In order to find the magnitude of a vector, we use the Pythagorean theorem. The magnitude, also known as the length or the norm, of a vector, is the square root of the sum of the squares of its components.
In this case, we are given two vectors A and B, which are defined as
A = 5i + 7j
B = 2i + 3j.
The i and j components represent the x and y values of the vector respectively.
To find the magnitude of vector A-B, we need to first find the difference between the two vectors. This can be done by subtracting the components of vector B from the corresponding components of vector A. So,
A-B = (5i + 7j) - (2i + 3j) = 3i + 4j.
Now we can use the Pythagorean theorem to find the magnitude of this vector. The square root of the sum of the squares of the x and y components of the vector is the magnitude of the vector. So, the magnitude of
A-B = √(3^2 + 4^2)
A-B = √(9 + 16)
A-B= √25
A-B = 5. Therefore, the answer is (b) 5.
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An automobile manufacturer claims that its car has a 57.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 210 cars, they found a mean MPG of 57.4. Assume the standard deviation is known to be 1.9. A level of significance of 0.1 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.
Answer:
The value of test statistic
|Z| = |-2.2883| = 2.2883
Step-by-step explanation:
Step(i):-
Given that the mean of the Population = 57.7miles/gallon
The standard deviation of the Population = 1.9
The mean of sample x⁻ = 57.4
Given that the sample size 'n' =210
level of significance = 0.1
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{57.4-57.7}{\frac{1.9}{\sqrt{210} } }[/tex]
Z = -2.2883
|Z| = |-2.2883| = 2.2883
Final answer:-
The value of test statistic
|Z| = 2.2883
1. Clare has $150 in her bank account. She buys a bike for $200. What is Clare’s account balance now?
2. If Clare earns $75 the next week from delivering newspapers and deposits it in her account, what will her account balance be then?
Answer:
1. -$50 2. $25
Step-by-step explanation:
150-200= -50
-50+75=25
a circle with the diameter of 40 inches. what is the area?
Answer:
A= 1256
Step-by-step explanation:
The formula for area of a circle is [tex]A=\pi r^{2}[/tex]
1. Diameter is DOUBLE of radius, so the diameter must be divided by 2. 40/2 = 20.
2. Then, plug in the values into the area formula. A= 3.14[tex](20^{2})[/tex]
3. Solve. A= 1256. (Remember that 20 squared is 20x20)
what is the meaning of XII in roman numeral
Answer:
its 12 in mathematics....
The population of a city decreases by 4.6% per year. If this year's population is
329,000, what will next year's population be, to the nearest individual?
Answer:
Your answer
313866
Mark it as Brainlist answer. Follow me to get more answer
Step-by-step explanation:
Solve the Antiderivative.
Answer:
I got the same as the top so I think that's the answer
I WILL GIVE BRAINLIEST!!!! ~PLEASE HELP (all the answers for all the questions please for the second and first picture)
Answer:
Question 6: I know that (8 + 9) + 3 is equal to 8 + (9 + 3) because of the associative property states that you can change the grouping of addends in any order you want. The benefit to using this property is that you can first add numbers that you can combine more easily. For example, (743 + 51) + 49 can be written as 743 + (51 + 49) or 743 + 100. It is more straightforward to add the numbers that equal 100 first and then add the final number.
Question 3: -3(4x + 3) + 5x [Given]; -12x - 9 + 5x [Distributive Property]; -12x + 5x - 9 [Commutative Property]; -7x - 9 [Combine like-terms]. [tex]\frac{1}{2}[/tex] (6k + 10) + 5k [Given]; 3k + 5 + 5k [Distributive Property]; 3k + 5k + 5 [Commutative Property]; 8k + 5 [ Combine like-terms].
Question 4: 4(2 - 5) - 8 = 4 * (-3) - 8 = -12 - 8 = -20; 4 * 2 - 28 = 8 - 28 = -20.
Question 5: 15 * 3 - 2(2 * 3 + 6) = 45 - 2(6 + 6) = 45 - 2(12) = 45 - 24 = 21; 11 * 3 - 12 = 33 - 12 = 21.
To complete her holiday wrapping, Bella needs identical
strips of ribbon measuring 3.5 feet each. She has 85 feet of
ribbon in total. About how many pieces of ribbon can she
cut from this long strip?
Answer:
24
Step-by-step explanation:
Answer:
The answer would be At least 20 box.
Step-by-step explanation:
i anwerd it in the lesson and got it right. Hope this helps. :)
What is 9% of 2 trillion
Answer: 180000000000
Step-by-step explanation:
Answer:
180000000000
Step-by-step explanation:
Solving
This figure is made up of two rectangular prisms.
12 in.
What is the volume of the figure?
in.
Enter your answer in the box.
2 in.
7 in.
in
21 in.
1
2.
3
4
Answer:
The question is invalid. Please provide a diagram.
When 2 times a number is increased by 9, the answer is the same as
when 30 is decreased by the number. Find the number. HELP ME
Answer:
its 7
Step-by-step explanation:
why did u delete my answer if its right?
Out of 4/10, 3/4, 2/5, and 1/3 which fraction is the biggest?
Answer:
3/4
Step-by-step explanation:
3/4 = .75
4/10 = .40
2/5 = .40
1/3 = .33
Answer:
3/4 is greater then 4/10 and 2/5 is greater then 1/3 and that's all I know
Step-by-step explanation:
[tex] \frac{ \sqrt{40} }{ \sqrt{3} } [/tex]
Answer:
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{2\sqrt{30} }{ 3 }[/tex]
Step-by-step explanation:
Given
[tex]\frac{ \sqrt{40} }{ \sqrt{3} }[/tex]
Required
Simplify
[tex]\frac{ \sqrt{40} }{ \sqrt{3} }[/tex]
Rationalize:
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{40} }{ \sqrt{3} }*\frac{ \sqrt{3} }{ \sqrt{3} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{40*3} }{ \sqrt{3*3} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{120} }{ \sqrt{9} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{120} }{ 3 }[/tex]
Expand the numerator
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{4*30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{4}*\sqrt{30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ 2*\sqrt{30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{2\sqrt{30} }{ 3 }[/tex]
Which of the following points have a distance of five units between them? Select all that apply 
A.)(-2,5) and (3,7)
B.)(10,5) and (7,9)
C.)(1,10) and (6,5)
D.)(-4,-8) and (-4,-5)
E.)(2,-5) and (6,-8)
Answer:
C. (1, 10) and (6, 5)
Step-by-step explanation:
To find the point with a distance of 5 units.
Let the points be x and y.
x = x1 and x2
y = y1 and y2
x2 - x1 = 5 units
y2 - y1 = 5 units.
A quick look at the options, we can tell that the correct option is C.
From points (1, 10) and (6, 5)
x1 = 1, x2 = 6, y1 = 10 and y2 = 5
Substituting into the equation above, we have;
x2 - x1 = 6 - 1 = 5 units
y2 - y1 = 5 - 10 = -5 units.
Therefore, option C with points (1,10) and (6,5) have a distance of five units between them.
7/16+3/8
Simplify or answer in regular fractions or improper fractions
Answer:
hope it helps you
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Answer:
13/16
Step-by-step explanation:
Turn [tex]\frac{7}{16} +\frac{3}{8}[/tex] into [tex]\frac{7}{16} +\frac{6}{16}[/tex]
If both denominators are the same the number it makes it easier to add.
Since 8*2 is 16 you have to do 3*2 in order for 3/8 and 6/16 to be equivalent.
then add the top numbers, not the bottom bc the bottom stays the same.
7+6=13 so the answer is 13/16
hope that helps:)
Write the ratio as a fraction in lowest terms. Be sure to make necessary conversions:
12 feet to 15 inches
------/---------
Answer:12533
Step-by-step explanation:
13x+7=215
×=
Solve the equation and enter the value of x
Answer:
x=16, have a great day
Step-by-step explanation:
Answer:
x = 16
Step-by-step explanation:
13x + 7 = 215
13x = 208 (Subtract 7 from both sides.)
x = 16 (Divide both sides by 13)
-1 subtracted by 2.5
Answer:
-3.5
Step-by-step explanation:
Please help right now which of the following is a major challenge to volcano preparedness
Answer:
D or C I think
Step-by-step explanation:
How do someone overrun so much lava and disaster kits are eated by lava so
Find the value of x.
a) 21
b) 27
c) 31
d) 34
Answer:
21 is the answer
a question arises how?? right
so, 3x+1
3×21+1
63+1
64
Answer:
a) 21
Step-by-step explanation:
Since, in the figure
64° = (3x+1)° [Vertically Opposite Angles]
=> (3x+1)° = 64°
=> 3x = 64° - 1° = 63°
[tex] => x = \frac{63}{3} [/tex]
=> x = 21 (Ans)
brian is buying cans of baked beans for a camping trip.each can is 15 ounces.if he buys 7 cans,about how many pounds of beans is he buying?
2 pounds
5 pounds
7 pounds
10 pounds
Answer:
about 7 pounds
Step-by-step explanation:
NOTE: 16 ounces equals a pound
so, we would do 15x7 which equals 105 ounces. then we would do 105/16 since 105 is the ounces in total and 16 ounces=1 pound. so our answer would equal to 6.5625. which rounded off would be about 7 pounds. I hope this is correct /helps!:)
The store bought a table for $150, and sold it for $240. What percentage was the markup?
Answer:50%
Step-by-step explanation:
Answer:
the bought 65% porcentege
please help me solve this geometry problem:)
Given:
The endpoints of a line segment are (-5,12) and (-5,0).
To find:
The coordinates of a points which divides the line segment in 2:1.
Solution:
Section formula: If a point divides a line segment in m:n.
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Let point P divides the given line segment in 2:1. They, by using section formula, we get
[tex]P=\left(\dfrac{2(-5)+1(-5)}{2+1},\dfrac{2(0)+1(12)}{2+1}\right)[/tex]
[tex]P=\left(\dfrac{-10-5}{3},\dfrac{0+12}{3}\right)[/tex]
[tex]P=\left(\dfrac{-15}{3},\dfrac{12}{3}\right)[/tex]
[tex]P=\left(-5,4\right)[/tex]
Therefore, the coordinate of the point that partitions the given segment in the ratio 2:1 are (-5,4).
A scientist wanted to measure the constant rate of the current in a particular section of the river. She released a tracker into the river. The tracker sent her back the following information:
After 3.5 seconds since the tracker was released into the river the tracker had traveled 5.5 meters.
After 10.9 seconds since the tracker was released into the river the tracker had traveled 16.5 meters.
What is the constant rate of the current?
Answer:
1.486m/s
Step-by-step explanation:
The rate of change is defined as the change in distance divided by the change in time
Rate = ∆distance/∆time
Distance = 16.5 and 5.5
Time = 10.9 and 3.5
When we put this into the formula above, we have:
Rate of change = 16.5 - 5.5 / 10.9 - 3.5
= 11/7.4
= 1.486m/s
The constant rate of change has been calculated to be equal to 1.486m/s
You can use the fact that the rate of the change of a value when some other independent value changes is the ratio of change in the dependent variable to the change in the independent variable.
The constant rate of the current is given by 1.4865 meters per second.
How to measure the rate of change of something as some other value changes?Suppose that we have to measure the rate of change of y as x changes, then we have:
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where we have
[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]
Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.
(5 change per 3 unit can be rewritten as 5/3 change per 1 unit)
How to measure the constant rate of the current for the given situation?The distance traveled by the tracker depends on the time passed.
Let the variable "t" tracks the amount of time passed and let the variable "d" tracks the distance traveled by the tracker, then we have:
[tex]\rm At \: t = t_1 = 3.5, d=d_1 = 5.5 \: m\\At \: t = t_2 = 10.9, d = d_2 = 16.5 \: m[/tex]
Thus, the constant rate of current is obtained by
[tex]Rate = \dfrac{d_2 - d_1}{t_2 - t_1} = \dfrac{16.5 - 5.5}{10.9 - 3.5} = \dfrac{11}{7.4} \\\\Rate \approx 1.4865 \: \text{meters per second}[/tex]
Thus,
The constant rate of the current is given by 1.4865 meters per second.
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Given that a linear function goes through the points (3,2) and (5, 6) determine the slope
of the line.
Answer:
2
Step-by-step explanation:
The formula of slope from 2 points is change in y divided by change in x, so you can apply that to this problem.
First, find the change in y between the two points. To do this, do y2 - y1.
y2 = 6 and y1 = 2, so you have 6 - 2 = 4.
Next, find the change in x between the two points. To do this, do x2 - x1.
x2 = 5 and x1 = 3, so you have 5 - 3 = 2.
All you're really doing here is finding the distance between the x values and the y values of the points, if that makes sense.
The last step is to do change in y divided by change in x, so 4 / 2 = 2.
This means that the slope of the line is 2.
At a recent soccer game at Red Bulls stadium, 7500 fans were rooting for the New England Revolution while 17,500 fans were rooting for the New York Red Bulls. What percent of the soccer fans were rooting for the New England Revolution?
Answer:
30%
Step-by-step explanation:
add the number of fans together: 7500+17500 = 25000
write as fraction, fans of New England Revolution over total number: 7500/25000
simplify or use calculator: 3/10 or 0.3
convert fraction or decimal to percentage: 30%
Find the midpoint between each pair of points.
13. (7,-2) (-4,2)
BONUS POINTS IF RIGHT
vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson-distributed. Determine the following: a. The percentage of time the machine is busy b. The average number of customers waiting in line c. The average time customers spend in the system d. The average number in the system
Answer:
0.667 ;
0.667 customers ;
0.0166708 hour ;
1.334 customers
Step-by-step explanation:
Given that:
Service time (μ) = 30 seconds ; 2 customers per minute ; 2 * 60 = 120 customers per hour
Arrival time, λ = 80 customers per hour
a.) percentage of time machine is busy (p) ; Utilization factor :
P = λ/ μ = 80 / 120 = 0.667
b.) average number of customers waiting in line Li = p² / 2(1-p)
= 0.667² / 2(1-0.667) = 0.667 customers
c) Average time customer spend in the system = Li/λ + 1/μ
= (0.667 / 80) + (1 / 120)
0.0083375 + 0.0083333
= 0.0166708 hour
= 0.0166708 * 60 = 1.00025 minutes
D) average number in the system ;
Li + p
= 0.667 + 0.667 = 1.334 customers
Daniel has a total collection of 200 marbles. 10% of them are red. How many are red marbles in his collection? What is missing in the problem?
Answer:
40(i think)
Step-by-step explanation:
WHAT IS THE PRUDTUCT OF 7\9 AND 6 A. 1 4/9 B. 3 7\9 C. 4 2\3 D. 7 5\7
Answer:
C.
Step-by-step explanation: