If Charlie’s Chocolate Fudge costs $1.95 perpound, how many pounds can you buy for $10.00?Set up a proportion.Make sure that the units match going across.Cross multiply to solve,X =_____ pounds for $10.
Answers
Let's use a rule of three:
This way,
[tex]x=\frac{10\cdot1}{1.95}\Rightarrow x=5.13lbs[/tex]We could buy 5.13 pounds
Related Questions
which point on the grid below has coordinates (-9, -2)?
Answers
Answer:
A
Explanation:
Given the point (-9,-2):
[tex]\begin{gathered} (x,y)=(-9,-2) \\ \implies x=-9,y=-2 \end{gathered}[/tex]As seen in the graph, the point on the grid that has the coordinates (-9,-2) is point A.
Shelley has a bag containing three balls: one red, one yellow, and one green. All balls are equally likely to be chosen. Shelley will choose one ball without looking in the bag. What is the probability that Shelley will choose the yellow ball out of the bag? A. 2/3 B. 3/1 C. 3/3 D. 1/3
Answers
Answer:
D. 1/3
Explanation:
In the bag, there are one red, one yellow, and one green ball.
Number of yellow ball = 1
Total number of balls = 3
Thus, the probability that Shelley will choose the yellow ball out of the bag:
[tex]=\frac{1}{3}[/tex]T
Answer: D
Step-by-step explanation: There is 3 balls, lets say that is 3/3, and a yellow ball is 1, which is 1/3
[tex]5 \times 5[/tex]what is 5 times 5
Answers
5 times 5 = 25
5 x 5 = 25
5 + 5 + 5+ 5 +5 = 25
Answer:
answer is going to be 25
Step-by-step explanation:
so pretend you have 5 bags of 5 apples, this should stand for 5(bags of apples) and 5(apples in each bag), if you add the apples all together it will be 25 in total, or just try adding 5 five times: 5+5+5+5+5
[tex]x2 = 49[/tex]what's the answer
Answers
Solve the equation:
[tex]x^2=49[/tex]The simplest method to solve the equation is to apply the square root on both sides of the equation:
[tex]\sqrt{x^2}=\sqrt{49}[/tex]Since the square and the square root are inverse functions, they cancel out, leaving us with the equation:
[tex]x=\sqrt{49}[/tex]We must find a number such that its square results in 49. That number is 7. But we must recall that there is another number that produces 49 when squared. That number is -7.
This gives us two solutions. It can be written:
[tex]x=\pm7[/tex]The equation has two solutions:
x = 7, x = -7
Which conjecture is possible to prove?A. All quadrilaterals with at least one side length of 3 are congruent.B. All rectangles with at least one side length of 3 are congruent.C. All rhombuses with at least one side length of 3 are congruent.D. All squares with at least one side length of 3 are congruent.
Answers
All the sides of a square are equal, therefore, if at least one side length is congruent, all of them are.
Thus,
The correct answer is option D.
The organizer of a conference is selecting workshops to include. She will select from 6 workshops about chemistry and 7 workshops about biology. In how many ways can she select 4 workshops if 2 or fewer must be about chemistry?
Answers
Given that there are 6 workshops about chemistry and 7 workshops about biology.
So the total number of workshops available are,
[tex]\begin{gathered} =6+7 \\ =13 \end{gathered}[/tex]The number of ways of selecting 'r' objects from 'n' distinct objects is given by,
[tex]^nC_r=\frac{n!}{r!\cdot(n-r)!}[/tex]The total number of ways of selecting 4 workshops having no workshop about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 0 chemistry)}=^7C_4 \\ n(\text{ 0 chemistry)}=\frac{7!}{4!\cdot(7-4)!} \\ n(\text{ 0 chemistry)}=\frac{7\cdot6\cdot5\cdot4!}{4!\cdot3!} \\ n(\text{ 0 chemistry)}=\frac{7\cdot6\cdot5}{3\cdot2\cdot1} \\ n(\text{ 0 chemistry)}=35 \end{gathered}[/tex]The total number of ways of selecting 4 workshops having exactly 1 workshop about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 1 chemistry)}=^7C_3\cdot^6C_1 \\ n(\text{ 1 chemistry)}=\frac{7!}{3!\cdot(7-3)!}\cdot\frac{6!}{1!\cdot(6-1)!} \\ n(\text{ 1 chemistry)}=\frac{7\cdot6\cdot5\cdot4\cdot3!}{3!\cdot4!}\cdot\frac{6\cdot5!}{1!\cdot5!} \\ n(\text{ 1 chemistry)}=\frac{7\cdot6\cdot5\cdot4}{4\cdot3\cdot2\cdot1}\cdot6 \\ n(\text{ 1 chemistry)}=210 \end{gathered}[/tex]The total number of ways of selecting 4 workshops having exactly 2 workshops about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 2 chemistry)}=^7C_2\cdot^6C_2 \\ n(\text{ 2 chemistry)}=\frac{7!}{2!\cdot(7-2)!}\cdot\frac{6!}{2!\cdot(6-2)!} \\ n(\text{ 2 chemistry)}=\frac{7\cdot6\cdot5!}{2!\cdot5!}\cdot\frac{6\cdot5\cdot4!}{2!\cdot4!} \\ n(\text{ 2 chemistry)}=\frac{7\cdot6}{2\cdot1}\cdot\frac{6\cdot5}{2\cdot1} \\ n(\text{ 2 chemistry)}=315 \end{gathered}[/tex]Consider that the number of ways to select 4 workshops if 2 or fewer must be about chemistry, will be equal to the sum of the individual cases when the number of chemistry workshops in the selection are either 0 or 1 or 2.
This can be calculated as follows,
[tex]\begin{gathered} \text{ Total}=n(\text{ 0 chemistry)}+n(\text{ 1 chemistry)}+n(\text{ 2 chemistry)} \\ \text{Total}=35+210+315 \\ \text{Total}=560 \end{gathered}[/tex]Thus, the total number of ways is 560.
A cube is dilated by a factor of 3.5.The volume of the resulting cube is ___ times the volume of the original cube.
Answers
A volume of a cube is given by V=L^3 where L is its side length. If a cube is dilated by a factor of 3.5, it means that its sidelength is increased by a factor of 3.5, i.e. if S is the first length, the new length L satisfies L=3.5*S. Now, the old cube's volume v was v=S^3, after it has expanded to the new sidelength L its new volume V is V=L^3. Using the equation L=3.5*S we can replace L in the equation for V like follows:
V=(3.5*S)^3
Expanding the product we get
V=[(3.5)^3]*(S^3)=42.875*(S^3)
We previously noticed that the prior volume of the cube was v=S^3. Replacing v for S^3 in the previeus equation gives us:
V=42.875v
Thus, the factor by wich the volume of the original cube was scaled up is 42.875
Content attributionQUESTION 441 POINTThe area of a rectangle is 19.68 square centimeters. The width is 4.8 centimeters. What is the length?Provide your answer below:centimetersD0
Answers
In order to calculate the length of the rectangle, we can use the formula for the area of a rectangle:
[tex]A=L\cdot W[/tex]Where A is the area, L is the length and W is the width.
If the area is equal to 19.68 cm² and the width is equal to 4.8 cm, let's calculate the length:
[tex]\begin{gathered} 19.68=4.8\cdot L\\ \\ L=\frac{19.68}{4.8}\\ \\ L=4.1\text{ cm} \end{gathered}[/tex]Therefore the length of the rectangle is equal to 4.1 cm.
what is the value of B ( area of the base) for the following triangular prism?40 ft^248 ft^260 ft^224ft^2
Answers
SOLUTION:
The base of the prism is a triangle and the formula for finding the area of a triangle is "half base multiplied by height".
From the figure of the prism given the base and height of the triangle is 6 ft and 8 ft.
[tex]\begin{gathered} \frac{1}{2\text{ }}\text{ x 6 x 8} \\ \\ \frac{48}{2} \\ \\ 24ft^2 \end{gathered}[/tex]CONCLUSION:
The area of the base of the given triangular prism is 24 squared feet ( the fourth option).
Use this graph of y = 2x2 - 12x + 19 to find the vertex. Decide whether thevertex is a maximum or a minimum point.TV-5O A. Vertex is a minimum point at (1,3)B. Vertex is a minimum point at (3,1)C. Vertex is a maximum point at (1,7)D. Vertex is a maximum point at (3,1)
Answers
For a parabola, the vertex is the critical point, in other words, it is the maximum or the minimum of the function.
From the graph, we can see that the minimum (the minimum value of y) of the graph is 1. The vertex is the point (3,1).
Moreover, as we mentioned the vertex is always the minimum or the maximum, in this case, it is the minimum since the rest of the graph is 'above' that point.
The answer is option B. Vertex is a minimum point at (3,1)
Given the function f(x) = 2x2 - 5x + 1. Calculate the following values: f(-2) = f(-1) = f(0) = f(1) = f(2) Question Hon
Answers
Given function is
[tex]f(x)=2x^2-5x+1[/tex]Substitute the value of -2 in the equation we get
[tex]\begin{gathered} f(-2)=2(-2)^2-5\times-2+1_{} \\ =8+10+1 \\ =19 \end{gathered}[/tex]Similarly find other values
[tex]\begin{gathered} f(-1)=2(-1)^2-5\times-1+1_{} \\ =2+5+1 \\ =8 \end{gathered}[/tex]And then similarly f(1)=-2 and f(2)=-1 and f(0)=1
[tex]\begin{gathered} f(0)=2(0)^2-5\times0+1_{} \\ =0+0+1 \\ =1 \end{gathered}[/tex][tex]\begin{gathered} f(0)=2(0)^2-5\times0+1_{} \\ =0+0+1 \\ =1 \end{gathered}[/tex]What is the ratio of fish to dinosaurs?3 dinosaurs 10 fish
Answers
Answer
10/3
or 3.33
Solution
[tex]\frac{10\text{ fish}}{3\text{ dinosaurs}}\text{ = }\frac{10}{3}=3.33[/tex]So I am struggling in math and I could use some help to try and get through it
Answers
Given the functions:
[tex]\begin{gathered} f(x)=-5x+2 \\ g(x)=-2x²-3 \end{gathered}[/tex]to find f(7), we can make x = 7 on the function f to get the following:
[tex]\begin{gathered} f(7)=-5(7)+2=-35+2=-33 \\ \Rightarrow f(7)=-33 \end{gathered}[/tex]in a similar way, we can find g(5) by making x = 5 on the function g:
[tex]\begin{gathered} g(5)=-2(5)²-3=-2(25)-3=-50-3=-53 \\ \Rightarrow g(5)=-53 \end{gathered}[/tex]therefore, f(7) = -33 and g(5) = -53
I need help but not all are boxes are used
Answers
Given:
[tex]y=3x-5\text{ and y=-6x+4}[/tex]Aim:
We need to find the solution to the given system of equations.
Explanation:
Consider the equation y =3x-5.
Substitute y =-6x+4 in the equation y =3x-5.
[tex]-6x+4=3x-5[/tex]Solve for x.
Add 6x to both sides of the equation.
[tex]-6x+4+6x=3x-5+6x[/tex][tex]4=3x-5+6x[/tex][tex]4=9x-5[/tex]Add 5 to both sides of the equation.
[tex]4+5=9x-5+5[/tex][tex]9=9x[/tex]Divide both sides by 9.
[tex]\frac{9}{9}=\frac{9x}{9}[/tex][tex]x=1[/tex]Substitute x =1 in the equation y =3x-5.
[tex]y=3(1)-5[/tex][tex]y=-2[/tex]The solution of the given system of equations is x=1 and y =-2.
Final answer:
[tex](1,-2)[/tex]Consider the relation y = −3|x + 5| − 6. What are the coordinates of the vertex?
Answers
Solution:
Given the relation below
[tex]y=-3|x+5|-6[/tex]The general form, an absolute value function is
[tex]y=a|x-h|+k[/tex]The vertex coordinates are (h, k)
Solving to find the vertex below
[tex]\begin{gathered} x+5=x-h \\ 5=-h \\ h=-5 \\ k=-6 \\ (h,k)\Rightarrow(-5,-6) \end{gathered}[/tex]Hence, the coordinates of the vertex is
[tex](-5,-6)[/tex]You have $10,000 in a savings account. You want to take most of the money out and invest it in stocks and bonds. You decide to invest nine times as much as you leave in the account. You also decide to invest five times as much in stocks as in bonds. How much will you invest in stocks, how much in bonds, and how much will youleave in savings?
Answers
Answer:
7,500 in stocks
1,500 in bonds
1,000 in savings
Explanation:
First, let's call x the quantity that you will leave in saving and y the quantity that you will invest in stocks and z the quantity that you will invest in bonds.
Now, we can formulate the following equations:
x + y + z = 10,000
y + z = 9x
y = 5z
Because you have 10,000 in savings, you decide to invest nine times as much as you leave in the account, and you also decide to invest five times as much in stocks as in bonds.
So, we can rewrite the expressions as:
x + y + z = 10,000
-9x + y + z = 0
y - 5z = 0
Now, we can multiply the second equation by -1 and sum this equation with the first one as:
-9x + y + z = 0
(-9x + y + z)*(-1) = 0*(-1)
9x - y - z = 0
Then, the sum is equal to:
x + y + z = 10,000
9x - y - z = 0
10x - 0 - 0 = 10,000
10x = 10,000
x = 10,000/10
x = 1,000
Replacing x on the second equation, we get:
9x - y - z = 0
9*1,000 - y - z = 0
9,000 - y - z = 0
-y - z = - 9,000
Now, we can add the equation with the third one as:
-y - z = - 9,000
y - 5z = 0
0 - 6z = -9,000
-6z = -9000
z = -9000/(-6)
z = 1,500
Finally, using the third equation, the value of y is equal to:
y = 5z
y = 5*1500
y = 7,500
Therefore, you will invest 7,500 in stocks, 1,500 in bonds and you will leave 1,000 in savings.
Assume that when adults with smartphones are randomly selected, 49% use them in meetings or classes. If 11 adult smartphone users are randomly selected, findthe probability that fewer than 4 of them use their smartphones in meetings or classes.The probability is
Answers
Answer: 12.66%
First, we will solve the probability that 3 adults, 2 adults, 1 adult and no adult use their smartphones in meetings or classes,
To solve for this, we will use the following equation
[tex]11Cn\times0.49^n\times0.51^{11-n}[/tex]*Probability of adults using their phones for meetings or classes are 0.49.
1 - 0.49 = 0.51
*Probability of adults NOT using their phones are 0.51
Now, with the values of n at:
n = 0
n = 1
n = 2
n = 3
[tex]11Cn\times0.49^n\times0.51^{11-n}=11C0\times0.49^0\times0.51^{11-0}=0.0006[/tex][tex]11Cn\times0.49^n\times0.51^{11-n}=11C1\times0.49^1\times0.51^{11-1}=0.0064[/tex][tex]11Cn\times0.49^n\times0.51^{11-n}=11C2\times0.49^2\times0.51^{11-2}=0.0308[/tex][tex]11Cn\times0.49^n\times0.51^{11-n}=11C3\times0.49^3\times0.51^{11-3}=0.0888[/tex]Now, we will add these altogether to get the probability that fewer than 4 of them use their smartphones in meetings or classes.
[tex]0.0006+0.0064+0.0308+0.0888=0.1266=12.66\%[/tex]The answer would be 12.66%.
in an election being held by the associated students organization, there are eight candidates for president, five for five president, five for secretary, and seven for treasurer. How many different possible outcomes are there for this election?
Answers
we have
eight candidates for president
five for secretary
seven for treasurer
therefore
The different possible outcomes is giving by
(8)*(5)*(7)=280 outcomes
the answer is 280 outcomesadrienne earns 98$ for working 8 hours. if she earned 453.25$, how many hours did she work?
Answers
Answer: 37 hours
Step-by-step explanation:
98/8 = 12.25
453.35/12.25 = 37
solve and graph the following inequality: x + 19 > 31
Answers
You have the following inequality:
x + 19 > 31
subtract 19 both sides and simplify:
x > 31 - 19
x > 12
The graph of the previous inequality is:
You buy a house for $299,00. If you make a 20% down payment, how much would you pay in total per month for the 30 year loan if you pay $3200/year in taxes, $1050/year in insurance and $28/month forthe home owners association?
Answers
Charlene calculated that the monthly patyment, including interests is $ 692.88.
Taxes = $ 3,200 annually, if we divide it by 12, we will find the monthly amount, this way:
3,200/12 = $ 266.67
Insurance = $ 1,050 annually, if we divide it by 12, we will find the monthly amount, this way:
1,,050/12 = $ 87.50
Home owners association = $ 28
Therefore, the monthly payment would be:
692.88 + 266.67 + 87.50 + 28
You can finish the calculation, Charlene!
help pls 1st blank - Graph A, Graph B, Graph C, Graph D 2nd blank - Yes or No 3rd blank - inside or outside
Answers
SOLUTION
From the question,
Let x represent acres for apple orchard
Let y represent acres for peach orchard
Since the farmer can afford a maximum of 54 acres of land, that means
[tex]x+y\le54[/tex]The apple orchard requires 3000 gallons of water, while the peach requires 800 gallons of water. But the farmers irrigation system can deliver a maximum of 80,000 gallons per day, puting in an equation, we have
[tex]3000x+800y\le80,000[/tex]From his apple orchard, he expects to get a profit of $3,400 per year and from peach, a profit of $1,600 per year.
His expected profit will be determined using the equation
[tex]\begin{gathered} P=3400x+1600y \\ \text{where P is the expected maximum profit } \end{gathered}[/tex]So, we will plot the following points
[tex]\begin{gathered} x+y\le54 \\ 3000x+800y\le80,000 \end{gathered}[/tex]This will help us to get the required region needed to find the expected maximum profit
We can see that this is the same with graph B from the question
Now, we will substitute the following points from the graph into the equation of the maximum expected profit. Which ever that gives us the highest value becomes the answer.
For point (0, 54) we have
[tex]\begin{gathered} P=3400x+1600y \\ P=3400(0)+1600(54) \\ P=0+86,400 \\ P=86,400 \end{gathered}[/tex]For Point (16.727, 37.273), we have
[tex]\begin{gathered} P=3400x+1600y \\ P=3400(16.727)+1600(37.273) \\ P=56,871.8+59,636.8 \\ P=116,508.6 \end{gathered}[/tex]Finally, for point (26.667, 0) we have
[tex]\begin{gathered} P=3400x+1600y \\ P=3400(26.667)+1600(0) \\ P=90,667.8+0 \\ P=90,667.8 \end{gathered}[/tex]We can see that the maximum profit is $116,508.60, from
point (16.727, 37.273)
Hence the division of land that will maximize his expected profit is
16.73 acres of land for apple orchard
37.27 acres of land for peach orchard
Now, looking at the graph, the point (30, 20) lies outside the required region, so the farmer cannot maximize his profit at 30 acres for apple orchard and 20 acres for peach orchard.
Hence the answer is No, because the point (30, 20) lies outside the solution region.
Simplify:6.2n - 8.3 + -9.1 + 1.4n
Answers
ANSWER
7.6n - 17.4
EXPLANATION
We have the expression that we want to simplify.
We have:
6.2n - 8.3 + (-9.1) + 1.4n
The first step is to collect like terms:
=> 6.2n + 1.4n - 8.3 - 9.1
Now, simplify:
7.6n - 17.4
That is the answer.
Solve the equation. (Enter your answers as a comma-separated list.)2b2 − 18 = −9b
Answers
Given
The equation,
[tex]2b^2-18=-9b[/tex]To solve for b.
Explanation:
It is given that,
[tex]2b^2-18=-9b[/tex]That implies,
[tex]\begin{gathered} 2b^2-18=-9b \\ 2b^2+9b-18=0 \\ 2b^2-3b+12b-18=0 \\ b(2b-3)+6(2b-3)=0 \\ (2b-3)(b+6)=0 \\ 2b-3=0,b+6=0 \\ 2b=3,b=-6 \\ b=\frac{3}{2},b=-6 \end{gathered}[/tex]Hence, the answer is 3/2, -6.
how do I write an equation as a multiple of a unit fraction using 3×3/7
Answers
EXPLANATION
An equation can be written as a multiply of a unit fraction using the following relationship:
[tex]x(3\cdot\frac{3}{7})[/tex]For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.Part A: Write a function in for the geometric sequence where the first term is 11 and the common ratio is 4 .Part B: Find the first five terms in the geometric function.Part C: In one paragraph, using your own words, explain your work for Step A and Step B.
Answers
Remember that the formula for a geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]PART A:
With the data given, the formula for the sequence is:
[tex]a_n=11_{}\cdot4^{n-1}[/tex]PART B:
[tex]\begin{gathered} a_1=11\cdot4^{1-1}\rightarrow a_1=11 \\ a_2=11\cdot4^{2-1}\rightarrow a_2=44 \\ a_3=11\cdot4^{3-1}\rightarrow a_3=176 \\ a_4=11\cdot4^{4-1}\rightarrow a_4=704 \\ a_5=11\cdot4^{5-1}\rightarrow a_5=2816 \end{gathered}[/tex]PART C:
For part A, we took the general formula for the geometric sequence and plugged in the first term and the common ratio provided.
For part B, we replaced n for all the numbers from 1 through 5 to get the first 5 terms of the sequence.
Solve each inequality). 2|4t-1|+6>20
Answers
To answer this question we will use the following property:
[tex]|a|>b>0\text{ if and only if }a>b\text{ or }a<-b.[/tex]Subtracting 6 from the given inequality we get:
[tex]\begin{gathered} 2|4t-1|+6-6>20-6, \\ 2|4t-1|>14. \end{gathered}[/tex]Dividing the above inequality by 2 we get:
[tex]\begin{gathered} \frac{2|4t-1|}{2}>\frac{14}{2}, \\ |4t-1|>7. \end{gathered}[/tex]Then:
[tex]4t-1>7\text{ or }4t-1<-7.[/tex]Solving the above inequalities we get:
1)
[tex]4t-1>7.[/tex]Adding 1 to the above inequality we get:
[tex]\begin{gathered} 4t-1+1>7+1, \\ 4t>8. \end{gathered}[/tex]Dividing the above by 4 we get:
[tex]\begin{gathered} \frac{4t}{4}>\frac{8}{4}, \\ t>2. \end{gathered}[/tex]The above inequality in interval notation is:
[tex](2,\infty).[/tex]2)
[tex]4t-1<-7.[/tex]Adding 1 to the above inequality we get:
[tex]\begin{gathered} 4t-1+1<-7+1, \\ 4t<-6. \end{gathered}[/tex]Dividing the above result by 4 we get:
[tex]\begin{gathered} \frac{4t}{4}<-\frac{6}{4}, \\ t<-\frac{3}{2}. \end{gathered}[/tex]The above inequality in interval notation is:
[tex](-\infty,-\frac{3}{2}).[/tex]Answer:
[tex](-\infty,-\frac{3}{2})\cup(2,\infty).[/tex]Gregory left a $8 tip on a $46 restaurant bill. What percent tip is that? Give your answer to two decimal places if necessary.
Answers
Answer:
17.39%
Step-by-step explanation:
Considering that $46 was the restaurant bill and Gregory left an extra tip of $8, the percent is:
[tex]\begin{gathered} \frac{8}{46}=0.1739\text{ } \\ \end{gathered}[/tex]0.1739 = 17.39%
This tip represents 17.39%.
Statement Reason
1. AEEC;BDDC 1. given
2. ∠AEC is a rt. ∠; ∠BDC is a rt. ∠ 2. definition of perpendicular
3. ∠AEC ≅ ∠BDC 3. all right angles are congruent
4. ? 4. reflexive property
5. △AEC ~ △BDC 5. AA similarity theorem
What is the missing statement in step 4?
Answers
The missing Statement is 4. ∠EAC ≅ ∠EAC 4. reflexive property
In △AEC and △BDC
We need to know the missing statement in step 4
Statement Reason
1. AE⊥EC;BD⊥DC 1. given
2. ∠AEC is a rt. ∠; ∠BDC is a rt. ∠ 2. definition of perpendicular
3. ∠AEC ≅ ∠BDC 3. all right angles are congruent
4. ∠EAC ≅ ∠EAC 4. reflexive property
5. △AEC ~ △BDC 5. AA similarity theorem
Therefore, the missing Statement is 4. ∠EAC ≅ ∠EAC 4. reflexive property.
To learn more about similarity properties refer here
https://brainly.com/question/24184322
#SPJ1
how do i find the volume to the nearest 1 decimal place?
Answers
Solution:
The volume of a cylinder is expressed as
[tex]\begin{gathered} V=\pi\times r^2\times h \\ where \\ V\Rightarrow volume\text{ of the cylinder} \\ r\Rightarrow radius\text{ of its circular ends} \\ h\Rightarrow height\text{ of the cylinder} \end{gathered}[/tex]Given the cylinder below:
we have
[tex]\begin{gathered} height\text{ of the cylinder = 4 cm} \\ diameter\text{ of the circular end = 2 cm} \end{gathered}[/tex]but
[tex]\begin{gathered} radius=\frac{diameter}{2} \\ \Rightarrow r=\frac{d}{2}=\frac{2cm}{2}=1\text{ cm} \end{gathered}[/tex]Thus, the volume of the cylinder is evaluated by substituting the values of 4 cm and 1 cm for h and r respectively into the volume formula.
[tex]\begin{gathered} V=\pi\times1cm\times1cm\times4cm \\ =12.56637 \\ \approx12.6\text{ cubic centimeters} \end{gathered}[/tex]Hence, the volume of the cylinder, to the nearest 1 decimal place is
[tex]12.6\text{ cubic centimeters}[/tex]