Answer: 84 cubes
Step-by-step explanation: Given, The dimension of the rectangular prism are, 1 1/3 ft. * 1 * 2 1/3 = 4/3 * 7/3 = 28/9 cube ft.
Now, the volume of a cube = side³, if side = 1/3 ft., Then the volume of each cube, V = (1/3)³ = 1/27 cube ft.
Hence, the number of cubes that can be packet in the prism = V/V1 = 28/9 / 1/27 = 27*28/9 = 3 * 28 = 84
A) The number of small cubes which can be packed in the rectangular prism are 180.
B) The volume of the rectangular prism in terms of the small cube and a unit cube will be 180 units³
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
Length = 2 1/4 feet
Width = 1 feet
Height = 1 1/4 feet
And, The lengths of the sides of a small cube are 1 /4 foot each.
Now,
Since, The volume of rectangular prism = Length x width x height
Substitute all the values, we get;
⇒ The volume of rectangular prism = 2 1/4 × 1 × 1 1/4
= 9/4 × 1 × 5/4
= 45/16 ft³
= 2.81 ft³
And, The Volume of one cube = Side³
Here, The length of side of cube = 1/4 feet = 0.25 feet
Hence, The Volume of one cube = Side³
The Volume of one cube = 0.25³
The Volume of one cube = 0.015625 ft³
So, The number of small cubes that can be packed in the rectangular prism = Volume of rectangular prism / Volume of cube
= 2.81 /0.015625
= 180
B) The length, the width and the height of the rectangular prism in term of units cubes is:
Length = 2 1/4 feet / 0.25 feet = 2.25 / 0.25 = 9 units
Width = 1 feet / 0.25 feet = 4 units
Height = 1 1/4 feet / 0.25 feet = 1.25 / 0.25 = 5 units
So, The volume of the rectangular prism in terms of the small cube and a unit cube is,
Volume = 9 x 4 x 5
= 180 units³
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A sporting goods store is having a sale in which all sleeping bags are discounted by 20%. Priya has a coupon for $5 off the regular price of a sleeping bag. The store first applies this coupon and then takes 20% off the reduced price. If Priya pays $34.40 for the sleeping bag, what was the original price, x, before the sale and without the coupon?
the original price was "x", which oddly enough is the 100%.
now, let's pluck out of "x" 5 bucks, so that makes it "x-5", that's our new adjusted 100%, from which the lady at the counter is happy to apply a 20% discount. Now, if the lady discounts 20% off of that "x-5" amount, what Priya is really paying for the sleeping bag is just 100% - 20% = 80%, and we happen to know that that 80% was really $34.40.
now, if "x - 5" is the 100%, and we know that 34.40 is the 80%, what the heck is "x"?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x-5 & 100\\ 34.40& 80 \end{array} \implies \cfrac{x-5}{34.40}~~=~~\cfrac{100}{80} \implies \cfrac{ x-5 }{ 34.40 } ~~=~~ \cfrac{ 5 }{ 4 } \\\\\\ 4x-20=172\implies 4x=192\implies x=\cfrac{192}{4}\implies x=48[/tex]
If xx and yy vary directly and yy is 40 when xx is 5, find yy when xx is 6.
Answer:
41
Step-by-step explanation:
20 points to whoever answers this asap <3
Joe and Andrew shot baskets in a school fair. Joe made 9 baskets, which is 2 baskets more than Andrew. Supply the correct numbers to complete the equation that can be used to determine the number of baskets, b, that Andrew made.
Answer:
The answer to the question is 7. This is the number of baskets that Andrew made, as calculated using the equation b = 9 - 2.
Step-by-step explanation:
Which frequency table matches the data?
Answer: A
Step-by-step explanation: hope it helps
SOMEONE HELP ME PLEASE I DONT KNOW HOW TO DO THIS!!!
if you're a tad confused, o represents one of the options and you're supposed to fill it in. x represents number for bags
A coffee shop sells bags of coffee for a regular price of $8 per bag. Chang bought some bags and used a coupon for $10 off his entire purchase. After applying the coupon, he paid $30.
How many bags of coffee did he buy?
(a) Write an equation to help answer the question above.
Choose the correct form below and fill in the blanks using only 8, 10, and 30.
(The variable x is used to represent the number of bags.)
ox+o=o OR o×-o=o
(b) Write an expression to help answer the question above.
Choose the correct form below and fill in the blanks using only 8, 10, and 30.
o+o/o OR o-o/o
(c) How many bags of coffee did Chang buy? answer: _x_ bags
If the number of bags is x, the cost of them is 8x.
After applying a $10 coupon the total was $30.
Part (a)Set equation:
8x - 10 = 30Part (b)Solve it for x:
8x = 30 + 108x = 40x = 40/8x = 5Part (c) Answer: 5 bagsWhich expression is equivalent to 2E-3/2E-5
a. 2E2
b. 1/2E2
c. 2E8
d. 1/2E8
E=exponent
Answer:
a 2E2
Step-by-step explanation:
[tex]\frac{2^{-3} }{2^{-5} }[/tex] When powers have the same bases and you are dividing, you subtract the exponents.
[tex]2^{-3 - -5}[/tex] = [tex]2^{-3+5}[/tex] = [tex]2^{2}[/tex]
Which table shows a function that is decreasing only over the interval (–1, ∞)?
What answer is it and why? To me it seems it can either be C or D (One all the way to the right on the top row and one all the way to the bottom right), but I'm not sure why it would be either one over the other and would need an explanation. If it is neither C nor D I need an explanation on how to solve this question correctly.
Answer: The table to the farthest right the last one.
Explanation:
The interval (-1, ∞) represents x-values anywhere from -1 and higher.
As such, you are looking for a table with y-values that decrease as the x-values increase.
Starting from -1 -
The first option: -5, -2, -1, 2. This is increasing.
The second option: -7, -6, 1, -1. This increases from -7 to -6 to 1.
The third option: -1, 2, 1, -6. This increases from -1 to 2.
The fourth option: 1, 0, -4, -8. This decreases across all coordinates in the range specified.
Answer:
The last graph (d) represents it
z/2>2
hey help me please
Answer:
Z > 4
Step-by-step explanation:
Need Answered ASAP. Rewrite 12x^4y^3 − 48x^3y^4 using a common factor.
Answer:
Step-by-step explanation:
12x^2y^3-36x^5y^3-48x^4y4
factor out 12
12(x^2y^3-3x^5 y^3 - 4x^4 y^4
consider X^2 y^3 - 3x^5 y^3
4x^4 y^4 Factor out x^2y^3
x^2 y^3 (1-3x^3 -4x^2 y)
Rewrite the complete factored expression
12x^2 y^3 (1-3x^3-4x^2y)
ok, my let’s try this again. can someone please help fill out the ? for this table.
