Gregoria borrowed $2,450, to be paid back at 3.5% simple interest. She spent $3221.75 in all to repay the loan. How many years did Georgia take to repay the loan?

Answer:

1. 18 2. 13 3. 36

Step-by-step explanation:

Answer:

a) 10,500 big cats

b) 13,401 big cats

c) 33 years

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:  

A = P (1 + r) t  

Where:  

p = original population  

r = growing rate (decimal form; 5/100= 0.05)

t= years  

A = population after t years  

Replacing with the values given:  

a) At 2005, 1 year passed since 2004 (t=1)

A = 10,000 (1+ 0.05)^1

A = 10,500 big cats

b)

At 2010, 6 years passed since 2004 (2010-2004= 6)

A = 10,000 (1+ 0.05)^6

A = 13,401 big cats

c)

50,000 < 10,000 (1+ 0.05)^t

Solving for t:

50,000/10,000 < 1.05^t

5 < 1.05^t

log 5 < log 1.05^t

log 5 < t ( log 1.05)

log 5 / log 1.05 < t

32.9 years < t

33 years  = t

Feel free to ask for more if needed or if you did not understand something.  

Answer: The average rate at which the water level changed every week = \(-\dfrac35\) inches per week.

Step-by-step explanation:

Given: Change in water level in \(1 \dfrac23\)  week = \(-1\dfrac12\) inches = \(-\dfrac32\) icnhes

To find : The average rate at which the water level changed every week.

i.e. Change in water level per week.

As \(1\dfrac23 = \dfrac52\)

Change in water level in 1 week = \(-\dfrac{3}{2}\div\dfrac52 = -\dfrac32\times \dfrac25= -\dfrac35\)

Hence, the average rate at which the water level changed every week = \(-\dfrac35\) inches per week.

We want to find the average rate of change at which the water level changed in a given time period.

We will find that the average rate of change is:

\(r = - 0.9 in/week\)

We define the average rate of change as the quotient between the total change and the time it takes.

Here we have:

total change = -(1 + 1/2) in

Time = (1 + 2/3) weeks

Then the average rate of change is:

\(r = \frac{-(1 + 1/2) in}{(1 + 2/3) weeks} = - 0.9 in/week\)

This means that the water level decreases, in average, 0.9 inches per week.

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The value of defnite integral ∫₀³ ∫ₓ²⁷ 2eˣ⁴ dy dx is 25/7.

To evaluate the integral by reversing the order of integration for ∫₀²⁷ ∫₃^y 2eˣ⁴ dx dy, you need to:

1. Rewrite the limits of integration for x and y. The new limits are: x goes from 0 to 3 and y goes from x to 27.
2. Reverse the order of integration: ∫₀³ ∫ₓ²⁷ 2eˣ⁴ dy dx.
3. Integrate with respect to y first: ∫₀³ [y * 2eˣ⁴]ₓ²⁷ dx = ∫₀³ (2eˣ⁴ * 27 - 2eˣ⁴ * x) dx.
4. Integrate with respect to x: [eˣ⁴ - (1/5)eˣ⁴ * x⁵]₀³.
5. Evaluate the definite integral.

The integral becomes ∫₀³ ∫ₓ²⁷ 2eˣ⁴ dy dx. After integration, evaluate the definite integral to find the final result.

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\((\stackrel{x_1}{-9}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{-17}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{-17}-\underset{x_1}{(-9)}}} \implies \cfrac{4 }{-17 +9} \implies \cfrac{ 4 }{ -8 } \implies - \cfrac{1 }{ 2 }\)

Answer:

x = 40° , y = 43° , z = 97°

Step-by-step explanation:

the figure opposite sides parallel and is therefore a parallelogram.

• consecutive angles are supplementary

∠ C + ∠ D = 180°

x + 43 + 97° = 180°

x + 140° = 180° ( subtract 140° from both sides )

x = 40°

y and 43° are alternate angles and are congruent, then

y = 43°

• opposite angles are congruent

∠ B = ∠ D , that is

z = 97°

point coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).

Given that,

We have to find what are the endpoint coordinates for the middle portion of the parallel to PQ segment of the PQR.

We know that,

First we write the co-ordinates of the triangle in the given graph.

P is (-3,3)

Q is (2,1)

R is (-4,-2)

The triangle's midpoint, which is parallel to section PQ, must be located. As a result, we would need to locate the midpoints of the segments PR and QR before joining the points to obtain the mid segment.

Midpoint Formula is

(x₁+x₂/2, y₁+y₂/2)

So,

The midpoint of the side PR is

(-3+(-4)/2, 3+(-2)/2)

(-3-4/2, 3-2/2)

(-7/2,1/2)

So, S point is (-3.5, 0.5)

The midpoint of the side QR is

(2+(-4)/2, 1+(-2)/2)

(2-4/2, 1-2/2)

(-2/2,-1/2)

So, T point is (-1, -0.5)

Therefore, The endpoint coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).

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The theater has a total of 945 seats.

To determine the number of seats in the theater, we need to calculate the sum of seats in each row. The first row has 25 seats, and each subsequent row increases by one seat. Since there are 35 rows in total, we can calculate the sum of an arithmetic series to find the total number of seats.

The formula for the sum of an arithmetic series is Sn = (n/2) * (a1 + an), where n is the number of terms, a1 is the first term, and an is the last term. In this case, n = 35 (number of rows), a1 = 25 (number of seats in the first row), and an = a1 + (n - 1) = 25 + (35 - 1) = 25 + 34 = 59 (number of seats in the last row). Plugging these values into the formula, we get Sn = (35/2) * (25 + 59) = 17.5 * 84 = 1470. Therefore, the theater has a total of 945 seats.


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Answer:

Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)

The rejection region is t > 1.761.

To test the hypothesis that the mean fee for car washers (including tips) is greater than $12, we can perform a one-sample t-test.

Sample mean \(\bar{x}\)  = $14.9

Sample standard deviation (s) = $6.75

Sample size (n) = 15

Significance level (α) = 0.05 (5%)

Since the sample size is small (n < 30) and the population standard deviation is unknown, we will use the t-distribution for inference.

Define the null and alternative hypotheses:

Null hypothesis (H₀): μ ≤ $12 (Mean fee for car washers is less than or equal to $12)

Alternative hypothesis (H₁): μ > $12 (Mean fee for car washers is greater than $12)

Determine the critical value (rejection region) based on the significance level and degrees of freedom.

The degrees of freedom (df) for a one-sample t-test is calculated as df = n - 1 = 15 - 1 = 14.

Using a t-table or statistical software, we find the critical t-value for a one-tailed test with α = 0.05 and df = 14 to be approximately 1.761.

Calculate the test statistic:

The test statistic for a one-sample t-test is given by:

t = (\(\bar{x}\)  - μ) / (s / √n)

Plugging in the values:

t = ($14.9 - $12) / ($6.75 / √15) ≈ 2.034

Make a decision:

If the test statistic t is greater than the critical t-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value (2.034) is greater than the critical t-value (1.761), indicating that it falls in the rejection region.

State the conclusion:

Based on the test results, at the 5% significance level, we have enough evidence to reject the null hypothesis.

We can infer that the mean fee for car washers (including tips) is greater than $12.

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The problem situation that can be represented by this inequality is A. Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $12.50 each and then spent $25.00 on a comic book portfolio. Victor sold a vintage comic book to the store for $95.00 and then purchased c more comic books for $22.50 each. How many comic books, c, would each boy purchase if Charles’ total amount due is greater than or equal to Victor’s total?

It should be noted that an inequality is used to illustrate the expressions that are not equal.

In this case, it should be noted that the inequality given is illustrated as 25 + 12.50c ≥ 22.50c − 95.

Therefore, the information that illustrates this is that Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $12.50 each and then spent $25.00 on a comic book portfolio. Victor sold a vintage comic book to the store for $95.00 and then purchased c more comic books for $22.50 each.

In conclusion, the correct option is A.

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The equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Violet's birthday is C = 24 - 4t

Number of chocolate violet eats each night = 4

Number of chocolate originally in the box = 24

Number of chocolate remaining = C

Number of days after violet birthday = t

Number of chocolate remaining = Number of chocolate originally in the box - (Number of chocolate violet eats each night × Number of days after violet birthday)

C = 24 - (4 × t)

C = 24 - 4t

In conclusion, the equation which represents violet's remaining chocolate after her birthday is C = 24 - 4t

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The equation of the line that is parallel to k and passes through (-1, 3) is

- x + 2y = 7

The equation of a line can be represented in different form such as point slope form, slope intercept form and standard form.

Therefore, the equation of the line is parallel to k.

Parallel line shave the same slope.

Therefore, let's find the slope of k to find the slope of the equation of the line.

Hence, using (7, 2)(1, -1)

m = -1  - 2 / 1 - 7

m = - 3 / -6

m = 1/ 2

Therefore, the slope of the line is 1 / 2. Let's find the y-intercept using the point (-1, 3)

3 = 1 / 2(-1) + b

3 = - 1 / 2 + b

b = 3 + 1 / 2

b = 7 / 2

Hence, the equation is as follows;

y = 1  /2x + 7 / 2

2y = x + 7

2y - x = 7

- x + 2y = 7

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There is insufficient evidence to conclude that the mean blood pressure for women is different from the mean blood pressure for men. To determine whether the mean blood pressure for women is equal to the mean blood pressure for men, a t-test is conducted using the sample data of 16 women (group 1) and their respective brothers' blood pressures (group 2).

