Answer:
The equation that shows how the cost of the baby shower, y, depends on the number of guests, x is:
y = 9x + 43
In this equation, x represents the number of guests and y represents the cost of the baby shower. The term 9x represents the cost of food for each guest, multiplied by the number of guests. The term 43 represents the cost of decorations that has already been spent. Therefore, the total cost of the baby shower can be calculated by multiplying the number of guests by the cost of food per guest and adding the cost of decorations that have already been spent.
Answer: y = 9x + 43
Step-by-step explanation: y = cost of the baby shower
x = number of guests
$9 per guest would be 9x
Both circles have the same center. The circumference of the inner circle is 18.84 feet. What is the area of the shaded region?
The area of the shaded region is π(R + 3)² - 9π where R is teh radius of the outer circle
Calculating the area of the shaded regionThe circumference of the inner circle is 18.84 feet
So, we have
2πr = 18.84
Divide by 2π
r = 18.84/2π
Evaluate
r = 3.0
So, the area of the inner circle is
A = πr²
This gives
A = π * 3²
Evaluate
A = 9π
The shaded area is
Area of big - Area of inner circle
So, we have
Shaded area = π(R + 3)² - 9π where R is teh radius of the outer circle
Read more about area at
https://brainly.com/question/24487155
#SPJ1
solve
2|x| = 3 i need help
Answer: [tex]x_1 = -\frac{3}{2} \\x_2 = \frac{3}{2} \\\\[/tex]
X could equal either -3/2, or 3/2 because x is made into an absolute value
Answer:
[tex]x = 1 \frac{1}{2} \: \\ x = - 1 \frac{1}{2} [/tex]
Step-by-step explanation:
If we're solving for x, then we should divide both sides by 2 and then simplify.
[tex](2 |x| = 3) \div 2[/tex]
[tex] |x| = \frac{3}{2} [/tex]
This gives us the final answer of
[tex]x = ±\frac{3}{2} [/tex]
Which can be simplified into:
[tex]x = 1\frac{1}{2} , \: - 1\frac{1}{2} [/tex]
Which is a function
For each relation, we would determine whether or not it is a function as follows;
Relation 1 is: B. not a function
Relation 2 is: A. function.
Relation 3 is: B. not a function
Relation 4 is: A. a function.
How to determine the relations that represent functions?In Mathematics and Geometry, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).
This ultimately implies that, an independent value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the value on the y-coordinate of a cartesian coordinate.
Based on relations 1 and 3, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).
Read more on function here: brainly.com/question/3632175
#SPJ1
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
We have,
Equation of circle: x²+ y² – 2x – 8 = 0
The standard equation of a circle is
x² + y² + 2gx + 2fy + C= 0
where Centre is (-g, -f)
and, radius = √g²+f²-C
from given equation the center is
2gx = -2x
x= -1
and, 2fy = 0
f = 0
So, the Centre = (-(-1), 0) = (1, 0)
Now, r = radius = √g²+f²-C
r= √1²+0²-(-8)
r=√9
r = 3 units
Hence, the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Learn more about Equation of Circle here:
https://brainly.com/question/29288238
#SPJ1
(4 radical 3)- 4i in polar form
The solution is the number in polar form 4 - 4i is
4 Root(2) (cos(-45) + i sin(-45)).
We know that,
Polar form of a complex number is r( cos(theta) + i sin(theta) )
r is equal to the total distance created by the rectangular coordinates of the complex number
r = Root(4^2 + (-4)^2) = Root(32) = 4 Root(2)
To find theta, if a > 0, use arctan(b/a), where:
a = the first number
b = the second number
arctan (-4/4) = -45 degrees (-0.7854 radians)
The answer is 4 Root(2) (cos(-45) + i sin(-45))
To learn more on complex number click:
brainly.com/question/19467739
#SPJ1
complete question;
Express the number in polar form 4 - 4i
Calculate the standard deviation of the sum
S=I+O.
O as = $227.69
Oos= $1,301.25
O as = $1,508.48
as = $6,348.75
The standard deviation of the sum S = I + O is [tex]$1,508.48[/tex]. The Option C is correct.
