Bailey’s Cakes and Pastries baked a three-tiered cake for a wedding. The bottom tier is a rectangular prism that is 18 centimeters long, 12 centimeters wide, and 8 centimeters tall. The middle tier is a rectangular prism that is 12 centimeters long, 8 centimeters wide, and 6 centimeters tall. The top tier is a cube with edges of 4 centimeters each. What is the volume of each tier and of the entire cake?
1,728 cubic centimeters
2,368 cubic centimeters
2,664 cubic centimeters
64 cubic centimeters
576 cubic centimeters
38 cubic centimeter
16 cubic centimeters
The top tier
The middle tier
The bottom tier
The entire tier
Answers
Answer:
I hope this helps
Step-by-step explanation:
Related Questions
Write an inequality that represents the verbal expression. All real numbers greater than or equal to 74
Answers
x represents all real numbers, and that is the greater than symbol.
Determine whether the given value is a statistic or a parameter. upper a sample of students is selected and it is found that 25 % own a computer.a sample of students is selected and it is found that 25% own a computer.
Answers
Check my answers please -
The yearly attendance at a local move theatre is 42,000 and grows continuously at a rate of 5.9% each year. what is the approximate attendance at the movie theater in seven years?
A. 43,467
B. 59, 346
C. 63, 476
D. 62, 737 **
The number of customers that visit a local small business is 29,600 and has been continuously declining at a rate of 2.9% each year. what is the approximate number of customers that visit the buisness in 10 years?
A. 22,149 **
B. 21,874
C. 39,558
D. 22,054
Answers
I can tell you for sure that the answer to the first one is
C) 63,475
and the second is
A) 22,149
The attendance at the movie theater in seven years will be 63,476. Then option C is correct. And the number of customers that visit the business in 10 years will be 22,149. Then option A is correct.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The yearly participation at a neighborhood movie theater is 42,000 and develops ceaselessly at a pace of 5.9% every year. Then the attendance at the movie theater in seven years will be given as,
[tex]\rm y = 42,000 \times (e)^{0.059\times 7}\\\\y = 42,000 \times (e)^{0.413}[/tex]
Simplify the equation further, then we have
y = 42,000 × 1.5113
y = 63,476
The quantity of clients that visit a neighborhood private venture is 29,600 and has been persistently declining at a pace of 2.9% every year.
Then the number of customers that visit the business in 10 years will be given as,
[tex]\rm y = 29,600\times (e)^{-0.029\times 10}\\\\y = 29,600 \times (e)^{-0.29}\\[/tex]
Simplify the equation further, then we have
y = 29,600 × 0.748
y = 22,149
More about the exponent link is given below.
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Mario bought $5 worth of stamps at the post office. He bought ten more 6-cent stamps than 10-cent stamps. The number of 8-cent stamps was three times the number of 10-cent stamps. He also bought two 20-cent stamps. How many of each kind of stamp did he purchase?
Answers
That is $0.40.
He spent $4.60 on the other stamps.
He bought x 6-cent stamps, y 10-cent stamps, and z 8-cent stamps.
y + 10 = x
z = 3y
6x + 10y + 8z = 460
6(y + 10) + 10y + 8(3y) = 460
6y + 60 + 10y + 24y = 460
40y + 60 = 460
40y = 400
y = 10
x = y + 10 = 10 + 10 = 20
z = 3y = 3(10) = 30
He bought
20 6-cent stamps
10 10-cent stamps
30 8-cent stamps
2 20-cent stamps
Simplify 12 to the sixteenth power over 12 to the fourth power
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So, it looks like this. 12^16 / 12^4. Do the "Quotient Rule." (A.K.A, subtracting both powers. 12^16 / 12^4 = 12^12. 12^12 = 8,916,100,448,256. (Yes, it's a scarily huge number..)
Hope this helps! ☺♥
Solve.
