find the apr (rounded to the nearest tenth of a percent) for the loan described below. purchase a living room set for $3,500 at 10% add-on interest for 3 years.

n = -0.5714

Step-by-step explanation:

[tex]{ \tt{1.8n + 0.2 = 3.2n + 1}}[/tex]

[tex]{ \tt{1.8n = 3.2n + 1 - 0.2}}[/tex]

[tex]{ \tt{1.8n = 3.2n + 0.8}}[/tex]

[tex]{ \tt{1.8n - 3.2n = 0.8}}[/tex]

[tex] { \tt{ - 1.4n = 0.8}}[/tex]

Divide both sides by -1.4 then,

[tex]{ \tt{ \frac{ - 1.4}{ - 1.4}n = - \frac{ 0.8}{1.4}}} [/tex]

Let us convert 0.8 to 8 and 1.4 to 14 by shifting the points. Then,

[tex]{ \tt{n = - \frac{8}{14}}} [/tex]

[tex]{ \tt{n = - \frac{4}{7}}} [/tex]

[tex]{ \blue{ \boxed{ \green{\sf{n = -0.571428571}}}}} [/tex]

Answer:

x=11

Step-by-step explanation:

Answer:Consumidores primarios: comen a los productores. Consumidores secundarios: comen a los primarios. Consumidores terciarios: comen a los carnívoros. Descomponedores: se alimentan de restos de seres vivos.

Step-by-step explanation:Consumidores primarios: comen a los productores. Consumidores secundarios: comen a los primarios. Consumidores terciarios: comen a los carnívoros. Descomponedores: se alimentan de restos de seres vivos.

Hello..!

¿What is consumidores primarios?

They are the ones that eat plants. They are herbivores or are parasites of these.

Answer:

f(x) = 1/2x + 3

Answer:

3/2

Step-by-step explanation:

(y2-y1)/(x2-x1)

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

-3/-2

the slope of the line is 3/2

Based on the box plot, the number of students that gained more than 48 marks is 80 students.

In Mathematics, the five-number summary of any box and whisker plot include the following:

By critically observing the box and whisker plots which represent the scores of students in a test, we can reasonably and logically deduce that the third quartile (75%) is 70 and the median score is 48. Therefore, we would calculate the total number of students as follows:

Total number of students = 75/100 × T

120 = 0.75T

T = 120/0.75

T = 160 students.

From the median score of 48, the number of students that gained more than 48 marks is given by:

Students = 50/100 × 160

Students = 50/100 × 160

Students = 80 students.

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Answer:thhe one on top good

Step-by-step explanation:

Any algebraic expression can be represented graphically. The given problem can be solved as shown in the image attached.

A polynomial in one variable is also an algebraic expression. It can be written in the form aˣn. Here, n is a non-negative integer and a is a real number. The a is also called the coefficient of the term.

The given problem also consists of a polynomial in one variable. It can be solved as such.

We have been told that = y = -3x+7

We need to graph this. For this, we plot at least two values for x and y -

x  = 0 and y = 7

x = 1 and y = 4

We plot both these coordinates on the graph which has been attached below.

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Answer:

The answer is 923.6111 because 166430÷180 is 923.6111

A spurious correlation is the implied causal relationships between events that are statistically  linked.

Spurious correlation;

A spurious correlation (or spuriousness) in statistics is an apparent causal relationship between two variables. Any reported dependencies between variables are solely the result of chance or are both a result of an unidentified confounder when there is misleading correlation.

When the price of higher education and the cost of living both rise, for instance, this doesn't necessarily indicate a causal link between the two factors because higher education tuition isn't always the result of rising living costs.

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The length of the chord is 6

Simply said, a circle is a rounded form without any edges or line segments. It has the geometric form

The circle's general equation is written as follows: x2 + y2 + 2gx + 2fy + c = 0. The center of the circle in this general form of the equation of a circle is (-g, -f), and its radius is given by r = g2+f2cg2+f2c.

The circle's general equation is written as follows: x2 + y2 + 2gx + 2fy + c = 0. The coordinates of the circle's center and radius are determined using this general form. The equation in this case represents a circle that does not pass through the origin because c is a constant term.

We possess

4x2+4y2−12x+32y=27…(1)

We shall have y=0 when the specified circle intersects the x-axis, therefore

4x2+4y2−12x+32y=27

=>4x2−12x=27

=>4x2−12x−27=0…(2)

The answers to (2) are:

x1=−3/2

x2=9/2

Thus, the supplied circle intersects the x-axis at the following points:

A(−3/2,0) and B(9/2,0)

The length of the chord we want is defined as the distance d between these sites. The well-known formula for calculating the distance between points A and B is used to calculate the distance d:

d=root((9/2−(−3/2))^2+(0−0)^2)

√=6^2

=6

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Answer:

Step-by-step explanation:

32

If the rate of change is constant, the volume of the water in the pond by the year 2030 will be 147 gallons.

Define volume.

Any three-dimensional solid's volume is just the amount of space it takes up. It can be any shape like a cube, cuboid, cone, cylinder, etc. Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. The SI unit of volume is cubic units.

Solution Explained:

Based on the conditions given in the question, we formulate as follows

(612 X (2024 - 2020) + (612 - 798) X (2030 - 2020) / (2024-2020)

= (612 X 4 - 186 X 10) / 4
= (2448 - 1860) / 4
= 588 / 4
= 147

Therefore, by 2030 the volume of the water in the pond will be 147 gallons.

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x + y ≤ -4 and 3x + 2y ≤ -5

======================================================

Explanation:

The given point has coordinates of x = 3 and y = -7.

Let's plug those coordinates into the first inequality of choice A.

x+y < -4

3 + (-7) < -4

-4 < -4

The last statement is false. A number cannot be smaller than itself.

Since the last inequality is false, it causes the first to be false for those x,y values. Therefore, we rule out choice A.

--------------

We'll do the same idea for the first inequality in choice B

x + y ≤ -4

3 + (-7) ≤ -4

-4 ≤ -4

This time we get a true statement at the end. The key difference is the "or equal to" portion.

Let's check the other inequality of choice B

3x + 2y < -5

3(3) + 2(-7) < -5

9 - 14 < -5

-5 < -5

We run into a similar issue as we did with choice A. We have no choice but to cross choice B off the list as well.

--------------

Choice C is eliminated for the same reason choice A was.

Choice D is the final answer because both inequalities involve "or equal to". So the -5 < -5 is now -5  ≤ -5 which is true.

It turns out that (3, -7) is on the boundary of each shaded region. It's at the intersection of the two boundary lines x+y = -4 and 3x+2y = -5.

D. x + y ≤ -4

3x + 2y ≤ -5

To see if (3, -7) satisfies both inequalities.

x + y ≤ -4:

Substitute x = 3 and y = -7 into the first inequality:

3 + (-7) ≤ -4

-4 ≤ -4

Since -4 is less than or equal to -4, the first inequality is true for the point (3, -7).

3x + 2y ≤ -5:

Substitute x = 3 and y = -7 into the second inequality:

3(3) + 2(-7) ≤ -5

9 - 14 ≤ -5

-5 ≤ -5

Since -5 is equal to -5, the second inequality is also true for the point (3, -7).

(✿◕‿◕✿)

The fraction of the container that is empty, based on the capacity of the container and the water added, is 12 / 25

The fraction of the container that is empty can be found by the formula:

= (Capacity of container - Amount of water added ) / Capacity of container

Capacity of container = 2.5 liters

Amount of water added = 1 . 3 liters

The fraction of the container which is empty is:

= (2 . 5 - 1.3) / 2.5

= 1.2 / 2.5

= (1 . 2 x 10) / ( 2 . 5 x 10)

= 12 / 25

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The value of the expression 2b plus 4a minus a minus 2 plus 12b is 3a + 14b - 2.

Expression:

An expression is defined as the a combination of operators, constants and variables. And it may consist of one or more operands, and zero or more operators to produce a value.

Given,

Here we have the statement "2b plus 4a minus a minus 2 plus 12b".

Now, we have to find the simplified form of this statement.

In order to find the simplified form,

First we have to convert the statement into expression form, then we get

2b plus 4a minus a minus 2 plus 12b = 2b + 4a - a - 2 + 12b

Now, we have to combine the like terms, then we get,

=> (2b + 12b) + (4a - a) - 2

Perform the appropriate arithmetic operations, then we get the simplified form of the expression as,

=> 14b + 3a - 2

Now, we have to arrange them in order then we get,

=> 3a + 14b - 2

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The constant of proportionality in terms of dollars per hour is A 40.

The constant of proportionality is used to illustrate the constant relationship between the variables.

In this case, a 3 hour lesson costs $120.00 and the cost of a lesson is proportional to the duration, in hours, of the lesson.

The constant will be the division of the values. This will be:

= $120 / 3

= $40

The correct option is A

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0.86 of the exam scores are between 68 and 77.99 points

Since the set of computer science exam scores are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x-μ)/σ

Where

X = computer science exam scores.

μ = mean score

σ = standard deviation

From the information given,

μ = 71.33 points

σ = 333 points

We want to find the proportion of the exam scores are between 68 and 77.99 points. It is expressed as

P(68 < x ≤ 77.99)

For x = 68,

z = (68 - 71.331)/333 = - 0.01

Looking at the normal distribution table, the probability corresponding to the z score is -0.01

For x = 68,

z = (77.99 - 71.33)/333 = 0.25

Looking at the normal distribution table, the probability corresponding to the z score is 0.25

P(68 < x ≤ 77.99) = 0.25 + 0.01 = 0.26

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The value of the blocks he used is 80 blocks.

The difference is that expressions, which are essentially mathematical "phrases," do not contain an equal sign. Equations have an equal sign and demonstrate that two mathematical expressions are equivalent. An algebraic equation is 2x + b = 14, but 2x + b is an algebraic expression.

Arithmetic operations are the most fundamental type of mathematical expression. Any combination of numbers and a mathematical operation, such as multiplication, addition, subtraction, or division, are considered arithmetic operations.

Given ,

A)How many blocks has he used?

150-70

= 80

B) 35 - 20

= 15

70/15

= 4

Therefore the value of the blocks he used is 80 blocks

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Andre made a mistake after getting 14x=8x. He divided each side by x, but this is not valid since x may be 0 and dividing by 0 gives an undefined result.

Andre should have collected the like terms in order to have all the variables x on one side before taking the difference.

Inequality expression

Given the inequality expression solved by andre expressed as:

14x + 3 ≤ 8x + 3

Simplify to have:

14x - 8x ≤ 3-3

6x ≤ 0

x ≤ 0

Hence andre should have collected the like terms in order to have all the variables x on one side before taking the difference.

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The slope of the line from the equation is 2/3.

The line:

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.

The formula of a line:

y = mx + c

m = slope

c = y-intercept

Here we are provided with the equation:

8x - 12y = 108

12y = 8x - 108

y = 2/3x - 9

So by equating we get the slope:

m = 2/3

Therefore the slope is 2/3.

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If we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, then 56 sample size should be used and if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, then 22 sample size should be used.

In the given question,

A preliminary sample conducted by the wall street journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes.

(a) We have to estimate the population mean time for previews at movie theaters with a margin of error of seconds, what sample size should be used.

Assuming the confidence interval 98% and margin error of 75 seconds.

We can write 98% as 0.98.

So the value of z at 98% confidence interval using the standard table of z is 2.326.

Standard Deviation= 4 minutes

Converting minutes in seconds so,

Standard Deviation= 4*60

Standard Deviation= 240

Margin of error is 75 seconds.

So the sample size = (Value of z * Standard Deviation)/Margin Error

Sample Size = ((2.326*240)/75)^2

Sample Size = (558.24/75)^2

Sample Size = (7.4432)^2

Sample Size = 55.401

Approx value of Sample Size = 56

Hence, if we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds, then 56 sample size should be used.

(b) We have to estimate if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, what sample size should be used.

The given margin of error is 75 seconds.

Now converting the error in minute by dividing 60.

Now the margin of error = 75/60=5/6 minute

Standard Deviation= 4 minutes

The confidence interval 98% and margin error of 75 seconds.

We can write 98% as 0.98.

So the sample size = (Value of z * Standard Deviation)/Margin Error

sample size = {(0.98*4)/(5/6)}^2

sample size = {6(0.98*4)/5}^2

sample size = (6*3.92/5)^2

sample size = (23.52/5)^2

sample size = (4.704)^2

sample size = 22.13

Approx value of Sample Size = 22

Hence, if we want to estimate the population mean time for previews at movie theaters with a margin of error of minute, then 22 sample size should be used.

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NORAL follows a hyperbolic path.

Equation of hyperbola; x²/6400 + y²/33600 = 1

Given,

The coordinates where the two NAROL transmitters are located = (-200, 0) and (200, 0)

The distance from receiver to these transmitters = 160 miles

We have to find the standard form of the hyperbola that the receiver sits on ;

Here,

The transmitters behave as foci of the hyperbola.

The center of hyperbola; (h, k) = (0, 0)

The distance from center to focal point,

c = 200

Square both sides

c² = 40,000

The distance from the receiver to the transmitters  is given as:

2a = 160

Divide both sides by 2

a = 80

Square both sides

a² = 6400

We have:

b² = c² - a²

This gives

b² = 40000 - 6400

b² = 33600

The equation of a hyperbola is:

(x - h)²/a² + (y - k)²/b² = 1

So, we have:

(x - 0)²/6400 + (y - 0)²/33600 = 1

Therefore,

The equation of the hyperbola is:

x²/6400 + y²/33600 = 1

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Answer:

Equation: 3x - 4 = 6 - 2x

Solution: x = 2

Step-by-step explanation:

Look at the key.

Left side of the equal sign:

A grey rectangle means x.

There are 3 grey rectangles on the left side, so that is 3x.

A white square means -1.

There are 4 white squares on the left side, so that means -4.

Altogether, the left side is 3x - 4.

Right side of the equal sign:

A black square means 1.

There are 6 black squares, so that means 6.

A white rectangle means -x.

There are 2 white rectangles, so that means -2x.

Altogether, the right side is 6 - 2x.

Put both sides together, and you have

3x - 4 = 6 - 2x

Solve the equation:

Add 2x to both sides.

5x - 4 = 6

Add 4 to both sides.

5x = 10

Divide both sides by 5.

x = 2

Answer:

Equation: 3x - 4 = 6 - 2x

Solution: x = 2

The equation that represents the altitude h of the balloon over time.

h = 1500t.

Option B is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 5 is an equation.

3x + 5x = 5 is an equation.

We have,

A hot air balloon rises 1,500 feet in 25 minutes.

This means,

25 minutes = 1,500 feet

h = altitude

The equation that represents the altitude h of the balloon over time.

h = 1500t.

Thus,

The equation that represents the altitude h of the balloon over time.

h = 1500t.

Option B is the correct answer.

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All the equations that have 10² = 100 as a solution are given as follows:

We have to solve the equations and verify if the solution is equals to 100.

All the equations have the following format:

ax = b

Isolating the variable x, the solutions are given as follows:

x = b/a.

The first equation is:

0.031x = 31

The solution is:

x = 31/0.031 = 1000 = 10³.

The second equation is:

0.501x = 501

The solution is:

x = 501/0.501 = 1000 = 10³.

The third equation is:

4.08x = 408.

The solution is:

x = 408/4.08 = 100 = 10². (one of the correct options).

The fourth equation is:

0.97x = 97.

The solution is:

x = 97/0.97 = 100 = 10². (one of the correct options).

The fifth equation is:

0.55x = 550.

The solution is:

x = 550/0.55 = 1000 = 10³.

The equations are:

The problem asks for which of these equations 10² = 100 is a solution.

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Answer:

Step-by-step explanation:

Domain is the input

Range is the output

Function is the equation that is set up by the given information

1)

Domain   2 to 8

Range   1 to 6

Yes, this is a function

2)

Domain  2 to 3

Range  7 to 13

No, this is not a function , b/c functions need a 1 to 1 correspondence

3)

Domain  0 to 4

Range   -1 to 5

No, this is not a function , b/c functions need a 1 to 1 correspondence

The probability that the sample mean will be between 181 and 185 is 0.3039.

Given,

The mean of a population, μ = 180

Standard deviation, σ = 36

Number of sample observations, n = 84

We have to find the probability that the sample mean will be between 181 and 185;

Lets convert 181 and 185 into z scores;

z = (x - μ) / (σ/√n)

z = (181 - 180) / (36/√84)

z = 1/3.93

z = 0.25

z = (185 - 180) / (36/√84)

z = 5 / 3.93

z = 1.27

Lets look z score table;

The area to the left of z = 0.25 is 0.5987

The area to the left of z = 1.27 is 0.8980

The probability that the z is between 0.25 and 1.27 would be 0.8980 – 0.5887 = 0.3039.

That is,

The probability that the sample mean will be between 181 and 185 is 0.3039.

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Answer:

30 inches

Step-by-step explanation:

1 ft=12 inches

We multiply this fraction by 12

2 1/2x12

5/2x12/1

60/2

30 inches

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1/9 is Square root of expression .

What in mathematics is a square root?

= √1/x²  * √x²/81

= √x²/ x² * 81

= √1/81

= 1/9

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