Janice bought a new car. the total amount she needs to borrow is $35,000 . she plans on taking out a 5-year loan at an apr of 4%. what is the monthly payment ?

The sum of the measures of the interior angles is 1260 degrees

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

An interior angle = 140 degrees

The sum of interior angles of a regular polygon is:

S = (n - 2) × 180

Where n is the number of sides of a polygon

Also, we have

S = 140n

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

140n = (n - 2) × 180

Expand

140n = 180n - 360

This gives

40n = 360

Divide

n = 9

Recall that

S = (n - 2) × 180

So, we have

S = (9 - 2) × 180

Evaluate

S = 1260

Hence, the sum of the measures of the interior angles is 1260 degrees

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To determine the total cost of the laptop each month if you make no payments, we need to calculate the balance on the credit card after each month, including the simple interest charged.

Starting balance = $550

Month Balance Interest Total Cost
0 $550 $0 $550
1 $616 $66 $616 + $66 = $682
2 $689.92 $73.92 $689.92 + $73.92 = $763.84
3 $770.15 $80.23 $770.15 + $80.23 = $850.38
4 $857.09 $86.94 $857.09 + $86.94 = $944.03
5 $951.19 $94.10 $951.19 + $94.10 = $1045.29

To calculate the balance for each month, we multiply the previous balance by 1.12, which represents the 12% interest charged. For example, for month 1, the balance is $550 * 1.12 = $616.

To calculate the interest charged each month, we subtract the previous balance from the new balance. For example, for month 1, the interest charged is $616 - $550 = $66.

To calculate the total cost each month, we add the new balance to the interest charged.

For example, for month 1, the total cost is $616 + $66 = $682.

Note that if you make no payments on the credit card, the balance will continue to grow each month due to the interest charged.

It is always advisable to make at least the minimum payment each month to avoid high interest charges and potential late fees.

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A. True. A compound event may consist of two dependent events. Dependent events are those in which the outcome of the first event affects the outcome of the second event. For example, drawing a card from a deck and not replacing it before drawing a second card would be an example of dependent events.

The ordered pairs of the inequality expression is (0, 4)

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

The inequality expression  y>1/2x+3

To determine the ordered pairs of the inequality expression, we set x - 0 and then calculate the value of y

Using the above as a guide, we have the following:

y > 1/2 * 0 + 3

Evauate

y > 3

This means that the value of y is greater than 3 say y = 4

So, we have (0, 4)

Hence, the ordered pairs of the inequality expression is (0, 4)

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We will use the Poisson distribution, which is a probability distribution that models the number of events occurring in a fixed interval of time or space, given the average rate of occurrence and assuming that the events are independent and randomly distributed.

For this problem, we will assume that the number of days with 0.01 inch or more precipitation in Lewiston, Idaho, follows a Poisson distribution with parameter λ = 8.7.

(a) To find the probability that there are exactly 9 days with 0.01 inch or more precipitation, we can use the Poisson probability mass function:

P(X = k) = e^(-λ) * λ^k / k!

where X is the random variable representing the number of days with 0.01 inch or more precipitation, λ is the parameter of the Poisson distribution, and k is the number of events we are interested in.

Plugging in the values, we get:

P(X = 9) = e^(-8.7) * 8.7^9 / 9! ≈ 0.151

Therefore, the probability that there are exactly 9 days with 0.01 inch or more precipitation is approximately 0.151.

(b) To find the probability that there are at most 9 days with 0.01 inch or more precipitation, we can use the cumulative distribution function of the Poisson distribution:

P(X ≤ k) = ∑i=0^k e^(-λ) * λ^i / i!

Plugging in the values, we get:

P(X ≤ 9) = ∑i=0^9 e^(-8.7) * 8.7^i / i! ≈ 0.503

Therefore, the probability that there are at most 9 days with 0.01 inch or more precipitation is approximately 0.503.

(c) To find the probability that there are more than 9 days with 0.01 inch or more precipitation, we can subtract the probability of having 9 or fewer days from 1:

P(X > 9) = 1 - P(X ≤ 9) ≈ 0.497

Therefore, the probability that there are more than 9 days with 0.01 inch or more precipitation is approximately 0.497.

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The cost to manufacture 2000 headphones as the number of headphones varies inversely with the cost of manufacture is $32

Let x = number of headphones

y = cost of manufacturing headphones

The cost of manufacturing a certain type of headphones is inversely proportional to the number of headphones.

The equation for inversely proportional is

x₁ y₁ = x₂ y₂

x₁ = 8000 , y₁ = 8 , x₂ = 2000 y₂ = ?

Putting the value in the equation we get ,

8000 × 8 = 2000 × y₂

64000/2000 = y₂

y₂ = 32

Cost of manufacturing 2000 headphones is 32 .

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Answer:

30%

Step-by-step explanation:

If there are only 2 categories:

Students at lunch and students studying, then the whole is 100%

100% - 70% = 30%

Helping in the name of Jesus.

Distribute

50+30(2x+10)

50+30×2x+30×10

50+60×+300

add the number

50+300+60×

350+60x

60x+350

common factors

10(6x+35)

Therefore, the perimeter of the rectangle is 38 units that is option C.

A coordinate is a set of numbers or values that specifies the position or location of a point or object in a space. In mathematics, coordinates are used to describe the position of a point in a plane, a space or a higher-dimensional object. Coordinates can be represented by ordered pairs or tuples, where the first value corresponds to the position on the horizontal axis, and the second value corresponds to the position on the vertical axis.

Here,

First, we need to find the distance between points A and B to determine the length of the rectangle:

Distance AB = |yB - yA|

= |8 - 2|

= 6

Next, we need to find the distance between points B and C to determine the width of the rectangle:

Distance BC = |xC - xB|

= |6 - (-7)|

= 13

Since opposite sides of a rectangle are equal in length, we know that the distance between points A and D is also 13, and the distance between points C and D is also 6.

Therefore, the perimeter of the rectangle is:

Perimeter = 2 * (length + width)

Perimeter = 2 * (13 + 6)

Perimeter = 2 * 19

Perimeter = 38

So the answer is (C) 38.

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Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.

Since Daniel read 77 pages in $\frac{2}{5}$ of an hour, we can set up the proportion:

$\frac{77}{\frac{2}{5}} = x$

where $x$ is the number of pages he would read in 1 hour.

To solve for $x$, we can simplify the left side of the equation by multiplying both the numerator and denominator by 5, which gives:

$\frac{77 \times 5}{2} = x$

Simplifying this expression gives:

$192.5 = x$

Therefore, if Daniel continues reading at the same rate, he will read 192.5 pages in one hour. However, since the number of pages must be a whole number, we can round this answer to the nearest whole number to get:

$x \approx 193$

So, Daniel will read approximately 193 pages in one hour if he continues reading at the same rate.

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Step-by-step explanation:

4% tax is .04 in decimal:

($  50  + 30 ) * .04    = 3.20 tax    

The equation in two variables that describes how the amount of cat food in the bag changes over time is: A = 10 - 0.3t
Where A represents the amount of cat food left in the bag after t days, and t represents the number of days that have passed since Simon bought the bag.

The variable A is the dependent variable because it depends on the value of t. As time passes and t increases, the amount of cat food left in the bag decreases. The variable t is the independent variable because it is the input that determines the value of A.

For example, after one day (t = 1), Simon will have used 0.3 pounds of cat food and there will be 9.7 pounds left in the bag (A = 10 - 0.3(1) = 9.7). After two days (t = 2), he will have used 0.6 pounds of cat food and there will be 9.4 pounds left in the bag (A = 10 - 0.3(2) = 9.4), and so on.

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Her profit when 0 people attend is -$50 and each person pays 10

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

y = 10x - 50.

The graph is added as an attachment

This means that

x = 0

So, we have

y = 10(0) - 50.

y = -50

She made a loss of 5-

This represents her profit when 0 people attend

This represents the slope of the function

The slope of the function is 10

So, each person pays 10

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The value of ∠APB = 180°. It is a straight line.

Given the information, we can deduce that the line passing through the center O of circle C2 and point A also passes through point B, as AB is the intersection of the two circles.

Now, consider the line segment AP. Since PAT is tangent to circle C1 at point A, we know that ∠APT = 90°. Additionally, since AB is a diameter of circle C1, we know that ∠ABP = 90°.

Using these angles, we can see that ∠APB is equal to the sum of ∠APT and ∠ABP. Therefore,

∠APB = ∠APT + ∠ABP = 90° + 90° = 180°.

So, we have shown that ∠APB is a straight line.

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P(X ≤ 1) = P(X = 0) + P(X = 1) ≈ 0.901

So the probability that at most 1 customer in the sample orders for delivery is approximately 0.901, rounded to three decimal places.

To solve this problem, we can use the binomial distribution since we have a fixed number of trials (6) and each trial can result in one of two outcomes (ordering for delivery or not).

Let X be the number of customers in the sample who order for delivery. Then X follows a binomial distribution with parameters n = 6 and p = 0.11 (the probability of ordering for delivery).

We want to find the probability that at most 1 customer orders for delivery. This can be written as:

P(X ≤ 1) = P(X = 0) + P(X = 1)

To calculate these probabilities, we can use the binomial probability formula:

P(X = k) = (n choose k) *[tex]p^k[/tex]*[tex](1 - p)^(n - k)[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.

Using this formula, we can calculate:

P(X = 0) = (6 choose 0) * 0.11^0 * [tex]0.89^6[/tex] ≈ 0.530

P(X = 1) = (6 choose 1) * 0.11^1 * 0.89^5 ≈ 0.371

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Answer: Linear Function: y = -10x + 15    Exponential Function:  

y = 15(1/3)(to the power of x)

Step-by-step explanation:

Linear Function:

First we need to find the slope by using the slope equation: (y2 - y1)/(x2 - x1)

In which, it should be (5 - 15)/(1 - 0)

So, we know that the slope is -10, and we already know that the y-intercept is 15, so, we are going to plug it in to the slope-intercept formula, which is

y = mx + b,

In which, it would become y = -10x + 15

Exponential Function =

The exponential function is y = ab(to the power of x)

Let's list out the points onto the equation, 15 = ab(0) and 5 = ab(1)

Know let's solve for each variable.

1. 15 = ab(0)

2. 15/b(0) = a

3. 15 = a

Know we know that a is 15, we can solve for b.

1. 5 = (15)b(1)

2. 5/15 = b(1)

3. 1/3 = b

Know we know that b is equal to 1/3, let's plug it into the equation.

y = 15(1/3)(to the power of x)

Answer:

238 ft²

Step-by-step explanation:

Base area is l*w and there are two of these so 2(7*7) = 98

Then there 4 faces that have dimensions 4(7*5)=140

98+140=238

The probability of getting two numbers whose sum is 12 when rolling a single number cube twice is 1/36.

To find the probability of getting two numbers whose sum is 12 when a single number cube is rolled twice, we'll first need to identify the favorable outcomes.

A number cube has six faces, numbered from 1 to 6. When it is rolled twice, there are 6 x 6 = 36 equally-likely outcomes. To find the probability, we can use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

The first step is to identify the favorable outcomes, which are the pairs of numbers that add up to 12. Since we are dealing with a number cube that has faces numbered 1 to 6, there is only one possible pair that satisfies this condition: (6,6).

Now that we have determined the favorable outcome, we can find the probability:

Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 1 (for the pair 6,6) / 36

Thus, the probability of getting two numbers whose sum is 12 when rolling a single number cube twice is 1/36.

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The value of measure of angle WPN is,

⇒ m ∠WPN = 108°

We have to given that;

Parallel lines EN, BH, and RK, with transversal PW are shown.

And, m ∠ BMV = 108° and m ∠KVS = 72°

Now, We get by definition of vertically opposite angle;

m ∠ BMV = m ∠PWN = 108°

Hence, By definition of alternate angle we get;

⇒ m ∠PWN = m ∠WPN = 108°

Thus, The value of measure of angle WPN is,

⇒ m ∠WPN = 108°

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Leslie’s annual social security deduction is $3551.70.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Leslie’s  annual salary is $57,285. 50 and her annual social security deduction is 6.2% of the annual salary. We can say:

Annual social security deduction = 6.2/100 * 57,285. 50

Annual social security deduction = $3551.70

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For given equation x = (-b ± √(b²-4ac))/2a the equation in the form c= is: c = -x²(a/b) - x.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division.

What is goal of equation?

The goal of solving an equation is to determine the value or values of the variable that make the equation true. Equations are used extensively in mathematics and science to describe relationships between quantities and to solve problems.

Starting with the equation:

x = (-b ± √(b²-4ac))/2a

We can simplify and rearrange it to the form c= as follows:

Multiply both sides by 2a to get rid of the denominator:

2a x = -b ± √(b²-4ac)

Add b to both sides:

2a x + b = ± √(b²-4ac)

Square both sides:

(2a x + b)² = b² - 4ac

Expand the left side:

4a² x² + 4abx + b² = b² - 4ac

Simplify:

4a² x² + 4abx = -4ac

Divide both sides by 4a:

x² + bx/a = -c/a

Rearrange to the form c=:

c = -x²(a/b) - x

Therefore, the equation in the form c= is:

c = -x²(a/b) - x

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Answer:

A, C, F

Step-by-Step:

The amplitude is whatever the coefficient is behind the trig function

. 0.587 in scientific notation is 5.87 x 10^-1.

Scientific notation is a way of writing numbers that are very large or very small in a compact and standardized way. In scientific notation, a number is expressed as a coefficient multiplied by 10 raised to some power.

For example, the number 0.587 can be written in scientific notation as 5.87 x 10^-1. The coefficient 5.87 is obtained by moving the decimal point one place to the right, while the negative exponent -1 indicates that the decimal point has been moved one place to the left, to the tenth place.

Scientific notation is commonly used in scientific and engineering fields where very large or very small numbers are often encountered, and it allows for easier calculation and comparison of these values.

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The y-values that a function approaches when the x-values are extremely large or extremely small is called the function's asymptotic behavior.

When we talk about the asymptotic behavior of a function, we are referring to what happens to the values of the function as the input (x-values) either tends to positive infinity or negative infinity.

In other words, we are interested in how the function behaves when the input values become extremely large or extremely small.

To understand asymptotic behavior, let's consider two types of asymptotes: horizontal and vertical asymptotes.

Horizontal Asymptotes:

A horizontal asymptote is a horizontal line that a function approaches as the x-values become extremely large or extremely small. We usually denote horizontal asymptotes as y = c, where c is a constant.

For example, let's consider the function f(x) = (2x^2 + 3) / (x^2 - 1). As x approaches positive or negative infinity, we can observe the following behavior:

As x becomes extremely large or extremely small, the function becomes closer and closer to the line y = 2. Therefore, we say that y = 2 is a horizontal asymptote for this function.

Vertical Asymptotes:

A vertical asymptote is a vertical line that the function approaches as the x-values approach a particular value. It typically occurs when there is a division by zero or when the function tends to infinity at a specific point.

For example, consider the function g(x) = 1 / (x - 2). As x approaches 2 from either side (but never equal to 2), we can observe the following behavior:

As x approaches 2 from the left (x < 2), the function g(x) becomes increasingly negative, tending towards negative infinity.

As x approaches 2 from the right (x > 2), the function g(x) becomes increasingly positive, tending towards positive infinity.

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Answer:

Step-by-step explanation:

Let's call the two angles in the ratio of 4:13 "x" and "y".

We know that the sum of all three angles in a triangle is always 180 degrees.

So, we can set up an equation:

10 + x + y = 180

We also know that x and y are in a ratio of 4:13, which means we can write:

x = 4k

y = 13k

where "k" is a constant that we need to find.

Substituting these expressions for x and y into the equation, we get:

10 + 4k + 13k = 180

17k = 170

k = 10

Now we can find the values of x and y:

x = 4k = 4(10) = 40

y = 13k = 13(10) = 130

Therefore, the measures of the two angles in the ratio of 4:13 are 40 degrees and 130 degrees, respectively.

Nataly saved s/64.

The original prices for the items are:

Skirt: s/78

Blouse: s/65

Jacket: s/240

The discounted prices Nataly paid are:

Skirt: s/69

Blouse: s/52

Jacket: s/198

To find out how much Nataly saved, we need to calculate the difference between the original prices and the discounted prices, and then add them up:

savings = (78 - 69) + (65 - 52) + (240 - 198)

savings = 9 + 13 + 42

savings = s/64

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The mean of the given stem and leaf plot is 24.5 and the median of the data is 25.

The stem and leaf plot represents the given data as:

| 2 | 4, 5, 6, 9

| 3 | 1, 4, 5, 5, 7, 8

| 4 | 2, 5, 7, 8, 9

To find the mean, we need to add up all the values and divide by the total number of values.

Mean = (24 + 25 + 26 + 29 + 31 + 34 + 35 + 35 + 37 + 38 + 42 + 45 + 47 + 48 + 49) / 15

= 367 / 15

= 24.5

To find the median, we need to arrange the data in order and find the middle value. As there are 15 data points, the median will be the average of the 8th and 9th data points.

Data in order: 24, 25, 25, 26, 29, 31, 34, 35, 35, 37, 38, 42, 45, 47, 48

Median = (35 + 37) / 2

= 36.

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Answer:

366 times

Step-by-step explanation:

Answer:

3x + 5 = 4x - 40

x = 45

5y - 50 = y

4y = 50

y = 25/2