Explanation:
The area of the circle with radius 10 is...
A = pi*r^2
A = pi*10^2
A = 100pi
The surface area of the sphere with radius 5 is...
SA = 4pi*r^2
SA = 4pi*5^2
SA = 100pi
Both results are the same, so the claim is true. We can think of surface area as the amount of wrapping paper needed to cover the sphere.
The coordinates of point T are (0,2). The midpoint of ST is (5,-3). Find the coordinates of point S.
The other endpoint is
(Type an ordered pair.)
Step-by-step explanation:
the midpoint is exactly halfway in each coordinate direction.
so, whatever we have to add ti or subtract from the coordinates of T to get to the midpoint, we have to add to or subtract from the midpoint to get to S.
for x we get
0 + 5 = 5
so, we need to add another 5 to get the x coordinate of S.
that is then 5 + 5 = 10
for y we get
2 - 5 = -3
so, we need to subtract another 5 to get the y coordinate of S.
that is then
-3 - 5 = -8
S = (10, -8)
At a restaurant, Isabel and Nancy received a bill for $12.42. If they leave a tip of 15%, how much will each girl pay if they equally divide the total amount? Round where necessary.
Answer:
$7.14
Step-by-step explanation:
Given:
Isabel , Nancy = 2 humans
Bill = $12.42
Tip = 15%
To Find:
How much will each girl pay if they equally divide the total amount?
Solve:
$12.42 × 15% = 1.863
1.863 ≈ 1.86
$12.42 + 1.86 = 14.28
14.28 ÷ 2 = 7.14
Therefore each girl pays $7.14 .
~Kavinsky
Which of the following equations can be used to find the length of EF in the
triangle below?
OA. EF = 24 +12
OB. (EF)2 = 242 +12²
OC. EF = 24-12
D. (EF)2 = 242-12²
D
24
E
12 F
W
The equation which can be used to find the length of EF is option A which is EF=[tex]\sqrt{24^{2} -12^{2} }[/tex].
Given the length of base of right angled triangle is 12 and the hypotenuse be 24.
We are to find the length of EF and tell which equation can be used to find the length of EF.
We know that pythagoras theorem applies in a right angled triangle.
Pythagoras theorem says that in a right angled triangle the square of the hypotenuse is equal to the sum of square of base and perpendicular.
[tex]H^{2} =B^{2} +P^{2}[/tex]
In this triangle we are only given base and hypotenuse and we have to find EF which is perpendicular.
[tex](DE)^{2} =(EF)^{2} +(DF)^{2}[/tex]
EF=[tex]\sqrt{DE^{2}-DF^{2} }[/tex]
=[tex]\sqrt{(24)^{2} -(12)^{2} }[/tex]--1
=[tex]\sqrt{576-144}[/tex]
=[tex]\sqrt{432}[/tex]
Hence the equation which can be used to find the length of Ef is option A which is EF=[tex]\sqrt{24^{2} -12^{2} }[/tex].
Question is incomplete as it should include the figure also.
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Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.
2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).
The transformations that would be used on the blue segment CD to get it to match with the red segment C2D2 is to effect a 180° clockwise rotation, so that C remains at (3, -10) and D assumes (3, -11). Recall that original coordinates were: C (3, -10); D (5, -10).
What is transformation in math?A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure.
The pre-Image is the original shape of the item, and the Image during the transformation is the final shape and location of the object. The following are different types of transformation in math:
TranslationRotationReflection; and Dilation.What transformations would you use on the blue triangle to get it to match with the red triangle?The type of transformation that will be used here is called reflection.
D retains it's original coordinates of (5, -10); E goes to (6, -11) and F (6, -10).
Which line segments on the boat are parallel?The line with the coordinates [(4, -11) and (4, -10) that is EF is parallel to [(3,-11) and (3, -10).
Parallel lines are lines that are always the same width apart in a plane. Parallel lines never cross.
Which line segments on the boat are perpendicular?The lines that are perpendicular are: AB with coordinates A(3, -9) & B(3, -11) and CD with coordinates (3, -10) and (5, -10). Lines that intersect each other forming a right angle are called perpendicular lines.
The line segments on the boat that have a slope of zero are:
EF, AB AC, BC. A line with zero slope is one that has a constant value shown along the y-axis that does not vary over the line's points.
The line segments on the boat that are undefined are:
CD, CF, and DF. The gradient or slope of any vertical line that travels up or down is the undefined slope.
The slope (m) is calculated as:
(Y2-Y1)/(X2 - X1)
Given that:
Y1 = 5
Y2 = 4
X1 = -10
X2 = -11
Hence,
m = (5-4)/(-11 -10)
m = -0.048
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A=
B=
What are the coordinates for a and b?
Help me please asap thanks so much
Answer:
A = (0, b)
B = (a, b)
Step-by-step explanation:
A is straight up from the origin and is the same height as b so it's (0, b)
B is straight up from C so the x is the same so it's (a, b)
In the figure, what is the ratio of the area of square KLMN to the area of LOK?
the ratio of the area of square KLMN to the area of LOK is 2a^2/b h
How to determine the ratioFrom the image given, we can deduce the following;
KLMN is a squareLOK is a triangleThe formula for area of a square is
Area = a^2
Where, 'a' is the side
The formula for area of a triangle
Area = 1/ 2 base × height
Now, let's find the ratio
Ratio = area of KLMN/ area of LOK
Ratio = [tex]\frac{a^2}{\frac{1}{2} bh}[/tex]
Ratio = [tex]\frac{a^2}{\frac{bh}{2} }[/tex]
make the expression linear
Ratio = 2a^2/bh
The ratio of the area of square KLMN to the area of LOK is 2a^2/bh
Thus, the ratio of the area of square KLMN to the area of LOK is 2a^2/b h
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PLEASE HELP!!!!!!!!!!!!!!!!!!
Answer:
[tex]\sin\left(x+\frac{\pi}{7} \right)[/tex]
Step-by-step explanation:
[tex]\sin\left(x+\frac{\pi}{7} \right)=\sin \frac{\pi}{7}\cos x +\cos \frac{\pi}{7} \sin x[/tex]
PLEASE HELP ASAP, I WILL GIVE 40 POINTS IF THE RIGHT ANSWER, AND BRAINLEST, ASAP
Answer:
8 types of sandwiches.
Step-by-step explanation:
she has choices of :
1 turkey sandwich
1 roast beef sandwich
1 ham sandwich
1 white sandwich
1 white bread sandwich
1 American sandwich
1 swiss sandwich
1 colby cheese sandwich.
Answer:
8 types
Step-by-step explanation:
she had alot of choice like :
Turkey, roast beef, ham, swiss, corby cheese, wheat or whitebread and american sandwhich .
Kenton watched 2000 adult men and women board a cruise ship. half of the adults were women. if 20$\%$ of the women and 9$\%$ of the men were wearing sunglasses, what was the total number of men and women wearing sunglasses?
Total number of men and women wearing sunglasses = 290
According to the question,
Total number of men and women = 2000
half of the adults were women = 1/2 × 2000
Number of women = 1000
Number of men = (Total adults) - (Number of women )
Number of men = 2000 - 1000
= 1000
given,
20% of women were wearing sunglasses = 20/100 × 1000
= 200
9% of men were wearing sunglasses = 9/100 × 1000
= 90
Total number of adults wearing glasses = 200 + 90
= 290
What is the percentage?In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.
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10 Points !!!!!!!!!!!
Using proportions, the length of x is of 2.9.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The triangles are similar, that is, they have the same angles, hence the corresponding sides are proportional, by the following rule of three:
x/7 = 5/12
Applying cross multiplication:
12x = 35
x = 35/12
x = 2.9.
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In triangle r s t, angle r = 63 degrees, angle t = 90 degrees, side r s = 23 and side s t = 10.4. which ratios are correct?
The correct ratios are: cos 27=23/RT, sec 27= 23/10.4 and cot 63 = RT/10.4
What is trigonometry ratio in tringle?
Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.In triangle RST, angle T= 90° and angle R= 63°
As the total of all angle in any triangle is 180°, so the measure of the angle S = 180°- (90°+63°)
S= 180°- 153°
S= 27°
According to the rule of trigonometric ratios,
cos(θ) = [tex]\frac{hypotenuse}{opposite}[/tex]
sec(θ) = [tex]\frac{hypotenuse}{adjacent}[/tex]
cot(θ) = [tex]\frac{adjacent}{opposite}[/tex]
In respect of angle R (63°), side RS(23) is hypotenuse , ST(10.4) is opposite and RT is adjacent.
cos(63°) = [tex]\frac{23}{10.4}[/tex]
sec(63°) = [tex]\frac{23}{RT}[/tex]
cot(63°) = [tex]\frac{RT}{10.4}[/tex]
Now, in respect of angle S(27°), hypotenuse is RS(23), adjacent is ST(10.4) and opposite is RT.
So, cos(27°) = [tex]\frac{23}{RT}[/tex]
sec(27°) = [tex]\frac{23}{10.4}[/tex]
cot(27°) = [tex]\frac{10.4}{RT}[/tex]
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Find the value of n in this equation.
Answer:
D. 9=========================
GivenTriangle with:
Base of n² -3,Midsegment of 39.To findThe value of n.SolutionAs per definition of midsegment, it is connecting the midpoints of two sides and its length is half the length of the opposite side of the triangle.
So we have:
(n² - 3)/2 = 39Solve it for n:
n² - 3 = 78n² = 81n = √81n = 9Correct choice is D.
The tens digit of a two-digit number is 5 greater than the units digit. If you subtract twice the reversed number from the original number, the result is a fourth of the original number. Find the original number
Answer:
The number is 72.
Step-by-step explanation:
Let the number be xy.
x = y + 5
10x + y - 2(10y + x) = 0.25(10x + y)
10x - 2x + y - 20y = 2.5x + 0.25y
5.5x - 19.25y = 0
Substituting for x:
5.5y + 27.5 - 19.25y = 0
-13.75y = -27.5
y = 2.
So x = 2 + 5 = 7.
(a) if x is the sample mean young's modulus for a random sample of n = 64 sheets, where is the sampling distribution of x centered, and what is the standard deviation of the x distribution?
The standard deviation of the x distribution is 0.2.
According to the statement
we have given that the the sample n is 64 and we have to find the standard deviation of the given sample.
So, For this purpose, we know that the
The standard deviation of the sample is the standard deviation of population divided by the square root of the length of the sample.
In this problem, we have that the value of alpha is
[tex]\alpha = 1.6[/tex]
Suppose that for aluminum alloy sheets of a particular type,
If X is the sample mean Young's modulus for a random sample of n = 64 sheets, and the standard deviation of the X distribution is given by
[tex]s = \frac{\alpha}{\sqrt{64} }[/tex]
then solve it then the standard deviation
s = {1.6} / {8 }
s = 0.2
So, The standard deviation of the x distribution is 0.2.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Given that Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively.
a. If X is the sample mean Young's modulus for a random sample of n = 64 sheets, the sampling distribution of X centered at 70 GPa, and the standard deviation of the X distribution is given by
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The function f(x) = –Two-sevenths (five-thirds)x is reflected over the y-axis to create g(x). Which points represent ordered pairs on g(x)? Check all that apply.
The values of the function if the function f(x) is reflected over y-axis is g(x) = 10/21x
Reflection of coordinatesReflection is a transformation technique that changes the position of an object on an xy-plane.
If the function f(x) is reflected over y-axis, the resulting function is y = f(-x). Given the following function;
f(x) = -2/7(5/3)x
This can also be written as;
f(x) = -10/21 x
Replace x as -x
f(-x) = -10/21(-x)
f(-x) = g(x) = 10/21x
Hence the values of the function if the function f(x) is reflected over y-axis is g(x) = 10/21x
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The second highest point measured above sea level is the summit of
Kangchenjunga which is 8,586m above sea level and the lowest point is
challenger deep at the bottom of Mariana Trench which is 10,911 m below
the sea level. What is the vertical distance between these two points? Collect
some more information about these two points and present them withimages.
Answer:
19497 m
Step-by-step explanation:
The vertical distance between the given points is:
10911 + 8586 = 19497 mAnswer:
19,497m
Step-by-step explanation:
8,856-(-10,911)
=8856+10,911
=19,497m
Isabel made $176 for 8 hours at work At the same rate, how many hours would she have to work to make 374
Answer:
17 hours
Step-by-step explanation:
We first want to figure out how much money shes making per hour.
We can simply divide 176 by 8 getting us 22
Since we know she makes 22 dollars an hour we can divide 374 by 22 getting us 17.
Now we know it would take 17 hours to make 374 dollars
If you want to double check you can simply multiply 17 by 22 which would get you 374
Answer: 17 hours
Step-by-step explanation
Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→0 e3x − 1 − 3x x2
It looks like the limit is
[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2}[/tex]
L'Hôpital's rule works in this case; applying it twice gives
[tex]\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2} = \lim_{x\to0} \frac{3e^{3x} - 3}{2x} = \lim_{x\to0} \frac{9e^{3x}}{2} = \boxed{\frac92}[/tex]
What is the step that comes after 3x(x+1)-5(x+1) when factoring by grouping?
Answer:
Separating the 3x and -5 apart from the (x+1)
Step-by-step explanation:
It would turn out to be (3x-5)(x+1) !
Factor out x+1 from the expression
(x+1) x (3x-5)
how do you solve this?
we are given x here, so we already know that our first coordinate is equal to -2.
in order to find the next coordinate, we have to substitute x for -2 in the y=mx+b equation.
the equation is
[tex]y = \frac{2}{3} x + 23[/tex]
so in substituting x for -2 we get
[tex]y = \frac{2}{3} ( - 2) + 23[/tex]
all we need to do is multiply ⅔ by -2, which gives us -1,3333.
we now have
[tex]y = - 1.3333 + 3[/tex]
so we add them together and get :
[tex]y = 1.666666[/tex]
hope this helps!!<3
A school counselor tests the level of depression in fourth graders in a particular class of 20 students. The counselor wants to know whether the kind of students in this class differs from that of fourth graders in general at her school. On the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. From reports, she is able to find out about past testing. Fourth graders at her school usually score 5 on the scale, but the variation is not known. Her sample of 20 fifth graders has a mean depression score of 4.4. Use the .01 level of significance.
1. The counselor calculates the unbiased estimate of the population's variance to be 15. What is the variance of the distribution of means?
A) 15/20 = 0.75
B) 15/19 = 0.79
C) 152/20 = 11.25
D) 152/19 = 11.84
2. Suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. She figures her t score to be -.20. What decision should she make regarding the null hypothesis?
A) Reject it
B) Fail to reject it
C) Postpone any decisions until a more conclusive study could be conducted
D) There is not enough information given to make a decision
3. Suppose the standard deviation she figures (the square root of the unbiased estimate of the population variance) is .85. What is the effect size?
A) 5/.85 = 5.88
B) .85/5 = .17
C) (5 - 4.4)/.85 = .71
D) .85/(5 - 4.4) = 1.42
1. The variance of the distribution of means option A) 15/20 = 0.75
2. The decision that counselor should make regarding the null hypothesis is that: option "Fail to reject it"
3. The effect of the size is: option c: (5 − 4.4)/.85 = .71
What is the variance about?Note that:
Sample size = 20.
Note that for us to be able to get the answer in question one, we have to divide the unbiased estimate for the population variance by the use of 20 so that we can be able to get our unbiased estimate for the variance: And as such;
15/20 = 0.75.
The term fail to reject implies that the null hypothesis is one that has not been disproven or wrong and therefore the use of the term "failure to reject." It is one that should not be taken with acceptance.
Therefore, 1. The variance of the distribution of means option A) 15/20 = 0.75
2. The decision that counselor should make regarding the null hypothesis is that: option "Fail to reject it"
3. The effect of the size is: option c: (5 − 4.4)/.85 = .71
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A point having a negative abscissa and negative ordinate is in quadrant ____.
Answer:
III
Step-by-step explanation:
This is a fact - A point having a negative abscissa and negative ordinate is in quadrant III.
Dagogo uploads 333 videos on his channel every month. each video averages 151515 minutes in length and gets an average of 150{,}000150,000150, comma, 000 new views. the average ratio of likes-to-views of dagogo's videos is 1:51:51, colon, 5. dagogo wants to reach a total of 9{,}000{,}0009,000,0009, comma, 000, comma, 000 views on his channel. assuming these rates continue, for how many months does dagogo need to upload videos to get to 9{,}000{,}0009,000,0009, comma, 000, comma, 000 views on his channel?
To acquire 90000000 views on his channel, he has to upload 20 videos every month.
According to the given information:Every month, he posts 3 videos to his channel. An average number of people watch each video. = 1500000
In search of:
How many months must pass before he begins to receive 90,000,000 views on his channel?
Step 1
On his channel, he posts three videos each month.
The average number of views per video is.
3 Videos Receive Views
= 3 * 1500000
= 4,500,000 Views
Number of 4,500,000 views each month
Complete 90000000 Views
Step 2
Total Views/Months = Total Views/Total Views
Days in a month = 90000000/4500000
= 20
20 Monthly months in the number
To acquire 90000000 views on his channel, he has to upload 20 videos every month.
20 Months is the right response, so.
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in the diagram below all angles are given in degrees(°)
find X with 50°,3x,X,X+110
The value of x in the angles of Quadrilateral is 52 degree.
According to the statement
we have given a four angles and we have to find the value of x in these give angles.
From given 4 angles it is clear that the these angles are of a quadrilateral.
And we know that the
A quadrilateral is a four-sided polygon, having four edges and four corners.
And the sum of all angles of a quadrilateral is 360 degree.
so,
50° + 3X + X + (X+110) = 360 degree
50° + 4X + (X+110) = 360 degree
50° + 5X + 110 = 360 degree
160° + 5X = 360
5X = 360-100
5X = 260
X = 52 degree.
So, The value of x in the angles of Quadrilateral is 52 degree.
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A motorcycle is traveling at a constant speed of 45 miles per hour. how many feet does it travel in 6 seconds? remember that 1 mile is 5280 feet.
Answer:
The total number of feet travelled by the motorcycle is 396 feet
Step-by-step explanation:
Using the constant speed relationship with the distance:
v = s/t
From the above equation the distance travelled will be:
s = v * t (i)
We are given with the v, that is:
v = 45 miles per hour
Converting in to feet per second.
v = (45 * 5280)/3600 feet / s
v = 66 feet per second
Now, put that v and t in equation (i)
s = 66 * 6
s = 396 feet
A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the base. There will be between 20,000 square feet and 50,000 square feet of construction material used for the outside of the building. What would be the maximum possible side length of the base of the building? Round your answer to the nearest foot.
A.
89 feet
B.
141 feet
C.
71 feet
D.
45 feet
The maximum possible side length of the base of the building is; C: 71 feet.
How to determine the maximum side length of a Pyramid?The given parameters of the new building in the shape of a square pyramid that is to be constructed are as follows:
Base is expressed as b
Slant height (l) is expressed as 5b
The lateral surface area of the square pyramid is calculated from the formula given as;
LSA = 2bl
Thus, the lateral surface area is expressed as;
L = 2 * b * 5b
L = 10b²
The total surface area is calculated using the formula:
T = L + b²
Thus, plugging in the value of 10b² for L gives the total surface area as;
T = 10b² + b²
T = 11b²
The maximum surface area is 50,000 square feet and so we can find b from the following expression;
11b² = 50000
Divide both sides of the equation by 11 to get;
b² = 50000/11
b = √(50000/11)
b = 71 feet to the nearest foot.
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In the diagram, the straight line ABC is parallel to EFG and DB is parallel to FC. Given that ABD=38 degrees and DFE=62 degrees. Find angle BDF and CFG
Based on the calculations, the measure of angle BDF and CFG are 100° and 38° respectively.
The condition for two parallel lines.In Geometry, two (2) straight lines are considered to be parallel if their slopes are the same (equal) and they have different y-intercepts. This ultimately implies that, two (2) straight lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
What is the alternate interior angles theorem?The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.
Based on the alternate interior angles theorem, we can infer and logically deduce the following properties from the diagram (see attachment):
<ABD = <BDH = 38°<DFE = <HDF = 62°For angle BDF, we have:
<BDF = <BDH + <HDF
<BDF = 38° + 62°
<BDF = 100°.
Since angles BDF and DFC are linear pair, they are supplementary angles. Thus, we have:
∠BDF + <DFC = 180°
<DFC = 180 - ∠BDF
<DFC = 180 - 100
<DFC = 80°.
For angle CFG, we have:
∠DFE + <DFC + <CFG= 180°
<CFG = 180° - ∠DFE - <DFC
<CFG = 180° - 62° - 80°
<CFG = 38°.
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Find the unit price of 70lbs of honey for $123.99. round your answer to nearest cent if necessary
Answer:
$1.77 per pound
Step-by-step explanation:
To find the unit price we divide the cost over the weight: 123.99/70 = 1.77128571 = 1.77
URGENT What is the discontinuity and zero of the function f(x)= (x^2 - 4x - 21)/(x + 7)
Answer:
when x=-7
Step-by-step explanation:
if u are solving a function like this, u must not have a division by zero so if we put x=-7 in the function we hav a division by zero
Jessica fills a cube shaped tank that has an edge of 70 cm with water from a tap. Water flows into the tank at a rate of 7L per minute. How long will it take to fill the tank fully?
The volume of the tank is (70 cm)³ = 343,000 cm³.
Now,
1 mL = 1 cm³
1 L = 1000 mL
so we convert the given rate to
[tex]\dfrac{7\,\rm L}{1\,\rm min} \cdot \dfrac{1000\,\rm mL}{1\,\rm L} \cdot \dfrac{1\,\mathrm{cm}^3}{1\,\rm mL} = \dfrac{7000\,\mathrm{cm}^3}{1\,\rm min}[/tex]
Then the time it will take to fill up the tank is
[tex]343,000\,\mathrm{cm}^3 \cdot \dfrac{1\,\rm min}{7000\,\mathrm{cm}^3} = \boxed{49\,\rm min}[/tex]
