The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 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 11 feet from a wall to its left.
Samuel throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor.
Does Samuel's dart land on the dartboard?
Answers
Answer:
Yes, Samuel dart does land on the dart board
Step-by-step explanation:
The given parameters are;
The height from the floor to the bulls eye = 5 feet 8 inches
The size of the standard board = 18 inches diameter
The distance of the bulls eye from the wall to the left = 11 feet
The distance the dart Samuel throws land from the left wall = 11.5 feet
The distance above the ground, the dart Samuel throws land = 5.5 feet
Whereby Samuel throws the dart directly at the dartboard, we have;
The location of the bulls eye = (11, 5.67)
The equation of the circle representing the dart board = (x - 11)² + (y - 5.67)² = 0.75² = 0.5625
The unit of the radius is in feet
The position of Samuel's dart is represented by the coordinate, (11.5, 5.5)
Plugging in the coordinates of the position of Samuel's dart into the equation of the circle of the dart board gives;
(11.5 - 11)² + (5.5 - 5.67)² = 0.2789 ≈ 0.528²
Therefore, given that the square of the distance of the position of Samuel's dart is less than the square of the radius of the dart board, we have;
Yes, Samuel dart does land on the dart board.
From the parameters given to find out if Samuel's dart landed on the dartboard, we can say that;
Samuel's dart does not land on the dartboard.
We are given;
Height from the floor to the bulls eye = 5 ft 8 in = 5.67 ft
Diameter of the standard dartboard = 18 in = 1.5 ft
Thus, radius; r = 1.5/2 = 0.75 ft
Distance of the bulls eye from the wall to the left = 11 ft
Distance of dart thrown by Samuel from the left wall = 11.5 ft
Height of dart thrown by Samuel above the ground = 5.5 ft
We know that general equation of a circle is;
(x - a)² + (y - b)² = r²
Since Height from the floor to the bulls eye is 5.67ft,then a = 5.67 ft
And also since Distance of the bulls eye from the wall to the left = 11 ft, then b = 11 ft
Thus;
(x - 11)² + (y - 5.67)² = 0.75²
(x - 11)² + (y - 5.67)² = 0.5625
Now, since he throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor. Thus;
r² = (11.5 - 11)² + (5.5 - 5.67)²
r² = 0.2789
r² of 0.2789 gotten here is lesser than 0.5625 gotten earlier, we can conclude that Samuel's dart does not land on the dart board.
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
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Answers
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i hope this helps and i'm sorry if it's wrong!
Duncan had 3.8 gallons of paint and used 1.89 gallons for a poster. How much paint did Duncan have left after painting the posture.
Answers
3.8-1.89= 1.91 gallons
Answer:
1.91
Step-by-step explanation:
Duncan had 3.8 and used 1.89 obviously we can't subtract right now so we have to add a 0 to 3.8 so it would 3.80 - 1.89 = 1.91
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Answers
Answer:
d = 10 inches
Step-by-step explanation:
It is given that,
The length, breadth and the height of a rectangular box is 8 inches×10 inches ×6 inches
We need to find the length of its longest diagonal.
In a rectangle, 6 inches will act as perpendicular and 8 inches will be base. The diagonal can be calculated using Pythagoras theorem as follows :
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Answers
Answer: She got 30 questions right and 6 questions wrong.
Step-by-step explanation:
Let x = Number of correct questions, y = Number of wrong questions
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Answer:
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What is multiplication?Multiplication is a mathematical arithmetic operation.
The process of adding the same number many times is repeated addition.
Multiplication is a repeated addition.
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Given:
Last year,
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Answers
Answer:
The equipment elevator is positioned 481 feet closer and the miner equipment is positioned 342 feet closer relative to the surface. The equipment elevator is deeper.
Step-by-step explanation:
The rate that both elevators descend are the same according to the information given in the question.
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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credits to the owner:lisboa, another brainly expert
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Answer: The answer for 1. is B For 2 its c and for 3 its D
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
The average fun size Snickers bar has the mass of 20.1 grams with a standard deviation of 0.7 grams What percent of Snickers bars have a mass more than 21.5 grams?
Answers
Step-by-step explanation:
The “fun size” of a Snickers bar is supposed to weigh 20 grams. Because the penalty for selling Snickers candy bars that weigh less than 20 grams is so severe, the manufacturer calibrates the machine so that the mean weight is 20.2 grams. The quality control manager at the candy company is concerned that the candy produced does not weigh 20.2 grams. She obtains a random sample of 64 candy bars and weighs them. She finds that the mean weight of this sample is 20.05 grams with standard deviation 0.72. By answering the following questions, test the claim that the Snickers bars have a mean weight less than 20.2 grams at the level of α = 0.01.
1. Select from the following list all the requirements that are met in this problem scenario for this test: (circle your choice(s))
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b. The population standard deviation is known.
c. The sample taken is a random sample.
d. The population standard deviation is unknown. e
. The degrees of freedom is 0.01.
f. The sample size is greater than 30.
2. Which of the following statements is correct?
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b) Statistics describe population characteristics.
c) We use statistics to estimate the value of parameters.
d) We use parameters to estimate the value of statistics
Expert Answer
The percent of Snickers bars which have a mass more than 21.5 grams is equal to 2.28%.
To find the percentage of Snickers bars with a mass more than 21.5 grams,
use the concept of standard normal distribution.
Calculate the z-score for 21.5 grams.
The z-score is a measure of how many standard deviations a particular value is away from the mean. It can be calculated using the formula:
z = (x - μ) / σ
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Here
x = 21.5 grams
μ = 20.1 grams (mean)
σ = 0.7 grams (standard deviation)
z = (21.5 - 20.1) / 0.7
z = 1.4 / 0.7
z = 2
The percentage of values greater than the z-score in the standard normal distribution calculator.
The percentage of values greater than 2 standard deviations from the mean is approximately 2.28%.
Therefore, approximately 2.28 percent of Snickers bars have a mass more than 21.5 grams.
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the solution of equation x × 3=0 is
Answers
Answer:
x=0
Step-by-step explanation:
Regroup terms:
3x=0
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Answers
-2/3, -1/4, 1/3, 2/5
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Negatives are always the smallest.
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Determine the transformations that produce the graph of the functions g(x)=0.2log(x+14)+10 and h(x)=5log(x+14)−10 from the parent function f(x)=logx. Then compare the similarities and differences between the two functions, including the domain and range.
Answers
Let's focus on g(x) for now.
0.2 = 1/5
f(x) = log(x) is the parent function
0.2*f(x) = 0.2*log(x) .... vertical compression by factor of 5
0.2*f(x+14) = 0.2*log(x+14) .... shift 14 units to the left
0.2*f(x+14)+10 = 0.2*log(x+14)+10 .... shift 10 units up
g(x) = 0.2*log(x+14)+10
The transformations to go from f(x) to g(x) are:
vertical compression by factor of 5shift 14 units to the leftshift 10 units upThe domain of g(x) is x > -14 to ensure that x+14 > 0. This is so we avoid applying a log to 0 or a negative value. The parent function domain was x > 0. Note how the domain shifted 14 units to the left (step 2)
======================================================
Now onto h(x)
f(x) = log(x)
5f(x) = 5log(x) .... vertical stretch by factor of 5
5f(x+14) = 5log(x+14) ... shift 14 units left, just like earlier
5f(x+14)-10 = 5log(x+14)-10 ... shift 10 units down
h(x) = 5log(x+14)-10
The transformations to go from f(x) to h(x) are:
vertical stretch by factor of 5shift 14 units to the left (same as g(x))shift 10 units down (instead of up compared to g(x))This time h(x) is taller compared to f(x), while g(x) is more vertically squished compared to f(x). Both involve being shifted 14 units to the left, so both g(x) and h(x) have the same domain. Vertical shifting and compressing/stretching does not affect the domain.
The range of f(x), g(x) and h(x) is the set of all real numbers.
which line is perpendicular to a line that has a slope of 1/2
Answers
Answer:
It’s line AB
Step-by-step explanation:
The equation for like AB is y=1/2x+0 and is perpendicular to HJ
What number should be subtracted from 3/7 to get 5/7
Answers
which is bigger. 34 1/2 or 34.5
Answers
Answer: They are equal.
Step-by-step explanation:
34 1/2 equals 34.5 in decimal form
34.5 equals 34 1/2 in fractional form
(.5 equals 1/2)
Question 6
A person standing 35 feet from a street light casts a shadow as shown. What is the height h of the street light? Assume the triangles
are similar
61
101
a
26 ft
30 ft
b
С
45 ft
27 ft
d
Answers
Answer:
Option (D)
Step-by-step explanation:
From the figure attached,
Since, ΔABD and ΔECD are the similar triangles,
Their corresponding sides will be proportional.
[tex]\frac{AB}{EC}=\frac{BD}{CD}[/tex]
[tex]\frac{h}{6}=\frac{(x+10)}{10}[/tex]
10h = 6(x + 10)
Since, the person is standing 35 feet from a street light,
x = 35 feet
By substituting the value of x in the equation,
10h = 6(35 + 10)
10h = 270
h = 27 ft
Therefore, height of the street light will be 27 feet.
Option (D) is the answer.
A kayak is originally priced at $100. The online retailer gives a discount and the kayak is now priced at $75. Enter the percentage discount for the cost of the kayak.
Answers
Answer:
25%
Step-by-step explanation:
Discount:
$100 * .25 = $25
New Price:
$100 - $25 = $75
4y+2x+30 if x=2and y=5
Answers
Answer:
54
Step-by-step explanation:
First let's replace the values x and y.
4y + 2x + 30 will become (4 * 5) + (2 * 2) + 30
Then we do order of operations.
(4 * 5) is 20..
20 + (2 * 2) + 30
Then we do (2 * 2) which is just four.
20 + 4 + 30
Lastly we add it all up.
24 + 30 = 54
I hope this helps, I hope it's not wrong, but I don't think it is.
Which theorem correctly justifies why the lines m and n
are parallel when cut by transversal k?
converse of the corresponding angles theorem
converse of the alternate interior angles theorem
converse of the same side interior angles theorem
converse of the alternate exterior angles theorem
Answers
Casey bought 3/8 pound of plums and 5/12 pound of bananas. How many pounds of fruit did he buy?
Answers
Answer:
19/24 pounds
Step-by-step explanation:
To find the total number of pounds, we should add 3/8 and 5/12. They both have different denominators, so we have to find the least common multiple between 12 and 8. The least common multiple between 12 and 8 is 24. 12 should be multiplied by 2 to get 24 (5 too) and 8 should be multiplied by 3 to get 24 (3 too).
[tex] \frac{3}{8} + \frac{5}{12} [/tex]
[tex] \frac{3 \times 3}{8 \times 3} + \frac{5 \times 2}{12 \times 2} [/tex]
[tex] \frac{9}{24} + \frac{10}{24} [/tex]
[tex] \frac{19}{24} [/tex]
PLSS!!!! HELP!!! ME I WILL MARK U!!!!
Answers
Answer:
562
Step-by-step explanation:
Plug in the values of x, y, and z provided.
(5(5)-1)^2-2(7)
Solve.
(25-1)^2-14
(24)^2-14
576-14
562
Answer: 562
Step-by-step explanation:
(5x+y)^2-2z
first put in the known values. (5(5)+(-1))^2-2(7)
(25+-1)^2-14
Second, do 25+-1=24
(24)^2-14
Third, do 24 squared
576-14
Subtract
562