One hexagonal prism has dimensions that are triple the dimensions of a similar hexagonal prism. If the volume of the smaller prism is 4.75 cm3, what is the volume of the larger prism?
4.75 cm3
14.25 cm3
42.75 cm3
128.25 cm3
Answers
Answer:
128.25 cm³
Step-by-step explanation:
Volume of an hexagonal prism:
The volume of an hexagonal prism is given by:
\(V = \frac{3\sqrt{3} a^2h}{2}\)
In which a and h are the dimensions.
Triple the dimensions
This means that the volume will be multiplied by 3^3, 27(as there are 3 terms which are dependent of the dimensions, a² and h).
If the volume of the smaller prism is 4.75 cm3, what is the volume of the larger prism?
27*4.75 = 128.25 cm³
128.25 cm³ is the answer
Answer:
128.25 cm3
Step-by-step explanation:
Related Questions
SOMEONE PLEASE HELP
The number of chips of different colors in Gail's bag is shown below
-2 blue chips
-4 pink chips
-8 white chips
Gail takes out a chip from the bag randomly without looking, She replaces the chip and then takes out another chip from the bag. What is the probability that Gail takes out a white chip in both draws?
Answers
Answer:
8 over 15 multiplied by 7 over 14 is equal to 56 over 210
8 over 15 plus 7 over 14 is equal to 217 over 210
8 over 15 plus 8 over 15 is equal to 16 over 15
8 over 15 multiplied by 8 over 15 is equal to 64 over 225
She's taking it out and then she replaces it
and so that means the denominator would stay 15 both times
and since it's a white chip in both draws, it would be 8/15 * 8/15
Find the volume of a cone of radius 3.5cm and vertical height 12 cm.
Answers
Answer:
Volume ≈ 153.93804 cm^3
Rounded to the nearest whole number, the volume of the cone is approximately 154 cm^3.
Step-by-step explanation:
a party rental company has chairs and tables for rent the total cost to rent three chairs and eight tables is $58 the total cost to rent 5 chairs and two tables is $23 what is the cost to rent each chair in East table
Answers
Let 'c' be the cost to rent one chair and let 't' be the cost to rent one table.
Then, since three chairs and eight tables cost $58, then:
\(3c+8t=58\)also, the cost to rent 5 chairs and two tables is $23,then:
\(5c+2t=23\)we have the following system of equations:
\(\begin{cases}3c+8t=58 \\ 5c+2t=23\end{cases}\)now, if we multiply by -4 the second equation, we get:
\(\begin{gathered} -4\cdot(5c+2t=23) \\ \Rightarrow-20c-8t=-92 \end{gathered}\)then, if we add this equation with thte first equation from the system, we get the following:
\(\begin{gathered} 3c+8t=58 \\ -20c-8t=-92 \\ ----------- \\ -17c=-34 \\ \Rightarrow c=\frac{-34}{-17}=2 \\ c=2 \end{gathered}\)now that we have that c = 2, we can use this value to find the cost of the tables with the first equation:
\(\begin{gathered} 3(2)+8t=58 \\ \Rightarrow6+8t=58 \\ \Rightarrow8t=58-6=52 \\ \Rightarrow t=\frac{52}{8}=6.5 \\ t=6.5 \end{gathered}\)therefore, the cost to rent each chair is $2 and the cost to rent each chair is $6.5
is 13/10 irrational or rational
Answers
Answer:
Yes
Step-by-step explanation:
Both 13 and 10 are integers, meaning 13.10 is rational.
Emma has a rain gauge on her deck to measure the amount of rain that falls in the area. After a storm with steady rain, there were 4.23 inches of water in the rain gauge. If the storm lasted 3 hours, how much water did the rain gauge collect every hour?
Answers
The rain gauge collected 1.41 inches of water every hour.
In the question ,
it is given that ,
amount of water collected in the rain gauge = 4.23 inches
time for which the rain lasted = 3 hours
So the amount of water collected in the rain gauge every hour can be calculated using the formula
amount of water collected every hour = (total amount of water)/( total time it rained)
Substituting the values of amount of water collected and time for which it rained , in the formula we get
amount of water collected every hour = 4.23/3
= 1.41 inches
Therefore , the rain gauge collected 1.41 inches of water every hour.
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Point B has coordinates (1,2). The x-coordinate of point A is -11. The distance between point A and point B is 15 units. What are the possible coordinates of point A?
Answers
Answer:
We know that the x-coordinate of point A is -11, and that the distance between point A and point B is 15 units. Let's call the y-coordinate of point A "y". Then we can use the distance formula to find the two possible values of y:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1,y1) = (-11,y) is the coordinates of point A, and (x2,y2) = (1,2) is the coordinates of point B. Substituting the values, we get:
15 = sqrt((-11 - 1)^2 + (y - 2)^2)
15 = sqrt(144 + (y - 2)^2)
15^2 = 144 + (y - 2)^2
225 = 144 + (y - 2)^2
81 = (y - 2)^2
y - 2 = ±9
y = 2 ± 9
So the possible coordinates of point A are (-11,11) and (-11,-7).
Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.50. During one busy period, Kyle served 21 cups of coffee, using 294 ounces of coffee, while collecting a total of $24.35. How many cups of each size did Kyle fill?
Kyle filled ___ 10-oz cup(s), ___ 14-oz cup(s), and ___ 20-oz cup(s).
Answers
Kyle filled 6 10-oz cup(s), 11 14-oz cup(s), and 4 20-oz cup(s).
Let's define the variables:
x = number of 10-oz cups of coffee sold.
y = number of 14-oz cups of coffee sold.
z = number of 20-oz cups of coffee sold.
We know that:
Kyle served 21 cups of coffee, then:
x + y + z = 21
He used 294 ounces of coffee, then:
x*10 oz + y*14 oz + z*20 oz = 294 oz
He collected a total of $24.35, then:
x*($0.95) + y*($1.15) + z*($1.50) = $24.35
Then we have a system of 3 equations:
x + y + z = 21
x*10 oz + y*14 oz + z*20 oz = 294 oz
x*($0.95) + y*($1.15) + z*($1.50) = $24.35
To solve this, the first thing we need to do is isolate one of the variables in one of the equations, let's isolate x in the first one.
x = 21 - y - z
Now we can replace this in the other two equations to get:
(21 - y - z)*10 oz + y*14 oz + z*20 oz = 294 oz
(21 - y - z)*($0.95) + y*($1.15) + z*($1.50) = $24.35
Now we can simplify these two equations:
y*4 oz + z*10 oz = 294 oz - 210oz = 84 oz
y*($0.20) + z*($0.55) = $24.35 - $19.94 = $4.40
Now we need to do the same thing, we need to isolate one of the variables in one of the equations, we can isolate z in the first one:
z*10 oz = 84oz - y*4 oz
z = (84oz - y*4 oz)/10oz
z = 8.4 - y*0.4
Now we can replace this in the other equation:
y*($0.20) + ( 8.4 - y*0.4)*($0.55) = $4.40
Now we can solve this for y.
y*($0.20) + $4.62 - y*$0.22 = $4.40
y*$0.02 = $4.40 - $4.62 = $0.22
y = $0.22/$0.02 = 11
Now that we know the value of y, we can use:
z = 8.4 - y*0.4
z = 8.4 - 11*0.4 = 4
Now that we know the value of z and y we can use:
x = 21 - y - z
x = 21 - 11 - 4 = 6
Then we found:
x = 6
y = 11
z = 4
this means that:
Kyle filled 6 10-oz cup(s), 11 14-oz cup(s), and 4 20-oz cup(s).
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For each of the following determine a unit rate using the information given. Show the division that leads to your answer. Use appropriate units. All rates will be whole numbers. At a theatre, Mia paid $35 for five tickets
Answers
Answer:
Step-by-step explanation:
cool
S={(3,p),(3,0),(4,q),(1,4)}
Answers
Answer:
S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:
(3,p): The first element is 3 and the second element is p.
(3,0): The first element is 3 and the second element is 0.
(4,q): The first element is 4 and the second element is q.
(1,4): The first element is 1 and the second element is 4.
The radius of a circle is 4 miles. What is the length of a 45° arc?
45°
r=4 mi
Answers
The length of a 45° arc with a radius of 4 miles is approximately 3.14 miles, calculated using the formula for arc length.
To determine the length of a 45° arc given a radius of 4 miles, we can use the formula: Arc length = (angle measure / 360°) x 2πr, where r is the radius of the circle and π is a constant equal to approximately 3.14.
Substituting the given values into the formula, we get: Arc length = (45° / 360°) x 2π(4 mi)Arc length = (1/8) x 2π(4 mi)Arc length = (1/8) x 8π Arc length = π
The length of the 45° arc is approximately 3.14 miles.
Summary: To find the length of a 45° arc of a circle, we use the formula: Arc length = (angle measure / 360°) x 2πr. Given a radius of 4 miles, we can substitute the values into the formula to get the length of the 45° arc, which is approximately 3.14 miles.
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12. The wheel of a machine rotates at the rate of 300 rpm (rotation per minute). If the diameter of the wheel is 80 cm,what are the angular (in radian per second) and linear speed (in cm per second) of a point on the wheel?
Answers
SOLUTION
From the question, the wheel of the machine rotates 300 times per minute.
One rotation is 360 degrees.
