A rectangular prism with a volume of 101010 cubic units is filled with cubes with side lengths of \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction unit.
How many \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction unit cubes does it take to fill the prism?
Answers
now, we're assuming that the prism has a volume of 10³ and is filled with cubes of sides 1/2 long, Check the picture below.
now notice the bottom-right part of the picture, if we put two small cubes next to each other, they add up to 1, so to get 10 units from that, we'll need 20 of those halves, or 20/2 = 10, meaning we'll need 20 cubes side by side to make a length of 10 horizontally.
The same will be true for getting cubes to make up 10 vertically, we'll need 20, the same is true to fill up from back to front, we'll need 20 cubes.
so we can say that the rectangular prism will need 20 cubes from front to back, 20 horizontally and 20 vertically, that'll be 20*20*20 cubes, or 20³ or 8000 cubes.
mind you that we used a Cube for the prism, but the same will be true if we were to rearrange the cubes and make the prism taller or wider, same 8000 cubes will fill it in.
Related Questions
The table shows the proof of the relationship between the slopes of two parallel lines. What is the missing reason for step 2?
A.
Pythagorean theorem
B.
application of the distance formula
C.
application of the slope formula
D.
transitive property
Answers
The missing reason for step 2 is the application of the slope formula option (C) application of the slope formula is correct.
What is a distance formula?It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
As we know,
Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
From the graph of two parallel lines:
r ║ s
The slope is the ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Thus, the missing reason for step 2 is the application of the slope formula option (C) application of the slope formula is correct.
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a) x+(3x÷2y)
b) (b⁹)²×b⁵÷b¹¹=
c) (4²)⁶×4⁷÷4¹⁶=
Answers
Answer:
a) x+3x/2y or (3x+2xy)/2y
b) b^12
c) 4^3 or 64
Step-by-step explanation:
Solve x2+6x+7=0
A.x=-1 and x=-5.
B. 3+ √2
C.-3+ √2
D. -3+ √2
———-
2
Answers
Answer:
-3+ √3 or -3- √3
Step-by-step explanation:
whats the solution.?
Answers
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(x-4)=0
STEP
1
:
Equation of a Straight Line
1.1 Solve y-x+4 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-x+4 = 0 and calculate its properties
Step-by-step explanation:
Add 4 to both sides
x=-1/5x+6
Add 1/5x to both sides
6/5x=6
Multiply each side by 6/5
X=7.2
2/3 plus 1/4 plzzzzzzzzzzzzzzzzzz
Answers
11/12
Answer:
1. find the least common denominator (LCD) of 2/3, 1/4 in other words, find the Least Common Multiple (LCM) of 3,4
Least Common Multiple (LCM) of 3,4 LCD = 12
Least Common Multiple (LCM) of 3,4 LCD = 122.
Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.
Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.2_x_4_ + _1 x 3__
Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.2_x_4_ + _1 x 3__3 x 4 4x3
Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.2_x_4_ + _1 x 3__3 x 4 4x33. Simplify denominators are Now The Same.
8/12 + 3/12
4. join the denominators
__8+3_____
12
5. Answer 11/12
Btw the Lines are Just For Separating numbers.
Find the values of sin, cosine, and tangent, for
Answers
sin=3/5
cos=4/5
tan=3/4
[tex]sin = \frac{opposite}{hypotenuse} = \frac{3}{5} = 0.6\\\\cos = \frac{adjacent}{hypotenuse} = \frac{4}{5} = 0.66666666666666666666666666666667\\\\tan = \frac{opposite}{adjacent} = \frac{3}{4} = 0.75\\\\hypotenuse = 5[/tex]
HOPE THIS HELPS :)
help :( explain the meaning of -500 in context to the problem,
a plane flies directly from a city in Pennsylvania to a city in Ecuador. the equation below estimates the distance (d), In miles, from the city in Ecuador of the airplane (t) hours after taking off from the city in Pennsylvania
d=2565-500t
Answers
The equation of the distance of the plane from the city in Ecuador is a
linear equation that has a constant rate of change.
The -500 is the rate at which the distance of the plane from Ecuador changes every hour.Reasons:
The equation that estimates the distance of the plane from the city in
Ecuador is d = 2565 - 500·t
Where;
d = The distance in miles from the city in Ecuador
t = The time in hours after taking off from the city in Pennsylvania
Required:
The meaning of -500 in the context of the problem.
