The day Sunshine City was formed, it had a population of 100 people. However, the city grew exponentially over the following years. Its population could be modeled by this equation: , where p represents population, and t represents the time in years.

(1) What is the theoretical domain for Sunshine City’s population equation?

(2) What is the theoretical range for Sunshine City’s population equation?

(3) Assuming the model holds true, how many people will live in Sunshine City 20 years after it was founded? Round to the nearest tenth, and be sure to label your answer.

(4) Look at your answer to 2(c). Is it part of the practical range of the function? Why or why not? Explain the difference between the practical range and theoretical range of the function.

Answer:

Step-by-step explanation:

1254p(b/(8p))=156.75b

The number of boats must be an integer because you can’t have a fraction of a boat so

b=157

Answer:

2 x + 3 y

Step-by-step explanation:

The nominal rate per annum compounded half-yearly, equivalent to an effective rate of 14.5% per annum, is approximately 14.900625%.

To convert an effective rate to a nominal rate compounded half-yearly, we can use the formula:

Nominal rate \(= (1 + r/m)^m - 1\)

Where:

r = effective rate

m = number of compounding periods per year

In this case, the effective rate is 14.5% per annum, and we want to convert it to a nominal rate compounded half-yearly.

Since compounding is done semi-annually, m would be 2.

Plugging in the values:

Nominal rate \(= (1 + 0.145/2)^2 - 1\)  

Simplifying the expression inside the parentheses:

Nominal rate \(= (1 + 0.0725)^2 - 1\)

Calculating the exponent:

Nominal rate \(= (1.0725)^2-1\)

Performing the calculations:

Nominal rate = 1.14900625 - 1

Nominal rate = 0.14900625

Converting the nominal rate to a percentage:

Nominal rate = 14.900625%

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Answer:

9x - 2x + 62 = 9x + 24

Number of correct answer each obtained = 19

Step-by-step explanation:

Given that:

Number of correct answers = x

POINTS for correct answers = 9

POINTS for incorrect answers = - 2

SCHOOL A:

Number of correct answers = x

Number of incorrect answers = x

Initial point = 62

Initial point + 9(number of correct answers) + - 2(number of incorrect answers)

62 + 9x - 2x

SCHOOL B :

Number of correct answers = x

Number of incorrect answers = 0

Initial point = 24

Initial point + 9(number of correct answers) + - 2(number of incorrect answers

24 + 9x

Since they end up tied :

School A = School B

62 + 9x - 2x = 24 + 9x

9x - 2x + 62 = 9x + 24

Number of correct answers gotten :

9x - 2x + 62 = 9x + 24

7x + 62 = 9x + 24

7x - 9x = 24 - 62

-2x = - 38

x = 19

Hence, Number of correct answers each obtained = 19

(1) The value of x is determined as 16.8.

(2) The measure of length VX is calculated as 4.1.

(3) The measure of angle UWV is 69.5⁰.

The value of the missing lengths of the triangle is calculated by applying the following formula;

(1) For the two similar triangles, the value of x is calculated as follows;

20 / (28 - x) = 30 / x

20x = 30 (28 - x )

20x = 840 - 30x

20x + 30x = 840

50x = 840

x = 840 / 50

x = 16.8

(2) The measure of length VX is calculated by applying trig ratios.

tan 63 = 8 / VX

VX = 8 / tan 63

VX = 4.1

(3) The measure of angle UWV is calculated as follows;

angle T = 360 - (94 + 127) = 139

angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)

angle UWV = 69.5⁰

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Answer:

Step-by-step explanation:

Give me a sec to work it out

The value of a in the equation 60°a = [? ]° is dependent on the value of [? ].

To solve for a in the equation 60°a = [? ]°, we need to isolate a on one side of the equation. We can do this by dividing both sides of the equation by 60°:

60°a / 60° = [? ]° / 60°

This simplifies to:

a = [? ]° / 60°

Since we don't have the value of [? ]°, we cannot determine the exact value of a. However, we can simplify the expression by canceling out the ° units:

a = [? ] / 60

Therefore, the value of a is dependent on the value of [? ].

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₋2.3 < ₋8/3 is the correct answer.

Given, we need to compare the terms.

₋8/3 = ₋2.67

therefore, 2.3 is less than 2.667

hence we form it as ₋2.3 < ₋2.67

we form: ₋2.3 < ₋8/3

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Answer:

25

Step-by-step explanation:

Step-by-step explanation:

7

√

15

32

=

0.85

Explanation:

sin 2t = 2sin t.cos t

Knowing

cos

t

=

−

7

8

, find sin t.

Trig identity:

sin

2

a

=

1

−

cos

2

a

-->

sin

2

t

=

1

−

cos

2

t

=

1

−

49

64

=

15

64

sin t = +- sqrt15/8.

Arc t is in Quadrant III, then, sin t is negative.

sin

2

t

=

2

(

−

7

8

)

(

−

√

15

8

)

=

7

√

15

32

=

0.85

hope this helps :)

The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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Answer:

44

Step-by-step explanation:

Answer:

1 iteration: x =  

5/4

2 iteration: x =  

11/8

3 iteration: x =  

21/16

Step-by-step explanation:

Hope this helps!

The probability of a z-score smaller than -1.54 using a normal distribution table is roughly 0.06162. As a result, there is a roughly 0.06162 percent chance that the average thickness of the 100 sheets is less than 3.83 mm.

1.  A. True

B. False

C. True

D. True

2. The histograms indicate that option B, or 290, is the most likely number for the population mean.

3.A candy bar's weight has a normal distribution with a mean of 50 grammes and a standard deviation of 2 grammes. A normal distribution describes the weight of the four candy bars in a pack, with a mean of 50 grammes and a standard deviation of 1 gramme (since the standard deviation of the sum of independent random variables is the square root of the sum of their variances). In light of this, the likelihood that the average weight of the bars in a randomly chosen pack is 4 or more grammes less than stated is as follows:

P(z -4) = P(x 46) = P((x - )/(/n) (46 - 50)/(1/4))

As there is no method to calculate this likelihood due to the exceedingly low probability, option E is the correct response.

4. B. We repeatedly choose 15-person random samples from a population with a normal distribution.

5.The standard error is 1.1/100 = 0.11mm, and the sample mean's sampling distribution's mean is also 4mm. The z-score for a sample mean of 3.83mm is as follows:

z = (3.83 - 4) / 0.11 = -1.54

The probability of a z-score smaller than -1.54 using a normal distribution table is roughly 0.06162. As a result, there is a roughly 0.06162 percent chance that the average thickness of the 100 sheets is less than 3.83 mm.

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Answer: 1.25

Step-by-step explanation: 5 / 4 = 1.25

Answer:

Acute

Step-by-step explanation:

acute triangle has angles with measurement less than 90

Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

The domain of the function g ( x ) = √ x − 3 / x − 11 is R - 11.

Inputs are assigned outputs by functions. The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

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Answer:

≈4,365%.

Step-by-step explanation:

1) для нахождения требуемой вероятности необходимо найти вероятность каждого из пяти выниманий, а затем перемножить их;

2) при каждом вынимании вероятности:

\(P_1=\frac{C^1_{10}*C^1_{10}}{C^2_{10}}=\frac{10}{19};\\P_2=\frac{C^1_9*C_9^1}{C^2_{18}}=\frac{9}{17};\\P_3=\frac{C^1_8*C_8^1}{C^2_{16}}=\frac{8}{15};\\P_4=\frac{C^1_7*C^1_7}{C^2_{14}}=\frac{7}{13};\\P_5=\frac{C^1_6*C^1_6}{C^2_{12}}=\frac{6}{11};\)

3) требуемая вероятность:

P=P₁*P₂*P₃*P₄*P₅≈0,04365.

Answer:6/5 or 1.2

Step-by-step explanation:

4/5 divided by 2/3

=4/5 *3/2

=12/10

=6/5

=1.2

Answer:

AAS

Step-by-step explanation:

because here it is given that two angle are

equal

and a side is common between both traingle

so, both traingle are congruent by

AAS

hope it helps

The number of grasses is 17.

The number of trees is 36.

The number of weeds is 29.

Two linear equations would be formed given the information in the question. A linear equation is an equation that is made up of a single variable that is raised to the power of one. When drawn on a graph, a linear equation is a straight line.

Let g represent the number of grasses

Weeds  = 2g - 5

Trees  =2g + 2

82 = 2g + 2 + g + 2g -5

The first step is to determine the value of g. To determine the value of g, take the following steps:

Combine similar terms:

82 - 2 + 5 = 2g + g + 2g

Add similar terms together:

85 = 5g

Divide both sides of the equation by 5

g = 85/5

g = 17

Weeds = 2(17) - 5

= 34 - 5 = 29

Trees  =2(17) + 2

34 + 2 = 36

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The range is the best measure of variability for this data, and its value is 4.

The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).

The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:

Range = Maximum value - Minimum value = 4 - 0 = 4

Therefore, the range is the best measure of variability for this data, and its value is 4.

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9514 1404 393

Answer:

Step-by-step explanation:

In scientific notation, the decimal point is placed immediately to the right of the most-significant digit. The exponent of 10 is the number of digits to the right of the most significant digit.

  186,000 mi/s = 1.86×10^5 mi/s

  671,000,000 mi/h = 6.71×10^8 mi/h

Comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.

A multiple of the denominators of two or more fractions can be used as a common denominator to add, subtract, or compare the fractions. As fractions with dissimilar denominators cannot be added together or directly compared, they must be changed into comparable fractions with the same denominator. We must determine the least common multiple (LCM) of the fraction denominators in order to determine a common denominator. The lowest number that is a multiple of both denominators is known as the LCM. Once we have the common denominator, we may multiply the numerator and denominator by the same factor to change each fraction to an equal fraction with the same denominator.

The two values are 9/10 and 3/2.

Taking the LCM we have:

9/ 10 and 15/10

Now comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.

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On number line we can compare 9/10 and 3/2 as 9/10 < 3/2.

What is number line?

A number line is a visual representation of numbers in order, usually shown horizontally. It is a line with a starting point and an endpoint that represent the smallest and largest numbers, respectively.

To compare 9/10 and 3/2 on a number line, we need to first convert them to the same denominator. The least common multiple of 10 and 2 is 10, so we can convert 3/2 to 15/10:

9/10 = 0.9

3/2 = 15/10 = 1.5

Now, we can plot these two numbers on a number line:

We can see that 9/10 is to the left of 3/2 on the number line.

Therefore we can compare 9/10 and 3/2 as 9/10 < 3/2.

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The similarities between matrix factorization and content-based filtering and/or collaborative filtering are given below.

What is matrix factorization and collaborative filtering?

A group of cooperative filtering algorithms used in recommender systems is called matrix factorization. The user-item interaction matrix is broken down into the product of two rectangular matrices with lower dimensions by matrix factorization algorithms.

Collaborative filtering makes recommendations by simultaneously comparing similarities between users and items, addressing some of the drawbacks of content-based filtering.

collaborative filtering: user-based for example, CF calculates users' similarities in the item space. Then taking similar users's interest to do a recommendation for the target user. CF is one case of neighborhood methods.

matrix factorization amounts to mapping features of user and item via linear combination to latent factor space respectively.

Then calculating the similarity via inner-product of latent user factor and latent item factor.

CF covers local information of target user for the sake of neighborhood methods, while MF covers global information.

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Length of cuboid = 4 cm

Width of cuboid = 2 cm

Height of cuboid = 4 cm

Volume of cuboid :

\( = \tt{Length × Width × Height }\)

\( = \tt{4 \times 2 \times 4}\)

\( =\bold{\color{plum}\tt 32 \: cm {}^{3} }\)

Therefore, the volume of this cuboid = 32 cm³

Answer:  

I think the answer is -3/4

Step-by-step explanation:

Let x = a number

(2x)(5) = 9x - (3/4)

10x = 9x - (3/4)

Subtract 9x on both sides of equation.

x = -3/4