To find the time it will take for a train
to travel from Springfield to Franklin,
d
where d
use the expression s,
represents distance and s represents
speed.
Find the time if the train travels
at a speed of 79
miles per
hour.

A) Isosceles

E) Obtuse

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.

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.

The largest angle in the triangle is 98 degrees, which is obtuse. This means that the triangle is obtuse.

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]

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:

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].

Answer:

translate down 6 units and left 3 units

answer:

[tex]\frac{-23}{6}[/tex] or -3.8333 (repeating)

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.

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

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.

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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Answer:

All three sides and angles are different in measurement.

Step-by-step explanation:

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.

Answer:

X=-1 or x=1/3

Step-by-step explanation:

That is the explanation in the photo

Answer:14

Step-by-step explanation: i did the math probly wrong but i made an educated guess

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,

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.

Answer:

A. Square

Step-by-step explanation:

Hmm yes looks very much like a square if you ask me. This is right!!

The type of toy the kids enjoyed the most is the doll.

The 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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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

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.

The volume of a rectangular prism is:

Volume = Length * Width * Height

From the question, we have the following prisms:

So, 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.

Read more about volumes at:

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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

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)

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.

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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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

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

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