In this article, I will show you how to find the area of a circle and express your answer in terms of pi (π). First, you'll need to familiarize yourself with the formula for calculating the area of a circle:
A = π * r²
Let's define our variables:
A: area of the circle
π: pi (a mathematical constant that is approximately equal to 3.141492 . . .)
r: radius of the circle (the distance from the circle's center point to its edge)
Typically, to find the area of a circle, we would simply plug in the circle's radius for r and 3.141592 for π. If so, our answer would be a number.
Therefore, the answer is 16π.
George wants to watch all 23 games that a football team will play at home next season.
He can buy
a season ticket costing £425
or 23 separate tickets costing £24 each ticket.
What percentage of the total cost of 23 separate tickets does George save by buying a
season ticket?
The percentage of the total cost of 23 separate tickets that George saves by buying a season ticket is 23%.
What are percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
As the cost of the separate ticket is £24, and there are a total of 23 games, therefore, the total cost of the 23 games separate ticket can be written as,
= £24 × 23
= £552
Now, the cost of the season ticket is £425, therefore, the percentage of the total cost of 23 separate tickets that George saves by buying a season ticket can be written as,
[tex]\rm Percentage = \dfrac{\text{Total cost of 23 seperate ticket}-\text{Cost of season ticket}}{\text{Total cost of 23 seperate ticket}} \times 100\%[/tex]
[tex]\rm Percentage = \dfrac{552-425}{552} \times 100\% = \dfrac{127}{552} \times 100\% = 23\%[/tex]
Hence, the percentage of the total cost of 23 separate tickets that George saves by buying a season ticket is 23%.
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In a class test, (2) marks are given for every correct answers and (-1) marks for every
incorrect answers and no marks for not attending any questions.
Sreya scored 30 marks. If she got 16 correct answers, how many questions has she attempted
incorrectly?
Using a system of equations, it is found that she attempted two questions incorrectly.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this question, the variables are:
Variable x: Number of questions attempted correctly.Variable y: Number of questions attempted incorrectly.Sreya scored 30 marks, with 16 correct questions, hence, considering the amount of points for each question, we have that:
2x - y = 30.
Since x = 16:
32 - y = 30
y = 2.
She attempted two questions incorrectly.
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a school plans to start selling snacks at their basketball games they want to know what your snacks would be most popular
Answer:
takis
Step-by-step explanation:
everyone in gen z loves takis for some reason
The perimeter of a rectangle is 60 cm. Its width measures
16 cm. What is its length?
Let x = the length of the rectangle. Choose the equation that represents this
problem.
O A. 2x+32 = 60
B. X+ 16 = 60
O C. 2x-32 = 60
D. 2x+ 16 = 60
Answer:
Option a :- 2x+32 = 60
Step-by-step explanation:
Formula to calculate perimeter:-- P=2(l+w)
2(l+w) = P
2l + 2w = P
2x + 2(16) = 60
2x + 32 = 60
[tex] \therefore [/tex] The equation that represents this problem = 2x+32 = 60
1) For what values is the statement true? sin(x+20)°=cos(y−10
x=20, y=60
x=20, y=50
x=30, y=40
x=30, y=60
2)In right triangle ABC with right angle C, sinA=4/5 and cosA=3/5. What is sinB+cosB?
1/5
7/5
35/12
5/7
3)In a right triangle ABC where sinA=cosB, what are the measures of acute angles A and B if the measure of angle A is three times the measure of angle B?
The measure of angle A is 67. 5° and the measure of angle B is 22. 5°.
The measure of angle B is 135° and the measure of angle A is 45°.
The measure of angle A is 135° and the measure of angle B is 45°.
The measure of angle B is 67. 5° and the measure of angle A is 22. 5°.
4)What is the value of b that makes the equation cos(17b+26)°=sin(15b)° true?
13
2
9. 5
3
Answer:
1) X =20° ,Y=60°
2) 7/5
3) first is correct
4) 2
airplane leaves City A and flies 142 km due north to City B. It then turns through an angle of 57° and flies 108 km to City C. What angle 8 with respect to
due north could the pilot have used to fly directly from City A to City C? See the figure below.
City
108 km
Carry your intermediate computations to at least four decimal places.
Round your answer to the nearest tenth of a degree.
Answer:
24.3°
Step-by-step explanation:
A suitable calculator can add the vectors directly. (See attached.) In this calculation, bearing angles are measured clockwise from north, so the initial vector has an associated angle of 0 degrees.
__
We can find the angle of interest by considering the distances north and east that city C is from city B. The relevant trig functions are ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
__
location of C relative to BThe direct distance from B to C is the hypotenuse of a right triangle whose right angle is at point "D" due north of B and due west of C. The distances of interest are ...
sin(57°) = DC/BC
DC = BC·sin(57°) = (108 km)sin(57°) ≈ 90.5764 km
cos(57°) = BD/BC
BD = BC·cos(57°) = (108 km)cos(57°) ≈ 58.8210 km
__
angle of C from AAnd the angle of interest can be found from ...
tan(θ) = DC/AD = (90.5764 km)/(142 km +58.8210 km) ≈ 0.451031
θ = arctan(0.451031) ≈ 24.3°
The pilot could have flown on a bearing of 24.3° to get to city C directly from city A.
_____
Additional comment
We can ignore the fact that bearing angles are measured CW from north, while conventional angles on a Cartesian plane are measured CCW from "east" (+x). Each coordinate system can be mapped to the other by flipping the map over along a NE-SW line (y=x), aligning the +x axis with north and the +y axis with east.
The diagram we used in working this problem is shown in the second attachment.
A meal that serves 6 people contains 5,364 calories.
How many calories are in each serving?
Enter your answer in the box.
The amount of calories in each serving of the meal given the amount of calories in 6 servings is 894 calories.
What does division mean?Division is the process of obtaining the quotient of a number by grouping a number into equal parts using another number. The sign used to denote division is ÷.
How many calories are in each serving?Calories in each serving = total calories / number of people
5364 / 6 = 894 calories
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Is the following number rational or irrational?
-2π
Choose 1 answer:
А
Rational
00
B
Irrational
Answer:
B, Irrational number
Step-by-step explanation:
Irrational number because
[tex]\pi[/tex]
is Irrational number
A high school has 1,300 students, 320 of which are seniors. An administrator surveys 50 seniors and finds that 18 seniors plan to attend community college the year after they graduate. What is the population
The population of seniors who plan to attend community college is; 115.
Population and Sample sizeAccording to the task content;
It follows that the 50 senior students were surveyed and only 18 wanted to attend community college.On this note, the number of seniors who want to attend community college among the 320 seniors is;
(18/50) × 320 = 115.2.On this note, it follows that the number of seniors who want to attend community college is; 115 seniors.
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© There are 5 times as many females as males on the maths course at university. What fraction
of the course are female?
Give your answer in its simplest form.
Answer: 5/6
Step-by-step explanation: Females are 5 times more
Ratio of female to male will be 5:1
Female will be 5/6 and males will be 1/6
Determine which function has the greatest rate of change as x approaches infinity. f(x) = 4x 50 g(x) = 3x − 4 h(x) = 2x2 9x − 4 there is not enough information to determine the answer.
The slope of the h(x) is 4x as the value of x increases the slope of h(x) will approach to the infinity.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The functions are given below.
[tex]\rm f(x) = 4x+ 50\\\\ g(x) = 3x - 4 \\\\h(x) = 2x^2+ 9x- 4[/tex]
The slope of the f(x) and g(x) will be 4 and 3 respectively.
And the slope of the h(x) is 4x as the value of x increases the slope of h(x) will approach to the infinity.
The graph is shown below.
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The radius of a circle is 4 m. Find its area to the nearest whole number.
Answer:
16π or around 50.26
Step-by-step explanation:
A=πr²
A=π(4)²
A=16π
A=16(3.1415926)
A=50.26
Below are some perfect square root numbers. What would the next perfect square root be?
[tex] \sqrt{4} [/tex]
[tex] \sqrt{9} [/tex]
[tex] \sqrt{16} [/tex]
[tex] \sqrt{25} [/tex]
What is the probability that a hand of 5 cards chosen randomly and without replacement from a standard deck of 52 cards (which has 4 kings and 4 queens) contains the king of spades, exactly 1 other king, and exactly 2 queens
Answer: Approximately 0.0003047
As a fraction, it is equal to exactly 792/(2,598,960)
===========================================================
Explanation:
The king of spades must be in the hand, and we can pick any other king. There are 3 ways to pick the other king. Then there are 4 C 2 = 6 ways to pick the two queens. The 4C2 refers to the nCr notation. Or you could use Pascal's Triangle.
Overall, there are 3*6 = 18 ways to pick the king of spades, another king, and exactly 2 queens.
Then we have one more card to pick that isn't a king nor a queen. There are 4+4 = 8 cards that are either a king or queen, leaving 52-8 = 44 cards that are neither.
So there are 18*44 = 792 ways to pick a king of spades, another king, exactly 2 queens, and some other card that isn't a king nor queen.
This is out of 52C5 = 2,598,960 possible five card hands.
The probability we're after is roughly 792/(2,598,960) = 0.0003047
Side note: order does not matter with card hands.
Maria is making a candle in the shape of a cylinder. she wants the candle to have a height of 3 cm and a radius of 2 cm. how much wax does maria need? 12pi cm3 12pi cm2 18pi cm3 20pi cm2
The amount of wax that Maria will need to fill up the cylinder in this scenario is 12pi cm3 which is denoted as option A.
What is a Cylinder?This is defined as a a three-dimensional solid that holds two parallel bases joined by a curved surface usually at a fixed point and the volume is πr²h where r is radius and h is height.
Volume = πr²h
= π × 2² × 3
= 12π cm³
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Answer:
its A
Step-by-step explanation:
1. Suppose an online retailer has determined that if a potential customer spends more than 5 minutes on their site, that the probability of them making a purchase is 0.40. If 12 customers who spent more than 5 minutes on the site were randomly selected, what is the probability that more than 7 will make a purchase
Using the binomial distribution, it is found that there is a 0.056 = 5.6% probability that more than 7 will make a purchase.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
There are 12 customers, hence n = 12.The probability of any of them making a purchase is of p = 0.4.The probability that more than 7 will make a purchase is given by:
P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12).
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{12,8}.(0.4)^{8}.(0.6)^{4} = 0.042[/tex]
[tex]P(X = 9) = C_{12,9}.(0.4)^{9}.(0.6)^{3} = 0.012[/tex]
[tex]P(X = 10) = C_{12,10}.(0.4)^{10}.(0.6)^{2} = 0.02[/tex]
[tex]P(X = 11) = C_{12,11}.(0.4)^{11}.(0.6)^{1} \approx 0[/tex]
[tex]P(X = 12) = C_{12,12}.(0.4)^{12}.(0.6)^{0} \approx 0[/tex]
Then:
P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.042 + 0.012 + 0.02 + 0 + 0 = 0.056.
0.056 = 5.6% probability that more than 7 will make a purchase.
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You normally pay your line cooks $22 per hour, but one has worked overtime and should be paid time and a half. What is
the correct overtime pay per hour?
Answer:
$33 per hour
Step-by-step explanation:
"Time and a half" means the overtime rate is 1 1/2 times the base rate.
overtime rate = (1 1/2) × $22/hour = $(22 +1/2(22))/hour = $33/hour
The correct overtime rate is $33 per hour.
Consider the two solids shown.
What is the difference between the number of vertices of the two solids?
one
three
four
six
can somebody help me and explain how to do this
Answer:
=> 24m²
Step-by-step explanation:
Area of small rectangle = l×b
=> 2m× 3m
=> 6m²
Area of large rectangle = L×B
=> 9m × 2m
=> 18 m²
Area of figure = area of small rectangle + area of large rectangle
=> 18 m² + 6m ²
=> 24m²
y=[? ]°
Please help me!!
homework problem lol
Answer:
G is the answer hope that helpd
A boat is 122 meters from the base of a lighthouse. The lighthouse is 34 meters tall. The angle formed with the lighthouse and sea level is 90 degrees.
A boat is 122 meters from the base of a lighthouse that is 34 meters above sea level. What is the angle of elevation from the boat to the top of the lighthouse? Round to the nearest degree.
°
Answer:
about 16°
Step-by-step explanation:
Make sure your calculator is in degree mode.
Drawing the right triangle, we see that the shorter leg is 34 meters, and the longer leg is 122 meters. So the angle of elevation is:
[tex] \tan( \alpha ) = \frac{34}{122} [/tex]
[tex] \alpha = { \tan }^{ - 1} \frac{34}{122} = 15.57[/tex]
Answer: 16
Step-by-step explanation:
got it right on edge :)
Your experiment is using a one-tailed test with an alpha level of .05. Your alternative hypothesis predicts an increase in test scores. The correct value of z crit for this test is ____________.
Answer:
The correct value of z crit for this test is +1.645
Step-by-step explanation:
There is a leak in a container that holds a certain nontoxic gas. Each hour, it loses 10% of its volume.
Write an equation that models the amount of gas left in the container after x hours, assuming there were 300 cubic centimeters in the container before the leak. Then use your equation to determine the amount of gas left in the container after 11 hours. Round your answer to the nearest tenth.
Answer:
94.1 cm^3 to nearest tenth.
Step-by-step explanation:
Each hour 100 - 10 = 90% of the gas remains.
90% = 0.90.
At 0 hours the volume = 300 cm^3
The equation is
Amount (V) after x hours = 300(0.90)^x.
The amount after 11 hours:
V = 300(0.90)^11
= 94.14
Answer:
y = 300(0.9)^x
94.1 cm³
Step-by-step explanation:
This is an exponential decay.
y = 300(0.9)^x
where x is the number of hours, and y is the amount after x hours.
y = 300(0.9)^11
y = 94.1
write an explicit formula for each geometric sequence
1000,200,40,...
Answer:
[tex]\text Explicit \ Formula :\ a_{n}= 1000\times (\frac{1}{5}) ^{n-1}[/tex]
Step-by-step explanation:
Let [tex]\left( a_{n}\right)[/tex] be our geometric sequence
The explicit formula for [tex]\left( a_{n}\right)[/tex] is :
[tex]a_{n}= a_1\times r^{n-1}[/tex]
where r is the common ratio
a1 is the first term
We notice that :
200/1000 = 1/5
40/200 = 1/5
⇒ r = 1/5
[tex]a_1 = 1000\ \ (given)[/tex]
Conclusion:
[tex]a_{n}= 1000\times (\frac{1}{5}) ^{n-1}[/tex]
Liz is taking guitar lessons and practices every night. Yesterday, she played a total of 40 chords in 8 minutes. Today, she will play chords for 5 minutes.
If she plays at the same rate, how many chords will Liz play today?
Answer:
25
Step-by-step explanation:
If you divide by eight, it is equivalent to five cords per minutes.
Now you know that she plays five cords per minute, right?
So you want to multiply five by five, because she plays a total of five minutes.
pls help me with this
PLEASEEE HELP !!
Matching equations with diagrams & finding unknown ancies
is on line WY. Find the value of b.
Which equation(s) and angemeurerents go with the
diagram. Choose ALL that apply
(Select all that apply.)
Answer: b+95+34=180, b+129=180, 51
Step-by-step explanation:
b+95+34=180 works because the angles add to form a straight angle.
From this, we can obtain b+129=180 by adding the two constants.
Subtracting 129 from both sides, we get b=51.
The Red Mills Children's Hospital has raised 70% of the money they need for medical supplies. If they need a total of $900, how much money has the hospital raised so far?
Answer:
$630
Step-by-step explanation:
They raised 70% of $900.
70% of $900 = 70% × $900 = 0.7 × $900 = $630
Who invented mathematics??