Answer:
[tex]\|a\| = 5\sqrt{13}[/tex].
[tex]\|b\| = 3\sqrt{29}[/tex].
Step-by-step explanation:
Let [tex]m[/tex],[tex]n[/tex], and [tex]k[/tex] be scalars such that:
[tex]\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}[/tex].
[tex]\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}[/tex].
[tex]\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}[/tex].
The question states that [tex]\| a + b \| = 34[/tex]. In other words:
[tex]k\, \sqrt{8^{2} + 15^{2}} = 34[/tex].
[tex]k^{2} \, (8^{2} + 15^{2}) = 34^{2}[/tex].
[tex]289\, k^{2} = 34^{2}[/tex].
Make use of the fact that [tex]289 = 17^{2}[/tex] whereas [tex]34 = 2 \times 17[/tex].
[tex]\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}[/tex].
[tex]k^{2} = 2^{2}[/tex].
The question also states that the scalar multiple here is positive. Hence, [tex]k = 2[/tex].
Therefore:
[tex]\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}[/tex].
[tex](a + b)[/tex] could also be expressed in terms of [tex]m[/tex] and [tex]n[/tex]:
[tex]\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}[/tex].
[tex]\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}[/tex].
Equate the two expressions and solve for [tex]m[/tex] and [tex]n[/tex]:
[tex]\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}[/tex].
[tex]\begin{cases}m = 5 \\ n = 3\end{cases}[/tex].
Hence:
[tex]\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}[/tex].
[tex]\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}[/tex].
In a math class of 28 students, 14 boys and 14 are girls. On a unit test, 5 boys and 9 girls made an A grade. A student is chosen at random from the class. What is the probability of choosing a girl or an A student?
A. 0.82
B. 0.68
C. 0.14
D. 0.50
Answer:
The probability of choosing a girl is 1/2.
The probability of choosing an A student who is a BOY is 5/28.
1/2 = 14/28, and 14/28 + 5/28 = 19/28. This can be simplified to 0.68
Thus, the answer is B. 0.68
Let me know if this helps!
The required probability of choosing a girl or an A student is 0.82. Option A is correct.
Given that,
In a math class of 28 students, 14 boys and 14 are girls. On a unit test, 5 boys and 9 girls made an A grade.
A student is chosen at random from the class. What is the probability of choosing a girl or an A student is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Total sample space = 28
Number of girls = 14
Number of boys = 14
Number of girls A grade student = 9
probability of a girl = 14/28 = 0.5
probability of A grader girl = 9 / 28 = 0.32
Now the probability of choosing a girl or an A grader girl student,
= 0.32 + 0.5
= 0.82
Thus, the required probability of choosing a girl or an A student is 0.82. Option A is correct.
Learn more about probability here:
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Evaluate the following
expression using x = 6:
8(3x + 1)
Anyone know the answer
Answer:
152
Step-by-step explanation:
Substitute the given value for x.
[tex]8(3(6)+1)\\8(18+1)\\8(19)\\152[/tex]
Answer:
152
Step-by-step explanation:
8(3x+1)
Let x = 6
8(3*6+1)
Multiply inside the parentheses
8(18+1)
Add inside the parentheses
8(19)
Multiply
152
PLEASE SOMEONE HELP ME ANSWER THIS !!!!
Write the equations of the linear and exponential functions that pass through the points (0, 15) and (1, 5)
Linear Equation, y = mx+b
Exponential Equation, y = a(b)^x
PLEASE ANSWER IT I HAVE AN IMAGE ATTACHED IF NEEDED !!!!
Step-by-step explanation:
Part A: Linear Equation.
One of the points is (0,15). This means 0,15 is the y intercept so b=15.We can find the slope
[tex] \frac{5 - 15}{1 - 0 } = \frac{ - 10}{1} = - 10[/tex]
So our equation is
[tex]y = - 10x + 15[/tex]
Part B: Exponential Equation
We know that
[tex]15 = a \times b {}^{0} [/tex]
B to the zero power is 1 so
[tex]15 = a[/tex]
This means a =15. Now let find b.
[tex]5 = 15 \times b {}^{1} [/tex]
[tex] \frac{1}{3} = b[/tex]
So the equation is
[tex]y = 15( \frac{1}{3} ) {}^{x} [/tex]
regroup and factorise:
x(x+2)+x+2
⇒x (x+2) + x + 2
⇒x² + 2x + x + 2
⇒x² + 3x + 2
✯ Now factorising☛ By Splitting the middle term method
⇒x² + 3x + 2
⇒x² + 2x + x + 2
⇒ x(x+2)+1(x+2)
⇒ (x+1) (x+2)
Write the name of the definition, postulate, property or theorem that justifies the statement about the diagram.
