Answers
1. If the cake rises by ¹/₃ as it bakes, the number of cups of cake batter needed for the four cakes is 140.
2. If ¹/₄ in. is used between layers and ¹/₂ in. is used on the top and sides, the number of cups of icing needed for the four cakes is 47.
How are the numbers determined?The number of cups of cake batter and icing can be determined using the mathematical operations of multiplication, addition, division, and subtraction.
First, the volumes of each cake and its batter are calculated using the given dimensions and the rise.
Using the division operation, the number of cups of cake batter for each cake is determined and multiplied by four.
We understand that the normal volume of the cake will increase with the icing, helping us to calculate the increased volume after the icing.
The difference between the two volumes becomes the volume of the icing required, which is divided by 14.4 in³ to get the number of cups of icing required.
a) Cups of Cake Butter:The volume of each cake = Length x Width x Height
Length = 14 inches
Width = 12 inches
Height = 4 inches (2 x 2)
= 12 x 14 x 4
= 672 in³.
Rise of the cake as it bakes = ¹/₃
The normal volume before rising = 1
Risen volume = 1¹/₃
1¹/₃ = 672 in³
The normal volume of cake batter before the ¹/₃ rise = 504 in³ (672/1¹/₃).
1 cup = 14.4 in³, the total cups for each cake = 35 cups (504 in³/14.4 in³).
The total cups of cake batter for the 4 cakes = 140 cups (35 x 4).
b) Cups of Icing:The total quantity of icing = 1¹/₄ (¹/₄ + ¹/₂ + ¹/₂).
The new volume after the icing = 840 in³ (672 x 1¹/₄)
The difference in volume after the icing = 168 in³ in (840 in³ - 672 in³)
If 1 cup = 14.4 in³, the cups of icing for each cake = 11.67 cups (168 in³/14.4 in³).
The total cups of icing for the 4 cakes = 47 cups (11.67 x 4).
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Question Completion:Four double-layered cakes, each 12.0 in. x 14.0 in., have been ordered for a special event. Each layer is 2.0 in. high.
a) If the cake rises by ¹/₃ as it bakes, how many cups of cake batter are needed? (1 cup = 14.4 in³. Hint: The ¹/₃ rise should be treated as a constant.)
b) How many cups of icing are needed if ¹/₄ in. is used between layers and ¹/₂ in. is used on the top and sides? (Assume icing is not layered on top of the icing. 1 cup = 14.4 in³.)
Related Questions
Fill in the missing number to complete the linear equation that gives the rule for this tablex: 4, 5, 6, 7y: 32, 40, 48, 56y = ?x
Answers
according to the equation and information given we can see that the equation is in the form
[tex]y=kx[/tex]in which k is the constant of proportionality
use one of the points to find the constant
[tex]\begin{gathered} 32=k(4) \\ k=\frac{32}{8} \\ k=8 \end{gathered}[/tex]replace withone of the points to see if its true in all the points
[tex]\begin{gathered} 40=8\cdot5 \\ 40=40 \end{gathered}[/tex]according to this the equation for the table will be
[tex]y=8x[/tex]Find the surface area of the triangular prism. 13 in. 5 in. 4 in. 12 in.
Answers
The first face is a triangle with height 5in and base 12in
Traingular face area = 1/2 x bh
=1/2 x 12 x 5
= 30 in^2
The area of the other triangular base = 30 in^2
Area of left side face = Length x breadth
= 5 x 4 = 20in^2
Area of the slant face = Length x breadth
= 13 x 4 = 52in^2
Area of the bottom face = Length x breadth
= 12 x 4 = 48in^2
Total surface area = 30 in^2 + 30 in^2 + 20in^2 + 52in^2 + 48in^2
=180in^2
Finding Slope
HELP ME PLS
Answers
The slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
The first point = (-5,6)
The second point = (-9,-6)
The slope of the line defined as the change in y coordinates with respect to the change in x coordinates.
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = [tex]\frac{-6-6}{-9-(-5)}[/tex]
= -12/-4
= 3
Hence, the slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
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wich time of line are shown in the figure
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Solution
Step 1
Two distinct lines intersecting each other at 90° or at right angles are perpendicular to each other.
Hence apply this to question 8 the type of lines shown in the figure is perpendicular lines. Option C
Step 2
To explain this as stated above line A and line B intersect each other at a right angle hence line A and B are perpendicular lines. The line segments are seen below.
Draw a line connecting each sphere to its volume in terms of π and round it to the nearest tenth. (Not all of the values will be used.)
Answers
Remember that
The volume of a sphere is equal to
[tex]V=\frac{4}{3}\pi r^3[/tex]N 1
we have
D=9 units
r=9/2=4.5 units
substitute
[tex]\begin{gathered} V=\frac{4}{3}\pi(4.5)^3 \\ V=121.5\pi\text{ unit3} \\ V=381.5\text{ unit3} \end{gathered}[/tex]N 2
we have
r=2 units
[tex]\begin{gathered} V=\frac{4}{3}\pi2^3 \\ V=10.6\pi\text{ unit3} \\ V=33.5\text{ unit3} \end{gathered}[/tex]N 3
we have
D=14 units
r=14/2=7 units
[tex]\begin{gathered} V=\frac{4}{3}\pi7^3 \\ V=457.3\pi\text{ unit3} \\ V=1,436\text{ unit3} \end{gathered}[/tex]N 4
we have
r=9 units
[tex]\begin{gathered} V=\frac{4}{3}\pi9^3 \\ V=972\pi\text{ unit3} \\ V=3,052.1\text{ unit3} \end{gathered}[/tex]4. AABC = ADBC by SSS. Select one set of corresponding parts that could be marked congruent by CPCTC.B.A11CDO CBDAO ZA ZDOZCZ ZBO ACBC
Answers
We are given two triangles that are congruent and we are asked to mark the parts that are congruent by CPCTC, this stands for Corresponding Parts of Congruent Triangles are Congruent. This means that when two triangles are congruent then their corresponding sides and angles are also congruent.
We notice that the following segments are corresponding segments and therefore congruent:
[tex]\begin{gathered} AB=BD \\ AC=DC \\ CB=CB \end{gathered}[/tex]And also the following angles are corresponding angles and therefore congruent:
[tex]\begin{gathered} \angle A=\angle D \\ \angle ABC=\angle DBC \\ \angle ACB=\angle DCB \end{gathered}[/tex]Therefore, from CPCTC we know that the corresponding parts are:
[tex]\angle A=\angle D[/tex]Alyssa will correctly label the numbers 48.4, 48482, 48.09, and 48on the number line below.
Answers
The numbers under consideration are:
[tex]48.4,\text{ 48}\frac{1}{2},\text{ 48.09, 48}\frac{3}{5}[/tex]Converting all the numbers to decimal:
[tex]\begin{gathered} 48\frac{1}{2}=\text{ 48+0.5 = 48.5} \\ 48\frac{3}{5}=\text{ 48 + }0.6\text{ = 48.6} \end{gathered}[/tex]Therefore, the numbers can be written as:
48.4, 48.5, 48.09, and 48.6
Out of these numbers, only 48.6 is closest to 49
[tex]48\frac{3}{5}\text{ is closest to 49}[/tex]Classify the triangle with side lengths 8,13,20. a) Acute b) Right c) Obtuse
Answers
for right angles triangle,
hyposenuse square should be equal to sum of square of other two sides
it fails that law so its not right angled triangle
7. Explain It Draw a net for a triangular pyramid. Explain how you know your dagram is correct.
Answers
The definition of geometry net is the 2-dimensional shape that if folded, it will produce or yield to the 3-dimensional image
Since the triangular pyramid, has 4 sides (4 triangular faces), when we unfold it on the edges from one tip/corner, it will produce a 2-dimensional image of 3 triangles attached to the sides of one triangle
Find a unit vector u in the direction of v. Verify that ||0|| = 1.v = (4, -3)U =
Answers
Answer
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Explanation
The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.
u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)
v = <4, -3> = 4i - 3j
Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5
u = (4i - 3j)/5 = (4i/5) - (3j/5)
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Hope this Helps!!!
Answer
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Explanation
The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.
u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)
v = <4, -3> = 4i - 3j
Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5
u = (4i - 3j)/5 = (4i/5) - (3j/5)
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Hope this Helps!!!
2. State two (2) values of θ (theta) to the nearest degree forsin θ = − 0. 966
Answers
To find a value of θ theta given a value of sin(θ) we must use the arcsin function, it receives a value of an sin as argument and returns the value of the angle θ. Then we must use a calculator and input
[tex]\begin{gathered} \theta=\arcsin\left(x\right) \\ \\ \theta=\arcsin(-0.966) \\ \\ \theta=−75 \end{gathered}[/tex]The result is already rounded to the nearest degree. Therefore, one value of θ that satisfies sin θ = −0.966 is θ= -75°
Now to find the other value we will look at the symmetry in the trigonometric circle:
Then, the other value of theta will be
[tex]\begin{gathered} \theta_2=-75°-30° \\ \\ \theta_2=105° \end{gathered}[/tex]Final answer:
[tex]\begin{gathered} \theta=-75° \\ \theta_2=-105° \end{gathered}[/tex]how do i expand -4(-x-8)
Answers
Answer:
4x+32
Step-by-step explanation:
mutiply the -4 to both numbers inside parentheses. negative * negative= positive. -4*-x=4x, -4*-8=32
1. Juan bought fruit from the grocery store. The variables below define his purchase. Juan's bananas cost half as much as apples. Which equations can be used to model his purchase? Select each correct equation.* a = the number of apples he bought b = the number of bananas he bought x= the cost of an apple in dollars y= the cost of a banana in dollars A- a= 1/2 bb- y=1/2 xc- a=2bd- x=2ye- y=2af- b=1/2 x
Answers
Juan's bananas cost half ( 1/2) as much as apples.
x= the cost of an apple in dollars
y= the cost of a banana in dollars
Multiply the cost of an apple by 1/2 (half). that expression must be equal to the cost of a banana.
y = 1/2 x (option b)
A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week. X, and grade-point average, y. Shefound that a linear relation exists between the two variables. The least-squares regression line that describes this relation is ý = -0.0579x + 2.9408(Round to the nearest hundredth as needed.)(Part b) Interpret the slope.For each additional hour that a student spends playing video games in a week, the grade-point average will decrease by 0.0579 points, on average.(Part c) if appropriate, interpret the y-intercept.A. The grade-point average of a student who does not play video games is 2.9408.B. The average number of video games played in a week by students is 2.9408.C. It cannot be interpreted without more information.
Answers
exactly For sentence A "The grade-point average of a student who does not play video games is 2.9408" we can verify as follows:
That means this sentence "The grade-point average of a student who does not play video games is 2.9408" is true.
For sentence B "The average number of video games played in a week by students is 2.9408" is not exactelly correct because the average number of hours of video game played is not specified.
For sentence C "It cannot be interpreted without more information" let's look over an illustration.
We can see, we can interpret the y-intercept as the moment where x = 0 which means when the student does not play a video game. So this sentence is false.
I mean the correct sentence is sentence A.
102,410,000,000,000,000,000,000,000 in scientific notation round to two digits after the decimal
Answers
We have a big integer and want to write in scientific notation.
To do this we need to count how many places we need to move the decimal point.
In this case we need to move the decimal point to left so the exponent of 10 will be positive.
So,
[tex]\begin{gathered} 102,410,000,000,000,000,000,000,000=1.0241\cdot10^{29} \\ \text{Round to two digits after the decimal:} \\ 1.02\cdot10^{29} \end{gathered}[/tex]We move the decimal point 29 places to left so the exponent of 10 is 29.
Drag each number to the correct location on the table
Answers
Step-by-step explanation:
There is no table attached, please recheck and resend.
Convert to fractional Notation 4 19/100
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to solve this we need to convert the number 4 to a fraction with denominator 100 and add both fractions
to do that we can multiply 4 and 1 by 100, like this:
[tex]\frac{4\cdot100}{1\cdot100}=\frac{400}{100}[/tex]now we can add the fractions
[tex]\frac{400}{100}+\frac{19}{100}=\frac{419}{100}[/tex]So the answer is: 419/100
Amplitude, period, and phase shift of sine and cosine functions
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We are given that
[tex]y=-2+2\cos (2x-\frac{\pi}{3})[/tex]Note: Given the cosine function
[tex]y=a\cos (bx-c)+d[/tex]then
[tex]\begin{gathered} Amplitude=a \\ Period=\frac{2\pi}{b} \\ PhaseShift=\frac{c}{b} \\ VerticalShift=d \end{gathered}[/tex]Comparing the question with what is written in the note
We have
[tex]\begin{gathered} a=2 \\ b=2 \\ c=\frac{\pi}{3} \\ d=-2 \end{gathered}[/tex]We want to find
(a). Amplitude
From the given question, the amplitude (a) is
[tex]\begin{gathered} a=2 \\ Amplitude=2 \end{gathered}[/tex](b).Period
From the given question, the period is
[tex]\begin{gathered} Period=\frac{2\pi}{b} \\ Period=\frac{2\pi}{2} \\ Period=\pi \end{gathered}[/tex](c). Phase Shift
From the given question, the phase shift is
[tex]\begin{gathered} PhaseShift=\frac{c}{b} \\ PhaseShift=\frac{\pi}{3}\times\frac{1}{2} \\ PhaseShift=\frac{\pi}{6} \end{gathered}[/tex]Which graph represents the solution of −2x≤4(x−6)?
Answers
Answer:
See attachments.
Step-by-step explanation:
Given inequality:
[tex]-2x\leq 4(x-6)[/tex]
Solve the inequality by first expanding the brackets:
[tex]\implies -2x\leq 4x-24[/tex]
Subtract 4x from both sides:
[tex]\implies -2x-4x\leq 4x-24-4x[/tex]
[tex]\implies -6x\leq -24[/tex]
Divide both sides by -6 (remembering to reverse the inequality sign as we are dividing by a negative number).
[tex]\implies \dfrac{-6x}{-6}\leq \dfrac{-24}{-6}[/tex]
[tex]\implies x\geq 4[/tex]
When graphing inequalities on a coordinate plane:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Therefore, to graph the given inequality on a coordinate plane:
Draw a solid line at x = 4.Shade above the line (i.e. shade to the right of the line).(See attachment 1).
When graphing inequalities on a number line:
< or > : open circle.≤ or ≥ : closed circle.< or ≤ : shade to the left of the circle.> or ≥ : shade to the right of the circle..Therefore, to graph the given inequality on a number line:
Place a closed circle at 4.Shade to the right of the circle.(See attachment 2).
complete the table to show the total change in the average mean daily in the price of for stocks over a five-day.
Answers
Answer: -$0.26, -$0.7, $0.65, and -$1.6
The number of days = 5
Average price = Total change in price / the number of days
For Stock A
Total change in price = -$1.30
Average price = - 1.30 / 5
Average price = -$0.26
STOCK B
Average change in price = -$0.14
From, Average price = Total price / number of days
Total price = Average price x number of days
Total price = -0.14 x 5
Total price = - $0.7
For stock C
Average price = 3.25 / 5
Average price = $0.65
Stock D
Average price = Total price / number of days
Total price = Average price x number of days
Total price = -0.32 x 5
Total price = - $1.6
The answer are -$0.26, -$0.7, $0.65, and -$1.6
Simplify the expression by combing like terms.21v + 8 - 12v - 7 + 3t - t
Answers
We need to simplify the like terms.
"The like terms are whose with the same variable and exponent"
Therefore, the like terms are:
21v - 12v = 9v
8 - 7 = 1
3t - t = 2t
Now, the result is :
9v + 2t + 1
Hence, the correct answer is option D.
Jim baked 48 cookies with 4 scoops of flour. How many scoops of flour does Jim need in orderto bake 96 cookies? Assume the relationship is directly proportional.
Answers
Given:
Jim baked 48 cookies with 4 scoops of flour.
So, the unit rate will be = 48/4 = 12 cookies/scoop of flour
So, for 96 cookies, the number of scoops of flour will be =
96/12 = 8
So, the answer will be 8 scoops of flour
how many shirts can Jeanette sew at most of and still have 1. spool of thread left
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Answer:
The number of shirts sewn at most, when there is just 1 spool of thread left is;
[tex]5\text{ shirts}[/tex]Explanation:
Given a graph that relates the number of spools of thread left to the number of shirts sewn.
We want to find the number of shirts sewn at most, when there is just 1 spool of thread left.
To get that, let us draw a straight horizontal line from y=1 (spools of thread remaining =1) to join the line of the graph and also trace it down.
Tracing the line down we can observe that it is at shirt sewn equals 5.
So, the number of shirts sewn at most, when there is just 1 spool of thread left is;
[tex]5\text{ shirts}[/tex]Need help with my math yall please??
Answers
The value of the expression after simplification is found as -3.
What is termed as simplification?Simplify simply way of making something easier to understand. Simply or simplification in mathematics refers to reducing an expression/fraction/problem to a simpler form. It simplifies the problem by calculating and solving it. We can —Simplify fractions by removing all common factors from the numerator and denominator as well as composing the fraction in its simplest form.By grouping as well as combining similar terms, you can simplify mathematical expressions. This helps make the expression simple to understand and solve.For the given expression;
5x + 8 = 2x - 1
Subtract 8 from both side.
5x + 8 - 8 = 2x - 1 - 8
Simplify
5x = 2x - 9
Subtract both side by 2x.
5x - 2x = 2x - 9 - 2x
3x = -9
Divide both side by 3.
3x/3 = -9/3
x = -3
Thus, the value of the expression is found as -3.
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What is a feature of function g if g(x) = log (x-4) -8
Answers
The domain and range of the logarithmic function are
[tex]\begin{gathered} \text{domain}(\log x)=(0,\infty) \\ \text{range}(\log x)=(-\infty,\infty) \end{gathered}[/tex]Therefore, if
[tex]g(x)=\log (x-4)-8[/tex]We require that
[tex]\begin{gathered} x-4>0 \\ \Rightarrow x>4 \end{gathered}[/tex]Notice that the -8 term does not affect the range of function g(x); thus,
[tex]\begin{gathered} \text{domain}(g(x))=(4,\infty) \\ \text{range}(g(x))=(-\infty,\infty) \end{gathered}[/tex]Set g(x)=-8; then,
[tex]\begin{gathered} \Rightarrow\log (x-4)-8=-8 \\ \Rightarrow\log (x-4)=0 \\ \Rightarrow x=5 \end{gathered}[/tex]Therefore, y=-8 is not an asymptote of g(x), and, as shown above, the domain and range of g(x) are x>4, y->all real numbers.
Calculate the limit when x->4 as shown below,
[tex]\lim _{x\to4}g(x)=(\lim _{x\to4}\log (x-4))-8=(-\infty)-8=-\infty[/tex]Therefore, there is a vertical asymptote at x=4
Answer:
Hope this helps ;)
Step-by-step explanation:
If joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters. How far was joey from home?
Answers
The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
The group's total number of items decreases or becomes lower when we subtract from it.
It is known that East and West are the opposite of each other.
So, 15 2/3 towards the east let's take it positively.
And 21 3/4 towards left let's consider it negative.
So, the distance from the home
⇒ | ( 15 + 2/3) - (21 +3/4) |
⇒ | 15 -21 + 2/3 - 3/4 |
⇒ | -6 + (8 - 9)/12 |
⇒ | -6 - 1/12 |
⇒ | -(6 +1/12) |
⇒ 6 1/12
Hence "The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters".
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prove the formula sin 3 A + sin A = 4 sin A cos2A
Answers
We proved that formula using the trigonometry relations sin3A + sinA = 4sinAcos^2A.
In the given question,
We have to prove the formula sin 3A+sin A = 4sinAcos^2A
The given expression is sin 3A+sin A = 4sinAcos^2A
To prove the formula we take the left side terms to the right side terms
The left side is sin 3A+sin A.
As we know that sin 3A = 3sinA − 4sin^3A
To solve the left side we put the value of sin 3A in sin 3A+sin A.
=sin 3A+sin A
=3sinA − 4sin^3A+sin A
Simplifying
= (3sinA+sin A) − 4sin^3A
= 4sinA − 4sin^3A
Taking 4sinA common from both terms
= 4sinA(1 − sin^2A)
As we know that cos^2A=1 − sin^2A. So
= 4sinAcos^2A
We proved the right hand side.
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helpppppppppppppppppppppppppppppp
Answers
Answer:
[tex]f^{-1}[/tex](x) = x/2 - 3/2
Step-by-step explanation:
Swap x and y and solve for y.
Original equation:
y = 2x + 3
Swapped equation:
x = 2y + 3
Now, solve for y:
x -3 = 2y
y = (x-3)/2
If it's wrong, it might just be the way you format your answer, since Pearson (what I assume you're using) is specific about that.
Maybe, [tex]f^{-1}[/tex](x) = x/2 - 3/2 or [tex]f^{-1}[/tex](x) = (x-3)/2
A parallelogram has an area of 364.5 cm2. If the base is 27 cm, What is the height?
Answers
Answer:
Height = 13.5cm
Explanation:
The area of a parallelogram is obtained using the formula below:
[tex]\text{Area}=\text{Base}\times Height[/tex]Substituting the given values:
[tex]\begin{gathered} 364.5=27\times\text{Height} \\ \text{Height=}\frac{364.5}{27} \\ H\text{eight}=13.5\operatorname{cm} \end{gathered}[/tex]The graph shows a dilation of trapezoid TRAP with respect to the origin which statements are true about the figures select three
Answers
A dilation means an elongation of the sides of a figure
So in a dilation the sides are bigger than at the original figure
A key formula for found dilation is Pithagoras theorem
For calculate T'R'
T'R' is the exact diagonal of OT' and OR', that means
OT' + OR' = T'R' in vectorial sum
OT'^ 2 + OR'^ 2 = T'R'^2. In numerical sum
So then T'R'^2 = 5^2 + 5^2 = 50.
and T'R'= √50
Now find TR to find the factor of dilation that is
T'R'/TR