A wire of length 15 is cut into two pieces which are then bent into the shape of a circle of radius r and a square of side s . Then the total area enclosed by the circle and square is the following function of s and r If we solve for s in terms of r , we can reexpress this area as the following function of r alone:
Thus we find that to obtain maximal area we should let r= To obtain minimal area we should let r=

Answer:

Target

Step-by-step explanation:

$4.40/8 is 0.55 and $7.08/12 is 0.59

Answer: 02

Step-by-step explanation: w

Answer:

  a.  18.5 million

  b.  2002

Step-by-step explanation:

Given that A = 18.5·e^(0.1708t) models a population t years after 2000, you want to know the population in 2000 and when it will reach 26.6 million.

The year 2000 is 0 years after 2000, so we can find the population using t=0 in the given equation.

  A = 18.5·e^(0.1708·0) = 18.5·e^0 = 18.5

The population in 2000 was 18.5 million.

We can solve for t to find the year in which the population reached 26.6 million:

  26.6 = 18.5·e^(0.1708t)

  26.6/18.5 = e^(0.1708t)

  ln(266/185) = 0.1708t

  t = ln(266/185)/0.1708 ≈ 2.13 . . . . . . 2.13 years after 2000

The population will reach 26.6 million in the year 2002.

__

Additional comment

The population of 26.6 million represents about a 44% increase over the initial population of 18.5 million. The exponential term tells you the rate of growth is 17.08% compounded continuously. Thus we expect the larger population to be reached in a time slightly less than 44/17 ≈ 2.6 years.

(These numbers were found using a calculator. It is sufficient to do the estimating by realizing that 1.50·18 = 27, and 17·3 = 51, so the growth to 26.6 from 18.5 is less than 50% and will take less than 3 years.)

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Answer:

c

...................

Answer:

the answer is the option C

Answer:

  1/3log₂(x) +1/3log₂(y) +1/3log₂(z)

Step-by-step explanation:

You want the complete expansion of ...

  [tex]\log_2{\sqrt[3]{x\cdot y\cdot z\vphantom{b}}}[/tex]

The rules of logs and exponents relevant to this expansion are ...

  [tex]\log_b{(xy)}=\log_b{(x)}+\log_b{(y)}\\\\\log_b{(x^a)}=a\cdot\log_b{(x)}\\\\\sqrt[n]{\vphantom{b}a}=a^{\frac{1}{n}}[/tex]

Applying these rules to the given expression, we get ...

  [tex]\log_2{\sqrt[3]{x\cdot y\cdot z\vphantom{b}}}=\log_2{((xyz)^{\frac{1}{3}})}=\dfrac{1}{3}\log_2{(xyz)}\\\\=\boxed{\dfrac{1}{3}\log_2{(x)}+\dfrac{1}{3}\log_2{(y)}+\dfrac{1}{3}\log_2{(z)}}[/tex]

Answer: 5.25>1 3/4>-5/2>-8.345

Step-by-step explanation:

Percent is from the Latin adverbial phrase per centum meaning “by the hundred.”

Using concepts of percentage,

3 is 16.63% of 22.

22 is 13.41% of 164.

0.88 is 4% of 22.

8 is 22% of 36.36.

1.1 is 5% of 22.

A percentage is a number or ratio expressed as a fraction of 100.

Let 3 be x% of 22.

=x/100*22=3

=x=3*100/22=13.63

3 is 13.63% of 22.

Let 22 be y % of 164.

=y/100*164=22

=y=22*100/164=13.41

13.41% of 164 is 22.

4% of 22 = 0.88

=4/100*22=0.88

Let 8 is 22% of z.

=22/100*z=8

=8*100/22=36.36

5% of 22 = 1.1

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There are total 42,072,307,200 different passwords are possible .

What are combinations ?

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.

Combinations can be confused with permutations. However, in permutations, the order of the selected items is essential. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), while in permutations, the arrangements are different.

Given: A password is required to log into a system that only recognizes numbers and letters of the alphabet

Since , there are total 26 letters and 10 numbers are possible that can be used to create a password . Hence , there are 36 character in total to be used.

Also , repetition of character is not allowed. Therefore , the chance of selecting every character decreases by 1 in comparison to its preceding character .

