Answer:
[tex](\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )[/tex]
Step-by-step explanation:
The unit vector for a nonzero vector, say u, in the direction of u is given by:
û = [tex]\frac{u}{|u|}[/tex] ---------------(i)
Where;
|u| = magnitude of vector u
From the question;
u = (4, -4)
First let's calculate the magnitude of u as follows;
|u| = [tex]\sqrt{(4)^2 + (-4)^2}[/tex]
|u| = [tex]\sqrt{16 + 16}[/tex]
|u| = [tex]\sqrt{32}[/tex] = [tex]4\sqrt{2}[/tex]
Now, substitute u and |u| into equation (i) as follows;
û = [tex]\frac{(4, -4)}{4\sqrt{2} }[/tex]
û = [tex](\frac{4}{4\sqrt{2} }, \frac{-4}{4\sqrt{2} } )[/tex]
û = [tex](\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )[/tex]
Therefore, the unit vector is [tex](\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} } )[/tex]
A visitor guide for a downtown area lists many restaurants. Which of the following is an example of a quantitative variable the guide could report for each restaurant? A. the zip code of the restaurant B. the number of seats in the restaurant C. the type of cuisine the restaurant offers D. a restaurant critic’s letter grade (A–F)
The correct answer is B. The number of seats in the restaurant
Explanation:
The number of seats is a quantitative variable because this is expressed using numbers and can be understood through numbers. For example, the average of seats in the restaurants in the area can be calculated by finding the total of seats and dividing the number into the number of restaurants.
On the other hand, the type of cuisine and the restaurant critic's letter grade do not involve numbers but qualities, which make them qualitative variables. Also, even if zip codes are expressed using numbers these cannot be understood through them, for example, you cannot add two zip codes.
Answer:
B
Step-by-step explanation:
Jen classifies the number 4.567 as an irrational number because it does not repeat. Is Jen correct? Explain.
Answer: Jen is wrong about her classification.
Step-by-step explanation:
First of all, we know that the definition of an irrational number is that they are numbers that cannot be represented by a simple fraction and that they are never repeating decimals and they never end.
So, considering this, Jen is wrong because, yes it does not repeat but it DOES END unless it is not written in this problem that it continues on irrationally like pi. Hence, this number is not irrational.
The Jen classifies the number 4.567 as an irrational number is false.
It is required to find the number is rational and irrational numbers.
What is real number?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
Given :
Jen's argument
We have
4.567 as an irrational number
The above claim is false because
4.567 =
4567/1000
When we divide the above number in the form of p/q and q≠0 then then number is rational number.
Therefore, the Jen classifies the number 4.567 as an irrational number is false.
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Find the indicated side of the
triangle.
Answer:
8
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
0.4, 0.04, 0.44, 0.444, 0.404, 0.044 in order smallest first
I'm pretty sure it's 0.04, 0.044, 0.4, 0.404, 0.44, 0.444.
Which one of the following correctly states the VaR for a 3-year period with a 2.5 percent probability?
a) Prob[Rp, I E(Rp) x 3 - 1.960 x Op V3]
b) Prob[Rp, I S E(Rp) x 13 - 1.645 x Op 3]
c) Prob[Rp, T = E(Rp) x V3 - 1.960 x Op 3]
Answer: Option A
Prob[Rp,T ≤ E(Rp) × 3 - 1.960 × σp √3]
Step-by-step explanation:
It should be noted that, the VaR for a 3-year period with a 2.5 percent probability is Prob[Rp,T ≤ E(Rp) × 3 - 1.960 × σp √3]. Therefore, option A only is correct while other options are wrong
Answer:
A: Prob[Rp, I E(Rp) x 3 - 1.960 x Op V3]
Step-by-step explanation:
Which of the following is most likely the next step in the series?
o
Answer:
C
Step-by-step explanation:
the first shape has 6 edges, the second shape has 5 edges, the third shape has 4 edges, therefore the fourth shape has 3 edges (c)
What is the average of 74 and 57?
Answer:
65.5
Step-by-step explanation:
(74 + 57)divided by 2 = 65.5
38 animals are at the aquarium. 22 animals are manatees and the rest are sea lions.
How many of the animals are sea lions?
22 manatees
? sea lions
38 animals
Answer:
16
Step-by-step explanation:
38-22=16
16 sea lions
Answer:
38-22=16.
16 sea lions.
Help will give brainliest
Answer:
[tex](-1)+(-3)=-4[/tex]
Step-by-step explanation:
We were originally on -1.
But we jumped to -4.
-4 is 3 spaces to the left of -1.
In other words, we subtract 3 into -1.
Another way of saying this is that we added -3 to -1.
Therefore, our equation is:
[tex](-1)+(-3)=-4[/tex]
A bag contains 30 pieces of candy. There are 15 grape, 7 cherry, 3 lemon, 5 strawberry. What is the probability of drawing a strawberry? (Please simplify your answer) 3 3 5 5 1/6 1/6 1/5
Answer:
[tex]Probability = \frac{1}{6}[/tex]
Step-by-step explanation:
Given
Grape = 15
Cherry = 7
Lemon = 3
Strawberry = 5
Total = 30
Required
Determine the probability of picking a strawberry
The probability of drawing a strawberry is calculated by dividing the number of strawberry by the total number of fruits as follows;
[tex]Probability = \frac{Strawberry}{Total}[/tex]
Substitute 5 for Strawberry and 30 for Total
[tex]Probability = \frac{5}{30}[/tex]
Divide the numerator and denominator by 5
[tex]Probability = \frac{1}{6}[/tex]
Hence, the required probability is [tex]\frac{1}{6}[/tex]
This question relates to concepts covered in Lectures 1 & 2. You can use any of the excel files posted to work through the question. Demand at a store can be modeled by a random variable which takes the following values across four different scenarios that occur with following probabilities. Scenario Low: D1 = 10 with probability P1=0. 1 Scenario Medium 1: D2 = 30 with probability P...2=0,4 Scenario Medium 2. D3 = 60 with probability p. 3-0.4 Scenario High: 04 = 90 with probability p_4=0.7 What is the mean of this demand distributional?
Answer:
mean of this demand distribution = 100
Step-by-step explanation:
To find the mean of this demand distribution;
Mean = Expected vale = E[x]
for discrete provability function,
we say E[x] = ∑(x.p(x))
x p(x) x.p(x)
10 0.1 1
30 0.4 12
60 0.4 24
90 0.7 63
∴ ∑(x.p(x)) = ( 1 + 12 + 24 + 63 )
∑(x.p(x)) = 100
7. If a school has 70 computers in the ratio of 3 desktops for every 4 laptops, how many
are desktops? Explain your answer.
Step-by-step explanation:
As ratio of desktops to laptops=3:4
Take no. of desktops= 3x
Take no. of Laptops=4x
Total no. of desktops+ Total no. of laptops = Total no. of computers
3x+4x=70
7x=70
x=10
Hence, the total no, of desktops= 3x
Hence, Total no. of desktops= 3×10
=30 desktops
Write 3,141,500 in scientific notation.
Answer:
The answer is 3.14 * 10^-6
Answer:
3.1415 * 10^6
Step-by-step explanation:
Scientific notation is of the form a* 10 ^b where a is between 1 and less than 10
3,141,500
Move the decimal 6 places to the left
The exponent is the number of places you move the decimal
Since we move it to the left, it is positive
3.141500 * 10^6
Drop the trailing zeros
3.1415 * 10^6
Which of the following statements are always true? Justify your answers. a. If A + B = C, then AD' + BD' = CD' b. If A'B + A'C = A'D, then B + C = D c. If A + B = C, then A + B + D = C + D d. If A + B + C = C + D, then A + B = D
Answer:
a. True
B. False
C. True
D. False
Step-by-step explanation:
a.) A+B = C then AD' + BD' = CD'
AD'+BD' = D'(A+B)
and we already have that A+B = C
such that D'C = C'D
this statement is true
b.) A'B + A'C = A'D then B+C = D
let's have A = 1 and B= 0, C= 0 and D = 1
A'(0) + A'(0) = 1(1)
0+0 = 1
0 = 1
This is false because 0 is not equal to 1
c.) A+ B=C then A+B+D= C+D
If A+B+D= C+D
Then A+B=C
The statement is true
d.) A+B+C=C+D
A+B = D
let's equate A = 0
B= 0
C= 1
D= 1
from a+b = D
We have
0+0 = 1
0 is not equal to 1
The statement is false
Answer:
a. True
B. False
C. True
D. False
Step-by-step explanation:
a.) A+B = C then AD' + BD' = CD'
AD'+BD' = D'(A+B)
and we already have that A+B = C
such that D'C = C'D
this statement is true
b.) A'B + A'C = A'D then B+C = D
let's have A = 1 and B= 0, C= 0 and D = 1
A'(0) + A'(0) = 1(1)
0+0 = 1
0 = 1
This is false because 0 is not equal to 1
c.) A+ B=C then A+B+D= C+D
If A+B+D= C+D
Then A+B=C
The statement is true
d.) A+B+C=C+D
A+B = D
let's equate A = 0
B= 0
C= 1
D= 1
from a+b = D
We have
0+0 = 1
0 is not equal to 1
The statement is false
Step-by-step explanation:
195.21 is 24.10% of what number?
Turn the percentage into a decimal.
24.10 / 100 = 0.241
Divide.
195.21 / 0.241 = 810
Therefore, 195.21 is 24.10% of 810
Best of Luck!
help I need to determine the slopes
Answer:
y-int: (0, -45)
x-int: (-10, 0)
Step-by-step explanation:
x-intercept is the x-value when y = 0
y-intercept is the y-value when x = 0
x-int:
When y = 0, x = -10, so (-10, 0)
y-in:
when x = 0, y = -45, so (0, -45)
Enter the correct answer in the box replacing the values of m and b
Answer: f(x) = -2X + 5
Step-by-step explanation:
A ball player is at bat 55 times as hits the ball 33 times. Want ratio of his times at bat does he not hit the ball?
Answer:55:33
Step-by-step explanation:
55:33
PART 5 - Mathematical knowledge
If 4x + 12 = 0, then x=
A -16
B -12
С-3
D
1/3
Click the button or type the letter tot
Answer: C) -3
Step-by-step explanation: 4(-3) + 12 = 0
is 7.69669669 a rational number
Answer:
yes it is
Step-by-step explanation:
hope this helps✨
f(x)=-4x+1 Find the average rate of change from 2 to 5.
Answer:
- 4
Step-by-step explanation:
The slope of the line is the average rate of change of f(x)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
f(x) = - 4x + 1 ← is in slope- intercept form
with m = - 4 ← average rate of change
Hector works in a gas station and earns $15.50 per hour. Last week he worked 29 hours. What was his gross pay?
Answer:
449.50
Step-by-step explanation:
because gross pay is before taxes and everything else and he worked 29 hours so 15.50 × 29 = $449.50
The amount of money that Hector works in a gas station will be $449.50.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Hector works in a service station and procures $15.50 each hour. Last week he worked 29 hours.
The total cost that Hector can earn will be given as,
⇒ $15.50 x 29
⇒ $449.5
The gross pay that Hector works in a corner store will be $449.50.
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Round 630,379,982 to the nearest hundred thousand
Answer:
630,400,000
Step-by-step explanation:
630,379,982
The 3 above that is bold, between the 0 and the 7, is in the hundred thousands place.
To round to a place, change all digits to the right of that place to zero. If the digit immediately to the right is 0 through 4, you're done. If the digit immediately to the right is from 5 to 9, then you raise the digit you are rounding to by 1.
Step 1. Make all digits to the right of the hundred thousands digit 0.
630,300,000
Step 2. Since the digit immediately to the right of the hundred thousands digit was a 7, which is from 5 to 9, the digit we are rounding to goes up by 1. The 3 becomes 4.
630,400,000
Answer: 630,400,000
Can you please help me with this I’ll give you a Brainly list please it’s hard
Answer:
Your answer will be 6+6-17 hope this helps :)
Step-by-step explanation:
give an example of a set of five different numbers whose mean is 290
Answer:
200,300,290,320,340
Step-by-step explanation:
If the mean of five numbers = 290
Then the total sum of the five numbers should be= 290*5
= 1450
an example of a set of five different numbers whose mean is 290
= 200,300,290,320,340
Summation of the above
=( 200+300+290+320+340)
= 1450
So the above set of numbers is a good example of a set of five different numbers whose mean is 290
Can someone help? This is from Kahn Academy
Answer:
B. [tex] \frac{ {7}^{36} }{ {9}^{24} } [/tex]
Step-by-step explanation:
[tex] \bigg( {9}^{6} . {7}^{ - 9} \bigg ) ^{ - 4} \\ \\ = {9}^{6 \times ( - 4)} \times {7}^{ - 9 \times ( - 4)} \\ \\ = {9}^{ - 24} \times {7}^{36} \\ \\ = \frac{ {7}^{36} }{ {9}^{24} } \\ [/tex]
What is 4 4/5+7 3/5-6
Answer:
17.4
Step-by-step explanation:
44/5 = 8.8
73/5 = 14.6
8.8 + 14.6 = 23.4
23.4 - 6 = 17.4
You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You also know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?
Answer:
y = 7.8x + 26
Step-by-step explanation:
Given the following :
Pearson's r = 0.78
Average consumption of ice cream = 5 grams per week (m) with Standard deviation (sd) = 1.5 grams
Average weight = 65 kg with standard deviation of 15kg
Formular for the regression line :
General regression formula :
y = mx + c
y = predicted variable ; m = slope or gradient ; x = predictor variable ; c = intercept
Gradient (m) = change in y / change in x
m = (sd y / sd x) * r
m = (sd weight / sd ice cream) × r
m = (15 / 1.5) × r
m = 10 × 0.78 = 7.8
Intercept:
mean of weight(y) - [Slope×mean of icecream(x)]
65 - [7.8 × 5]
65 - 39 = 26
Hence,
y = 7.8x + 26
Which step in the problem-solving process includes the following statement? Identify the information the problem gives you. A. Understand B. Look back C. Solve D. Plan
Answer:plan
Step-by-step explanation:
Which number rounds to 4.3 when rounded to the nearest tenth?
Answer:
it is the same 4.3
Step-by-step explanation:
this numbers didn't add one number when you round(0,1,2.3.4)
this numbers(5,6,7,8,9), you add one number when you add
4.3 (the three is the tenth)and no number after it so its stell the same
The rounding number of 4.3 when rounded to the nearest tenth is 4.3
Here,
The number is 4.3
We have to find the rounding number of 4.3 nearest tenth.
What is Rounding number?
A method of approximating a number to its nearest place value is called Rounding of Numbers.
Now,
The number is 4.3
To round the decimal number to its nearest tenth, look at the hundredth place.
But here is no any number on hundredth number, hence no change occur for rounding 4.3 to the nearest tenth.
So, The rounding number of 4.3 when rounded to the nearest tenth is same as the number 4.3
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