1. A soup company uses a cylindrical can for their soup with a radius of 4 cm.
If the volume of the can is 240π cm3, what is the height of the can?
Explain how you determined the answer.
2.Consider a cylinder with radius 4 cm and a height of 12 cm.
Describe how to calculate the volume of the given cylinder and what the volume means.
3.A cracker company wants to make a rectangular box to hold their crackers.
They want the height of the box to be 10 inches and the width to be 4 inches.
Explain how to calculate the length the box needs to be in order for the volume of the box to be 200 cubic inches.
Answers
Cylinder
V = [tex] \pi r^2[/tex]
Rectangle
V = L x W x H
In the first problem, we have a cylinder and we are looking for the height. We know the volume (240), and we know the radius (4). We can use these values to fill in our formula, and then solve for the missing height. (This process is shown in the image).
In the second problem, we have a cylinder and we are looking for the volume. We know the radius (4), and we know the height (12). We can use these values to fill in our formula, and then solve for the volume. (This process is shown in the image).
In the third problem, we have a rectangle and we are looking for the length. We know the height (10), we know the width (4), and we know the volume (200). We can use these values to fill in our formula, and then solve for the length. (This process is shown in the image).
Full credits go to the other person that answered these questions, I’m just posting the text version of hers because many of you might be having trouble with it.
So, here it is:
1. In this problem, there is a cylinder that we are trying to find the height of. We know the radius which is 4, and we know that the volume which is 240.
V = πr^2
Volume: πr^2h
240 = π4^2h
240/16 = 16π(h)/16
H = 15cm
2. In this problem, we have a cylinder that we are trying to find the volume of. We know the radius which is 4, and we know the height which is 12.
Volume = πr^2h
V = π4^2(12)
= 16 π(12)
V = 192 π^2
3. In this problem, we have a rectangle that we are looking for the length of. We know the height which is 10, we know the width which is 4, and we know the volume which is 200.
Volume = L*W*H
200 = L*4*10
200/40 = 40L/40
L = 5in
Hope I helped!
Related Questions
What is the volume of a cube with an edge length of 3.2 meters? Enter your answer, as a decimal, in the box.
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a photograph measuring 4 inches wide and 5 inches long is enlarge to make a wall mural. If the mural is 120 inches wide, how long is the mural?
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4x=120×5
x=600÷4
x=150 inches
find the difference (-ab+9a-1)-(5ab-3)
Answers
Hope this helps!! ;))
Have a grat day!! <3
If f=6 and g=8, what does h equal
Answers
The value of h in this given alphabetical series is 10.
What is an arithmetic sequence?The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the. sequence. The nth term of an arithmetic sequence is given by. aₙ = a + (n – 1)d
Given, f=6 and g=8
Since, there is no additional data is given I will assume this is the question of Alphabetic sequence.
In Alphabet Series section, a string of alphabets, either in a single file or in combination form a sequence. This sequence comes together following a definite rule. The candidate is expected to detect this rule and answer the questions at the end.
So,
the value of f = 6 and g = 8
Since, Alphabetic order after f and g is h, i ,j, k, l, .....
