Your friend says that the magnitude of vector (8 , 3) is 4 times that of vector (2 , 3) since 8 is 4 times 2 . Explain why your friend's statement is incorrect.
Answers
With the help of the Magnitude formula, we can say that Magnitude of 1st vector is more than the 2nd vector.
A vector is an object that has both magnitude and direction. To find the size of a vector, we need to calculate the length of the vector. Variables such as velocity, distance, force, and momentum are vector variables. But velocity, mass, distance, volume, temperature, etc. is a scalar quantity. A vector has both magnitude and direction, while a scalar has only one magnitude.
The Magnitude of a vector is the length of the vector. The Magnitude value of vector a is represented by ∥a∥.
For a two-dimensional vector a= (a1, a2), the formula for its Magnitude is written below.
By using the Magnitude formula, we can say that Magnitude of 1st vector is more than the 2nd vector.
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Related Questions
A survey finds that 110 people ate breakfast and 30 people skipped breakfast. Of those who ate
breakfast, 10 people felt tired. Of those who skipped breakfast, 10 people felt tired. Make a
two-way table that shows the conditional relative frequencies based on the breakfast totals.
Answers
Here is the two-way table :
Felt tired Did not feel tired Total
Ate breakfast 0.0714 0.7142 0.7857
Did not eat breakfast 0.0714 0.1428 0.2143
Total 0.1428 0.8572 1
What is the two way table?A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns. A conditional relative frequency is the ratio of the frequency of a class to the total frequency.
People who ate breakfast and did not feel tired = 110 - 10 = 100
People who did not breakfast and did not feel tired = 30 - 10 = 20
Felt tired Did not feel tired Total
Ate breakfast 10 100 110
Did not eat breakfast 10 20 30
Total 20 130 140
Felt tired Did not feel tired Total
Ate breakfast 10 / 140 100 / 140 110 / 140
Did not eat breakfast 10 / 140 20 / 140 30 / 140
Total 20 / 140 130 / 140 140 / 140
Felt tired Did not feel tired Total
Ate breakfast 0.0714 0.7142 0.7857
Did not eat breakfast 0.0714 0.1428 0.2143
Total 0.1428 0.8572 1
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Elena has $225 in her bank account. She takes out $20 each week for w weeks. After w weeks she has d dollars left in her bank account.
Write an equation that represents the amount of money left in her bank account after w weeks.
Answers
Answer:
y20=225x or y225+x20 ir can be
Which system of equations is represented by the matrix below?
[4 0 5
2 -117
Answers
47576777...................
Find the inverse of each function. Is the inverse a function?
f(x)=2x² /5 +1
Answers
Yes , the given function is an inverse function which is given by [tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex] .
An inverse function or anti -function is defined as a function that can be inverted into another function. Simply put, if the function 'f' makes x into y, the inverse of 'f' makes y into x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f-1 or F-1.A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function.An inverse function returns the original value that the function provided the output for.We have given a function [tex]f(x)=\frac{2x^2}{5} +1[/tex]. ....(1)
Let y = f(x)
[tex]y=\frac{2x^2}{5} +1\\y-1=\frac{2x^2}{5} \\\\\frac{5(y-1)}{2} =x^2\\\\\sqrt{\frac{5(y-1)}{2} } =x[/tex] ......(2)
Swap the values of x and y, then the inverse is then
[tex]x=f^{-1}(y)[/tex] ...(3)
Comparing equation (2) and (3) , we get
[tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex]
We can check that this is really an inverse function or not
Putting in [tex]x=\sqrt{\frac{5(y-1)}{2} }[/tex] equation (1) , we get
[tex]f(f^{-1}(y))=\frac{2(\sqrt{\frac{5(y-1)}{2} })^2}{5} +1\\\\\y=\frac{2\frac{5(y-1)}{2} }{5} +1\\\\y=\frac{5(y-1)}{5} +1\\\\y=y-1+1\\\\y=y[/tex]
As LHS = RHS which means inverse function is correct .
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Devon has 4 3/4 bags of soil to put in hs flower bed each bag will cover 15 ft2 how many squares will he be able to cover
Answers
Devon will be able to cover 71.25 ft² of flower bed.
The number of bags of soil Devon has = [tex]4\frac{3}{4}[/tex]
Converting mixed fraction to fraction
Number of bags of soil = (4×4+3)/4
Performing multiplication and addition in numerator to find the number of bags of soil with Devon
Number of bags of soil = 19/4
Now, it is stated that area covered by 1 bag = 15 ft²
So, 19/4 bags will cover area = 15×(19/4)
Performing multiplication and division to find the area covered by the bags of soil
Area covered by bags of soil Devon has = 71.25 ft²
Hence, the area covered by bags of soil Devon has is 71.25 ft²
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The complete question is -
Devon has 4 3/4 bags of soil to put in his flower bed. Each bag will cover 15 ft2. How many square feet will he be able to cover?
Let g(x)=3 x+2 and f(x)=x-2 / 3 . Find each value.
(g⁰g)(1)
Answers
Value for (g⁰g)(1) = 17
What is the domain of the function (g⁰g)(1)?Now, (g⁰g)(x) = g[g(x)]
let g(x) = 3x + 2
(g⁰g)(x) = g(3x + 2)
(g⁰g)(1) = g(5)
(g⁰g)(1) = 3(5) + 2
(g⁰g)(1) = 17
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About how much farther did she bike on Wednesday than Thursday?
Answers
the answer is 71 miles far
The graph below describes the journey of a train between two cities.
a) Work out the
acceleration, in km/h²,
in the first 15 mins
b) Work out the distance
between the two cities.
c) Work out the average
speed of the train during
the journey.
Answers
The acceleration in first 15 minutes = 200 km/h²
The distance between the two cities = 125 km
Average Speed of train during the journey = 62.5 km/hr
According to the given question:
Each block of horizontal is 1/8 hr = 7.5 min
Each block of vertical is 10 km/hr
Time Velocity (km/hr)
0 Min ( 0 hr) 0
15 Min (1/4 hr) 50
45 Min (3/4 hr) 50
60 MIn ( 1 hr) 100
90 Min ( 3/2 hr) 100
120 Min ( 2hr) 0
The acceleration in first 15 minutes = (1/4 hr) = (50 - 0)/(1/4 - 0) = 50/(1/4)
= 200 km/h²
The distance between the two cities =
= (1/2)(0 + 50)(1/4 - 0) + 50 * (3/4 - 1/4) + (1/2)(50 + 100)(1 - 3/4) + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)
= 25/4 + 25 + 75/4 + 50 + 25
= 125
Distance between two cities = 125 km
Average Speed of train during the journey = 125/2 = 62.5 km/hr
Therefore,
The acceleration in first 15 minutes = 200 km/h²
The distance between the two cities = 125 km
Average Speed of train during the journey = 62.5 km/hr
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x/a=y/b solve for x please help my homework is due today
Answers
WITHOUT GRAPHING identify the coordinates of A(-3, 7), B(4, 9), and C(0, -2) after the following transformations. 1. Translation 2 units up and 7 units right.
Answers
The points A(-3, 7), B(4, 9), and C(0, -2) is translated 2 units up and 7 units right to get A'(4, 9), B'(11, 11), and C'(7, 0)
What is transformation?Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.
Dilation is a transformation that affects the size of a figure.
The points A(-3, 7), B(4, 9), and C(0, -2) is translated 2 units up and 7 units right to get A'(4, 9), B'(11, 11), and C'(7, 0)
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A school dedicated 50% of the courtyard area for students to start a garden. The students want to know how much of the 632 yard the will be able to use?
Answers
The students will have 316 yards of the courtyard
The number of yards left for the students can be calculated as follows;
A school dedicated 50% of the courtyard area for students to start a garden
= 50/100
= 0.5
The number of yards is 632, the number of yards left for the students can be calculated as follows
= 0.5 × 632
= 316
Hence 316 yards are left for the students
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The Brandywine Dance Team is buying equipment and T-shirts. The equipment costs $356 and the T-shirts cost $12 each. The team spent a total of $644
Answers
The number of T-shirts bought by the Brandywine Dance Team is 24.
How is the number of T-shirts determined?The number of the T-shirts that the Brandywine Dance Team purchased is determined using basic mathematical operations of division, subtraction, addition, and multiplication.
First, the cost of the equipment is subtracted from the total cost spent by the team. The remainder refers to the cost of the T-shirts. Since one T-shirt costs $12, the total quantity of T-shirts bought is 24.
Data and Calculations:The total amount spent = $644
The cost of the equipment = $356
The remainder after the equipment = $288 ($644 - $356)
Unit cost of T-shirts = $12
The number of T-shirts bought = 24 ($288/$12)
Thus, the Brandywine Dance Team bought 24 T-shirts.
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Question Completion:How many T-shirts were purchased by the Team?
Enterprise will allow you to rent a car for $10 per day plus a $20 fee. Hertz will allow you to rent a car for $40 a
day. After how many days, x, will Enterprise cost more than Hertz?
Answers
Yes..............................
The data show the traveler spending in billions of dollars for a recent year for a sample of the states. find the range, variance, standard deviation for the data. 20.1, 33.5,21.7,58.4,23.2,110.8,30.9,24.0,74.8,60.0
Answers
We know that the measures of dispersion tend to see how numbers are scattered around the mean. In this case, we are asked to find three of the measures of dispersion which are; range, variance and standard deviation.
We first have to arrange the data in the proper order as follows;
20.1, 21.7, 23.2, 24.0, 30.9, 33.5, 58.4, 60.0, 74.8, 110.8
It is now easier for us to find the range of the data set as the difference between the largest and the smallest value; 110.8 – 20.1 = 90.7
The mean of the dataset is = 20.1 + 21.7+ 23.2 + 24.0 + 30.9 + 33.5 + 58.4 + 60.0 + 74.8 + 110.8/10
= 45.74
Now;
Variance = (20.1 - 45.74)^2 + (21.7 - 45.74)^2 + (23.2 - 45.74)^2 + (24.0 - 45.74)^2 + (30.9 - 45.74)^2 + (33.5 - 45.74)^2 + (58.4 - 45.74)^2 + (60.0 - 45.74)^2 + (74.8 - 45.74)^2 + (110.8 - 45.74)^2/10
= 657.4 + 577.9 + 508.1 + 472.6 + 220.2 +149.8 + 160.3 + 203.3 + 844.5 + 4233/10
= 802.71
Standard deviation = √variance = √802.71
= 8.96
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What would happen to a monthly payment if the interest rate increased?
OA. The payment would go up.
B. The payment would go down.
OC. The payment would remain the same.
OD. None of the above
Answers
Work out the following, giving your answers in their simplest form:
a) 4/7 / (1 3/4)
b) 5 3/5 / (2 2/3)
Answers
The simplest form of the following are -
a) 4/7 / (1 3/4) = 16/49
b) 5 3/5 / (2 2/3) = 21/10
The word simplify means to make something easier to do or understand. So, reducing or simplifying fractions means we make the fraction as simple as possible. We do this by dividing the numerator and the denominator by the largest number that can divide into both numbers exactly.
We have been given that
a) 4/7 / (1 3/4)
Rewrite as -
= (4/7) / (1× 3/4)
= (4/7) / (7/4)
= (4/7) × (4/7)
= 16/49
b) 5 3/5 / (2 2/3)
Rewrite as -
= (5× 3/5) / (2× 2/3)
= (5× 3/5) / (8/3)
= (28/5) / (8/3)
= (28/5) × (3/8)
= 7/5 × 3/2
= 21/10
= 2.1
Thus , the following are in order of simplicity:
a) 4/7 / (1 3/4) = 16/49
b) 5 3/5 / (2 2/3) = 21/10
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I need some help with these it's hard for me can some help asap
Answers
Answer:
C and B
Step-by-step explanation:
Evaluate g(5) then substitute the value obtained into f(x)
g(5) = [tex]\sqrt{5-1}[/tex] = [tex]\sqrt{4}[/tex] = 2 , then
f(2) = 3(2) + 1 = 6 + 1 = 7
-----------------------------------------------------------------------------
f(x) = [tex]\frac{x^2+3}{(x-4)(x+8)}[/tex]
the denominator of f(x) cannot be zero as this would make f(x) undefined.
equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.
(x - 4)(x + 8) = 0
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 8 = 0 ⇒ x = - 8
the vertical asymptotes are x = 4 and x = - 8
Which angles are vertical to each other?
Answers
ashley drove 605 miles in 11 hours at the same rate how long would it take her to drive 495 miles
Answers
Answer:
9 hours
Step-by-step explanation:
605 miles/11 hours = 55miles/hour
495 miles (time) = 495 / 55 =9
So, 9 hours
i need all 3 im confused on them
Answers
Answer:
1. 5/12 in exact form and 0.416 in decimal form
2. 26/3 in exact form and 8.6 in decimal form and 8 2/3 in mixed number form.
On each "6" there's a - on top!
Write each expression in simplest form. (x¹/₄ / y⁻³/₄)¹²
Answers
The given expression can be written in its simplest form by solving the exponents.
There are two types of exponent rules that will be applied to the expression. First, we will solve the negative exponent then we will multiply the exponents.
According to the negative exponent rule: x^-n=1/x^n.
Hence, applying the rule to the base term in the denominator, 1/y^⁻³/₄= y^³/₄
Therefore, x^¹/₄ / y^⁻³/₄= x^¹/₄ y^³/₄
According to the multiplication of exponent rule: (x^n)^m=x^nm
Hence, applying the rule to the expression,
(x^¹/₄ y^³/₄)^12=x^¹/₄*12 y^³/₄*12
Multiplying the powers and simplifying,
x^¹/₄*12 y^³/₄*12=x^3y^9
The simplest form of the expression (x^¹/₄/y^⁻³/₄)^12 is x^3y^9.
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what is 2169 rounded to the nearest hundred
Answers
Answer: 2169 rounded to the nearest hundred is 2200
Step-by-step explanation: Since 6 in the tenth place is greater than 5 the number in the hundred place which is 1 goes up to 2. That is how you get 2200
If a person walks
mile in 1 hour, how far does that person walk
in 1 3/4 hours at that rate?
Answers
7/4 miles distance does that person walk.
What is distance?
The length or width between two objects, points, lines, etc. remoteness is the state or fact of something or someone being physically distant from another. A straight line in space It would take too long to walk seven miles in one hour. a distance; a space: The ship was encircled by a sizable body of water.We can use a ratio to solve
1 mile x miles
----------------= ---------------
1 hour 1 3/4 hours
Changing to improper fractions
1 mile x miles
----------------= ---------------
1 hour 7/4 hours
Using cross products
1 * 7/4 = 1 * x
7/4 = x
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The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $ 1200 . The party must have 13 adult chaperones.
b. The class wants to promote the event by giving away 30 spots to students in a drawing. How does the model change? Now how many paying students must attend so the cost for each is no more than $ 7.50 ?
Answers
The function model will be -
Divide the cost by the number of pupils to split it, and you'll get the function C=1200 / n.
How many pupils must enroll in order for the price per pupil to not exceed $7.50?1200/N ≤ 7.50
1200 / 7.50 ≤ N
N ≥ 1200/7.5
N ≥ 160
To keep the price per kid to no more than $7.50, there must be more than 160 participants.
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what is the slope of the line that passes through the points (6, -5) and (6, -4)?
Answers
Answer (y2 -y1) / (x2 - x1)
hope this helps
Answer:
(y2 -y1) / (x2 - x1)
Step-by-step explanation:
Use that formula. The answer should be -3/0 which doesn't make sense. Are you sure you have your x values correct? Since in that case, it would be a straight line and the equation for that would be x = 6 since it is a straight line up with no y-intercept.
Find the domain and range. Graph each relation.
1. {(0, 0), (1, -1),(2, -4).(3,-9),(4, -16)}
Answers
The domain of the relation: {0, 1, 2, 3, and 4}
The range of the relation: {0, -1, -4, -9, -16}
The graph for the relation is in the attachment.
What is the Domain is a Relation?A domain of a relation can be defined as the set of x-values or inputs of a relation.
What is the Range of a Relation?The set of all output or y-values that correspond to the x-values in a set of ordered pairs.
Given the relation, {(0, 0), (1, -1),(2, -4), (3,-9), (4, -16)}
The domain of the relation is: {0, 1, 2, 3, and 4} (these are all the input of the relation)
The range of the relation is: {0, -1, -4, -9, -16} (these are all the output of the relation)
The graph for the relation is in the attachment.
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At the local movie theatre, there are 115 boys, 92 girls, and 28 adults.
a. Write the ratio of the number of boys to the number of girls.
115:92
b. Write the same ratio using another form (: vs. to ).
115 to 92
c. Write the ratio of the number of boys to the number of adults.
115:28
d. Write the same ratio using another form.
115 to 28
Answers
A. The ratio of the number of boys to the number of girls is; 115:92
B. The same ratio using another form is; 115 to 92
C. The ratio of the number of boys to the number of adults is; 115:28
D. The same ratio using another form is; 115 to 28
What is the Ratio?We are told that there are 115 boys, 92 girls, and 28 adults. Thus;
Number of boys = 115
Number of girls = 92
Number of Adults = 28
Now, we want to find some ratios and they are;
A) The ratio of boys to the number of girls = 115 : 92
B) Now, when we have a ratio of a:b, in words, it simply means a to b. Thus, our ratio of boys to girls here can be expressed as;
115 to 92
C) The ratio of the number of boys to the number of adults is;
115:28
D) Similar to answer B above, the ratio of the number of boys to the number of adults can also be expressed as; 115 to 28
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PLSSSPLSS PLS HELP ME WILL GET BRIANLIEST
Answers
π/√2 = 2.22144
5/√3 = 2.88675
3+2√2 = 5.82843
4+8/√50 = 5.13137
So the 1st one and the 2nd one would be the right answers
Kim has a part-time job assembling bicycles for a local store. each day, she earns $20 plus $15 for each bike assembled. kim's boss daily goal is to assemble no more than 6 bicycles a day. if x represents the number of bikes assembled, the total amount she earns can be represented by . what is the range for the function for this situation?
Answers
The range of the function represented by y = 15x + 20, where y is Kim's daily earnings and x is the number of bikes she assembles, is $20 ≤ y ≤ $110.
The range of a function is the set of values of y possible values of the dependent variable after substituting values for the independent variable(domain).
The total amount she earns can be represented by
y = 15x + 20
where y is her daily earnings and x is the number of bikes she assembles
If Kim's boss daily goal is to assemble no more than 6 bicycles a day, then the value of x will only range from 0 to 6(whole number).
domain : {x| 0 ≤ x ≤ 6}
where x is a whole number
Substituting the minimum and maximum value of x in the function.
y = 15(0) + 20 when x = 0
y = 20
y = 15(6) + 20 when x = 6
y = 110
range : $20 ≤ y ≤ $110
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(Use the following statement to answer questions 10-16.)
“If a number is greater than -500, then the number is greater than 500.”
Determine the truth value of the conditional statement. Explain.
Answers
The truth value of the conditional statement is false
How to determine the truth value of the conditional statement?The conditional statement is given as
“If a number is greater than -500, then the number is greater than 500.”
The above conditional statement is false
This is so because
Not all numbers greater than -500 are greater than 500
Take for instance 499 is greater than -500, but less than 500
Hence, the truth value of the conditional statement is false
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