Perform the multiplication. Simplify the answers. 2 √30*( √5+ √6+ √10+ √15)
Answers
The simplified expression of \(2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})\)is \(10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}\)
The expression is given as:
\(2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})\)
Expand the expression
\(2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2\sqrt{30} \times \sqrt5+ 2\sqrt{30} \times \sqrt6+ 2\sqrt{30} \times \sqrt{10} + 2\sqrt{30} \times \sqrt{15}\)
Factor out 2
\(2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{30} \times \sqrt5+ \sqrt{30} \times \sqrt6+ \sqrt{30} \times \sqrt{10} + \sqrt{30} \times \sqrt{15})\)
Combine the radicals
\(2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{150} + \sqrt{180}+ \sqrt{300} + \sqrt{450})\)
Expand the expression
\(2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(\sqrt{25 \times 6} + \sqrt{9 \times 20}+ \sqrt{100 \times 3} + \sqrt{225\times 2})\)
Evaluate the roots
\(2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) = 2(5\sqrt{6} + 3\sqrt{20}+ 10\sqrt{3} + 15 \sqrt{2})\)
Expand
\(2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15}) =10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}\)
Hence, the simplified expression of \(2\sqrt{30} \times (\sqrt5+ \sqrt6+ \sqrt{10} + \sqrt{15})\)is \(10\sqrt{6} + 6\sqrt{20}+ 20\sqrt{3} + 30\sqrt{2}\)
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Related Questions
Using the graph below, describe the acceleration, position, and force at each of the
points listed in reference to how it changes from the previous section.
1
2
3
4
5.
Answers
Answer:
Step-by-step explanation:
(1). 2 m / s²
(2). 0 m / s² { Change from the previous section is - 2 m / s² }
(3). - 8 m / s² { Change from the previous section is - 8 m / s² }
(4). - 1 m / s² { Change from the previous section is + 7 m / s² }
(5). 0 m / s² { Change from the previous section is + 1 m / s² }
PLEASE HELP!!!!!!!!!!!!!!
Answers
Answer:
24
Step-by-step explanation:
36:45 = x:30
36 x 30 = 1080
1080/45 = 24
Please don’t lie to me and tell the right answer and if you do get it correct I will give you a shout out thanks
Answers
Answer:
Part A = 7
Part B = 1
I hope this is right, sorry if it isn't
Answer:
See below
Step-by-step explanation:
5 cups cheese / ( 2/3 cup cheese/plate ) =
5 * 3/2 = 15/2 = 7 1/2 or 7 full plates
2/3 cup cheese / plate * 9 plates =
2/3 * 9 = 6 cups cheese total
she has 5 cups to start.....she will need 1 cup more
there are an equal number of red, green, orange, yellow, purple, and blue candies in a bag of 42 candies. joey picks a candy at random. what is the probability that joey picks a red candy? a. b. c. d.
Answers
The probability that Joey picks a red candy is 1/6.
To calculate the probability of Joey picking a red candy, we need to determine the total number of red candies and the total number of candies in the bag.
Given that there are an equal number of red, green, orange, yellow, purple, and blue candies, and a total of 42 candies, we can determine the number of red candies.
Since there are 6 colors in total and an equal number of each, the number of red candies is:
Number of red candies = Total number of candies / Number of colors
Number of red candies = 42 / 6 = 7
Now, we can calculate the probability of Joey picking a red candy:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = Number of red candies / Total number of candies
Probability = 7 / 42
Probability = 1/6
Therefore, the probability that Joey picks a red candy is 1/6.
Your question is incomplete but this is the general answer
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which equation has a solution of k=6.5
Answers
Consider the complete question is "Which equation has a solution of k = 6.5? A. -3k = 19.5 , B. -1 + k = 7.5 , C. -7k = -45.5 , D. -2 + k = -8.5."
Given:
Solution of equation is k=6.5.
To find:
The equation.
Solution:
In option A,
\(-3k=19.5\)
\(k=\dfrac{19.5}{-3}\)
\(k=-6.5\neq 6.5\)
In option B,
\(-1+k=7.5\)
\(k=7.5+1\)
\(k=8.5\neq 6.5\)
In option C,
\( -7k = -45.5\)
\( k =\dfrac{ -45.5}{-7}\)
\( k =6.5\)
In option D,
\(-2+k=-8.5\)
\(k=-8.5+2\)
\(k=-6.5\neq 6.5\)
Therefore, the correct option is C.
If 1760 litres of fuel is sold in 5 days, in how many days will 3872 litres be sold
Answers
It will take 11 days to sell 3872 liters of fuel at the same rate as 1760 liters sold in 5 days.
We can use the following proportion to solve the problem:
1760 liters / 5 days = 3872 liters / x days
Where x is the number of days it will take to sell 3872 liters of fuel.
We can use the unitary method to solve this problem.
Let's start by finding out how much fuel is sold in one day. To do this, we need to divide the total amount of fuel sold (1760 liters) by the number of days it was sold for (5 days):
1760 liters ÷ 5 days = 352 liters per day
Now we can use this rate to find out how many days it will take to sell 3872 liters of fuel:
3872 liters ÷ 352 liters per day = 11 days (rounded to the nearest whole number)
Therefore, it will take 11 days to sell 3872 liters of fuel at the same rate as 1760 liters sold in 5 days.
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Researchers are interested in learning more about the age of women when they marry for the first time so they survey 500 married or divorced women and ask them how old they were when they first married. The collection of the ages of the 500 women when they first married is a ______
A) Population
B) Statistic
C) Parameter
D) Sample
Answers
The collection of the ages of the 500 women when they first married is a Sample.
The collection of the ages of the 500 women when they first married is a Sample.
What is a Sample?
A sample is a subset of the population. The sample is chosen to represent the entire population. The purpose of using the sample is to draw a conclusion about the population.
The sample is used to represent the population that is being studied. The collection of the ages of the 500 women when they first married is a sample since it is a subset of the entire population of women.
Researchers use a sample to learn more about the population. It's essential to choose the sample carefully so that it accurately represents the population.
The other options include:
A population is the entire group that you want to draw conclusions about.
A statistic is a numerical value calculated from a sample of data.
Parameter is a numerical value calculated from an entire population of data.
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For f(x) = x + 1 and g(x) = 2x^2 - x - 3, find (f/g)(x).
Answers
Answer:
\(\frac{1}{2x-3}\)
Step-by-step explanation:
(\(\frac{f}{g}\) )(x)
= \(\frac{f(x)}{g(x)}\)
= \(\frac{x+1}{2x^2-x-3}\) ( factorise the denominator )
= \(\frac{x+1}{(2x-3)(x+1)}\) ← cancel the common factor (x + 1) on numerator/ denominator
= \(\frac{1}{2x-3}\)
Is the ordered pair (- 2 2 A solution of the linear inequality?
Answers
No, the ordered pair (-2, 2) is not a solution of the linear inequality because it does not satisfy the inequality.
An ordered pair is a pair of numbers that are related to each other in a specific order. An ordered pair can be used to represent a point on a graph. In order for an ordered pair to be a solution of a linear inequality, it must satisfy the inequality. This means that the ordered pair must make the inequality true when it is substituted into the equation. For example, if the linear inequality is "x + 2 > 3," then for (-2, 2) to be a solution, it must make the inequality true. This would mean that -2 + 2 > 3, which is not true, so (-2, 2) is not a solution of the linear inequality.
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44. The Loveland town council wants to build a bandstand. Architects were asked to submit plans. In the plan shown, the floor has the shape of a regular octagon. a) What is the area of the floor of the bandstand in this plan? 20 ft b) What would the dimensions be of a square bandstand with the same area as the octagon above? c) Which one has the largest perimeter?
Answers
Area of the floor of the bandstand in regular octagon is 1931.2 ft²
dimensions of a square bandstand with the same area as the octagon is 43.94 ft
square bandstand has largest perimeter.
floor has the shape of a regular octagon
Area of a regular octagon = 2a²(1+\(\sqrt{2}\))
a = length of the side of the octagon
here a = 20 ft
Area = 2a²(1+\(\sqrt{2}\)) = 2(20)(20)(1+\(\sqrt{2}\))
= 800(1+1.414)
= 800(2.414)
= 1931.2 ft²
square bandstand with the same area as the octagon
Area of square = b²
b = length of the side of the square
1931.2 = b²
b = 43.94 ft
Perimeter of regular octagon = 8a
= 8(20)
= 160ft
Perimeter of Square = 4b
= 4(43.94)
= 175.78ft
area of the floor of the bandstand in regular octagon is 1931.2 ft²
dimensions of a square bandstand with the same area as the octagon is 43.94 ft
square bandstand has largest perimeter.
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suppose v is finite-dimensional, t 2 l.v / has dim v distinct eigenvalues, and s 2 l.v / has the same eigenvectors as t (not necessarily with the same eigenvalues). prove that st d ts.
Answers
As, stx = tsx for every eigenvector x of t, and eigenvectors corresponding to distinct eigenvalues are linearly independent, we can conclude that st = ts.
To prove that st = ts, where v is finite-dimensional, t and s are linear operators on v, t has dim v distinct eigenvalues, and s has the same eigenvectors as t (not necessarily with the same eigenvalues), we can use the fact that eigenvectors corresponding to distinct eigenvalues are linearly independent.
Let's consider an eigenvector x of t with eigenvalue λ. We can write this as tx = λx. Now, since s has the same eigenvectors as t, we can write this as sx = λx.
Now, let's consider the product stx. Using the definitions of s and t, we have stx = s(λx) = λ(sx).
Since sx = λx, we can substitute this in the above equation to get stx = λ(λx) = λ²x.
On the other hand, let's consider the product tsx. Using the definitions of s and t, we have tsx = t(λx) = λ(tx).
Since tx = λx, we can substitute this in the above equation to get tsx = λ(λx) = λ²x.
Since stx = tsx for every eigenvector x of t, and eigenvectors corresponding to distinct eigenvalues are linearly independent, we can conclude that st = ts.
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25w +40J 120
According to the inequality, at what rate does Mwamini drink juice, and what is her time limit?
Answers
I think not sure
PLEASEEEE HELPPPP MEEEE I HAVE A FREAKING 36 IN GEOMETRYYYY
Answers
Answer:
Suppose in a triangle △ABC, if sides AB and AC are equal, then △ ABC is an isosceles triangle where ∠ B = ∠ C. The theorem that describes the isosceles triangle is if the two sides of a triangle are congruent, then the angle opposite to them are also congruent
A transformation was performed on the following figure. Which transformation was applied to ΔSRT?
A(Reflection over the x axis
B(Reflection over the y axis
C(Dilation of 1/2
D(Translation
Answers
If a transformation was performed on the following figure, the transformation applied to ΔSRT is given as translation
What is the transformation that is called translationTranslation is a transformation in which a figure or shape is moved without rotating, flipping, or resizing it. This movement is in a straight line, either horizontally, vertically, or diagonally. The figure's orientation changes but its size, shape, and angles remain the same. In other words, a translation moves a figure to a new location without changing its appearance. It is also called a slide. The direction and distance of the slide are specified by a vector.
For example, if we translate a triangle to the right by 3 units and up by 2 units, we will obtain the same triangle, but at a different location on the coordinate plane.
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An 84-foot building casts a 98-foot shadow. What is the angle that the sun hits the building? HINT: Draw a picture.
Answers
Answer:
40.6°
Step-by-step explanation:
The building and the shadow are perpendicular to each other (or intersect at a 90° angle).
Meaning that this is a triangle problem.
We are making a triangle from the building to the shadow and a diagonal line connecting the ends of both.
We need to find the angle at the top of the building. The opposite side of the angle is 84. The adjacent side is 98.
Opposite / Adjacent = Tan X
So if we go to the calculator:
\(tan^{-1} (\frac{84}{98}) = 40.6\)
The answer is 40.6 degrees.
15 points and brainliest for the answer
Polygon ABCD is similar to polygon FGHI. Each side of polygon ABCD is 5 1/2 times longer than the corresponding side of polygon FGHI. Determine the perimeter of polygon ABCD.
Answers
Answer:
71.5
Step-by-step explanation:
(3 + 3 + 2 + 5) * 5 1/2 = 71.5
Calculate the interest on a 90-day, 9% note for $50,000 (Use a 360 day year to compute interest Round your answer to the nearest dollar ) A. S375 B. S4.500 O C. $1,125 O D. $2,250
Answers
The correct answer is C. $11,250.
To calculate the interest on a 90-day, 9% note for $50,000, we can use the simple interest formula:
Interest = Principal × Rate × Time
Given:
Principal (P) = $50,000
Rate (R) = 9% = 0.09 (decimal)
Time (T) = 90 days
Since the interest is calculated based on a 360-day year, we need to convert the time in days to a fraction of a year:
Time (T) = 90 days / 360 days = 0.25 (fraction of a year)
Now we can calculate the interest:
Interest = $50,000 × 0.09 × 0.25
Interest = $11,250
Rounded to the nearest dollar, the interest on the 90-day, 9% note for $50,000 is $11,250.
Therefore, the correct answer is C. $11,250.
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a researcher studies a group of 25 preschool children in order to answer questions about the entire population of preschool children. what general categories of statistical techniques will this researcher be using?
Answers
The researchers use inferential statistics.
Inferential statistics uses measurement from a sample, comparing groups and making generalizations about the large population. Inferential statistics are based on a test statistic calculated based on a formula. The test statistic along with degrees of freedom to determine the difference between the study population. With inferential statistics, the researcher will draw conclusions from extrapolations.
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how do u find the sum of (5x-2) + (4x+6)
Answers
\( \: \: \: \: \: \: \: \: (5x - 2) + (4x + 6) \\ \\ = > 5x - 2 + 4x + 6 \\ \\ = > 5x + 4x - 2 + 6 \\ \\ = > \green{\boxed { 9x + 4}}\)
Answer:
9x+4
Step-by-step explanation:
First, remove the unnecessary parentheses from (5x-2)+(4x+6) making it 5x-2+4x+6 because when there is a + in front of an expression in parentheses, the expression remains the same.
Next, collect like terms, turning 5x-2+4x+6 into 9x-2+6.
Now, calculate the sum and you should get 9x+4.
What is inequality algebraically |x+9|<7
Answers
The inequality |x+9|<7 can be written as -16<x<-2.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
we have the inequality:|x+9|<7
By Definition of Absolute Value.
-(x+9)<7 and x+9<7
-x-9<7
-x<16
x>-16..(1)
and
x+9<7
x<-2...(2)
-16<x<-2
Hence, the inequality |x+9|<7 can be written as -16<x<-2.
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i need hlp with this question offer I 50 points
Answers
We can start by multiplying both sides of the equation by the reciprocal of 2/3, which is 3/2, to get rid of the fraction:
```
2/3 ( ) = -5 + 4x
(3/2) * 2/3 ( ) = (3/2) * (-5 + 4x)
( ) = -15/2 + 6x
```
Now we can compare this expression to the possible answer choices to see which one makes the equation true:
A: -15/2 + 6X --> This is the same expression we just solved for, so it must be the correct answer.
B: 10/3 + 8/3X --> This expression does not match our solution.
C: 5 2/3+3 1/3X --> This expression does not match our solution.
D: -15+12X --> This expression does not match our solution.
Therefore, the answer is A: -15/2 + 6X.
Isabella flew 720 miles in 120 minutes. How many miles per minute did
she fly?
Answers
Answer:
6 miles per minute.
Step-by-step explanation:
All you need to do is, divided 720 into 120, and you will get your answer. :)
i need help with 1-9 please help!!
Answers
Answer:
1
Step-by-step explanation:this is so easy
Here is part of a shopping bill for clothing.
Work out the cost of the jacket before the discount.
Answers
Answer:
how are we supposed to answer this
Answer:
Hewo ❤
Step-by-step explanation:
❤ how are you? ❤
In triangle ABC above, what is m
Answers
Answer:
15*
Step-by-step explanation:
Change from rectangular to spherical coordinates. (Let rho ≥ 0, 0 ≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π.) (a) (0, −9, 0) (b) (-1,1,-sqrt(2))
Answers
The point (0, −9, 0) in rectangular coordinates can be written in spherical coordinates as (9, π/2, π). The point (-1,1,-√2) in rectangular coordinates can be written in spherical coordinates as (2, 5π/4, π/4).
(a) The point (0, −9, 0) in rectangular coordinates can be written in spherical coordinates as (9, π/2, π), where ρ = 9 is the distance from the origin to the point, θ = π/2 is the angle between the positive x-axis.
The projection of the point onto the xy-plane, and ϕ = π is the angle between the positive z-axis and the line segment connecting the origin and the point.
(b) The point (-1,1,-√2) in rectangular coordinates can be written in spherical coordinates as (2, 5π/4, π/4), where ρ = 2 is the distance from the origin to the point, θ = 5π/4 is the angle between the positive x-axis.
The projection of the point onto the xy-plane, and ϕ = π/4 is the angle between the positive z-axis and the line segment connecting the origin and the point.
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(5,-4); y = 1/5 x - 4
Answers
y = 1/5x - 5 is the equation of slope-intercept form .
What is slope-intercept form explain?
A line's equation can be written in the slope-intercept form such that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are instantly visible. This form is frequently known as the y = mx + b form.equation y = 1/5 x - 4
compare y = mx + c , m = 1/5
put points (5,-4) in equation
y = mx + c
- 4 = 1/5 * 5 + c
- 4 = 1 + c
c = -5
put value of c in equation
y = 1/5x - 5
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i am stuck on this question and i’m not sure how to graph it
Answers
Given the function:
\(f\left(t\right)=e^{0.4t}\)For t = -4,
\(f\left(t\right)=e^{0.4(-4)}=e^{-1.6}=0.2\)For t = -2,
\(f(t)=e^{0.4(-2)}=e^{-0.8}=0.4\)For t = 0,
\(f(t)=e^{0.4(0)}=e^0=1\)For t = 2;
\(f(t)=e^{0.4(2)}=e^{0.8}=2.2\)For t = 4,
\(f(t)=e^{0.4(4)}=e^{1.6}=5\)Then we graph the points
(-4,0.2) (-2, 0.4) (0,1) (2, 2.2) and (4,5)
and we get the graph:
Decide which chi-square test (goodness-of fit, homogeneity, or independence) would be most appropriate for the given situation.
A car insurance company performed a study to determine whether an association exists between age and the frequency of car accidents. They obtained the following sample data.
Age Group
Under 25 25-45 Over 45 Total
Number of accidents in past 3 years 0 74 90 84 248
1 19 8 12 39
1 7 2 4 13
Total 100 100 100 300
A. Test for Homogeneity.
B. Test for Independence.
C. Test for Goodness-of-fit.
Answers
Answer:
C. Test for Goodness-of-fit.
Step-by-step explanation:
C. Test for Goodness-of-fit would be most appropriate for the given situation.
A. Test Of Homogeneity.
The value of q is large when the sample variances differ greatly and is zero when all variances are zero . Sample variances do not differ greatly in the given question.
B. Test for Independence.
The chi square is used to test the hypothesis about the independence of two variables each of which is classified into number of attributes. They are not classified into attributes.
C. Test for Goodness-of-fit.
The chi square test is applicable when the cell probabilities depend upon unknown parameters provided that the unknown parameters are replaced with their estimates and provided that one degree of freedom is deducted for each parameter estimated.
Which solid has 12 edges?
Answers
A cube has 6 faces, 8 vertices, and 12 edges.
What is the Polyhedron?
A polyhedron is a 3D shape that has flat faces, straight edges, and sharp vertices (corners). The word "polyhedron" is derived from a Greek word, where 'poly' means "many" and hedron means "surface".Thus, when many flat surfaces are joined together they form a polyhedron. These shapes have names according to their faces which are usually polygons.
A cube or a cuboid is a three dimensional shape that has 12 edges, 8 corners or vertices, and 6 faces.
The difference between a cube and a cuboid is that a cube has all edges equal which makes every face a square while a cuboid has two square faces and four rectangular faces.
In any convex polyhedron, if V is the number of vertices or corners, F is the number of faces and E is the number of edges, then V + F = E + 2.
Therefore, A cube has 6 faces, 8 vertices, and 12 edges.
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