cos (theta) = √21/5
Step-by-step explanation:
sin (theta) = 2/5
(sin (theta))^2 = 4/25
4/25 + (cos (theta))^2 = 1
(cos (theta))^2 = 1 - 4/25 = 21/25
cos (theta) = √21/5
55 points see attachment below
Answer:
f(3) = -20
Step-by-step explanation:
To find the value of a function, substitute the number for the variable and do the arithmetic.
f(x) = -2x^2 +x -5 . . . . . . given
f(3) = -2(3^2) +(3) -5 . . . . function value for x = 3
f(3) = -2(9) +3 -5 = -18 +3 -5
f(3) = -20
8 Select all of the
correct forms of 806,510.
800 + 6 + 500 + 10
eight hundred
six thousand, five hundred ten
800,000
+ 6,000 + 500 + 10
D eight hundred six, five ten
E 80,000 + 6,000 + 500 + 10
3/4 fraction plus 7/12 fraction - (-4)
I WILL GIVE U 40 POINTS
answer:
[tex]\frac{-23}{6}[/tex] or -3.8333 (repeating)
How many solutions does the system have? You can use the interactive graph below to find the answer. \begin{cases} y=x+1 \\\\ y=2x-5 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=x+1 y=2x−5 Choose 1 answer: Choose 1 answer: (Choice A) A Exactly one solution (Choice B) B No solutions (Choice C) C Infinitely many solutions
Answer:
Exactly 1 solution
Step-by-step explanation:
The equations are both in slope intercept form: y=mx+b We can use the y-intercept and slope to identify points on each line.
The line given by the first equation y= 1x+1 has a y-intercept of (0, 1) and a slope of 1, so another point on that line is (0 + 1, 1 + 1)= (1, 2).
Now we have two points to graph this line. In a similar manner, we will find that the line given by y=2x-5 passes through (0, -5) and (0 + 1, -5 + 2)= (1, -3). We can use those lines to graph the points.
Upon graphing our system of equations, we see that the lines intersect exactly once.
Since the lines intersect exactly once, the system has exactly one solution.
The system of equation has exactly one solution.
What is the system of equation?Simultaneous equations are any equations with the same number of unknowns that may be solved at the same time. The system of equations is a simultaneous equation.
Given, the system of equation;
y = x+1 { equation 1}
y = 2x-5 { equation 2}
Subtracting equation 2 to equation 1;
2x-x = 5+1
x = 6
And y = 7
The solution set is (6,7).
Therefore, the system of equation has unique solution.
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Describe the the cross section
A.Square
B.Pentagon
C.Trapezoid
D.Cube
Answer:
A. Square
Step-by-step explanation:
Hmm yes looks very much like a square if you ask me. This is right!!
Tom and his sister both decided to get part-time jobs afterschool at competing clothing stores. Tom makes $15 an hour and recieves $3 in
commission for every item he sells. His sister makes $7 an hour and recieves $5 in commission for every item she sells. How many items
would each of them have to sell to make the same amount of money in an hour?
Answer:
Each of them would sell four items.
Step-by-step explanation:
Tom - 15+3+3+3+3= $27
His sister - 7+5+5+5+5= $27
Clamentine and jake make cookies for the school bake sale. Clamentine baked 72 cookies. Jake baked twice as many as clementine. How many cookies did they bake altogether?
Answer:
Jake has 144 cookies.
Step-by-step explanation:
Let's say Clementine is x.
Clementine: x
Jake: 2x
Now, let's substitute x with 72 since the number is given.
This means that Jake has 72 * 2 cookies which are 144.
3х + 4y = 5
6х + 8y = 10
Use a polar coordinate system to plot the point with the given polar coordinates. Then find another representation (r,0) of this point in which:
(a) r> 0, 2x <0 < 4x.
(b) r<0,0<0<2R.
(c) r> 0, -2x <0<0.
(10,pi/3)
Step 1: Plotting the Point
Make a polar coordinate system.
It looks like this ( look at the first photo)
Step 2: Graph the polar function
r=10.
Here since our first coordinate is 10, our radius of our point will be 10.
This basically means we will have a circle with a radius of 10. ( look at the second photo).
Step 3: Look for the angle pi/3,
So that how u graph polar coordinates.
Next, a polar form can have multiple representations.
a. Here we want a radius of to be positve, so our r will stay 10.
We want our angle to lie between 2 pi and 4 pi.
So we just add 2 pi to pi/3.
[tex] \frac{\pi}{3} + 2\pi = \frac{\pi}{3} + \frac{6\pi}{3} = \frac{7\pi}{3} [/tex]
So another angle is
[tex](10, \frac{7\pi}{3} )[/tex]
B. We want r to be negative so
[tex]10( - 1) = - 10[/tex]
And we want our angle to be in between 0 and 2 pi. so we add pi to our angle.
[tex] \frac{\pi}{3} + \pi = \frac{\pi}{3} + \frac{3\pi}{3} = \frac{4\pi}{3} [/tex]
So our new representation is
[tex]( - 10, \frac{4\pi}{3} )[/tex]
C. Finally, we want our r to be positvr and our angle to be negative and in between -2pi and 0.
So we just subtract 2 pi.
[tex] \frac{\pi}{3} - 2\pi = \frac{\pi}{3} - \frac{6\pi}{3} = - \frac{5\pi}{3} [/tex]
So our new representation is
[tex](10, - \frac{5\pi}{3}) [/tex]
1. If a triangle of area 95 square units has a height of length 19 units, calculate
the base of the triangle.
Choose the correct simplification of (3xy6)2(y3)3. 9x2y21 6x2y21 9x2y14 6x2y14
Answer:14
Step-by-step explanation: i did the math probly wrong but i made an educated guess
Movies at the rental store are $3.75 each. Snacks and drinks are $1.89 each. Round each amount to the nearest dollar to estimate the cost to rent 3 movies and buy popcorn, a soda, and a candy bar.
Answer:
$14.00
Step-by-step explanation:
First you round 3.75 to 4.00 because 7 is greater than 5 so it would turn the 3 to 4 than add the zeros it's 4.00. Second You multiply by three so 4.00 × 3 you will get 12.00. Than you round 1.89 to 2.00 because 8 is greater than 5 so it would turn to the 1 to the 2 than add the zeros it's 2.00. Finally you add them together and get $14.00
True or False: A scalene obtuse triangle has sides of all different lengths, and it
contains one obtuse angle.
a. True
b. False
Answer:
All three sides and angles are different in measurement.
Step-by-step explanation:
Sixth-grade students were asked, "What grade are you in?" Explain why this is not a statistical question.
Isabel works for a company that makes toys. She is trying to figure out what types of toys kids enjoy
playing with most. She started with a survey that asks about whether kids liked dolls or trains. She
surveyed 80 kids. Of the kids who don't like dolls, 30% more kids like trains than don't like trains.
out the rest of his table.
The type of toy the kids enjoyed the most is the doll.
Evaluation of toys enjoyed mostThe total number of kids evaluated = 80
The percentage of kids that like train = 30%
The percentage of kids that like doll = 70%
30% of 80 = 30/100×80
= 2400/100
= 24
70% of 80 = 70/100×80
= 5600/100
= 56
Therefore, the type of toy the kids enjoyed the most is the doll.
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Fu Da spent a whole day traveling. 5/8 of the journey was spent by the airplane and 1/4 of the remainder was by the train. He spent 6 3/4 h on the bus journey.
a) How long did Fu Da spend on the train journey?
b) How much longer did Fu Da spend on the airplane than on the bus?
Answer:
A) 13.5 Hours
B) 27 Hours
Step-by-step explanation:
So the total journey was 54 hours.
5/8 of that would be 33 and 3/4 hours or how long the airplane journey was.
1/4 would be 13 and a half hours or how long the train journey was
And the remaing amount was the 6 3/4 hours which was the bus journey
So the answers are Fu Da spent 13 and a half hours on the train journey and he spent 27 more hours on the plane than the bus
A bag contains 5 red marbles, 6 blue marbles and 4 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that all three marbles drawn will be blue?
Answer:
4.4%
Step-by-step explanation:
The overall probability is the product of the individual probabilities.
Total number of marbles: 15
Original number of blue marbles: 6
First drawing (6 blue and 15 total):
p(blue) = 6/15 = 2/5
Second drawing (5 blue and 14 total):
p(blue) = 5/14
Third drawing (4 blue and 13 total):
p(blue) = 4/13
p(blue followed by blue followed by blue) = 2/5 × 5/14 × 4/13 = 40/910 = 4/91
p(blue followed by blue followed by blue) = 4/91 = 0.043956... = 4.4%
CAN SOMEBODY SOLVE THE EQUATION
Answer:
Step-by-step explanation:
Given
y = x^2 + 10x + 21
Complete the square
y = x^2 + 10x + 21 Put brackets around the first 2 terms
y = (x^2 + 10x) + 21 Take 1/2(10) and square it. Add inside the brackets.
y = (x^2 + 10x + 5^2) + 21 Subtract 5^2 after 21
y = (x^2 + 10x + 25) + 21 - 25 Make (x^2 + 10x + 25) into a perfect square.
y = (x + 5)^2 - 4
Answer: (x + 5)^2 - 4
A. Transform F using the rule (x, y) → (-x, y)
B. Describe the transformation precisely.
C. Does the transformation result in a a congruent figure?
Answer:
A: Use these points to plot the shapes reflection (-3,4) (-3,6) (-5,6) (-7,4)
B: The transformation would be described as a reflection over the y axis
C: The transformation does result in a congruent figure because the shape doesn't change in size or shape and in length or width
Step-by-step explanation:
So our plots from the figure are: (3,4) (3,6) (5,6) (7,4)
This rule (x, y) → (-x, y) is used for the type of transformation that is a reflection but over the y axis.
So using the rule (x, y) → (-x, y) are new points would be:
(-3,4)
(-3,6)
(-5,6)
(-7,4)
count the number of cubic units to find the volume of the following rectangular prisms and cube
The volume of the rectangular prism is the number of cubes in it
The calculated volumes of the rectangular prisms are 32 and 36 unit cubes, respectively.
How to determine the volumes of the prisms?The volume of a rectangular prism is:
Volume = Length * Width * Height
From the question, we have the following prisms:
4 units by 4 units by 2 units3 units by 4 units by 3 unitsSo, the volumes are:
Volume= 4 * 4 * 2
Volume= 32
Volume= 3 * 4 * 3
Volume= 36
Hence, the volumes of the rectangular prisms are 32 and 36 unit cubes, respectively.
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Which scenario shows an example of conditional probability?
a
The probability of getting heads when flipping a coin five times
b
The probability of winning a raffle
c
The probability of pulling a red marble out of a bag that contains one red marble and nine blue marbles
d
The probability of it raining when it is cloudy
Answer:
Id say D but im noot 100% positive so im sorry if its wrong
Step-by-step explanation:
A donut store has 11 different types of donuts. You can only buy a bag of 3 of them, where each donut has to be of a different type from the rest. How many different bags of 3 can you make
Answer:
[tex]165[/tex].
Step-by-step explanation:
Since repetition isn't allowed, there would be [tex]11[/tex] choices for the first donut, [tex](11 - 1) = 10[/tex] choices for the second donut, and [tex](11 - 2) = 9[/tex] choices for the third donut. If the order in which donuts are placed in the bag matters, there would be [tex]11 \times 10 \times 9[/tex] unique ways to choose a bag of these donuts.
In practice, donuts in the bag are mixed, and the ordering of donuts doesn't matter. The same way of counting would then count every possible mix of three donuts type [tex]3 \times 2 \times 1 = 6[/tex] times.
For example, if a bag includes donut of type [tex]x[/tex], [tex]y[/tex], and [tex]z[/tex], the count [tex]11 \times 10 \times 9[/tex] would include the following [tex]3 \times 2 \times 1[/tex] arrangements:
[tex]xyz[/tex].[tex]xzy[/tex].[tex]yxz[/tex].[tex]yzx[/tex].[tex]zxy[/tex].[tex]zyx[/tex].Thus, when the order of donuts in the bag doesn't matter, it would be necessary to divide the count [tex]11 \times 10 \times 9[/tex] by [tex]3 \times 2 \times 1 = 6[/tex] to find the actual number of donut combinations:
[tex]\begin{aligned} \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}[/tex].
Using combinatorics notations, the answer to this question is the same as the number of ways to choose an unordered set of [tex]3[/tex] objects from a set of [tex]11[/tex] distinct objects:
[tex]\begin{aligned}\begin{pmatrix}11 \\ 3\end{pmatrix} &= \frac{11 !}{(11 - 3)! \times 3 !} \\ &= \frac{11 !}{8 ! \times 3 !} \\ &= \frac{11 \times 10 \times 9}{3 \times 2 \times 1} = 165\end{aligned}[/tex].
Hi pls guys uf you know pls help me this is my last chance ok this theta pls guys help me
The table shows the colors of the cars sold from a dealership over the last month
Based on this information, which prediction about next month's car sales is
most reasonable?
Answer:
The anser is B
Step-by-step explanation:
There are twice as many silver cars as blue cars
12 x 2 = 24 24 / 12 = 2
Which data set contains an outlier?
{30, 31, 31, 32, 34, 37}
{11, 12, 12, 12, 13, 13, 14, 14}
{6.1, 6.8, 7.3, 8, 9.1, 9.5}
{14, 15, 16, 20, 22, 25, 51}
Answer:
The last one {14,15,16,20,22,25, and 51}
Step-by-step explanation:
This set shows an outlier because 51 is a huge jump from 25 which causes it to be the outlier.
The data set {14,15,16,20,22,25,51} contains an outlier. So, option D is correct.
What is an outlier:An outlier is an extreme value in a data set that is either much larger or much smaller than all the other values.A data point is an outlier if it is over 1.5 times the IQR below the first quartile [tex](Q_1)[/tex] or 1.5 times the IQR above the third quartile [tex](Q_3)[/tex].How to calculate an outlier:To calculate an outlier for a given data, arrange the data in the ascending orderSeparate the data into two sections or groupsFind the medians for each group. The median for the first group is said to be the first quartile [tex](Q_1)[/tex] and the median for the second group is said to be the third quartile [tex](Q_3)[/tex]Find the difference between them by [tex](Q_3)[/tex] minus [tex](Q_1)[/tex] which is called the interquartile range (IQR).Then, if the data points are over 1.5 times the IQR below the first quartile [tex](Q_1)[/tex] or 1.5 times the IQR above the third quartile [tex](Q_3)[/tex] is said to have an outlier.Calculating the outlier for the given data sets:Option A:
{30, 31, 31, 32, 34, 37}
There is an even number of data points.
Diving into 2 groups- {30,31,31} and {32,34,37}
So, [tex]Q_1[/tex]=31 and [tex]Q_3[/tex]=34
Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=34-31=3
Then 1.5×3=4.5
[tex]Q_1[/tex]-4.5=31-4.5=26.5
[tex]Q_3[/tex]+4.5=34+4.5=38.5
So, for this data set, there are no outliers either below or above.
Option B:
{11,12,12,12,13,13,14,14}
There is an even number of data points.
Diving into 2 groups- {11,12,12,12} and {13,13,14,14}
So, [tex]Q_1[/tex]=[tex]\frac{12+12}{2}=12[/tex] and [tex]Q_3[/tex]=[tex]\frac{13+14}{2}=13.5[/tex]
Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=13.5-12=1.5
Then 1.5×1.5=2.25
[tex]Q_1[/tex]-2.25=12-2.25=9.75
[tex]Q_3[/tex]+2.25=13.5+2.25=15.75
So, for this data set, there are no outliers either below or above.
Option C:
{6.1,6.8,7.3,8,9.1,9.5}
There is an even number of data points.
Diving into 2 groups- {6.1,6.8,7.3} and {8,9.1,9.5}
So, [tex]Q_1[/tex]=6.8 and [tex]Q_3[/tex]=9.1
Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=9.1-6.8=2.3
Then 1.5×2.3=3.45
[tex]Q_1[/tex]-3.45=6.8-3.45=3.35
[tex]Q_3[/tex]+3.45=9.1+3.45=12.55
So, for this data set, there are no outliers either below or above.
Option D:
{14,15,16,20,22,25,51}
There is an odd number of data points.
Diving into 2 groups- {14,15,16,20} and {20,22,25,51}
So, [tex]Q_1[/tex]=[tex]\frac{15+16}{2}=15.5[/tex] and [tex]Q_3[/tex]=[tex]\frac{22+25}{2}=23.5[/tex]
Then [tex]Q_3[/tex] - [tex]Q_1[/tex]=23.5-15.5=8
Then 1.5×8=12
[tex]Q_1[/tex]-8=15.5-8=3.5
[tex]Q_3[/tex]+8=23.5+8=35.5
In this data set, some values are above the value of 35.5 (35.5<51).
So, this data set is said to have outliers.
Therefore, Option D is correct.
The required data set is {14,15,16,20,22,25,51}.
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The formula below is used to convert a tempreture in degrees Farenheit,F to a tempreture in degrees Celsuis ,C.C = 5/9 (f-32) What is the tempreture in degrees celsuis that is equivalent to a tempreture of 40f?
Answer:
4.4 degrees C.
Step-by-step explanation:
C = 5/9 (F - 32)
When F = 40:
C = 5/9( 40 - 32)
= 5/9 * 8
= 40/9
= 4.4 degrees C,
There are three different size bags of the same dog food shown below with the price for each bag. Based on the price per ounce, order the bags from
least expensive to most expensive.
= 32oz for $7 37
= 48oz for $9.50
= T2oz for $17.99
Answer:addaddition
Step-by-step explanation:
just adddd all
A piece of machinery depreciates $7000 the first year,
$6800 the second year, and $6600 the third year. If the
rate of depreciation is constant, what is the amount of
depreciation of the piece of machinery in the sixth year?
Answer:
6000 in the 6th year 39000 total
Step-by-step explanation:
depreciates 200 per year
7000 6800 6600 6400 6200 6000
How many distinguishable permutations are there of the letters in BUBBLE?
There are 6 letters, hence 6! = 720 total permutations of BUBBLE. But there are 3 indistinguishable copies of B, so we divide by the number of ways we can rearrange them, 3! = 6. Then there are
6!/3! = 720/6 = 120
distinguishable permutations of BUBBLE.
Someone please help me!!
98
41
A. Isosceles
B. Scalene
C. Acute
D. Right
E. Obtuse
F. Equilateral
A) Isosceles
E) Obtuse
Step-by-step explanation:Ways to Define a Triangle
Triangles can be defined in two ways: by angles and by sides. Equilateral, isosceles, and scalene are based on side length. Acute, right, and obtuse are based on angle measurements. Triangle may only fall under one category for side length and one for angle measure (2 categories total).
Side Length
First, let's define equilateral, isosceles, and scalene.
Equilateral - All 3 sides of the triangle are congruent (equilateral are always acute angles).Isosceles - 2 of the sides are congruent.Scalene - There are no congruent sides; each side has a different length.The triangle above has 2 congruent sides as shown by the tick marks on the left and right sides. This means the triangle is isosceles.
Angle Measurements
Now, let's define acute, right, and obtuse.
Acute - All 3 angles are less than 90 degrees; all angles are acute.Right - 1 of the angles is exactly 90 degrees; it has a right angle.Obtuse - 1 of the angles is greater than 90 degrees; there is an obtuse angle.The largest angle in the triangle is 98 degrees, which is obtuse. This means that the triangle is obtuse.
Please help me Im quite confused!!
Answer:
B
Step-by-step explanation:
As stated in the problem x is the number of hours that he works.
x = 6y
All of the other answers establish y as 6, but B is the only answer that has 6 Infront of y (Pretty much multiplying it)
If you were to plug 6 into Y you would get 6(6)
6 times 6 equals thirty six.
x ≠ 36