how many cubic blocks with a side length of 1/6 cm are needed to fill the volume of this prism?The answer choices are 4,8,9,32.
Answers
Given the figure, we can deduce the following information:
Height=1/2 cm
Length=1/2 cm
Width= 1/6 cm
To determine the number of cubic blocks with a side length of 1/6 cm needed to fill the volume of the given prism, we first note that a cube has equal sides. So, the dimensions of the cube must be:
Height= 1/6 cm
Length=1/6 cm
Width=1/6 cm
Next, we get the volume of the cube by using the formula:
[tex]\begin{gathered} Volume\text{ of the cube}=(Height)(Length)(Width) \\ =(\frac{1}{6})(\frac{1}{6})(\frac{1}{6}) \\ Simplify \\ =\frac{1}{216}\text{ }cm^3\text{ } \end{gathered}[/tex]Then, we get the volume of the given prism using the same formula:
[tex]\begin{gathered} Volume\text{ of the given prism}=(He\imaginaryI ght)(Length)(W\imaginaryI dth) \\ =(\frac{1}{2})(\frac{1}{2})(\frac{1}{6}) \\ =\frac{1}{24}\text{ }cm^3\text{ } \end{gathered}[/tex]Now, we find the number cubic blocks by using the formula:
[tex]\begin{gathered} Number\text{ }of\text{ cubic blocks}=\frac{Volume\text{ of the given prism}}{Volume\text{ of the cube}} \\ =\frac{\frac{1}{24}}{\frac{1}{216}} \\ Simplify \\ =9 \end{gathered}[/tex]Therefore, the answer is 9.
Related Questions
the ratio of students to faculty is 25 to 2. how many faculty members will be needed for a student population of 623? rounded to the nearest whole number
Answers
We have a ratio of students to faculty members is 25 to 2.
For a students population of 623, the number of faculty members will be:
[tex]623\text{ students}\cdot\frac{2\text{ faculty members}}{25\text{ students}}=49.84\text{ faculty members}\approx50\text{ faculty members}[/tex]50 faculty members will be needed for a student population of 623.
The rear window of Alex's van is shaped like a trapezoid with an upper base measuring 36 inches, a lower base measuring 48 inches, and a height of 21 inches. An 18-inch rear window wiper clears a 150° sector of a circle on the rear window. as shown in the diagram below. a. What is the area, in square inches, of the entire trapezoidal rear window Show on explain low you on your answer.
Answers
The area of a trapezoid is computed as follows:
[tex]A=\frac{a+b}{2}\cdot h[/tex]where a and b are the bases, and h is the height of the trapezoid. Replacing with a = 48, b = 36, and h = 21, we get:
[tex]\begin{gathered} A=\frac{48+36}{2}\cdot21 \\ A=42\cdot21 \\ A=882in^2 \end{gathered}[/tex]The area of the entire trapezoidal rear window is 882 square inches
Translate the following: "twice the sum of a number and 7
is negative fifteen"
Answers
A variable is a letter or term that represents an unknown number, value, or quantity. Variables are especially useful in algebraic expressions or algebra.
What is meant by variables?In the context of a mathematical problem or experiment, a variable is a quantity that can change. A variable is typically represented by a single letter. Variables are commonly represented by the letters x, y, and z. Any property, number, or quantity that can be measured or counted is defined as a variable.A variable is also referred to as a data item. Age, gender, business income and expenses, country of birth, capital expenditure, class grades, eye color, and vehicle type are all variables.In research, a variable is simply a person, place, thing, or phenomenon that you want to quantify in some way.let a number be x
then "twice the sum of a number be 2x
given
"twice the sum of a number and 7 is negative fifteen"
⇒ 2x + 7 = -15
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10 Millie and her gr
made this plan for a garden.
They will plant flowers in
8 square feet of the garden.
They will plant vegetables in
the rest of the garden.
10 feet
2 feet
FOR
129
FOR FOR
20 CAP
4 feet
7 feet
9 feet
6 feet
Part A
Which of these can be used
to model the area of the
vegetable garden?
A2 x 10
B6X7
©6x9
D 10 x 7
Part B
What is the total area of the
garden in square feet?
Answers
Part A) Option c is correct answer. 6 x 9 can be used to model the area of the vegetable garden.
Part B) Total area of the garden in square feet is 62 square feet.
What do you mean by area?
Area is a unit of measurement used to describe a region's size on a flat or curved surface. While a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.
To calculate the area we first individually calculate the area of the garden with flowers and vegetables,
Area of the garden where flowers are planted:
Area = length x breadth
Area = 4 x 2 = 8 square feet
Area of garden where vegetables are planted:
Area = 6 x 9 = 54 square feet
Total area of the garden = 8 + 54
Total area of the garden = 62 square feet
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In a square box problem, the:Top number is the product of those left and rightBottom number is the sum of those at left and rightComplete this square box problem
Answers
Answer
Draw the box to complete the table.
Next,
To get the top, multiply both the left and the right = 11 x (-3)
= -33
To get the top, add both the left and the right = 11 + (-3) = 11 - 3 = 8
Based off of the diagram below, correctly categorize each of the angle pairs. Some angle pairs go to more than one category. There are a few incorrect angle pairs as well. The incorrect pairs DO NOT get categorized.For context, line CD intersects line AB at point E.Line EG is perpendicular to line AB at point E.
Answers
Vertical angles = angle AEC and angle DEB
Adjacent angles = GEF and angle CEG also GEF and FEB also DEB and BEF
AED and DEB, also AED and AEC
Complementary angles = angle GEF and angle FEB, and angle AEC and angle CEG
That's all. None of the angles are complementary
what is seven times negative three / 7(-3)
Answers
-21
1) Let's calculate this product:
7 (-3) Multiply 7 by -3
-21
2) So, seven times negative three is equal to -21 that is the same as adding seven times the number -3. Remember different signs in a product turns to out to a negative result.
17. Critique Reasoning Lisa used a number line to model 2(3). Does her number line make sense? Explain why or why not. 8-7-6-5-4-3-2-1 0
Answers
Reasoning Criticism Lisa modeled 2 with a number line (3). Her logical number line is -6.
What is meant by number line?A number line is a graphical representation of numbers on a straight line. A number line has numbers that are sequentially placed at equal distances along its length. It can be extended in any direction indefinitely and is usually represented horizontally. A number line is a horizontal line with mathematical increments spaced evenly.The numbers on the line will determine how to answer the number on the line. The number's use is determined by the question that goes with it, such as plotting a point. The number line is a straight line with divisions at equal intervals, similar to a scale.Therefore, Reasoning Criticism Lisa modeled 2 with a number line (3). Her logical number line is -6.
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f(x)=4x+6 and g(x)=1/2 * f(x)
What is the function rule for function g?
g(x)=
Answers
Answer: 2x + 3
Step-by-step explanation:
f(x) = 4x + 6
g(x) = 1/2 * f(x)
Plug f(x) into the g(x) equation.
g(x) = 1/2 * (4x + 6)
Now simplify,
g(x) = 2x + 3
Can someone answer this question for me please, I really need the help:
Answers
Answer:
4x² +28x +49
Step-by-step explanation:
You want a polynomial equivalent to the area of the figure shown.
PolynomialThe polynomial can represent the sum of three areas:
blue area + green area + yellow area
= 4x² +4(7x) +7²
= 4x² +28x +49
A rectangular safe can hold 5,184 cubic inches. Gold bars that are 3 inches by 6 inches by 2 inches fit to completely fill the safe. What is the volume of each gold bar?11 in.336 in.318 in.315 in.3
Answers
Given:
Rectangular safe hold 5184 cubic inches
Gold bar,
3 inches by 6 inches by 2 inches
Find-:
The volume of each gold bar
Explanation-:
The gold bar is in a rectangular shape
So volume is:
[tex]V=\text{ Length}\times\text{ Width}\times\text{ Height }[/tex]The dimension of the gold bar is 3 inches by 6 inches by 2 inches.
[tex]\begin{gathered} V=3\times6\times2 \\ \\ V=36\text{ in}^3 \end{gathered}[/tex]Volume of each gold bar is 36.
A 220 m wire is cut into three pieces. The second piece is 2 times as long as the first. The third piece is 4 times as long as the second. How long is each piece?
Answers
The first piece = 20m
The second piece = 40m
The third pice = 8x = 160m
Explanation:Given:
Total length of wire = 220m
2nd piece = 2 times the 1st piece
3rd piece = 4 times the 2nd
To find:
The length of each of the piece
The wire was cut into 3:
1st piece + 2nd piece + 3rd piece = 220m
let the first length = x
2nd length = 2 (1st length) = 2(x)
2nd length = 2x
3rd length = 4(2nd piece) = 4(2x)
3rd length = 8x
[tex]\begin{gathered} x\text{ + 2x + 8x = 220} \\ simplify: \\ 11x\text{ = 220} \end{gathered}[/tex][tex]\begin{gathered} divide\text{ both sides by 11:} \\ \frac{11x}{11}=\frac{220}{11} \\ x\text{ = 20} \end{gathered}[/tex]The first piece = 20m
The second piece = 2x = 2(20) = 40m
The third pice = 8x = 8(20) = 160m
Dilate the following points by each scale factor (k) provided. P(3, 4) by k=1/2 And N(4, 15) by k=2
Answers
Dilations involve multiplication, so we have that the dilation with scale factor 1/2 of the point (3,4) is (1.5, 2)
[tex]\frac{1}{2}\cdot(3,4)=(\frac{3}{2},\frac{4}{2})=(1.5,2)[/tex]and the dilation with scale factor 2 of the point (4,15) is (8, 30)
[tex]2\cdot(4,15)=(2\cdot4,2\cdot15)=(8,30)[/tex]Vector v has an initial point at (8, 4) and a terminal point at (−8, 10). What is -1/2 times vector v?
Answers
In order to find a vector multiplication by a scalar, we follow the rule:
[tex]u\ast(n_1,n_2)_\Rightarrow(un_{1,}un_2)[/tex]then, if we apply it to the vector v, we need to find the dimensions of the vector, for that we subtract the initial point from the terminal point,
[tex](-8-8,10-4)\Rightarrow(-16,6)[/tex]then, multiply by the scalar -1/2,
[tex]-\frac{1}{2}\ast(-16,6)\Rightarrow(8,-3)[/tex]Answer:
[tex](8,-3)[/tex]Evaluate (You can use which ever first step you
selected above)
Answers
[tex] \frac{3 \times 3 \times 2^{ - 4} \times 2^{0} }{(3 \times 2 ^{ - 3}) ^{2} } \\ = \frac{3^{ 1+1 } \times 2^{ - 4 + 0} }{3 \times 2 ^{ - 3 \times 2} } \\ = \frac{ {3}^{2} \times {2}^{ - 4} }{3 \times {2}^{ - 6} } \\ = 3^{2 - 1} \times 2^{ - 4 - ( - 6)} \\ = 3 \times {2}^{ - 4 + 6} \\ = 3 \times {2}^{2} \\ = 3 \times 4 \\ = 12[/tex]
I USED THE LAWS OF EXPONENTS.
IF YOU DO NOT KNOW THEM PLEASE TELL ME AS SOON AS POSSIBLE TO ARRANGE FOR YOU.
Find the equation of the circle (2, 3) and radius 4
Answers
Answer: [tex](\text{x}-2)^2+(\text{y}-3)^2 = 16[/tex]
=========================================================
Explanation:
The general circle template is
[tex](\text{x}-\text{h})^2+(\text{y}-\text{k})^2 = \text{r}^2[/tex]
(h,k) = center
r = radius
Assuming the center is (2,3) then we have h = 2 and k = 3. We also have a radius of r = 4.
[tex](\text{x}-\text{h})^2+(\text{y}-\text{k})^2 = \text{r}^2\\\\(\text{x}-2)^2+(\text{y}-3)^2 = 4^2\\\\(\text{x}-2)^2+(\text{y}-3)^2 = 16\\\\[/tex]
Use the formula h = 16t2, where t is time in seconds and h is the distance in feet traveled by a free-falling body or object to solve the following problem.
A diver dives from a cliff that has a height of 125 feet. Determine the time of the dive.
The dive lasted approximately
seconds.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
If a diver dives from a cliff that has a height of 125 feet, The dive lasted approximately 2.80 seconds
A diver dives from a cliff that has a height of 125 feet
The formula h = 16t², where t is time in seconds and h is the distance in feet traveled by a free-falling body or object
125 = 16t²
125/16 = t²
t = √(125/16)
t = √125/√16
t = 5√5 /4
t = 1.25 x 2.23
t = 2.795
t = 2.80
Therefore, if a diver dives from a cliff that has a height of 125 feet, The dive lasted approximately 2.80 seconds
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(calc exponential growth and decay calculus!) a principal amount of $5000 is deposited into an account paying interest at a rate of 6 percent continuously compounded. what will the account balance be after 3 years
Answers
SOLUTION
Given:
The formula is given as:
[tex]\begin{gathered} P(t)=? \\ P_0=\text{ \$5000} \\ t=3years \\ r=\frac{6}{100}=0.06 \end{gathered}[/tex][tex]\begin{gathered} P(t)=5000e^{0.06(3)} \\ P(t)=5986.08681\approx\text{ \$}5986.09 \end{gathered}[/tex]Final answer:
14. Write a quadratic equation that cannot be factored.
Answers
Given:
Quadratic equation
To write a quadratic equation that cannot be factored or cannot be solved by factoring, we note first that factoring is the easiest method to solve a quadratic equation as long as the equation is easily factorable. If not, we'll need alternative approaches like employing the quadratic formula.
We also note that factoring cannot always be used to solve quadratic equations.
Below is an example of an equation that can be solve by factoring:
[tex]\begin{gathered} x^2-3x-10=0 \\ (x-5)(x+2)=0 \end{gathered}[/tex]Now, the equation that cannot be factored or cannot be solved by factoring is:
[tex]x^2+x-1=0[/tex]We cannot apply factoring to the above equation. Therefore, the answer is:
[tex]x^2+x-1=0[/tex]