Answer:
[tex]\theta = 108.29[/tex]
Step-by-step explanation:
Given
[tex]u = <2,6>[/tex]
[tex]v = <4,-7>[/tex]
Required:
Calculate the angle between u and v
The angle [tex]\theta[/tex] is calculated as thus:
[tex]cos\theta = \frac{u.v}{|u|.|v|}[/tex]
For a vector
[tex]A = <a,b>[/tex]
[tex]A = a * b[/tex]
[tex]cos\theta = \frac{u.v}{|u|.|v|}[/tex] becomes
[tex]cos\theta = \frac{<2,6>.<4,-7>}{|u|.|v|}[/tex]
[tex]cos\theta = \frac{2*6+4*-7}{|u|.|v|}[/tex]
[tex]cos\theta = \frac{12-28}{|u|.|v|}[/tex]
[tex]cos\theta = \frac{-16}{|u|.|v|}[/tex]
For a vector
[tex]A = <a,b>[/tex]
[tex]|A| = \sqrt{a^2 + b^2}[/tex]
So;
[tex]|u| = \sqrt{2^2 + 6^2}[/tex]
[tex]|u| = \sqrt{4 + 36}[/tex]
[tex]|u| = \sqrt{40}[/tex]
[tex]|v| = \sqrt{4^2+(-7)^2}[/tex]
[tex]|v| = \sqrt{16+49}[/tex]
[tex]|v| = \sqrt{65}[/tex]
So:
[tex]cos\theta = \frac{-16}{|u|.|v|}[/tex]
[tex]cos\theta = \frac{-16}{\sqrt{40}*\sqrt{65}}[/tex]
[tex]cos\theta = \frac{-16}{\sqrt{2600}}[/tex]
[tex]cos\theta = \frac{-16}{\sqrt{100*26}}[/tex]
[tex]cos\theta = \frac{-16}{10\sqrt{26}}[/tex]
[tex]cos\theta = \frac{-8}{5\sqrt{26}}[/tex]
Take arccos of both sides
[tex]\theta = cos^{-1}(\frac{-8}{5\sqrt{26}})[/tex]
[tex]\theta = cos^{-1}(\frac{-8}{5 * 5.0990})[/tex]
[tex]\theta = cos^{-1}(\frac{-8}{25.495})[/tex]
[tex]\theta = cos^{-1}(-0.31378701706)[/tex]
[tex]\theta = 108.288386087[/tex]
[tex]\theta = 108.29[/tex] (approximated)
82,77,72,67 find the sequince
Answer:
Subtract 5 as you go along the pattern.
82-5=77-5=72-5=67...
Step-by-step explanation:
answer the following
Step-by-step explanation:
–(11/4) = 11 : (–4) = –11/4 = 11/-4
(PLEASE HELP) You buy your dream house and want to redesign the front of the house. The budget for the
front of the house is $1,800. You spent $90 of the budget on fresh flowers. What percent of the
budget did you spend on fresh flowers?
budget did you spend on fresh flowers?
Answer:
Step-by-step explanation:
1620.
Answer:
5%
Step-by-step explanation:
90/1800 = x/100
0.05 = x/100
0.05 * 100 = x
5 = x
1.800 * 5% = 90
can someone help me with this question please? ASAP
Answer:
pentagram lookin symbol its c btw
Step-by-step explanation:
Write the given linear system without the use of matrices. Assume X = x y z . X' = 7 6 −9 5 1 1 0 −3 4 X + 0 3 1 e6t − 8 0 4 e−3t
Answer:
X= 3
Step-by-step explanation:
a) Solve by determinant method: x - y = 2, 2x + 3y = 4
Answer:
x = 2
y = 0
Step-by-step explanation:
x - y = 2
2x + 3y = 4
Using creamers rule of determinants, we have;
D =
|1 1|
|2 3|
Thus; D = (1 × 3) - (1 × 2)
D = 1
Dx =
|2 1|
|4 3|
Dx = (2 × 3) - (1 × 4)
Dx = 2
Dy =
|1 2|
|2 4|
Dy = (1 × 4) - (2 × 2)
Dy = 0
Thus;
x = Dx/D = 2/1
x = 2
y = Dy/D = 0/1
y = 0
Find the derivation of the following functions with they corresponding variables
Answer:
d(f(t))/dt = –56/(t^8) – (5/6)/t^(7/6) + 12t^3 – 2t + (1/3)t^(2/3))
Step-by-step explanation:
To find the derivative of f(t), we have to find the derivative of each component of the function to make it easier.
d(8/(t^7))/dt = d(8xt^-7)/dt = –7 x 8 x t^-8 = –56t^-8 = -56/(t^8)
d(5/(t^(1/6)))/dt = –(1/6) x 5 x t^(-7/6) = –(5/6)/t^(7/6)
d(3t^4)/dt = 4 x 3 x t^3 = 12t^3
d(t²)/dt = 2t
d(t^⅓)/dt = ⅓t^(-2/3) = (1/3)t^(2/3))
d(12)/dt = 0.
Therefore,
d(f(t))/dt = –56/(t^8) – (5/6)/t^(7/6) + 12t^3 – 2t + (1/3)t^(2/3))
If -1 2/3 is subtracted from 5 1/2, what will be the result?
a. negative
b. greater than 4
c. positive, but less than 4
d. equal to 4
C
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
When subtracting a negitive number from a positive number the difference ends up being a positive. The answer is 7, therefore, greater than 4.
which ordered pair is the solution of the system of equations shown?
y= -x + 5
y= 5x-6
Answer(1.833,3.167)
Step-by-step explanation:
Antonio bought a box of cookies for $3.84.
If there are 24 cookies in the box, how much did Antonio pay per cookie?
Explain your thinking using 3-5 complete sentences.
Answer:
24 cookies in a box, and it costs 3.84. since the whole thing costs 3.84, to find the unit rate of each cookie, you need to divide the price by the amount of cookies. 3.84 divided by 24 is equal to 0.16. so the price per cookie would be 16 cents.
that's how you find the answer, maybe try to reword it to get the 3-5 sentences you need.
the double number line shows that 4 bottles of water cost 10 dollars at a music festival
Answer:
That means that each water is $2.50, das crazy tho
Step-by-step explanation:
At 60 km per hour it takes archie 10 hours to travel from his house in Manila to his house in the province. If his rate will be 120 km per hour, how long will it take him to reach his house in the province from Manila
A. 5 hours
B. 8.5 hours
C. 6 hours
D. 7.5 hours
Pls i need it now
Answer:
a
Step-by-step explanation:
5 hours
1. A recipe calls for lb of flour for 1 batch. How many batches can be made with each of the following amounts? a. 1 lb b. lb c. lb
In a sample of 14 CEOs, they spent an average of 12.9 hours each week looking into new product opportunities with a standard deviation of 4.9 hours. Find the 95% confidence interval.a. (10.3, 15.5)b. (8.0, 17.8)c. (10.1, 15.7)d. (9.9, 15.9)
Answer:
c. (10.1, 15.7)
Step-by-step explanation:
The calculation of the 95% confidence interval is shown below:
Given that
n = sample = 14
average = [tex]\bar x[/tex] = 12.9
Standard deviation = s = 4.9
Based on the above information
[tex]\alpha = 1 -0.95 = 0.05[/tex]
n - 1 = 14 - 1 = 13
[tex]t_{\alpha}\ value = 2.16[/tex]
Now the 95% confidence interval is
[tex]= \bar x + \pm\ t \times \frac{s}{\sqrt{n} } \\\\= 12.9 \pm 2.16 \times \frac{4.9}{\sqrt{14} } \\\\= 12.9 \pm 2.8287[/tex]
= (10.1, 15.7)
hence, the correct option is c.
Graph the solution set for the inequalíty
y> 2x-5 by following these steps:
Step 1: ldentify the slope and y-intercept.
slope = y-intercept =
Please help me
Answer:
Slope= 2
Y-intercept= -5
Step-by-step explanation:
This inequality is in slope-intercept form which means we can get both striaght from the inequaltiy. Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. In this inequality m would be 2 and b would be -5, so those are your answers.
A health club down the street has an initial joining fee of $100, and then you pay $5 each time you visit the gym. if Calvin spends $195, how many times did he visit the gym?
Variable: Equation:
Solve (show all steps):
Answer:
19
Step-by-step explan
Multiply by 5 until you get to 95 :)
What is the product of 14/5
Answer:
2.8
Step-by-step explanation:
Just divide and get the answer
A lifeguard can swim at a speed of 6 feet per second and run at a speed of 10 feet per second. The lifeguard is standing at the edge of a beach, looking at the ocean to the south. The lifeguard sees a drowning child in the ocean 100 feet east (down the shore) and 80 feet south (out at sea). How far should the lifeguard run before they start swimming?
The requried distance run and swam by the lifeguard is 100 - x. and √[x² + 80²] respectively.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The question seems to be incomplete, there must be a figure that illustrates the situation,
Since, as of the given data, he might run x distance less toward the east as of the 100 feet east, and than swim, the distance is given as,
= √[x² + 80²].
And the distance run = 100 - x.
Thus, the requried distance run and swam by the lifeguard is 100 - x. and √[x² + 80²] respectively.
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Which graph represents an even function?
Answer:
one that looks like triangle
Step-by-step explanation:
(11/18-4/9)+1/6 pemdas fraction
Answer:
1/3
Step-by-step explanation:
11/18 - 4/9 + 1/6
= 1/6 + 1/6
= 1/3
The value of the fraction is 1/3.
What is PEMDAS Rule?PEMDAS rule is the same as BODMAS rule.
PEMDAS is the abbreviation for Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction.
Given fraction is : (11/18 - 4/9) + 1/6
We have a parenthesis (brackets) in the given expression. First solve the operations inside the bracket.
And multiply the fraction 4/9 with 2 on both numerator and denominator.
(11/18 - 4/9) + 1/6 = (11/18 - 8/18) + 1/6
= 3/18 + 1/6
There is only an operation of addition left.
Multiplying both numerator and denominator of 1/6 with 3,
(11/18 - 4/9) + 1/6 = 3/18 + 3/18
= 6/18
= 1/3
Hence the value of the fractional expression given is 1/3.
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identify the k-value that makes the relationship shown in the table below proportional.
Answer:
The value of k that makes the relationship shown in the table below proportional is [tex]\mathbf{\frac{1}{2}}[/tex]
Step-by-step explanation:
The relation is proportional if [tex]y=kx \:or\:k=\frac{y}{x}[/tex]
Putting values of x and y to find k.
For x =2 and y =1 k is: [tex]k=\frac{y}{x}=\frac{1}{2}[/tex]
For x =4 and y =2 k is: [tex]k=\frac{y}{x}=\frac{2}{4} =\frac{1}{2}[/tex]
For x =6 and y = 3 k is: [tex]k=\frac{y}{x}=\frac{3}{6} =\frac{1}{2}[/tex]
For x = 8 and y = 4 k is: [tex]k=\frac{y}{x}=\frac{4}{8} =\frac{1}{2}[/tex]
For x =10 and y = 5 k is: [tex]k=\frac{y}{x}=\frac{5}{10} =\frac{1}{2}[/tex]
So, The value of k that makes the relationship shown in the table below proportional is [tex]\mathbf{\frac{1}{2}}[/tex]
Is 3abc an expression?
Answer:
yes
Step-by-step explanation:
an expression is like an equation without the equal sign, or according to the Oxford Dictionary: "a collection of symbols that jointly express a quantity."
Answer:
Yes
Step-by-step explanation:
An expression is a collection of symbols that jointly express a quantity, which means a set of symbols that equals a number. a,b, and c are all variables, meaning that its a expression
Alex’s printer can print 8 photos in 12 minutes.
Khalil’s printer can print 24 photos in 1 hour.
Select all the processes you could use to help determine how much longer it will take Khalil’s printer to print 120 photos than Alex’s.
Answer:
What are the choices?
Step-by-step explanation:
How would you write the number displayed on the calculator screen in standard form
Answer:
E is short for 10^x. The number that comes after the E is the power of 10.
So its 7.6*10^12
now that scientifically notation
For standard your gonna need to simplify that
so we know 10^12 is 1000000000000
Multiply the 7.6
7600000000000
hope I helped :)
Can someone help me with this please?
Answer:
-12
Step-by-step explanation:
subtracting a negative from a negative makes a greater negative, basically adding to the negative
Answer:
-8 is the answer correct
Step-by-step explanation:
Hurry please!!!!!!!!! It’s a timed test!!!!!!!
The function /(x) is shown on the graph.
What is f(0)?
A.12 only
B. 2 and 3 only
C. -2, -1, -1, and 2 only
D. -2,-1, 1, 2 and 12
Answer:
c
Step-by-step explanation:
(a) An article in a medical journal suggested that approximately 14% of such operations result in complications. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.08
This question is incomplete, the complete question is;
Surgical complications: A medical researcher wants to construct a
99.5% confidence interval for the proportion of knee replacement surgeries that result in complications.
- An article in a medical journal suggested that approximately 14% of such operations result in complications. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.08?
Answer: a sample of operations needed is 149
Step-by-step explanation:
Given that;
confidence interval = 99.5% = 0.995 so
margin of error E = 0.08
p = 14% = 0.14
now we obtain the critical value of z t the 99.5 confidence interval
∝ = 1 - confidence interval
∝ = 1 - 0.995
∝ = 0.005
∝/2 = 0.0025
obtaining the area of probability in the right tail
Area of probability to the right is = 1 - 0.0025 = 0.9975
from probability table; critical value of t =2.81
using the formula
n = p( 1 - p ) [ (z_∝/2)/E)² ]
so we substitute
n = 0.14 ( 1 - 0.14 ) [ 2.81 / 0.08 )²
n = (0.14 × 0.86 ) × 1233.7656
n = 148.5453 ≈ 149
Therefore , a sample of operations needed is 149
HURRY PLEASE IM TIMED AND THIS IS IMPORTANT. Which list of numbers is shown on the number line below?
A number line going from negative 3 to positive 2. There are 4 equal spaces between each number. A point is halfway between negative 3 and negative 2. A point is between the second and third mark between negative 2 and negative 1. A point is on the mark 1 space to the right of 0. A point is halfway between 1 and 2.
Negative 2.5, 1 and three-fourths, 50 percent, 1.5
Negative 2.5, negative 1 and one-third, 50 percent, 1.5
Negative 2.5, negative 1 and three-fourths, 25 percent, 1.5
Negative 2.5, negative 1 and one-third, 25 percent, 1.5
Answer:
D.
Step-by-step explanation:
Answer:
this person is right the answer is D
Step-by-step explanation:
have a good day good luck on the test
edg 2022
Which graph shows the solution to the systern of linear inequalities? x+3y>6 y>2x+4
Answer: y>2x+4
Step-by-step explanation:
Tommy was trying to solve the system of a linear equation and a quadratic equation shown below. 2x – y = –1 x2 – 5x – y = –7 Tommy had completed the following steps in his algebraic solution process but could not factor the resulting quadratic, x2 – 7x – 1, to complete the problem. Step I: y = 2x + 1 Step II: x2 – 5x – (2x + 1) = –7 Step III: x2 – 5x – 2x – 1 = –7 Step IV: x2 – 7x – 1 = –7 Determine the step in which Tommy made his mistake and justify your reasoning.
Answer:
Step IV; Tommy must set the quadratic expression equal to 0 before factoring.
plz give brainlyest
It is found that in Step IV; Tommy must set the quadratic equations equal to 0 before factoring and then solving.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given that the system of a linear equation and a quadratic equation.
2x – y = –1
x² – 5x – y = –7
Now Tommy had completed the following steps in his algebraic solution process but could not factor the resulting quadratic equation as;
x² – 7x – 1,
Step I: y = 2x + 1
Step II: x² – 5x – (2x + 1) = –7
Step III: x² – 5x – 2x – 1 = –7
Step IV: x² – 7x – 1 = –7
Therefore, we conclude that in Step IV; Tommy must set the quadratic equations equal to 0 before factoring and then solving.
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