Answer:
Step-by-step explanation:
l
Option C corresponds to the vectors scalar projection and dot product, which are uv = 2.24 and u v = 7.07.
To find the scalar projection (uv) and the dot product (u · v) of vectors u and v, use the following formulas:
Scalar Projection (uv) of u onto v:
uv = |u| × cos(ϴ)
Dot Product (u · v) of u and v:
u · v = |u| × |v| × cos(ϴ)
u = ⟨1, 3⟩ and v = ⟨2, 1⟩, and cos(ϴ) = √(2)/2,
calculate the magnitudes of u and v first:
|u| = √(1² + 3²) = √10
|v| = √(2² + 1²) = √5
Now, calculate the scalar projection (uv) and the dot product (u · v):
Scalar Projection (uv) of u onto v:
uv
= |u| × cos(ϴ)
= √10 × √(2)/2
= √(10/2)
= √5 ≈ 2.24
Dot Product (u · v) of u and v:
u · v
= |u| × |v| × cos(ϴ)
= √10 × √5 × √(2)/2
= √(1052)/2
= √100/2
= √50
≈ 7.07
Therefore, the scalar projection and dot product of the vectors is equal to option c. uv = 2.24 and u · v = 7.07.
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An ice cream cone with a diameter of 2 inches and a height of 3.5 inches is filled with ice cream and more ice cream on top in the form of a hemisphere with the radius equal to the radius of the cone. Compute the total volume of ice cream it contains.
Answer:
11pi/6 in^3 or
5.760 in^3 to the nearest thousandth.
Step-by-step explanation:
Volume of ice cream = volume of the cone + volume of the hemisphere
= 1/3 pi r^2 h + 1/2 * 4/3 pi r^3
= 1/3 pi 1^2 * 3.5 + 2/3 pi 1^3 (as the radius = 1/2 * diameter)
= (7/6 + 2/3) pi
= 11pi/6 in^3.
There are 40 boys in 6th grade. The number of girls in 6th grade is 30. Carly says that means the ratio of the number of boys in 6th grade to the number of girls in 6th grade is 4:7. Is Carly correct? If not, what is the correct answer?
Answer:
Carly is wrong. The correct answer is 4:3
Step-by-step explanation:
40/10=4
30/10=3
Answer:
Carlie is wrong
Step-by-step explanation:
The correct answer is 4:3
49 increased by twice a number m
W
49(2m)
2m - 49
49 + 2m
2m + 49
Answer:
The answer to this question is 49＋2m.
Answer:
49 + 2m
Explanation:
49 is being Increased by so you would be adding a certain ammount to 49
3) There were 35 children and 10 adults at a barbeque.
a. What is the ratio of adults to
children at the barbeque?
b. What is the ratio of children to
total people at the barbeque?
c. Five more children came to the
barbeque. Now what is the ratio
of children to total people?
Answer:
3. a. 10:35= 2:7
b.35:45=7:9
c.40:50=4:5
A 10-foot by 12-foot wall has two windows that measure 3 feet by 5 feet each.
5 feet
5 feet
10 feet
3 feet
3 feet
12 feet
If the windows are not to be painted, what percent of the wall will be painted?
12 ft maybe? i dunno im sorry if this is wrong
5. Ellen wants to rent a bike. They charge a $12 service
fee plus $16 per hour and she can spend at most $140,
how many hours can she rent the bike?
Answer:
5
Step-by-step explanation:
cuz 12 +16 is 28, 140÷28 is 5
Answer:
16h + 12 = 140
Step-by-step explanation:
She can ride the bike for 8 hours.
The perimeter of a triangle is
17
x
−
5
units. One side is
3
x
+
5
units and another is
8
x
−
3
units. How many units long is the third side?