2x + 6 - 7x = 21
Answers
-5x+6+21 (what happen to one side happens to the others
-5x=21 (divide by five)
x= -3
Now you have -5x + 6 = 21.
subtract 6 from both 6 and 21, the 6 cancels out and 21-6=15.
You’re left with -5x=15
Divide 5 on both sides, -5 cancels out, and you’re left with
x=-3
sorry this was messy and i hope this made sense!
How many ways can you split 12 people into 3 groups?
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how do u do that 2*2/2*2
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------ =
2 * 2
4
-- =
4
1
[tex] \frac{2 x 2}{2 x 2} [/tex] = [tex] \frac{4}{4} [/tex]
Now, all you would have to do is simplify your answer.
[tex] \frac{4}{4} [/tex] = 1
The sum would be 1.
I hope this helps!
What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y= x/3−1 ?
Answers
y= -3x+b
Now, we can substitute in the point given to find the intercept.
2= -3(4)+b
2= -12+b
b=14
Finally, put in everything we've found to finish the equation.
y= -3x+14
POINTS POINTS POINTS POINTS POINTS! harder question!
45(34- 2)
Answers
Solve the stuff in the parenthesis first
45(32)
Multiply
1440
Have an awesome day! :)
Answer:
answer is 1440,ok
Step-by-step explanation:
Help me Solve this and explain to me the steps thank you
Answers
recall that a flat-line is always 180°, also recall that all interior angles in a triangle are 180°, therefore x + 95 + 54 = 180. Surely you'd know what "x" is.
Karen Johnson rode her 27” bicycle to the store and back. The store is 1 mile from Johnson’s Home. Approximately how many rotations did Johnson’s bicycle wheels make in going to the store and back
Answers
Any number that is divisible by 2 is also divisible by 8. Find a counter example to show that the conjecture is false. 24 28 16 32
Answers
Just to clarify, a correct statement would be “any number divisible by 8 is also divisible by 2.”
Hope this helps!
Two airplanes left the same airport and arrived at the same destination at the same time. The first airplane left at 8:00 a.m. and traveled at an average rate of 496 miles per hour. The second airplane left at 8:30 a.m. and traveled at an average rate of 558 miles per hour. Let x represent the number of hours that the first plane traveled. How many hours did it take the first plane to travel to the destination? Enter an equation that can be used to solve this problem
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then for first plane d = 496x
and for second plane its d = 558/(x - 0.5) , so:-
496x = 558x - 279
62x = 279
x = 4.5 hours
The first plane took 4 and a half hours
Answer:
4.5 hours
[tex]496 x= 558 x-279[/tex]
Step-by-step explanation:
We are given that two airplanes left the same airport and arrives at the same destination at the same time.
We have to find the number of hours taken by first plane to travel to the destination and find the equation that can be used to solve this problem
We are given that the first airplane left at 8:00 a.m
Let y be the distance traveled by the first airplane
The average rate of first airplane =496 miles per hour
The average rate of second airplane =558 miles per hour
Let x represents the number of hours that the first airplane traveled.
The number of hours that the second plane traveled =x-0.5
Because the second airplane take half an hour less than the first airplane
We know that [tex] distance=speed\times time [/tex]
[tex]d=496 x[/tex]
[tex]d=558(x-0.5)[/tex]
[tex]496 x= 558 x-279[/tex]
[tex]279=558 x-496 x[/tex]
[tex]279=62 x[/tex]
[tex]x=\frac{279}{62}[/tex]
x=4.5 hours
Hence, the first airplane takes 4.5 hours to travel to the destination.
If a and b are positive numbers, find the maximum value of f(x) = xa(7 â x)b on the interval 0 ⤠x ⤠7.
Answers
Final Answer:
The maximum value of f(x) = xa(7 - x)b on the interval 0 ≤ x ≤ 7 occurs when x = 7/2 for a > 0 and b > 0.
Explanation:
To find the maximum value of f(x) on the interval 0 ≤ x ≤ 7, we'll use calculus. First, take the derivative of f(x) with respect to x.
f'(x) = a * (7 - x)^b * x^(a-1) - b * a * (7 - x)^(b-1) * x^a
Setting f'(x) = 0 to find critical points:
a * (7 - x)^b * x^(a-1) - b * a * (7 - x)^(b-1) * x^a = 0
Solving for x gives x = 7/2. To determine if this point is a maximum, minimum, or inflection point, we'll use the second derivative test.
f''(x) = a * (7 - x)^(b-1) * x^(a-2) * ((a - 1) * x - 7) - b * a * (7 - x)^(b-2) * x^(a-1) * ((b - 1) * x - 7)
When x = 7/2, f''(7/2) > 0, indicating a concave-up shape and confirming it as a local minimum. Therefore, the maximum value of f(x) occurs at the endpoints of the interval, x = 0 and x = 7, or potentially at x = 7/2 if it surpasses these values.
For a > 0 and b > 0, plugging in x = 7/2 into f(x) = xa(7 - x)b yields the maximum value of the function within the given interval.
Understanding the critical points through derivatives helps identify where the maximum or minimum points occur in the function. In this case, x = 7/2 stands as the point of maximum value within the interval 0 ≤ x ≤ 7 when a and b are both positive.
a) Simplify the expression and explain each step. (2 points)
4(3x + 2) – 2
b) Factor the expression completely. (1 point)
20b – 16
Answers
12x+8-2
12x+6
2x+1 simplified expression
Answer:
a) [tex]4\left(3x+2\right)-2=12x+6[/tex]
b) [tex]20b-16= 4\left(5b-4\right)[/tex]
Step-by-step explanation:
a) To simplify the expression you must:
Expand [tex]4(3x + 2)[/tex]:
Apply the distributive law: [tex]\:a\left(b+c\right)=ab+ac[/tex]
[tex]a=4,\:b=3x,\:c=2\\\\4\left(3x+2\right)=4\cdot \:3x+4\cdot \:2[/tex]
Simplify [tex]4\cdot \:3x+4\cdot \:2= 12x+8[/tex]
[tex]12x+8-2[/tex]
Subtract the numbers: [tex]4\left(3x+2\right)-2=12x+6[/tex]
b) To factor the expression [tex]20b - 16[/tex] you must:
Rewrite 16 as [tex]4\cdot 4[/tex] and 20 as [tex]4\cdot 5[/tex]
[tex]20b-16=4\cdot \:5b-4\cdot \:4[/tex]
Factor out common term 4
[tex]20b-16= 4\left(5b-4\right)[/tex]
N an algebra classroom, a teacher has created an estimation game using a jar of pennies. six students remain in the contest. each student makes one guess and their guesses are as follows: 62, 52, 59, 42, 49, 65. one guess is 12 away from the exact number of pennies in the jar while the other guesses are 1, 4, 6, 9, and 11 pennies away. determine exactly how many pennies are in the guessing jar.
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please help
its really important
Answers
--------------------------------------------
Use the given table to compute the row and column totals. We simply add up values to get these totals.
Boys: 108+23 = 131 meaning that there are 131 boys total so this value will go in row 1 of the "total" column attached to the right side of the given table. See figure 1.
Girls: 99+16 = 115 will go right under 131.
Right-Handed: 108+99 = 207 will go under 99 in the "right handed" column in the "total" row.
Left-handed: 23+16 = 39 will go next to the 207 in the same total row as before
--------------------------------------------
We have the row and column totals computed. Now onto the next step.
Copy the entire table (with row and column totals) to another sheet of paper or just below the table you just wrote out. This new second table will be built upon and altered. First, erase the bottom "total" row. Now divide everything in row 1 by the total
108/131 = 0.82442748091603 which rounds to 0.82
23/131 = 0.17557251908397 which rounds to 0.18
So we'll have 0.82 and 0.18 fill in for the first row of the "Boys" row. See figure 2.
Do the same for the second row. Divide everything in this row by the total 115
99/115 = 0.8608695652174 which rounds to 0.86
16/115 = 0.1391304347826 which rounds to 0.14
The values 0.86 and 0.14 will go in the first two columns of row 2.
The totals will divide by each other to lead to 1
131/131 = 1
115/115 = 1
which explains why we have two '1's in the very right column. They represent 100%
Again, see figure 2 to see how the values are placed.
--------------------------------------------
We'll follow similar steps as before in the previous section. Copy the table from figure 1 but now erase the entire right-hand column marked "total".
Divide everything in column 1 by the total 207
108/207 = 0.52173913043479 which rounds to 0.52
99/207 = 0.47826086956521 which rounds to 0.48
207/207 = 1
Divide everything in column 2 by the total 39
23/39 = 0.58974358974359 which rounds to 0.59
16/39 = 0.41025641025641 which rounds to 0.41
39/39 = 1
See figure 3 to see how the values are filled in. The values in red are the results we got in this section. The '1's have already been filled in by your teacher.
--------------------------------------------
Side Note: In figure 2, the red values in the "Boys" row add up to 1
0.82+0.18 = 1
The same can be said for the "girls" row too
0.86+0.14 = 1
In figure 3, the red values in the "right handed column" add to 1
0.52+0.48 = 1
And similarly for the "left-handed" column
0.59+0.41 = 1
These four facts are not coincidences. For instance, 82% of the boys are right-handed so that leaves 18% left-handed boys (see row1 of figure 2). So 82% + 18% = 100% which is represented by 0.82+0.18 = 1
A bag contains 44 red balls and 55 blue balls. 22 balls are selected at random. find the probability of selecting 22 red balls.
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# of random pairs of balls: 12C2 = 66
The probability of selecting 22 red balls is [tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
A bag contains 44 red balls and 55 blue balls
The total number of balls=44+55=99
22 balls are selected at random from bag.
We need to find the probability of selecting 22 red balls.
The probability of selecting 22 red balls from 44 balls
[tex]^{44} C_{22}[/tex]
2,104,098,963,720
and [tex]^{99} C_{22}[/tex] is 5.7190121704386E+21
So probability of selecting 22 red balls is
[tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
Hence, the probability of selecting 22 red balls is [tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
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Which value is needed to create a perfect square trinomial from the expression x2 + 8x + _____?
Answers
hope this helps
that will equal x²+ 8x + 16
It would be 16.
Hope This Helps You!
Good Luck :)
- Hannah ❤
The larger of two supplementary angles measures 20° less than four times the measures of the smaller angle .find the degree measure of each angle
Answers
From that knowledge we can write up some equations.
Let angle 1 = x, and angle 2 = y
x + y = 180
"The larger of two supplementary angles measures 20° less than four times the measure of the smaller angle"
(Let x be the larger angle)
x+20 = 4y
Since there are two different equations, and two variables, this means we have a set of simultaneous equations.
We can solve this via the substitution method or the elimination method.
I choose to solve it via the substitution method cause of personal preference.
x + y = 180 => x = 180- y
x+20 = 4y => x = 4y - 20
Make them equal each other..
180 - y = 4y - 20
200 = 5y
40 = y
Now that we know y we can sub it into any equation to find x
x + 20 = 4y
x + 20 = 4(40)
x + 20 = 160
x = 140
So the angles are 40° and 140°
We want to create a system of equations that allows us to find the values of two supplementary angles.
We will find that the larger angle measures 140° and the smaller one measures 40°.
------------------------
Two angles A and B are supplementary if their measures add up to 180°, so we have:
A + B = 180°.
Let's assume that B is the larger one, we also do know that:
"The larger is 20° less than 4 times the smaller"
Then we can write:
B = 4*A - 20°.
Then our system of equations is:
A + B = 180°.
B = 4*A - 20°.
To solve it we need to isolate one variable in one of the equations and replace it on the other equation. Here we can see that B is already isolated on the second equation, so we can replace it in the first one to get:
A + B = 180°.
A + (4*A - 20°) = 180°
Now we can solve this for A:
A + (4*A - 20°) = 180°
5*A - 20° = 180°
5*A = 180° + 20° = 200°
A = 200°/5 = 40°
Now that we know the value of A we can get the value of B:
B = 4*A - 20° = 4*40° - 20° = 140°
Then the larger angle measures 140° and the smaller measures 40°
If you want to learn more, you can read:
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Given the number 2464829438 what is the next number?
Answers
24648294389
Hope I helped :)
You have the answer?
Answers
1/2 divided by 5=1 over blank I need to know the blank number
Answers
1 over 2 divided by 5 equals 1 over 2 times 1 over 5, which equals 1 over 10
Algebra help please.
Find the value of 21 + 4(3^2 - 5).
25
37
100
Answers
the answer would be 37
{12x + 4y = 15232x + 12y = 42012x + 4y = 15232x + 12y = 420 In the equations, xx represents the cost of a chicken lunch and yy represents the cost of a vegetarian lunch. Which is the cost of the vegetarian lunch?
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What is the definition to an equation?
Answers
OR
A mathematical statement that 2 expresion are equal.
Sam deposited $350 into a savings account that paid 5% in simple interest. When he withdrew his money 8 months later, how much interest did he receive?
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I = P x R% x T
I is simple interest
P is principal, which is the amount u deposit in
R% is the rate
And T means the time
However, this question didn't list whether 5% is per annual or per monthly.
Suppose it's oer annual,
From the numbers, we can substitute in
Interest = 350 x (5%/12) x 8
Note that since the amount of time is in months, and one year has 12 months, so we need to change the rate into per monthly.
Interest = 350 x (5%/12) x 8
Answer = $11.66666676
But suppose it's per monthly.
This time we don't need to divide the rate by 12.
Interest= 350 x 5% x 8
=$140
I need a little help please Brainliest
Answers
For the first image, the median range would be 88. In order to find the median, you'll place all your numbers in numerical order (smallest to largest). If there are an odd amount of numbers, find the one directly in the middle. If there is an even amount, you'll take the two most central ones and find the mean, that will tell you the median. Therefore, B (88) would be the answer to your first one.
The second one would be C (20.4). It's asking for the mean. In order to find the mean of a set of numbers, you'll simply add up all of the numbers and divide by how many numbers are in your number set. That gives you the mean.
Describe in words a sequence of transformations that maps ∆ABC to ∆A'B'C'.
Transformation #1
Transformation #2
Write an ordered-pair rule for each transformation in the sequence.
Transformation #1
Transformation #2
Answers
Answer: The required sequence of transformations is
Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒ (-y, x).
Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).
Step-by-step explanation: We are given to describe in words a sequence of transformations that maps ∆ABC to ∆A'B'C'.
From the figure, we note that
the co-ordinates of the vertices of triangle ABC are A(0, 4), B(0, 0) and C(2, 3).
And, the co-ordinates of the vertices of triangle A'B'C' are A'(-2, -3), B'(2, -3) and C'(-1, -1).
We see that if triangle ABC is rotated 90 degrees in anticlockwise direction about the origin, then its co-ordinates changes according to the following rule :
(x, y) ⇒ (-y, x).
That is
A(0, 4) ⇒ (-4, 0),
B(0, 0) ⇒ (0, 0),
C(2, 3) ⇒ (-3, 2).
Now, if the vertices of the rotated triangle are translated 2 units right and 3 units down, then
(x, y) ⇒ (x+2, y-3).
That is, the final co-ordinates after rotation and translation will be
(-4, 0) ⇒ (-4+2, 0-3) = (-2, -3),
(0, 0) ⇒ (0+2, 0-3) = (2, -3),
(-3, 2) ⇒ (-3+2, 2-3) = (-1, -1).
We see that the final co-ordinates are the co-ordinates of the vertices of triangle A'B'C'.
Thus, the required sequence of transformations is
Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒ (-y, x).
Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).