Answer:
w = 61❬cos 280.389°, sin 280.389°❭
Step-by-step explanation:
The "trigonometric form" of a vector is ...
(magnitude)❬cos(angle), sin(angle)❭
This is sometimes abbreviated ...
magnitude cis(angle)
__
This form immediately eliminates choices A and D, as those have the trig functions reversed. The signs on the unit vectors i and j tell you the vector has a 4th-quadrant angle, so will be between 270° and 360°. Only answer choice B makes any sense.
w = 61❬cos 280.389°, sin 280.389°❭
_____
Additional comment
The angle is computed from ...
θ = arctan(y/x) = arctan(-60/11) = -79.611°
Expressed as a positive angle in the range [0, 360°), that will be ...
360° +(-79.611°) = 280.389°
__
The abbreviation "cis" is mentioned as an aid to remembering the (x, y) coordinates are the cosine and sine of the angle, in that order.
153 apples, 255 oranges, 357 pears are to be distributed to a group of children. Suppose each child in the group receives an equal number for each type of fruit.
a) Find the least possible number of children in the group
b) the maximum possible number of children in the group
c) the least possible number of apples, oranges and pears each child can receive
d) the maximum possible number of apples, oranges and pears each child can receive.
Answer:
Below in bold.
Step-by-step explanation:
a) we need the grestest common factor of theses values
153 = 3 * 3 * 17
255 = 3 * 5*17
357 = 3 * 7 * 17
The GCF = 3 * 17 = 51.
a) the least possible number of children is 3.
b) The maximum number is 51 ( as 51 is the GCF of the given values).
c) the least possible number of fruits is when b) occurs, that is:
153/51, 255/51 and 357/51
= 3 apples , 5 oranges and 7 pears.
d) the maximum number of fruits is :
153/3, 255/3 and 357/3
= 51 apples , 85 oranges and 119 pears.
Answer:
a) 3 children
b) 51 children
c) 3 apples, 5 oranges and 7 pears
d) 51 apples, 85 oranges and 119 pears
Step-by-step explanation:
lnc - Least possible number of children in group
mnc - maximum possible number of children in group
a - Apples
o - Oranges
p - Pears
a = 153
o = 255
p = 357
a)
To solve this, find the highest divisor for the apples, oranges and pears.
[tex]a = \frac{153}{51} [/tex]
[tex]a = 3[/tex]
[tex]o = \frac{255}{85} [/tex]
[tex]o = 3[/tex]
[tex]p = \frac{357}{119} [/tex]
[tex]p = 3[/tex]
In order for each child to get 51 apples, 85 oranges and 119 pears, there would need to be a minimum of 3 children in the group.
[tex]lnc \: = 3[/tex]
b)
To solve this, find the lowest divisor for the apples, oranges and pears.
[tex]a = \frac{153}{3} [/tex]
[tex]a = 51[/tex]
[tex]o = \frac{255}{5} [/tex]
[tex]o = 51[/tex]
[tex]p = \frac{357}{7} [/tex]
[tex]p = 51[/tex]
In order for each child to get 3 apples, 5 oranges and 7 pears, there would need to be a maximum of 51 children in the group.
[tex]mnc = 51[/tex]
c)
In a group of 51, each child will get:
- 3 apples
- 5 oranges
- 7 pears
d)
In a group of 3, each child will get
- 51 apples
- 85 oranges
- 119 pears
Ay a benefit concert eight bands have volunteered to perform but there is only enough time for five of the bands to play how many lineups are possible
Using the permutation formula, as the order is important, it is found that 6720 lineups are possible.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 5 bands are selected from a set of 8, hence:
[tex]P_{8,3} = \frac{8!}{3!} = 6720[/tex]
6720 lineups are possible.
More can be learned about the permutation formula at https://brainly.com/question/25925367
The length of one leg of a right triangle is 9 ft. The length of the hypotenuse is 3 feet longer than the other leg. Find the length of the hypotenuse and the other leg.
The length of the hypotenuse is ___ ft.
Answer:
The length of the hypotenuse is 14 ft[tex] \: [/tex]
Step-by-step explanation:
We'll solve this using the Pythagorean theorem, we know that,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^{2}= (Base) {}^{2} + (Perpendicular {)}^{2} }}}[/tex]
So, As it is given in the question that, the length of one leg of a right triangle is 9 ft and the length of the hypotenuse is 3 feet longer than the other leg and we are to find the length of the hypotenuse and the other leg.
[tex] \: [/tex]
Let us assume the other leg as x ft and therefore the hypotenuse will be (x + 3) ft.
[tex] \: [/tex]
Now, substituting the values in the formula :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad (x + 3 {)}^{2} = (9 {)}^{2} + (x) {}^{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (x {)}^{2} + 2.x.3 + {(3)}^{2} =81 + (x) {}^{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad \cancel{ (x {)}^{2}} + 2.x.3 +9 =81 + \cancel{(x) {}^{2} }}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 6x + 9 =81 }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 6x =81 - 9 }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 6x =72 }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{72}{6} }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\frak {\qquad x =12 }}} \\ \\ [/tex]
Therefore,
The length of other leg is 12 ft . And the length of hypotenuse is (12 + 2) ft = 14 ft
Louise buys five raffle ticket out of 1000 sold.she does not win the first prize.what is the probability that she will win the second prize
Answer:
1 in 999 i guess
Step-by-step explanation:
What primarily drew early civilizations to the places they first populated?
A. Religious freedom
B. Governmental policies
C. Economic development
D. Physical geography
According to information from a college admissions office, 62% of the students there attended public high schools, 26% attended private high schools, 2% were home schooled, and the remaining students attended schools in other countries. Among this college's Honors Graduates last year there were 47 who came from public schools, 29 from private schools, 4 who had been home schooled, and 4 students from abroad. Is there any evidence that one type of high school might better equip students to attain high academic honors at this college
The p-value shows that onea type of high school might not be better equip students to attain high academic honors at this college.
What is a p-value?A p-value simply means a statistical measurement that is used to validate a hypothesis against the observed data.
Here, from the table, the p-value is 0.0393. Since the p-value is less than the level of significance which is 0.05, we are going to reject the null hypothesis.
It simply means that the observed values don't support the proportion given. Here, the p-value shows that one type of high school might not be better equip students to attain high academic honors at this college.
Learn more about p-value on:
https://brainly.com/question/4621112
Please help me solve and show all steps, thank you!!!
Answer:
y = -2x² + 12x - 14
Step-by-step explanation:
Isolate the "-2" in (x - 3)² by using brackets:
⇒ y = -2(x - 3)² + 4⇒ y = -2[(x - 3)²] + 4Using the formula (a - b)² = a² - 2ab + b²:
⇒ y = -2[(x - 3)²] + 4⇒ y = -2[x² - 2(x)(3) + 3²] + 4Open the brackets on the R.H.S
⇒ y = -2[x² - 6(x) + 9] + 4⇒ y = -2x² + 12(x) - 18 + 4Simplify the expression on the R.H.S
⇒ y = -2x² + 12(x) - 18 + 4⇒ y = -2x² + 12x - 14If you help me ill give you brainliest!
Alice is making a necklace. She has a chain that is 400 mm long. She puts forty 1.7 mm beads, twenty-seven 6.5 mm beads, and eight 3.4 mm beads on the chain. How much of the 400 mm chain is left without bead?
Answer:
129.3mm chain left without beads
Step-by-step explanation:
Equation:
400mm long chain - [(40 x 1.7mm) + (27 x 6.5mm) + (8 x 3.4mm)]
= chain left without beads
Calculation:
40 beads x 1.7mm = 68mm
27 beads x 6.5mm = 175.5mm
8 beads x 3.4mm = 27.2mm
(68mm + 175.5 mm + 27.2mm) = 270.7mm chain with beads
400mm chain - 270.7mm chain with beads
= 129.3mm chain left without beads
Activity 1
Use ∆XYZ to find each trigonometric ratios.
Answer:
1. Cos X =
2. Sin X = 3/5
3. Cos Y = 4/5
4. Sin Y = 3/5
5. Sec Y = 5/4
6. CSC X = 5/3
Step-by-step explanation:
(XY)² = (YZ)² + (XZ)²
=> (XY) ² = 3² +4²
=> (XY) ² = 9 + 16
=> (XY) ² = 25
=> (XY) = √25
=> (XY) = 5
What is the range of the function f(x) = 3x2 6x – 8?
The domain of the function 3x² + 6x – 8 is a real number and the range of the function 3x² + 6x – 8 will be (-11, ∞).
What are domain and range?The domain means all the possible values of the x and the range means all the possible values of the y.
The function is given below.
f(x) = 3x² + 6x – 8
The range of the function will be
f(x) = 3x² + 6x – 8
f(x) = 3x² + 6x + 3 – 11
f(x) = 3(x² + 2x + 1) – 11
f(x) = 3(x + 1)² – 11
Then the range of the function will be from -11 to infinity.
More about the domain and range link is given below.
https://brainly.com/question/12208715
Find the circumference of the circle.
113.04 feet
18.84 feet
d = 6 ft.
28.26 feet
37.68 feet
9.42 feet
male the question little more clear
Cason read an article claiming that 98.6\%98.6%98, point, 6, percent of births in his country happen in a hospital, 0.5\%0.5%0, point, 5, percent in a home, 0.4\%0.4%0, point, 4, percent in a birthing center, and 0.5\%0.5%0, point, 5, percent in other places. He wondered if the locations of births at his state followed this distribution, so he took a random sample of 200020002000 births and recorded where they happened. Here are his results:
Location Hospital Home Birthing center Other
Births 196819681968 141414 888 101010
He wants to use these results to carry out a \chi^2χ
2
\chi, squared goodness-of-fit test to determine if the distribution of birthing locations in his state disagrees with the claimed percentages.
What are the values of the test statistic and P-value for Cason's test?
Answer:
D) X^2 = 1.608;
P-value > 0.25
Step-by-step explanation:
Correct on Khan
In a triangle, a 32° angle is between two sides of 12 feet
and 16 feet. What is the length of the third side, in feet?
Round to one decimal place.
Answer:
please check photo for detailed analysis
James spent $98 at the mall. He purchased a pair of shoes for $55 and 2 t-shirts. Write an equation to show how much each t-shirt cost.
Type an equation that matches the situation. Use x for the variable.
Helpppppp plssss!!!!!!
Incorrect:
A-Reflection across line AC
B-Reflection across line BD
C-vertical translation
Correct:
D-Rotation about the center of the square
Thank you so much Please consider brainliest! <3
the diameter of fishing line varies. Fishing lines can have a diameter as small as 2 x 102 and as large
Answer:
We know that:
small diameter = 2 * 10^-2 in
large diameter = 6 * 10^-2 in
We want to know how many times larger is the thin diameter compared to the large one.
We will do this as follows:
large diameter = k * small diameter
where k is the number of times that we want to find
6 * 10^-2 = k * 2 * 10^-2
k = (6 * 10^-2) / (2 * 10^-2)
k = 3
This means that the large diameter is 3 times the small one.
Step-by-step explanation:
Find the area of a regular pentagon with a radius of 9 yds. show all six steps.
Answer:
192.6 square yards
Step-by-step explanation:
The area of a regular pentagon can be found using the formula for any regular polygon.
A = (n/2)r²·sin(360°/n) . . . . radius r, n sides
For a pentagon, the number of sides is 5, so this becomes ...
A = 2.5r²·sin(72°)
__
Using the given value of radius, the area is ...
A = 2.5(9 yd)²·sin(72°) = 2.5 · 81 · 0.951057 yd²
A ≈ 202.5 · 0.951057 yd²
A ≈ 192.589 yd²
The area of the pentagon is about 192.6 square yards.
_____
Additional comment
We're not sure what "six steps" you're supposed to follow. The necessary steps appear to be ...
determine an appropriate area formula for the given informationevaluate the formula for the given dimensionsHere, the formula for a pentagon can be simplified somewhat by precomputing the value of 2.5×sin(72°) ≈ 2.37764129074. Then the formula for the area is ...
A = 2.37764129074·r² . . . . . area of regular pentagon with radius r
PLEASE HELP ITS A MATH PROBLEM !!! A smart phone costs $800 and loses 2/5 of its value every year.
How much is the phone worth after 3 years?
Question options:
$69.12
$288.00
$798.80
$172.80
* i will award brainlist
Answer:
$172.80
Step-by-step explanation:
The phone cost $800
Decreases by 2/5 every year. So the cost would be 3/5 (instead of doing 800 - 800 *2/5 its easier to just do 800*3/5)
Here is a equation for this question:
[tex]800* (\frac{3}{5})^{t}[/tex]
t = time in years
So we can plug in 3 for t
[tex]800* (\frac{3}{5})^{3}[/tex]
[tex]800* (\frac{27}{125})[/tex]
[tex]172.8[/tex]
So the phone is now worth $172.80
Hope this helps! :)
Which of the following correlation coefficients represents the weakest correlation?
A. 0.3
B.-0.1
C.0.4
D.-0.9
i barely remember 7th grade stuff :')))
i am practicing for the TSI so please explain! <3 TY!
The correlation coefficient that represents the weakest correlation amongst the given options is -0.1.
What is correlation?Correlation is a statistical measure used to measure the relationship that exists between two variables. A value of one represents a perfect correlation. A value of zero signfies that the variables have no relationship.
So, the correlation coeffieicent with a value closest to zero would have the weakest correlation.
To learn more about negative correlation, please check: https://brainly.com/question/27246345
8(p-6) > 4(p-4)
How do I solve?
Answer:
p > 8
Step-by-step explanation:
8p - 48 > 4p - 16
plus 48 on both sides
8p > 4p + 32
minus 4p on both sides
4p > 32
divide 4 on both sides, 32 ÷ 4 = 8, so,
p>8
Answer:
P > 8 ??? I don't know if this is right and if its not then sorry lol
Step-by-step explanation:
Multiply 8(p-6) and 4(p-4)
You will get 8p - 48 > 4p - 16
Then add 48 to -16
Then you will get 8p > 4p + 32
Then subtract 4p from 8p
Then you will get 4p > 32
Then divide 4 from 4p and 32
Then you will get p > 8
6. How many real-number solutions does the equation have?
0=3x62+18x+27
a. one solution
b. two solutions
c. no solutions
d. infinitely many solutions
I think it's A but I'm not too sure...
Answer:
well for starters
the answer you get when you factor it out is 3(x+3)(x+3)
i know that would mean x=-3 but i dont know how the big 3 would effect anything. hope this helps
What is the area of this right triangle?
36
ft
2
36 ft 2
54
ft
2
54 ft 2
108
ft
2
108 ft 2
135
ft
2
I think it is exactly 90ft
Normal Distributions
According to the College Board, the probability that a student forgets to bring their ID with them when they take their SAT is 3%. A random sample of
500 students was selected. Let p-hat be the proportion of the sample which forgot their ID.
1. What is the mean of the sampling proportion?
2. What is the standard deviation of the sampling proportion?
(Round to the nearest thousandth. )
The mean of the sampling proportion is 0.03 and the standard deviation of the sampling proportion is 0.008 if the probability that a student forgets to bring their ID with them when they take their SAT is 3%. and a random sample of 500 students was selected.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
We have:
p = 0.03
n = 500 students
[tex]\rm {\hat p} - Normal[/tex]
So the mean:
[tex]\rm \mu _\hat p \ = \ p \ = \ 0.03[/tex]
For standard deviation:
[tex]\rm \sigma_p = \sqrt{\frac{pq}{m} }[/tex]
q = 1 - p = 1 - 0.03 = 0.97
[tex]\rm \sigma_p = \sqrt{\frac{0.03\times 0.97}{500} }[/tex]
[tex]\rm \sigma_p = 0.008[/tex]
Thus, the mean of the sampling proportion is 0.03 and the standard deviation of the sampling proportion is 0.008 if the probability that a student forgets to bring their ID with them when they take their SAT is 3%. and a random sample of 500 students was selected.
Learn more about the standard deviation here:
brainly.com/question/12402189
#SPJ1
///////////////////////////////////////////////////
Answer:
x = 27°
Step-by-step explanation:
[tex]m < 2 = 2\% \times 180 \\ = 36 \\ \\ m < 2 = 65\% \times 180 \\ = 117 \\ \\ [/tex]
Now,
[tex]x = 180 - (36 + 117) \\ \\ x = 180 - 153 \\ \\ x = 27[/tex]
What conjecture can you make about the tangent of complementary angles?
Answer:
Step-by-step explanation:
If the sum of two angles is one right angle or 90°, then one angle is said to be complementary of the other. Thus, 25° and 65°; θ° and (90 - θ)° are complementary to each other.
Suppose a rotating line rotates about O in the anti-clockwise sense and starting from its initial position
AABC is translated 4 units to the left and 8 units up. Answer the questions to find the
coordinates of A after the translation.
1. Give the rule for translating a point 4 units left and 8 units up. (2 points)
Answer:
(3, 13)
Step-by-step explanation:
Original coordinates of A
A = (7, 5)After translating left 4 units
A' = (7 - 4, 5)A' = (3, 5)After translating up 8 units
A'' = (3, 5 + 8)A'' = (3, 13)The diagram shown is two intersecting lines. The measure of 5 is 47°.
Please solve this on paper! I'll give brainliest to the best explanation. Thank you so much <3
Answer:
The measure of angle 7 is 47°
The value of x = 69
Step-by-step explanation:
(a) The measure of angle 7 is also 47° { therefore angle 5 angle 7 are vertically opposite angles so they are equal }
(b) if the angle 6 is represented by (2x-5) so the equation will be (2x-5) + angle 5 = 180° { linear pair}
(c)
=> 2x-5+47 = 180
=> 2x + 42 = 180
=> 2x = 180 -42
=> 2x = 138
=> x = 138/2
=> x = 69
Answer:
See below ↓↓↓
Step-by-step explanation:
(a) ∠7 = ∠5 (vertically opposite angles)
∠7 = 47°It is equal to 47 degrees, because the when a transversal cuts through a straight line, the angles which lay opposite to each other are equal(b) ∠5 and ∠6 form a line, so their sum is equal to 180°, which is the angle of a straight line. Therefore, our equation :
47 + 2x - 5 = 180(c) Solving for x :
2x + 42 = 1802x = 138x = 69°find the greatest common factor of 54 and 72. use a model to justify your answer
what is the best game that you think of
Answer:
The best game I can think of is the game of life
Step-by-step explanation:
Simply because its fun to have different experiences each time you play and can chose whatever
Answer:
Mobile- Animal crossing pocket camp
Step-by-step explanation:
I love this game :3
It's really relaxing and a fun way to pass a few minutes. -Crispin