Answer:
9
Step-by-step explanation:
Start with the total amount Dan paid and subtract the part of the payment that is for the ticket.
450-315=135
Assuming that all of that $135 was for luggage fees and each pound over the limit costs $15, then the question is, how many times did Dan pay $15 until he'd paid the full $135 luggage fee.
So divide $135 by $15.
135/15=9
So his luggage weighted 59 pounds, which is 9 pounds over the limit.
Let |u| = 10 at an angle of 45° and |v| = 13 at an angle of 150°, and w = u + v. What is the magnitude and direction angle of w?
|w| = 9.4; θ = 72.9°
|w| = 9.4; θ = 107.1°
|w| = 14.2; θ = 72.9°
|w| = 14.2; θ = 107.1°
Recall that for two vector x and y making an angle θ with each,
x • y = ||x|| ||y|| cos(θ)
If we replace y with x, we see that
x • x = ||x|| ||x|| cos(0) = ||x||² ⇒ ||x|| = √(x • x)
Using the last identity, the magnitude of w is
||w|| = √(w • w)
but since w = u + v, we have
w • w = (u + v) • (u + v)
The dot product distributes over sums and is commutative, so
w • w = (u • u) + (u • v) + (v • u) + (v • v)
… = ||u||² + 2 (u • v) + ||v||²
… = ||u||² + 2 ||u|| ||v|| cos(θ) + ||v||²
If u has a direction of 45° with the positive x-axis, v has a direction of 150°, then the angle between u and v is |45° - 150°| = 105°. So,
||w|| = √(||u||² + 2 ||u|| ||v|| cos(150°) + ||v||²)
… = √(10² + 2 • 10 • 13 cos(150°) + 13²)
… ≈ 14.2
Using the parallelogram rule for vector addition (see attached sketch), the sum of the angle between w and u and 45° is equal to the direction of w.
If φ is the angle between w and u, then
w • u = ||w|| ||u|| cos(φ)
… = 14.2 • 10 • cos(φ)
but we also have
w • u = (u + v) • u
… = (u • u) + (v • u)
… = ||u||² + ||u|| ||v|| cos(105°)
… = 10² + 10 • 13 • cos(105°)
… ≈ 66.4
Then
14.2 • 10 • cos(φ) ≈ 66.4
cos(φ) ≈ 0.467
φ ≈ 62.1°
and so the direction of w is 62.1° + 45° ≈ 107.1°.
Write and solve an absolute value inequality.
18. Students are guessing the number of jelly beans in a jar. Each student who guesses
within 15 of the correct amount will win a prize. The correct amount of jelly beans in the
jar is 389. Write and solve an absolute value inequality to represent this situation.
Express your solution as a compound inequality.
Compound inequalities are used to combine several inequalities
The solution as a compound inequality is [tex]374<x <404[/tex]
Assume the correct amount of jelly beans in the jar is x.
15 away from x can be represented as 15 - x or x - 15
The correct number of jelly beans is given as 389.
So, when the statement is represented as an absolute inequality, we have:
[tex]|x - 15| < 389[/tex]
Express as compound inequality:
[tex]389 - 15<x <389 + 15[/tex]
Evaluate like terms
[tex]374<x <404[/tex]
Hence, the solution as a compound inequality is [tex]374<x <404[/tex]
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Sin(180-A)/tan(180-A) × cot(90-A)/tan(90+A) × cos(-A)/ cos(270-A) Please solve
so tan = me sun bathing for 2.5 second
The ratio of the measures of the sides of a triangle is 5:7:8. Find the measures of each angle in the triangle.
Answer:
45°, 63°, 72°
Step-by-step explanation:
The sum of ratio units is 5+7+8=20, so each stands for 180°/20 = 9° of angle. Multiplying the ratio values by 9° gives the angle values:
45° : 63° : 72°
How much momentum does a 50 kg mass moving west at 10 m/s have?
Answer:
(a) 500 kg·m/s west
Step-by-step explanation:
Momentum is the product of mass and velocity.
p = mv
p = (50 kg)(10 m/2 west)
p = 500 kg·m/s west
Helppp! I dont completly get the conceptttt
help with this please
Help help help help math math
Answer:
y = -2x - 1
See image
Step-by-step explanation:
The "slope-intercept" form of the equation is the
y = mx + b form
So you need to find the slope (m) and the y-intercept (b), which you are able to find on the image in the question.
Slope (m) tells how steep a line is and whether it goes up or down from left to right. It also works just like directions, from any point on the line to any other point on the line.
The y-intercept (b) is the point on the line where the line crosses the y-axis.
The slope is -2 and the y-intercept is -1
So the equation is
y = -2x - 1
See image
6+√27/4-√3 can be written in the form r +s√3/13
where are both r and s integers
what are the values of r and s
[tex]r = \left(\dfrac{33}{13}\right)[/tex]
[tex]s = \left(\dfrac{10}{13}\right)[/tex]
Step-by-step explanation:
Let's multiply and divide the given fraction by the conjugate of the denominator:
[tex]\dfrac{6+\sqrt{27}}{4-\sqrt{3}}×\dfrac{4+\sqrt{3}}{4+\sqrt{3}}[/tex]
[tex]\;\;\;\;= \dfrac{24 + 6\sqrt{3} + 4\sqrt{3} + \sqrt{27}\sqrt{3}}{13}[/tex]
[tex]\;\;\;\;=\frac{1}{13}(24 + 10\sqrt{3} + \sqrt{81})[/tex]
[tex]\;\;\;\;=\frac{1}{13}(33 + 10\sqrt{3})[/tex]
[tex]\;\;\;\;=\left(\dfrac{33}{13}\right) + \left(\dfrac{10}{13}\right)\dfrac{\sqrt{3}}{13}[/tex]
We can see here that
[tex]r = \left(\dfrac{33}{13}\right)[/tex]
[tex]s = \left(\dfrac{10}{13}\right)[/tex]
The value of the variable 'r' and 's' will be 33 and 18, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The two equations are given below.
(6 + √27) / (4 - √3) and (r + s√3) / 13
Simplify the expression (6 + √27) / (4 - √3), then we have
[tex]\rightarrow \dfrac{6 + \sqrt{27}} { 4 - \sqrt3} \times \dfrac{4 + \sqrt3} { 4 + \sqrt3} \\\\[/tex]
⇒ [(6 + 3√3)(4 + √3)] / (4² - 3)
⇒ [(24 + 6√3 + 12√3 + 9)] / (16 - 3)
⇒ (33 + 18√3) / 13
Compare the expression (33 + 18√3) / 13 with (r + s√3) / 13, then the value of r and s will be given as,
r = 33
s = 18
The value of the variable 'r' and 's' will be 33 and 18, respectively.
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Which of the following equations describes the graph shown above
Answer: D
Step-by-step explanation:
this is in y=Mx+ b form. M stands for the slope and b stands for the y intercept, or where the line intersects with the y-axis.
Going left to right, the line slopes downwards, therefore it is a negative Slope. This narrows down your answer to either a or d. the slope is -1 because you can only ever write x by itself if it means 1x. In this case it is negative so it would look like this: -x
for the y-intercept, simply look at where the line passes through the y-axis. In this case, it is positive 2.
your finished equation would be: y=-x+2
i hope this is helpful
Help help math math math
Answer:
10
Step-by-step explanation:
substitute -8 into x.
f(-8)=-8+18=10
Answer:
10
Step-by-step explanation:
What is the value of (-2.8)+0+(-2.6)+6.4
What functions have a range of {y £ R | -
Answer:
the second and the fourth have a range of real no
Solve each inequality 3+1/2(3-x)<_7
Answer:
x > 5
Step-by-step explanation:
multiply the fractions, break up the fraction, group like terms, convert integer into a fraction, combine the fraction, combine the numerator, etc. hope this helps.
a dogs hair grew 2 1/2 inches in 12 1/2weeks how long will the hair grow in 1 week?
Answer:
0.2 inches
Step-by-step explanation:
12.5 weeks = 2.5 inches
1 week = p inches
Cross multiply
12.5p = 2.5
Divide both sides by 12.5
p = 2.5 / 12.5
p = 0.2 inches
Hence, the length grown in 1 week is 0.2 inches
Hope I Helped You:)
Write an equation in standard form for the line that passes through (-1, -2) and (3, 0).
(dy)/(dx) = (x ^ 2)/(1 + y)
Which equation best matches the graph shown below?
Answer:
B
Step-by-step explanation:
because it is actually move to right
Answer:
y= -3(x+1)(x+3)
Step-by-step explanation:
the lowest coordinate of it is -3 and the x-coordinates are 1 and 3
work out the volume of the cone giving your answer to 3 significant figures 7cm 24cm 25cm
Answer:
1230
Step-by-step explanation:
[tex]\frac{\pi }{3}[/tex] x 49 x 24 = 1230 cm^3
Find the perimeter of a regular polygon with an interior angle of 90° and side length 3.5 ft.
Please be accurate and explain.
Answer:
p=14 ft
Step-by-step explanation:
The figure that meets these conditions is the square
The perimeter:
4(3.5) = 14 ft.
Hope this helps
Write the phrase "one more than the product of six and nine" as a mathematical expression.
Answer:
6.9+1
Step-by-step explanation:
hope it helps
[tex]\huge\mathfrak\blue{ ☃ }[/tex]
Answer:
the product of six and nine is fifty five
Solve for x/3= −9
SHOW WORK
Answer:
x =-27
Step-by-step explanation:
X/3= -9
or,X=-9×3(cross multiplication)
or, X=-27
The formula for finding the perimeter of a rectangle is P = 2L + 2W. If a rectangle has a perimeter of 68 inches and the length is 14 inches longer than its width, find the width.
Enter a number answer only.
Answer:
Width = 10 inches
Step-by-step explanation:
Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.
We can establish the following values to help us solve for the width of a rectangle:
Perimeter (P) = 68 inches
Length (L) = 14 + W inches
Width (W) = unknown
Solve for the Width (W)P = 2(L + W) ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.
Divide both sides by 2:
[tex]\displaystyle\mathsf{\frac{P}{2}\:=\:\frac{2(L\:+\:W)}{2}}[/tex]
[tex]\displaystyle\mathsf{\frac{P}{2}\:=L\:+\:W}[/tex]
Substitute the value of the Perimeter and the length (L) into the formula:
[tex]\displaystyle\mathsf{\frac{68}{2}\:=14\:+W\:+\:W}[/tex]
Combine like terms on the right-hand side, and simplify the left-hand side of the equation:
[tex]\displaystyle\mathsf{34\:=14\:+2W}[/tex]
Subtract 14 from both sides:
34 - 14 = 14 - 14 + 2W
20 = 2W
Divide both sides by 2 to solve for the width (W):
[tex]\displaystyle\mathsf{\frac{20}{2}\:=\:\frac{2W}{2}}[/tex]
W = 10 inches
Therefore, the width of the rectangle is 10 inches.
Double-check:Verify whether the derived value for the width is correct:
P = 2L + 2W
68 = 2(14 + 10) + 2(10)
68 = 2(34) + 20
68 = 48 + 20
68 = 68 (True statement).
Thus, the length of the rectangle is 34 inches, and the width is 10 inches.
HELP!!!! PLEASE NO LINK SCAM THO
Which graph shows all natural numbers less than 3?
OA)
-4 -3 -2 -1
+
4
o
1
2
3
+
+
OB) -4 -3 -2 -1
+
2 3
o
1
4
+
+
OC) -4 -3 -2 -1
+ +
2 3 4
o
1
OD)
-4 -3 -2 -1
+ +
+
0 1 2 3 4
Answer: C
Step-by-step explanation:
Answer:
The Answer Is B
Step-by-step explanation:
What is the slope of the line that passes through the points (4,1) and (6, 2)?
Answer:
1-2
Step-by-step explanation:
honestly idek what this stuff is I just need points
i need help with this
Answer:
Yes Jeff is the correct answer
Step-by-step explanation:
Which of the following is most likely the next step in the series?
A.
B.
C.
D.
Each consecutive element of the series has one less blue points than the before element, with that, we conclude that the correct option is D, where there is only one blue point.
Which of the following is most likely the next step in the series?
Here we can see a series of 3 elements.
the first element is a circle with 4 blue points on its circumference, such that the points are connected to form a rectangle.
The next element is a circle with 3 blue points on it, such that when the points are connected a triangle is formed.
The third element is a circle, this time with 2 points, and the connection forms a segment.
So what we can see is that in each consecutive element the number of blue points on the circumference of the circles decreases by one, so the logical conclusion is that the next element will have only one point on its perimeter, then the correct option is D, where we can see only one blue point on the perimeter of the circle.
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F(x)=2x^2+7 what is the value f(-2)
Answer:
f(x)=2(x+7/4)^2-49/8
Step-by-step explanation:
To convert from Standard Form to Slope-Intercept Form the strategy is to solve for which variable?
b
m
y
x
Answer: y
Step-by-step explanation:
Slope intercept form is written as
Y=mx+b, so you’d solve for the variable y
It is the policy of stores owned by the Talkara Co. to give out bonuses to salespeople every six months. The size of the bonus is determined by averaging (taking the mean of) the two highest and the lowest monthly sales totals from the six-month period, taking 8% of the result, and splitting it evenly among the salespeople. The graph below shows sales for the most recent bonus period.If there are six salespeople, how much money will each one receive, to the nearest dollar? a. $243 b. $309 c. $324 d. $355
Answer:
c. $324
Step-by-step explanation:
The solution is,
A) 83/400= 0,2075
B) 100/400=0,25
C) 42/400= 0,105
D) 42/100= 0,42
E) The special training program was effective.
What is division?Division can be stated as the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
Explanation:
Total population= 400 salespeople
Received a bonus last year= 83 salespeople
Attended a special sales training program= 100 salespeople
Both attended sales training and received a bonus= 42 salespeople
a) You need to calculate the number of salespeople that receive a bonus over total population
83/400= 0,2075 The proportion of salespeople that receive a bonus is 0,2075
b) You need to calculate the number of salespeople that attended a special program over total population
100/400= 0,25 The proportion of salespeople that attended a special program is 0,35
c) 42/400= 0,105 The proportion of salespeople that receive a bonus and attended a special program is 0,105
d) You need to calculate the proportion of people that having attended received a bonus.
42/100= 0,42 The proportion of salespeople that receive a bonus having attended a special program is 0,42
e) The special training program was effective. The proportion of people that receive a bonus over the total population that didn't attend the program (41/300=0,14) is inferior to the proportion of salespeople that attend the program and receive a bonus. Meaning that there are more chances of receiving a bonus taking a training program.
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Complete question:
A company employs 400 salespeople. Of these, 83 received a bonus last year, 100 attended a special sales training program at the beginning of last year, and 42 both attended the special sales training program and received a bonus. (Note: the bonus was based totally on sales performance.) a) What proportion of the 400 salespeople received a bonus last year? b) What proportion of the 400 salespeople attended the special sales training program at the beginning of last year? c) What proportion of the 400 salespeople both attended the special sales training program and received a bonus? d) What proportion of the salespeople who attended the special sales training program received a bonus? e) Based on your answers to parts a and d, does the special sales training program seem to have been effective? Explain your answer.