Answer: her interest in 3 years is $45
Step-by-step explanation:
For simple interest, the principal is not compounded. The interest is only on the original capital. The formula for simple interest is expressed as
I = PRT/100
Where
I represents the interest on the principal
P represents the initial amount
R represents the interest rate.
T represents the time in years.
From the information given
P = $300
R = 5%
T = 3 years
I = 300×5×3)/100
I = 4500/100 = 45
It is 4 o’clock. What is the measure of the angle formed between the hour hand and the minute hand?
If it's 4 o'clock, the hour hand will be on the 4 and the minute hand will be on the 12.
This takes 4 partitions/pieces of the clock, and there are 12 different partitions. That's 4/12, or 1/3 of the entire clock.
The total clock is a 360 degree angle.
360 * (1/3) = 120
1/3 of 360 degrees is 120 degrees.
Since the angle between the minute and hour hand takes up 1/3 of the clock, the angle is 120 degrees.
Let me know if you need any clarifications, thanks!
30% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?
Answer:
30% companies will offer both wireless internet and free on-board snacks.
Step-by-step explanation:
Percentage of major companies who equip their planes with wireless internet access = 30%
Percentage of major airlines who offer passengers free on-board snacks = 70%
Therefore, from the given information, the maximum percentage of the companies who offer both wireless internet facility as well as on-board snacks may be 30% only.
Bryce has heard that gas appliances are cheaper to use and can lower utility costs. He is interested in purchasing a new gas stove for his kitchen to replace his electric stove. Assuming that the stove gets used one hour per day, use the following chart to determine how much Bryce will save each year in utility costs by purchasing the gas appliance.
Answer:
C. $29.20
Step-by-step explanation:
The difference between using an electric stove and a gas stove everyday is 13 cents - 5 cents= 8 cents.
Saving 8 cents everyday.
Therefore for a year, Bryce will save 8 cents × 365days = 2920 cents
Then 2920 cents = $(2920÷100)
=$29.20
Answer:
C. $29.20
Step-by-step explanation:
Find the indicated term of the geometric sequence. a8 for 4, -12, 36, ...
Answer:
76
Step-by-step explanation:
Answer:
The 8th term of geometric sequence is -8748
ie., [tex]a_{8}=-8748[/tex]
Step-by-step explanation:
Given geometric sequence is 4,-12,36,...
Geometric sequence can be written as
[tex]a_{1},a_{2},a_{3},..,[/tex]
[tex]a_{1}=4=a[/tex]
[tex]a_{2}=-12=ar[/tex]
[tex]a_{3}=36=ar^2[/tex]
and so on.
common ratio is [tex]r=\frac{a_{2}}{a_{1}}[/tex]
[tex]r=\frac{-12}{4}[/tex]
[tex]r=-3[/tex]
[tex]r=\frac{a_{3}}{a_{2}}[/tex]
[tex]r=\frac{36}{-12}[/tex]
[tex]r=-3[/tex]
Therefore [tex]r=-3[/tex]
Geometric sequence of nth term is [tex]a_{n}=ar^{n-1}[/tex]
To find the 8th term:
[tex]a_{8}=ar^{8-1}[/tex]
[tex]a_{8}=ar^{7}[/tex]
here a=4 and r=-3
[tex]a_{8}=ar^{7}[/tex]
[tex]=4\times (-3)^7[/tex]
[tex]=4\times (-2187) [/tex]
[tex]=-8748[/tex]
[tex]a_{8}=-8748[/tex]
Therefore the 8th term of geometric sequence is -8748
4n-12=12-4n(If there is no solution, type in "no solution") n= Answer
Answer:
n = 3
Step-by-step explanation:
What is the simple interest earned on $3,672 at 4.5% for three years?
$459.72
$594.86
$518.36
$495.72
Answer: interest at the end of 3 years is $495.72
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 3 years
P = $3,672
R = 4.5%
Therefore
I = (3672 × 4.5 × 3)/100
I = 49572/100
I = 495.72
What is the area of a right triangle with the given vertices? A(3,1) , B(5,4) , C(6,−1)
Answer:
[tex]\frac{13}{2}[/tex] square units
Step-by-step explanation:
We are given that vertices of a right triangle are A(3,1) ,B(5,4) and C(6,-1).
