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2 years ago

9

at the Phoney Interior Design Store each salesperson receives a 7.5% commission on sales. What would the salesperson earn if she

sold $1,750 in home furnishings?

1 answer:

leva [86]2 years ago

5 0

They would receive $131.25

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A rectangular garden has a width that is 8 feet less than twice the length. Find the dimensions if the perimeter is 20 feet.

krok68 [10]

Answer:

length = 6 feet

width = 4 feet

Step-by-step explanation:

To find the dimensions of the rectangle, you can set up a variable and an expression that will equal the perimeter of the figure. Given l = length, width is '8 feet less than twice the length' or w = 2l - 8.

The general formula for perimeter of a rectangle is:

2w + 2l = P, where w = width and l = length

Using the variable and expression from above and the perimeter of 20 feet:

2(2l - 8)+ 2l = 20

distribute: 4l - 16 + 2l = 20

combine like terms: 6l - 16 = 20

add 16 to both sides: 6l - 16 + 16 = 20 + 16 or 6l = 36

divide and solve for 'l': 6l/6 = 36/6, or l = 6 feet

solve for 'w': w = 2(6) - 8 or w = 12 - 8 = 4 feet

4 0

2 years ago

A bacteria sample can be modeled by the function f(x) - 350(1.20) which gives the number of bacteria in the sample at the end of

marissa [1.9K]

Answer: A) The initial number of bacteria is 350.

Step-by-step explanation:

Exponential growth equation: $f(x)=A(1+r)^x$ , where A=Initial value, r= growth rate. (i)

Given: A bacteria sample can be modeled by the function $f(x) = 350(1.20)$ which gives the number of bacteria in the sample at the end of x days.

Here, $f(x)=350(1+0.20)$

Compare this equation to (i) , we get A = 350 and r= 0.20 = 20% (growth rate)

So, the best interpretation of one of the values in this function are:

A) The initial number of bacteria is 350.

3 0

2 years ago

Sofia is working two summer jobs, making $12 per hour babysitting and making $8 per hour clearing tables. In a given week, she c

Mamont248 [21]

The possible values for the number of whole hours clearing tables that she must work to meet her requirements is 2, 3 hours

<em><u>Solution:</u></em>

Amount earned in babysitting = $ 12 per hour

Amount earned in clearing tables = $ 8 per hour

In a given week, she can work a maximum of 17 total hours and must earn a minimum of $180

Sofia worked 14 hours babysitting

Therefore,

Amount earned at babysitting = 14 x 12 = 168

Thus, Sofia earned $ 168 at babysitting

Sofia must earn a minimum of $ 180

Remaining amount to be earned = 180 - 168 = 12

Thus, Sofia must earn $ 12 from clearing tables

Amount earned in clearing tables = $ 8 per hour

So, she must work for atleast 1.5 hours to get $ 12 from clearing tables

She can work a maximum of 17 total hours and Sofia worked 14 hours babysitting

Remaining is 17 - 14 = 3 hours

Thus possible values for the number of whole hours clearing tables that she must work to meet her requirements is 2 hours or 3 hours

3 0

2 years ago

What is the following product? RootIndex 3 StartRoot 16 x Superscript 7 Baseline EndRoot times RootIndex 3 StartRoot 12 x Supers

KengaRu [80]

Answer:

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}\sqrt[3]{3x} }$

Step-by-step explanation:

Given

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9}$

Required

Find the products

From laws of indices;

$\sqrt[m]{a} * \sqrt[m]{b} = \sqrt[m]{a*b}$

So;

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{16x^7 * 12x^9}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{16* x^7 * 12 * x^9}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{16*12* x^7 * x^9}$

From laws of indices

$a^m * a^n = a^(m+n); So,$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{16*12* x^{7+9}}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{16*12* x^{16}}$

Expand 16 * 12

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{4*4*4*3* x^{16}}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{4^3 *3* x^{16}}$

From laws of imdices

$a^{\frac{1}{m}} = \sqrt[m]{a}$

So;

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4^3 *3* x^{16}})^{\frac{1}{3}}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4^{3*{\frac{1}{3}}} *3^{{\frac{1}{3}}}* x^{16*{\frac{1}{3}}}})$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{\frac{1}{3}}}* x^{\frac{16}{3}}}$

Divide 16 by 3 (Write as ,mixed number)

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{\frac{1}{3}}}* x^{5\frac{1}{3}}}$

Split mixed numbers

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{\frac{1}{3}}}* x^{5+\frac{1}{3}}}$

Apply law of indices

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{\frac{1}{3}}}* x^{5}*{x ^\frac{1}{3}}}$

Reorder

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 * x^{5}*3^{{\frac{1}{3}}}*{x ^\frac{1}{3}}}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}*3^{{\frac{1}{3}}}*{x ^\frac{1}{3}}}$

Apply law of indices

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}*\sqrt[3]{3} *\sqrt[3]{x} }$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}*\sqrt[3]{3*x} }$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}*\sqrt[3]{3x} }$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}\sqrt[3]{3x} }$

6 0

2 years ago

The function A(b) relates the area of a trapezoid with a given height of 10 and

Natali5045456 [20]

The function of the trapezoid area is:

A(x)=(B+b)*h/2

Where B and b are the bases and h is the height.

With the given data: h=10 B and b =7 and x (it may vary which one is bigger)

-----------

So that function becomes:

A(x)=(7+x)*10/2

A(x)=(7+x)*5

----------

So if you want the inverse function, you have to operate to find x:

A(x)/5=7+x

A(x)/5-7=x

----------

So the new function is:

x(A)=A/5-7

6 0

2 years ago