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2 years ago

According to the rational root theorem, which statement about f(x)= 12x^3-5x^2+6x+9 is true?

Mathematics

2 answers:

Lubov Fominskaja [6]2 years ago

4 0

Any rational root of f(x) is a factor of 9 divided by a factor of 12

which is answer D

scZoUnD [109]2 years ago

3 0

If there are any rational roots, it would be a factor of your constant term (9) divided by a factor of the high-order coefficient (12).

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The manager of a grocery store estimates that 74% of customers will make a purchase.

Lina20 [59]

Answer:

A - Per 100 people, cashier should expect 26 customer until he finds a costumer that makes a purchase.

B - The probability is 1/4

Step-by-step explanation:

The estimated chance of a customer making a purchase = 74%

So, if a TOTAL of 100 people visit the grocery store on any random day,

then 74 % of customers

= 74% of 100

= 74 people will make purchases.

⇒ Out of total 100 people visiting, 74 people will make a purchase.

So, the number of people NOT making a purchase = 100 - 74 = 26

⇒ Out of total 100 people visiting, 26 people will NOT make a purchase.

Also, 26 = 26% of 100

Part A :

So, in order to make a purchase, cashier should expect 26% of customers because the percentage of NOT purchasing is 26%.

Hence, per 100 people, cashier should expect 26 customer until he finds a costumer that makes a purchase.

Part B :

The percentage of customer making a purchase = 74%

The percentage of people NOT making a purchase = 26%

So, for every 3 customer making a purchase there is a 1 person NOT making a purchase.

So, the probability is 1/4

6 0

2 years ago

What is the cube root of -729a9b6

Harman [31]

ANSWER

$\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2}$

EXPLANATION

We want to find the cube root of

$- 729 {a}^{9} {b}^{6}$

We express this symbolically as:

$\sqrt[3]{- 729 {a}^{9} {b}^{6} }$

The expression under the radical called the radicand.

We need to express this radical in exponential form using the property,

${x}^{ \frac{m}{n} } = \sqrt[n]{ {x}^{m} }$

Applying this rule gives us:

$\sqrt[3]{- 729 {a}^{9} {b}^{6} } = ({- 729 {a}^{9} {b}^{6}})^{ \frac{1}{3} }$

$\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3} {a}^{9} {b}^{6}})^{ \frac{1}{3} }$

Recall that

$({a}^{m} )^{n} = {a}^{mn}$

We apply this rule on the RHS to get,

$\sqrt[3]{- 729{a}^{9} {b}^{6} } = ({- {9}^{3 \times { \frac{1}{3} } } {a}^{9 \times { \frac{1}{3} } } {b}^{6 \times { \frac{1}{3} } }})$

This simplifies to

$\sqrt[3]{- 729{a}^{9} {b}^{6} } = - 9 {a}^{3} {b}^{2}$

3 0

2 years ago

Read 2 more answers

A barrel in Jim's yard contains 60 gallons of water. Water leaks out of the barrel at a rate of 1 gallon every 10 minutes. Creat

emmainna [20.7K]

Answer:

$y=-0.10x+60$

Step-by-step explanation:

Let

y -----> gallons of water remaining in the barrel

x-----> number of minutes elapsed

we know that

Water leaks out of the barrel at a rate of 1 gallon every 10 minutes

$1/10=0.10\frac{gal}{min}$

The linear equation that represent this situation is

$y=-0.10x+60$

The graph in the attached figure

7 0

2 years ago

Read 2 more answers

A cone is cut out of the center of a pyramid with a rectangular base. The rectangular base has side lengths of 15 and 10 units.

Mekhanik [1.2K]

Answer:

Volume of shaded portion = (600 - 36π) units³

Step-by-step explanation:

Volume of the shaded portion = Volume of pyramid - Volume of cone

Volume of pyramid = ⅓*l*w*h

Where,

l = length of base of pyramid = 15 units

w = width of base of pyramid = 10 units

h = height of pyramid = 12 units

Plug in the values to find the volume of the pyramid

Volume of pyramid = ⅓*15*10*12 = 5*10*12 = 600 units³

Volume of Cone = ⅓πr²h,

Where,

r = radius = ½ of diameter = ½ of 9 = 3 units

h = height = 12 units

Volume of Cone = ⅓*π*3²*12 = ⅓*π*9*12

= π*3*12 = 36π units³

Volume of shaded portion = (600 - 36π) units³

3 0

2 years ago

In 2012, on average, about $9.46\times10^{-1}$ pound of potatoes was produced for every $2.3\times10^{-5}$ acre harvested. How m

muminat

Answer:

4.113 × 10⁴ pounds per acre = 41,130 pounds per acre to the nearest pounds per acre

Step-by-step explanation:

9.46 × 10⁻¹ pounds of potatoes were produced for every 2.3 × 10⁻⁵ acre harvested. The average pounds of potatoes harvested per acre would be pounds of potatoes/acres harvested = 9.46 × 10⁻¹ pounds/2.3 × 10⁻⁵ acre = 4.113 × 10 ⁻¹⁻⁻⁵ = 4.113 × 10⁵⁻¹ = 4.113 × 10⁴ pounds per acre = 41,130 pounds per acre to the nearest pounds per acre.

6 0

2 years ago