for exercises 17 and 18, find the acute angle between the given lines by using vectors parallel to the lines. y
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For Exercises 17 And 18, Find The Acute Angle Between The Given Lines By Using Vectors Parallel To The Lines.
y = x , y = 2 x + 3
The acute angle between the lines y = x and y = 2 x + 3 is 18.4349°.
We are given the lines:
y = x
y = 2 x + 3
The formula for finding the angles between two vectors is given by:
cos θ = u · v / | u | | v|
We know that (0,0) and (1, 1) lies on the line y = x.
Now, vector u for the line y = x will be:
u = (1,1) - (0,0) = {1, 1}
(0,3 ) and (1, 5) lies on the line y = 2 x + 3
Similarly, vector v will be equal to:
v = (1, 5) - (0, 3) = {1, 2}
cos θ = {1, 1} · {1, 2} / √1 + 1 √1 + 4
cos θ = 1 + 2 / √10
cos θ = 3 / √10
θ = cos⁻¹ ( 3 / √10)
θ = 18.4349°
Therefore, the acute angle between the lines y = x and y = 2 x + 3 is 18.4349°.
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a consumer affairs investigator records the repair cost for 1010 randomly selected vcrs. a sample mean of $72.82$72.82 and standard deviation of $24.17$24.17 are subsequently computed. determine the 90�% confidence interval for the mean repair cost for the vcrs. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
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Consumer affairs investigator records the repair cost for 10 randomly selected VCRs. A sample mean of $72.82 and standard deviation of $24.17 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the VCRs. Assume the population is approximately normal. Construct the 90% confidence interval. Round your answer to two decimal places.
We get that the critical value of the 90 % confidence interval is 1.833 and the interval is (58.81, 86.83).
We are given that the number of VCRs are 10.
So, we get that:
Sample size = n = 10
Now, we get the degree of freedom as:
d o f = n - 1
d o f = 10 - 1
d o f = 9
For 90% confidence interval , critical value will be:
t (0.10, 9) = 1.833
Lower limit of 90% confidence interval will be:
Lower interval = Mean - t (0.10,9) × s / √n
= 72.82-1.833 × 24.17 /√10
= 58.81
Upper limit of 90% confidence interval will be:
Upper interval = Mean + t (0.10,9) × s /√n
= 72.82 + 1.833 × 24.17/√10
= 86.83
Therefore, we get that the critical value of the 90 % confidence interval is 1.833 and the interval is (58.81, 86.83).
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Help please! For highschool algebra! You will get 20 points and no links please :)
Answer: a. 12x+19
b. 67
Step-by-step explanation:
a. P=a+b+c+d
P=x+7+2x+2+8x+x+10
P=x+2x+8x+x+7+2+10
P=3x+9x+19
P=12x+19
b. P=12(4)+19
P=48+19
P=67
large pies cost $5, and small pies cost $2. if 45 pies were sold for $120, how many small pies were sold ?
Answer:
35 small pies
Step-by-step explanation:
Framing system of linear equations and solving:Let the number of large pies be 'l' and
The number of small pies be 's'.
Total pies sold = 45
⇒ l + s = 45 ------------(I)
l = 45 - s -------(II)
Cost of 45 pies = $120
Cost of 1 large pie = $5
Cost of 'l' large pies = 5*l = 5l
Cost of 1 small pie = $2
Cost of 's' small pie = 2*s = 2s
5l + 2s = 120 --------------(III)
Solving : substitution method
Substitute l = 45 -s in equation (III)
5*(45 - s) + 2s = 120
5*45 - 5*s + 2s = 120
225 - 5s + 2s = 120 {Combine like terms}
225 - 3s = 120
-3s = 120 - 225 {Subtract 225 from both sides}
-3s = -105
s = -105 ÷ (-3) {Divide both sides by (-3)}
s = 35
Substitute s = 35 in equation (II),
l = 45 - s
= 45 - 35
l = 10
[tex]\sf \boxed{\text{\bf 35 small pies were sold}}[/tex]
with show work please!
x-4 1/3=9 2/3 ive been trying to find the answer to this for hours someone please help
Answer:
x = 14
Step-by-step explanation:
1. Change the equation to x + -4 1/3 = 9 2/3
2. Add 4 1/3 to each side of the equation to get rid of the -4 1/3
3. You will be left with x = 14
need help !! Please somebody help
Answer:
The bottom Option
Note:
Due to my sus vibes from your questions, this is the last one I am answering from you. this is basic and easy if you read it.
Ginny Brown hoped her crops would get 3 3/4 inches of rain this month. The newspaper said the area received 3.8 inches of rain. Was that more or less than Ginny hoped for? By how much?
Answer:
More, by 0.05 or [tex]\frac{1}{20}[/tex] inches more.
Explanation:
Find out if the amount of rain was more or less by subtracting the desired outcome from the real outcome. If the answer comes out as positive then the amount of rain was more and if the answer is negative, it was less.
Workout:
[tex]\sf real \ outcome - desired \ outcome[/tex]
[tex]3.8 - 3\dfrac{3}{4}[/tex]
[tex]3.8 - 3.75[/tex]
[tex]0.05[/tex]
Hence, The rain was more than ginny expected by 0.05 inches more.
let v = (2, 3, 1), w = (1, 1, 1), and 3u + 2v 4w = (1, 2, 3). find (a) the vector u (b) the linear combination: 2u 3v + 5w
The vector u is [tex]\frac{-7}{3} i -\frac{8}{3}j -k[/tex].
The linear combination 2u + 3v + 5w is 19/3 i + 17/3 j + 6k.
According to the given question.
v = (2, 3, 1)
w = (1, 1, 1)
And
3u + 2v + 4w = (1, 2, 3)
From,
v = (2, 3, 1)
⇒ v = 2i + 3j + 1k
w = (1, 1, 1)
⇒ w = i + j + j
a). Let vector u be xi + yj + zk
Here,
3u + 2v + 4w = (1, 2, 3)
⇒ 3u + 2v + 4w = i + 2j + 3k
⇒ 3(xi + yj + zk) + 2(2i + 3j + k) + 4(i + j +k) = i + 2j + 3k
⇒ 3xi + 3yj + 3zk + 4i + 6j + 2k + 4i + 4j + 4k = i + 2j + 3k
⇒3xi + 3yj + 3zk + 8i + 10j + 6k = i + 2j + 3k
⇒ 3xi + 3yj + 3zk = i + 2j + 3k - 8i -10j -6k
⇒ 3xi + 3yj + 3zk = -7i -8j -3k
⇒ xi + yj + zk = (1/3)(-7i -8j-3k)
⇒ xi + yj + zk = [tex]\frac{-7}{3} i -\frac{8}{3}j -k[/tex]
b). The linear combination
2u + 3v + 5w
= 2(-7/3i -8/3j - k ) + 3(2i + 3j + k) + 5(i + j + k)
= -14/3 i -16/3j -2k + 6i + 6j + 3k + 5i + 5j + 5k
= -14/3 i -16/3j -2k + 11i + 11j + 8k
= 19/3 i + 17/3 j + 6k
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I don’t really understand how to get this one :/
in function notation, we get that the transformed function is:
g(x) = -2*f(x - 10) + 800
How to identify the transformation?
Here the parent function is:
f(x) = x^2
And the transformed function is the one graphed in the lower right side of the given image.
Notice that the y-intercept of the transformed function is y = 600.
The x-intercepts are x = -10 and x = 30
Then the polynomial is something like:
y = a*(x + 10)*(x - 30)
Using the fact that the y-intercept is y = 600, then:
600 = a*(0 + 10)*(0 - 30) = a*-300
600/-300 = a = -2
The transformed function is:
g(x) = -2*(x + 10)*(x - 30)
Expanding that:
g(x) = -2( x^2 + 10x - 30x - 300)
Completing squares we get:
g(x) = -2*( x^2 - 20x - 300)
= -2*(x^2 - 2*10*x - 300)
Now we can add and subtract 100, so we get:
-2*(x^2 - 2*10*x - 300 + 100 - 100)
-2*( (x - 10)^2 - 400)
Finally, expanding that:
g(x) = -2*(x - 10)^2 + 800
Writing it in function notation, we get that the transformed function is:
g(x) = -2*f(x - 10) + 800
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Sebastian started watching a movie at 17:30 (5:30 pm).
The movie was 1 hour and 54 minutes but partway through he paused it for 15 minutes.
What was the time when he finished the movie?
Give your answer using the 24 hour clock.
Using the diagram and the given angle measure to find the other three angle measures
Based on the given.
If [tex]m∠2 = 59°[/tex]
Then, [tex]m∠4 = 59 °[/tex]
(reason: vertically opposite angles are equal)
If [tex]m∠4 = 59 °[/tex]
Then, [tex]m∠1⟹ 180 - 59 = 121 °[/tex]
(reason: angles on a straight line = 180°)
If [tex]m∠1 = 121°[/tex]
Then, [tex]m∠3 = 121°[/tex]
(reason: vertically opposite angles are equal)
Therefore:
[tex]m∠1 = 121°[/tex]
[tex]m∠3 = 121°[/tex]
[tex]m∠4 = 59 °[/tex]
See attached image for the placement of the values.
5. The box plot represents the distribution of the number of points scored by a cross country team at 12 meets.
Answer:5 teams
Step-by-step explanation:
Is this answer correct?
Answer:
yes this is correct
Step-by-step explanation:
this is correct because angle gqh is adjacent to mqk, meaning they are the same degree which would mean kqg and hqm are adjacent
A stack of one dozen cookies with diameter of 5in. exactly fits in a cylindrical container of volume 176.715 in^3. which is the thickness of each cookie?
The thickness of each cookie is 0.75 inch.
The cookies are in cylindrical container, hence, the shape of cookies will also be cylindrical. Now, the volume of cylinder is given by the formula : V = πr²h, where V refers to volume, r refers to radius and h represents height.
So, volume of 12 cookies will be equal to the cylindrical container.
Radius of cookies = Diameter÷2
Radius of cookies = 5÷2
Radius of cookies = 2.5 inches
Taking π as 3.14
Volume of a stack of cookies = 3.14×2.5²×h
Volume of a stack of cookies = 19.625h
Relating both the volumes to find the value of h
19.625h = 176.715
h = 176.715 ÷ 19.625
Performing division to find the height
h = 9 inches
So, height of 12 cookies is 9 inches
Height of 1 cookie = 9 ÷ 12
Height of 1 cookie = 0.75 inch
Thus, the thickness of each cookie is 0.75 inch.
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7/4 to 4 is the same as x to 32
Answer:
14
Step-by-step explanation:
7/4:4 = x:32
x = 32(7/4) / 4 = 14
62 + 14 ÷ 2 - 8
Which operation appears first in the given expression?
Which operation did you select first in order to evaluate the expression?
Which operation is not included in the expression?
(the number problom goes with all questions)
The addition is the operation that appears first, the division is the operation that is selected first in order to evaluate and multiplication is the operation that is not included in the given expression.
The given expression can be evaluated using the BODMAS rule which tells the order of priority to give to solve an equation with multiple operations
BO stands for Bracket off means to solve the bracket first
D stands for division
M stands for multiplication
Stands for addition
S stands for subtraction
Now we should look at the expression given which is 62 + 14 ÷ 2 - 8
Although the addition operation appears first in the given expression, we would select the division operation first that can be bracketed because of BODMAS rule and then addition and then Subtraction at last which results
62 +( 14 ÷ 2) - 8
62 + 7 -8
69 -8
61
Hence, Using the BODMAS rule the expression is solved and the result is 61
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ASAP!!! PLEASE HELPPP!!Write an equation for the following sentence, then solve for the unknown value.
3 times the difference of a number and 8 is less than 15.
Answer:
3(x - 8) < 15
Step-by-step explanation:
3(x - 8) < 15
3x - 24 < 15
3x < 39
x < 13
in the eight-term sequence $a$, $b$, $c$, $d$, $e$, $f$, $g$, $h$, the value of $c$ is 5 and the sum of any three consecutive terms is 30. what is $a h$?
The value of A + H is 25 for the given sequence.
What is a series?A sequence's series is the total number of terms in the sequence.
A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.
Given that sum of any three consecutive terms is 30
Since c = 5
So a + b + c = 30
a + b = 25
⇒ (a+b)+(c+d+e)+(f+g+h)
⇒ 25 + 30 + 30 = 85
Now,
a+b+c+d+e+f+g+h = 85
a + h +(b+c+d)+(e+f+g) = 85
a + h + 30 + 30 = 85
a + h = 25
Hence "The value of A + H is 25 for the given sequence".
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Sebastian has 100$ he spits it to four of his friends how much does sebastian give?
Answer: $25 to each friend
Step-by-step explanation: 100 divided by 4 = 25
I need help with this question!
the angle measures less than 90°, thus, the correct classification is acute.
Which is the correct classification for the angle ∠JML?
First, let's define the possible angles that we have here:
Obtuse: With a measure larger than 90° and smaller than 180°Acute: With a measure between 0° and 90°Right: With a measure of 90°Straight: With a measure of 180°.Notice that the angles HML and LMK should add up to 180°, then we can write:
∠HML + ∠LMK = 180°
132° + ∠LMK = 180°
∠LMK = 180° - 132° = 48°
Now we can see that:
∠JML = ∠JMK + ∠LMK
∠JML = 41° + 48° = 89°
So the angle measures less than 90°, thus, the correct classification is acute.
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help with this question please! with show work
A hippopotamus can run 6 kilometers in 15 minutes. At this rate, how far can the hippopotamus run in 1 minute? __ kilometer(s) per minute
Answer:
15 minutes=1km
1 minute=?
(15m:m)×1km
minutes cancel minutes
15×1km=15km
Members of a softball team raised $1943.50 to go to a tournament. they rented a bus for $1148.50 and budgeted $53 per player for meals. write and solve an equation which can be used to determine x, the number of players the team can bring to the tournament.
The number of players the team can bring to the tournament are 15
Firstly we need to form the equation. The components of equation based on given information are as follows -
Total amount raised by softball team = Cost of bus + Cost of meal × number of players
Let the number of players be represented with x.
1943.50 = 1148.50 + 53×x
Rewriting the equation
53x = 1943.50 - 1148.50
Performing subtraction to Right Hand Side of the equation
53x = 795
Shifting 75 to Right Hand Side of the equation
x = 795 ÷ 53
Performing division at Right Hand Side of the equation
x = 15
Hence, 15 players the team can bring to the tournament.
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A recipe calls for of a cup of milk for 12 cookies. How many cups of milk are needed to make 72 cookies?
Answer: 6 cups of milk
Step-by-step explanation:
Set-up proportion
[tex]\frac{1}{12} =\frac{x}{72}[/tex]
1*72=72/12=6
6 cups of milk
the area of a certain state is 840000 square miles. what is this area in scientific notation?
1. 8.4x10.-4
2. 84x10.-3
3. 84x10.3
4. 8.4x10.5
please help
Answer:
4. 8.4×10^5
Step-by-step explanation:
The exponent of ×10 is the amount of places that you move the decimal. When the exponent is negative, you move the decimal to the left and when it is positive, you move it to the right. Number 1 and 2 are wrong right away because they move the decimal to the left which is not what we want. Number 3 is wrong because there are not enough 0's when we move the decimal. So, option 4 is correct. I hope this helps!
If 21% of a number is 3, find 7% of that number.
Answer:
7% of the number is 1.
Step-by-step explanation:
21%=3
Divide both sides by 3
7%=1
Answer:
1
Step-by-step explanation:
let x be the number.so.......
if 21%of a number means 21÷100*the number(x)=3
21÷100×X=3 so when we solve this first we have to criss-cross and then 21*X=3*100
then we both divide by 21 in order to get x .so x is going to be 100 divided by 7
then.......
we are asked to get how much percent of 100÷7 is 7% so...let the answer be y
7÷100*X=y
7÷100*100*7 =Y
when calculated the answer will possibly be 1 :)))
please answer this its due by 12
Answer:
4. 4(x+1)
5. 7(d+4)
6. y(y+3)
Answer:
I could be totally wrong but ill tr7
Step-by-step explanation:
4. 12 OR 4x+4
5. 56 (28+28)
6. y^2 + 3y
4 ÷ 2/5
Help (( 15 points ))
[tex]4 \div \frac{2}{5} [/tex]
[tex]4 \times \frac{5}{2} [/tex]
[tex]2 \times 5[/tex]
[tex]10[/tex]
Answer:10
Step-by-step explanation:
first step 4× 5/2
second step 4x5
2
third step is to simplify 20/2 which is
10
please help!
not sure how to solve 6
write the slope intercept form of the equation of the line through the given point with the given slope
Answer: x = 1
Step-by-step explanation:
Since the slope is undefined, that means it will be a vertical line. The equation of a vertical line is: x = h, where h is the x-value/coordinate it runs through. Based on your given point (1, 3), the x-coordinate is 1, so that makes the equation of your line x = 1.