Answer:
[tex]V=V_p-V_cV=27.712 cm^3 - 4.019 cm^3V=23.693 cm^3V=23.6 cm^3[/tex]
Step-by-step explanation:
Given that:
Diameter of the cylinder: d=1.6 cm
Apothem of the hexagon: a=2 cm
Assuming the thickness of the steel hex nut: t=2 cm
Volume of metal in the hex nut: V=?
[tex]V=V_p-V_c[/tex]
[tex]\texttt {Volume of the prism}: V_p\\\\\texttt {Volume of the cylinder}: V_c[/tex]
Prism:
[tex]V_p=Ab h[/tex]
Ab=n L a / 2
Number of the sides: n=6
Side of the hexagon: L
Height of the prism: h=t=2 cm
Central angle in the hexagon: A=360°/n
A=360°/6
A=60°
[tex]\tan \frac{A}{2} =\frac{L}{2} / a[/tex]
[tex]\tan \frac{60}{2} =\frac{L}{2} / 2cm[/tex]
[tex]\tan 30 =\frac{L}{2} / 2cm[/tex]
[tex]\frac{\sqrt{3} }{3} =\frac{\frac{L}{2} }{2}[/tex]
[tex]2\frac{\sqrt{3} }{3} =\frac{L}{2}[/tex]
[tex]L=4\frac{\sqrt{3} }{3}[/tex]
[tex]Ab=n *L *\frac{a}{2}[/tex]
[tex]Ab=6(4\frac{\sqrt{3} }{3} )(2cm)/2[/tex]
[tex]=24\frac{\sqrt{3} }{3} cm^2\\\\=8\sqrt{3} cm^2[/tex]
[tex]V_p=Ab h[/tex]
[tex]=(8\sqrt{3} )cm^2(2cm)\\\\=16\sqrt{3} cm^3\\\\=16(1.732)cm^3\\\\=27.712cm^3[/tex]
Cylinder:
[tex]V_c=\pi\frac{d^2}{4} L[/tex]
π=3.14
d=1.6 cm
Height of the cylinder: h=t=2 cm
[tex]V_c=3.14\times\frac{1.6^2}{4} \times2\\\\=3.14\times\frac{2.56}{4} \times 2\\\\=2.0096\times2\\\\=4.019cm^3[/tex]
[tex]V=V_p-V_cV=27.712 cm^3 - 4.019 cm^3V=23.693 cm^3V=23.6 cm^3[/tex]
Answer:
23.6
Step-by-step explanation:
Edge 2020
what is the equation of the line? please help !!!! first and correct answer will get brainesttt
Answer:
y=1/2x-4
Step-by-step explanation
can anyone answer this questionin 4 Step I'll mark that person has branily please
Answer:
[tex] - \frac{11}{28} [/tex]
Step-by-step explanation:
[tex] \frac{2}{5} \bigg( - \frac{3}{7} \bigg) - \frac{1}{6} \times \frac{3}{2} + \frac{1}{14} \times \frac{2}{5} \\ \\
= - \frac{6}{35} - \frac{3}{12} + \frac{1}{35} \\ \\
= \frac{1 - 6}{35} - \frac{1}{4} \\ \\
= \frac{ - 5}{35} - \frac{1}{4} \\ \\
= \frac{ - 1}{7} - \frac{1}{4} \\ \\
= \frac{ - 1\times 4-1\times 7}{7\times 4} \\\\
= \frac{ - 4- 7}{28} \\\\
= -\frac{ 11}{28} \\\\
[/tex]
Please help! Correct answer only please! I need to finish this assignment by today.
The aspect ratio of a rectangular shape is it's length divided by it's width (L/W). If the aspect ratio of a chalkboard is 4:3 and the width is 7 in,
what is the length of the chalkboard?
A. 6.67 in
B. 9.33 in
C. 12 in
D. 14 in
Answer:
B
Step-by-step explanation:
If the ratio of the length of the chalkboard to the width is 4:3, this means that the length of this one is 7* 4/3=28/3. This can be rewritten as approximately 9.33 inches, or answer choice B. Hope this helps!
50a^3-18ab^2 guys plz factorise this for me
Answer:
2a(5a+3b)(5a−3b)
Step-by-step explanation:
Both terms have 2a, so take out the 2a and you will get your answer.
Answer:
2a(5a - 3b)(5a + 3b)
Step-by-step explanation:
50a³ - 18ab² = 2a(25a² - 9b²) = 2a(5a - 3b)(5a + 3b)
The product of a number and its ___________ is
A).opposite
B)reciprocal
C)factor
D)quotient
Answer:
Most definitely reciprocal
what is the quotient of the rational expression below? 3x+1/x+8 ÷ x-7/5x
Answer:
8x^2 + 45/5x
Step-by-step explanation:
write the division as a fraction
3x+ 1/x + 8/x - 7/5x
using a=a/1, convert the expression into a fraction
3x/1 - 7/5x
calculate the product
3x/1 - 7x/5
expand the fraction to get the least common denominator
5 x 3x/ 5 x 1 - 7x/5
multiply the numbers
15x/5 - 7x/5
write all numerators above the common denominator
15x - 7x/5
collect like terms
8x/5
write the factor as a product
8/5 x + 1/x + 8/x
calculate the product
8x/5 + 5 x 1/5x + 5 x 8/5x
expand the fraction to get the least common denominator
X x 8x/X x 5 + 5/5x + 5 x 8/5x
multiply the numbers
X x 8x/X x 5 + 5/5x + 40/5x
calculate the product
8x^2/5x + 5/5x +40/5x
write all numerators above the common denominator
8x^2 + 5 + 40/5x
add the numbers and that's the answer
8x^2 + 45/5x
(that was l o n g)
Find the distance from point B to point C. Please help 25 points!!
Answer:
9.6 = BC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opposite/ adjacent
tan 58 = BC / 6
Multiply each side by 6
6 tan 58 = BC
9.602007174 =BC
Round to the nearest tenth
9.6 = BC
Answer:
BC= 9.6
Hope it helps :)
Grace wanted to pick a card randomly from a regular deck of 52 cards. Fifty of the cards were regular playing
cards, and the rest of the cards were jokers. What is the probability that Grace picks a joker?
Answer:
2:52 or 1:26 (simplest form)probability.
if a certain number x is doubled, the result is less than or equal to 12. find the range of values of the number
Answer:
2x≤12
2x/2 ≤12/2
x≤6
therefore x=6
x+x
6+6=12
La distancia en Km. De Santo Domingo a Puerto Plata está dada por la expresión D = 4x³- 10x² -6. ¿Cuál es la distancia aproximada de santo Dom. A Puerto Plata si X = 6 km?
Answer:
The distance when x = 6km is D = 498 KM
Step-by-step explanation:
Here, given the formula for the distance, we want to find the distance D given the value of x to be 6km
What we do simply here is to substitute the value 6km as x in the equation
The equation is
D = 4x^3 - 10x^2 -6
Substituting x = 6, we have
D = 4(6^3) -10(6^2) -6
D = 864-360-6
D = 498 km
If p=3(2q+r), express q in terms of p and r.
Answer:
[tex]q=\frac{1}{6}p- \frac{1}{2}r[/tex]
Step-by-step explanation:
[tex]p=3(2q+r)[/tex]
[tex]2q+r=\frac{p}{3}[/tex]
[tex]2q=\frac{p}{3} -r[/tex]
[tex]q=\frac{p}{6}- \frac{r}{2}[/tex]
In a box-and-whisker plot, the interquartile
range is a measure of the spread of the
middle half of the data. Find the interquartile
range for the data set: 10, 3, 7, 6, 9, 12, 13.
Answer:
IQR=8
Step-by-step explanation:
write numbers in ascending order
3 6 9 10 12 13
find the middle, in this case, it's two numbers (10 and 12)
3 6 are on the left, find the middle between them; 3+6/2
4.5
12 and 13 are on the right, find the middle between them;
12+13/2
12.5
IQR=12.5-4.5
which image shows -1 7/8 on a number line
Answer:
C
Step-by-step explanation:
C goes past -1 and almost reaches -2 so you know it will include some sort of fraction.
If you count the tick marks, C is on the 7th tick mark which is the one before -2. This represents 7/8 because 8/8 would be right on -2.
So, C shows -1 and 7/8
The sticker price is the price you must pay for the vehicle
True or False
it's true...........
Answer:
False
Step-by-step explanation:
Verified correct with test results.
Which number is less than 0.37? A. 0.72 B. 0.5 C. 0.35 D. 0.41
Answer:
0.35 is less than 0.37 because 35 < 37.
Answer:
C is the correct answer
Step-by-step explanation:
A line segment has endpoints at (4.-6) and (0,2).
What is the slope of the given line segment?
What is the midpoint of the given line segment?
What is the slope of the perpendicular bisector of the given line segment?
What is the equation, in slope-intercept form, of the perpendicular bisector?