360 degrees in radians is
\(360\degree=2\pi\text{ radians }\)A minute = 60 seconds. So the angular speed w, in radians per seconds become
\(w=\frac{300\times2\pi}{60\text{ seconds }}=\frac{300\times2\pi}{60}=10\pi\text{ rad/secs}\)Hence the angular speed is
\(10\pi\text{ rads/sec}\)The angular speed w is related to the linear speed v by the formula
\(\begin{gathered} v=rw \\ where\text{ v = linear speed = ?} \\ w=angular\text{ speed = 10}\pi\text{ rads/secs} \\ r=radius\text{ =}\frac{diameter}{2}=\frac{80}{2}=40\text{ cm } \end{gathered}\)Substituting into the formula, we have
\(\begin{gathered} v=rw \\ v=40\times10\pi \\ v=400\pi\text{ cm/secs } \\ v=1256.63706\text{ cm/secs } \end{gathered}\)Hence the linear speed is 1256.64 cm/secs to the nearest hundredth
What is 6 times 6? #ifyouknowitquestion!
Answers
Answer:
36
Step-by-step explanation:
Help please i would appreciated it
here is the picture is about Row Ops
Answers
The matrix operation add -4(row 1) to row 3 is\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)
Evaluating the matrix expressionFrom the question, we have the following parameters that can be used in our computation:
\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\4&-1&6&-8\end{array}\right]\)
From the question, we understand that
We are to add -4(row 1) to row 3
This means that
row 3 = row 3 - 4 * row 1
When these values are evaluated, we have
4: 4 - 4 * 1 = 0
-1: -1 - 4 * 2 = -9
6: 6 - 4 * 1 = 2
-8: -8 - 4 * -5 = 12
This means that we relace 4, -1, 6, and -8 in row 3 with 0, -9, 2 and 12
Using the above as a guide, we have the following:
\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)
Hence, the result of the matrix expression is \(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)
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I triangle ABC is dilated by a scale factor of 3 with a center of (2.1). what is the location of A?
Answers
Pedro earns $94.50 for 6 hours of work. If he makes a constant hourly wage, which table represents the relationship between the number of hours he works and his total earnings?
please help me
Answers
Answer:
The answer is most likely A.
The reason why, is because since the earning in 6 hours is $94.50, so the hourly wage would be, $15.75 because:
94.50/6 = 15.75
Graph B, for the first hour, the amount of dollars is correct, but in 11 hours, it says 25.75, which is not correct so Graph B cannot be it.
Graph C, shows that at hour 1, that it is 15.75 dollars, but at hour 2 16.75, as well with hour 3, 17.75. The graph is showing an increase of 1 dollar per hour, which is not correct so graph C is not it.
Graph D shows that at hour 6, there is $94.50, which is correct, but at hour 12, its 100.50. This is not true because , the hour has increased by 6, and when it increased by 6, the amount of pay increased by 6 as well, which is not the right way in which you would do so.
Option A is correct!
Step-by-step explanation:
Hope it helps! =D
can anyone help me answer this?
Answers
Answer:
an equation to determine how many pairs of shoes, p, Roger must sell in a day to meet his daily earnings goal is:
f (p) = 4.50p + 40
the number of pairs of shoes he must sell to meet his daily earnings goal is:
p = 16 (pair of shoes)
suppose a certain home improvement outlet knows that the monthly demand for framing studs is 2,500 when the price is $3.25 each but that the demand is 3,900 when the price is $2.83 each. assuming that the demand function is linear, write its equation. use p for price (in dollars) and q for quantity.
Answers
The demand function is linear, so we can write it in the form of:
q = a - bp
Where a and b are constants and q is the quantity demanded and p is the price. We have two points, one at a price of $3.25 with a quantity of 2,500, and another at a price of $2.83 with a quantity of 3,900.
We can use these two points to solve for the values of a and b in the equation.
Plugging in the first point:
2500 = a - (3.25)b
Plugging in the second point:
3900 = a - (2.83)b
We can then solve this system of equation by substituting the first equation with the second one
3900 = a - (2.83)b
=2500 + 1400 = a - (3.25)b + (2.83)b
=a - (0.42)b
So the equation is:
q = 3900 - 0.42p
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Solve using the tangent formula(real answers please)
Answers
Answer:
21.17
Step-by-step explanation:
tan= opposite/ adjacent
tan(36)= x/29
0.73= x/29
x= 21.17
A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 170 gallons of a mixture that contains 80% pure antifreeze, how many gallons of each brand of antifreeze must be used?
first brand: ?
Second brand ?
please dont answer if you dont know it.
Answers
The quantity of first brand is 102 gallons and quantity of second brand is 68 gallons
Given,
The first brand of antifreeze = 70% pure antifreeze
The second brand of antifreeze = 95% pure antifreeze
The quantity of mixture = 170 gallons contains 80% pure antifreeze
We have to find the quantity of each brand of antifreeze must be used;
Now,
The quantity of first brand = x gallons
The quantity of second brand = y gallons
Then,
x + y = 170
x = 170 - y ....(1)
70x / 100 + 95y / 100 = (80 × 170) / 100
70x + 95y = 13600
Now, putting the value of x from equation 1:
70 (170 - y) + 95y = 13600
11900 - 70y + 95y = 13600
11900 + 25y = 13600
25y = 13600 - 11900
25y = 1700
y = 1700/25
y = 68
Now, putting this value of y in equation 1:
x = 170 - 68
x = 102
Therefore,
The quantity of first brand is 102 gallons and quantity of second brand is 68 gallons
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please help with this
Answers
help i will give you 5 star if you answer this math question
Answers
Answer:
12
Step-by-step explanation:
12>6
12 is factor of 36 36/12=3
12 is factor of 48 48/12=4
9x + 6y = 1164 x+y =144
Answers
how do you find answer to 9/35 - 1/5?
Answers
Answer:
2/35
Step-by-step explanation:
\(\frac{9}{35}-\frac{1}{5}=\frac{9}{35}-\frac{7}{35}=\frac{2}{35}\)
What’s the answer
5 3/7 - 2 1/5
Answers
Answer:3.22
Step-by-step explanation:
Hope this helps
See attachment for math work and answer.
Solve the quadratic equation by completing the square
X^2+14x+35=0
First choose the appropriate form and fill in the blanks with the correct numbers
Then solve the equation if there is more than one solutionseparate them with commas
Answers
Answer:
x= -7±√14
Step-by-step explanation:
Using the quadratic equation, Use the quadratic formula to find the solutions.
−
b
±
√
b
2
−
4
(
a
c
)
2
a
-
b
±
b
2
-
4
(
a
c
)
2
a
Substitute the values
a
=
1
a
=
1
,
b
=
14
b
=
14
, and
c
=
35
c
=
35
into the quadratic formula and solve for
x
x
.
−
14
±
√
14
2
−
4
⋅
(
1
⋅
35
)
2
⋅
1
-
14
±
14
2
-
4
⋅
(
1
⋅
35
)
2
⋅
1
Simplify.
Tap for more steps...
x
=
−
7
±
√
14
x
=
-
7
±
14
The result can be shown in multiple forms.
Exact Form:
x
=
−
7
±
√
14
x
=
-
7
±
14
Decimal Form:
x
=
−
3.25834261
…
,
−
10.74165738
…
Oliver drove the first 90 miles of his journey in 1.5 hours and the remaining 120 in 3 hours. What was the average speed on the second part of Oliver’s journey?
Answers
Answer:
Step-by-step explanation:
90 miles + 120 miles = 210 total miles
1.5 hours + 3 hours = 4.5 total hours.
Average speed = 210 miles / 4.5 hours = 46 2/3 miles per hour
Answer:
40
Step-by-step explanation:
I know meth
Please helppp meeee for brainliest!! ❤️❤️
Answers
Answer:
I'm sorry but I couldn't see the hole question
Steven earns extra money babysitting. He charges $35.00 for 4 hours and $70.00 for 8
hours.
Enter an equation to represent the relationship. Let x represent the number of hours
Steven babysits and y represent the amount he charges.
The equation is y =
Answers
Answer:
Step-by-step explanation:
35/4 = 8.75
70/8 = 8.75
x= 1 (hour) y = 8.75$
Answer:
y= 35x/4
Step-by-step explanation:
We can solve this by plotting a graph of these values of (4,35) and (8,70). We find that this graph is a straight line. Meaning we can solve it in the form Y = mx, where m is the gradient. there is no y intercept as our range is greater than x =0. So the gradient will be 70-35/8-4, which is 35/4. Simply substitute it into the formula to obtain y= 35x/4!
Write the letter of the definition next to the matching word as you work through the lesson.
Answers
The matching word are as follows:- center of dilation - C,corresponding angles - D,dilation - E,scale factor (of a dilation) - A,similar polygons - B respectively.
What are corresponding angles?Corresponding angles are a pair of angles that have the same relative position at the intersection of two lines when one line is crossed by a transversal.
They are located in corresponding (matching) positions in congruent or similar figures, and are congruent if the figures are similar.
center of dilation: C.The fixed point that is parallel to each point on the pre-image and the corresponding point on the picture during a dilatation
corresponding angles: D.a pair of angles in two congruent or similar figures that are in the same relative position
dilation: E. The transformation in which each point on the image lies on the same line as the corresponding point on pre-image and a fixed point called the center of dilation.
scale factor (of a dilation): in a dilation, the constant rate between the distance from the center of dilation and a point on the image and the distance from the center of dilation and the matching point on thepre-image
similar polygons: B.two or further polygons in which corresponding angles are harmonious and the lengths of corresponding sides are in proportion.
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Need help solving this problem 35)210.35
Answers
Answer: The answer is 0.16638935108
Step-by-step explanation: