The probability is 1/10.
The equation x(x+5) = -n can be rewritten as x^2 + 5x + n = 0. To find the solutions of this equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 5, and c = n.
For there to be no real solutions, the discriminant (b^2 - 4ac) must be negative. The discriminant is 5^2 - 4(1)(n) = 25 - 4n. So for there to be no real solutions, 25 - 4n < 0, or n > 6.25.
Since the integer n is between 1 and 10 inclusive, the only value that would not have a real solution is n = 7. Therefore, the probability that for the randomly chosen n there exist no real solutions is 1/10.
To learn more about probability visit: brainly.com/question/30034780
#SPJ4
Help me with this question for BRAINLIEST
Last year, Christine had $20,000 to invest. She invested some of it in an account that paid 8% simple interest per year, and she invested the rest in an account that paid 10% simple interest per year. After one year, she received a total of $1920 in interest. How much did she invest in each account?
First account:
Second account:
Answer:
First account: $16,000
Second account: $4,000
Step-by-step explanation:
Let x be the amount Christine invested in the 8% account and y be the amount she invested in the 10% account. We know from the problem that:
x + y = $20,000 (the total amount she had to invest)
0.08x + 0.1y = $1920 (the total amount of interest she received)
We can use the first equation to solve for one variable in terms of the other.
x = $20,000 - y
Now we substitute this expression into the second equation:
0.08($20,000 - y) + 0.1y = $1920
Solving for y:
0.08x + 0.1y = $1920
0.08($20,000 - y) + 0.1y = $1920
1,600 - 0.08y + 0.1y = $1920
-0.08y = -320
y = $4,000
Now, we know that Christine invested $4,000 in the 10% account, we can use the first equation again to find out how much she invested in the 8% account:
x + y = $20,000
x + $4,000 = $20,000
x = $16,000
So Christine invested $16,000 in the 8% account and $4,000 in the 10% account
Aume that y varie inveraly with x. If y equal 7 when x equal 2/3, find y when x =7/3
If y equals 7 when x equal 2/3, so when x =7/3 the y is equal to 14/7
If y varies inversely with x, this means that the product of x and y is a constant. So if we know that y = 7 when x = 2/3, then we can set up the equation: x*y = k, where k is the constant.
Substituting the known values we get: (2/3)*7 = k.
So we know that k = 14/3
Now, we can use this value of k to find the value of y when x = 7/3.
x*y = k
(7/3)*y = 14/3
y = 14/7
So, when x = 7/3, y = 14/7
To learn more about the product, visit:
brainly.com/question/3211849
#SPJ4
Evaluate: 2−1 × 23 /24
Answer:
0.9583
Step-by-step explanation:
(2-1) * (23÷24)
1*0.983
=0.9583
Answer:
[tex]\frac{23}{24} = 0.95[/tex]
Step-by-step explanation:
According to BODMAS
1. Kevin regularly travels from Manchester to Oxford.
He travels on two different trains.
His first train is from Manchester to Birmingham and his second train is from Birmingham to
Oxford.
On the 1st train, the probability that a seat has a table is 3/5
On the 2nd train, the probability that a seat has a table is
3/10
The 1st train has a total of 400 seats.
(a) Work out an estimate for the number of these 400 seats that have a table.
Answer:
240 seats with tables
Step-by-step explanation:
Let's start by making our fraction out of 10 on the first train to make it easier on us, this fraction would be [tex]\frac{6}{10}[/tex]. Then, to get the number of seats on this train that would have a table, we need to multiply 400 by our fraction, giving us:
[tex]400 * \frac{6}{10} = 2400/10 = 240[/tex]
So, the 1st train should have approximately 240 seats with tables.
Hope this helped!
The volume of a rectangular prism is given by the expression10x3 + 46x2 – 21x – 27. The area of the base of the prism is given by the expression 2x2 + 8x – 9. Which of the following expressions represents the height of the prism? (V = Bh)
8x - 3
3x - 5
5x + 3
42x + 3
The height of the prism is 5x + 3 units.
What is volume?
A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.
Given:
The volume of a rectangular prism is given by the expression
10x^3 + 46x^2 – 21x – 27. The area of the base of the prism is given by the expression 2x^2 + 8x – 9.
We have to find the height of prism.
Volume of the rectangular prism = Base × Height
The expression is in the Question be
10x ³ + 46 x² - 21x -27
And the area of the base of the prism is given by the expression
2x² + 8x - 9 .
Put in the formula
10x ³ + 46 x² - 21x -27 = 2x² + 8x - 9 × Height
The factor of 10x ³ + 46 x² - 21x -27 are (5x +3 )(2x² + 8x - 9) .
put in the formula
(5x +3 )(2x² + 8x - 9) = (2x² + 8x - 9) × Height
Cancelled 2x² + 8x - 9 on both side.
(5x+3)unit = Height
Hence, the height of the prism is 5x + 3 units.
To know more about volume, click on the link
https://brainly.com/question/2887044
#SPJ1
You are going to use an incline plane to lift a heavy object to the top of a shelving unit with a height of 5 ft. The base of the incline plane is 14 ft
from the shelving unit. What is the length of the incline plane?
an incline plane to lift a heavy object to the top of a shelving unit with a height of 5 ft. The base of the incline plane is 221 ft from the shelving unit
How does the length of the inclined plane affect its slope?A ramp or inclined plane, which is a flat support surface tilted at an angle from vertical with one end higher than the other, is used to help raise or reduce a weight.This implies that as the plane lengthens, the task will become easier in terms of force, but the distance will always need to adjust proportionally. This is due to the fact that the angle of elevation of the ramp lowers as length increases. The Pythagorean Theorem is used to compute the slope length, where rise and run are the vertical and horizontal distances, respectively: [tex]rise^{2} + run^{2} =slope length^{2}[/tex]The inclination plane is long, measuring [tex]5^{2} +14^{2} =221ft^{2}[/tex] .To learn more about incline plane refer to :
https://brainly.com/question/26262923
#SPJ1
Ted runs a coffee-distributing company with monthly fixed costs of $3600. he also spends $1.50 for each 16 ounce bag of coffee that he sells (%). during the month of september, his total costs were $12,000. which of the
following equations represent his total september costs? select all that apply.
3600 1.50x 12,000
1.50(2400x12,000
1.50(3600+) 12,000
3601.50 x 12.000
1.50 + 3600x12,000
(3600+ 1.50) x 12.000
The correct equations to represent Ted's total September costs are: (3600+ 1.50) x 12.000 1.50(3600+) 12,000.
What is cost?Cost is the total expenditure or loss incurred in the production, acquisition, or use of a product or service. It can be calculated as the sum of fixed costs (such as rent and labor costs) plus variable costs (such as materials and energy). Cost can be expressed both in monetary terms (such as dollars or euros) or in terms of resources (such as time or effort). In business, cost is a crucial factor for determining profitability and should be taken into consideration when making decisions about production, sales, and pricing strategies.
The first equation calculates the cost of the fixed monthly costs plus the cost of the 16 ounce bags of coffee multiplied by the total number of bags sold. The second equation calculates the cost of the 16 ounce bags of coffee multiplied by the fixed monthly costs plus the total number of bags sold.
To know more about cost click-
https://brainly.com/question/25109150
#SPJ4
In parallelogram ABCD, AB = 14cm. The altitude corresponding to AB is 6 cm and the altitude corresponding to BC is 7 cm. Find AD.
If in parallelogram ABCD, AB = 14cm. The altitude corresponding to AB is 6 cm and the altitude corresponding to BC is 7 cm. The AD is 8.57.
How to find AD?Given data:
AB= 14cm
Altitude corresponding AB =6cm
Altitude corresponding to BC =7cm
So,
1/2 × AB × altitude 1 = 1/2 × AD × altitude 2
AB × altitude 1 =AD × Altitude 2
10 × 6 = AD × 7
60 = AD × 7
AD = 60/7
AD = 8.57
Therefore we can conclude that AD is 8.57.
Learn more about altitude here:https://brainly.com/question/1159693
#SPJ1
Angle addition postulate
Answer:
the sum of two adjacent angle measures will equal the angle measure of the larger angle that they form together
Step-by-step explanation:
angle addition postulate formula is ∠AOB + ∠BOC = ∠AOC
Sorry, but may I ask what the answer to this question is?
Which is not a combination that can be made if Joe has a pair of yellow, orange, black, and blue shoes with yellow, red, and brown shoelaces?
A. orange shoes with red shoelaces
B. black shoes with yellow shoelaces
C. blue shoes with brown shoelaces
D. yellow shoes with black shoelaces
Answer:
D
Step-by-step explanation:
There are no black shoelaces
How do I do this help me please
Answer: x = 81
Step-by-step explanation:
Quite a straightforward question.
Given equation is 61+20=x
So you just need to add 61 and 20 to get the value of x,
x=81
The inverse of f(x) would be represented by:
f(x)
ƒ¹(x)
f(x)-¹
fog(x)
None of the choices are correct.
If g(x) is the inverse function of f(x) and[tex]$f^{\prime}(x)=\frac{1}{1+x^4}$[/tex], then [tex]$g^{\prime}(x)$[/tex] is [tex]1+[\mathrm{g}(\mathrm{x})]^4\end{aligned}[/tex]
What is Inverse function?By applying the formula x=-b/2a to find the quadratic's vertex, the result can then be used to replace y in the original equation. Substitute the vertex into the equation y=a(x-h)2+k in the vertex form. (A will not change; h is x; and K is y.) It is referred to as being in standard form when the quadratic function f(x) = a(x - h)2 + k is not equal to zero. The graph opens either upward or downward depending on whether an is positive or negative. The vertex is the point, while the vertical line x = h is the line of symmetry (h,k).
Correct option is A)
[tex]& \mathrm{g}=\mathrm{f}^{-1} \\[/tex]
[tex]& \mathrm{f}(\mathrm{g}(\mathrm{x}))=\mathrm{x}[/tex]
Differentiate w.r.t.x
[tex]& \mathrm{f}^{\prime}(\mathrm{g}(\mathrm{x})) \cdot \mathrm{g}^{\prime}(\mathrm{x})=1 \\[/tex]
[tex]& \therefore \frac{1}{1+(\mathrm{g}(\mathrm{x}))^4} \cdot \mathrm{g}^{\prime}(\mathrm{x})=1 \\[/tex]
[tex]& \mathrm{~g}^{\prime}(\mathrm{x})=1+[\mathrm{g}(\mathrm{x})]^4\end{aligned}[/tex]
The complete question is,
If [tex]$\mathrm{g}(\mathrm{x})$[/tex]is the inverse function of [tex]$\mathrm{f}(\mathrm{x})$[/tex] and [tex]$\mathrm{f}^{\prime}(\mathrm{x})=\frac{1}{1+\mathrm{x}^4}$[/tex], then [tex]$\mathrm{g}^{\prime}(\mathrm{x})$[/tex]is
A [tex]$1+[\mathrm{g}(\mathrm{x})]^4$[/tex]
B [tex]$1-[g(x)]^4$[/tex]
C [tex]$1+[\mathrm{f}(\mathrm{x})]^4$[/tex]
D [tex]$\frac{1}{1+[\mathrm{g}(\mathrm{x})]^4}$[/tex]
To learn more about Inverse function refer to:
https://brainly.com/question/3831584
#SPJ1
State the fifth and seventh terms of the sequence -2, -3, -4½..
Answer:
see explanation
Step-by-step explanation:
there isa common difference between consecutive terms, that is
[tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-3}{-2}[/tex] = [tex]\frac{3}{2}[/tex]
[tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{-4\frac{1}{2} }{-3}[/tex] = [tex]\frac{3}{2}[/tex]
this indicates the sequence is geometric with nth term
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = - 2 and r = [tex]\frac{3}{2}[/tex] , then
[tex]a_{n}[/tex] = - 2 [tex](\frac{3}{2}) ^{n-1}[/tex] , thus
a₅ = - 2 ([tex](\frac{3}{2}) ^{4}[/tex] = - 2 × [tex]\frac{81}{16}[/tex] = - [tex]\frac{81}{8}[/tex]
and
a₇ = - 2 [tex](\frac{3}{2}) ^{6}[/tex] = - 2 × [tex]\frac{72 9}{64}[/tex] = - [tex]\frac{729}{32}[/tex]
Add and Subtract Fractions Quiz
Select the correct solution for the expression.
2/5+3/8
A. 2/5+3/8=5/13
B. 16/40+15/40=31/40
C. 10/40+24/40=34/40
D. 2/5+3/8=6/40
Answer:
B.
