The diagram shows a cube with sides of length 8 meters. A smaller cube with
sides of length 3.5 meters has been out out of the larger cube.
a) Find the volume, in cubic centimeters of the large aube before the
small cube is out out. Write your answer in scientific notation
Find the volume of the solid after the small cube is removed. Write your
answer in scientific notation. Round the coefficient to the nearest tenth
Answers
Answer:
a) 512 cm^3
b) 469.125 cm^3
Step-by-step explanation:
8*8*8 = 512 cm^3
or
8^3 = 512 cm^3
3.5^3 = 42.875
512 - 42.875 = 469.125 cm^3
You can round the second answer down
Related Questions
Consider the function g(x) shown below over a domain of [1,∞).
g(x) = 2(x – 1)2 – 3
Part A
Determine g–1(x).
Part B
Identify the domain and range of g(x) and g–1(x). Represent the domains and ranges in inequality, interval, and set notation. Describe the relationship between the domains and ranges of g(x) and g–1(x).
Part C
Graph g(x) and g–1(x). Describe the relationship between the graphs of g(x) and g–1(x).
Answers
The inverse of a function may or may not be a function
The function g(x) is given as:
[tex]g(x) = 2(x - 1)^2 - 3[/tex]
(a) Inverse function g^-1(x)
We have:
[tex]g(x) = 2(x - 1)^2 - 3[/tex]
Replace g(x) with y
[tex]y = 2(x - 1)^2 - 3[/tex]
Swap the positions of x and y
[tex]x = 2(y - 1)^2 - 3[/tex]
Add 3 to both sides
[tex]x + 3 = 2(y - 1)^2[/tex]
Divide both sides by 2
[tex]\frac{x + 3}2 = (y - 1)^2[/tex]
Take square roots of both sides
[tex]\sqrt{\frac{x + 3}2} = y - 1[/tex]
Add 1 to both sides
[tex]1 + \sqrt{\frac{x + 3}2} = y[/tex]
Rewrite as:
[tex]y = 1 + \sqrt{\frac{x + 3}2}[/tex]
Express as inverse function of g
[tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]
Hence, the inverse function of g is [tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]
(b) The domain, and the range of g(x) and g^-1(x)
Function g(x)
The function g(x) is a quadratic function.
So, the domain is:
Inequality: [tex]-\infty < x < \infty[/tex]Interval: [tex](-\infty ,\infty)[/tex]Set: {R}The range is:
Inequality: [tex]f(x) \ge -3[/tex]Interval: [tex][-3 ,\infty)[/tex]Set: [tex]\{y|y\ge -3\}[/tex]Function g^-1(x)
The function g^-1(x) is a square root function.
So, the domain is:
Inequality: [tex]x \ge -3[/tex]Interval: [tex][-3 ,\infty)[/tex]Set: [tex]\{x|x\ge -3\}[/tex]The range is:
Inequality: [tex]-\infty < y < \infty[/tex]Interval: [tex](-\infty ,\infty)[/tex]Set: {R}The domain of g(x) is the range of g^-1(x), while the range of g(x) is the domain of g^-1(x).
(c) The graph
See attachment for the graph
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Help Please 100 pts for the answer! Need answer ASAP
Answers
Answer:
-25/1 or -25
Step-by-step explanation:
Answer:
-25/1 or -25
Step-by-step explanation:
there hope this will help a lot
i need atleast 5 volunteers for the magic trick
Answers
What magic trick??
Are you gonna do a magic??
Sorry for a lot of questions.
A parachutist has made thousands of successful jumps. His assumption is that when he pulls the rip cord, that parachute will open.
What are the null and alternative hypothesis?
Describe a Type I error along with the consequence.
Describe a Type II error along with the consequence.
What is a more serious error in this context? Justify your answer.
Most parachutes have a backup in case the ripcord malfunctions. Does the guard against Type I or Type II errors? Explain.
