Convert the following component vectors to a linear combination:
< 20 , 14 , -23 >
The component vectors to a linear combination is given by the equation
A = 20 i^ + 14 j^ - 23 k^
What is the product of vectors?The dot product, or inner product, of two vectors, is the sum of the products of corresponding components. Equivalently, it is the product of their magnitudes, times the cosine of the angle between them . The dot product , also known as the inner product, of u and v to be the number u ⋅ v given by
u ⋅ v = u₁v₁ + u₂v₂ + u₃v₃
An equivalent definition, typically used in physics, is
u ⋅ v = ∣u∣ ∣v∣ cos θ,
where θ is the angle between u and v
Two nonzero vectors are perpendicular, or orthogonal, if and only if their dot product is equal to zero
Given data ,
Let the component vectors be represented as A
The value of A is
< 20 , 14 , -23 > be equation (1)
On simplifying the equation to the linear combination , we get
< 20 , 14 , -23 > = 20 i^ + 14 j^ - 23 k^
So , the linear combination of the vectors is given by the equation ,
A = 20 i^ + 14 j^ - 23 k^
Hence , the equation is 20 i^ + 14 j^ - 23 k^
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Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
3 is divided by the difference of 4 and a number.
Answer:
Submit Answer
Il
DELL
******
attempt 1 out of 2
The given statement can be written as expression given by -
y = 3 ÷ (4 - x)
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is the statement as -
"3 is divided by the difference of 4 and a number"
Assume the number to be {x}. Then, we can write the expression as -
3 ÷ (4 - x)
Let this expression is equivalent to {y}. We can write -
y = 3 ÷ (4 - x)
Therefore, the given statement can be written as expression given by -
y = 3 ÷ (4 - x)
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4. What is the area of the shaded region in the figure below?
67
A
IT or 20.30 e
8
67
B
3 feet
IT or 17.50
12
10
O or 3.49
0
D
5
IT or 1.90 Ft
8
Equations of Exponential Functions
A 30-gram sample of bacteria has some unknown disease that is killing the bacteria. The amount of bacteria is measured each day and the results are shown in the table.
What is the amount of bacteria on the 8th day?
a. On the eighth day, the bacteria is 1.72 grams
b. On the eighth day, the bacteria is 19.90 grams
c. On the eighth day, the bacteria is 6.23 grams
d. On the eighth day, the bacteria is 6271.89 grams
Please select the best answer from the choices provided
Answer:
B. On the eighth day, the bacteria is 19.90 grams
Step-by-step explanation:
I calculated it logically
Plz help me well mark brainliest if correct!!.....
Answer:
A
Step-by-step explanation:
The oil painting classes lastes two hours on Saturday
Estimate the answer by rounding the divisor to the nearest whole number.
196,900÷4.084
Answer:
48,213
Step-by-step explanation:
The full answer is 48,212.5367, but because there is a 5 in the tenths place you round the whole number up
9514 1404 393
Answer:
49,000
Step-by-step explanation:
The divisor is 4.084. When it is rounded to the nearest whole number, it is 4.
Then the division problem becomes ...
196,900/4 ≈ 49,000 . . . . . . showing just 2 significant digits for the estimate
__
The point of an estimate is to obtain an approximate answer that is within a few percent of the actual answer. Here, rounding 4.084 to 4.000 gives an error on the order of .084/4 ≈ 2.1%. Because we're using a smaller divisor, the value we obtain for our estimate will be too large by about that amount.
Often, an estimate that has 1 or 2 significant digits is "close enough" for the purpose. Because a change in our estimated value of 1 in the least significant digit is a change of about 2%, we judge this estimate to be "close enough", given the rounding we did to start. Keeping 3 significant digits in our estimate would claim an accuracy that it does not have.
IF ITS CORRECT ILL GIVE BRAINLEIST
Draw a line plot to represent the data
Answer:
Make sure you include the words ^-^
Step-by-step explanation:
A manager samples the receipts of every fifth person who goes through the line. Out of 50 people, 6 had
a mispriced item. If 900 people go to this store each day, how many people would you expect to have a
mispriced item?
Answer:
48
Step-by-step explanation:
Can you please help me
9514 1404 393
Answer:
x = 90°
y = 30°
Step-by-step explanation:
The relevant relations are ...
an inscribed angle is half the measure of the arc it interceptsthe sum of angles in a triangle is 180°the sum of arcs of a circle is 360°Arc AB is half a circle, so is 180°. Inscribed angle C intercepts that arc, so is half its measure: x = 90°.
The angles of a triangle total 180°, so y has the value that makes the sum of angles be 180°.
y = 180° -90° -60°
y = 30°
_____
Additional comment
It is worth remembering that a triangle inscribed in a semicircle is a right triangle. This tells you right away that x=90°.
Cylinder A has a radius of 7 inches and a height of 5 inches. Cylinder B has a volume of 490TT. What is the percentage change in volume from cylinder A to cylinder B?
50% decrease
0.75% increase
150% decrease
O 100% increase
Refer to the second stanza of the poem, at the
top of page 2. What can be inferred about the
setting based on the evidence in this stanza?
5
Answer:
A: the forest is at this moment being threatened by severe weather
Step-by-step explanation:
Plz help me well mark brainliest if correct!!
Answer:
A) 32 cm
Step-by-step explanation:
the rectangle could be 12cm x 4cm, giving an area of 48 sq cm
and a perimeter of 24+8 or 32 cm
If x = 5, then which inequality is true?
F -2x ≥ 12
G. x – 2 < 7
H. 2x > 12
J. x – 7 > 2
Directions: Solve these equations by using addition. You will need to use your fraction and decimal skills to solve these equations.
A number increased by 1 2/3 is equal to 8
Answer:
6 and 1/3
Step-by-step explanation:
8 minus 1 is 7 and 7 minus 2/3 is 6 1/3. Therefore the number you started with is 6 and 1/3. Hope this helps :)
4. ABCD below is a rectangle. BE=6x+2 and ED=4x+6. Find the length of AC.
Answer:
28 units
Step-by-step explanation:
ABCD is a rectangle. AC and BD are diagonals intersecting at point E.
Diagonals of a rectangle bisect each other.
[tex] \therefore BE = ED[/tex]
[tex] \therefore 6x + 2 = 4x + 6[/tex]
[tex] \therefore 6x - 4x= 6-2[/tex]
[tex] \therefore 2x= 4[/tex]
[tex] \therefore x= \frac{4}{2} [/tex]
[tex] \therefore x= 2 [/tex]
[tex] \therefore 6x + 2= 6*2+2= 12+2= 14 [/tex]
[tex] \therefore BE= 14\: units [/tex]
[tex] \because BD = 2BE[/tex]
[tex] \therefore BD = 2(14)= 28\: units [/tex]
[tex] \because AC = BD[/tex] (diagonals of a are equal in measure)
[tex] \therefore AC = 28\: units [/tex]
A tissue box in the shape of a rectangular prism has a surface area of 158 square inches . The width is 5 inches and the height is 3 inches . What is the length of the tissue box ?
Answer Choices - A. 8.0
B. 8.5
C. 9.0
D . 10.5
Answer:
A. 8.0 inches
you will have to use the formula A= 2(LW + LH + WL)
Two distinct intersecting lines intersect at a single point. Is it true or false
Answer before 11:59 plzzz
Which statement best applies to the function y = x squared?
a.
The domain only includes numbers greater than or equal to 0.
c.
Both the domain and range only include numbers greater than or equal to 0.
b.
The range only includes numbers greater than or equal to 0.
d.
The domain and range include all real numbers.
Answer:
b. The range only includes numbers greater than or equal to 0.
Step-by-step explanation:
Any square of a number will never lead to a negative number
The range of an equation is it's numerical possibilities for y
Since a square of a negative number never leads to a negative y
The answer is therefore, the range can only be zero and above
(otherwise the roots would be imaginary)
The diameter of cork of a Champagne bottle is supposed to be 1.5 cm. If the cork is either too large or too small, it will not fit in the bottle. The manufacturer measures the diameter in a random sample of 36 bottles and finds their mean diameter to be 1.4 cm with standard deviation of 0.5 cm. Is there evidence at 1% level that the true mean diameter has moved away from the target?
Answer:
[tex]t_{n-1,\alpha/2}=3.59114678[/tex]
Therefore we do not have sufficient evidence at [tex]1\%[/tex] level that the true mean diameter has moved away from the target
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=36[/tex]
Mean diameter [tex]\=x=1.4[/tex]
Standard deviation [tex]\sigma=0.5cm[/tex]
Null hypothesis [tex]H_0 \mu=1.5[/tex]
Alternative hypothesis [tex]\mu \neq 1.5[/tex]
Significance level [tex]1\%=0.001[/tex]
Generally the equation for test statistics is mathematically given by
[tex]t=\frac{\=x-\mu}{\frac{s}{\sqrt{n} } }[/tex]
[tex]t=\frac{1.4-1.5}{\frac{0.5}{\sqrt{36} } }[/tex]
[tex]t=-1.2[/tex]
Therefore since this is a two tailed test
[tex]t_{n-1,\alpha/2}[/tex]
Where
[tex]n-1=36-1=>35[/tex]
[tex]\alpha=/2=0.001/2=>0.0005[/tex]
From table
[tex]t_{n-1,\alpha/2}=3.59114678[/tex]
Therefore we do not have sufficient evidence at [tex]1\%[/tex] level that the true mean diameter has moved away from the target
Without graphing, find the slope of the line that goes through (-3,-2) and (-1,-5)
Helpp!! I’m stuck on this!!
(1,0) m=-5
Formula
Y-Y1 = m(x-x1)
Slope form
Slope form -
y - y1 = m(x - x1)
y - 0 = -5(x - 1)
y = -5x + 5
Please help me with these questions if can explain i am a bit confused at it
On solving the provided question, we can say that - he re the slope value is using the formula y/x = k => [tex]k = 2/3[/tex]
what is slope?A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
Use the point (3, 2) and divide y by x using the formula y/x = k.
[tex]k = 2/3[/tex]
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Write and solve a system of equations for each of the following problems. You must write two questions for each problem, thank you
1. Ella is a landscape photographer. She sells small prints for $50 each, and large prints for $75
each. One weekend she sold a total of 52 prints for a total of $2975. How many of each size print did
Ella sell?
2. At a hot air balloon festival, Georges's balloon is at an altitude of 40 meters and rises at a rate of
10 meters per minute. William's balloon is at an altitude of 165 meters and descends at a rate of 15
meters per minute. In how many minutes will both balloons be at the same altitude? What is that
altitude?
The system of equations that satisfy the given problems is x + y = 52 and 50x + 75y = 2975, and the value of x = 15 and y= 37.
What is system of equations?A system of linear equations consists of two or more equations and looks for common answers.
1. Let us suppose small prints = x
Large prints = y
Total prints sold can be written as follows:
x + y = 52
The total cost of the prints can be written as follows:
50x + 75y = 2975
The system of equations is:
x + y = 52 . . . equation 1
50x + 75y = 2975 . . .equation 2
Using equation 1 we have:
x = 52 - y
Substituting the value of x in equation 2 we have:
50(52 - y) + 75y = 2975
2600 - 50y + 75y = 2975
25y = 2975 - 2600
25y = 375
y = 15
Now, substituting the value of y in equation 1 we have:
x + 15 = 52
x = 52 - 15
x = 37
Hence, the solution of the system of equations is y = 15 and x = 37.
2. Let us suppose the altitude = x.
The rising balloon can be thus written as:
40 +10x
The descending balloon can be written as:
165 - 15x
Solving the system of equations by substituting the value of x we get x= 5.
Hence, the altitude at which both the balloons are at the same height is 5m.
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PLEASE HELP ME RIGHT NOW DUE TOADY ASAP
Answer:
A 0.9102
Step-by-step explanation:
A correlation coefficient tells us the strength of the linear relationship between two variables. It is measured on a scale from +1 to -1.
The gradient is positive as it is going up the slope, so the correlation coefficient is positive. We can rule out B.
A correlation coefficient of 0 suggests there is no correlation, however, the scatter graph shows a positive correlation, so we can rule out C.
A correlation coefficient of 1 implies that there is a perfect positive correlation, so all the scatter points lie in a straight line. In the scatter graph given, the points do not all lie on a straight line, so we can rule out D.
Hence, the correlation coefficient is A, 0.9102
how to solve this equation for x x/3+7-5
the answer is right there
A spinner had four lettered sections. The table shows the results of an experiment spinning the pointer.
Letter Frequency
Q 15
R 8
S 3
T 24
Fine the probability of each letter in the simplest form.
PLEASE ANSWER FAST.!!!!
Answer:
Q 3/10 R 4/25 S 3/50 T 12/25
Step-by-step explanation:
Q 15/50 3/10
R 8/50 4/25
S 3/50 3/50
T 24/ 50 12/25
Answer:
Q = 30%
R = 16%
S = 6%
T = 48%
Step-by-step explanation:
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the mean of 100 nummerical observations is 51.82
If the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that mean of 100 nummerical observations is 51.82
We need to find the sum of all the observations
The formula to find mean is mean=Sum of observations/ Number of observation
From given mean=51.82
Number of observations =100
Let us take x as sum of all 100 numbers
So 51.82=x/100
Now apply cross multiplication
x=51.82×100
x=5182
Hence, if the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.
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Does anyone know? 6th grade work I need help please :( no link answer please
Answer:
Step-by-step explanation:
you add all them up
Answer:
C.
Step-by-step explanation:
there is a measuement of 12 cm missing.
Just multiply all the sides!