Step-by-step explanation:
You need to find a common denominator. In this case, 40. Convert 2/5 to 16/40 and 3/8 to 15/40. Add the numerators (16 + 15) together. The denominator stays the same.
A rectangular field measures 63.9m by 104.6metres find the minimum number of poles to be Erected for fencing if they are to be at most 2.4meters apart.
The minimum number of poles to be Erected for fencing are 26.
What is the perimeter of a rectangle?The perimeter of a rectangle is -
P = 2{L + B}
Given is that a rectangular field measures 63.9 meters by 104.6 meters.
The perimeter of the rectangular field will be -
P = 2(63.9 + 104.6)
P = 2(168.5)
P = 337
Let the total number of poles that can be erected are {x}. Then, we can write that -
2.4x ≤ 63.9
x ≤ (63.9/2.4)
x ≤ 26.66
x = 26 {approx.}
Therefore, the minimum number of poles to be Erected for fencing are 26.
To solve more questions on rectangles, visit the link below -
brainly.com/question/12802031
#SPJ1
Kevin is travelling from Manchester to Oxford tomorrow.
(b) Complete the probability tree diagram to show the outcomes of Kevin's seating on the two
trains.
Label clearly the branches of the probability tree diagram.
The probability tree diagram has been started in the space below.
315
Seat on the
first train
with a
table
without
a table
Seat on the
second train
Answer:
I don't know the answer to this question
What is the volume of the cylinder? Round to the nearest hundredth and approximate using π = 3.14.
cylinder with a segment from one point on the circular base to another point on the base through the center labeled 2.6 feet and a height labeled 4.4 feet
23.35 cubic feet
35.92 cubic feet
71.84 cubic feet
93.4 cubic feet
Answer:
23.35 cubic feet
Step-by-step explanation:
The volume of a cylinder can be calculated using the formula: V = π * r^2 * h, where r is the radius of the circular base, h is the height of the cylinder.
To find the radius, we use the formula for the circumference of a circle: C = 2πr
The circumference of the circular base is 2.6 feet, so we can set this equal to 2πr and solve for r: 2.6 = 2πr, r = (2.6) / (2π) = 0.816
Now that we know the radius, we can substitute it into the volume formula: V = π * (0.816)^2 * 4.4 = 23.35 cubic feet
So the answer is 23.35 cubic feet, which closest to A. 23.35 cubic feet
amy was born on a tuesday. what is the probability that exactly two of her three best friends were also born on tuesday? express your answer as a common fraction.
The probability of being born on a Tuesday is= 18/343
What is probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The likelihood that an event will occur increases with its probability.
A straightforward illustration is tossing a fair (impartial) coin.
The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).
Hence, The probability of being born on a Tuesday is= 18/343.
learn more about probability click here:
brainly.com/question/13604758
#SPJ4
what is the procedure for completing the square to find the center and radius of a circle?
By completing squares in both the variables and try to get the general equation of the form:
(x - a)^2 + (y - b)^2 = R^2
How is the procedure to identify the center and radius of the circle?A general circle equation for a circle whose center is (a, b) and the radius is R, is:
(x - a)^2 + (y - b)^2 = R^2
So, if we have an equation like:
x^2 + cx + d + y^2 + h*y + l = m
We just need to complete squares in both x and y, such that we end with an equation of the form of:
(x - a)^2 + (y - b)^2 = R^2
Learn more about circle equations at:
https://brainly.com/question/1559324
#SPJ1
Using Pythagoras' theorem, calculate the length of the hypotenuse in this right-angled triangle. Give your answer in centimetres (cm) to 1 d.p. 4.8 cm 2 cm Not drawn accurately
Answer: 5.2 cm
Step-by-step explanation:
4.8 squared + 2 squared is 23.04 + 4, which is 27.04. The square root of that is 5.2
Identify the surface with the given vector equation. r(s, t) = (s, t, t^2-s^2) elliptic cylinder circular paraboloid hyperbolic paraboloid plane circular cylinder
Therefore , the solution of the given problem of equation comes out to be x² + z²= y, a circular paraboloid.
What is equation?When a math formula employs the equals symbol (=), it appears to be a rule that connects two expression and denotes equality. An equation in algebra is a factual declaration that shows that several mathematical variables are all equal. For instance, the values ptdc + 6 and 12 in the equation obd + 6 = 12 have an equal sign. The link between the words on either side of each letter is described by a mathematical formula. The sentence and the insignia are frequently same.
Here,
The vector solution is r(s, t) = s, t, t² - s².
When comparing to r(s, t) = x, y, and z, x = s, y = t, and z = 2 - s²
So, z = y² - x²
, a hyperbolic paraboloid (2)
r(s, t) = s sin³t, s², s cos³t is the vector equation that is presented.
When comparing with withr(s, t) = x, y, and z,
x = ssin³t, y = s², and z = s* cos³t²
As a result, x2 + z2 = s2 (sin23t + cos23t),
sin23t + cos23t = 1,
x² + z² = s², s² = y, and x² + z²= y,
a circular paraboloid.
Therefore , the solution of the given problem of equation comes out to be x² + z²= y, a circular paraboloid.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ4
Suppose you want to have 800,000 for retirement in 35 years your account earns 9% interest how much would you need to deposit in the account each month
Therefore , the solution of the given problem of interest rate comes out to be $271.94 you will be depositing every month.
What is interest, exactly?The original capital is multiplied by the interest rate, the loan term, and other factors to calculate simple interest. A simple return is equal to the principal plus interest hrs. This method of calculating interest is the simplest. The most typical method is to calculate it as a fraction of the principal amount. For instance, he was only liable for paying his portion of the interest if he acquired $100 from a buddy and agreed to repay the money on 5% interest. $x (0.05) = $5. When you make loans or lend money, you both have to pay interest. Interest is frequently determined as a percentage of a loan.
Here,
Given : interest = 9%
time =35 years
amount = 800000
Using formula :
=> FV.( r / [tex](1+r) ^{n}[/tex] -1)
=> 800000 (0.09/12 / [tex](1 + 0.09/12 )^{12*35}[/tex] - 1 )
=> 271.94
Therefore,
the total amount you deposit will only be
=> 35*12 times $271.94, or
roughly total amount => 35*12*271.94= 114214.8 dollars, out of the estimated $800,000.
The balance will be what the account earns or accumulates over the next 35 years.
Therefore , the solution of the given problem of interest rate comes out to be $271.94 you will be depositing every month.
To know more about interest visit:
https://brainly.com/question/28792777
#SPJ1
pls help super simple !!
The values of the expression are given by the inequality below:
11/3 < 5/x + 2 < 9/2
How to find the possible values of the expression?Here we want to find the possible values of the expression:
5/x + 2
Where we have the restriction:
2 < x < 3
Notice that x is on the denominator, so when x takes the largest value x = 3, we will have a lower bound for the expression:
5/3 + 2 = 5/3 + 6/3 = 11/3
When x takes the smallest value, we will get the upper bound:
5/2 + 2 = 5/2 + 4/2 = 9/2
Then the possible values of the expression are:
11/3 < 5/x + 2 < 9/2
Learn more about inequalities:
https://brainly.com/question/24372553
#SPJ1
according to westgard and clia, how many specimens should be run by each method on the same day for 8 to 20 days to compare a test method with a comparative method?
According to Westgard and CLIA , 40-100 specimens should be run by each method on the same day for 8 to 20 days to compare a test method with a comparative method.
CLIA stands for Clinical Laboratory Improvement Amendments . The regulations under CLIA includes, the federal standards which is applicable to all U.S. facilities or sites which are test human specimens for health assessment or it is used to diagnose, prevent, or treat disease.
The Federal Register is the official daily publication for federal agencies and the organization's notices, proposed regulations, and final rules, as well as executive orders and other presidential papers. The regulations published in the Code of Federal Regulations and enforced by federal agencies are known as final rules.
To learn more about CLIA
brainly.com/question/29342147
#SPJ4
The quadratic regression equation y = –0.1x2 + 143.99x – 13,242.84 models expected company profits in terms of the number of pairs of shoes sold.
Based on the regression equation, approximately how much profit can the company expect if it sells 400 pairs of shoes?
$28,400
$41,600
$44,300
$60,400
The approximate profit can the company expect if it sells 400 pairs of shoes will be 28,400. Then the correct option is A.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The quadratic regression equation y = –0.1x² + 143.99x – 13,242.84 models expected company profits in terms of the number of pairs of shoes sold.
The profit can the company expect if it sells 400 pairs of shoes will be given as,
y = –0.1(400)² + 143.99(400) – 13,242.84
y = – 16,000 + 57,596 – 13,242.84
y = 28,354
y ≈ 28,400
The approximate profit can the company expect if it sells 400 pairs of shoes will be 28,400. Then the correct option is A.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ1
the region inside the cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ)
The region inside cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ) is equal to [tex]\frac{\pi}{4}[/tex]
Now, According to the question:
We will first draw both of them on the same plane and then find their point of intersection. Then using the given information, we will shade the region whose area we have to find.
The point of intersection of r = 1 + cos(θ) and r = 3 cos(θ)
1 + cos(θ) = 3 cos(θ)
1 = 2 cos(θ)
=> cos(θ) = 1/2
=> θ = [tex]cos^-^1[/tex][tex]\frac{1}{2}[/tex]
=> θ = ±[tex]\frac{\pi }{3}[/tex]
So, two curves intersect at θ = ± [tex]\frac{\pi }{3}[/tex]
Area of the cardioid,
[tex]A_1 = \int\limits^\pi _\frac{\pi }{3} {\frac{1}{2}(1+cos\theta)^2 } \, d\theta= \frac{1}{2} \int\limits^\pi _\frac{\pi }{3} (1+cos^2\theta+2cos\theta) } \, d\theta=\frac{1}{2}[/tex]
[tex]\int\limits^\pi _\frac{\pi }{3} {(1 + \frac{cos2\theta+1}{2} +2cos\theta)} \, d\theta[/tex]
=> [tex]A_1 = \frac{1}{2}[\theta+\frac{1}{2}(\frac{sin2\theta}{2} +\theta)+2sin\theta ]^\pi _\frac{\pi }{3}[/tex]
=> [tex]A_1= \frac{1}{2}[\frac{3\pi }{2}+0+0-\frac{\pi }{2}-\frac{\sqrt{3} }{8} -\sqrt{3} ][/tex]
=> [tex]A_1= \frac{1}{2} [\pi +\frac{-9\sqrt{3} }{8} ]\\\\A_1 = \frac{\pi }{2} - \frac{9\sqrt{3} }{16}[/tex]
Area of the circle,
[tex]A_2 = \int\limits^\frac{\pi }{2} _\frac{\pi }{3} {\frac{1}{2}(3cos\theta)^2 } \, d\theta \\\\A_2 = \frac{9}{2} \int\limits^\frac{\pi }{2} _\frac{\pi }{3} \frac{cos2\theta+1}{2}d\theta\\ \\A_2 = \frac{9}{4}[\frac{sin2\theta}{2}+\theta ]^\frac{\pi }{2}_\frac{\pi }{3}[/tex]
[tex]A_2 = \frac{9}{4}[0+\frac{\pi }{2} -\frac{\sqrt{3} }{4} -\frac{\pi }{3} ][/tex]
[tex]A_2=\frac{9}{4}[\frac{\pi}{6}-\frac{\sqrt{3} }{4} ][/tex]
[tex]A_2= \frac{3\pi }{8}-\frac{9\sqrt{3} }{16}[/tex]
Area of the shaded region,
[tex]A = A_1-A_2[/tex]
[tex]A = \frac{\pi }{2} - \frac{9\sqrt{3} }{16} - \frac{3\pi }{8}+\frac{9\sqrt{3} }{16}[/tex]
[tex]A = \frac{\pi }{8}[/tex]
This is the area of the shaded region in the first and the second quadrant. We see that by symmetry, the area of the shaded region in the first and the second quadrant is equal to the area of the shaded region in the third and the fourth quadrant.
So, the total area is 2 ×[tex]\frac{\pi}{8}[/tex] = [tex]\frac{\pi}{4}[/tex]
Hence, the region inside cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ) is equal to [tex]\frac{\pi}{4}[/tex]
Learn more about Area of the circle at:
https://brainly.com/question/28642423
#SPJ4
Match each rational expression to its simplest form.
2m²
2(m-2)
m².. 2m.t.d
1
m²-3m +2
m
926
06
M
774
m²-m-2
m²
The simplification of rational expressions can be achieved by using the Greatest Common Factor (GCF).
How do you write a rational expression in simplest form?Take the common terms in the numerator and denominator and remove them from the expression to make it simpler.
The simplification of rational expressions can be achieved by using the Greatest Common Factor (GCF).Similar to fractions with variables in the denominators, rational expressions appear like them (and often numerators too).
For instance, the expression x 2 x + 3 is a rational expression: x squared, divided by x, plus 3, end fraction.
1)2m^2-4m)/2(m-2)
=[2m(m-2m)]/2(m-2)
= 2m/2
=m
2)m^2-2m+1/m-1
= (m-1)^2/(m-1)
=(m-1)(m-1)/(m-1)
=(m-1)
3)m^2-3m+2/m^2-m
=m^2-m-2m+2/m(m-1)
=m(m-1)-2(m-1)/m(m-1)
= (m-1)(m-2)/m(m-1)
=(m-2)/m
To learn more about rational expression refer
https://brainly.com/question/10242441
#SPJ1
How do you this help please
Answer:
Step-by-step explanation:
The height of her pear tree is 20 inches
First subtract 46 from 26 to get 20. So 20+26=46inches
x=20
Step-by-step explanation:
you know how to transform an equation ?
you need to apply the same operating to both sides of the equation. always. otherwise the equality relation is destroyed.
x + 26 = 46
to get to "x = ..." the "+ 26" is in the way.
clearly we need to subtract 26. but we need to do it on both sides.
x + 26 - 26 = 46 - 26
x = 20
that simply means the last tree is 20 in.
it is 26 in shorter than 46 in (fig tree).
that's all there is to it.
select the correct answer. it is estimated that approximately one-half of all aluminum cans will be recycled each year. if a soft drink company produces 350,000 cans one year, how many cans are still in use after 4 years of recycling and re-using, using this function? nt
After 4 years of recycling and re-using, approximately average one-half of the original 350,000 cans produced by the soft drink company would still be in use.
1. 350,000 cans produced in 1 year
2. 50% of cans recycled each year
3. 50% of 350,000 cans = 175,000 cans
4. After 4 years, 175,000 cans still in use.
Each year, it is predicted that about half of all aluminum cans will be recycled. This means that if a soft drink company produces 350,000 cans one year, then after four years, approximately one-half of the original cans produced would still be in use. This can be calculated by taking the initial number of cans produced (350,000), multiplying it by fifty percent (50%), and then multiplying that number by four (4). The final result is that after four years of recycling and re-using, approximately 175,000 cans would still be in use.
Learn more about average here
https://brainly.com/question/24057012
#SPJ4
Gertrude takes out a $5,500 subsidized stafford loan, which must be paid back in ten years. gertrude will graduate four years after taking out the loan. if the loan has an interest rate of 6.8%, compounded monthly, and gertrude makes monthly payments, how much interest will she pay by the time the loan is repaid? round all dollar values to the nearest cent. a. $4,462.40 b. $1,213.28 c. $1,713.69 d. $2,094.80 please select the best answer from the choices provided a b c d
$2094.28 interest will she pay by the time the loan is repaid.
What is compounded monthly?
Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.
As we know the formula of per month installments
[tex]E.M.I = \frac{P*r*(1+r)^n}{(1+r)^n^-^1}[/tex]
By putting the value of P (loan applied for)=$5500
r (Monthly rate of interest) [tex]= \frac{6.8}{12*100}[/tex]
n = number of monthly installments = 10 × 12 = 120
[tex]E.M.I = \frac{5500*(\frac{6.8}{12*100} )(1+\frac{6.8}{1200} )^1^2^0}{(1+\frac{6.8}{1200} )^1^2^0-1}\\ E.M.I= \frac{5500*0.00567*1.971}{1.971-1}\\ E.M.I = \frac{61.461}{0.971} \\E.M.I = 63.29[/tex]
E.M.I.=$63.29
Total Installments of loan =120
Therefore total amount paid against loan = $63.39 × 120 = 7594.28
So interest paid = 7594.28 - 5500= $2094.28
Hence, $2094.28 interest will she pay by the time the loan is repaid.
To know more about compounded monthly, click on the link
https://brainly.com/question/1397205
#SPJ4