Suppose you went skydiving and pull the ripcord and it does not function. You have time to pull it again or pull the back up but not both. What would you do?
Answers
The null hypothesis is the one in which any statement which is the claim of the experiment is chosen to decide the results for .
The alternate hypothesis is the opposite of the null hypothesis.
Type I Error: Type I Error occurs when H0 is true but it is rejected and Ha is accepted.
Type II Error: Type II Error occurs when Ha is true but it is rejected and the false null hypothesis H0 is accepted which is wrong decision.
In this case the null hypothesis is
H0: On pulling the rip cord the parachute will open.
Ha: On pulling the rip cord the parachute will not open.
In this experiment the alternate hypothesis Ha :On pulling the rip cord the parachute will not open is accepted then type I error occurs.
In this experiment the null hypothesis H0 :On pulling the rip cord the parachute will not open is accepted then type II error occurs.
In this experiment Type I Error is a more serious error because the true null hypothesis H0: the parachute will open is rejected.
In this experiment Type II Error is a more serious error.
Type I and Type II Errors are independent of the confidence interval.
When the parachute has a backup in case of ripcord malfunctions then the confidence level of the hypothesis can be 100 percent. That is we are 100 percent sure that the parachute will land safely and there will be no accidents.
This is does not guard the type I and type II errors because these are made on the wrong decision.
The null and alternate hypotheses can be understood here
https://brainly.com/question/19132215
https://brainly.com/question/15681523
Type I and II Errors can be understood
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Find DY if PY= 6
and DP= 10.
Answers
The relationship between sides DY, PY and DP is that they form a right-angled triangle.
The value of side length DY is 8 units
Side length DY can be calculated using the following Pythagoras theorem.
So, we have:
[tex]DP^2 =DY^2 + PY^2[/tex]
Substitute values for DP, DY and PY
[tex]10^2 =DY^2 + 6^2[/tex]
Evaluate the squares
[tex]100 =DY^2 + 36[/tex]
Subtract 36 from both sides
[tex]64 =DY^2[/tex]
Take square roots of both sides
[tex]8 =DY[/tex]
Rewrite as:
[tex]DY = 8[/tex]
Hence, the value of side length DY is 8 units
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Find the greatest common factor and the least common multiple of 16 and 20. The prime factorizations of each number are given.
.
Answers
Answer:
GCF 4, LCM 80
Step-by-step explanation:
Since both 16 and 20 have two 2s as factor, their greatest common factor is 4.
The LCM is found by multiplying all of the remaining factors by the LCM:
16 still has (2 x 2), 20 still has (5), times the GCF (4) so 2 x 2 x 5 x 4 = 80.
What is 2/3, 7/6, 3 1/9, and 5 5/18 written as a decimal?
Please give an explanation and a correct answer!
I will give brainliest to whoever answers first!
Answers
Step-by-step explanation:
[tex] \frac{2}{3} = 2 \times \frac{1}{3} = 2 \times 0.333 = 0.666 \\ \\ \frac{7}{6} = 7 \times \frac{1}{6} = 7 \times \frac{1}{2} \times \frac{1}{3} = 7 \times 0.5 \times 0.333 = 1.1655 \\ \\ 3 \frac{1}{9} = 3 + \frac{1}{9} = 3 + ( \frac{1}{3} \times \frac{1}{ 3} ) = 3 + (0.333 \times 0.333) = 3 \times 0.11088 = 3.11088 \\ \\ 5 \frac{5}{18} = 5 + (5 \times \frac{1}{18} ) = 5 + (5 \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{2} ) = 5 +(5 \times 0.333 \times 0.333 \times 0.5) = 5 + 0.27722 = 5.27722[/tex]
estimate quotients using compatible numbers lesson 4.5 answer key
Answers
4 its the correct answer do it
Step-by-step explanation:
its correct
Need help ASAP!!!!!!
Answers
Answer:
graph b
Step-by-step explanation:
Please help me solve this. warning: an equation may have no solution, one solution or more than one solution.
5x-13=2x-9-4+3x
Answers
I got the answer and steps for this math problem,
Answer:
[tex]5 \times - 13 = 2 \times - 9 - 4 + 3 \times \\[/tex]
= 1 5/9 or 1 .5555556.
Step-by-step explanation:
Please comment if I'm
wrong...
A function f(x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box below.
f(x) = ____
Answers
Answer:
mx+b
Step-by-step explanation:
One way to express linear function rules is called slope-intercept form. Sometimes, f(x)=mx+b is used. In either case, m and b describe the general characteristics of the line. m indicates the slope, and b indicates the y-intercept.
The required function of the line would be y = 2x + 1 which is shown in the given graph.
What is the function rule in slope-intercept form?The slope-intercept form is one rule to represent linear function rules. f(x)=mx+b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.
According to the given figure,
We clearly see that the coordinates of the y-intercept would be (0, 1).
The value of the x-coordinate is 1 when y-coordinate is 3.
Here the line passes through points (0, 1) and (1, 3).
Let the required linear function would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]
x₁ = 0, y₁ = 1
x₂ = 1, y₂ = 3
⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]
⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]
⇒ y - 3 = (2)[x -1]
⇒ y - 3 = 2x - 2
⇒ y = 2x - 2 + 3
⇒ y = 2x + 1
Therefore, the required function of the line would be y = 2x + 1 which is shown in the given graph.
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simplify as much as possible please u get 50 points thank you
Answers
-8 -8
28 = 4y
/4 /4
7 = y
y = 7
Answer:
y = 7
Step-1: Subtract 8 both sides
⇒ [tex]36 = 4y + 8[/tex]
⇒ [tex]36 - 8 = 4y + 8 - 8[/tex]
⇒ [tex]28 = 4y[/tex]
Step-2: Divide 4 both sides
⇒ [tex]28 = 4y[/tex]
⇒ [tex]\frac{28}{4} = \frac{4y}{4}[/tex]
⇒ [tex]7 = y[/tex]
pls help on my maths question
Answers
Answer:
Somewhat illegible but looks like the equation should be:
S = u t + 1/2 a t^2
100 = 20 + 1/2 * a * 4 where t = 2
a* 4 = 160
a = 40
Ralph is on a diet. He currently weighs 248
pounds. How many pounds would he need
to lose if he wishes to weigh at most 195
pounds?
Answers
Answer:
53
Step-by-step explanation:
248-195 is 53
you should take his weight and then subtract the amount he wants to weigh
Answer:
53 pounds
Step-by-step explanation:
248 minus 195 which gives you 53
He needs to lose 53 pounds.
Hope that helped!
An airplane is 280 feet long. Charlie makes a scale model of the airplane at 1:140 of its actual size. How long is the model?
Answers
Answer:
2 feet long
Step-by-step explanation:
Which of the following is equivalent to the expression below? (2^5)(2^6)
(A) 2^11
(B) 2^30
(C) 4^11
(D) 4^30
Answers
Answer:
(A) 2^11
Step-by-step explanation:
helppppppppppppppppppppppppppppppppppppppp
Answers
show that
[tex] \frac{2}{3 + \sqrt{7} } = 3 - \sqrt{7} [/tex]
I don't know what to do
please help with the steps.
for brainliest
Answers
Answer:
multiply by (3-√7)/(3 -√7) and simplify
Step-by-step explanation:
When there are radicals or complex numbers in the denominator, you can rewrite the expression so it has a real, rational denominator. You do this by multiplying numerator and denominator by the conjugate of the denominator. That value is the denominator with its sign changed.
This takes advantage of the factoring of the difference of squares.
(a -b)(a +b) = a² -b²
__
[tex]\dfrac{2}{3+\sqrt{7}}=\dfrac{2}{3+\sqrt{7}}\times\dfrac{3-\sqrt{7}}{3-\sqrt{7}}=\dfrac{2(3-\sqrt{7})}{3^2-(\sqrt{7})^2}=\dfrac{2}{9-7}\times(3-\sqrt{7})\\\\=\boxed{3-\sqrt{7}}[/tex]
if we changed the –0.14 to a 2 in the equation, what would happen to the graph?
