a sector with angle 120 degrees has a radius of r+4cm and its area is the same as the area of a circle with radius r cm.
By forming an equation in terms of 'r', show that r²-4r-8=0
Answer:
If area of sector = area of circle
1/3π(r+4)^2= πr^2
r^2-4r-8 =0
what is a sector?A sector is a cut out section of a circle. It is of two radii and an arc .
The area of a sector is angle substended/ 360 x area of a circle
area of a circle is πr^2
if area of circle is equal to the area of sector
120/360×π(r+4)^2=πr^2
divide both side by π
1/3(r+4)^2=r^2
multiply both sides by 3
(r+4)^2=3r^2
opening the bracket
(r+4)(r+4)=3r^2
r^2+ 8r +16=3r^2
3r^2-r^2- 8r -16=0
2r^2- 8r -16=0
divide all by 2
r^2- 4r -8=0
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your flight has been delayed: at denver international airport, 83% of recent flights have arrived on time. a sample of 14 flights is studied. round the probabilities to four decimal places.
1.0000 percent is the probability that all 12 flights will arrive on time.
What is probability?Simply put, the probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. Probability of an event P(E) = (Number of favorable outcomes)÷ (Sample space).So, the problem meets all requirements for a binomial experiment, written as:
[tex]P(X=x)\left(\begin{array}{l}n \\x\end{array}\right) p^x(1-p)^{n-x}[/tex]
Now, p=0.85 and n=14, the probability that precisely 14 people arrived on time are calculated as follows:
[tex]\begin{aligned}&P(X \geq 1)=1-P(X=0) \\&=1-\left(\begin{array}{c}12 \\0\end{array}\right) 0.85^0(1-0.85)^{12} \\&=1-1.297 \times 10^{-10} \\&=1.0000\end{aligned}[/tex]
Therefore, 1.0000 percent is the probability that all 12 flights will arrive on time.
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The complete question is given below;
Your flight has been delayed: At Denver International Airport, 85% of recent flights have arrived on time. A sample of 14 flights is studied. Round the probabilities to at least four decimal places. Find the probability that all 12 of the flights were on time.
Drag the numbers below to put them in order from least to greatest:
8.66 8.6 8.611 8.641 8.63 8.691
8.6 8.63 8.66 8.611 8.641 8.691
quick question thx!!
What is the slope of the line that passes through the points (7, -4) and (11,−4)?
The slope of the linear equation is 0, so this is a horizontal line.
What is the slope of the line?
A linear equation is of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
Particularly, if a a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we have the points (7, -4) and (11,−4), then the slope is:
a = (-4 + 4)/(11 - 7) = 0
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3) Two rooms in a house need to be painted.
Each room can be painted either white or
yellow.
Answer:
Paint them white as it looks better
Step-by-step explanation:
Yellow is a very bad choice to paint a room
Light travels 1.8x 10^7 kilometers in one minute. How far does it travel in 8 minutes
Answer:
Step-by-step explanation:
Distance covered in 1 minute= 1.8x 10^7 kilometers
So, by unitary method,
distance covered in 8 minutes= 1.8 x 10^7 kilometers x 8
= 14.4 x 10^7 kilometers
The maximum slope of a wheelchair ramp is 1:12. For a wheelchair ramp made with these specifications, what angle does the ramp make with the ground? Round your answer to the nearest hundredth.
a
8.24
b
4.76
c
6.91
d
5.39
Answer: B
Step-by-step explanation: Maximum slope for hand-propelled wheelchair ramps should be 1" of rise to every 12" of length (4.8 degree angle; 8.3% grade). To the nearest hundredth would be 4.76 so, B.
A scale drawing of a car is presented in the following three scales. Order thescale drawings from smallest to largest. Explain your reasoning. (There areabout 1.1 yards in a meter, and 2.54 cm in an inch.)A. 1 in to 1 ftB. 1 in to 1 mC. 1 in to 1 yd?
The smallest drawing will be the one that has the smallest drawing unit with respect to the the actual unit.
We have:
A. 1 in to 1 ft
B. 1 in to 1 m
C. 1 in to 1 yd
If we put them all in meters, we have:
A. 1 in to 0.3048 m
B. 1 in to 1 m
C. 1 in to 1/1.1 = 0.90... meters
Then, the small drawing will be B, as 1 meter is the largest actual unit.
Second, will be B, that has 1 in by approximately 0.9 meters.
Third and last, option A, which drawing has an scale of 1 in in 0.3048 meters.
We can calculate the scale as a ratio between the drawing units and actual units, expressed in the same units.
For example, for A, we have:
[tex]\frac{1\text{ in}}{1\text{ ft}}\cdot(\frac{1\text{ ft}}{12\text{ in}})=\frac{1}{12}[/tex]So the scale is 1:12.
NOTE: look that we have cancelled all the units with this operation.
For B, we have:
[tex]\frac{1\text{ in}}{1\text{ m}}\cdot(\frac{2.54\text{ cm}}{1\text{ in}})\cdot(\frac{1\text{ m}}{100\text{ cm}})=\frac{2.54}{100}=\frac{254}{10000}[/tex]For C, we have:
[tex]\frac{1\text{ in}}{1\text{ yd}}\cdot(\frac{1\text{ yd}}{3\text{ ft}})\cdot(\frac{1\text{ ft}}{12\text{ in}})=\frac{1}{36}[/tex]You can verify that B has the smallest scale (0.0254)
Please help me find the equation of the parallel line.
Given: 5x-2y=10, (3,-5)
I know that the formula is y-y1=m(x-x1) but what do I do with the 2y?
Thank you!
Answer:
mperpendicular = −2/5
Step-by-step explanation:
If the length of a room is 4.02m, the width of a room is 3.37m, and the height of a room is 2.35m, what is the volume of the room m^3? after figuring out the volume, then find out the mass of the air kg in the room.
The value for the volume of the room is 31. 84 cubic centimeters(cm³)
The mass of the air in the room is 41. 39 kg
How to determine the volume of the roomThe formula for calculating the volume of the room is expressed as;
Volume = l × w × h
Where;
l is the length of the roomw is the width of the roomh is the height of the roomFrom the information given, we have to substitute the values of the measurements of the room into the formula.
We have;
Volume, v = 4. 02 × 3. 37 × 2. 35
Volume, v = 31. 84 cubic centimeters(cm³)
To determine the mass of the air in the room, we use the formula for mass which is expressed as;
Mass = Density × volume
Given that;
Density of air = 1. 3kg/m³Volume of the room = 31. 84 cubic centimeters(cm³)Substitute the values
Mass = 1. 3 × 31. 84
Mass = 41. 39 kg
Hence, the volume is 31. 84 cubic centimeters(cm³)
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Kevin and Randy Muise have a jar containing coins, all of which are either quarters or nickels. The total value of the coins in the jar is $. How many of each type of coin do they have?
Hi! The total amount in the jar did not post properly. can you provide this?
The babysitter charges $8 per hour plus $4 for gas to come to the house. If the babysitter earned $36, how many hours did the sitter work?
Answer: 8x + 3, where x is the number of hours
ASAP I have a couple more minutes, please help! This lesson is called "The Pythagorean Theorem"
Answer: Number 5. is B-7CM
Number 8. is y=2/x
Step-by-step explanation:math
Estimate the answer to 783 + 329 by rounding each number to the nearest hundred
Answer:
1100
Step-by-step explanation:
783 rounded to the nearest hundred is 800
329 rounded to the nearest hundred is 300
800+300=1100
The estimation of 783 + 329 = 1100.
What is Rounding off?Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.
Given:
783 + 329
Now rounding off nearest hundred
783 rounded off to 800
and, 329 rounded off to 300.
So, 800+ 300 = 1100
Hence, the estimation is 1100.
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Explain why the equation 4|x| + 30 = 2 has no solution.
Answer:
the answer will be a negative answer
Step-by-step explanation:
Esimate the value of 13 squared, between which two whole numbers
Answer:
168 and 170
Step-by-step explanation:
£12000 borrowed for 17 months at a rate of 12.5% p.a.
Answer:
1062.50
Step-by-step explanation:
Interest = PRT / 100.
= 12000 × 12.5 × 17 /100 × 24
= 1062.50
Salma fills an aquarium to a depth of 4/5 meters in 8 minutes.
What is the unit rate in minutes per meter?
The unit rate is 10 minutes per meters.
What is rate of time?
Time is in units of seconds, minutes, hours, or years. Rate is distance per time, so its units could be mph, meters per second, or inches per year.
rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute.
Given,
she fills 4/5 meters in 8 minutes.
let x be the time she fills minutes per liter.
4/5 meters ⇔ 8 minutes
1 meter ⇔ x minutes
Cross multiplying
4/5*x = 1*8
x = 5*8/4
x = 10 minutes
The unit rate is 10 minutes.
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Can you help me with this math question
Answer:
40
Step-by-step explanation:
[tex]m \angle 2=20^{\circ}[/tex] (angle sum of triangle)
[tex]m\angle 1=40^{\circ}[/tex] (angle sum of triangle)
Please help what is the answer???
Match the trigonometry formula to its correct ratio. Reduce the ratio if necessary.
Matching the trigonometry formula to its ratio, we get
4/3 → tan A
4/5 → sin A
3/5 → cos A
Trigonometrical ratiosFrom the question, we are to match the given trigonometry formulas to their correct ratios.
From SOH CAH TOA, we have that
sin (angle) = opposite / hypotenuse
cos (angle) = adjacent / hypotenuse
tan (angle) = opposite / adjacent
Considering angle A,
Opposite = 16
Adjacent = 12
Hypotenuse = 20
Thus,
tan A = 16 / 12 = 4 / 3
sin A = 16 / 20 = 4 / 5
cos A = 12 /20 = 3 / 5
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O skaters are racing toward the finish
race. The first skater has a 40 meter
d and is traveling at a rate of 12 meters
second. The second skater is travelin
ate of 14 meters
per
second. How long
it take for the second skater to pass
st skater?
The first skater has a 40 meter d and is traveling at a rate of 12 meters second, second skater is traveling rate of 14 meters per second. it will take 20 seconds for second skater to pass the first skater.
What is the definition of time?Time is continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in conscious experience. Time is often referred to as fourth dimension, along with three spatial dimensions.
Time has long been an important subject of study in religion, philosophy, and science, but defining it in manner applicable to all fields without circularity has consistently eluded scholars. Nevertheless, diverse fields such as business, industry, sports, the sciences, and performing arts all incorporate some notion of time into their respective measuring systems.
12x+40=14x
40=2x
x=20
it will take 20 seconds for second skater to pass the first skater.
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(3x³+4x² − x + 7) ÷ (x + 2)
Answer:
I think this is the answer
Step-by-step explanation:
Cedar just graduated from college. he accepted a position with a firm at an annual salary of 45,000. using the department of housing and urban development guidelines, what is the maximum amount cedar should pay for rent on a monthly basis?
The maximum amount Cedar should pay for monthly rent is 13,500.
We need to know the maximum amount of monthly rent cost to solve this problem. In this country, the department of housing and urban development has ruled that the maximum monthly rent cost is 30% of gross profit.
Max cost = 30% Gross
From the question above, the given parameter is
Gross profit = 45,000
By substituting the given parameter, the maximum monthly rent cost is
Max cost = 30% Gross
Max cost = 30% x 45,000
Max cost = 13,500
Hence, the monthly rent cost should have a maximum amount of 13,500.
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A 32 ounce box of Fruit Loops cost $3.99 and a 24 ounce box of Honey Nut Cheerios cost $3.29.
Which is the better deal and why? What is the price of each
Answer:
32 ounce box of fruit loops is a better deal
Step-by-step explanation:
32 ounce of fruit loops is about $0.12 an ounce
24 ounce box of Honey Nut Cheerios is about $0.14 an ounce
*Similarity & transformations (practice) | Khan...
Pedro was curious if circles A and B (with X and Y being on each circle, respectively) were
similar, so he tried to map one figure onto the other using rigid transformations.p
1
Loading
COUP
Pedro concluded:
PO
X
"It's not possible to map circle A onto circle B using a sequence of rigid transformations, so
the circles are not similar."
Choose 1 answer:
What error did Pedro make in his conclusion?Perdo concluded: “it’s not impossible to map circle a onto circle b using a sequence of rigid transformations so the circles are not similar”. What error did Pedro make in his conclusion?
A round plane figure whose boundary ( circumference) consists of the points equidistant from a fixed point (the center). In the above question Pedro was wrong.
What is a circle?All the points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in plane draws to keep its distance from a specific point constant.
The tactic Pedro frequently used is ineffective since applying strict transformation to one figure and then onto another will only demonstrate whether the figures are congruent, not whether they are comparable.
Keep in mind that resemblance, as opposed to congruence, is about the proportionality between the dimensions of those figures. Therefore, when we overlay the figures, they won't match.
Pedro should divide each set of matching coordinates to demonstrate similarity; if all divisions provide the same outcome, the figures are said to be comparable.
Therefore, Pedro was not wrong.
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is 89.396668... a rational number
Answer: yes it is rational
Step-by-step explanation:
Answer: 89.396668... is a rational number
Step-by-step explanation:
Please Answer Fast!
There is a line that includes the point (-8, -8) and has a slope of. What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = [tex]\frac{1}{4}[/tex] x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = [tex]\frac{1}{4}[/tex] , then
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute (- 8, - 8 ) into the partial equation
- 8 = - 2 + c ⇒ c = - 8 + 2 = - 6
y = [tex]\frac{1}{4}[/tex] x - 6 ← equation of line
Which ordered pairs are in the solution set of the system of linear inequalities y > -1/3x +2 y < 2x + 3
The ordered pairs in the solution set of the system of linear inequalities y ≥ -1/3x +2 and y < 2x + 3 are (2, 2), (3, 1), and (4, 2).
What is the system of inequalities?One or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. A linear inequality solution is an ordered pair that resolves all of the system's inequalities, and the inequality's graph is a representation of all of the system's solutions.Given linear inequalities represented in the graph are:
y ≥ -1/3x +2
y < 2x + 3
In the graph, the shaded region above the solid line denotes the inequality,
y ≥ -1/3x +2
The shaded area on the right side of the dotted line denotes the inequality's solution set,
y < 2x + 3
And the common area of these inequalities will denote the solution set of the system of linear inequalities.
Ordered pairs are (2, 2), (3, 1), and (4, 2) and will therefore be located in the shared shaded area.
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Write a statement and an expression to represent the tape diagram. Then evaluate your
expression.
22|9|22|9
22|9|22|9|22|9|22|9|
Statement:
Expression:
Value of Expression:
In the picture there are two tape diagram. From the tape diagram we got x as 7 and y as 18.
Given that,
In the picture there are two tape diagram.
1st diagram is A and 2nd diagram is B.
Diagram A has 3 blocks are x and the total of those diagram is 21.
We get,
x+x+x=21
3x=21
x=21/3
x=7
Now,
Diagram B has 2 blocks are y and 3 and the total of those diagram is 21.
We get,
y+3=21
y=21-3
y=18
Therefore, from the tape diagram we got x as 7 and y as 18.
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