Solution:
By using dimensional analysis, we have;
Given that d is in miles and t is in hours, 2,565 is in miles, and 500 × t is in
miles.
Therefore, -500 is in miles per hour, which is the speed of the plane.
The -500 therefore, in the context, is the number of miles, the rate, by
which the plane becomes closer to the city in Ecuador every hour.
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We can analice through a dimensional evaluation, every term in any equation.
Solution is:
The term - 500 × t
represents, the quantity of miles travel in the time t
Looking carefully each term in the equation:
d = 2565 - 500×t
And knowing:
d, is distance in milest, is time in hoursThe fact that, adding and subtracting are mathematical operations with homologous quantities. By homologous quantities we must understand that we add and subtract apples plus or (minus) apples. We never add pencils plus boxesWe are able to answer the question.
Then in the expression
d = 2565 - 500×t
As d is in miles, we must understand that 2565 is the total distance of the trip, also in miles, should and the product -500×t must also be in miles. According to that, the number 500 is necessarily in miles/hours (the speed of the plane), and the negative sign for 500 means that the total distance 2565 miles should be subtracted from the total time of travel.
For instance if t = 1 hour
d = 2565 miles - 500 (miles)/hour × 1 (hour)
As we can see we are able to determine the total time of fly, as the total distance between the cities is 2565, and 500 is the speed of the plane (constant during the whole trip).
For the whole trip
d = 2565 miles then total fly time is:
2565 (miles)/ 500 (miles/hour)×t
To get . t = 5.13 h
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Question 1 (1 point)
Find the measure of the angle marked 4x
Answers
we need the image to solve the problem
Jenny is a great saver! She has $80 in her savings account. She deposits $25 each week into her account. She wants to save at least $300 before she begins to withdraw money from her account. Which of the following inequalities can Jenny use to determine when she can withdraw money from her account?
Answers
Answer:
[tex]80+25x\geq 300[/tex]
Step-by-step explanation:
Since she already has 80$ in the account it will be the starting point.
To those 80$ she adds 25$/w.
Since the amount of week is what needs to be determined we'll refer to it as x.
So far we have 80 + 25x.
Now since she only wants to withdraw once she has at least 300$, it means that the amount has to be either equal to 300 or more than 300.
Which gives us [tex]80+25x\geq 300[/tex]
Part 2: Find the area of each of the given shapes below. If a shape has shading, find the area of the shaded region only. NO LINKS!
Answers
Answer:
b. 256 m²
d. 324 cm²
f. 35 in²
Step-by-step explanation:
b.The shaded area is the difference between the areas of the outer rectangle and the inner one:
A = (24 m)(12 m) -(8 m)(4 m) = 288 m² -32 m² = 256 m²
__
d.The steps are all the same height and width. Their height is (18 cm)/3 = 6 cm, so the height of the middle step is 2×6 cm = 12 cm. The area of the figure will be the product of the base and the average step height:
A = (27 cm)(12 cm) = 324 cm²
You might be able to visualize this as cutting off the top step even with the middle on and placing it on top of the bottom step.
__
f.The triangle area formula applies.
A = 1/2bh = 1/2(4" +10")(5") = 35 in²
_____
Additional comment
The formula for area of a rectangle is ...
A = LW . . . . . the product of length and width
SCO
Sarah put 15 gumdrops on the roof of her
gingerbread house. How many gumdrops
will she need to make 16 more houses
exactly like this one?
MY
gumdrops
Answers
Answer: 240 gumdrops
Step-by-step explanation:
1 house: 15 gumdrops
16 houses : 240 gumdrops
1 x 16 = 16
15 x 16 = 240
Which of the following is equal to 2,952 ÷ 24?
A.
(2,400 ÷ 24) + (480 ÷ 24) + (72 ÷ 24)
B.
(2,400 + 24) ÷ (480 + 24) ÷ (72 + 24)
C.
(2,400 + 24) + (480 + 24) + (72 + 24)
D.
(2,400 ÷ 24) - (480 ÷ 24) - (72 ÷ 24)
Answers
Answer:
A
Step-by-step explanation:
After doing long division we then know that 2,952 ÷24 = 123
We 1st follow pemdas knowing this we solve the equations in parenthesis 1st
(2,400 ÷ 24) + (480 ÷ 24) + (72 ÷ 24)
2,400 ÷ 24 = 100
480 ÷ 24 = 20
72 ÷ 24 = 3
We can then rewrite the equation as
100 + 20 + 3 We then solve left to right
100 + 20 = 120
120 + 3 = 123
A bag contains 42 red,45 green, 20 yellow and 32 purple candies you pick one candy at random find the probability that it is green or yellow
Answers
Answer:
Probability 29%
Step-by-step explanation:
Answer:
65/139
Step-by-step explanation:
Just did this problem
A survey found that in a sample of 75 families, 26 owned dogs. A survey done 15 years ago found that in a sample of 60 families, 26 owned dogs. Find the 95% confidence intervals of the true difference in the proportions.
Answers
The difference in the proportions of both surveys goes from a maximum of 12.57% to a minimum of 4.76%.
Given that a survey found that in a sample of 75 families, 26 owned dogs, while a survey done 15 years ago found that in a sample of 60 families, 26 owned dogs, to find the 95% confidence intervals of the true difference in the proportions, the following calculation must be performed:
75 = 100 26 = X 26 x 100/75 = X 34.66 = X 34.66 x 0.95 = 32.93 34.66 x 1.05 = 36.40 60 = 100 26 = X 26 x 100/60 = X 43.33 = X 43.33 x 0.95 = 41.16 43.33 x 1.05 = 45.50 45.50 - 32.93 = 12.57 41.16 - 36.40 = 4.76
Therefore, the difference in the proportions of both surveys goes from a maximum of 12.57% to a minimum of 4.76%.
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What is the common difference in the sequence below? 9, 2, -5, -12, ......
Select one:
a. -5
b. -6
c. -8
d. -7
Answers
Answer:
-7
Step-by-step explanation:
a=9 a2=2 a3=-5 a4=-12
d = a4-a3 ,a3-a2, a2-a.
so:
d = -12-(-5) =-12+5 =-7
also;
d = -5-2 = -7
and
d= 2-9 =-7
so the common difference is -7
Answer:
-7
Step-by-step explanation:
We know that
Common difference = a2 - a1
=> 9 - 2
=> -7
Ann received a $90 gift card for a coffee store. She used it in buying some coffee that cost $8.04 per pound. After buying the coffee, she had $65.88 left on her
card. How many pounds of coffee did she buy?
pounds
5
?
Answers
Answer:
3 lbs of coffee
Step-by-step explanation:
$90.00 - $65.88 =$24.12 (spent 24.12 on the coffee)
24.12/8.04 = 3
Answer:
3 ponds of Coffee. take what she spent, and subtract it from the total. Then divide that number by the cost of 1 lb. of coffe. You get 3. 3 pounds.
Given the following computer output, select the correct least-squares regression line:
Answers
The correct form of the regression line is [tex]\log time = 0.699 + 0.500\cdot \log length[/tex] (Correct choice: D).
According to the information presented in the figure, we know the following function:
The independent variable is 'length'.The dependent variable is 'time'.The regression line is of the form: [tex]\ln y = A + B\cdot \ln x[/tex].Hence, the correct form of the regression line is:
[tex]\log time = 0.699 + 0.500\cdot \log length[/tex] (Correct choice: D)
The correct form of the regression line is [tex]\log time = 0.699 + 0.500\cdot \log length[/tex] (Correct choice: D).
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Answer:
D: logTime=0.699 + 0.500
Step-by-step explanation:
0.699 is the x value which can be found in data under Coef and Constant. The y value can be found under coef and log(length)
Enter the correct answer in the box. Write your answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign. HELP MEEE ASAPPPP ILL GIVE BRAINLIEST!!!!!!
Answers
Answer:
y > - x - 4
Step-by-step explanation:
1) Find the equation of the line
2) The equation of the line is y = - x - 4
3) Identify where the graph is shaded
4) It is shaded above and to the right of the line
5) This means that it is more positive/ greater than the unshaded areas
6) Switch the = sign to > to signify the inequality
7) All done!
Step-by-step explanation:
the delimiter line is going through the points (-4, 0) and (0, -4).
the line function
y = mx + b
m is the slope of the line, b is the y-intercept (the y value when x = 0).
the slope is the ratio of "y coordinate change / x coordinate change" when going from one point to another.
so, for the 2 found points :
x changes by +4 (from -4 to 0)
y changes by -4 (from 0 to -4).
the slope m is then
-4/+4 = -1
and the y-intercept is -4 (as explained).
so, the line is
y = -x - 4
and the graphic says that all values greater than our equal to the line values are valid, so
y >= -x - 4
Find the values of the variables.
isosceles trapezoid
Side measures are: 4, 2x, 2x + 2 and 4x +3
X=
Answers
Answer:
x=-1/2
Step-by-step explanation:
2x+2=4x+3
-1=2x
x=-1/2
Find the value of k so that (x + 3) is a factor of H(x) = 3x^3 – 2x^2 + kx – 3.
A. 34
B. 20
C. -20
D. -34
E. 32
Answers
Explanation:
3(-3)³ - 2(-3)² + (-3)k - 3 = 0
-81 - 18 - 3k - 3 = 0
3k = -102
k = -34.
Find BC.
А В
С
ош
=
=
AD = 10.5
AB = 2
СЕ = 11.5
AE = 15
BC = [?]
=
Answers
Answer:
8,5
Step-by-step explanation:
BC=AD-AB
BC=10,5-2
BC=8,5
Ryan and Caiden both bought roses from the market. If Ryan paid $174.93 for 7 dozen roses, how much did Caiden pay for 4 dozen roses?
Will give the crown thing
Answers
2.08 x 48 = $99.84
2 years,18 month.express the first quantity as a percentage of the second quantity
Answers
Answer:
2 years= 12 months
12÷18×100= 66.67%( approx)
2) 20cm=200mm
225÷200×100
=112.5%
Step-by-step explanation:
Answer:
2 years= 12 months
12÷18×100= 66.67%( approx)
Step-by-step explanation:
Sin(180-A)/tan(180-A) × cot(90-A)/tan(90+A) × cos(-A)/ cos(270-A) Please solve
Answers
so tan = me sun bathing for 2.5 second
Help help help help help
Answers
Answer:
8
Step-by-step explanation:
The answer is 8 because there are 2 possibilities for each coin you flip heads and tails so if you flip three coins all at once you get 2*2*2, which equals to 8.
I hope this help!
A circle has a radius of 2/2 units and a center at (-5, 1). Which point is located on the circle?
(-3,1)
(-3,2)
(-3,3)
(-3,4)
Answers
Answer:
(-3,1)
Step-by-step explanation:
2/2 x (-5,1)
Then the circle is (-3,1)
Julie goes to the store to buy grapes. Grapes cost $1.09 per pound. Write an equation to help Julie determine the total amount, y, she will pay for a given number of pounds of grapes, x?
Answers
Answer:
y=1.09x
Step-by-step explanation:
helppppppppppppppp me
Answers
Answer:
I think it is A hope this helps
Step-by-step explanation:
The diagonal of an isosceles trapezoid with angle to the base is equal to 30. Find the length of the height of the trapezoid if it is known that the midline of this trapezoid is equal to 8 cm.
Answers
Answer:
4.62 cm to nearest hundredth.
Step-by-step explanation:
If the parallel sides are x and y then:
x + y = 2*8 = 16
x + y = 16
If we drop a perpendicular line from one of the upper points on the trapezoid we have the height. Let the upper point be C and the point on the base be A. Let the point on right of the base be B.
AC is the height of the trapezoid. AB is the baseline of the triangle CAB.
In triangle CAB the angle B is 30 degrees.
As this is a 30-60-90 degree triangle
AC/AB = 1/√3 so AC = AB/ √3.
As the trapezoid is isosceles:
AB = x + 0.5(y - x)
AB = 0.5x + 0.5y
So AC = 1 /√3 (0.5x + 0.5y)
= 1 /√3 (0.5x + 0.5(16 - x)) (Substituting for x)
= 1 /√3 (0.5x + 8 - 0.5x)
=8 / √3
. = 4.6188 cm
Determine the value of x for the following equation: 9(x + 2) = 72
Answers
Divide both sides by 9
x+2=8
Subtract 2 from both sides
x=6
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
So, first we divide the equation by 9 on both sides to get: [tex]\frac{9\left(x+2\right)}{9}=\frac{72}{9}[/tex]
Then, we simplify to get [tex]x+2=8[/tex]
Now, to leave x alone we subtract 2 from both sides ([tex]x+2-2=8-2[/tex]) to get our final answer of [tex]x=6[/tex]
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