[tex]\sqrt[3]{-8x^{24}y^{36}} = \sqrt[3]{-8}\cdot \sqrt[3]{x^{24}}\cdot \sqrt[3]{y^{36}}[/tex]
[tex]\sqrt[3]{8}=-2[/tex] because [tex](-2)(-2)(-2)= -8[/tex]
[tex]\sqrt[3]{x^{24}}=x^8[/tex] because [tex](x^8)(x^8)(x^8)=x^{24}[/tex]
[tex]\sqrt[3]{y^{36}}=y^{12}[/tex] because [tex](y^{12})(y^{12})(y^{12})=y^{36}[/tex]
Therefore [tex]\sqrt[3]{-8x^{24}y^{36}} = -2x^8y^{12}[/tex]
Answer:
[tex]-2x^8y^{12}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt[3]{-8x^{24}y^{36}}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}:[/tex]
[tex]\implies \sqrt[3]{-8}\sqrt[3]{x^{24}}\sqrt[3]{y^{36}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies \left(-8\right)^{\frac{1}{3}}\left(x^{24}\right)^{\frac{1}{3}}\left(y^{36}\right)^{\frac{1}{3}}[/tex]
Rewrite 8 as 2³:
[tex]\implies \left(-2^3\right)^{\frac{1}{3}}\left(x^{24}\right)^{\frac{1}{3}}\left(y^{36}\right)^{\frac{1}{3}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies -2^{\frac{3}{3}}x^{\frac{24}{3}}y^{\frac{36}{3}}[/tex]
Simplify:
[tex]\implies -2x^8y^{12}[/tex]
A car rental charges an initial fee of $42 and a daily fee of $12. A costumer pays a total of $138. How many days did the customer rent the car?
Answer: 8 days
Step-by-step explanation: 138-42 = 96 then you divide that by daily fee of 12 to get 8 days
Find the 7th term in the
sequence
1, -3, 9, -27, . . .
Answer:
81,-247, 729
Step-by-step explanation:
each time its multiplying it by -3
so -27x-3=81
Answer: 729
Step-by-step explanation: The thing that happens every time is -3 is multiplied: 1, -3, 9, -27, 81, -243, 729
hope this helps!
please give brainliest!
can anybody help please?
A box is a cuboid with dimensions 26 cm by 15 cm by 20 cm all measured to the nearest centimetre. Disc cases are cuboids which measure 1.6 cm by 14.2 cm by 19.3 cm all measured to the nearest millimetre. 20 cm If the disc cases are stacked as shown, show that it may not be possible for 16 cases to fit in the box. box measurements: 26 cm 15 cm 20cm disc measurements: 1.6 cm 19.3 cm 14.2 cm
The number of discs that can be filled in the box is 17.
length of box , l =26 cm , breadth , b =15 cm , height = 20 cm
So,the volume of the box = l × b × h
= 26 × 15 ×20 cm³
= 7800 cm³
Now length of a disc case, l= 1.6 cm
breadth ,b =14.2 cm
height, h =19.3 cm
So the volume of a disc case = 1.6×14.2×19.3 cm³
= 438.496 cm³
No of disc cases can be stacked inside the box
= 7800 ÷ 438.496
=7800000÷438.496
= 17.8
Hence 17 disc cases can be fitted into the box.
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9. The perimeter and the ratio of the
length to the width of a rectangle are
given. Find the length and width of the
rectangle.
Perimeter: 132 cm 1:w = 7:4
Answer:
Length: 42, width: 24
Step-by-step explanation:
Perimeter: 132
L: W = 7:4
7u+7u+4u+4u= 22u (Length + length + width + width)
132/22= 6 (1u)
6x4= 24 (Width/ 4u)
6x7=42 (length/7u)
recheck:
42+42+24+24= 132cm
perimeter= 132
What is the value for x and y? and how do you use the systems to figure them out?
The value of x is 22.37 and y is 20
What is Interior angle?
An angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon.
What is Exterior angle?
An exterior angle (also called an external angle or turning angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.
We know, the sum of interior angle is 180 degree
The given interior angles is ,
3y + 5 and 5y + 15
So, equate to 180°
3y + 5 + 5y + 15 = 180°
Solve for 'y'
8y + 20 = 180
4(2y + 5) = 180
2y + 5 = 45
2y = 45 - 5
2y = 40
y = 20
Now, we know the sum of exterior angle is 360 degree
The given exterior angle is,
17x - 70 and 2x + 5
So, equate to 360°
17x - 70 + 2x + 5 = 360°
Now, solve for 'x'
19x - 65 = 360
19x = 360 + 65
19x = 425
x = 22.368 or 22.37
Hence, the value of x is 22.37 and y is 20
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wall-to-wall carpeting is installed in a room that is ft long and ft wide. the edges of the carpet are held down by tack strips. how many feet of tack-strip material are needed?
If wall-to-wall carpeting is installed in a room 21 ft long and 17 ft wide and the edges of the carpet are held down by tack strips, the feet of tack-strip material needed are 76 ft calculated by determining the perimeter of the rectangle room.
Tack strips are thin pieces of wood studded with nails or tacks in the installation of carpets. These thin strips are placed along all the edges of the carpet. In order to determine the length of the tack strips needed to hold the wall to wall carpeting installed in a rectangular room of 21 ft by 17 ft. The formula of the perimeter of a rectangle is:
P = 2 (length + width)
P = 2 (21 + 17)
P = 2 (38)
P = 76 ft
Hence, the feet of tack-strip material needed are 76 ft.
Note: The question is incomplete. The complete question is Wall-to-wall carpeting is to be installed in a rectangular room that is 21 ft long and 17 ft wide. The edges of the carpet are to be held down by tack strips. How many feet of tack-strip material is needed?
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The comprehensive graph of a polynomial function y=f(x) is shown
how many real zeros does the function f have?
There is only 1 real zero of the function.
What are Zeros of a Function?
The zeros of a function are the values of the function's variables that fulfil the equation and yield the function's value of 0. The zeros of a function can be represented graphically as the x-coordinates (x-intercepts) where the graph intersects the x-axis.
Solution:
As mentioned above,
The zeros of a function can be represented graphically as the x-coordinates (x-intercepts) where the graph intersects the x-axis.
So,
We can see that there is only one point where the graph intersects the x-axis.
Therefore, it can be said that there is only 1 real zero of the function.
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Pete,Joe, and Blake shared a large pizza. The pizza was cut into eight pieces. Pete ate two pieces, Joe ate two piece, and Blake ate one piece. Which fraction is equivalent to the amount of pizza that was eaten by all the boys.
Answer:
Pete ate 2, Joe ate two, and Blake ate 1
2 + 2 + 1 = 5
They ate 5 out of 8 slices. The boys ate 5/8 of the pizza
20 points
need help with this
Answer:
D
Given the inequation symbols > and < , the lines will be dotted.
The points A(0,5), B(4,2), and C(0,2) form the vertices of a right triangle in the coordinate plane. What is the equation of the line that forms the hypotenuse
Answer:
y = - [tex]\frac{3}{4}[/tex] x + 5
Step-by-step explanation:
the hypotenuse is the line AB
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A (0, 5 ) and (x₂, y₂ ) = B (4, 2 )
m = [tex]\frac{2-5}{4-0}[/tex] = [tex]\frac{-3}{4}[/tex] = - [tex]\frac{3}{4}[/tex]
the line AB crosses the y- axis at A (0, 5 ) ⇒ c = 5
y = - [tex]\frac{3}{4}[/tex] x + 5 ← equation of hypotenuse
Find the perimeter of the figure below. Use 3.14 for pi
10 m
16 m
I hope this is the last on I need help with!-
I need an answer immediately and i will give a lot of points
╔══╗
╚╗╔╝
╔╝ (¯`v´¯)
╚══`.¸.*when you answer*
Answer:
72.52
Step-by-step explanation:
circumference of a circle formula = [tex]2\pi r[/tex]
where r is the radius
the radius is half of diameter, and the diameters for all semicircles are given.
so the radius for the smaller semicircles is 10/2 which is 5
so [tex]2\pi 5[/tex] = 2(3.14)(5) = 31.4
31.4 is the circumference of the whole circle, since we have 2 semicircles with the same radius, we don't need to divide this by 2, we will simply use 31.4 for instead of doing this exact calculation again for the other small semicircle.
for the larger cemicircle, the diameter is 16 so the radius will be 16/2 which is 8
[tex]2\pi 8[/tex] = 2(3.14)(8) = 50.24
since 50.24 is the circumference of an entire circle, we will have to divide this by 2 to d=find the circumference of the semicircle.
50.24/2 = 25.12
Now we will simply add up the lengths of the borders,
31.4 + 25.12 + 16 = 72.52
Answer:
57.7 meters total perimeter for the object.
Step-by-step explanation:
See the attached worksheet. Break up the object into three circles and one rectangle. Label them to keep track of the work. The object's perimeter is coprised of:
- One side of rectangle R (16 m)
- 1/2 the circumference of circles b and c, each with a radius of 5 m
- 1/2 the circumference of circle a, with a circumference of 8 m.
The perimeter of a circle is 2πr. The perimeter of circles b and c is 31.4 meters in total, which is reduced to (1/2) or 15.7 m total. Circle a contributes 26 meters to the object's perimeter.
The sum of these measurements is (16m) + (15.7m) + (26m) = 57.7 meters total perimeter for the object.
If n is the greater of two consecutive
numbers, write an expression for the other
number.
The expression for the other number is (n-1) when n is the greater of two consecutive numbers.
Given that,
We have to write an expression for the other number if n is the greater of two successive numbers.
We know that,
One is equal to the difference between any two consecutive numbers.
Let us take
x be the smaller of two consecutive number
n be the larger of two consecutive numbers
We have that
n-x=1
Solve for x
x=n-1
Therefore, The expression for the other number is (n-1) when n is the greater of two consecutive numbers.
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A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, what is the total weight in tons of all the wheat that will be placed on the first 59 squares? (Assume that each grain of wheat weighs 1/7000 pound. Remember that 1 ton2000 lbs.)
The number of grains on square 59 will be 5.7646075230342 x 10^17grains.
How to calculate the number of grain?No. of grains on the first square = 1 = 2^0
No. of grains on the second square = 2 = 1*2 = 2¹
No. of grains on the third square = 4 = 2*2 = 2²
No. of grains on the fourth square = 8 = 2*4 = 2³
From the pattern it could be seen that amount of wheat is doubled for every next square
So, the number of grains in the nth square = 2^n-1
Therefore, No. of grains on 59th square
= 2^59 -1 =
= 5.7646075230342 x 10^17
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A phone receives signals from a transmitter that is
13 km west and 21 km south of it.
What is the bearing from the phone to the
transmitter?
Give your answer to the nearest degree.
Answer:
301.76
Step-by-step explanation:
I'll add a diagram for better understanding.
Look at the diagram
The angle with a question mark in purple is the the bearing from the phone to the transmitter.
To figure out that angle we will have to figure out the angle inside the triangle on that side and we will subtract that from 360 to find the answer.
Since this is a right angled triangle, we can use SOH CAH TOA to figure out the angle inside.
For the angle we have to figure out, 21 is the opposite and 13 is adjacent.
so we will use TOA
tan[tex]x\\[/tex] = O/A
tan[tex]x[/tex] = 21/13
tan inverse(21/13) = [tex]x[/tex]
[tex]x[/tex] = 58.2405
This is the phone's angle inside the triangle
subtract this from 360 to find the bearing
360 - 58.2405 = 301.76
The graph of the function y = -2 can be described as ________________.
Responses
curved
curved
horizontal
horizontal
vertical
vertical
diagonal
The graph of the function y = -2 can be described as Horizontal.
Given, a function y = -2.
As, we can see that the given function is an one variable function.
And the functions in one variable have straight line graph.
Now, the function y = -2 has a graph that will be parallel to the x-axis.
So, the function y = -2 has a graph that will be horizontal as the x-axis is horizontal in cartesian plane.
Hence, the graph of the function y = -2 can be described as Horizontal.
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7) Find the discriminant to determine the number of roots, then solve the quadratic equation
using the quadratic formula.
2x² + 7x-4 = 0
The Determinant of the equation is 17
What is the determinant of the equation?
The determinant is a scalar variable in mathematics that is a function of the elements of a square matrix. It enables the characterization of some characteristics of the matrix as well as the linear map expressed by the array. The determinant is nonzero, in particular, if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a matrices product is the product of their determinants (the preceding property is a corollary of this one). The determinant is a scalar variable in mathematics that is a function of the elements of a square matrix. It enables the characterization of some attributes of the matrix as well as the vertical map presented by that of the array.
Given equation is 2x² + 7x - 4 = 0
Therefore, determinant = (7)² - 4x2x(-4)
= 49 - 32
= 17
Hence, the determinant of the given equation is 17
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If a board of directors consists of 18 people, how many ways can a chief executive officer, a director, a treasurer, and a secretary be selected?.
There are 204 possible methods to choose a chief executive officer, a director, a treasurer, and a secretary, if there are 18 members on the board of directors.
What is combination?Combinations are mathematical procedures that count how many different ways a collection of items might be arranged when the order in which they are chosen is immaterial. Regardless of the order in which the things are chosen, a combination is the choice of all or part of a collection of objects. A combination is "an arrangement of items where the order of the components is unimportant," according to the definition. When these two terms are combined, "Selection of things" is meant, where the order of the items is not important.
Here,
If the order doesn't matter then we have a combination, if the order do matter then we have a permutation.
18C4=18!/(18-4)!(4)!
=18!/14!4!
=18*17*16*15/4*3*2*1
=3*17*4
=204 ways
A chief executive officer, a director, a treasurer, and a secretary be can be selected in 204 ways If a board of directors consists of 18 people.
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10. Suppose the length and width of the rectangle are doubled. What effect would this have on the area? 15 points!!!!
Answer:
area increases by a factor of 4
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = lw ( l is length and w is width )
doubling the length and width , that is
l = 2l and w = 2w , then
A = 2l × 2w = 4lw
that is the area is increased by a factor of 4
Calculer 1,2% de 130 £
in a certain chemical the of zinc to copper is 4 to 15 if a jar contains 600 grams of copper how much zinc is there
The amount of zinc in the jar is 160 grams.
According to the question,
We have the following information:
In a certain chemical the of zinc to copper is 4 to 15 and a jar contains 600 grams of copper.
Let's take the amount of zinc in a chemical to be 4x and that of copper to be 15x.
So, we have the following expression:
15x = 600
Dividing both the sides by 15 will give us the value of x:
x = 600/15
x = 40 grams
Now, we will put this value of x in the amount of zinc:
4x grams
4*40
160 grams
Hence, the amount of zinc in the given jar is 160 grams.
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Lauren and Chris buy 60 rolls of paper towels in bulk. They use up 1 roll every week and a half. How many weeks will it take them to run out of rolls of paper towels?
Total number of rolls are 60, they used 1 and half roll per week. So, 40 weeks will it take them to run out of rolls of paper towels.
What are Paper towels?Paper towels are the disposable paper made up from the paper. It is an absorbent, which designed to absorb liquid. It is made up of pulp like tissue paper which are meant to be single time use only.
Paper towel is made up of cellulose fibers who are bigger in size consist of many small molecules linked together. Paper towels are used in drying, wiping, cleaning, toilets etc.
For given information,
Total rolls= 60
They used up 1 roll in 1.5 week or 1 week and half
So,
60 + 60*1/2
60+30= 90 weeks
Thus, total number of rolls are 60, they used 1 and half roll per week. So, 40 weeks will it take them to run out of rolls of paper towels.
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the overall speedup of a system that spends 40% of its time in calculations with a processor upgrade that provides for 100% greater throughput is
The overall speedup of such a system that spends 40% of its time performing calculations is 1.25 when a processor upgrade results in 100% more throughput.
What is defied as the processor upgrade?One of the most efficient and affordable changes you can do to a more aged system is swapping the processor with a speedier one. In some circumstances, you can significantly increase CPU performance at a little cost. Not every system is a good candidate for a processor upgrade, which is unfortunate.The overall speedup of a machine that spends 40% of its time processing data with a processor upgrade that offers 100% more throughput answers the issue.
Thus, with a CPU upgrade that results in 100% more throughput, a system that spends 40% of its time performing calculations sees an overall speedup of 1.25.
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A chool i arranging a field trip to the zoo. The chool pend 683. 47 dollar on pae for 38 tudent and 3 teacher. The chool alo pend 334. 78 dollar on lunch for jut the tudent. How much money wa pent on a pa and lunch for each tudent?
25.48 was spent on a pass and lunch for each student.
Total money spend on passes = 683.47
Total no. of people = 38 + 3
= 41
Money spend on pass for each person = 683.47/41
= 16.67
Total money spend on lunch = 334.78
Total no. of students = 38
Money spend on lunch for each student = 334.78/38
= 8.81
Total = 16.67 + 8.81
= 25.48
Hence, 25.48 was spent on a pass and lunch for each student.
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Question 3(Multiple Choice Worth 2 points)
(03.03 MC)
What are the zeros of the function f(x) = x² - 4x² - 5?
