Write and solve an inequality that means a number plus six is less than or equal to twenty-four.
Answer:
Inequality: x + 6 ≤ 24
Solution: x ≤ 18
Step-by-step explanation:
Plus: "+" → to add something to something else
Less than or equal to: "≤" → the expression on the left side of the inequality sign is smaller than the expression on the right side of the sign.
Let x be the unknown number.
A number plus 6 is less than or equal to twenty-four:
x + 6 ≤ 24
To solve the found inequality, subtract 6 from both sides:
⇒ x + 6 - 6 ≤ 24 - 6
⇒ x ≤ 18
Therefore, the solution to the inequality is x ≤ 18. The unknown number x can be any real number equal to or less than 18.
No be n
n+6≤24Solve
n≤24-6n≤18Solution set
(-oo,18]
(1 point)Let S be the part of the plane 2x+2y+z= 1 which lies in the first octant, oriented upward. Find the flux of the vector field
F = 2i+2j + 2k across the surface S.
The flux is 9.
What is Flux?Flux is the presence of a force field in a specified physical medium, or the flow of energy through a surface.
Given:
2x+2y+z= 1
F = 2i+2j + 2k
Now,
r = xi + yj + z( 1-2x-2y) K
dr/dx= i - 2k
dr/dy = j-2k
dr/dx* dr/dy
= ( i - 2k) * (j-2k)
= 2i + 2j + k
F(x)= 2i+2j + 2k
F(x). da = 4 +4 +2 = 10 dxdy
Hence, flux
= [tex]\int\limits^1_0 {\int\limits^{1-2y}_0 {10 } \, dx dy } \,[/tex]
= [tex]\int\limits^1_0[/tex] 10(1-2y) dx
= [tex]\int\limits^1_0[/tex] 10-2y
= 10(1) - (1)²
=9
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The plane has intercepts (1/2, 0, 0), (0, 1/2, 0), and (0, 0, 1). Parameterize [tex]S[/tex] by the vector function
[tex]\vec s(u,v) = \dfrac{(1-u)(1-v)}2 \, \vec\imath + \dfrac{u(1-v)}2 \, \vec\jmath + v \,\vec k[/tex]
with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. (More explicitly, we have the parameterization
[tex]\vec s(u,v) = (1-v)((1-u) p_1 + u p_2) + v p_3[/tex]
where [tex]p_i[/tex] denote the given points.)
The normal vector to [tex]S[/tex] is
[tex]\vec n = \dfrac{\partial\vec s}{\partial u} \times \dfrac{\partial\vec s}{\partial v} = \dfrac{1-v}2\,\vec\imath + \dfrac{1-v}2\,\vec\jmath + \dfrac{1-v}4\,\vec k[/tex]
Then the flux of [tex]\vec F = 2\,\vec\imath+2\,\vec\jmath+2\,\vec k[/tex] across [tex]S[/tex] is given by the surface integral,
[tex]\displaystyle \iint_S \vec F \cdot d\vec\sigma = \iint_S \vec F \cdot \vec n \, dA[/tex]
[tex]\displaystyle = \int_0^1 \int_0^1 \left(2\,\vec\imath+2\,\vec\jmath+2\,\vec k) \cdot \left(\frac{1-v}2\,\vec\imath + \frac{1-v}2\,\vec\jmath + \frac{1-v}4\,\vec k\right) \, du \, dv[/tex]
[tex]\displaystyle = \frac52 \int_0^1 \int_0^1 (1-v) \, du \, dv[/tex]
[tex]\displaystyle = \frac52 \int_0^1 (1-v) \, dv = \boxed{\frac54}[/tex]
||
Writing ratios for real-world situations
There are 3 red marbles and 8 blue marbles in a bag.
Answer:
3:11 or 8:11
Step-by-step explanation:
I think your missing some imformation! I'm guessing the ratio of picking a red marble is 3:8 while a blue marble is 8:3
Based on local population projections for 2010, school district 31 will lose 5 teaching positions, district 222 will lose 5 teachers, and district 225 will lose 2. Write a
signed number that represents the total number of teachers that these three school districts are projected to lose.
What is the signed number that represents the total number of positions that these three districts are projected to lose?
Answer:
2+3+4 = 9
Add the three numbers of the three school districts that project to lose.
julie ran a race 2 minutes faster than teri did. if teri ran the race in 28 minutes, what equation would be used to find the number of minutes teri took to run the race
Th equation that can be used to find the umber of minutes Teri ran is m + 2 = 28 minutes.
How many minutes did it take Teri to run the race?Addition is a mathematical operation that is used to determine the sum of two or more numbers.
The total minutes run by Julie = minutes ran by Teri + 2
28 = m + 2
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the probability that Luis will pass his test is 0.82. find the probability that he will fail his statistic test
The probability of failure for Luis will be 0.18.
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability of passing is = 0.82
We know that the maximum probability of happening any event is 1 or 100 per cent if the probability of passing of the person is 0.82 then the probability of failure will be calculated as:-
Probability of failing = 1 - probability of passing
Probability of failing = 1 - 0.82
Probability of failing = 0.18
Therefore the probability of failure for Luis will be 0.18.
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10 problems for 50 points
Answer:
1. F
2. F
3. T
4. F
5. F
6. T
7. T
8. F
9. F
10. T
Step-by-step explanation:
1. For the rays to be opposite, they need to have the same starting point and go in different directions. Rays AP and BP use Point A and Point B, respectively, for their starting points.
2. They do not lie on the same line.
3. Points A, B, C, D all lie in the same plane therefore making them coplanar.
4. Points X, Y do not lie in the same plane as A, B.
5. Point X does not lie in the same plane as C, D, B
6. A, P, B are all points on the same line therefore any two of them could be used to represent the same line.
7. PX and PY start at the same point and go in the opposite directions, defining them as opposite rays.
8. Plane AXY cannot be defined as point X and Y are not in a plane.
9. Lines AB and CD cannot both be in a different plane.
10. Both rays sum up to equal Line XY.
which expression is equivalent to...
Answer:
[tex]\frac{y^{12} }{5}[/tex]Step-by-step explanation:
1) Cancel [tex]x^5[/tex].
[tex]\frac{9y^{16} }{45y^4}[/tex]
2) Take out the constants.
[tex]\frac{9}{45} \times\frac{y^{16} }{y^4}[/tex]
3) Simplify [tex]\frac{9}{45}[/tex] to [tex]\frac{1}{5}[/tex].
[tex]\frac{1}{5} \times\frac{y^{16} }{y^4}[/tex]
4) Simplify.
[tex]\frac{y^{16} }{5y^4}[/tex]
5) Use Quotient Rule: Use Quotient Rule: [tex]\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}[/tex].
[tex]\frac{{y}^{16-4}}{5}[/tex]
6) Simplify [tex]16-4[/tex] to [tex]12[/tex].
[tex]\frac{y^{12} }{5}[/tex]
When we're solving minimum or maximum problems, are we h or the constant k? looking for the constant
In solving minimum and maximum problems, result we are looking for would be the constant, k.
What is being solved for in minimum and maximum problems?When looking for the minimum functional value, we are looking for the constant, k because it can be thought of as the absolute minimum value.
An open parabola would then have k as the maximum functional value which means that the constant k is the value being sought.
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Mountain Climbing Gym has a gym registration fee of $30 and then charges $55 per month for all access climbing.
Susie wanted to model what she has spent in total on the climbing gym at any given month in the future.
Fill in the blanks for the equation if C = total Cost and m = number of months.
Answer:
C=55m + 30
Step-by-step explanation:
You would multiply 55 by the number of months so you'd get 55m, and since 30 is a one time fee you would just add 30 to your monthly payment.
7
2
3
Mark this and return
f(x)
The functions f(x) and g(x) are graphed.
3
-6-5-4-3-2-1₁-
"AssessmentViewer(Ant
N
5
-2+
-3-
6
g(x)
7
2 3 4 5 6 x
8
Which represents where f(x) = g(x)?
Of(2)= g(2) and f(0) = g(0)
f(2)= g(0) and f(0) = g(4)
Of(2)= g(0) and f(4) = g(2)
Of(2)= g(4) and f(1) = g(1)
Save and Exit
Answer: Option 1
Step-by-step explanation:
The graphs intersect at x=0 and x=2, meaning f(2)=g(2) and f(0)=g(0).
The functions have the intersecting points at x = 2 and x = 0 and the relation is f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the first function be represented as f ( x )
Let the second function be represented as g ( x )
Now , the function f ( x ) is a parabolic function and g ( x ) is a linear function
And , the intersecting points of both f ( x ) and g ( x ) are
x = 2 and x = 0
So , both the functions f(x) and g(x) intersect at two points, one at x = 2 at the x-axis in the graph and one at y = 4 at y-axis of the graph
Therefore , f ( 0 ) = g ( 0 ) and f ( 2 ) = g ( 2 )
Hence , the functions are solved
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Can someone help me? I’ll give brainliest to whoever gets it right first
Answer:
the measure of line AD is 8
Step-by-step explanation:
lines AD and BC are equal, due to the markings on the lines
this means that if line BC is 8, than line AD is also 8
Factoring using GCF 15cd + 30c^2d^2
Answer:
15cd(1 + 2cd)
Step-by-step explanation:
greatest common factor is 15cd
[tex]15cd*1 + 15cd*2cd\\= 15cd(1 + 2cd)[/tex]
How many solutions exist for the given equation?
3(x - 2) = 22 -x
Answer:
One solution
Step-by-step explanation:
The equation can be rewrite as 3x - 6 = 22 - x
so we try to get all the x on one side so we add x and 6 to both sides so we get 4x = 28 then we divide by 4 both side and get x=7
Find the inverse of the function.
y=x+9
Answer: [tex]y=x-9[/tex]
Step-by-step explanation:
To find the inverse of a function you must first swap the places of x and y
[tex]x=y+9[/tex]
Now solve for y
Step 1: Flip the equation.
[tex]y+9=x[/tex]
Step 2: Subtract 9 from both sides.
[tex]y+9-9=x-9\\y=x-9[/tex]
help! asap! algebra 2
We can subtract the function that represents the cost in 2000 from the function that represents the cost in 1990.
Doing this gives us [tex](-20t^{2}+1000)-(-10t^{2}+1500)=\boxed{-10t^{2}-500}[/tex]
Fireside Shop offers chimney caps for $120 less trade discounts of 25/10. The same chimney cap is being offered at Builder's Supply for $111 less trade discounts of 25/5. What is the price difference between the two companies?
The difference in price between the two companies is $81-$79.56 = $1.44
Fire side Shop
Price of Chimney cap =$120
First Discount = 25% of(120)=$30
Price after 1st Discount = $120-$30=$90
Second Discount = 10% of 90=$9
Price after 2nd Discount = $90-$9=$81
Builders' Supply
Price of Chimney Cap= $111
First Discount= 25% of 111 = $27.75
Price after 1st Discount = $111 - $27.75 = $83.75
Second Discount = 5% of $83.75 = $ 4.1875
Price after 2nd Discount = $83.75 - $4.1875 = $79.5625 ≈ $79.56
Therefore,
a) Builders supply offers the lower price.
b) Difference in price = $81-$79.56 = $1.44
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The function G is defined by g (X) =X^2+2
Find g(4n)
Answer:
the answer is 4gn Puig IT in
When treated with an antibiotic, 92% of all the dolphins are cured of an ear infection. If 7 dolphins are treated, find the probability that exactly 4 are cured.
The probability is
(Round your answer to 4 decimal places.)
The probability that exactly 4 are cured from 7 dolphins is 0.0128
What is Probability ?Probability is the likeliness of an event to occur and it has a range of 0 to 1, where 0 means unlikely and 1 indicates certainty of the event to happen.
It is given that the 92% of all the dolphins are cured of an ear infection ,When treated with an antibiotic
If there are total dolphins given as 7
On the basis of given data
The dolphin that cannot be cured is given by
1 - p = 1 - (92/100) = 0.08 = 8/100
q = (8/100)
n= 7
r = 4
Therefore by Binomial Distribution
[tex]P = ^nC_r p^r q^{n-r}[/tex]
Putting the values
[tex]P = ^7C_4 (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]
[tex]P = \dfrac{7!}{4! \;3!} (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]
P = 0.0128
Therefore the probability is 0.0128.
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Find the perimeter of the following shape, given its curves are made from parts of circles.
Give your answers in terms of .
4cm
4cm
4cm
The diagram is not drawn to scale.
The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute.
A 2-row table with 10 columns. The first row is labeled time (minutes) with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4, 4.5. The second row is labeled temperature (degrees Celsius) with entries 75, 79, 83, 86, 89, 91, 93, 94, 95, 95.5.
According to the line of best fit, at what time will the temperature reach 100°C, the boiling point of water?
5
5.5
6
6.5.
According to the given table the line of best fit is
f(x)=4.54x+77.84
The term "line of best fit" describes a line that passes across a scatter plot of data points and best captures their connection. Statisticians often utilise regression analysis software or manual computations to arrive at the geometric equation for the line using the least squares approach. A straightforward linear regression study of two or more independent variables will provide a straight line.
Hence, as asked by the question we need to find the time at which the tempurature will become 100°C.
To find that let us put f(x)=100 and find out the value of x for which it is satisfied.
4.54x+77.84=100
⇒[tex]x=\frac{100-77.84}{4.54}=4.88[/tex]
⇒x≈5
Therefore the time at which the tempurature is 100°C is 5 minutes.
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Select the correct answer from each drop-down menu. Consider this system of equations: (equation A) (equation B) The solution for the system of equations is .
The solution for the system of equations is: (99/13, 150/13)
Given the two expression 2/3x+3/5y=12 and 5/2y-3x=6
We have to find solution of two given expression.
To find the value of x, we have to eliminate y by making y the subject of formula in any of the equations.
Multiply equation A by 5/3 t.o get,
5/3(2/3x) + 5/3(3/5y) = 5/3(12)
10/9x + y = 20
y = 20 - 10/9x
substituting for y into equation b, we have:
5/2(20 - 10/9x) - 3x = 6
50 - 25/9x - 3x = 6
52/9x = 44
52x = 396
The expression that gives the value of x is: 52x = 396
Hence, x = 396/52 = 99/13
y = 20 - 10/9(99/13) = 20 - 110/13 = 150/13
Hence The solution for the system of equations is: (99/13, 150/13)
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100 adults were asked how they keep fit.
Each adult goes to the gym, runs or cycles.
45 of these adults are female.
30 of the 52 adults who go to the gym are female.
35 adults run.
9 males cycle.
One of the females is chosen at random.
Write down the probability that she runs.
The probability that a female chosen runs = 0.24
How to find the probability?We are given;
Number of adults surveyed = 100
Total number of females = 45
Total Number of Males = 55
Number of female adults that go to gym = 30
Number of adults that run = 35
Number of males that cycle = 9
Thus;
From the probability table attached, we can say that;
Number of females that can run = 11
Probability that she runs = 11/45
Probability that she runs = 0.24
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Two buses leave a station at the same time and travel in opposite directions. One bus travels12m/hrslower than the other. If the two buses are 765 miles apart after 6 hours, what is the rate of each bus?
distance = speed * time
the first bus speed = x
second bus = x - 12
the sum of distance = 765 miles
first distance = 6x
second distance = 6 (x -12)
6x + 6(x-12) = 765
x + x -12 = 127.5
2x = 139.5
x = 69.75 mi/h which is the faster bus
the second bus speed = 57.75 mi/h
Match each fraction to a reasonable estimate.
(-6/11)
(-7/9)
(-3/13)
(-1/4)
(-3/4)
(-1/2)
Which one goes with each?
Answer:
-6/11 goes with -1/2
-7/9 goes with -3/4
-3/13 goes with -1/4
Step-by-step explanation:
6/11 is close to 6/12 which is the same as 1/2, so -6/11 goes with -1/2
7/9 is close to 6.75/9 which is 3/4, so -7/9 is close to -3/4
3/13 is close to 3/12 which is the same as 1/4, so -3/13 goes with -1/4
The value of x for the function f(x) = 100+ 0.3x is 210, when
f(x) = 121. True Or False
Answer:
false
Step-by-step explanation:
the answer is x=70
Using the diagram, if angle 3 + angle 4 is a straight line then what is the total
measure?
Answer: 180 degrees
Step-by-step explanation:
Angles on a line add to 180 degrees since they form a straight angle.
4+0.4+0.0024 in Standard Form
Answer:
In standard form thats 4.4024
In standard form, 4+0.4+0.0024 can be written as 4.4024
Concept: Any number we can write as a decimal number, between 1.0 and 10.0, multiplied by 10, is said to be in the normal range. 1.23 × 108;
If you look closely, 1.23 is a decimal number between 1.0 and 10.0 so we have a standard form 123,000,000 as 1.23 × 108.
Given: 4+0.4+0.0024
In this case,4 is the integral value and 0.4 is at the first decimal place followed by 0.0024 at the third and 4th decimal place so combining them all together and writing them in standard form we get,4.4024
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Which graph represents the function f(x)=−3x−2?
Answer:
Step-by-step explanation:
round 0.3391 to the nearest thousandth
Answer:
0.339
Step-by-step explanation:
Hope it helped!
Hii!
___________________________________________________________
Answer: 0.339
Explanation:
Rounding Rules
There are two rounding rules that will help us whenever we need to round a number! These are the rules.
If the number that you need to round is followed by a digit that is less than 5, you round down.If the number that you need to round is followed by a digit that is either greater than or equal to 5, you round up.---
Now that we know the rules, let's get down to solving our problem! ^^
The nearest thousandth is 3 decimal places.
_._ _ _ <==== Nearest thousandth
The third number after the decimal point is 9. After it is a digit that is less than 5. According to the rounding rules, we should round down.
[tex]\boldsymbol{0.3391=== > 0.339}[/tex]
--
Hope that this helped! Best wishes.
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