We have to find the area of triangle.
We know that area of triangle=[tex]\frac{1}{2}\mid (x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))\mid [/tex]
[tex]x_1=3,x_2=5,x_3=6[/tex]
[tex]y_1=1,y_2=4,y_3=-1[/tex]
Substitute the values in the formula then we get
Area of right triangle =[tex]\frac{1}{2}\mid (3(4+1)+5(-1-1)+6(1-4))\mid [/tex]
Area of right triangle =[tex]\frac{1}{2}\mid (15-10-18)\mid [/tex]
Area of right triangle =[tex]\frac{1}{2}\times 13=\frac{13}{2}[/tex] square units
5+3r=5r-19(if there is no solution,type in ''no solution'')r= Answer
Answer: 12 = r
Step-by-step explanation: When we have this kind of a setup, we want to put our variables together on one side of the equation and our numbers together on the other side of the equation.
First, let's put our variables on the right side by subtracting 3r from both sides of the equation. That gives us 5 = 2r - 19.
Now we can move our numbers to the left by adding 19 to both sides of the equation and we get 24 = 2r.
Divide both sides by 2 and 12 = r
Note:
Don't just do this problem in your head. It's extremely important to develop the habit of putting all your steps down on paper or digitally. It will really pay off for you down the line.
Let R and S be partial orders on a nonempty set A prove that T = R intersection S is also a partial order on A.
Answer:
See proof below
Step-by-step explanation:
We denote (x,y)∈R as xRy, and we also use the similar notation xSy for (x,y)∈S. Remember that R and S are reflexive, antisymmetric and transitive relations (the definition of partial order).
To prove that R∩S⊆A is a partial order, we will prove that R∩S is reflexive, antisymmetric and transitive.
Reflexive: Let a∈A. R is reflexive thus aRa. S is also reflexive, then aSa. Then (a,a)∈R and (a,a)∈S which implies that (a,a)∈R∩S, that is, a(R∩S)a for all a∈A.Antisymmetric: Let a,b∈A and suppose that a(R∩S)b and b(R∩S)a hold. In particular, aRb and bRa. Since R is antisymmetric, a=b.Transitive: Let a,b,c∈A and suppose that a(R∩S)b and b(R∩S)c hold. Then aRb, bRc, aSb and bSc are true. The first two statements imply by the transitivity of R that aRc. Similarly, from the last two we have that aSc. Thus a(R∩S)c as we wanted to prove.The posterior lobe of the pituitary gland is NOT a true endocrine gland because ________. A it is unable to function as an endocrine tissue because it is actually part of the neural system due to its location B it is strictly a part of the neural system and has little or nothing to do with hormonal release C embryonically it was an endocrine tissue, but in the adult human it is no longer functional
Isn't this Anatomy and Physiology?
If 10 50-74 is written as an integer in base decimal notation, what is the sum of the digits in that integer?
Answer:
The required sum of the digits in that integer is 440.
Step-by-step explanation:
Consider the provided expression.
[tex]10^{50}-74[/tex]
We need to find the sum of the digits in that integer.
For [tex]10^2[/tex] = 100 (3 digits)
Now subtract 74 from it.
100-74=26
For [tex]10^3[/tex] = 1000 (4 digits)
Now subtract 74 from it.
1000-74=926
For [tex]10^4[/tex] = 100000 (5 digits)
Now subtract 74 from it.
10000-74=9926
Similarly,
[tex]10^50[/tex] = 1000....[51 digits]
Now subtract 74 from it.
[tex]10^50-74=99999....26[/tex]
The number of 9 after subtracting 74 is 3 less than the number of digits.
Therefore, the number of 9 after subtracting 74 from [tex]10^50[/tex] must be: 51-3=48
The sum of the digits is = 9×48 + 2 + 6 = 432 + 2 + 6 = 440.
Hence, the required sum of the digits in that integer is 440.
Final answer:
The sum of the digits in the integer 10⁵⁴ - 74 is 476, which is calculated by adding the contribution of the 52 nines and the digits in '26'.
Explanation:
To determine the sum of the digits of the integer written in base decimal notation for 10⁵⁴ - 74, we first need to understand what 10⁵⁴ represents. This value is a 1 followed by 54 zeros in decimal form. When we subtract 74 from this value, we alter only the last two non-zero digits. This results in a number that looks like 999...9926, where the '9's continue until the last two digits, which are '26'.
To find the sum of the digits, we simply add up the '9's and '26'. Since there are 52 nines (54 digits minus the last two which are '26'), and each nine contributes nine to the sum, we can calculate this part of the sum as 52 multiplied by 9. Then we also add the sum of the digits in '26'.
Therefore, the sum of digits in 10⁵⁴ - 74 is (52 × 9) + 2 + 6 = 468 + 8 = 476.
For the given pentagon ABCDE the diagonal
EC
∥
AB
. I, G, F, H are midpoints of
BC
,
CD
,
DE
,
EA
respectively. The length of
FG
is 50% more than the length of AB. Find the area of the quadrilateral HFGI, if A△ADB = 16sq. in.
Answer:
28 in²
Step-by-step explanation:
Without constraining the problem unduly, we can make the assumption that AB = 2 inches. Then the altitude from AB to D is h in ...
Area ABD = (1/2)(AB)h
16 in² = (1/2)(2 in)(h)
16 in = h . . . . . . . . . . . divide by 1 in
__
The altitude D to AB is the sum of the heights from D to EC (h1) and from AB to EC (h2). That is ...
16 = h1 + h2
We also know that the height from FG to EC is 1/2 the height from D to EC, hence (1/2)h1. Likewise, the height to midsegment HI from either EC or AB is half the height from EC to AB, hence (1/2)h2. This means the total height of the quadrilateral HFGI is (1/2)h1 + (1/2)h2 = (1/2)(h1 +h2) = 8.
__
We are given that FG is 50% longer than AB, so its length will be ...
FG = AB×(1 + .5) = (2 in)(1.5) = 3 in
Since FG is the mid-segment of triangle CDE, base EC is twice its length, or ...
EC = 2×FG = 2(3 in) = 6 in
__
Mid-segment HI is the average of the base lengths of trapezoid ABCE, so is ...
HI = (EC +AB)/2 = (6 + 2)/2 = 4
__
Now, we know the height and base lengths of trapezoid HFGI, so we can find its area as ...
A = (1/2)(b1 +b2)h = (1/2)(3 in + 4 in)(8 in) = 28 in²
The area of quadrilateral HFGI is 28 square inches.
_____
You can make any assumption you like about the dimension of AB, and the rest of the dimensions scale accordingly. The result is still the same.
Solve for x. The triangles in each pair are similar.
Answer:
Step-by-step explanation:
Triangle TML is similar to triangle TVU. Side TV measures 36 and side TM meaures 9; side TV is 4 times longer than side TM. Same with sides VU and ML. VU is 4 times longer than ML. That means that side TU is 4 times longer than side TL. Side TL measures x - 4; side TU measures 24 + x - 4 which is x + 20. That means that x + 20 = 4(x - 4) and x + 20 = 4x - 16 and
3x = 36 so
x = 12
Ray hired sun and peter to help him move .Sun charged a $20 flat fee and $30 per hour.Peter charged $25 per hour. Write an expression for ray's total cost if sun and peter each work h hours.
Answer:
Step-by-step explanation:
Ray hired sun and peter to help him move.
Let h represent the number of hours that each of them worked.
Let y represent Ray's total cost for hiring Sun and Peter for h hours.
Sun charged a $20 flat fee and $30 per hour. The total amount that Sun charges would be
20 + 30h
Peter charged $25 per hour. The total amount that Peter charges would be
25h
An expression for Ray's total cost if Sun and Peter each work h hours would be
y = 20 + 30h + 25h
y = 20 + 55h
Answer:
[20+(30+25)]h or (20+55)h
Step-by-step explanation:
20 will not be changed.
Total cost per hour is 55
add $20
Hope this helps
A random sample of 384 people in a mid-sized city (city one) revealed 112 individuals who worked at more than one job. A second random sample of 432 workers from another mid-sized city (city two) found 91 people who work at more than one job. Find a 99% confidence interval for the difference between the proportions of workers in the two cities who work at more than one job.Select one:a. (0.003, 0.159)b. (0.021, 0.141)c. (-0.159, 0.004)d. (0.031, 0.131)e. Sample sizes aren't large enough to justify using z-procedures
Answer:
99% confidence interval is:
(0.00278 < P1 - P2< 0.15921)
Step-by-step explanation:
For calculating a confidence intervale for the difference between the proportions of workers in the two cities, we calculate the following:
[tex][(p_{1} - p_{2}) \pm z_{\alpha/2} \sqrt{\frac{p_{1}(1-p_{1})}{n_{1}} + \frac{p_{2}(1-p_{2})}{n_{2}} }[/tex]
Where [tex]p_{1}[/tex] : proportion sample of individuals who worked
at more than one job in the city one
[tex]n_{1}[/tex]: Number of respondents in the city one
[tex]p_{1}[/tex] : proportion sample of individuals who worked
at more than one job in the city two
[tex]n_{1}[/tex]: Number of respondents in the city two
Then
α = 0.01 and α/2 = 0.005
and [tex]z_{\alpha/2} = 2.575[/tex]
[tex]p_{1} = \frac{112}{384} = 0.2916[/tex]
[tex]p_{2} = \frac{91}{432} = 0.2106[/tex]
[tex]n_{1}= 384[/tex] and [tex]n_{2}= 432[/tex]
The confidence interval is:
[tex][(0.2916 - 0.2106) \pm 2.575 \sqrt{\frac{0.2916(1-0.2916)}{384} + \frac{0.2106(1-0.2106)}{432} }[/tex]
(0.00278 < P1 - P2< 0.15921)
There are three grades in the school. One grade has 1/3 of the students, one grade has 1/4 of the students. What fraction of students is in the remaining grade?
Answer:
Step-by-step explanation:
Let x represent the total number of stdents that has all grades in the school.
There are three grades in the school. One grade has 1/3 of the students, this means that number of students that belongs tho this grade is 1/3 × x = x/3
One grade has 1/4 of the students, this means that number of students that belongs to this grade is 1/4 × x = x/4
Total number of students in both grades would be x/3 +/x/4 = 7x/12
The number of students in the remaining grade would be
x - 7x/12 = 5x/12
fraction of students in the remaining grade would be
(5x/12)/x = 5/12
Answer:
2/4
Step-by-step explanation:
i dont want to think
Graph the linear equation.
x = - 9
help in any way u can please
This is a vertical line that goes through all points with an x-coordinate of -9.
To graph it, I can give you a couple of points this line goes through so you can draw it more easily.
Points that are on line: (-9,0) and (-9,1)
Find the LCM of 2, 10 and 6
Answer:
30
Plz click the thxs button or mark brainliest!
Yours Truly.
Answer:
30
Step-by-step explanation:
2 2 10 6
3 1 5 3
5 1 5 1
1 1 1
2*3*5 30
Which graph represents the solution set of the system of inequalities? How do you know?
{x+y<1 2y≥x−4
Answer:
Step-by-step explanation:
It is the fourth one
Hope this helps
Mark me as brainiest
What is the value of \dfrac{d}{dx}\left(\dfrac{2x+3}{3x^2-4}\right) dx d ( 3x 2 −4 2x+3 )start fraction, d, divided by, d, x, end fraction, (, start fraction, 2, x, plus, 3, divided by, 3, x, squared, minus, 4, end fraction, )at x=-1x=−1x, equals, minus, 1 ?
The question asks for the derivative of the function (2x+3)/(3x^2-4) at x=-1. Using the quotient rule, we find the derivative and then substitute x=-1 into it to get the required value.
Explanation:The question aims to find the derivative of the function f(x) = (2x + 3) / (3x^2 - 4) and then find its value at x = -1. To do this, we need to use the Quotient Rule which is (f(x)/g(x))' = (g(x)*f'(x) - f(x)*g'(x))/(g(x))^2.
Here f(x) = 2x + 3 and g(x) = 3x^2 - 4. So, the derivative of the function becomes f'(x) = ( (3x^2 - 4)*2 - (2x + 3)*6x ) / (3x^2 - 4)^2 which simplifies to (6x^2 - 8 - 12x^2 - 18x) / ( 9x^4 - 24x^2 + 16). Now, substitute x = -1 into f'(x) to get the desired value.
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Ben drinks tea at an incredible rate. He drinks 3\dfrac123 2 1 3, start fraction, 1, divided by, 2, end fraction liters of tea every \dfrac23 3 2 start fraction, 2, divided by, 3, end fraction of an hour. Ben drinks tea at a constant rate.
Answer:
[tex]5\frac{1}{4}[/tex] liters per hour.
Step-by-step explanation:
Consider the question: Ben drinks tea at an incredible rate. He drinks [tex]3\frac{1}{2}[/tex] liters of tea every [tex]\frac{2}{3}[/tex] of an hour. Ben drinks tea at a constant rate. How many liters of tea does he drink in one hour?
To find the liters of tea drank by Ben in one hour, we will divide amount of tea drank by time taken as:
[tex]3\frac{1}{2}\text{Liters}\div \frac{2}{3}\text{ hour}[/tex]
Convert mixed fraction into improper fraction:
[tex]\frac{7}{2}\text{Liters}\div \frac{2}{3}\text{ hour}[/tex]
Convert division problem into multiplication problem by flipping the 2nd fraction:
[tex]\frac{7}{2}\text{ Liters}\times \frac{3}{2}\text{ hour}[/tex]
[tex]\frac{21}{4}\frac{\text{ Liters}}{\text{ hour}}[/tex]
[tex]5\frac{1}{4}\frac{\text{ Liters}}{\text{ hour}}[/tex]
Therefore, Ben drinks [tex]5\frac{1}{4}[/tex] liters per hour.
Answer:
He drinks 21/4, or 5 1/4, liters of tea in 1 hour
Step-by-step explanation:
The following question is missing: How much does he drink in one hour?
Given that he drinks 3 1/2 (= 7/2) liters of tea every 2/3 of an hour, and we want to know how much he drink in 1 hour, then the following proportion must be satisfied:
7/2 liters / x liters = 2/3 hour / 1 hour
x = (7/2)/(2/3) = 7/2 * 3/2
x = 21/4 = 5 1/4 liters
PLEASE HELP IM TERRIBLE AT MATH!!!! WILL GIVE BRAINLIEST!!!
Divide 3x^2 + 4x − 4 by x + 2.
A. x − 2
B. x + 6
C. 3x − 2
D. 3x + 6
Answer:
It is C
Step-by-step explanation:
(3x-2)(x+2)
3x(x)+3x(2)-2(x)-2(2)
3x^2+6x-2x-4
3x^2+4x-4 <----------
(Im bad at explaining but that is right trust me :P)
Please Help me!!!!!! Thank you so much
Answer:x1 = 1, x2 = - 1, x3 = 3
Step-by-step explanation:
x1 + 2x2 - x3 = - 4 - - - - - - - - - -1
x1 + 2x2 + x3 = 2 - - - - - - - - - -2
- x1 - x2 + 2x3 = 6 - - - - - - - - - -3
Let us eliminate x1 and x2. Subtracting equation 2 from equation 1, it becomes
-2x3 = - 6
x3 = -6/-2
x3 = 3
Adding equation 2 to equation 3, it becomes
x2 + 3x3 = 8 - - - - - - - - - - - 4
Substituting x3 = 3 into equation 4, it becomes
x2 + 3 × 3 = 8
x2 + 9 = 8
x2 = 8 - 9 = -1
Substituting x2 = -1 and x3 = 3 into equation 2, it becomes
x1 + 2 × -1 + 3 = 2
x1 - 2 + 3 = 2
x1 + 1 = 2
x1 = 2 - 1 = 1
Let us check by substituting x1 = 1, x2 = -1 and x3 = 3 into equation 1. It becomes
1 + 2 × - 1 - 3 = - 4
1 - 2 - 3 = - 4
-1 - 3 = - 4
-4 = - 4
The rate (in liters per minute) at which water drains from a tank is recorded at half-minute intervals. Use the average of the left- and right-endpoint approximations to estimate the total amount of water drained during the first 3 min. t (min) 0 0.5 1 1.5 2 2.5 3 r (l/min) 44 40 37 34 30 27 23
