Solve the following exponential equations

Answer:

s = 0.75 inches

Step-by-step explanation:

Let s = side length of the original square

s + 3 = side length of the new square

Area of a square = s²

A = s²

A = (s+3)²

A = s² + 6s + 9

Area multiplied by 25 = 25 * s²

So,

s² + 6s + 9 = 25s²

25s² - s² - 6s - 9 = 0

24s² - 6s - 9 = 0

8s² - 2s - 3 = 0

a = 8

b = -2

c = -3

s = -b ± √b² - 4ac / 2a

= -(-2) ± √(-2)² - 4(8)(-3) / 2(8)

= 2 ± √4 - (-96) / 16

= 2 ± √100 / 16

= 2 ± 10/16

s = 2 + 10/16 or 2-10/16

= 12/16 or -8/16

= 0.75 or -0.5

side length can not be negative

Therefore, s = 0.75

A = s²

A = (0.75)²

= 0.5625

A = (s+3)²

= (0.75+3)²

= 3.75²

= 13.95

Answer:

11,000

Step-by-step explanation:

You would multiply 1,500 by 7 and then add 500.

The algorithm described simulates a random variable with a binomial distribution of parameters p and n.

The given algorithm involves generating random numbers and incrementing a variable X based on certain conditions. The variable X represents the number of successes or "1" outcomes in a sequence of n independent Bernoulli trials, where each trial has a probability of success equal to p.

In each iteration of the loop, the algorithm generates a random number between 0 and 1 (denoted as RND) and compares it to the probability parameter p. If the generated random number is less than or equal to p, the variable X is incremented by 1.

This process is repeated for a total of n trials, resulting in the count of successes, which follows a binomial distribution. The binomial distribution represents the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success, given by parameter p. Therefore, the algorithm simulates a random variable with a binomial distribution of parameters p and n.

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A confidence interval for the population mean (BMI) based on a

random

sample of 45 people, a normal distribution should be used because the sample is random and the population is known.

In this scenario, the sample size is sufficiently large (n = 45), and the population standard

deviation

(σ = 6.16) is known. When these conditions are met, the appropriate distribution to construct a confidence interval for the population mean is the normal distribution. The central limit theorem states that when the sample size is large, the distribution of the sample mean approaches a

normal

distribution regardless of the shape of the population distribution.

Using the normal distribution, we can calculate the

standard

error of the mean (SEM) by dividing the population standard deviation by the square root of the sample size: SEM = σ / √n. In this case, the SEM would be 6.16 / √45. The confidence

interval

can then be calculated by multiplying the SEM by the appropriate critical value for the desired level of confidence (e.g., 95%) and adding/subtracting it to/from the sample mean.

Therefore, to construct a confidence interval for the population mean BMI, we would use a normal

distribution

because the sample is random, and the population standard deviation is known.

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Answer:

a protractor is not needed to constant a perpendicular bisecter

Step-by-step explanation:

please mark brainliest

Answer: She ate 12 apples

Step-by-step explanation: 18 divided by 2 is 9 add 2 of 9 to the other 9 and you get 12 hope I helped

Answer:

she ate 10 apples

Step-by-step explanation:

I thought of it because there is only 18 apples all together

The value of arc ABD is  determined as 236⁰.

Option C.

The value of arc ABD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

arc BA = 2 x 48⁰ (interior angles of intersecting secants)

arc BA = 96⁰

arc BD = 2 x 70⁰ (interior angles of intersecting secants)

arc BD = 140⁰

arc ABD = arc BA + arc BD

arc ABD = 96⁰  + 140⁰

arc ABD = 236⁰

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Answer:

B

Step-by-step explanation:

equation for volume of a cone = [tex]V=\frac{1}{3}\pi r^2h[/tex]

plug in - [tex]V=\frac{1}{3} \pi (4)^2(7)[/tex]

Answer:

we have

volume of cone =1/3 πr²h=1/3×π×4²×7ft³

so

v=1/3 π(4²)(7)ft³

Answer:

3.25

Step-by-step explanation:because you have to divide the years with the inches so in each year i would grow about 3.25 inches

Here are the solutions to each problem, which include the center and radius for each circle:7. Center: (6, -3); Radius: 6.9. Center: (-7, 10); Radius: 13.11. Center: (1, -2); Radius: 1/2.8. Center: (0, 9); Radius: 3/2.10. Center: (7/2, 3/2); Radius: 5/2.12. Center: (2, 0); Radius: 1.

The solution is given as follows;7. x² - 12x + y² + 6y = - 9.

We start by grouping the x and y terms separately, then completing the square by adding half of the coefficient of the respective variable and squaring the result. x² - 12x + y² + 6y = - 9(x² - 12x + __) + (y² + 6y + __) = - 9 + __ + __

Now, we'll fill in the blanks in the parentheses so that the trinomials are perfect squares: (x² - 12x + 36) + (y² + 6y + 9) = - 9 + 36 + 9.

This simplifies to: (x - 6)² + (y + 3)² = 36.

The center of the circle is (6, −3), and its radius is 6.9. x² + y² + 14x - 20y - 20 = 0.

First, we group the x terms and the y terms separately:x² + 14x + y² - 20y = 20.

Now, we'll complete the square in both x and y. x² + 14x + y² - 20y = 20(x² + 14x + __) + (y² - 20y + __) = 20 + __ + __.

We'll fill in the blanks so that the trinomials are perfect squares.

To find the terms to add, we take half of the coefficient of the variable and square it. (x² + 14x + 49) + (y² - 20y + 100) = 20 + 49 + 100

Simplifying, we get (x + 7)² + (y - 10)² = 169.

The center of the circle is (-7, 10), and its radius is 13.x - 2x + y + 3/2y = -1

We first rearrange the terms. x - 2x + y + 3/2y = -1-x - 1/2y = -1

We then complete the square in x and y as follows. x - 2x + y + 3/2y = -1(x - 1) - (1/2)(y + 2) = -1/2(x - 1)² - 1/4(y + 2)² = 1/2

The center of the circle is (1, -2) and its radius is 1/2.8. - 3x² - 3y² + 27y + 61 = 0

We rearrange and group the terms. - 3x² - 3y² + 27y = -61

We then complete the square. - 3x² - 3(y² - 9y + 81/4) + 27(81/4) = -61 - 3(81/4)(x² + (y - 9/2)² = 405/4

The center of the circle is (0, 9) and its radius is 3/2.10. x² + y² - 7x - 3y - 1 = 0

We rearrange and group the terms. x² - 7x + y² - 3y = 1

We then complete the square. x² - 7x + 49/4 + y² - 3y + 9/4 = 1 + 49/4 + 9/4(x - 7/2)² + (y - 3/2)² = 25/4

The center of the circle is (7/2, 3/2), and its radius is 5/2.12. 4x² - 16x + 4y² + 16 = 0

We rearrange and group the terms. 4x² - 16x + 4y² = -16

We then complete the square. 4(x² - 4x + 4) + 4y² = 0(x - 2)² + y² = 1

The center of the circle is (2, 0), and its radius is 1.

Completing the square is a method used to turn quadratic expressions in standard form into perfect squares. It’s often used to find the center and radius of circles.

Here are the solutions to each problem, which include the center and radius for each circle:7. Center: (6, -3); Radius: 6.9. Center: (-7, 10); Radius: 13.11. Center: (1, -2); Radius: 1/2.8. Center: (0, 9); Radius: 3/2.10. Center: (7/2, 3/2); Radius: 5/2.12. Center: (2, 0); Radius: 1.

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Answer:

16.25 grams are left

exponential

Step-by-step explanation:

Half the material will decay every 12-hour period (the other half will remain).

Initial amount (at time t = 0):  520 grams

Time t = 12:  260 grams are left

Time t = 24:  130 grams are left

Time t = 36:  65 grams are left

Time t = 48:  32.5 grams are left

Time t = 72:  16.25 grams are left

Radioactive decay is modeled by an exponential function.  The function can't be linear because for them, equal time steps would produce equal reductions in the amount of material.

The function h(x) = 4sec(π/4(x+3)) represents a graph with a stretching factor of 4 and a period of 8π/4 = 2π. The correct graph representation of h(x) = 4sec(π/4(x+3)) needs to show these characteristics. The correct answer would be (b).

The function h(x) = 4sec(π/4(x+3)) has a stretching factor of 4, which means that the amplitude of the function is multiplied by 4, causing the graph to be vertically stretched.

The period of the function is given by P = 2π/π/4 = 8π/4 = 2π. This means that the graph will complete two periods within the interval [-P, P], which in this case is [-2π, 2π].

The asymptotes of the function occur at x = -P/2 and x = P/2. Substituting the value of P = 2π, the asymptotes are x = -π and x = π. These vertical asymptotes indicate where the graph approaches infinity or negative infinity as x approaches these values.

To determine the correct graph representation of h(x) = 4sec(π/4(x+3)), you would need to choose the graph option that shows the stretching factor of 4, a period of 2π, and vertical asymptotes at x = -π and x = π.

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An example of a commutative ring R with 1, a prime ideal P, and no zero divisors but R is not an integral domain is the ring R = Z/6Z, where Z is the set of integers and 6Z is the ideal generated by 6.

The ring R = Z/6Z consists of the residue classes of integers modulo 6. The elements of R are [0], [1], [2], [3], [4], and [5], where [a] denotes the residue class of a modulo 6.

In this ring, addition and multiplication are performed modulo 6. For example, [2] + [3] = [5] and [2] * [3] = [0].

R has a multiplicative identity, which is the residue class [1]. It is commutative since addition and multiplication are performed modulo 6.

The ideal P = 2R consists of the elements [0] and [2]. P is a prime ideal since R/P is an integral domain, which means there are no zero divisors in R/P. However, R itself is not an integral domain because [2] * [3] = [0] in R, showing that zero divisors exist in R.

Therefore, the ring R = Z/6Z, with the prime ideal P = 2R, satisfies the given conditions.

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The final concentration in the tank is 0.045 kg/L, which is the same as the concentration of the incoming solution.

To solve the problem, we can use the formula:

C1V1 + C2V2 = C3V3

where C1 is the initial concentration, V1 is the initial volume, C2 is the concentration of the incoming solution, V2 is the volume of the incoming solution, C3 is the final concentration, and V3 is the final volume.

We know that the initial volume of the tank is 1000 L and it contains 90 kg of salt. To find the initial concentration, we need to convert the mass of salt to concentration by dividing it by the total volume:

90 kg / 1000 L = 0.09 kg/L

This means that initially, the concentration of salt in the tank is 0.09 kg/L.

Next, we need to calculate how much salt enters and leaves the tank during a given time period. Since the incoming solution has a concentration of 0.045 kg/L and enters at a rate of 8 L/min, it brings in:

0.045 kg/L x 8 L/min = 0.36 kg/min

The outgoing solution has the same concentration as the final concentration in the tank, so we can use this formula to find it:

C1V1 + C2V2 = C3V3

(0.09 kg/L)(1000 L) + (0.045 kg/L)(8 L/min)(t min) = C3(1000 L + 8 L/min)(t min)

Simplifying and solving for C3, we get:

C3 = (0.09 kg/L)(1000 L) + (0.045 kg/L)(8 L/min)(t min) / (1000 L + 8 L/min)(t min)

At steady state, when the amount of salt entering and leaving the tank is equal, we can set the incoming and outgoing terms equal to each other:

0.36 kg/min = C3(8 L/min)

Solving for C3, we get:

C3 = 0.045 kg/L

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First find the center, then graph all the points that are at a distance of R units from that center.

A circle of radius R is the set of all points that are at a distance R from a given point (the center of the circle).

So to graph it, we need to know these two things, radius and center.

Once we do, first we graph the center on the coordinate plane.

Once we find the center, we can find all the poiints that are at a distance of R units from our center, so we need to graph these. Once we do, we will have the graph of our circle on the coordinate plane.

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Answer:

what is your question? it seems the answer would be 12 just by looking at this, but still what is the question exactly?

Step-by-step explanation:

Answer: if you are dividing the answer will be 12

(i wrote two since it dosent say what we need to do

if you are multiplying you answer will be 192

hope it helped!

Step-by-step explanation:

Answer:

1. (-125 a - 5.75) x + b c (605 x - 550 x^2) + 10.75

2. -125 a x + x (-550 b c x + 605 b c - 5.75) + 10.75

3. 0.25 (-500 a x - 220 b c (10 x - 11) x - 23 x + 43)

Step-by-step explanation:

The volume of the room with the given dimensions is 84 cubic meters.

The volume of a room can be calculated by multiplying its length, width, and height. In this case, the given dimensions are:

Length (L) = 7 m

Width (W) = 4 m

Height (H) = 3 m

To find the volume, we can use the formula:

Volume = Length × Width × Height

Substituting the given values:

Volume = 7 m × 4 m × 3 m

Simplifying:

Volume = 84 m³

Therefore, the volume of the room with the given dimensions is 84 cubic meters.

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Answer:

r = c / 2π

Step-by-step explanation:

c = 2πr is the formula for the circumference of a circle of radius r.

We can solve this for r:

r = c / (2pi)

or

r = c / 2π

Answer:

The function stated by Tucker is incorrect.

V(t) = 4600(0.8)^t

Step-by-step explanation:

Given the function :

V(t)=4,600(0.4)2t

The initial value of equipment = 4600

Decay rate = 40% of very 2 years

The value of equipment t years after purchase

The exponential decat function goes thus :

V(t) = Initial value * (1 - decay rate)^t

The Decay rate per year = 40% /2 = 20% = 0.2

V(t) = 4600(1 - 0.2)^t

V(t) = 4600(0.8)^t

Based on a random sample of 50 home theater systems, the 90% confidence interval for the population mean price is approximately $110.81 to $119.19, assuming a population standard deviation of $19.50.

To construct a 90% confidence interval for the population mean of home theater systems, we can use the following formula

Confidence Interval = Sample Mean ± Margin of Error

The margin of error depends on the level of confidence and the standard deviation of the population. Given that the sample size is large (n = 50) and we know the population standard deviation is $19.50, we can use the z-distribution.

First, we need to find the critical value (z) for a 90% confidence level. Using a standard normal distribution table or calculator, the critical value for a 90% confidence level is approximately 1.645.

Next, we calculate the margin of error (E) using the formula:

Margin of Error (E) = z * (Population Standard Deviation / sqrt(n))

E = 1.645 * ($19.50 / √(50))

E ≈ $4.19

Now we can construct the confidence interval:

Confidence Interval = Sample Mean ± Margin of Error

Confidence Interval = $115 ± $4.19

Confidence Interval ≈ ($110.81, $119.19)

Therefore, we can say with 90% confidence that the population mean of home theater systems is between approximately $110.81 and $119.19.

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This indicates that the Australian dollar appreciated by 5.80%. the correct answer is (a) appreciated; 5.80.

To determine whether the Australian dollar appreciated or depreciated and by what percentage, we can calculate the percentage change in value between today and yesterday.

The formula for calculating the percentage change is:

Percentage Change = (New Value - Old Value) / Old Value * 100

Using this formula, we can calculate the percentage change:

Percentage Change = (0.73 - 0.69) / 0.69 * 100

Percentage Change = 0.04 / 0.69 * 100

Percentage Change ≈ 5.80

The percentage change is approximately 5.80%. This indicates that the Australian dollar appreciated by 5.80%.

Therefore, the correct answer is (a) appreciated; 5.80.

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To find the equation of a parabola given its focus and directrix, we use the standard form of the equation of a parabola which is:

[tex]\frac{(y-k)^2}{4a} = x-h[/tex]

Where (h,k) is the vertex of the parabola, and a is the distance between the vertex and the focus (or between the vertex and directrix, they're equal).

Therefore, the answer is option D, (y-3)²-4(x-3).

Using this formula, let's first find the vertex of the parabola. Since the directrix is a horizontal line, the vertex lies halfway between the focus and directrix on the y-axis. Thus, the vertex is at (3,3).

Since the focus is above the vertex, a is positive, and its value is the distance between the vertex and focus:

a = 4 - 3

= 1

Substituting these values into the standard form of the equation of a parabola gives:

[tex]\frac{(y-3)^2}{4(1)} = x - 3$$[/tex]

[tex]\frac{(y-3)^2}{4} = x - 3$$[/tex]

Multiplying both sides by 4 gives:

y - 3 = 2(x - 3)

y = 2x - 3

Therefore, the answer is option D, (y-3)²-4(x-3).

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Answer:

(2, 7) is not an ordered pair for the function.

Step-by-step explanation:

The number of shoppers on the first day is 150, and each subsequent day the number of shoppers increases by 15%.

Number of shoppers on the first day: The shopping mall recorded a total of 150 shoppers on their first day of business.

Increase in shoppers each day: Starting from the second day, the number of shoppers increases by 15% compared to the previous day.

To calculate the number of shoppers on each day, we can use the following steps:

Day 1: The number of shoppers on the first day is given as 150.

Day 2: To find the number of shoppers on the second day, we need to increase the number of shoppers from the previous day by 15%.

Number of shoppers on Day 2 = Number of shoppers on Day 1 + (15/100) * Number of shoppers on Day 1

Day 3: Similarly, to find the number of shoppers on the third day, we increase the number of shoppers from the second day by 15%.

Number of shoppers on Day 3 = Number of shoppers on Day 2 + (15/100) * Number of shoppers on Day 2

We can continue this process for each subsequent day, using the number of shoppers from the previous day to calculate the number of shoppers for the current day.

By following these steps, we can determine the number of shoppers on each day, starting from the first day and increasing by 15% each day compared to the previous day.

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Im gonna label the long side of a rectangle a and the smaller side b.

For the perimeter, 2a + 2b = 34

For the area, a x b = 66

if a is 11 and b is 6, the equation for perimeter would be 22 + 12 = 34.

So a = 11 and  b = 6

Answer:

Longer side = 11

Shorter side = 6

Step-by-step explanation:

L x W = 66,  then W = 66/L

2L + 2W = 34

substitute for W:

2L + 2(66/L) = 34

2L + 132/L = 34

multiply both sides of the equation by L:

2L² + 132 = 34L

divide both sides by 2:

L² + 66 = 17L

L² - 17L + 66 = 0

factor:

(L - 11)(L - 6) = 0

L = 11 or L = 6

if L = 11, then W = 6

if L = 6 then W = 11

As per the given details, the dog is approximately 0.6249 * 3 = 1.8747 meters from the house.

The angle recognized in the problem is the angle of depression. The angle of depression is the attitude between the horizontal line and the line of sight from an observer looking downward.

To calculate approximately how a ways the canine is from the residence, we are able to use trigonometry.

Since the angle of despair is given as 32º and the boy is 3 meters above the floor, we will use the tangent characteristic to find the space.

tan(32º) = (dog's distance / boy's height)

tan(32º) = d / 3

3 * tan(32º) = d

The dog is approximately 0.6249 * 3 = 1.8747 meters from the house.

To calculate how high the boy is above the floor, we are able to again use trigonometry. Since the canine is 7 meters from the residence and the attitude of melancholy is given as 32º, we are able to use the tangent characteristic to discover the peak of the boy.

tan(32º) = (boy's height / dog's distance)

tan(32º) = h / 7

7 * tan(32º) = h

Therefore, the boy is approximately 0.6249 * 7 = 4.3743 meters above the ground.

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Answer:

0.075 inches per year

Step-by-step explanation:

The average rate of change is measured as

( difference in diameter ) ÷ ( difference in years )

= ( 251 - 248 ) ÷ ( 2005 - 1965 )

= 3 inches ÷ 40 years

= 0.075 inches per year