Answer:
60 months
$9,000
4.6%
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.5cm}\underline{Simple Interest Formula}\\\\$ A = P(1 + rt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
A = $5,000P = $4,000r = 5% = 0.05Substitute the given values into the formula and solve for t:
[tex]\implies 5000=4000(1+0.05t)[/tex]
[tex]\implies \dfrac{5000}{4000}=1+0.05t[/tex]
[tex]\implies1.25=1+0.05t[/tex]
[tex]\implies 0.05t=1.25-1[/tex]
[tex]\implies 0.05t=0.25[/tex]
[tex]\implies t=\dfrac{0.25}{0.05}[/tex]
[tex]\implies t=5\; \rm years=60\; months[/tex]
Given:
A = $11,160r = 8% = 0.08t = 36 months = 3 yearsSubstitute the given values into the formula and solve for P:
[tex]\implies 11160=P(1+0.08 \cdot 3)[/tex]
[tex]\implies 11160=P(1.24)[/tex]
[tex]\implies P=\dfrac{11160}{1.24}[/tex]
[tex]\implies P=\$9000[/tex]
Given:
A = $3,207P = $3,000t = 18 months = 1.5 yearsSubstitute the given values into the formula and solve for r:
[tex]\implies 3207=3000(1+r \cdot 1.5)[/tex]
[tex]\implies \dfrac{3207}{3000}=1+1.5r[/tex]
[tex]\implies 1.069=1+1.5r[/tex]
[tex]\implies 1.5r=1.069-1[/tex]
[tex]\implies 1.5r=0.069[/tex]
[tex]\implies r=\dfrac{0.069}{1.5}[/tex]
[tex]\implies r=0.046[/tex]
[tex]\implies r=4.6\%[/tex]
Therefore, the completed table is:
[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \vphantom{\dfrac12} \rm BALANCE & \rm PRINCIPAL & \rm INTEREST \; RATE & \rm TIME \\\cline{1-4} \vphantom{\dfrac12} \$5,000 & \$4,000 & 5\% & \rm 60 \; months\\\cline{1-4} \vphantom{\dfrac12} \$ 11,\!160 & \$9,000 & 8\% & \rm 36 \; months \\\cline{1-4} \vphantom{\dfrac12} \$3,207 & \$3,000 & 4.6\% & \rm 18 \; months\\\cline{1-4} \end{array}[/tex]
If x and y vary directly and y is 40 when x is 10, find y when x is 15.
Answer:
y is 60 when x is 15
Step-by-step explanation:
the ratio of x to y is 1:4
May some pls help my head hurts
Answer:
20 minutes
Step-by-step explanation:
we can solve with an equation
9 : 12 = 15 : x
x = 12 × 15 : 9
x = 180 : 9
x = 20
-------------------------
check
9 : 12 = 15 : 20
3 : 4 = 3 : 4
the answer is good
Help, i have to do this in the next like 30 seconds -_-
I think your answer is 2/3
I am not sure
Which story problem can be solved using the expression 5 divided by ¼?
Group of answer choices
-Alex cuts ¼ of a pizza into 5 slices. What part of the pizza is one of the slices he cuts?
-Nicole cuts 5 feet of string into ¼ - foot pieces. How many pieces does she cut?
-Suzy needs 5 pieces of ribbon that are each ¼ yard long. What is the total length of the ribbon?
-Sammy pours ¼ cup of honey equally into 5 teacups. How much honey does he pour into each teacup?
Thank u! <3
Answer: Nicole cuts 5 feet of string into ¼ - foot pieces. How many pieces does she cut?
Step-by-step explanation:
Nicole cuts 5 feet of string into ¼ - foot pieces. How many pieces does she cut?
When you cut one piece of string into smaller pieces, that is the same as dividing.
5/1/4 is the same as 5*4/1
=20
PLEASE HELP MY ASSIGNMENT IS OVERDUE
In the triangle ABC, AB = (x + 3)cm, BC = (x + 2)cm, AC = x cm and angle BAC = 60degrees
Find the value of x.
Answer:
x = 5---------------------------------
Side BC is opposite to ∠BAC and adjacent sides are AB and AC.
Use the law of cosines:
BC² = AB² + AC² - 2AB*AC*cos ∠BAC
Substitute and solve for x:
(x + 2)² = (x + 3)² + x² - 2x(x + 3) cos 60°x² + 4x + 4 = x² + 6x + 9 + x² - 2(x² + 3x)*1/2x² + 4x + 4 = 2x² + 6x + 9 - x² - 3xx² + 4x + 4 = x² + 3x + 94x - 3x = 9 - 4x = 5A tree that is 14 feet tall casts a shadow that is 7 feet long. What is the distance from the top of the tree to the tip of the shadow? Round to the nearest tenth.
15.7 feet
12.1 feet
4.6 feet
2.6 feet
Answer:
2.7
Step-by-step explanation:
Need Answered ASAP. As part of the training for the cross-country team, you must run a total of 20 miles per week. You ran 6.3 miles in the first two days of the week. If you run the same amount each day for the remaining five days, how many miles must you run per day to complete the 20 miles?
Write and solve an equation to determine the number of miles, m, you must run per day.
Answer: 1.48 miles
Step-by-step explanation:
6.3 x 2 = 12.6
20 - 12.6 = 7.4
7.4/5 = 1.48
You have 2 different savings accounts. For Account A, the simple interest earned after 21 months is $5.95. For Account B, the simple interest earned after 30 months is $36.00. If the interest rate is %3.4 for Account A and %2.4 for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
Answer: Principal amount is A = $250.09
Principal amount is B = $400.
Account B earned you the most interest the first month
The formula for simple interest is expressed as
I = PRT/100
Where
P = the principal or initial amount of money invested.
R = interest rate
T = time
On account A,
I = $6.94
R = 3.7%
T = 9 months = 9/12 = 0.75 years.
Using the formula:
On account B,
I = $13.80
R = 2.3%
T = 18 months = 18/12 = 1.5 years
Using the formula:
To determine the account that earned more interest in the first month we divide the interest by the number of months.
$6.94/9 = $0.7711
$13.80/18 = $0.7667
Account B earned you the most interest the first month because $0.7667 is higher than $0.7711.
Answer:
Principal amount is A = $250.09
Principal amount is B = $400.
Account B earned you the most interest the first month
The formula for simple interest is expressed as
I = PRT/100
Where
P = the principal or initial amount of money invested.
R = interest rate
T = time
On account A,
I = $6.94
R = 3.7%
T = 9 months = 9/12 = 0.75 years.
Using the formula:
On account B,
I = $13.80
R = 2.3%
T = 18 months = 18/12 = 1.5 years
Using the formula:
To determine the account that earned more interest in the first month we divide the interest by the number of months.
$6.94/9 = $0.7711
$13.80/18 = $0.7667
Account B earned you the most interest the first month because $0.7667 is higher than $0.7711.
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Hope it helps.
PLEASEEEE HELPPPPPPPPP
Answer: The difference between the angle measure is 152 degrees
Step-by-step explanation: Supplementary angles are angles that add up to 180
So if one angle is x in this case, the other will be 14x
Adding both ;
x + 14x = 180
15x = 180
x = 180/15
x = 12
The other angle is 14 * 12 = 168
The difference between the two will be;
168-12 = 156
Answer:
168
Step-by-step explanation:
m<B + m<C = 180 since the angles are supplementary.
m<B = 14m<C since the measure of angle B is 14 times the measure of angle C.
m<B + m<C = 180
14m<C + m<C = 180
15m<C = 180
m<C = 180/15
m<C = 12
m<B = 14m<C = 14 × 12
m<B = 168
Answer: 168
When Jackson works more than 40 hours in a week, he earns 1.5 times his normal hourly rate for each of the extra hours. Jackson worked 43 hours one week. What was his total pay before deductions? Justify your answer.
Answer:
44.5 hr
Step-by-step explanation:
40x+(3*1.5x) = 40x+4.5x = 44.5x
An equation is written in standard form, match each word with the expression that is used to find it.
Answer:
slope : opposite of a
y-intercet:b/c
x-intercet:a/b
Step-by-step explanation:
The zoom feature on a copier sets the percent size of a copy. Lebron wants to make a 200% copy of a photograph. The original photo has a width of 5 in. What width will the copy be?
a) 2.5in
b) 10in
c) 25in
d) 100in
Write the mixed number 4 ⅜ as an improper fraction.
Thank u!
Answer:
[tex]\frac{35}{8}[/tex]
Step-by-step explanation:
Another name for 1 is [tex]\frac{8}{8}[/tex] so 4 can be [tex]\frac{8}{8}[/tex] + [tex]\frac{8}{8}[/tex] + [tex]\frac{8}{8}[/tex] + [tex]\frac{8}{8}[/tex] = [tex]\frac{32}{8}[/tex]. we can now add this to [tex]\frac{3}{8}[/tex]
[tex]\frac{32}{8}[/tex] + [tex]\frac{3}{8}[/tex] = [tex]\frac{35}{8}[/tex]
Which expression has like terms?
Group of answer choices
8x - 4y
8x - 4x
13c + 13d
4 + 4y
thx!
Evaluate the expression: 2 × 14 ÷ (3² − 2)
Group of answer choices
3
8
4
6
Answer: 4
Step-by-step explanation:
2 × 14 ÷ (3² − 2)
28 / (9-2)
28/7
4
[tex]2\times14\div(3^2-2)[/tex]
[tex]14\times2=28[/tex]
[tex](3^2-2)=7[/tex]
[tex]28\div7[/tex]
[tex]=\fbox{4}[/tex]
A circle’s circumference is 600 m.
What is a good approximation of the circle’s area? 1. 300\ m^{2} 2. 3,000\ m^{2} 3. 30,000\ m^{2} 4. 300,000\ m^{2}
The area of the circle is approximately 30,000 [tex]m^{2}[/tex]
The circumference of the circle is given as 600m.
And we know that circumference = [tex]2\pi r[/tex] where r is the radius of the circle.
Therefore,
[tex]2\pi r = 600[/tex]
[tex]r = \frac{600}{2\pi }[/tex]
[tex]r = \frac{300}{\pi }[/tex]
Now, we know that area of the circle = [tex]\pi r^{2}[/tex]
Putting the value of r in this, we get
area = [tex]\pi (\frac{300}{\pi } )^{2}[/tex]
area = [tex]\pi.\frac{300}{\pi } .\frac{300}{\pi }[/tex]
Therefore, area of the circle = 28,647.889 [tex]m^{2}[/tex]
Therefore, the correct answer is 30,000 [tex]m^{2}[/tex]
To learn more about circle and it's area, refer to:
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"Based on the table, which best predicts the end behavior of the graph of f(x)?"
How do I figure out the answer to this question? I need a step-by-step explanation to the answer of the question.
Answer: How you figure out the answer to this question is figure out if it's a line by a constant rate of change
Step-by-step explanation: Because you gotta make sure before you plug in an answer you need to make sure it's a line
Distribute the negative sign to each term inside the parenthesis. - (9k-5p+7e-2)
Step-by-step explanation:
Distribute the negative sign to each term inside the parenthesis.
- (9k-5p+7e-2)
To distribute the negative sign to each term inside the parenthesis:
a negative and positive = -
a positive and positive = +
a negative and negative = +
- (9k-5p+7e-2)
- 9k + 5p - 7e + 2
Step-by-step explanation:
(-9k+5p-7e+2)
-×-=+
-×+=-
+×+=+
This Is a Math Test. Help please ASAP! 30 POINTS!
Use the following model to answer the question.
3 groups are shown. Each group shows 2 tens rods and 6 ones cubes.
Which division problem is shown by the model?
A. 0.66÷3=0.22
B. 0.66÷3=0.26
C. 0.78÷3=0.62
D. 0.78÷3=0.26
Answer:
D
Step-by-step explanation:
well, it all starts with a check, what calculations in the answer options are even correct.
A. is correct. 0.66/3 = 0.22
B. is incorrect
C. is incorrect
D. is correct. 0.78/3 = 0.26
so is it A or B ?
one group of 2 tens and 6 ones : how much is that ?
2×10 + 6×1 = 20 + 6 = 26
3 groups of 26 means
3×26 = 78
so, the combination of the 3 groups would either show that
3×26 = 78
or
78/3 = 26
and that is the same as showing
0.78/3 = 0.26
because
0.78 = 78/100
0.26 = 26/100
therefore
78/100 / 3 = 26/100
78/100 = 3×26/100 = 78/100
correct.
Enter the expression −3−8 as an equivalent addition expression.
Answer:
8 + 3
Step-by-step explanation: