Answers
Solution:
Given a right right rectangular prism with made of of unit cubes
Note that A unit cube has 6 square faces with each side 1 unit long
Volume of a unit cube = 1 x 1 x 1 = 1 cubic unit
Total unit cubes present = 60 unit cubes.
To find the volume of the prism by whole unit cube:
The volume of the prism with the whole unit cube = volume of 1 unit cube x 60 = 1 x 60 = 60 cubic units
To find the volume with 1/2 unit cube:
If the divide each of the 60 units cubes into half, we will have a total of 120 half unit cubes
Volume of a half unit cube = (Volume of a unit cube) / 2
= 1/2 = 1/2 cubic unit
Thus, The volume of the prism with the half unit cubes = 120 x volume of a half unit cube
= 120 x 1/2 = 60 cubic units
In conclusion, the difference between finding the volume of the prism by whole unit cubes and 1/2 unit cubes is that the that the volume of each 1/2 unit cube will be multiplied by 120 while that of each whole unit cube will be multiplied by 60
Related Questions
PACKAGING A juice manufacturer is creating new cylindrical packaging. The height of the cylinder is to be 3 inches longer than the radius of the can. The cylinder is to have a volume of 628 cubic inches. Use 3.14 for π.
Answers
The radius and height of a cylinder with volume 628 cubic inches are 5 inches and 8 inches respectively.
Volume of a CylinderThe volume of a given cylinder with radius r and height h can be calculated using the formula πr^2h.
In this question, we have the volume of the cylinder given as 628 cubic inches. The height of the cylinder is 3 inches longer than the radius of the can.
Lets assume the radius of the cylinder is equal to r
Substituting the values into the equation;
[tex]v = \pi r^2 h\\628 = \pi r^2 (r + 3)\\628 = 3.14* r^2(r+3)\\r = 5[/tex]
The radius of the equation is 5 inches and the height of the equation is 8 inches.
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please help me I DONT REMEMBER HOW TO DO THIS
Answers
Answer:
The answer is 6.72 x 10⁷
Step-by-step explanation:
The answer is 6.72 x 10⁷ because I solved it and I got this answer.
A 5-ounce bottle of glue costs $2.85. What is the unit price?
Answers
Answer:
$0.57 per ounce
Step-by-step explanation:
2.85/5 = 0.57
Answer:
Step-by-step explanation:
First, set up an equation: $2.85/5 oz.
Next, divide both the numerator and denominator by 5. NOTE: do them one at a time.
2.85/5=$0.57
5/5=1
So, the unit rate is $0.57/oz.
Which expression will have a positive value?
Responses
the product of a negative number and a positive number
the product of a negative number and a positive number
the sum of a negative number and a negative number
the sum of a negative number and a negative number
the quotient of a positive number and a negative number
the quotient of a positive number and a negative number
the quotient of a negative number and a negative number
Answers
Answer:negative
Step-by-step explanation: the product of a negative number and a positive number
Odalis invierte $1200 en una cuenta y gana 7% anual ¿ su inversión crecerá a Qué cantidad en 5 años
Answers
$1683.06
1) Desde que Odalis invierte $1200 podemos escribir
$1200
7% anualmente ( 0.07)
Tiempo: 5 anos
2) Vamos aplicar esta formula:
[tex]\begin{gathered} A=P(1+\frac{0.07}{1})^{1\cdot5} \\ A=1200(1+\frac{0.07}{1})^{1\cdot5} \\ A=1200(1.07)^5 \\ A=\text{ }1683.06 \end{gathered}[/tex]Considerando una capitalización anual, tenemos al termino un valor de $1683.06
Carol earns a 13% commission on the sales she makes. Complete the table by determining the amount of commission she earned each week.
Answers
The commission on $950 = 13/100 x 950 = $ 123.5
The commission on $2200 = 13/100 x 2200 = $286
The commission on $3000 = 13/100 x 3000 = $390
The commission on $2600 = 13/100 x 2600 = $338
Each commission = 13/100 x the amount in question
A recipe book shows measurement conversions for pints to cups. It shows that 1.5 pints equals 3 cups and 2.5 pints equals 5 cups.
Write an equation that shows the proportional relationship between pints and cups where p represents pints and n represents cups.
p equals 3 over 1.5 times n
n equals 1.5 over 3 times p
p = 0.5n
n = 0.5p
Answers
The equation that t shows the proportional relationship between pints and cups is p = 3 over 1.5 times n
What is the equation?The mathematical operation that would be used to determine the equation is division. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.
In order to determine the proportional relationship, divide the measurement for cups by the measurement for pints.
p = 3 / 1.5n
p = 2n
p = 5 / 2.5
p = 2
This means that one pint represents two cups.
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+Find the number to add to x2 + 14x to make it a perfect square trinomial. Write that trinomial as the square of a binomial.O add 49; (x + 7)?o add 196; (x + 14)2o add 28: (x + 14)2O add 14; (x + 7)?
Answers
A binomial square have the following form:
[tex](x+a)^2=x^2+2ax+a^2[/tex]So, from the coefficient of the second term, we can get the value a and with the value a we can calculate a² for the value of the third term, that is, the value we need to add to make it a perfect square.
We have the expression:
[tex]x^2+14x[/tex]By comparing the second terms, we see that:
[tex]\begin{gathered} 14=2a \\ 2a=14 \\ a=\frac{14}{2} \\ a=7 \end{gathered}[/tex]Since we have a, we can calculate a²:
[tex]a^2=7^2=49[/tex]So, this means the number we need to add is 49 and, since a is 7, the trinomial can be rewritten as:
[tex]x^2+14x+49=(x+7)^2[/tex]So, add 49 and the square binomial is:
[tex](x+7)^2[/tex](ignore the answer i selected i accidentally clicked it) Pleez help
Answers
Okay, here we have this:
We need to find the inverse of the following function:
[tex]f\mleft(x\mright)=\mleft(\frac{x^5}{7}\mright)^{\frac{1}{7}}-1[/tex]First we will replace x with y:
[tex]x=\mleft(\frac{y^5}{7}\mright)^{\frac{1}{7}}-1[/tex]Now, let's clear y:
[tex]\begin{gathered} \mleft(\frac{y^5}{7}\mright)^{\frac{1}{7}}-1=x \\ \mleft(\frac{y^5}{7}\mright)^{\frac{1}{7}}=x+1 \\ \frac{y^5}{7}=(x+1)^7 \\ y^5=7(x+1)^7 \\ y=\sqrt[5]{7(x+1)^7} \end{gathered}[/tex]Finally we obtain that the correct answer is the second option.
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 49 minutes of calls is$13.08 and the monthly cost for 86 minutes is $16.41. What is the monthly cost for 72 minutes of calls?Monthly costin dollars)
Answers
Answer
The monthly cost for 72 minues of calls = $15.15
Explanation
Let the monthly cost in dollars of the long distance phone plan be represented by y.
Let the total calling time in minutes be represented by x.
We are told that montly cost in dollars of the long distance phone plan, y, is a linear function of the total calling time in minute, x. In mathematical terms and using the equation of a straight line model,
y = a + bx
where
a = fixed amount paid monthly
b = dollar per unit time rate charged on the calls
when x = 49 minutes, y = 13.08 dollars
13.08 = a + 49b ........... equation 1
when x = 86 minutes, y = 16.41 dollars
16.41 = a + 86b ........... equation 2
Combining these simultaneous equations
a + 49b = 13.08 .............. equation 1
a + 86b = 16.41 .............. equation 2
Subtract equation 1 from equation 2
a - a + 86b - 49b = 16.41 - 13.08
37b = 3.33
Divide both sides by 37
(37b/37) = (3.33/37)
b = 0.09 dollars per minute.
We can now solve for a
when b = 0.09
a + 49b = 13.08
a + 49(0.09) = 13.08
a + 4.41 = 13.08
a = 13.08 - 4.41
a = 8.67 dollars
So, the linear function that relates the montly cost in dollars of the long distance phone plan, y, to the total calling time in minute, x is
y = a + bx
a = $8.67 and b = $0.09 per minute
y = 8.67 + 0.09x
When total calling time in minutes, x = 72 minutes, we can now calculate the monthly cost, y.
y = 8.67 + 0.09x
y = 8.67 + 0.09(72)
y = 8.67 + 6.48
y = $15.15
Hope this Helps!!!
4≤9x-10≤3
Help please school test tomorrow
Answers
Answer:
[tex]\frac{14}{9}[/tex] ≤[tex]\frac{13}{9}[/tex]
Step-by-step explanation:
4 ≤ 9x - 10 ≤ 3 add 10 from the far left, the middle and the far right.
+10 +10 =10
14 ≤ 9 x ≤13 Divide all the way through by 9
[tex]\frac{14}{9}[/tex]≤x≤
The Scooter Company manufactures and sells electric scooters. Each scooter cost $200 to produce, and the company has a fixed cost of $1,500. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x − 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?
Answers
The total profit of the company is represented by the equation -2x^2-600x-1500
Cost of each scooter = $200
Fixed cost of each scooter = $1500
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. The coefficient of x2 must be a non-zero term (a 0) in order for an equation to meet the definition of a quadratic equation.
Function of revenue R(x) = 400x -2x^2
Let x represent each electric scooter sold
The total cost of the scooter = Fixed cost + variable cost number of scooters sold
= 1500 + 200x
Profit = Revenue - Cost
= 400x - 2x^2 - 1500 + 200x
= 600x - 2x^2 -1500
-2x^2 - 600x -1500
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The circle below has center K, and its radius is 9 m. Given that m
Answers
Solution
for this case we can find the lenght of the arc LM like this:
[tex]LM=2\pi r(\frac{80}{360})=2\pi(9m)(\frac{80}{360})=4\pi[/tex]And the answer for this case would be 4pi
The temperature in Fairbanks was -27 degrees F. Phoenix was 100 degrees F warmer than Fairbanks. What was the temperature in Phoenix?
Answers
Step 1: Given data
Fairbanks temperature - -27 degrees
Phoenic temperature is 100 warmer than Fairbanks temperature
Step 2: Find the temperature of Phoenix.
Since the temperature of Phoenix is 100 warmer than that of Fairbank, then you will add 100 to the temperature of Fairbank.
Step 3: Final answer
The temperature of Fairbank = -27 + 100
= 73 degrees
Miguel and Arjun performed different operations on 12 and 2. Miguel divided 12 by 2: 12 ÷ 2 = x x = 6 Arjun multiplied 12 by 2: 12 × 2 = y y = 24 Which statements are true about Miguel’s and Arjun’s work? Check all that apply. Both operations resulted in the same answer. The product of 12 and 2 is represented by y. The difference between 12 and 2 is represented by x. Miguel found the quotient of 12 and 2. Arjun found the sum of 12 and 2.
Answers
A spectator is viewing the six cars of a roller coaster as it travels down a hill at an amusement park. Which is closest to the total length of the six cars? (G.8c, 1 point) 380 20 ft- O A. 12.3 ft B. 15.8 ft C. 25.6 ft D. 32.5 ft
Answers
We have the following:
We can calculate the answer by means of the trigonometric ratio of the sine, as follows
[tex]\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]replacing:
[tex]\begin{gathered} \sin 38=\frac{20}{x} \\ x=\frac{20}{\sin 38} \\ x=32.48 \end{gathered}[/tex]Thefeore, the answer is D. 32.5 ft
What is the equation of the line that passes through the point (5,-5) and has a slope of -1/2
Answers
Answer: y= -1/2x - 2.5
Step-by-step explanation:
Slope: y= mx+ b
m being the slope
b being the y intercept
You're given the slope, so you substitute m for -1/2
y=mx+b
y = -1/2x + b
You have the coordinates (5, -5) which you can substitute (the line passes through that point.)
-5 = -1/2(5) + b
-5 = -2.5 + b
+2.5 +2.5
-2.5= b
y= -1/2x + 2.5
Check:
-5 = -1/2(5) - 2.5
-5 = -2.5 - 2.5
-5 = -5
I'm trying to solve for x by rounding to the nearest hundredth ? can anyone help me please ?
Answers
Notice that you are asked to find side "x" in a right angle triangle. and that side "x" is adjecent to the given acute angle of 47 degrees.
Since in this triangle you know the values of the adjacent angle (47 degrees) and that of the hypotenuse (3), you can use the trigonometric function that uses those, that is the "cosine" function of the angle:
Recall that :
[tex]\cos (\theta)=\frac{adjacent}{\text{hypotenuse}}[/tex]so, we can solve for the unknown "adjacent" side (x) multiplying both sides by the hypotenuse value (3), and get:
[tex]\begin{gathered} \text{adjacent}=\text{hypotenuse}\cdot\cos (47) \\ x\text{ = 3 }\cdot\text{ cos(47}^{\circ})=2.04599 \end{gathered}[/tex]Therefor, rounding this to two decimals we get:
x = 2.05
which agrees with answer "D" in your list.
the highest temperature ever recorded for today's date in a certain town was 15 Celsius
Answers
To find out the difference, subtract the minimum value from the maximum value
so
15-(-23)=15+23=38 degrees
answer is 38 degrees
expression is 15-(-23)
a rectangle is drawn so that the width is 1 foot shorter than the length. the area of a rectangle is 30 square feet. find the length of the rectangle.___feet
Answers
If the width (W) of the rectangle is 1 ft shorter than its length (L), then we can write the following equatiion:
W = L - 1
now since we know the formula for the area of a rectangle:
Area = length x width
Area = L * W
30 = L * (L - 1)
where we have substituted the width W using the expression in terms of the length in the first equation we wrote.
then we multiply as indicated:
30 = L^2 - L
and write all terms on one side of the equal sign:
L^2 - L - 30 = 0
we try solving this quadratic equation by grouping:
L^2 - 6 L + 5 L - 30 = 0
L (L - 6) + 5 (L - 6) = 0
(L - 6) * (L + 5) =0
then there are two possible solutions to make that product equal to zero:
L = 6
or
L= -5
We pick the POSITIVE answer since we are looking for a length
therefore the length of the rectangle is 6 feet.
Type a "6" in the blank of your question.
What is the slope of the line that passes through the points (7, -4) and (11. -4)?
Write your answer in simplest form.
Answers
The slope of the line for the given coordinate point is: slope = 0
What is slope of the line?
In mathematics, the slope of the line is the ratio of the change in the y-axis and x-axis. Basically, it tells the steepness of the line. Depending upon the slope value, the line is categorized as parallel or perpendicular or constant line.
According to the question, the given coordinate points for the calculation of the slope of the line are as follows:
Points: (7, -4) and (11, -4) ⇒ x1 = 7; y1 = -4; x2 = 11; y2 = -4
The formula for the slope of the line is as follows:
Slope = (y2 - y1)/(x2 - x1)
Slope = (-4 - (-4))/(11 - 7) = 0
Hence, the slope of the line for the given coordinate point is: slope = 0
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Kim bought an outfit that cost $24.50. She had to pay 6.55% sales tax.What was the total amount of her purchase?a. $1.60b. $26.10c. $28.24d. $31.05
Answers
Given
Cost = $24.50
Tax = 6.55%
Procedure
The total cost of the product would be the cost plus the value of taxes.
[tex]\begin{gathered} P=C+C\cdot T \\ P=24.50+24.50\cdot6.55\text{ \%} \\ P=26.10 \end{gathered}[/tex]The total amount would be $26.10
A plane travels 20 degrees east of south what is its compass heading?
Answers
If the angle of elevation of the sun is 61.7° when a building casts a shadow of 56.5 feet, what is the height of the building rounded to the nearest tenth of a foot?
Answers
SOLUTION
Let us use a simple diagram to interprete the question
In the diagram above, the dark stuff below represents the shadow and the rectangular bar represents the building. I have labelled the height of the building as h.
So we will use the right-angled triangle formed to find h
As we can see h represents the opposite side and 56.5 feet represents the adjacent side of the right-angle triangle. So we will use TOA
[tex]\text{TOA tan }\theta=\frac{opposite}{\text{adjacent}}[/tex]So we have
[tex]\begin{gathered} \text{ tan }\theta=\frac{opposite}{\text{adjacent}} \\ \text{ tan }61.7\degree=\frac{h}{56.5} \\ 1.8572015=\frac{h}{56.5} \\ \text{cross multiplying, we have } \\ h=1.8572015\times56.5 \\ h=104.931887 \end{gathered}[/tex]Hence the answer is 104.9 feet to the nearest tenth
Match each equation with an equivalent equation. Some of the answer choices are not used.
3x+5=4x+8
3(x+5)=4x+8
3x+4x=8-5
Answers
The equivalent equations in the given choices are : 3x+5=4x+8 and 3x+4x=8-5.
What are equivalent equations?
Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.
The equations that are equivalent are :
3x+5=4x+8 and 3x+4x=8-5
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Type in the answer to each problem, be sure to include the correct sign with your final answer.
Answers
Remember that when adding positive and negative numbers,there are a couple of rules to follow. For example, in this case:
[tex]-8+6[/tex]first, notice that since 8 is greater than 6, then the result will be a negative number.
Then, we substract 6 from 8 to get 2, so the final result would be:
[tex]-8+6=-2[/tex]Next, if we want to add two negative numbers, then we add the numbers and keep the negative sign, for example:
[tex]-2-3[/tex]Notice that 2 plus 3 is 5, and since both 2 and 3 are negative,we have that:
[tex]-2-3=-5[/tex]If we want to substract a negative number from another negative number, like in thiscase:
[tex]-9-(-4)[/tex]just remember that anything that is inside of a parenthesis with a negative sign will change its sign, then, we have the following:
[tex]-9-(-4)=-9+4[/tex]applying the same rules as before we have:
[tex]-9+4=-5[/tex]On the remaining cases, we have the following results:
[tex]\begin{gathered} 5-7=-2 \\ +4+3=7 \end{gathered}[/tex]Content attribution QUESTION 11.1 POINT Find the perimeter of the figure.
Answers
Let us assume that the dimension of each square is 1 unit by 1 unit
The figure is a rectangle. The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
By counting the squares,
length = 7 * 1 = 7 units
width = 2 * 1 = 2 units
Perimeter = 2(7 + 2)
Perimeter = 18 units
The price of the item has risen to $133 today. Yesterday it was $95. Find the percentage increase.
Answers
Answer:
40%
Step-by-step explanation:
133-95=
38/95=
40%
In 1990, the profit of the Gamna company was $10,007,911. each year after 1990, profits fell by $37,104 on average. construct a linear model for this scenario and use it to solve for the profits in the year 2020.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
initial profit = $10,007,911
profits fell per year = $37,104
linear model = ?
profits (2020) = ?
Step 02:
linear model:
x = years
y = 10007911 - 37104 x
Step 03:
profits (2020):
x = 30
y = 10007911 - 37104 (30)
y = 8894791
The answer is:
linear model: y = 10007911 - 37104 x
profits (2020): $8,894,791
In which set(s) of numbers would you find the number49integerO rational numberOreal numberO natural numberwhole numberO irrational number
Answers
Rational numbers, Real numbers, Natural numbers, whole number
Explanation:[tex]49\text{ can also be written as }\frac{49}{1}[/tex]Rational numbers can be written as a fraction. 49 can be written as a fraction
Real numbers consists of natural numbers, whole umbers, integers and rational numbers.
Since it is already a rational number, then it is also a real number
Natural numbers are counting numbers from 1 to positive infinity. 49 is between 1 to positive infinity.
Hence, it is a natural number
whole numbers start from 0 to positive infinity. 49 is between 0 to positive infinity.
Hence, it is a whole number
Irrational numbers cannot be written in the form of fraction. SInce 49 can be written as fraction, it is not an irrational number
Hence, the set(s) of numbers would you find the number 49 are Rational numbers, Real numbers, Natural numbers, whole number
