Let $a_1 a_2 a_3 \dotsb a_{10}$ be a regular polygon. A rotation centered at $a_1$ with an angle of $\alpha$ takes $a_4$ to $a_8$. Given that $\alpha < 180^\circ$, find $\alpha,$ in degrees

I'll do the first two questions of each activity to get you started. The remaining unanswered questions will follow similar steps compared to the other questions in the same activity group.

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Activity 5, Problem 1

To find the mean, we first add up the values

4+8+2+8+5+9 = 36

Then we divide over n = 6 because there are 6 values in this data set.

36/n = 36/6 = 6

=======================================================

Activity 5, Problem 2

Follow the same idea as the previous problem.

Add the values:  9+8+8+13+12 = 50

Divide by the number of values: 50/n = 50/5 = 10

=======================================================

Activity 6, Problem 1

The median is the middle-most number. Think of a median of a highway or freeway.

In order to find the median, we first need to sort the data values from smallest to largest.

The original set {7,3,9,9,2,5,8} sorts to {2, 3, 5, 7, 8, 9, 9}

If we erased the first and last items, we get this smaller subset

{3, 5, 7, 8, 9}

repeat again to get

{5,7,8}

At this point its clear the middle most value is 7

But if you wanted, you could cross the first and last values from the list to end up with {7}

=======================================================

Activity 6, Problem 2

We could do the same trick as the previous problem, but I'll use a slightly different route this time.

We'll need to sort {10,8,4,11,9} into {4, 8, 9, 10, 11}

There are n = 5 items in that set. The middle slot would be at slot n/2 = 5/2 = 2.5 = 3

The value 9 is in slot 3 of the sorted items.

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Activity 7, Problem 1

The mode is the most frequent value of a set. It repeats the most often.

The set {5,6,7,3,5,4} sorts to {3,4,5,5,6,7}

The value "5" shows up the most. It shows up twice when everything else shows up exactly once only.

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Activity 7, Problem 2

Using the same idea in the previous problem, the set {7,4,11,9,7,3} has the mode 7 because it shows up the most of any other value.

Here's the sorted set: {3,4,7,7,9,11}

Sorting is optional with finding the mode in contrast to being mandatory when it comes to finding the median.

3 gallons => 54 miles

so

1 gallon => 54 : 3 = 18 miles

then

8 gallons => 18x 8= 144 miles

Answer:

2.744 cubic milimeters

Step-by-step explanation:

Here,

Length ( l ) = 1.4 mm

Base ( b ) = 1.4 mm

Height ( h ) = 1.4 mm

l = b = h = 1.4 mm = a

To find : Volume

This shape is a cube.

Formula : -

Volume of cube = a³

Volume of cube

= 1.4³

= 1.4 x 1.4 x 1.4

= 2.744 cubic milimeters

[tex] \huge\fbox\orange{ANSWER} [/tex]

[tex] \mathsf \purple{v = l \times w \times h}[/tex]

[tex] \mathsf \pink{v = 1.4 \times 1.4 \times 1.4}[/tex]

[tex] \mathsf \purple{v = 2.744 {mm}^{3} }[/tex]

2.74 cubic millimeters

Answer:

16.4 units to the nearest tenth.

Step-by-step explanation:

sin 66 = 15 / x

x *  sin 66 = 15

x = 15 / sin 66

= 16.4196

Done!

Answer:

  isosceles obtuse triangle

Step-by-step explanation:

The attached graph shows a plot of the three lines.

The triangle is an isosceles obtuse triangle in the 2nd quadrant.

_____

It is convenient to let a graphing calculator plot these lines. If you're going to plot them by hand, it usually works best to choose values of the variables for the variable that has the largest coefficient (3 in two of the equations). That way, you're not trying to plot coordinates that contain fractions.

There are 1.5625 grams of the radioactive substance that would remain after 60 seconds.

The exponent of a number represents the total time required to multiply that number. 8 8 8 may be stated as 83 since 8 is multiplied by itself three times. In this case, 3 is the 'exponent' or 'power' that indicates how many times 8 is multiplied by itself, and 8 is the 'base' that represents the integer being multiplied.

The exponent is given as:

y = a (1 - r)ˣ

As per the question, we have

a = 100, and r = 0.50 and x = 6

Substitute the known values in the above formula, and we get

y = 100 × (1-0.50)⁶

y = 100 × (0.50)⁶

y = 100 × 0.015625

Apply the multiplication operation, a

y = 1.5625

So, after 60 seconds, 1.5625 grams of the radioactive substance would remain.

Learn more about the exponent here:

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Answer:

x coordinate is +3 and y coordinate is +1

Step-by-step explanation:

just count three squares right and one square down from D

Answer:

[tex] (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656{x}^{} + 46656 [/tex]

Step-by-step explanation:

we want to solve the following binomial:

[tex](x + 6 {)}^{6} [/tex]

There is a handy way to expand powers of binomials which is known as binomial theorem . and it describes the algebraic expansion of powers of a binomial. binomial theorem is given by

[tex] \displaystyle (a + b {)}^{n} = \sum _{k = 0 }^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]

comparing (x+6)⁶ to (a+b)ⁿ , we get

now substitute them on the formula which yields:

[tex] \displaystyle (x + 6 {)}^{6} = \sum _{k = 0 }^{n} \binom{6}{k} {x}^{6 - k} \cdot {6}^{k} [/tex]

converting the summation notation into sum yields:

[tex] \displaystyle (x + 6 {)}^{6} = \binom{6}{0} {x}^{6 - 0} \cdot {6}^{0} + \binom{6}{1} {x}^{6 - 1} \cdot {6}^{1} + \binom{6}{2} {x}^{6 - 2} \cdot {6}^{2} + \binom{6}{3} {x}^{6 - 3} \cdot {6}^{3} + \binom{6}{4} {x}^{6 - 4} \cdot {6}^{4} + \binom{6}{5} {x}^{6 - 5} \cdot {6}^{5} + \binom{6}{6} {x}^{6 - 6} \cdot {6}^{6} \\ \implies(x + 6 {)}^{6} = \binom{6}{0} {x}^{6 } \cdot 1 + \binom{6}{1} {x}^{5} \cdot {6} + \binom{6}{2} {x}^{4} \cdot 36+ \binom{6}{3} {x}^{3} \cdot 216 + \binom{6}{4} {x}^{2} \cdot 1296+ \binom{6}{5} {x}^{} \cdot 7776+ \binom{6}{6} {x}^{0} \cdot 46656 \\ \implies(x + 6 {)}^{6} = 1 \cdot {x}^{6 } \cdot 1 + 6 \cdot{x}^{5} \cdot {6} + 15 \cdot {x}^{4} \cdot 36+ 20 \cdot {x}^{3} \cdot 216 + 15 \cdot{x}^{2} \cdot 1296+ 6 \cdot {x}^{} \cdot 7776+ 1 \cdot {x}^{0} \cdot 46656 \\ \implies \boxed{ (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656 {x}^{} + 46656 }[/tex]

and we're done!

Answer:

88

Step-by-step explanation:

86 is 98% of 87.755102040816 which rounded to the nearest whole number is 88.

Answer:

x = -1

Step-by-step explanation:

"An undefined slope" indicates that the line in question is a vertical one.  The coordinate x = -1 tells us that the equation of the line is just that:  x = -1.

Step-by-step explanation:

please mark me as brainlest

Answer:

(x + 1)(x - 6)

Step-by-step explanation:

We can factor x^2 - 5x - 6 using grouping:

Hope this helps!!

Answer:

[tex]y = (-3/2)\, x + (-2)[/tex].

Step-by-step explanation:

If [tex](x_{0},\, y_{0})[/tex] is on the equation of the line [tex]y = m\, x + b[/tex], then substituting [tex]x = x_{0}[/tex] and [tex]y = y_{0}[/tex] into the equation would still give an equality: [tex]y_{0} = m\, x_{0} + b[/tex].

