Becky needs a $5,000 loan in order to buy a boat. Which loan option would allow her to pay the LEAST amount of interest?
A)
A 24-month loan with a 6.25% annual simple interest rate.
B)
A 30-month loan with a 5.75% annual simple interest rate.
0)
A 36-month loan with a 4.00% annual simple interest rate.
D)
A 42-month loan with a 3.75% annual simple interest rate.

Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

The probability of the event for the given odds in favor (4 to 7) is found as 4/11.

To continue solving, we must represent the ratio as a fraction.

Thus, we have the depiction shown below.

Odds ratio equals 4/7

We use the following equation to translate the aforementioned odd's expression into a probability expression.

This is displayed as

P = (Odds + 1)/(Odds).

Replace the unknown values in the equation above.

The following equation is what we have.

P = (4/7)/(4/7 + 1)

Analyze the amount

This results

P = (4/7)/(11/7)

Put the quotient in product form.

P = (4/7) * (7/11)

Evaluate

P = 4/11

Thus, the probability of event for the given odds in favor (4 to 7) is found as 4/11.

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Answer:

We need to determine 50% of 100 now and the procedure explaining it as such

Step 1: In the given case Output Value is 100.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 100 = 100%.

Step 4: In the Same way, x = 50%.

Step 5: On dividing the pair of simple equations we got the equation as under

100 = 100% (1).

x = 50% (2).

(100%)/(x%) = 100/50

Step 6: Reciprocal of both the sides results in the following equation

x%/100% = 50/100

Step 7: Simplifying the above obtained equation further will tell what is 50% of 100

x = 50%

Therefore, 50% of 100 is 50

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The minimum profit occurs at L = 0, where Q = 0.

To find the value of L that maximizes the profit Q = L²\(e^{(0.01L)\).

We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.

Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.

Testing for critical points:Q = L²\(e^{(0.01L)\)

Q' = \(2Le^{(0.01L)\) + \(0.01 L^2e^{(0.01L)\)

= 0(2L + 0.01L²) \(e^{(0.01L)\)

= 0L (critical point) or 200 \(e^{(0.01L)\)

= 0 (extraneous, ignore)

2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)

The only critical point is at L = 0.

Testing for maximum or minimum:Q'' = \(2e^{(0.01L)\) + 0.02Le^(0.01L) + 0.0001L²\(e^{(0.01L)Q''(0)\)

= \(2e^{(0)\) = 2Since Q''(0) > 0,

The critical point at L = 0 is a minimum.

Therefore, there is no value of L that maximizes the profit.

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The values of L that will maximize the profit are 0 and -200

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

\(Q = L\²e^{0.01L\)

Differentiate the function

So, we have

\(Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}\)

Set the equation to 0

\(\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0\)

Cross multiply

\(L \cdot (L + 200) \cdot e^{0.01L} =0\)

When expanded, we have

L = 0, L + 200 = 0 and \(e^{0.01L} =0\)

When solved for L, we have

L = 0 and L = -200

Hence, the values of L are 0 and -200

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In mathematics, Euclid's three undefined terms are:

These terms are considered undefined because they cannot be defined in terms of simpler objects.

"Hugot" is a colloquial term in the Philippines that refers to a type of emotional expression, often expressed in the form of a quote or a line from a song or a movie.

The "hugot" line is meant to be a reflection of a personal feeling or experience and can be used to express longing, heartbreak, unrequited love, and other emotions.

Here are some hugot lines that illustrate these three undefined terms:

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Therefore, the solution to the inequality 3(y + 1/4) > 3/4 is y > 0.

An inequality is a mathematical statement that shows a relationship between two values, which are not necessarily equal. Inequalities are represented using symbols such as > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to). Inequalities are commonly used in algebra and other areas of mathematics, as well as in real-world applications such as finance, economics, and science. They can be used to represent constraints or limits on a variable, such as the maximum or minimum value that it can take.

Here,

We can solve the inequality 3(y + 1/4) > 3/4 by first distributing the 3 to the expression inside the parentheses:

3y + 3/4 > 3/4

Next, we can simplify by subtracting 3/4 from both sides:

3y > 0

Finally, we can solve for y by dividing both sides by 3:

y > 0/3

y > 0

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Answer:

54

Step-by-step explanation:

the sum of all angles of a triangle must equal 180.

180 - 76 - 50 = 54

Answer:

54

the sum of all angles of a triangle must equal 180.

180 - 76 - 50 = 54

Answer:

a calculator

Step-by-step explanation:

Options :

a.) shape unknown with mean of 2.8 and a standard deviation of 0.4 b.) approximately normal with mean of 2.8 and standard deviation of 4 C.) shape unknown with mean of 2.8 and standard deviation of 4 d.) approximately normal with mean of 2.8 and standard deviation of 0.4

Answer: d.) approximately normal with mean of 2.8 and standard deviation of 0.4.

