What is the interquartile range for the data set?

Could you please double check my answer for me?

Answer:

The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.

Step-by-step explanation:

To find the absolute extrema values of [tex]f(x) = 6x^3 - 9x^2 - 108x + 6[/tex]  on the closed interval [−3, 4] you must:

1. Locate all critical values. We need to find the derivative of the function and set it equal to zero.

[tex]\frac{d}{dx}f(x)= \frac{d}{dx}\left(6x^3-9x^2-108x+6\right)=\\\\f'(x)=\frac{d}{dx}\left(6x^3\right)-\frac{d}{dx}\left(9x^2\right)-\frac{d}{dx}\left(108x\right)+\frac{d}{dx}\left(6\right)\\\\f'(x)=18x^2-18x-108[/tex]

[tex]18x^2-18x-108=0\\18\left(x^2-x-6\right)=0\\18\left(x+2\right)\left(x-3\right)=0\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=-2,\:x=3[/tex]

2. Evaluate f(x) at all the critical values and also at the two values -3 and 4

[tex]\left\begin{array}{cc}x&f(x)\\-3&87\\-2&138\\3&-237\\4&-186\end{array}\right[/tex]

3. The absolute maximum of f(x) on [-3, 4] will be the largest number found in Step 2, while the absolute minimum of f(x) on [-3, 4] will be the smallest number found in Step 2.

Therefore,

The absolute maximum of f(x) on [-3, 4] is 138 and the absolute minimum of f(x) on [-3, 4] is -237.

[tex] |\Omega|=25\cdot24=600\\
|A|=11\cdot14+14\cdot13=154+182=336\\\\
P(A)=\dfrac{336}{600}=\dfrac{14}{25}=56\% [/tex]

The probability of selecting a black seven or a red three will be 1/13.

What is Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

You randomly select one card from a​ 52-card deck.

Now,

Number of black sevens = 2

Number of red three = 2

So, The probability of selecting a black seven or a red three is;

= (2 + 2) / 52

= 4 / 52

= 1 / 13

Thus, The probability of selecting a black seven or a red three will be 1/13.

Learn more about the probability visit:

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Answer:

(-1,-3)

Step-by-step explanation:

I just took the test, and I got 100%!!!

Option B= $23000 is the answer.

Explanation:

Let the bakery's sales for the month be represented by = x

As given, the bakery has total receipts for the month = $24150

Rate of sales tax = 5%

This implies that total monthly sales(x) + sales tax on 'x' = 24150

[tex]x+\frac{5x}{100}=24150[/tex]

[tex]x+0.05x=24150[/tex]

[tex]1.05x=24150[/tex]

x=23000

Hence, the bakery's sale for the month is $23,000

Answer:

( 9 ,0)

Step-by-step explanation:

Given  : [tex]\frac{(x -5)^{2}}{7} - \frac{(y+3)^{2}}{9} = 1.[/tex] is shifted to the right by 4 units and upward by 3 units

To find :  New center of the hyperbola .

Solution : We have given

[tex]\frac{(x -5)^{2}}{7} - \frac{(y+3)^{2}}{9} = 1.[/tex]

Center of hyperbola is  ( 5 , -3)

By the transformation rule f(x) →→ f(x -h) + k it mean f(x) is shifted to right by h unit and k unit up.

Then Center of hyperbola is shifted to the  right by 4 units and upward by 3 units.

( 5 , -3)  →→ (5 + 4 , -3 + 3

( 5 , -3)  →→ ( 9 ,0)

Therefore, new center is  ( 9 ,0).

Answer:

The statement is false

B is correct

Step-by-step explanation:

Given: [tex]f(x)=\log_{0.5}x[/tex]

Increasing function.

Log function:

[tex]y=\log_ax[/tex]

If 0<a<1 then y is decreasing function.

If a>1 then y is increasing function.

Now, we compare the given function

[tex]\log_ax\rightarrow \log_{0.5}x[/tex]

a=0.5

0.5<1

If 0<a<1 then y is decreasing function.

Therefore, f(x) is decreasing. But we are given f(x) is increasing.

Hence, The statement is false

The soup can is 6 cm tall and has a radius of 3.5cm. If you were to pull the label off the can in one complete piece,what would the area of the label be ? Use 22/7 for p.  

Please help !!!

A)22 sq.cm

B)42 sq.cm

C)132 sq.cm

D)152 sq.cm

Solution:

Radius of cylindrical soup can= 3.5 cm

Height of cylindrical soup can= 6 cm

Area of cylinder =2πrh

So, Area of label of cylindrical soup can=2πrh

Plugging in the value of r and h in the formula

Area of label=2*π*3.5*6

Multiplying the constants, we get

Area=2*π*21

Area=42π

Plugging in the value of π

Area=42*[tex]\frac{22}{7}[/tex]

Multiplying the numerators

Area=[tex]\frac{924}{7}[/tex]

Area=132 sq.cm

Answer: Option (C)

Area of label= 132 sq. cm

Answer:

AB = 12 units                    

Step-by-step explanation:

We are given the following information in the question:

DB is the median of the triangle.

AC = 24 units

Property of median of a triangle:

Thus, DB divides AC in two equal parts.

Thus, we could say:

AB = BC

We have to find the length of AB.

[tex]\text{AB} = \displaystyle\frac{AC}{2} = \frac{24}{2} = 12\text{ units}[/tex]

Thus, AB is 12 units.

It is the c)25-y^2-y^2 by 16-9 = 1

Answer:
∠1 and ∠2,
∠3 and ∠4,
∠5 and ∠6

Explanation:
Supplementary angles are angles opposite each other that share the same line that is being dissected by a perpendicular line. The sum of their angles will always equal 180 degrees.

Angles 1 and 2 are an example of such supplementary angles. They share the horizontal line but are being dissected by descending line which creates their angles.

Angles 3 and 4 are more of the same. They share the somewhat-vertical line and are dissected by a different descending line that created them.

Lastly, Angles 5 and 6 are also supplementary angles. They share the somewhat-vertical line and are dissected by the horizontal line, resulting in their angles.

Angles 7 and 8 are not supplementary angles. Rather, they are vertically-opposite angles, or vertical angle pairs, two angles lying opposite each other existing at the point where two lines intersect. These angles have the same exact measurement and their sum will never equal 180 degrees.

Answer:

  2.7 dm

Step-by-step explanation:

You want to know the number of decimeters in 27 centimeters.

The SI prefix "deci-" means 1/10.

The SI prefix "centi-" means 1/100.

This tells you that 10 cm = 1 dm.

  27 cm = (27 cm) × (1 dm)/(10 cm) = 2.7 dm

Jenny had 2.7 dm of hair cut off.