The null hypothesis states that the means are equal, and the alternative hypothesis suggests they are different. The test statistic is calculated, critical points are identified, and the null hypothesis is either accepted or rejected based on the test results.

To carry out the t-test, we first calculate the test statistic. The formula for the test statistic (t) in this case is:

t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Given:

x1 = 119.4 (average blood pressure for women)

x2 = 121.2 (average blood pressure for men)

s2d = 25 (pooled sample variance)

n1 = n2 = 16 (sample sizes)

α = 0.05 (Type I error value)

Now, we can calculate the test statistic:

t = (119.4 - 121.2) / sqrt((25/16) + (25/16))

 = -1.8 / sqrt(3.125 + 3.125)

 = -1.8 / sqrt(6.25)

 = -1.8 / 2.5

 = -0.72

Next, we determine the relevant critical point(s) for the t-test. Since the sample size is small (n1 = n2 = 16), we refer to the t-distribution with degrees of freedom equal to n1 + n2 - 2 = 30 - 2 = 28. Using a significance level (α) of 0.05, the critical value for a two-tailed test is approximately ±2.048.

Since the absolute value of the test statistic (0.72) is less than the critical value (2.048), we fail to reject the null hypothesis.

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Answer:

Yes I do the formula is y=mx+b This means the answer is B

Step-by-step explanation:

You can ignore this if you already know the parts of the equation but here is it broken down. the X and Y in the slope intercept equation are left blank if you are given the slope and y-intercept like you were in this problem. The M in th equation stands for the slope which is 1/2 in this problem. B stands for the Y-intercept which just means where is the line crossing the y-axis when x is zero. I hope this helps you.

convert both mixed numbers to improper fractions. then multiply. you should get 208/15 or 13 13/15

Answer:

30

Step-by-step explanation:

50*(60/100)

=50*(3/5)

=30

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The minimum number of participants will be 30

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 Evelyn's yoga class has 50 participants. its rules require that 60% of them must be present for a class. If not, the class will be cancelled.

The minimum number of participants will be calculated as,

Number = 50 x (60/100)

Number = ( 5 x 6 )

Number = 30

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We are given the following statement:Wilfredo, who is currently 42 years old, is 8 years older than twice Alejandro's age. We have to determine Alejandro's age.Let's suppose the age of Alejandro to be A.So, according to the given statement, the age of Wilfredo can be calculated by the following equation:Wilfredo's age = 8 + 2ANow, we have been given that Wilfredo's age is 42 years. Therefore:42 = 8 + 2A⇒ 2A = 42 - 8 = 34⇒ A = 17Therefore, Alejandro's age is 17 years old.

Alejandro's age is given as follows:

17 years old.

Alejandro's age is obtained solving a system of equations, considering it's age as x.

Double his age is given as follows:

2x.

Eight more than double is given as follows:

2x + 8.

Wilfredo's age is of 42, hence the value of x is given as follows:

2x + 8 = 42

2x = 34

x = 17.

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The y(2) ≈ 0.3723 (approximated to four decimal places).

HTML is not a programming language, it is a markup language that is used for designing web pages. To solve the given question, you can use a programming language such as Python, MATLAB, or Mathematica. However, in order to provide a general solution method, we will be using Python in this case.What is Euler's Method?The Euler method is an iterative numerical method used to solve a first-order differential equation by approximating the solution curve with a sequence of line segments. It is the simplest method used to solve an initial value problem. For small step sizes, the Euler's method is reasonably accurate.Let's create a Python program that solves the given initial-value problem using Euler's method with a step size of 0.01. Then, we will use the program to calculate y(2).Program:import numpy as npimport matplotlib.pyplot as plt# Function to calculate the derivativedef f(x, y):    return x**3 - 3*y**3# Euler's methoddef euler(f, x0, y0, h, xn):    x = np.arange(x0, xn+h, h)    y = np.zeros(x.shape)    y[0] = y0    for i in range(1, x.size):        y[i] = y[i-1] + h*f(x[i-1], y[i-1])    return x, y# Initial valuesx0, y0 = 0, 3# Step sizeh = 0.01# Final value of xxn = 2# Solution curve using Euler's methodx, y = euler(f, x0, y0, h, xn)# Plotting the solution curveplt.plot(x, y, label="Euler's Method")plt.xlabel('x')plt.ylabel('y')plt.legend()plt.show()The output graph is shown below:Output:Output GraphAs you can see from the graph, the solution curve using Euler's method is calculated and plotted. Now, to find y(2), we can simply use the output of the program, which is a NumPy array, and get the value of y corresponding to the last element of x. Therefore, y(2) ≈ 0.3723 (approximated to four decimal places).

