The standard height from the floor to the bull’s-eye at which a standard dartboard is hung at 5 feet 8 inches. A standard dartboard is 18 inches in diameter. Suppose a standard dartboard is hung at standard height so that the bull’s-eye is 10 feet from the wall to its left. Sasha throws a dart at the dartboard that land at point 10.25 Feet from the left wall and 5 feet above the floor. Does Sasha’s dart land on the dartboard? Drag the choices into the boxes to correctly complete the statements.
Answers
Answer:
Hello! I'm sorry I couldn't get to your question sooner. I just completed this quiz!
The equation of the circle that represents the dartboard is (x-10)^2 + (y-17/3)^2 = 9/16, where the origin is the lower-left corner of the room and the unit of the radius is feet.
The position of Sasha's dart is represented by the coordinates (10.25,5). Sash's dart does land on the dartboard.
This quiz was completed on k12, lesson 3.03.
The question is an illustration of equation of circles.
The equation of the dartboard circle is: [tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]Sasha's dart lands on the dartboard becauseFrom the question, we understand that:
[tex]\mathbf{h = 5\ ft\ 8\ in }[/tex] ---- the height at which the dartboard was hung
[tex]\mathbf{d = 18\i n }[/tex] ---- the diameter of the dartboard
[tex]\mathbf{B = 10ft}[/tex] --- the bull's eye
[tex]\mathbf{D = (10.25ft, 5ft)}[/tex] --- Sasha's dart
Equation of the circle
First, we convert all units to feet
This is done by dividing inches units by 12
[tex]\mathbf{h = 5\ ft\ 8\ in }[/tex]
[tex]\mathbf{h = 5\ ft\ + \frac{8}{12}\ ft }[/tex]
[tex]\mathbf{h = 5\ ft\ + \frac{2}{3}\ ft }[/tex]
Take LCM
[tex]\mathbf{h = \frac{15 + 2}{3}\ ft }[/tex]
[tex]\mathbf{h = \frac{17}{3}\ ft }[/tex]
[tex]\mathbf{d = 18\i n }[/tex]
[tex]\mathbf{d = \frac{18}{12}ft}[/tex]
[tex]\mathbf{d = \frac{3}{2}ft}[/tex]
Divide by 2 to calculate radius
[tex]\mathbf{r = \frac{3}{2*2}ft}[/tex]
[tex]\mathbf{r = \frac{3}{4}ft}[/tex]
The equation of the circle is represented as:
[tex]\mathbf{(x - a)^2 + (y - b)^2 = r^2}[/tex]
In this case:
[tex]\mathbf{a = B = 10ft}[/tex] -- the distance between the bull's eye and the wall
[tex]\mathbf{b = h = \frac{17}{3}\ ft }[/tex] ---- the height at which the dartboard was hung
So, we have:
[tex]\mathbf{(x - a)^2 + (y - b)^2 = r^2}[/tex]
[tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = (\frac 34)^2}[/tex]
Evaluate the exponents
[tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]
Hence, the equation of the circle is: [tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]
Does Sasha’s dart land on the dartboard?
Yes her dart lands on the dartboard because
[tex]\mathbf{D = (10.25ft, 5ft)}[/tex] is within the circumference of the dartboard
Read more about equation of circles at:
https://brainly.com/question/23988015
Related Questions
Last year, 50 students attended the winter carnival. This year, 60 students attended the carnival. Which statement below correctly describes the percent
change from last year to this year?
A
An increase of 10%
B
A decrease of 10%
С
An increase of 20%
D
A decrease of 20%
Answers
Answer:
C. An increase of 20%
Step-by-step explanation:
50/100 = 60/x
Cross products
50 x = 6000
Divide 50 by both sides
x = 120
60 is 120% of 50, so there is a 20% increase
Hope this helps!
-Jerc
Identify next 3 numbers in this sequence 2,6,3,9,6,18,15
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Find the value of x and measure of ∠3
∠3=2x+7
∠6=6x+21
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Answer:
the answer is four
Step-by-step explanation:
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32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
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Valerie runs track and field. At meets, Valerie lkes to buy protein bars, bananas and sports drinks Protein bars are $1. bananas are S0.50, and sports drinks are S2. Valerie has S10 to spend. She will spend no more than twice as much on sports drinks as bananas and at least three times as much on bananas as protein bars. Let represent the number of protein bars. represent the number of bananas. and represent the number of sports drinks that Valerie buys. Which statements are true regarding Valerie's situation? Select all that apply A: p + 0.5b + 2d < 10 B: 0.5d + b + 3p < 10. C: d < 2b. D: b > 3p. E: 2d < b. F: 3b > p
Answers
Complete Question
Valerie runs track and field. At meets, Valerie likes to buy protein bars, bananas, and sports drinks. Protein bars are $1, bananas are $0.50, and sports drinks are $2. Valerie has $10 to spend. She will spend no more than twice as much on sports drinks as bananas and at least three times as much on bananas as protein bars.
