Answer:
3617.28 grams
Step-by-step explanation:
Find the volume of the metal as following:
[tex]V_{metal}=V_{external}-V_{internal}[/tex][tex]V_{external} = \pi d_{external}^2h/4=\pi *10^2*16/4=1256[/tex] cm³[tex]V_{internal} = \pi d_{internal}^2h/4=\pi *8^2*16/4=803.84[/tex] cm³[tex]V_{metal}=1256-803.84 = 452.16[/tex] cm³Find the mass:
[tex]mass = volume*density[/tex][tex]mass = 452.16*8=3617.28[/tex] gramsAnswer:
3619.1 grams (nearest tenth)
Step-by-step explanation:
Volume of a cylinder
[tex]V=\pi r^2 h[/tex]
where:
r is the radius.h is the height.The radius of a circle is half its diameter.
Find the volumes of the external and internal cylinders by substituting the given values into the formula for volume of a cylinder:
[tex]\implies \textsf{Volume of the external cylinder}&=\pi \cdot 5^2 \cdot 16=400 \pi \; \sf cm^3[/tex]
[tex]\implies \textsf{Volume of the internal cylinder}&=\pi \cdot 4^2 \cdot 16=256 \pi \; \sf cm^3[/tex]
Find the volume of the cylindrical hollow metal pipe by subtracting the volume of the internal cylinder from the volume of the external cylinder:
[tex]\begin{aligned}\implies \textsf{Volume of the metal pipe}&=\sf Volume_{external}-Volume_{internal}\\&=400 \pi - 256 \pi\\& = 144 \pi \sf \; cm^3\end{aligned}[/tex]
Density formula
[tex]\rho=\dfrac{m}{V}[/tex]
where:
ρ = densitym = massV = volumeGiven:
ρ = 8 g/cm³V = 144π cm³Substitute the given values of density and the found volume into the density formula and solve for m:
[tex]\begin{aligned}\implies \rho&=\dfrac{m}{V}\\8&=\dfrac{m}{144 \pi}\\m&=8 \cdot 144\pi\\m&=1152 \pi \\m&=3619.11473...\\m&=3619.1\; \sf g \;(nearest\;tenth)\end{aligned}[/tex]
Therefore, the mass of the pipe is 3619.1 grams (nearest tenth).
Note: I have used the exact value of π (not a rounded value).
Sarah spent 2 h more travelling by train than she did by bus. The train averaged 70 km/h and the bus 50 km/h. The total distance travelled was 740 km. How far did she travel by bus?
Answer:
250 km
Step-by-step explanation:
Sarah traveled a total of 740 km, 2 hours more at a speed of 70 km/h than at a speed of 50 km/h. You want to know how far she traveled at 50 km/h.
SetupThe relations between time, speed, and distance are ...
distance = speed × time
time = distance/speed
If 'd' represents the distance (km) Sarah traveled by bus (at 50 km/h), then the time (hours) required was ...
time = d/50
The time at 70 km/h is 2 hours more, and the total distance is ...
total distance = (distance at 50 km/h) + (distance at 70 km/h)
740 = d + 70(d/50 +2)
SolutionSimplifying the equation, we have ...
740 = 2.4d +140
600 = 2.4d . . . . . . . . subtract 140
d = 250 . . . . . . . . . . . divide by 2.4
Sarah traveled 250 km by bus.
two concentric circles have radii 11 and 22 two points on the outer circle are chosen independently and uniformly at random. what is the probability that the chord joining the two points intersects the inner circle?
Answer: Two concentric circles have radii $1$ and $2$. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle?
$\textbf{(A)}\ \frac{1}{6}\qquad \textbf{(B)}\ \frac{1}{4}\qquad \textbf{(C)}\ \frac{2-\sqrt{2}}{2}\qquad \textbf{(D)}\ \frac{1}{3}\qquad \textbf{(E)}\ \frac{1}{2}\qquad$
Solution
Let the center of the two circles be $O$. Now pick an arbitrary point $A$ on the boundary of the circle with radius $2$. We want to find the range of possible places for the second point, $A'$, such that $AA'$ passes through the circle of radius $1$. To do this, first draw the tangents from $A$ to the circle of radius $1$. Let the intersection points of the tangents (when extended) with circle of radius $2$ be $B$ and $C$. Let $H$ be the foot of the altitude from $O$ to $\overline{BC}$. Then we have the following diagram.
[asy] scale(200); pair A,O,B,C,H; A = (0,1); O = (0,0); B = (-.866,-.5); C = (.866,-.5); H = (0, -.5); draw(A--C--cycle); draw(A--O--cycle); draw(O--C--cycle); draw(O--H,dashed+linewidth(.7)); draw(A--B--cycle); draw(B--C--cycle); draw(O--B--cycle); dot("$A$",A,N); dot("$O$",O,NW); dot("$B$",B,W); dot("$C$",C,E); dot("$H$",H,S); label("$2$",O--(-.7,-.385),N); label("$1$",O--H,E); draw(circle(O,.5)); draw(circle(O,1)); [/asy]
We want to find $\angle BOC$, as the range of desired points $A'$ is the set of points on minor arc $\overarc{BC}$. This is because $B$ and $C$ are part of the tangents, which "set the boundaries" for $A'$. Since $OH = 1$ and $OB = 2$ as shown in the diagram, $\triangle OHB$ is a $30-60-90$ triangle with $\angle BOH = 60^\circ$. Thus, $\angle BOC = 120^\circ$, and the probability $A'$ lies on the minor arc $\overarc{BC}$ is thus $\dfrac{120}{360} = \boxed{\textbf{(D)}\: \dfrac13}$.
See Also
2 (x + 1) <\= 12
X <\= ?
Answer: x<1
Step-by-step explanation:
Nine friends vote on their favorite fruit. Only one person in the group votes for kiwi.
Choose the decimal that is equivalent to this fraction.
0.1
The decimal which represents the fraction of the people who vote for kiwi among all 9 people is 1/9 it's 0.1111111.
What is a fraction?It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
As per the given,
Number of people who vote on their favorite fruit = 9
Number of people who vote for kiwi = 1
The fraction of person vote kiwi to vote on their favorite fruit = 1/9
In decimal form 1/9 = 0.1111111.
Hence "The decimal which represents the fraction of the people who vote for kiwi among all 9 people is 1/9 it's 0.1111111".
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Find the measure of angle b
Simplify the expression √9x^3/25y^2 and be sure to explain your steps!
The value of the expression given as√9x^3/25y^2 is 3x^3/25y^2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to simplify the value of the expression?The expression is given as
√9x^3/25y^2
Evaluate the square root of 9 in the expression
So, we have the following equation
√9x^3/25y^2 = 3x^3/25y^2
The above expression cannot be further simplified
Hence, the solution to the expression is 3x^3/25y^2
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At lunch time a restaurant sold 6 times as many salads as they sold cups of soup . If they sold two cups of soup how many salads did they sell
Which one is the right answer??
Grace and Kian are building towers. Each one of Grace’s blocks is 8cm tall. Each one of Kian's blocks is 12 cm tall.
They both build towers that are exactly the same height. What is thensmallest height that their towers could be? Give your answer in centimetres.
The smallest height of the tower is 24 cm.
What is an expression?An expression contains terms with addition, subtraction, multiplication, and division.
Example: 44 + 3x + 4y = 7 is an expression.
We have,
Grace:
Blocks = 8 cm
Kian:
Blocks = 12 cm
Now,
Grace and Kian both have the same height.
This means,
The least common multiples of 8 and 12.
4 x 2 = 8
4 x 3 = 12
So,
4 x 2 x 3 = 24
Thus,
The smallest height of the tower is 24 cm.
