We can start by using the formula for inverse square law: F = k/d^2. where F is the force, d is the distance between the magnets, and k is a constant.
We can use the given information to solve for k: 4 = k/0.06^2, k = 4 * 0.06^2, k = 0.0144
Now we can use the value of k to find the force when the magnets are 0.03 meters and 0.1 meters apart: F1 = 0.0144/0.03^2 = 16, F2 = 0.0144/0.1^2 = 0.144
The work required to move the magnets is equal to the change in potential energy between the initial and final positions.
We can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy plus its change in potential energy. Since the magnets are not moving, their kinetic energy is constant, so the work done on them is equal to their change in potential energy: W = Uf - Ui
where W is the work, Uf is the final potential energy, and Ui is the initial potential energy. The potential energy of the magnets is given by: U = -k/d
where k is the constant we found earlier and d is the distance between the magnets.
Therefore, the initial potential energy is: Ui = -0.0144/0.03 = -0.48
And the final potential energy is: Uf = -0.0144/0.1 = -0.144
So the work required to move the magnets is: W = -0.144 - (-0.48) = 0.336 Joules
Therefore, the work required to move the magnets from 0.03 meters apart to 0.1 meters apart is 0.336 Joules (rounded to three decimal places).
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Graph the line. Y = -3×
Answer:
here it is
Step-by-step explanation:
-3 represents the slope. Since its 3/1, this means which point on the slope is 3 to side and 1 either up or down. Since the slope is negative, it goes down.
The formula for a slope is y = mx + b. Since we don’t have the b, that means it is 0. B represents the y intercept or when the line crosses the y axis.
Do certain car colors attract the attention of the police more than others, so that they are more likely to get speeding tickets? A few years ago a curious newspaper columnist tabulated the car color on a random sample of 120 speeding citations at the local courthouse. Here are his results:
Color Red White/Silver Gray/Black Other
Number of Speeding Tickets 16 33 39 32
He then went to the state motor vehicle registry and obtained data on the distribution of car colors for all cars registered in his state: Red 14%, White/Silver 35%, Gray/Black 23%, Other 28%.
To answer the question poised above about car color and speeding tickets, the appropriate null hypothesis is:
Group of Answer Choices:
-The observed number of speeding tickets is the same for all four color groups
-The observed counts are equal to the expected counts.
-At least one of the four car color percentages is different from the other three.
-The distribution of car colors for the speeding citations is the same as the distribution of colors for cars on the highway.
-The observed counts are all equal to 30
The appropriate null hypothesis for a random sample of car's color and speeding tickets is equals to the observed counts are equal to the expected counts.
The curious newspaper columnist tabulate the car color on a random sample. The above table showed car color and their corresponding speeding tickets. Sample size, n = 120
Registed red colour cars in his state
= 14%
Registed white/silver colour cars in his state= 35%
Registed gray/black colour cars in his state = 23%
Registed others colour cars in his state
= 28%
We habe to determine the right choice for null hypothesis from the options. For this, here we have to use chi square test of goodness of fit to test this hypothesis. We know that in chi square test, they arevalready given the observed frequencies. Then we have to find out the expected frequencies using the given percentages. So here we have to findout whether the expected frequency and observed frequency are equal or not. So the null hypothesis is The observed counts are equal to the expected counts.
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Write the equation for the parabola/quadratic function containing the points
(-1, 1), (1, -5), and (2, 1).
Answer:
The equation for the parabola (quadratic function) that passes through the points (-1, 1), (1, -5), and (2, 1) is y = (6/49)(x - 2/3)^2 - 1.
Step-by-step explanation:
To write the equation of a quadratic function (parabola) given three points, we can use the vertex form of the equation:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola and a is a scaling factor that determines the shape of the parabola.
To find the vertex of the parabola, we can use the formula:
h = (x1 + x2 + x3) / 3
k = (y1 + y2 + y3) / 3
where (x1, y1), (x2, y2), and (x3, y3) are the given points.
Substituting the given points into these formulas, we get:
h = (-1 + 1 + 2) / 3 = 2/3
k = (1 - 5 + 1) / 3 = -1
So the vertex of the parabola is (2/3, -1).
Now, we can substitute this vertex and one of the given points (e.g. (-1, 1)) into the vertex form equation and solve for a:
1 = a(-1 - 2/3)^2 - 1
2 = a(7/3)^2
a = 6/49
So the equation of the parabola is:
y = (6/49)(x - 2/3)^2 - 1
Answer: y = -2x^2 + 6x - 4
Step-by-step explanation:
The equation for this parabola/quadratic function is y = -2x^2 + 6x - 4. To arrive at this equation, we use the fact that the equation for a parabola/quadratic function is y = ax^2 + bx + c, where a, b, and c are constants. We can then substitute in the coordinates of each point to solve for a, b, and c.
For the point (-1,1), we have 1 = -2(-1)^2 + 6(-1) + c, so c = 5.
For the point (1,-5), we have -5 = -2(1)^2 + 6(1) + 5, so -2 = -2.
For the point (2,1), we have 1 = -2(2)^2 + 6(2) + 5, so -4 = -4.
And therefore, the equation is y = -2x^2 + 6x - 4.
A banner is made of a square and a semicircle. The square has side lengths of 24 inches. One side of the square is also the diameter of the semicircle. What is the total area of the banner? Use 3.14 for π.
The total area of the banner is approximately 800.54 square inches.
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners
The area of the square is side length squared, or 24² = 576 square inches.
The diameter of the semicircle is also the side length of the square, so it is 24 inches.
Radius = 24/2=12 inches
The area of a semicircle is half of the area of a circle with the same radius. The area of a circle is π times the radius squared, so the area of the semicircle is:
1/2×π×12²=72π
Add Area of the square and the area of the semicircle:
576 + 72π = 800.54
Therefore, the total area of the banner is approximately 800.54 square inches.
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Use sigma notation to write the Taylor series about x=x0 for the function. e^−x,x0=−1.
Taylor series =∑k=0∞
Answer:
Step-by-step explanation:
To write the Taylor series for the function f(x) = e^(-x) about x = x0 = -1, we first need to find the k-th derivative of f(x) and evaluate it at x = -1.
f(x) = e^(-x)
f'(x) = -e^(-x)
f''(x) = e^(-x)
f'''(x) = -e^(-x)
f''''(x) = e^(-x)
...
The k-th derivative alternates between e^(-x) and -e^(-x), depending on the parity of k.
To evaluate the k-th derivative at x = -1, we substitute -1 into the k-th derivative expression and simplify:
f^k(-1) = (-1)^k * e^1
Now we can write the Taylor series using the formula:
f(x) = f(x0) + (x - x0) f'(x0) / 1! + (x - x0)^2 f''(x0) / 2! + (x - x0)^3 f'''(x0) / 3! + ...
Plugging in the values we obtained earlier, we have:
f(-x0) = e
f'(-x0) = -e
f''(-x0) = e
f'''(-x0) = -e
f''''(-x0) = e
...
Substituting these values into the formula, we get:
f(x) = e - (x + 1)e + (x + 1)^2 e / 2! - (x + 1)^3 e / 3! + (x + 1)^4 e / 4! - ...
Using sigma notation, we can write this as:
f(x) = ∑_{k=0}^∞ (-1)^k (x + 1)^k e / k!
where ∑_{k=0}^∞ represents the sum from k = 0 to infinity.
Please helppppppp meeee
The range, given the cost of surfboard rentals, would be $ 140.
The interquartile range of the cost of surfboard rentals is $ 56.
There is an outlier which is the cost of 6 days of rentals which is $ 168.
How to find the range and interquartile range ?To find the range, the formula is :
= Largest cost - Lowest cost
To find these costs, find the cost of the days of rentals :
1 day : 2 days 3 days :
= 28 x 1 = 28 x 2 = 28 x 3
= $ 28 = $ 56 = $ 84
6 days :
= 28 x 6
= $ 168
The range is therefore :
= 168 - 28
= $ 140
To find the Interquartile range, first find the First Quartile and the Third Quartile after ordering the costs:
Order of costs :
28, 28, 28, 56, 56, 56, 84, 84, 84, 168
First quartile position :
= 1 / 4 x ( n + 1 )
= 1 / 4 x ( 10 + 1 )
= 3 rd position which is $ 28
Third quartile position :
= 3 / 4 x ( n + 1 )
= 3 / 4 x ( 10 + 1 )
= 8 th position which is $ 84
The Interquartile range is :
= 84 - 28
= $ 56
The outlier is the cost of 6 days which is $ 168. This is a rental as it is much larger than other costs.
