ANSWER:
20.93 cubic cm
STEP-BY-STEP EXPLANATION:
We can calculate the volume of the crayon by adding the volume of the cone and the volume of the cylinder.
First the volume of the cylinder would be:
[tex]\begin{gathered} V_1=\pi\cdot r^2\cdot h \\ \text{replacing:} \\ V_1=3.14\cdot1^2\cdot6 \\ V_1=18.84 \end{gathered}[/tex]Now, the volume of the cone:
[tex]\begin{gathered} V_2=\frac{1}{3}\cdot\pi\cdot r^2\cdot h \\ V_2=\frac{1}{3}\cdot3.14\cdot1^2\cdot2 \\ V_2=2.09 \end{gathered}[/tex]Now we add them and we have:
[tex]\begin{gathered} V_T=V_1+V_2 \\ V_T=18.84+2.09 \\ V_T=20.93 \end{gathered}[/tex]The volume of the crayon is 20.93 cubic cm
Algebraic fractions are fractions that contain variables, exponents, and operations with polynomials.O TrueO False
Solution
An algebraic fraction is a fraction whose numerator and denominator are algebraic expressions.
Algebraic fractions are fractions that contain variables, exponents, and operations with polynomials.
O True Answer
O False
Diagram of the adjacent picture frame has outer dimensions = 24 cm x 28 cm and inner dimensions 16 cm x 20 cm. Find the area of each section of the frame, if the width of each section is same.
The area of the inner section is 320 cm^2
The area of the bigger section is 96 cm^2 (bigger trapezoid)
The area of the smaller trapezoid is 80 cm^2
Here, we want to calculate the area of each section of the frame
As we can see, there are 5 sections of the frame
The inner section represented by a rectangle and 4 adjoining shapes looking like a trapezoid
The inner part of the frame is a rectangle that measures 16 cm by 20 cm
Now, for the trapezoid part, we have 2 different sets
The first two set, has a longer length 28 cm, and shorter length of 20 cm
The second set has a longer length of 24 cm and a shorter length of 16 cm
Now, to get the area of the trapezoid, we need the height of the trapezoid which is called the width in this case. This measure corresponds to a measure of 4 cm on the two sets
Mathematically, the area of a trapezoid is;
[tex]A\text{ = }\frac{1}{2}(a\text{ + b)h}[/tex]Where a is the longer length and b is the shorter length with h representing the width of 4 cm
For the bigger trapezoid, we have;
[tex]\frac{1}{2}(28+20)4=96cm^2[/tex]For the smaller trapezoid, we have;
[tex]\frac{1}{2}\times(24_{}+16)\text{ 4 = }80cm^2[/tex]Then, we have the inner section as;
[tex]\begin{gathered} \text{Area = length }\times\text{ width} \\ =\text{ 16 cm }\times20cm=320cm^2 \end{gathered}[/tex]could you please help
From the trapezoid,
x + ( 31 + 38 ) + y = 180 ------------ equ 1
x + y + 69 = 180
x + y = 180 - 69
x + y = 111 .................... equ 2
Also, x + 31 + 90 = 180
x + 121 = 180
x = 180 -121
x = 59.....................equ 3
put x = 59 in equ 2 ,
59 + y = 11
y = 111 - 59
y = 52 ------------------equ 4
Stephan owns a landscaping company. Today, he is mowing three lawns: one is of an acre, one is į of an acre, and oneis 14 acres. How many acres of lawn is Stephan going to mow today? Simplify your answer and write it as a mixedfraction if necessary.21 acres
The acres of lawn mowed by Stephen is the total of the fractions of each of the mowed lawns.
Thus, we have:
[tex]\frac{1}{4}+\frac{1}{2}+1\frac{1}{3}[/tex]Simplifying the fraction above, we have:
[tex]\begin{gathered} \frac{1}{4}+\frac{1}{2}+\frac{4}{3} \\ \text{The L.C.M of 4, 2 and 3 is 12} \\ \text{Thus, we have:} \\ \frac{3+6+16}{12}=\frac{25}{12} \\ 2\frac{1}{12} \end{gathered}[/tex]Hence, the correct option is Option A.
Find the range of allowable values based on the given information. round to the nearest tenth. 50; can vary by 30%
The allowable values are;
[tex]35\text{ to 65}[/tex]Here, we want to get the allowable values for the given information
To do this, we need to find the percentage value
That would be;
[tex]\frac{30}{100}\times50\text{ = 15}[/tex]Now, the allowable values can be in both direction
Greater than 50 or less than 50
When greater, we add; when lesser, we subtract
Thus, we have it as;
[tex]\begin{gathered} 50-15\text{ to 50+15} \\ 35\text{ to 65} \end{gathered}[/tex]Which of the following equations could represent a town with an initial population of 875 people and an annual growth rate of approximately 2%?y=875 - 1.02V=875 -1.02%y = 875(2)Dy=875 (1.02)
Answer:
D. y=875(1.02)^x
Explanation:
Initial population = 875 people
Growth rate = 2%
The population after x years can be modeled below:
[tex]\begin{gathered} y=875(1+2\%)^x \\ =875(1+\frac{2}{100})^x \\ =875(1+0.02)^x \\ y=875(1.02)^x \end{gathered}[/tex]The correct choice is D.
Graph the inequality.3x+4y>4
Given the inequality equation below:
[tex]3x+4y>4[/tex]Find the y-intercept
[tex]\begin{gathered} set\text{ x=0} \\ 3x+4y=4 \\ 3(0)+4y=4 \\ 4y=4 \\ y=\frac{4}{4}=1 \\ y-intercept\rightarrow(0,1) \end{gathered}[/tex]Find the x-intercept
[tex]\begin{gathered} set\text{ y=0} \\ 3x+4y=4 \\ 3x+4(0)=4 \\ 3x=4 \\ x=\frac{4}{3} \\ x-intercept\rightarrow(\frac{4}{3},0) \end{gathered}[/tex]Find the shaded area
[tex]\begin{gathered} set\text{ x=0, and y=0} \\ 3x+4y>4 \\ 3(0)+4(0)>4 \\ 0+0>4 \\ 0>4\rightarrow false \\ Shade\text{ the side of the line where \lparen0,0\rparen is not includedand use dot line} \end{gathered}[/tex]Hence, the graph is
sean is given a solution in which the population of a family of rabbits grows according to he equation....
No, the problem is not asking for
Here, we simply want to check if the method used is correct to find the number of months it will take for the population of Rabbits to be 500
The method used in this case is wrong
What should have been done is to substitute the value of 500 for y
Afterwards, we can proceed to find the value of t which is the number of months using technology
So the correct answer is the second option
Write in form y=mx+b-3y = -6x - 24
Let's solve the equation for y:
[tex]\begin{gathered} -3y=-6x-24 \\ y=\frac{-6x-24}{-3} \\ y=\frac{-6x}{-3}-\frac{24}{-3} \\ y=2x+8 \end{gathered}[/tex]Therefore we have:
[tex]y=2x+8[/tex]For this equation we have that the slope is 2 and the y-intercept is 8.
A cart weighing 200 pounds rests on an incline at an angle of 40°. What is the required force to keep the cart at rest? Round to the thousandths place.
Given:
There are given that the car weighed 200 pounds on an incline at an angle of 40 degrees.
Explanation:
To find the required force, first we need to draw the triangle.
So,
Now,
We need to find the value for x:
So,
To find the value for x, we need to use the sine function.
Then,
[tex]sin40=\frac{x}{200}[/tex]Then,
[tex]\begin{gathered} s\imaginaryI n40=\frac{x}{200} \\ x=sin40^{\circ}\times200 \\ x=128.5575 \\ x=128.558 \\ \end{gathered}[/tex]Final answer:
Henc
Answer:
128.558
Step-by-step explanation:
On a unit circle, 0 = 30°. Identify the terminal point and tan e.
A unit circle is a circle with a radius of 1 unit.
The angle θ = 30⁰'
The terminal points are:
[tex]undefined[/tex]Rita is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of English is Fun she sells. Suppose that x and y are related by the equation 1900+110x=Y.
, if she does not sell any of English,x = The number of copies of English is Fun she sells
y = Total pay
[tex]y=1900+110x[/tex]Therefore,
a.
Her change in total pay for each copy of English is fun can be computed below.
(0, 1900) (1, 2010)
[tex]m=\frac{2010-1900}{1-0}=110[/tex]Her change in total pay for each copy of English is fun she sells = $110
b.
Her total pay if she does not sell any of English is fun is the y-intercept. Therefore,
[tex]\begin{gathered} y=1900+110x \\ y=1900+110(0) \\ y=\text{ \$1900} \end{gathered}[/tex]Her total pay if she does not sell any of English is fun = $1900
Note you can model it to the slope-intercept equation.
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{change in total pay for each copy of English is fun she sells } \\ b=\text{Her total pay if she does not sell any of English is fun} \end{gathered}[/tex]
Write an equation for the quadratic that passes through: (0,9),(−6,9), (−5,4)
The general form of a quadratic is:
[tex]y=ax^2+bx+c[/tex]We need to plug in the 3 pair of points into "x" and "y" and simultaneously solve the 3 equations for a, b, and c.
Putting (0,9):
[tex]\begin{gathered} 9=a(0)^2+b(0)+c \\ c=9 \end{gathered}[/tex]Putting (-6,9):
[tex]\begin{gathered} 9=a(-6)^2+b(-6)+c \\ 9=36a-6b+9 \\ 36a=6b \\ a=\frac{6b}{36} \\ a=\frac{b}{6} \end{gathered}[/tex]Putting (-5,4):
[tex]\begin{gathered} 4=a(-5)^2+b(-5)+9 \\ 4=25a-5b+9 \\ 25a-5b=-5 \end{gathered}[/tex]We substitute a=b/6 into this equation and solve for b:
[tex]\begin{gathered} 25(\frac{b}{6})-5b=-5 \\ \frac{25b}{6}-5b=-5 \\ \frac{25b-30b}{6}=-5 \\ -5b=-30 \\ b=6 \end{gathered}[/tex]Thus, "a" will be:
[tex]\begin{gathered} a=\frac{b}{6} \\ a=\frac{6}{6} \\ a=1 \end{gathered}[/tex]Thus, we have a = 1, b = 6, c = 9
The equation is:
[tex]\begin{gathered} y=1x^2+6x+9 \\ y=x^2+6x+9 \end{gathered}[/tex]Find the slope intercept equation of the line that has the given characteristics. Slope 1.3 and y intercept (0,-6)
We want to find the equation of the line in slope intercept form with the following values.
Slope = 1.3 and y-intercept ( 0, -6)
The equation of a line with slope m and y intercept (0,c) is;
[tex]y=mx+c[/tex]Thus, the equation of the line is;
[tex]y=1.3x-6[/tex]Which of the following is not a true postulate.Through any three noncollinear points there is exactly one planeThrough any two points there is exactly one plane.If two distinct lines intersect, then they intersect in exactly one point.If two distinct planes intersect, they intersect in exactly one line.
Answer:
Through any two points there is exactly one plane.
Step-by-Step explanation:
Postulate: Statement that is believed to be true, just without proof.
The first one is correct, that is, it is a true postulate.
The third statement is correct.
The fourth statement is also correct.
The answer is the second postulate.
It is stated that:
Through any two points there is exactly one plane.
But the correct postulate is:
Through any two points there is exactly one line.
So the answer is:
Through any two points there is exactly one plane.
If there are three black, four white, two blue, and four gray socks in a drawer, what would be the probability of picking a black sock as a fraction in simplest form?1/103/91/33/13
The probability of getting a black sock out of the drawer is given by the ratio between the amount of black socks in the drawer by the total amount of socks in the drawer.
We know that we have 3 black socks, now we just need to calculate the total amount of socks. We have three black, four white, two blue, and four gray socks in a drawer, then, the total is given by
[tex]3+4+2+4=13[/tex]We have a total of 13 socks in the drawer, therefore, the probability of getting a black sock out of the drawer is given by
[tex]\frac{3}{13}[/tex]And this is the fraction in the most simplified version.
A grain bin is in the combined shape of a right cylinder and right cone, both of which have diameters of 10 feet.(a) Find the volume of the cylindrical portion of the bin to the nearest cubic foot.(b) Find the volume of the conical portion of the bin to the nearest cubic foot.(c) The bin is to be filled completely with dry corn that weighs 45 lbs per cubic foot. Of there are 2,000 pounds per ton, how many total tons of corn can be placed in the bin?
ANSWER :
a. 628 cubic foot
b. 52 cubic foot
c. 1.17 ton
EXPLANATION :
The volume formula of a cylinder is :
[tex]V=\pi r^2h[/tex]The volume formula of a cone is :
[tex]V=\frac{1}{3}\pi r^2h[/tex]From the problem, we have a diameter of 10 ft, so the radius is r = 5 ft
Cylinder's height is 8 ft and cone's height is 2 ft
a. volume of cylinder part :
[tex]\begin{gathered} V=\pi(5)^2(8) \\ V=628ft^3 \end{gathered}[/tex]b. volume of cone part :
[tex]\begin{gathered} V=\frac{1}{3}\pi(5)^2(2) \\ V=52ft^3 \end{gathered}[/tex]c. The combine volume is 628 + 52 = 680 cubic foot
A dry corn weighs 45 lbs per cubic foot.
That will be :
[tex]52ft^3\times\frac{45lbs}{ft^3}=2340lbs[/tex]There are 2000 pounds per ton, so that will be :
[tex]2340lbs\times\frac{1ton}{2000lbs}=1.17ton[/tex]Compare the Mixed Numbers. Convert the imroner fraction to mixed nu
1) Comparing those Mixed numbers we can stat which is greater, lesser than, or equal by dividing the numerator by the denominator and adding to the whole number:
[tex]\begin{gathered} 2\frac{5}{8}=\frac{8\cdot2+5}{8}=\frac{21}{8}=2.625 \\ 2\frac{1}{2}=\frac{2\cdot2+1}{2}=\frac{5}{2}=2.5 \\ 2\frac{5}{8}>\text{ 2}\frac{1}{2} \\ 2\frac{2}{8}=2\frac{1}{4}\text{ } \\ 1\frac{3}{8}<2\frac{3}{8} \\ 1\frac{5}{8}=\frac{8\cdot1+5}{8}=\frac{13}{8}=1.625 \\ 2\frac{3}{4}=2.75 \\ 1\frac{5}{8}<2\frac{3}{8} \\ \\ 1\frac{2}{4}=1\frac{1}{2}=1+0.5=1.5 \\ 1\frac{2}{8}=1\frac{1}{4}=1.25 \\ 1\frac{2}{4}>1\frac{2}{8} \\ \\ 2\frac{7}{8}>1\frac{7}{8} \end{gathered}[/tex]So there are cases when the fraction is the same we just need to compare the whole number.
But in most cases, dividing the numerator by the denominator and writing it as a decimal number is really helpful
3) So the answers are:
[tex]1\frac{3}{8}<2\frac{3}{8},2\frac{2}{8}=2\frac{1}{4},\text{ }2\frac{5}{8}>\text{ 2}\frac{1}{2},\text{ }1\frac{5}{8}<2\frac{3}{8},\text{ }1\frac{2}{4}>1\frac{2}{8},\text{ }2\frac{7}{8}>1\frac{7}{8}[/tex]6-4x=6x-8x-8. what does x =
Start by balancing it out.
First +4x to both sides:
6=6x-4x-8
Then +8 to both sides:
14=6x-4x
As 6x-4x=2x
14=2x
Finally, divide both sides by 2:
7=x
So, the answer is x = 7
Error Analysis A store is instructed by corporate headquarters to put a markup of 11% on all items. Anitem costing $18 is displayed by the store manager at a selling price of $2. As an employee, you noticethat this selling price is incorrect. Find the correct selling price. What was the manager's likely error?The correct selling price is $ ). (Round to the nearest dollar as needed)Enter your answer in the answer box and then click Check Answer
The item cost $18 and the selling prices must aim a markup os 11%
Therefore, the selling price of this item should be 1.11*18 = $19.98
Rounding to the nearest dollar, the price should be $20
Then, the manager's likely error was doesn't display the "0" algarism for the selling price.
A car is traveling at a steady speed. It travels 1 1/2 miles in 2 1/4 minutes. How far will it travel in 47 Minutes ? In 1 hour ?The car will travel ( blank) miles in 47 minutes (Simplify your answer. Type an integer, proper fraction, or mixed number.)
1 1/2 miles ---> 2 1/4 minutes
x miles -------> 47 minutes
[tex]\begin{gathered} x\times2\frac{1}{4}=1\frac{1}{2}\times47 \\ x\times\frac{9}{4}=\frac{3}{2}\times47 \\ \frac{9}{4}x=70.5 \\ \frac{9}{4}x\times\frac{4}{9}=70.5\times\frac{4}{9} \\ x=\frac{94}{3}=31\frac{1}{3} \end{gathered}[/tex]answer: 31 1/3 miles in 47 minutes
for 1 hour = 60 minutes
[tex]\begin{gathered} \frac{9}{4}x=\frac{3}{2}\times60 \\ \frac{9}{4}x=90 \\ \frac{9}{4}x\times\frac{4}{9}=90\times\frac{4}{9} \\ x=40 \end{gathered}[/tex]answer: 40 miles in 1 hour
Answer:
1 1/2 miles ---> 2 1/4 minutes
x miles -------> 47 minutes
answer: 31 1/3 miles in 47 minutes
for 1 hour = 60 minutes
answer: 40 miles in 1 hour
Step-by-step explanation:
Solve the problem. Students in a math class took a final exam. They took equivalent forms of the exam in monthly intervals thereafter. The average score S(t), in percent, after t months was found to be given by 6) - 70-20In (t.1). *20. Find Slu). 20 OSTU - 70 STO OSD- t + 1 20 0 st) SO) = -20 In
Find the derivative of S(t)=70-20ln(t+1)
[tex]\begin{gathered} \frac{dS(t)}{dt}=0-20\cdot\frac{1}{t+1}\cdot1 \\ \frac{dS(t)}{dt}=\frac{-20}{t+1} \\ \end{gathered}[/tex]The derivative is -20/t+1
If four friends collected 9 1/3 bags of treats and shared them among themselves equally,how many bags of treats did each person get?
It is given that four friends collected 9 1/3 bags of treats.
[tex]9\frac{1}{3}=\frac{28}{3}\text{ bags}[/tex]Now 28/3 bags divided equally among 4 friends will be:
[tex]\frac{\frac{28}{3}}{4}=\frac{28}{12}=\frac{7}{3}=2\frac{1}{3}\text{ bags}[/tex]Hence the total number of bags that each person will receive is 7/3 bags or 2 1/3 bags.
Write the equation of a perpendicular and parallel line to the following: (in picture)
anIf we have an equation of the form
[tex]y=mx+b[/tex]then the equation of the perpendicular will be
[tex]y=-\frac{1}{m}x+c[/tex]where c is any arbitrary constant determined by the point the line must pass through,
Now in our case, we have
[tex]y=-10x+20[/tex]Therefore, the equation of the perpendicular line will be
[tex]y=\frac{1}{10}x+c[/tex]We must choose c such that the above line passes through (-2,2).
Putting in y = 2 and x = 2 from (-2, 2) gives
[tex]2=\frac{1}{10}(-2)+c[/tex][tex]2=-\frac{1}{5}+c[/tex][tex]\therefore c=\frac{11}{5}.[/tex]Hence, the equation of a line perpendicular y = -10x + 20 and passing through (-2, 2) is
[tex]y=\frac{1}{10}+\frac{11}{5}[/tex]Now we find the equation of a line parallel to y = -10x+20 and passing through (-2,2).
Now, the slope of the parallel line is the same as that of the original equation; therefore the equation for the parallel line we have is
[tex]y=-10x+k[/tex]We find k by using the point (-2,2) and substituting x = -2 and y = 2 into the above equation to get
[tex]2=-10(-2)+k[/tex][tex]2=20+k[/tex][tex]\therefore k=-18.[/tex]Hence, the equation of the parallel line is
[tex]y=-10x-18[/tex]Multiply Polynomials. Find the product and write answers in standard form
Step 1
Given;
[tex]5m^3(n^6)(6n^5)[/tex]Required; To multiply the polynomials
Step 2
Write the answers in standard form.
Rearrange the question and write like terms close to each other
[tex]5\times6\times n^6\times n^5\times m^3[/tex]Simplify using the following law of indices
[tex]a^b\times a^n=a^{b+n}[/tex][tex]\begin{gathered} 5\times6=30 \\ n^6\times n^5=n^{6+5}=n^{11} \\ m^3=m^3 \end{gathered}[/tex]Hence the combined answer will be;
[tex]30m^3n^{11}[/tex][tex]5m^3(n^6)(6n^5)=30m^3n^{11}[/tex]Answer;
[tex]30m^3n^{11}[/tex]1. 12,5); x+y=72x-3y = 1 What are the steps
As the given lines are:
[tex]\begin{gathered} x+y=7\ldots\ldots\ldots\ldots(1) \\ 2x-3y=-11\ldots\ldots\ldots.(2) \end{gathered}[/tex]To find the system of linear equation:
multiply equation (1)by 3 and then add in equation 2:
[tex]\begin{gathered} 3(x+y)+2x-3y=3(7)-11 \\ 3x+3y+2x-3y=21-11 \\ 5x=10 \\ x=2 \end{gathered}[/tex]Now put the value of x in equation 1:
[tex]\begin{gathered} 2+y=7 \\ y=5 \end{gathered}[/tex]7. Quinn had 3 more than two times the number of marbles Rowan has. Together they have 77marbles. How many marbles does each child have?
Explanation:
Let the number of marbles Rowan has = x
Two times x = 2x
3 more than two times the number of marbles Rowan has = 2x + 3
Quinn = 2x + 3
Together they have = 77 marbles
Rowan marbles + Quinn marbles = 77
x + (2x + 3) = 77
x + 2x + 3 = 77
Collect like terms:
3x = 77-3
3x = 74
Divide through by 3:
x = 74/3
x = 24.7
Given: a = 7 and b = 2 Then the m∠A=_?_ . ROund to the nearest degree. Enter a number answer only.
m∠A of the given rectangular triangle is 74.05°.
Why is Pythagoras useful?In two dimensions, the Pythagorean Theorem is helpful for navigation. You may calculate the shortest distance using it and two lengths. … The two legs of the triangle will be north and west, and the diagonal will be the shortest line separating them. Air navigation can be based on the same ideas.Three positive numbers a, b, and c make up a Pythagorean triple if their sum, a2 + b2, equals their sum, c2. A typical way to write such a triple is (a, b, c), and a well-known example is (3, 4, 5). For any positive integer k, (ka, kb, kc) is a Pythagorean triple if (a, b, c) is one as well.Given :
a = 7
b = 2
∠c =90°
according to Pythagoras theorem
c =[tex]\sqrt[n]{a^2 + b^2}[/tex]
c = [tex]\sqrt{7^2 + 2^2}[/tex]
c≈7.28011.
to find m∠A
Sin A = [tex]\frac{opp. side}{Hypotenuse}[/tex] = 7/7.28011 = 0.9615
∠A = sin⁻¹ 0.9615
m∠A = 74.05°.
To learn more about Pythagorean Theorem refer,
https://brainly.com/question/343682
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You have 3 black cups, 10 Green cups, 9 purple cups, and 19 gray cups. what is the ratio between purple and green cups?
We chave 9 purple cups and 10 green cups, so we can write the ratio between purple and green cups as 9:10 or "9 to 10".
Answer: 9:10
I need help can u help me?
Mark has ten pens.
Kate has 5 times as many pens as mark has
Number of pen kate has = 5 (number of pens of Mark)
y is the number of Kates pen
y = 5( Number of pens of Mark)
y=5(10)
y= 5 x 10
Answer : C) y = 5 x 10
Answer:
Where is the math question?