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The average income of 5 members in a family is $36,500. The average income of a neighboring family with 2 members is $52,000. What is the average income of both families combined?
Answer:
$40928.57
Step-by-step explanation:
(5·36500 + 2·52000) / (5 + 2) = 40928.57
Alyssa buys 3 bottles of orange juice at the corner store for a total cost of $3.54. If
each bottle costs the same amount, how much is 19 bottles of juice?
Answer the whole attachment for 100 points and brainlyist
Using it's concept, it is found that:
a) The percent error is of 16.67%.
b) To get the same percent error, the amount of error needs to be the same. Because the estimate was 40 people below the attendance, an estimate of 40 people above the actual attendance will give the same percent error. Therefore, the other estimate that gives the same percent error is an amount of 280 people.
How to find the percent error?
The percent error is given by the difference between the actual and the expected amount, divided by the expected amount and multiplied by 100%.
In the context of this problem, the amounts are given as follows:
Actual amount: 200 people.Expected amount: 240 people.Hence the percent error is given as follows:
(240 - 200)/240 x 100% = 16.67%.
For item b, we want to have the same absolute difference between the actual amount and the expected amount, that is:
|Actual - Expected| = 40.
Meaning that there are two possible outcomes:
Actual - Expected = -40 -> Item a.Actual - Expected = 40 -> Actual = 280.Which gives the answer to item b, completing the sentences.
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7. What is the cost of a book that was sold for $500 and at a profit of $ 230?
The most appropriate choice for Profit and loss will be given by-
Cost price of the book is $270
What is Profit and loss?
The price at which an article is bought is known as cost price and the price at which the article is sold is known as selling price.
If the selling price of an article is more than the cost price, the difference between the selling price and the cost price gives the profit.
If the selling price of an article is less than the cost price, the difference between the cost price and the selling price gives the loss.
Here,
Selling price of book = $500
Profit = $230
In case of profit, cost price is always less than the selling price
Cost price of the book = Selling price - profit
= $(500 - 230)
= $270
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Solve this equation for x in terms of the other pronumerals.
x/a - x/2a = b
Answer:
x=2a*b
Step-by-step explanation:
(2x-x)/2a=b
x=2a*b
Draw a picture: The area of a square is 81 square centimeters, then find the length of the sides and diagonals.
The length of a side of the square is 9 centimeters. The length of the diagonal is 12.73 centimeters.
What is the length of the side and diagonal?A square is an object that has four sides of equal length. A square has two diagonals that biscect each other at 90°. The diagonals are of equal length. The diagonals of a square divide the square into two right triangles.
Area of a square = length²
Length = √area
√81 = 9cm
Pythagoras theorem can be used to determine the length of the diagonal.
The Pythagoras theorem: a² + b² = c²
Where:
a = lengthb = basec = hypotenuse9² + 9²
= 81 + 81
= √162 = 12.73 cm
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Write the equation of the line in fully simplified slope-intercept form.
Step-by-step explanation:
a slope-intercept form :
y = ax + b
"a" is the slope, "b" is the y-intercept (the y-value when x = 0).
the slope is the ratio (y coordinate change / x coordinate change) when moving from on point on the line to another.
"b" we can read off the graph : when x = 0, then y = -5.
so, b = -5.
for the slope let's pick 2 points. your teacher has kindly marked already points with integer coordinates.
so, I pick (3, 1) and (4, 3).
x changes by +1 (from 3 to 4).
y changes by +2 (from 1 to 3).
so, the slope is
+2/+1 = 2/1 = 2
the equation is
y = 2x - 5
Answer: y=2x-5
Step-by-step explanation:
Choose two points on the graph: (0,-5) and (3,1)
The straight line equation is: y=mx+b
1)
[tex]\displaystyle\\\boxed {The\ slope\ m\ =\frac{y_2-y_1}{x_2-x_1} }[/tex]
[tex]\displaystyle\\x_1=0\ \ \ \ \ x_2=3 \ \ \ \ y_1=-5\ \ \ \ y_2=1\\\\ Hence,\\\\m=\frac{1-(-5)}{3-0} \\\\m=\frac{1+5}{3} \\\\m=\frac{6}{3} \\\\m=2\\\\Thus,\ y=2x+b\ \ \ \ \ (1)[/tex]
2)
To determine the coefficient b, take any of the two points,
for example, (0,-5), that is, x=0 y=5
Substitute these values into formula (1):
[tex]-5=2*0+b\\-5=0+b\\-5=b\\Thus,\ b=-5[/tex]
The result is y=2x-5
The table shows the cost for ordering a certain number of pieces of chicken. What is the value of x if the cost is proportional to the number of chicken pieces ordered?
Answer:
$9.00
Step-by-step explanation:
if 2 pieces of chicken ordered --> $3.00
6 pieces of chicken ordered --> x
(cross multiplication)
[tex]x= \frac{6*3}{2}[/tex]
so x = 9
then, 6 pieces of chicken ordered is $9.00
Chec
Nathan sells jewelry and earns a 9.75% commission on every piece
he sells. How much commission would he earn on a bracelet that
sold for $220? Use any strategy
Answer:
$21.45
Step-by-step explanation:
You want to know the amount of a 9.75% commission on $220.
CommissionThe amount of the commission is the product of the commission rate and the sales amount to which it is applicable. A 9.75% commission on $220 will be ...
9.75% × $220 = 0.0975 × $220 = $21.45
Nathan would earn a commission of $21.45 on the sale.
__
Additional comment
We know that a 10% commission can be found by moving the decimal point on the sale amount. A 10% commission on $220 will be $22.
The commission rate of 9.75% is 1/4% less than 10%. 1/4% can be found in two steps: find 1%, then find 1/4 of that.
As with 10%, the 1% amount can be found by moving the decimal point. 1% of $220 is $2.20. One-quarter of that will be $2.20/4 = $1.10/2 = $0.55.
This is the amount we must subtract from the 10% value to make it be 9.75%.
The 9.75% commission amount is $22.00 -0.55 = $21.45.
(The point of using a strategy like this is that you can do the math mentally.)
ASAP help with 8th grade math, 50 points
Answer:
The height is 7 units the length is 12 units.
Step-by-step explanation:
It's 6 and 6 for the graph one.
A farmer has bushels to sell at a roadside stand. sells an average of
each day. Represent the total change in the number of bushels for sale after.
The total change in the number of bushels for sale is 64.1 bushels.
Given
A farmer has 160 bushels of apples to sell at her roadside stand. Every day, she sells around a 13 7/10 bushel.
Let us calculate the overall change in the number of bushels she has available for sale after 7 days.
137/10
Now we'll figure out how many bushels she'll sell in seven days.
7 x 137/10
95.9
In 7 days, the farmer will sell 95.9 bushels. To calculate our overall change, subtract this figure from the total number of bushels of apples.
165 - 95.9 = 64.1
Thus, a total of 64.1 bushels have been added to the amount of bushels available for sale.
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yo ___ 14 anos (expressing age
Answer:
tengo
Step-by-step explanation:
i am hispanic
Let and .
Which transformations are needed to transform the graph of f(x) to the graph of g(x)?
Select EACH correct answer.
Question 3 options:
Horizontal translation 1 units right.
Vertical translation 1 unit down.
Horizontal translation 3 units right.
Horizontal translation 1 unit left.
Vertical translation 3 units up.
Vertical translation 3 units down.
The transformations that are needed to transform the graph of f(x) to the graph of g(x) include the following:
Horizontal translation 1 unit left.Vertical translation 3 units down.What is a translation?In Mathematics, the translation of a geometric figure to the right simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image and translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
Given the following function:
Function, f(x) = 4^x
Next, we would translate f(x) 1 unit left based on this horizontal translation rule:
f'(x) = f(x + 1)
f'(x) = 4^{x + 1}
Now, we would apply a vertical translation 3 units down based on this horizontal translation rule:
f''(x) = f'(x) - 3
f''(x) = 4^{x + 1} - 3
Therefore, function g(x) = 4^{x + 1} - 3
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PLS HELP ME... just confused on this question about what I need to do
5. What is an equation of the line in slope-intercept form?
m=2/7 and the y-intercept is (0, -12)
Oy=2/7x+12
Oy=2/7x-12
Oy=12x-2/7
Oy=12x+2/7
Answer:
[tex]y=\dfrac{2}{7}x-12[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given:
slope = ²/₇y-intercept = (0, -12)The y-intercept is the y-value when x = 0.
Substitute the slope and y-intercept into the formula to create the equation of the line in slope-intercept form:
[tex]\implies y=\dfrac{2}{7}x-12[/tex]
There were fifty-nine people in line at lunch when sixteen more got in line. How many people were there total in line?
answer: 59+16=75
75 total in line
PLEASE HELP! What is one over seven raised to the third power equal to?
one over ten
three over twenty-one
one over three hundred forty-three
three over two thousand four hundred one
Answer: 1/343
Step-by-step explanation:
the coefficient of x³ in the expansion (2x-1)³
Answer: 8
Step-by-step explanation:
Since the expression is raised to the 3rd power, the highest exponent x will have will be 3. So in order to get the coefficient you multiply 2x by itself 3 times, getting (2x)³ = (2 * 2 * 2)(x * x * x) = (8)(x³) = 8x³
[tex]\qquad \qquad \textit{binomial theorem expansion} \\\\ \qquad \qquad (2x-1)^{3}~\hspace{4em} \begin{array}{cccl} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(2x)^{3 }(-1)^0\\ 2&+3&(2x)^{2}(-1)^1\\ 3&+3&(2x)^{1}(-1)^2\\ 4&+1&(2x)^{0}(-1)^3 \end{array} \\\\\\ 1(8x^3)+3(-4x^2)+3(2x)+1(-1)\implies \text{\LARGE 8}x^3-12x^2+6x-1[/tex]
Please help me with this asappppp
The perimeter of the rectangle is 32 feet.
Perimeter of the rectangle:
The perimeter of a rectangle is stated that the sum of all the sides of a rectangle.
Through the definition, the perimeter of a rectangle,
P = 2 (a + b) units
where
“a” is the length of the rectangle
“b” is the width of the rectangle
Given,
Here we have the diagram of the rectangle and the measurements are given in it.
And we need to find the perimeter of the rectangle.
Through the given diagram, we know that, the values of
length = 12 feet
width = 4 feet
Now, we have to apply the values on the formula in order to solve it,
So, the perimeter is,
P = 2 ( 12 + 4)
When we simplify it then we get,
P = 2 (16)
After the multiplication we get the result as
P = 32 feet.
Therefore, the perimeter of the rectangle is 32 feet.
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Stephanie is helping her band collect money to fund a field trip the band decided to sell chocolate bars each bar sells for $1.50 and each box contains 20 bars below is a partial table of monies collected for the different number of boxes sold
O P=20($1.50)
If they sell 100 boxes of chocolates, they will make $3,000 in profit.
Given that each chocolate bar costs $1.50 and that there are 20 chocolate bars in a box, multiplication is required to get the profit for the entire box. Using this information, we discover that each chocolate box costs $30, multiplied by 100 boxes to equal $3000.
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daisy has one cucumber that is 3 inches long and another cucumber that is 5 inches long she cuts the cucumbers into (3)/(8)-slices and adds them to a salad how many (3)/(8)-inches thick slices does daisy have
Answer:
21 slices of 3/8 inch
Step-by-step explanation:
Daisy would have 21.This is because 3 times 8 divided by 3 is 8.And 5 times 8 divided by 3 is 13 (you have to ignore the remainder) 8 plus 13 is 21