Step-by-step explanation:

Given that :

Population Mean (m) = 2.8

Population Standard deviation (s) = 4

Sample size = 100

The mean of the sampling distribution is equal to the population mean, according to the central limit theorem. As the size of the sample increases, the mean if the sample distribution converges to that if the population mean.

Hence, sample mean = 2.8

The sample standard deviation (standard error) :

Standard Error = population standard deviation / √sample size

= s/√n

= 4 / √100

= 4/10

= 0.4

Using the Central Limit Theorem, it is found that the correct description of the sampling distribution of the sample means is:

Approximately normal, with mean of 2.8 and standard deviation of 0.4.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

In this problem, the population has an unknown distribution, with mean \(\mu = 2.8\) and standard deviation \(\sigma = 4\)

The sampling distribution of the sample means of size 100 has:

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Answer:

The answer is 24

Step-by-step explanation:

24/4 is 6 and then you add 6 to 3 which is 9

Answer:

24

Step-by-step explanation:

x/4+3=9

x/4=9-3

x/4=6

4 times x/4 = 6 times 4

x=24

Answer:

\(\frac{2}{\frac{1}{24} }\)

Step-by-step explanation:

2/x = 48

48x = 2

x = (2)/ (1/24)

\(\frac{2}{\frac{1}{24} }\) = 48

Given the equation:

using the general formula to find the solutions:

From the given equation :

a = 3 , b = 13 and c = 14

So,

so, x = (-13+1)/6 = -12/6 = -2

OR x = (-13-1)/6 = -14/6 = -7/3

So, the answer is the options: D. -7/3 and E. -2

9514 1404 393

Answer:

  a) 98

  b) directly

  c) k = 14 pages per hour

Step-by-step explanation:

a) In order to answer the first question, we must assume that the number of pages varies directly with the amount of time. Further, we must find the constant of variation:

  p = kt

  56 = k(4)

  k = 56/4 = 14 . . . . pages per hour

Then in 7 hours, the student will read ...

  p = 14(7) = 98 . . . pages

__

b) As we said in part (a), the variation is direct.

__

c) As we found in part (a), the constant of variation is 14 pages per hour.

\(-21x^{2}-588\)

let me know if anything is unclear, I'm happy to help!

Answer:

Sophia should start her homework at 5:55

Step-by-step explanation:

If it takes her 10 minutes to go to school, 30 minutes to do her homework, and 25 minutes to eat dinner, you should add those numbers together to get 65 because then you can subtract 65 minutes from 7:00 so you get the time she needs to start her homework in order to get to school at 7:00. So basically 10+30+25=65 and then 65 minutes subtracted from 7:00 is 5:55.

I hope this helps you :D

Answer:

5:55 pm

Step-by-step explanation:

30+25+10=65

or

1 hour and 5 minutes

Answer:

x=11

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

-10 = -2x + 12

-10 - 12 = -2x + 12 - 12

-22 = -2x

-22/-2 = -2x/-2

11 = x

Check:

-10 = -2*11 + 12

-10 = -22 + 12

Answer:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Now we know that point D, which we can write as (x, y), is at a distance of 8 units from the origin.

Where the origin is written as (0, 0)

We also know that point D is 6 units away along the y-axis.

Then point D could be:

(x, 6)

or

(x, -6)

Now, let's find the x-value for each case, we need to solve:

\(8 = \sqrt{(x - 0)^2 + (\pm6 - 0)^2}\)

notice that because we have an even power, we will get the same value of x, regardless of which y value we choose.

\(8 = \sqrt{x^2 + 36} \\\\8^2 = x^2 + 36\\64 - 36 = x^2\\28 = x^2\\\pm\sqrt{28} = x\\\pm 5.29 = x\)

So we have two possible values of x.

x = 5.29

and

x = -5.29

Then the points that are at a distance of 8 units from the origin, and that are 6 units away along the y-axis are:

(5.29, 6)

(5.29, -6)

(-5.29, 6)

(-5.29, -6)

Answer:

What statements, the statements aren't listed in the question?

Step-by-step explanation:

Answer:If we compare the p value and the significance level assumed we see thatso we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can conclude that the true mean is not different from the specification at 1% of signficance.  

Step-by-step explanation:

The machine is working properly based on the convincing evidence provided by the sample.

For the null hypothesis, we would test that:

H0 : p = 2

For the alternate hypothesis, we would test that:

Ha > p = 2

In Mathematics, the test statistics of a given sample is calculated by using this formula:

\(Z=\frac{x\;-\;u}{\frac{\sigma}{\sqrt{n} } }\)

Where:

Substituting the given parameters into the formula, we have;

\(Z=\frac{2.024\;-\;2}{\frac{0.205}{\sqrt{200} } }\\\\Z=\frac{0.024}{\frac{0.205}{14.14} }\\\\Z=\frac{0.024}{0.0145 }\)

Z = 1.66.

For the p-value:

P(Z > Zo) = P(Z > 1.66)

P(Z > 1.66) = P(Z < -1.66)

P(Z < -1.66) = 0.0485.