And common factor is 2
Thus,
The value of h = 8+2 = 10
The value of i = 10+2 = 12
The value of j = 12 +2 =14
And so on
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Find the discriminant of the quadratic $3x^2 - 7x + 6.$
Answers
3 x^2 - 7 x + 6 = 0
Divide both sides by 3:
x^2 - (7 x)/3 + 2 = 0
Subtract 2 from both sides:
x^2 - (7 x)/3 = -2
Add 49/36 to both sides:
x^2 - (7 x)/3 + 49/36 = -23/36
Write the left hand side as a square:
(x - 7/6)^2 = -23/36
Take the square root of both sides:
x - 7/6 = (i sqrt(23))/6 or x - 7/6 = -(i sqrt(23))/6
Add 7/6 to both sides:
x = 7/6 + (i sqrt(23))/6 or x - 7/6 = -(i sqrt(23))/6
Add 7/6 to both sides:
Answer: x = 7/6 + (i sqrt(23))/6 or x = 7/6 - (i sqrt(23))/6
Answer:
Discriminant of the quadratic is-23
Step-by-step explanation:
The given quadratic function is [tex]3x^2-7x+6[/tex]
Comparing with the expression [tex]ax^2+bx+c[/tex]
a = 3, b = -7, c = 6
The discriminant of the quadratic is given by [tex]D=b^2-4ac[/tex]
Substituting the known values, discriminant of the quadratic is
[tex]D=(-7)^2-4(3)(6)\\\\D=49-72\\\\D=-23[/tex]
Therefore, discriminant of the quadratic is-23
Gcf of 28x3 and 16x2y2
Answers
The greatest common factor (GCF) of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex] is the greatest common factor (GCF) of and [tex]16x^{2} y^{2}[/tex] is [tex]4x^{2}[/tex] .
To find the greatest common factor (GCF) of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex]
, we need to identify the common factors between the two expressions.
The prime factorization of is [tex]2.2.7.x.x.x.[/tex]
The prime factorization of [tex]16x^{2} y^{2}[/tex] is [tex]2.2.2.2.x.x.y.y.[/tex]
Now, let's identify the common factors:
Both expressions have [tex]2.2.x.x[/tex] in common.
So, the greatest common factor (GCF) of and [tex]16x^{2} y^{2}[/tex] is [tex]4x^{2}[/tex] .
COMPLETE QUESTION:
Circle the GCF of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex]
[tex]28x^{3}[/tex]: [tex]2.2.7[/tex].*•*•*
[tex]16x^{2} y^{2}[/tex]:[tex]2.2.2.2.x.x.y.y[/tex]
The area of a rectangle playgrond is 78 square meters. If the length of the playground is 13 meters, what is its width?
Answers
78 = length * 13
[tex] length = \frac{78}{13} [/tex] use a calculator to find out the answer then,
Answer:
6 meters.
Step-by-step explanation:
Let w represent width of the rectangle.
We have been given that the area of a rectangle playground is 78 square meters. The length of the playground is 13 meters.
We know that area of a rectangle is width times length of rectangle. We can represent our given information in an equation as:
[tex]\text{Area of rectangle}=\text{Length}\times \text{Width}[/tex]
[tex]78\text{ m}^2=13\text{ m}\times \text{Width}[/tex]
[tex]13\text{ m}\times \text{Width}=78\text{ m}^2[/tex]
[tex]\frac{13\text{ m}\times \text{Width}}{13\text{ m}}=\frac{78\text{ m}^2}{13\text{ m}}[/tex]
[tex]\text{Width}=6\text{ m}[/tex]
Therefore, the width of the rectangle is 6 meters.
a jope rope is 9 feet long how long is the jump rope in yards
Answers
If there is a 30% increase in the operation charge for using a service,$82.70 remains to be paid.how much is the original bill ?
Answers
1) Given that lines L and M are parallel, which of the statements is true? A) ∠ DEF ≅ ∠ EBC B) ∠ ABC ≅ ∠ DEF C) ∠ ABC ≅ ∠ EBC D) ∠ BEF ≅ ∠ ABC
Answers
Greyson's mom used 4 out of 12 eggs to make pancakes. Then she used 3 out of 12 eggs to make cupcakes. What fraction of a dozen eggs did she used in all? ( Hint: 1 dozen = 12)
Answers
NBDHBbhjnsjkbhBSDBWjcd
Well . . .
4 out of 12 eggs makes the fraction 4/12 for pancakes.
3 out of 12 eggs makes the fraction 3/12 for cupcakes.
4/12 + 3/12 + 7/12
If you don’t know how to do it here you go judging by how easy the question is -
Only add the numerator (top) and keep the denominator (bottom) the same.
Hope this helps :)
The table shows data for a random sample of 20 students out of middle school. Use the sample to draw an inference about each measure. Explain your reasoning.
Answers
A standard coffee mug has a capacity of 16 fluid ounces. If Annie needs to fill 12 mugs mugs with coffee, how many quarts of coffee does she need?
Answers
16 is half of 32 so 1 quart fills 2 mugs meaning that she needs 6 quarts of coffee
the fish tank in Paul's bedroom has a pump that will recirculate 75 gallons of water in 1/4 of an hour. Find the unit rate in gallons per hour.
a. 5 gallons per hour
b. 18.75 gallons per hour
c. 300 gallons per hour
d. 187.5 gallons per hour
Answers
(1/4) hour---------> 0.25 hour
if the pump recirculate 75 gallons of water in -------------> 0.25 hour
X gallons of water in-----------------------------------------> 1 hour
X=75/0.25----------> x=300 gallons /hour
the answer is 300 gallons /hour
Picture is attached need help fast thanks
Answers
[tex] \sqrt[3]{ 8^{x} } [/tex]
Verbally we can say we are taking cube root of [tex] 8^{x} [/tex]. Cube root is equivalent to raising the power to [tex] \frac{1}{3} [/tex].
So, we can say we raising [tex] 8^{x} [/tex] to the power [tex] \frac{1}{3} [/tex].
In expression form, this will be:
[tex] ( 8^{x} )^{ \frac{1}{3} } \\ \\ = 8^{ \frac{x}{3} } [/tex]
Therefore, third option is the correct answer
please help! determine whether the number is closest to 0, or 1. explain why. (a. 10/9) (b. 9/16) (c. 2/15) theyre not answer choices.
Answers
A number greater than 1 is closer to 1 than to 0.
A number between 0 and half is closer to 0 than to 1.
A number between half and 1 is closer to 1 than to 0.
Now we need to see if the given numbers are less than 0, greater than 1, between 0 and half, or between half and 1.
a. 10/9 is greater than 1, so it is closer to 1 than to 0.
b. 9/16 is between half and 1, so it is closer to 1.
c. 2/15 is between 0 and half, so it is closer to 0.
A candy wrapping robot can wrap 434 pieces of candy in five minutes. How many pieces of candy can it wrap in any number of minutes
Answers
y=86.8x (y is total candies wrapped, x is the number of minutes)
What is the answer to 3(t-7)=6t
Answers
3(t) = 3t
3(-7) = -21
3t -21 = 6t
isolate the -21 by subtracting 3t from both sides
-21 + 3t = 6t
-21 + 3t (-3t) = 6t (-3t)
-21 = 3t
divide 3 from both sides to isolate the t
3t = -21
3t/3 = -21/3
t = -21/3
t = -7
t = -7 is your answer
hope this helps
PLEASE HELP. WILL OFFER 50 POINTS AND BRAINLIEST FOR CORRECT ANSWER!
Graph the two lines
2x + 3y = 18
3x -4y > 16.
Give the Domain and Range, Slope, and Y-intercept for each line. Graph each equation above on the graph below and show all work. Give the Domain and Range, Slope, and Y-intercept for each line. Explain in detail how you got each answer.
2x + 3y = 18 3x -4y > 16
Slope-Intercept Form: Slope-Intercept Form:
Domain: Domain:
Range: Range:
Slope: Slope:
Y-intercept: Y-intercept:
Answers
Answer:
For Equation 1:
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]Y-intercept: 6For Equation 2:
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\frac{3}{4}[/tex]Y-intercept: -4Step-by-step explanation:
We are given two lines - one is an equation and one is an inequality.
Neither are in slope-intercept form (y = mx + b), so we need to make these adjustments.
Slope-intercept form has two key parts to the equation: m, which is the slope of the line and b, which is the y-intercept of the line.
Equation 1
[tex]\displaystyle2x+3y=18\\\\3y = -2x + 18\\\\y = -\frac{2}{3}x+6[/tex]
With this, we can now determine the domain, range, slope, and y-intercepts for this line.
For Equation 1, because our equation is in slope-intercept form, we can find the slope and the y-intercept.
Our equation is [tex]y=-\frac{2}{3}x+6[/tex]. Therefore, our m is [tex]-\frac{2}{3}[/tex] and our b is 6.
Because the equation is linear, there is no instance in which the line will not meet an x- or y-value. Therefore, our domain and range is all real numbers, or [tex]\mathbb{R}[/tex].
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]Y-intercept: 6Equation 2
[tex]\displaystyle3x-4y>16\\\\-4y>-3x+16\\\\y < \frac{3}{4}x-4[/tex]
Now that we have solved the inequality, we can determine our slope, the domain, and the range of the function.
We can use the same tactic as before - m is our slope and b is our y-intercept. Therefore, [tex]\frac{3}{4}[/tex] is our slope and -4 is our y-intercept.
Because the inequality represents a line, our domain is all real numbers, or [tex]\mathbb{R}[/tex]. If we were to plug in any number for x, y would be true for that value. Therefore, our range is also all real numbers, or [tex]\mathbb{R}[/tex].
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\frac{3}{4}[/tex]Y-intercept: -4which expression is equivalent to 20-4x/4
a. 5-x
b. 5-4x
c. 20-x
d. 80-16x
Answers
The expression (20-4x)/4 equals 5 - x.
Given is an expression (20-4x)/4 we need to find an equivalent expression to it,
A mathematical expression or equation that is equivalent to another expression or equation is one that has the same value or meaning.
In other words, if two phrases yield the same result or depict the same mathematical relationship, they are deemed equal.
So,
By multiplying each word in the brackets by 4, it is possible to simplify the formula (20-4x)/4.
This results in:
(20/4) - (4x/4)
Simplifying even more
5 - x
Therefore, the expression (20-4x)/4 equals 5 - x.
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I need to know the answer
Answers
PLEASE MATH EHLP WILL GIVE BRAINLIEST!!!
What is the trigonometric ratio for sin C ?
Enter your answer, as a simplified fraction, in the boxes.
Answers
=root of 324=18
therfore altitude =18cm,hypotenuse =82
sinC=Opposite/hypotenuse=18/82=9/41
Answer:
The trigonometric ratio for [tex]\sin C[/tex] is [tex]\frac{9}{41}[/tex]
Step-by-step explanation:
Given : A right triangle ABC with ∠B = 90° and AC = 82 and BC = 80
We have to find the value of [tex]\sin C[/tex]
Since, Sine is defined as the ratio of perpendicular to its hypotenuse.
Mathematically written as [tex]\sin\theta=\frac{Perpendicular}{Hypotenuse}[/tex]
For the given triangle ABC, we have
Using Pythagoras theorem, For a right angled triangle, sum of square of base and perpendicular is equal to the square to its hypotenuse.
[tex](AC)^2=(AB)^2+(BC)^2[/tex]
Substitute, we get,
[tex](82)^2-(80)^2=(AB)^2\\\\ 6724-6400=(AB)^2\\\\ 324=(AB)^2\\\\ \Rightarrow AB =18[/tex]
[tex]\theta=C[/tex]
So, perpendicular = AB and Hypotenuse = AC
[tex]\sin C=\frac{AB}{AC}[/tex]
[tex]\sin C=\frac{18}{82}=\frac{9}{41}[/tex]
Thus, The trigonometric ratio for [tex]\sin C[/tex] is [tex]\frac{9}{41}[/tex]
A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best describes the change in the radius of the original circle? increased by a factor of 8 increased by a factor of 4 increased by a factor of 16 increased by a factor of 12
Answers
Answer:
Increased by a factor of 4
Step-by-step explanation:
-4x-15y=-17
-x+5y=-13
[tex] - 4x - 15y = - 17 \\ - x + 5y = - 13[/tex]
Answers
we are given the following system of equations
[tex] - 4x - 15y = - 17[/tex]
[tex] - x + 5y = - 13[/tex]
if you look at the x variables in both equations you can see that we can easily eliminate them by multiplying the bottom equation by -4 as so