+√5 ti
±2, ti
±5, ti
+√2 ti
Question 4(Multiple Choice Worth 2 points)
The solution to the equation are 5 or -1 after applying the quadratic formula.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
It is given that:
x² - 4x² - 5 = 0
The above equation is a quadratic equation:
Using the quadratic formula:
[tex]\rm $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
Plug the values in the formula:
[tex]\rm $x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(-5)}}{2(1)}$[/tex]
After solving:
x = 5 or -1
Thus, the solution to the equation is 5 or -1 after applying the quadratic formula.
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What is the next term in the sequence 4, 11, 18, 25, ...?
Answer: 32
Step-by-step explanation: you have to count by 7 everytime
follow the steps to find the area of the Shaded region. use trigonometry to find the height of the triangle. ROUND TO THE FOURTH DECIMAL PLACE!
HINT: Not 51 cm
Applying the trigonometry ratio, SOH, the height, h = 6.2172 cm.
Area of the region that is shaded in the circle = 47.1784 cm²
What are the Trigonometric Ratios?Recall the formulas for the trigonometric ratios, which are given as SOHCAHTOA, where:
SOH is sin ∅ = opp/hypCAH is cos ∅ = adj/hypTOA is tan ∅ = opp/adj.Find the height, h, of the triangle using the sine ratio of trigonometry:
∅ = 51°
Opposite length = h
Hypotenuse = 8 cm
sin 51 = h/8
h = 8(sin 51)
h = 6.2172 cm
Area of the triangle = 1/2(base)(height) = 1/2(8)(6.2172)
Area of the triangle = 24.8688 cm²
Area of the sector = /360 × r² = 129/360 × (8²)
Area of the sector = 72.0472 cm²
Area of the shaded region = area of the sector - area of the triangle
= 72.0472 - 24.8688
= 47.1784 cm²
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1. in 2009, 33% of americans felt that one parent should stay home to raise the children instead of using day care. in a poll conducted in 2011, 416 out of 1015 americans believed that one parent should stay home. at a 99% level of confidence, is there sufficient evidence to conclude that the percentage has increased from its 2009 value?
Answer: Yes
Step-by-step explanation: To show that the percentage has increased we would need to prove that 416/1015 with a 99% level of confidence or a 1% margin of error to do this we divide 416 by 1015
This equals 0.40985221674
Which can be rounded to 0.41 or 41% since there is a one percent margin of error we can assume that this is enough evidence, because if 1% of the poll's recipients mistakenly voted for a option they did not really think was true it would not be enough to change 41% to 33%
Hope this helps!
if they want to be 99% sure that their estimate will be within 3% of the true population percentage, how large of a sample do they need?
If they want to be 99% sure that their estimate will be within 3% of the true population percentage then the required sample size is n = 4161.
When there is no known population, the sample size can be calculated by determining the minimal sample size needed to accurately estimate proportions while taking the standard normal deviation into account.
We have been given the confidence level = c= 99%
Estimate percentage= 3%
We want to find the sample size when the true percentage is not given
Therefore Assume that true proportion = p = 0.5
Therefore the sample size is calculated as:
N= p(1-p) (zc/e) square
N = 4161
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Translate the sentence into an inequality. The product of w and 7 is at most -25
Answer:
7w ≤ -25
Step-by-step explanation:
If 7 x W is at most -25 then it cant be greater than -25 but can be equal to it.
Hope this helped!
Simplify them please(a and b)
a. [tex]a^{3}[/tex].
b. [tex]\frac{1}{2c^{6}}[/tex].
Step-by-step explanation:Exercise "a".1. Write the expression.[tex]\frac{a^{4} }{a}[/tex]
2. Subtract 1 from the exponent of both numerator and denominator.[tex]\frac{a^{4-1} }{a^{1-1} }=\\ \\\frac{a^{3} }{a^{0} }=\\\\ \frac{a^{3} }{1 }=\\ \\a^{3}[/tex]
3. Final answer.[tex]a^{3}[/tex]
----------------------------------------------------------------------------------------------------------
Exercise "b".1. Write the expression.[tex]\frac{2c^{-4} }{c^{2}}[/tex]
2. Move the numerator down to the denominator by changing the sign of the exponent.[tex]\frac{1}{c^{2}*2c^{4} }[/tex]
3. Multiply.[tex]\frac{1}{2c^{6}}[/tex]
