Step-by-step explanation:
Hello!!!
Let's workout with this figure.
BC is a chord, O is the centre and OA is the perpendicular bisector.
AB = 1/2 of BC (according to circle's theorem)
so, A B = 1/2 × 25.6
Therefore, the measure of AB is 12.8.
now, let's have a small work with triangle AOB.
as it is a Right angled triangle, taking angle B as refrence angle we get,
p=x
b=12.8
h= OB = 16 (it is also a radius.)
now,
by Pythagoras relation we get,
[tex]p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]
or, x = root 16^2- 12.8 ^2
by simplification, we get;
the measure of x is 9.6.
Therefore, the value of x is 9.6.
Hope it helps...
Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. Does the situation involve permutations, combinations, or neither? Choose the correct answer below. A. B. C. Neither. A line of people is neither an ordered arrangement of objects, nor a selection of objects from a group of objects.
Answer:
C. Neither
Step-by-step explanation:
The permutation is a selection of objects from a given sample in an ordered manner .
The combination is a selection of objects from a given sample irrespective of an order of arrangement.
The given line of people is neither an ordered arrangement of objects, nor a selection of objects from a group of objects So it fits neither of the combinations or permutations.
So the best answer is neither.
(-1, 4) and (-2, 2).
Answer:
Slope : 2
slope-intercept: y = 2x + 6
Point-slope (as asked): y - 4 = 2 (times) (x + 1)
standered: 2x - y = -6
Step-by-step explanation:
How many variables terms are in the expression 3xcube y+5xsquare+y+9
Answer: Please Give Me Brainliest, Thank You!
2
Step-by-step explanation:
There are two variables here, X and Y
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Perform the following computation with radicals. Simplify the answer.
V6 18
311
123 45
6
7
8
+
x
Question: Perform the following computation with radicals. Simplify the answer. √6 • √8
Answer:
[tex] 4\sqrt{3} [/tex]
Step-by-step explanation:
Given, √6 • √8, to perform the computation, we would simply evaluate the radicals and try as much as possible to leave the answer in the simplest form in radicals.
Thus,
[tex] \sqrt{6}*\sqrt{8} = \sqrt{6*8} [/tex]
[tex] = \sqrt{48} [/tex]
[tex] = \sqrt{16*3} = \sqrt{16}*\sqrt{3}[/tex]
[tex] = 4\sqrt{3} [/tex]
Please answer this correctly without making mistakes
Answer:
7/10 mi
Step-by-step explanation:
The total distance is 3 miles = 30/10 miles.
The other distances added gives 7/10+7/10+9/10 = 23/10
Therefore the last hop from Kingwood to Silvergrove is 30/10 - 23/10 = 7/10
What is the rise over run for the slope -11/9
Answer: 11 down and 9 right
Step-by-step explanation:
Slope IS rise over run where the top number of the fraction (numerator) determines the vertical distance --> positive is up, negative is down
and the bottom number of the fraction (denominator) determines the horizontal distance --> positive is right, negative is left.
Given slope = -11/9
the numerator is -11 so the "rise" is DOWN 11 units
the denominator is 9 so the "run" is RIGHT 9 units
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9
Answer:
The Width = 65.44 inches
The Height = 36.81 inches
Step-by-step explanation:
We are told in the question that:
The width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9
Using Pythagoras Theorem we known that:
Width² + Height² = Diagonal²
Since we known that the size of a television is the length of the diagonal of its screen in inches.
Hence, for this new TV
Width² + Height² = 75²
We are given ratio: 16:9 as aspect ratio
Width = 16x
Height = 9x
(16x)² +(9x)² = 75²
= 256x² + 81x² = 75²
337x² = 5625
x² = 5625/337
x² = 16.691394659
x = √16.691394659
x = 4.0855103303
Approximately x = 4.09
For the newer 75 inch tv set
The Height = 9x
= 9 × 4.09
= 36.81 inches
The Width = 16x
= 16 × 4.09
= 65.44 inches.