Answer:
see explanation
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, - 6) and (x₂, y₂ ) = (0, 2)
m = [tex]\frac{2+6}{0-4}[/tex] = [tex]\frac{8}{-4}[/tex] = - 2
---------------------------------------
Find the midpoint using the midpoint formula
M =( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
= [tex]\frac{4+0}{2}[/tex] , [tex]\frac{-6+2}{2}[/tex] ) = (2, - 2 )
-----------------------------------------------
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
----------------------------------------------
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = [tex]\frac{1}{2}[/tex] , thus
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (2, - 2) into the partial equation
- 2 = 1 + c ⇒ c = - 2 - 1 = - 3
y = [tex]\frac{1}{2}[/tex] x - 3 ← equation of perpendicular bisector
Answer:
-2(2, -2)1/2y= 1/2x - 3Step-by-step explanation:
Points given: (4, -6) and (0, 2)
Slope intercept form of the line going through the given pints:
y= mx+b
m= (y2-y1)/(x2-x1)= (2+6)/(0-4)= -2 slope is -2y= -2x+b ⇒ -6= -2*4+b ⇒ b= 8-6= 2 ⇒ y= -2x+2
Mid point= (x1+x2)/2, (y1+y2)/2= (4+0)/2, (-6+2)/2= (2, -2)The slope of the perpendicular bisector is the negative reciprocal of the line segment which it is dividing:
m'= -1/m= -1/-2= 1/2Equation of perpendicular bisector:
y= 1/2x+bIt passes through the mid point: (2, -2), so
b= y - 1/2x= -2 - 1/2*2= -2 -1= -3So the equation of perpendicular line:
y= 1/2x - 3Jeremy’s bank account started at a balance of $124 this week. Since then, he wrote a check, which decreased his balance by $147. Jeremy was then charged an overdraft fee, decreasing his balance by $32. Finally, he deposited a paycheck, which increased his balance by $567. What is Jeremy’s ending balance after these transactions, in dollars?
Answer:
$512
Step-by-step explanation:
His bank account started at a balance of $124.
He wrote a check, which decreased his balance by $147. His new balance is:
124 - 147 = -$23
Jeremy was then charged an overdraft fee, decreasing his balance by $32. That is:
-23 - 32 = -$55
He deposited a paycheck, which increased his balance by $567. His account balance will become:
-55 + 567 = $512
His account balance after those transactions is $512.
what is the midpoint of the segment shown below?
Answer:
(5, 1/2)
Step-by-step explanation:
To find the midpoint
Take the sum of the x coordinates and divide by 2
(5+5)/2 = 10/2 = 5
Take the sum of the y coordinates and divide by 2
(4+-3)/2 = 1/2 = 1/2
The midpoint is ( 5, 1/2)
It is answer D
Its is exactly in between these to values
they paid $13 for each pepperoni pizza and $11for each plain pizza the club bought total of 18 pizzas for the party and paint a total of $212 Drag and drop the numbers to the boxes to create an equation which models this situation if x=the number of pepperoni pizza and y=the numbers of plain pizza boght
Complete question;
A booster club paid for pizzas for an end of season party. They paid $13 for each pepperoni pizza and $11 for each plain pizza. The club bought a
total of 18 pizzas for the party and paid a total of $212.
Drag and drop the numbers to the boxes to create an equation which models this situation if x = the number of pepperoni pizzas and y = the number of plain pizzas bought.
Answer:
13x + 11y = 212
Step-by-step explanation:
They bought 2 different recipe of pizza. The first is the pepperoni pizza and the second kind is the plain pizza. The pepperoni pizza cost $13 each while the plain Pizza cost $11 each. The total number of pizza bought is 18 in number.
The total cost of the pizza is also $212.
number of pizza bought = 18
total cost of pizza = $212
x = the number of pepperoni pizzas
y = the number of plain pizzas
The number of pepperoni pizzas multiply by the cost for each will give the cost of the pepperoni pizzas. This same method is applied to get the cost of the plain pizzas.
Therefore, adding the individual cost of the kinds of pizza will give the total cost of the pizzas.
13x + 11y = 212
Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by 3 and add 1. Now repeat the process with your new number. If you keep going, you'll eventually end up at 1. Explain why you get 1 every time. I don't know why I end up with 1 every single time. Can someone help me please?
Answer:
Because the process by itself will force the numbers to be eventually reduced to an even number whose half is always another even number. For example, if you start taking the number 3, the result will be 10; then, the result of 10 will be 5; then, the result will be 16. When you get 16, the result will be 8, then 4, then 2 and finally 1.
Step-by-step explanation:
If 30% of a company's advertising budget is $7,200, then what is the full advertising budget?
Answer:
$24000
Step-by-step explanation:
Let the full advertising budget of the company be $x.
Therefore, 30% of x = $7,200
[tex]\frac{30}{100} \times x= 7200 \\\\x = \frac{100}{30} \times 7200\\\\x = 100 \times 240\\\\x = \$24000[/tex]
Hence, full advertising budget of the company is $24000.
screenshot below-mathematics ,help please!!
Answer:
(a) range = difference between highest
mark and lowest mark
range of marks = 10 - 6
= 4
(b) total students = marks × frequency
(6×5)+(7×4)+(8×7)+(9×10)+(10×4)
= 30+28+56+90+40
= 244 students
(c) total frequency = 5+4+7+10+4
= 30
mean mark = total students/total
frequency
= 244/30
= 8.133
Answer:range-4 , no. of students-30, mean mark is 26
Step-by-step explanation:
At my friend’s middle school the ratio of teachers to students is 1:9. If there are 45 teachers at the school, how many students are there? Show your work or explain how you determine your answer.
Write a literal/explicit equation to model the situation above. Where Y is the number of students and X the number of teachers at the school
Answer:
405 students
Step-by-step explanation:
1=teachers
9=students
1=45 teachers
9=y students
y=9 x 45
y=405 students
Write and solve an equation to represent the following situation: an electrician earns an hourly wage of $13.50 plus a $75 bonus. If he made $149.25, how many hours, h, did he work?
list the integers that satisfy both these inequalities 2x+9 0 x > -12 put the answer on the first line
Answer:
The Answer is 5
Step-by-step explanation:
What is the rate of change of the amount earned with respect to hours worked for this function?
hours per dollar
hours per dollar
3 dollars per hour
13 dollars per hour
Question:
The graph shows the amount of money Miguel earns after working x hours. What is the rate of change of the amount earned with respect to hours worked for this function? hours per dollar hours per dollar 3 dollars per hour 13 dollars per hour
Answer: 13 dollars per hour
Step-by-step explanation:
The rate of change (ROC) for the point defined on the graph can be deduced by calculating the ratio of the difference between the two coordinate points given, similar to calculating the gradient or slope :
Point a = (5, 65) = (x2, y2)
Point b = (2, 26) = (x1, y1)
Calculating the gradient or slope :
Rate of change = (y2 - y1) / (x2 - x1)
Rate of change = (65 - 26) / (5 - 2)
Rate of change = 39 / 3
= 13 dollars per hour
Answer:
I think that the answer is D
What would the base be to the solution to
4^8*4^2?
Answer:
It can would be 4
Step-by-step explanation:
When you multiply exponents you add the exponents
so you get 4^10
What is the 9th square number.
On Monday, Avi walked from his home to the school track and walked
4 laps around the track for a total of 3.5 miles. On Saturday, Avi ran from
his home to the school track, ran 2 laps, and then ran home for a total of
4 miles. Let x represent the distance from Avi’s home to the school track,
and let y represent the distance of one lap around the track.
1. Write a system of equations to represent this situation.
2. What is the distance from Avi’s home to the school track and around
the track?
3. On Saturday, Avi walked from his home to the school track, walked 6
times around the track, and then walked home. How far did he walk in all?
Avi knows that the distance from his home to the library and back is
at least 2.5 miles. He also knows that the distance from his home to
the library and then to the school track is less than 3 miles. Let p
represent the distance from Avi’s home to the library, and let q
represent the distance from the library to the school track.
4. Write a system of inequalities to represent this situation.
5. Can the distance from Avi’s home to the library be 2 miles and the
distance from the library to the school track be 1 mile?
9514 1404 393
Answer:
x+4y=3.5; 2x+2y=4x=1.5; y=0.56 miles2p≥2.5; p+q<3NoStep-by-step explanation:
1. x +4y = 3.5 . . . . variables are defined in the problem statement
2x +2y = 4
__
2. Subtract half the second equation from the first.
(x +4y) -(1/2)(2x +2y) = (3.5) -(1/2)(4)
3y = 1.5
y = 0.5
x = 2 -y = 1.5
The distance from home is 1.5 miles; the distance around the track is 0.5 miles.
__
3. 2x +6y = 2(1.5) +6(0.5) = 3+3 = 6
Avi walked 6 miles on Saturday.
__
4. 2p ≥ 2.5 . . . . variables are defined in the problem statement
p +q < 3
__
5. No.
2 + 1 < 3 is NOT TRUE
The final velocity, V, of an object under constant acceleration can be found using the formula v2=v2+2as, where v is the initial velocity (in meters per second), a is acceleration (in meters per second), and s is the distance (in meters). What is the formula solved for a?
Answer: a = (V^2 - v^2)/2s
Step-by-step explanation:
The equation for the final velocity is:
V^2 = v^2 + 2*a*s
where V is the final velocity, v is the initial velocity, a is the acceleration and s is the distance.
Now, we want to solve this formula for a, this would mean isolate a in one side of the equation, this is pretty simple, first we pass subtract v^2 in both sides.
V^2 - v^2 = v^2 + 2*a*s - v^2
V^2 - v^2 = 2*a*s
now we can divide by 2*s in both sides:
(V^2 - v^2)/2s = 2*a*s/2s = a
a = (V^2 - v^2)/2s
