4. Compare/contrast the data sets below. Which data set has a range of 9, a mean of
15, a median of 14, and a mode of 11? How do you know (show work)? Why do the
other choices fail to meet the criteria? State one reason why each of the other
choices fail.
A. 11, 11, 13, 15, 20
B. 5, 11, 14, 14, 31
C. 11, 11, 14, 19, 20
D. 6, 10, 14, 15, 15

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π              → A + B = π - C

                                              → B + C = π - A

                                              → C + A = π - B

                                              → C = π - (B +  C)

Use Sum to Product Identity:  cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]

Use the Sum/Difference Identity: cos (A - B) = cos A · cos B + sin A · sin B

Use the Double Angle Identity: sin 2A = 2 sin A · cos A

Use the Cofunction Identity: cos (π/2 - A) = sin A

Proof LHS → Middle:

[tex]\text{LHS:}\qquad \qquad \cos \bigg(\dfrac{A}{2}\bigg)+\cos \bigg(\dfrac{B}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)[/tex]

[tex]\text{Sum to Product:}\qquad 2\cos \bigg(\dfrac{\frac{A}{2}+\frac{B}{2}}{2}\bigg)\cdot \cos \bigg(\dfrac{\frac{A}{2}-\frac{B}{2}}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)[/tex]

[tex]\text{Given:}\qquad \quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{\pi -(A+B)}{2}\bigg)[/tex]

[tex]\text{Sum/Difference:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\sin \bigg(\dfrac{A+B}{2}\bigg)[/tex]

[tex]\text{Double Angle:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\sin \bigg(\dfrac{2(A+B)}{2(2)}\bigg)\\\\\\.\qquad \qquad \qquad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+2\sin \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A+B}{4}\bigg)[/tex]

[tex]\text{Factor:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\bigg[ \cos \bigg(\dfrac{A-B}{4}\bigg)+\sin \bigg(\dfrac{A+B}{4}\bigg)\bigg][/tex]

[tex]\text{Cofunction:}\quad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\bigg[ \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{\pi}{2}-\dfrac{A+B}{4}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =2\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{A-B}{4}\bigg)+\cos \bigg(\dfrac{2\pi-(A+B)}{4}\bigg)\bigg][/tex]

[tex]\text{Sum to Product:}\ 2\cos \bigg(\dfrac{A+B}{4}\bigg)\bigg[2 \cos \bigg(\dfrac{2\pi-2B}{2\cdot 4}\bigg)\cdot \cos \bigg(\dfrac{2A-2\pi}{2\cdot 4}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad =4\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -A}{4}\bigg)[/tex]

[tex]\text{Given:}\qquad \qquad 4\cos \bigg(\dfrac{\pi -C}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -A}{4}\bigg)\\\\\\.\qquad \qquad \qquad =4\cos \bigg(\dfrac{\pi -A}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -C}{4}\bigg)[/tex]

LHS = Middle [tex]\checkmark[/tex]

Proof Middle → RHS:

[tex]\text{Middle:}\qquad 4\cos \bigg(\dfrac{\pi -A}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi-B}{4}\bigg)\cdot \cos \bigg(\dfrac{\pi -C}{4}\bigg)\\\\\\\text{Given:}\qquad \qquad 4\cos \bigg(\dfrac{B+C}{4}\bigg)\cdot \cos \bigg(\dfrac{C+A}{4}\bigg)\cdot \cos \bigg(\dfrac{A+B}{4}\bigg)\\\\\\.\qquad \qquad \qquad =4\cos \bigg(\dfrac{A+B}{4}\bigg)\cdot \cos \bigg(\dfrac{B+C}{4}\bigg)\cdot \cos \bigg(\dfrac{C+A}{4}\bigg)[/tex]

Middle = RHS [tex]\checkmark[/tex]

Answer:

4¹⁰

Step-by-step explanation:

4³ × 4⁷ = 4³⁺⁷ = 4¹⁰

Answer:13

Step-by-step explanation:

13^2

5 1.80, the crackers cost $1.80 per box: 20 3 1.80 5 36. So, 20 boxes cost $36.00.

Answer:

$36

Step-by-step explanation:

To find how much one box costs you divide 9÷5 = 1.8

Then you take 1.8 × 20 = 36

If you want me to go over it in depth, let me know! Have a great day!

Answer:

It is 4

Step-by-step explanation:

4

4 8

4 8 12

as you can tell 4 is your answer.

Answer:

1. -5

2. 1/3 (1 third)

3. -3

4. -1\2 (negative one and a half)

5.-4

6. 1.66666

Step-by-step explanation:

1.  Let's solve your equation step-by-step. ( x + 5 ) ( x − 2 ) = 0 Step 1: Simplify both sides of the equation. x 2 + 3 x − 10 = 0 Step 2: Factor left side of equation. ( x − 2 ) ( x + 5 ) = 0 Step 3: Set factors equal to 0. x − 2 = 0 or x + 5 = 0 x = 2 or x = − 5.        <—— this is for the first explanation

2. Step 1: Simplify both sides of the equation. 6 x 2 + 13 x − 5 = 0 Step 2: Factor left side of equation. ( 3 x − 1 ) ( 2 x + 5 ) = 0 Step 3: Set factors equal to 0. 3 x − 1 = 0 or 2 x + 5 = 0 x = 1 3 or x = − 5 2 Answer: x = 1 3 or x = − 5 2

<———— this is for the second explanation

3.Step 1: Factor left side of equation. ( x + 1 ) ( x − 4 ) = 0 Step 2: Set factors equal to 0. x + 1 = 0 or x − 4 = 0 x = − 1 or x      

<———- this is for the third explanation

4.Step 1: Factor left side of equation. ( 2 x + 1 ) ( x − 3 ) = 0 Step 2: Set factors equal to 0. 2 x + 1 = 0 or x − 3 = 0 x = − 1 2 or x = 3

<—————- this is for the fourth explanation

5. Step 1: Add 16 to both sides. x 2 − 16 + 16 = 0 + 16 x 2 = 16 Step 2: Take square root. x = ± 16 x = 4 or x = − 4

<—————- this is for the fith explanation

6. Step 1: Add 25 to both sides. 9 x 2 − 25 + 25 = 0 + 25 9 x 2 = 25 Step 2: Divide both sides by 9. 9 x 2 9 = 25 9 x 2 = 25 9 Step 3: Take square root. x = ± 25 9 x = 1.666667 , − 1.666667

<—————- this is for the sixth explanation

Hope this helps :)

Answer: False

Step-by-step explanation: First, you are going to multiply the numbers in the first set of parenthesis, getting 72. Now, have 72 take the place of 12x6 in the equation. Your new equation looks like this: 0.3 x 72 = 0.4(12-3).

Going off of step one, you will be doing the same thing with the second set, but you will be subtracting instead. You will get 9, and plug it place of the parenthesis. Your equation now looks like o.3 x 72 = 0.4 x 9.

Next, you will multiply the set of numbers on the left side of the equal sign, getting 21.6. You now have an equation of 21.6 = 0.4 x 9.

Going off of step 3, you are going to do the exact same thing we did in step 3. Multiply 0.4 and 9, and you will get 3.6. The equation now looks like 21.6 = 3.6.

Now, the inequality is false because the left-hand side and right-hand side are two completely different numbers. A bigger number cannot be equal to a smaller number.

Hope this helps!

Answer:

12

Step-by-step explanation:

4x3=12

Think about the rule when multiplying powers together.

When multiplying two powers that have the

same base, simply add their exponents.

In this problem, each power has a base

of a and our exponents are m and n.

So adding these exponents together, we have a^m + n.

Answer:

Step-by-step explanation:

Let the height (the dependent variable) be h.

Let the independent variable (x) be y

h = 8y + 10

So at birth, these creatures are 10 cm long. At each birthday, they are another 8 cm.

Take the fifth year which is where the table begins.

y= 8*5 + 10

y = 40 + 10

y = 50 cm which is exactly what you got.

The dimensions of this rectangle are 4 units by 3 units

4 units * 3 units = 12 sq units

We need to multiply the 80mph by the 1.6 to make it KPH

When done correctly we get the answer of 128KPH

The limit is 128kph

HOPE THIS HELPED. DONT FORGET TO MARK THIS AS THE BRAINLIEST ANSWER AND GIVE IT A 5 STAR SO OTHER PEOPLE CAN BE HELPED BY THIS ANSWER!! HAVE A NICE DAY!

Answer: It is A

Step-by-step explanation:

In the given figure D) DC/BC has the same ratio as AB/BC.

The interior angle bisector theorem states that in a triangle the angle bisector of an angle divides the opposite side to the angle in the ratio of the remaining two sides.

In ΔABC m∠A = 28° and the ratio is taken for the sides which is opposite to the given angle BC and the side which not base AB.

Given the ratio AB/BC.

∴ In ΔBCD in which m∠B is also 28° we have to take the same sides opposite side is DC and the side which is not the base BC.

So, in the triangles ABC and ABD The ratio which has the same value as AB/BC is BC/DC.

learn more about the exterior angle theorem of a triangle here :

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Answer:

[tex]x<-8[/tex]

Step-by-step explanation:

So we have the inequality:

[tex]3x-1>4x+7[/tex]

Add 1 to both sides. The left side cancels:

[tex]3x>4x+8[/tex]

Subtract 4x from both sides. The right side cancels:

[tex]-x>8[/tex]

Divide both sides by -1. Since we're dividing by a negative, we flip the sign:

[tex]x<-8[/tex]

And we're done!

Our solution is all numbers less than -8.

Answer:

x = -8

Step-by-step explanation:

I will be the brainliest, its hard to explain on a document, i could make you avideo how to do these problems, im a math teacher.

Answer:

B) (-2,3)

Step-by-step explanation:

Graph all your points. No count the distance from point A to B. divide in half .

[tex] \huge \purple {\tt {x + \frac{7}{6} = 2x - \frac{7}{6}}} [/tex]

[tex] \large {\tt {The \: answer \: in \: reduced}} [/tex]

[tex] \large {\tt { improper \: fraction \: form.}} [/tex]

[tex] \huge \pink {\tt {x + \frac{7}{6} = 2x - \frac{7}{6}}} [/tex]

[tex] \huge \blue {\tt {or, \: x - 2x = - \frac{7}{6} - \frac{7}{6}}} [/tex]

[tex] \huge \red {\tt {or, \: - x = \frac{ - 14}{6} = \frac{ - 7}{3}}} [/tex]

[tex] \huge \green {\tt {or, \: x = \frac{7}{3}}} [/tex]

[tex] \huge \orange {\tt {x = \frac{7}{3}}} [/tex]

Answer:

see below

Step-by-step explanation:

 g(x) = 1/2 | x+2| -3

y = Cf(x)   0 < C < 1 compresses it in the y-direction

y = f(x + C)      C > 0 moves it left

y = f(x) + C C < 0 moves it down

1/2 compression in the y direction moved to the left 2 units and down 3 units

Given: g(x) = 1/2|x + 2| - 3

0 < c < 1 means at the y-axis and makes it smaller

y = cf(x)

1/2 compression

c > 0 means that you move it to the left

y = f(x + c)

2 units to the left

c < 0 means that you move it down

y = f(x) + c

3 units down

Best of Luck!

Answer:

A, D, E

Step-by-step explanation:

like with division if you multiply the same thing on both sides it is still equal

The  ratios are equivalent to 8 : 12 are A 4 : 6 , D 24 : 36 and E 56 : 84.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 8, and b= 12,

[tex]a:b = 8 : 12\\\\ = \dfrac{8}{12} = \dfrac{2 \times 4}{2 \times 6} \\= \dfrac{2}{3} \\\\a : b = 2 : 3[/tex]

So, the  ratios are equivalent to 8 : 12

A 4 : 6

D 24 : 36

E 56 : 84

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

Learn more about ratio here:

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Answer:

9 dimes and 17 quarters

Step-by-step explanation:

9+17=26 coins

9 dimes = 90 cents

17 = 425 cents

90+425= 515 cents or $5.15

Hope this helps! :)

Answer:

8

Step-by-step explanation:

Answer:  9 1/10      91/10

Step-by-step explanation:

Answer:

9 1/10 and 91/10

Step-by-step explanation:

hope it helps :)

brainliest pls? have a good day/night

Answer:

D

Step-by-step explanation:

Answer:

1 1/3

Step-by-step explanation:

Firstly, 1 2/3 is converted into an improper fraction being 5/3. Next, 1/5 of 5/3 is one portion of 5 equal portions. You can split 5/3 into five equal portions of 1/3. Therefore, 1/3 cup of honey was used to make the honey glaze. Lastly, that is subtracted from the 1 2/3 to end up with 1 1/3.

The required amount of honey left is given as 1 1/3.

Given that,
Ben wants to try a new honey-glazed salmon recipe. He starts with 1 2/3 cups of honey. He uses 1/5 of it to make the glaze.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Amount of honey = 1 2/3 = 5 / 3
Amount of honey used is 1/5 times = 1/5 [5 / 3] = 1 / 3
Amount of honey left = 5/3 - 1/3 = 4/3 or 1 1/3

Thus, the required amount of honey left is given as 1 1/3.

Learn more about arithmetic here:

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Answer:

m∠XAZ = 40°

Step-by-step explanation:

Since ∠YAU, ∠YAZ and ∠XAZ are the angles based at a point on a straight line, and the sum of the all angles on a line is 180°.

Therefore, m∠YAU + m∠YAZ + m∠XAZ = 180°

50° + 90° + m∠XAZ = 180°

m∠XAZ = 180° - 140°

             = 40°

Therefore, measure of angle XAZ is 40°.

Answer:

It depends.

Step-by-step explanation:

If it is two straight lines, then no, there is no way for the lines to intersect in more than one place. If the line is a parabola, then the lines would intersect in 2 places. It depends on what type of line you have.  

Hi there! :)

2t + 8 ≥ -4(t + 1)

Distribute the coefficient outside of the parenthesis:

2t + 8 ≥ -4(t) -4(1)

2t + 8 ≥ -4t - 4

Add 4t to both sides:

6t + 8 ≥ -4

Subtract 8 from both sides:

6t ≥ -12

Divide both sides by 6:

t ≥ -2.

Answer: t ≥  -2/3

Step-by-step explanation:

Answer:

IT'S A BELIEVE PLZZZZZZZz

Step-by-step explanation:

Answer:

The cost at Store A is $2.00 greater than at Store B.

Step-by-step explanation:

i had the same quiz this was correct

Answer:

The answer is 1

Step-by-step explanation: