5) A woman wants to borrow $12,000 to buy a car. She wants to repay the loan by monthly installments
for 4 years. If the interest in the loan is 10.5% per year, compounded monthly, what is the amount of
each payment?

The equation of the line that passes through the point ((0, 3) & (3, 0) is y = -1x - 3.

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).

To find the slope of the line, we can use the slope formula:

m = (y2 - y1)/(x2 - x1)

We have given the line passes through the points(0, 3) & (3, 0),

so, m = (0-3)/(3-0)

= -3/3

m = -1

The y-intercept is the point where the line intersects the y-axis. This point is (0, b), where b is the y-intercept.

Since the given line passes through the point (3, 0), we can substitute these values into the slope-intercept form of the equation to find the y-intercept:

y = mx + b

0 = -1 * 3 + b

b = -3

Solving for b gives us:

b = -3

Therefore, the equation of the line that passes through the point ((0, 3) & (3, 0) is y = -1x - 3.

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Answer:

-2.5

Step-by-step explanation:

For a quadratic equation [tex]ax^2 + bx+c=0[/tex], the sum of the roots is [tex]-b/a[/tex].

Here, [tex]b=5[/tex] and [tex]a=2[/tex], so the sum is [tex]-2.5[/tex].

7.14 unit² is the area of the rectangle shown on the coordinate plane

The length and breadth of the rectangle multiplied together provide the area of the rectangle. To determine the area occupied by a rectangle within its perimeter, we compute the area of the rectangle.

Consider rectangle with vertices A(-1,-2), B(-3,-4), C(-6,-1) and D(-4,1). The area of the rectangle is:

Area = length × width

Now, find the length and the width:

Length (BC) = [tex]\sqrt{[-3-(-6)]^2 + [(-4)-(-1)]^2}[/tex]

or, BC = [tex]\sqrt{(3)^2 +(-3)^2}[/tex]

or, BC = [tex]\sqrt{18}[/tex] unit

Width (AB) = [tex]\sqrt{[(-1) -(-3)]^2 + [(-2)-(-4)]^2}[/tex]

or, AB = [tex]\sqrt{(2)^2 +(2)^2}[/tex]

or, AB = [tex]\sqrt{8}[/tex] unit

Then the area of the rectangle ABCD is

Area(ABCD) = length (BC) × width (AB)

or, Area(ABCD) = [tex]\sqrt{18} *\sqrt{8}[/tex]

or, Area(ABCD) = 7.14 unit²

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Step-by-step explanation:

based on the geometric mean theorem

h² = pq

h = height of the main right-angled triangle.

p and q are the segments of the baseline of the main right-angled triangle.

12² = 36x

144 = 36x

x = 144/36 = 4

so, DC is 4 units long.

Answer:

4 and 1/2

Step-by-step explanation:

left side must be ewual to right side. after you substract 12x-4x you get 8x+2 on right side. you than find a number on the left side, whit which you have to multiply 2x to get 8x(same number as on the other side) and you get 4. lastly you have to find a number that gives you 2 when multiplied with 4 and it is 1/2

Answer:

D) [tex]x^2+8x+16=(x+4)^2[/tex]

Step-by-step explanation:

[tex]x^2+8x+(8/2)^2=x^2+8x+16=(x+4)^2[/tex]

Answer:

$4,140.00

Step-by-step explanation:

Interest = principle x rate x time

I = 3600 x .03 x 5

I = 540

Add the interest to what is already in the account

540 + 3600

4140

The income of the man is 24000.

Step-by-step explanation:

income of man =24000

Let the income of man be x

According to the question,

20%*x = 4800

0.2x=4800

As a result, x =24000

(4800*10= 48000/2= 24000)

So the income of a man is 24000.

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Man's income is, 24000 rupees.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given, 20% of an income of a man is Rs 4,800.

To find the income:

Use percentage formula,

let m be the man's income.

So, m x 20 / 100 = 4800

Rearranging,

m = 4800 x 100 / 20

m = 24000

Therefore, the income is, 24000 Rs.

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Step-by-step explanation:

since it's -14 then it will be√-14

√-14=√-2 multiplied is by √7

so that will be √-2√7

Answer:

4.67 (nearest hundredth)

Step-by-step explanation:

In 3 weeks, Landscape Elementary uses 14 reams of paper.

In 1 week, Landscape Elementary uses 14/3 reams of paper. = 4.66666...

The digit at thousandth place is 6 and it is more than 5. Thus add 1 with hundredth digit.

4.66666... = 4.67 (nearest hundredth)

An inequality that can be used to determine how much material, x, Paul should buy is x ≥ 196.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other.

Given:

Paul is making picture frames.

He wants to make at least 8 picture frames and needs 24.5 inches of material for each frame.

To find the total material for 8 frames:

Multiply by 8 to material for one form

24.5 x 8

= 196 inches

To write an inequality that can be used to determine how much material, x, Paul should buy:

x ≥ 196 inches.

To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more.

You must flip the inequality sign if you multiply or divide either side by a negative number.

Therefore, the inequality is x ≥ 196.

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By using the unitary method the boy's actual height is 3 meters.

The unitary method is used to solve a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

The unitary method's formula is to find the value of a single unit and then multiply that value by the number of units to get the required value.

Given:

12 meters is the height of a boy statue.

The scale used was 4 meters = 1 foot.

1 metre = 1/4 feet

Assume the boy's actual height = H foot

By using the unitary method of unit conversion.

According to the question,

The actual height of the boy = height of the statue×  scale used for 1 meter.

H = 12 × ¼

H = 12/4

H = 3 meters

By using the unitary method the boy's actual height is 3 meters.

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By using the unitary method the boy's actual height is 3 meters.

The unitary method is used to solve a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

The unitary method's formula is to find the value of a single unit and then multiply that value by the number of units to get the required value.

Given:

12 meters is the height of a boy statue.

The scale used was 4 meters = 1 foot.

1 metre = 1/4 feet

Assume the boy's actual height = H foot

By using the unitary method of unit conversion.

According to the question,

The actual height of the boy = height of the statue×  scale used for 1 meter.

H = 12 × ¼

H = 12/4

H = 3 meters

By using the unitary method the boy's actual height is 3 meters.

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Answer:

= about 1436.75504

Step-by-step explanation:

V = 4/3 π r³

Applying the properties of a rhombus, the value of each angle listed are:

m∠JKL = 72°

m∠MLK = 108°

m∠JMK = 36°

m∠MJL = 54°

m∠KNL = 90°

A rhombus is a quadrilateral with the following properties:

Given, m∠JKM = 36°, apply the properties of a rhombus to solve the missing values.

m∠JKL = 2(36)

m∠JKL = 72°

m∠MLK = 180 - 72 [adjacent angles are supplementary in a rhombus]

m∠MLK = 108°

m∠JMK = 36°

m∠MJL = 1/2(m∠MLK)

m∠MJL = 1/2(108)

m∠MJL = 54°

m∠KNL = 90° [bisection of the diagonals of a rhombus at right angles).

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The table for the function y = 5^x should be completed as follows;

x           y

-1          0.2

0           1

1            5

2           25

A graph of the given function y = 5^x with the points (0, 1) and (1, 5) is shown in the image attached below.

In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

Next, we would determine the ordered pairs that would complete the table for the function y = 5^x as follows;

When x = -1, the value of y is given by;

y = 5^-1

y = 0.2 or 1/5.

When x = 0, the value of y is given by;

y = 5^0

y = 1

When x = 1, the value of y is given by;

y = 5^1

y = 5

When x = 2, the value of y is given by;

y = 5^2

y = 25

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Answer:

x ≈ 10.6

y = 15

Step-by-step explanation:

The opposite angles in an inscribed quadrilateral are supplementary.

Therefore:

(4y+14) + (7y+1) = 180

=> 11y + 15 = 180

=> 11y = 165

=> y = 15

7x+1 + 105 = 180

=> 7x + 106 = 180

=> 7x = 74

=> x ≈ 10.6

Answer: 20/48

(simplified) 5/12

Step-by-step explanation:

We will use 6/8 - 2/6 for our example

6/8 - 2/6

Multiply the denominator on the right side by the denominator on the left side: 6x8 = 48

Make 48 the denominators on both sides: /48,  /48

Now multiply the denominator on the left side with the numerator on the  left side: 6x6 = 36

Make the first fraction's numerator 36: 36/48

Now multiply the denominator on the left side by the numerator on the right side: 8x2 = 16

Now make 16 the numerator of the second fraction: 16/48

Now that the denominators are the same, we can subtract!

36/48-16/48 = 20/48

Now to simplify:

divide 20/48 by 4 = 5/12

So the answer is 20/48 and when it is simplified it comes out to 5/12

This is how you subtract fractions with different denominators.

You can use the same method when adding, the only difference is that instead of adding in the last step, you add instead!

Answer:

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

We need to find the remainder when -5x³ + 2x + 3  is divided by x + 2.

According to the remainder theorem, the remainder is the value of the polynomial when x = - 2:

The matching choice is B.

Answer:

B.  39

Step-by-step explanation:

Divide the polynomials using long division:

[tex]\large \begin{array}{r}-5x^2+10x-18\phantom{)}\\x+2{\overline{\smash{\big)}\,-5x^3\;\;\;\;\;\;\;\;\;\;\;+2x+3\phantom{)}}}\\{-~\phantom{(}\underline{(-5x^3-10x^2)\phantom{-b)))))))}}\\10x^2+2x+3\phantom{)}\\-~\phantom{()}\underline{(10x^2+20x)\phantom{)))}}\\-18x+3\phantom{)}\\-~\phantom{()}\underline{(-18x-36)\phantom{}}\\39\phantom{)}\\\end{array}[/tex]

The solution is the quotient plus the remainder divided by the divisor.

Solution

[tex]-5x^2+10x-18+\dfrac{39}{x+2}[/tex]

a) The Test statistic of the hypothesis is; 0.23

b) The p-value from the test statistic is; 0.409

c) The final conclusion is there is not sufficient evidence to determine whether the antidepressant drug had an effect on changing working habits after one year.

Test statistic is defined as a number, calculated from a statistical test, used to find if your data could have occurred under the null hypothesis. In this case, we are dealing with proportions and as such the test statistic has the formula;

z = (p1 - p2)/standard error

p1 = 14/167 = 0.084; s1 = √(0.084 * 0.916/167) = 1.285

p2 = 316/833 = 0.38; s2 = √(0.38 * 0.62/833) = 0.0168

Hence, for the distribution of differences, the mean and the standard error are given as follows:

Mean: p = 0.38 - 0.084 = 0.296

Standard error: s = √(1.285² + 0.0168²) = 1.2854

a) Test statistic = p/s = 0.296/1.2854

Test statistic = 0.23

b) From p-value from z-score calculator, we get that;

p-value = 0.409

c) The p-value is greater than the significance value of 0.04, we fail to reject the null hypothesis and conclude that there is not sufficient evidence to determine whether the antidepressant drug had an effect on changing working habits after one year.

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The dimensions of the rectangular garden to maximize the area is length = width = 75 meters.

Let l be the length and w be the width of the rectangular garden.

We need to find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.

The perimeter of the  rectangular garden = 300 meters

We know that the perimeter of the rectangle =2(length + width)

300 = 2(l + w)

l + w = 150               .......(1)

Now, the maximum area of a  rectangular garden is when Length  = width

So, for equation 1

l + l = 150

l = 75 meters

So, w = 75 meters

And the area of the rectangular garden = length * width

                                                               = 75 * 75

                                                               = 5625 m²

So the maximum area of the  rectangular garden is 5625 m²

Therefore, the dimensions of the garden to maximize the area is length = width = 75 meters and maximum area is  5625 m²

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Solving proportional relationship and options given we have value of x in second row as 5 and in third row as 8, value of y in third row as 2.4

What is proportional constant ?

The ratio between two proportional quantities' constant values is known as the constant of proportionality.

When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship.

The Direct Variation and Inverse Variation types of proportions between the two provided quantities determine the proportionality constant's value.

To show proportional relationship we need to have  [tex]\frac{y}{x}[/tex] as a constant value k.

From first set of data, we can have our constant k as

[tex]k=\frac{.6}{2} =0.3[/tex]

Now to fill 2nd row of table we have value of y given and as discussed above  [tex]\frac{y}{x}[/tex]  will remain constant. So, solving we get

 [tex]x = \frac{1.5}{0.3} = 5[/tex]

So, value of x in second row will be 5

For third row we can substitute as value of x as 8 and value of y as 2.4 that will give us proportional constant as calculate in above cases.

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Answer:

-7

Step-by-step explanation:

(-4)2 | -7 - (-5)| -23

-4*2=-8

-7- -5=-2

|-2|=2

-8*2=16

16-23=-7

If there is a problem with this answer please feel free to tell me, thanks :)

The length of the congruent triangles are as follows:

BC = 36

EF = 36

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

ΔABC≅ΔDEF

Let's find the length of the given sides as follows:

BC = x + 20

EF = 2x + 4

Therefore,

BC = EF

x + 20 = 2x + 4

x - 2x = 4 - 20

- x = -16

x = 16

Therefore,

BC = x+20 = 16 + 20 = 36

EF = 2x+4 = 2(16) + 4 = 32 + 4 = 36

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The equation of a line into slope is 1/2x+1

A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.

Y equals mx plus b is actually the slope intercept form. Because it provides both a slope and an intercept, the form is known as a slope intercept form.

A line's slope and y-intercept are expressed in the following formula: y=mx+b. The y-intercept, which is usually represented in coordinate form as (0,b), is the point where the line crosses the y-axis.

y=1/2x+1

8y-4x=8

Add 4x to both sides.

8y=4x+8

Divide 8 (the one with y) by both sides.

y=1/2x+1

Therefore the equation of a line into slope is 1/2x+1

The complete question is : 8y−4x=8 Put the following equation of a line into slope-intercept form, simplifying all fractions.

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Answer:

a) {A,E,I}

b) {red, orange, yellow, green, blue, violet, indigo}

c) {9,18,27,36,45}

d) {12,14,16,18,20,22}

Lol I'm not sure if I did all of these correct :]

(Also what is this for? Like the coding class or something? (Just curious))

12 bottles of soda cost  $15.84  next week

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Price of  5 bottles = $6

Price of  1 bottle = 6/5 = $1.2

10% of 1.2 = (10/100)*1.2 = 0.12

new price of 1 bottle = 1.2+ 0.12 = $1.32

Price of  12 bottles = 12*1.32 = $15.84

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The total years taken to double the money according to Compounding will be 13.75 years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 2%

amount = $1700

Total amount = $2200

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/400)^4t

T = A[tex](1+r/400)^{4t[/tex]

2200 = 1700(1 +2/400)^4t

22/17 = (1 +1/200)^4t

22/17 = (1.005)^4t

1.29 = (1.005)^4t

taking log on both sides

0.11/0.002 = 4t

t = 13.75 years.

Hence the time taken to double the money is 13.75 years.

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The points that make both equations true are, (0,3) and (-3,3).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The graph of the equations is attached with the answer below. The points are (0,3) and (-3,3).

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The thing that the horizontal line signifies in the confidence interval plot is D. These horizontal lines are placed to help you visually locate the dot.

A confidence interval is a range of values that contains the value of an unknown population parameter. Given the characteristics of your sample data, these intervals represent a plausible domain for the parameter.

Confidence intervals are calculated using a specified confidence level and are derived from sample statistics. Confidence intervals are used by statisticians to quantify uncertainty in a sample variable. These horizontal lines are placed to assist you in visualizing the dot.

In conclusion, the correct option is D.

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Answer:

Below

Step-by-step explanation:

a)  All possible rolls  ( 36 of them)

1   1 , 2 , 3 , 4 , 5 , 6

2   1, 2, 3, 4, 5 , 6

3    1 , 2 , 3 , 4,5,6

4  1,2,3,4,5,6

5  1,2,3,4,5,6

6  1,2,3,4,5,6

b) underlined above    21 out of 36    or 7/12

c )   3 out of 36    1/12

d )  11/36