The distance between Dallas, Texas and Omaha, Nebraska is 631.4 miles.
The distance between Dallas, Texas and Omaha, Nebraska can be calculated using the Haversine Formula. This formula calculates the great circle distance between two points on a sphere, taking into account the curvature of the Earth. The formula is as follows:
d = 2r arcsin( sqrt[ sin^2((lat2 - lat1)/2) + cos(lat1)cos(lat2)sin^2((lon2 - lon1)/2)] )
In this case, the latitude of Dallas, Texas is 32° 47' 39'' N and the latitude of Omaha, Nebraska is 41° 15' 50'' N. Since the two cities are on the same longitude, we can assume that the longitude for both cities is 0°.
Plugging these values into the formula, we get:
d = 2(4000 miles) arcsin[ sqrt[ sin^2((41° 15' 50'' N - 32° 47' 39'' N)/2) + cos(32° 47' 39'' N)cos(41° 15' 50'' N)sin^2((0° - 0°)/2)] ]
d = 631.4 miles
Therefore, the distance between Dallas, Texas and Omaha, Nebraska is 631.4 miles.
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the accompanying sketch represents a maze of oneway streets in a city in the united states. the traffic volume through certain blocks during an hour has been measured. suppose that the vehicles leaving the area during this hour were exactly the same as those entering it.
Based on the sketch, it appears that the traffic flow in the city would remain the same during the hour. All of the vehicles entering the area would leave it, meaning that the same number of vehicles would remain in the area for the entire hour.
1. The sketch shows a maze of one-way streets in a city in the United States.
2. The traffic volume through certain blocks during an hour has been measured.
3. Suppose that the vehicles leaving the area during this hour were exactly the same as those entering it.
4. This means that the same number of vehicles would remain in the area for the entire hour, as the vehicles entering the area would be the same as those leaving it.
Based on the sketch, it appears that the traffic flow in the city would remain the same during the hour. All of the vehicles entering the area would leave it, meaning that the same number of vehicles would remain in the area for the entire hour.
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which of the following is/are true? (select all that apply) group of answer choices if augmented matrices of two linear systems are row equivalent, the systems have the same solution set. the row replacement operation, when performed on a matrix, results in interchanging two rows.
two matrices are called row equivalent if one matrix can be transformed into another by applying a sequence of elementary row operations. in an echelon form of a matrix, all entries in a column below the leading entry are zero. the reduced echelon form of a matrix is not defined uniquely.
The following statements are true: if augmented matrices of two linear systems are row equivalent, the systems have the same solution set; two matrices are called row equivalent if one matrix can be transformed into another by applying a sequence of elementary row operations; in an echelon form of a matrix, all entries in a column below the leading entry are zero; the reduced echelon form of a matrix is not defined uniquely.
The row replacement operation, when performed on a matrix, results in interchanging two rows. This statement is not true. Row replacement operations can also be used to add multiples of one row to another, it doesn't necessarily interchange two rows.
The statement "if augmented matrices of two linear systems are row equivalent, the systems have the same solution set." is true. Row equivalence is a property of matrices that describes how two matrices can be transformed into one another by performing elementary row operations. If two matrices are row equivalent, it means that they can be transformed into the same row echelon form, which implies that they have the same row space, and therefore the same solution set.
The statement "two matrices are called row equivalent if one matrix can be transformed into another by applying a sequence of elementary row operations." is true. Two matrices are row equivalent if one matrix can be transformed into another by applying a sequence of elementary row operations, such as row interchanges, row scaling, and row replacement.
The statement "in an echelon form of a matrix, all entries in a column below the leading entry are zero." is true. An echelon form of a matrix is a matrix that has the following properties: all non-zero rows are above any rows of all zeroes, the leading entry of a non-zero row is to the right of the leading entry of the row above it. In an echelon form of a matrix, all entries in a column below the leading entry are zero.
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What is the greatest number of consecutive integers
that sum to –11? PLS NOW
Answer:
It is not possible for the sum of consecutive integers to be -11. The sum of n consecutive integers is n times the average of the first and last integers. The average of any two integers is a fraction, which when multiplied by n, will always yield a fraction, which cannot equal -11. Therefore it is not possible to have n consecutive integers that sum to -11.
Each of 12 refrigerators of a certain type has been returned to a distributor because of the presence of a high-pitched oscillating noise when the refrigerator is running. Suppose that 5 of these 12 have defective compressors and the other 7 have less serious problems. If they are examined in random order, let X = the number among the first 6 examined that have a defective compressor. Compute the following:
(i) P(X = 1)
(ii) P(X ≥ 4)
(iii) P(1≤X ≤3)
(a) .1136, .1212 and 0.7955 respectively.
(b) .1136, .1212 and 0.1136 respectively.
(c) .1136, .1212 and 0.8712 respectively.
(d) .1136, .039 and 0.7955 respectively. (e) .1136, .039 and 0.8712 respectively.
The probability of one defective compressor among the first 6 examined, the probability of four or more defective compressors among the first 6 examined, and the probability of 1 to 3 defective compressors among the first 6 examined are 0.1136, 0.1212, and 0.7955 respectively.
(a) .1136, .1212 and 0.7955 respectively.
(i) P(X=1) = C(5,1) / C(12,6) = 5/66 = 0.1136
(ii) P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = C(5,4) / C(12,6) + C(5,5) / C(12,6) + C(5,6) / C(12,6) = .1212
(iii) P(1≤X ≤3) = P(X = 1) + P(X = 2) + P(X = 3) = C(5,1) / C(12,6) + C(5,2) / C(12,6) + C(5,3) / C(12,6) = 0.7955
The probability of one defective compressor among the first 6 examined is P(X = 1) = C(5,1) / C(12,6) = 5/66 = 0.1136. The probability of four or more defective compressors among the first 6 examined is P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = C(5,4) / C(12,6) + C(5,5) / C(12,6) + C(5,6) / C(12,6) = .1212. The probability of 1 to 3 defective compressors among the first 6 examined is P(1≤X ≤3) = P(X = 1) + P(X = 2) + P(X = 3) = C(5,1) / C(12,6) + C(5,2) / C(12,6) + C(5,3) / C(12,6) = 0.7955.
Therefore, the probability of one defective compressor among the first 6 examined, the probability of four or more defective compressors among the first 6 examined, and the probability of 1 to 3 defective compressors among the first 6 examined are 0.1136, 0.1212, and 0.7955 respectively.
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for a nrw musical adult tickets cost 5 dollars and students cost three 56 tickets were sold for a total of 232
Answer: We can set up a system of equations to represent the given information:
Let x be the number of adult tickets sold
Let y be the number of student tickets sold
x + y = 56 (the total number of tickets sold is 56)
5x + 3y = 232 (the total amount of money made is 232 dollars)
To find the number of adult and student tickets sold, we can use the first equation to solve for one of the variables in terms of the other, and then substitute that into the second equation.
x + y = 56
x = 56 - y
Now we can substitute this value of x into the second equation:
5(56 - y) + 3y = 232
280 - 5y + 3y = 232
280 = 8y
y = 35
So, 35 student tickets were sold, and 56 - 35 = 21 adult tickets were sold.
Step-by-step explanation:
andre measured the lenghts of 10 sticks to the nearest inch. the lenghts of the sticks were 3,3,4,3,3,5,4,6,5 and 4 inches
The 4th line plot picture correctly shows the data of the lengths of the sticks that were 3, 3, 4, 3, 3, 5, 4, 6, 5 and 4 inches.
What is line plot?A line plot is a graph that uses symbols to represent data above a frequency number line. It is used to arrange the data simply and is very simple to understand.
A line plot is a graphical representation of data on a number line which uses dots, crosses, or any other symbol. The scale of the graph is represented by each mark, which corresponds to a particular quantity.
The data on a number line can be graphically represented using symbols using a line plot graph. In contrast to a line graph, no cartesian plane or x and y axes are used in this data representation. Simple lines are drawn on a number line to represent a line plot graph.
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Full question:
Andre measured the lengths of 10 sticks to the nearest inch. the lenghts of the sticks were 3,3,4,3,3,5,4,6,5 and 4 inches. Click on the line plot that shows these data. Lengths of Sticks (in inches) Lengths of Sticks (in inches) Lengths of Sticks (in inches) Lengths of Sticks.
What is the cost of 6 pencils at 60 cents a dozen
To determine the cost of 6 pencils at 60 cents a dozen, we need to convert the price per dozen to the price per pencil. We know that a dozen is equal to 12, so we can use the following formula:
Price per pencil = (Price per dozen) / (Number of items per dozen)
So, in this case:
Price per pencil = (60 cents) / (12 pencils)
To convert cents to dollars, we divide by 100.
Price per pencil = (60/100) $ = 0.6 $
To find the total cost for 6 pencils we multiply the price per pencil by the number of pencils
Cost of 6 pencils = 6 * 0.6 = 3.6 $
So the cost of 6 pencils at 60 cents a dozen is 3.6 $.
Use the ALEKS calculator to evaluate each expression.
Round your answers to the nearest thousandth.
Do not round any intermediate computations.
log√7 =
Log 23/6=
Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current amount.
Logarithmic evaluationLog√7 = 1.659Log 23/6 = 0.862It is a rapid increase in the quantity of something over a period of time. Exponential growth can be seen in populations, investments, and other areas.It is characterized by a doubling or tripling of the original amount within a specified period of time.This type of growth is often caused by compounding, where gains from one period are reinvested in the next period, leading to a rapid increase in the overall amount.Exponential growth is often seen in the early stage of a business, when it is experiencing rapid growth due to investments or other factors.However, exponential growth can also lead to rapid decline if not managed properly.This is called logarithmic evaluation, which involves using logarithms to simplify complex expressions.To learn more about logarithmic evaluation refer to:
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given a pair of similar triangles find the missing length x and the missing angles a,b,c
Angles of similar triangles are always congruent a: 63, b: 88, c: 29 and x = 53.75
Find the missing length?Based on the information available, there are numerous equations for calculating the area of a triangle. As indicated in the calculator above, please use the Triangle formula for additional information and equations for calculating the area of a triangle as well as determining the sides of a triangle using whatever information is available.
find the ratio between the two triangles:
40 on the left corresponds to 50 on the right = 40/50 = 43/x
to find x:
40x = 43 × 50
40x = 215
x = 215/40
x = 53.75
"angles of similar triangles are always congruent."
a: 63
b: 88
c: 29
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Full question:
Given a pair of similar triangles, find the missing length x and the missing angles A, B, and C.
The doctor orders 500,000 Unlts of penicillin for the patient: The capsules avallable are 200,OOUnits and 100,000 Units Wlth the fwest capsules how many capsules would be given per dosc? (____) 200,000 mo capsuics (____) 100,000 ma capsulcs
Patient needs to 500,000 unit of penicillin, then according to capsule availability we shall provide the 2 capsules of 200,000 unit and 1 capsule of 100,000 unit.
The doctor orders 500,000 unit of penicillin for the patient. the capsule available are 200,000 unit and 100,000 units.
we have to find out the number of capsules required for 500,000 unit,
let's see,
we have 200,000 unit of penicillin and 100,000 units of penicillin available,
patient need of 500,000 unit of penicillin,
so we shall provide the 2 capsule of 200,000 units of penicillin and 1 capsule of penicillin 100,000 unit to the patient,
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Last year, The Lakewood Times had a total of 4,770 subscribers. This year, after the paper
was bought out, it had 6,201 subscribers. What is the percent of increase in the number of
subscribers?
%
The Lakewood Times had a 30.4% increase in the number of subscribers after it was bought out.
What is the percentage increase?
Percent increase is a way of measuring how much something has increased relative to its original value. It is expressed as a percentage, and it is calculated by taking the difference between the new value and the original value, and then dividing that difference by the original value, and then multiplying by 100.
Formula: % increase = (new value - original value) / original value x 100
To find the percent increase, you can use the formula:
% increase = (new value - old value) / old value x 100
In this case, the percent increase would be:
% increase = (6201 - 4770) / 4770 x 100 = 30.4%
Hence, The Lakewood Times had a 30.4% increase in the number of subscribers after it was bought out.
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what is the unit rate of 6/11 1/6
Answer:
Step-by-step explanation:
Answer:
36/11 or 3.2727
Step-by-step explanation:
A unit rate is a rate with 1 in the denominator.
Since you didn't specify, I assume 6/11 per 1/6 rate.
Divide 6/11 by 1/6
[tex]\frac{6}{11} /\frac{1}{6}[/tex]
Multiply the reciprocal:
[tex]\frac{6}{11} *\frac{6}{1}=\frac{36}{11}[/tex]
use the method of midpoint rectangles (do not use the integral or antiderivative) to approximate the area under the curve f ( x )
The method of midpoint rectangles is a numerical integration technique used to approximate the area under a curve.
It is based on the idea of breaking up the area under the curve into a series of rectangles and approximating the area of each rectangle using the midpoint of the interval.
For example,
Let's say we want to approximate the area under the curve f(x) = x^2 from x = 0 to x = 2 using the method of midpoint rectangles.
We divide the interval into n = 4 subintervals of width 0.5.
We can calculate the midpoints of the intervals as follows:
interval 1: (0,0.5)
interval 2: (0.5,1)
interval 3: (1,1.5)
interval 4: (1.5,2)
We find the height of each rectangle as the value of f(x) at the midpoint of the interval.
interval 1: f(0.25) = 0.25^2 = 0.0625
interval 2: f(0.75) = 0.75^2 = 0.5625
interval 3: f(1.25) = 1.25^2 = 1.5625
interval 4: f(1.75) = 1.75^2 = 3.0625
We multiply the width of each rectangle (0.5) by the height of each rectangle to find the area of each rectangle:
interval 1: 0.5 * 0.0625 = 0.03125
interval 2: 0.5 * 0.5625 = 0.28125
interval 3: 0.5 * 1.5625 = 0.78125
interval 4: 0.5 * 3.0625 = 1.53125
Finally, we add the areas of all the rectangles to find the total approximate area under the curve:
0.03125 + 0.28125 + 0.78125 + 1.53125 = 2.64375
Hence, using this method the area under the curve f(x) = x^2 from x = 0 to x = 2 is approximately 2.64375.
Note: The precision of the result will depend on how many rectangles you use, and how small you make the rectangles.
The more rectangles we use and the smaller width of each rectangle, the more accurate our result will be.
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Find three sets of points that are on the line y=5/3x-2
Note that these points are not different from each other and are on the same line y = 5/3x - 2.
Any point on this line will have the coordinates (x, y) such that y = 5/3x - 2.
What are the points on a line?Generally, A point on a line is any place along that line that is represented by a set of coordinates in either two- or three-dimensional space, denoted by the letters x, y, or x, y, z, respectively.
An equation, such as y = mx + b, may be used to define a line in a mathematical context. In this equation, m refers to the slope, while b refers to the y-intercept.
Any point that can be made to fit into this equation is up for grabs.
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what property states that if two sides are congruent, then the angles opposite to them are congruent as well?
The converse of the Pythagorean Theorem states that if two sides of a triangle are congruent, then the angles opposite to them are also congruent. This property is known as the Corresponding Angles Postulate.
The Pythagorean Theorem states that the sum of the squares of the lengths of the two sides of a right triangle are equal to the square of the length of the hypotenuse. The theorem is written as a^2 + b^2 = c^2. The converse of the Pythagorean Theorem states that if two sides of a triangle are congruent, then the angles opposite to them are also congruent. This property is known as the Corresponding Angles Postulate. To prove this postulate, we can start with an arbitrary triangle ABC. If we extend the side AC to D, then we can create a line parallel to BC, creating two similar triangles, ABC and ADC. Since similar triangles have corresponding angles that are congruent, then angle A = angle D. Since side AC is congruent to side AD, then angle A is also congruent to angle B. This proves the Corresponding Angles Postulate.
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Find the mistake: Explain what the person did incorrectly while solving the problem or how you would solve it.
5x + 8 = 2x + 20
5x + 8 = 2x + 20
-2x -2x
3x + 8 = 20
-8 -8
3x = 12
times each side by 3
x = 36
Solve for the indicated variable.
H = kx - kx0 for x
Answer:
5.0 if you love life
Step-by-step explanation:
The volume of a cylinder is 282.6 cubic yards. The radius measures 3 yards. What is the height of the cylinder rounded to the nearest yard? Use 3.14 for π. PLEASE HELP WANTED TTYY!!!
Answer:
10 yards
Step-by-step explanation:
You want the height of a cylinder of radius 3 yards that has a volume of 282.6 cubic yards, using pi = 3.14.
VolumeThe volume of a cylinder is given by ...
V = πr²h
Using the given values, this is ...
282.6 yd³ = 3.14(3 yd)²·h = 28.26h yd²
Dividing by the coefficient of h, we find it to be ...
h = (282.6 yd³)/(28.26 yd²) = 10 yd
The height of the cylinder is 10 yards.
A ball is thrown straight downward from the top of a tall building. The initial speed of the ball is10 m/s. It strikes the ground with a speed of60 m/s. How tall is the building? 28. A baseball is thrown straight downward with an initial speed of40ft/sfrom the top of the Washington Monument (555fthigh). How long does it take to reach the ground, and with what speed does the baseball strike the ground?
The tall of the building is 175m and the baseball strikes the ground in 4.53 seconds, 195 ft/s.
Assume that the acceleration due to gravity is 10m/s2.
The equation for the ball’s velocity in the downward direction is
v(t) = at + v₀.
Here
v₀=10m/s a=10m/s² v(t)=60m/s
Solving this for t we get the:
[tex]t =\frac{60m/s-10m/s}{10m/s^2}\\ \\t=\frac{50m/s}{10m/s^2}\\[/tex]
t=5s
The total distance traveled will be
[tex]x(t)=\frac{1}{2} at^2+v_{0} +x_{0}[/tex]
Here x₀ = 0 and we get:
[tex]x(t)=\frac{1}{2} (10m/s^2)(5s)^2+(10m/s)(5s)[/tex]
x=125m+50m
x=175m
The given values are:
u = 50 ft/s
h = 555 ft
g = 32 ft/s²
Let the time taken by the ball to reach the ground be t and the velocity of the ball as it hits the ground be v.
Use the third equation of motion
v²=u²+2as
v²=50²+2*32*555
v = 195 ft /s
Thus, the ball strikes the ground with a velocity of 195 ft/s.
Use the first equation of motion
v = u + at
195 = 50 + 32 t
32 t = 145
t = 4.53 second
Thus, the ball reaches the ground in 4.53 seconds.
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Regina bought a handmade quilt at original cost $120 to sale in her quilt store. She marked the price of 55%. What is the amount of markup
Color Number of Stickers Brown 86 Green 24 Yellow 32 Orange 21 Red 21 Blue 30 How is the histogram for the stickers from the large package distributed?
(Algebra 2 Normal Distribution)
The distribution of the histogram for the large packages colors is given as follows:
Right skewed.
How to obtain the distribution of the histogram?The distribution depends on whichever of the mean or the median is greater, as follows:
Hence the distribution is defined as follows:
Mean greater than median: Positively(right) skewedMean less than the median: Negatively(left) skewedThe ordered data-set is given as follows:
21, 21, 24, 30, 32, 86.
The median is the mean of the two-middle values, hence:
Median = (24 + 30)/2
Median = 27.
The mean is the sum of all the observations divided by the number of observations, hence:
Mean = (21 + 21 + 24 + 30 + 32 + 86)/6
Mean = 35.67.
Mean > median, hence the distribution is right skewed.
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The Cincinnati zoo had 25 snakes last year and this year they have 30 snakes what is the percent increase in snakes from last year to this year
The percentage increase in snakes from last year to this year at the Cincinnati Zoo is 20%.
What is the percentage increase?The percentage increase refers to the ratio of the increase in the number of snakes in the zoo.
The percentage increase can be computed as the quotient of the amount of increase divided by the previous number of snakes, multiplied by 100.
The number of snakes in the zoo last year = 25
The number of snakes in the zoo currently = 30
The increase in the number of snakes = 5 (30 - 25)
The percentage increase = 20% (5/25 x 100)
Thus, we can conclude that the number of snakes in the Cincinnati Zoo has increased by 20 percent since last year.
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What conditions must be met for the results of an ANOVA test to be reliable? Check all that apply.
A) The observations must be independent of each other and randomly selected from their populations.
B) The variances for each population must be approximately equal to each other.
C) The populations from which each group is drawn must be approximately Normal.
D) The hypothesized means of the populations from which each group is drawn must be approximately equal
The results of the ANOVA test may not be reliable.
The conditions that must be met for the results of an ANOVA test to be reliable are that the observations must be independent of each other and randomly selected from their populations (A). Additionally, the variances for each population must be approximately equal to each other (B). This can be tested with the F-test, which is calculated by dividing the variance of the sample means by the variance of the individual observations. This test is used to determine if the variability between the groups is greater than the variability within the groups. If the F-test returns a value greater than 1, then the variances are not equal and the results of the ANOVA test may not be reliable. Lastly, the populations from which each group is drawn must be approximately Normal (C). This can be tested with a Shapiro-Wilk test or a visual inspection of a histogram or qqplot. If the populations are not normally distributed, then the results of the ANOVA test may not be reliable. The hypothesized means of the populations from which each group is drawn must be approximately equal (D). This can be tested with a t-test or a confidence interval. If the means are significantly different, then the results of the ANOVA test may not be reliable.
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angle bisector altitude median centroid orthocenter circumcenter incenter find missing values worksheet
Two straightforward equations are all that are left for us to solve. Therefore, the x and y values determine the coordinates of the orthocenter.
What is angle?When two rays or straight lines intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points meet. The Latin word "angulus," which means "corner," is where the term "angle" first appeared.
Its coordinates are determined using the orthocenter formula. Let's take a look at the triangle ABC in the illustration above. AD, BE, and CF are the perpendiculars that are drawn from the vertices A(x1,y1), B(x2,y2), and C(x3,y3), respectively. The three elevations come together at point O.
The slope of the triangle's sides must first be determined using the following formula:
m = y2 - y1/x2 - x1
The slope of the triangle ABC's altitudes will now be the line's perpendicular slope.
Line slope perpendicular to the plane is -1/m
Let mAC be the slope of the AC. Hence,
mAC = y3 - y1/x3 - x1
Similarly, mBC = (y3 - y2)/(x3 - x2)
Now, the corresponding altitudes' slopes are as follows:
BE slope: mBE = -1/mAC
AD slope: mAD = -1/mBC
Now, in order to determine the equations of the lines that coincide with BE and AD, we will use the slope point form equation of a straight line.
Hence,
mBE = (y - y2)/(x - x2)
mAD = (y - y1)/(x - x1)
As a result, we are left with two equations that are simple to answer. The orthocenter's coordinates are thus determined by the values of x and y.
The complete question is :
The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.
For an acute angle triangle, the orthocenter lies inside the triangle.For the obtuse angle triangle, the orthocenter lies outside the triangle.For a right triangle, the orthocenter lies on the vertex of the right angle.Take an example of a triangle ABC.
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Vertical angles: Which of the sets of angles are vertical angles?
a
a and b
a and c
O a and d
Ob and c
Ob and d
Oc and d
b
There are two vertical angles created by the intersection of two lines.
What is meant by vertical angles?An isosceles triangle has a vertical angle that is twice as large as the total of its base angles. Angles that are vertically opposed to one another are always equal to one another. A vertical angle and the angle to which it is next are also supplementary angles; that is, they sum up to 180 degrees. For instance, if two lines make an angle with X = 45°, the opposing angle will also be 45°.Two vertical angle pairs make up a total of four angles, which always sum to 360 degrees.Angles that come from each pair of vertical angles are referred to as neighboring angles and are additional (the angles sum up to 180 degrees).To learn more about vertical angles, refer to:
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43.How's the economy? A poll conducted by the American Research Group asked individuals their views on how the economy will be a year from now. Respondents were given four choices: Better than today, Same as today, Worse than today, and Undecided. Are these choices nominal or ordinal?
It is nominal because they all mean the same thing
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 35% salt and Solution B is 60% salt. She wants to obtain 150 ounces of a mixture that is 45% salt. How many ounces of each solution should she use?
Answers:
90 ounces of solution A.
60 ounces of solution B.
====================================================
Explanation:
x = amount of solution A
150-x = amount of solution B
Each amount is in ounces and they add to 150 ounces.
Solution A is 35% salt, so we get 0.35x ounces of pure salt from solution A.
Solution B is 60% salt, so we get 0.60*(150-x) = 90-0.60x ounces of pure salt from solution B.
We want 150 ounces of 45% salt solution, which means we want 150*0.45 = 67.5 ounces of pure salt when everything is mixed.
Here's a table showing this info
[tex]\begin{array}{|c|c|c|} \cline{1-3}& \text{Mixture} & \text{Pure Salt}\\\cline{1-3}\text{Solution A} & \text{x} & 0.35\text{x}\\\cline{1-3}\text{Solution B} & 150-\text{x} & 0.60(150-\text{x}) = 90-0.60\text{x}\\\cline{1-3}\text{Total} & 150 & 150*0.45 = 67.5 \\\cline{1-3}\end{array}[/tex]
Cleaning up the table a bit shows
[tex]\begin{array}{|c|c|c|} \cline{1-3}& \text{Mixture} & \text{Pure Salt}\\\cline{1-3}\text{Solution A} & \text{x} & 0.35\text{x}\\\cline{1-3}\text{Solution B} & 150-\text{x} & 90-0.60\text{x}\\\cline{1-3}\text{Total} & 150 & 67.5 \\\cline{1-3}\end{array}[/tex]
Focus on the "pure salt" column.
We want the 0.35x and 90-0.60x to add to 67.5
So,
0.35x+(90-0.60x) = 67.5
90-0.25x = 67.5
-0.25x = 67.5-90
-0.25x = -22.5
x = -22.5/(-0.25)
x = 90
She must use 90 ounces of solution A.
150-x = 150-90 = 60 ounces of solution B must be used as well.
-------------------
Check:
35% of 90 = 0.35*90 = 31.5 ounces of pure salt comes from solution A.
60% of 60 = 0.60*60 = 36 ounces of pure salt comes from solution B.
31.5+36 = 67.5 ounces of pure salt in total, which matches with the value mentioned earlier. The answers are confirmed.
Not all visitors to a certain company's website are customers,. In fact, the website administrator estimates that about 12% of all visitors to the website are looking for other websites. Assuming that this estimate is correct, find the probability that, in a random sample of 5 visitors to the website, exactly 2 actually are looking for the website
This question involves the binomial probability distribution. The probability of exactly 2 successful outcomes (in this case, visitors who are looking for the website) in 5 trials (visitors to the website) can be calculated using the formula:
P(X = 2) = (5C2)(0.12)^2(0.88)^3
Where C represents the binomial coefficient and 0.12 and 0.88 represent the probability of a successful outcome (looking for the website) and unsuccessful outcome (not looking for the website), respectively.
Calculating this gives:
P(X = 2) = (5C2)(0.12)^2(0.88)^3 = 100.01440.4712 = 0.066
So the probability that, in a random sample of 5 visitors to the website, exactly 2 are looking for the website is 0.066 or about 6.6%.
If a fair die is rolled 3 times, what is the probability, to the nearest thousandth, of getting exactly 1 three?
The probability of getting exactly 1 three, to the nearest thousandth is 0.347.
What is Binomial Distribution?Binomial distribution is the distribution of a random variable X for which there are only two possibilities. The probability p for the success and the probability of 1-p for the failure, which consist of n trials.
The binomial distribution has the formula,
P(x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ
where x : number of times for a specific outcome within n trials
p : probability of success in each trial
n : number of trials
Given that a fair die is rolled 3 times.
Here, n = 3, x = 1
p = probability of getting three for 1 trial = 1/6
1 - p = 1 - 1/6 = 5/6
P(1) = ³C₁ (1/6)¹ (5/6)³⁻¹
= 0.347
Hence the probability of getting exactly 1 three is 0.347.
Learn more about Binomial Distribution here :
https://brainly.com/question/14565246
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Teachers in a district have been teaching for a mean of 8 years with a standard deviation of 3 years, and the distribution of years teaching is strongly skewed to the right. Suppose we took random samples of 30 teachers from this district and calculated x as the sample mean of how long each group of teachers had been teaching. We can assume that the teachers in each sample are independent.
Answer:C. Approx. Normal
Step-by-step explanation:
