The problem involves calculating the speed of the current in a river using the given data: the speed of a boat in still water, the distance traveled downstream and upstream, and the total time taken. An application of the concept of relative speed helps solve the problem by setting up an equation reflecting the speeds during the downstream and upstream runs, then solving for the speed of the current.
Explanation:The problem demonstrates an application of relative speed in the context of a boat moving in a stream. Let's denote the speed of the boat by 'b', the speed of the stream by 's', the time taken to move downstream by 't1', and the time taken to move upstream by 't2'. The speed of the boat in still water is given as 24 mph.
When moving downstream, the boat and the stream are going in the same direction, so their speeds add up: the actual speed will be b+s (24 mph + s). On the other hand, when moving upstream, the boat is going against the stream, so the actual speed is b-s (24 mph - s).
The total time taken to go 15 miles downstream and return is 80 minutes or 4/3 hours. Therefore, using the formula for time (time = distance/speed), we can set up the following equation: 15/(24+s) + 15/(24-s) = 4/3
Solving this equation will give us the value of 's', which represents the speed of the stream.
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The speed of the stream is 6mph.
To find the speed of the stream, we can use the concept of relative speed.
When the boat is going downstream (with the current), the effective speed is increased by the speed of the stream. So, the effective speed downstream is v + s
When the boat is going upstream (against the current), the effective speed is decreased by the speed of the stream. So, the effective speed upstream is V- s
1. Time taken downstream
[tex]\[ t_d = \frac{\text{Distance}}{\text{Speed}} = \frac{15}{v + s} \][/tex]
2. Time taken upstream
[tex]\[ t_u = \frac{\text{Distance}}{\text{Speed}} = \frac{15}{v - s} \][/tex]
3. Total time for the round trip
The total time taken for the round trip is the sum of the time taken downstream and upstream.
[tex]\[ \frac{15}{v + s} + \frac{15}{v - s} = \frac{80}{60} \] (converted minutes to hours)[/tex]
Now, let's substitute v = 24 into the equations and solve for \( s \), the speed of the stream.
Once we have s we can find the speed of the stream.
[tex]\[ \frac{15}{24 + s} + \frac{15}{24 - s} = \frac{4}{3} \][/tex]
Multiplying both sides of the equation by ( (24 + s)(24 - s) to clear the denominators:
[tex]\[ 15(24 - s) + 15(24 + s) = \frac{4}{3}(24 + s)(24 - s) \][/tex]
Taking the square root of both sides:
s= 6
Therefore, the speed of the stream is 6 mph.
Quadratic formula what is the expression for discriminant
Answer:
b^2-4ac
Step-by-step explanation:
By looking at that part after substituting and calculating, you can tell these things about the solution
Kayla hit 4 homeruns at batting practice
out of 12 pitches thrown. What is the
experimental probability that Kayla will hit a
homerun at batting practice?
Answer:
[tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given,
Total number of trial = 12
Total number of favorable event = 4
Experimental probability of hitting home run is
[tex]P(home\ run)=\dfrac{Favorable\ event}{Total\ trial}[/tex]
[tex]P(home\ run)=\dfrac{4}{12}[/tex]
[tex]P(home\ run)=\dfrac{1}{3}[/tex]
Answer:1/3
Step-by-step explanation:Answer:
Step-by-step explanation:
Given,
Total number of trial = 12
Total number of favorable event = 4
Experimental probability of hitting home run is
PLEASE HELP ASAP
Fiona must find the length indicated by the dotted line for
the tiles she is installing. She knows that each polygon is a
regular hexagon with a perimeter of 7.5 in.
What is the length of the dotted line? Round to the nearest
hundredth.
2.50 in.
3.75 in.
5.00 in.
6.25 in.
Answer:
3.75 in.
Step-by-step explanation:
Fiona must find the length indicated by the dotted line for the tiles she is installing. She knows that each polygon is a regular hexagon with a perimeter of 7.5 in.
3 regular hexagons are connected at their sides. A dotted line is drawn through the middle of the 3 hexagons. The top image is a reflection of the bottom image. The dotted line is the length of one side and the distance from one point of the hexagon to the opposite point.
What is the length of the dotted line? Round to the nearest hundredth.
2.50 in.
3.75 in.
5.00 in.
6.25 in.
The length of the dotted line in the hexagon is 3.75 cm.
What is a hexagon?A polygon with 6 sides is called a hexagon.
Finding the length across one entire hexagon :-
We can draw 6 small triangles from the center of the hexagon. The top vertex of this triangle will be 60°; this is because there are 6 angles, and 360.
The sum of the measures of the angles in a triangle is 180°; taking out the top angle, we have 180-60 = 120°.
Since the triangle is isosceles, the base angles will be equal to 120/2 = 60
The bottom two angles will also be 60°.
This makes the triangle equiangular, which also makes it equilateral; all 3 sides will be 1.25.
Hence,
This means across the dotted line we have 1.25+1.25+1.25 = 3.75.
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Helllllllppppp ....,.:,:::;;,:()$?;;:/&//&
Answer:
The answer is 41>6t+7
Step-by-step explanation:
It said that he wants to earn "more than" $41 so the inequality sign is more than. Then it says $6 per hour so 6t. Then you add $7
Sandy plays tennis once every 6 six days. Jim plays once every 8 eight days. If they both played tennis today, in how many days will they play on the same day again?
Answer: 24 days
Step-by-step explanation:
Sandy plays tennis once every 6 six days while Jim plays tennis once every 8 eight days.
To get the number of days they will play on the same day again, we find the lowest common multiple for the numbers.
The lowest common multiple is the smallest positive integer which is evenly divisible by both 6 and 8.
6 = 6, 12, 24, 30
8 = 8, 16, 24, 32
The lowest common multiple is 24.
In 24 days, they will play on the same day again
can you actually help me with this so i can finish the math work if so thank you so much
Answer:
adbbcbaca
Step-by-step explanation:
What is the mean of the data set below? Round to the nearest tenth when necessary. 40, 40, 52, 41, 62
Answer:
47
Step-by-step explanation:
add all the numbers and divide them by however many numbers there are.
Answer: The mean is 47.
There are 5 numbers.
To find the mean of them we add them and divide the sum by 5.
Mean = [tex]\frac{\left(40+40+52+41+62\right)}{5}=\frac{235}{5}=47[/tex]
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On a game show, a contestant randomly chooses a chip from a bag that contains numbers and strikes. The theoretical probability of choosing a strike is 1/8. The bag contains 7 strikes. How many chips are in the bag?
Answer:
Let x be the number of chips.
\frac{8}{x}=\frac{1}{5}
x = 40
The answer is: There are 40 chips in
Easy Question means Easy points
Topic: Volume
Focus on Scenario 2
Answer:
20,000 cm³
Step-by-step explanation:
The shape is a triangular prism
Base area × height
½ × 20 × 25 × 80
20,000 cm³
Answer:
20,000 cm³
Reason Why I know is because I had to do this very same thing :P
Which graph shows a quadratic function with a discriminant value of 0 ?
D. Graph D. A graph that shows a quadratic function with a discriminant value of 0 is graph D.
In Mathemeatics, the number of zeros for any quadratic function by using the discriminant formula as follows;
Discriminant, D = b² - 4ac
where:
a, b, and c are constants.
Note:
If D equals 0, the quadratic equation has only one real solution.
If D is greater than 0, the quadratic equation has two real solutions.
If D is less than 0, the quadratic equation has two complex solutions
In this context, we can logically deduce that only graph D shows a quadratic function with a discriminant value of 0 because it has only one real solution (x = 1).
Enrico buys 3/8 of cheddar cheese and 4/8 pounds of Swiss cheese .How much cheese did Enrico buy in all?
Answer: 7/8 pounds of cheese
Step-by-step explanation:
Add the two numbers.
4/8 + 3/8 = 7/8.
That is your answer.
What is the final amount if 457 is decreased by 1% followed by a further 3% decrease? Give your answer rounded to 2 DP.
Answer:
438.86
Step-by-step explanation:
1. 457 x 0.99 = 452.43 - Decreased by 1%
2. We need to decrease 452.43 again but this time by 3% - 452.43 x 0.97
3. This gives us an answer of 438.8571
4. Finally we need to round this to 2DP, the 7 (438.8571) rounds up so the number to the left increases. This leaves an answer of 438.86
Hope this helps :D
my equation is f(x)= x^2-16x-100 and i am using the complete the box method im really stuck
Answer:
x2-16x+100=0
Two solutions were found :
x =(16-√-144)/2=8-6i= 8.0000-6.0000i
x =(16+√-144)/2=8+6i= 8.0000+6.0000i
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2-16x+100
The first term is, x2 its coefficient is 1 .
The middle term is, -16x its coefficient is -16 .
The last term, "the constant", is +100
Step-1 : Multiply the coefficient of the first term by the constant 1 • 100 = 100
Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is -16 .
-100 + -1 = -101
-50 + -2 = -52
-25 + -4 = -29
-20 + -5 = -25
-10 + -10 = -20
-5 + -20 = -25
For tidiness, printing of 12 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 - 16x + 100 = 0
Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2-16x+100
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 8.0000
Plugging into the parabola formula 8.0000 for x we can calculate the y -coordinate :
y = 1.0 * 8.00 * 8.00 - 16.0 * 8.00 + 100.0
or y = 36.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-16x+100
Axis of Symmetry (dashed) {x}={ 8.00}
Vertex at {x,y} = { 8.00,36.00}
Function has no real roots
Solve Quadratic Equation by Completing The Square
2.2 Solving x2-16x+100 = 0 by Completing The Square .
Subtract 100 from both side of the equation :
x2-16x = -100
Now the clever bit: Take the coefficient of x , which is 16 , divide by two, giving 8 , and finally square it giving 64
Add 64 to both sides of the equation :
On the right hand side we have :
-100 + 64 or, (-100/1)+(64/1)
The common denominator of the two fractions is 1 Adding (-100/1)+(64/1) gives -36/1
So adding to both sides we finally get :
x2-16x+64 = -36
Adding 64 has completed the left hand side into a perfect square :
x2-16x+64 =
(x-8) • (x-8) =
(x-8)2
Things which are equal to the same thing are also equal to one another. Since
x2-16x+64 = -36 and
x2-16x+64 = (x-8)2
then, according to the law of transitivity,
(x-8)2 = -36
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-8)2 is
(x-8)2/2 =
(x-8)1 =
x-8
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-8 = √ -36
Add 8 to both sides to obtain:
x = 8 + √ -36
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1
Since a square root has two values, one positive and the other negative
x2 - 16x + 100 = 0
has two solutions:
x = 8 + √ 36 • i
or
x = 8 - √ 36 • i
Solve Quadratic Equation using the Quadratic Formula
2.3 Solving x2-16x+100 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -16
C = 100
Accordingly, B2 - 4AC =
256 - 400 =
-144
Applying the quadratic formula :
16 ± √ -144
x = ——————
2
In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written (a+b*i)
Both i and -i are the square roots of minus 1
Accordingly,√ -144 =
√ 144 • (-1) =
√ 144 • √ -1 =
± √ 144 • i
Can √ 144 be simplified ?
Yes! The prime factorization of 144 is
2•2•2•2•3•3
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 144 = √ 2•2•2•2•3•3 =2•2•3•√ 1 =
± 12 • √ 1 =
± 12
So now we are looking at:
x = ( 16 ± 12i ) / 2
Two imaginary solutions :
x =(16+√-144)/2=8+6i= 8.0000+6.0000i
or:
x =(16-√-144)/2=8-6i= 8.0000-6.0000i
Two solutions were found :
x =(16-√-144)/2=8-6i= 8.0000-6.0000i
x =(16+√-144)/2=8+6i= 8.0000+6.0000i
Step-by-step explanation:
1. According to the box and whisker plot below, what was the lower quartile weight of Frank's
classmates?
Weights of Frank's Classmates (in lbs.)
50 75 100 125 150
HHHHHHHHH
a) 65
b) 75
c)
95
d) 125
B
Step-by-step explanation:
I hoped this helped
Based on the provided box and whisker plot, the lower quartile (Q1) represents the 25th percentile of the data, which means 25% of the data points are below this value. To find the lower quartile weight of Frank's classmates, we need to identify the middle value of the lower half of the data.
The box and whisker plot separates the data into four quartiles: the lower whisker, the box (which contains Q1), the median (Q2), and the upper whisker. The box covers the interquartile range (IQR), which contains the middle 50% of the data.
Let's find the lower quartile (Q1) based on the provided data:
Weights of Frank's Classmates (in lbs.): 50, 75, 100, 125, 150
Step 1: Arrange the data in ascending order: 50, 75, 100, 125, 150
Step 2: Find the position of Q1:
Position of Q1 = (25/100) * (Total number of data points + 1)
Position of Q1 = (25/100) * (5 + 1)
Position of Q1 = (25/100) * 6
Position of Q1 = 1.5
Since the position is not a whole number, we need to take the average of the data points at positions 1 and 2.
Step 3: Calculate Q1:
Q1 = (Data at position 1) + [(Position of Q1 - Integer part of Position of Q1) * (Data at position 2 - Data at position 1)]
Q1 = 50 + [(1.5 - 1) * (75 - 50)]
Q1 = 50 + [0.5 * 25]
Q1 = 50 + 12.5
Q1 = 62.5
So, the lower quartile weight of Frank's classmates is 62.5 lbs.
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please please please help
Answer:
The inverse of the function is ±sqrt( (x+4)/2
Step-by-step explanation:
Set the function equal to y
y = 2x^2 -4
Exchange x and y
x = 2y^2 -4
Solve for y
Add 4 to each side
x+4 = 2y^2 -4+4
x+4 = 2y^2
Divide each side by 2
(x+4)/2 = 2/2y^2
(x+4)/2 = y^2
Take the square root of each side
±sqrt( (x+4)/2 )= sqrt(y^2)
±sqrt( (x+4)/2 )= y
The inverse of the function is ±sqrt( (x+4)/2
The height of a right circular cylinder is 1.5 times the radius of the base. What is the ratio of the total surface area to the lateral (curved) surface area of the cylinder?
Let r represent the radius of cylinder.
We have been given that the height of a right circular cylinder is 1.5 times the radius of the base. So the height of the cylinder would be [tex]1.5r[/tex].
We will use lateral surface area of pyramid to solve our given problem.
[tex]LSA=2\pi r h[/tex], where,
LSA = Lateral surface area of pyramid,
r = Radius,
h = height.
Upon substituting our given values in above formula, we will get:
[tex]LSA=2\pi r\cdot (1.5)r[/tex]
Now we will find the total surface area of cylinder.
[tex]TSA=2\pi r(r+h)[/tex]
[tex]TSA=2\pi r(r+1.5r)[/tex]
[tex]TSA=2\pi r(2.5r)[/tex]
[tex]\frac{TSA}{LSA}=\frac{2\pi r(2.5r)}{2\pi r(1.5r)}[/tex]
[tex]\frac{TSA}{LSA}=\frac{2.5r}{1.5r}[/tex]
[tex]\frac{TSA}{LSA}=\frac{25}{15}[/tex]
[tex]\frac{TSA}{LSA}=\frac{5}{3}[/tex]
Therefore, the ratio of total surface area to lateral surface area is [tex]5:3[/tex].
The formula in cell B1 is =A$2. Autofill is used by dragging B1's autofill box across to C1, D1, and E1. What formulas will appear in C1, D1, and E1, respectively?
Answer:
=A$2, =A$2, =A$2
Step-by-step explanation:
Autofill is used in excel to fill a series of cells automatically. If the formula in cell B1 is =A$2. On using autofill by dragging B1's autofill box across to C1, D1, and E1, =A$2, =A$2, =A$2 appear in C1, D1, and E1, respectively. Excel tries to guess and insert next values on the basis of selected data.
Answer:
Step-by-step explanation:
A$2 A$3 A$4
you invest 3200 in an account that pays an interest rate of 7.25% compounded continuosly
HELP 100 POINTS GIVEN 1. An inground non-diving swimming pool has the following dimensions. It is 33 feet long and 14 feet wide. On the
shallow end, it is 3 feet 6 inches deep and slopes gradually to a depth of 5 feet 4 inches. A picture is below. What
shape(s) can be used to estimate the volume of the pool.
2. What volume formula(s) will be used for the shape listed in
number 1
3. The pool has dimensions that are in both feet and inches. Perform unit conversions on this step
4. Apply the dimensions from number 3 to the formula(s) listed in number 1 and calculate the approximate volume of
the pool.
5. Write the answer from number 4 in scientific notation. It can be approximated.
Answer:
14inches farenheight
Step-by-step explanation:
Answer:
14 inches farenheit
Step-by-step explanation:
which prism has a greater volume prism a has 17 more cubic units of volume than prism B prism B has 3 more cubic units of volume than prism a prism B has 8 more cubic units of volume than prism a
Answer:
B
Step-by-step explanation:
I also took a test
The correct answer is that neither prism has a greater volume they must have the same volume.
Let denote the volume of prism A as [tex]\( V_A \)[/tex] and the volume of prism B as [tex]\( V_B \).[/tex] According to the problem statement, we have the following relationships:
1. Prism A has 17 more cubic units of volume than prism B:
[tex]\[ V_A = V_B + 17 \][/tex]
2. Prism B has 3 more cubic units of volume than prism A:
[tex]\[ V_B = V_A + 3 \][/tex]
3. Prism B has 8 more cubic units of volume than prism A:
[tex]\[ V_B = V_A + 8 \][/tex]
However there is a contradiction in the last two statements. Prism B cannot have both 3 more cubic units and 8 more cubic units than prism A. This suggests there might be a typographical error in the problem statement.
Assuming there is a mistake and we only consider the first two statements, we can solve for the volumes by setting the two equations equal to each other since both right-hand sides are equal to [tex]\( V_B \):[/tex]
[tex]\[ V_B + 17 = V_A + 3 \][/tex]
Now, we can solve for [tex]\( V_A \)[/tex]in terms of[tex]\( V_B \)[/tex] using the first equation:
[tex]\[ V_A = V_B + 17 \][/tex]
Substitute \( V_A \) into the second equation:
[tex]\[ V_B = (V_B + 17) + 3 \][/tex]
Simplify the equation
[tex]\[ V_B = V_B + 20 \][/tex]
This simplifies to:
[tex]\[ 0 = 20 \][/tex]
This is not possible, which means our initial assumption that the two statements could be true simultaneously is incorrect. The only logical conclusion, given the contradictory information, is that neither prism has a greater volume; they must have the same volume. This is the only way to satisfy the condition that each prism has more volume than the other by different amounts.
Therefore, the volumes of prism A and prism B are equal:
[tex]\[ V_A = V_B \][/tex]
This resolves the contradiction in the problem statement. The volumes of the two prisms must be the same for the given conditions to hold true.
Examine the number line and select all the statements that are true.
The sum of B and C is negative.
the product of A and B > the product of A and D
|A| < |D|
A - B = -2 2/3
A + D = B
The quotient of C and B is equivalent to -2/3
Answer:
the sum of B and C is negative
A + D = B
The quotient of C and B is equivelent to -2/3
Step-by-step explanation:
The quotient of C and B is equivalent to -2/3. Therefore, the correct option is option D among all the given options.
What is number line?A picture of numbers along a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, a whole number is a collection of numbers that contains all counting numbers.
Comparing numbers is made simpler by writing them on a number line. As seen in the aforementioned graphic, the integers to the left are smaller compared to the integers for the right. As an illustration, the numbers 0 and 1 are less than each other, as are the numbers -1 and -2. The sum of B and C is negative.
Therefore, the correct option is option D.
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what is p if 7/p = 3/10
Answer:
23 1/3 or 70/3 =p
Step-by-step explanation:
7/p = 3/10
Using cross products
7*10 = 3p
70 = 3p
Divide each side by 3
70/3 = 3p/3
70/3 =p
or as a mixed number
23 1/3 =p
Find the surface area of this triangular prism.
Your answer would be 900m².
We can find this by finding the area of each of the shapes that make up the surface of this prism.
First there is the bottom of the prism, which would be 11 × 24 = 264m².
Then you have the two triangles on the sides of the prism, which are both (10 × 24)/2 each, which equals 120m² for each triangle. This means that the area for both triangles is 120 × 2 = 240m².
Next we have the area of the back of the prism, which is 11 × 10 = 110m².
Finally we need to find the area of the rectangle on top of the prism, which is 11 × 26 = 286m²
This means your final answer would be the sum of all of these, which is 264 + 240 + 110 + 286 = 900m².
I hope this helps!
find the x and the area of the shape perimeter is 64.5
Answer:
x=8
A = 192
Step-by-step explanation:
The perimeter is the sum of the outer lengths
17.9 + 22.6 + 3x = 64.5
Combine like terms
40.5 +3x = 64.5
Subtract 40.5 from each side
40.5 +3x -40.5 = 64.5 - 40.5
3x =24
Divide each side by 3
3x/3 = 24/3
x = 8
The area of a triangle is given by
A = 1/2 bh
The base is 3x = 3(8) =24
and the height is 2x = 2(8) =16
A = 1/2 (24) * 16
A =192
C/ 8= 9. What does c equal
Answer: 72
72/8 will get you 9. To see if the answer is correct Multiply 9*8.
Answer:
72
Step-by-step explanation:
c/8 = 9
Multiply each side by 8
c/8 * 8 =9*8
c = 72
Can anybody find the measure of arc KL and arc JK?
click on image for full picture
Answer:
Arc KL = 30°
Arc JK = 90°
Step-by-step explanation:
Arc KL is a connected to a central angle with the measurement of 30°. Because it is a central angle, the arc's measurement will be the same as the central angle's measurement:
Arc KL = 30°
Arc JK is connected to a central angle that has a right angle measurement sign. A right angle = 90°. Because it is a central angle, the arc's measurement will be the same as the central angle's measurement:
Arc JK = 90°
~
Answer:
arc kl= 30
arc jk=90
Step-by-step explanation:
Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 17 feet by 17 feet by 2 inches for a patio if the concrete costs $64.00 per cubic yard?
Answer:
$114.17
Step-by-step explanation:
First we need to convert cubic yard to cubic feet.
One yard is equivalent to three feet, so one cubic yard is 3^3 = 27 cubic feet.
So the cost of one cubic feet is 64/27 = $2.3704
We also need to convert from inches to feet.
One inch is 1/12 feet, so 2 inches is 2/12 = 1/6 feet
Now we need to find the volume of the slab:
Volume = 17 * 17 * (1/6) = 48.1667 ft3
Now, to find the cost, we can use a rule of three:
1 cubic feet -> $2.3704
48.1667 cubic feet -> X
X = 48.1667 * 2.3704 = $114.1743
An artist is creating a sculpture where a globe with a diameter of 48 inches sits in a cone like a scoop of ice cream. She wants the cone of her sculpture to be geometrically similar to an actual ice cream cone that has a diameter of 2 1/2 inches and a height of 6 inches. What should be the height of the cone in the artist’s sculpture?
We have been an artist is creating a sculpture where a globe with a diameter of 48 inches sits in a cone like a scoop of ice cream. She wants the cone of her sculpture to be geometrically similar to an actual ice cream cone that has a diameter of 2 1/2 inches and a height of 6 inches.
We will use proportions to solve our given problem.
[tex]2\frac{1}{2}=2.5[/tex]
[tex]\frac{\text{Height of sculpture}}{\text{Diameter of sculpture}}=\frac{\text{Height of cone}}{\text{Diameter of cone}}[/tex]
[tex]\frac{\text{Height of sculpture}}{48}=\frac{6}{2.5}[/tex]
[tex]\frac{\text{Height of sculpture}}{48}\cdot 48=\frac{6}{2.5}\cdot 48[/tex]
[tex]\text{Height of sculpture}=6\cdot 19.2[/tex]
[tex]\text{Height of sculpture}=115.2[/tex]
Therefore, the height of the sculpture should be 115.2 inches.
Answer:
115 1/5
Step-by-step explanation:
This is 100% the answer because I took a test with this question and that was the correct answer
Please mark as brainliest :)~
Simplify the expression.
100^(1/2)-125^(1/3)
PLEASE HELP OFFERING 24 POINTS
Analyzing Student Work
Analyze Marika's steps. Which statement is true about
her work?
Marika solved the equation (6x +15)2 + 24 = 0. Her work
is below.
1. (6x + 15)2 = -24
2. V6x +15)2 = -24
In step 2, Marika should have simplified / -24 to be
4-6
3. 6x + 15 = -25
4. 6x = -2.5 - 15
-256-15
5. X=
There are no real solutions to this equation because
the square root of a negative number is not a real
number
There should be two real solutions to this equation
because -24 = +25.
Marika correctly solved this equation.
Answer:B
Step-by-step explanation:
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