Answer:
The components of [tex]\vec{b}[/tex] parallel and perpendicular to [tex]\vec {a}[/tex] are [tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex] and [tex]\vec b _{\perp} = \frac{1}{2}\,i+\frac{3}{2}\,j-3\,k[/tex], respectively.
Step-by-step explanation:
Let be [tex]\vec b = 2\,i+j-3\,k[/tex] and [tex]\vec a = 3\,i-j[/tex], the component of [tex]\vec b[/tex] parallel to [tex]\vec a[/tex] is calculated by the following expression:
[tex]\vec b_{\parallel} = (\vec b \bullet \hat{a}) \cdot \hat{a}[/tex]
Where [tex]\hat{a}[/tex] is the unit vector of [tex]\vec a[/tex], dimensionless and [tex]\bullet[/tex] is the operator of scalar product.
The unit vector of [tex]\vec a[/tex] is:
[tex]\hat{a} = \frac{\vec {a}}{\|\vec a\|}[/tex]
Where [tex]\|\vec {a}\|[/tex] is the norm of [tex]\vec a[/tex], whose value is determined by Pythagorean Theorem.
The component of [tex]\vec{b}[/tex] parallel to [tex]\vec {a}[/tex] is:
[tex]\|\vec {a}\| = \sqrt{3^{2}+(-1)^{2}+0^{2}}[/tex]
[tex]\|\vec {a}\| = \sqrt{10}[/tex]
[tex]\hat{a} = \frac{1}{\sqrt{10}} \cdot (3\,i-j)[/tex]
[tex]\hat{a} = \frac{3}{\sqrt{10}}\,i -\frac{1}{\sqrt{10}} \,j[/tex]
[tex]\vec{b}\bullet \hat{a} = (2)\cdot \left(\frac{3}{\sqrt{10}} \right)+(1)\cdot \left(-\frac{1}{\sqrt{10}} \right)+(-3)\cdot \left(0\right)[/tex]
[tex]\vec b \bullet \hat{a} = \frac{5}{\sqrt{10}}[/tex]
[tex]\vec b_{\parallel} = \frac{5}{\sqrt{10}}\cdot \left(\frac{3}{\sqrt{10}}\,i-\frac{1}{\sqrt{10}}\,j \right)[/tex]
[tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex]
Now, the component of [tex]\vec {b}[/tex] perpendicular to [tex]\vec{a}[/tex] is found by vector subtraction:
[tex]\vec{b}_{\perp} = \vec {b}-\vec {b}_{\parallel}[/tex]
If [tex]\vec b = 2\,i+j-3\,k[/tex] and [tex]\vec {b}_{\parallel} = \frac{3}{2}\,i-\frac{1}{2}\,j[/tex], then:
[tex]\vec{b}_{\perp} = (2\,i+j-3\,k)-\left(\frac{3}{2}\,i-\frac{1}{2}\,j \right)[/tex]
[tex]\vec b _{\perp} = \frac{1}{2}\,i+\frac{3}{2}\,j-3\,k[/tex]
Define p ~ q by the equation p ~ q = p2q3– 3q. Then 2 ~ 3 = A) 108 B) 27 C) 99 D) 117 E) 89
Answer:
C
Step-by-step explanation:
We know that p = 2 and q = 3 so:
2 ~ 3
= 2² * 3³ - 3 * 3
= 4 * 27 - 9
= 108 - 9
= 99
8.2 more than the quotient of h and 6 is w
Answer:
8.2 + (h÷6=w)
Translate each of the following English statements into logical expressions. The domain of discourse is the set of all real numbers.
(a) There are two numbers whose ratio is less than 1.
(b) The reciprocal of every positive number is also positive.
(c) There are two numbers whose sum is equal to their product.
(d) The ratio of every two positive numbers is also positive.
(e) The reciprocal of every positive number less than one is greater than one.
(f) There is no smallest number.
(g) Every number besides 0 has a multiplicative inverse.
(h) Every number besides 0 has a unique multiplicative inverse.
Answer:
A) З x,y : ( x/y < 1, y/x < 1 )
B) ∀ Y : ( Y > 0 = 1/Y > 0 )
C) з x,y : ( x+y = xy )
D) ∀ x,y : [ ( x>0 ) ∧( y > 0 ) = (( x/y > 0 ) ∧ ( y/x > 0 ))
E ) ∀ y : [ ( y > 0 ) ∧ ( y < 1) = ( 1 / y > 1 )
F) n ( ( з x ∀ y ( x <y ) )
G) ∀x (( x ≠ 0 ) = ( зy ( xy = 1 ) ))
H) ∀x ( (x≠0) = ( з! y (xy = 1))
Step-by-step explanation:
since the domain of discourse is a set of all real numbers the logical expressions of the English statements are expressed with respect to real number:
A) З x,y : ( x/y < 1, y/x < 1 )
B) ∀ Y : ( Y > 0 = 1/Y > 0 )
C) з x,y : ( x+y = xy )
D) ∀ x,y : [ ( x>0 ) ∧( y > 0 ) = (( x/y > 0 ) ∧ ( y/x > 0 ))
E ) ∀ y : [ ( y > 0 ) ∧ ( y < 1) = ( 1 / y > 1 )
F) n ( ( з x ∀ y ( x <y ) )
G) ∀x (( x ≠ 0 ) = ( зy ( xy = 1 ) ))
H) ∀x ( (x≠0) = ( з! y (xy = 1))
In translating English written expressions to logical expressions, we have to know the domain of the discourse. The domain of discourse can be said to be a set of all real numbers that the logical expressions of the English statements are expressed with respect to their real numbers. And as such, we arrive at each of this.
A) З x,y : ( x/y < 1, y/x < 1 )
B) ∀ Y : ( Y > 0 = 1/Y > 0 )
C) з x,y : ( x+y = xy )
D) ∀ x,y : [ ( x>0 ) ∧( y > 0 ) = (( x/y > 0 ) ∧ ( y/x > 0 ))
E ) ∀ y : [ ( y > 0 ) ∧ ( y < 1) = ( 1 / y > 1 )
F) n ( ( з x ∀ y ( x <y ) )
G) ∀x (( x ≠ 0 ) = ( зy ( xy = 1 ) ))
H) ∀x ( (x≠0) = ( з! y (xy = 1))
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How many models of 100 do you need to model 3600 Please answer this full question for me and fill in the blanks to the entire question thank you so much
Answer:
a=36, b=3, c=36, d=66
Step-by-step explanation:
a=3600/100=36
b=30*100/1000=3
c=30*100+(36*100)=66 hundreds
Direct Variation - Guided Practice #3 - Karen earns $28.50 for working six hours. If the amount m she earns varies directly with h the number of hours she works, how much will she earn for working 10 hours? $57.00 $74.50 $47.50 $64.50 O
Answer:$47.50
Step-by-step explanation:First you need to find how much she earns per hour or the unit rate by dividing the money she earned (28.50) by the hours she worked(6) which equals to $4.75.Then you take that number and multiply it by the 10 hours which equals $47.50.
An area of 4 square yards is qual to 36 square feet. 10 square yards is equal to how many square feet
Answer:
90 square feetStep-by-step explanation:
square square
yards feet
4 36
10 x
[tex]x = \dfrac{36\cdot10}{4}=9\cdot10=90[/tex]
Use the Ratio Test to determine if the following series converges absolutely or diverges.
sigma^infinity_n = 1 (- 1)^n n^2 (n + 2)!/n!7^n
Since the limit resulting from the Ratio Test is_______, the series converges absolutely.
(Simplify your answer.)
Answer:
Since the limit resulting from the ratios test is = 1 / 729 which is < 1 the series converges absolutely
Step-by-step explanation:
Since the limit resulting from the ratios test is = 1 / 729 which is < 1 the series converges absolutely
ATTACHED BELOW IS THE DETAILED SOLUTION of the above answer
You move up 2 units and down 8 units. You end at (-2, -3). Where did you start?
Answer:
(-2, 3)
Step-by-step explanation:
Let's work backwards.
You start at (-2, -3).
Instead of "moving up 2 units", we "move down 2 units".
Moving up or down means changing the Y axis FYI.
(-2, -5)
Instead of "moving down 8 units", we "move up 8 units".
(-2, 3)
Answer:
(0,5)
Step-by-step explanation:
2 + -2 =0
-3 +8 =5
so its( 0,5)
HOPE THIS HELPS!!!!!!!!!!!!!!!!!!
8 old rings for every 1 new ring - 16 old rings for every 2 new rings is proportional or not proportional
Answer:
Proportional
Step-by-step explanation:
If you simplify 8/16 down as a fraction it would be 1/2 which is the same as 1/2 for the other one. You can also times the new rings by 8 which equals the old rings.
Assume the acceleration of the object is a(t) = −32 feet per second per second. (Neglect air resistance.) A balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 80 feet above the ground.(a) How many seconds after its release will the bag strike the ground? (b) At what velocity will it hit the ground?
Answer:
(a) 2.79 seconds after its release the bag will strike the ground.
(b) At a velocity of 73.28 ft/second it will hit the ground.
Step-by-step explanation:
We are given that a balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 80 feet above the ground.
Assume the acceleration of the object is a(t) = −32 feet per second.
(a) For finding the time it will take the bag to strike the ground after its release, we will use the following formula;
[tex]s=ut+\frac{1}{2} at^{2}[/tex]
Here, s = distance of the balloon above the ground = - 80 feet
u = intital velocity = 16 feet per second
a = acceleration of the object = -32 feet per second
t = required time
So, [tex]s=ut+\frac{1}{2} at^{2}[/tex]
[tex]-80=(16\times t)+(\frac{1}{2} \times -32 \times t^{2})[/tex]
[tex]-80=16t-16 t^{2}[/tex]
[tex]16 t^{2} -16t -80 =0[/tex]
[tex]t^{2} -t -5 =0[/tex]
Now, we will use the quadratic D formula for finding the value of t, i.e;
[tex]t = \frac{-b\pm \sqrt{D } }{2a}[/tex]
Here, a = 1, b = -1, and c = -5
Also, D = [tex]b^{2} -4ac[/tex] = [tex](-1)^{2} -(4 \times 1 \times -5)[/tex] = 21
So, [tex]t = \frac{-(-1)\pm \sqrt{21 } }{2(1)}[/tex]
[tex]t = \frac{1\pm \sqrt{21 } }{2}[/tex]
We will neglect the negative value of t as time can't be negative, so;
[tex]t = \frac{1+ \sqrt{21 } }{2}[/tex] = 2.79 ≈ 3 seconds.
Hence, after 3 seconds of its release, the bag will strike the ground.
(b) For finding the velocity at which it hit the ground, we will use the formula;
[tex]v=u+at[/tex]
Here, v = final velocity
So, [tex]v=16+(-32 \times 2.79)[/tex]
v = 16 - 89.28 = -73.28 feet per second.
Hence, the bag will hit the ground at a velocity of -73.28 ft/second.
Which digit is in the thousandths place 1.356.209
Answer:
9
Step-by-step explanation:
The thousandths place is the third digit after the decimal place. In this case, the digit in the thousandths place is 9. Note that this is the thousandths place, not the thousands place.
There was a total of $548 collected for tickets to the school musical. The adult tickets cost $6 and the student tickets cost $4. If 12 more student tickets were sold than adult tickets, then find the number of adult tickets sold.
Answer:
1) 6A + 4S = 548
2) A +12 = S multiplying by 4
2) 4A -4S = -48 then we add equation 1)
1) 6A + 4S = 548
10A = 500
50 Adult Tickets were sold and
62 Student Tickets were sold.
Double Check
50 * $6 = $300
62 * $4 = $248
Total = $548 Answer is correct!!!
Step-by-step explanation:
An agency is studying the income of store managers in the retail industry. A random sample of 25 managers reveals a sample mean of $45,420. The sample standard deviation is $2,050. Use 90% confidence level to determine the confidence interval.
Answer:
The Confidence Interval = ($44,745.55 , $46,094.45)
Step-by-step explanation:
The formula for Confidence Interval =
Confidence Interval = Mean ± z × Standard deviation/√n
Where n = number of samples = 25 managers
Standard deviation = $2,050
Mean = $45,420
z = z score of the given confidence interval
= z score of 90% confidence interval
= 1.645
Confidence Interval = $45,420 ± 1.645 × $2,050/√25
= $45,420 ± 1.645 × $2,050/5
= $45,420 ± 674.45
Confidence Interval =
$45,420 - 674.45 = $44,745.55
$45,420 + 674.45 = $46,094.45
Therefore, the Confidence Interval = ($44,745.55 , $46,094.45)
HELP ASAP ROCKY!!! will get branliest.
Step-by-step explanation:
Haley: 10x + 155
brother: 230-15x
10x+155=230-15x
25x + 155 = 230
25x = 75
x = 3 weeks
10(3)+155= 30+155= $185 for Haley
230-15(3)= 230-45= $185 for brother
solve for x 3/5=x/11 give your answer as an improper fraction in its simplest form
Answer:
[tex]\huge \boxed{x = \frac{33}{5} }[/tex]
Step-by-step explanation:
[tex]\displaystyle \sf \frac{3}{5} =\frac{x}{11}[/tex]
Cross multiply.
[tex]\sf x \cdot 5=3 \cdot 11[/tex]
[tex]\sf 5x=33[/tex]
Divide both sides by 5.
[tex]\displaystyle \sf x = \frac{33}{5}[/tex]
The value is an improper fraction in simplest form.
The solution of the given fractions 3/5=x/11 in the improper fraction will be 6 3/5.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
As per the given,
3/5 = x/11
x/11 = 3/5
x = (3/5)11
x = 33/5
x = (30 + 3)/5
x = 30/5 + 3/5
x = 6 + 3/5 = 6 3/5
Hence "The solution of the given fractions 3/5=x/11 in the improper fraction will be 6 3/5".
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A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. The p-value is between
Answer:
The P-value is between 2.5% and 5% from the t-table.
Step-by-step explanation:
We are given that a random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years.
Let [tex]\mu[/tex] = true average age of all the students at the university.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 24 years {means that the average age of all the students at the university is less than or equal to 24}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 24 years {means that the average age of all the students at the university is significantly more than 24}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average age = 25 years
s = sample standard deviation = 2 years
n = sample of students = 16
So, the test statistics = [tex]\frac{25-24}{\frac{2}{\sqrt{16} } }[/tex] ~ [tex]t_1_5[/tex]
= 2
The value of t-test statistics is 2.
Also, the P-value of test-statistics is given by;
P-value = P( [tex]t_1_5[/tex] > 2) = 0.034 {from the t-table}
The P-value is between 2.5% and 5% from the t-table.
a truck can be rented from company A for $80 a day plus $0.40 per mile .company B charges $20 s day plus 0.80 per mile to rent the same truck. find the number of miles in a day at which the rental cost for company A and company B are the same?
Answer:
Step-by-step explanation:
.40m + 80 = .80m + 20
-.40m + 80 = 20
-.40m = -60
m = 150 miles in a day
7.) When rounding to the nearest 10, what is the largest number that will
round to 80?
2.) 84
b.) 85
c.) 79
d.) 86
9514 1404 393
Answer:
(a) 84
Step-by-step explanation:
The largest integer that will round to 80 is one that does not have 5 or more in the ones place: 84.
__
The largest decimal number of a particular precision is 84.99999... (some finite number of 9s). If there are an infinite number of 9s, the number can be shown to be equal to 85, which would round to 90.
A typical adult human body contains approximately 2.500 L of blood plasma. How many grams of blood plasma are in the typical adult human body? The density of blood plasma is 1.03 g/mL.
Answer:
2,575 grams of blood plasma are in the typical adult human body
Step-by-step explanation:
Density is the property that matter, whether solid, liquid or gas, has to compress into a given space, so it relates the amount of mass per unit volume. So the density of a substance is the quotient between mass and volume:
[tex]density=\frac{mass}{volume}[/tex]
In this case, you know:
density=1.03 [tex]\frac{g}{mL}[/tex]mass= ?volume= 2.5 L= 2,500 mL (being 1 L= 1,000 mL)Replacing:
[tex]1.03\frac{g}{mL} =\frac{mass}{2,500 mL}[/tex]
and solving, you get:
mass= 1.03 [tex]\frac{g}{mL}[/tex] *2,500 mL
mass= 2,575 g
2,575 grams of blood plasma are in the typical adult human body
Candy is sold 5 pieces for $2.50. What is the unit rate cost per piece of candy
Answer:
the unit rate is 0.50 per piece
Step-by-step explanation:
divide $2.50 by 5
It takes Three hours for a highway worker to mow the grass on a stretch of highway. It takes 6 hours for a different highway worker to mow the grass on the same stretch of highway. How many hours will it take for the two highway workers to mow the grass together on this stretch of highway?
