $142,573
Dividends: $650
Rental income: $8,500
Total income before deductions: $151,723
Next, we need to subtract their eligible deductions. In this case, they are able to reduce their income by $12,500, which could include things like contributions to a retirement account or health savings account, self-employed expenses, or student loan interest payments. Let's assume that the full $12,500 deduction applies to their situation.
Adjusted gross income calculation:
Total income before deductions: $151,723
Minus eligible deductions: $12,500
Adjusted gross income: $139,223
Therefore, Kendra and Allen Tovsky's adjusted gross income is $139,223.
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Which expression is equivalent to √64 a6
Answer:
√64 a⁶
or, √2⁶a⁶
or, √(2a)⁶
or, (2a)³
=8a³
The table shows the number of brothers and sisters of the students in year 7.
What percentage of students have more than 1 brother or sister?
Number of brothers and sisters
Year 7 Male students
Year 7 Female students
1
62
118
2
24
3
8
14
4
6
104
200
The percentage of students with more than 1 brother or sister is 41%.
How to calculate percentage?To find the percentage, first complete the table:
118 - 62 = 56 female students with 1 brother and sister.
8 + 14 = 22 7th years with 3 brothers and sisters.
118 + x + 22 + 6 = 200, x = 200 - 146, x = 54 7th years with 2 brothers and sisters.
54 - 24 = 30 male students with 2 brothers and sisters.
62 + 30 + 8 + y = 104, y = 104 - 100, y = 4 male students with 4 brothers and sisters.
6 - 4 = 2 female students with 4 brothers and sisters.
56 + 24 + 14 + 2 = 96 total female students of 7th year.
The percentage of students with more than i brother and sister is:
54 + 22 + 6 = 82 students or 200 - 118 = 82 students.
% = 82 / 200 x 100 = 41%.
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A new therapy for Psoriasis is being tested and subjects have their PASI score taken before and after treatment. The distribution of their scores are shown in the following boxplot: A. Find the approximate 25th percentile (___), median (___), and 75th percentile (____) for the PASI scores pre treatment. B. Find the approximate 25th percentile ), median ), and 75th percentile ) for the PASI scores post treatment C. The effectiveness (i.e. the lower the score, the better) of the therapy is O A. Based on the post-treatment median being much lower than the median at baseline, the treatement appears to be ineffective OB. Based on the post-treatment median being much higher than the median at baseline, the treatement appears to be effective O C. Based on the post-treatment median being much lower than the median at baseline, the treatement appears to be effective OD. Based on the post-treatment median being much higher than the median at baseline, the treatement appears to be ineffective
The answer is option (C) based on the post-treatment median being much lower than the median at baseline, the treatment appears to be effective.
A) To find the approximate 25th percentile, median, and 75th percentile for the PASI scores pre-treatment, we can look at the boxplot. The box in the plot represents the middle 50% of the data, and the line inside the box represents the median. The whiskers show the range of the data, and any points outside of the whiskers are considered outliers.
From the given boxplot, we can see that the median is around 13, the 25th percentile is around 9, and the 75th percentile is around 19 for the PASI scores pre-treatment.
B) To find the approximate 25th percentile, median, and 75th percentile for the PASI scores post-treatment, we can again look at the boxplot.
From the given boxplot, we can see that the median is around 4, the 25th percentile is around 2, and the 75th percentile is around 8 for the PASI scores post-treatment.
C) The effectiveness of the therapy can be determined by comparing the pre-treatment and post-treatment PASI scores. As the goal is to have lower PASI scores post-treatment, a lower median PASI score post-treatment as compared to pre-treatment is an indication of the effectiveness of the therapy. Therefore, based on the post-treatment median being much lower than the median at baseline, the treatment appears to be effective.
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(b) the weights of the empty cardboard containers have a mean of 20 grams and a standard deviation of 1.7 grams. it is reasonable to assume independence between the weights of the empty cardboard containers and the weights of the eggs. it is also reasonable to assume independence among the weights of the 12 eggs that are randomly selected for a full carton. let the random variable x be the weight of a single randomly selected grade a egg.
0.1038 is the probability that a randomly selected full carton of Grade A eggs will weigh more than 850 grams.
0.413 is the mean of X?
0.643 is the standard deviation of X
As per the data given:
Each full carton of Grade A eggs consists of 1 randomly selected empty cardboard container and 12 randomly selected eggs.
The weights of such full cartons are approximately normally distributed with a mean of 840 grams and a standard deviation of 7.9 grams.
[tex]\mu=840[/tex]
[tex]\sigma = 7.9[/tex]
(a) Here we have to determine the probability that a randomly selected full carton of Grade A eggs will weigh more than 850 grams
Here, a full carton [tex]$y \sim N(840,7.9)$[/tex]
[tex]& \mu=840 \\[/tex]
As, z = [tex]$ \frac{y-840}{7.9} \sim N(0.1) \\[/tex]
[tex]$P(y > 850)= & P\left(z > \frac{850-840}{7.9}\right)=1-P(z < 1.26) \\[/tex]
[tex]= & 1-\phi(1.26) \\[/tex]
= 1 - 0.8962
= 0.1038
(b) Here, B is the weight of the carton [tex]$\sim N(20,1.7)$[/tex]
Weight of each egg [tex]$x=\frac{y-B}{12} \\[/tex]
[tex]& x \sim N\left(\frac{1}{12}(\epsilon(y)-\epsilon(B)), a\right)^{\prime}[/tex]
Here we have to determine the mean of x
Here [tex]$ \epsilon(x)=\epsilon \frac{\epsilon(y)-\epsilon(B)}{12} \\[/tex]
[tex]$ =\frac{840-20}{12} \\[/tex]
[tex]$& =\frac{820}{12} \\[/tex]
[tex]\epsilon(x) & =68.33 \\[/tex]
[tex]\alpha^2=v(x) & =\left(\frac{1}{12}\right)^2[v(y)-v(B)][/tex] as independent
[tex]$& =\frac{1}{12^2}\left[(7.9)^2-(1.7)^2\right][/tex]
[tex]$& =\frac{1}{144}[62.41-2.89] \\[/tex]
[tex]$ & =\frac{1}{144}[59.52] \\ &[/tex]
= 0.413
(ii) Here we have to determine the standard deviation
[tex]\sigma =\sqrt{0.413} \\ &[/tex]
[tex]\sigma[/tex] = 0.643
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Each full carton of Grade A eggs consists of 1 randomly selected empty cardboard container and 12 randomly selected eggs. The weights of such full cartons are approximately normally distributed with a mean of 840 grams and a standard deviation of 7.9 grams.
(a) What is the probability that a randomly selected full carton of Grade A eggs will weigh more than 850 grams?
(b) The weights of the empty cardboard containers have a mean of 20 grams and a standard deviation of 1.7 grams. It is reasonable to assume independence between the weights of the empty cardboard containers and the weights of the eggs. It is also reasonable to assume independence among the weights of the 12 eggs that are randomly selected for a full carton.
Let the random variable X be the weight of a single randomly selected Grade A egg.
i) What is the mean of X?
ii) What is the standard deviation of X?
Evaluate 2x + 3y if x =2 and y = 8
A random sample of 31 charge sales showed a sample standard deviation o $50. A 90% confidence interval estimate of the population standard deviation is:
A 1715.10 - 4055.68
B 1596.45-4466.73
C 39.96-66.83
D 41.39-63.68
A 90% confidence interval estimate of the population standard deviation is 1596.45-4466.73
We can use the chi-square distribution to construct a confidence interval for the population standard deviation, where the lower and upper limits are given by:
[tex]\sqrt{(n-1)*s^2/chi2(alpha/2,n-1)) }[/tex] and [tex]\sqrt{(n-1)*s^2/chi2(1-alpha/2,n-1)}[/tex]
Standard Deviation is a measure that shows how much variation (such as spread, dispersion, spread,) from the mean exists.
Where n is the sample size, s is the sample standard deviation, alpha is the significance level, and chi2 is the chi-square distribution function.
Substituting the given values, we get:
Lower limit
= [tex]\sqrt{(31-1)*50^2/chi2(0.05/2,31-1)}[/tex]
= 1596.45
Upper limit
= [tex]\sqrt{(31-1)*50^2/chi2(1-0.05/2,31-1)}[/tex]
= 4466.73
Therefore, a 90% confidence interval estimate of the population standard deviation is 1596.45-4466.73.
Hence, the correct answer is B) 1596.45-4466.73
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