The following are the statement justifications and explanatory reasons ;
(a) AD + DB = AB; Is justified by segment addition postulate
Reason
Segment addition postulate states that let A and B represent two points,
Then a third D can be on the line joining A and B, if and only if the
relationship between the points is according to the equation, AD + DB = AB
only
(b) m∠1 + m∠2 = m∠CDB; Is justified by angle addition postulate
Reason
Angle addition postulate states that given that a point B lies between an angle m∠AOC, then we have;
m∠AOC = m∠AOB + m∠BOC
(c) ∠2 ≅ ∠6; Is justified by vertically opposite angles theorem
Reason
Vertical angles formed by the crossing of two lines are always equal
(d) If D is the midpoint of [tex]\overline{AB}[/tex], then AD = [tex]\dfrac{1}{2}[/tex]×AB; Definition of midpoint
Reason
The midpoint of a line is the point that is of equal distance from both ends of the of the line. It is the point halfway between the endpoints
(e) If [tex]\underset{DF}{\rightarrow}[/tex] bisects ∠CDB then ∠1 ≅ ∠2; Definition of angle bisector
Reason
An angle bisector is a ray or line that divides an angle into two angles that are congruent
(f) m∠ADF + m∠FDB = 180°; Linear pair postulate
Reason
The linear pair postulate states that where we have two angles that form a linear pear (their addition forms a straight line), then the two angles are supplementary (their sum is 180°)
(g) ∠ADF and ∠4 are supplements, then m∠ADF + m∠4 = 180°; Definition of supplementary angle
Reason
Supplementary angle are defined as angles that when added together, have a sum of 180°
(h) If ∠4 is complementary to ∠5, and ∠6 is complementary to ∠5, then ∠4 ≅ ∠6; Transitive property
Reason
Transitive property states that given three real numbers, a, b, and c, if a = b and c = b, then a = c
Learn more about angle properties postulates, and theorems here;
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PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Could you please please help me with these questions this is my last attempt and it's due today
Answer:
70.20%
Step-by-step explanation:
Since you seem to be in a rush, let's go for a concise answer.
Let's add 146 and 344 to get 490, and do 344 / 490. This gives us the decimal proportion of ice cream cones that was sold. 344 / 490 = 0.70204.
Excellent. To get the percentage, let's multiply 0.70204 by 100 to get 70.204%. Rounding this to the nearest hundredth gives us 70.20%.
Hope this helps!
Note: This question seems to be badly worded, your 42.44% is correct if it's percentage of ice cream bowls in ice cream cones. I'm assuming that it's the percentage of all ice cream. :)
PLS HELP ME ON THIS ANSWER I WILL MARK YOU AS BRAINLIEST IF YOU KNOW TGE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
LOL
Answer:
D. The over 30s have a larger range and interquartile range than the under 30s
Step-by-step explanation:
In a data set, the range is the difference between the maximum and minimum. So, the range for under 30s is 20, while the range for over 30s is 24. Additionally, the interquartile range is the difference between Q3 and Q1. For a boxplot, Q3 is the line where the box ends and Q1 is the line where the box begins. Therefore, the IQR for the under 30s is 8, and the IQR for over 30s is 11. So, D must be correct.
The sum of a rational number and an irrational number is irrational.
Always true,sometimes true, never true
=========================================================
Explanation:
We can prove this by contradiction.
Let's say
A = some rational numberB = some irrational numberC = some other rational numberand
A+B = C
We'll show that a contradiction happens based on this.
If A is rational, then A = p/q where p,q are two integers. The q cannot be zero.
If C is rational, then C = r/s for some other integers. We can't have s be zero.
Note the following
A+B = C
B = C - A
B = r/s - p/q
B = qr/qs - ps/qs
B = (qr - ps)/qs
B = (some integer)/(some other integer)
This shows B is rational. But this is where the contradiction happens: We stated earlier that B was irrational. A number cannot be both rational and irrational at the same time. The very definition "irrational" literally means "not rational".
In short, I've shown that if A+B = C such that A,C are rational, then B must be rational as well.
The template is
rational + rational = rational
Therefore, we've shown that if A is rational and B is irrational, then C cannot possibly be rational. C is irrational.
Another template is
rational + irrational = irrational
A factory inspector found flaws in 3 out of 18 wooden boxes. What is the experimental probability that the next wooden box will be flawed?
Write your answer as a fraction or whole number.
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\frac{1}{6}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Box Probability}}\\\\\rightarrow \frac{\text{# of boxed flawed}}{\text{# of boxes checked}} \\\\\rightarrow \frac{3}{18}\\\\\rightarrow \frac{3/3}{18/3}\\\\\rightarrow\boxed{\frac{1}{6}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
What is x in the diagram below?
Answer:
3rd option, 2√10
Step-by-step explanation:
x²=4×10
or, x=√(4×10)
or, x=2√10
Answer: C, 2√10
Step-by-step explanation:
The chance of solving a problem by A and B is and 1/3 and 2/5 respectively. What is the probability the problem will be solved?
a)2/15
b)1
c)9/15
d)11/15
Books shows "c" as the answer.. I am confused..
We want to compute the probability P(A or B) because we could either solve it following path A, path B, or doing both paths.
P(A) = 1/3
P(B) = 2/5
P(A and B) = P(A)*P(B) assuming A,B are independent
P(A and B) = (1/3)*(2/5)
P(A and B) = 2/15
--------
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 1/3 + 2/5 - 2/15
P(A or B) = 5/15 + 6/15 - 2/15
P(A or B) = (5 + 6 - 2)/15
P(A or B) = 9/15
We could reduce this to 3/5, but it appears your teacher has chosen not to.
would you Rather geometry
Walk on a line or A line segment
why?
Simplify (Asap️ )
please answer this if you know
(full steps required )
(please no spam answers)
see the attachment hope this helps you
In Circle H with m<GKJ=38, Find the m<GHJ
Answer:
the angle GHJ would be 76 because the central angle is always double the measurement of the inscribed angle
What is the quotient?
(-3)
(-3)²
O-9
1
o
1
9
100
O 9
Answer:
(-3)
Step-by-step explanation:
follow me if you want
Whats different for the functions
Solve the inequality 8 + n > 4.
Answer:
n>-4
Step-by-step explanation:
8+n>4
n>4-8
n>-4
Answer:
-4
Step-by-step explanation
Subtract 8 from 4 to get -4.
N = -4
God Bless.
PLS HELP ME ON TTHIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION WHILE YOU ANSWER THE QUESTION!!
Which of the following is not a step in creating a box plot?
A. Order the data
B. Find the values for the five-number summary
C. Create a number line
D. Add all of the numbers in the data set and divide by the number of data items in the set
9514 1404 393
Answer:
D (compute the mean)
Step-by-step explanation:
A box plot is a visual representation of the 5-number summary of a set of data. It is plotted against a number line.
The 5-number summary of the data set is most easily determined from an ordered set of the data, so ordering the data is usually the first step. Since the 5-number summary is plotted against a number line, the next steps are finding the 5-number summary, and creating a suitable number line.
__
The business of adding the data and dividing by the number of data items is a description of computing the mean of the data. That value is not part of the 5-number summary, and is not needed in the creation of the box plot.
Rationalize the denominator and simplify:
a) (√3 - √2)/( √3+√2)
b) (5+2√3)/(7+4√3)
c) (1+√2)/(3 - 2√2)
Answer:
A) (√3-√2)/(√3+√2)
Step-by-step explanation:
i think so
The question is
"Mia has a large bag of sweets, If i share the sweets equally among 1,2,3,4,5 or 6 people, there will always be 1 sweet left over"
with step by step pls :(
Answer:
61
or
421
Step-by-step explanation:
Find the L.C.M. of 2,3,4,5,6 and add 1.
2| 2-3-4-5-6
-------------------
2| 1-3-2-5-3
---------------------
3| 1-3-1-5-3
----------------------
5| 1-1-1-5-1
----------------------
| 1-1-1-1-1-1
L.C.M.=2×2×3×5=60
reqd. number=60+1=61
if i distribute between 2,3,4,5,6 people then reqd number is 61
if Mia is also among those people or she gets also share
then the people are2,3,4,5,6 or 7
L.C.M. of 2,3,4,5,6,7=60×7=420
so reqd number is 420+1=421
Find the measure of the indicated angle to the nearest degree.
Answer:
? ≈ 37°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex] , then
? = [tex]cos^{-1}[/tex] ([tex]\frac{4}{5}[/tex] ) ≈ 37° ( to the nearest degree )
Between which two numbers does 46 lie?
A.
between 8 and 9
B.
between 6 and 7
C.
between 5 and 6
D.
between 7 and 8
Answer:
So the sqrt(46) is between 6 and 7
Step-by-step explanation:
sqrt(46)
5*5 = 25
6*6=36
7*7=49
So the sqrt(46) is between 6 and 7
a piece of work can be done by 24 men in 15 days.in how many days can 18 men do the same work?
18 people is 25% less people so will take 25% longer
25% of 15 is 3.75
3.75+ 15 = 18.75 days ?
find the missing side of the triangle.
Answer:
x = 17
Step-by-step explanation:
x ^2 = 8^2+ 15^2
√x^2 =√64+225
x=17
Answer:
17cm.
Step-by-step explaination:
The given triangle is a right angled triangle.
Using Pythagorean Theorem,
a² + b² = c²
Putting the given values in the equation;
(15)² + (8)² = c²
225 + 64 = c²
289 = c²
17² = c² (square root of 289 = 17)
17 = c
c = 17
Therefore, the missing side of the triangle is equal to 17 cm.
Factorize:
6 + 13mn + 7m² n²
explanation
Answer:
1(6+13mn+7m^2n^2)
Step-by-step explanation:
The coefficients and variables in this equation have a common factor of 1, therefore the equation will go back to it's original state if you use 1 as the common factor.
I hope this helps and sorry if am wrong
josh is standing on the top of a building that is 425 feet tall. He throws a penny up into the air with an initial of 32 ft/sec. How long does it take for the penny to hit the ground?
Y = -4.9x^2 + 32x + 425
A. 10 seconds
B. 6.25
C. 400
D. 0 seconds
Answer:
A
Step-by-step explanation:
cause it will be more faster just because it is in a solid phase or it is solid
The time taken to hit the ground is 6.25 sec.(Option B)
How to calculate time?
It is given that penny follows the trajectory:
[tex]y = -4.9x^2 + 32x + 425[/tex]
Differentiating it we get:
[tex]\dfrac{dy}{dx} =-9.8x+32[/tex]
At y=425, it is obvious that x=0
So dy/dx at x=0 is 32.
Now the vertical component of the velocity is 32sinФ (where Ф is the angle at which penny is thrown).
Ф[tex]=\tan^{-1}(32)[/tex]
Vertical component=[tex]32*\sin(\tan^{-1}(32))[/tex]=31.98 ft/sec
Now applying the equation of motion: acceleration=-32ft/sec^(2)
u=31.98ft/sec s=-425 t=?
[tex]s=ut+\frac{1}{2} at^{2}[/tex]
[tex]-425=31.98t-16t^2[/tex]
[tex]16t^2-31.98t-425=0[/tex]
Solving the quadratic equation we get:
t=6.249 sec≅6.25 sec
Therefore, the time taken is 6.25 sec.
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what is the degree of the polynomial below
Answer:
d
Step-by-step explanation:
trust me gang
Answer:
the degree is the value of the highest exponent... 4x^3 the exponent is a three
answer "D"
Step-by-step explanation:
For the function F defined by F(x)=x2−2x+4, find F(|−4|).
A. 8
B. 4
C. 12
D. 28
Answer:
12
Step-by-step explanation:
F(x)=x^2−2x+4
Let x = |-4| = 4
F(|-4|)=4^2−2(4)+4
= 16 -8+4
= 8+4
= 12
Jerry sold 320 tickets for the school play. He sold x adults tickets for $8 each and y child tickets for $5 each. He sold $1900 worth of tickets. Write a system of equations to model the situation.
What is the equation?
Answer:
x + y = 320
8x + 5y = 1900
Step-by-step explanation:
The equation x + y = 320 represents how 320 tickets were sold in total, from combining the adult and child tickets sold.
Since adult tickets are $8 each, the money from adult ticket sales can be represented by 8x.
The money from child ticket sales can be represented by 5y.
The equation 8x + 5y = 1900 represents how $1900 worth of tickets were sold.
So, the system of equations for the situation is:
x + y = 320
8x + 5y = 1900
Answer:
y = 220
x = 100
Step-by-step explanation:
x + y = 320
8x + 5y = 1900
x = 320 - y
8(320 - y) + 5y = 1900
2560 - 8y + 5y = 1900
2560 -3y = 1900
-2560 -2560
-------------------------
-3y = -660
----- -------
-3 -3
y = 220
x + 220 = 320
-220 -220
----------------------
x = 100