Answer:
i did'nt understand the question
Step-by-step explanation:
sorry
Solve the equation. Check your solution. (1/2 is a fraction for one half
s-1/2=1/2
Answer:
[tex]s = 1[/tex]
Step-by-step explanation:
Given
[tex]s - \frac{1}{2} = \frac{1}{2}[/tex]
Required
Solve for s
[tex]s - \frac{1}{2} = \frac{1}{2}[/tex]
Add [tex]\frac{1}{2}[/tex] to both sides
[tex]s - \frac{1}{2} + \frac{1}{2} = \frac{1}{2} + \frac{1}{2}[/tex]
Take LCM
[tex]s + \frac{-1+1}{2} = \frac{1+1}{2}[/tex]
[tex]s + \frac{0}{2} = \frac{2}{2}[/tex]
[tex]s +0 = 1[/tex]
[tex]s = 1[/tex]
How much will the store be selling the cans of spam if they want to make a 420% profit?
Answer:
how many cans?
Step-by-step explanation:
if you have a GCF of x is that a root?
Answer:
No,
Step-by-step explanation:
No, GCF is not a root, it is the coefficient of x.
A virus takes 13 days to double its original population (A = 2A0). How long will it take to triple its population? Round to
the nearest tenth.
Answer:
20.6
Step-by-step explanation:
The exponential function to solve the problem.
A = [tex]A_0[/tex] [tex]e^{rt}[/tex]
A = population in time t.
[tex]A_0[/tex] = Initial population.
r = growth rate.
t = time
The number of days taken to triple the population is 20.7 days.
What is a function?
A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The exponential function to solve the problem.
A = [tex]A_0[/tex] [tex]e^{rt}[/tex]
A = population in time t.
[tex]A_0[/tex] = Initial population.
r = growth rate.
t = time
Now,
A = 2[tex]A_0[/tex]
t = 13
A = [tex]A_0[/tex] [tex]e^{rt}[/tex]
[tex]2A_0[/tex] = [tex]A_0e^{13r}[/tex]
2 = [tex]e^{13r}[/tex]
Taking logs on both sides.
log 2 = 13r log e
0.30 = 13r
r = 0.30/13
r = 0.023
Now,
A = 3[tex]A_0[/tex]
A = [tex]A_0[/tex] [tex]e^{rt}[/tex]
3 = [tex]e^{rt}[/tex]
log 3 = rt
0.48 = 0.023t
t = 0.48/0.023
t = 20.7 days.
Thus,
The number of days taken to triple the population is 20.7 days.
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Someone please help me !!!!!
A company claims that its laptops have an average battery life of at least 12 hours. How would you formulate this
Options:
H0 :
H0 : µ =12
H0 > 12> H1
None of these
Answer:
None of these
Step-by-step explanation:
The answer is
H0 : µ ≧ 12
Ha : µ<12
We formulate the null and alternative hypothesis here to state that battery life of the laptop lasts at least 12 hours(more than but not less, null hypothesis) or that it lasts less than 12 hours(alternative hypothesis).
The null hypothesis is the one being tested to know whether we would reject it or not in which case we choose the alternative hypothesis. To test the hypotheses, we do a t test using a significance level of say 0.05(95% confidence interval) and find our p value in order to compare and decide if the null hypothesis would be rejected or not based on statistical significance.
(MC)
The leg of a right triangle is 3 units and the hypotenuse is 11 units. What is the length, in units, of the other leg of the triangle?
1. 112 units.
2. square root 112 units.
3. 130 units.
4. square root 130 units.
Answer:
Square root 112 Units.
Step-by-step explanation:
See the image attached for the work.
4/ PLEASE HELP ME ON THIS. ASAP
Answer: a,b,d,e are all right beacuse they all relate to the question
Step-by-step explanation:
c how ever is no shown on the graph and is therefor wrong
What are the answers and how?
Answer:
a) [tex]x=2p-4[/tex]
b) our team scored 44 points
Step-by-step explanation:
Your basketball team scored 4 fewer than twice as many points p as the other team.
a) Write algebraic expression
Let x is your basketball team score, the expression will be:
[tex]x=2p-4[/tex]
b) The other team scored 24 points. How many points did your team score?
p=24
we need to find x
[tex]x=2p-4\\Put \ p=24\\x=2(24)-4\\x=48-4\\x=44[/tex]
So, our team scored 44 points
Identify the next three numbers in this sequence : 2,8,4,16,12
Answer:
18, 14, 20
Step-by-step explanation:
Answer:
I got A 18,14, and 20
Step-by-step explanation:
PLZ CORRECT ME IF I AM WRONG PLZ AND THANK YOU
A contestant in a weight-loss competition wants to lose an average of at least 8 pounds per month during a five-month period. Based on the progress report, how many pounds must the contestant lose in the fifth month to meet the goal?
Answer:
Can you import the progress report picture please
Step-by-step explanation:
So we can solve it
Help. I don’t understand this.
Answer:
f(6)=2
f(2)=4
f(0)=7
f(5)=1.5
f(x)=1 x=4
Step-by-step explanation:
f(x)=y.The numbers represent the x values. As you are plugging in a number for x. Just look at the graph on the x-axis to get the y-values.
The average number of pounds of meat that a person consumes a year is 218.4 pounds. Assume that the standard deviation is 25 pounds and the distribution is approximately normal. If a sample of 40 individuals is selected, find the probabil
Answer:
The answer is "0.9217".
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]\mu = 218.4 \\\\ \sigma = 25\\\\\bar{x}= 224 \\\\ n = 40 \\\\[/tex]
[tex]z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\\[/tex]
[tex]= \frac{224 - 218.4}{\frac{25}{\sqrt{40}}} \\\\= 1.4167\\\\\to P( \bar{x}< 224) = P(z< 1.4167) = 0.9217[/tex]
find the slope of the line please help
Answer:
2/5 I think I'm not sure tho :/
Answer:
Slope is -1/2 this is the answer 1 down and 2 across.
Step-by-step explanation:
Can I have brainiest
HELPPPP PLEASSSSEEEiffgxhxgxgkxgjxgxutx
Graph y=-3x+4
Please Help
Answer:
(-2,10)
(-1,7)
(0,4)
(1,1)
(2,-2)
(3,-5)
Step-by-step explanation:
Answer:
your anwer is x=-1/3y+4/3
Step-by-step explanation:
Please choose all linear functions with slope that is greater than jamals linear function.
Answer:
a b
Step-by-step explanation:
On a camping trip, there are 7 girls for every 3 boys. If there are 60 kids total, how many girls are there?
Answer:
There would be 42 girls and 18 boys.
Step-by-step explanation:
Multiply7 by 6 since 7 + 3 is 10 x 6 = 60.
in a felony case the purpose of a grand jury is to
Answer:
In a felony case, the purpose of a grand jury is to decide if the evidence warrants prosecution. In a felony case, the purpose of a grand jury is to decide if the evidence warrants prosecution
Answer:
decide if the evidence warrants prosecution
Step-by-step explanation:
a house was valued at 362000. over several years the value increased by 16% giving the house a new value
Answer:
419,920 is the new value when it's increased by sixteen percent
1. The temperature is -2℃. If the temperature rises by 15℃, what is the new temperature?
2. At midnight the temperature is -6℃. At midday the temperature is 9℃. By how much did the temperature rise
Please need right now
Answer:
1. The new temperature would be 13°C (-2+15)
2. The temperature rose 15°C (9-(-6))
The sum of two triangles is 136 degrees. How many degrees is the third angle
Answer:
44°
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesGeometry
All angles in a triangle add up to 180°Step-by-step explanation:
Step 1: Set up Equation
136° + x° = 180°
Step 2: Find missing angle
Subtract 136 on both sides: x = 44I need Help please!:D
Answer:
70
Step-by-step explanation:
42/6=7. 42000/600=70. Add the zeroes!
Answer:
70
Step-by-step explanation:
42,000 ÷ 600=70
600x70=42,000
42,00÷70=600