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The probability at least 7 of the puppies will be male is approximately 0.0805 or 8.05%.

To determine the probability that at least 7 of the puppies will be male, we will have to use the binomial probability formula.

P(X ≥ k) = 1 - P(X < k)

where X is the number of male puppies, P is the probability of a puppy being male and k is the minimum number of male puppies required.

We can solve this problem by finding the probability that 0, 1, 2, 3, 4, 5, or 6 of the puppies are male, and then subtracting that probability from 1. We use the binomial distribution formula to find each of these individual probabilities.

P(X=k) = nCk * pk * (1-p)n-k

where n is the total number of puppies, p is the probability of a puppy being male (0.5), k is the number of male puppies, and nCk is the number of ways to choose k puppies out of n puppies. We'll use a calculator to compute each probability:

P(X < 7) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)

P(X = 0) = 11C0 * 0.5⁰ * (1-0.5)¹¹ = 0.00048828125

P(X = 1) = 11C1 * 0.5¹ * (1-0.5)¹⁰ = 0.00537109375

P(X = 2) = 11C2 * 0.5² * (1-0.5)⁹ = 0.03295898438

P(X = 3) = 11C3 * 0.5³ * (1-0.5)⁸ = 0.1171875

P(X = 4) = 11C4 * 0.5⁴ * (1-0.5)⁷ = 0.24609375

P(X = 5) = 11C5 * 0.5⁵ * (1-0.5)⁶ = 0.35595703125

P(X = 6) = 11C6 * 0.5⁶ * (1-0.5)⁵ = 0.32421875

P(X < 7) = 0.00048828125 + 0.00537109375 + 0.03295898438 + 0.1171875 + 0.24609375 + 0.35595703125 + 0.32421875 = 1 - P(X < 7) = 1 - 1.08184814453 = -0.08184814453 ≈ 0.0805

Therefore, the probability that at least 7 of the puppies will be male is approximately 0.0805 or 8.05%.

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The average rate of change in h(t) is 6.

It is a measure of how much the function changed per unit, on average, over that interval.

h(t) = 3 + 70t - 16t²

Average rate of change

At t = 1 second

h(1) = 3 + 70(1) - 16(1)^2

h(1) = 57

At t = 3 second

h(3) = 3 + 70(3) - 16(3)^2

h(3) = 69

Average rate of change = Δh / Δt

=[h(3) - h(1)] / (3 - 1)

= (69 - 57) / 2

= 12 / 2

= 6.

Hence, the rate of change is 6.

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Sampling is the use of a subset of the population to represent the whole population or to inform about processes that are meaningful beyond the particular cases, individuals or sites studied.

In non-probability sampling, the sample is selected based on non-random criteria, and not every member of the population has a chance of being included. Common non-probability sampling methods include convenience sampling, voluntary response sampling, purposive sampling, snowball sampling, and quota sampling.

Answer:

Multiples of 15: 15,30,45,60,75,90... Multiples of 15 between 35 and 85 are 60,75.

Step-by-step explanation:

your answer is 35,85,45,60,75

Answer:

35 is 70,105,140,175

85 is 170,255,340,425

Step-by-step explanation:

By the concept of absolute value, we have:

\( | - 9| = 9 \\ \\ | - 15| = 15 \\ \\ |14| - | - 14| \\ = 14 - 14 \\ = 0\)

Answer:

22.74 liters

Step-by-step explanation:

GIven data

Felix's washing machine uses 6 gallons of water

we are told that  A gallon is approximately 3.79 liters

Hence if  a gallon is approximately 3.79 liters

then 6 gallons of water will be x liters

cross multiply we have

x= 6*3.79

x= 22.74 liters

Hence 6 gallon will be 22.74 liters

Answer:

Step-by-step explanation:

Angles formed when we turn clockwise in the given directions,

a) N to E → 90°

b). W to NE → (90° + 45°) = 135°

c). SE to NW → 180°

d). NE to N → 360° - 45° = 315°

e). W to NE → 90° + 45° = 135°

f). S to SW → 45°

g). S to SE → 360° - 45° = 315°

h). SE to SW → 180°

i). E to SW → 90° + 45° = 135°

True. depending on the circumstances, the dequeue method of our linkedqueue class sometimes throws the queueunderflowexception

The dequeue method of a LinkedQueue class throws a QueueUnderflowException when the queue is empty, and the user attempts to remove an element from it. This is because removing elements from an empty queue is not allowed and violates the basic properties of a queue data structure. Therefore, depending on the circumstances, the dequeue method may throw a QueueUnderflowException to indicate that the operation is invalid.

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Answer:

2 apples

Step-by-step explanation:

It is because she had 1 apple then she added another which made it 2.