Answers
If -0.14 is changed to 2, the graph would become a positive graph, or it would be steeper, because it has a positive slope
The equation of the graph is given as:
[tex]y = -0.14x + 3[/tex]
The above equation is a linear equation, which is represented as:
[tex]y =mx + c[/tex]
Where m represents the slope of the linear equation.
By comparison, we have:
[tex]m = -0.14[/tex]
i.e. the slope of the equation [tex]y = -0.14x + 3[/tex] is -0.14
When -0.14 is replaced with 2, the equation becomes
[tex]y = 2x + 3[/tex]
And the slope of the new equation [tex]y = 2x + 3[/tex] is
[tex]m =2[/tex]
2 is greater than -0.14, and 2 is positive.
This means that the graph would become a positive graph, or it would be steeper, because it has a positive slope
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3. Rich has t dollars in his checking account. On June 3, he deposited
w, h, and v dollars, and cashed a check for k dollars. Write an alge-
braic expression that represents the amount of money in his account
after the transactions.
Answers
b = his end total after the transactions
Roberto is a fan of the Los Angeles Angels baseball team. Since he works at night he only
goes to day games. Last year he attended all 16 home day games and saw his team win 11
and lose only 5 games, for a winning percentage of 68.8%. In their other games the team won
69 and lost 77, for a winning percentage of 47.3%.
Even though the p-value for a test
comparing these winning percentages is very small, explain how confounding prevents us
from concluding that Roberto’s attendance at those games is the cause of the Angels success
in those games.
Answers
Step-by-step explanation:
There are other factors than Roberto coming that could have affected the outcome of the game. For example, maybe the night games were against better teams to generate better ratings in prime time. Moreover, maybe the Angels do better at home due to home-field advantage. There are many factors such as these that could explain why Roberto witnessed such a high win rate at the games he went to, so it cannot be concluded that Roberto's attendance caused the Angels to win.
One week Culver earned $375.50 regular pay and $65.50 overtime pay. His net pay for the week was $230.90. How much did he have withheld for deductions?
Answers
Answer:
He had $210.1 after deductions.
Step-by-step explanation:
Add his regular pay and overtime pay together
$375.50 + $65.50 = $441
Now subtract his net pay from the total that he makes before deductions - with his overtime and regular pay.
$441 - $230.90 = $210.1
In \triangle KLM,△KLM, \overline{KL}\cong \overline{MK} KL ≅ MK and \text{m}\angle M = 43^{\circ}.m∠M=43 ∘ . Find \text{m}\angle L.m∠L.
Answers
Based on the definition of an isosceles triangle, the measure of angle L is: 43°
Recall:
An isosceles triangle has two side lengths that are equal in size, and also the angles opposite the equal sides are congruent.Given that KL ≅ MK in △KLM, it means △KLM is an isosceles triangle.
If m∠M = 43°, therefore, m∠M = m∠L (equal angles directly opposite KL and MK).
This implies that: m∠L = 43°
In summary, based on the definition of an isosceles triangle, the measure of angle L is: 43°
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what is (2i)^2? and is it a real or imaginary number?
Answers
Answer:
4i
Step-by-step explanation:
Distribute the 2, you get 4i.
It's imaginary because it has an i with it
Answer:
-4, real
Step-by-step explanation:
Hi there!
‘i’ is characterized as the sqrt of -1 or, alternatively, i^2= -1
If the problem is asking us to square i, then we know that it is going to equal -1. If we distribute the exponent, we would also square the 2, making it become 4. Now that we have done that, we multiply -1 and 4 to get a final answer of -4. This would be a real number as it is not imaginary.
I hope this can help!
Using ruler and compasses only, construct a parallelogram KLMN, so that KL = 8 cm, LM = 6 cm and angle KLM = 135°.