In this question, since [tex](-2,\, 1)[/tex] is a point on the line [tex]y = m\, x + b[/tex], equality shall still hold after substituting in [tex]x = (-2)[/tex] and [tex]y = 1[/tex]:

[tex]1 = m\times (-2) + b[/tex].

Similarly, since [tex](2,\, -5)[/tex] is a point on this line, equality shall still hold after substituting in [tex]x = 2[/tex] and [tex]y = (-5)[/tex]:

[tex](-5) = m\times 2 + b[/tex].

The unknowns of both equations are [tex]m[/tex] and [tex]b[/tex].

Solve this system of two equations and two unknowns:

[tex]\left\lbrace\begin{aligned}& (-2)\, m + b = 1\\ & 2\, m + b = (-5)\end{aligned}\right.[/tex].

[tex]\left\lbrace\begin{aligned}& m = -\frac{3}{2} \\ & b = -2\end{aligned}\right.[/tex].

Therefore, the equation of this line would be:

[tex]y = (-3/2)\, x + (-2)[/tex].

Given -

ie. d = 6yd

ps - use 3.14 for a

To find -

Solution -

As we know the formula to find the perimeter of the semicircle is 2r + πr.

But A.T.Q we are only provided with the diameter. As we know that the radius is half of the diameter. ie, r = d/2.

Hence, d = 6

r = 6/2

r = 3 yd

Perimeter of semicircle = 2r + πr

Perimeter of semicircle = 2(3) + 3.14(3)

Perimeter of semicircle = 15.42 yd

Hence forth the semicircle's perimeter is 15.42 yd

The diameter of a semicircle is 6 yards. Find the perimeter of the semicircle?

Given :

Need to find :

Solution :

[tex] \small \blue {\underline {\underline{{ \orange{\rm{ First \: we \: need \: to \: calculate \: the \: radius \: of \: the \: semicircle }}}}}}[/tex]

We know,

[tex] \large \star \: \: \large \underline{\boxed{ \rm{ Radius = \dfrac{Diameter}{2}}}}[/tex]

[tex] \small\rm{ Radius = \dfrac{6}{2} = 3 \: yards}[/tex]

[tex] \small{ \underline{ \underline{\rm \red{ Now \: we \: will \: calculate \: the \: perimeter \: of \: the \: semicircle }}}}[/tex]

We know,

[tex] \large\star \: \: \large \underline{\boxed{ \rm{ Perimeter_{(semicircle)} = πr + 2r}}}[/tex]

Where,

Substituting the values we get

[tex] \small\bf{ Perimeter_{(semicircle)} = 3.14 × 3 + (2 × 3)}[/tex]

[tex] \small\rm{ Perimeter_{(semicircle)} = 9.42 \: + 6}[/tex]

[tex] \small\boxed{ \rm{ Perimeter_{(semicircle)} = 15.42 \: yards}}[/tex]

[tex] \rule{92mm}{3pt}[/tex]

Answer:

60 degrees

Step-by-step explanation:

well, angle x is on a line with a little square that means 90 degrees and a 30 degree angle, so you would simply add those two angles together 90+30=120 and then subtract by 180 because a straight line is always 180 degrees which is 180-120=60 degrees.

point grab lol

Answer:

x+y=4

Step-by-step explanation:

hello :

note :  by identity  you have   x²-y² = (x-y)(x+y)

in this exercice : 2x²-2y² = 2(x²-y²) = 2 (x-y)(x+y)

means :   2 (x-y)(x+y) = 40

but x-y = 5

so : 2(5)(x+y) =40

x+y=40/10

x+y=4

Directly solving the linear equations, we will see that:

Let's start with the first one:

3 - x = 11 + x

First, move all the terms with x to the left side and the ones without to the right side:

-x -x = 11 - 3

-2x = 8

Now we divide both sides by -2

x = 8/-2 = -4

x = -4

2) 2x + 7 = 3x + 1

Same procedure:

2x - 3x = 1 - 7

-x = -6

x = -6/-1 = 6

x = 6

3) 8 - 2x = 4 + x

-2x - x = 4 - 8

-3x = -4

x = -4/-3 = 4/3

4) 4x + 2 = 2x + 6

4x - 2x = 6 - 2

2x = 4

x = 4/2 = 2

x = 2

So we solved all linear equations.

If you want to learn more about linear equations, you can read:

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Answer:

No.

Step-by-step explanation:

the result is 17 / 5, Which is not = 3 / 2

Answer:

Step-by-step explanation:

Solve this problem by multiplying the fraction from left to right.

Dividing is another option.

3/5=0.6

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

B) 240

Step-by-step explanation:

If you want an explanation, just ask.

Hope this helps! Pls give brainliest!

Answer: A

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees, so the unknown angle is 180-90-45=45 degrees.

Answer:

a

Step-by-step explanation:

[tex]423 \times 10 {}^{2} [/tex]

[tex]2 \times 10 {}^{3} [/tex]

[tex]92 \times 10 {}^{5} [/tex]

[tex]4 \times 10 {}^{3} [/tex]

[tex]80 \times 10 {}^{6} = 8 \times 10 {}^{7} [/tex]

[tex]32 \times 10 {}^{9} [/tex]

Answer:

4.23*10^4

2*10^3

9.2*10^7

4*10^3

8*10^7

3.2*10^10

Answer:

12

Step-by-step explanation:

the ratio of the 2 numbers = 3 : 4 = 3x : 4x ( x is a multiplier ) , then

3(3x) + 2(4x) = 68 , that is

9x + 8x = 68

17x = 68 ( divide both sides by 17 )

x = 4

smaller number = 3x = 3 × 4 = 12

The dimensions of the picture size to fit in the frame are 14 inches by 11 inches.

It is known the frame is 17 inches tall but this includes 1.5 inches of the wooden frame. This means that 3 inches of the frame (1.5 inches x 2) do not count for the size of the picture.

We already know the picture can be 14 inches tall and the total area is 238 square inches including the 1.5 wooden frame.

Learn more about inches in: https://brainly.com/question/17533009

The expressions that represent the total number of berries in the Berry Blast smoothies that Luther made today is 3 + b = 20

Let the number of strawberries be x

Let the number of b berries be y

If at work today, he made 20 Berry Blast smoothies, then;

x + y = 20

SInce x = 3 and y = b, then;

3 + b = 20

The expressions that represent the total number of berries in the Berry Blast smoothies that Luther made today is 3 + b = 20

Learn more on system of equation here: https://brainly.com/question/847634

Answer:

17 stops on 1 ticket

Step-by-step explanation:

Answer:

17 stops on 1 ticket

Step-by-step explanation:

Answer:

1t = 1000kg

22.69 x 1000= 22690 kg

22690 kg ÷ 100 = 226.9

I would usually round it to 227 but I would say 226, since they are asking how many full bags she sold.

Answer:

the guy above if right it is D

Step-by-step explanation:

I did the work on Acellus and pick D IT GAVE ME A CHECK MARK

The reason that supports the statement 7 in the given proof is D. Subtraction property of equality.

Subtraction property of equality is defined as, if an equation is of the form,

a = b,

then any number subtracted from both sides makes the equation same.

a - c = b - c

Here, given a proof for the value of x.

In the 6th step, by substitution,

55 = 5x + 10

This is an equation.

We need term in x on one side and a constant term on other side.

For that, if we subtract both sides by 10,

55 - 10 = 5x + 10 - 10

45 = 5x

So here the subtraction property of equality is used.

Hence the correct option is D.

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Answer:

y = 4

Step-by-step explanation:

because 5 x 4 = 20 and 20 × 4 = 80 and so on y is equal to four