20.
(05.07 MC)

A scatter plot is made to model the amount of money left to pay on a mortgage. The data used for the scatter plot are shown in the table:

Number of Months 3 5 1 2 0 4
Money Owed $114,000 $100,000 $118,000 $116,000 $120,000 $112,000


What does the y-intercept of the model represent? (1 point)

The amount of the mortgage that has been paid that month

The monthly payments

The original amount of the mortgage

The number of months it takes to pay off the mortgage

Step-by-step explanation:

Let simplify the identity

[tex] \frac{ \csc {}^{2} (x) - \sec {}^{2} (x) }{ \csc {}^{2} (x) + \sec {}^{2} (x) } [/tex]

[tex] \frac{ \frac{1}{ \sin {}^{2} (x) } - \frac{1}{ \cos {}^{2} (x) } }{ \frac{1}{ \sin {}^{2} (x) } + \frac{1}{ \cos {}^{2} (x) } } [/tex]

Combine Like Fractions

[tex] \frac{ \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } }{ \frac{ \sin {}^{2} (x) + \cos {}^{2} (x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } } [/tex]

Multiply by reciprocals.

[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } \times \frac{ \cos {}^{2} (x) \sin {}^{2} (x) }{ \sin {}^{2} (x) + \cos {}^{2} (x) } [/tex]

Pythagorean Identity

[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{1} [/tex]

Double Angle Identity

[tex] \frac{ \cos(2x) }{1} [/tex]

[tex] \cos(2x) [/tex]

Now, we need to find cos 2x. Given that we have tan x.

Note that

[tex] \cos {}^{2} (x) - \sin {}^{2} (x) = \cos(2x) [/tex]

So let find cos x and tan x.

We know that

[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]

We know that

[tex] \tan(x) = \frac{o}{a} [/tex]

[tex] \sin(x) = \frac{o}{h} [/tex]

[tex] \cos(x) = \frac{a}{h} [/tex]

So naturally,

[tex] \tan(x) = \frac{ \frac{o}{h} }{ \frac{a}{h} } = \frac{o}{a} [/tex]

So we need to find the hypotenuse,

remember Pythagorean theorem.

[tex]h {}^{2} = {o}^{2} + {a}^{2} [/tex]

Here o is 1

h is root of 5.

So

[tex] {h}^{2} = {1}^{2} + ( \sqrt{5} ) {}^{2} [/tex]

[tex] {h}^{2} = 1 + 5[/tex]

[tex] {h}^{2} = 6[/tex]

[tex]h = \sqrt{6} [/tex]

Now, we know h, let plug in to find sin x and cos x.

[tex] \sin(x) = \frac{1}{ \sqrt{6} } [/tex]

[tex] \cos(x) = \frac{ \sqrt{5} }{ \sqrt{6} } [/tex]

Let's find these values squared

[tex] \sin {}^{2} (x) = \frac{1}{6} [/tex]

[tex] \cos {}^{2} (x) = \frac{5}{6} [/tex]

Finally, use the trig identity

[tex] \frac{5}{6} - \frac{1}{6} = \frac{2}{3} [/tex]

So part I.= 2/3

ii. Use the definition of sine and cosine and Pythagorean theorem

Let sin x= o/h

Let cos x= a/h.

So

sin x squared is

[tex] \sin {}^{2} (x) = \frac{o {}^{2} }{h {}^{2} } [/tex]

[tex] \cos {}^{2} (x) = \frac{ {a}^{2} }{h {}^{2} } [/tex]

By definition,

[tex] \frac{ {o}^{2} }{ {h}^{2} } + \frac{ {a}^{2} }{h {}^{2} } = 1[/tex]

[tex] \frac{ {o}^{2} + a {}^{2} }{h {}^{2} } = 1[/tex]

Remember that

[tex]{ {o}^{2} + {a}^{2} } = {h}^{2} [/tex]

So

[tex] \frac{ {h}^{2} }{h {}^{2} } = 1[/tex]

[tex]1 = 1[/tex]

2sin(x) - 1 =0

first, simplify and isolate sin(x)

2sin(x) - 1 = 0

2sin(x) = 1

sin(x) = 1/2

Then, do sin inverse of 1/2 which is 30 degrees

150 degrees also works because when you set 30 degrees as the reference angle in quadrant 2, you get 150 degrees. 180-30 = 150

C is the answer

cranberry juice = 350 ml

blueberry juice = 2 liters = 2000 ml

Ratio of cranberry juice : blueberry juice = 350 : 2000 = 7 : 40

The simplest ratio is 7 : 40    or    7/40

Answer:

x=12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

12-1 is 11 and than 9 times 1 is 9

The exponent is negative , The exponent represents the number of places the decimal moves. , Option A and D is the correct answer.

The complete question is

Which statements describe writing 0.00000000003 in scientific notation? Check all that apply.

A.The exponent is negative.

B. The exponent is positive.

C.The coefficient is 0.3.

D.The exponent represents the number of places the decimal moves.

E.The decimal moves to the right.

Scientific Notation means writing a decimal number in the form of 10ˣ .

It is given that

A nitrogen molecule is 0.00000000003 meters larger than an oxygen molecule.

= 3 × 10⁻¹¹

(scientific notation)

The exponent is negative , The exponent represents the number of places the decimal moves. , Option A and D is the correct answer.

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Answer:

y = (5/3)x + 4

Step-by-step explanation:

The general equation for slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. Since you have been given both of these values, you can plug them into the formula to find your answer.

slope (m) = 5/3

y-intercept (b) = 4

y = mx + b

y = (5/3)x + 4

Answer:

[tex]\mathrm{Slope=== > 0}[/tex]

Step-by-step explanation:

Hi student, let me help you out!

.............................................................................................................

First, let's recall the slope formula: [tex]\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}}[/tex], where y2 and y1 are y-coordinates; x2 and x1 are x-coordinates.

Plugin the values: [tex]\mathrm{\cfrac{0-0}{-17-(-9)}}[/tex].

Upon simplifying, we obtain [tex]\mathrm{\cfrac{0}{-17+9}}[/tex].

Upon simplifying this further, we obtain [tex]\mathrm{\cfrac{0}{-9}}[/tex].

0 divided by anything results in 0.

✨ ∴, the slope of this particular line is 0, and this line looks something like this: [tex]\rule{200}{1}[/tex].

See, it's a horizontal line, with a rise of 0, meaning that it goes up 0 units.

Hope this helped you out! Ask in comments if even the slightest queries arise.

Best Wishes!

[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]

[tex]\underline{\rule{300}{5}}[/tex]

Answer:

[tex]\frac{13}{33}[/tex]

Step-by-step explanation:

we require 2 equations with the repeating digits placed after the decimal point.

let x = 0.3939.... (1) ← multiply both sides by 100

100x = 39.3939... (2)

subtract (1) from (2) thus eliminating the repeating digits

99x = 39 ( divide both sides by 99 )

x = [tex]\frac{39}{99}[/tex] = [tex]\frac{13}{33}[/tex] ← in simplest form

Step-by-step explanation:

0.39 repeating as a fraction

= 13/33

Semiperimeter is used to find the area of various shapes including the equilateral triangle (False).

Semiperimeter is a term used in geometry to refer to half the perimeter of a polygon. It is generally used in formulas for triangles.

However, it is also part of calculations related to other geometric shapes. According to the above, it can be inferred that the semiperimeter can be used to find the area of various geometric figures.

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The correct answer is option A which is segment D which is closer to home.

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

From the given graph we can see that in segment D the distance between the home and the person is lesser than all the segments given in the graph.

Therefore the correct answer is option A which is segment D which is closer to home.

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Answer:

[tex]2y - 8x = 3[/tex]

Step-by-step explanation:

[tex]y - 4x = 9[/tex]

[tex]2y - 8x = 18[/tex]

So 2y - 8x = 3 is parallel to y - 4x = 9.

The statements that would complete the proof where ∠2 ≅ ∠7 by the transitive property are:

∠2 ≅ ∠3

∠3 ≅ ∠7

The transitive property states that if x = y, and y = z, then x = z.

From the image given below, we have:

∠2 ≅ ∠3 because they are vertical angles which must be congruent.

∠3 ≅ ∠7 because corresponding angles are congruent.

Applying the transitive property, we can state that: ∠2 ≅ ∠7.

Therefore, the statements that would complete the proof are:

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Answer:

103mm or 53mm

Step-by-step explanation:

--A------B------C--

AB=78mm BC=25mm AC=AB+BC=103mm

--A----C---B---

AB=78mm BC=25mm AC=AB-BC=53mm

-B---A---C-

is impossible because BA<BC but 78mm>25mm

Answer:

Should be C

Step-by-step explanation:

Only the same power number can be use to add or subtract :)

But why is A, B and C same kinda stuff?

Answer:

-2x³ - 7x².

Step-by-step explanation:

- (4x³ + x²) + 2(x³ - 3x²)

= - 4x³ - x² + 2x³ - 6x²    Simplifying like terms:

= -2x³ - 7x².

The expression that represents the product of negative three-fourths x and –8x is 6x^2

The statement is given as:

the product of negative three-fourths x and –8x

Rewrite properly as:

-3x/4 * -8x

Divide 4 and 8 by 4

-3x * -2x

Multiply -3 and -2

6x * x

Multiply x and x

6x^2

Hence, the expression that represents the product of negative three-fourths x and –8x is 6x^2

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Answer:

answer is 6x2 or D

Step-by-step explanation:

Answer:

big bodie built

Step-by-step explanation:

i used to be dusty

Based on the calculations, the value of the given prefix expression is equal to 2205.

The preorder traversal of a tree (T) are typically used in discrete mathematics to determine the value of a prefix expression on a specific expression tree.

For the preorder traversal of this tree (T), we would start from the right most expression:

Prefix expression = * + 3 + 3 ↑ 3 + 3 3 3

Prefix expression = * + 3 + 3 ↑ 3 6 3

Prefix expression = * + 3 + 3  3⁶  3

Prefix expression = * + 3 3 729 3

Prefix expression = * + 3 732 3

Prefix expression = * 735 3   ⇒ 735 × 3

Value = 2205.

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Complete Question:

Given the following prefix expression:

* + 3 + 3 ↑ 3 + 3 3 3

What is the value of the prefix expression?

Answer:

no they did not make enough money

Step-by-step explanation:

Glass: 35 ×0.50 = 17.5

plastic: 50 × 0.25 = 12.5

aluminum: 22 × 0.75 = 16.5

17.5 + 12.5 + 16.5 = $46.5

Answer:

A. All squares are rectangles because both are quadrilaterals, have 90-degree angles and the opposite sides are parallel.

Step-by-step explanation:

This is the only true statement because all squares are rectangles just with equal sides, the angles will always be 90-degrees.

Hope this helps!

If not, I am sorry.

The equation of line is y = 92x – 182631. The slope is 92 and the y-intercept is the negative 182631. And the health expenditure in 2010 will be 2289.

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

[tex]\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)[/tex]

In MODE, (second line), fix the number of decimal places to be 2.

Then the slope and the y-intercept values of the Lin Reg line will round to the nearest hundredth.

(x₁, y₁) → (1997, 1093)

(x₂, y₂) → (2002, 1553)

Then we have

y – 1093 = [(1553 – 1093) / (2002 – 1997)] (x – 1997)

y – 1093 = [460  / 5] (x – 1997)

y – 1093 = 92 (x – 1997)

           y = 92x – 182631

If x = 2010, then the value of y will be

y = 92 × 2010 – 182631

y = 184920 – 192631

y = 2289

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Answer:

3

Step-by-step explanation:

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

Answer:  [tex]\textsf{x = 1000}[/tex]

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

Given: [tex]\textsf{log(x) = 3}[/tex]

Find: [tex]\textsf{The value of x}[/tex]

Solution:  In order to solve for x we need to get rid of the log which means that we need to put it to the power of the same number as the base.  When a base isn't displayed it defaults to 10 so we raise everything to the base of 10.

Get rid of log

Therefore, the final answer would be that x is equal to 1000.

Answer:

24

Step-by-step explanation:

The question is saying, how many three digit numbers can be made from the digits 3, 4, 6, and 7 but there can't be two of the same digit in them. For example 346 fits the requirements, but 776 doesn't, because it has two 7s.

Okay, on to the problem:

We can do one digit at a time.

First digit:

There are 4 digits that we can choose from. (3, 4, 6, and 7)

Second digit:

No matter which digit we chose for the first digit, there is only going to be 3 of them left, because we already chose one, and you can't repeat that same digit. So there are 3 options.

Third digit:

Using the same logic, there are only 2 options left.

We have 4 choices for the first digit, 3 choices for the second, and 2 for the third.

Hence, this is 4 * 3 * 2 = 24 three-digit numbers that can be made.

Answer:

transitive property

Step-by-step explanation:

Generally proofs flow naturally from one step to the next.  Consequently, each step usually follows from the previous step, and the Reason given justifies why that change is valid.

From statement 8, note that [tex]90^{o}=m\angle{ABD}[/tex]

For statement 9, the proof asserts that [tex]m\angle{ABC}=m\angle{ABD}[/tex]

What changed between line 8 and 9?  The left side of the equation lost it's 90 degrees, and it became the measure of angle ABC.

So, what justifies changing the 90degrees into a measure of an angle (specifically, the measure of angle ABC)?

Recall from statement 3, that [tex]m\angle{ABC}=90^{o}[/tex].

The "substitution property" would be a valid reason for step 9, (but of the given options, that isn't one, so we must look for another valid reason).

Recall that the transitive property states:

[tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]

There are three parts,

1. the first part needs a=b

2. the second part needs b=c

3. the third part produces a=c

Notice that in the second part, b=c, and then for the third part, on the left side, the "b" disappears, and the "a" sort of appears out of nowhere.

Statement 8 is like the second part, and statement 9 is like the third part.

Replacing "a" with [tex]m\angle{ABC}[/tex], replacing "b" with [tex]90^{o}[/tex], and replacing "c" with [tex]m\angle{ABD}[/tex], we can update the transitive property and see how it applies to our situation:

Original transitive property:  [tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]

Updated transitive property:  [tex]\text{If }m\angle{ABC}=90^{o}\text{ and }90^{o}=m\angle{ABD}, \text{then }m\angle{ABC}=m\angle{ABD}[/tex]

In order to use the transitive property, we need the first part and the second part to be true, and then it will be a valid reason for the last part to be true.  The first part was already proven back in statement 3, the second part was just proven in statement 8, so the conclusion (the third part) is valid and can be statement 9, because of the transitive property.

The point F lies on 4.5 in the number line.

Number line is a One dimensional representation of point referring by a number only.

We know that if a point divides a line joining the points at x,y in the number line respectively in m:n ratio then that point lies on = (my+nx)/(m+n) in the number line.

Here in the give problem that,

Point D lies on -6 in number line

Point E lies on 8 in number line

And F lies between D and E points and DE:EF = 3:1

So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.

So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5

Hence the point F lies on 4.5 in the number line.

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Answer: 4.5

Step-by-step explanation:

A ratio shows us the number of times a number contains another number. The maximum amount of purple that Susan can make is 25 ml.

A ratio shows us the number of times a number contains another number.

Susan makes purple paint by mixing red and blue paint in a ratio of 2:3. Now, if Susan wants to use the complete red paint then,

Purple paint she can make = 2/3 × 6/6 = 12 ml of red paint / 18 ml of blue paint

If Susan wants to use the complete blue paint then,

Purple paint she can make = 2/3 × 5/5 = 10 ml of red paint / 15 ml of blue paint

As per the first condition 18ml of blue paint is needed which is not possible, therefore, the second case is possible.

Thus, Susan needs to mix 10 ml of red paint and 15 ml of blue paint. Therefore, the amount of paint that Susan will make is,

Total Paint = 10ml + 15ml = 25ml

Hence, the maximum amount of purple that Susan can make is 25 ml.

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Using it's concept, it is found that there is a 0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering the situation described, the ways that alternate colored balls can be taken with the probabilities given as follows:

Hence the probability that the first three balls are drawn out of the box alternated in colour is given by:

[tex]p = \frac{5}{8} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex].

0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

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12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.

An equation is an expression that shows the relationship between two or more variables and numbers.

It took 4 days for 4 butterflies to give birth to 4 larvae. After 4 days, each butterfly produces a larvae

Hence for 12 butterflies in 12 days:

number of larvae = 12 butterflies * (12 days /4 days per larvae) = 36 larvae

12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.

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