Answers
The steps to construct a parallelogram using a ruler and a compass are;
1. Draw a starting line segment l linger than 8 cm.
2. Mark point K on the line segment.
3. Widen the compass to a radius of 8 cm using the ruler.
4. Place the compass at point K and with the 8 cm radius mark point L on the line l.
5. At point L construct a 45° angle as follows;
Draw arcs that intersect line l on both sides of point L.From each of the intersection points, draw arcs that intersect each other on on the upper area adjacent to line l.From the intersection point in the previous step, draw a line to point L to get a perpendicular line to line l.Draw arcs to intersect the perpendicular line and line l on the other side of point L from K.From the points the arc intersects the perpendicular line draw arcs of the same radius to intersect at a point X to the right of the perpendicular line.The above steps bisects the 90° angle of the perpendicular lines.
Join point X to point L with a straight line to form ∠XLM = 135° (90° + 45° = 135°)6. Adjust the radius of the compass to give an opening of 6 cm and from point L draw an arc to intersect XL at M.
7. At point M construct a line YM at 45° angle to the line l.
8. From point M draw an arc to intersect YM and label the point as point N.
9. Join point M and N to complete the construction of the parallelogram KLMN.
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Is x+2y=6
2x-3y=26
have no solution,one solution, or infinity many solution
Answers
Answer:
1
Step-by-step explanation:
x + 2y = 6, multiply by 2 = 2x + 4y = 12
2nd equation: 2x - 3y = 26
It has one solution
Answer: One solution
Step-by-step explanation:
Convert both equations into slope-intercept form:
x+2y=6
2y=6-x
[tex]y=\frac{6-x}{2}[/tex]
Slope = 6/2 = 3
2x-3y=26
y=2x-26/3
Slope = 2/3
Therefore, he system of equations have one solution because their slopes are not equal.
A number is les than or equal to -11
Answers
Answer:
-12 is the answer for this question
Step-by-step explanation:
make me as brainlist
Answer:
[tex]x\leq-11[/tex]
Step-by-step explanation:
What is the smallest integer $k>2000$ such that both $\dfrac{17k}{66}$ and $\dfrac{13k}{105}$ are terminating decimals?.
Answers
The smallest integer greater than 2000 for both the fractions [tex]\frac{17k}{66} \ and \ \frac{13k}{105}[/tex] to be terminating decimals is 2079.
GivenK is greater than 2000.
[tex]k> 2000\\[/tex].
Given fractions are
[tex]\dfrac{17k}{66} \ and \ \dfrac{13k}{105}[/tex].
How to find the smallest integer greater than 2000 for the fractions to be terminating decimals?In order for the decimal equivalents to be terminating, the only factors that can remain in the denominators are 2 and 5.
Here, the given denominators are 66 and 105 respectively.
Now factors of 66 will be 2,3,11.
And the factors of 105 will be 3,5,7.
So, the value of k must be multiples of 3, 7, and 11. The LCM of these numbers will be,
[tex]3\times 7\times 11=231[/tex]
Now the value of K must be greater than 2000, so the multiple of 231 which is greater than 2000 is its [tex]9^{th}[/tex] multiple,
[tex]231\times9=2079[/tex]
Hence 2079 is the smallest integer greater than 2000 for both the fractions [tex]\frac{17k}{66} \ and \ \frac{13k}{105}[/tex] to be terminating decimals.
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I need help plz asp
Answers
9
Step-by-step explanation:
woody is 5
buzz is 3
mr potato head is 3
rex is 7
alien is 1
A rental car company charges $35 per day to rent a car and $0.15 for every mile driven. Enola wants to rent a car, knowing that:
She plans to drive 450 miles.
She has at most $260 to spend.
Write and solve an inequality which can be used to determine xx, the number of days Enola can afford to rent while staying within her budget.
Answers
Answer:
260≤67.5+35x
Step-by-step explanation: