Answer:
[tex]A=81\pi $ m^2[/tex]
Step-by-step explanation:
Circumference of the column [tex]=18\pi $ meters[/tex]
Circumference of a circle[tex]=2\pi r[/tex]
Therefore:
[tex]2\pi r =18\pi $ meters\\2r=18\\r=18 \div 2\\$Radius, r=9 meters[/tex]
Area of a Circle [tex]=\pi r^2[/tex]
Since radius of the cross section of the column =9 meters
Area of the cross section of the column
[tex]=\pi *9^2\\=81\pi $ m^2[/tex]
Answer:
81pi
Step-by-step explanation:
how many ways can 7 different runners finish in first, second, and third places in a race?
Answer:
210
Step-by-step explanation:
There are 7 * 6 * 5 ways to finish. This is because we have 3 slots:
For 1st place, there are 7 people that could take that place, so we have 7
For 2nd place, there are 6 people, because one person already took 1st, so they cant be second as well.
For 3rd place, there are 5 people, because 2 people already took first and second place, and neither of them can be third then.
So we have:
7*6*5 = 210
Answer:
210 ways
Step-by-step explanation:
For 1 st place there are 7 different runners
Now there are only 6 options
For 2nd place there are 6 different runners
Now there are only 5 options
For 3rd place there are 5 different runners
7*6*5
Which expressions are equivalent to RootIndex 3 StartRoot 128 EndRoot Superscript x? Select three correct answers.
128 Superscript StartFraction x Over 3 EndFraction
128 Superscript StartFraction 3 Over x EndFraction
(4RootIndex 3 StartRoot 1 EndRoot)x
(4 (2 Superscript one-third Baseline) ) Superscript x
(2)x
Answer:
(A)[tex]128^{x/3}[/tex]
(D)[tex](4(2^{1/3}))^x[/tex]
Step-by-step explanation:
We want to determine which of the expression is equivalent to:
[tex]\sqrt[3]{128}^ x[/tex]
By the law of indices:
[tex]\sqrt[3]{128}=128^{1/3}\\$Therefore:\\\sqrt[3]{128}^ x \\=(128^{1/3})^x\\=128^{x/3}[/tex]
Similarly:
[tex]\sqrt[3]{128}^ x \\=\sqrt[3]{64*2}^ x\\=(4\sqrt[3]{2})^ x\\=(4(2^{1/3}))^x[/tex]
The expressions that are equivalent to (∛128)ˣ are; (128)^(x/3) and (4(2^(1/3))ˣ
How to use law of indices?We want to find the expression that is equivalent to (∛128)ˣ
From law of indices, we have that;
(∛128)ˣ = [(128)^(1/3)]ˣ
This can be further expressed as;
(128)^(x/3)
Similarly, we have the simplified expression at;
[(128)^(1/3)]ˣ = (64 * 2)^(x/3)
⇒ (4³ * 2)^(x/3)
⇒ (4(2^(1/3))ˣ
Read more about law of indices at; https://brainly.com/question/11761858
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A classroom will be assembled so that the desks fit within an area that is 8 m by 12 m. The desks will be surrounded by a border that will be the same width on all sides of the rectangular room, to
allow for walking space. The area of the border will equal 20% of the area of the space that the desks
occupy. What is the width of the border, to the nearest hundredth of a meter?
Answer:
0.46 m
Step-by-step explanation:
area of desks: 8 m by 12 m = 8 m * 12 m = 96 m^2
20% of this area is 20% * 96 m^2 = 19.2 m^2
The area of the border is 19.2 m^2.
Let the path around the desks have width x.
The area of desks plus path is a rectangle 2x + 8 by 2x + 12.
area of desks plus path = (2x + 8)(2x + 12)
= 4x^2 + 24x + 16x + 96 = 4x^2 + 40x + 96
The area of the border is the area of the rectangle that includes the border minus the rectangle that has just the desks.
area of border = (4x^2 + 40x + 96) - (96) =
= 4x^2 + 40x
Above, we have the area of border = 19.2, so we get this equation:
4x^2 + 40x = 19.2
4x^2 + 40x - 19.2 = 0
x^2 + 10x - 4.8 = 0
We now use the quadratic formula to solve the equation for x.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{10^2 - 4(1)(-4.8)}{2(1)} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{100 + 19.2 )}{2} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{119.2 )}{2} [/tex]
[tex] x = 0.46 [/tex] or [tex] x = -10.46 [/tex]
We discard the negative solution.
Answer: the border is 0.46 m wide.
Two similar cardboards have areas of 24cm² and 150cm². If the length of the bigger one is 10cm ,what is the length of the smaller one,?
Answer:
4 cm
Step-by-step explanation:
You want the length of the smaller of two similar pieces of cardboard when the larger has an area of 150 cm² and a length of 10 cm, while the smaller has an area of 24 cm².
Scale factorThe scale factor for lengths is the square root of the scale factor for areas. It will be ...
√(24/150) = 0.4 . . . . . . = smaller / larger
The smaller cardboard has a length of ...
0.4 × 10 cm = 4 cm
__
Additional comment
Sometimes folks like to write this as a proportion:
[tex]\dfrac{\text{smaller length}}{\text{larger length}}=\sqrt{\dfrac{\text{smaller area}}{\text{larger area}}}[/tex]
Solving this for "smaller length" gives the expressions we used above:
smaller length = (larger length) × √(smaller area/larger area)
someone please help
Answer:
See explanation for answers
Step-by-step explanation:
prism = 12*4 + 5*4 + 12*4 + 5*4 + 12*5 + 12*5 = 256 ft²
lateral surface area of pyramid = 4*1/2*5*5 = 50 ft²
area of square base of the pyramid = 5*5 = 25 ft²
total exposed surface area of the figure = 256 + 50 - 25 = 281 ft²
What is the diameter of a circle with a radius of 9.5 cm ?
Answer:
9.5(2) = 19 is the diameter
Step-by-step explanation:
Answer:
19 cm
Step-by-step explanation:
Diameter is twice the radius, thus 2 x 9.5 cm = 19 cm
anybody know this :( please help
Answer:
the set of all the real values which are strictly greater than zero which is all positive real numbers
Step-by-step explanation:
In interval notation: (0, ∞)
Any exponential function with a positive base and positive multiplier will have a horizontal asymptote at y=0 and will extend to +∞. That's what this one does.
Range of a function--
The range of a function is the set of all the values that are attained by a function.
We are asked to find the range of the function f(x)
the set of all the real values which are strictly greater than zero
x > 0
please mark me brainliest :)
How can you tell if an expression is a perfect square trinomial? Explain.
Answer:
Step-by-step explanation:
A perfect square trinomial is the square of a binomial.
One of the special products and factors formulas that you should know is
(a + b)^2 = a^2 + 2ab + b^2; another is (a - b)^2 = a^2 - 2ab + b^2.
So, if you are given a trinomial and can use either of the above identities to rewrite it as the square of a binomial, you've got it.
The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?
Answer:
Step-by-step explanation:
If the longest side is 6.2 cm, and it is twice the length of the shortest, then we can write an equation as 2x=6.2, where x is the short side length.
Then, since a triangle has 3 sides, the medium side length is 14.5-6.2-x.
Hope that helped,
-sirswagger21
The price of an item has been reduced by 15%. The original price was $17
Answer:
17/100*85= $14.45
Step-by-step explanation:
Divide by 100 and multiply by (100-15) 85 to get the result.
Use the circle to answer the questions.
A circle with radius 5.4 centimeters.
The diameter is
cm.
The circumference in terms of Pi is
Using 3.14 for Pi, the approximate circumference of the circle is
cm.
Answer:
C = 10 π cm
Step-by-step explanation:
Diameter is 2 x radius = 2*5.4 = 10.8 cm
radius r = 5 cm
diameter d = 10 cm
circumference C = 31.4 cm
area A = 78.5 cm2
In Terms of Pi π
circumference C = 10 π cm
area A = 25 π cm²
Formulas: Circle Formulas in terms of Pi π, radius r, and diameter d
Radius and Diameter:
r = d/2
d = 2r
Area of a circle:
A = πr2 = πd2/4
Circumference of a circle:
C = 2πr = πd
Answer:
c
Step-by-step explanation:
got it right on my test
1. Using the scale 1 in.: 4 ft, find the dimensions in a blueprint of an 8 ft-by-12 ft
room
Answer:
2 in by 3 in
Step-by-step explanation:
1 in = 4 ft Divide both sides with 4
0.25 in = 1 ft
0.25 * 8 = 2 in
0.25 * 12 = 3 in
2 in by 3 in
Answer: 2 in by 3 in
Step-by-step explanation:
1 in = 4 ft Divide both sides with 4 0.25 in = 1 ft 0.25 * 8 = 2 in 0.25 * 12 = 3 in 2 in by 3 in
Solve 5 + x - 14 = x - 7
Answer:
No solution
Step-by-step explanation:
5+x-14=x-7
-9+x=x-7
2+x=x
2=0
No solution
Point P partitions the directed segment from A to B into 1:3 ratio. Q partitions the directed segment from B to A into a 1:3 ratio. Are P and Q the same point? Why or why not?
Answer:
Point Q is further from A than point P, therefore, they are not the same point
Step-by-step explanation:
The given information are;
Point P partitions the directed segment from A → B into the ratio of 1:3
Point Q partitions the directed segment from B → A into the ratio of 1:3
We note that the properties of a directed segment are that it has a length and direction with a defined starting or initial point.
Hence the two segments when arranged in the same direction are;
A B and B A
Hence point P is at a the point 1/(1 + 3) or 1/4 of AB or 1/4 times the length of AB from A
Point Q is at a the point 1/4 of B/A or 1/4 times the length of AB from B which is 3/4 times the length of AB from A
Therefore, point Q is further from A than point P which means they are not the same point.
Answer:
No, P is One-fourth the distance from A to B, and Q is One-fourth the distance from B to A.
Step-by-step explanation:
A vehicle with a particular defect in its emission control system is taken to a succession of randomly selected mechanics until r = 15 of them have correctly diagnosed the problem. Suppose that this requires diagnoses by 20 different mechanics (so there were 5 incorrect diagnoses). Let p = P(correct diagnosis), so p is the proportion of all mechanics who would correctly diagnose the problem. What is the mle of p?
Answer:
the mle of P=0.833
Step-by-step explanation:
X=incorrect answer
And probability of success to be denoted as P
Here X posses a binomial distribution along with 'r' and 'p'parameter
CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLATION
Which of the following is the complete factorization of 10x - 3 - 3x2? -(3x + 1)(x - 3) -(3x - 1)(x - 3) (3x - 1)(x + 3)
Answer:
[tex]=-\left(3x-1\right)\left(x-3\right)[/tex]
Step-by-step explanation:
[tex]10x-3-3x^2\\\mathrm{Factor\:out\:common\:term\:}-1\\=-\left(3x^2-10x+3\right)\\\mathrm{Factor}\:3x^2-10x+3:\quad \left(3x-1\right)\left(x-3\right)\\3x^2-10x+3\\\mathrm{Write\:in\:the\:standard\:form}\:ax^2+bx+c\\=3x^2-10x+3\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(3x^2-x\right)+\left(-9x+3\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}3x^2-x\mathrm{:\quad }x\left(3x-1\right)\\3x^2-x\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\=3xx-x[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x\\=x\left(3x-1\right)\\\mathrm{Factor\:out\:}-3\mathrm{\:from\:}-9x+3\mathrm{:\quad }-3\left(3x-1\right)\\-9x+3\\\mathrm{Rewrite\:}9\mathrm{\:as\:}3\cdot \:3\\=-3\cdot \:3x+3\\\mathrm{Factor\:out\:common\:term\:}-3\\=-3\left(3x-1\right)\\=x\left(3x-1\right)-3\left(3x-1\right)\\\mathrm{Factor\:out\:common\:term\:}3x-1\\=\left(3x-1\right)\left(x-3\right)\\=-\left(3x-1\right)\left(x-3\right)[/tex]
Penny had a bag of marbles. She gave one-third of them to Rebecca, and then one-fourth of
the remaining marbles to John. Penny then had 24 marbles left in the bag. How many marbles were
in the bag to start with?
pls explain.
Given That:
x - (Rebecca's share + John's share) = 24
x - (x/3 + x/4) = 24
12x/12 - (4x / 12 + 3x / 12) = 24
5x/12 = 24
5x = 24 x 12
5x = 288
x = 57 or 58
May you help please
Answer:
Option A
Step-by-step explanation:
We are given the inequality 4x + 6 [tex]\leq[/tex] 18;
[tex]4x + 6 \leq 18,\\4x \leq 12,\\\\x \leq 12 / 4,\\x \leq 3,\\\\Conclusion - Option A[/tex]
As you can tell, the second step was derived through the subtraction of 6 from either side of the inequality sign. 18 - 6 is 12, which resulted in the simplified inequality [tex]4x \leq 12[/tex]. Dividing 4 on either side, we derived [tex]x \leq 3[/tex], which is Option A
Multiply and simplify
V8xyz3 . V10x3y2z
Answer:
Step-by-step explanation:
[tex]\sqrt{8xyz^{3}}*\sqrt{10x^{3}y^{2}z} =\sqrt{8xyz^{3}*10x^{3}y^{2}z}\\\\ =\sqrt{2*2*2*2*5*x^{1+3}*y^{1+2}*z^{3+1}} \\\\\\=\sqrt{2^{4}*5*x^{4}*y{3}*z^{4}} \\\\=2^{2}*x^{2}*y*z^{2}\sqrt{5y} \\\\\\=4x^{2}yz^{2}\sqrt{5y}[/tex]
Which of the following does not come from domesticated animals?
a. milk from cows, sheep, and goats
c. fertilizer to help crops grow better
b. labor to pull the plows
d. furs for shelter and warmth
If a student with 2 absences got a score of 12 what would be the score for a student who had 3 absences
The scatter plot below shows the relationship between two variables, x and y. Which kind best fits the data?
Answer:
The last one on the bottom right
Step-by-step explanation:
When we are trying to fit a line for a number of points, we can fix this line at several points on the graph. However, out of the several lines that we can fit, only one of these lines would work perfectly and it is called the line of best fit.
The reason why it is called the line of best fit is that it is drawn in a manner in which it leaves equal number of points above it as below it.
Supposed we have 15 points for our graph with the line of the slope passing thorough 5, the line of best fit in this case would leave 5 points above and another 5 below the line.
Leaving 6 and 4 is also manageable, but in case where 3 and 7 are left above and below the line, then it becomes a problem
Thus, out of all the representations we have, the one on the bottom right best works
If A = T, then SM ___ MO. > = < NEED HELP
Answer:
I'm not sure but I think the answer is >
Step-by-step explanation:
It looks rig but if I were u I wouldn't trust me
i just did the quiz, It's > !
What is the smallest number that can be added to 2018·2019·2020 so that the result of the addition is a perfect cube? Please answer soon!
Answer:
[tex]802[/tex]
Step-by-step explanation:
[tex]18^3=5832[/tex]
[tex]19^3=6859[/tex]
[tex]2018+2019+2020=6057[/tex]
[tex]6859-6057=802[/tex]
Check.
[tex]6057+802=6859[/tex]
[tex]\sqrt[3]{6859} =19[/tex]
Answer:
2019.
Step-by-step explanation:
Let x = 2018, then x + 1 = 2019 and x + 2 = 2020.
x(x + 1)(x + 2)
= x(x^2 + 3x + 2)
= x^3 + 3x^2 + 2x ................(A)
Now the perfect cube of x + 1 is:
(x + 1)^3 = x^3 + 3x^2 + 3x + 1
If we add x + 1 to (A) we get this expression so the answer is x + 1
= 2019.
Simplify 7(A-6)
A-6
7A-42
7A-6
Answer:
7A - 42
Step-by-step explanation:
7(A-6)
Distribute
7*A - 7*6
7A - 42
Find the SURFACE AREA of this composite solid. Show work
Answer:
8
Step-by-step explanation:
4+4
6-6+8
what is 1.8 increased by 10??
Answer:
zdsczsczscs
Step-by-step explanation:
Record 3 2/25 as a decimal. Please help!!!!!
Answer:
1.28 is the decimal form
Step-by-step explanation:
and 128/100 or 128% is the percentage for 32/25.
// have a great day //
what is log 8/3 base 5
Answer:
3 to the power of 8 / 5
Step-by-step explanation:
what should be added in the polynomial x3-6x2+11x+8 so that it is completely divisible by 1-3x +x2
Answer:
The value to be added to the polynomial x³ - 6·x² + 11·x + 8 so that it is completely divisible by 1 - 3·x + x² is -(x + 11)
Step-by-step explanation:
By long division, we have;
[tex]{\left ({x^{3}-6x^{2}+11x+8} \right )\div 1 - 3x + x^{2}}[/tex] = x - 3
-(x³ - 3·x² + x)
-3·x² + 10·x + 8
-(-3·x² + 9·x -3)
x + 11
Therefore, -(x + 11) should be added to the polynomial x³ - 6·x² + 11·x + 8 so that it is completely divisible by 1 - 3·x + x².
That is (x³ - 6·x² + 11·x + 8 - x - 11) ÷ (1 - 3·x + x²) = x - 3.
