Check the picture below.
Please help ASAP! Unit 5.4-5.5 Pre-Calculus question needed so I can retake a test!
Using half angle formula,
the exact value of sin(α/2) = √[5(√5 + 2)]/10the exact value of tan(α/2) = 1/(√5 - 2)What are half angle formula?Half angle formulas are equations that contain the half angles of the trigonometric ratios.
How to find the exact value of sin(α/2)?Given that tanα = -1/2 and π/2 < α < π
To find sin(α/2), we use the half angle formula
sin(α/2) = √[(1 - cosα)/2]
Also, tan²α + 1 = sec²α = 1/cos²α
⇒ cosα = ±1/√(1 + tan²α)
Since π/2 < α < π
cosα = -1/√(1 + tan²α)
Substituing this into the equation for sin(α/2), we have
sin(α/2) = √[(1 - cosα)/2]
sin(α/2) = √[(1 - (-1/√(1 + tan²α)))/2]
Substituting tanα = -1/2 into the equation, we have
sin(α/2) = √[(1 + 1/√(1 + tan²α))/2]
sin(α/2) = √[(1 + 1/√(1 + (-1/2)²))/2]
sin(α/2) = √[(1 + 1/√(1 + 1/4))/2]
sin(α/2) = √[(1 + 1/√(5/4))/2]
sin(α/2) = √[(1 + 1/√5/2)/2]
sin(α/2) = √[(1 + 2/√5)/2]
sin(α/2) = √[(√5 + 2)/√5)/2]
sin(α/2) = √[(√5 + 2)/2√5
sin(α/2) = √[(√5 + 2)/2√5 × √5/√5
sin(α/2) = √[5(√5 + 2)]/2 × 5
sin(α/2) = √[5(√5 + 2)]/10
So, sin(α/2) = √[5(√5 + 2)]/10
b. How to find the exact value of tan(α/2)?Using the half angle formula,
tan(α/2) = sinα/(1 + cosα)
Using the trigonometric identity cosα = ±1/√(1 + tan²α)
cosα = ±1/√(1 + (-1/2)²)
cosα = ±1/√(1 + 1/4)
cosα = ±1/√(5/4)
cosα = ±1/√5/2
cosα = ±2/√5
Since π/2 < α < π
cosα = -2/√5
Also, since the trigonometric identity sinα = ±√(1 - cos²α)
So, sinα = ±√(1 - (-2/√5)²)
sinα = ±√(1 - 4/5)
sinα = ±1/√5
Since π/2 < α < π
sinα = +1/√5
Substituting cosα = -2/√5 and sinα = +1/√5 into the equation for tan(α/2), we have
tan(α/2) = sinα/(1 + cosα)
tan(α/2) = +1/√5/(1 + (-2/√5))
tan(α/2) = +1/√5/(1 - 2/√5)
tan(α/2) = +1/√5/(√5 - 2)/√5)
tan(α/2) = 1/(√5 - 2)
So, tan(α/2) = 1/(√5 - 2)
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How many solutions does the pair of equations y 0 and y =- 7 have?
The pair of equations y = 0 and y = -7 have no solutions.
The pair of equations y = 0 and y = -7 have no solutions because the equations are not equal. The left side of the equation is y = 0, while the right side of the equation is y = -7. Since the two sides of the equation do not have the same value, there is no solution that can satisfy both equations.
The pair of equations y = 0 and y = -7 have no solutions because the two equations are not equal. The left side of the equation is y = 0, while the right side of the equation is y = -7. Since the two sides of the equation do not have the same value, there is no solution that can satisfy both equations simultaneously. This can be confirmed by substituting the value of y on the left side into the equation on the right side. Since the value of y would be 0 on the left side and -7 on the right side, they cannot be equal and thus there is no solution. Therefore, the pair of equations y = 0 and y = -7 have no solutions.
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Mario obtains a 30/7 balloon mortgage to finance $245,500 at 5. 25%. How much principal and interest will he have already paid when his balloon payment is due?
O $113,875. 44
O $112,519. 78
O $127,304. 57
O $216,988. 63
113875.44746 is principal and interest will he have already paid when his balloon payment is due.
What exactly does "interest rate" mean?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off. The amount you pay for borrowing money, expressed as a percentage of the entire loan amount, is what you will pay in interest if you are a borrower.
The financial fee for borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR). Lenders may charge interest for the use of their money, or borrowers may charge interest for the use of those funds.
=PMT(5.25%/12,12*30,-245500)*12*7
= 113875.44746
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On a field trip there are 3 chaperones for every 20 minutes. How many children are there?
Answer:that doesn’t seem possible to figure out
Step-by-step explanation:
?
Is 0 a positive or negative integer?
Number Zero is neither positive nor negative.
A whole number, an integer can be positive, negative, or zero but cannot be a fraction or a decimal because it is a whole number. The natural numbers (1, 2, 3,...), their opposites (-1, -2, -3,...), and zero are all considered to be integers. Numerous branches of mathematics use integers, but number theory and algebra place a special emphasis on them.
Zero is not an integer that may be either positive or negative. It is regarded as a non-negative or neutral number. The absolute value of zero is also zero in terms of magnitude. |0| = 0. In the set of integers, zero is also regarded as the identity element of addition and the absorbing element of multiplication.
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Can someone help me solve the first math problem please in a quadratic model
a) The maximum Height of Projectile is 843.75 m
b) The projectile reach its maximum at t= 12.5 sec.
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .
It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.
Given:
h(t) = -5t² +120t + 125
a) For the maximum height, h= 0
-5t² +120t + 125 = 0
t² - 24 t - 25 = 0
t² - 25t + t - 25 = 0
t( t- 25) + 1(t-25)= 0
(t-25)(t+1)=0
t= 25, -1
So, Max height is reached after half the total flight time, t= 25/2
So, h(25/2 )= -5(25/2)² +120(25/2) + 125
= -5 x 156.25 + 1500+ 125
= 843.75 m
b) The projectile reach its maximum at t= 12.5 sec.
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The frequency distribution shows the average number of pupils per teacher in some states of the United States. Find the variance and standard deviation for the data. Round your answers to one decimal place.
As per the given frequency distribution, the value of variance is 9.8 and the value of standard deviation is 3.126
The term frequency distribution is defined as the distribution of a variable is the pattern of frequencies, meaning the set of all possible values and the frequencies associated with these values
Here we have the following frequency distribution with average number of pupils per teacher in some states of the United States.
While we looking into the table we have identified the value of variance as,
But in order to calculate the variance we must need the value of mean, it can be calculated as follows:
= >Mean (x) = ∑(f(x)) / ∑f
Apply the values on it, then we get
=> 660/42 = 15.71
Now, the value of variance is calculated as
=> Variance = ∑(f(x)²) / ∑f - (Mean²)
Apply the values on it, then we get,
=> [10782/42] - [15.71] = 9.8
Then through the variance the value of standard deviation is calculated as,
=> standard deviation = √9.8 = 3.126
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the volume of a cube is decreasing at a constant rate of 1327 cubic feet per second. at the instant when the volume of the cube is 528528 cubic feet, what is the rate of change of the surface area of the cube? round your answer to three decimal places (if necessary).
The required rate of change of the surface area of the cube is 66 sq,feet/second.
Explain Rate change with respect to time.The momentum of a variable is represented by the rate of change, which is used to mathematically express the percentage change in value over a specified period of time. R = (D2 - D1)/T is a general formula for calculating the rate of change.
According o question:[tex]\frac{V}{dt}[/tex] = 1327 cubic feet per second
volume(V) = 528528 cubic feet
We know that
V = a^3
528528 = a^3
a = 80.85
Differentiate w, r, t
[tex]\frac{V}{dt}[/tex] = 3a^2[tex]\frac{da}{dt}[/tex]
1327 = 3(80.85)^2da/dt
da/dt = 0.068
Now,
Surface area(S) = 6a^2
Differentiate w, r, t
dS/dt = 12a(da/dt)
dS/dt = 12(80.85)(0.068)
dS/dt = 66 Sq.feet/second
Thus, required rate of change of the surface area of the cube is 66.
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HELP FOR BRAINLIEST!! ASAP PLS
Using the linear function, the monthly cost for 6 HCF is $36.72.
What is the monthly cost for 6 HCF?If the monthly water bill is a linear function with a slope of 1.65, it means that for every additional HCF used, the cost increases by $1.65.
Let's denote the monthly cost as C(HCF) and the number of HCF used as HCF. We know that C(12) = $46.62.
Now, to find the monthly cost for 6 HCF (C(6)), we can use the slope information:
C(12) = $46.62
C(12) - C(6) = $46.62 - C(6) = (12 HCF - 6 HCF) * 1.65
C(6) = $46.62 - (6 HCF * 1.65)
Now, let's calculate:
C(6) = $46.62 - (6 * 1.65)
C(6) = $46.62 - 9.90
C(6) = $36.72
So, the monthly cost for 6 HCF is $36.72.
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An employee at a construction company is ordering interior doors for some new houses that are being built. there are 6 one-story houses and 2 two-story houses on the west side of the street which require a total of 72 doors. on the east side there are 5 one-story houses and 7 two-story houses which require a total of 124 doors. assuming that the floor plans for one-story houses are identical and so are the two-story houses, how many doors does each type of house have?
The number of doors in one-story building are 8 and the number of doors in two-story building are 12.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, an employee at a construction company is ordering interior doors for some new houses that are being built.
Let the number of doors in one-story houses be x and the number of doors in two-story houses be y.
There are 6 one-story houses and 2 two-story houses on the west side of the street which require a total of 72 doors.
Here, 6x+2y=72 -------(I)
On the east side there are 5 one-story houses and 7 two-story houses which require a total of 124 doors.
5x+7y=124 -------(II)
Multiply equation (I) by 7, we get
42x+14y=504 -------(III)
Multiply equation (II) by 2, we get
10x+14y=248 -------(IV)
Subtract equation (IV) from (III), we get
32x=256
x=8
Substitute x=8 in equation (I), we get
48+2y=72
2y=24
y=12
Therefore, the number of doors in one-story building are 8 and the number of doors in two-story building are 12.
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In the sequence 2,5,8,11,...,X,...,which expression describes the number after x? explain your choice a.X+3 b. x-3 c.3x d. x divided by 3
Answer:
A- x+3
Step-by-step explanation:
each number is growing by 3
Tabitha’s account balance is $3,800. Of this, $750 is for rent. Tabitha wants to keep a balance greater than $500. Write an inequality describing how much she can withdraw and still meet these conditions
The inequality describing how much she can withdraw is x < 3550
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
Inequalities are used in expression for non equal comparison of variables.
Let x represent the amount of money that can be withdrawn.
Tabitha’s account balance is $3,800. Of this, $750 is for rent. Hence:
Money remaining = 3800 - 750 = 3050
Tabitha wants to keep a balance greater than $500. Hence:
3050 - x > 500
x < 3550
The inequality is x < 3550
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Na
PRE-ALGEBRA REVIEW
1. An appliance store offers a loan to buy a
refrigerator for $2,700 at an 8% simple interest
rate with equal monthly payments for 2 years.
What is the monthly payment?
A. $124.50
B. $127.50
C. $130.50
D. $132.50
The monthly payment is $130.50. Therefore, option C is the correct answer.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.
Given that, principal =$2700, rate of interest =8% and time =2 years
Here, SI=(2700×8×2)/100
= 43200/100
= $432
Amount =Principal+Interest
= 2700+432
= $3132
We know that 2 years =24 months
Now, the monthly payment = 3132/24
= $130.50
Therefore, option C is the correct answer.
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the difference between the two numbers is 3 and their product is 28
Answer:
4 and 7
Step-by-step explanation:
7-4=3
4x7=28
3.4.Sarah, Lilly and Paula make R1 200 profit from selling cakes. Determine how much profit each girl receives if they invested in the ratio 1:2:3.
Profit made by each girl Sarah, Lilly and Paula respectivly are R 200 , R 400 and R 600
What is Ratio and Proportion ?A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. Indicators of proportions include "::" and "=".
The amount of investment done by each girl Sarah, Lily and Paula respectivly is x, 2x and 3x
So, the profit will be
x + 2x + 3x = 1200
⇒6x =1200
⇒ x = 200
Profit made by each girl respectivly are x = R 200 , 2x = R 400 and 3x = R 600.
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Tara has read 95\%95%95, percent of the books she owns. If Tara owns 160160160 books, how many of her books has she not read?
The number of the books owed by Tara which she has not read would be = 152 books.
What is percentage?Percentage is defined as the part of the value that can be expressed as per 100 of the whole given value. This can be represented with a symbol such as %..
The number of books owned by Tara = 160 books
The percentage of books read by Tara = 95%
Therefore, 95% of her books = 95/100 × 160
= 15200/100
= 152 books.
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In the figure below ABCDE A’B’C’D’E’
Which transformation maps figure ABCDE onto figure A’B’C’D’E’?
Answer: Rotation around the origin
Step-by-step explanation:
If you rotate ABCDE around the point (0,0), you will see that it maps onto A'B'C'D'E'.
. What series of steps would result in the correct solution to the equation
-8(0.5y - 3) = 3
Answer:
y = 21/4 or 5[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
step 1: multiply -8 and 0.5y to get -4y
step 2: multiply -8 and -3 to get 24
now you have distributed -8 and have removed parentheses to get:
-4y + 24 = 3
subtract 24 from each side to get:
-4y = -21
divide each side by -4 to get:
y = 21/4 or 5[tex]\frac{1}{4}[/tex]
The sum of the perimeters of 2 different regular hexagons is 66 and the difference between their perimeters is 30. If x represents the side length of the larger regular hexagon and y represents the side length of the smaller regular hexagon, which of the following systems of equations can be used to find the dimensions of the regular hexagons?
Perimeter of rectangular hexagon = 6 × length of side, length of side of given hexagon = 30/6 =5 cm and perimeter of new figure = Number of outer sides × length of each side =10×5=50 cm
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
Perimeter of rectangular hexagon = 6 × length of side
length of side of given hexagon = 30/6 =5 cm
perimeter of new figure = Number of outer sides × length of each side
=10×5=50 cm
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work out the area of this shape
Answer: 127
Step-by-step explanation:
the image has steps
Answer:
the answer is 127 cm^2 ig
HELP PLS -----------------
The TQ is a chord, PR is a secant line and WU is a tangent line.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
A chord of a circle is the line segment joining two points on the circle.
Line segments TQ and QV are chords.
TV is also a chord, which is the diameter.
A secant line is a line which intersects the circle at two different points.
Line PR is a secant line which intersects the circle at T and Q.
A tangent line is a line which intersects the circle at exactly one point.
Line WU is a tangent line which intersects the circle at V.
Hence the chords in the given figure are TQ and QV, secant line is PR and tangent line is WU.
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12. The distribution of pH levels for all community swimming pools in a large county is approximately normal with mean 7.5 and standard deviation 0.2. According to swimming pool studies, the safest pH levels for water in swimming pools are between 7.2 and 7.8. (a) One community swimming pool in the county will be selected at random. What is the probability that the selected pool has a pH level that is not considered safe? The county health inspector will select a random sample of 4 community swimming pools in the county to investigate the pH levels. (b) Describe the sampling distribution of the sample mean for samples of size 4. ("Describe" means find the shape center and variability.) (©) Consider the situation in which the health inspector finds the sample mean of the 4 pools to be outside the safe pH levels. As a result, the inspector declares that the population mean is not 7.5. However, if the population mean really is 7.5, the inspector will have made an error. Such an error is called a Type I error. Find the probability that the inspector will make a Type I error with the sample of 4 pools. Show your work.
The probability that the selected pool has a pH level that is not considered safe pool is 0.1336.
The given parameters are:
a =7.5
b= 4
Start by calculating the probability that a pool is safe.
This is represented as: P (7.2 <x<7.8)
Calculate the z-scores for x=7.2 and 7.8 using:
So, we have:
P(7.2<x<78) P (-1.5 <x<1.5)
This gives.
P(7.2<x<7.8) = P(<1.5)-P(z<-1.5)
Using z table of probabilities, we have:
P(7.2<x<7.8) = 0.9332-0.0668
P(7.2<x<7.8) = 0.8664
The probability that the pool is not safe is calculated using the following complement formula.
P (Not Safe) = 1-P(Safe)
So, we have:
P (Not Safe) = 1-0.8664
P (Not Safe) = 0.1336
So, the probability that the pool is not safe is 0.1336.
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what information relevant to calculating area do we
have available for this triangle?
e
which method should we use to calculate the area for
this triangle?
12
10
what is the area of this triangle calculated to the
nearest hundredth of a square unit?
d 7 f
done
On solving the provide question, we can say that Area of the triangle, [tex]A = \sqrt{s( s - a )( s - b )( s - c )} \\[/tex] = 34.98 sq units
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here,
in this triangle
[tex]A = \sqrt{s( s - a )( s - b )( s - c )} \\[/tex]
and here
s = a+b+c/3
a = 10
b = 7
c =12
s = 10+7+12 / 3
s = 14.5
A = 34.98 sq units
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Which of the following is not a quadratic equation?
a)(x−2)2+1=2x−3
b)x(x+1)+8=(x−2)(x−2)
c)x(2x+3)=x2+1
d)(x−2)3=x3−4
The equation x(2x+3) = x² + 1 is the quadratic equation and the remaining equation (x²)² + 1 = 2x³, (x + 1) + 8 = (x²)(x²), and (x²)³ = (x³)⁴ are not in quadratic equation.
The term quadratic equation in math is defined as an equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.
Here we have to find the equation that was not in the form of the quadratic equation.
As per the definition, we have know that the quadratic equation must be in the form of
=> ax² + bx + c = 0
So, here we have to look into the given expression, then w e have identified that only the equation x(2x+3) = x² + 1 is in the quadratic form.
Because the quadratic equation only have the highest power value of 2.
And the remaining are not the quadratic equation.
Therefore, option (a), (b) and (d) are the resulting options.
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people with acrophobia (fear of heights) sometimes enroll in therapy sessions to help them overcome this fear. typically, seven or eight therapy sessions are needed before improvement is noticed. a study was conducted to determine whether the drug d-cycloserine, used in combination with fewer therapy sessions, would help people with acrophobia overcome this fear. each of 27 people who participated in the study received a pill before each of two therapy sessions. seventeen of the 27 people were randomly assigned to receive a d-cycloserine pill, and the remaining 10 people received a placebo. after the two therapy sessions, none of the 27 people received additional pills or therapy. three months after the administration of the pills and the two therapy sessions, each of the 27 people was evaluated to see if he or she had improved. was this study an experiment or an observational study? provide an explanation to support your answer. when the data were analyzed, the d-cycloserine group showed statistically significantly more improvement than the placebo group did. based on this result, would the researchers be justified in concluding that the d-cycloserine pill and two therapy sessions are as beneficial as eight therapy sessions without the pill? justify your answer. a newspaper article that summarized the results of this study did not explain how it was determined which people received d-cycloserine and which received the placebo. suppose the researchers allowed the therapists to choose which people received d-cycloserine and which received the placebo, and no randomization was used. explain why such a method of assignment might lead to an incorrect conclusion.
(a)- The study was experimental.
(b)- No, the researchers would not be justified in doing so.
(c)- Such a method leads to an incorrect conclusions for justifiable reasons.
This problem involves minute statistical knowledge and assesses the student's ability to differentiate between an experiment and an observation and also his/her potential to make justifiable logics as to draw conclusions for a scientific research. The explainations are-
Part - (a)
The study was not an observation, it was an experiment because the treatments involving D-Cycloserine or placebo were imposed by the researchers on the people with acrophobia.
Part (b) -No, the experiment was designed to compare the D-Cycloserine group with a control group that received a placebo . The researchers can conclude that the D-Cycloserine and two therapy sessions show significantly more improvement than a placebo and two therapy sessions. However, there is no basis for comparison with the other group of people with acrophobia who received eight therapy sessions and no pill.
Part (c)-
We can cite an example that if the therapists were allowed to choose who received a placebo and who received D-Cycloserine, they might assign the people with more severe acrophobia with the other group. Thus, the improvement after only two therapy sessions can be related to the initial severity of the acrophobia rather than to the effects of D-Cycloserine.
Therefore, the answers are -
(a)- The study was experimental.
(b)- No, the researchers would not be justified in doing so.
(c)- Such a method leads to an incorrect conclusions for justifiable reasons.
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Tim drives at an average speed of 80 km per hour for 3 hours 45 minutes.
Work out how many kilometres Tim drives.
Answer:
To solve this problem, we will use the following steps:
Step 1: Convert the minutes to hours by dividing the minutes by 60: 45 minutes / 60 = 0.75 hours
Step 2: Add the hours and minutes together to find the total time: 3 hours + 0.75 hours = 3.75 hours
Step 3: Multiply the total time by the average speed to find the distance: 3.75 hours * 80 km/hour = 300 km
Final Answer: Tim drives 300 km.
select the correct answer. a classmate finds that it takes 1.090 seconds for a tossed ball to touch ground. how many significant figures are in this measurement? a. 4 b. 3 c. 2 d. 1
Significant figures are in this measurement 1.090
In a number, to determine the number of significant figures following three rules are used:
The digits which are non-zero are always significant.
Any zeros between two digits which are non-zero are significant.
In the decimal portion, trailing zeros are significant.
Significant figures = Numbers that carry meaning in the measurements of a number.
The number is 1.090, it has two non-zero digits, 1 zero in between two non-zero digit and one trailing zero thus, all of them are significant figures.
Therefore, it has 4 significant figures : 1.090
Significant figures are in this measurement 1.090
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Factor completely:
a^n + a^n+1
Answer:
a^n(a+1)
This is just to reach the minimum character limit.
Complete the following probability distribution table: Probability Distribution Table X P(X)20 0.2 49 0.453 ? 80 0.3 Get help: Written Example
0.1 is probability in distribution table.
What are examples and probability?
The quantity of success-producing options. the total number of outcomes that could occur.
For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.
Here X is a random variable. P(X) is its probabilities corresponding to the different values of X.
now according to the properties of probability theory we know that sum of probabilities is 1.
so here to find the value of the probability of X coresponding to the value 53 we should use the following steps:
sum of given probabilities =(0.2+0.4+0.3) = 0.9
required probability = 1 - sum of given probabilities = 1 - 0.9 = 0.1
hence the complete probability table is
X P(X)
20 0.2
49 0.4
53 0.1
80 0.3
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At what point do the curves r1 (t) = t, 4 - t, 35 + t^2 and r2 (s) = 7 - s, s - 3, s^2 intersect? Find their angle of intersection, \theta, correct to the nearest degree.
At point, the parametric curves cross (4, 1, 32).
What are parametric functions?t functions expressed as x = f(y) = y = f(x) = (some function of the variable x) (some function of the variable y).
It is frequently more easier to view functions of two or more variables (although we'll keep it at two here) as parametric functions, particularly in physical science.
The introduction of the idea of time makes parametric functions the most simple to understand.
Imagine tracing a parabola-like function from left to right as time passes.
Then, it is simple to begin considering how the x-coordinate and the y-coordinate change as a function of time: x = f(t), y = g. (t). In this sense, time is actually referred to as the parameter.
We will investigate functions for which a point exists in this section.
Hence, At point, the parametric curves cross (4, 1, 32).
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