The total area of the painting and frame is 112 in²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
Let x represent the length of the smaller edge.
One edge of a painting is 6 in. longer than the other edge. Hence:
Longer edge = x + 6
The painting has a 2-inch-wide frame.
Smaller edge length with frame = x + 2 + 2 = x + 4
Longer edge length with frame = (x + 6) + 2 + 2 = x + 10
Total area = (x + 4)(x + 10)
Total area = x² + 14x + 40
The longer side of the frame is 14 inches long, hence:
x + 10 = 14
x = 4 in
Total area = x² + 14x + 40 = 4² + 14(4) + 40 = 112 in²
The total area is 112 in²
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solve my homework and your smart and the brainiest person i know
Answer:
How are we supposted to do your homework if we dont have a picture or explanation of it??
Step-by-step explanation:
A drilling crew dug to a height of -323 feet during their first day of drilling. On the second day, the crew dug down 1933 feet more than on the first day. Describe the height of the bottom of the hole after the second day.
The height of the bottom of the hole after the second day is 2579 feet.
What is Addition?Mathematicians employ the action of addition to combine numbers. The sum of the given numbers is the outcome of addition, or the total of the given numbers.
As per the given data:
Drilling on first day = 323 feet.
Drilling on second day = drilling on first day + 1933 feet
Drilling on second day = 323 feet + 1933 feet
= 2256 feet
Total drilling = Drilling on first day + Drilling on second day
= 323 feet + 2256 feet
= 2579 feet
Hence, the height of the bottom of the hole after the second day is 2579 feet.
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Question below
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Answer: The answer t your question is the second one
Step-by-step explanation:
The angle of elevation from your hand to a kite is 65∘ and the distance from your hand to the kite is 287 feet. How high is the kite when your hand is 5 feet from the ground?
The height of the kite from the ground is 620.5 feet.
How to find the height of the kite?The angle of elevation from your hand to a kite is 65∘ and the distance from your hand to the kite is 287 feet.
Therefore, the height of the kite when your hand is 5 feet from the ground can be found as follows:
The situation forms a right angle triangle. Therefore, the height of the kite can be found using Pythagoras's theorem.
Hence,
tan 65 = opposite / adjacent
tan 65 = h / 287
cross multiply
h = 287 × tan 65
h = 615.473486186
Therefore,
height of the kite = 615.473486186 + 5
height of the kite = 620.5 feet
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RATIONAL EXPRESSIONS Restriction on a variable in a denominator: Quadra Find all excluded values for the expression. That is, find all values of u for which the expression is und (u-7)/(u^(2)-14u+49) If there is more than one value, separate them with comma
The excluded values of u in the expression (u-7)/(u^2-14u+49) are 7.
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Draw the image of the indicated translation of the given pre image please
The coordinates of the pre-images are (-7, 8); (-7, 5); (4, 8), and (2, 5), and the pre-image is given below.
Transformation:
A transformation of a quadrilateral refers to any process that changes the size, position, or shape of a four-sided polygon.
To draw the pre-mage, find the coordinates of the pre-mage as given below and plot the points in a graph
Here we have
The coordinates of the quadrilateral are (-4, 5); (-4, 2); (7, 5), and (5, 2)
Given T < -3, 3 > (x, y)
Hence, the coordinates of the pre-images are
(-4, 5) => (-4 -3, 5 + 3 ) = (-7, 8)
(-4, 2) => (-4 -3, 2 + 3) = (-7, 5)
(7, 5) => (7 -3, 5 + 3) = (4, 8)
(5, 2) => (5 - 3, 2+3) = (2, 5)
Therefore,
The coordinates of the pre-images are (-7, 8); (-7, 5); (4, 8), and (2, 5), and the pre-image is given below.
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Arrange in order from least to greatest (Radicals)
a. 4√3
b. 3√5
c. 5√2
d. 2√10
e. 2√13
f. 3√6
Therefore, the order from least to greatest is:d<f<a<b<c<e
d. 2√2 x √5 ≈ 5.66, f. 3√2 x √3 ≈ 6.00, a. 4√3 = 4 x √(3) ≈ 6.93, b. 3√5 ≈ 6.71, c. 5√2 ≈ 7.07, e. 2√13 ≈ 7.21
Arranging radicals( surds) in order from least to greatest,To arrange these radicals in order from least to greatest, we need to simplify them and compare the values. We can start by simplifying the radicals using prime factorization.
a. 4√3 = 4 x √(3) = 4 x√(3)
b. 3√5 = 3 x √(5)
c. 5√2 = 5 x√(2)
d. 2√10 = 2 x √(25) = 2 x √(2) x √(5) = 2√2 x√5
e. 2√13 = 2 x √(13)
f. 3√6 = 3 x √(23) = 3 x √(2) x √(3) = 3√2 x √3
Now, we can compare the values of the radicals by comparing their coefficients and the values inside the radical:
a. 4√3 = 4 x √(3) ≈ 6.93
b. 3√5 ≈ 6.71
c. 5√2 ≈ 7.07
d. 2√2 x√5 ≈ 5.66
e. 2√13 ≈ 7.21
f. 3√2 x √3 ≈ 6.00
Therefore, the order from least to greatest is:
d. 2√2 x √5 ≈ 5.66
f. 3√2 x √3 ≈ 6.00
a. 4√3 = 4 x √(3) ≈ 6.93
b. 3√5 ≈ 6.71
c. 5√2 ≈ 7.07
e. 2√13 ≈ 7.21
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4 Let f(x)= with f(0) = 2 and f(1) = 9. Find a and k and then evaluate the function f(2). a +5ekx a = (Type an exact answer in simplified form. Use integers or fractions for any numbers in the express
The value of the function at x = 2 is 11.8.
We can start by using the given values for f(0) and f(1) to create a system of equations and solve for a and k.
f(0) = 2 = a + 5ek(0)
f(1) = 9 = a + 5ek(1)
Simplifying the first equation gives us a = 2 - 5ek(0) = 2. Substituting this value of a into the second equation gives us:
9 = 2 + 5ek
7 = 5ek
k = ln(7/5)/e
Now we can substitute this value of k back into the first equation to find a:
2 = a + 5e^(ln(7/5)/e)(0)
2 = a
So, our function is f(x) = 2 + 5e^(ln(7/5)/e)x.
To evaluate f(2), we simply plug in x = 2:
f(2) = 2 + 5e^(ln(7/5)/e)(2)
f(2) = 2 + 5(7/5)^2
f(2) = 2 + 5(49/25)
f(2) = 2 + 9.8
f(2) = 11.8
Therefore, the value of the function at x = 2 is 11.8.
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how do you solve 83 = y/5?
Answer: 415
83 = [tex]\frac{y}{5}[/tex]
83(5) = y
415 = y
Answer:
y = 415
Step-by-step explanation:
83 = y/5
83 x 5 = y
415 = y
Question 4. (10 points) For what value(s) of the constant λ will y = e^(λx) be a solution of the differential equation y′′ −3y′ + 2y = 0 ? If there are no such λ's state that.
The values of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0 are λ = 1 and λ = 2.
To find the value(s) of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0, we can substitute y = e^(λx) into the differential equation and solve for λ.
First, we need to find the first and second derivatives of y = e^(λx):
y′ = λe^(λx)
y′′ = λ^2e^(λx)
Now, we can substitute these derivatives into the differential equation:
λ^2e^(λx) − 3λe^(λx) + 2e^(λx) = 0
e^(λx)(λ^2 − 3λ + 2) = 0
Since e^(λx) cannot equal 0, we can set the expression in parentheses equal to 0 and solve for λ:
λ^2 − 3λ + 2 = 0
(λ − 1)(λ − 2) = 0
λ = 1 or λ = 2
Therefore, the values of the constant λ that will make y = e^(λx) a solution of the differential equation y′′ −3y′ + 2y = 0 are λ = 1 and λ = 2.
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A survey asked 1,200 students which movie genre was their favorite. The results of the survey are shown in the circle graph.
Favorite Movie Genre
Science Fiction
10%
Comedy
20%
Drama
15%
Action
45%
Romance
10%
How many total students chose romance and science fiction movies?
Total students=1,200
Total number of students whose favorite movie genre is Romance= 10%
So,
10% of total students= 10% of 1,200
Therefore, the Total students who chose romance= 10/100*1200=120
Similarly, 10% of students chose Science fiction, and the total number of students who chose science fiction=10/100*1200=120
Therefore,
Total students who chose romance=120
Total students who chose science fiction=120
p(x)=7x^(3)-10x^(2)+8x-5 According to the rational zero theorem, the possible zeros for p(x) are +-((1,5)/(1,7))
Yes, according to the Rational Zero Theorem, the possible zeros of the polynomial p(x) are +-(1,5/1,7). The only factorization that works in this case is p/q = 1.5/1.7, which yields the zeros +-(1,5/1,7).
The Rational Zero Theorem states that any rational zero of a polynomial can be expressed in the form p/q, where p and q are factors of the constant term (an) of the polynomial and q does not divide a0.
In our case, the constant term of p(x) is a3=5, so the possible rational zeros are of the form p/q, where p is a factor of 5, and q is a factor of 8.
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CL 7-121. Kelly started the proof below to show that if TC ~=TM and AT bisects cTM, then CA~=MA. Copy and complete her proof.
Using the statements given for congruency the proof is -
TC ≅ TM Given
AT bisects ∠CTM Given
∠ATC ≅ ∠ATM Definition of bisect
AT ≅ AT Reflexive property
Δ ATC ≅ Δ ATM SAS theorem
CA ≅ MA ≅ Δs → ≅ parts
What is congruency?
If two shapes are similar in size and shape, they are congruent. We can also state that if two shapes are congruent, then their mirror images are identical.
A diagram of a diamond ACTM is given.
The line segment TC is equal and congruent to line segment TM.
This statement is already given in the question.
The line segment AT bisects angle CTM.
This statement is already given in the question.
The angle ATC is equal and congruent to angle ATM.
This statement is the definition of bisect.
The line segment AT is equal and congruent to line segment AT.
This statement is true by the reflexive property of the triangles.
Triangle ATC is equal and congruent to triangle ATM.
This statement is true by Side-Angle-Side (SAS) theorem of the triangles.
The line segment CA is equal and congruent to line segment MA.
This statement is true as the triangles are congruent to each other and congruent triangles have congruent parts.
Therefore, the proof is complete.
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HELP HELP HELP
a student divided 3p^4-8x^2-11x+1 by x-2 using LONG DIVISION. Where did they go wrong?
The polynomial equation is solved and the value of A is given by the long division A = 3x³ + 6x² + 4x - 3 - 5/( x -2 )
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the polynomial equation be represented as A
Now , let the first equation be p
p = 3x⁴ - 8x² - 11x + 1
Let the second equation be q
q = ( x - 2 )
And , the value of A = p/q
On simplifying , we get
A = ( 3x⁴ - 8x² - 11x + 1 ) / ( x - 2 )
From the long division of polynomials , we get
Step 1 :
A = 3x³ + [ ( 6x³ - 8x² - 11x + 1 ) / ( x - 2 ) ]
The student went wrong while multiplying the quotient 3x³ with the divisor -2 , it should have been 6x³ instead of 6x²
Step 2 :
A = 3x³ + 6x² + [ ( 4x² - 11x + 1 ) / ( x - 2 ) ]
Step 3 :
A = 3x³ + 6x² + 4x + [ ( -3x + 1 ) / ( x - 2 ) ]
Step 4 :
A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]
Therefor , the long division is solved , A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]
Hence , the polynomial is A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]
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Mrs.. Tomas says that the number of the students in her class this week has no variability. Her student, Peirce, says that it does not have a variability because someone could be absent. Do you agree or disagree? Why or why not?
