Answers
Answer:
See below
Step-by-step explanation:
[tex] \overrightarrow a= \bigg(\frac{5}{\sqrt 34},\:\frac{3}{\sqrt 34}\bigg)[/tex]
We have to show that [tex] \overrightarrow a[/tex] is an unit vector.
To show this, we will find the modulus of [tex] \overrightarrow a[/tex] and if its value is 1, it will be a unit vector.
So,
[tex] | \overrightarrow a| = \sqrt{\bigg(\frac{5}{\sqrt 34} \bigg) ^{2}+\bigg(\frac{3}{\sqrt 34}\bigg)^{2} } \\ \\ | \overrightarrow a| = \sqrt{\frac{25}{ 34} +\frac{9}{ 34} } \\ \\ | \overrightarrow a| = \sqrt{\frac{25 + 9}{ 34} } \\ \\ | \overrightarrow a| = \sqrt{\frac{34}{ 34} } \\ \\ | \overrightarrow a| = \sqrt{1} \\ \\ | \overrightarrow a| = 1[/tex]
Thus, [tex] \overrightarrow a[/tex] is a unit vector.
Related Questions
0.8 as a fraction??
You can give your answer
Answers
Answer: 4/5
Step-by-step explanation:
0.8 = 8/10 = 4/5
Answer:
4/5
Step-by-step explanation:
Marge conducted a survey by asking 350 citizens whether they frequent the city public parks. Of the citizens surveyed, 240 responded favorably.
What is the approximate margin of error for each confidence level in this situation?
0.07
0.03
0.04
0.05
0.06
99%
95%
90%
Answers
Answer:
The margin of error for a 99% confidence interval is of 0.0639, that is, approximately 0.06.
The margin of error for a 95% confidence interval is of 0.0486, that is, approximately 0.05.
The margin of error for a 90% confidence interval is of 0.0408, that is, approximately 0.04.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
350 citizens, 240 responded favorably:
This means that [tex]n = 350, \pi = \frac{240}{350} = 0.6857[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
[tex]M = 2.575\sqrt{\frac{0.6857*0.3143}{350}} = 0.0639[/tex]
The margin of error for a 99% confidence interval is of 0.0639, that is, approximately 0.06.
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
[tex]M = 1.96\sqrt{\frac{0.6857*0.3143}{350}} = 0.0486[/tex]
The margin of error for a 95% confidence interval is of 0.0486, that is, approximately 0.05.
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
[tex]M = 1.645\sqrt{\frac{0.6857*0.3143}{350}} = 0.0408[/tex]
The margin of error for a 90% confidence interval is of 0.0408, that is, approximately 0.04.
Can someone please help me
Answers
Answer:
135ft^3
Step-by-step explanation:
Volume for triangular prism = 1/2bhl
v=1/2*6*5*9= 135
calculate the slope line that passes through points (0,3) (2,9)
Answers
2 - 0 = 2
Finally do 6 divided by 2 and you get 3.
The slope is 3
Simplify the following expression
6y + 8 - 2y + 5y - 9
Answers
Answer: 9y-1
:))))))))))))))))))))
Which of the following numbers is a perfect square?
1 489
2 485
3 490
4 484
Answers
Answer:
3490 is the perfect square
Answer:
490 is the correct answer
Step-by-step explanation:
HELP ASAP!!!!! 20PTS!!
Answers
Answer:
the answer is 80!!!!!!!!!!
Step-by-step explanation:
Jason has 5 boxes and 3 cases of soup cans Each box contains 6 cans and each case contains 36 cans How many cans of soup does Jason have altogether?
1. 138
2. 198
3. 288
4. 3,240
Answers
step one - find the cans of soup in boxes
5 times 6 is 30, so there are 30 cans in boxes
step two - find the cans of soup in cases
3 times 36 is 108, so there are 108 cans in cases
step 3 - add them together to find the total number of cans
30+108=138
hope this helps!
2.
Thomas drove 45 miles in 1 hour. At this rate, how many miles will he drive in 4 hours?
Answers
Answer:
180
Explanation:
45*4=180
Answer:
I agree with the other answer- 45 x 4= 180 miles
Covert 2/3 years to months
Answers
thank you hope this helps
Answer:
7.9 or if you need to round it,it will be 8
Step-by-step explanation:
dont have a explanation nut i hopes this help.
Five friends went to the zoo.
• Tickets cost $8.50 each.
• Each person purchased a drink for $3.50
• Three of the people had a discount coupon for $2.50 off the cost of admission,
• The friends split the total cost equally.
How much did each person spend?
А A
$10.13
B. $10.50
c С
$11.50
D
$12.00
Answers
Answer:
B . 10.50
Why ? Because 8.50+3.50=12 , Then 12 × 5 = 60 , 2.50×3=7.5 , 60-7.5= 52.5 . divide 52.5 by 5 = 10.50 . So each friend paid 10.50
A square picture frame with each side length represented by 3x -
5 has a perimeter of 52 inches. What is the value of x?
A. x = 3
u
B. x = 5
C. x = 6
D. x = 13
Answers
Answer:
C. X=6
Step-by-step explanation:
Length of one side =52/4= 13
3X-5= 13
3x = 13+5
X= 18/3
X= 6
Which quadratic relation has a y-intercept of 8?
O y = 0.5(x + 2)(x + 4)
O y = 0.5 (x - 2)(+ 8)
O y = 0.5(x2 -2x - 16)
O y = 0.5 (x2 -2x + 16)
Answers
Answer:
y = 0.5 (x^2 -2x + 16) has a y-intercept of 8.
Step-by-step explanation:
The x-coordinate of every y-intercept is zero. To determine which of the four quadratics given here has a y-intercept of 8, we need only substitute 0 for x in each; if the result is 8, we've found the desired quadratic.
O y = 0.5(x + 2)(x + 4) becomes y = 0.5(2)(4) = 4 (reject this answer)
O y = 0.5 (x - 2)(x + 8) becomes y = 0.5(-2)(8) = -8 (reject)
O y = 0.5(x2 -2x - 16) becomes y = 0.5(-16) = -8 (reject)
O y = 0.5 (x2 -2x + 16) becomes y = 0.5(16) = 8 This is correct; that '8' represents the y-intercept (0, 8).
A carpenter buys a box containing 0.6 kilogram of nails. Each nail has a mass of 5 grams. How many nail are in the box?
Answers
600grms/5gms=120 nails
Will the product of 22.65 x 0.999 be greater than or less than 22.65? Without calculating, explain how you know.
Answers
It will be less since as common knowledge, it's a decimal so it'll be a little bit less
ollities
Assignment
Active
Calculating a Z-Score from a Percentile
The prices of paperbacks sold at a used bookstore are Complete the sentences.
approximately Normally distributed, with a mean of $7.85 To find the Z-score for the 56th percentile means that
and a standard deviation of $1.25.
the area above the z-score will be
and the
Use the z-table to answer the question.
area below the Z-score will be
The Z-score for the 56th percentile is
V
Answers
Answer:
Complete the sentences.
To find the z-score for the 56th percentile means that
the area above the z-score will be ✔ 0.44 and the
area below the z-score will be ✔ 0.56.
The z-score for the 56th percentile is ✔ 0.15
*you typed the question weird, but I hope this helps*
Answer:
To find the z-score for the 56th percentile means that the area above the z-score will be
✔ 0.44
and the area below the z-score will be
✔ 0.56
.
The z-score for the 56th percentile is
✔ 0.15
.
Step-by-step explanation:
edge 2023
6. Use the bar diagram to help you solve the equation 4x - 12 = 16.
Answers
adding 12 to both side
4x - 12 + 12 = 16 + 12
4x = 28
devide both side by 4
4x ÷4 = 28÷4
x = 7
Answer:
1. 4x=16+12
2. 4x=28
3. 4x over 4=28 over 4
4. 4 is cancelled by 4 and x will remainder =7
5. x=7
that's it good luck
Please solve this math question.
Answers
Answer:
none of these
Step-by-step explanation:
the side lengths are are 2√5/5, 2, and 4.
sin(x) = opp/hyp
sin(x) = 2/2√5
If 70% of a number is 126 and 95% of the same number is 171, find 25% of that number.
Answers
Answer:
45
Step-by-step explanation:
70%=126
100%=?
100×126=12600÷70
=180
100=180
25=?
25×180÷100
=45
Solve for w. Only use numbers in your answer.
8w - 15 = 57
w =
Answers
Answer:
w = 9
Step-by-step explanation:
1. Add 15 from both sides: 8w = 72
2. Divide my 8: w = 9
Answer:
the answer for this question is 9
PLEASE SOMEONE HELP ME
Answers
Answer:
X=22
Step-by-step explanation:
90-68=22
D) y= x - 3/2
HELP ME PLS
Answers
Answer:
i think it's A
Step-by-step explanation:
How many distinct variables does the expression below
contain?
2x^5+xy^4-zx
Answers
What is the equation of the line that passes through the point (-6, -6) and has a
slope of - 1/3
Answers
Answer:
The equation of the line is [tex]y = -\frac{1}{3}x - 8[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Slope of - 1/3
This means that [tex]m = -\frac{1}{3}[/tex]
So
[tex]y = -\frac{1}{3}x + b[/tex]
Through the point (-6, -6)
This means that when [tex]x = -6, y = -6[/tex]. So
[tex]y = -\frac{1}{3}x + b[/tex]
[tex]-6 = -\frac{1}{3}(-6) + b[/tex]
[tex]b + 2 = -6[/tex]
[tex]b = -8[/tex]
The equation of the line is [tex]y = -\frac{1}{3}x - 8[/tex]
It takes 7 gardeners 8 hours to plant 1 680 seedlings on a piece of land.
Calculate (in hours and minutes) how long it would take 12 gardeners to
plant the seedlings
Answers
Answer:
4 hours, 40 minutes
Step-by-step explanation:
1680 ÷ 8 hours = 210 seeds per hour for 7 gardeners
30 seeds per hour per gardener
30 x 12 = 360 seeds per hour for 12 gardeners
4.66 hours to plant. which is 4 hours and 40 minutes
If the cafeteria has 80 customers on Tuesday, which prediction for Tuesday is NOT supported by the data in the table
Answers
Answer:
the day.
step-by-step: you dont need the day
Answer:
G
Step-by-step explanation:
A person invested 3,900 in an account growing at a rate allowing the money to double every 7 years. How much money would be in the account after 18 years to the nearest dollar
Answers
Answer:
23182 or 23181.5109105
Step-by-step explanation:
Show your work for this one
Answers
Step-by-step explanation:
multipy the two sides by 2
n+4= -16
move the constant to the right change its sign
n= -16 - 4
calculate the difference
N= - 20
Answer:
[tex]n=-20[/tex]
Step-by-step explanation:
1) Subtract 2 from both sides.
[tex]\frac{n}{2} =-8-2[/tex]
2) Simplify −8−2 to −10.
[tex]\frac{n}{2} =-10[/tex]
3) Multiply both sides by 2.
[tex]n=-10*2[/tex]
4) Simplify 10 * 2 to 20.
[tex]n=-20[/tex]
Therefor, the answer is n = - 20.
an employer pays three workers x,y,z a total amount of 6100 a month. x is paid 125% of the amount y is paid; which represent 80% of the amount z is paid. how much does x receive a month
Answers
Answer:
X earns $ 2,178.57, as does Z, while Y earns $ 1,742.85.
Step-by-step explanation:
Since an employer pays three workers X, Y and Z a total amount of $ 6100 a month, of which X is paid 125% of the amount Y is paid; which represents 80% of the amount Z is paid, to determine how much does X receive a month the following calculation must be performed:
X = 1.25Y
Y = 0.8Z
Z = Z
Z + Y + X = 6,100
Z + 0.8Z + (1.25 x 0.8Z) = 6,100
Z + 0.8Z + Z = 6,100
2.8Z = 6,100
Z = 6,100 / 2.8
Z = 2,178.57
Y = 0.8 x 2,178.57 = 1,742.85
X = 1,742.85 x 1.25 = 2,178.57
2,178.57 + 2,178.57 + 1,742.85 = X
6,099.99 = X
Thus, X earns $ 2,178.57, as does Z, while Y earns $ 1,742.85.
A kite is flying at the end of a 20-meter string. If the string makes an angle of 55° with the ground, how many meters above the ground, to the nearest meter, is the kite
Answers
The total distance of Kite from the ground is 16.38 meters and this can be determined by using the trigonometric function.
Given :
A kite is flying at the end of a 20-meter string. The string makes an angle of 55° with the ground.The following steps can be used in order to determine the total distance of Kite from the ground:
Step 1 - The trigonometric functions can be used in order to determine the total distance of Kite from the ground.
Step 2 - The sine function is used to measure the distance. The mathematical expression of the sine function is:
[tex]\rm sin\theta = \dfrac{P}{H}[/tex]
where P is the perpendicular and H is the hypotenuse.
Step 3 - Now, substitute the values of the known terms in the above expression.
[tex]\rm sin55 = \dfrac{Distance}{20}[/tex]
Step 4 - Simplify the above expression.
Distance = 16.38 meters
For more information, refer to the link given below:
https://brainly.com/question/13710437