A $900 item on the sale of 20% discount the
Money off: $180
Amt. of tax: $50.40
Money paid: $770.40
Final price: $770.40
what is discount ?
A discount is a reduction in the price of an item or service, often offered as a promotion or incentive to encourage customers to make a purchase. The discount is usually expressed as a percentage of the original price and represents the amount of money that the customer can save on the purchase.
For example:
Percentage discount: a certain percentage of the original price is deducted from the selling price. For example, a 20% discount on a $100 item would reduce the price to $80.
According to the question:
To calculate the final price of the item with sales tax, we can follow these steps:
Calculate the amount of money off by multiplying the original price by the discount percentage:
Money off = 0.20 x $900 = $180.
Calculate the price after the discount by subtracting the money off from the original price:
Price after discount = $900 - $180 = $720.
Calculate the amount of sales tax by multiplying the price after discount by the tax rate:
Amount of tax = 0.07 x $720 = $50.40.
Calculate the money paid by adding the price after discount and the amount of tax:
Money paid = $720 + $50.40 = $770.40.
Therefore, the final price with 7% sales tax is $770.40.
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M6U3L15: Representing ratios using tables
Set of practical problems
Complete the table to show the amounts of yellow and red paint needed for different numbers of batches of the same shade of orange paint.
Yellow paint (quarts)
Red paint (quarts)
5
6
Explain how you know that these amounts of yellow paint and red paint will give the same shade of orange as the mixture in the first row of the table.
A car is traveling at a constant speed, as shown by the double number line.
How far does the car travel in 14 hours? Explain or demonstrate your reasoning.
The olive trees in an orchard produce 3000 pounds of olives per year. It takes 20 pounds of olives to produce 3 liters of olive oil. How many liters of olive oil can this orchard produce in a year? If you get stuck, consider using the board.
Olives (pounds)
Olive oil (litres)
20
3
100
3000
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1)The completed table is
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
2) The car travels 98 miles in 14 hours.
3) The orchard can produce 450 liters of olive oil in a year.
What is a ratio?
A ratio is a quantitative comparison between two or more quantities, indicating how many times one quantity contains another. It is expressed as the quotient of the two quantities or in the form of a fraction. Ratios can be represented in various ways, including as decimals, percentages, or fractions.
Complete the table to show the amounts of yellow and red paint needed for different numbers of batches of the same shade of orange paint.
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
To get the same shade of orange paint, we need to mix yellow and red paint in a certain ratio. This ratio will determine the hue, saturation, and brightness of the final color. In this case, we can see that the ratio of yellow to red paint is 5:3 in the first row of the table, and 6:3.6 (which simplifies to 5:3) in the second row. This means that we need the same amount of yellow and red paint for each batch of orange paint, in a 5:3 ratio.
A car is traveling at a constant speed, as shown by the double number line.
The distance traveled by the car is directly proportional to the amount of time it travels. This means that the ratio of distance to time is constant. From the given double number line, we can see that the car travels 21 miles in 3 hours. Therefore, the ratio of distance to time is 21:3 or 7:1. To find how far the car travels in 14 hours, we can set up a proportion:
distance/time = 7/1
distance/14 = 7/1
distance = 7 x 14
distance = 98 miles
Therefore, the car travels 98 miles in 14 hours.
The olive trees in an orchard produce 3000 pounds of olives per year. It takes 20 pounds of olives to produce 3 liters of olive oil.
To find how many liters of olive oil the orchard can produce in a year, we need to divide the total weight of olives by the amount of olives needed to produce one liter of oil, and then multiply by the conversion factor:
Liters of oil = (Pounds of olives / Pounds per liter) x Conversion factor
Liters of oil = (3000 / 20) x 3
Liters of oil = 150 x 3
Liters of oil = 450
Therefore, the orchard can produce 450 liters of olive oil in a year.
Hence,
1)The completed table is
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
2) The car travels 98 miles in 14 hours.
3) The orchard can produce 450 liters of olive oil in a year.
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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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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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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
Question below
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V
Answer: The answer t your question is the second one
Step-by-step explanation:
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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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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SSD Provided Links O RATIONAL EXPRESSIONS Simplifying a ratio of factored polynomials: Linear factors Simplify. (18(3x-4))/(6(x-8)(3x-4)) You may leave the numerator and denominator of your answer in
The simplified ratio of factored polynomials is 18/(6(x-8)).
What is polynomial?A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial is x^2 + 5x + 6.
The question is asking to simplify the ratio of factored polynomials (18(3x-4))/(6(x-8)(3x-4)). To simplify this ratio, we can divide the numerator and denominator by the common factors.
The numerator and denominator both have the factor of 3x-4, so we can divide both the numerator and denominator by this common factor.
The numerator then becomes 18/(6(x-8)) and the denominator becomes 1.
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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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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
3 + 10x+ 4x as an algebradic expression
Answer: 10x² + 3x + 4
Step-by-step explanation: I hate math.
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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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]
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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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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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
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
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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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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Shaquille baked 4 times as many chocolate chip cookies as vanilla cupcakes. He baked 48 chocolate chip cookies. Write an equation that can be used to find the number of vanilla cupcakes, x, that Shaquille baked.
Shaquille baked 12 vanilla cupcakes and the equation to depict the number of vanilla cookies is 48 = 4x.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution technique. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve. Learn about the graphical approach and the algebraic method before beginning to solve the linear equations using the substitution method.
Let us suppose the number of vanilla cupcakes = x.
The chocolate chip cookies are:
48 = 4x
x = 12
Hence, Shaquille baked 12 vanilla cupcakes and the equation to depict the number of vanilla cookies is 48 = 4x.
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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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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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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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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:
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)
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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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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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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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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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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