Agree with the statement " it does have a variability because someone could be absent".
What is meant by variability?
The degree to which the data points in a statistical distribution or data collection deviate from the average value and from one another is virtually by definition the measure of variability. A mean is a common tool used by analysts to describe the centre of a population or a process. Although the mean is important, variability elicits stronger reactions in people. Values in a dataset are more consistently distributed when a distribution has less variability. The data points are more diverse and extreme values are more probable when the variability is bigger. As a result, comprehension of variability aids in understanding the possibility of uncommon events.
Peirce says that there is variability because someone could be absent.
I agree with Peirce's statement.
Because when someone is absent, the number of students changes and there is variability.
Now the range of variability changes with how many students are absent.
If there are only a few students absent, then the variability can be low.' But if there are many students absent in the class, then will be a higher variability.
Therefore there can be variability when someone could be absent.
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What types of angles are shown by the window-glass shapes? Or, what kind of angles could there be?
In the given window there are both acute and obtuse angles are shown.
What is Coordinate system?a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space
We have to find the types of angles are shown by the window-glass shapes
An angle is formed when two straight lines or rays meet at a common endpoint.
As we observe the angles are less than 180 degrees.
Angles between 0 and 90 degrees are called acute angles.
Angles between 90 and 180 degrees are known as obtuse angles.
Hence, In the given window there are both acute and obtuse angles are shown.
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Nadia has log that are 3 m long how many logs does she need when the river is 12 m
Answer:
Step-by-step explanation:4. 12 divided by 3 is 4 so 4
Of the following parent functions, which one has D = (XER) and R = ([-1, 1], 2 points YER) (in interval form)? (Select all that apply) *
linear
quadratic
exponential
reciprocal
absolute value
square root
sine
cosine
The correct answer is sine and cosine.
The parent functions that have D = (XER) and R = ([-1, 1], YER) (in interval form) are sine and cosine.
Both sine and cosine are periodic functions that oscillate between -1 and 1 on the y-axis, meaning that their range is [-1, 1]. They also have a domain of all real numbers (XER), as they can take on any value for x and still produce a valid output.
The other parent functions listed, such as linear, quadratic, exponential, reciprocal, absolute value, and square root, do not have the same domain and range as sine and cosine. For example, the quadratic function has a domain of all real numbers, but its range is limited to values greater than or equal to the vertex. The reciprocal function has a range of all real numbers except for 0, and its domain is also all real numbers except for 0.
Therefore, the correct answer is sine and cosine.
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what’s the value of k that transforms f into g
Answer:
Below
Step-by-step explanation:
'k' shifts the graph of f(x) UP by ' k' units k = 6 ( look how far the y-axis intercepts are shifted UP= 6 units from -2 to + 4)
The diameter of a circle is 13 in. Find its area to the nearest whole number.
Answer:
area=22/7×13=40.85=41 is the nearest whole number
help plssssssssssssssssssssss
Step-by-step explanation:
the height is 17 feet and the distance from the wall is 8 feet
using pythogras theorem
[tex] {h}^{2} + {b}^{2} = {hypotenuse}^{2} \\ {h}^{2} + {8}^{2} = {17}^{2} \\ h = \sqrt{( {17}^{2} - {8}^{2} } \\ h = 15[/tex]
There are 12 people at a Restaurant and the menu has 13 items.
How many different ways can they order?
The answer is 106993205379072 different ways that the 12 people can order from the 13 items on the menu.
There are a total of 12 people at a Restaurant and each person can order one of the 13 items on the menu. Therefore, the total number of different ways that they can order is 1312 = 106993205379072.
This is because for each of the 12 people, there are 13 choices for what they can order. So for the first person, there are 13 choices, for the second person there are 13 choices, and so on. Multiplying all of these choices together gives us the total number of different ways that they can order:
13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 * 13 = 106993205379072
So the answer is 106993205379072 different ways that the 12 people can order from the 13 items on the menu.
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Identify the number of solutions of the polynomial equation. Then find all the solutions. 4x^(5)-8x^(4) +6x^(3)=0
The number of solutions of the polynomial equation, 4x^(5)-8x^(4) +6x^(3)=0 is 5 and the solutions are x=0, x=3/2, and x=1.
The polynomial equation at hand is of degree 5, which means that the highest power of the variable present in any term is 5.
Therefore, we can infer that the equation can be written in the form of ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0, where a, b, c, d, e, and f are constants and x is the variable. To solve this equation, we can try factoring it:
4x^(5)-8x^(4) +6x^(3)=0
2x^(3)(2x^(2)-4x+3)=0
2x^(3)(2x-3)(x-1)=0
The solutions are x=0, x=3/2, and x=1.
Therefore, the number of solutions of the polynomial equation is 5 and the solutions are x=0, x=3/2, and x=1.
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3 + 10x+ 4x as an algebradic expression
Answer: 10x² + 3x + 4
Step-by-step explanation: I hate math.
A_(t)=([1,3,2],[2,5,t],[4,7-t,-6]) For what values of t does A_(t) have an inverse? Find the rank of A_(t) for each value of t.
The rank of At is the number of linearly independent rows or columns in the matrix. Since At has an inverse for all values of t, the rank of At is 3 for all values of t.
In order to determine the values of t for which At has an inverse, we need to find the determinant of At. If the determinant of At is not equal to 0, then At has an inverse. The determinant of At is given by:
|At| = (1)(5)(-6) + (3)(t)(4) + (2)(2)(7-t) - (4)(5)(2) - (7-t)(t)(1) - (-6)(2)(3)
Simplifying the above expression, we get:
|At| = -30 + 12t + 28 - 14t - 40 - 5t2 + 12
Combining like terms, we get:
|At| = -5t2 - 2t - 30
Setting the determinant equal to 0, we get:
-5t2 - 2t - 30 = 0
Using the quadratic formula, we can find the values of t for which the determinant is equal to 0:
t = (-(-2) ± √((-2)2 - 4(-5)(-30)))/(2(-5))
t = (2 ± √(4 - 600))/(-10)
t = (2 ± √(-596))/(-10)
Since the square root of a negative number is not a real number, there are no real values of t for which the determinant of At is equal to 0. Therefore, At has an inverse for all values of t.
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Find the inverse function of f(x) = - Vx+1+6. Specify the domain for f^-1(x) f^-1(x)__________ Domain of f-1(x) using interval notation:________
The inverse function of f(x) = - Vx+1+6 is f^-1(x) = - Vx-7. The domain of f^-1(x) is [-1, ∞), or in interval notation, [-1, ∞).
The inverse function of f(x) = -√x+1 + 6 can be found by following the steps below:
1. Swap the x and y values, so y = -√x+1 + 6 becomes x = -√y+1 + 6
2. Solve for y by isolating it on one side of the equation:
x - 6 = -√y+1
(x - 6)² = y+1
y = (x - 6)² - 1
3. The inverse function is therefore f^-1(x) = (x - 6)² - 1
The domain of f^-1(x) can be found by considering the restrictions on the original function. Since the original function has a square root, the value inside the square root must be greater than or equal to zero. This means that:
x+1 ≥ 0
x ≥ -1
So, the inverse function of f(x) = -√x+1 + 6 is f^-1(x) = (x - 6)² - 1, and the domain of f^-1(x) is [-1, ∞).
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Write the decimal number that has the specified place values. 4 ones, 0 hundredths, 6 tens, 9 hundreds, 8 tenths
The answer of decimal number that has the specified place values is 964.8.
To write the decimal number, we need to understand the place value of each digit.
The place values are as follows:
- 9 hundreds = 900
- 6 tens = 60
- 4 ones = 4
- 8 tenths = 0.8
- 0 hundredths = 0.00
To write the decimal number, we add the place values together:
900 + 60 + 4 + 0.8 + 0.00 = 964.8
Therefore, the decimal number that has the specified place values is 964.8.
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Find the following for the function f(x)=3x^2+3x−3 (a) f(0) (b) f(3) (c) f(−3) (d) f(−x) (e) −f(x) (f) f(x+2) (g) f(3x) (h) f(x+h)
a) f(0) = 3(0)^2 + 3(0) - 3 = -3
b) f(3) = 3(3)^2 + 3(3) - 3 = 33
c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
e)−f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3
We are asked to find the following for the function f(x)=3x^2+3x−3: (a) f(0) (b) f(3) (c) f(−3) (d) f(−x) (e) −f(x) (f) f(x+2) (g) f(3x) (h) f(x+h)
(a) f(0) = 3(0)^2 + 3(0) - 3 = -3
(b) f(3) = 3(3)^2 + 3(3) - 3 = 33
(c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
(d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
(e) −f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
(f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
(g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
(h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3
I hope this helps! Let me know if you have any further questions.
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The 1989 U.S. Open golf tournament was played on the East Course of the Oak Hills Country Club in Rochester, New York. During the second round, four golfers scored a hole in one on the par 3 sixth hole. The odds of a professional golfer making a hole in one are estimated to be 3,708 to 1, so the probability is 1/3,709. There were 174 golfers participating in the second round that day.
a. What is the probability that no one gets a hole in one on the sixth hole? (Round your answer to 5 decimal places.)
b. What is the probability that exactly one golfer gets a hole in one on the sixth hole? (Round your answer to 5 decimal places.)
The probability of no one getting a hole in one on the sixth hole during the 1989 U.S. Open golf tournament is 0.95431 and the probability of exactly one golfer getting a hole in one on the sixth hole is 0.04478.
The probability of an event occurring is the number of favorable outcomes divided by the number of possible outcomes. In this case, the probability of a professional golfer making a hole in one is 1/3,709.
a. To find the probability that no one gets a hole in one on the sixth hole, we need to find the probability that each of the 174 golfers does not get a hole in one. The probability of not getting a hole in one is 1 - (1/3,709) = 3,708/3,709. The probability that no one gets a hole in one is (3,708/3,709)^174 = 0.95431. Therefore, the probability that no one gets a hole in one on the sixth hole is 0.95431.
b. To find the probability that exactly one golfer gets a hole in one on the sixth hole, we need to find the probability that one golfer gets a hole in one and the rest do not. The probability of one golfer getting a hole in one is 1/3,709 and the probability of the rest not getting a hole in one is (3,708/3,709)^173. There are 174 ways this can happen, so the probability is 174 * (1/3,709) * (3,708/3,709)^173 = 0.04478. Therefore, the probability that exactly one golfer gets a hole in one on the sixth hole is 0.04478.
In conclusion, the probability of no one getting a hole in one on the sixth hole during the 1989 U.S. Open golf tournament is 0.95431 and the probability of exactly one golfer getting a hole in one on the sixth hole is 0.04478.
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Which variable makes most sense to use as the explanatory variable and which should be used as the response variable and which is not a variable?
1. Cold 2. Health Condition 3. Placebo 4.Vitamin C 5. Treatment
The explanatory variable is the one that is thought to influence or cause changes in the response variable. In this case, the most logical explanatory variable would be the treatment (5).
Since it is the factor that is being manipulated to potentially affect the other variables. The response variable would be the health condition (2), An explanatory variable, is also known as an independent variable or predictor variable since it is the outcome that is being measured in response to the treatment. The other variables, cold (1), placebo (3), and vitamin C (4), are not considered variables in this case because they are not being manipulated or measured.
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