Chance of selecting first character = 36

Chance of selecting second character = 35

Similarly for seventh = 30

Thus , different passwords that are possible  using 7 numbers or letters, without reusing any of them = 36*35*34*33*32*31*30 = 42,072,307,200 .

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The rate of change is 7 more of function A than the slope of function B.

Slope is calculated as the ratio of "vertical change" to "horizontal change" between any two points on a line, or any two points. When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line.

Since y=8x+3,

The rate of change in equation A is equal to the slope m m=8.

The rate of change, m=1, is given in equation B.

y=mx+ is the solution to equation B.

By substituting the values we get,

y=x+4

Calculate the difference between the rates of change of function A and function B.

8-1=7

Therefore, the rate of change is 7 more of function A than the slope of function B.

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Answer:

[tex]x = 3, -1[/tex]

Explanation:

math

The original cost of the speaker will be equal to $125.3. The correct option is D.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a waterproof speaker sells for $179, which is marked up by 30% of the selling price.

The cost price of the speaker will be calculated as,

Cost price = 179 x 0.7

Cost price = $125.3

Therefore, the original cost of the speaker will be equal to $125.3. The correct option is D.

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83.01dB is approximate combined sound pressure level.

What is sound pressure level?

The result of the pressure changes in the air caused by sound waves is sound pressure, often known as sound pressure level. The hearing threshold is the lowest sound pressure that a human can hear, and the pain threshold is the maximum sound pressure that a person can tolerate.

The difference between sound pressure at the pain threshold and the hearing threshold is a million times higher.

We have sound pressure level denoted as (Lp) of each machine

i.e 80 dB,(given).

Therefore, we can calulate sound pressure level from both machines combined by given formula,

SPL = 10 * Log(10^(SPL(1) /10)  + 10^(SPL(2) /10) +10^(SPL(3) /10) + ............)

   where,

      SPL= sound pressure level(dB)

 => SPL = 10 * Log(10^(80 /10) + 10^(80 /10))

 => SPL = 10 * Log(10^8 + 10^8)

 => SPL = 10 * 8.301

 => SPL = 83.01dB

Hence, 83.01dB is approximate combined sound pressure level.

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The concurrent parts in the given ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD.

Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size. These triangles may be moved, flipped, twisted, and turned to get a similar effect. When relocated, they are parallel to one another. The concurrence sign is '≅'.

Here we have,

ABDE is an isosceles trapezoid.  

Draw 2 diagonals in a given trapezoid

Then the 2 diagonal  will divide the trapezoid into 4 triangles

Here ΔAOB, ΔBOD, ΔEOD, and AOE

From the formed triangles

ΔAOB and ΔEOD will be two concurrent triangles

Then Side AB ≅ Side ED  

ΔBOD and AOE will be two concurrent triangles

Side AE ≅ Side BD    

Therefore,

The concurrent parts in the given ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD.    

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Answer: n=11 m=3

Step-by-step explanation:

2n+2=3n-9

n=11

3m+6=n+4

3m+6=11+4

3m+6=15

3m=9

m=3

The doubling period of a bacterial population is 15 minutes. the initial population at time t=0 is 351.56. the size of the bacterial population after 3 hours is:359,997.44.

y = total amount of bacteria

a = initial bacterial at time 0

b = growth factor

t=120 minutes =15 minutes 8 times

So,

t=8

90000 =  a (2)^8

90000 = a (256)

90000/256 = a

351.56 = a (initial population)

Equation:

y = 351.56 (2)t

After 3 hours (15 minutes 10 times), or at t = 10

y = 351.56 (2)^10

y= 359,997.44

Therefore the initial population at time t=0 is 351.56. the size of the bacterial population after 3 hours is:359,997.44.

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Answer:

book c has 130 pages

Step-by-step explanation:

let book a = x pages

book b      = 2x

book c      = 2x + 30

according to the question:

x + 2x +2x + 30 = 280

5x + 30 = 280

5x = 280-30

5x = 250

x = 250/5

x = 50

thus book c has 2(50) + 30 = 130 pages

Present Value of Annuity = $4,000 × 26.1948  = $104779.2

What is a present value?

The worth of an anticipated revenue stream assessed as of the valuation date is known as the present value in the fields of economics and finance.

Here, we have

Where , Annuity Amount = $4,000            

n = No. of periods = 8 years × 4 quarters per year = 32 periods but since the first payment is at beginning of the quarter,

Then, n = 31 when considered for PVAF

r  = 5.4% / 4 quarters = 1.35%,

Present value of Annuity  = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n, r)

PVAF(n₀,r) when the first payment is at beginning of n i.e.

n₀ = 1 + { [1-(1+r)^ -n ]/r }

= 1 + { [1-(1+0.0135)^ {-31}]/0.0135 }

= 1 + [ (1 - 0.65987 ) ] / 0.0135]

= 1 + 25.1948

= 26.1948

PVAF(32,35%) = 26.1948

Hence, Present Value of Annuity = $4,000 × 26.1948  = $104779.2

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f(x) = x² + 2x + 2

Solution:

Given vertex (1,1)

a = 1

Formula of quadratic equation  is :

y = a(x + b)² + c

where, a =1, x=x, b = x1, c = y1

Substituting  the values in the equation, we get

y = x² + 2x + 2

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A quadratic function to model the graph to the right is f(x) = x² + 2x + 2

What is a quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Solution:

Given vertex (1,1)

a = 1

Formula of quadratic equation  is :

y = a(x + b)² + c

where, a =1, x=x, b = x1, c = y1

Substituting  the values in the equation, we get

y = x² + 2x + 2

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82.9 score should be assigned for A’s and 74.4 should be assigned for B’s

In this question we have been given the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points.

It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students.

We need to find what scores should be assigned A’s and B’s.

μ = 70, σ = 10

Using standard normal table,

P(X > x) = 10%

P(X > x) = 0.10

1 - P(X ≤ x) = 0.10

P(X ≤ x) =1−0.10

             =0.90

Using standard normal z table,

(x - 70)/10 = 1.29

x = 82.9 (score for A’s)

Now, P(X > x) = 33% (top 33% = 10% for A’s+23 % for B’s)

P(X>x) = 0.33

1 - P(X ≤ x) = 0.33

P(X ≤ x) = 1 - 0.33

             = 0.67

Using standard normal z table,

(x - 70)/10 = 0.44

x = 74.4 (score for B’s)

Therefore, the score for A = 82.9 and the score for B = 74.4

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The equation of the line is y = x - 2.

What is the equation of the line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Key Concept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

We have,

y-intercept(c) = −2 and

the line is equally inclined to the axis i.e., the same angle to the x-axis and y-axis(say)=θ

but the angle between the axes is 90°

2θ = 90° ⇒ θ = 45°

As slope and y-intercept are given.

The equation of a line is y = mx + c

c = -2 and

m = tan45°

as the line is equally inclined to the axes.

c = -2 and m = 1

Hence, the equation of the line is y = x - 2.

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if the markup is 11%, well, we simply add that to the cost of the item, in this case 18.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{11\% of 18}}{\left( \cfrac{11}{100} \right)18}\implies 1.98~\hfill \underset{selling~price}{\stackrel{18 ~~ + ~~1.98}{\text{\LARGE 19.98}}}[/tex]

a) If only your employer makes the monthly deposits into your retirement account for the future value of $500,000 in 40 years at 7% APR, your employer contributions should be $190.49.

b) If only your employer makes the monthly deposits into your retirement account for the future value of $500,000 in 40 years at 4% APR, your employer contributions should be $423.03.

The future value represents the amount expected to be the balance in the investment account after a period.

The future value can be used to determine the periodic payments required to meet the target balance, using an online finance calculator.

N (# of periods) = 480 months (40 years x 12)

I/Y (Interest per year) = 7%

PV (Present Value) = $0

FV (Future Value) = $500,000

Results:

PMT (Periodic deposits) = $190.49

Sum of all periodic payments = $91,435.07

Total Interest = $408,564.93

N (# of periods) = 480 (40 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

FV (Future Value) = $500,000

Results:

PMT (Periodic deposits) = $423.03

Sum of all periodic payments = $203,052.33

Total Interest = $296,947.67

Thus, the periodic deposits to meet the future value will depend on the interest rate.

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If the three side lengths are all different then you will only get one triangle. However, if two or more of the side lengths are the same then you can get more than one triangle.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total

Three diagonals must meet at three different locations to form a triangle. There are five possible arrangements of three diagonals. We categorize them according on how many different diagonal endpoints there are. The quantity of triangles with 3, 4, and 5 endpoints will be counted directly.

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The events P(A) = 0.22 P(B) = 0.45, P(A and B) = 0.099 and rolling a pair of dice at the same time are independent events. Others are dependent events.

Independent events are events for which the occurrence of this event does not depend on any other events.

Dependent events are those events for which it's occurrence depends on other events.

Two events A and B are independent, if

P(A | B) = P(A)

P(A and B) = P(A) × P(B)

P(A) = 0.65, P(B) = 0.25 and P(A and B) = 0.40

P(A) × P(B) = 0.65 × 0.25 = 0.1625 ≠ P(A and B)

∴ A and B are dependent events.

P(A) = 0.22 P(B) = 0.45 and P(A and B) = 0.099

P(A) × P(B) = 0.22 × 0.45 = 0.099 = P(A and B)

∴ A and B are independent events.

P(A) = 0.42 P(B) = 0.62 and P(A| B) = 0.2604

P(A| B) = 0.2604 ≠ P(A)

∴ A and B are dependent events.

If you roll a pair of dice at the same time, probability for any number to occur on dice 1 does not affect the probability of any number to occur on dice 2.

∴ A and B are independent events.

If you choose two marbles from a bag, when the first marble is chosen, then the second marble you choose will not be the first marble in any case. So second event depends on the first event.

∴ A and B are dependent events.

Hence, as P(A and B) = P(A) × P(B) satisfies for the events P(A) = 0.22 P(B) = 0.45, P(A and B) = 0.099, is is independent events. Also rolling a pair of dice at the same time is also independent events. The rest of the events are dependent events as it does not satisfies the condition for independent events.

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Answer:

1120

Step-by-step explanation:

Given the information below:

The Relative Frequency of selling a pan style pizza =

Therefore, if Valentino's Pizzeria were to sell 4000 pizzas, the expected number of Pan style pizza sold will be:

Number of Pan Style Pizza Sold = Relative Frequency of pan Style Pizza Purchase X Total Number of Sales

They should expect to sell 1120 pan Style pizzas.

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 4500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A=4500\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1 \cdot 10}-1}{\frac{0.04}{1}} \right]\left(1+\frac{0.04}{1}\right) \\\\\\ A=4500\left[ \cfrac{(1.04)^{10}-1}{0.04} \right](1.04) \implies A \approx 56188.58[/tex]

so every year you were putting in 4500 bucks, so for 10 years that'd be a total deposits for 4500*10 = 45000, so let's squeeze out the 45000 from the the total, that gives us 56188.58 - 45000 ≈ 11188.58.

so, if we take 56188.58 to be the 100%, what's 11188.58 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 56188.58 & 100\\ 11188.58& x \end{array} \implies \cfrac{56188.58}{11188.58}~~=~~\cfrac{100}{x} \implies 56188.58x=1118858 \\\\\\ x=\cfrac{1118858}{56188.58}\implies x\approx \stackrel{\%}{19.91}[/tex]

Being a female and participating in sports are independent events for the provided data because P(girl) = P(girl participates in sports)

These are the occurrences that are independent of other occurrences.

Occurrences A and B are independent events when the likelihood of one occurring is unaffected by the occurrence of the other.

Probability of independent events formula:

"P(A∩B) = if A and B are independent occurrences P(A).P(B)

Finding the chance that an event will occur is the focus of this area of mathematics."

P(A) = n(A)/n(S), where n(A) is the number of positive outcomes and n(S) is the total number of possible outcomes for an event A.

For given question,

We have been given a table that shows the results broken down by gender.

            Play sports         Do not play sports       Total

Boy            95                          45                        140

Girl             76                           59                       135

Total          171                            104                     275

Using the definition of probability:

⇒ P(girl)  = Number of girls/ Number of students

⇒ P(girl) = 135/275

⇒ P(girl) = 0.49                    ....................(1)

Now we find the probability of girls that play a sport.

Using the definition of probability:

P(girl plays a sport)

= Number of girls who plays a sport/ number of students who plays a sport

= 76/ 171

= 0.44                                    ......................(2)

From (1) and (2),

P(girl) = P(girl plays a sport)

Thus, being a girl and playing a sport are Independent events.

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