From the z-table, a z-score of 1.66 corresponds has a p-value of 0.0485. Therefore, the p-value for this test is 0.0485 < 2 while assuming a confidence level of 95%.

In conclusion, we fail to reject the null hypothesis because 0.0485 < 2.

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The equation -6 = 0 is not true, which means that there is no solution to the equation 9t+6 in standard form. This is because we cannot write the equation in the form \(ax + by = c\)  , since there is no value of c that would satisfy the equation.

To write 9t+6 in standard form, we need to rearrange the expression to have the variables first, followed by the constant term. The standard form of a linear equation is:

\(ax + by = c\)

where a, b, and c are constants, and x and y are variables.

To rearrange 9t+6, we first need to group the t term and the constant term together. We can do this by adding 0t to the expression:

\(9t + 0t + 6\)

Now, we can rearrange the terms so that the variable term comes first:

\(9t + 0t = 9t\)

Finally, we can write the expression in the standard form:

\(9t + 0t = 9t + 6\)

This can be simplified further by removing the 0t term:

\(9t = 9t + 6\)

We can now move the constant term to the other side of the equation by subtracting 6 from both sides:

\(9t - 6 = 9t + 6 - 6\)

\(9t - 6 = 9t\)

\(-6 = 0\)

Therefore, The equation  \(-6 = 0\) is not true, which means that there is no solution to the equation   \(9t+6\) in standard form. This is because we cannot write the equation in the form  \(ax + by = c\)  , since there is no value of c that would satisfy the equation.

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Answer:

-7

Step-by-step explanation:

If it is 7 below (a key word, which you can connect to 'negative'), then you just write it as -7.

Answer:

633222

Step-by-step explanation:

just put them in order from biggest - smallest

Answer: 15.77

Step-by-step explanation: We know that Milans car had 19.57 gallons of fuel, so I subtracted 19.57 - 3.8 to get my answer.

The y-intercept of the linear function means that her initial distance from the finish line is of 10 kilometers.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 10, hence the intercept b is given as follows:

b = 10.

The y-values represent the distance in the context of this problem, hence the initial distance is of 10 km.

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Answer:

a. Angel has a greater flat fee

b. Difference = $130

Step-by-step explanation:

Given

Rose:

\(Flat\ Fee = \$50\)

\(Rate = \$12\)

Angel

Guests --- Charges

10 -------- $180

15 -------- $255

25 -------- $405

30 -------- $480

Solving (a): Who charges the greater flat fee?

We have that the flat fee of Rose is:

\(Flat\ Fee = \$50\)

For Angel, we need to determine the equation of the given table

Start by calculating the slope (m) of the table

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where x and y represent any two corresponding values of the guests and the charges.

\((x_1,y_1) = (10, 180)\)

\((x_2,y_2) = (30, 480)\)

So: \(m = \frac{y_2 - y_1}{x_2 - x_1}\) becomes

\(m = \frac{480 - 180}{30 - 10}\)

\(m = \frac{300}{20}\)

\(m = 15\)

Next, we calculate the equation using:

\(y - y_1 = m(x - x_1)\)

Where

\(m = 15\)

\((x_1,y_1) = (10, 180)\)

\(y - 180 = 15(x - 10)\)

\(y - 180 = 15x - 150\)

Add 180 to both sides

\(y - 180 + 180 = 15x - 150 + 180\)

\(y= 15x + 30\)

From the equation above:

The slope = 15 --- This represents the hourly rate

and

y intercept = 30 --- This represents the flat fee

This is better represented as:

Angel

\(Flat\ Fee = \$30\)

\(Rate = \$15\)

and

Rose:

\(Flat\ Fee = \$50\)

\(Rate = \$12\)

By comparison, Angel has a greater flat fee

Solving (b): Difference between total charges of 50 guests for both caterers.

For angel, the equation is:

\(y= 15x + 30\)

and x = 50.

So:

\(y = 15 * 50 + 30\)

\(y = 750 + 30\)

\(y = 780\)

For Rose,

First, we need to determine the equation.

\(Flat\ Fee = \$50\)

\(Rate = \$12\)

The equation is:

\(y = Flat\ Fee + Rate * x\)

\(y = 50 + 12 * x\)

So, the total charges for 50 guests is:

\(y = 50 + 12 * 50\)

\(y = 50 + 600\)

\(y = 650\)

The difference is then calculates as:

\(Difference = 780 - 650\)

\(Difference = \$130\)

Answer:

\(7x + 5y \leqslant 30\)

Answer:

You cannot solve this, but you can try to simplify it: 16^x = −2x + −23/4

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Answer:

9.7

Step-by-step explanation:

The mean is the same as the average value of a data set and is found using a calculation.

Add up all of the numbers and divide by the number of numbers in the data set.

Hope this helps! :)

Answer: 9.7

Step-by-step explanation:

Mean means to add up the values and divide it by how many numbers there are, so 10 + 8 + 12 + 10 + 7 + 11 + 13 + 6 + 15 + 5 = 97, then 97 / 10 = 9.7