[tex] - 4x - 15y = - 17[/tex]
[tex] - 4( - x + 5y = - 13)[/tex]
simplify and we get
[tex] - 4x - 15y = - 17[/tex]
[tex]4x - 20y = 52[/tex]
now we can combine like terms on each side with the x's cancelling and get
[tex] - 35y = 35[/tex]
now divide off -35
[tex]y = - 1[/tex]
great now we can go back to our original system and pick a equation and substitute y back in to find x lets use
[tex] - x + 5y = 13[/tex]
so now we substitute y and get
[tex] - x + 5( - 1) = 13[/tex]
[tex] - x - 5 = 13[/tex]
[tex] - x = 17[/tex]
[tex]x = - 17[/tex]
now we put x and y into one coordinate (x,y)
so now our FINAL ANSWER IS
(-17,-1)
2 - 4x = 14 A) -4 B) -3 C) 0 D) 3 Eliminate
Answers
Hope this helps
subtract 2 from both sides
-4x = 12
divide both sides by -4
x= -3
ANSWER: B) -3
Hope this helps! :)
A sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7 : 6. The store donates 24 soccer balls. How many basketballs does the store donate
The store donates __ basketballs
Answers
Derek uses a $50 gift card to purchase 3 books for $12 each and a calendar for $9.What is the amount left on the card ?
Answers
Evan's mother used 1/3 pound of beef, 1/2 pound of shrimp, and 3 pounds of pasta to make dinner for 4 people.
Use this information to answer ALL FOUR PARTS below.
Question:
Part A:
Each person will receive an equal share of beef with none left over. What is the amount, in pounds, of each serving of beef?
Part B:
Each person will receive an equal share of shrimp with none left over. What is the amount, in pounds, of each serving of shrimp?
Part C:
Each person will receive an equal share of pasta with none left over. What fraction represents the amount, in pounds, of each serving of pasta?
Part D:
Evan only ate 1/2 of the pasta that he received. What is the amount, in pounds, of pasta did Evan eat? Explain how you got this answer step-by-step using math vocabulary.
Answers
Part B: 1/2 / 4 = 1/8. Each person gets 1/8 pound of shrimp.
Part C: 3 / 4 = 3/4. Each person gets 3/4 pound of pasta.
Part D: If we're talking about pasta, then Evan ate 3/8 pound of pasta. Half of 3/4 (the amount of pasta given to everyone) is 3/8, so if Evan ate 1/2 of his share (3/4), he ate 3/8 pounds of pasta.
Hope this helps! Have an awesome day :)
|-2x+6|=-8 absolute value equations
Answers
The left side must be non-negative. (An absolute value is always 0 or positive.) The right side is negative. There can never be any point of intersection.
Carlos and Maria drove a total of 233 miles in 4.4 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.
Answers
Equation 1: x + y = 4.4
x = 4.4 - y
Equation 2: 55x + 50y = 233
55(4.4 - y) + 50y = 233
242 - 55y + 50y = 233
-5y = 233-242
-5y = -9
y=9/5 or 1.8 hours Maria drove
To find time Carlos drove:
x=4.4 - 1.8
x = 2.6 hours
Answer:
Time of driving of Maria = 1.8 hours
Step-by-step explanation:
Let a be time drove by Carlos and b be the time drove by Maria.
Carlos and Maria drove a total of 233 miles in 4.4 hours.
Total time = 4.4 hours
a + b = 4.4 ------------------eqn 1
Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour.
Speed of Carlos = 55 miles per hour
Speed of Maria = 50 miles per hour
Total distance = 233 miles
That is
55 a + 50 b = 233----------------------eqn 2
eqn 1 x 50
50 a + 50 b = 220---------------------------eqn 3
eqn 3 - eqn 2
55 a + 50 b - 50 a - 50 b = 233 - 220
5a = 13
a = 2.6
Substituting in eqn 1
2.6 + b = 4.4
b = 1.8
Time of driving of Maria = 1.8 hours