In 2010, the population of a city was 74,000. From 2010 to 2015, the population grew by 8%. From 2015 to 2020, it fell by 6%. To the nearest 100 people, what was the population in 2020?

a. exponential function is[tex]y = 397,000*(1+0.03)^t[/tex] b. Rounding to the nearest thousand, the population after 15 years will be 605,000

A mathematical function with the following formula is an exponential function:

[tex]f(x) = a^x[/tex]

where x: input variable and an is a positive constant known as the base. As x increases or decreases, the value of the function either rises or falls exponentially. In other words, the function always increases or decreases at a rate that is proportionate to its current value.

a. The formula: can be used to create an exponential function that depicts the population after t years.

[tex]y = y 0 * (1 + r)^t[/tex]

where t: number of years, r: yearly growth rate expressed as a decimal, and y 0 is the initial population.

The initial population in this instance is 397,000, and the yearly growth rate is 3%, or 0.03 in decimal form. The exponential function that depicts the population after t years is as follows:

[tex]y = 397,000 * (1 + 0.03)^t[/tex]

b. We may change the exponential function we discovered in part a to include t = 15 to determine the population after 15 years:

[tex]y = 397,000 * (1 + 0.03)^(15)y = 605,464[/tex]

After 15 years, the population will be roughly 605,000, to the nearest thousand.

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Therefore, the minimum number of people in the second group is 4.In order to calculate the minimum size of the second group, we must use the median formula.

In order to calculate the minimum size of the second group, we must use the median formula. The median is calculated by finding the middle number in a set of numbers when the numbers are arranged in ascending order. In this case, the median is 4, which means that half of the people bought more than 4 cups of coffee and the other half bought less than 4 cups of coffee.In order to calculate the minimum size of the second group, we must multiply the median number of cups (4) by the total number of people in both groups (n). This means that 4n = sum of all cups bought.Now, we know that the first group bought a total of 17 cups of coffee, so we can rearrange the equation to solve for n.17 = 4n - sum of all cups bought by the second group 17 = 4n - (sum of all cups bought by the second group) 17 - 4n = -(sum of all cups bought by the second group)n = (17 - (sum of all cups bought by the second group))/4 .Therefore, the minimum number of people in the second group is 4.

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minimum number of people in the second group is 4

In linear equation, 33  is the cost of supply when q=20 .

What is the most effective way to explain linear equations?

An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x). A linear equation is an algebraic equation of the form y=mx+b.

                          In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.

demand function D(q) = 100 - 5q

 supply function s(q) = 0.75q

 for equilibrium point

              D(q) = S(q)

  100 - 5q = 0.75q

 0.75q + 5q = 100

   2.25q = 100

    q = 100/2.25

     q = 400/ 9

so, supply functions's value at q = 400/9

        s(400/9) = 0.75 * 400/9

                    = 100/3

                    = 33.33

                  ≈ 33

  the value of the supply functions at q = 400/9  = 33

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The value of the determinants are

D=13

Dx =26

Dy =52

Dz =26

The determinant of a matrix is ​​a scalar value calculated for a given square matrix. Linear algebra deals with the determinant, it is calculated using the elements of a square matrix. It can be thought of as a scaling factor for the matrix transformation. Useful for solving a system of linear equations, calculating the inverse of a matrix, and numerical operations.

Given system is

x+ y-z= 4

3x+4y-3z=16

9x- 3y+4z=14

from the system the determinants become,

D=  1   1  -1

      3  4  -3

      9   -3  4

D= 1(16-9)-1(12+27)-1(-9-36)

   =7-39+45

   13

Dx=4   1  -1

      16  4  -3

      14   -3  4

   =26

Dy=1  4  -1

      3  16  -3

      9   14  4

   =52

Dz=1  1  4

      3  4  16

      9   -3  14

 =26

Hence, D=13, Dx=26, Dy=52, Dz=26

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The ratio of red to yellow pots of flowers can be written as 32:24, 8:6, or 4:3. To calculate the ratio with fractions, you can divide 32 by 24 to get 8/6, which can be simplified to 4/3.

To calculate with decimals, divide 32 by 24 to get 1.3333, which can be written as 1.33:1. To calculate the ratio with a percentage, divide 32 by 24 to get 1.3333, then multiply that by 100 to get 133.3%. This can be written as 133.3%:100%. The ratio of red to yellow pots of flowers is 8:6, or 4:3. This means for every 6 yellow pots of flowers, there are 8 red pots of flowers. Dividing 8 by 6 yields 1.3333, which can be written as 1.33:1, or 133.3%:100%. This means for every 100% of yellow pots of flowers, there are 133.3% of red pots of flowers. To calculate the fraction, divide 32 by 24 to get 8/6, which can be simplified to 4/3. This means for every 3 yellow pots of flowers, there are 4 red pots of flowers.

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The answer of the given question is (a)  Joseph would pay approximately $646.56 in interest over nine months. (b) Joseph would pay approximately $200.34 more in interest than Andres over nine months due to his lower credit worthiness.

An interest rate is the percentage at which a lender charges a borrower for the use of money or other assets. It is essentially cost of borrowing money. The interest rate is usually expressed as an annual percentage of the amount borrowed or invested, and can be fixed or variable depending on the terms of the loan or investment.

(a) Assuming Joseph receives the highest interest rate of 25.74%, the interest he would pay in nine months with an average monthly balance of $3,350 can be calculated as follows:

Interest rate per month = (25.74% / 12) = 0.02145

Average monthly balance = $3,350

Interest paid per month = (0.02145 x $3,350) = $71.84

Interest paid in nine months = ($71.84 x 9) = $646.56

Therefore, Joseph would pay approximately $646.56 in interest over nine months.

And assuming Andres receives the lowest interest rate of 17.74%, the interest he would pay in nine months with an average balance of $3,350 can be calculated as follows:

Interest rate per month = (17.74% / 12) = 0.0148

Average monthly balance = $3,350

Interest paid per month = (0.0148 x $3,350) = $49.58

Interest paid in nine months = ($49.58 x 9) = $446.22

Therefore, Andres would pay approximately $446.22 in interest over nine months.

(b) The difference in interest paid by Andres and Joseph can be calculated as follows:

Interest paid by Joseph - Interest paid by Andres = $646.56 - $446.22 = $200.34

Therefore, Joseph would pay approximately $200.34 more in interest than Andres over nine months due to his lower credit worthiness.

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The rate of change of volume with respect to time at t=2 minutes is 240π cm³/min.

At t=0, the radius of the sphere is r=1. At t=2 minutes, the radius will be r=2. The volume of a sphere is V=4/3πr³, so the volume of the sphere at t=2 minutes will be V=4/3π(2)³=33.5π.

The rate of change of volume with respect to time (dV/dt) can be calculated by taking the derivative of the volume equation with respect to time.

dV/dt = 4πr²dr/dt

At t=2 minutes, r=2 and dr/dt=30 cm/min.

dV/dt = 4π(2)²(30 cm/min)

    = 240π cm³/min

Therefore, the rate of change of volume with respect to time at t=2 minutes is 240π cm³/min.

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Answer: its a taco

Step-by-step explanation: taco

Answer: neither

Step-by-step explanation:

sandwich is a sandwich, a taco is a taco.

The recommended warranty length for Benjamin’s company is 58 months. This should give the company a good balance between covering a reasonable number of water heaters and still making a profit.

Profit is a financial gain that is realized when the amount of revenue generated from a business activity exceeds the expenses, costs and taxes needed to sustain the activity. It is the difference between total revenue and total costs incurred during an accounting period.

In order to answer this question, we must use the standard deviation formula to calculate the number of months in which 10% of the water heaters will need to be serviced. This is done by subtracting 1.28 times the standard deviation from the mean, which is 60 months. In this case, the result is 57.44 months. Because Benjamin’s company cannot offer a warranty of less than one month, we must round this number up to 58 months.

This formula gives us a warranty length that is statistically the most likely to cover 10% of all water heaters that need to be serviced. This warranty length also works in the company’s favor as it is long enough to cover most water heaters that need servicing, but not so long that the company is covering an unnecessarily large number of water heaters.

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Answer:

2

Step-by-step explanation:

I'm assuming that one x means one recipe. Two recipes require more than 2.5 cups but less than 4 cups.

All possible real zeros of the polynomial are values of x that would make the result 0. To find these values, we set the polynomial equal to 0 and solve for x. In this case, the real zeros are x=-2, 1.5, 1, and 2.5. In this case, we will use the Synthetic Division to evaluate f(x) when x=5.

Synthetic Division is a simplified way of dividing polynomials. It can be used to divide a polynomial of any degree by a linear factor to find the zeroes of a polynomial. It is a useful tool for quickly solving many problems without having to go through the lengthy process of long division.

To do this, we will create a synthetic division table with the coefficients of the polynomial. The first row of the table will be the coefficients of the polynomial, starting from the highest power: 3x⁴, -14x³ -10x², 25x, and 0. The second row will begin with the value of x, in this case 5, followed by the coefficients of the polynomial.

Starting from the left, we will divide the first coefficient, 3, by 5, then multiply the result by 5, and subtract the first row from the second row. This process is repeated for each coefficient, until the last coefficient is 0. The last number in the second row is the remainder when the polynomial is divided by (x-5). In this case, the remainder is -45.

The highest power is 4, so the graph will decrease to the left and increase to the right. The negative coefficient (-14x³) indicates that the graph will decrease more drastically to the left than to the right.

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Answer: c. 60

Each interior angle = 720/6 = 120°.

When the hexagon is extended create an exterior angle, its measure is given by;

x + 120 = 180°.

x = 180° - 120°

x = 60°

If the right-fielder throws the ball to second base, the distance she throws the ball is 40.6 ft.

option D.

The distance between the right fielder and the second base is calculated by applying sine rule as shown below.

Angle of the right - fielder = 180 -  (68 + 40 ) (sum of angles in a triangle)

Angle of the right - fielder = 72⁰

Apply the sine rule as shown below;

let the distance between the second base and the right - fielder = x

x/sin 40 = 60 ft / sin72

multiply both sides by sin 40

x = (sin 40 / sin 72) x 60 ft

x = 40.55 ft

x ≈ 40.6 ft

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a. Ex is read as "the expected value of all x values,"

What is sigma ?

Ex is a mathematical notation that represents the expected value of a random variable X. The expected value of X is the theoretical long-run average value of X that is expected to occur when X is repeatedly observed or measured under identical conditions. The expected value is calculated by summing the product of each possible value of X and its probability of occurrence. Mathematically, it is denoted as E(X) or Ex. The expected value is a fundamental concept in probability theory and statistics and is used in various applications such as decision-making, risk assessment, and financial analysis.

Sigma (written as Σ) is a mathematical symbol that represents the sum of a series of numbers or terms. It is often used in mathematics and statistics to denote a sum of a set of values. The symbol is written as an uppercase Greek letter sigma and appears as an elongated "S".

For instance, if we have a series of n numbers, a₁, a₂, ..., aₙ, then the sum of these numbers is represented by the following formula using the sigma notation:

∑ᵢ₌₁ⁿ aᵢ = a₁ + a₂ + ... + aₙ

Here, i is the index that takes on the values from 1 to n, and aᵢ is the ith term in the series. The sigma notation allows us to express the sum of the terms in a compact and convenient way. We can also use sigma notation to represent other types of mathematical expressions involving sums, such as infinite series or double sums.

b. Sigma * x² is read as "the sum of the squared values of all x values,"

c. Sigma (x- overline x ) is read as "the sum of the deviations from the mean x bar."

d. (Sigma*x)² is read as "the square of the sum of all x values."

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By solving, vertical asymptote at x = -4 and horizontal asymptote at y = -1/4.

What are vertical and horizontal ?

Vertical asymptotes are vertical lines that occur when the denominator of a function approaches zero, resulting in the function becoming undefined.

Horizontal asymptotes are horizontal lines that a graph approaches as x approaches positive or negative infinity.

To find the vertical asymptote, we set the denominator equal to zero and solve for x:

-4x - 16 = 0

-4x = 16

x = -4

Therefore, the equation has a vertical asymptote at x = -4.

To find the horizontal asymptote, we need to examine what happens to the function as x becomes very large or very small. We can do this by dividing the numerator and denominator by the highest power of x in the denominator, which in this case is x:

f(x) = (x-4)/(-4x-16) = (x/x - 4/x) / (-4/x - 16/x)

= (1 - 4/x) / (-4 - 16/x)

As x becomes very large (either positive or negative), the terms involving 4/x and 16/x become very small, and we are left with:

f(x) ≈ (1 - 0) / (-4 - 0) = -1/4

So, the equation has a horizontal asymptote at y = -1/4.

Using this information, we can choose the appropriate graph for the situation. The graph of the equation will approach the vertical asymptote at x = -4, and approach the horizontal asymptote at y = -1/4, as x gets very large or very small. The graph should look something like this: Attachment 1

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Answer:

Part A:

To graph the system of equations, we need to plot the two equations on the same coordinate axes.

First, let's graph the inequality 2x + 4y ≤ 24. We can start by graphing the equation 2x + 4y = 24 (by setting it equal to the maximum value of 24).

When x = 0, 2(0) + 4y = 24, which gives y = 6. When y = 0, 2x + 4(0) = 24, which gives x = 12. So we have the points (0, 6) and (12, 0) on the line.

Next, we need to decide which side of the line to shade. Since the inequality includes "less than or equal to," we will shade the side of the line that contains the origin, which is the side where 2x + 4y < 24.

Now, let's graph the equation x + y = 7. When x = 0, y = 7. When y = 0, x = 7. So we have the points (0, 7) and (7, 0) on the line.

Again, we need to decide which side of the line to shade. Since the inequality includes "greater than or equal to," we will shade the side of the line that contains the point (0, 0), which is the side where x + y > 7.

Putting it all together, the graph should look like the image I provided.

Part B:

The solution to the system of equations is the shaded region on the graph where the two shaded regions overlap. This region represents all the possible combinations of pokemon and bakugan cards that Noah can purchase for at least 7 of his friends using the $24 he has.

Part C:

To determine whether the point (2, 3) is included in the solution, we need to check whether it satisfies both equations.

Plugging in x = 2 and y = 3 to the first equation, we get 2(2) + 4(3) = 16, which satisfies the inequality 2x + 4y ≤ 24.

Plugging in x = 2 and y = 3 to the second equation, we get 2 + 3 = 5, which does not satisfy the inequality x + y ≥ 7.

Therefore, the point (2, 3) is not included in the solution.

Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]

[tex]csc(-x)-1~~ = ~~\cfrac{cot^2(x)}{csc(-x)+1} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{cot^2(x)}{csc(-x)+1}\implies \cfrac{~~ \frac{ cos^2(x)}{sin^2(x) } ~~}{\frac{1}{sin(-x)}+1}\implies \cfrac{~~ \frac{ cos^2(x)}{sin^2(x) } ~~}{\frac{1}{-sin(x)}+1}\implies \cfrac{~~ \frac{ cos^2(x)}{sin^2(x) } ~~}{1-\frac{1}{sin(x)}} \\\\\\ \cfrac{~~ \frac{ cos^2(x)}{sin^2(x) } ~~}{\frac{sin(x)-1}{sin(x)}}\implies \cfrac{ cos^2(x)}{sin^2(x) }\cdot \cfrac{sin(x)}{sin(x)-1}\implies \cfrac{ cos^2(x)}{sin(x)[sin(x)-1] }[/tex]

[tex]\cfrac{ cos^2(x)}{-sin(x)[1-sin(x)] }\implies \cfrac{ -cos^2(x)}{sin(x)[1-sin(x)] } \\\\\\ \cfrac{ -cos^2(x)}{sin(x)[1-sin(x)] }\cdot \cfrac{1+sin(x)}{1+sin(x)}\implies \cfrac{-cos^2(x)[1+sin(x)]}{sin(x)\underset{ \textit{difference of squares} }{[1-sin(x)][1+sin(x)]}} \\\\\\ \cfrac{-cos^2(x)[1+sin(x)]}{sin(x)[1-sin^2(x)]}\implies \cfrac{-cos^2(x)[1+sin(x)]}{sin(x)[cos^2(x)]}[/tex]

[tex]\cfrac{-[1+sin(x)]}{sin(x)}\implies \cfrac{-1-sin(x)}{sin(x)}\implies \cfrac{-1}{sin(x)}-\cfrac{sin(x)}{sin(x)}\implies \cfrac{1}{-sin(x)}-1 \\\\\\ \cfrac{1}{sin(-x)}-1\implies \boxed{csc(-x)-1 }[/tex]

Answer:

(-3,1)

Step-by-step explanation:

The solution is where in the graph, both lines intersect. In this case they are intersect at (-3,1), so the answer is (-3,1)

The solution to [tex]-2x(-2)^-4/(-2)^-2[/tex]can be found by converting the expression into a rational exponent form. The expression can be written as[tex]-2(-1/2)^4/(-1/2)^[/tex]2.

The solution to [tex]-2x(-2)^-4/(-2)^-2[/tex]can be found by converting the expression into a rational exponent form. The expression can be written as[tex]-2(-1/2)^4/(-1/2)^[/tex]2. By raising both the numerator and denominator to the same exponent, the expression can be simplified to [tex]-2(-1/2)^2/-1.[/tex]Next, we can simplify the rational exponent to [tex]-2(-1/4)/-1.[/tex] After simplifying, we can then rewrite the expression in a standard form as 8/1. Therefore, the solution to[tex]-2x(-2)^-4/(-2)^-2[/tex] is -1/2.To calculate the solution step by step, we can use the following formula:Step 1:[tex]-2x(-2)^-4/(-2)^-2[/tex]Step 2: [tex]-2(-1/2)^4/(-1/2)^2[/tex] Step 3: [tex]-2(-1/2)^2/-1[/tex] Step 4: [tex]-2(-1/4)/-1[/tex]Step 5: -1/2Therefore, the solution to[tex]-2x(-2)^-4/(-2)^-2[/tex]is -1/2.

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Answer: 1.05 dollars

Step-by-step explanation:

Since an 8 minute phone call is 1.20 dollars, we divide 1.2 by 8 to get the price per minute of .15. This means we now multiply by seven to get 1.05 dollars.

Answer:

D)720

Step-by-step explanation:

It 720 because it is correct .

The volume of the cylinder is equal to 300π cubic feet.

What is meant by volume?

Volume is the measure of space within a particular 3D object in mathematics. For instance, a fish tank measures three feet long by one foot wide by two feet high. The volume is calculated by multiplying the length, the breadth, and the height, or 3x1x2, which equals six. The fish tank, therefore, has a 6 cubic foot volume.

It is given that the radius and height of the cone and cylinder are the same.

The volume of the cone is 100π cubic feet.

The volume of a cone is [tex]\frac{1}{3} \pi r^{2} h=100\pi[/tex]

The volume of a cylinder is [tex]\pi r^{2}h[/tex].

Therefore the volume of a cylinder is 3 times the volume of a cone with the same radius and height.

Therefore the volume of the cylinder is equal to 300π cubic feet.

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Based on the parameters, the width of the rectangular gate is 5.7 feet

From the question, we have the following parameters that can be used in our computation:

Brace = 7 feet

Height = 4 feet

Using the Pythagoras theorem we have the following equation

Width^2 = Brace^2 - Height^2

substitute the known values in the above equation, so, we have the following representation

Width^2 = 7^2 - 4^2

Evaluate

Width^2 = 33

Take the square root

Width = 5.7

Hence, the width is 5.7 feet

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Answer:

.4 or 2/5

Step-by-step explanation:

Answer:

Area of Parallelogram Using Diagonals ; Using Base and Height, A = b × h ; Using Trigonometry, A = ab sin (x) ; Using Diagonals, A = ½ × d1 × d2 .....

Using Diagonals: A = ½ × d1 × d2 sin (y)

Using Base and Height: A = b × h

Using Trigonometry: A = ab sin (x)

The required probability of getting at least one red card is [tex]\frac{3}{4}[/tex].

A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The probability of getting at least one red card can be found by calculating the probability of getting two black cards and then subtracting that from 1 (since the sum of the probabilities of all possible outcomes must be 1).

The probability of getting a black card on the first draw is 26/52 = 1/2, and the probability of getting a black card on the second draw (assuming the first card was replaced) is also 1/2. Therefore, the probability of getting two black cards is:

[tex]$\frac{26}{52} \cdot \frac{26}{52} = \frac{1}{4}$$[/tex]

So the probability of getting at least one red card is:

[tex]$1 - \frac{1}{4} = \frac{3}{4}$$[/tex]

Therefore, the probability of getting at least one red card is [tex]\frac{3}{4}[/tex].

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Answer:

3/4 i took the test

Step-by-step explanation:

Answer:

The probability of selling three cars next week is approximately 0.0733, or 7.33%.

Step-by-step explanation:

We can use the Poisson distribution to solve this problem, since it models the number of events (in this case, the number of cars sold) that occur in a fixed period of time, given a known rate of occurrence.

The Poisson distribution has the following formula:

P(x) = (e^(-λ) * λ^x) / x!

where:

In this case, we know that the rate of occurrence (λ) is 1.1 cars per week, and we want to calculate the probability of selling 3 cars (x = 3) next week. Substituting these values into the Poisson distribution formula, we get:

P(3) = (e^(-1.1) * 1.1^3) / 3!

P(3) = (0.332871 * 1.331) / 6

P(3) = 0.0733

Therefore, the probability of selling three cars next week is approximately 0.0733, or 7.33%.

Answer:

0.0733, or 7.33%.

Step-by-step explanation:

The answer above is correct.

Answer:

x=0

Step-by-step explanation:

Answer:

Since each customer's decision to make a purchase is independent of other customers' decisions and there is a fixed probability of 0.52 for each customer to make a purchase, we can model the number of customers who make a purchase, X, using a binomial distribution.

The probability histogram of a binomial distribution is approximately symmetric when the probability of success (p) is close to 0.5, and becomes more skewed as p gets closer to 0 or 1. In this case, p = 0.52, which is close to 0.5, so the probability histogram of X is approximately symmetric.

Therefore, the answer is: approximately symmetric.

Step-by-step explanation:

Answer:

d. approximately symmetric

Step-by-step explanation:

Answer:

  3

Step-by-step explanation:

You want to simplify the product (3^(1/2))·(3^(1/2)).

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  a^1 = a

Your expression simplifies as follows:

  [tex]\displaystyle 3^{\frac{1}{2}}\times3^{\frac{1}{2}}=3^{\frac{1}{2}+\frac{1}{2}}=3^1=\boxed{3}[/tex]

__

Additional comment

This is a demonstration that 3^(1/2) = √3, the value that gives 3 when it is multiplied by itself.