Answer:
Simone is 16 and Olivia is 12
Step-by-step explanation:
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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How much was made if 900 raffle tickets were sold at 5 for $20?
Answer:
$3600
Step-by-step explanation:
900/5=180
180*20=3600
Answer:
$3600
Step-by-step explanation:
Since they are being sold 5 at a time, divide 900 by 5 first to get 180. Then, since every 5 are worth 20$, multiply 20 by 180 to get $3600.
1. If a triangle of area 95 square units has a height of length 19 units, calculate
the base of the triangle.
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)
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
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.
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:
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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Natalia is a girl in a math class with a total of 11 girls and 9 boys. If the teacher selects one student at random to go to the board, what is the probability that Natalia will be selected?
A box of pens contains a total of 28 pens. If 4 of the pens are red and the rest are blue, what is the probability that the first pen pulled from the box will be red?
Katelyn has a package of 24 jelly beans. There are 9 cherry jelly beans in the package. What is the probability that the first jelly bean Katelyn pulls out of the package will be a cherry jelly bean?
A marble is drawn at random from a bag containing 2 blue marbles, 3 yellow marbles, and 7 orange marbles. What is the probability that the marble is not yellow and not blue?
(Five Stars & Thanks to whoever answers first)
Answer:
First, let's find how many students there are in total:
11 girls + 9 boys
= 20 students.
Out of those 20 students, we are trying to find the probability if Natalia will be selected first.
There is only one Natalia.
So, out of those students, the probability of selecting Natalia is a:
1/20 probability
(if wanted to convert into a percentage):
1/20 x 100
= 5% probability
Since we already know there are 28 given pens in total and 4 of them are red pens, there is a:
4/28 chance of selecting a red pen which can be simplified to a 1/7 probability.
(if wanted to convert into a percentage):
1/7 x 100
= 14% probability
Since we already know there are 24 jelly beans in total and 9 of them are cherry beans, there is a:
9/24 chance/probability of selecting a cherry jelly bean.
(if wanted to convert into a percentage):
9/24 x 100
= 37.5% probability
Let's first figure out how many marbles there are in total.
2 + 3 + 7
= 12 marbles in total.
Now let's exclude the marbles that are blue and yellow, leaving us with 7 orange marbles.
So the probability of selecting a marble that isn't blue/yellow is a:
7/12 probability
(if wanted to convert into a percentage)
7/12 x 100
= 58% probability
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
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
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
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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3/4 fraction plus 7/12 fraction - (-4)
I WILL GIVE U 40 POINTS
answer:
[tex]\frac{-23}{6}[/tex] or -3.8333 (repeating)
Evaluate the expression. – 5×(6+ – 5 1/ 2 )– – 1 4 /5. Write your answer as a fraction or as a whole or mixed number.
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
3х + 4y = 5
6х + 8y = 10
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:
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!!
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.
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,
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]
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].
Sixth-grade students were asked, "What grade are you in?" Explain why this is not a statistical question.
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
PLEASE HELP! TIMED!
Find the perimeter of a triangle with the measurements of 5cm, 9cm, and 11cm.
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.
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
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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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