Mystery Measures
Determine as many angle measures as you can by
creating different designs.
Record your results and strategies on the worksheet.

Answer:

A. 0.3204

B. 0.59049

Step-by-step explanation:

Data:

The total number of combinations:

= [tex](10)^5=100000[/tex]

A.

The number of ways = [tex]10*9*8*7=30240[/tex]

                                                                           [tex]\frac{30240}{100000}[/tex]

The probability for an event P taking place = [tex]=0.3024[/tex]

B.

Number of ways to arrange the subjects = [tex](9)^4=59049[/tex]

                             [tex]\frac{59049}{100000}[/tex]

The probability = [tex]=0.59049[/tex]

Answer:

[tex]\textsf{13)} \quad y=(x+5)^2+4[/tex]

[tex]\textsf{14)} \quad y=-\dfrac{1}{2}(x-2)^2-3[/tex]

Step-by-step explanation:

Vertex form of a parabola:  

[tex]y=a(x-h)^2+k[/tex]  where (h, k) is the vertex

From inspection of the graph, the vertex is (-5, 4)

[tex]\implies y=a(x+5)^2+4[/tex]

To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.

Using point (-4, 5):

[tex]\implies a(-4+5)^2+4=5[/tex]

[tex]\implies a(1)^2+4=5[/tex]

[tex]\implies a+4=5[/tex]

[tex]\implies a=1[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]y=(x+5)^2+4[/tex]

From inspection of the graph, the vertex is (2, -3)

[tex]\implies y=a(x-2)^2-3[/tex]

To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.

Using point (0, -5):

[tex]\implies a(0-2)^2-3=-5[/tex]

[tex]\implies a(-2)^2-3=-5[/tex]

[tex]\implies 4a-3=-5[/tex]

[tex]\implies 4a=-2[/tex]

[tex]\implies a=-\dfrac{1}{2}[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]\implies y=-\dfrac{1}{2}(x-2)^2-3[/tex]

#1

Equation

As there is no y inetercept present and the function is same as general quadratic equation y=x^2 just change in coordinates a=1

Final equation

#2

y=a(x-2)²-3

Use (4,-5)

Equation

Answer:

(1,4)

Step-by-step explanation:

Since x is already "alone", you can plug 3y-11 into the x-value for the first equation to get 3(3y-11)+5y=23. Now distribute 3 to the numbers in the parentheses. In the end, the solution to this is (1,4).

Answer:

x=1, y=4

Step-by-step explanation:

Substitute x = 3y - 11

3(3y - 11) + 5y = 23 |

Simplify

|14y – 33= 23 |

Isolate y for 14y-33=23

y=4

For x =3y - 11

Substitute y = 4

X=3• 4- 11

Simplify

X=1,

Answer:

-2

Step-by-step explanation:

→ -9x + 1 = -x + 17

→ -9x + x = 17 - 1

→ -8x = 16

→ x = -16/8

→ [ x = -2 ]

Answer:

[tex]\boxed{\sf distance \: between \: the \: objects \: \: is \: 2.5 \: cm}[/tex]

Step-by-step explanation:

According to universal law of gravitation every object in the universe attracts every other particles that surrounds it with a force which is inversely proportional to the square of their distance of separation & directly proportional to

the product of their masses, given by standard formula.

[tex]A = G \cdot \frac{m_1.m_2}{ {d}^{2} } [/tex]

where A,d & G are force of attraction, distance of separation & proportionality constant respectively.

Given:

A1 = 2 units

d1= 5 cm

A2 = 8 units

To find:

Distance of separation when the force of attraction is 8 units d2 = ?

Solution:

Substituting the given values in above at each point,

[tex]A_1 = G \cdot \frac{m_1.m_2}{ {d_1}^{2} } \\ 2 = G \cdot \frac{m_1.m_2}{ {5}^{2} } \\ \sf similarly \: at \: second \: point \: of \: attraction \\ A_2 = G \cdot \frac{m_1.m_2}{ {d_2}^{2} } \\ 8 = G \cdot \frac{m_1.m_2}{ {d_2}^{2} } \\ \sf \: \: dividing \: both \: of \: the \: equation \\ \frac{2}{8} = \frac{G \cdot \frac{m_1.m_2}{ {5}^{2} }}{G \cdot \frac{m_1.m_2}{ {d_2}^{2} } } \\ \sf \: G \: m_1 and \: m_2 \: are \: \: constant \: hence \\ \sf they \: can \: be \: cancelled \: out \\ \frac{2}{8} = \frac{ \frac{1}{ {5}^{2} } }{ \frac{1}{ {d_2}^{2} } } \\ \sf rearranging \: above \: equation \\ \frac{1}{4} = \frac{{d_2}^{2} }{ {5}^{2} } \\ {d_2}^{2} = \frac{ {5}^{2} }{4 } \\ {d_2}^{2} = \frac{25}{4} \\ {d_2}^{2} = 6.25 \\ \sqrt{{d_2}^{2} } = \sqrt{6.25} \\ \boxed{ \sf{d_2} = 2.5 \: cm}[/tex]

Answer: the distance between the two objects is 2.5 cm, if the attraction between them is 8 units.

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[tex](\stackrel{x_1}{12}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{12}}}\implies \cfrac{5+7}{-8}\implies \cfrac{12}{-8}\implies -\cfrac{3}{2}[/tex]

Answer:

Step-by-step explanation:

C

Answer:

25%

Step-by-step explanation:

Answer:

14/15

Step-by-step explanation:

P(S or T) = P(S) + P(T) = 3/5 + 1/3

= 9/15 + 5/15 = 14/15

To know the area of a regular hexagon:

  ⇒ must know the formula:

          [tex]Area = \frac{3\sqrt{3} }{2} s^2[/tex]

Consider the information given:

Let's solve:

  [tex]Area=\frac{3\sqrt{3} }{2} (5)^2=64.95cm^2[/tex]

Answer: 65.0 cm²

Hope that helps!

Answer:

64.1 cm²

Step-by-step explanation:

Central Angle = 360 °

∴ ∠AOB = 360 ° / 12

⇒ Tan 30° = AB/ 4 · 3

⇒ AB = 4.3 tan 30°

∴ (ΔAOB) = 1/2 × AB × OB

= 1/2 × 4.3 tan 30° × 4.3

= 5.34 cm

∴ Area of regular hexagon = 12 (a⊃(ΔAOB))

= 12 (5.34 cm²)

= 64.1 cm²

Answer:

Number 1

Step-by-step explanation:

Vertex is (−1,−13)

[tex]~~~~~6x^2 +12x -7 =0\\\\\implies x^2 +2x - \dfrac 76=0\\\\\implies x^2+2x = \dfrac76\\\\\implies x^2 +2x +1 = \dfrac 76 +1\\\\\implies (x+1)^2 = \dfrac{13}6\\\\\implies x+1 = \pm \sqrt{ \dfrac{13}6}\\\\\implies x = -1 \pm\sqrt{\dfrac{13} 6}\\\\\text{Hence,}~ x = -1 +\sqrt{\dfrac{13} 6}~~ \text{and}~~ x = -1-\sqrt{\dfrac{13} 6}[/tex]

The appropriate hypotheses for this test are

Erica filled 70

Jen filled 10

Heather filled 10

Tonya filled 10

A company is started by four friends.

The company was Erica’s idea,

So she wants to fill 70% of the orders. Jen, Heather, and Tonya each agree to fill 10% of the orders.

A hypothesis is a statement that proposes a result that will be tested to get a verified result.

A hypothesis is not hundred percent true, that is why it is always put to test.

The hypothesis is singular while the hypothesis is plural.

Making a hypothesis in this case is an attempt to predict an answer or result that will be verified by doing the experiment.

We can conclude by saying that a hypothesis is not hundred percent true.

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Answer:

535km

Step-by-step explanation:

train speed = 321/3 km per hour = 107kmh

in 5 hours, travel distance = speed x time = 107 x 5 = 535km

Answer:

Step-by-step explanation:

Discussion

The object of this is make w by itself on one side of the equation.

Equation

x = 3 (y + w) - 1               Add 1 to both sides of the equation.

x + 1 = 3(y + w) - 1 + 1      Combine

x + 1 = 3(y + w)                 Remove the Brackets

x + 1 = 3y + 3w                 Notice y and w are affected by the 3. Subtract 3y

x + 1 - 3y = 3y-3y + 3w   Combine

x + 1  = 3w                       Divide both sides by 3

(x +1)/3 = 3w/3  

(x + 1)/3 = w

Answer: (x + 1)/3 = w

Answer:

Using the Empirical Rule, we find that .997 (99.7%) of students have grade point averages that are between 1.23 and 3.81.

Step-by-step explanation:

Calculate the z-scores corresponding to a GPA of 1.23 and 3.81.

We want to find the area between the z-scores of -3 and 3.

The Empirical Rule tells us that 99.7% of the data lies within three standard deviations under the normal curve.

Therefore, the area between -3 < z < 3 is about .997, or around 99.7%.

use tan since you are given the opposite and adjacent sides

tan θ = [tex]\frac{opp}{adj}\\\\[/tex]

tan θ = [tex]\frac{2}{12}[/tex]

use the inverse of tan to find the angle

θ = [tex]tan^{-1}(\frac{2}{12})[/tex]

θ = 9.462322208...

θ = 9.46°

Answer:

3 hrs

Step-by-step explanation:

Answer:  False

Reason: It should be x-a instead of x+a

A graph is a way to represent a lot of data in such a visual format. The correct option is C, he/she should use graph B.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

If an employee wants to request a raise, the graph he/she should use to support his or her case is graph B. Because that graph is showing all thought the company is earning good profit the salary of the employees is still reducing.

Hence, the correct option is C, he/she should use graph B.

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The experimental probability that the bottle landed on its base by the data recorded is; 3/10.

It follows from the frequency recorded for the bottle landing on it's base and side that; base = 9 and side = 21.

The total possible outcome is 30.

On this note, the required probability is; 9/30 = 3/10.

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Answer:

it's the 'D' ..............,..

Answer:

volume

Step-by-step explanation:

the amount of space enclosed by an object or shape, how much 3-dimensional space

Answer:

1/5

Step-by-step explanation:

there are 15 pens totally, there are 3 red pens.

probability-> 3/15=1/5

Answer:

-1

Step-by-step explanation:
4+(-5) is basically 4-5 which is -1

[tex]\huge[\sum_{k=0}^{4}(k)][/tex] [tex] = 0+1+2+3+4=\boxed{10} [/tex]

=[tex]\huge(\binom {5}{2}) [/tex] [tex] =(5!)/(3! \times 2!) = (5\times 4)/(2)= \boxed{10}[/tex]

Since there are 5 teams..

The number of matches played in a 5 team round Robin is 10.

A round-robin tournament is a sports competition where each player or team competes against every other player or team; each contestant faces off against the other contestant in turn. A round-robin tournament differs from an elimination tournament in that participants are eliminated after a set number of losses.

From 5 teams we choose 2 to form combinations (need combinations of 2 different teams to play a match).

Here, 5C2 = 5!/2!(5-2)!

= 5×4×3×2!/2!×3!

= 10

Hence, the number of matches played in a 5 team round Robin is 10.

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