Divide. Write the quotient in lowest terms. 3 3/4 ÷ 5/7
Rewrite 3 3/4 as an improper fraction
3 3/4 = 15/4
Now you have
15/5 / 5/7
When you divide fractions, change the division to multiplication and flip the second fraction over:
15/4 x 7/5
Now multiply the top numbers together and the bottom numbers together:
( 15 x 7) / (4 x 5) = 105/20
Write as a proper fraction:
105/20 = 5 1/4
if P(x)=1+6x-5x^2 represents the profit in selling x thousand Boombotix speakers, how many speakers should be sold to maximize profit?
Answer:
600
Step-by-step explanation:
[tex]p(x) = 1 + 6x - 5x^2[/tex]
x max = [tex]-b/2a[/tex]
a = -5
b = 6
-6/2(-5) = 6/10 = 3/5 = .6
.6 thousand = 600
600 speakers should be sold.
Alternatively, you can check the vertex of the parabola formed.
Algebra Review
Write an algebraic expression for each verbal expression.
1. the sum of one-third of a number and 27
2. the product of a number squared and 4
3. Write a verbal expression for 5n^3 +9.
Answer:
Step-by-step explanation:
1. The sum of one-third of a number and 27
= [tex]\frac{1}{3}\times x +27\\= 1/3x +27[/tex]
2. The product of a number squared and 4
[tex]Let\:the\:unknown\: number\: be \:x\\\\x^2\times4\\\\= 4x^2[/tex]
3.Write a verbal expression for 5n^3 +9.
The sum of the product and of 5 and a cubed number and 9
Use the model to show to help find the sum 0.34 plus 0.49
Answer/Step-by-step explanation:
The idea to use in solving this problem using the model, is to express the number of shaded boxes in fraction form.
Thus, the blue red shaded boxes has 34 boxes shaded out of 100 boxes. This represents [tex] \frac{34}{100} [/tex]. This will give us 0.34.
The other shaded boxes represents [tex] \frac{49}{100} = 0.49 [/tex].
Using the model, we can solve 0.34 + 0.49.
Add both fractions together.
[tex] \frac{34}{100} + \frac{49}{100} = \frac{34+49}{100} [/tex]
[tex] \frac{83}{100} = 0.83 [/tex]
Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for itself since the time it takes to produce the product using the new machine is significantly less than the production time using the old machine. To test the claim, independent random samples were taken from both machines. You are given the following results.
New Machine Old Machine
Sample Mean 25 23
Sample Variance 27 7.56
Sample Size 45 36
As the statistical advisor to Ajax, would you recommend purchasing Allied's machine? Explain.
Answer:
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
Step-by-step explanation:
We must evaluate the differences of the means of the two machines, to do so, we will assume a CI of 95%, and as the interest is to find out if the new machine has better performance ( machine has a bigger efficiency or the new machine produces more units per unit of time than the old one) the test will be a one tail-test (to the left).
New machine
Sample mean x₁ = 25
Sample variance s₁ = 27
Sample size n₁ = 45
Old machine
Sample mean x₂ = 23
Sample variance s₂ = 7,56
Sample size n₂ = 36
Test Hypothesis:
Null hypothesis H₀ x₂ - x₁ = d = 0
Alternative hypothesis Hₐ x₂ - x₁ < 0
CI = 90 % ⇒ α = 10 % α = 0,1 z(c) = - 1,28
To calculate z(s)
z(s) = ( x₂ - x₁ ) / √s₁² / n₁ + s₂² / n₂
s₁ = 27 ⇒ s₁² = 729
n₁ = 45 ⇒ s₁² / n₁ = 16,2
s₂ = 7,56 ⇒ s₂² = 57,15
n₂ = 36 ⇒ s₂² / n₂ = 1,5876
√s₁² / n₁ + s₂² / n₂ = √ 16,2 + 1.5876 = 4,2175
z(s) = (23 - 25 )/4,2175
z(s) = - 0,4742
Comparing z(s) and z(c)
|z(s)| < | z(c)|
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
The very hight dispersion of values s₁ = 27 is evidence of frecuent values quite far from the mean
If A and B are independent events with P( A) = 0.35 and P( B) = 0.55, then P( A| B) is:_________.
a. .19
b. 1.57
c. .64
d. .91
Answer:
P( A| B)= 0.35. None of the options are correctStep-by-step explanation:
Two events A and B are said to be independent if the occurrence of one of the events does not affect the other occurring. For example, the event of tossing two coins is an independent event since they occur simultaneously. Two events are therefore independent if the following are true.
P(A|B) = P(A)
P(B|A) = P(B)
P(A and B) = P(A)P(B)
If A and B are independent events with P( A) = 0.35 and P( B) = 0.55,
then P( A| B) is a probability of A occurring provided that B has occurred. This is known as conditional probability for an independent event.
From the condition above for independent events, P(A|B) = P(A) and since P(A) = 0.35, hence P(A|B) =0.35
Solve for x: 3(x + 1)= -2(x - 1) + 6.
Answer:
x=1
Step-by-step explanation:
3(x + 1)= -2(x - 1) + 6.
Distribute
3x+3 = -2x+2+6
Combine like terms
3x+3 = -2x+8
Add 2x to each side
3x+3+2x = 8
5x+3 = 8
Subtract 3 from each side
5x =5
Divide by 5
x =1
pls help:Find all the missing elements:
Answer:
B = 48.7° , C = 61.3° , b = 12Step-by-step explanation:
In order to find B we must first angle C
To find angle C we use the sine rule
That's
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]
From the question
a = 15
A = 70°
c = 14
So we have
[tex] \frac{15}{ \sin(70) } = \frac{14}{ \sin(C) } [/tex]
[tex] \sin(C) = \frac{14 \sin(7 0 ) }{15} [/tex]
[tex]C = \sin^{ - 1} ( \frac{14 \sin(70) }{15} ) [/tex]
C = 61.288
C = 61.3° to the nearest tenthSince we've found C we can use it to find B.
Angles in a triangle add up to 180°
To find B add A and C and subtract it from 180°
That's
A + B + C = 180
B = 180 - A - C
B = 180 - 70 - 61.3
B = 48.7° to the nearest tenthTo find b we can use the sine rule
That's
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |a| }{ \sin(B) } [/tex]
[tex] \frac{15}{ \sin(70) } = \frac{ |b| }{ \sin(48.7) } [/tex]
[tex] |b| = \frac{15 \sin(48.7) }{ \sin(70) } [/tex]
b = 11.9921
b = 12.0 to the nearest tenthHope this helps you
I need help with these questions asap, I will post pictures if you know them all answer them in the order of the photos from 1-5 thank you.
Answer:
1. step 4
2.idk
3. step 2
4.-5n = 1 ---------> n= -1/5
n + 15 = -10 -------> -25
n/5 = -1/5 ------> n = -1
n - 13 = -12 ------> n = 1
5. cant see the drop down menu or possible answers
but if an answer is the addition one thing
then the second one is the subtraction thing
Step-by-step explanation:
(3) In a group of 60 seldiers have enough food for
20 days - How many soldiers should leave the group
so that the food is enough for 100 days ? Find it.
Answer:
48 soldiers
Step-by-step explanation:
60 soldiers 20 days
x soldiers 100 days
60 x 20 = 1200 = 100x
Therefore x = 1200/100 = 12
60 - 12 = 48
Hope that helped!!! k
Answer:
30 Soldiers
Step-by-step explanation:
Given:
1) No of soldiers=60
No of days=20
2) No of days=100
No of soldiers=?
No of soldiers to leave=?
Solution:
Let us use the cross multiplication method.
Let x be the no of soldiers.
No of days No of soldiers
1) 20 60
2) 100 x
by cross multiplying,
20x=100 x 60
20x=600
x=600/20
x=30 soldiers
Therefore, No of soldiers to leave =60-30=30 soldiers
Find the distance between points P(5, 1) and Q(3, 4) to the nearest tenth.
3.6
5
9.4
13
Answer:
≈ 3.6
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (P(5, 1) and (x₂, y₂ ) = Q(3, 4)
d = [tex]\sqrt{(3-5)^2+(4-1)^2}[/tex]
= [tex]\sqrt{(-2)^2+3^2}[/tex]
= [tex]\sqrt{4+9}[/tex]
= [tex]\sqrt{13}[/tex] ≈ 3.6 ( to the nearest tenth )
Answer:
3.6
Step-by-step explanation:
Look above bru
An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:
418 421 421 422 425 428 431 435 437
438 445 447 448 453 458 462 465
(c) Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.) Note that it is plausible that the given sample observations were selected from a normal distribution and there are no outliers.
(___ , ___)
Does the interval suggest that 441 is a plausible value for true average degree of polymerization?
Yes or No
Does the interval suggest that 451 is a plausible value?
Yes or No
Answer:
Step-by-step explanation:
Form a set of values we get
n = 17
And with the help of a calculator
μ₀ = 438,47
σ = 14,79
Normal Distribution is : N ( 438,47 ; 14,79 )
c)
CI = 95 % means α = 5 % α/2 = 2,5 % α/2 = 0,025
and as n < 30 we should use t-student distribution with n -1 degree of freedom df = 16. t score for 0,025 and 16 s from t-table 2,120
By definition:
CI = [ μ₀ ± t α/2 ; n-1 * σ/√n ]
CI = [ μ₀ ± 2,120* 14,79/√17 ]
CI = [ μ₀ ± 7,60 ]
CI = [ 438,47 ± 7,60 ]
CI = [ 430,87 ; 446,07 ]
95% confidence interval for true average degree of polymerization is [430.87 ; 446.07] and this interval suggest that 441 is a plausible value for true average degree of polymerization and also this interval does not suggest that 451 is a plausible value.
Given :
Sample = [ 418, 421, 421, 422, 425, 428, 431, 435, 437, 438, 445, 447, 448, 453, 458, 462, 465 ]95% confidence interval.The total number of values given is, n = 17
Mean, [tex]\mu_0=438.47[/tex]
Standard Deviation, [tex]\sigma = 14.79[/tex]
The normal distribution is given by: N (438.47 ; 14.79)
If Cl is 95% then [tex]\alpha[/tex] is 5% and [tex]\alpha /2[/tex] is 2.5%
[tex]\alpha /2 = 0.025[/tex]
Now, use t-statistics distribution with (n-1) degree of freedom df = 16
So, the t score for 0.025 and 16 s from t-table 2.120.
[tex]\rm Cl = [\mu_0 \pm t_{\alpha /2};(n-1)\times \dfrac{\sigma}{\sqrt{n} }][/tex]
[tex]\rm Cl = [\mu_0 \pm 2.120\times \dfrac{14.79}{\sqrt{17} }][/tex]
[tex]\rm Cl = [\mu_0 \pm 7.60][/tex]
Cl = [430.87 ; 446.07]
Yes, the interval suggests that 441 is a plausible value for true average degree of polymerization.
No, the interval does not suggest that 451 is a plausible value.
For more information, refer to the link given below;
https://brainly.com/question/2561151
A Markov chain has 3 possible states: A, B, and C. Every hour, it makes a transition to a different state. From state A, transitions to states B and C are equally likely. From state B, transitions to states A and C are equally likely. From state C, it always makes a transition to state A.
(a) If the initial distribution for states A, B, and C is P0 = ( 1/3 , 1/3 , 1/3 ), find the distribution of X2
(b) Find the steady state distribution by solving πP = π.
Answer:
A) distribution of x2 = ( 0.4167 0.25 0.3333 )
B) steady state distribution = [tex]\pi a \frac{4}{9} , \pi b \frac{2}{9} , \pi c \frac{3}{9}[/tex]
Step-by-step explanation:
Hello attached is the detailed solution for problems A and B
A) distribution states for A ,B, C:
Po = ( 1/3, 1/3, 1/3 ) we have to find the distribution of x2 as attached below
after solving the distribution
x 2 = ( 0.4167, 0.25, 0.3333 )
B ) finding the steady state distribution solving
[tex]\pi p = \pi[/tex]
below is the detailed solution and answers
What is the sum of the complex numbers −9−i−9−i and −5−i−5−i?
Answer:
The sum of the complex numbers will be - 28 - 4i
Step-by-step explanation:
We have the sum −9−i−9−i + −5−i−5−i. Let's group like elements and simplify this expression,
−9−i−9−i + −5−i−5−i ( Group like terms )
- i - i - i - i - 9 - 9 - 5 - 5 ( Add like terms )
- i - i - i - i = - 4i, - 9 - 9 = - 18, and - 5 - 5 = - 10
- 18 - 10 = - 28 ( Substitute )
Solution : - 28 - 4i
About how many feet are in 3.6 kilometers? 1 m = 39.37 in
Answer:
11811 feet
Step-by-step explanation:
Hope it helps!
There are about 11,812 feet in 3.6 kilometers.
To convert kilometers to feet, we need to use the conversion factor:
1 kilometer = 3,280.84 feet.
Now, to find how many feet are in 3.6 kilometers,
we can multiply 3.6 by the conversion factor:
So, 3.6 kilometers x 3,280.84 feet/kilometer
= 11,811.504 feet.
Thus, Rounded to a whole number, there are about 11,812 feet in 3.6 kilometers.
Learn more about Unit Conversion here:
https://brainly.com/question/14573907
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Select the correct answer from each drop-down menu.
A cross section is the intersection of a
Solid or point and a plane or plane. Helpp
Answer:
solid, plane
Step-by-step explanation:
A cross section is the intersection of a solid and a plane.
Answer:
A cross section is the intersection of a solid and a plane.
Step-by-step explanation:
Got this right on plato, hope it helps :P
A random sample of 11 students produced the following data, where x is the hours spent per month playing games, and y is the final exam score (out of a maximum of 50 points). The data are presented below in the table of values.
x y
14 46
15 49
16 37
17 42
18 37
19 31
20 25
21 23
22 20
23 15
24 12
What is the value of the intercept of the regression line, b, rounded to one decimal place?
Answer:
b = - 3.7
Step-by-step explanation:
here are the data values:
x y XY X²
14 46 644 196
15 49 735 225
16 37 592 256
17 42 714 289
18 37 666 324
19 31 589 361
20 25 500 400
21 23 483 441
22 20 440 484
23 15 345 529
24 12 288 576
now we are required to find the summation (total) of all values of X, Y, XY and X².
∑X = 209
∑Y = 337
∑XY = 5996
∑X² = 4081
The formular for finding b is given as:
b = n∑XY - (X)(Y) / n∑X² - (∑X)²
= 11(5996) - (209)(337) / 11(4081) - (209)²
= 65956 - 70433 / 44891 - 43681
= -4477/ 1210
= -3.7
The question asked us to find the value of b but we can go further to find the equation of the regression line:
a = ∑Y - b∑X / n
= 337 - (-3.7)(209)/ 11
=1110.3/11
= 100.94
the equation is:
Y = 100.94 - 3.7X
I hope you find my solution useful!
=
whats is 5% in words?
Here are a few ways 5% could be written in words:
-five percent
-five thousandths (0.05)
Hope this helps! :)
Answer:
0.05
Step-by-step explanation:
Assuming you mean as a decimal...
5/100 = 0.05
ALTERNATIVELY
5% = Five Percent
0.05 = Five Thousandths, Zero Point Zero Five
algebra and trigonometry difference
Answer:
Algebra deals with knowing the value of unknown variables and functional relationships, while trigonometry touches on triangles, sides and angles and the relationship between them.
Algebra is more on polynomial equations, x and y while trigonometry more on sine, cosine, tangent, and degrees.
Trigonometry is much more complicated than algebra but algebra has its uses in our daily lives, be it calculating distance from point to another or determining the volume of milk in a milk container.
Step-by-step explanation:
Answer:
Although both Algebra II and Trigonometry involve solving mathematical problems, Algebra II focuses on solving equations and inequalities while Trigonometry is the study of triangles and how sides are connected to angles.
hope this answer helps u
pls mark as brainliest .-.
How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Enter your answers to one decimal place.) 147 153 170 172 185 181 182 185 181 170 181 167 153 145
Answer:
Mean: 169.4
Median: 171
Mode: 181
Step-by-step explanation:
I first sorted the numbers by value, least to greatest.
145 147 153 153 167 170 170 172 181 181 181 182 185 185
We can see that 181 occurs the most, 3 times, so it's the mode.
The median of this set will be the middle number(s).
When we take away 6 numbers from both sides we are left with 170 and 172, and the mean of these two numbers is 171. So the median is 171.
We can add all the numbers and divide by 14 to get the mean.
[tex]147+153+170+172+185+181+182+185+181+170+181+167+153+145=2372\\\\2372\div14\approx169.4[/tex]
Hope this helped!
Suppose we want to choose 6 colors, without replacement, from 14 distinct colors. (a) How many ways can this be done, if the order of the choices matters? (b) How many ways can this be done, if the order of the choices does not matter?
Answer:
(a) 2,162,160
(b) 3,003
Step-by-step explanation:
(a) order matters
You can choose from 14 for the first pick. Then you have 13 left for the second pick. Then you have 12 left for the third pick. Keep going until you have 9 left for the 6th pick. The number when order matters is:
total = 14 * 13 * 12 * 11 * 10 * 9 = 2,162,160
(b) Order does not matter
Start with the same number as above for picking 6 out of 14. Since order does not matter, we divide by the number of ways you can arrange 6 items.
Since there are 6! ways of arranging 6 items,
total = 2,162,160/6! = 3,003
The number of ways when the order matters are 121080960.
The number of ways when order does not matters are 3003.
Given,
Choose 6 colors, without replacement, from 14 distinct colors.
We have to find:
- How many ways can this be done, if the order of the choices matters.
- How many ways can this be done if the order of the choices does not matter.
What are permutation and combination?We use permutation when the order of the arrangements matters.
It is given by:
[tex]^ nP_r[/tex] = n! / r!
We use combination when order does not matter.
It is given by:
[tex]^nC_{r}[/tex] = n! / r! (n-r)!
Find the number of ways when order matters.
We have,
n = 14 and r = 6
[tex]^{14}P_{6}[/tex]
= 14! / 6!
= (14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6!) / 6!
= 4 x 13 x 12 x 11 x 10 x 9 x 8 x 7
= 121080960
Find the number of ways when order does not matter.
We have,
n = 14 and r = 6
[tex]^{14}C_{6}[/tex]
= 14! / 6! 8!
= 14 x 13 x 12 x 11 x 10 x 9 / 6 x 5 x 4 x 3 x 2
= 7 x 13 x 11 x 3
= 3003
Thus,
The number of ways when the order matters are 121080960.
The number of ways when order does not matters are 3003.
Learn more about combination here:
https://brainly.com/question/28134115
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4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced? Answer: A= the cube with side length 6 cm, B= the cube with side length 8 cm, C= the cube with side length 10 cm, D= the cube with side length 12 cm. On one side of the scale : , on the other side of the scale
Answer: The cube with side length of 12cm is alone in one plate, the other 3 cubes are in the other plate.
Step-by-step explanation:
We have 4 cubes with side lengths of:
6cm, 8cm, 10cm and 12cm.
Now, some things you need to know:
If we want a scale to be balanced, then the mass in both plates must be the same.
The volume of a cube of side length L is:
V = L^3
And the mass of an object of density D, and volume V is:
M = D*V.
As all the cubes are of the same material, all of them have the same density, so the fact that we do not know the value of D actually does not matter here.
Then we want to forms two groups of cubes in such a way that the total volume in each plate is the same (or about the same), the volumes of the cubes are:
Cube of 6cm:
V = (6cm)^3 = 216cm^3
Cube of 8cm:
V = (8cm)^3 = 512cm^3
Cube of 10cm:
V = (10cm)^3 = 1000cm^3
cube of 12cm
V = (12cm)^3 = 1728cm^3
First, if we add the volumes of the first two cubes, we have:
V1 = 216cm^3 + 512cm^3 = 728cm^3
Now we can see that we add 1000cm^3 the volume will be equal to the volume of the larger cube, so here we can also add the cube with side length of 10cm
Then the volume of the 3 smaller cubes together is:
V1 = 216cm^3 + 512cm^3 + 1000cm^3 = 1728cm^3.
Then, if we want to have the same volume in each plate, then we need to have the 3 smaller cubes in one plate, and the larger cube in the other plate.
6. If x + 2 is the only factor of the polynomial P(x),then P(2) is:
Options:
A. Cannot be determined
B. Not Zero
C. R(2)
D. Zero
Answer:
P(x) = x + 2p(2) = 2 + 2 p(2) = 4So option B is the answer.
If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) is Not Zero. Therefore, the option B is the correct answer.
What is standard form of a polynomial?Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.
Given information;
If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) :
P(x) = x + 2
p(2) = 2 + 2
p(2) = 4
The P(2) is Not Zero.
Therefore, the option B is the correct answer.
Learn more about standard form of a polynomial here:
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