Answers
The volume of blocks = 27n³cm3.
volume of the cube box = 216n⁹ cm3.
Solution:Here given,
6n³cm is the length of the cube-shaped box's side.
3n cm is the side length of the cube-shaped blocks.
We must calculate the volume of the box and the blocks.
The formula for cube volume is,
S³ = V
where s is the cube's side length
by substituting the values,
(6n³)³ cm3 box volume
= 216 n⁹ cm³
(3n)³ cm3 is the volume of the blocks.
= 27n³ cm³
As a result, the volume of the blocks is 27n³cm3 and the volume of the box is 216 n⁹ cm³.
To learn more about volume of cube refer to :
https://brainly.com/question/19891526
#SPJ13
Answer:
A) Volume of one block = 27n³ cm³
Volume of the box = 216n⁹ cm³
B) 8n⁶ blocks will fit in one box.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cube}\\\\$V=s^3$\\\\where:\\ \phantom{ww}$\bullet$ $V$ is the volume. \\\phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}[/tex]
Part AThe side length of the cube-shaped block is 3n cm.
Substitute the given side length into the formula to find the volume of the block:
[tex]\begin{aligned}\implies \textsf{Volume of one block}&=(3n)^3\\&=3^3 \cdot n^3\\&=27n^3\;\sf cm^3\end{aligned}[/tex]
The side length of the cube-shaped box is 6n³ cm.
Substitute the given side length into the formula to find the volume of the box:
[tex]\begin{aligned}\implies \textsf{Volume of one box}&=(6n^3)^3\\&=6^3 \cdot (n^3)^3\\&=216n^9\; \sf cm^3\end{aligned}[/tex]
Part BTo find the number of blocks that will fit in the box, divide the volume of the box by the volume of one block:
[tex]\begin{aligned}\implies \textsf{Number of blocks}&=\dfrac{\textsf{Volume of box}}{\textsf{Volume of block}}\\\\& = \dfrac{216n^9}{27n^3}\\\\&=\dfrac{216}{27} \cdot \dfrac{n^9}{n^3}\\\\&=8 \cdot n^{9-3}\\\\&=8n^6\end{aligned}[/tex]
Related Questions
in the diagram below , the measure of arc SQ is 160 degrees and the measure of arc PR is 102 degrees . find the value of x .
Answers
Given:
The measure of angle of arrc SQ is 160°.
The measure of angle of arc PR is 102°.
The objective is to find the measure of angle x.
Since, the angle x is away from te center of the circle.
Then, the formula to find the value of angle x is,
[tex]x=\frac{PR+SQ}{2}[/tex]Now, substitute the given values in the above formula.
[tex]\begin{gathered} x=\frac{102+160}{2} \\ =\frac{262}{2} \\ =131\degree \end{gathered}[/tex]Hence, the value of x is 131°.
Can someone please help answer the attached?
Answers
The variables we need to use in the question are defined. We will call the price of a knife as [tex]k[/tex] and the price of a spoon as [tex]s[/tex].
The total price of [tex]12[/tex] spoons and [tex]16[/tex] knives is then given. Let's write knives instead of [tex]4[/tex] spoons.
[tex]12s+16k=105.64[/tex][tex]3k+16k=105.64[/tex][tex]k=5.56[/tex] per knife.===================================================
Explanation:
k = cost of one knife
s = cost of one spoon
costs are in pounds
12s = cost of 12 spoons
16k = cost of 16 knives
12s+16k = 105.64 pounds is the total cost
We can replace k with 4s because of the phrasing "a knife is 4 times the cost of a spoon". Whatever s might be, quadruple it and it leads us to the value of k.
So,
12s+16k = 105.64
12s+16(4s) = 105.64
12s+64s = 105.64
76s = 105.64
s = 105.64/76
s = 1.39 pounds is the cost of one spoon
k = 4s = 4*1.39 = 5.56 pounds is the cost of one knife
----------------------
Check:
1 spoon = 1.39 pounds
12 spoons = 12*1.39 = 16.68 pounds
1 knife = 5.56 pounds
16 knives = 16*5.56 = 88.96 pounds
12 spoons + 16 knives = 16.68+88.96 = 105.64 pounds total
This fully verifies the answer.
find the missing fraction 1/2+ blank=7/8
Answers
To solve this problem we change the structure from
1/2 + ? = 7/8
to
7/8 - 1/2 = ?
Now we need to subtract the fractions and find the difference. To do this, make the denominators (the bottom numbers on the fractions) the same.
1/2 = 4/8
then subtracts the numerator
7/8 - 4/8 = 3/8
there is your answer... 3/8
Vince and Wendy share $2000 in the ratio Vince : Wendy = 19 : 21. Calculate the amount of money that Vince receives
Answers
workout:
19+21=40
2000÷40=50
Vince=50×19=950
Wendy=50×21=1050
-u can check by adding 950+1050=2000 (which means the ratio is correct)
Answer:
(vince:wendy)= 950:1050
Answer:
V:W
19:21
19 + 21 = 40
19 over 40 × 200
Vince received $950
The midpoint of AB is M(0, -7). If the coordinates of A are (-2,-6), what arethe coordinates of B?Answer:Submit AnswerPASSA
Answers
Explanation:
The coordinates are given below are
[tex]\begin{gathered} A(-2,-6) \\ M(0,-7) \\ B=(x,y) \end{gathered}[/tex]The image is given below as
To calculate the coordinate of A,we will use the formula below
[tex]M=\frac{(x_1+x_2}{2},\frac{y_1+y_1}{2})[/tex]By substituting the values, we will have
[tex]\begin{gathered} M=\frac{x_1+x_2}{2},\frac{y_{1}+y_{1}}{2} \\ (0,-7)=\frac{-2+x)}{2},(\frac{-6+y}{2}) \\ \frac{-2+x}{2}=0,\frac{6+y}{2}=-7 \\ -2+x=0,6+y=-14 \\ x=2,y=-14+6 \\ x=2,y=-8 \end{gathered}[/tex]Hence,
The coordinate of B will be
[tex]B=(2,-8)[/tex]The function g(x) is defined as g(x) = -2x^2 - 4x + 2 The value of g(-3)
Answers
There are 125 people in a sport centre.
59 people use the gym.
70 people use the swimming pool.
55 people use the track.
25 people use the gym and the pool.
30 people use the pool and the track.
17 people use the gym and the track.
6 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
Answers
Probability that the person selected at random from the sport centre of 125 people is a fraction of 1/4 or 0.25.
Probability of an eventThe probability of an event is the fraction of the required number of outcome divided by the number of possible outcomes.
We shall determine the answer to the question as follows;
People in the sport centre = 125
People who used the 3 facilities = 6
People who accessed only gym = 59 - (6 + 11 + 19) = 26
People who accessed only track event = 55 - (6 + 11 + 24) = 14
People who accessed only swimming pool event = 70 - (6 + 19 + 24) = 21
People who accessed only gym and swimming pool events = 29 - 6 = 19
People who accessed only gym and track events = 17 - 6 = 11
People who accessed only swimming pool and track events = 30 - 6 = 24
Total number of people who accessed at least any one of the facilities = 121
The number of people who did not access any of the facility = 125 - 121 = 4, which is the number of possible outcomes for our required outcome.
Therefore, the probability that the person selected doesn't use any facility = 1/4
Learn more about probability here: https://brainly.com/question/25870256
#SPJ1
Find the area of ABC with verticles A(4,-3), B(9,-3) and C(10,-11)
Answers
Answer:
Step-by-step explanation:
The area of the triangle when the vertices of the triangle are given can be calculated by the following formula:
Area of triangle = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)| where the vertices are A(Ax, Ay), B(Bx, By), C(Cx, Cy)
Now, we have been given the values of vertices as A(4, -3) B(9,-3) , and C(10, −11)
Therefore,
By applying the formula and substituting the given values, we get
Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|
Area = 0.5 * |44|
Area = 22
Hence, the area of triangle ABC with the given vertices is 22 square units
To know more about the areas of triangle visit the link:
https://brainly.com/question/24207603
what is the formula to find the circumference of a circle?
Answers
Answer:
C = 2 \pi r
Step-by-step explanation:
A function is a fifth-degree polynomial. how many turning points can it have? exactly four exactly five four or less five or less
Answers
A fifth-degree polynomial function can have five turning points in its graph.
What is a quintic function?In other terms, a polynomial of degree 5 defines a quintic function. When graphed, normal quintic functions resemble normal cubic functions since they have an odd degree, with the possible exception that they might contain an extra local maximum and/or local minimum. 9x5– 2x + 3x4– 2 – A leading term to the fifth degree and a term to the fourth degree are both included in this four-term polynomial. It is known as a polynomial of fifth degree.The given polynomial must be factored as much as feasible in order to solve a polynomial equation of degree 5. We can solve for the variable after factoring by equating factors to zero.Examples of polynomials with degrees include the following: The degree of the polynomial 5x5+4x2-4x+3 is 5To learn more about quintic functions, refer
https://brainly.com/question/12700460
#SPJ4
Answer:
The correct is answer is option C: "four or less"
The answers to the next part of the question on Edge are options A and C :)
Step-by-step explanation:
Hope this helped!
Brainliest would be greatly appreciated - Have a great day :3
Solve the following equation: 5(n + 2) = 3(1 + 2n)
Answers
Answer: n=7
Step-by-step explanation:
First distribute the numbers to get 5n+10=3+6n
Next Subtract 6n from both sides to get -n=10=3
Finally divide both sides my -1 to get rid of the -n to get n=7
Hope this helps :)
what is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean? reducing the process standard deviation causes a - select your answer - in the number of defects.
Answers
A low standard deviation implies that the data exists grouped around the mean, whereas a large standard deviation indicates that the data exists more dispersed.
What is meant by standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data exists grouped around the mean, whereas a large standard deviation indicates that the data exists more dispersed.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Because it aids in comprehending measurements when the data is scattered, standard deviation is significant. The standard deviation of the data will be higher the more evenly dispersed the data is.
To learn more about standard deviation refer to;
https://brainly.com/question/475676
#SPJ4
Please help, i really need help
Answers
Answer: m<1 = 146 degrees, m<3 =146 degrees, m<4 = 34 degrees
Step-by-step explanation:
Since m<2 and m<4 are vertical angles, they will be equal to each other.
By using straight lines, we can easily find out that m<1 = 180-34 = 146
Since m<1 and m<3 are vertical angles, they are equal to each other.
Hope this helped :))
Angle 1: is 146 degrees. Since angle 4 and angle 1 are linear angles they are equal to 180. So subtract 180 and 34 to get 146
Angle 3: is 146 because angles 1 and 3 are vertical and congruent.
Hope this helps :)
Please help this is urgent your effort is appreciated
Answers
Answer:
3
Step-by-step explanation:
Door prizes for entrants in a young inventors competition are $100, $50, $25 and $10. In how many ways can the door prizes be awarded if there are 23 entrants?.
Answers
The total number of ways the prizes are awarded is 8855.
The prizes for entrants in a young inventors competition are $100, $50, $25, and $10.
Which are of total 4 types of prizes.
If there are 23 entrants in the competition the prizes can be awarded in the following ways by using Combinations.
Total number of ways = ²³C₄
= [tex]\frac{23!}{4! * (23 - 4)!}[/tex]
= 8855
The total number of ways the prizes are awarded is 8855.
To learn more about Combinations click here:
https://brainly.com/question/13387529
#SPJ4
If α and β are the roots of the equation ax2+bx+c=0,αβ=4ax2+bx+c=0,αβ=4 and a,b,,c are in A. P then α+β=
Answers
Considering the sum and the product of the roots of the quadratic equation, it is found that the numeric value of the expression is given as follows:
[tex]\alpha + \beta = -2.5[/tex]
What are the sum and the product of the roots of a quadratic equation?A quadratic equation is defined as follows:
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
The roots of the equation are given as follows:
[tex]\alpha, \beta[/tex]
The sum of the roots is given as follows:
[tex]\alpha + \beta = -\frac{b}{a}[/tex]
The product of the roots is given as follows:
[tex]\alpha\beta = \frac{c}{a}[/tex]
In the context of this problem, the product is of 4, as [tex]\alpha\beta = 4[/tex] hence:
c/a = 4
c = 4a.
The coefficients are in an arithmetic progression, hence:
b = a + d. (d is the common difference of the sequence).c = a + 2d.We have that c = 4a, hence:
4a = a + 2d
2d = 3a
d = 1.5a.
Hence coefficient b is calculated as follows:
b = a + d = a + 1.5a = 2.5a.
Then the sum of the roots is given as follows:
[tex]\alpha + \beta = -\frac{b}{a} = -\frac{2.5a}{a} = -2.5[/tex]
More can be learned about quadratic equations at https://brainly.com/question/24737967
#SPJ1
Your mom Paid $8 for 10 Granny Smithapples and bought 15 Golden Delicious at60 cents an apple. What is her average costper apple?
Answers
First, let's find the total cost of all the apples:
[tex]8+(0.6\cdot15)=17[/tex]Now, we divide this by the total amount of apples bought. In our case, we know that there were 10 Granny Smith apples and 15 Golden Delicious, for a total of 25 apples.
[tex]\frac{17}{25}\rightarrow0.68[/tex]Therfore, we can conclude that the average cost per apple was $0.68
Sean weighs 10 lb more than twice Brad’s weight. If Brad gains 10 lb, together they will weigh 230 lb. How much does each weight now?
Answers
Using equations the weight of both Sean and Brad is 156 lbs and 73 lbs.
What do we mean by equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.as in 3x + 5 = 15, for example.There are many different types of equations, including linear, quadratic, cubic, and others.The three primary forms of linear equations are point-slope, standard, and slope-intercept.
So, the weight of Sean and Brad.
Let, Brad, be 'x'.Then Sean be '2x + 10'So, the equation will become:
x + 2x + 10 = 230
Now, solve this equation for 'x' as follows:
x + 2x + 10 = 2303x = 230 - 103x = 220x = 220/3x = 73.33Rounding off: 73 lbs
Then,
Brad weights ⇒ 73 lbsSean weights ⇒ 2(73) + 10 = 156 lbsTherefore, using equations the weight of both Sean and Brad is 156 lbs and 73 lbs.
Know more about equations here:
brainly.com/question/28937794
#SPJ13
what do you divide by 15 to get to 9
Answers
Answer:
aproamitly 1.66666666667
Step-by-step explanation: 15/9=1.66666666667 thus
15/1.66666666667=9
Answer: it's 135 the other dude used a calculator probs
Alysa buys 23 boxes of toothpicks. There are 255 toothpicks in each box. Which equation and solution show the number toothpicks, t, in all the boxes?
Answers
Answer:
255 ^t because the amount if toothpicks depend on the number of boxes she/he gets.
Which of the following statements is true about the graph shown?
The equation y = 4.5x is correctly represented by the graph.
The graph is incorrect and the line should go through the point (3, 13.5).
The graph is incorrect and the line should go through the point (4.5, 4.5).
The graph does not show a proportional relationship
Answers
Answer: A
Step-by-step explanation:
Which graph shows the line y-4-2(x+1)?
Answers
(Just for extra information;
slope: 2
Y-intercept: (0,6)
X | Y
——
0 | 6
1 | 8
NEEED HELP PLSSSS . Find x in triangles Geometry.
Answers
Answer:
10) x = 76,12) x = 8, Perimeter = 77 units=========================
Question 10The triangle is isosceles as marked.
The two opposite angles of equal sides are equal, one of them is x and the angle in between them is 28°.
Use angle sum of the triangle:
2x + 28 = 1802x = 152x = 76Question 12Same as previous question, we have an isosceles triangle. Equal sides are:
3x + 5 = 5x - 115x - 3x = 5 + 112x = 16x = 8Find the perimeter by substituting the value of x:
P = 3*8 + 5 + 5*8 - 11 + 2*8 + 3 = 77 unitssomeone please help me!!!
Answers
Im going to answer for the first one.So angles 1 and 2 are corresponding angles and so they are equal because line k and line p and parellel
Find the inverse of the given function.
5. f= {(1,3), (2,-5), (3,6)}
Answers
Check the picture below.
A survey was given to people who own a sertain car. What percent of the people surveyed were completely satisfied with the car
Answers
The percent of the people surveyed were completely satisfied with the car is 55%.
How to calculate the percentage?Number of people completely satisfied = 1155
Number of people somewhat satisfied = 755
Number of people not satisfied = 190
Total number of people = 1155 + 755 + 190 = 2100
Therefore, the percent of the people surveyed were completely satisfied with the car will be:
= Number of people completely satisfied / Total number of people × 100
= 1155 / 2100 × 100
= 55%
Learn more about percentage on:
brainly.com/question/24304697
#SPJ1
4.74 do you own a tablet? a study20 conducted in june 2015 examines ownership of tablet computers by us adults. a random sample of 959 people were surveyed, and we are told that 197 of the 455 men own a tablet and 235 of the 504 women own a tablet. we want to test whether the survey results provide evidence of a difference in the proportion owning a tablet between men and women. state the null and alternative hypotheses, and define the parameters. give the notation and value of the sample statistic. in the sample, which group has higher tablet ownership: men or women? use statkey or other technology to find the p-value.
Answers
Null hypothesis, [tex]H_{0}[/tex] P.1 = P2 (The proportion of tablets owned by men and women are equal.)
Alternative hypothesis,[tex]H_{0}[/tex] P1[tex]\neq[/tex]P2 (The proportion of tablets owned by men and women are not equal.)
Sample proportion for men who own tablets ≈0.433
Sample proportion for women who own tablets ≈0.466
p value of the test is 0.3320.
Test whether the survey results provide evidence of a difference in the proportion owning a tablet between men and women.
Let p, be the proportion of all men who own tablets and p, be the proportion of all women who own tablets.
Null hypothesis, [tex]H_{0}[/tex] P.1 = P2 (The proportion of tablets owned by men and women are equal.)
Alternative hypothesis,[tex]H_{0}[/tex] P1[tex]\neq[/tex]P2 (The proportion of tablets owned by men and women are not equal.)
The notations for the sample statistic are p p1 p2
Pooled proportion p = [tex]\frac{x_{1}+x_{2} }{n_{1}+n_{2} }[/tex]= 197+235/455+504
≈ 0.45
Sample proportion for men who own tablets,
p1 = [tex]\frac{x_{1} }{n_{1} }[/tex]= 197/455
≈0.433
Sample proportion for women who own tablets,
p2 = [tex]\frac{x_{2} }{n_{2} }[/tex] = 235/506
≈0.466
Since p1<p2 women group has higher tablet ownership.
Sample statistic, p1-p2
= 0.433-0.466
p value of the test is 0.3320.
What is Null hypothesis?In mathematics, statistics deals with the study of surveys and reports of numerical data. For questions, we need to define a hypothesis. In general, there are two types of hypotheses. One is the null hypothesis and the other is the alternative hypothesis.
In probability and statistics, the null hypothesis is the general statement or default state that zero or nothing will happen. For example, there is no association between groups or no association between two measured events. Here, a hypothesis is generally assumed to be true until other evidence is presented to disprove the hypothesis.
To learn more about null hypothesis, refer;
https://brainly.com/question/19263925
#SPJ4
How many cups will stack to the top of the door frame?
Explain why...
Answers
Answer:
157 cups
Step-by-step explanation:
First, convert in to cm
83.375 in * 2.54 Cm/in = 211.77 cm
Each cup adds 1.3 cm to the (9.2 - 1.3 cm) base (Base is 7.9)
211.77 = 7.9 + 1.3 x X is the number of cups
X = 156.9 = ~ 157 cups
Find the measure of
Answers
Answer: ∠BDG = 50°
Step-by-step explanation:
We know that a straight line is equal to 180°, meaning that line CDF is 180°.
Next, we know that angle CDB, angle BDG, and angle GDF should all add up to be 180°, since we know CDF is equal to 180°.
Lastly, with all this information in mind, we will set up an equation and solve.
130° + BDG = 180°
∠BDG = 50°
a ladder 10 feet long rests against a vertical wall. let be the angle between the top of the ladder and the wall, and let be the distance from the bottom of the ladder to the wall. if the bottom of the ladder slides away from the wall, how fast does change with respect to when ?
Answers
Rate of change of x with respect to [tex]\alpha[/tex] when [tex]\alpha =\frac{\pi }{3}[/tex] is 5ft/s.
Since the ladder is 10ft long resting against a vertical wall.
Let the angle between the top of the ladder and the wall is [tex]\alpha[/tex] .
And let the distance from the bottom of the ladder to the wall is x.
Thus we need to find the rate of change of x with respect to [tex]\alpha[/tex] when [tex]\alpha =\frac{\pi }{3}[/tex]
Consider L to be the length of the ladder.
Then, L = 10ft
Thus, we get the relation between the angle and distance x i.e.
x = L [tex]\sin \alpha[/tex]
On differentiating the above equation,
[tex]\frac{dx}{dt} =L \cos \alpha[/tex]
Now after putting the values [tex]\alpha =\frac{\pi }{3}[/tex] in above equation, we get,
[tex]=(10)\cos(\frac{\pi }{3} )=(10)(\frac{1}{2} )=5[/tex]
Therefore, [tex]\frac{dx}{dt} =5[/tex] ft/s
To learn more about differentiation visit:
https://brainly.com/question/954654
#SPJ4