Mrs. Santiago's consumer science class is making two different-size cheesecakes for
a fundraiser.
The large cheesecake has a diameter of 12 inches
The small cheesecake has a diameter of 4 inches
Part A: If the pans are both 3 inches deep, how many times greater is the volume
Of the large pan than that of the small pan? Show your work
Part B: When shipped, the large cheesecakes will be packaged in a box with dimensions of 12 in x
12 in x 3 in. What percentage of the box does the large cheesecake take up?
Show all work for each part and give at least 2 sentences explaination for each part.
Answers
Answer:
Part A: 9 times
Part B: 79%
Step-by-step explanation:
Part A:
Volume of the large pan = πr²h
Where,
radius (r) = ½(diameter) = ½(12) = 6 in.
height (h) = 3 in.
Volume = π*6²*3
Volume of the large pan = 339.29 in.³
Volume of the small pan = πr²h
r = ½(4) = 2 in.
h = 3 in
Volume of small pan = π*2²*3
Volume of the small pan = 37.7 in.³
✔️To determine how many times the volume of the large pan is greater than the small pan, divide the volume of the larger by the smaller:
= 339.29/37.7 ≈ 9
✅The volume of the large pan is about 9 times greater than the volume of the smaller pan.
Part B:
✔️Find the volume of the box:
Volume of box = L*W*H
Where,
L = 12 in.
W = 12 in.
H = 3 in.
Volume of the box = 12*12*3 = 432 in.³
Divide the volume of the large pan over the volume of the box and multiply by 100%
Thus:
339.29/432 × 100
= 78.5393519 ≈ 79%
The large cheesecake takes up about 79%
Related Questions
Write an equation for the line that passes through E(4, -3) and is parallel to the line
0 = 5x - 7y - 27 Write the equation in general form.
Answers
Answer:
y= 5x/7 -27/7
if they are parallel there gradient is the same
m1=m2
y-y1=m(x-x1)
plug in the gradient and points E
y-(-3)=5/7( x-4)
y= 5/7(x) -20/7 +3
final answer
y= 5/7(x) +1/7
A rectangle measures 15 cm by 10 cm is given, if the length of side is
increased by 20%, find the increase of area in percentage.
Answers
Answer:
20 % increase in Area
Step-by-step explanation:
1. Original Rectangle Area = 150cm ²
2. 20% of 15 is 3
3. Increased length is equal to 18
4. Increased Rectangle Area = 180cm ²
5. Ten percent of 150 = 15.
6. 15x2(ten percent) = 30. Which give us 150+30 equal to 180.
7. 2 ten percent equals 20%
8. Answer is 20%.
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Answers
Answer:
B) Unequal
Step-by-step explanation:
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Can someone please help me with this. ANYONE!
Answers
Answer:
Step-by-step explanation:
1 OF 3OR5
Quadrilateral MNQP has vertices as shown. If the figure is translated 4 units left and 3 units down, what are the coordinates of N'? *
Answers
Explanation:
Point N is at (1,3)
We apply the rule [tex](x,y) \to (x-4,y-3)[/tex] which will translate the point 4 units to the left and 3 units down.
The old x coordinate x = 1 becomes x-4 = 1-4 = -3
The old y coordinate y = 3 becomes y-3 = 3-3 = 0
The point N(1,3) moves to N ' (-3, 0)
Use one of your new conjectures to find the lettered angles measures.
t+p =
Answers
Diagram attached
Answer:
72 degrees
Explanation:
From the diagram, angle on a straight line add up to 180 degrees.
180 degrees - 144 degrees = 36 degrees.
Sum of the angles in a triangle= 180 degrees
Angles x and the other are congruent(the marks from the diagram indicate).
Therefore sum of the congruent angles= 180 degrees - 36 degrees = 144 degrees
Angle x= 144/2= 72 degrees
Kate is 1 year and six months younger than her sister. If her sister is 14 years and 2 months old, how old is Kate?
Answers
Answer:
Kate is 13years and 4 months old,I suggest.
What trig ratio would you use to solve for x?
O Cosine
O Tangent
O Sine
Answers
Answer: Cosine
This is because cosine involves the adjacent over hypotenuse
cos(angle) = adjacent/hypotenuse
Which best describes the relationship between the line that passes through the points (-6, -1) and (-11, 1) and the line
that passes through the points (-3, -8) and (-5, -13)?
A. perpendicular
B. parallel
C. neither perpendicular nor parallel
D. same line
Answers
Answer: A. perpendicular
Step-by-step explanation: First, you have to determine the slope of both lines and you can do so using the slope formula: (y2 - y1)/(x2 - x1). You should get the slope -2/5 for the first line and 5/2 for the second. Because one line has a slope that is the negative reciprocal of the other, these lines are perpendicular.
Convert 150 base 10 to a binary
number.
Answers
Answer:
10010110
Step-by-step explanation:
A binary number is basically a number in base 2. So, each place represents a power of two. The ones place represents 1 or 2^0, the tens represents 2 or 2^1, the hundreds represents 4 or 2^2 and so on. To find the highest place needed to make in the number in binary, we find the greatest power of two that is below 150. In this case, it is 128. We can start by writing 128 in binary:
10000000
Now, we subtract 128 from 150 and find the largest power of two that is smaller than the difference. The largest power of 2 smaller than 22 is 16, so we put a one in the place for 2^4:
10010000
We can subtract 16 from 22 to get what is leftover to continue the process. We get 6, and the largest power of 2 smaller is 4. We can place a one in the hundreds place to represent it:
10010100
What is left is 6-4 or 2, which is just 2^1, so we can place it in the tens place:
10010110
Rotate the triangle 90° anti-clockwise about the cross.
Answers
Answer:
see below
Step-by-step explanation:
-90 degrees, the rule is (x, y) --------> (-y, x)
The leftmost point is at (1,1) so it will be at (-1, 1)
The top right point is at (4,1) so it will be at (-1,4)
The bottom right point is at (4,-1) so it will be at (1,4)
The profit for a car company can be represented by the function P=−0.5 x² +4 x+ 12,
where P is the profit in hundred thousands of dollars and x represents the number of cars sold in thousands. What is the maximum profit the company can make?
Answers
Answer:
3x+12
Step-by-step explanation:
-0.5x*2+4x+12
Multiply 0.5x*2=x
= -x+4x+12
Add similar elements -x+4x+12
= 3x+12
Need help on this question asap please
Answers
Answer:
3rd choice
Step-by-step explanation:
Similar triangles have congruent angles and proportional sides
They look similar but size may vary
I will give brainliest if you add details:
A recent study asked the same 15 students their favorite subject at three different times: in elementary school, in middle school, and when getting ready to graduate from high school.
What percentage of students said that Math was their favorite subject in elementary school?
What is the percent of change for History being the favorite subject between elementary school and graduating from high school?
Answers
Answer:
53 1/3% for the first answer, and 33 1/3% increase for the second answer
Step-by-step explanation:
Ok, lets start up witht eh first question.
We need to find the percentage of studens that find math the be their favorite subject in elementary school.
We know that there are 15 kids in total.
We specificly see that 8 of those kids like math the most.
To find percentage, divide 8 by 15.
Using a calculator you should find 53 1/3% of the students found math to be their favorite subject.
Next we need to find the percentag eof change that history is over elementary school to high school.
This might sound confusing, but this is basically just a change of 3 students to 4 students.
To find percentage, just divide 3 by 4:
This gets you 33 1/3%
Hope this helps!
6. If the set A = {-2, 1, 3), then the set A is a subset of the set of?
Answers
Answer:
Step-by-step explanation:
We could invent set B: {-2, 1, 3, 5, 6, 10} and then correctly state tht set A is a subset of B, because {-2, 1, 3} is also found in A.
give me one secondddd..
Answers
Answer:
mark me as a brainleast
Step-by-step explanation:
iam not undeerstand on your qiestion write it beautiful words
in isosceles Triangle RST below what is the value of y
Answers
Answer:
second option
Step-by-step explanation:
y + y + 38 = 180 degree ( sum of interior angle of a triangle is 180 degree)
2y = 180 - 38
y = 142/2
y = 71 degree
Answer:
71 degrees
Step-by-step explanation:
Hi there!
All the interior angles of a triangle add up to 180 degrees.
Knowing this, we can construct the following equation:
[tex]180=y+y+38\\180=2y+38[/tex]
Subtract 38 from both sides
[tex]180-38=2y+38-38\\142=2y\\71=y[/tex]
I hope this helps!
An article bought for $125 was sold %175. The percentage profit
Answers
Answer:
40% profit
Step-by-step explanation:
There is a profit of $50.
If you were to find the percentage, you would divide 50 by 125. This would give you 0.4
Write the slope-intercept form of the linear equation that has a slope of 3
and a y-intercept of -1.
Answers
Answer:
y = 3x - 1
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope
b = y-intercept
m∠RST =______because they are __________ (Fill in the blanks)
Answers
Answer:
∠RST = ∠SRU because they are alternate angles.
Step-by-step explanation:
Hope it helps .
Simplify variable expressions involving like terms and the distributive property
Answers
Answer:
gracias por los puntos xd
What is the area of this figure? Round to the tenth if necessary.
Answers
Answer:
b) 850.1 centimeters.Step-by-step explanation:
To find the area of this figure, we must first find the areas of the shapes that compose this figure.
This figure is made up of a rectangle and a semicircle.
Remember: To find the area of a semicircle, multiply the radius by itself twice, then multiply the product pi, lastly divide the product by 2.
[tex]a=\pi r^2/2[/tex]
3.14 will be used for pi!
To find the area of a rectangle, multiply the length by the width. The product is the area of the rectangle.
[tex]a=lw[/tex]
Now, let's solve.
The diameter of the semicircle is 32 centimeters.
To find the radius of a semicircle, divide the diameter by 2.
[tex]32/2=16[/tex]
The radius of the semicircle is 16 centimeters.
Now that we have the radius, we can find the area of the semicircle.
[tex]\pi 16^2/2=401.92[/tex]
The area of the semicircle is 401.92 centimeters.
Furthermore, we find the area of the rectangle.
[tex]14*32=448.[/tex]
The area of the circle is 448 centimeters.
Next, we add the areas of both shapes to find the area of this figure.
[tex]401.92+448[/tex]
[tex]=849.92[/tex]
The final step is to round 849.92 to the nearest tenth.
Even though 849.92 to rounded to the nearest tenth is 849.9, there is no answer choice for this. The closest one to this answer is choice 'b.'
I, therefore, believe the area of this figure is 850.1 centimeters.
I don’t understand the problem or question
Answers
Answer:
Part A
a. Could be a parallelogram but cannot be a rectangle
Part B
c. 100°
Step-by-step explanation:
Part A
The polygon constructed by Andrew = Four sided polygon having no right angles
From the given four sided polygon (quadrilateral) options, the options which can have no right angles are the parallelogram, and rhombus
The rectangle, and square both have 4 right angles
Therefore, the polygon can be either a parallelogram or a rhombus, but cannot be either a rectangle or square
The correct option is therefore, 'His polygon could be a parallelogram but cannot be a rectangle'
Part B
The given parameters of the rhombus EFGH are;
Angle E = 3·x + 5, angle H = 4·x
The characteristics of a rhombus are;
The sum of the interior angles of a rhombus = 360°
The opposite angles of a rhombus are equal
The sum of the adjacent angles = 180° (The adjacent angles are supplementary)
Therefore, in the rhombus EFGH, we have;
Angle E, and angle H are supplementary angles
∴ Angle E + angle H = 180°
Substituting the values of angle E and angle H gives;
3·x + 5 + 4·x = 180°
7·x = 180° - 5 = 175°
x = 175°/7 = 25°
Angle H = 4·x
∴ Angle H = 4 × 25° = 100°
Angle H = 100°
Angle F = angle H = 100°
Therefore, angle F = 100°
Sarah accepted a new job at a company with a contract guaranteeing annual raises. Sarah's salary after working for nn years can be determined using the equation S=90000+3500n.S=90000+3500n. What is the slope of the equation and what is its interpretation in the context of the problem?
Answers
Answer:
Slope = 3500
Sarah's salary will increase by 3500 per year
Step-by-step explanation:
Given that Sarah's salary after working n years is given as :
S=90000+3500n
The equation given is similar to a linear equation :
y = bx + c ;
Where, b = slope of the linear equation
Therefore, relating the equation to that of a linear model ; the slope, b is equivalent to 3500 in Sarah's salary equation.
Slope is simply described as the rate of change, the change in y per unit change in x ;
Therefore, this means Sarah's salary will increase by 3500 per year
what is the value of J
Answers
Answer:
Step-by-step explanation:
Since all 3 of these angle come off a straight line, they all add up to equal 180. Thus,
2j + 32 + 6j - 2 + 30 = 180 and
8j + 60 = 180 and
8j = 120 so
j = 15
The product of two rational numbers is 9⁄7 and one of them is 15⁄14. Then the other rational number is
Answers
Answer:
The other rational number in the operation given is:
6/5Step-by-step explanation:
To obtain the number in the operation given, we're gonna represent the operation:
r * 15/14 = 9/7Where:
r = the other rational number.Now we are going to solve r to identify its value in numbers:
r * 15/14 = 9/7[tex]r = \frac{\frac{9}{7} }{\frac{15}{14}}[/tex] (We pass a number that is multiplying to the left of the equal, to divide to the right of the equal symbol)[tex]r = \frac{6}{5}[/tex]As you can see, when we operate, the result is 6/5, and we can prove this multiplying as we had in the original equation, replacing r by 6/5:
r * 15/14 = 9/76/5 * 15/14 = 9/79/7 = 9/7In this form, we know the result is correct.
Determinar el valor de las siguientes progresiones:
1)4, 12, 36, 108,…
2)4, 20, 100, 500,…
3)5, 10, 20, 40,…
Answers
Answer:
Step-by-step explanation:
1) . .324, 972, 2916
2) ...2500, 12500, 62500
3). . 80, 160, 320
Will give branliest
Find l.
l= [?] in
Answers
h=15 and r= d/2= 12/2= 6
So, (15^2+6^2)=
225+36= 261
L= Square Root of [261] in
i need help as soon as possible please and thank you
Answers
Step-by-step explanation:
yes that's the answer
can you please give me brainliest
and use DESMOS app for drawing graphs
a) Model this situation with a linear system:
To rent a car, a person is charged a daily rate and a fee for each kilometre driven. When Chena
rented a car for 6 days and drove 320 km, the charge was $286.00. When she rented the same car
for 10 days and drove 900 km, the charge was $605.00.
b) Determine the daily rate and the fee for each kilometre driven.
Answers
Answer:
The daily rate is $ 29 and the fee for each kilometer driven is $ 0.35.
Step-by-step explanation:
Since to rent a car, a person is charged a daily rate and a fee for each kilometer driven, and when Chena rented a car for 6 days and drove 320 km, the charge was $ 286.00, while when she rented the same car for 10 days and drove 900 km, the charge was $ 605.00, to determine the daily rate and the fee for each kilometer driven the following calculation must be performed:
286 = 6 days and 320 km
320/6 = 53,333 km
286/6 = $ 47,666
Thus, the value of 1 day and 53,333 km is $ 47,666.
605 = 10 days and 900 km
900/10 = 90 km
605/10 = $ 60.5
Thus, the value of 1 day and 90 km is $ 60.5.
90 - 53,333 = 36,666
60.5 - 47.666 = 12.833
12,833 / 36,666 = value per kilometer traveled
0.35 = value per kilometer traveled
(286 - (0.35 x 320)) / 6 = X
(286/112) / 6 = X
174/6 = X
29 = X
(605 - (0.35 x 900)) / 10 = X
(605 - 315) / 10 = X
290/10 = X
29 = X
Therefore, the daily rate is $ 29 and the fee for each kilometer driven is $ 0.35.
