Answer:
30√2 cm
Step-by-step explanation:
Maximum length of the rod = Length of the diagonal of the cuboid
Length of diagonal of cuboid = [tex]\sqrt{l^2+w^2 + h^}[/tex]
where l = length, w =width and h = height
For this particular cuboid,
Diagonal length = [tex]\sqrt{30^2+24^2 + 18^2}[/tex]
[tex]\sqrt{800 + 576 + 324} \\\\\\= \sqrt{1500}\\\\= 30\sqrt{2} \text{ cm}[/tex]
SSS stands for ___ Congruence Postulate ( will mark Brainliest )
Answer:
I believe it stands for Side, Side, Side
Step-by-step explanation:
When two triangles with all three sides are equal they're SSS
Identify each pair of angles as corresponding, alternate interior, alternate exterior, consecutiveinterior, vertical, or adjacent. Explain step-by-step
Given: Pair of parallel lines and a transversal with angles x and y.
Required: To determine which type of angles are formed by x and y.
Explanation: Consider the following figure below showing a pair of parallel lines and a transversal
In the figure, line l is parallel to line m, and line n is the transversal.
Further alternate angles are the pair:
[tex](\angle1&\angle8),(\angle2&\angle7),(\angle3&\angle6),(\angle4&\angle5)_[/tex]The angles lying inside the parallel lines are alternate interior, while the angles lying outside the parallel lines are the alternate exterior.
While the corresponding angles are the pair:
[tex](\angle2&\angle6),(\angle1&\angle5),(\angle3&\angle7),(\angle4&\angle8)[/tex]Finally, the consecutive interior angles are the pair of non-adjacent angles that lie on the same side of the transversal. In the figure above, the consecutive interior angles are:
[tex](\angle4&\angle6),(\angle3&\angle5)[/tex]Hence the given pair of angles x and y are consecutive interior angles.
Final Answer: Option D is correct.
Terms from two sequences are given in tables below. Which of the following statements are true? Select all that apply.
As per the terms from the two sequences given in tables as attachment hereby along with the question statement, the following statements from the provided options are true.
(i) [(a₁) > (g₂)]
(iv) Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ).
As per the question statement and the reference tables attached thereby along with the question, we are provided with terms from the two sequences in table format, and five statements based on the sequences.
We are required to determine which statements among the five, are true.
To solve this question, we will use the trial-and-error method, where we will consider individual statement and assess it's honesty.
First statement is [(a₁) > (g₂)], which is true. As we can see from the table, that, [(a₁) = 10] and [(g₂) = 4], i.e., (10 > 4), or, [(a₁) > (g₂)].
Second statement is that, "The constant difference for (aₙ) is 10" which is False. We can clearly see from the table that, (a₁ = 10), (a₂ = 15), (a₃ = 20), (a₄ = 25) and so on, and [(25 - 20) = (20 - 15) = (15 - 10) = 5], i.e.,
[(a₄ - a₃) = (a₃ - a₂) = (a₂ - a₁) = 5]. Hence, the common difference for (aₙ) is 5, and not 10.
Third statement is that, "(aₙ) can be modelled by a linear function, and (gₙ) can be modelled by an exponential function" which is true for the first part, but false for the second, making the complete statement false as whole.
From the left hand side table, we can see that, (a₂ = 15) and (a₁ = 10),
Or, [a₂ = (10 + 5)]
Or, [a₂ = (a₁ + 5)]
Similarly, (a₃ = 20),
Or, [a₃ = (15 + 5)]
Or, [a₃ = (a₂ + 5)]
That is, we can generalise (aₙ) as
[aₙ = {(aₙ₋₁) + 5}] where, (n = 2, 3, 4, 5...) and (a₁ = 10).
Hence, (aₙ) can be modelled by a linear function.
But from the right hand side table, we can see that, (g₂ = 4) and (g₁ = 2),
Or, [g₂ = (2 * 2)]
Or, [g₂ = 2g₁]
Similarly, (g₃ = 8),
Or, [g3 = (2 * 4)]
Or, [g₃ = 2g₂], it goes on for (gₙ).
Therefore, we can generalise (gₙ) as
[gₙ = 2*(gₙ₋₁)] where, (n = 2, 3, 4, 5...) and (g₁ = 2).
Here, (gₙ) can also modelled as a linear function and not as a exponential function (which goes in the form of "xⁿ").
Coming to the fourth statement, "Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ)" is true, as from both the tables,
For (n = 5), [aₙ = a₅ = (a₄ + 5) = (25 + 5) = 30],
And [gₙ = g₅ = (2 * g₄) = (2 * 16) = 32], which is greater than 30,
Or, [(g₅) > (a₅)].
Similarly, for (n = 6), (a₆ = 35) while (g₆ = 64), i.e., [(g₆) > (a₆)], and it continues for greater values of "n".
Coming to the last statement, that [a₁₀ > g₆], is false. As we can observe from the both the tables and their sequence,
For (n = 5), (aₙ = 50), for (n = 6), (aₙ = 35), for (n = 7), (aₙ = 40), for (n = 8), (aₙ = 45), for (n = 9), (aₙ = 50) and for (n = 10), (aₙ = 55),
While on the other hand, for (n = 5), (gₙ = 32) and for (n = 6), (gₙ = 64).
Since (64 > 55), therefore, [(g₆) > (a₁₀)].
Sequence: In mathematics, a sequence is an enumerated collection of objects in a particular order, and repetitions being allowed.To learn more about Sequence, click on the link below.
https://brainly.com/question/21961097
#SPJ1
can you help me with this? i got it wrong
1) Let's sketch this out so that we can better understand it
2) Reminding ourselves of the metric relations of a right triangle we can write out the following:
[tex]\begin{gathered} h^2=m\cdot n \\ YO^2=26\cdot12 \\ YO=\sqrt[]{312} \\ OZ=\sqrt[]{26.12} \\ OZ=\sqrt[]{312} \\ YZ=\sqrt[]{312}+\sqrt[]{312} \\ YZ=2\sqrt[]{312} \\ YZ=35.3 \end{gathered}[/tex]Note that the radius intersects that chord with a 90º angle so it bisects that chord.
Given equal probabilities of the birth of a xy or xx, what is the probability that a group of four siblings includes all xy? all xx? all xy or all xx?.
The probability of all XY in a group of four siblings is 1/16 (6.5%), and also the probability of all XX offspring is 1/16 (6.5%).
Let us first know how do chromosomes work?
Long DNA molecules called chromosomes contain all or a portion of an organism's genetic code. Males receive one X and one Y chromosome from each parent, whereas females receive two X chromosomes from each parent.
For females, the likelihood or probability of inheriting two X chromosomes is 1/2 (50%) while for men, the probaility of receiving one X chromosome and one Y chromosome is similarly 1/2.
Therefore, the probability that all XY siblings are present in a group of 4 siblings is:
[tex]1/2 * 1/2 * 1/2 * 1/2 = 1/16[/tex]
Also the probability that a family of four siblings or offspring includes all XX is
[tex]1/2 * 1/2 * 1/2 * 1/2 = 1/16[/tex]
To learn more about offspring click here:
https://brainly.com/question/414761
#SPJ4
The probability of all XY in a group of four siblings is 1/16 (6.5%), and also the probability of all XX offspring is 1/16 (6.5%).
For females, the likelihood or probability of inheriting two X chromosomes is 1/2 (50%) while for men, the probability of receiving one X chromosome and one Y chromosome is similarly 1/2.
Therefore, the probability that all XY siblings are present in a group of 4 siblings is:
1/2*1/2*1/2*1/2=1/16
Also the probability that a family of four siblings or offspring includes all XX is
1/2*1/2*1/2*1/2=1/16
learn more about of probability here:
https://brainly.com/question/11234923
#SPJ4
Is the following statement true or false? The cube root of zero is zero.
The statement that The cube root of zero is zero is true .
What is cube root ?The number that results in the original number after being multiplied three times is known as the cube root of a number.[tex]\sqrt[3]{}[/tex] The sign is used to represent a number's cube root in radical form.
