A walk alongside a railway track is represented on a map by an 86 mm straight line.

The walk is 17.2 km.

What is the scale of the map?

Answers

Answer 1

First we turn the 17.2 km into mm. To do that we turn it into 17,200 m then into 1,720,000 cm then into 17,200,000 mm. Then we just divide 17.2 million by 86 so 17,200,000÷86=200,000. so we know that the scale of the map is 1:200,000. Also pls mark as brainliest answer thx.


Related Questions

Someone please help me with these Natural Logarithms questions!!!!!

I give lots of points who ever answers with an explanation of why that is the answer

Answers

The solution to the equations using natural logarithm as shown below.

How to use natural logarithm to solve equations?

To solve an equation of this nature, you need to know that the reverse of natural logarithm (ln) is exponential (e). Let apply this idea.

PART 1

Using natural logarithm to solve equations:

2eˣ = 4

eˣ = 4/2

eˣ = 2   (take "ln" of both sides to get rid of "e")

x = ln 2

x = 0.693

eˣ = 72

x = ln 72

x = 4.277

e⁴ˣ = 25

4x = ln 25

x = (ln 25)/4

x = 0.805

e³ˣ = 124

3x = ln 124

x = (ln 124)/3

x = 1.607

PART 2

ln(x -3) = 2    (take "e" of both sides to get rid of "ln")

x - 3 = e²

x = e² + 3

x = 7.389 + 3

x = 10.389

ln 2t = 4

2t = e⁴

t = e⁴/2

t = 27.299

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Consider the line shown on the graph.

Answers

The equation of the given line in the graph in slope intercept form is: y = 2x + 7

How to find the equation of a line?

The general formula for the equation of a line in slope intercept form is:

y = mx + b

where:

m is slope

b is y-intercept

From the given graph, the y-intercept is b = 7

Let us pick two coordinates which are:

(-3.5, 0) and (0, 7)

Thus:

(y - 0)/(x + 3.5) = (7 - 0)/(0 + 3.5)

y = 2(x + 3.5)

y = 2x + 7

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8 Use the results of problem 5 and problem 6. Find the
sum of all the probabilities for Leon's experiment and
for Celia's experiment. Compare the sums and explain
the result.
Show your work.

Answers

Sum of all probabilities for Leon's experiment and for Celia's experiment are 1.

What is a probability?

The study of random events and their likelihood of occurring is the focus of the probability field, which is a subfield of statistics. It is used to predict and estimate the likelihood of future events.

Based on the problems 4, 5 and 6 as discuss in figure, we have to find out the sum of all the probabilities for Leon's experiment and for Celia's experiment.

The Results of problem 5 and problem 6 are shown in below figure.
So, The sum of all the probabilities for Leon's experiment and for Celia's experiment are;

Leon:   [tex]\frac{2}{20} + \frac{3}{20} + \frac{5}{20} +\frac{4}{20} +\frac{6}{20} = \frac{20}{20} =1[/tex]

Celia:   [tex]\frac{4}{24} + \frac{3}{24} + \frac{7}{24} +\frac{6}{24} +\frac{4}{24} = \frac{24}{24} =1[/tex]

Solution: Sum of all probabilities for Leon's experiment and for Celia's experiment are 1.

Possible explanation: It is certain that 1 of the 5 possible outcomes will result. The probability of any of the outcomes occurring is 1.

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Full question -

Let y = - 4j- 21 Find the vector - 6v
-6v=

Answers

The vector 6v is -24j - 126.

What is vector?

In mathematics, a vector is a mathematical object that represents a quantity that has both magnitude (size) and direction. Vectors are used to describe physical quantities that have both magnitude and direction, such as velocity, force, and displacement.

Given the vector v = -4j - 21, we can find the vector 6v by multiplying each component of v by 6:

6v = 6(-4j - 21)

Distributing the 6:

6v = -24j - 126

So the vector 6v is -24j - 126.

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Complete question: Let v = - 4j- 21 Find the vector 6v.

there are 49 pong-pong balls in a machine, each bearing a number from 1 to 49. The machine randomly spits out 6 pong-pong balls. If the numbers on the ping-pong balls match the six numbers that you chose, you win.

Answers

The probability of winning the game is 1 / 13,983,816 or 0.00000715 or 0.000715%.

Finding probability:

To solve the problem we use probability and combinatorics.

To calculate the probability of winning the game, we used the formula for calculating combinations to determine the total number of possible outcomes and then counted the number of favorable outcomes.  

Here we have

There are 49 pong-pong balls in a machine, each bearing a number from 1 to 49. The machine randomly spits out 6 pong-pong balls.

The probability of winning the game depends on the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes is the number of ways to choose 6 ping-pong balls out of 49,

This can be calculated using the combination formula:

C(49, 6) = 49! / (6! × (49-6)!) = 49! / (6! × 43!) = 1,39,83,816

Therefore,

There are 13,983,816 possible outcomes when 6 ping-pong balls are randomly selected from 49.

To calculate the number of favorable outcomes,

Count the number of ways to choose 6 ping-pong balls that match the 6 numbers that you chose.

There is only one way to choose all 6 numbers correctly, so the number of favorable outcomes is 1.

Therefore, the probability of winning the game is:

= 1 / 13,983,816 = 0.00000715 or 0.000715%.

Therefore,

The probability of winning the game is 1 / 13,983,816 or 0.00000715 or 0.000715%.

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The distribution of scores on a standardized test is approximately normal with
a standard deviation of 40. Suppose a sample of 100 students had a mean
score of 180.23.
Find the margin of error for a 90% confidence interval for the mean score of all
students on this test. Round your answer to two decimal places.

Answers

Answer: The margin of error (ME) for a 90% confidence interval using a normal distribution with a known population standard deviation is given by:

ME = z* (σ/√n)

where z* is the z-score corresponding to the desired confidence level (in this case, 90% confidence), σ is the population standard deviation, and n is the sample size.

Using a z-score table or calculator, we find that the z-score corresponding to a 90% confidence level is 1.645.

Substituting the given values, we have:

ME = 1.645 * (40 / √100) = 6.58

Therefore, the margin of error for a 90% confidence interval for the mean score of all students on this test is 6.58. We can report the 90% confidence interval as:

180.23 ± 6.58 or (173.65, 186.81)

Step-by-step explanation:

5. Which expression is 16 times as large as 18,233 — 4,006? (18,233 - 4,006) + 16 (18,233 — 4,006) × 16 (18,233 - 4,006) ÷ 16 (18,233 x 16) – 4,006 A (B) (D)​

Answers

The expression is 16 times as large as 18,233 — 4,006 (B) 16(18,233 - 4,006).

Expression calculation.

The expression (18,233 - 4,006) + 16 represents the sum of the difference between 18,233 and 4,006 (which is 14,227) and 16 times that difference.

To break it down further:

First, we calculate the difference between 18,233 and 4,006, which is 14,227.

Then, we multiply 14,227 by 16 to get 227,632.

Finally, we add the original difference of 14,227 to the product of 16 and the difference to get the final answer, which is 241,859.

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A triangular prism is 21 centimeters long and has a triangular face with a base of 16 centimeters and a height of 15 centimeters. The other two sides of the triangle are each 17 centimeters. What is the surface area of the triangular prism?

Answers

The surface area equation for a triangular prism is SA = bh + pl

b = base length [16 cm]h = height [15 cm]p= perimeter  l = length [21 cm]

You have been given most of your information, but you need to find the perimeter. The problem has given you the lengths needed to find the perimeter, so add the lengths together to get the perimeter!

P = a + b + c

P = 21 + 17  17

P = 55

Now you have all your information. Plug into the Surface area equation to find the surface area of the triangular prism:

SA= bh + pl

SA = (16)(15) + (55)(21)

SA= 240 + 1155

SA= 1395 cm ²

*connected parenthesis indicated multiplication*

The surface are of this triangular prism is 1395 square centimeters

find the reduced racial form of each expression:
1: 3^√4/9m^2 ?
2:√63-√700–√112 ?
3: (a^2b^8/a^1/3)^3/4 ?
4: ^4√1024x^9y^12 ?
5:4^3√81 - 2^3√72 - ^3√24 ?
6: ^5√2pq^6 • 2 √2p^3q ?
HELP PLEASE ILL DO ANYTHING. (show explanation pls)

Answers

The reduced radical forms of the expressions provided are as follows:

1.  3^(4/9m)

2. -11√7

3. a^(1/2) * b^6

4.  2x^(9/4) * y^3

5. 16 - ^3√24

6. 4p^(9/10)q^(7/10)

What is a reduced radical form?

A reduced radical form is a way of simplifying expressions that contain radicals such as square roots and cube roots, as much as possible. In a reduced radical form, the radical is simplified to its lowest possible terms.

To obtain the reduced radical forms of the expresions, we can proceed with the workings:

1. 3^(√4/9m^2) = 3^(2/3 * 1/3√4m^2) (since √4 = 2)

= (3^(2/3))^(1/3√4m^2)

= (3^(2/3))^(2/3m)

= 3^(4/9m)

2. √63 = √(9 * 7) = 3√7

√700 = √(100 * 7) = 10√7

√112 = √(16 * 7) = 4√7

√63 - √700 - √112 = 3√7 - 10√7 - 4√7

= -11√7

3. (a^2b^8/a^1/3)^3/4 = (a^2/1/3√a)^3/4 * b^8^3/4

= (a^(2/3))^3/4 * b^6

= a^(1/2) * b^6

4. ^4√1024x^9y^12 = (^4√1024) * (^4√x^9) * (^4√y^12)

= 2 * x^(9/4) * y^(12/4)

= 2x^(9/4) * y^3

5. 4^3√81 = 4^3 * 3 = 64

2^3√72 = 2^3 * 2√9 = 16√9 = 48

^3√24 can't be simplified any further

4^3√81 - 2^3√72 - ^3√24

= 64 - 48 - ^3√24 or  16 - ^3√24.

6. ^5√2pq^6 • 2 √2p^3q

= 2p^(3/5)q^(6/5) * 2p^(3/2)q^(1/2)

= 4p^(9/10)q^(7/10)

So, the results are the simplified or reduced forms of the expressions.

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In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.3 inches, and standard deviation of 8.3 inches.
What is the probability that the height of a randomly chosen child is between 37.55 and 42.55 inches? Do not round until you get your your final answer, and then round to 3 decimal places. Use GeoGebra!

Answer=

Answers

Answer: To solve this problem, we need to standardize the values of 37.55 inches and 42.55 inches using the given mean and standard deviation.

Z-score for 37.55 inches:

z = (x - μ) / σ

z = (37.55 - 55.3) / 8.3

z = -2.1355

Z-score for 42.55 inches:

z = (x - μ) / σ

z = (42.55 - 55.3) / 8.3

z = -1.5386

Now, we can use a standard normal distribution table or a calculator to find the probability of a random variable being between these two standardized values. Using GeoGebra, we can find this probability by following these steps:

Click on the "Functions" icon and select "NormalCDF" function.

Enter the lower and upper limits of the range, which are -2.1355 and -1.5386, respectively.

Enter the mean and standard deviation values, which are 0 and 1 for a standard normal distribution.

Click on the "Evaluate" button to find the probability.

The resulting probability is 0.059, rounded to 3 decimal places.

Therefore, the probability that the height of a randomly chosen child is between 37.55 and 42.55 inches is approximately 0.059.

Step-by-step explanation:

A bag of M&M's has 6 red, 3 green, 8 blue, and 5 yellow M&M's. What is the probability of randomly picking: (give answer as a reduced fraction) 1) a yellow? 2) a blue or green? 3) an orange?

Answers

The probability of randomly picking a yellow M&M is 5/22.

There are no orange M&M's in the bag, so the probability of randomly picking an orange M&M is 0.

What is the probability of randomly picking 1) a yellow? 2) a blue or green? 3) an orange?

There are 22 M&M's in the bag in total. We can use this information to answer the following:

The probability of randomly picking a yellow M&M is 5/22.

The of randomly picking a blue or green M&M is the sum of the probabilities of picking a blue M&M and a green M&M, since these events are mutually exclusive(i.e., they cannot occur at the same time). The probability of picking a blue M&M is 8/22, and the probability of picking a green M&M is 3/22. Therefore, the probability of picking a blue or green M&M is (8/22) + (3/22) = 11/22.

There are no orange M&M's in the bag, so the probability of randomly picking an orange M&M is 0.

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A department store manager has monitored the number of complaints received per week about poor service. The probabilities for numbers of complaints in a week, established by this review, are shown in the table. Answer Number of complaints 012 3 4 5 Probability 0.13 0.21 0.44 0.070. 0.06 0.09Save your answer What is the variance of complaints received per week? Please round your answer to the nearest hundredth Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.

200 word answer

Answers

To calculate the variance of complaints received per week, we first need to find the mean or expected value of the number of complaints. This can be calculated by multiplying the number of complaints in each category by its corresponding probability, and then adding up the results.

Expected value = (0 x 0.13) + (1 x 0.21) + (2 x 0.44) + (3 x 0.07) + (4 x 0.06) + (5 x 0.09) = 2.54

Next, we can use the following formula to calculate the variance:

Variance = Σ[(x - µ)²P(x)]

where Σ = sum, x = number of complaints, µ = expected value, and P(x) = probability.

Using this formula and the probabilities given in the table, we get:

Variance = (0 - 2.54)²(0.13) + (1 - 2.54)²(0.21) + (2 - 2.54)²(0.44) + (3 - 2.54)²(0.07) + (4 - 2.54)²(0.06) + (5 - 2.54)²(0.09) = 1.4856

Rounding this answer to the nearest hundredth, we get a variance of 1.49.

In conclusion, the variance of complaints received per week is 1.49, meaning that the number of complaints is quite spread out around the mean, which is 2.54. This could indicate that the department store has some variability in its service quality, as the number of complaints can vary widely from week to week.

Which is the closest to the area of the shaded region in the given square containing a circle? (Use ≈ 3.14.)
10 m
21.5 square meters
50 square meters
O 78.5 square meters
O 100 square meters
5m

Answers

The area of the shaded region in the specified figure of the square containing a circle is 21.5 m², which is the first option

21.5 square meters

What is a square?

A square is a quadrilateral with all sides of the same length and four interior angles which are right angles.

The figure is a composite figure comprising of a square and a circle

The radius of the circle, r = 5 meters

The side length of the square = 10 meters

The value of π = 3.14

The area of the square = 10 m × 10 m = 100 m²

The area of the circle = π × (5 m)² = 25·π m²

The area of the shaded region is the difference between the area of the square and the area of the circle, therefore;

The area of the shaded region = (100 - 25·π) m²

The area of the shaded region is therefore; (100 - 25 × 3.14) m² = 21.5 m²

The area of the shaded region is 21.5 square meters

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The expression below is equal to -20g plus a constant term. -8(2.5g-4.25)+5.25 What is the value of the constant term?

Answers

Answer:

We can simplify the expression -8(2.5g-4.25)+5.25 by distributing the -8:

-8(2.5g-4.25)+5.25 = -20g + 34 + 5.25

Simplifying further, we can combine the constant terms:

-8(2.5g-4.25)+5.25 = -20g + 39.25

So the value of the constant term is 39.25.

Working with Actual Interest Earned
Daniela puts $550 in a CD that earns 3.5% APR, compounded quarterly,
for 2 years. She is taxed at a rate of 15% on the interest she earns.
The total amount of interest is $33.75.
What percentage of the original principal is this?

Answers

the tax and interest represent 6.5% of the original principal

Spencer is working with his finande advisor to create some personal financial goals for the next year. One of his goals is to reduce the amount of debt
he has. Which statement could
his goal specific and timely?
He should focus intust his student loan debt and give himself a deadline of five years.
B. He should ask
end to be his accountability partner and remind him of his goal every two weeks.
le should review.
current finances to determine how much he can allocate to his goal.
He should pay
the minimum payment on his credit card statement each month.

Answers

Answer: A. He should focus on his student loan debt and give himself a deadline of five years. This statement specifies a particular type of debt and sets a time-bound goal, making it both specific and timely.

Step-by-step explanation:

2.Each curve is a transformation of the graph of the parent function y = √x.
Write an equation for each curve.
A.
B.
C.
D.

Answers

Since each curve is a transformation of the graph of the parent function y = √x, an equation for each curve are as follows;

A. y = √(-x + 2)

B. y = -√(x - 1) + 3

C. y = √(x - 3)

D. y = √x - 2

E. y = -√(x + 2)

What is a translation?

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

N represents an integer.g(x) and f(x) represent the parent functions.

In order to write an equation that models curve A, we would have to apply a reflection and horizontal translation to y = √x by 2 units left.

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Find the value of x. Write your answer in simplest form.

Answers

Answer:

C

Step-by-step explanation:

using the sine ratio and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{5}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = 5[tex]\sqrt{2}[/tex]

Find the value of y in 3/5 y=6

Answers

since 3/5 y is 6 to find what 1/5 y is we divide 6 by 3 which is 2 so 1/5 y=2. Now to find the value of y we multiply that by 5 and since 2*5=10 y=10. Also pls mark as brainliest answer

I need help solving this thank you

Answers

The negation is the fourth option.

6 + 3 ≠ 9 or 6 - 3 ≠ 9

How to write the negation?

The negation of an equation is an inequality such that we just change the equal sign, by the "≠" sign.

Here we start with the two equations.

6 + 3 = 9 or 6 - 3 = 9

Just change the equal signs for different signs:

6 + 3 ≠ 9 or 6 - 3 ≠ 9

That is the negation, fourth option.

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Consider 8 = − 2/3x. 1 Which is the BEST first step to take when solving the given equation?

Answers

multiply each side by -3/2

A wall is 2000 sq ft. A gallon of paint covers 400 sq ft. Complete the conversion factor: 1 gallon / ? sq ft

Answers

To cover a 2000 sq ft wall, we will need 5 gallons of paint.

what is area?

Area is the measure of the size of a two-dimensional surface or region, expressed in square units. It is a fundamental concept in geometry and is used to quantify the amount of space inside a shape, such as a square, rectangle, triangle, or circle. The unit of measurement for area varies depending on the system used, but in the International System of Units (SI), the standard unit of area is the square meter (m²). In everyday life, we often use other units of area such as square feet, square inches, or square centimeters.

To find the conversion factor, we need to divide the number of square feet by the number of square feet covered by one gallon of paint:

Conversion factor = 1 gallon / (400 sq ft/gallon)

So, for a wall that is 2000 sq ft, we can use this conversion factor to find the number of gallons of paint needed:

Number of gallons = (2000 sq ft) / (400 sq ft/gallon) = 5 gallons

Therefore, to cover a 2000 sq ft wall, we will need 5 gallons of paint.

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Find the value of x from the given figure.​

Answers

The value of x from the given figure is given as follows:

144º.

What is a straight angle?

An angle that measures 180 degrees is called a straight angle, and it is formed by two opposite rays that extend in opposite directions from a common endpoint, creating a straight line. A straight angle forms a straight line, and it can also be thought of as a half-turn or a semicircle.

The two opposite rays in this problem have the measures given as follows:

x.x/4.

Hence the equation to find the value of x is given as follows:

x + x/4 = 180

x + 0.25x = 180

1.25x = 180

x = 180/1.25

x = 144º.

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Mr. Howard's phone has
4 rows of buttons. There are
3 buttons in each row. How
many buttons are on
Mr. Howard's phone?
buttons

Answers

Answer:

12

Step-by-step explanation:

since there are 4 rows, and in each row, there are 3 buttons, then you would end up with

4 (rows) x 3 (buttons per row)

this gives you 12 buttons on the phone.

Answer:

Step-by-step explanation:

Each row has 3 buttons.

There are 4 rows in total 3x4= 12buttons

if f(x)=7x-5, determine f^-1(18)

Answers

To find the inverse of the function f(x) = 7x - 5, we need to solve for x in terms of y (or f^(-1)(x)). First, let's replace f(x) with y:

y = 7x - 5

Now, we need to solve for x:

1. Add 5 to both sides:

y + 5 = 7x

2. Divide both sides by 7:

(x = (y + 5) / 7)

Now we have the inverse function, f^(-1)(x) = (x + 5) / 7. We can use this to find f^(-1)(18):

f^(-1)(18) = (18 + 5) / 7f^(-1)(18) = 23 / 7So, f^(-1)(18) = 23/7.

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Answers

The x-axis is where the circle centre is located. Three units make up the circle's radius. This circle's radius coincides with the radius of the circle whose equation is x² + y² = 9.

What is the circle's equation when its centre is on the x-axis?

The y coordinate of a circle's centre will be 0 if the circle's centre is on the x-axis. The circle's equation will therefore have the generic form x2 + y2 + 2gx + c = 0, where g and c are constants.

Circle's standard equation is written as:

x²+y²+2gx+2fy+C=0

Centre is (-g, -f)

radius = √g²+f²-C

Given a circle whose equation is : x²+y²-2x-8=0

Get the centre of the circle

2gx = -2x

2g = -2

g = -1

Similarly, 2fy = 0

f = 0

Centre = (-(-1), 0) = (1, 0)

This demonstrates circle's centre is on the x-axis.

r = radius = √g²+f²-C

radius = √1²+0²-(-8)

radius =√9 = 3 units

The circle has a radius of three units.

For the circle x²+y²=9, radius is expressed as:

r² = 9

r = 3 units

As a result, this circle's radius matches that of the circle whose equation is x² + y² = 9.

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How much will the monthly payment be for a new car priced at $29,950 if the current finance rate is 36 months at 3.16%? Include financing the 8% TT&L and make a 25% down payment.

Answers

By using loan amortization formula, we conclude that, the monthly payment for the new car, including financing and fees, would be $715.49.

What is loan amortization?

Loan amortization is the process of paying off a debt with regular, fixed payments over time, typically with interest. An amortization schedule shows how each payment is allocated between the principal amount and the interest owed, as well as the remaining balance of the loan after each payment.

According to given information:

To calculate the monthly payment for a car loan with financing, we need to use a loan amortization formula. The formula takes into account the loan amount, the interest rate, the length of the loan term, and any other fees or charges.

First, we need to calculate the total loan amount. We start with the price of the car ($29,950) and add the TT&L (8% of $29,950 = $2,396), then subtract the down payment (25% of $31,346 = $7,836.50).

Total loan amount = $29,950 + $2,396 - $7,836.50 = $24,509.50

Next, we need to calculate the monthly interest rate. We divide the annual interest rate (3.16%) by 12 (the number of months in a year).

Monthly interest rate = 3.16% / 12 = 0.2633%

Finally, we can use the loan amortization formula:

Monthly payment = [tex][P x (r(1+r)^n)] / [(1+r)^n - 1][/tex]

Where P is the principal amount (total loan amount), r is the monthly interest rate, and n is the number of months in the loan term.

Plugging in the values:

Monthly payment = [tex][$24,509.50 x (0.002633(1+0.002633)^{36})] / [(1+0.002633)^{36} - 1] = $715.49[/tex]

Therefore, the monthly payment for the new car, including financing and fees, would be $715.49.

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Translate in two ways each of these statements into logical expressions using predcates quantifiers and logical connective first let the domain consist of the students in your class and second let it consist of all people a) everyone in your class has a cellular phone

Answers

For all x, P(x) (using universal quantifier ∀) and  It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:

1. For all x in S, P(x) (using universal quantifier ∀)

2. It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)

If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:

For all x, P(x) (using universal quantifier ∀)

It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)Let S be the set of students in your class and P(x) be the predicate "x has a cellular phone". Then, we can represent the statement "everyone in your class has a cellular phone" as:

For all x in S, P(x) (using universal quantifier ∀)

It is not the case that there exists an x in S such that ~P(x) (using negation ¬ and existential quantifier ∃)

If we want to represent the same statement for all people, we can use the same predicate P(x) and consider the domain of all people. Then, the statement "everyone has a cellular phone" can be represented as:

1. For all x, P(x) (using universal quantifier ∀)

2. It is not the case that there exists an x such that ~P(x) (using negation ¬ and existential quantifier ∃)

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Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? .

Answers

5x^2 + 20x - 7 = 0
The first step to solve this using completing the square is to move the constant to the right. The constant is -7, so we will add 7 to both sides.
5x^ 2 + 20x = 7
Now we will divide the equation by 5. Because to complete the square, you must divide the equation by the coefficient of x^2.
x^2 + 4x = 7/5
Now we must figure out what to add to both sides to complete the square. To find that, you will half the coefficient of the x term and then square it. 4/2 = 2. 2^2=4. So we will add 4 to both sides.
x^2 + 4x + 4 = 7/5 + 4
Factor the left side.
(x + 2)^2 = 7/5 + 4
Calculate the right side.
(x + 2)^2 = 27/5
Now we will solve for x.
x = -3√(15)/5 -2
x = 3√(15)/5 -2
There are your two solutions. Hope this helped!

A car corporation produce 1420 more cars this month then last. Write a signed number to represent this month’s change in production

Answers

The car corporation produced 1420 more cars this month than last, so the signed number to represent this month's change in production would be +1420.

What is number system?

The signed number system is a way of representing positive and negative numbers. It includes a sign (+ or -) and a numerical value. In the case of the car corporation's change in production, the sign is positive (+) because the production increased, and the numerical value is 1420.

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