The length of the vector x=5e1+3e2+2e3+4e4+2e5−4e6 is √79.
What is the magnitude of vector x?The given vector x can be expressed as a linear combination of the standard basis vectors in R6. We calculate the length (magnitude) of x using the formula ||x|| = √(x₁² + x₂² + x₃² + x₄² + x₅² + x₆²), where x₁, x₂, x₃, x₄, x₅, and x₆ are the coefficients of the standard basis vectors e1, e2, e3, e4, e5, and e6 respectively.
In this case, x = 5e1 + 3e2 + 2e3 + 4e4 + 2e5 - 4e6, so we substitute the coefficients into the formula:
||x|| = √((5)² + (3)² + (2)² + (4)² + (2)² + (-4)²)
= √(25 + 9 + 4 + 16 + 4 + 16)
= √(74 + 5)
= √79
Therefore, the length of vector x, ||x||, is √79.
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The length of one leg of an isosceles right triangle is 3 ft. What is the perimeter of the triangle?
O3+3√√2 ft
O 3+3-√√3 ft
O 6+3 √√2 ft
O6+3√3 ft
Step-by-step explanation:
Solution
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Verified by Toppr
Correct option is A)
In an isosceles right angled triangle, the two sides on the right angle are equal.
Let the equal sides be a.
Hence, hypotenuse of the isosceles right angled triangle =
a
2
+a
2
=
2
a
Given, perimeter of the triangle =(6+3
2
)m
⇒a+a+
2
a=(6+3
2
)m
⇒a(2+
2
)=3(2+
2
)m
⇒a=3m
In the isosceles right triangle, the base and height =a
Hence, area of the triangle =
2
1
×base×height =
2
1
×3×3=4.5m
2
I keep believing the answer is either 18,000 or 1,800 but im incorrect. Can someone please help me?? I use the formula A^2 *2*A*L=SA
The base is a square, so the area of the square is (10 cm)² = 100 cm²
To find the area of each triangle use the formula
base • height
10 cm • 9 cm = 90 cm²
now multiply by the number of triangles
90 cm • 4 = 360 cm²
Add the area of the square:
100 cm² + 360 cm² = 460 cm²
I hope it's correct
Answer:
SA = 280 cm²
Step-by-step explanation:
SA = area of base + area of 4 congruent triangles
= 10² + (4 × [tex]\frac{1}{2}[/tex] × 10 × 9 )
= 100 + (2 × 10 × 9)
= 100 + 180
= 280 cm²
O Work out the length of x.
Give your answer rounded to 3 significant figures.
12.4 mm
8.6 mm
X
Answer:
8.9mm
Step-by-step explanation:
To solve for x, we use the Pythagoras theorem.
Pythagoras theorem states that in a right angled triangle, the square of the Hypotenus is equal to the sum of the square of the other two sides.
The Hypotenus is the longest side, or the side facing the right angle.
From the question above,
[tex]12.4 {}^{2} = \: 8.6 {}^{2} + x {}^{2} \\ \\ 153.76 \: = 73.96 \: + x {}^{2} \\ \\ collecting \: liketerms \\ \\ x { \: }^{2} = 153.76 - 73.93 \\ = 79.83 \\ \\ squareroot \: bothsides \\ \\ \sqrt{x {}^{2} } = \sqrt{79.83} \\ \\ x = 8.9[/tex]
Select all the true statements. Logarithms may be used to linearize data. Powers may be used to linearize data. Roots may be used to linearize data. If a data set is linearized by taking the common logarithm (log) or natural logarithm (ln) of the y-values, then the data follows a power model. If a data set is linearized by taking the pth root of the y-values, then the data follows a power model.
The true statements are:
Logarithms may be used to linearize data.
Powers may be used to linearize data. Roots may be used to linearize data.
If a data set is linearized by taking the common logarithm (log) or natural logarithm (ln) of the y-values, then the data follows a power model.
Another format for writing exponents is in logarithms.
The use of a logarithm can be utilized to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. Exponent and logarithm are inverse forms of one another. A logarithm is defined using an exponent.
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Answer:
A.Logarithms may be used to linearize data.
B.Powers may be used to linearize data.
C.Roots may be used to linearize data.
E.If a data set is linearized by taking the pth root of the y-values, then the data follows a power model.
Step-by-step explanation:
Yes
At a charity fundraiser, each female attendant donated $1,200 and each male attendant donated $800. If the average donation at the fundraiser was $900, what was the ratio of the number of female attendants to the number of male attendants.
The ratio of the number of female attendants to the number of male attendants is 21/17
RatioAmount donated by female attendant = $1200Amount donated by male attendant = $800Average donation = $900let
number of female attendant = xnumber of male attendant = y900 = 1200x + 800y / (x + y)
900x + 900y = 1200x + 800y
900x + 1200x = 800y + 900y
2100x = 1700y
x : y = 2100 / 1700
x : y = 21 ; 17
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I need help anyone with graphs
The given function shows imply that the graph g(x) is shifted two units right and three units up.
Option B is correct.
What is the transformation of a function?The transformation of a function occurs in a fancy way such that a function maps itself. f: x → x.
From the given information:
Let's take a look at the function f(x) that goes through 0 just when x = 0. Now we want to move it to the right by 2. It implies that it has to go through 0 when x = +2.
Now, we have to add 2 to x, then the function becomes f'(x) = f(x-2) will be shifted by 2 units to the right.
Similarly, the same scenario occurs when shifting up. Again imagine your function passes 0 when x = 0. We have to add 3. Now, the function f’’(x) = f(x) + 3 will be shifted by 3 units up.
Combining the two transformations, we have:
g(x) = f(x-2) + 3Therefore, we can conclude that the function implies that the graph g(x) is shifted two units right and three units up.
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The distribution of probabilities for each outcome of a random variable that sums to 1.00 is called a Group of answer choices random variable probability distribution conditional probability sample space
The distribution of probabilities for each outcome of a random variable that sums to 1.00 is called a Probability Distribution.
According to the statement
we have to find the under which probability type The distribution of probabilities for each outcome of a random variable that sums to 1.00.
So,
For this purpose, we know that the
A probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range.
and the above written definition of probability is satisfied the condition that the The distribution of probabilities for each outcome of a random variable that sums to 1.00.
Due to this reason The Probability Distribution is a correct option.
So, The distribution of probabilities for each outcome of a random variable that sums to 1.00 is called a Probability Distribution.
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Two random samples were done to determine how often people in a community go to the dentist. the first sample surveyed 10 people as they entered their workplaces. the first sample found that the mean time between visits to the dentist was 7.5 months. the second sample surveyed 50 people as they entered the local grocery store. the second sample found that the mean time between visits to the dentist was 18.1 months. which statements are true? check all that apply. the first sample is likely to be more representative of the population. the second sample is likely to be more representative of the population. the second sample will give a better representation because it is larger. the first sample is not biased. community members probably visit the dentist about once every 18 months.
Answer:
B, C and E
Step-by-step explanation:
PLEASE HELP I've been struggling on this one :(
Answer: The answer is (x+2)(x-4)(x-4)
Or as a short form you can write it as [tex](x+2) (x-4)^{2}[/tex]
Step-by-step explanation:
Answer is very lengthy but I am 100% sure that's the correct answer
Answer:
(x³ - 6x² + 32) = (x - 4)²(x + 2)
Step-by-step explanation:
(x³ - 6x² + 32)/(x - 4) =
x² - 2x - 8
----------------------------------
x - 4 | x³ - 6x² + 0x + 32
x³ - 4x²
----------
-2x² + 0x
-2x² + 8x
----------------
-8x + 32
-8x + 32
-------------
0
(x³ - 6x² + 32) = (x - 4)(x² - 2x - 8) = (x - 4)(x - 4)(x + 2) =
= (x - 4)²(x + 2)
13. Define the domain of the following
For the given diagram, the domain of the graph will be within the range [-2, 8]. Hence the required domain are {-2, 0, 1, 2, 8}
Domain of a functionThe domain of a function are the independent variable of the function for which it exists,
For graphs, the domain exists on the x-axis of the curve or line on the xy plane.
For the given diagram, the domain of the graph will be within the range [-2, 8]. Hence the required domain are {-2, 0, 1, 2, 8}
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Some articles were bought at 6 for rupees 5 and sold at 5 for rupees 6. find the gain percent
44% is the answer
6 Article price at buying =5 Rs
1 Article price at buying = 5/6...(i)
5 Articles sold at Rs. 6
1 Articles cost at sold = 6/5 ....(ii)
% Gain=((6/5 - 5/6)/ 5/6) * 100
= 11/25 * 100 = 44%
Profit is a general increase in an asset or the value of an asset. If the item's current price is higher than the original purchase price, you will make a profit. For accounting and tax purposes, profits can be categorized in several ways: B. Gross profit and net profit, or realized profit and unrealized (paper) profit.
The definition of victory is profit, benefit, or increase. An example of profit is a 5% increase in income over the past year. An example of a win is a 5 point lead over another team.
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Explain why the standard deviation of a set of data is always given as a positive number, but data points can have a negative overall standard deviation.
The reason why the standard deviation of a set of data is always given as a positive number is because the individual values are squared.
What is the standard deviation?The term standard deviation is used to express how much numbers depart from the mean value. Now we know that the standard deviation for each of the data points is the square of the difference between the score and the mean.
Given that the value that is extracted from each data point is squared, the standard deviation of a set of data is always given as a positive number, but data points can have a negative overall standard deviation.
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Find the value of X. Round to the nearest tenth HELP ASAP!!!!
Answer: 22.5
Step-by-step explanation:
[tex]\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5[/tex]
Decide if the random variable x, is discrete or continious: x represents the temperature in degrees Fahrenheit on July 4th in Juneau, Alaska
Answer:
Continuous
Step-by-step explanation:
Degrees don't always have to be integers. It can be 32.3 degrees, 32.31 degrees, etc.
Calculate the slope of a line that goes through (3,3) and (8,1).
Answer:
slope formula= y2-y1/x2-x1
=1-3/8-3
= -2/5
pls mark as brainliest thanks!
find the slope of the line on the graph
Answer:
4
Step-by-step explanation:
Slope=rise/run
there is a increase of 4 in y for every increase of 1 in x
Solve the triangle. A = 46°, a = 31, b = 27
A. B = 38.8°, C = 115.2°, c ≈ 34.3
B. B = 38.8°, C = 95.2°, c ≈ 25.7
C. B = 38.8°, C = 95.2°, c ≈ 42.9
D. Cannot be solved
Answer:
C. B=38.8, C=95.2, c=42.9
Step-by-step explanation:
Find B by using sine rule
sin 46/31=sin B/27
sin B= 27 sin 46/31
B=sin‐¹(0.627)
B=38.8
Find C
C= 180-(A+B)
C=180-(38.8+46)
C=95.2
Using sine rule, Find c
31/sin 46=c/sin 95.2
c=31 sin 95.2/sin 46
c=42.9
A company has $36,000 to hire a mathematician and his or her secretary. Out of respect for the mathematician's training, the mathematician will be paid $8000 more than the secretary. How much will each be paid
The money paid to the secretary is $14000 and the money paid to mathematician is $22000.
What is an equation?A mathematical statement that establishes the equality of two mathematical expressions is the called an equation.
Total money available for hiring = $36000
Let the money given to secretary = X
Money given to the mathematician = X + 8000
X + (X + 8000) = 36000
2X = 28000
X = 14000
Money given to secretary is $14000.
Money given to the mathematician is $22000.
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Find the length of the segment indicated. Assume that lines which appear to be tangent are tangent. Round to one decimal place if necessary.
Answer: 13.6
Step-by-step explanation: Use a theorem which exists s. then you use pythagoreom
The length of the segment indicated is 13.6
Finding the length of the segment indicated.From the question, we have the following parameters that can be used in our computation:
The circle
Assuming that lines which appear to be tangent are tangent, we have
?² = (2 * 6)² + 6.4²
Evaluate
?² = 184.96
So, we have
? = 13.6
Hence, the length of the segment indicated is 13.6
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when evaluating (6.28x10^12)\(3.14x10^4)
Answer:??? rest of the question I think is what will be the exponent of 10 in the quotient? answer is 8
Step-by-step explanation:
NL and MK are diameters of circle J.
Circle J is shown. Line segments M K and N L are diameters. Line segment J P is a radius. Angle M J N is 62 degrees and angle N J P is 90 degrees.
Complete the statements about circle J.
Arc M P is a
and measures
degrees.
Arc M L N is a
and measures
degrees.
Arc M P is a minor arc and measures 152°
Arc M L N is a major arc and measures 298° .
Given that NL and MK are diameters of circle J.
Size of arc MP is 62+90=152°, since MP is smaller than MLN
then it is a minor arc. Hence the correct statement is:
M P is a minor arc and measures 152°.
Size of M L N is 360-62=298°, thus it is a major arc. Hence the
correct statement is:
MLN is major arc and measures 298°.
Arc M P is a minor arc and measures 152°
Arc M L N is a major arc and measures 298° .
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Answer:
Complete the statements about circle J.
Arc M P is a
✔ minor arc
and measures
✔ 152
degrees.
Arc M L N is a
✔ major arc
and measures
✔ 298
degrees.
Step-by-step explanation:
edge 2022
Let tan(x)=2/5
What is the value of tan(2π−x)
please!
Answer:
-0.4 or [tex]\frac{-2}{ 5}[/tex]
Step-by-step explanation:
[tex]tan^-^{1} ({\frac{2}{5} })=21.80\\[/tex]
tan ( 2π-21.80)
but 2π = 360
Therefore our question becomes:
tan ( 360-21.80)=tan(338.2)= -0.4
There are 50 pennies in a roll. if you have 110 rolls of pennies, how many pennies do you have?
Answer:
The answer to your question is 5500
Step-by-step explanation:
[tex]50x 110 = 5500\\[/tex]
I hope this helps and have a good day!
The center of circle q has coordinates (-2, 1). if circle q passes through r (6, 7), what is the length of its diameter?
There are multiple strategies we can use to find the diameter of a circle. For this question, we must calculate the length of the radius first and multiply by 2 to find the diameter.
Solving the QuestionWe're given the centre and a point on the circumference: [tex](-2,1),(6,7)[/tex].
Find the distance between them using the distance equation:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Plug in the given points:
[tex]d=\sqrt{(-2-x_1)^2+(1-y_1)^2}\\d=\sqrt{(-2-6)^2+(1-7)^2}\\d=\sqrt{(-8)^2+(-6)^2}\\d=\sqrt{64+36}\\d=\sqrt{100}\\d=10[/tex]
Therefore, the radius of the circle is 10 units.
Multiply the radius by 2 to find the length of the diameter:
10 × 2
= 20
Therefore, the length of the diameter is 20 units.
Answer20 units
If x = 3 (y 2) minus 1 what is the value of w in terms of x and y? w = startfraction x minus 3 y over 3 endfraction w = startfraction x minus 3 y 1 over 3 endfraction w = x minus 3 y 1 w = startfraction x 1 over 9 y endfraction
The value of w from the given equation is w=(x-3y+1)/3.
Given an equation x=3(y+w)-1 and we have to find the value of w in terms of x and y.
Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation.
The given expression is x=3(y+w)-1 and we have to find the value of w. To find the value we have to first solve the right side of the equation.
x=3y+3w-1
Now take w at one end and all other variables in other end.
3w=x-3y+1
Now divide both sides by 3.
3w/3=(x-3y+1)/3
Now cancel 3 from numerator and denominator in left side.
w=(x-3y+1)/3
Hence the value of w in the equation x=3(y+w)-1 is w=(x-3y+1)/3.
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Identify the range of the function shown in the graph.
OA. -1 sy≤ 1
OB. {-1, 1)
OC. y> -1
-10
D. y is all numbers.
10
8
8-
2
48
-6
88
-10-
The range of the attached function is 0 ≤ y ≤ 8
How to determine the range?The complete question is added as an attachment
From the graph, we have the following highlights
Vertex = MaximumVertex = (0, 8)This means that the y value do not exceed 8, and the minimum is 0
Hence, the range of the attached function is 0 ≤ y ≤ 8
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PLSSS THIS NEEDS TO BE DONE QUICKLY
Answer: 433.33 cm^3
Step-by-step explanation: Since the base is a square, volume = base area × height / 3
10*10 = 100, 100 * 13 = 1300, divided by 3 = 433.33 cm^3
how many 2/7 are 150
Answer:
42.8571
Step-by-step explanation:
We would need to divide 150 by 7 and multiply it by 2 to get the answer.
150/7 = 21.42857
21.42857*2 = 42.8571
What is the perimeter of the trapezoid
The perimeter of the trapezoid is 18 lines
How to determine the perimeterFormula for perimeter of a trapezoid is given as;
Perimeter = a + b+ c + d
a = 1
b = 4
c = 4
d = 9
Perimeter = 1 + 4 + 4 + 9
Perimeter = 18
Thus, the perimeter of the trapezoid is 18 lines
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Help me with this question please