Expand and simplify:
(x+2)(x+3)

Answer:   [tex]78.5\ cm^2[/tex]

Step-by-step explanation:

From the given we can see that there is a  rectangle is rotated about a line bisecting its length in segment of 5 cm in each.

Since the base will be a circle, then the area of the base will be :-

[tex]\text{Area of base}=\pi r^2\\\\\\\Rightarrow\text{Area of base}=3.14\times(5)^2\\\\\\\Rightarrow\text{Area of base}=78.5\ cm^2[/tex]

Hence, the base area of the resulting figure = [tex]78.5\ cm^2[/tex]

The approximate base area of the rectangle is rotated about a line bisecting its length in segments of 5 cm in each is 78.5.

From the given, we can see that there is a  rectangle is rotated about a line bisecting its length in segments of 5 cm in each.

Since the base will be a circle, then the area of the base will be

A=pir^2

Where r is the radius of the circle.

A=3,14(5)^2

A=78.5.

Therefore, the approximate base area of the resulting figure is 78.5.

To learn more about the area visit:

https://brainly.com/question/25292087#SPJ3

Answer:

The piecewise-defined function to model the salesperson's total monthly salary (in $) is,

[tex]f(x)=\begin{cases}2000 & \text{ if } x\leq 40,000 \\2000+0.05(x-40000) & \text{ if } x>40000\end{cases}[/tex]

Step-by-step explanation:

It is given that the salesperson makes a base salary of $2000 a month. Once he reaches $40,000 in total sales, he earns an additional 5% commission on the amount in sales over $40,000.

Let the x represents the amount of sales and f(x) represents the salary of salesperson.

It means till the sale of $40,000, the salary of the salesperson is constant, i.e., $2000.

[tex]f(x)=2000[/tex]    for   [tex]x\leq 40,000[/tex]

He will get commision of 5% on the amount in sales over $40,000.

[tex]f(x)=2000+\frac{5}{100}(x-40000)[/tex]  for  [tex]x>40,000[/tex]

Therefore the piecewise-defined function to model the salesperson's total monthly salary (in $) is,

[tex]f(x)=\begin{cases}2000 & \text{ if } x\leq 40,000 \\2000+0.05(x-40000) & \text{ if } x>40000\end{cases}[/tex]

The piecewise-defined function to model the salesperson's total monthly salary (in $) as a functionis [tex]\boxed{f\left( x \right)=\left\{\begin{gathered}2000{\text{ if }}x \leqslant 40000 \hfill\\2000 + 0.05\left( {x - 40000} \right){\text{ if }}x > 40000 \hfill\\\end{gathered}\right.}[/tex].

Further explanation:

The piecewise defined function is defined as a function that takes different values in different interval. It is defined on the sequence of intervals.

Given:

The base salary is [tex]\$ 2000[/tex].

He will earn [tex]5\%[/tex] additional commission on the amount sales over [tex]\$ 40000[/tex].

Explanation:

The base salary of a salesperson in a month is $2000.

If the salesperson reaches to $40000, he will earns 5% additional commission on the amount sales over [tex]\$ 40000[/tex].

The person get [tex]\$ 2000[/tex] if sale less than  [tex]\$ 40000[/tex].

[tex]f\left( x \right) =2000{\text{ for }}x \leqslant 40000[/tex].

The value of the function for less than $40000 is  [tex]f\left( x \right)=2000[/tex].

If he sales over 40000 the amount he will get can be expressed as follows,

[tex]f\left( x \right)=2000+\dfrac{5}{{100}}\left( {x - 40000} \right)[/tex] for[tex]x > 40000.[/tex]

The value of the function for greater than 40000 is  [tex]f\left( x \right)=2000 + \dfrac{5}{{100}}\left({x - 40000} \right)[/tex].

The piecewise-defined function to model the salesperson's total monthly salary (in $) as a functionis [tex]\boxed{f\left( x \right)=\left\{\begin{gathered}2000{\text{if }}x \leqslant 40000\hfill\\2000 + 0.05\left( {x - 40000}\right){\text{if }}x > 40000 \hfill \\\end{gathered}\right.}[/tex]

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear Equation

Keywords: solving equation, inverse operation, isolate, variable, addition property, good guess, solution, order of operations, reverse order, two solution, linear equation.

The that stacy picked it out of bowl #1 is 0.6

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Bowl 1 has 10 chocolate chip and 30 plain cookies, while Bowl #2 has 20 of each.

So, P[tex](H_1|E)[/tex]

= P( E| [tex]H_1[/tex]) P([tex]H_1[/tex]) / [  P( E| [tex]H_2[/tex]) P([tex]H_2[/tex] )+  P( E| [tex]H_1[/tex]) P([tex]H_1[/tex])  

= (0.75 x 0.5) / (0.75 x 0.5 + 0.5 x 0.5)

= 0.375 / (0.375 + 0.25)

= 0.6

Hence, the probability is 0.6

Learn more about Probability here:

https://brainly.com/question/30034780

#SPJ5

1. For that accurate reason, CD and AB will be congruent. the answer here is B) A congruent segment. 2. Option (A) is the right answer. We can construct a perpendicular bisector usind the given steps.

1. Form opening the compass to the length of AB you are setting the radius of the circle the compass could create to the same length of AB then by intersecting with the ray C, we have to copied the length of AB to ray C.

For that accurate reason, CD and AB will be congruent.

Therefore, The answer here is B) A congruent segment.

2. Given a segment with endpoints A and B.

By using the construction step we will draw the following figure that  represents a perpendicular bisector XY of line segment AB.

Hence, Option (A) is the right answer. We can construct a perpendicular bisector usind the given steps.

Learn more about this concept here;

https://brainly.com/question/2485485

#SPJ2

since they are both negative numbers just subtract 7 from 54

54-7 = 47

To write 19.4 in expanded form, you can break down the number into its place values. The digit 1 is in the tens place, the digit 9 is in the ones place, and the digit 4 is in the tenths place. Therefore, 19.4 in expanded form is 10 + 9 + 0.4.

To write 19.4 in expanded form, we break down the number into its place values. The digit 1 is in the tens place, the digit 9 is in the ones place, and the digit 4 is in the tenths place. So, we can write 19.4 in expanded form as 10 + 9 + 0.4.

https://brainly.com/question/25632734

#SPJ11

Answer:

A)up

Step-by-step explanation:

Given : f(x)=log x +3

            g(x)= log x

To Find :

The graph of f(x) = log x + 3 is the graph of  g(x) = log x translated 3 units

a)up

b)down

c)left

d) right

Solution:

Rule: f(x)→f(x)+b

So, the graph f(x) is translated up by b units

So, on comparing given f(x) with rule , we can say that the graph g(x) is translated up by 3 units

Thus option A is correct.

Hence The graph of f(x) = log x + 3 is the graph of  g(x) = log x translated 3 units up

To find (g-f)(3), evaluate g(3) and f(3), then subtract f(3) from g(3).

To find (g-f)(3), we need to subtract the function f(x) from g(x) and then evaluate the result at x = 3. Let's first simplify the expressions for f(x) and g(x):

f(x) = 4 - x^2

g(x) = 6x

Now substitute these into (g-f)(3) and simplify:

(g-f)(3) = g(3) - f(3)

= 6(3) - (4 - 3^2)

= 18 - (4 - 9)

= 18 - (-5)

= 23

Therefore, (g-f)(3) is equivalent to 23.

https://brainly.com/question/12056604

#SPJ2

[tex]\(1138368400\)[/tex] different outcomes possible when considering all the events together.

Coin Toss: Since each toss is independent of the others, the total number of outcomes for 4 tosses is:

[tex]\(2 \times 2 \times 2 \times 2 = 2^4 = 16\)[/tex].

Die Roll: A standard six-sided die has 6 faces, each with a different number from 1 to 6. When the die is rolled once, there are 6 possible outcomes. If the die is rolled 2 times, the number of different outcomes is:

[tex]\(6 \times 6 = 6^2 = 36\)[/tex]

Card Draw: When drawing a card from the deck, there are 52 possible outcomes. If a second card is drawn without replacing the first, there are now 51 possible outcomes for the second card (since one card has already been drawn). Continuing this pattern, for the third card, there are 50 possible outcomes, and for the fourth card, there are 49 possible outcomes.

The number of different outcomes for drawing 4 cards without replacement is: [tex]\(52 \times 51 \times 50 \times 49\)[/tex].

[tex]\[ \text{Total Outcomes} = (\text{Coin Toss Outcomes}) \times (\text{Die Roll Outcomes}) \times (\text{Card Draw Outcomes}) \][/tex]

[tex]\[ \text{Total Outcomes} = 16 \times 36 \times (52 \times 51 \times 50 \times 49) \][/tex]

[tex]\[ \text{Total Outcomes} = 6^2 \times 52 \times 51 \times 50 \times 49 \][/tex]

[tex]\[ \text{Total Outcomes} = 36 \times 52 \times 51 \times 50 \times 49 \][/tex]

[tex]\[ \text{Total Outcomes} = 36 \times 31625400 \][/tex]

[tex]\[ \text{Total Outcomes} = 1138368400 \][/tex]

An equation is formed of two equal expressions. The value of y for the given equation is (1.5x - 6)/3.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

1.5x - 3y = 6

Subtract 1.5x from both the sides of the equation,

1.5x - 3y - 1.5x = 6 - 1.5x

-3y = 6 - 1.5x

Divide both the sides of the equation by -3,

-3y/(-3) = (6 - 1.5x)/(-3)

y = (1.5x - 6)/3

Hence, the value of y for the given equation is (1.5x - 6)/3.

Learn more about Equation here:

https://brainly.com/question/14686792

#SPJ2

The Greates Common Factor (GCF) is:   2

The value that is equivalent to 6 times 5 squared is 150.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, and exponentiation) that represents a mathematical relationship or a quantity.

Expressions in mathematics can be evaluated or simplified to produce a single value or to represent a more simplified form of the original expression.

6 times 5 squared can be written in a few different ways:

6 x 5²

6 x 25

150

So the expressions that are equivalent to 6 times 5 squared are:

6 x 5²

6 x 25

The value that is equivalent to 6 times 5 squared is 150.

To know more about an expression follow

https://brainly.com/question/1859113

#SPJ2

1/3 = 0.33333 ( repeating)

4/5 = 0.8 (terminating)

Answer:

84/6=14

Step-by-step explanation:

read the answer

Rounding the coefficients to four decimal places:

[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]

The logistic equation governing the number of people exposed to the advertisement in the community is given by:

[tex]\[ \frac{{dn}}{{dt}} = kn \left(1 - \frac{n}{M}\right) \][/tex]

Where:

n(t)  is the number of people exposed to the advertisement at time t

k  is the growth rate constant

M  is the limiting number of people who will see the advertisement

Given:

[tex]\( n(0) = 500 \)[/tex]

[tex]\( n(1) = 1000 \)[/tex]

[tex]\( M = 50000 \)[/tex]

We first need to find the growth rate constant \( k \):

[tex]\[ 1000 = 500 \times \left(1 - \frac{500}{50000}\right) \times k \][/tex]

[tex]\[ 1000 = 500 \times \left(1 - \frac{1}{100}\right) \times k \][/tex]

[tex]\[ 1000 = 500 \times \frac{99}{100} \times k \][/tex]

[tex]\[ k = \frac{1000 \times 100}{500 \times 99} \][/tex]

[tex]\[ k = \frac{2000}{99} \][/tex]

Now, we integrate to find [tex]\( n(t) \)[/tex]:

[tex]\[ \int \frac{{dn}}{{n(1 - \frac{n}{50000})}} = \int \frac{{2000}}{{99}} dt \][/tex]

[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t + C \][/tex]

Using the initial condition [tex]\( n(0) = 500 \)[/tex], we find[tex]\( C \)[/tex]:

[tex]\[ -\ln|1 - \frac{500}{50000}| = 0 + C \][/tex]

[tex]\[ -\ln\left(\frac{99}{100}\right) = C \][/tex]

So, the equation becomes:

[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t - \ln\left(\frac{99}{100}\right) \][/tex]

Solving for n(t) :

[tex]\[ |1 - \frac{n}{50000}| = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ 1 - \frac{n}{50000} = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ \frac{n}{50000} = 1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ n(t) = 50000 \times \left(1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)}\right) \][/tex]

This is the solution for [tex]\( n(t) \)[/tex]. Now, rounding the coefficients to four decimal places:

[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]

c=PI*d

divide both sides by PI to get d by itself

d = c/PI