Let p represent the number of protein bars, b represent the number of bananas, and d represent the number of sports drinks that Valerie buys.
Which statements are true regarding Valerie's situation? Select all that apply A: p + 0.5b + 2d < 10 B: 0.5d + b + 3p < 10. C: d < 2b. D: b > 3p. E: 2d < b. F: 3b > p
Answer:
The statements that are true regarding Valerie's situation:
A: p + 0.5b + 2d < 10
C: d < 2b
D: b > 3p
Step-by-step explanation:
Lets represent
The number of protein bars as p.
The number of bananas as b.
The number of sports drinks that Valerie buys as d.
From the question:
We are told
Protein bars are $1
Bananas are $0.50
Sports drinks are $2.
She will spend no more than twice as much on sports drinks as bananas
d ≤ 2b = d < 2b
At least three times as much on bananas as protein bars.
b ≥ 3p = b > 3p
We are also told that:
Valerie has $10 to spend.
Hence:
$1 × p + $0.50 × b + $2 × d < $10
= p + 0.5b + 2d < 10
Therefore, the statements that are true regarding Valerie's situation:
A: p + 0.5b + 2d < 10
C: d < 2b
D: b > 3p
**PLEASE HELP THIS IS DUE TODAY** when the sun's declination is at the highest point, what direction does the sun rise and set?
Answers
People living in a society where one person rules by force have which type of government?
Answers
Answer:
An autocracy is a government structure in which the ultimate political authority is concentrated in one person's hands.
Hope this helps please give me brainliest!
God bless!
An autocracy.
An autocracy is a system of government in which a supreme political power is concentrated in the hands of one person.
20x+x-2=4 rational equation
Answers
Answer:
x = 2/7
Step-by-step explanation:
Step 1: Write equation
20x + x - 2 = 4
Step 2: Solve for x
Combine like terms: 21x - 2 = 4Add 2 to both sides: 21x = 6Divide both sides by 21: x = 6/21Simplify: x = 2/7Step 3: Check
Plug in x to verify it's a solution.
20(2/7) + 2/7 - 2 = 4
40/7 + 2/7 - 2 = 4
42/7 - 2 = 4
6 - 2 = 4
4 = 4
Answer:
x = 2/7
Step-by-step explanation:
Collect like terms:
20x + x = 21x ----> 21x - 2= 4
Move the constant to the right hand side and change the sign of the constant:
21x = 4 + 2
Calculate:
21x = 4 + 2 ---> 21x = 6
Divide both sides by 21:
21/21 and 6/21 = 2/7
Solution:
x = 2/7 or x= 0.285714
The length of a rectangle is 10 meters more than the width. If 3 meters is added to both the length and the width, the new area will be 299 square meters. Find the length and width of the original rectangle.
HELP HELP HELP HELP
Answers
Answer:
L = 20
W = 10
Step-by-step explanation:
L = (w + 10)
NL = (w + 13)
Divide 299 by 13:
299 ÷ 13 = 23
So, 23 x 13 = 299
L = 23
W = 13
Subtract 3 from both to get the original length and width
AsKevin Selma madelyn Louis
Answers
What does it mean to divide a number by
a fraction (e.g., ¾)?
Answers
Answer: You can divide a number by a fraction by flipping over the fraction and multiplying them together.
Step-by-step explanation:
For example:
Lets say we wanted to divide 8 by 3/4
8÷[tex]\frac{3}{4}[/tex]
Change the division symbol into multiplication, and flip over the fraction (a great way to remember doing this is to remember the phrase Copy Dot Flip - Copy the first digit as it is, put a dot for multiplication, and then flip the fraction over)
8 ·[tex]\frac{4}{3}[/tex]
Now, just multiply and reduce/simplify the fraction if needed
Final answer is [tex]\frac{32}{3}[/tex], no need to simplify or reduce
Hope that helps!!
4 Rosie has 150 caramel
apples to sell. Each caramel apple is covered with one topping.
of the caramel apples are covered with peanuts.
are covered with chocolate chips.
• The rest are covered with sprinkles.
How many caramel apples are covered with sprinkles?
F
50
G 80
H 70
J 30
7.3B
Answers
Answer:
I'd say 50
Step-by-step explanation:
I just divided 150 by 3 since I only saw 3 toppings.
At 7:00 one Summer morning Harry and Hermione hopped into their speedy more motorboat and left Hogwarts dock. They arrived at Dumbledore Wharf 35 minutes later. During the busy summer months a car ferry departs from Dumbledore wharf every five minutes. Tourists crowd onto the ferry for the 55 minute ride to Hogswarts dock. If Harry and Hermione followed the route that the car ferries take, how many car ferries did they see on their trip?
Answers
9514 1404 393
Answer:
19
Step-by-step explanation:
If we assume that the car ferries start at or before 6:05, and each 5 minutes thereafter, and if we count the ferries at the dock on either end, the total number seen is the number of ferries encountered in ...
55 +35 = 90 . . . minutes
That is, it is the number already in transit when they leave, plus the number that start while they are traveling.
That's 90/5 +1* = 19 ferries.
_____
The attached diagram can give an idea. Each up-sloping line represents a ferry in-transit. The left side is Dumbledore Wharf; the right side is Hogwarts dock. Each horizontal unit represents the distance traveled by a ferry in 5 minutes. Each vertical unit represents a 5-minute interval.
The down-sloping line represents the motorboat travel. The dots at either end of the latter line represent car ferries that are at the dock, just arriving or just-departing. Altogether, there are 17 places where the lines cross, in addition to the boats at the docks.
__
* the +1 is because the number of points defining intervals is 1 more than the number of intervals.
Choose the best explanation that describes in words what the numerical value of the slope tells you.
a. Every increase in coral growth of one centimeter will result in an average of 5.25 fewer degrees Celsius of sea surface temperature per year.
b. Every increase in coral growth of one centimeter will result in an average of 5.25 more degrees Celsius of sea surface temperature per year.
c. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 more centimeters of coral growth per year.
d. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.
Answers
Data for the question :
Sea surface temperature 26.7 26.6 26.6 26.5 26.3 26.1
Growth 0.85 0.85 0.79 0.86 0.89 0.92
Answer:
d. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.
Step-by-step explanation:
Given the data :
Surface Temperature (X) : 26.7 26.6 26.6 26.5 26.3 26.1
Growth (Y) : 0.85 0.85 0.79 0.86 0.89 0.92
Using a regression calculator, we can find the model equation and extract the slope :
The regression equation obtained is :
y=5.039-0.1578x
From y = mx + c
Where m = gradient or slope
c = intercept
x and y are predictor and predicted variables respectively.
Hence, the gradient or slope (m) of the model = - 0.157. We have a negative slope, hence, increase in x will result una decrease in y.
The slope thus means: for every 1 degree increase in sea surface temperature (x), there is an average decline of about 0.1578 cm in growth per year.
f(x) = -x^2+10x-6
Find f(-5)
Answers
9514 1404 393
Answer:
f(-5) = -81
Step-by-step explanation:
Put -5 where x is and do the arithmetic.
f(-5) = -(-5)^2 +10(-5) -6
f(-5) = -25 -50 -6
f(-5) = -81
Answer:
-81
Step-by-step explanation:
what does they y represent in the equation y=mx+b
Answers
Answer:
The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Step-by-step explanation:
The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept.
Please help ASAP! All questions.
Answers
Answer:
I think i don't really know its been awhile for me.
Step-by-step explanation:
But i think you do 2 x 10 and what ever you get from that you multiply by 5 and what get from that you divide by 24.
I may not be right.
So please don't hate i tried.
A stack of books is 62 inches high. How high is it in feet and inches?
Answers
Answer:
5 feet and .16667 inches
Step-by-step explanation:
if you where to simplify the inches it would be 2 inches because the 6 next to the 1 is greater then five making the 1 a 2
Analyzing a Linear Function Expressed in Different Ways Choose the true statements. A linear function is expressed by a graph of a line that crosses both axes at the origin. An equation is written in slope-intercept form to express the same function as shown in the graph. From just this information, what statements can be made? A) The slope of the equation must be positive. B)The y-intercept of the equation is zero. C) It is possible that the line on the graph is horizontal. D) The slope of the equation must be negative.
Answers
Answer: The answer is option B and option C.
Answer:
B and C
Step-by-step explanation:
Help me out please I need help
Answers
you just need to figure out what the difference of an hour and a minute is. an hour=60 minutes so you would want to divide 420 by 60 to get your answer
Shen is on the swim team. Each week he swims a total of 5000 meters. How many kilometers does he swim each week?
Be sure to include the correct unit in your answer.
Answers
Answer:
5 km
Step-by-step explanation:
to convert m to km you have to divide by 1000.
5000/1000=5
hope this helps!
you just purchased new tennis shoes for basketball for $99 the cost for washing will be $2.00. you will wear them 110 times between basketball practice and games. what is the cost per wearing?
Answers
Answer:
Step-by-step explanation:
espera y termino y te ayudo vale que me falta poco vale
Please Assist!
What is the answer to this question???
Answers
Answer:
[tex](3.5,0.5)[/tex]
Step-by-step explanation:
Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )[/tex]
Simply plug in your coordinates into the midpoint formula to find midpoint:
P(5, -3)
Q(2, 4)
[tex](\frac{5+2}{2},\frac{-3+4}{2} )[/tex]
[tex](\frac{7}{2},\frac{1}{2} )[/tex]
[tex](3.5,0.5)[/tex]
Can someone plz plz help me with the last 2 problems #5 and #6
Answers
i believe your answers would be
1/2c+7 and 2H-9
Select all the expressions that are rational numbers.
a. 3.14159…
b. –9.1234567123…
c. –9.293847210103938…
d. 227
e. –26
Answers
Answer:
d,e
Step-by-step explanation:
rational numbers are positive and negative whole numbers.
Answer:
d,e
Step-by-step explanation:
Write the product using exponents.
(-4).(-4).(-4).y.y
Answers
Answer:
(-4)^3 * y^2
Step-by-step explanation:
hope it helps.
A young reptile is 0.6 foot long. An adult reptile is 19.5 times as long. How many feet longer is the adult reptile than the young reptile?
Answers
11.7ft-0.6ft = 11.1 ft
answer is 11.1 ft longer
Ritika bought 5 meters of cloth from the market. She cut off 2 3/4 meters and gave it to Aditi. What length of cloth is left with her?
Answers
Answer:
I think its 3/2
hope it will help you
By the end of Tina’s bike ride, she traveled a distance of 40 kilometers. How many miles did Tina ride? (1 mile ≈ 1.6 kilometers)
help plz brainless you help me
Answers
Answer:
24.85 or rounded to 24.9
Step-by-step explanation:
Conversion
K H D____D C M
The number of miles did Tina ride when (1 mile ≈ 1.6 kilometers) so it should be considered as the 25 miles.
Calculation of the number of miles:Since
By the end of Tina’s bike ride, she traveled a distance of 40 kilometers.
And we know that
1 mile ≈ 1.6 kilometers
So,
[tex]= 40 \div 1.6[/tex]
= 25 miles
hence, The number of miles did Tina ride when (1 mile ≈ 1.6 kilometers) so it should be considered as the 25 miles.
Learn more about miles here: https://brainly.com/question/13208356
Suppose that Haley encounter two traffic lights on her commute to GGC campus. Based on
her past experience, she judge that the probability is 0.35 that the first light will be red when she gets to it,
0.45 that the second light will be red, and 0.20 that both lights will be red. Let R1 denote the event that the
first light is red, and let R2 denote the event that the second light is red.
a) Determine the probability that at least one light will be red. (Show how you calculate this.)
b) Determine the conditional probability that the second light will be red given that the first light is
red. (Show how you calculate this.)
c) Are the events R1 and R2 independent? Justify your answer numerically.
d) Are the events R1 and R2 disjoint (mutually exclusive)? Justify your answer numerically.
Answers
Answer:
Explained below.
Step-by-step explanation:
The information provided is,
P (R₁) = 0.35
P (R₂) = 0.45
P (R₁ ∩ R₂) = 0.20
(a)
Compute the probability that at least one light will be red as follows:
P (at least one light will be red) = P (R₁ ∪ R₂)
= P (R₁) + P (R₂) - P (R₁ ∩ R₂)
= 0.35 + 0.45 - 0.20
= 0.60
Thus, the probability that at least one light will be red is 0.60.
(b)
Compute the conditional probability that the second light will be red given that the first light is red as follows:
[tex]P(R_{2}|R_{1})=\frac{P(R_{1}\cap R_{2})}{P(R_{1})}[/tex]
[tex]=\frac{0.20}{0.35}\\\\=0.571428\\\\\approx 0.57[/tex]
Thus, the conditional probability that the second light will be red given that the first light is red is 0.57.
(c)
If two events, say A and B are independent then:
P (A|B) = P (A).
The value of P (R₂ | R₁) = 0.57.
And the value of P (R₂) = 0.45
P (R₂ | R₁) ≠ P (R₂)
Thus, the events R₁ and R₂ are not independent.
(d)
If two events, say A and B are mutually exclusive then:
P (A ∩ B) = 0
The value of P (R₁ ∩ R₂) = 0.20.
Thus, the events R₁ and R₂ are not mutually exclusive.