======================================================
Explanation:
Any vector of the form v = (a,b) will have a length of |v| = sqrt(a^2+b^2).
This is derived from the pythagorean theorem. It's the same as saying the distance from (0,0) to (a,b) is sqrt(a^2+b^2).
In this case, a = 3 and b = -4, which means...
|v| = sqrt(a^2+b^2)
|v| = sqrt(3^2+(-4)^2)
|v| = sqrt(9+16)
|v| = sqrt(25)
|v| = 5
The vector is 5 units long.
Note: we have a 3-4-5 right triangle
Pleaseeeee help me with this question
Calculate the average rate of change in the amount of the surcharge for non-account holders between 2004 and 2008. Write the result in a sentence of interpretation. (Round your answer to two decimal places.)
Answer:
The average rate of change in the amount of the surcharge for non-account holders between 2004 and 2008 is $0.08
Step-by-step explanation:
Given
[tex]s(t) = 0.72 * 1.081^t[/tex]
[tex]3 \le t \le 13[/tex]
[tex]t \to[/tex] years since 2001
Required
Average rate of change between 2004 and 2008
In 2004,
[tex]t = 2004 - 2001[/tex]
[tex]t =3[/tex]
So:
[tex]s(t) = 0.72 * 1.081^t[/tex]
[tex]s(3) = 0.72 * 1.081^3[/tex]
[tex]s(3) = 0.9095[/tex]
In 2008,
[tex]t = 2008 - 2001[/tex]
[tex]t = 7[/tex]
So:
[tex]s(t) = 0.72 * 1.081^t[/tex]
[tex]s(7) = 0.72 * 1.081^7[/tex]
[tex]s(7) = 1.2420[/tex]
The average rate of change (m) is calculated as:
[tex]m = \frac{s(a) - s(b)}{a - b}[/tex]
In this case:
[tex](a,b) = (3,7)[/tex]
So, we have:
[tex]m = \frac{s(3) - s(7)}{3 - 7}[/tex]
[tex]m = \frac{s(3) - s(7)}{-4}[/tex]
Substitute values for s(3) and s(7)
[tex]m = \frac{0.9095 - 1.2420}{-4}[/tex]
[tex]m = \frac{-0.3325}{-4}[/tex]
[tex]m = 0.083125[/tex]
[tex]m = 0.08[/tex] --- approximated
what degree of rotation about the origin will cause the triangle below to map onto itslef
Answer:
[tex]360^o[/tex]
Step-by-step explanation:
Given
The attached plot
Required
Which degree maps the triangle onto itself
The degrees that can map a point, line, or shape onto itself are:
[tex]\theta=360,720,1080,1440, 1800, 2160, 2520, 2880, 3240, 3600[/tex]
i.e. multiples of 360
Looking at the given options
[tex](a)\ 360^o[/tex] is correct because it can be found in the listed multiples
In other words, it will map point [tex](x,y)[/tex] to point [tex](x,y)[/tex]
PLEASE HELP ASAPPP!!
Answer:
34
Step-by-step explanation:
im pretty sure its 34.
vertical angles are basically angles from the opposite side of each other, so saying that one of the angles is 68 degrees and they're vertical angles, means that the other unknown angle is 68 degrees.
but in this case it'll be 34 since ur multiplying 2 with 34
2(34) = 68
i hope this helped
A cylinder has a height of 10 millimeters and a radius of 3 millimeters. What is its volume?
Use - 3.14 and round your answer to the nearest hundredth.
Answer:
18312.5mm³
Step-by-step explanation:
Given parameters:
Height of cylinder = 18mm
radius = 18mm
Unknown:
Volume of the cylinder = ?
Solution:
The volume of cylinder is given as;
Volume = π r ² h
Insert the given parameters and solve;
Volume = 3.14 x 18² x 18
Volume = 18312.5mm³
Answer:
282.6
Step-by-step explanation:
volume= h*(pie*r^2)
3*3=9
9*pie=28.26
10*28.6=282.6
15,60,240,... Find the 6th term .
Answer:
61440
Step-by-step explanation:
15 x 4= 60
60 x 4= 240
240 x 4= 960
960 x 4= 3840
3840 x 4 = 15360
15360 x 4= 61440
The 6th term = 15360.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
the given sequence 15,60,240,...
1st trem = 15
common ratio = 4
so, 6th term = 15* 4^5
=15360
hence, The 6th term = 15360.
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ2
It is well known that steroid usage is banned in athletes. As a result, athletes are randomly tested. The steroid test procedures are believed to be equally effective on both steroid users as well as non-steroid users. The effective rate is 98%. Assume 90% of the athletes are clean (not steroid users). Suppose an athlete is tested as a steroid user (and thus could be disqualified from the Summer Olympics games), what is the probability that the athlete is actually clean (i.e., not a steroid user)
Answer:
18% that the athlete is disqualified but is actually clean
Step-by-step explanation:
In order to find the probability of two events happening together, in this case the athlete being disqualified and being clean, we need to multiply the probabilities. So,
It is a 90% chance that the athlete is clean and a 2% chance that the test fails so multiply the two
.9 * .2 = .18
This means that it is an 18% chance that the athlete is clean but is still disqualified.
Tina's user ID is a 5-digit number.
• 9 is in the ten thousands place.
• The digit in the ones place is two less than the digit in ten thousand place.
• Digit in the thousands place is one less than digit in ten thousand place.
• 4 is in the tens place.
• Digit in the hundreds place is the number of sense organs.
What is Sara’s user ID number? _____________
Answer:
98547
Step-by-step explanation:
find the radius of a circle if the circumference is 66cm
Answer:
Approximately 10.5, or 10.5095541.
Step-by-step explanation:
To find the radius given the circumference of a circle, we first have to divide the circumference by pi, or an estimation of 3.14. This will give us the diameter.
Since we know that the radius of a circle is simply half the diameter, we divide the number we got from the problem above by 2. This will give you your answer!
Answer:
r = 10.50
Step-by-step explanation:
Circumference =
[tex]2\pi \: r[/tex]
[tex] 66 = 2\pi \: r[/tex]
[tex] \frac{66}{2\pi} = r[/tex]
r = 10.5
i know the answer but i need a thorough explanation on how to do this. pls answer the questions i have for brainliest thank you
Answer:
i think because it's powered by 4
PLEASE HELP! 30 POINT!!!
What is the value of y when x = 3 in this equation
Y = 2x + 2
Answer:
5
7
8
12
Answer:
Step-by-step explanation:
8
The table shows the number of miles driven and the number of gas used in 4 cars.Which car drives the most miles per gallon of gas
Answer:
Car C
Step-by-step explanation:
Miles per gallon = miles traveled / gallon of gas used
Miles per gallon :
Car A = 19 / 1 = 19 miles per gallon
Car B = 39 / 3 = 13 miles per gallon
Car C = 42 / 2 = 21 miles per gallon
Car D = 48 / 3 = 16 miles per gallon
Car with most miles per gallon is car C
11. How can you solve the system? Complete the
sentence
(3x + 3y = 9
-6x – 4y = -14
Multiply 3x + 3y = 9 by ?and add
it to -6x – 4y = -14.
X Х
Answer:
Multiply by 2.
Step-by-step explanation:
Given the following simultaneous equations;
3x + 3y = 9 ......equation 1
-6x – 4y = -14 ......equation 2
To solve the equation by elimination, we would multiply eqn 1 by 2;
6x + 6y = 18
-6x – 4y = -14
Adding them together, we have;
0x + 2y = 4
2y = 4
y = 4/2
y = 2
To find the value of x;
3x + 3y = 9
3x + 3(2) = 9
3x + 6 = 9
3x = 9 - 6
3x = 3
x = 3/3
x = 1
Therefore, to solve the system of equations, you will multiply 3x + 3y = 9 by 2 and add it to -6x – 4y = -14.
increase 21 kobo by 35%
Answer:
28.35
Step-by-step explanation:
you can use mathswatch or hegarty maths to help u
The question is in the picture (:
Answer:
[tex] \frac{(x - 2)(x + 2)}{x - 8} [/tex]
Robin has colored pants in a drawer that she wears for work. She has the following pants:
6 red pants
9 yellow pants
8 blue pants
2 orange pants
If Robin picks a pair of pants from the drawer without looking, the probability that she will pick a red or yellow pair of pants is
i need help asap pls anyone i will be so thankful
Answer:
3/5 times or 60%
Step-by-step explanation:
Answer:
3/5 or 60%
Step-by-step explanation:
The total amount of pants are 6 + 9 + 8 + 2 = 25. The amount that are red or yellow are 9 + 6 = 15. The probability is 15/25, or 3/5, or 60%
How much would you have to deposit today to have an accumulated amount of 20,000 in 20 years if yearly interest is 4.75% compounded continuously?
(3)^4 times (3)^3 simplified version using exponents
Answer:
I'm pretty sure your answer is [tex]3^1^1[/tex]
Step-by-step explanation:
PLEASE HELP ME ASP !!!
Answer:
x=11
Step-by-step explanation:
22*y=32
y=16/11
So,
x*16/11=16
x=11
Answer:A
Step-by-step explanation:
Two figures have a similarity ratio of 3 : 7. If the area of the larger figure is 294 cm2, which is the area of the smaller figure?
Answer:
The area of the smaller figure is 126 cm^2.
Step-by-step explanation:
3:7 ratio
Divide 294 by larger ratio.
294/7 = 42
Multiply 42 by the smaller ratio.
42 x 3 = 126
3 to the fourth power +9
Answer:
81
Step-by-step explanation:
3*3=9
9*3=27
27*3=81
Answer: 90
Step-by-step explanation:
3 to the fourth power = 81
81 + 9 = 90
Came someone help me answer this one?
Answer:
Let x = ducks
Let y = goats
Equation 1: x+y=38
Equation 2: 2x+4y=90
Step-by-step explanation: (Work)
The question says two kinds of animals, so let x be "ducks" and y be "goats."
Number one equation: x+y=38
Number two equation: 2x+4y=90
Explanation:
The x+y=38 represents how many animals there will be if you add both the ducks and goats.
The 2x+4y=90 represents the legs of the animals, the 2x represents the 2 legs of the ducks and the 4y represents the 4 legs of the goats.
in 2007 the poverty threshold for a family of four two of whom were related children was $21027 at the same time the poverty threshold for a family of four three of whom were related children was 21100 for each of the preceding years the difference between these two thresholds was less than $100 what is the conclusion you can draw from this
Answer:
MINIMUM WAGE does not increase much over time
Step-by-step explanation:
Based on the information given the conclusion you can draw from this is that MINIMUM WAGE DOES NOT INCREASE OR TEND TO GO UP MUCH OVER TIME Since the MINIMUM WAGES of the poverty threshold of whom TWO were related children was the amount of $21,027 and the poverty threshold of whom THREE were related children was the amount of $21,100 indicating that the minimum wages only increase from $21,027 to $21,100 given us the amount of $73 ($21,027 -$21,100) which is less than the amount of $100 as the difference between these TWO THRESHOLDS for each of the preceeding year.
Find 35% of a number is 70 find the number
Answer:
200.
Step-by-step explanation:
35% = 0.35 so
0.35x = 70
x = 70 / 0.35
= 200.
Answer:
200
Step-by-step explanation:
Let the number = x
35% of x = 70
35/100 * x = 70 Multiply by 100
35x = 70 * 100
35x = 7000 Divide by 35
x = 7000/35
x = 200
7th grade math help :)
The population of a certain town is known to increase at a rate proportional to the current population. If the population doubles every 15 years, and the current population is 32,000, then what will be the population in 11 years g
Answer:
The population in 11 years will be of 53,199.
Step-by-step explanation:
Equation for a population that doubles every n years.
The population of an specie, after t years, considering that is doubles after n years, is given by an equation in the following format:
[tex]P(t) = P(0)(2)^{\frac{t}{n}}[/tex]
In which P(0) is the initial population.
The population doubles every 15 years, and the current population is 32,000
This means that [tex]n = 15, P(0) = 32000[/tex]. So
[tex]P(t) = P(0)(2)^{\frac{t}{n}}[/tex]
[tex]P(t) = 32000(2)^{\frac{t}{15}}[/tex]
What will be the population in 11 years?
This is P(11). So
[tex]P(t) = 32000(2)^{\frac{t}{15}}[/tex]
[tex]P(11) = 32000(2)^{\frac{11}{15}}[/tex]
[tex]P(11) = 53199[/tex]
The population in 11 years will be of 53,199.
Find the coordinates of the points that are 10 units away from the origin and have a y- coordinate equal to -8
Answer:
(-6, -8) and (6, -8)
Step-by-step explanation:
Think of this as a right triangle
The hypotenuse is 10
The "y" leg is |-8| = 8
x² + 8² = 10²
x² + 64 = 100
x² = 36
x = ±6
two points
(-6, -8) and (6, -8)
Please help me with this question
9514 1404 393
Answer:
(x, y) = (5, 2)
Step-by-step explanation:
Given:
LP = x
MP = 2y+3
NP = y+3
KP = 3x -8
KP = MP, LP = NP
Find:
x, y
Solution:
The given relations between the segment lengths let us write two equations:
KP = MP
3x -8 = 2y +3 ⇒ 3x -2y -11 = 0 [eq1]
LP = NP
x = y +3 ⇒ x -y -3 = 0 [eq2]
__
Subtracting 3 times [eq2] from [eq1] gives ...
(3x -2y -11) -3(x -y -3) = 0
y -2 = 0 . . . . . . . . simplify
y = 2 . . . . . . . . . . add 2
Substituting this value into [eq2] gives ...
x = 2 + 3 = 5
The values of x and y are ...
x = 5, y = 2
A dozen apples costs $2.35. At this rate, how much would 5 apples cost?
Answer:
0.95 is your answer
Step-by-step explanation:
Answer:
$.98
Step-by-step explanation:
so if a dozen apples cost $2.35 that can be represented by the equation 12x=2.35
so solve that for x because that is the price of a single apple
so then if you just leave it because it is a weird decimal then x times 5(to figure out how much 5 apples cost) is
(2.35/12) * 5 = 47/48 or about $.98
so five apples cost $.98
Amy runs 10 miles in 85 minutes. At the same rate, how many minutes would she take to run 8 miles?
9514 1404 393
Answer:
68 minutes
Step-by-step explanation:
At the same rate, she will run 8/10 of the distance in 8/10 of the time.
(8/10)(85 minutes) = 68 minutes
It would take Amy 68 minutes to run 8 miles.