Answer:
The probability that two randomly selected tulip bulbs are both red is 0.11
The probability that the first bulb selected is red and the second is yellow is 0.13
The probability that the first bulb selected is yellow and the second is red is 0.13
Step-by-step explanation:
A bag of 29 tulip bulbs contains:
10 red tulip bulbs
11 yellow tulip bulbs
8 purple tulip bulbs
Part 1:What is the probability that two randomly selected tulip bulbs are both red?
No. of red tulips = 10
So, probability of getting red tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]
= [tex]\frac{10}{29}[/tex]
Since 1 bulb is drawn . So, total no. of bulbs remaining = 28
And that 1 bulb is drawn from red bulbs . So, remaining red bulbs = 9
So, probability of getting red bulb in second draw = [tex]\frac{9}{28}[/tex]
Thus the probability that two randomly selected tulip bulbs are both red:
= [tex]\frac{10}{29}\times\frac{9}{28}[/tex]
= [tex]\frac{45}{406}[/tex]
= [tex]0.11[/tex]
Hence the probability that two randomly selected tulip bulbs are both red is 0.11
Part 2: What is the probability that the first bulb selected is red and the second is yellow?
No. of red tulips = 10
So, probability of getting red tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]
= [tex]\frac{10}{29}[/tex]
Since 1 bulb is drawn . So, total no. of bulbs remaining = 28
No. yellow bulbs =11
So, probability of getting yellow bulb in second draw = [tex]\frac{11}{28}[/tex]
Thus the probability that the first bulb selected is red and the second is yellow
= [tex]\frac{10}{29}\times\frac{11}{28}[/tex]
= [tex]\frac{55}{406}[/tex]
= [tex]0.13[/tex]
Hence the probability that the first bulb selected is red and the second is yellow is 0.13
Part 3: What is the probability that the first bulb selected is yellow and the second is red?
No. of yellow tulips = 11
So, probability of getting yellow tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]
= [tex]\frac{11}{29}[/tex]
Since 1 bulb is drawn . So, total no. of bulbs remaining = 28
No. red bulbs =10
So, probability of getting red bulb in second draw = [tex]\frac{10}{28}[/tex]
Thus the probability that the first bulb selected is red and the second is yellow
= [tex]\frac{11}{29}\times\frac{10}{28}[/tex]
= [tex]\frac{55}{406}[/tex]
= [tex]0.13[/tex]
Hence the probability that the first bulb selected is yellow and the second is red is 0.13
The ratio of sues age to her fathers age is 2:7 in three years their ages will total 60, how old is sue and her dad right now
A sequence in which each term is found by adding the same number
The width of a square-based storage tank is 3m less than its height. The tank has a capacity of 20 m3. If the dimensions are integer values in metres, what are they?
Morgan calculated that he spent 305 minutes doing homework one week and 284 minutes doing homework the next week. How much more time did he spend doing homework the first week?
who good at the math
The equation of line KL is y=-1/2x-6. The equation line WX is 7x-14y=-42. Rewrite the equation of line WX in slope-intercept form and determine if the two lines are parallel.
The equation of line WX in slope-intercept form is,
⇒ y = 1/2x + 3
And, Lines WX and Kl are not parallel lines because its slopes are not equal to each other.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation of line KL is,
⇒ y = - 1/2x - 6.
And, The equation line WX is,
⇒ 7x - 14y = - 42
Now,
The equation of line WX in slope-intercept form is,
⇒ 7x - 14y = - 42
⇒ 7x + 42 = 14y
⇒ 14y = 7x + 42
⇒ y = 7x/14 + 42/14
⇒ y = 1/2x + 3
Hence, Slope of equation of line WX is,
⇒ y = 1/2x + 3
⇒ dy/dx = 1/2
⇒ m = 1/2
And, Slope of equation of line KL is,
⇒ y = - 1/2x - 6
⇒ dy/dx = - 1/2
⇒ m = - 1/2
We know that;
Slopes of parallel lines are equal.
Hence, Lines WX and Kl are not parallel lines because its slopes are not equal to each other.
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If h(x) = -3x - 10, find h(-3).
Answer
-1
2.3
-19
1
...?
A1+a2+a3=180 solve for a1
what is 4.09 rounded to the nearest
Assume the function has an inverse. Without solving for the inverse find the indicated function values: f(x)=x^3+4x-1, (a) f^-1 (-1) (b) f^-1 (4) ...?
To find the indicated function values of the inverse of a function, substitute the given values into the original function and solve for x.
Explanation:To find the indicated function values of the inverse of the function f(x)=x^3+4x-1, without solving for the inverse function, we substitute the given values into the original function and solve for x.
(a) To find f^-1(-1), we substitute -1 into the function: f(-1)=(-1)^3+4(-1)-1 = -1+(-4)-1 = -6.
(b) To find f^-1(4), we substitute 4 into the function: f(4)=(4)^3+4(4)-1 = 64+16-1 = 79.
What is the prime factorization of 126
The prime factorization of the number 126 is 2,3,3, and 7.
What is prime factorization?Any number can be represented as a sum of prime numbers by prime factorization. A number with exactly two factors, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2,3, and 3.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the number is 126. The prime factorization of the number 126 will be calculated as:-
126 = 2 x 3 x 3 x 7
Hence, the prime factorization of the number 126 is 2,3,3, and 7.
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A fast food restaurant sells between 164 and 328 hamburgers per day. If the company profits $82.00 per 82 hamburgers sold, approximately how much does the company profit in one year from hamburgers?
PLZZZZZZ HELPPPP
What did the inventor of the 10 ton truck so often say
Answer:
This is an equation in which we have to find the slope of the line. We are supposed to draw the line for the two given points.
Step-by-step explanation:
The equation and the graph are solved as:
For graph One: B=(4,4)(1,2) for that m= 2/3. E=(2,0)(-4,4), for this m=-2/3. O=(1,-3)(-3,-4),m=1/4.for Second graph: I=(-1,-3)(2,3), m=2. E=(-4,-3)(-2,-1), m=-2. O=(-3,0)(-1,5),m=5/2. for the third graph:E=(0,2)(5,-1),m=-3/5. D=(5,6)(2,-1), m=7/3.L=(-5,2)(0,-3),m=-1.for the fourth graph: D=(0,0)(2,-6),m=-3. G=(4,5)(-2,4),m=1/6. S=(2,-3)(-5,-3), m=0.Now the Graphical data and the results are attached to the answer, given hope it helps out.
graph the line y=3/4x-2
Step-by-step explanation: First, notice that this line is in slope intercept or more commonly known as y = mx + b form because y is by itself on one side of the equation.
Our slope or m therefore is the coefficient of the x-term which in this case is 3/4. Our b or y-intercept is the constant term which in this case is -2.
To graph a line given the slope and y-intercept, we will first start with its y-intercept. The y-intercept of a line is the point where the line crosses the y-axis. Since our y-intercept is -2, we start by plotting the point that is down 2 units on the y-axis and we call that point A.
From there we take our slope of 3/4 so our rise is 3 and our run is 4 and we end up at point B. Now we can connect the two points and we have our line.
I attached the image of the line in the image provided.
What is the solution of the equation?
4p/6+27=39
A. 22
B. 99
C. 4
D. 18
In the formula A=\pi r^{2}, if the radius is 6 centimeters, what is the correct unit for the area of the circle?
A)\pi cm
B)cm^2
C)cm
D)cm^3
The formula for rate is r=d/t . Solve for d.
Write the standard form of the equation of the line that passes through the given points.
(5, 3) and (8, -2)
Which of the following is the inverse of the function {(1,2),(3,4),(6,8)}
A. {(6,8),(3,4),(1,2)}
B. {(2,1),(4,3),(6,8)}
C. {(2,1),(4,3),(8,6)}
D. {(2,1),(3,4),(8,6)}
Dayla earns $108.75 for working 15 hours of holiday open rap at this rate how much money will see you earn if she works 18 hours the next week explain
XY is the perpendicular bisector of JK. which of the following statements must be true? check all that apply?
A. XY and JK form four right angles
B. P is the midpoint of XY
C. m
D. XP=YP
E.JP=KP
F. XY perpendicualr to JK
According to the properties of a perpendicular bisector, XY will form four right angles with JK, XY is perpendicular to JK, and it must bisect JK into two equal parts, making statements A, D, E, and F true.
Explanation:The question tells us that XY is the perpendicular bisector of JK. This tells us a few things about the relationship between the two lines and the points on them:
XY and JK form four right angles: Because XY is a perpendicular bisector, it intersects line JK at a 90° angle.XY perpendicular to JK: This simply restates that the angle formed by the intersection of XY and JK is a right angle.JP=KP: Perpendicular bisectors not only intersect the other line at a right angle, but they also bisect it, which means they cut it into two equal parts. Thus, point J is as far from the point of intersection as point K, making JP equal to KP.XP=YP: This is also a property of the perpendicular bisector. It means that the point of intersection P is the midpoint of XY, making segment XP equal to segment YP.The options regarding P being the midpoint of XY and the statement that includes an undefined variable 'm' were ignored due to lack of context.
Final answer:
The statements that must be true when XY is the perpendicular bisector of JK are: XY and JK form four right angles, P is the midpoint of XY, XP = YP, and XY is perpendicular to JK.
Explanation:
To determine which of the statements must be true, we need to understand the properties of a perpendicular bisector. A perpendicular bisector of a line segment is a line that divides the line segment into two equal parts and forms a right angle with the line segment.
From this definition, we can conclude that the following statements must be true:
A. XY and JK form four right angles - Since XY is the perpendicular bisector of JK, it forms a right angle with JK at each point of intersection.
B. P is the midpoint of XY - The perpendicular bisector passes through the midpoint of the line segment it bisects.
C. XP = YP - Since P is the midpoint of XY, XP and YP have equal lengths.
F. XY is perpendicular to JK - This is the definition of a perpendicular bisector.
how to find a whole number in this question 4% of ... is 56?
the formula for finding the area of a circle is a equals pi r square. solve the formula for r.
Give 9.7814 correct to the nearest whole number
Final answer:
9.7814 rounded to the nearest whole number is 10, as the first digit after the decimal point is 7, which requires rounding up.
Explanation:
To find the nearest whole number to 9.7814, we need to look at the first digit after the decimal point. Since this digit is 7 (which is equal to or greater than 5), we round up the number. Rounding up changes 9.7814 to the next whole number, which is 10.
The general rule for rounding to the nearest whole number is:
If the first decimal place is 5 or greater, round up.If the first decimal place is less than 5, round down.Therefore, 9.7814 rounded to the nearest whole number is 10.
graph the equation. y = 4x - 3
Write 16 1/2 as an improper fraction
Sam is flying a kite. the length of the kite string is 80 meters, and it makes an angle of 75° with the ground. the height of the kite from the ground is meters.
Answer:
Height of the kite from ground is 77 m.
Step-by-step explanation:
Given: Length of the kite string = 80 m
Angle of elevation = 75°
To find: Height of the kite from the ground.
Figure is attached.
In ΔABC
using trigonometric ratio,
[tex]sin\,75^{\circ}=\frac{AB}{AC}[/tex]
[tex]0.97=\frac{AB}{80}[/tex]
[tex]AB=0.97\times80[/tex]
AB = 77.27 m
AB = 77 m (approx.)
Therefore, Height of the kite from ground is 77 m.
I HATE MATH (and im lazy)
Oliver borrowed $215 from his friend John. He used this money to advertise his tutoring services. Oliver earned 8 times the amount he borrowed in his first month of tutoring. Approximately how much did Oliver earn in his first month of tutoring?
Answer:
then f the teacher
Step-by-step explanation:
Does antibiotics help kill the common cold??
Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = 5(x + 8)2(x - 8)3
A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3
B. -8, multiplicity 2; 8, multiplicity 3
C. -8, multiplicity 3; 8, multiplicity 2
D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1
The given polynomial has roots -8 with multiplicity 2 and 8 with multiplicity 3. Hence option B is correct.
Use the concept of polynomial defined as:
An expression that contains exponents, variables, and constants that is combined using mathematical operations such as addition, subtraction, multiplication, and division is known as a polynomial.
The given polynomial is:
f(x) = 5(x + 8)²(x - 8)³
To find its root equate this polynomial to 0.
Then,
5(x + 8)²(x - 8)³ = 0
(x + 8)²(x - 8)³ = 0
(x + 8)(x + 8)(x - 8)(x - 8)(x - 8) = 0
Therefore,
x = -8, -8, 8, 8, 8
Hence,
It has root -8 with multiplicity 2 and 8 with multiplicity 3 which is option B.
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The complete question is:
Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = 5(x + 8)²(x - 8)³
A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3
B. -8, multiplicity 2; 8, multiplicity 3
C. -8, multiplicity 3; 8, multiplicity 2
D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1