The cube root of 0 will be calculated and explained here. First, observe that the mathematical symbol for the cube root of O is as follows:
[tex]\sqrt[3]{0}[/tex]
The number (n), which you can multiply twice by itself to get the number zero, is the cube root of zero. Alternatively, n×n×n should equal 0. Consequently, the following equation can be used to address the issue:
[tex]n^{3}[/tex] = 0
The answer to the cube root of 0 is as follows when the aforementioned equation is solved:
[tex]\sqrt[3]{0}[/tex]= 0
To learn more about cube root visit :
brainly.com/question/12726345
#SPJ10
let x denote the number of times harry potter manages to irritate professor snape in one day. let y denote the number of times ron weasley manages to irritate professor snape in one day. and let the joint probability mass function for (x, y) be given as
the probability that Ron will get in trouble with Professor Snape at least two times in one day is 0.7
We are given
X 0 1 2 3 4
P(X) 0.15 0.20 0.20 0.30 0.15
we want Ron Weasley to get in trouble at least two time in one day
that mean X 2
P(X 2) = P(X=2) + P(X=3) + P(X=4)
= 0.20+0.30+0.15
= 0.65= 0.7 (rounded to nearest tenth)
learn more about of probability here
https://brainly.com/question/18917250
#SPJ4
For questions 1-2, find the distance and midpoint of the segments given the endpoints. 1. AB with A(3, 4) and B(-1, 10) Midpoint
Given the points A(3,4) and B(-1,10), we can find the distance between them using the following function:
[tex]d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]then, we have the following:
[tex]\begin{gathered} (x_1,y_1)=(3,4)=A \\ (x_2,y_2)=(-1,10)=B \\ \Rightarrow d(A,B)=\sqrt[]{(-1-3)^2+(10-4)^2}=\sqrt[]{4^2+6^2}=\sqrt[]{16+36}=\sqrt[]{52} \\ =\sqrt[]{4\cdot13}=2\cdot\sqrt[]{13} \\ d(A,B)=2\cdot\sqrt[]{13} \end{gathered}[/tex]2/5 y 6/15 son equivalentes?
To know if 2/5 and 6/15 are equivalent, we do a multiplication, then,
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{2}{3}=\frac{2\times2}{5\times2}=\frac{4}{10} \ \ \longmapsto \ Not \ the \ result } \end{gathered}$} }[/tex]
Since if we try it with number 1, the result would be the same, then we continue with 2 being closer, then we continue with number 3, successively, until we reach the expected answer.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{2}{3}=\frac{2\times3}{5\times3}=\frac{6}{15} } \end{gathered}$} }[/tex]
2/5 and 6/15 are equivalent?, The two fractions are equivalent, (True).Calculate (9.5 × 106) + (4.2 × 106)
Give your answer in standard index form.
Answer:
1.4522 x [tex]10^{3}[/tex]
Answer the 4 question in the photo for EASY points ( 20 points )
The pink ribbon is shortest.
Purple > yellow > silver > pink
Can anyone help me with this?
Answer:
13 sec
Step-by-step explanation:
Prius' acceleration
60 mi/hr = 88 ft s
accel = change in v / change in time = 88 f/s / 10.3 s = 8.54 ft / s^2
F = ma = 2903 * 8.54 = 24802 lb ft/s^2
Now increase the mass to 4903 by adding a 2000 lb trailer (which, by the way is way past the towing capacity of an anemic Prius !)
F = ma
24802 = 4903 a shows a = 5.06 ft/s^2
45 mi/hr = 66 ft/s
a = change in v / change in time
5.06 = 66 / 5.06 = 13 sec
how many ways can you make a 5 digit password that can be any number (including zero) or letter (not case sensitive)? 916132832
These work out to 60,466,176 case insensitive combinations of letters.
There are 10 digits 0–9.
The are 26 letters in the modern alphabets.
However, you didn’t specify whether capital and lowercase letters count as the same letter or separate. In the former case, there are 26 letters, in the latter, there are 52.
There is also such a thing as lowercase numbers, but since they aren’t in common standard usage, I won’t count those.
You also didn’t specify that characters couldn’t be repeated, so I am going to assume that the same character can appear multiple times in a 5 character combination.
Also, since the combinations are an alphanumeric string of characters rather than a number, I will assume that leading zeroes are allowed.
So, there are either 36 (10 digits and 26 letters).
To find the number of combinations you multiply the number of possibilities for each character;
36 x 36 x 36 x 36 x 36
These work out to 60,466,176 case insensitive combinations of letters.
To learn more about Combinations click here:
brainly.com/question/28042664
#SPJ4
Work out, giving your answer in it's simplest form: 4 1/5 × 5/14
If BC= 6x+6 , AB= 8x+9 , and AC=142 find BC
The value of BC is 60.6.
What exactly is the segment addition property?According to the segment addition postulate, if we have two locations on a line segment, A and C, a third point B lies on the line segment AC if and only if the lengths between the points match the requirements of the equation AB + BC = AC.
Given:
BC = 6x+6
AB = 8x+9
AC = 142
We need to find BC.
As AB and BC combine to form AC, we add them together and equate them with the value of AC to determine the value of x.
Using the property of segment addition,
AB + BC = AC
8x + 9 + 6x + 6 = 142
Combine the variable terms and constants together,
14x + 15 = 142
14x = 142 - 15 (Subtracting both sides by 15)
14x = 127
x = 9.1
Hence the value of BC is,
BC = 6x + 6 = 6(9.1) + 6 = 60.6
To know more about segment addition property visit:
https://brainly.com/question/17423942
#SPJ10
Evaluate.
15÷(3+13)^2
Responses:
1 7/20
1 7/9
4 1/2
5 1/9
PLEASE HELP
Answer:
explain 15/256
3 1/8 times 3 1/2 times 4/5
Answer: 8.75
Step-by-step explanation:
3 1/8 into a decimal is 3.125
3 1/2 into a decimal in 3.5 or 3.50
4/5 into a decimal is 0.8 or .8
Then just multiply 3.125 and 3.5 and you get 10.9375
Next, multiply 10.9375 by 0.8 and you get 8.75
Therefore your answer is 8.75
Andre wants to make an open-top box by cutting out corners of a 22 inch by 28 inch piece
of poster board and then folding up the sides. The volume V(x) in cubic inches of the
open-top box is a function of the side length x in inches of the square cutouts.
Write an expression for V(x).
what is the volume of the box when x=6
The expression for volume is (28-2x)(22-2x)x and when x=6, the volume is 840 inch^3.
What is volume?
A 3D object's volume is the amount of actual space it occupies. It is a 2D shape's 3D equivalent of area. It is quantified in cubic units like cm3. It means that the amount of space a closed form can occupy in three dimensions depends on its volume. Volume is a gauge of a thing's potential. For instance, a cup is said to have a 100 ml capacity if the brim can hold 100 ml of water. Another way to measure volume is the amount of space a three-dimensional item takes up.
According to question,
Let x be the height of the cubic box
Length = (28-2x)
Breadth = (22-2x)
Volume = x(28-x)(22-x)
When x =6
Volume = 6(28-6×2)(22-6×2)
=6(10)(14)
=840 inch^3
To know more about volume, visit:
https://brainly.com/question/463363
#SPJ9
A rectangular park is 40 yards wide. then a city planner designs a path that is 1 yard wide to run all the way around the park.now the area of the park plus the path is 4200 square yards.how long is the park not counting the path?
The length of the park not counting the path is 98 yards
How to determine the length of the park
The formula for determining the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleFrom the information given, we have that;
The dimensions of the path having a width of 1 yard path around it are
(L+2) x (W+2)
We have to add 2 to the length and width because there will be a 1 yard path on all 4 sides of the rectangle
Given that the area is 4200 square yards; the original width is 40 yards
Now, substitute the values into the formula, we have;
Since Area = LW
4200 = (L+2)(W+2)
4200 = (L+2)(40+2)
Add the values
4200 = (L+2)(42)
expand the bracket
4200 = 42L + 84
collect like terms
4116 = 42L
Make 'L' the subject of formula
L = 98 yards
Hence, the length is 98 yards
Learn more about rectangles here:
https://brainly.com/question/25292087
#SPJ1
Answer:
98 yards
Step-by-step explanation:
Quadratic equation whose roots are -6 and 2 and whose leading coefficient is 2
Answer:
x² + 4x - 12
Step-by-step explanation:
Roots: -6 and 2
Leading coefficient: x²
(x + 6)(x - 2)
x(x - 2) + 6(x - 2)
x² - 2x + 6x - 12
x² + 4x - 12
I hope this helps!
:: 3x + 3 = 2(x + 7)
Answer: x= 11
Step-by-step explanation:
Answer:
x=11
Step-by-step explanation:
im assuming u r trying to find x
you need to solve the bracket first (2×x =2x , 7×2= 14)
After that move numbers with x to ur left, to make life easier
3x-2x= x
14-3 = 11
x=11
You can also use an area model to find the product of 253 x 34
Answer: 8602 is the answer to 253 x 34, do you want the other parts solved too?
Step-by-step explanation:
Ben orders t-shirts for $8.00 per t-shirt. There is a $6.00 flat fee for shipping. He only has $50.00 to spend. How many t-shirts can he
buy?
PLEASE PLEASE HELP RN 20 POINTS ADDED
Answer: The answer is 5 shirts
Step-by-step explanation:
8x + 6 = 50
subtract 6 from each side:
8x +6 (-6) = 50 (-6)
8x=44
divide by 8:
8x/8=44/8
x=5.5
round to single shirts:
x=5 shirts
Answer:
Step-by-step explanation: you have to divide 50 by 8 then get your answer of 6.25, but you also have to consider two things; the extra $6.00 flat fee, and you cant buy 6.25 shirts, so what we do is multiply 8 times 6 to get 48, but we have to consider the extra $6.00, so you take away 8 which gives you 5 shirts, plus the shipping fee so in all he can buy 5 shirts.
mark has 5 pants and 7 shirts in his closet. he wants to wear a different pant/shirt combination each day without buying new clothes for as long as he can. how many weeks can he do this for?
Mark has 35 unique combinations to choose from, so can he co go 5 weeks with this set of clothes
Number of pants in Mark's closet = 5
Number of shirts in Mark's closet = 7
Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.
He can choose amongst the pants in 5 ways, similarly, he can choose among the shirts in 7 ways
Total number of combinations = 5*7 = 35 unique combinations
So, if he wears one combination each day he can last 35 days or 5 weeks, without buying new clothes
Learn more about combination:
https://brainly.com/question/20211959
#SPJ4
A cyclists speed is 1.5 times faster than a walkers speed. they simultaneously start moving in the same direction from the same point and, after 1.5 hours, the distance between them is 12.5 miles. what are their speeds?
Answer:
The biker's pace is 25 miles per hour and the walker's speed is 50/3 miles per hour.
Answer:The speed of the walker is 16.67 miles per hour.
The speed of the cyclist is 25 miles per hour.
How to calculate the value?
Let the speed of a walker = x
Biker's speed = 1.5x
Their relative speed will be:
= 1.5x - x = 0.5x
Distance between them = 12.5 miles
Time taken = 1.5 hours.
It should be noted that distance will be:
= Speed × Time
12.5 = 1.5 × 0.5x
Divide through to get x
12.5 = 0.75x
x = 16.67 miles per hour.
Speed of cyclist = 16.67 × 1.5 = 25 miles per hour.
using a calculator,find the value of each mathematical statement.
PLSSS HELP
The exponents are solved below\
What are exponents?
Exponentiation is a mathematical process denoted by the symbol bn that involves two integers, the base b and the exponent or power n, and is spoken as "b (raised) to the (power of) n." Exponentiation corresponds to repeated multiplication of the base when n is a positive integer: bn is the product of multiplying n bases. Typically, the exponent is displayed as a superscript to the right of the base. In such scenario, bn is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, more succinctly, "b to nth." In other words, when a base raised to one exponent is multiplied by the same base raised to another exponent, the exponents accumulate.
The exponents are solved as follows
(10⁻²)⁹ = 10⁻¹⁸ = 1/10¹⁸
10⁻³ - 10⁻⁸ = 1/10³ - 1/10⁸ = (10⁵ - 10⁸)/10⁸ = 9.9999x10⁻⁴
To know more about exponents, click on the link
https://brainly.com/question/11761858
#SPJ9
HELP PLEASE ITS DUE BY MIDNIGHT
Please help due tonight
Answer:
C.
Step-by-step explanation:
The solution to a system of equations is the point where the two lines intersect. In this case, the lines intersect at Point C.
can someone please help me solve this math problem with solution too?? TYY!!
Answer: 2080
Step-by-step explanation:
62² −42²
3844−42²
3844−1764
2080
PLS HELP ASAP THIS QUESTION IS REALLY EASY
Answer:
x = -1, y = -1
Step-by-step explanation:
[tex]4x + 3 = - 8x - 9[/tex]
[tex]12x + 3 = - 9[/tex]
[tex]12x = - 12[/tex]
[tex]x = - 1[/tex]
[tex]y = 4( - 1) + 3 = - 4 + 3 = - 1[/tex]