Answer:
100.75 liters
Step-by-step explanation:
Data provided in the question:
t (min) 0 0.5 1 1.5 2 2.5 3
r (l/min) 44 40 37 34 30 27 23
Now,
left endpoint approximation
= 0.5 × ( 44 + 40 + 37 + 34 + 30 + 27 )
= 0.5 × 212
= 106
Right endpoint approximation
= 0.5 × ( 40 + 37 + 34 + 30 + 27 + 23 )
= 0.5 × 191
= 95.5
Therefore,
the average of the left- and right-endpoint approximations
= [ 106 + 95.5 ] ÷ 2
= 100.75 liters
The total amount of water drained during the first 3 min is: 100.75 liters/min.
Total amount of waterLeft endpoint approximation
r = 1/2 ( 44 + 40 + 37 + 34 + 30 + 27 )
r= 1/2 × 212
r= 106 L/m
Right endpoint approximation
r= 1/2 × ( 40 + 37 + 34 + 30 + 27 + 23 )
r= 1/2 × 191
r= 95.5 L/min
Average of the left- and right-endpoint approximations
Average= [ 106 + 95.5 ] ÷ 2
Average=201.5÷2
Average= 100.75 liters/min
Inconclusion the total amount of water drained during the first 3 min is: 100.75 liters/min.
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Molly is making Strawberry infused water for each ounce of strawberry juice she uses three times as many ounces of water she wants to make a total of 64 ounces of strawberry infused water
Answer:
The Total of 16 ounces of Strawberry juice and 48 ounces of water is used for making 64 ounces of Strawberry infused water.
Step-by-step explanation:
Let the amount of Strawberry juice in ounces be 'j'
Let the amount of water in ounce be 'w'
Given:
For each ounce of strawberry juice she uses three times as many ounces of water.
It means that amount of water in ounce is 3 times of amount of strawberry juice in ounce.
framing the equation we get;
[tex]w=3j[/tex]
Now we need how many ounces of strawberry juice and how many ounces of water does she need to make 64 ounces of strawberry infused water.
We know that Total Strawberry infused water is equal to sum of amount of Strawberry juice in ounces and the amount of water in ounces
Framing in equation form we get;
[tex]j+w=64[/tex]
But we know [tex]w=3j[/tex]
hence,
[tex]j+3j= 64\\\\4j=64\\\\j=\frac{64}{4} = 16 \ ounces[/tex]
Hence amount of Strawberry juice = 16 ounces
Amount of water = [tex]3j = 3\times16 =48 \ ounces[/tex]
Hence The Total of 16 ounces of Strawberry juice and 48 ounces of water is used for making 64 ounces of Strawberry infused water.
Laneka owns a cake shop.She is currently preparing cakes for two anniversary parties. The first cake has 3 small tiers and 1 medium tier and will serve a total of 100 guests. The second one has 3 small tiers and 2 medium tiers and will serve a total of 140 guests represent the situation with a system of equations
Answer:
The system of equations are [tex]\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.[/tex].
Step-by-step explanation:
Let 's' represents the number of guest small tier can serve.
Let 'm' represents the number of guest medium tier can serve.
Now Given:
For First cake:
Number of small tiers = 3
Number of medium tier = 1
Total serving guest = 100
Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.
Framing in equation form we get;
[tex]3s+m=100[/tex]
For Second cake:
Number of small tiers = 3
Number of medium tier = 2
Total serving guest = 140
Now Total serving guest is equal to sum of Number of small tiers multiplied by the number of guest small tier can serve and Number of medium tiers multiplied by the number of guest medium tier can serve.
Framing in equation form we get;
[tex]3s+2m=140[/tex]
Hence The system of equations are [tex]\left \{ {{3s+m=100} \atop {3s+2m=140}} \right.[/tex].
Which system of linear inequalities is represented by the graph?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]x+5y\geq 5[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the solid line [tex]x+5y=5[/tex]
The slope of the solid line is negative
The y-intercept of the solid line is (0,1)
The x-intercept of the solid line is (5,0)
[tex]y\leq 2x+4[/tex] ----> inequality B
The solution of the inequality B is the shaded area below the solid line [tex]y= 2x+4[/tex]
The slope of the solid line is positive
The y-intercept of the solid line is (0,4)
The x-intercept of the solid line is (-2,0)
therefore
The graph in the attached figure
The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians. What is the area of the shaded sector? 36Pi units squared 72Pi units squared 144Pi units squared 324Pi units squared
The question is missing the figure. So, it is attached below.
Answer:
Area of the shaded sector is 144π units squared.
Step-by-step explanation:
Given:
Central angle of the sector is, [tex]\theta=\frac{8\pi}{9}\ rad[/tex]
Radius of the circle is, [tex]R=18\ units[/tex]
We know that, area of a sector of a circle of radius 'R' and central angle [tex]\theta[/tex] is given as:
[tex]A=\frac{1}{2}R^2\theta[/tex]
Plug in [tex]\theta=\frac{8\pi}{9},R=18[/tex]. This gives,
[tex]A=\frac{1}{2}\times (18)^2\times \frac{8\pi}{9}\\\\A=(\frac{324\times 4}{9})\pi\\\\A=(36\times 4)\pi\\\\A=144\pi\ units^2[/tex]
Therefore, the area of the shaded sector is 144π units squared.
Answer: 144Pi units squared
Step-by-step explanation:
Suppose the size of a population of mustard plants is 6,000. According to genetic drift theory, what is the probability that a newly-arisen mutation will become fixed in this population?
Answer:
1/12,000
Step-by-step explanation:
Data provided in the question:
Size of a population of mustard plants = 6,000
Now,
According to genetic drift theory
The probability that a newly-arisen mutation will become fixed is given using the formula
⇒ 1 ÷ [ 2 × Size of a population of mustard plants ]
⇒ 1 ÷ [ 2 ×6,000 ]
⇒ [ 1 ÷ 12,000 ]
Hence,
probability that a newly-arisen mutation will become fixed in this population is 1/12,000
A rug has an area of x2+x−20 square feet. Which expression represents the dimensions of the rug? A (x+4)(x−5) B (x+2)(x−10) C (x−4)(x+5) D (x−2)(x+10)
Answer: the correct option is
C (x−4)(x+5)
Step-by-step explanation:
The area of the rug in square feet is expressed as
x^2+x−20
The given equation is a quadratic equation and the roots of the equation represents the dimensions of the rug. To simplify the equation, we would apply the factorization method.
We will get two numbers such that, their difference will be x and their sum will be -20x^2. The numbers are 5x and 4x. Therefore
x^2+ 5x - 4x −20 = 0
x(x + 5) - 4(x +5)
The roots are (x - 4)(x + 5)
The area of the rug is represented by the quadratic expression[tex]x^2 + x - 20,[/tex] which factors to (x + 4)(x - 5). This matches option A, verifying that these are the dimensions of the rug.
The student has a quadratic expression representing the area of a rug, which is[tex]x^2 + x - 20[/tex] square feet. To find the dimensions of the rug, we need to factor this expression. Factoring quadratic expressions involves finding two binomials that multiply to give the original quadratic expression. In this case, the correct factorization is (x + 4)(x - 5).
We can verify this by using the FOIL method (First, Outer, Inner, Last) to expand the binomials: (x + 4)(x - 5) = [tex]x^2 - 5x + 4x - 20 = x^2 - x - 20[/tex], which matches our original expression.
Thus, option A is the correct choice.