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mr. preston sponsors the creative writing club. he decided to make booklets of his students' poems and stories to hand out at the school's activity fair. he went to a local printing shop that charges $0.25 per page in the booklet and $1.00 to bind the pages together. the booklet mr. preston is making has p pages, and he plans to make 50 booklets. pick all the expressions that represent how much mr. preston will spend making the booklets. 12.50p 50.00 50(1.25p) 50(0.25p 1.00) 12.50p 50.00p submit
We can use algebraic equations to solve this kind of problems. The correct answer is 50.00( 0.25p+ 1.00). So option number 3 is correct.
The cost of printing a single page = 0.25
The cost of printing p pages = 0.25p
Cost of print 50 booklets with p pages = 50× 0.25p = 12.50p
Cost of binding 1 booklet = $1
Cost of binding 50 booklet = 50
Cost of 50 booklets = Cost of printing 50 booklets with p pages + cost for binding 50 booklets
= 12.5p + 50.00 = 50.00(0.25p+1.00)
So the correct answer is the third option , 50.00 ( 0.25p + 1.00)
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The coordinates of the vertices of triangle XYZ are X(-2, -1), Y(6, 8), and Z(8, 4). Triangle XYZ is dilated by a scale factor of 32
with the origin as the center of dilation to create triangle X’Y’Z’.
If (x, y) represents the location of any point on triangle XYZ, which ordered pair represents the location of the corresponding point on triangle X’Y’Z’?
Responses
(x+32, y+32)
(x+32, y+32)
(23x, 23y)
(23x, 23y)
(32x, 32y)
(32x, 32y)
(x+23, y+23)
Answer: A, i think
Step-by-step explanation: edge 2020
10. Solve the equation 0.5p - 3.45 = -1.2.
Answer:
p = 4.5
Step-by-step explanation:
0.5p - 3.45 = -1.2.
0.5p = -1.2 + 3.45
0.5p = 2.25
0.5p/0.5 = 2.25/0.5
p = 4.5
therefore p is equal to 4.5
select the net number of atp produced from eight molecules of glucose during the process of glycolysis
The net number of ATP produced from eight molecules of glucose during glycolysis is 32 ATP molecules.
Glycolysis is a metabolic pathway that breaks down glucose into two molecules of pyruvate, which in turn produces ATP. Each molecule of glucose yields two molecules of ATP and two molecules of NADH. Each NADH molecule, in turn, produces three more ATP molecules when it is oxidized in the electron transport chain. Therefore, the total number of ATP produced from one molecule of glucose is four. When eight molecules of glucose undergo glycolysis, the total number of ATP produced is 4 x 8 = 32 ATP molecules. hence 32 ATP molecules produced during the process of glycolysis.
The complete question is : select the net number of ATP produced from 8 molecules of glucose during the process of glycolysis is
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Each person in a group buys a ticket, a medium drink, and a large popcorn. Write an expression in simplest form that represents the amount of money the group spends at the movies. Interpret the expression.
Ticket $7.50
DRINKS
Small: $1.75
Medium: $2.75
Large: $3.50
POPCORN
Small: $3.00
Large: $4.00
Answer: 14.25x is the expression
It represents the total combined cost everyone paid.
=======================================================
Explanation:
Add up the price of a ticket, a medium drink, and a large popcorn.
7.50+2.75+4.00 = 14.25
Each person spends $14.25 for those three items.
If x is the unknown number of people, then 14.25x represents the total amount spent by everyone combined.
Example: x = 10 people, so 14.25x = 14.25*10 = 142.50 dollars total is spent by everyone combined.
Square ABDC is shown with diagonal CB. What's true about AABC and ADCB?
ΔABC and ΔDCB would be congruent triangles by the AAS postulate.
What is congruent geometry?In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
Here,
In a square, all sides are equal in length and all angles are right angles (90 degrees). Additionally, the diagonal of a square bisect each other at 90 degrees.
The lengths of AB, BC, CD, and DA are equal.
The angles ABC and CDA are both right angles (90 degrees).
The angles BAC and DCB are both 45 degrees.
So ΔABC and ΔDCB became congruent triangles by the AAS postulate.
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Use the following set definitions to specify each set in roster notation. Except were noted, express elements as Cartesian products as strings. A ={a}
B= {b, c } .
C = {a, b, d} a. Ax (B UC) b. Ax (BnC)
c. ( AxB) U (Ax C) d. (Ax B) n (Ax C) e. P(A x B) P(A) x P(B). Use ordered pair notation for elements of the Cartesian product.
Cartesian product are A.{aa, ab, ac, ad} B. {ab} C. {aa, ab, ad} D.{ab}
Given the set notations A = {a} B = {b, c} C = {a, b, d}
BUC = {a, b, c, d}
B∩C = {b}
a) A × (BUC) = {aa, ab, ac, ad}
b) A × (B ∩ C) = {ab}
c) (A × B) ∪ (A × C)
A × B = {ab, ac} and A × C = {aa, ab, ad}
(A × B) ∪ (A × C) = {aa, ab, ac, ad}
d) For (A × B) ∩ (A × C)
(A × B) ∩ (A × C) = {ab}
The symbol ∩ represents the intersection of sets. For example, the intersection of two sets X and Y can be expressed as X ∩ Y.
The union of two sets P and Q is denoted by P ∪ Q. This is the set of all distinct elements contained in P or Q. The symbol used to represent the union of sets is ∪. The intersection of two sets P and Q is denoted by P ∩ Q. This is the set of all distinct elements in both P and Q. The symbol for the set intersection is ∩. The intersection of two given sets, H. P and Q, is the set containing all elements common to both P and Q.
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the number of pumps in use at both a six-pump station and a four-pump station will be determined. give the possible values for each of the following random variables. (enter your answers in set notation.) (a) t
For each variable, the possible values are:
a) T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
b) X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
c) U = {0, 1, 2, 3, 4, 5, 6}
d) Z = {0, 1, 2}
Item a:
In total, there are 10 pumps, hence the possible values are all integers from 0 to 10, that is:
T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Item b:
In the first, there are 6 pumps, and in the second 4, hence, the difference ranges from -4 to 6, that is:
X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
Item c:
The maximum number in a station is 6 pumps, hence this variable ranges from 0 to 6.
U = {0, 1, 2, 3, 4, 5, 6}
Item d:
Either none of the stations has exactly two pumps in use, or one has or both, hence the variable ranges from 0 to 2.
Z = {0, 1, 2}
The question is incomplete. The complete question is:
"The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables. (Enter your answers in set notation.)
a. T = the total number of pumps in use
b. X = the difference between the numbers in use at stations 1 and 2.
c. U = the maximum number of pumps in use at either station
d. Z = the number of stations having exactly two pumps in use"
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Determine the lateral area and the surface area of each triangular prism by determining the area of the shape’s net.
The lateral area and the surface area of the right prism are 540 square yards and 1152 square yards, respectively.
How to determine the lateral area and the surface area of a triangular prism
Herein we find the case of a right prism with a triangular base, whose lateral area (A) and surface area (A'), both in square yards, must be determined.
The lateral area is the sum of the areas of three rectangular faces and the surface area is the sum of the lateral area and the area of the two triangles. Area formulas for rectangles and triangles are shown below:
Rectangle
A = w · l
Triangle
A = 0.5 · w · l
Where:
w - Width, in yardsl - Length, in yardsNow we determine the lateral area and the surface area of the prism:
Lateral area
A = (37 yd) · (5 yd) + (20 yd) · (5 yd) + (51 yd) · (5 yd)
A = 540 yd²
Surface area
A' = 540 yd² + 2 · 0.5 · (51 yd) · (12 yd)
A' = 1152 yd²
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If you paid $1,650.00 in property taxes on a house appraised at $112,000.00, what is the property tax rate in your neighborhood?
Express your answer rounded to the nearest hundredth of a percent
To calculate the property tax rate, you need to divide the property taxes by the appraised value of the property and then multiply by 100 to express the result as a percentage.
In this case, the property tax rate can be calculated as follows:
Property tax rate = (Property taxes / Appraised value) * 100%
= ($1,650.00 / $112,000.00) * 100%
= 0.014732142857142857 * 100%
= 1.47%
So, the property tax rate in your neighborhood is 1.47%, rounded to the nearest hundredth of a percent.
(Percent) Magnus is selling his clothes online. He is seling his leather jacket for $80 with an additional 5% for shipping and handling. How much would it cost someone to oder the leather jacket from magnus?
Answer:
$84.00
Step-by-step explanation:
$80.00 x .05 = $4.00
$80.00 + $4.00 = $84.00
Answer:
the cost is $84.00
Step-by-step explanation:
you take 80.00 x 5% tax that gives you $4.00 so the total is $84.00
Shelby drew a map of the appalachian trail using the scale 5 centimeters equals 400 kilometers. the map shows the appalachian trail to be 43.75centimeters. What is the actual length of appalachian trail?
PLEASE HELP ASAP
The solution is : 3500km is the actual length of appalachian trail.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
If 5cm represents 400km on the scale, and the map shows 43.75cm then,
Let ,
5cm .......400km
43.65cm......u
now, we get,
Hence by cross multiplication,
5cm* u=43.75cm × 400km
U =(43.75cm ×400km)/5cm
=(17500/5)km
=3500km
Hence, The solution is : 3500km is the actual length of appalachian trail.
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Find the area of the figure. (Sides meet at right angles.)
4 m
3 m
2 m
4 m
3 m
2 m
4 m
The area of the figure can be found to be 53 cm ²
How to find the area of the figure ?The figure given is a composite shape so to find the area of the figure, you need to divide the shape into two other shapes.
The area of the first shape is :
= Length x Width
= 5 x 4
= 20 m ²
The area of the second shape would be :
= Length x Width
= ( 3 + 5 + 3 ) x 3
= 11 x 3
= 33 cm ²
The area of the shape is :
= 20 + 33
= 53 cm ²
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Describe how technology improvements have changed the way we find and apply for jobs. How do you plan to use social media to find a job in the future?
Answer:
Technology improvements allow someone to look up jobs and be able to apply. This is much easier than going around yourself as it takes less time and effort. With technology we are capable of looking at ads of jobs and finding jobs in and around your area. Places such as indeed and linkedin have options for filters to allow you to adjust your search to salaries and areas that suit you.
Hope this helps, have a lovely day! :)
2. = {children who go to the park},
T= {children who play tennis},
G= {children who play golf}
120 children go to the park. 50 play tennis. 75 play golf. 25 do not play tennis or golf.
(a) Show this information in the Venn diagram.
[2]
[1]
(b) How many children play both golf and tennis?
Please let me knowwwwwwww!!!
Answer:
The 2nd option
Step-by-step explanation:
You can substitute values to replace X and if it alines with the graph then you know that is the correct answer choice
find the center, transverse axis, vertices, and foci of the hyperbola. ((x) with superscript (2)/121) - ((y) with superscript (2)/144)
Option C, center at (0, 0) transverse axis is x - axis vertices at (-11, 0) and (11, 0) foci at ([tex]-\sqrt{265}[/tex], 0) and ([tex]\sqrt{265}[/tex], 0) is the correct option.
The transverse axis is a line segment with vertices as its endpoints that traverses the hyperbola's center. The transverse axis's containing line is where the foci are located. The co-vertices serve as the endpoints of the conjugate axis, which is perpendicular to the transverse axis.
The transverse axis is located on the y-axis because of the equation's form, which is y^2a^2-x^2b^2 = 1. The vertices act as the graph's y-intercepts since the hyperbola is centered at the origin. Set x=0 and then solve for y to discover the vertices. Hence, the formula for a hyperbola with foci along the x-axis is x^2a^2-y^2b^2 = 1. The solution can be seen on the attached image below.
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Question correction:
See attached image below.
Straight angle
Obtuse angle
Match each angle description on the left with its possible angle measure, m, on the right.
Acute angle
90 m 180°
Right angle
Submit
Clear
questions
ncludi
Pass
m = 90°
m = 180°
0°
Answer:
makes no sense
Step-by-step explanation:
An empty fuel tank is filled using a cylindrical pipe with diameter 8 cm. Fuel flows along this pipe at a rate of 2 metres per second. It takes 24 minutes to fill the tank. Calculate the capacity of the tank. Give your answer in litres.
The capacity of the tank is 7234.56litres
What is capacity of a tank?Capacity refers to the amount of fluid a container can hold. It expressed in units like litres (l), millilitres (ml). Capacity is also known as volume of a substance.
The capacity of the cylindrical pipe is
V = πr²h
r = 8cm
if it takes the pipe 2m per second
then it's volume in one second is
V = 3.14 ×8 × 2× 100
V = 5024cm³/s
if it takes 24 minutes
24 minutes = 24 × 60 s
= 1440s
therefore volume of the tank = 1440 × 5024
= 7234560cm³
in litres = 7234560/1000
= 7234.56litres
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Someone help me with these math problems.
Answer:
<1=26
<2=154
<3=26
<4=26
<5=154
<6=154
<7=26
How many triangles are formed by the angles and sides unique triangle no triangle or many triangles? 53° and 27°
No triangle can form with the given measurements.
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
The given angles are 53° and 27°.
By using angle sum of property of a triangle, we get
53°+27°+x=180°
x=100°
It is not possible to draw a unique triangle with any 3 possible measurements of angles.
Therefore, no triangle can form with given measurements.
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ASAP!!!! Sixty-eight percent of U.S. adults oppose hydraulic fracturing (fracking) as a means of increasing the production of natural gas and oil in the United States. You randomly select six U.S. adults. Find the probability that the number of U.S. adults who oppose fracking as a means of increasing the production of natural gas and oil in the United States is (a) exactly 2, (b) less than four, and (c) at least three
The probability that the number of U.S. adults who oppose exactly 2, less than 4, and at least 3 will be 0.0727, 0.2925, and 0.9136, respectively.
What is the probability?Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as
[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]
The probability that the number of U.S. adults who oppose exactly 2 is given as,
P(2) = ⁶C₂ x (0.68)² x (1 - 0.68)⁴
P(2) = 0.0727
The probability that the number of U.S. adults who oppose less than four is given as,
P(x < 4) = ⁶C₁ x (0.68)¹ x (1 - 0.68)⁵ + ⁶C₂ x (0.68)² x (1 - 0.68)⁴ + ⁶C₃ x (0.68)³ x (1 - 0.68)³
P(x < 4) = 0.0137 + 0.0727 + 0.2061
P(x < 4) = 0.2925
The probability that the number of U.S. adults who oppose at least three is given as,
P (x ≥ 3) = 1 - ⁶C₁ x (0.68)¹ x (1 - 0.68)⁵ - ⁶C₂ x (0.68)² x (1 - 0.68)⁴
P (x ≥ 3) = 1 - 0.0137 - 0.0727
P (x ≥ 3) = 0.9136
The probability that the number of U.S. adults who oppose exactly 2, less than 4, and at least 3 will be 0.0727, 0.2925, and 0.9136, respectively.
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HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!
The measure of angle x is given as follows:
a. x = 30º.
How to obtain the angle measure?Angle y is complementary with the angle of 60º, meaning that the sum of their measures is of 90º, hence it's measure is given as follows:
y + 60 = 90
y = 30º.
Angle y and angle x form vertical angles, meaning that they are congruent, that is, they have the same measure, hence the measure of angle x is given as follows:
x = y = 30º.
Hence the correct option is given by option a.
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A data set comparing a woman's shoe size to her height is represented by the table.
Shoe Size Height (inches)
7.5 63
8 70.5
12 68
7 71
9 69.5
10 70
12 75
12.5 63
14 72
Using technology, calculate the line of best fit. Identify and interpret the slope in this scenario.
The slope of the line of best fit is 0.25. Each time the shoe size increases by one, the height increases by 0.25 inches.
The slope of the line of best fit is 0.25. Each time the shoe size increases by 0.25, the height increases by one inch.
The slope of the line of best fit is 66.6. Each time the shoe size increases by one, the height increases by 66.6 inches.
The slope of the line of best fit is 66.6. Each time the shoe size increases by 66.6, the height increases by one inch.
The line of best fit is given as follows:
y = 0.25x + 72.25.
The correct option regarding the slope is given as follows:
The slope of the line of best fit is 0.25. Each time the shoe size increases by one, the height increases by 0.25 inches.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points for this problem are given as follows:
(7.5, 63), (8, 80.5), (12, 68), (7, 71), (9, 69.5), (10, 70), (12, 75), (12.5, 63), (14,72)
Inserting these points into a calculator, the equation is given as follows:
y = 0.25x + 72.25.
The slope of 0.25 represents the rate of change of the output variable(height) relative to the input variable(shoe size).
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