How long will it take a population of 4000 to double if its annual growth rate is 7.1% round to the nearest year

The in this case, the distance covered by the car would be 120 miles. The equation Distance = Speed * Time allows us to determine the distance covered by an object when the speed and time taken are known.

To determine distance, we can rearrange the formula for speed:

Speed = Distance / Time. By multiplying both sides of the equation by Time, we can isolate Distance.

Distance = Speed * Time

The formula indicates that distance is equal to the product of speed and time. By multiplying the rate at which an object moves (speed) by the duration of travel (time), we can determine the total distance covered during that period.

The equation Distance = Speed * Time represents the relationship between distance, speed, and time.

It states that the distance covered is equal to the product of the speed at which an object is moving and the time it takes to travel that distance.

For example, if a car is traveling at a constant speed of 60 miles per hour for 2 hours, the distance it would cover can be calculated as follows:

Distance = 60 miles/hour * 2 hours = 120 miles.

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We have a problem where we have to relate the capacities of an old and a new computer.

We will call C1 the capacity of the old computer and C2 the capacity of the new computer.

We define the capacity as the inverse of the time it takes to complete the task T:

That means that the less time it takes to complete the task, the higher the capacity is.

We know that the capacity of the new computer is 4 times the capacity of the old computer:

If the computers work together they add their capacity, so we have:

We know that the time it takes for the two computers is 5 minutes, so we can write:

We then know that the time it takes for the new computer to complete the task on its ownis 6.25 minutes.

Answer: 6.25 minutes.

Answer :

⠀

Explanation :

\(\longrightarrow \sf \qquad {x}^{2} + 10x - 39 = 0\)

⠀

We have to find the two numbers a and b such that,

\(\longrightarrow \sf \qquad a + b = 10\)

\(\longrightarrow \sf \qquad a b = 39\)

⠀

Obviously, the two numbers are 3 and 13.

\(\longrightarrow \sf \qquad {x}^{2} - 3x + 13x - 39 = 0\)

\(\longrightarrow \sf \qquad {x}(x - 3)+ 13(x - 3) = 0\)

\(\longrightarrow \sf \qquad ({x}+ 13)(x - 3) = 0\)

⠀

Whether, the value of x :

\(\longrightarrow \sf \qquad {x}+ 13 = 0\)

\(\longrightarrow \pmb{\bf \qquad {x} = - 13}\)

⠀

Whether, the value of x :

\(\longrightarrow \sf \qquad {x} - 3 = 0\)

\({\longrightarrow { \pmb{\bf \qquad {x} = 3}}}\)

⠀

We are given with the equation x² + 10x - 39 = 0 and need to find x, so let's start ;

\({:\implies \quad \sf x^{2}+10x-39=0}\)

By using splitting the middle term method, Rewrite as ;

\({:\implies \quad \sf x^{2}+13x-3x-39=0}\)

\({:\implies \quad \sf x(x+13)-3(x+13)=0}\)

\({:\implies \quad \sf (x+13)(x-3)=0}\)

So, here either (x + 13) = 0 or (x - 3) = 0, when you equate both of them with 0, you will get x = -13 and x = 3

Hence, The required answer is -13 and 3

Answer:

Step-by-step explanation:

Given a + 1/a = 3, find its square:

Now find the square of (a - 1/a):

Substitute the value from the first square:

Since (a - 1/a)² = 5, its square root is:

Answer:

2736 square feet

Step-by-step explanation:210 minus 18(9 times 2 )equals 192 then 192 divided by 4 (4 because 4 side )equals 48 (48 is the width) to get the length 48 plus 9 equals 57 (57 is the length) to  get the area multiply length times width so 57 times 48 equals 2736 square feet

Answer:

Step-by-step explanation: bot

The function has the maximum revenue of $348,480 with the increasing rate of $33.

The highest and smallest values of a function, respectively, can either be found inside a specific range or distributed throughout the entire domain. They are also sometimes referred to collectively as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, accordingly.

Given data:

The overall revenue is thus:

y = (36 - 0.50x)(9600 + 160x)

Differentiate with respect to x.

y ' = (-0.50)(9600 + 160x) + 160(36 - 0.50x)

y' = -4800 - 80x + 5760 - 80x

y' = 960 - 160x

To find x, put y' = 0

960 - 160x = 0

x = 960/160 = 6 (critical point)

Function is decreasing in interval - [6, +∞)

Increasing Function in interval - (-∞, 6]

Thus, the function has the maximum value at x = 6.

maximum revenue f(6):

f(6) = (36 - 0.50x)(9600 + 160x)

f(6) = (36 - 0.50(6))(9600 + 160(6))

f(6) = $348,480

Rate : 36 - 0.50(6) = $33

The function has the maximum revenue of $348,480 with the increasing rate of $33.

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Answer: 4

Step-by-step explanation: +9-(-3)=12

81-78=3

so 12/3=4

The period is π/2 and the amplitude is 3.

Given data ,

Let the function be represented as the graph of f ( x )

where the function is plotted

Now , The period of a function is the length of one complete cycle of the function. It represents the distance along the x-axis over which the function repeats its pattern

And , The amplitude of a function is the maximum distance between the function's graph and its average value where it is a positive value

So , period: π/2; amplitude: 3

Hence , the period and amplitude are solved

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The Intel pays $7,760 to Bally Manufacturing on August 14.

The first step in calculating what Intel Corporation pays Bally on August 14 is to determine the net price of the machinery after the trade discount and the return of $100 due to defects.

The trade discount of 40% is calculated as follows:

Discount = List price × Discount rate

Discount = $13,100 × 0.40 = $5,240

So the net price of the machinery after the trade discount is:

Net price = List price - Discount

Net price = $13,100 - $5,240 = $7,860

After Intel returns $100 of machinery, the cost of the machinery is further reduced to:

Net price after return = Net price - Return

Net price after return = $7,860 - $100 = $7,760

Since the payment terms are 3/10 EOM (end of month), Intel receives a discount of 3% if payment is made within 10 days. The 10-day period begins on August 1 and ends on August 10 (the payment due date). Since Intel pays the bill on August 14, payment is late and the 3% discount does not apply.

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Answer:

given functions:

\(\sf f(x)=x^2+3x-7\)

\(\sf g(x)=3x+5\)

\(\sf h(x)=2x^2-4\)

solving steps:

(a)

\(\sf f(g(x))\)

\(\sf \sf f(3x+5)\)

\(\sf (3x+5)^2 + 3(3x+5)-7\)

\(\sf 9x^2+30x+25+9x+15-7\)

\(\sf 9x^2+39x+33\)

(b)

\(\sf h(g(x))\)

\(\sf h(3x+5)\)

\(\sf 2(3x+5)^2-4\)

\(\sf 18x^2+60x+50-4\)

\(\sf 18x^2+60x+46\)

(c)

\(\sf (h-f)(x)\)

\(\sf 2x^2-4-(x^2+3x-7)\)

\(\sf 2x^2-4-x^2-3x+7\)

\(\sf x^2-3x+3\)

(d)

\(\sf (f+g)(x)\)

\(\sf x^2 + 3x -7 +3x+5\)

\(\sf x^2+6x-2\)

Answer: The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.

Step-by-step explanation:

Hope this is right!!!!

I hope this helps you .

9514 1404 393

Answer:

  (f•g)(x) = 3x^3 +6x^2 -5x -10

Step-by-step explanation:

  (f•g)(x) = f(x)•g(x) = (x +2)(3x^2 -5)

  = x(3x^2 -5) +2(3x^2 -5) . . . . . . . . use the distributive property

  = 3x^3 -5x +6x^2 -10 . . . . . . . and again

  (f•g)(x) = 3x^3 +6x^2 -5x -10 . . . . put in standard form

Answer:

125.66

Step-by-step explanation:

C = 2πr = 2·π·20 = 125.66371

C) Carla's Cooking

Explanation:

Carla's Cooking: $1000

Alonzo' Appetizers: $1400

Ben's Bistro: $2250

Carla's cooking is the cheapest.

The rational function graphed in this problem is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x= -4 and x = 1.

Hence the denominator of the function is given as follows:

(x + 4)(x - 1).

The intercept is given as follows:

x = 0.

Hence the numerator is:

x.

Thus the function is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

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Answer:

20.. ... ...... .. ........

Answer:

C

Step-by-step explanation:

x²-9x<-8

x²-9x+(-9/2)²<-8+(-9/2)²

(x-9/2)²<-8+81/4

(x-9/2)²<(-32+81)/4

(x-9/2)²<49/4

|x-9/2|<7/2

-7/2<x-9/2<7/2

add 9/2

9/2-7/2<x-9/2+9/2<7/2+9/2

2/2<x<16/2

1<x<8

You forgot to include your slope but it should just follow the form y= mx+ b. where m is your slope and b is your y-intercept.

The probability of throwing 3 shots is 100% and the sample space is set of all possible real number.

Probability is the measure of the likelihood that a given event will occur. In this case, the event is a basketball player making a shot from the free throw line.

Since the player has a 40% success rate, we can calculate the probability of him making x number of shots, where x is the number of shots that he throws.

Since the shots are independent of each other, the sample space for x is the set of all possible numbers of shots that he can make, from 0 to the total number of shots (3 in this case).

Therefore, the sample space for x is {0, 1, 2, 3}, which means that the player has a 0% probability of making 0 shots, a 40% probability of making 1 shot, an 80% probability of making 2 shots, and a 100% probability of making all 3 shots

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Answer:

x-y=12

Step-by-step explanation:

Answer:

Volume of the rectanguler prism :

\( \sf v = \frac{21}{2} \: units {}^{2} \times \frac{8}{3} \: units\)

\( \sf v = \frac{21}{2} \times \frac{8}{3} = \frac{168}{6}\)

\( \sf v = \frac{168}{6} ( \frac{ \div 6}{ \div 6} = \frac{28}{1} )\)

\( \sf volume = \boxed{ \bold{ \red{28 \: {units}^{3} }}}\)

━━━━━━━━━━━━━━━━━

Hope it helps!

Answer:

r + s - 19

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

r - 7 + s - 12

Step 2: Simplify

Answer:

Step-by-step explanation:

y + 3 = -3/4(x - 8)

y + 3 = -3/4x + 6

y = -3/4x + 3

The total number of students in Ms. Morales's class is either 20 or 30, depending on the value of x.

Let the ratio of boys to girls in Ms. Morales's class be 3x:7x, where 3x represents the number of boys and 7x represents the number of girls.

The total number of students in the class is equal to the sum of the number of boys and the number of girls, which is 3x + 7x = 10x.

We don't know the value of x, but we do know that the class size is between 22 and 34 students.

Therefore, we can set up an inequality based on the total number of students:

22 ≤ 10x ≤ 34

Dividing all parts of the inequality by 10, we get:

2.2 ≤ x ≤ 3.4

Since x represents a whole number of students, the possible values for x are 3 (if there are 30 students in the class) or 2 (if there are 20 students in the class).

If x = 3, then the total number of students is:

10x = 10(3) = 30

If x = 2, then the total number of students is:

10x = 10(2) = 20

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Answer:

5

Step-by-step explanation:

A tech company bought a number of computers for its employees: 6 costing $1600 each, 4 costing $1200 each, and y costing $900 each, where y is a positive odd integer. what is the greatest possible value of y

Solution:

The median of a group of numbers is the middle number when the group of numbers have been arranged either in ascending of descending other. The median of an even group of numbers is the average of the two most middle most numbers while the median of an odd group of numbers is the middle number.

Since there are 6 computers costing $1600, 4 computers costing $1200 each and y computers costing $900 each. Since y is odd, hence y + 6 + 4 would be odd and the median would be the middle number.

Given that the median price = $1200, this means that the middle of the group of numbers is $1200

900, 900, ..., 1200, 1200, 1200, 1200, 1600, 1600, 1600, 1600, 1600, 1600

Since y is odd, for the median price to be $1200, y has to be 3 or 5.

If y = 3:

900, 900, 900, 1200, 1200, 1200, 1200, 1600, 1600, 1600, 1600, 1600, 1600

median = $1200

If y = 5:

900, 900, 900, 900, 900, 1200, 1200, 1200, 1200, 1600, 1600, 1600, 1600, 1600, 1600

Median = $1200

Therefore the greatest possible value of y is 5

By knowing that the median must be $1,200, we will see that the greatest possible value of y is y = 9.

We know that the company bought:

We know that y is a positive odd number.

We also know that the median is $1200, now we want to get the maximum value of y such that the median is $1200. (Remember that the median is the value of the middle element of the set).

Then we will have the distribution:

{ y elements,  $1200, the other 3 $1200 computers plus the 6 $1600 computers}

Notice that y (the number of elements at the left of the median) must be equal to the number at the right of the median.

At the right of the median, we have a total of 9 computers, then y must be equal to 9.

The greatest possible value of y is 9.

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