How do we calculate standard deviation of the sum S=I+O?In order to calculate standard deviation of the sum S = I + O on the information given from the question, we can use this formula: "SD(S) = sqrt[SD(I)^2 + SD(O)^2 + 2Cov(I,O)]".
Details:
SD(I) & SD(O) means standard deviations of in-state and out-of-state tuition.
Cov(I,O) means covariance between the two variables.
The two variables I and O are independent
Their covariance is zero
Now, we can solve the S.D. using the formula. The SD(S):
= sqrt[SD(I)^2 + SD(O)^2]
= sqrt[(1003.25)^2 + (1126.50)^2]
= sqrt[1006510.5625 + 1269002.25]
= sqrt[2275512.8125]
= 1508.48029901
= $1508.48
Read more about standard deviation
brainly.com/question/24298037
#SPJ1
Can u please solve the problem
The complete proof to show that ∠HIJ ≅ ∠EFG is:
Statement Reason
FG ⊥ EF Given
HI ⊥ IJ Given
m ∠EFG = 90° Definition of perpendicular lines
m ∠HIJ = 90° Definition of perpendicular lines
∠HIJ ≅ ∠EFG Substitution property
Proof of congruent anglesFrom the question, we to prove that the given angles are congruent.
The given angles are ∠HIJ and ∠EFG
To prove that angle HIJ is congruent to angle EFG we will complete the given table.
The given table is
Statement Reason
FG ⊥ EF Given
HI ⊥ IJ Given
m ∠EFG = 90° Definition of perpendicular lines
m ∠HIJ = 90° Definition of perpendicular lines
Now, we will complete the proof by adding the last statement and its reason
Statement Reason
FG ⊥ EF Given
HI ⊥ IJ Given
m ∠EFG = 90° Definition of perpendicular lines
m ∠HIJ = 90° Definition of perpendicular lines
∠HIJ ≅ ∠EFG Substitution property
Hence,
We have completed the proof by using the substitution property
Learn more on Proof of angles here: https://brainly.com/question/29969150
#SPJ1
A circular flower bed is 17 m in diameter and has a circular sidewalk around it that is 4 m wide. Find the area of the sidewalk in square meters. Use 3.14 for . The area of the sidewalk is m². (Round to the nearest whole number as needed.)
The area of the sidewalk is 264 sq. m.
What is area of a circle?A circle is a figure that is bounded by curved line called its circumference. Its area is the amount of space that he circle will cover on a 2 dimensional plane. It can be determined by:
area of a circle = πr^2
where r is the radius of the circle.
In the given question,
area of the circular flower = πr^2
r = d/2 (d is the diameter)
= 17/ 2
r = 8.5 m
area of the circular flower = 3.14*(8.5)^2
= 226.865 sq. m
area of the circular flower with sidewalk = πr^2
d = 4 + 17 + 4 = 25 m
so that,
r = 25/ 2 = 12.5 m
area of the circular flower with sidewalk = 3.14*(12.5)^2
= 490.625 sq. m
Area of the sidewalk = area of the circular flower with sidewalk - area of the circular flower
= 490.625 - 226.865
= 263.76 sq. m
The area of the sidewalk is 264 sq. m.
Learn more about the area of a circle at https://brainly.com/question/704946
#SPJ1
ayer compre 3/4 y hoy 1/2 cuantos kilogramos tengo en total porfaaaaaaaaaaa
Based on the above, Since Ana bought 3/4 kg of lanzones and 1/2 kg of apples, Ana bought 1 1/4 kilograms of fruits in all.
What is the kilograms?To be able to find out how many kilograms of fruits Ana bought in total, you have to add the amount of lanzones and apples she have.
Ana = 3/4 kg of lanzones
Ana = 1/2 kg of apples
So it will be:
3/4 + 2/4 = 5/4
Therefore, Ana will have bought a total of 5/4 kilograms of fruits.
To convert it to a mixed number, you need to divide the numerator by the denominator:
5 ÷ 4 = 1 remainder 1
So, the mixed fraction will be 1 1/4 kg.
Learn more about kilograms from
https://brainly.com/question/9301317
#SPJ1
See full question below
Ana bought 3/4 kg of lanzones and 1/2 kg of apples. How many kilograms of fruits did she buy in all?
I'm Serena. For a science project, my friend Jack and I are launching three model rockets, one after another. We launch the first rocket, and then 3 seconds later, we launch the next one. And we're launching the final rocket three seconds after that, from a platform that is 20 feet high.
For our project, we need to predict the paths for all three rockets. We also need to estimate when they will all be in the air at the same time. [A graph that shows "Height of rocket (feet)" on the y-axis and "Time (seconds)" on the x-axis is shown. A red downturned parabola is shown and labeled "Path of the first rocket."]
We have calculated the path of the first rocket. It looks like this: a parabola that opens down. The y-axis is the height of the rocket in feet, and the x-axis is the time in seconds.
My friend Jack thinks we need to recalculate the graphs for the other two model rockets. But since the rockets are all the same, I think we can just shift the graph of the first rocket to find the graphs for the other two. [The graph is duplicated in green and shifts to the right, and then again in blue and shifts to the right and up. Then the rockets blast off again.]
What do you think? How can we use the graph of the first rocket to create the graphs of the second and third rockets? When will all three rockets be in the air at the same time?Evaluate the Conjectures:
2. Do you agree with Serena that you can draw the graphs for the other two rockets by shifting the functions? Or do you think that Jack is correct that you need to recalculate the other two? Explain. (2 points)
Analyzing the Data:
Suppose that the path of the first model rocket follows the equation
h(t) = −6 • (t − 3.7)2 + 82.14,
where t is the time in seconds (after the first rocket is launched), and h(t) is the height of each rocket, in feet.
Compare the equation with the graph of the function. Assume this graph is a transformation from f(t) = –6t2. What does the term –3.7 do to the rocket's graph? What does the value t = 3.7 represent in the science project? (What happens to the rocket?)
Again assuming a transformation from f(t) = –6t2, what does the term 82.14 do to the rocket's graph? What does the value h(t) = 82.14 represent in the science project? (What is happening to the rocket?) (2 points)
Serena and Jack launch the second rocket 3 seconds after the first one. How is the graph of the second rocket different from the graph of the first rocket? Describe in terms of the vertical and horizontal shift.
What is the equation of the second rocket?
They launch the third rocket 3 seconds after the second rocket and from a 20-foot-tall platform. What will the graph of the third rocket look like? Describe in terms of the vertical and horizontal shift.
What is the equation of the third rocket?
Answer the following questions about the three rockets. Refer to the graph of rocket heights and times shown above.
a. Approximately when is the third rocket launched?
b. Approximately when does the first rocket land?
c. What is the approximate interval during which all three rockets are in the air?
Answer:
Regarding the conjecture of Serena and Jack:
Serena suggests that they can use the graph of the first rocket and shift it to find the graphs for the other two rockets. This means that the paths of the rockets are similar, and the only difference is the time of launch. Jack suggests that they need to recalculate the graphs for the other two rockets, which means that the paths of the rockets are different.
In this scenario, Serena is correct. Since the rockets are identical, they will follow the same path, but with a different time of launch. Thus, they can use the graph of the first rocket and shift it to the right to get the graph of the second rocket and shift it further to the right and up to get the graph of the third rocket.
Analyzing the equation:
The equation for the first rocket's path is h(t) = -6(t-3.7)^2 + 82.14. Assuming that the graph is a transformation from f(t) = -6t^2, the term -3.7 shifts the graph horizontally to the right by 3.7 seconds. This means that the first rocket was launched 3.7 seconds before the time t in the equation. The value t = 3.7 represents the time when the first rocket was launched.
The term 82.14 shifts the graph vertically up by 82.14 feet. This means that the initial height of the rocket is 82.14 feet above the ground. Therefore, the value h(t) = 82.14 represents the initial height of the rocket.
Equation of the second rocket:
The second rocket is launched 3 seconds after the first rocket. This means that the graph of the second rocket is a horizontal shift of the first rocket's graph by 3 seconds. Therefore, the equation of the second rocket is:
h(t) = -6(t-6.7)^2 + 82.14
This is because the launch time of the second rocket is t = 6.7 seconds (which is 3 seconds after the first rocket's launch).
Description of the third rocket's graph:
The third rocket is launched 3 seconds after the second rocket and from a 20-foot-tall platform. This means that the graph of the third rocket is a horizontal shift of the second rocket's graph by 3 seconds and a vertical shift upwards by 20 feet. Therefore, the equation of the third rocket is:
h(t) = -6(t-9.7)^2 + 102.14
This is because the launch time of the third rocket is t = 9.7 seconds (which is 3 seconds after the second rocket's launch).
Answers to the questions:
a. The third rocket is launched at approximately t = 9.7 seconds.
b. The first rocket lands when h(t) = 0. Solving -6(t-3.7)^2 + 82.14 = 0 gives t = 5.16 seconds (approximate).
c. The approximate interval during which all three rockets are in the air is from t = 6.7 seconds (when the second rocket is launched) to t = 14.46 seconds (when the first rocket lands).
Find the final amount for a $650 investment at 6.5% interest compounded continuously for 20 years.
After 20 years, the initial investment of $650 will have grown to $2,386.10
Now, let's consider the problem at hand: a $650 investment at 6.5% interest compounded continuously for 20 years. To calculate the final amount of the investment, we can use the formula:
A = P[tex]e^{rt}[/tex]
where A is the final amount, P is the initial investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate (in decimal form), and t is the time (in years).
Plugging in the values given in the problem, we get:
A = 650 x [tex]e^{0.065 \times 20}[/tex]
Simplifying this expression, we get:
A = 650 x [tex]e^{1.3}[/tex]
Using a calculator, we can find that [tex]e^{1.3}[/tex] is approximately 3.6693. Therefore, the final amount of the investment is:
A = 650 x 3.6693
A = $2,386.10
To know more about compound interest here
https://brainly.com/question/29335425
#SPJ1
Solve for the roots in the following equation. Hint: Factor both quadratic expressions.
(x4 + 5x2 - 36)(2x2 + 9x - 5) = 0
The roots of equation are 2 , -2, 3i, 1/5 and -5.
We have,
([tex]x^4[/tex] + 5x² -36)(2x² + 9x-5)=0
Now, factories each equation as
([tex]x^4[/tex] + 5x² -36)
= ([tex]x^4[/tex] + 9x² - 4x² -36)
= x²(x² + 9) - 4(x² + 9)
= (x² - 4)(x² + 9)
= (x-2)(x+2)(x²+9)
and, 2x² + 9x-5
= 2x² + 10x - x -5
= 2x(x+5)- (x+5)
= (2x -1)(x+5)
So, the factored form is (x-2)(x+2)(x²+9) (2x -1)(x+5)
and, the roots of equation are 2 , -2, 3i, 1/5 and -5.
Learn more about Factorization here:
https://brainly.com/question/2006173
#SPJ1
What is the quadratic regression equation that fits these data?
OA. 9-0.3x+30.3
X
1
2
3
4
5
OB.-29.8(0.99)
OC.9 -0.3x² + 30.3x -0.11
OD.9=2.4x2-14.4x+46.8
y
35
27
24
28
33
The quadratic regression equation for the data is given as follows:
y = 2.4x² - 14.4x + 46.8.
How to find the equation of quadratic regression?To find the quadratic regression equation, we need to insert the points (x,y) into a quadratic regression calculator.
The points for this problem are taken from the table, as follows:
(1, 35), (2, 27), (3, 24), (4, 28), (5, 33).
Inserting these points into a calculator, the equation is given as follows:
y = 2.4x² - 14.4x + 46.8.
More can be learned about quadratic functions at https://brainly.com/question/1214333
#SPJ1
Find the derivative of the given function.
y=4x² (5-7x)^8
Answer:
To find the derivative of the given function, we will use the product rule and the chain rule of differentiation.
Let u = 4x² and v = (5-7x)^8. Then, we have:
y = u * v
Using the product rule, we have:
y' = u' * v + u * v'
To find u' and v', we use the power rule and the chain rule:
u' = d/dx (4x²) = 8x
v' = d/dx (5-7x)^8 = 8(5-7x)^7 * (-7)
Now, we can substitute these values into the product rule formula:
y' = u' * v + u * v'
= 8x * (5-7x)^8 + 4x² * 8(5-7x)^7 * (-7)
Simplifying this expression, we get:
y' = 8x(5-7x)^7 * (40-56x-28x+49x)
= 8x(5-7x)^7 * (-14x+40)
Therefore, the derivative of the function y = 4x² (5-7x)^8 is y' = 8x(5-7x)^7 * (-14x+40).
NEED HELP FOR MATH HW! I need some help number 3 WITHOUT the use of a t1-83
The solution to the given inequality is −1.26354284<x<1.75564007 or x>4.50790277.
The given inequality is x³-5x²+10>0.
Solve for x by simplifying both sides of the inequality, then isolating the variable.
Inequality Form: −1.26354284<x<1.75564007 or x>4.50790277
Interval Notation:(−1.26354284,1.75564007)∪(4.50790277,∞)
Therefore, the solution to the given inequality is −1.26354284<x<1.75564007 or x>4.50790277.
To learn more about the inequalities visit:
https://brainly.com/question/20383699.
#SPJ1
3 more than the difference of 20 and a number m
Step-by-step explanation:
(20 - m) + 3
that's it. there is not more to it.
The algebra expression can be expressed as: 3 + (20 - m)
How to solve Algebra word problems?Algebraic word problems are defined as questions that require translating sentences to equations, and then solving those equations. The equations we need to write will only involve basic arithmetic operations. and a single variable. Normally, the variable represents an unknown quantity in a real-life scenario.
We are told that 3 more than the difference of 20 and a number m.
This can be expressed as:
3 + (20 - m)
That is the literal expression of the algebra word problem.
Read more about Algebra Word Problems at: https://brainly.com/question/21405634
#SPJ1
Claude Monet's Impression: Sunrise (1872) is considered a(n) ____ painting because it was completed out-of-doors.
plein-air
alfresco
alla prima
sfumato
Answer:
plein-air. Is the correct answer
Claude Monet's Impression: Sunrise (1872) is considered a plein-air painting because it was completed out-of-doors.
the sum of a numberator and a denominator of a fraction is 4140. when reduced fraction, it is 7/13
PLEASE HURRY
Let a = apple and c = cherry.
Mathland Bakery sells apple pies for $7.00 and cherry pies for $11.00.
The total number of pies sold in one day was 36. If the amount collected for all the pies that day was $304.00, how many of each type were sold?
Answer:
23 apple pies and 13 cherry pies were sold.
Step-by-step explanation:
Let's use the variables a and c to represent the number of apple and cherry pies sold, respectively.
From the problem, we know that:
The total number of pies sold is 36: a + c = 36
The total revenue from pie sales is $304.00: 7a + 11c = 304
We now have two equations with two unknowns. We can use substitution or elimination to solve for a and c. Here's one way to use substitution:
Solve the first equation for a: a = 36 - c
Substitute a = 36 - c into the second equation: 7(36 - c) + 11c = 304
Simplify: 252 - 7c + 11c = 304
Simplify further: 4c = 52
Solve for c: c = 13
Substitute c = 13 into the first equation to solve for a: a + 13 = 36
Simplify: a = 23
Therefore, 23 apple pies and 13 cherry pies were sold.
In the coordinate plane, the point X (-1, 0) is translated to the point X' (3, 1). Under the same translation, the points Y (2, 3) and Z (1, -2) are translated to Y' and Z', respectively. What are the coordinates of Y' and Z'?
The coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).
Here, we have,
To find the coordinates of Y' and Z', we need to apply the same translation that maps X to X'.
We know that the vector that connects X to X' is (3 - (-1), 1 - 0) = (4, 1).
So, to translate Y to Y', we add the vector (4, 1) to the coordinates of Y:
Y' = Y + (4, 1)
= (2, 3) + (4, 1)
= (6, 4)
Similarly, to translate Z to Z', we add the vector (4, 1) to the coordinates of Z:
Z' = Z + (4, 1)
= (1, -2) + (4, 1)
= (5, -1)
Therefore, the coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).
Learn more about translation here
brainly.com/question/29080541
#SPJ1
TALL BUILDING Rob wants to estimate how tall his school building is. The building casts a shadow that is 30 feet long. If Rob' is 6 feet tall and casts a shadow 2 feet long, how tall is the building?
The height of the building, found using the equivalent ratios of the corresponding sides of the similar triangles formed by Rob, the building and the shadows is 90 feet
What are similar triangles?Similar triangles are triangles that have the same shape but may have different sizes.
The length of the shadow cast by the building = 30 feet
Rob's height = 6 feet
The length of Rob's shadow = 2 feet long
The height of the building can be found from the similar right triangles formed by the building and the building's shadow and the triangle formed by Rob and Rob's shadow as follows;
Let h represent the height of the building, we get;
h/30 = 6/2 = 3
h = 30 × 3 = 90
The height of the building is 90 feet tall
Learn more on similar triangles here: https://brainly.com/question/29782808
#SPJ1
help me please quickly
the answer is B
B
because the answer B make the most sense to me and hopefully this helps
Pythagoras theorem: In a right triangle, if the hypotenuse, perpendicular, and base are its sides, then as per the theorem, the square of the hypotenuse side is equal to the sum of the square of the base and the square of the perpendicular. Hence, if we know any two sides, then we can easily find the third side of the triangle.
C. 20 ft, 20 ft, 50 ft correct?
What is the name of this shape?
A shape is shown with 4 sides of different lengths. Each side is not equal to the other.
A.
quadrilateral
B.
pentagon
C.
triangle
D.
hexagon
Who recommended that artists paint scenes of modern life?
Charles Baudelaire
John Ruskin
Louis Leroy
Sir Joshua Reynolds
Answer:
Charles Baudelaire recommended that artists paint scenes of modern life.
Charles Baudelaire was the one who recommended that artists paint scenes of modern life.
What is the value of x in this proportion? 27=−5x+3 Responses x=−2012 x equals negative 20 and 1 half x=−19 x equals negative 19 x=−16 x equals negative 16 x=−1412
The value of x in the equation 27=−5x+3 is -24/5
The given equation is 27=−5x+3
We have to find the value of x
Subtract 3 from both sides
27-3=-5x
24=-5x
Divide both sides by 5
x=-24/5
Hence, the value of x in the equation 27=−5x+3 is -24/5
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
Can someone help me please
Applying the Solution to a 3X3 System
At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?
Show up all steps please
Answer: there were 190 children, 140 parents, and 70 grandparents in attendance at the family reunion.
Step-by-step explanation: Let's denote the number of children, parents, and grandparents as "c", "p", and "g", respectively.
We are given three pieces of information:
The total number of people in attendance is 400:
c + p + g = 400
There were twice as many parents as grandparents:
p = 2g
There were 50 more children than parents:
c = p + 50
We can use this system of equations to solve for the unknown variables.
First, we can use equation (2) to express "p" in terms of "g":
p = 2g
Next, we can substitute this expression for "p" into equation (3) to get:
c = 2g + 50
Now, we can use equations (1) and (4) to eliminate "p" and "c" from the system and express "g" in terms of only known quantities:
c + p + g = 400
2g + 50 + p + g = 400 (substituting c=2g+50)
3g + p = 350 (simplifying)
We can then substitute the expression for "p" from equation (2) into this last equation to obtain:
3g + 2g = 350
Simplifying:
5g = 350
Solving for "g", we get:
g = 70
Now, we can use equation (2) to find "p":
p = 2g = 2(70) = 140
Finally, we can use equation (3) to find "c":
c = 2g + 50 = 2(70) + 50 = 190
Therefore, there were 190 children, 140 parents, and 70 grandparents in attendance at the family reunion.
A quiz consists of 20 multiple-choice questions, each with 4 possible answers. for someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 60 %.
The probability of passing the quiz by randomly guessing answers is very low, approximately 0.02%.
To pass the quiz with a minimum passing grade of 60%, a person needs to answer at least 12 questions correctly out of the 20 total questions.
If a person is making random guesses for all of the answers, the probability of guessing one question correctly is 1/4, since there are 4 possible answers for each question. The probability of guessing one question incorrectly is 3/4.
Using the binomial probability formula, we can find the probability of passing the quiz by correctly guessing at least 12 questions:
P(X >= 12) = 1 - P(X < 12)
where X is the number of questions answered correctly.
P(X < 12) = sum of the probabilities of getting 0, 1, 2, ..., or 11 questions correct:
P(X < 12) = C(20,0)(1/4)⁰(3/4)²⁰ + C(20,1)(1/4)¹(3/4)¹⁹ + ... + C(20,11)(1/4)¹¹(3/4)⁹
where C(20,0), C(20,1), ..., C(20,11) are the binomial coefficients.
We can use a calculator or a computer to evaluate this sum of probabilities, or we can use a normal approximation to the binomial distribution if we assume that np = 20(1/4) = 5 and n x (1-p) = 20 x (3/4) = 15 are both greater than 10.
Using the normal approximation, we can find the mean and standard deviation of the binomial distribution:
mean = np = 20(1/4) = 5
Standard deviation = √(np(1-p)) = √(20*(1/4) x (3/4)) = √(15/2) = 1.94 (rounded to 2 decimal places)
Then, we can standardize the distribution by subtracting the mean and dividing by the standard deviation:
z = (12 - 5) / 1.94 = 3.61 (rounded to 2 decimal places)
Using a standard normal distribution table or a calculator, we can find the probability of getting a z-score greater than 3.61:
P(Z > 3.61) = 0.0002 (rounded to 4 decimal places)
Therefore, the probability of passing the quiz by randomly guessing answers is very low, approximately 0.02%.
To know more about probability follow
https://brainly.com/question/30494044
#SPJ1
help please
Applying the Solution to a 3X3 System
At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?
Show up all steps please
The number of children, parents, and Grandparents that were in attendance are:
190 children140 parents70 grandparentsHow to find the number of people ?First, we should come up with equations that relate the number of children, parents, and Grandparents, given the information we know. The equations would have C for children, P for parents, and G for grandparents.
Total number of people:
C + P + G = 400
Parents to grandparents:
P = 2G
Children to parents:
C = P + 50
Substituting gives:
( P + 50 ) + P + ( P / 2 ) = 400
P + 50 + P + P / 2 = 400
(5 / 2) P + 50 = 400
(5 / 2 )P = 350
P = 140 parents
The children would be:
C = P + 50
= 140 + 50
= 190 children
The grandparents:
G = P/2
= 140/2
= 70 grandparents
Find out more on attendance at https://brainly.com/question/12531910
#SPJ1
in the diagram of a quadrilateral below the variables represent the lengths of the
sides, in inches
Answer
6-2
[not drawn to scale]
White an expression using the variables band that could be used to find the
perimeter of the quadrilateral.
-5
Show your work.
1 b = 11 and c = 15, what is the perimeter of the quadrilateral?
The perimeter of the quadrilateral is b + 2c - 2 inches
How to determine the perimeterTo determine the value of the perimeter, we need to know the properties of a quadrilateral.
These properties includes;
They are known to have four verticesThey are known to have four sides.The sum of all interior angles of a quadrilateral is 360°.They have two diagonals.A quadrilateral can be seen as a regular or irregular shapeThe perimeter of a quadrilateral is expressed as;
Perimeter = A + B + C + D
add the values of the sides
Substitute the values, we have;
Perimeter = b + c + b - 2 + c - b
collect the like terms
Perimeter = b + 2c - 2
Learn about quadrilaterals at: https://brainly.com/question/16691874
#SPJ1
West High School has 3,000 students. East High School has 1/10 as many students as West High School. How many students are there at East High School?
Answer:
There are 300 students at East High School.
Step-by-step explanation:
East High School has 1/10 as many students as West High School, which means that the number of students at East High School is equal to 1/10 of the number of students at West High School.
To find out how many students are at East High School, we can multiply the number of students at West High School by 1/10:
East High School = West High School x 1/10East High School = 3000 x 1/10East High School = 300
Therefore, there are 300 students at East High School.
Answer:
East High School has 1/10 × 3,000 = 300 students.