The scalar product between two vectors involves the cosine function of the angle between the lines of action of the two vectors.
What is the scalar product?The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of numbers of equal length (often coordinate vectors) and outputs a single number. The dot product of two vectors' Cartesian coordinates is frequently used in Euclidean geometry. Although other inner products can be defined in Euclidean space, it is frequently referred to as the inner product (or, less frequently, projection product) of Euclidean space (see Inner product space for more). The sum of the products of the matching entries of the two number sequences is the dot product, according to algebra. Geometrically, it is the result of adding the cosine of the angle between the two vectors and the Euclidean magnitudes of the two vectors.
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A heap of sand in the form of a square based pyramid is twice as tall as it is wide. If the volume, V, of the sand is 10 m3, find the height, h, of the heap. Give your answer, in metres, correct to two decimal places.
The height of the prism is 4.93 meter with a square base and having a volume of 10 m³
How to solve volumeVolume is the amount of space occupied by a three dimensional shape or object. Examples of shape with volume are cone, cube, cuboid, pyramid, prism and so on.
The volume of a pyramid = (1/3) * base area * height
Let base = b
height = 2 * base = 2b
Since volume is 10 m³, hence:
10 = (1/3) * b * b * 2b
b = 2.47 m, h = 2(2.47) = 4.93 m
The height of the prism is 4.93 meter with a square base and having a volume of 10 m³
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find the gradient-intercept form of the equation of the line which has a gradient of 5 and passes through the point (1, 11)
The gradient-intercept form of the equation of the line which has a gradient of 5 and passes through the point (1, 11) is y = 5x + 6
Gradient intercept form Or slope incept form of a linear equation is given by
y = mx + c
where m is the gradient or slope of the equation and c is the constant
As we are aware that the line passes through a point whose coordinates are (1, 11)
By putting the value of gradient/ slope, x coordinate in place of x in equation and y coordinate in place of y in equation we get
11 = 5 (1) +c
11= 5 + c
11-5 = c
6 = c
now, substituting the value of c in the Gradient/ slope intercept form
y = 5x + 6
Hence, The gradient-intercept form of the equation of the line which has a gradient of 5 and passes through the point (1, 11) is y = 5x + 6
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12=456 marking the first one bry
Answer:
38?
Step-by-step explanation:
I can't tell if you were dividing, but 456/12 is equal to 38. Same goes if you were looking for 456=12*x, which x is also 38.
Twelve buckets of water are needed to fill a small swimming pool. there are approximately 3.8 liters in 1 gallon. if each bucket holds 1.5 gallons, what is the volume of water, in liters, the pool holds?
Answer:68.4 liters
Step-by-step explanation: 1.5x12=18 18x3.8=68.4
7, 000 000 000 000 000 000
how do you read this
Answer: Seven trillion i think
Step-by-step explanation:
(+7) (–4) Write each multiplication expression as a repeated addition.
We get the repeated addition as ( - 4 ) + ( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ).
We are given a multiplication expression:
( + 7 ) ( - 4)
We need to write this expression as a repeated addition
Repeated addition means when we add the same digits many times that is repeatedly.
For example: 3 + 3 + 3 + 3 or 8 + 8 + 8 + 8 or 5 + 5 + 5 +5 etc.
Here, we can see that -4 is multiplied by 7
It means that - 4 will be added 7 times repeatedly to form the expression
So, we get that:
= ( - 4 ) + ( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 )
Therefore, we get the repeated addition as ( - 4 ) + ( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ).
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1.5, 21.5, 21.6 d: 20.0, 20.0, 20.0, 20.1, 20.2, 20.5, 20.5, 20.6, 20.7, 20.7, 21.0, 21.2, 21.5, 21.6, 22.1, 22.3 compute the standard deviation of the measurements for each method
Final answer:
The standard deviation from the method A is 2.87
The standard deviation from the method B is 1.35
The standard deviation from the method C is 0.42
The standard deviation from the method D is 0.75
What purposes does standard deviation serve?The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.
The statistical concept of standard deviation is used to quantify the variability or dispersion around an average. It is a measure of volatility technically. The discrepancy between the actual and average value is known as the dispersion. The standard deviation increases as the variability or dispersion increases.
A low standard deviation indicates that the data are tightly grouped around the mean, while a high standard deviation indicates that the data are widely dispersed (less dependable) (more reliable)
Explanation:
The highest standard deviation is found in procedure A. Given that it is not based on any actual measurements and is subject to wildly different subjective judgment, one would anticipate that it would be the largest.
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you roll 3 dice. if you get the same number, you earn 10 $. if you get two numbers the same, you get 5 $. if the numbers are all different, you lose 2 $. what is the expected win?
When you roll 3 dice, if if you get the same number, you earn 10 $. if you get two numbers the same, you get 5 $. if the numbers are all different, you lose $2, the expected win is $1.25.
Given,
You roll 3 dice.
In each dice there will be 6 outcomes
Total number of outcomes = [tex]6^{3}=216[/tex]
Conditions are
You earn $10, if you get same numbersYou earn $5, if you get two numbers sameYou loss $2, if the numbers are all differentWe can find the number of each cases by using the combination method
Number of cases all the outcomes are same =6
Number of cases you get two numbers same = [tex]6C_{2}[/tex]×3!
=90
Number of cases the numbers are all different= 6×5×4
=120
Therefore the expected win = (6×10+90×5-120×2)÷216
=270÷216
= $1.25
Hence, when you roll 3 dice, if if you get the same number, you earn 10 $. if you get two numbers the same, you get 5 $. if the numbers are all different, you lose $2, the expected win is $1.25.
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the hats of n persons are thrown into a box. the persons then pick up their hats at random (i.e., so that every assignment of the hats to the persons is equally likely). what is the probability that (a) every person gets his or her hat back?
The probability that every person gets his or her hat back is 1/n!
What are equally likely function?If each possibility in a sample space S has the same chance of happening, then all of the outcomes are equally likely. The following experiment shows how easy it is to compute the probability of a single result or an event if all outcomes in a sample space S are equally likely.
Think about the sample space for all hat assignments.
This has n! components (n hat picks for the first person, then n - 1 for the second, etc.),
with each occurrence having a chance of 1/n and being equally likely. Calculation is the issue.
The likelihood of a single element occurring, hence the response is 1/n!
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Write the domain for {(-4; 3), (2; 1), (0;3), (-3;-2)}
d=
Answer:
Element of xcomponent is called domain.
Step-by-step explanation:
Domain=(-4,2,0,-3)
Hope this helpful for you.
You invest $2,800 at a 6 nnual interest rate, stated as an apr. interest is compounded monthly. how much will you have in 1 year? in 1.5 years?
If, we invested $2,800 at a 6% annual interest rate. We will have $2972.70 in 1 year and $3063 in 1.5 year of time.
What is interest?In the fields of finance and economics, interest is defined as the payment of a sum over and above the principal amount (the amount borrowed) at a set rate by a borrower or deposit-taking financial institution to a lender or depositor. It is different from a fee that the borrower may pay to the lender or another entity. It also differs from a dividend, which is money given to shareholders (owners) by a company from its profit or reserve, but not at a set rate predetermined beforehand, but rather on a pro rata basis as a portion of the rewards received by risk-taking businesspeople when revenue is earned that exceeds all costs.
Calculations:
The Future value= fv= Pv x [tex](1+r/m)^{mt}[/tex]
R= Rate per period
mt= years x compounding
The Future value in 1 year= 2800x[tex](1+0.06/12)^{1x12}[/tex]
= $2972.70
The Future value in 1.5 years=2800x[tex](1+0.06/12)^{1.5x12}[/tex]
= $3063.00
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Abdoulaye is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he rolls a fair die in the shape of a cube that has six sides labeled 1 to 6 and spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange?
The number of different possible outcomes is 24
How to determine the number of different possible outcomes?The given parameters are:
Fair die = 6 sides
Spinner = 4 sections
The number of different possible outcomes is calculated using
Outcomes = Fair die * Spinner
This gives
Outcomes = 6 * 4
Evaluate
Outcomes = 24
Hence, the number of different possible outcomes is 24
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Evaluate 4 - 2(a - 3) for a=5
Answer: 0
Step-by-step explanation:
4 - 2(a - 3) =
4 - 2(5 - 3) =
4 - 2(2) =
4-4=0
Table: Is it a function? (yes/no) Why or why not?
Answer:
Yes
Step-by-step explanation:
Every x and y coordinate is different. The y-coordinates don't have the same x-coordinate, so the function passes the vertical line test. This function is called a discrete function since it's made up of individual points, not a line or curve.
Answer:
yes
Step-by-step explanation:
Different x and y coordinate
Different gradient of line graph
Therefore,it is a function.
Volume of Spheres
Volume of Spheres
Answer:
V ≈ 2,048 ft^3
Hope this helps :)
Step-by-step explanation:
The symbol ^ means raised to a power.
Formula for Volume of Sphere - V = 4/3 π r^3
1. To find the volume of a sphere, first find the radius with the given diameter 16.
16 ÷ 2 = 8
Radius = 8
2. Substitute r for 8 and solve, and 3 will be used for π.
V ≈ 4/3 • 3 • 8^3
V ≈ 4/3 • 3 • 512
V ≈ 4/3 • 1536
V ≈ 6144/3
V ≈ 2,048
(9x+1)+(-6x{2}-9x-4)
Answer:
12x - 3
Step-by-step explanation:
the top and bottom ends of a windshield wiper blade are 30 inches and 13 inches, respectively, from the pivot point. while in operation, the wiper sweeps through 135°.
The area swept by the wiper is 860.75 square inches, as calculated by the formula of area of a sector.
What is a sector and its area?A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.Area of a sector = [tex]\frac{1}{2}r^{2}\theta[/tex] (where the angle is in radians)Given:
Top end of windshield = 30 inchesBottom end of windshield = 13 inchesAngle made = 135 degrees = 3π/4 radiansTo find: Area swept by the wiper.
Finding:
As area of the sector = [tex]\frac{1}{2}r^{2}\theta[/tex],
Area swept by the wiper will be given by: (Area of the sector made by the top end of the windshield) - (Area of the sector made by the bottom end of the windshield)
=> Area swept by the wiper = [tex]\frac{1}{2}(30)^{2}\frac{3\pi}{4} - \frac{1}{2}(13)^{2}\frac{3\pi}{4}[/tex]
=> Area = [tex]\frac{1}{2}\frac{3\pi}{4}(900 - 169)[/tex]
=> Area = [tex]\frac{1}{2}\frac{3\pi}{4}(731)[/tex] ≈ 860.75 square inches
Hence, the area swept by the wiper is 860.75 square inches, as calculated by the formula of area of a sector.
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What is the quotient of the following division problem?
10703 ÷ 25 = ?
OA. 428 r3
OB. 427 r4
OC. 428 r4
O D. 429 r3
Answer is A, 10703 / 25 = 428 r3
In the question 2(8x - 1) = 20 i got 8/11 but the correct answer is 11/8 how do you determine which number goes on top and which goes on the bottom.
which conversion factors are used to multiply to 18 cm/s to get meters per minute? select each correct answer.
The conversion factor to convert cm/s to m/min is 3 / 5, it is gained by applying the knowledge of conversion of units to the given problem.
What do you mean by conversion of units?
Conversion of units deals with the method of converting a set of values given in a unit to another unit without changing its numerical value. Conversion can take place in both ways, from lower to higher units and vice-versa.
Calculation of the conversion factor to convert cm/s to m/min
We know that,
1 m = 100 cm
1 min = 60 s
To convert cm/s to m/min, we have
= 18 / (100 / 60)
= (18 × 3) / 5
= 54 / 5
= 10.8 m/min
Hence, the conversion factor used to convert cm/s to m/min is 3 / 5.
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the answer is A because to be honest im writing this so it will show me the right naswer but it should be A
The weather report predicted that the low temerature would be 93 degrees farenheit. The weather man said , "The low temperature was 13 degrees warmer than predicted!'' What was the low temperature, in degrees Farenheight?
Answer: 106!
Step-by-step explanation:
find the slope-intercept form of the equation of the line that has the given slope and passes through the given point
Answer: you didn't give me any numbers, so I can't give you an answer. But, I can help!
The slope intercept form is Y=mx+b
X and Y are your coordinates
m is the slope
b is the y-intercept.
As long as you know two of those, you can solve for the missing variable.
I hope this helps!!!
I am a multiple of 3 I am also a multiple of 4 the sum of my digits is a prime number I have 2 digits what number am I?
Answer:
the number 12
Step-by-step explanation:
the number 12 is a multiple of both 3 ans 4. the sum of the 2 digits in 12, is 3, which is a prime number. 12 only has 2 digits
q1: find the hexadecimal representation for each of the following binary numbers 1. 10101101 2. 00100111 q2: find the decimal representation for each of the following hexadecimal numbers 1. 8ef 2. 5ce q3: find the binary representation for each of the following decimal numbers 1. 53 2. 885 q4: find the answer for the following hexadecimal 1. 35 ab 2. aa – 22
The hexadecimal representation for the given question is 1. 0xAD 2. 0x27 and the decimal representation of the given question is 1. 10001110 2. 01011100
What do you mean by the term hexadecimal?The hexadecimal numeral system, usually known as base 16 or just "hex," is a positional numeral system used in mathematics and computing that uses the radix (base) of 16 to represent integers. Hexadecimal uses 16 different symbols as opposed to the decimal system's 10 symbols, with the most common being "0"-"9 to represent values 0 to 9 and "A"-"F" (or alternatively "a"-"f") to represent values 10 to 15. Hexadecimal numbers are frequently used by software engineers and system designers because they offer a human-friendly representation of binary-coded data. For example, an 8-bit byte might have values ranging from 00000000 to 11111111 in binary form, which can be succinctly represented as 00 to FF in hexadecimal. Each hexadecimal digit represents four bits (binary digits), often known as a nibble (or nybble).
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patricia will flip the coin 8 times. let a be the event that exactly 4 of the 8 flips are heads, and b be the event that the last two flips are tails. find p(a ∪ b).
The probability of an event of P(A∪B) is 49/128.
In this question,
Patricia will flip the coin 8 times.
The sample space is the flipping of a coin 8 times.
⇒ n(s) = 2⁸
⇒ n(s) = 256
Let A be the event that exactly 4 of the 8 flips are heads
⇒ n(A) = [tex]8C_4[/tex] [∵ [tex]nC_r=\frac{n!}{r!(n-r!)}[/tex]]
⇒ [tex]\frac{8!}{4!4!}[/tex] = 70
Then, P(a) = [tex]\frac{n(a)}{n(s)}[/tex]
⇒ [tex]\frac{70}{256}[/tex]
Let B be the event that the last two flips are tails
⇒ n(B) = [tex]8C_2[/tex]
⇒ [tex]\frac{8!}{2!6!}[/tex] = 28
Then, P(a) = [tex]\frac{n(b)}{n(s)}[/tex]
⇒ [tex]\frac{28}{256}[/tex]
Now, P(A∪B) = P(A) + P(B)
⇒ P(A∪B) = [tex]\frac{70}{256} + \frac{28}{256}[/tex]
⇒ P(A∪B) = [tex]\frac{70+28}{256}[/tex]
⇒ P(A∪B) = [tex]\frac{98}{256}[/tex]
⇒ P(A∪B) = [tex]\frac{49}{128}[/tex]
Hence we can conclude that the probability of an event of P(A∪B) is 49/128.
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−4 1/3÷−2 3/5 (I still don't know the answer to this and please I need help on this for my extra credit!! Thanks!
Answer:
-205/69
Step-by-step explanation:
-41/3÷23/5
reciprocate, then the sign changes
-41/3×5/23
=-205/69
helppppppppppppppppppppppppppppppppp
Answer:
S
Step-by-step explanation:
because an acute angle is and angle that is 89 or lower the rest are obtuse or right angle
Answer:
∠S
Step-by-step explanation:
An acute angle is an angle that is <90°, and in this case, angle S's measure is less than 90 or 15 in degrees, which both classify acute angles.
7 times as long as 3098 kilometers
Answer:21,686
Step-by-step explanation:7*3098=21,686
I need help ASAP DUE TODAY Please
Answer:
it's 9 squar feet ;) ........
Please help me with this question