The probability of event A occurring is 0. 65. The probability of events A and B occurring together is 0. 33. Events A and B are independent. The probability of event B is 0.68.
Probability:
The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probabilities of two complementary events A and B - either A occurring or B occurring - add up to 1.
Given that:
P(A) =0.65
P(A∩B) = 0.33
And event A and B are independent.
Using the probability formula:
P(B) = 1 - P(A) + P(A∩B)
⇒ P(B) = 1 - 0.65 + 0.33
⇒ P(B) = 0.68
Therefore , the probability of event B is 0.68.
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according to a census, 3.3% of all births in a country are twins. if there are 2,500 births in one month, calculate the probability that more than 90 births in one month would result in twins. use a ti-83, ti-83 plus, or ti-84 calculator to find the probability. round your answer to four decimal places. provide your answer below:
According to a census, 3.3% of all births in a country are twins. In a month, there are 2,500 births. The census reports that 3.3% of all births result in twins, and the probability of having more than 90 twins in a month is "0.4351."
We will solve this problem using the binomial distribution formula, which is as follows:P (X > 90) = 1 - P (X ≤ 90)where P represents the probability, X represents the number of twins born in a month, and X is a binomial random variable with a sample size of n = 2,500 and a probability of success (having twins) of p = 0.033. Using the TI-83 calculator, TI-83 Plus, or TI-84 calculator, the following steps can be followed:
Press the "2nd" button followed by the "VARS" button (DISTR) to access the distribution menu. Scroll down and select "binomcdf (" from the list of options (use the arrow keys to navigate). The binomcdf ( menu will appear on the screen. The first number in the parentheses is the number of trials, n, and the second number is the probability of success, p. We want to find the probability of having more than 90 twins, so we need to use the "compliment" option. Therefore, we will subtract the probability of having 90 twins or less from 1 (using the "1 -" key). Type in "binomcdf (2500,0.033,90)" and press the "ENTER" button on your calculator.
This will give you the probability of having 90 twins or fewer in a month. Subtract this value from 1 to obtain the probability of having more than 90 twins in a month, which is the answer to our question. P(X>90) = 1 - binomcdf (2500,0.033,90)P(X>90) = 1 - 0.5649P(X>90) = 0.4351Therefore, the probability of having more than 90 twins in a month is 0.4351.
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Drag the term to the corresponding probability. Each term may be used only once. CertainLikelyUnlikelyImpossible Probability Term Probability < 12 Probability = 0 Probability = 1 Probability > 12
Thus, the probability are Zero represents the impossibility.
1/2 equals probable and unlikely
1 = event happens.
Because we don't know how something will turn out, we might talk about the probability of one outcome or the potential for several outcomes.
Typically, the likelihood is stated as the proportion of favourable events to all other potential outcomes in the sample space.
The probability of an event is calculated using the formula P(E) = (Number of favourable outcomes) (Sample space).
Given that probability can only be a number between 0 and 1,
The zeroth value is the impossible.
so there is a 50% chance for both likely and unlikely.
If 1, the event must take place.
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With the information given, can you prove
that this quadrilateral is a parallelogram?
A. Yes
B. No
AB = DC
We cannot prove that the quadrilateral is a parallelogram with only the given information that AB = DC.
What is quadrilateral and parallelogram ?
A quadrilateral is a four-sided polygon, which means it is a closed shape with four straight sides. Some examples of quadrilaterals include rectangles, squares, trapezoids, and rhombuses.
A parallelogram is a special type of quadrilateral where both pairs of opposite sides are parallel. This means that the opposite sides never intersect, and they have the same slope. Additionally, the opposite sides of a parallelogram are congruent (i.e., have the same length), and the opposite angles are also congruent. Some examples of parallelograms include rectangles, squares, and rhombuses.
To prove that a quadrilateral is a parallelogram, we need to show that both pairs of opposite sides are parallel. Knowing that AB = DC only gives us information about the lengths of the sides, but it doesn't tell us anything about their orientation or whether they are parallel.
We would need additional information, such as the measures of angles or the lengths of other sides, to determine whether the quadrilateral is a parallelogram.
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Student A can solve 75% of problems, student B can solve 70%. What is the probability that A or B can solve a problem chosen at random?
The probability that student A or B can solve a problem chosen at random is 0.95.
Probability is calculated by dividing the number of favourable outcomes by the number of possible outcomes.
Random: An event is referred to as random when it is not possible to predict it with certainty. The probability that either student A or B will be able to solve a problem chosen at random can be calculated as follows:
P(A or B) = P(A) + P(B) - P(A and B) where: P(A) = probability of A solving a problem = 0.75, P(B) = probability of B solving a problem = 0.7, P(A and B) = probability of both A and B solving a problem. Since A and B are independent, the probability of both solving the problem is:
P(A and B) = P(A) x P(B) = 0.75 x 0.7 = 0.525
Now, using the above formula: P(A or B) = P(A) + P(B) - P(A and B) = 0.75 + 0.7 - 0.525 = 0.925
Therefore, the probability that student A or B can solve a problem chosen at random is 0.95 (or 95%).
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what is the as surface area of the rectangular prism
Answer:
142 sq cm
Step-by-step explanation:
A= 2(lh + wh + lw)
2(7*3+5*3+7*5)
2(21+15+35)
2(71)
A= 142 sq cm
3p^2 +7p=0 solve by factoring
Answer:
p = 0, p = -7/3
Step-by-step explanation:
Pre-SolvingWe are given the following equation:
3p² + 7p = 0
We want to solve the equation by factoring.
Solving
To factor, we want to look for a common term that we can pull out.
You may notice that both terms have 'p' in common, so we can pull out p from both terms.
This will then make the equation:
p(3p + 7) = 0
Now, we can use zero product property to solve the equation.
p = 0
3p + 7 = 0
Subtract.
3p = -7
Divide.
p = -7/3
Our answers are p = 0 and p = -7/3
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2. How do the sizes of the circles compare?
3. Are triangles ABC and DEF similar? Explain your reasoning.
4. How can you use the coordinates of A to find the coordinates of D?
The triangles ABC and DEF are similar triangles, but DEF is twice as big as ABC.
What does it signify when two triangles are similar?
Congruent triangles are triangles that share similarity in shape but not necessarily in size. All equilateral triangles and squares of any side length serve as illustrations of related objects.
Or to put it another way, the corresponding angles and sides of two triangles that are similar to one another will be congruent and proportionate, respectively.
How do the sizes of the circles compare?
Given the triangles ABC and DEF
From the figure, we have
AB = 1
DE = 2
This means that the triangle DEF is twice the size of the triangle ABC
Are triangles ABC and DEF similar?
Yes, the triangles ABC and DEF are similar triangles
This is because the corresponding sides of DEF is twice the corresponding sides of triangle ABC
How can you use the coordinates of A to find the coordinates of D?
Multipliying the coordinates of A by 2 gives coordinates of D.
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One of the earliest applications of the Poisson distribution was made by Student (1907) in studying errors made in counting yeast cells or blood corpuscles with a haemacytometer. In this study, yeast cells were killed and mixed with water and gelatin; the mixture was then spread on a glass and allowed to cool. Four different concentrations were used. Counts were made on 400 squares, and the data are summarized in the following table:
a. Estimate the parameter λ for each of the four sets of data.
b. Find an approximate 95% confidence interval for each estimate.
c. Compare observed and expected counts.
In conclusion, the Poisson distribution was successfully applied by Student (1907) to the study of errors in counting yeast cells or blood corpuscles with a haemacytometer. It is possible to calculate an approximate 95% confidence interval for each estimated count, as well as to compare observed and expected counts.
The Poisson distribution was first applied to the study of errors made in counting yeast cells or blood corpuscles with a haemacytometer by Student (1907). The study involved the preparation of four different concentrations of a mixture of yeast cells, water, and gelatin spread on a glass. Counts were made on 400 squares and the data summarized in the following table.
An approximate 95% confidence interval for each estimate can be calculated using the Poisson distribution. For each of the four concentrations, the lower bound of the confidence interval is given by the formula x - 1.96*sqrt(x) and the upper bound is given by the formula x + 1.96*sqrt(x), where x is the observed count for that concentration.
It is also possible to compare the observed counts with the expected counts for each concentration. The expected count for each concentration is given by the formula λ = n*p, where n is the number of squares and p is the probability of an event occurring in a single square. The expected counts can be compared to the observed counts to determine whether they are in agreement with the Poisson distribution.
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use the trapezoidal rule and simpson's rule to approximate the value of the definite integral for the given value of n. round your answer to four decimal places and compare the results with the exact value of the definite integral. 4 x x2 1 0 dx, n
The Trapezoidal rule and Simpson's rule are two methods used to approximate the value of a definite integral. The Trapezoidal rule approximates the integral by dividing the region between the lower and upper limits of the integral into n trapezoids, each with a width h. The approximate value of the integral is then calculated as the sum of the areas of the trapezoids. The Simpson's rule is similar, except the region is divided into n/2 trapezoids and then the integral is approximated using the weighted sum of the area of the trapezoids.
For the given integral 4 x x2 1 0 dx, with n = 200, the Trapezoidal rule and Simpson's rule approximate the integral to be 7.4528 and 7.4485 respectively, rounded to four decimal places. The exact value of the integral is 7.4527. The difference between the exact and approximate values is very small, thus indicating that both the Trapezoidal rule and Simpson's rule are accurate approximations.
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_____ is a relative measure of signal loss or gain and is used to measure the logarithmic loss or gain of a signal
Decibel is a relative measure of signal loss or gain and is used to measure the logarithmic loss or gain of a signal.
What is a decibel?
Decibel, also known as dB, is a logarithmic unit that measures the intensity of a sound or the strength of an electrical or electromagnetic signal. A decibel measures the relative amplitude of a sound or signal, rather than its absolute magnitude. Because decibels are logarithmic, they are used to express both large and small differences in amplitude. A difference of 1 decibel corresponds to a power ratio of approximately 1.26 to 1.
Logarithmic measure: A logarithmic scale is a scale that has a constant ratio between successive values. Decibels, for example, are a logarithmic scale. The decibel scale is used to measure the amplitude of sound waves and electrical or electromagnetic signals. Because decibels are logarithmic, they can be used to express a wide range of signal levels, from very weak to very strong.
Relative measure: Relative measure is a measure that compares one value to another. It is used in a variety of fields, including statistics, physics, and engineering. Decibels are a relative measure because they compare one signal to another. They are used to express the relative gain or loss of a signal, rather than its absolute magnitude.
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if the circumference of the moon is 6783 miles what is its diameter in miles
Answer:
C = 21,309.4
Step-by-step explanation:
Diameter of moon is miles is,
d = 2159.8 miles
We have,
The circumference of the moon is, 6783 miles
Since, We know that,
the circumference of circle is,
C = 2πr
Substitute given values,
6783 miles = 2 × 3.14 × r
6783 = 6.28 × r
r = 6783 / 6.28
r = 1079.9 miles
Therefore, Diameter of moon is miles is,
d = 2 x r
d = 2 x 1079.9
d = 2159.8 miles
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determine whether the set S spans R2. If the set does not span R2, then give a geometric description of the subspace that it does span. a, S = {(1, −1), (2, 1)} b, S = {(1, 1)} c, S = {(0, 2), (1, 4)}
a. S = {(1, -1), (2, 1)}Let's begin by calculating the determinant of the matrix composed of the vectors of S, and checking if it is equal to 0. Because the two vectors are not colinear, they should span R2.|1 -1||2 1| determinant is not 0, therefore S spans R2. No geometric description is required for this example.
b. S = {(1, 1)} The set S contains one vector. A set containing only one vector cannot span a plane because it only spans a line. Therefore, S does not span R2. Geometric description: S spans a line that passes through the origin (0, 0) and the point (1, 1).c. S = {(0, 2), (1, 4)} Let's again begin by calculating the determinant of the matrix composed of the vectors of S, and checking if it is equal to 0.|0 2||1 4| determinant is 0, thus S does not span R2. In this scenario, S only spans the line that contains both vectors, which is the line with the equation y = 2x.
Geometric description: S spans a line that passes through the origin (0, 0) and the point (1, 2).
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a) Work out the minimum number of hikers who could have walked between 6 miles and 17 miles. b) Work out the maximum number of hikers who could have walked between 6 miles and 17 miles. < Back to task Distance, a (miles) 0≤ x<5 5 ≤ x < 10 10 ≤ a < 15 15 ≤ x < 20 20 ≤ w Scroll down Watch video Frequency 3 2 9 8 4 Answer
9 hikers are the bare minimum that might have covered the range of 6 to 17 miles because that distance falls inside the typical interval of 10 x 15 miles.
What is meant by minimum and maximum value?Rearrange the function using fundamental algebraic concepts to determine the value of x when the derivative equals 0.
This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur.
To determine the minimum or maximum, rewrite the solution into the original function.
The greatest and smallest values of a function, either within a specific range (the local or relative extrema) or throughout the entire domain, are collectively referred to as extrema (PL: extrema) in mathematical analysis.
b) the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
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how to solve transversals find the angle measure (2x + 43) + (2x - 3) the answer
In a candy factory, each bag of candy contains 300 pieces. The bag can be off by 10 pieces.
Write an absolute value inequality that displays the possible number of candy pieces that a bag contains.
Answer:
[tex] |x - 300| \leqslant 10[/tex]
Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order.
y dA, D is bounded by y = x − 6; x = y2
D
The value of the double integral using the easier order, ydA bounded by y = x − 6; x = y² is 125/12.
The double integral, indicated by ', is mostly used to calculate the surface area of a two-dimensional figure. By using double integration, we may quickly determine the area of a rectangular region. If we understand simple integration, we can easily tackle double integration difficulties. Hence, first and foremost, we will go over some fundamental integration guidelines.
Given, the double integral ∫∫yA and the region y = x-6 and x = y²
y = x-6
x = y²
y² = y +6
y² - y - 6 = 0
y² - 3y +2y - 6 = 0
(y-3) (y+2) = 0
y = 3 and y = -2
[tex]\int\int\limits_\triangle {y} \, dA\\ \\[/tex]
= [tex]\int\limits^3_2 {y(y+6-y^2)} \, dx \\\\\int\limits^3_2 {(y^2+6y-y^3)} \, dx \\\\(\frac{y^3}{3} + 3y^2-\frac{y^4}{4} )_-_2^3\\\\\frac{63}{4} -\frac{16}{3} \\\\\frac{125}{12}[/tex]
The value for the double integral is 125/12.
Integration is an important aspect of calculus, and there are many different forms of integrations, such as basic integration, double integration, and triple integration. We often utilise integral calculus to determine the area and volume on a very big scale that simple formulae or calculations cannot.
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A toy maker needs to make $17,235 per month to meet his cost. Each toy sells for $45. How many toys does he need to sell in order to break even
Answer:
Step-by-step explanation:
i assume the figure he needs to "make" is the turnover and not the marginal profit - no indication of the cost of the toys he sells is given so it is impossible to work out the marginal profit of the each toy sold. (Though how the toymaker worked out the turnover required without knowing the cost of the toy is beyond me - though that didn't stop British Leyland pricing their best selling Mini in the 1970s.)
In this case divide the income required by the price of each toy, but as the income must be at least the required amount, any fractional part of a toy must be rounded *UP* to the next whole number.
17,235 ÷ 45 = 383 (so no rounding is needed).
He needs to sell 383 toys (made at zero marginal cost).
Aaron sampled 101 students and calculated an average of 6.5 hours of sleep each night with a standard deviation of 2.14. Using a 96% confidence level, he also found that t* = 2.081.confidence intervat = x±s/√n A 96% confidence interval calculates that the average number of hours of sleep for working college students is between __________.
The average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night
According to the given data,
Sample size n = 101
Sample mean x = 6.5
Standard deviation s = 2.14
Level of confidence C = 96%
Using a 96% confidence level, the value of t* for 100 degrees of freedom is 2.081, as given in the question.
Now, the formula for the confidence interval is:x ± (t* × s/√n)Here, x = 6.5, s = 2.14, n = 101, and t* = 2.081
Substituting the values in the above formula, we get:
Lower limit = x - (t* × s/√n) = 6.5 - (2.081 × 2.14/√101) = 6.28
Upper limit = x + (t* × s/√n) = 6.5 + (2.081 × 2.14/√101) = 6.72
Therefore, the 96% confidence interval for the average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night.
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Jacinta has 2 blue marbles, 4 red marbles, and 5 green marbles in a bag. All the
marbles are the same size. She will select one marble from the bag without looking. Ext
What is the probability that Jacinta will select a green marble? Write your answer as
fraction.
the probability of Jacinta selecting a green marble is 5/11. The total number of marbles in the bag is:
2 (blue) + 4 (red) + 5 (green) = 11
The probability of selecting a green marble can be found by dividing the number of green marbles by the total number of marbles:
P(selecting a green marble) = number of green marbles / total number of marbles
= 5 / 11
Therefore, the probability of Jacinta selecting a green marble is 5/11. Answer: 5/11.
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
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Goods with a cost price of R200 are sold at a mark-up of 100%. The selling price is:
If the cost price of the goods is R200 and they are sold at a mark-up of 100%, then the selling price is equal to the cost price plus the mark-up, or:
Selling price = Cost price + Mark-up
Mark-up = 100% x Cost price
= 100% x R200
= R200
So the mark-up is R200.
Selling price = Cost price + Mark-up
= R200 + R200
= R400
Therefore, the selling price of the goods is R400.
Which points satisfy both inequalities?
The pοint that satisfies bοth inequalities is the pοint inside this triangular regiοn.
What is inequality?An inequality is a mathematical statement that cοmpares twο values οr expressiοns and indicates whether they are equal οr nοt, οr which οne is greater οr smaller.
Since the shading is nοt included, we will need tο use the lines themselves tο determine the cοrrect regiοn οf the cοοrdinate plane.
The first inequality y > (3/2)x - 5 has a slοpe οf 3/2 and a y-intercept οf -5. This means the line will have a pοsitive slοpe and will be lοcated belοw the pοint (0,-5).
The secοnd inequality y < (-1/6)x - 6 has a negative slοpe οf -1/6 and a y-intercept οf -6. This means the line will have a negative slοpe and will be lοcated abοve the pοint (0,-6).
Tο find the pοint that satisfies BOTH inequalities, we need tο lοοk fοr the regiοn οf the cοοrdinate plane that is belοw the line y = (3/2)x - 5 AND abοve the line y = (-1/6)x - 6. This regiοn is the triangular-shaped area that is bοunded by the twο lines and the x-axis.
The pοint that satisfies bοth inequalities is the pοint inside this triangular regiοn.
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pleaseee im begging anyone for the steps of these questions i need them so urgently right now, i have the answer but not the steps pls anyone
Answer:
3. 79.9 mm²
4. 6.4 in
5. 177.5 mi²
6. 60.3°
Step-by-step explanation:
Given various quadrilaterals and their dimensions, you want to find missing dimensions.
Trig relationsIn all cases, one or more area formulas and trig relations are involved. The trig relations are summarized by the mnemonic SOH CAH TOA. The relevant relation for these problems is ...
Tan = Opposite/Adjacent
It is also useful to know that 1/tan(x) = tan(90°-x).
Area formulasThe formula for the area of a trapezoid is ...
A = 1/2(b1 +b2)h
The relevant formula here for the area of a parallelogram is ...
A = bs·sin(α) . . . . . where α is the angle between sides of length b and s
3. Parallelogram areaUsing the area formula above, we find the area to be ...
A = (21 mm)(9 mm)·sin(155°) ≈ 79.9 mm²
The area is about 79.9 square mm.
4. Trapezoid base 2The given figure shows two unknowns. We can write equations for these using the area formula and using a trig relation.
If we draw a vertical line through the vertex of the marked angle, the base of the triangle to the right of it is (b2-4). The acute angle at the top of that right triangle is (121°-90°) = 31°. The tangent relation tells us ...
tan(31°) = (b2 -4)/h ⇒ h = (b2 -4)/tan(31°)
Using the area formula we have ...
A = 1/2(b2 +4)h
and substituting for A and h, we get ...
20.8 = 1/2(b2 +4)(b2 -4)/tan(31°)
2·tan(31°)·20.8 = (b2 +4)(b2 -4) = (b2)² -16 . . . . . multiply by 2tan(31°)
(b2)² = 2·tan(31°)·20.8 +16 . . . . . . . add 16
b2 = √(2·tan(31°)·20.8 +16) ≈ 6.4 . . . . . . take the square root
Base 2 of the trapezoid is about 6.4 inches.
5. Trapezoid areaTo find the area, we need to know the height of the trapezoid. To find the height we can solve a triangle problem.
If we draw a diagonal line parallel to the right side through the left end of the top base, we divide the figure into a triangle on the left and a parallelogram on the right. The triangle has a base width of 10 mi, and base angles of 60° and 75°.
Drawing a vertical line through the top vertex of this triangle divides it into two right triangles of height h. The top angle is divided into two angles, one being 90°-60° = 30°, and the other being 90°-75° = 15°. The bases of these right triangles are now ...
h·tan(30°)h·tan(15°)and their sum is 10 mi.
The height h can now be found to be ...
h·tan(30°) +h·tan(15°) = 10
h = 10/(tan(30°) +tan(15°))
Back to our formula for the area of the trapezoid, we find it to be ...
A = 1/2(b1 +b2)h = 1/2(20 +10)(10/(tan(30°) +tan(15°)) ≈ 177.5
The area of the trapezoid is about 177.5 square miles.
6. Base angleThe final formula we used for problem 5 can be used for problem 6 by changing the dimensions appropriately.
A = 1/2(b1 +b2)(b1 -b2)/(tan(90-x) +tan(90-x))
112 = 1/2(20+12)(20-12)/(2·tan(90-x)) = (20² -12²)·tan(x)/4
tan(x) = 4·112/(20² -12²)
x = arctan(4·112/(20² -12²)) = arctan(7/4) ≈ 60.3°
Angle x° in the trapezoid is about 60.3°.
__
Additional comment
There is no set "step by step" for solving problems like these. In general, you work from what you know toward what you don't know. You make use of area and trig relations as required to create equations you can solve for the missing values. There are generally a number of ways you can go at these.
A nice scientific calculator has been used in the attachment for showing the calculations. A graphing calculator can be useful for solving any system of equations you might write.
The second attachment shows a graphing calculator solution to problem 5, where we let y = area, and x = the portion of the bottom base that is to the left of the top base. Area/15 represents the height of the trapezoid. This solution also gives an area of 177.5 square miles.
20m:600cm
Reduce the ratios to its simplest forms
Answer: 10:3
Step-by-step explanation: convert 600cm to 6m, then we will get 20m:6m, 2*10=20 and 2*3=6. then it will become 10:3
there exists a complex number $c$ such that we can get $z 2$ from $z 0$ by rotating around $c$ by $\pi/2$ counter-clockwise. find the sum of the real and imaginary parts of $c$.
The sum of the real and imaginary parts of $c$ is$$\operatorname{Re}(c) + \operatorname{Im}(c) = \frac{\operatorname{Re}(2c)}{2} + \frac{\operatorname{Im}(2c)}{2}$$$$= \frac{\operatorname{Re}(z_0+z_2)}{2} - \frac{\operatorname{Im}(z_0)}{2}(1-\cos(\theta/2)) - \frac{\operatorname{Re}(z_0)}{2}\sin(\theta/2)$$$$+ \frac{\operatorname{Im}(z_0+z_2)}{2} - \frac{\operatorname{Re}(z_0)}{2}(1-\cos(\theta/2)) + \frac{\operatorname{Im}(z_0)}{2}\sin(\theta/2).$$
The given problem can be solved using algebraic and geometric methods. We can use algebraic methods, such as the equations given in the problem, and we can use geometric methods by visualizing what the problem is asking. To start, let's translate the given problem into mathematical equations. Let $z_0$ be the original complex number. We want to rotate this point by 90 degrees counter-clockwise about some complex number $c$ to get $z_2$. Thus,$$z_2 = c + i(z_0 - c)$$$$=c + iz_0 - ic$$$$= (1-i)c + iz_0.$$We also know that this transformation will rotate the point $z_1 = (z_0 + z_2)/2$ by 45 degrees. Thus, using similar logic,$$z_1 = (1-i/2)c + iz_0/2.$$Now let's use the formula for rotating a point about the origin by $\theta$ degrees (where $\theta$ is measured in radians) to find a relationship between $z_1$ and $z_0$.$$z_1 = z_0 e^{i\theta/2}$$$$\implies (1-i/2)c + iz_0/2 = z_0 e^{i\theta/2}$$$$\implies (1-i/2)c = (e^{i\theta/2} - 1)z_0/2.$$We can solve for $c$ by dividing both sides by $1-i/2$.$$c = \frac{e^{i\theta/2} - 1}{1-i/2}\cdot\frac{z_0}{2}.$$We can now use the information given in the problem to solve for the sum of the real and imaginary parts of $c$. We know that rotating $z_0$ by 90 degrees counter-clockwise will result in the complex number $z_2$. Visually, this means that $c$ is located at the midpoint between $z_0$ and $z_2$ on the line that is perpendicular to the line segment connecting $z_0$ and $z_2$. We can use this geometric interpretation to solve for $c$. The midpoint of the line segment connecting $z_0$ and $z_2$ is$$\frac{z_0+z_2}{2} = c + i\frac{z_0-c}{2}.$$Solving for $c$, we get$$c = \frac{z_0+z_2}{2} - \frac{i}{2}(z_0-c)$$$$\implies 2c = z_0+z_2 - i(z_0-c)$$$$\implies 2c = z_0+z_2 - i(z_0- (e^{i\theta/2} - 1)(z_0/2)/(1-i/2)).$$We can now find the real and imaginary parts of $c$ and add them together to get the desired answer. Let's first simplify the expression for $c$.$$2c = z_0+z_2 - i(z_0 - (e^{i\theta/2} - 1)\cdot(z_0/2)\cdot(1+i)/2)$$$$= z_0 + z_2 - i(z_0 - z_0(e^{i\theta/2} - 1)(1+i)/4)$$$$= z_0 + z_2 - i(z_0 - z_0e^{i\theta/2}(1+i)/4 + z_0(1-i)/4)$$$$= z_0 + z_2 - i(z_0(1-e^{i\theta/2})/4 + z_0(1-i)/4)$$$$= z_0 + z_2 - i(z_0/4(1-e^{i\theta/2} + 1 - i))$$$$= z_0 + z_2 - i(z_0/2(1-\cos(\theta/2) - i\sin(\theta/2)))$$$$= z_0 + z_2 - i(z_0(1-\cos(\theta/2)) + z_0\sin(\theta/2) - i(z_0\cos(\theta/2))/2.$$Now we can find the real and imaginary parts of $2c$ and divide by 2 to get the real and imaginary parts of $c$. We have$$\operatorname{Re}(2c) = \operatorname{Re}(z_0+z_2) - \operatorname{Im}(z_0)(1-\cos(\theta/2)) - \operatorname{Re}(z_0)\sin(\theta/2)$$$$\operatorname{Im}(2c) = \operatorname{Im}(z_0+z_2) - \operatorname{Re}(z_0)(1-\cos(\theta/2)) + \operatorname{Im}(z_0)\sin(\theta/2).$$Thus, the sum of the real and imaginary parts of $c$ is$$\operatorname{Re}(c) + \operatorname{Im}(c) = \frac{\operatorname{Re}(2c)}{2} + \frac{\operatorname{Im}(2c)}{2}$$$$= \frac{\operatorname{Re}(z_0+z_2)}{2} - \frac{\operatorname{Im}(z_0)}{2}(1-\cos(\theta/2)) - \frac{\operatorname{Re}(z_0)}{2}\sin(\theta/2)$$$$+ \frac{\operatorname{Im}(z_0+z_2)}{2} - \frac{\operatorname{Re}(z_0)}{2}(1-\cos(\theta/2)) + \frac{\operatorname{Im}(z_0)}{2}\sin(\theta/2).$$
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Feng has a toy car collection he keeps 324 of the toy cars on his wall which is 81% of his entire collection what is the total number of toy cards in his collection
400 is the total number of toy cards in his collection. This will be the total number of toy cards in his collection if Feng keeps 324 of the toy cars on his wall which is 81% of his entire collection.
A fraction is a mathematical value that illustrates the components of a whole. In general, the whole can be any particular thing or value, and the fraction might be a portion of any quantity out of it. The top and bottom numbers of a fraction are explained by the fundamentals of fractions. The bottom number reflects the entire number of components, while the top number represents the number of chosen or coloured portions of the whole.
Based on the given conditions, formulate: 324/81%
Convert decimal to fraction: 324/81/100
Divide a fraction by multiplying its reciprocal 324 * 100 / 81
Reduce the expression to the lowest term: 4*100
Calculate the product or quotient: 400
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what percentage of defective lots does the purchaser reject? find it for . given that a lot is rejected, what is the conditional probability that it contained 4 defective components
The purchaser rejects 26.01% of the lots that contain five or more defective components, and the conditional probability of having four defective components given that the lot was rejected is 0.1653.
How do we calculate the probability?The percentage of defective lots that the purchaser rejects can be found by using the given formula. We can also calculate the conditional probability of having four defective components, given that the lot was rejected. Here's how to do it.
Let p be the probability that any component is defective. Then the probability that any component is non-defective is 1-p.
According to the given data, a lot is rejected if and only if there are at least five defective components in it. Let q be the probability that a lot is defective, i.e. the probability that there are five or more defective components in a lot.
Then, q = P(X ≥ 5), where X is the number of defective components in the lot. We can find the probability of rejecting a lot by subtracting the probability of accepting the lot from 1. So, we have:
P(reject) = 1 - P(accept)
P(accept) = P(X ≤ 4)
Now, we need to find q. We can do this by using the binomial distribution:
[tex]P(X = k) = C(n, k) * pk * (1-p)n-k[/tex]
where C(n, k) is the number of ways to choose k items out of n items. Here, n = 20 (the number of components in a lot). So,
[tex]q = P(X \geq 5) = 1 - P(X\leq 4) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)][/tex]
[tex]q = 1 - [C(20, 0) * p0 * (1-p)20-0 + C(20, 1) * p1 * (1-p)20-1 + C(20, 2) * p2 * (1-p)20-2 + C(20, 3) * p3 * (1-p)20-3 + C(20, 4) * p4 * (1-p)20-4][/tex]
[tex]q = 1 - [1 * p0.2 * (1-0.2)20-0 + 20 * p0.2 * (1-0.2)20-1 + 190 * p0.2 * (1-0.2)20-2 + 1140 * p0.2 * (1-0.2)20-3 + 4845 * p0.2 * (1-0.2)20-4][/tex]
[tex]q = 0.2601[/tex] (rounded to four decimal places)
So, the purchaser rejects 26.01% of the lots that contain five or more defective components.
Now, we need to find the conditional probability that a lot contained four defective components given that it was rejected. Let R be the event that a lot is rejected, and let F be the event that a lot contains four defective components.
Then, we have to find P(F | R), the conditional probability of F given R. We can use Bayes' theorem to find this:
P(F | R) = P(R | F) * P(F) / P(R)
where P(R | F) is the probability of rejecting a lot given that it contained four defective components, P(F) is the prior probability of a lot containing four defective components, and P(R) is the overall probability of rejecting a lot.
[tex]P(F) = C(20, 4) * p4 * (1-p)20-4 = 0.186[/tex]
[tex][tex]P(R) = P(X \geq 5) = q = 0.2601[/tex][/tex]
[tex]P(R | F) = P(X \geq 5 | X = 4) = P(X = 5) / P(X = 4) = C(20, 5) * p5 * (1-p)20-5 / C(20, 4) * p4 * (1-p)20-4[/tex]
[tex]P(R | F) = 0.2308[/tex]
So, we have:
[tex]P(F | R) = P(R | F) * P(F) / P(R)[/tex]
[tex]P(F | R) = 0.2308 * 0.186 / 0.2601[/tex]
[tex]P(F | R) = 0.1653[/tex] (rounded to four decimal places)
Therefore, the conditional probability of having four defective components given that the lot was rejected is 0.1653.
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A satellite TV company offers two plans. One plan costs $115 plus $30 per month. The other plan costs $60 per month. How many months must Alfia have the plan in order for the first plan to be the better buy?
Which of the following are true statements? Check all that apply. A. F(x)= 2 square x has the same domain and range as f(x)= square x. B. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2. C. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it horizontally by a factor of 1/2. D. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.
The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
Thus, Option B and Option D are correct.
What is function?A function is a relationship or expression involving one or more variables. It has a set of input and outputs.
A. F(x)= 2 square x has the same domain and range as f(x)= square x.
B. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.
D. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
Option A is false because multiplying the function by 2 will change the range of the function to include all non-negative real numbers (since the square of any number is non-negative).
Option B is true because multiplying the function by 2 will vertically shrink the graph by a factor of 1/2 (since the output values will be half the size of the original function).
Option C is false because multiplying the function by 2 will not affect the horizontal scale of the graph.
Option D is true because multiplying the function by 2 will vertically stretch the graph by a factor of 2 (since the output values will be twice the size of the original function).
Therefore, Option B and Option D are correct.
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(Do not use a calculator for this question) Given f(x)-73-12x + 5 answer the following: Is the function increasing or decreasing at x-3? List the interval A=B=where f(x) is decreasing. a F At what X-value does f(x) have a relative maximum?
The function is a set of ordered pairs (x, y), where x is an element of the domain and y is the corresponding element of the range. The notation f(x) is commonly used to denote the output value of the function for a given input value x.
The function is decreasing at x=3. The interval where f(x) is decreasing is (3,∞). The x-value at which f(x) has a relative maximum is x= -4.The derivative of the function f(x) is f'(x)=-12.At x=3, the derivative is negative, f'(3)=-12, so the function is decreasing at x=3.
The function is always decreasing since its derivative is constant and negative. Therefore, the interval where f(x) is decreasing is the entire real line, or (-∞, ∞).
Since the function is always decreasing, it does not have a relative maximum.
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La necesito por favor
Answer:
4(h+3) = 20
Step-by-step explanation:
Para empesar, disculpa si mi español no es perfecto, pero igual me encataria a ayudarte.
Pues, se sabe que estas temporadas de practica vienen en groupitos de horas a la ves. Dijo que cada dia, ella practica por alguans horas, las cuales suman a 20 en total. Como la problema nos dice que ella practica 4 veces a la semana, tienemos 4 de estos groupitos de horas. Por eso, la respuesa es 4(h+3) = 20, porque ella va por estas 4 temporadas de practicar 3 horas en la manana y quien sabe cuantos en la tarde. Addicionalmente, este"quien sabe" numero de horas se representa con h.
