======================================================
Explanation:
Vector u has magnitude 8 and direction 150 degrees.
So r = 8 and theta = 150
The polar form
r*(cos(theta)+i*sin(theta))
updates to
8*(cos(150)+i*sin(150))
---------------------
Use your calculator to evaluate that last expression to get it into a+bi form
8*(cos(150)+i*sin(150))
8*(-0.866025 + i*0.5)
-6.9282 + 4i
So this is the a+bi form of vector u. It's a rough approximation of it.
-----------------------
Repeat those steps for vector v
v = r*(cos(theta)+i*sin(theta))
v = 3*(cos(115)+i*sin(115))
v = 3*(-0.422618 + i*0.906308)
v = -1.267854 + 2.718924i
----------------------
We're converting each vector to a+bi form so that we can add the vectors.
The general idea is that if you want to add v = a+bi and w = c+di, then
v+w = (a+c)+(b+d)i
we simply add the corresponding real components together, and the imaginary components are added together as well.
-----------------------
Add up u and v
u+v = (-6.9282 + 4i) + (-1.267854 + 2.718924i)
u+v = (-6.9282 + -1.267854) + (4i + 2.718924i)
u+v = -8.196054 + 6.718924i
When rounding to four decimal places, the real and imaginary components are -8.1961 and 6.7189 respectively. These represent the x and y components of the vector.
So we can say vector u+v is approximately < -8.1961, 6.7189 >
The random variable X is normally distributed with mean of 80 and variance of 36. The 67th percentile of the distribution is
Answer:
82.64
Step-by-step explanation:
Mean = 80 ; σ² = 36 ; σ = √36 = 6
Using the relation :
P(Z < x) = (x - mean) / standard deviation
P(Z < x) = 0.67
Z = invNorm(0.67) = 0.44
Hence,
0.44 = (x - 80) / 6
Cross multiply :
6 * 0.44 = x - 80
2.64 = x - 80
2.64 + 80 = x
82.64 = x
Hence, X = 82.64
You roll a standard number cube. Find P (number greater than 5)
Answer:
1/6
Step-by-step explanation:
what is the slope of a line perpendicular to 3x+2y = 7?
Answer:
2/3
Step-by-step explanation:
First find the slope of the line
3x+2y = 7
Subtract 3x
2y = -3x+7
Divide by 2
y = -3/2x +7/2
This is in slope intercept form y = mx+b where m is the slope
The slope is -3/2
A line perpendicular is the negative reciprocal
-1/(-3/2)
2/3
The slope of the perpendicular line is 2/3
Answer:
Slope of the line perpendicular to the given line = 2/3
Step-by-step explanation:
The product of the slopes of lines perpendicular to each other is - 1
That is,
[tex]slope_{1} \times slope _ 2 = - 1\\[/tex]
Given equation of the line :
3x + 2y = 7
2y = - 3x + 7
[tex]y = -\frac{3}{2}x + \frac{7}{2}[/tex]
[tex]Therefore, \ slope \ of \ the \ given \ line \ , slope _1 = \ -\frac{3}{2}[/tex]
Find slope of the line perpendicular to the given line:
[tex]\frac{-3}{2} \times slope_2 = - 1\\\\slope_2 = - 1 \times \frac{2}{-3} = \frac{2}{3}[/tex]
A friend of yours can shoot free throws with 75% accuracy (she makes 75%
of her shots). If she attempts 25 free throws, what's the probability she'll
make at least 20?
Answer:
4
Step-by-step explanation:
Which expression is equivalent to square root 8x^7y^8?
Answer: 2x^3y^4 sqrt 2x or C on edge
Step-by-step explanation:
HELPPP ASAPPPP ONLY ONE WEEK OF SCHOOL LEFT
Answer:
D, no idea how the other one came to the conclusion that B would be right
f(0) is -3, but there is no zero point at -3 (-3/0)
The graph has no minimum value btw, just a maximum value of 1
pls brainliest
Is this correct? If not which is correct?
