Answer: =53.46 in²
Step-by-step explanation:
You need to first find the area of the circle then subtract the area of the polygon inside the circle.
We do not have the radius of the circle so we need to find the radius and apothem of the polygon first.
A(polygon) = 1/2 a P 8 sided figure(octagon)
a=apothem (that is the center of the shape to the center of a side creating a right angle
P=perimeter= 10(8) =80
to find the apothem you need to find the angle of the vertex and take half of it to make a right triangle so you can use trig to find a (picture of apothem attached.
To find the angle, all external angles add to 360 so 360/8 = 45 so the internal angles are 180-45=135
half of that for the right triangle is 67.5
half the side is 5 for the Right triangle, now use trig to find to find a
tan 67.5=\(\frac{a}{5}\)
a=5tan67.5
a=12.07
A(octagon)=1/2(12.07)(80
=482.84
now to find the circle we need to find radius of octagon which is same radius for circle
use trig to find hypotenuse of that triangle
cos 67.5 = 5/r
r=5/cos67.5
r=13.07
A(circle)=\(\pi\)r²
=\(\pi 13.07^{2}\)
=536.30
A(shaded)= A(circle)-A(octagon)
=536.30-482.84
=53.46 in²
The length of a rectangular field is represented by the expression 14x-3x^2+2y . The width of the field is represented by the expression 5x-7x^2+7y . How much greater is the length of the field than the width?
The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)
1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)
2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).
3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).
4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)
5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)
6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)
7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)
8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)
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In a School sports day, the number of points the 8th grade team scores is given by 3x + 2y + z,
is the red team; y is yellow team, and z is the blue team. What is the total number of points scored by 10* graders when red scores 3 three points, yellow 5 points, and blue 2 points?
The total number of points scored is given by the equation A = 23 points
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total points scored be represented as A
Now , the equation will be
Substituting the values in the equation , we get
A = 3x + 2y + z be equation (1)
where x = red team = 3 points
y = yellow team = 5 points
z = blue team = 2 points
So , A = 3 ( 3 ) + 2 ( 5 ) + 2
A = 9 + 10 + 2
A = 21 points
Hence , the equation is A = 21 points
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figures that formed by intersecting two inverted cones and a plane.
Answer:
hyperbola is formed by intersecting two inverted cones and a plane.
Find the product 0.31x 8
Answer:
0.31 x 8=2.48
(>'-'<)
Real world inequalities:
You must be 4 feet or taller to ride the roller coaster
\(\qquad\qquad\huge\underline{{\sf Answer}}\)
The required inequality that represent the given scenario is :
\(\qquad \tt \dashrightarrow \:x \geqslant 4\)
where, x is height in feet.
Let's interpret the information given:
4 feet or taller ⇒ the person can be 4 feet or above 4 feetLet's set 'x' as the hypothetical height of a person
Therefore the inequality should be x ≥ 4
⇒ we put x as greater than 4 since the person must be taller than 4
feet to ride the roller coaster
⇒ we also put the '_' under the inequality to signify that the person
can equal 4 feet in height and still be eligible to ride the roller
coaster
Hope that helps!
The coordinates of the point A are (10,-8) and the coordinates of point B are
(10,4). What is the distance, in units, between the point A and point B?
12 units between the two points
What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x?
Discriminant = b2 – 4ac
–8
4
8
16
Answer:
-8
Step-by-step explanation:
●Answer attached●
☆Hope it helps☆
Answer:
its option one
Step-by-step explanation:
What is the value of x in this triangle?
Answer:
83 degrees
Step-by-step explanation:
See attachment below:
To make rice in a factory, Linda mixes rice and water in the ratio 3 : 5. If she uses 30 cups of rice, how manycups of water does she need?
Given:
Linda mixes rice and water in a ratio of 3: 5.
She uses 30 cups of rice
Using the ratio and proportions:
Rice : Water
3 : 5
30 : x
So, if the number of cubs of water = x
the value of x will be calculated as follows using cross multiplication:
\(x=\frac{30\times5}{3}=10\times5=50\)so, the answer will be:
She needs 50 cups of water.
Help with the remaining one please!!
Answer:
\(h'(1)=4\sec^2(8)\)
\(h''(1)=32\sec^2(8)\tan(8)\)
Step-by-step explanation:
Given the following function.
\(h(x)=\tan(4x+4)\)
Find the following:
\(h'(1)= \ ??\\\\h''(1)= \ ??\\\\\\\hrule\)
Taking the first derivative of h(x). We will use the chain rule and the rule for tangent.
\(\boxed{\left\begin{array}{ccc}\text{\underline{The Chain Rule:}}\\\\\dfrac{d}{dx}[f(g(x))]=f'(g(x)) \cdot g'(x) \end{array}\right}\\\\\\\boxed{\left\begin{array}{ccc}\text{\underline{The Tangent Rule:}}\\\\\dfrac{d}{dx}[\tan(x)]=\sec^2(x) \end{array}\right}\)
\(h(x)=\tan(4x+4)\\\\\\\Longrightarrow h'(x)=\sec^2(4x+4) \cdot4\\\\\\\therefore \boxed{h'(x)=4\sec^2(4x+4)}\)
Now plugging in x=1:
\(\Longrightarrow h'(1)=4\sec^2(4(1)+4)\\\\\\\Longrightarrow \boxed{\boxed{h'(1)=4\sec^2(8)}}\)
Taking the second derivative of h(x). Using the chain rule again and the secant rule.
\(\boxed{\left\begin{array}{ccc}\text{\underline{The Secant Rule:}}\\\\\dfrac{d}{dx}[\sec(x)]=\sec(x) \tan(x) \end{array}\right}\)
\(h'(x)=4\sec^2(4x+4)\\\\\\\Longrightarrow h''(x)=(4\cdot 2)\sec(4x+4) \cdot \sec(4x+4)\tan(4x+4) \cdot 4\\\\\\\therefore \boxed{h''(x)=32\sec^2(4x+4)\tan(4x+4)}\)
Now plugging in x=1:
\(\Longrightarrow h''(1)=32\sec^2(4(1)+4)\tan(4(1)+4)\\\\\\\therefore \boxed{\boxed{ h''(1)=32\sec^2(8)\tan(8)}}\)
Thus, the problem is solved.
find the formula for g(x) if it is known that (x-3)=2x-6
Answer: g(x) = 2*x
Step-by-step explanation:
We want to find the formula of g(x) if we know that g(x - 3) = 2*x - 6
Well, the first step is to find the expression (x - 3) = y in the g(x - 3)
Then:
g(x - 3) = 2*x - 6 = 2*x - 2*3
Now we can just take the common factor 2, and write this as:
2*x -2*3 = 2*(x - 3) = 2*y
then:
g( x - 3) = g(y) = 2*y
if we just replace x by y, we get:
g(x) = 2*x
This is the formula of g(x)
There are 26 boys and 20 girls in a class.
The boys and the girls have some counters.
The mean number of counters that the boys have is 28.
The mean number of counters that the girls have is 19.
Work out the mean number of counters the 46 children have.
Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.
What is the mean?The mean refers to the average value.
The average is the quotient of the total value divided by the number of items in the data set.
The number of boys in the class = 26
The number of girls in the class = 20
The total number of boys and girls in the class = 46
The mean number of counters that the boys have = 28
The total number of counters that the boys have = 728 (28 x 26)
The mean number of counters that the girls have =19
The total number of counters that the girls have = 380 (19 x 20)
The total number of counters that the class has = 1,108 (728 + 380)
The average or mean number of counters in the class = 24 (1,108 ÷ 46)
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Sam says that the length of diagonal SQ is two times the length of diagonal OM.
Is Sam correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
Answer:
Sam is wrong.
Step-by-step explanation:
A diagonal of square or rectangle is equals to hypotenuse of a triangle. So you can apply Pythagoras Theorem to solve it :
Given that QS is 17.9 and OM is 11.3. So SQ is not 2 times greater than OM.
Which fraction represents 3 inches divided into 4 equal parts?
Answer:
0.75 inches?
Step-by-step explanation:
I did it on the calculator:
3 divided by 4 = 0.75
There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.10 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.04 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. What is the probability that the first machine produces an acceptable cork
Answer:
0.6827
Step-by-step explanation:
Given that :
Mean, μ = 3
Standard deviation, σ = 0.1
To produce an acceptable cork. :
P(2.9 < X < 3.1)
Recall :
Z = (x - μ) / σ
P(2.9 < X < 3.1) = P[((2.9 - 3) / 0.1) < Z < ((3.1 - 3) / 0.1)]
P(2.9 < X < 3.1) = P(-1 < Z < 1)
Using a normal distribution calculator, we obtain the probability to the right of the distribution :
P(2.9 < X < 3.1) = P(1 < Z < - 1) = 0.8413 - 0.1587 = 0.6827
Hence, the probability that the first machine produces an acceptable cork is 0.6827
What is the perimeter of a triangle with vertices (-1, 2). (-1, -1), and (3, -1)?
Answer:
perimeter = 12
Step-by-step explanation:
In a right-angled triangle, a² + b² = c²
where c is the hypotenuse, and a and b are opposite and adjacent, either way.
have a look at attached documents for answer and explanation
Shane wants to plant 28 marigold plants and 36 rose plants in his garden. What is the greatest number of rows possible if each row has the same number of marigold plants and the same number of rose plants.
Answer:
HCF=2*2=4
Step-by-step explanation:
Given : Shane wants to plant 28 marigold plants and 36 rose plants in his garden
To Find : the greatest number of rows possible each row has the same
number of marigold plants and the same number of rose plants.
Solution:
marigold plants = 28
rose plants = 36
To find the greatest number of rows possible if each row has the same
number of marigold plants and the same number of rose plants.
we need to find HCF of 28 and 36
28 = 2 x 2 x 7
36 = 2 x 2 x 3 x 3
HCF = 2 x 2 = 4
greatest number of rows possible is 4
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to solve 2/5 x = 14, you multiply both sides of the equation by 5/2. your friend divides both sides of the equation by 2/5. who is right? explain.
Both of you are correct because using either way can solve the equation for the value of x.
How to solve for x ?In the case of solving for x in 2/5 x = 14, the goal is to get rid of the fraction that is multiplying x on the left side. This can be done by either multiplying both sides of the equation by the inverse of 2 / 5 ( which is 5 / 2 ) or by dividing both sides by 2 / 5.
Doing either of these things would get rid of the 2 / 5 and give an answer to x as shown below :
Multiplying :
2/5 x = 14
5 / 2 x 2 / 5 x = 14 x 5 / 2
x = 35
Dividing :
2/5 x = 14
2 / 5 x / 2 / 5 = 14 / 2 / 5
x = 35
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find the positive suare root of the following number 57.27
The positive square root of 57.27 is approximately 7.5726, with further decimal places available through iterative approximation methods.
To find the positive square root of the number 57.27, we can use a calculator or mathematical operations.
Taking the square root of a number involves finding a value that, when multiplied by itself, gives the original number. In this case, we want to find the value that, when squared, equals 57.27.
Using a calculator, we can find the square root of 57.27 as approximately 7.5726. However, it's important to note that this is an approximation and may not be completely accurate due to rounding errors.
If we want to find a more precise answer manually, we can use iterative approximation methods. One such method is the Newton-Raphson method, which involves repeatedly refining an initial guess.
Starting with an initial guess of, let's say, 7, we can use the formula:
x(n+1) = (x(n) + (57.27/x(n)))/2,
where x(n) is the current approximation and x(n+1) is the next approximation. Iterating this formula a few times will converge to a more accurate value.
After a few iterations, we find that the positive square root of 57.27 is approximately 7.572615. This value can be further refined by performing more iterations or using more advanced numerical methods.
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Question:-
The area of two similar triangles are 81 cm2 and 49 cm² respectively. If one of the sides of the first triangle is 6.3 cm, find the corresponding side of the other triangle.
Let's assume that the corresponding side of the second triangle is \(\displaystyle\sf x\).
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:
\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)
To find \(\displaystyle\sf x\), we can solve the proportion above:
\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)
Taking the square root of both sides:
\(\displaystyle\sf \dfrac{x}{6.3} =\sqrt{\dfrac{49}{81}}\)
Simplifying the square root:
\(\displaystyle\sf \dfrac{x}{6.3} =\dfrac{7}{9}\)
Cross-multiplying:
\(\displaystyle\sf 9x = 6.3 \times 7\)
Dividing both sides by 9:
\(\displaystyle\sf x = \dfrac{6.3 \times 7}{9}\)
Calculating the value:
\(\displaystyle\sf x = 4.9\)
Therefore, the corresponding side of the second triangle is \(\displaystyle\sf 4.9 \, cm\).
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Answer:
Step-by-step explanation:
let's assume that the corresponding side of the second triangle is .
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:
To find , we can solve the proportion above:
Taking the square root of both sides:
Simplifying the square root:
Cross-multiplying:
Dividing both sides by 9:
Calculating the value:
Therefore, the corresponding side of the second triangle is 4.9cm
hope it helped u dear...........
A town has a population of 1500 people at time t = 0. In each of the following cases, write a formula for the population P, of the town as a function of year t.Need help answering part B(a) The population increases by 100 people per year.P=1500 + 100t people(b) The population increases by 2 percent a year P=_____ people
b)
We need to find the equation when the population increases by 2 percent a year.
Then, the equation must be an exponential function:
The population increases by 5% = 0.05 year
Hence, p= initial value + (1 + 0.05)^t
Replacing the values:
\(P=1500+(1.05)^t\)Below is a position-time graph of the O'Connor Panthers in pursuit of a victory over the
Marshall Rams.
100
80
Position
(ds) 60-
40
201
A 10
20
30
40
50
60
Time (s)
Find the total yardage traveled from 0-120 seconds.
70
-9
90
100
110
120
According to the information we can infer that the total yardage traveled from 0 to 120 seconds is 140 yards.
How to calculate the total yardage traveled?To calculate the total yardage traveled we have to consider the movement of the O'Connor Panthers. In this case we have to consider that the movement in the y axis.
In this case we can conclude that the total yardage traveled was 140 yards because:
From 0 to 20 seconds they moved 30 yards. From 20 to 40 seconds they moved 10 yards.From 40 to 60 seconds they moved 40 yards.From 60 to 80 seconds they didn't move.From 80 to 90 seconds they moved 20 yards.From 90 to 120 secons they moved 40 yards.30 + 10 + 40 + 20 + 40 = 140Learn more about yards in: https://brainly.com/question/28062239
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Which point is located on the x-axis of a coordinate grid?
A. (1, 1)
B. (1, 0)
C. (0, 1)
D. (2, 1)
Answer:
I believe it is B
Step-by-step explanation:
Remember - x,y. The 1 was found on the x-axis.
What is the area, in square inches, of the isosceles trapezoid below?
We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately
σ
=
24.4
. We would like to be 99.5% confident that the estimate is within 0.5 of the true population mean. How large of a sample size is required?
n
=
Using the z-distribution, it is found that a sample size of n = 18,805 is required.
What is a z-distribution confidence interval?The confidence interval is:
\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)
The margin of error is:
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which:
\(\overline{x}\) is the sample mean.z is the critical value.n is the sample size.\(\sigma\) is the standard deviation for the population.For this problem, the parameters are:
\(z = 2.81, \sigma = 24.4, M = 0.5\).
Hence we solve for n to find the needed sample size.
\(M = z\frac{\sigma}{\sqrt{n}}\)
\(0.5 = 2.81\frac{24.4}{\sqrt{n}}\)
\(0.5\sqrt{n} = 24.4 \times 2.81\)
\(\sqrt{n} = 48.8 \times 2.81\)
\((\sqrt{n})^2 = (48.8 \times 2.81)^2\)
n = 18,805.
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Answer:
Step-by-step explanation:
What if the estimate is within 1 of the population mean?
(3, 4, 5, ...} is finite or infinite
The given set is (3, 4, 5, ...} is infinite set.
A set with an infinite number of elements is one that cannot be numbered. A set that has no last element is said to be endless. A set that can be put into a one-to-one correspondence with a suitable subset of itself is said to be infinite. No issue with the in-class assignment.
The stars in the clear night sky, water droplets, and the billions of cells in the human body are just a few examples of endless sets of objects that surround us. A set of natural numbers, however, serves as the best illustration of an infinite set in mathematics. There is no limit to the amount of natural numbers.
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Find the exact value of tan(x-y) if sin x=8/17 cosy = 3/5
To solve the the question we proceed as follows:
From trigonometric laws
\((cos x)^2+(sin x)^2=1\)
\((cos x)^2+(sin x)^2=1\)
\(sin (x-y)=sin\) \(x\) \(sin\) \(y-sin\) \(y\) \(cos\) \(x\)
\(cos (x-y)=cos\) \(x\) \(cos\) \(y+sin\) \(x\) \(xin\) \(y\)
si \(x=\frac{8}{17}\)
\(cos\) \(x=sqrt(1-(sin x)^2)=sqrt(1-64/289)=sqrt(\frac{225}{289} )=\frac{15}{17}\)
\(cos\) \(y=\frac{3}{5}\)
\(sin\) \(x= sqrt(1- (cos x)^2)= sqrt(1-\frac{9}{25} )=sqrt(\frac{16}{25} )=\frac{4}{5}\)
thus
\(tan (x-y)=[sin (x-y)]/[cos (x-y)]\)
=[sin x cos y-sin y cos x]/[cos x cos y+sin x sin y]
plugging in the values we obtain:
\([8/17 *3/5-4/5*15/7]/[15/17*3/5+8/17*4/5]\)
simplifying
\([24/85-60/85]/[45/85+32/85]\)
\(=-\frac{36}{77}\)
Convert 506 minutes to hours and minutes.
Answer:
8 hours and 26 minutes
Step-by-step explanation:
To convert 506 minutes to hours and minutes, we can use the fact that there are 60 minutes in one hour.
First, we can divide 506 by 60 to find the number of hours:
506 ÷ 60 = 8 with a remainder of 26
This means that 506 minutes is equal to 8 hours and 26 minutes.
Therefore, the conversion of 506 minutes to hours and minutes is:
8 hours and 26 minutes
Write the equation of a line passing through (0, 6) and parallel to the line y = 3/2x-7
Using the table, what is the average daily balance of the credit card for the October 1 - October 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00. Day 1112131 Activity − Payment Purchase Purchase Adjustment −−2000+1500+1000 Closing Balance 100008000950010500
The balance based on the.data given in the table is shown below.
Balance from day 1 to 10 = 11000
Balance from day 11 to 21= 8000
Balance from day 21 to 30- 5500
Balance on day 31 7500
How to explain the balanceBalance from day 1 to 10= 11000
Balance from day 11 to 21= 8000 Balance from day 21 to 30 5500
Balance on day 31- 7500
The average daily balance of the credit card for the month of december is:
Average daily balance The ratio of total balance from each day in cycle to the total number of days in cycle.
Total balance from each day in cycle=
(11000 x 10)+(8000 × 10)+(5500 x 10) + (7500 x 1) = 104000
Average daily balance=104000 / 31
= 8145
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