Answer:
Step-by-step explanation:
4.5
The required time that two highway workers to mow the grass together on this stretch of highway is 2 hours,
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Rate of doing for highway workers A = 1 / 3
Rate of doing for highway workers B = 1 / 6
Now total rate,
= 1 / 3 + 1 / 6
= 2 + 1 / 6
= 3 / 6
= 1 / 2
Now,
it takes for the two highway workers to mow the grass together on this stretch of highway,
Time = 1 / 1 / 2
Time = 1 * 2 / 1
Time = 2 hours,
Thus, the required time that two highway workers to mow the grass together on this stretch of highway is 2 hours,
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y is 8 less than the product of 9 and x
Answer:
[tex]\huge \boxed{y=9x-8}[/tex]
Step-by-step explanation:
The product is the result after multiplying two or more values together.
A number less than a value means that the number is subtracted from that value.
[tex]y=9 \cdot x-8[/tex]
[tex]y=9x-8[/tex]
Are the ratios 0:5 and 0:20 equivalent?
0:5 and 0:20 are equivalent. You multiply both 0 and 5 by 4 to get 0 and 20.
i think i did it but im not sure if it even did anythig just wait
Answer:
x minus y: when it says "minus", it means substracting, so x - y.
The product of two numbers: If we call one x and the other y, the product of them is the same as multiplying them, so xy.
The product of two numbers is six: If we call one x and the other y, the product of them is the same as multiplying them and we know the result of doing so is 6, so xy = 6
Six less than a number is y: So if we substract x to a number, the result is y, so 6 - x = y
x substracted by y: this means we substract x from y, which is the same than y minus x, so y - x
y divided by x: this means y is being divided by x, so y/x
The sum of two numbers is six: That means we sum x and y, and the result is 6, so x + y = 6
x divided by y: This means x is being divided by y, so x/y
The sum of x and y: this means both numbers are summing, so x + y
Six times a number equals y: This means 6 per a number (let it be x) is equal to y, so 6x = y
In the underlined section, what do the colonists promise to do?
Answer:
obey the law :)
Step-by-step explanation:
Answer: Obey the law
Step-by-step explanation:
Find the sum for 2349 and 2009
4,358
hope this helps
A person makes an overseas phone call. The telephone company charges 65 cents for the first minute and then 75 cents for each minute thereafter. Because it's an overseas phone call, there is also a 55 cent service charge. If the phone call cost $ 19.20 , how many minutes did this person talk?
Answer:
25 minutes.
Step-by-step explanation:
A person makes an overseas call.
The telephone company charges 65 cents for the first minute.
Then 75 cents for each minute thereafter.
There is a 55 cent service charge.
1 dollar = 100 cents
65 cents = $0.65
75 cents = $0.75
55 cents = $0.55
For a phone call that cost $19.20 ;
Subtracting the service charge and the first minute charge from overall cost we get;
$19.20 - $0.55 - $0.65 = $18
For every additional minute there is a charge of $0.75
How many minutes make $18 ;
Cross multiplying this gives;
[tex]\frac{18}{0.75} * 1[/tex] = 24 minutes.
So the call lasted 24 minutes + 1 minute = 25 minutes.
Simply the answer and write as a mixed number if possible
3/4 divided by 9/10
Reduce the expression, if possible, by canceling the common factors.
Exact Form:
5/6
Answer:
27/40
Step-by-step explanation:
There is no possible way to simplfiy the equation
I have no clue how to do this equation please help me....[tex](-5)^5/(-5)^-6[/tex]
619
the answer is 619
Answer:
= -5¹¹
Step-by-step explanation:
[tex]\frac{-5^{5} }{-5^{-6} }[/tex]
= -5^(5+6)
= -5¹¹
Find the greatest common factor of the expressions.
5x^7, 30x
To find the GCF (greatest common factor) we must find the largest thing that can go into both of them.
We cannot divide by any exponents because only one has them, however we can divide by 5x.
5x^7, 30x
x^7, 6
So, the GCF is 5x
Hope this helps,
Jeron
P.S
If this helps, consider marking brainliest
edit:
Thank you :D
Answer:
5x.
Step-by-step explanation:
The GCF of 5 and 30 = 5.
The GCF of x^7 and x is x.