Suppose the x-axis of a density graph represents someone's height in inches. If the area under the density curve from 60 inches to 70 inches is 0.75, what is the probability of someone's height being anywhere from 60 inches to 70 inches? O A. 75% O B. 65% C. 70% D. 60% SUBMIT
OPTION A 75% is the correct answer
y=3x+2
y=3x−6
how many solutions does the system have
Answer:
no solutions
Step-by-step explanation:
The lines are parallel since they have the same slope
y = mx+b where m is the slope
They have different y intercepts (b)
The will never intersect so they have no solutions
4.
Andrew wants to buy a pair of jeans costing $60. Sales tax on his
purchase is 13%.
a)
How much tax will Andrew be charged?
Answer:
$7.80
Step-by-step explanation:
Find how much tax he will be charged by multiplying 60 by 0.13:
60(0.13)
= 7.8
So, he will be charged $7.80 in tax
Answer:
$7.80
Step-by-step explanation:
13% of 60 = 7.8
so in total 7.80 would be Andrew's TAX
[ Correct me if I'm wrong!! ]
The trapezoid above is cut into two triangles with a black line. Find the area of the two triangles and add the areas together. (HINT: Don't forget that you have to divide by 2 for the area of triangles!) No labels.
Answer:
[tex]42[/tex]
Step-by-step explanation:
The area of a triangle with base [tex]b[/tex] and height [tex]h[/tex] is given by [tex]A=\frac{1}{2}bh[/tex]. In the trapezoid, the two triangles share a height of 6, however one has a base of 6 and the other has a base of 8.
Area of smaller triangle (triangle on the left): [tex]\frac{1}{2}\cdot 6 \cdot 6=18\:\mathrm{cm^2}[/tex]
Area of larger triangle (triangle on the right): [tex]\frac{1}{2}\cdot 8 \cdot 6=24\:\mathrm{cm^2}[/tex]
Therefore, the sum of their areas are [tex]18+24=\boxed{42\:\mathrm{cm^2}}[/tex]
Answer:
Step-by-step explanation:
The triangle on the left is going to be a little trickier than the one on the right.
Right
height = 6
base = 8
Area = 1/2 * 6 * 8 = 24
Left
h=6
base = 6
Area = 1/2 * 6 * 6
Area = 18
Total Area = 18 + 24 = 42
Grandma Gertrude’s Chocolates, a family owned business, has an opportunity to supply its product for distribution through a large coffee house chain. However, the coffee house chain has certain specifications regarding cacao content as it wishes to advertise the health benefits (antioxidants) of the chocolate products it sells. In order to determine the mean % cacao in its dark chocolate products, quality inspectors sample 30 pieces. They find a sample mean of 4% with a standard deviation of 2%. What is the margin of error at 90% confidence?
a. 1.49%
b. 1.24%
c. 0.62%
d. 0.75%
e. 1.36%
Answer:
c. 0.62%
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 30 - 1 = 29
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 29degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.6991
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
Sample of 30, standard deviation of 2%.
Then
[tex]M = T\frac{s}{\sqrt{n}} = 1.6991\frac{2}{\sqrt{30}} = 0.62[/tex]
0.62%, so option c.
Write the equation of the ellipse 4x^2+9y^2+72x+108y+612=0 in standard form.
Answer:
(x+9)^2 + (y+6)^2
9 4 =1
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
Ashe and her two friends will run a relay race. The length of the race is 4/6 mile. If each person runs the same distance, how far will Ashe run?
Answer:
Ashe will run 6 miles
Step-by-step explanation:
4/6 x 3/1 = 12/6 divided by 6 (for numerator and denominator) = 6/1 = 6
Of the 85 learners that packed a lunch for the field trip, 60 have an apple in their lunch and 75 have an orange. All of the learners have at least one apple or orange in their lunch.
What is the probability that a learner chosen at random from the field trip has an orange but not an apple?
Using it's concept, it is found that there is a 0.1765 = 17.65% probability that a learner chosen at random from the field trip has an orange but not an apple.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, of the 85 learners, 75 - 60 = 15 have an orange but not an apple, hence the probability is given by:
p = 15/85 = 0.1765.
0.1765 = 17.65% probability that a learner chosen at random from the field trip has an orange but not an apple.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
If taina makes 5 dollars a hour for babysitting, and babysat for 5 hours on monday how much money did she make?
Answer:
25
Step-by-step explanation:
Take the amount earned per hour and multiply by the number of hours to determine the total amount earned
5 * 5 = 25
Answer:
25 dollars on monday
Step-by-step explanation:
5 dollars an hour times 5 hours
5x5=25
The numbers 24, 22, 34, 28, 29, 24, 25 29, a and b have a median of 27 and a mode of 29. Given that a
Answer: Median is 26,5 and modes are 24 and 29
Step-by-step explanation: In increasing order numbers are
22, 24 24, 25 , 28, 29 , 29 , 34. Because amount of number is even
median is (25 + 28) / 2 = 26,5 and modes are 24 and 29 because both
numbers exist twice
I need help help please help
middle left my guy lol..
what is the least common denominator of 1/3 and 4/7?? plsss explain
Answer:
21
Step-by-step explanation:
The smallest number that can go into both 3 and 7 as our denominators is 21. This can be worked about by multiplying them together.
(FYI: In some cases, if the product is even, it may not always work to multiply them together)
Answer:
21
hope this helps
have a good day :)
Step-by-step explanation:
3 multiples are 3, 6, 9, 12, 15, 18, 21, 24
7 multiples are 7, 14, 21, 28
so would need to change both denominators to 21 and multiple 7 and to 1/3 to get 7/21 and 3 to 4/7 to get 12/21
The perimeter of a square piece of gold is 28 millimeters. How long is each side?
Answer:
7 millimeters
Step-by-step explanation:
Perimeter is the distance around an object.
The object is a square so all sides are equal. This means that we can do 28mm / 4 and get our answer of 7 millimeters.
f(x) = 2x^2 – 3x - 9
g(x) = 4x^2 – 9
Find (f/g)(x)
Answer:
i dont get it sorry
Step-by-step explanation:
ayudaaaaa por favor
Answer:
La respuesta es treinta coma seis.
Espero que esto ayude.
When reaching mile marker 6 on the trail, Randy uses his GPS to find that his current elevation is 6220 feet. If he follows the trail until its end at mile marker 13, his elevation will be 8390 feet. What is the average change in elevation of Randy's position from mile marker 6 to mile marker 13, in feet per mile marker?
Answer:
310 feet per mile marker
Step-by-step explanation:
The average change will be the difference in elevation over the difference in mile markers. Randy’s elevation changed from 6220 feet to 8390 feet, which is a difference of
8390-6220=2170 feet. He started tracking at mile markers 6 to mile markers 13, which is a difference of
13-6=7 miles markers. The average change in elevation is 2170 feet / 7 mile markers = 310 feet per mile marker.
Lexie started her homework at 4:30 P.M. She finished at 5:05 P.M. How many seconds did it take her to finish her homework?
Answer:
2100 seconds
Step-by-step explanation:
4:30 P.M. → 5:05 P.M. there are 35 minutes in between.
1 minute = 60 seconds
35 minutes × 60 seconds = 2100 seconds
25/22 as a decimal rounded to the nearest hundredths
Answer:
Hi there!
Step-by-step explanation:
First thing we have to do is make 25/22 a proper fraction. That is 1 3/22. This converted to a decimal is 1.1(36) or, rounded to the nearest hundredth, that is 1.1 :)
Hope you enjoy!
How many lines intersect at point O?
A.2
B.1
C.4
D.3
Answer:
C. 4 because line o serve as the vertex for each angle there.
answered Which number line represents the solution to the inequality 4x +20 <40
Answer:
the one that has a hollow dot on 5 with the line pointing left
Step-by-step explanation:
4x+20<40
-20 -20
4x<20
/4 /4
x<5
:) ur welcome
-7 2/3 + ( -5 1/2) + 8 3/4 =
Answer:
- 53/12
Step-by-step explanation:
See the image below:)
What is the approximate volume of the cone? Use V=13πr2h
V
=
1
3
π
r
2
h
A 282.6 in3
282.6 in cubed
C 94 in3
94 in cubed
B 141 in3
141 in cubed
D 30 in3
30 in cubed
Will Mark Brainliest
Answer:
C is the correct answer
Step-by-step explanation:
1/3 × pi × 3² × 10 = 94.24777961
Can someone answer this for me (in the picture)