A 3cm x 2cm rectangle sits inside a circle with a radius of 4cm
What is the area of the shaded region
round your final answer to the nearest hundredth
Answers
The area of the shaded region is 44.24\ cm^{2}44.24 cm2
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the circle minus the area of rectangle
step 1
Find the area of circle
The area of the circle is equal to
A=\pi r^{2}A=πr2
we have
r=4\ cmr=4 cm
substitute
A=\pi (4)^{2}A=π(4)2
A=16\pi\ cm^{2}A=16π cm2
step 2
Find the area of rectangle
The area of rectangle is equal to
A=(3)(2)=6\ cm^{2}A=(3)(2)=6 cm2
step 3
Find the difference
16\pi\ cm^{2}-6\ cm^{2}16π cm2−6 cm2
assume
\pi=3.14π=3.14
16(3.14)\ cm^{2}-6\ cm^{2}=44.24\ cm^{2}16(3.14) cm2−6 cm2=44.24 cm2
Related Questions
If sinө= 7/25 , find the values of cosө and tanө
Answers
Step-by-step explanation:
sinx = p/h = 7/25
so
p = 7
h = 25
now
h^2 = p^2 + b^2
25^2 = 7^2 + b^2
or, 625 = 49 + b^2
or, 625-49 = b^2
or, 576 = b^2
or, b = [tex]\sqrt{576}[/tex]
so, b = 24
so
cosx = b/h = 24/25
tanx = p/b = 7/24
simplify the expression (3+4i) - (1-5i)
Answers
Answer:
9i + 2
Step-by-step explanation:
3 + 4i - 1 + 5i
=> 3 - 1 + 4i + 5i
=> 2 + 9i
=> 9i + 2
Answer:
9i + 2
Brainliest, please!
Step-by-step explanation:
(3 + 4i) - (1 - 5i)
3 + 4i - 1 + 5i
9i + 2
Factorize no i, l, o
Answers
Answer:
here ,
question no. L the question is incomplete.
rest all are solved hope this helped u ☺️
Todd is putting new oak baseboard trim in his living room. He has one piece that is 12 1/2 ft long and another that is 8 2/3 ft long. How much trim does he have total?
Answers
Answer:
21 1/6 ft
Step-by-step explanation:
Add the lengths together
12 1/2 + 8 2/3
Get a common denominator of 6
12 1/2 *3/3 + 8 2/3 *2/2
12 3/6 + 8 4/6
20 7/6
20 +6/6+1/6
21 1/6
Please solve this problem
Answers
take the help of the attachments.
define a ploynomial with real coeffients
Answers
Answer:
an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable is called polynomial. A polynomial with real coefficients is a product of irreducible polynomials of first and second degrees.
please help me solve this exercise.!!
find the value of tanx if sinx+cosx=1/5 and 0<x<π.
Answers
=============================================================
Explanation:
Let's square both sides and do a bit of algebra to get the following.
[tex]\sin(x) + \cos(x) = 1/5\\\\\left(\sin(x) + \cos(x)\right)^2 = \left(1/5\right)^2\\\\\sin^2(x) + 2\sin(x)\cos(x) + \cos^2(x) = 1/25\\\\\sin^2(x) + \cos^2(x) + 2\sin(x)\cos(x) = 1/25\\\\1 + 2\sin(x)\cos(x) = 1/25\\\\\sin(2x) = 1/25 - 1\\\\\sin(2x) = 1/25 - 25/25\\\\\sin(2x) = -24/25\\\\[/tex]
Now apply the pythagorean trig identity to determine cos(2x) based on this. You should find that cos(2x) = -7/25
This then means tan(2x) = sin(2x)/cos(2x) = 24/7.
From here, you'll use this trig identity
[tex]\tan(2x) = \frac{2\tan(x)}{1-\tan^2(x)}\\\\[/tex]
which is the same as solving
[tex]\tan(2x) = \frac{2w}{1-w^2}\\\\[/tex]
where w = tan(x)
Plug in tan(2x) = 24/7 and solve for w to get w = -4/3 or w = 3/4
So either tan(x) = -4/3 or tan(x) = 3/4.
If we were to numerically solve the original equation for x, then we'd get roughly x = 2.21; then notice how tan(2.21) = -1.345 approximately when your calculator is in radian mode.
Since tan(x) < 0 in this case, we go for tan(x) = -4/3
Match the vocabulary word to its correct definition.
1. mean
The mean is the average value of the data you collect. In statistics, you find the mean of your sample. Then you use that mean to approximate the mean of the entire population. If you want the mean of the data to be a good approximation of the mean of the entire population, your need to make sure that you collect a random sample. To find the mean, you find the sum of the data points you collected and divide it by the number of data points in the set. For example, if the data you collected was {3, 3, 6}. Then the mean would be (3 + 3 + 6) ÷ 3 = 12 ÷ 3 = 4. It's important to note that the mean does not have to be a data point in your set. You can generalize the formula as well. If you collect n data points {d1, d2, d3, … dn}, then the mean of your data set is . The Greek letter μ—pronounced "mu"—is used because the word "mean" begins with the letter "m." It is important that you divide by the number of data points in your set, n.
2. population
An experiment is a well-defined procedure under controlled conditions designed to gather data that tests a hypothesis. For example, you want to test the hypothesis that flowers grow faster when they are watered every other day as opposed to every day. Then you could water one set of plants every day and another set of plants every other day. What data would you collect? The height of each plant once a day. What conditions would you need to control? You would need to make sure that the groups of plants are treated the same in every other way by getting the same amount of sun and being maintained at the same temperature, etc.
3. experiment
Bias is the preference for a particular group or subset. In the example above, the bias was toward viewers who like sports. When your sample is not chosen at random, you introduce bias into your study. So, in a certain sense, a biased sample is the opposite of a random sample. Why? In a biased sample, some members of the population are more likely to be chosen than others. In a random sample, every member of the population is equally likely to be chosen. Bias may also occur in surveys. See "survey" below for more information on this type of bias.
4. sample
A population is the entire group you want to understand. So, in a certain sense, you can think of the population as the "opposite" of the sample because a sample is not the entire population. A sample is chosen subset upon that you use to draw conclusions about the entire population.
5. bias
Random means free from bias. So, if you choose a random sample from a population, every member of the population has an equal chance of being chosen. It should be pointed out that this "true randomness" is an ideal which is difficult to achieve in real world experiments conducted on real world populations. That is why statisticians make every effort to ensure their samples chosen as free from bias as is possible, that is, as randomly as possible under real world conditions.
6. survey
A sample is a subset chosen from a population. In most cases, you want a random sample. Why? A random sample has the best chance of accurately representing the entire population.
7. random
A survey is the means of collecting a sample. In statistics, a survey is often a question or set of questions. It is critical that the questions, like the sample itself, be free from bias. Bias in a question tends to favor one response. As an extreme example of a biased question about colors might be, "Don't you think blue is beautiful and yellow is yucky?" An unbiased form of the question might be, "Which color do you prefer, blue or yellow?" Though careful, statisticians might be concerned about the order in which the colors are offered, so that might further simplify the question to, "What is your favorite color?" This type of question is most free from bias because it does not suggest a response and therefore does not favor a response.
Answers
Answer:
1. mean-The mean is the average value of the data you collect. In statistics, you find the mean of your sample. Then you use that mean to approximate the mean of the entire population. If you want the mean of the data to be a good approximation of the mean of the entire population, your need to make sure that you collect a random sample. To find the mean, you find the sum of the data points you collected and divide it by the number of data points in the set. For example, if the data you collected was {3, 3, 6}. Then the mean would be (3 + 3 + 6) ÷ 3 = 12 ÷ 3 = 4. It's important to note that the mean does not have to be a data point in your set. You can generalize the formula as well. If you collect n data points {d1, d2, d3, … dn}, then the mean of your data set is . The Greek letter μ—pronounced "mu"—is used because the word "mean" begins with the letter "m." It is important that you divide by the number of data points in your set, n.
2. Population-A population is the entire group you want to understand. So, in a certain sense, you can think of the population as the "opposite" of the sample because a sample is not the entire population. A sample is chosen subset upon that you use to draw conclusions about the entire population.
3. Experiment-An experiment is a well-defined procedure under controlled conditions designed to gather data that tests a hypothesis. For example, you want to test the hypothesis that flowers grow faster when they are watered every other day as opposed to every day. Then you could water one set of plants every day and another set of plants every other day. What data would you collect? The height of each plant once a day. What conditions would you need to control? You would need to make sure that the groups of plants are treated the same in every other way by getting the same amount of sun and being maintained at the same temperature, etc.
4. Sample-A sample is a subset chosen from a population. In most cases, you want a random sample. Why? A random sample has the best chance of accurately representing the entire population.
5. Bais-Bias is the preference for a particular group or subset. In the example above, the bias was toward viewers who like sports. When your sample is not chosen at random, you introduce bias into your study. So, in a certain sense, a biased sample is the opposite of a random sample. Why? In a biased sample, some members of the population are more likely to be chosen than others. In a random sample, every member of the population is equally likely to be chosen. Bias may also occur in surveys. See "survey" below for more information on this type of bias.
6. Survey-A survey is the means of collecting a sample. In statistics, a survey is often a question or set of questions. It is critical that the questions, like the sample itself, be free from bias. Bias in a question tends to favor one response. As an extreme example of a biased question about colors might be, "Don't you think blue is beautiful and yellow is yucky?" An unbiased form of the question might be, "Which color do you prefer, blue or yellow?" Though careful, statisticians might be concerned about the order in which the colors are offered, so that might further simplify the question to, "What is your favorite color?" This type of question is most free from bias because it does not suggest a response and therefore does not favor a response.
7. Random-Random means free from bias. So, if you choose a random sample from a population, every member of the population has an equal chance of being chosen. It should be pointed out that this "true randomness" is an ideal which is difficult to achieve in real world experiments conducted on real world populations. That is why statisticians make every effort to ensure their samples chosen as free from bias as is possible, that is, as randomly as possible under real world conditions.
Step-by-step explanation:
It says what each of them are in each paragraph, you just need to match them up.
Hope this helps :)
find the value of x and y
Answers
Answer x = 25°
In triangle ABC
Angle BAC = BCA
= 50
Because its isoceles triangle and base angles are equal.
x + x + 80 = 180
2x = 100
x = 50
Angle ACD is exterior angle so 80 + 50
= 130
Triangle ACD is also Isoceles Angle x = Angle CDA
130 + x + x = 180
2x = 50
x = 25
the area of a parallelogram is 48cm².if the two adjacent sides are 8cm and 6cm, find the length of its diagonal .
Answers
Answer:
10cm
Step-by-step explanation:
Assuming the shape is a rectangle since it's already stated that it's a parallelogram, and the area is stated, we can use the Pythagorean theorem to find the length
[tex]a^{2} +b^2=c^2[/tex], where c will be the length
isolate c
[tex]c^2=a^2+b^2[/tex]
[tex]c=\sqrt{a^2+b^2}[/tex]
substitute for a and b
[tex]c=\sqrt{8^2+6^2}[/tex]
[tex]c=\sqrt{64+36}[/tex]
[tex]c=\sqrt{100}[/tex]
[tex]c=10[/tex]
If I Have 100 Dollars And i go to the bank and i ask for 30 more and use that money on a store and i have 12 Dollars Left How Much Did the Thing I Bought Cost/ How Much Money did i spend?
Answers
Answer:
$118
Step-by-step explanation:
First, find how much money you had after going to the bank:
100 + 30
= $130
Find how much money you spent at the store by subtracting 12 from 130:
130 - 12
= 118
So, you spent $118
which value of -7(x2-6)+2y when x=2 and y=6
Answers
Answer:
Solution
= -7 (x2 -6) +2y
= -7 ( 2*2 - 6 ) + 2 * 6
= -7 ( 4 - 6) + 12
= -7 - 2 + 12
= - 9 + 12
= 3
I hope this help u :)
FOR BRAINLIEST ANSWER THIS:
The area of a triangle is 12 square meters . The base is 2 meters longer than the height Find the height of the triangle .
Answers
Answer:
The height of the triangle is four meters.
Step-by-step explanation:
We are given that the area of a triangle is 12 square meters. The base is two meters longer than the height, and we want to determine the height of the triangle.
Recall that the area of a triangle is given by:
[tex]\displaystyle A = \frac{1}{2}bh[/tex]
Since the area is 12 square meters:
[tex]\displaystyle 12 = \frac{1}{2}bh[/tex]
The base is two meters longer than the height. In other words, we can write that:
[tex]b = h + 2[/tex]
Substitute:
[tex]\displaystyle 12=\frac{1}{2}(h+2)h[/tex]
Solve for h. Multiply both sides by two:
[tex]24 = (h+2)h[/tex]
Distribute:
[tex]h^2+2h=24[/tex]
Isolate:
[tex]h^2+2h-24=0[/tex]
Factor:
[tex](h+6)(h-4)=0[/tex]
Zero Product Property:
[tex]h + 6 = 0\text{ or } h -4 =0[/tex]
Solve for each case:
[tex]h = -6\text{ or } h = 4[/tex]
Since the height cannot be negative, we can ignore the first solution.
Thus, the height of the triangle is four meters.
Given: In Parallelogram ABCD,
• mA = (7y+13)º
• m2B = (106 - 2x)º
• mC = (10y - 32)º
• m2D = (3x – 4)º
What are the values of x and y
Answers
Answer:
x = 110
y = 15
Step-by-step explanation:
AB is parallel to CD
angle B and angle D are alternate and they are equal
106-2x = 3x-4
106 + 4 = 3x - 2x
110 = x
same goes for y
7y + 13 = 10y - 32
13 + 32 = 10y - 7y
45 = 3y divide both sides by 3
15 = y
This two-way frequency table shows the results of a survey of users of the mass-transit system in a city. People were asked their age and whether they used the system regularly (three or more times per week).
Answers
Answer:
if Q={1,3,5,7,9}Express it in description methods
Answer: With the condition that age is 30 or under, the sample space is restricted to the first column. This simplifies the problem to:
P(uses mass transit |age is 30 or under) = 125/575=0.217
Step-by-step explanation:
edmentum
The perimeter of a rectangle is 64 feet. If one side of the rectangle has a length of 20 feet. How long is the other side?
Please answer thanks
Answers
Answer:
b=12
Step-by-step explanation:
Perimeter=2*(l+b)
64=2*(20+b)
b=12
Answer:
The width is 12 feet
Step-by-step explanation:
If the length is 20 feet, the other side must be 20 feet as well. The perimeter is the addition of all sides of a rectangle. Length: 20 on one side, 20 on other side. Subtract the length from total perimeter and you get 24 feet remaining. Divide 24 by 2. 12 feet for the width.
help me please I need
[tex] {x}^{2} + 2x + 6 \\ {x}^{2} + 4x + 2[/tex]
Answers
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION..
hey, can i please get your intro? would you like to be my friend?
Myself Ojasvi
Class 8, 13
India
Erica recently invested in gold that is growing in value 4% annually. She invested $4000 initially. Find the value of her investment after 6 years.
Answers
Answer:
4% = 0.04
4000 = 0.04
6 years = 0.04
Step-by-step explanation:
Hope this helps!
Given the table below, determine which type of equation best models the data and use a calculator to find an equation of best fit.
Answers
Answer:
Hello,
Step-by-step explanation:
Best fit: quadratic y=5.3x²-9.3+6.1
with an total error of 0.4
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Data should be analyzed using each of the following except:
A. measures of central tendency
B. shape
C. population size
D. spread
Answers
Right now Jack’s age is greater than twice Fred’s age by 4. After 8 years, the sum of their ages is 59. Find Fred’s age.
Answers
Fred's age is 13 years
Let
Fred's age = x
Jack's age = 2x + 4
After 8 years:
Fred's age = x + 8Jack's age = 2x + 4 + 8= 2x + 12
Sum of their ages = 59Sum of their ages = Fred's age + Jack's age
59 = (x + 8) + (2x + 12)
59 = x + 8 + 2x + 12
59 = 3x + 20
59 - 20 = 3x
39 = 3x
x = 39/3
x = 13 years
Therefore, Fred's age = 13 years
https://brainly.com/question/24371832
The minimum mark to obtain a Grade A is 75. Cheryn managed to achieve an average of Grade A for three of her English quizzes. What is the minimum mark she scored in her first quiz if scored 76 and 89 marks in her second and third quiz, respectively?
Answers
9514 1404 393
Answer:
60
Step-by-step explanation:
Let m represent the mark Cheryn scored on her first quiz. Then her average is ...
(m +76 +89)/3 ≥ 75
m +165 ≥ 225 . . . . . . . . multiply by 3
m ≥ 60 . . . . . . . . . . . . subtract 165
Cheryn scored a minimum of 60 marks on her first quiz.
.....................
Answers
Answer:
2nd option is the correct one
log|x|-f(x)+k
Shaded areas ( What is the area of the shaded region? )
Answers
Answer:
119.43 cm²
Step-by-step explanation:
The shaded area (A) is calculated as
A = area of rectangle - area of circle
= (11 × 12) - π × 2²
= 132 - 4π
≈ 119.43 cm² ( to the nearest hundredth )
TRIGONOMETRY
Could someone please help me with 5.2 please...it would really help alot:)
Answers
sin(x+y) - sin(x-y) - 1 = cos(2x)
sin(90) - sin(x-y) - 1 = cos(2x)
1 - sin(x-(90-x)) - 1 = cos(2x)
-sin(2x-90) = cos(2x)
-1*(sin(2x)cos(90) - cos(2x)sin(90)) = cos(2x)
-1*(sin(2x)*0 - cos(2x)*1) = cos(2x)
-1*(0 - cos(2x)) = cos(2x)
-1*(-cos(2x)) = cos(2x)
cos(2x) = cos(2x)
This confirms the identity is true.
Notice that throughout this proof, I only changed the left hand side.
On the 5th line, I used the identity sin(A-B) = sin(A)cos(B)-cos(A)sin(B).
A shopkeeper marks the price of an article 25% above the cost price. Then he allows a discount of 10% of the marked price. Find the profit percentage.
Answers
here is your answer hope you will understand it
Please help explanation if possible
Answers
Answer:
Jordans' age = 31 ; Anna's age = 19
Step-by-step explanation:
Given the 2 equations relating their ages
J + A = 50 → (1)
J = 12 + A → (2)
Substitute J = 12 + A into (1)
12 + A + A = 50
12 + 2A = 50 ( subtract 12 from both sides )
2A = 38 ( divide both sides by 2 )
A = 19
Substitute A = 19 into (2)
J = 12 + 19 = 31
Then Jordans' age = 31 ; Anna's age = 19
Answer:
Step-by-step explanation:
J = 12 + A equation 1
J + A = 50 equation 2
Solving equation 2
J + A = 50
A = 50 - J equation 3
Putting value of A in equation 1
J = 12 + A
J = 12 + 50 - J
Bringing like terms on one side
J + J = 12 + 50
2J = 62
J = 62/2 = 31
Putting value of J in equation 3
A = 50 - J
A = 50 - 31 = 19
Checking answer by putting values in equation 2
J + A = 50
31 + 19 = 50
50 = 50
So the age of Jordan is 31 and Anna is 19
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!! Determine the Value of K in the diagram ( secant lines to circles).
Answers
Answer:
k = 10Step-by-step explanation:
According to intersecting secants theorem we have the following equation:
3x*(3x + 5x) = 2x*(2x + kx)Solve it for k:
3x*8x = 4x² + 2kx²24x² = (4 + 2k)x²24 = 4 + 2k20 = 2kk = 10Yet another calculus question :)
Given [tex]y = x^3 - 2x[/tex] for [tex]x \geq 0[/tex], find the equation of the tangent line to y where the absolute value of the slope is minimized.
I have tried taking both the first and second derivatives and setting them equal to 0 and using that as the answer, but they're incorrect. Could somebody please explain how to complete the question correctly? Thank you so much!
Answers
Answer: y = (-4/3)*sqrt(2/3)
This is the same as writing [tex]y = -\frac{4}{3}\sqrt{\frac{2}{3}}[/tex]
============================================================
Explanation:
The phrasing "where the absolute value of the slope is minimized" is an interesting way of saying "the tangent slope is 0". This is because absolute values are never negative, so the smallest it can get is 0.
Your teacher has given you
y = x^3 - 2x
which differentiates into
dy/dx = 3x^2 - 2
after using the power rule
The derivative function lets us determine the slope of the tangent. The slope is the dy/dx value. Since we want a slope of 0, we'll set 3x^2-2 equal to zero and solve for x. So you have the correct idea, but you won't involve the second derivative.
dy/dx = 0
3x^2 - 2 = 0
3x^2 = 2
x^2 = 2/3
x = sqrt(2/3)
Notice how I'm ignoring the negative version of this root. This is due to the fact that [tex]x \ge 0[/tex]
-------------------------
Now plug this x value back into the original equation to find its corresponding y coordinate.
y = x^3 - 2x
y = x(x^2 - 2)
y = sqrt(2/3)*( 2/3 - 2 )
y = sqrt(2/3)*( -4/3 )
y = (-4/3)*sqrt(2/3)
Note that x = sqrt(2/3) leads to x^2 = 2/3 after squaring both sides.
-------------------------
Therefore, the equation of this tangent line is y = (-4/3)*sqrt(2/3)
All horizontal lines are of the form y = k, for some constant k. This constant value is basically what number you want the horizontal line to go through on the y axis. That number would be (-4/3)*sqrt(2/3).
Determine the perimeter of triangleABC with A(2;3) B(3;-2) and C (-2;-3).
Answers
Answer:
Plot the coordinates on a graph and join them to form a triangle. After doing that, you can count the length of each triangular side and find the sum of the 3 sides. That will be your answer.
