Answer:
The diameter of the smaller can is ≅ 9.14 cm
Correct statement and question:
Two cylindrical cans are mathematically similar.
The larger can has a capacity of 1 liter and a diameter of 12 cm and the smaller can has a capacity of 440 ml.
Calculate the diameter, d, of the 440 ml can.
Source:
Previous question that can be found at brainly
Step-by-step explanation:
Let's recall that:
A. The formula of the volume of a cylinder is π*r²*h, where:
r is the radius of the cylinder (half of the length of the diameter) and h, represents the height of the cylinder.
B. 1 liter = 1,000 milliliters = 1,000 cubic centimeters
Therefore, we can find the height of the larger can, this way:
V = π*r²*h
Replacing with the value we know:
d = 12 ⇒ r = 6
1,000 = 3.1416 * 6² * h
1,000 = 113.0976h
h = 1,000/113.0976
h = 8.84 cm (rounding to the next hundredth)
Now we can find the ratio of the radius to the height of the larger can to find the measures of the smaller can, this way because the cylinders are mathematically similar:
Ratio = Radius/Height
Ratio = 6/8.84
Ratio = 0.6787
It means the radius of the smaller can is 0.6787 multiplied by the value of the height of the smaller can. Let x represent the height h of the smaller can, we can write this equation to solve for x:
V = π*r²*h
Replacing with the values we know:
height = x
radius = 0.6787x
440 = π * (0.6787x)² * x
440 = 3.1416 * 0.4606x² * x
440 = 1.4471x³
x³ = 440/1.4471
x³ = 304.06
∛x = ∛304.06
x = 6.73 ⇒ height of the smaller can = 6.73 cm and radius of the smaller can = 6.73 * 0.6787 = 4.57
If radius = 4.57 cm ⇒ diameter = 2 * 4.57 = 9.14 cm
The diameter of the smaller can is ≅ 9.14 cm
The diameter of the 440 ml can is approximately 9.12 cm.
To determine the diameter of the smaller can, we use the fact that the two cans are mathematically similar. This means that their dimensions have a constant ratio, known as the scale factor.
The capacity of the larger can is 1 liter (1000 ml), and the capacity of the smaller can is 440 ml.
The scale factor for volumes is given by:
Scale Factor (Volume) = (Volume of smaller can) / (Volume of larger can) = 440 ml / 1000 ml = 0.44
Since the cans are similar, the scale factor for the linear dimensions (such as diameter) is the cube root of the volume scale factor:
Scale Factor (Diameter) = ∛(Scale Factor (Volume)) = ∛(0.44)
Using a calculator, we find:
∛(0.44) ≈ 0.76
Now, we multiply the diameter of the larger can by this scale factor to find the diameter of the smaller can:
Diameter of the smaller can = Diameter of the larger can × Scale Factor (Diameter) = 12 cm × 0.76 ≈ 9.12 cm
Therefore, the diameter of the 440 ml can is approximately 9.12 cm.
Complete question:
Two cylindrical cans are mathematically similar.
The larger can have a capacity of 1 liter and the smaller can have a capacity of 440 ml.
Calculate the diameter, d, of the 440 ml can if the diameter of the larger can is 12 cm.
four minus x equals negative two. 4 - x = -2. whats x?
Answer:
X would have to equal 6. To work it out, you subtract 4 from each side to cancel out the 4. -x = -6. You have to make -x just x so you × each side by -1. You get x = 6.
Step-by-step explanation:
[tex]4 - x = - 2 \\ - x = - 2 - 4 \\ - x = - 6 \\ x = 6 [/tex]
Sam is building a rectangular deck with an area of 80 square feet. He wants the length of the garden to equal
6 feet more than 2 times the width.
a. Enter an equation that expresses the area of the deck in terms of the width, w, of the deck.
b. What is the width of the deck?
Answer:
a b c d e f g the jgh hgghg
Step-by-step explanation:
Final answer:
Provides equations to find the area and width of a rectangular deck based on given information.
Explanation:
a. Let the width of the deck be w. The length is given as 6 feet more than 2 times the width, which translates to 2w + 6. The area of a rectangle is length multiplied by width, so for this case, the equation expressing the area in terms of the width is w(2w + 6) = 80.
b. By solving the equation w(2w + 6) = 80, we find the width of the deck to be 10 feet.
If you can buy one can of pineapple chucks for $2 then how many can you buy with $10?
Answer:
5
Step-by-step explanation:
Because two times 5 equals ten
Answer:
5 cans.
Step-by-step explanation:
Divide 10 with 2 to get your answer.
10/2 = 5
5 cans of pineapple chucks can be bought with $10.
What is the volume of a rectangular pyramid with a height of 5.2 meters and a base 8 meters by 4.5 meters
Answer:
187.2
Step-by-step explanation:
just multiply everything
Azand sold some books at $44 each and used money to buy some concert tickets at $60 each. He had no money left over after buying the tickets. What is the least amount of money he could have earned from selling the books ? What is the least number of books he could have sold ?
The least amount of money Azand could have earned by selling books is $2640. This is because it would allow him to purchase an exact number of concert tickets without any money left over. Therefore, the least number of books he sold is 60.
Explanation:The subject of your question is Mathematics, specifically an application of simple arithmetic and algebra within the context of real world scenarios. To find out the least amount of money Azand could have earned from selling the books and the least number of books he could have sold, we need to realize one key piece of information: the total money spent on tickets (which is also the total money earned from the books) needs to be a multiple of both $44 (the cost of a book) and $60 (the cost of a ticket).
To find the lowest common multiple you simply multiply the numbers together. This gives $2640. Therefore, the least amount of money Azand could have earned by selling the books is $2640. The least number of books he sold can be calculated by dividing the total money by the cost of each book, $2640/$44, which equals 60. So he sold at least 60 books.
Learn more about simple arithmetic and algebra#SPJ12
30% of what number is 270,000?
Answer:81,000.
Step-by-step explanation:
please help me fast
How is the graph of y=-6x^2-4 different from the graph of y=-6x^2
It is shifted 4 units to the left.
It is shifted 4 units to the right.
It is shifted 4 units down.
It is shifted 4 units up.
Answer:
Step-by-step explanation:
it is shifted 4 units down.
y=f(x)
y=f(x)+a,a>0
it is shifted a units up .
y=f(x)-a ,a>0
it is shifted a units down.
Final answer:
The graph of y=-6x²-4 is the same as the graph of y=-6x² but shifted 4 units down. This shift is because a constant term (in this case -4) added or subtracted from a function results in a vertical shift of the graph.
Explanation:
The question asks how the graph ofy=-6x²-4 differs from the graph ofy=-6x². This is a situation where we are dealing with vertical shifts in quadratic functions. Looking at the function y = f(x), a subtraction of a constant term outside the function (not multiplying x) results in a vertical shift of the graph. Here, y=-6x²-4 is the same function as y=-6x², but with a vertical shift downwards by 4 units, resulting in the graph being shifted 4 units down.
For clarification and based on transformations, if we had a function f(x) = x² and transformed it to f(x) = x²- 4, the graph would shift vertically down by 4 units. Similarly, the graph of y=-6x², a downward-facing parabola with its vertex at the origin, will be shifted down by 4 units due to the -4 at the end of y=-6x²-4. Therefore, the correct answer is that the graph is shifted 4 units down.
What is an equation of the line that passes through the points (-2,1) and (-6,-5)
Answer: y = 3/2x+4 if you need to write it in slope intercept form and please give brainliest i will appreciate it.
will mark as a brainlist if i get help w these two
Step-by-step explanation:
Question 5
y = - 3x
Question 6
[tex]y = \frac{50}{x} \\ [/tex]
what is the mass of an object that experiences a gravitational force on earth of 2.5N
Answer:
The answer is 25
Step-by-step explanation:
you move the decimal back one place.
Travis bought a sticker for $2.53 and a belt for $5.68. He then used the rest of his money to buy a pizza. He spent a total of $14.24. How much money did Travis spend on the pizza?
$6.03
$8.21
$8.56
$11.71
Answer:
$6.03
Step-by-step explanation:
Let the amout Travis spent on pizza be reapresented as A.
Travis bought a sticker for $2.53,
Belt = $5.68
Pizza = ?
Total amount of money spent = $14.24
To get the amount spent on pizza , add up amount of everything he bought and equate them to total amount spent
That’s
$2.53 + $5.68 + A = $14.24
$8.21 + A = $14.24
Subtract $8.21 from both sides
$8.21 - $8.21 + A = $14.24 - $8.21
A = $6.03
Travis spent $6.03 on the pizza
(2,5) is the midpoint of (4,10) and (x, y)?
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+4}{2}~~,~~\cfrac{y+10}{2} \right)~~ = ~~\stackrel{midpoint}{(2~~,~~5)}\implies \begin{cases} \cfrac{x+4}{2}=2\\[1em] x+4=4\\ \boxed{x=0}\\[-0.5em] \hrulefill\\ \cfrac{y+10}{2}=10\\[1em] y+10=20\\ \boxed{y=10} \end{cases}[/tex]
Find the equation of the line passing through the points (5,2) and (10,6).
Please explain if you can!
Answer:
y = 4/5 x - 2
Step-by-step explanation:
Slope:
y₂ - y₁ / x₂ - x₁
6 - 2 / 10 - 5
4 / 5
y = 4/5 x + b
Solve for b by substituting one of the point's coordinate to the equation:
I'll use (5,2)
y = 4/5 x + b
(2) = 4/5 (5) + b
2 = 4 + b
2 - 4 = b
-2 = b
y = 4/5 x - 2
kasey's school starts at the time shown on the clock. what time does kasey's school start
While the exact time Kasey's school starts isn't provided, it can be inferred that the common school start time ranges from 8:00 a.m. to 8:30 a.m., based on the information given.
Explanation:The question involves reading a clock to determine what time Kasey's school starts. While the exact time is not provided in the given information, we can infer from various texts that a traditional school start time is typically around 8:00 a.m. In some contexts, like in the case of Jennifer Fuller, a teacher reflects on starting work at 7:45 a.m. which might hint at school starting shortly afterward, likely 8:15 a.m. However, considering the broader perspective given by multiple sources and the push for schools to start no earlier than 8:30 a.m. for teenagers' health, we can surmise that Kasey's school likely starts around 8:00 a.m. to 8:30 a.m., which is a common start time mentioned in the materials provided.
Two cubes have a scale factor of 4:1, what is the ratio of the surface areas of these cubes
Final answer:
The ratio of the surface areas of the two cubes with a linear scale factor of 4:1 is 16:1, because surface area is proportional to the square of the scale factor.
Explanation:
When working with scale factors in geometry, and specifically with cubes, the ratio of scale factors for linear dimensions affects the surface area and volume in specific ways. If two cubes have a scale factor of 4:1, the ratio of their surface areas is the square of the scale factor. Since the scale factor for the linear dimensions is 4, the ratio of the surface areas will be 42:12, or 16:1.
The surface area of a cube is calculated by multiplying the area of one face (length x width) by 6, as a cube has 6 faces. If one cube has a side four times as long as the other, each of its faces will be 42 times larger because area is a two-dimensional measurement. Thus, the surface area of the larger cube will be 16 times greater than that of the smaller cube, hence the ratio 16:1.
Amanda answered all the questions on her math test but got 10 answers wrong. She received 4 points for every correct answer, and there were no points for wrong answers. Her final score was 76 points.
Task: Write an equation to determine the total number of questions (q) on Amanda's math test.
Find the total number of questions on his math test.
Solution:
Given that,
Amanda answered all the questions on her math test but got 10 answers wrong
She received 4 points for every correct answer, and there were no points for wrong answers
Find the number of questions answered correctly:
Her final score was 76 points
4 points for every correct answer
Thus,
[tex]correct\ answers = \frac{76}{4} = 19[/tex]
From given.
Incorrect answers = 10
Let "x" be the total number of questions on his math test
Then,
x = correct answered questions + incorrect answered questions
x = 19 + 10
x = 29
Thus there are 29 total number of questions on his math test
Amanda's test had 29 questions in total.
Amanda answered all the questions on her math test but got 10 answers wrong. She received 4 points for every correct answer, with no points for wrong answers, and her final score was 76 points.
Step-by-Step Solution
1. Let q represent the total number of questions on the test.
2. The number of correct answers Amanda got is (q - 10).
3. Amanda's score for correct answers can be represented as 4 × (q - 10).
4. According to the problem, her score was 76 points, so we can set up the equation: 4 × (q - 10) = 76.
5. Simplify and solve for q:
4q - 40 = 76
4q = 116
q = 29
Therefore, the total number of questions on Amanda's math test is 29.
a dog groomer buys 7 packages of treats. Gourmet treats are sold in packs of 2. treats that help clean a dog's teeth are sold in packs of 5. the dog groomer buys 26 treats in all. how many packages of each did she buy?
Answer:
4 packs of 5
3 packs of 2
Step-by-step explanation:
5•4=20
2•3=6
20+6=26
Let's solve this problem using a system of equations. We'll use two variables:
Let \( x \) be the number of gourmet treat packages (each with 2 treats).
Let \( y \) be the number of dental treat packages (each with 5 treats).
We have two pieces of information that will translate into equations:
1. The dog groomer buys 7 packages in total: \( x + y = 7 \)
2. The dog groomer buys 26 treats in all: \( 2x + 5y = 26 \)
Now, we have a system of two equations with two variables:
\[ \begin{align*}
x + y &= 7 \quad \text{(Equation 1)} \\
2x + 5y &= 26 \quad \text{(Equation 2)}
\end{align*} \]
We will solve this system using the substitution or elimination method. Let's use substitution in this case. We can solve Equation 1 for \( x \):
\[ x = 7 - y \]
Next, we substitute \( 7 - y \) for \( x \) in Equation 2:
\[ 2(7 - y) + 5y = 26 \]
Expanding and simplifying,
\[ 14 - 2y + 5y = 26 \]
Combine the \( y \) terms:
\[ 3y = 26 - 14 \]
\[ 3y = 12 \]
Divide both sides by 3 to solve for \( y \):
\[ y = \frac{12}{3} \]
\[ y = 4 \]
Now that we have \( y \), we can find \( x \) using \( x = 7 - y \):
\[ x = 7 - 4 \]
\[ x = 3 \]
So, the dog groomer bought 3 packages of gourmet treats and 4 packages of dental treats.
To check if the solution is correct, we can plug the values back into the original equations:
Equation 1 (number of packages)
\[ 3 + 4 = 7 \] (Correct)
Equation 2 (total number of treats)
\[ 2(3) + 5(4) = 6 + 20 = 26 \] (Correct)
The solution is correct, and the problem is solved. The dog groomer bought 3 packages of gourmet treats and 4 packages of dental treats.
what is the area of this trapezoid HELP PLEASE
Answer:
Step-by-step explanation:
The answer is 44
Answer:
88 units^2
Step-by-step explanation:
split it into three shapes, a rectangle and two triangles. the find the area of these three different parts. add the areas you got, and you will get the total area of the trapezoid.
[tex]3.7x2.7 [/tex]
Can I please get step by step instructions for solving it!!!
Answer:
5.14
Step-by-step explanation:
[tex]3.7\times2.7[/tex]
Multiply the second numbers in both decimals to each other:
[tex].7\times.7=.14[/tex]
Now multiply the first numbers to each other:
[tex]3\times2=5[/tex]
[tex]=5.14[/tex]
Find the surface area of the triangular prism shown below.
I have no idea how to solve this
The surface area is the area of all the faces of the solid.
So, it is composed by the two triangles (front and rear) and the two lateral rectangles.
The triangles have base 12 and height 8 (both given), so their area is
[tex]A_t=\dfrac{12\cdot 8}{2}=12\cdot 4=48[/tex]
The rectangles have base 14 and height 10 (both given), so their area is
[tex]A_r=14\cdot 10=140[/tex]
Finally, there's a base rectangle with dimensions 14 and 12, which has area
[tex]A_b = 14\cdot 12 = 168[/tex]
The surface area is made of two lateral rectangles, one base rectangle and two triangles, so it is
[tex]S=2A_r+2A_t+A_b=96+280+168=544[/tex]
Answer: 544
Step-by-step explanation:
Edgar ran eee meters per second, and Mathieu ran mmm meters per second. The boys ran for ttt seconds.
The expression t(m-e)t(m−e)t, left parenthesis, m, minus, e, right parenthesis describes how many more meters Mathieu ran than Edgar ran during that time. We can also use the expression tm-tetm−tet, m, minus, t, e to represent the same quantity.
Match each amount in the situation with the expression that represents it.\
Answer:
The expression showing how many more meters Mathieu ran than Edgar ran during that time is [tex]t(m-e)[/tex].
Step-by-step explanation:
Edgar ran 'e' meters per second, and Mathieu ran 'm' meters per second. The boys ran for 't' seconds.
The expression [tex]t(m-e)[/tex] describes how many more meters Mathieu ran than Edgar ran during that time.
We can also use the expression [tex]tm-te[/tex] represent the same quantity.
We know that,
[tex]\text{Distance} =\text{Speed}\times \text{Time}[/tex]
Distance covered by Edgar = te
Distance covered by Mathieu = tm
Difference in distance [tex]d= tm - te=t(m-e)[/tex]
The expression showing how many more meters Mathieu ran than Edgar ran during that time is [tex]t(m-e)[/tex].
Mara found the length of time of an investment. The principal of the investment was $4,300, the interest rate was 6.2 percent, and
the interest was $2,666. Mara made an error in her work.
= prt
2666 = (4300) (0.062)
2666 = (266.6)
266.6
2666
0.14
What was Mara's error?
Mara did not substitute the values from the problem into the formula correctly
© Mara did not multiply correctly.
Mara did not divide correctly.
Mara divided when she should have multiplied.
Answer:
Mara did not divide correctly
Step-by-step explanation:
She had to divide 2666 by 266.6 which should have given her 10
Answer:
she did not divide correctly
Step-by-step explanation:
just did the test got it right
A Mexican restaurant sells quesadillas in two sizes: a "large" 10 inch-round quesadilla and a "small" 5 inch-
round quesadilla. Which is larger, half of the 10-inch quesadilla or the entire 5-inch quesadilla?
Answer:
Half of the 10-inch quesadilla is greater than the entire 5-inch quesadilla
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^2[/tex]
where
r is the radius
step 1
Find the area of the 10 inch-round quesadilla
we have
[tex]D=10\ in[/tex]
[tex]r=10/2=5\ in[/tex]
substitute
[tex]A=\pi (5)^2[/tex]
[tex]A=25\pi\ in^2[/tex]
step 2
Find the area of the 5 inch-round quesadilla
we have
[tex]D=5\ in[/tex]
[tex]r=5/2=2.5\ in[/tex]
substitute
[tex]A=\pi (2.5)^2[/tex]
[tex]A=6.25\pi\ in^2[/tex]
step 3
Which is larger, half of the 10-inch quesadilla or the entire 5-inch quesadilla?
Compare
half of the 10-inch quesadilla is equal to ----> [tex]\frac{1}{2}(25\pi)=12.5\pi\ in^2[/tex]
the entire 5-inch quesadilla ---->[tex]6.25\pi\ in^2[/tex]
therefore
Half of the 10-inch quesadilla is greater than the entire 5-inch quesadilla
There are 4 designd of necklaces available at a jewelry store. Each design is available in 3 types of stones. How many different combinations of 1 design and 1 stone of necklace can you have?
Answer:
12
Step-by-step explanation
4 designes of necklaces
in 3 different stones
4x3= 12 DIFFERENT DESIGHNES
I need help pls❗❗❗Its complicated
Answer:
The answer to 36 is -18
Step-by-step explanation:
x=-18 because 3×(-6)=(-6×-6) cancels
Help me on 16 and 17 please as fast as possible it’s due tomorrow
Answer:
Step-by-step explanation:
16.) 2/3
You add up the fractions and then reduce.
(5/12 + 3/12 = 8/12 = 2/3)
17.) No because if you add all the fractions together, you only get 7/8. This means the project is not complete yet.
Each of the letters of the word MISSISSIPPI are written on a piece of paper and then put into a bag. A piece of paper is drawn at random. What is the theoretical probability of NOT drawing an I?
The probability of not drawing an I is the number of non-I letters divided by the total number of letters, which is 7/11.
The word MISSISSIPPI has a total of 11 letters, with the following distribution: 4 I's, 4 S's, 2 P's, and 1 M. To find the theoretical probability of NOT drawing an I, we need to consider all the other letters that could be drawn instead. There are 11 - 4 = 7 letters that are not Is. Therefore, the probability of not drawing an I is the number of non-I letters divided by the total number of letters, which is 7/11.
A square with side length p has an area of 169 square centimeters. The following equation shows the area
of the square.
p2 = 169
What is the side length of the square in centimeters?
Answer:
13
Step-by-step explanation:
If you use the square root method, p^2 becomes p and 169 becomes 13.
Answer:
13
Step-by-step explanation:
The equation is basically
And 13x13 equals 169 so its 13
Can some help me find the volume and explain?
Area of the figure is 42 in²
Step-by-step explanation:
Step 1: The area of the figure can be found by calculating the sum of the areas of the rectangle and the right angled triangle.⇒ Area of the rectangle = length × width = 6 × 5 = 30 in²
⇒ Area of the triangle = 1/2 × base × height = 1/2 × 4 × 6 = 12 in²
∴ Area of the figure = 30 + 12 = 42 in²
Matt buys an item with a normal price of $25 and uses a 10% off cupon. How much does he save by using the coupon?
Answer:
$2.5
Step-by-step explanation:
The amount saved is 10% of $25
That’s
10% /100% x $25
0.1 x $25
$2.5
Amount saved is $2.5