You find a rare comic book at a yard sale and determine that the price of the comic book, y, measured in hundreds of dollars, after x years can be represented by the following graph.

Answer: C

Step-by-step explanation: You're Welcome

y = ½x +3

Step-by-step explanation:

Slope = m = ½

y-intercept = 3

Substitute values into Slope intercept form :

\(y = mx + b\)

Where m = slope

b = y intercept

\(y = \frac{1}{2} x + 3\)

Answer:

135

Step-by-step explanation:

Well you don ‘t have to worry about the first part since its just the equation with the unknown number while the second part has it already substituted in.

Solve the equation normally, follow orders of operations.

6(5)^2-15

5^2=25

25*6=150

150-15=135

Answer:

1.2 km

Step-by-step explanation:

The first thing that we should go over is the formula for the area of a trapezoid.

Recall that it is \(A= \frac{b_1 +b_2}{2} *h\)

From this image, we have the following information

\(b_1=2.5\\\\b_2=1.5\\\\A=2.4\)

Now, we can plug this information into our formula and then solve for h.

\(2.4=\frac{2.5+1.5}{2} *h\\\\2.4=\frac{4}{2} *h\\\\2.4=2h\\\\h=1.2\)

Another method that can be employed is to use the pythagorean theorem.

A trapezoid can be be broken into a rectangle and two triangles.

If we look at the difference in the sizes of the bases, the bottom base is 1 km larger. This means that the base of each triangle would be 0.5 km long.

As we have two side lengths of the triangle, we can now use the Pythagorean theorem to find the third side, which is h.

\((1.3)^2=h^2+(0.5)^2\\\\h^2=1.69-0.25\\\\h=\sqrt{1.44} \\\\h=1.2\)

Answer:

h=1.2 km

Step-by-step explanation:

This is the formula of a Trapezium

A=\(\frac{h(a+b)}{2}\)

\(2.4=\frac{(2.5+1.5)h}{2}\\ 2.4=\frac{4h}{2}\\ 2.4*2=4h\\4.8=4h\\h=1.2\)

Answer:

\(\textsf{a)}\quad P(t)=310000(1.0085)^t\)

where P is the population, and t is the number of years after 500 BC.

b)   42,013,000

Step-by-step explanation:

\(\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}\)

Define the variables:

The population in 500 BC is the initial value (when t = 0), therefore if the population was 310,000 in 500 BC:

If the population increases by 0.85% each year then the growth rate in decimal form is:

Therefore, the function that models the given scenario is:

\(\boxed{P(t)=310000(1.0085)^t}\)

where P is the population, and t is the number of years after 500 BC.

To use the function to calculate the population in 80 AD, first calculate the number of years (value of t):

⇒ 80 AD - 500 BC = 580 years

Therefore, to find the population in 80 AD, substitute t = 580 into the function:

\(\implies P(580)=310000(1.0085)^{580}\)

\(\implies P(580)=42013142.9844236...\)

Therefore, the population in 80 AD is 42,013,000 (to the nearest thousand).

Psychologist requires a sample size of at least 126 SI scores.

We may use the following calculation to get the minimal sample size required to estimate the mean SI score of smokers with a margin of error of 12 and a 90% confidence level:

\(n = [Z * (\sigma / E)]^2\)

Where:

Z = the z-score associated with the confidence level (90%), which can be found using a z-score table or calculator.

For a 90% confidence level, Z is approximately 1.645.

σ = the population standard deviation (82)

E = the desired margin of error (12)

Plugging in the values, we get:

n = [1.645 * (82 / 12)]^2

n = 126.2

We round up to the closest integer as the sample size must be a whole number in order to guarantee that the sample size is sufficient to fulfill the required confidence level and margin of error.

Thus, n = 126 is the required minimum sample size.

In order to estimate the mean SI score of smokers with 90% confidence that the estimate is within 12 of the actual population mean, the psychologist requires a sample size of at least 126 SI scores.

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The values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.

Given are two right triangles we need to find the missing sides,

We will use Trigonometric ratios to find the same.

We know that,

Sin a = perpendicular / hypotenuse

Cos a = base / hypotenuse

Tan a = perpendicular / base

1) Sin 60° = x / 4√3

x = √3/2 × 4√3

x = 6

Cos 60° = y / 4√3

1/2 × 4√3 = y

y = 2√3

2) Cos 60° = x / 98

x = 1/2 × 98

x = 49

Sin 60° = y / 98

√3/2 = y / 98

y = 49√3

Hence the values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.

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Answer:

The discount is $49.90 the final price is $449.10

Step-by-step explanation:

The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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Slope of line SP: -1

Slope of line FJ: -1

Point-Slope Form of Line FJ: \(y=-x-6\)

What to type inside the orange box? You must type "-x-6".

Concept. A parallel line to line SP. A parallel line is a line that has the same slope as another line, therefore, the line parallel to SP has the same slope of SP.

Let's solve!

1. Find the slope of line SP.

Line SP's expression is: \(y=-x-14\).

The slope of a linear function is always given by the coefficient of x when the equation is solved for y. Hence, the slope of line SP is -1, because x is being multiplied by -1.

2. Form the equation for line FJ.

Use the formula for finding linear equations: \(y-y_{1} =m(x-x_{1} )\), where m is the slope of the line, \(x_{1}\) is the x value of a point where the line passes, and \(y_{1}\) is the y value of a point where the line passes. \(x_1\) and \(y_1\) must be taken from a single point where the function passes.

Let's take the formula and find the equation for line FJ:

a. Substitute in the formula.

\(y-(0) =(-1)(x-(-6) )\)

b. Simplify.

\(y-(0) =(-1)(x-(-6) )\\ \\y=(-1)(x+6)\\ \\y=-x-6\)

3. Express your answers.

Slope of line SP: -1

Slope of line FJ: -1

Point-Slope Form of Line FJ: \(y=-x-6\)

Answer:

4x^2 - 12x + 9

Explanation:

(2x - 3)^2

(2x - 3)(2x - 3)

2x(2x - 3) -3 (2x - 3)

4x^2 - 6x - 3 (2x - 3)

4x^2 - 6x - 6x + 9

4x^2 - 12x + 9

Answer:

B

Step-by-step explanation:

Standard deviation is the average distance away from the mean, thus B is correct

Answer:

Step-by-step explanation:

\(\sqrt{2} cos x-1=0\\cos x=\frac{1}{\sqrt{2} } =cos (\frac{\pi }{4} ),cos (2\pi -\frac{\pi }{4} )\\cos x=cos(2n\pi +\frac{\pi }{4} ),cos(2n\pi +\frac{7\pi }{4} )\\x=2n\pi +\frac{\pi }{4} ,2n\pi +\frac{7\pi }{4} \\n=0\\x=\frac{\pi }{4} ,\frac{7\pi }{4}\)

Answer:

The Temperature was 35 Degrees F higher than the low temperature.

Step-by-step explanation:

Step-by-step explanation:

18:27

=18/27

=2/3 or 2:3

The slope of the line that passes through the points (0, -6) and (0, -5)is undefined.

Slope is line's inclination with regard to the horizontal is quantified numerically. In analytical geometry, a line, ray, or line segment's slope is the ratio of the vertical to horizontal distance between any two points on the line, ray, or line segment ("slope equals rise over run").

In differential calculus, the derivative of a function yields the slope of a line tangent to its graph, which represents the function's instantaneous rate of change with respect to changes in the independent variable.

Ok so slope is the change in y over change in x.

Your why changed from 6 to -5 so you can write this as -5 - 6

Your x didn’t change it went from 0 to 0

You can write this as 0-0

Now -11/0 is what you end up with as a slope.

Any number divided by 0 is undefined so your slope is undefined.

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Answer:

Step-by-step explanation:

Answer:

Part--1:

We know that a equation in point-slope form is represented by:

y-y1=m

where m is the slope of the line and  is a point through which the line passes.  

 Consider a equation in a point-slope form as:

This means that the slope of the line is: 5

and the line  passes through the point (1,5).

Part--2:

Now as we know that if a line has a slope as m then the perpendicular line has a slope: -1/m

Since,

Let this perpendicular line passes through (2,6)

Hence, the equation of a line in point slope form is given by:

Step-by-step explanation:

The tree is 4.2 m long in height.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Francisco is 1.5 meters tall.

Height of Shadow = 3.5 m

Now, Height of shadow of the tree = 9.8 m

let the Height of tree be x.

So, Using Direct proportion

1.5 / 3.5 = x / 9.8

9.8 × 1.5 = 3.5x

14.7 = 3.5x

x= 4.2 m

Hence, the height of the tree is 4.2 m long.

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Answer:

x = ±10

Step-by-step explanation:

4x² - 400 = 0

Add 400 to both sides

4x² = 400

Divide both sides by 4

x² = 100

Take the square root of both sides

x = ±10

The function y = (e⁻⁽ˣ⁺²⁾) / x + 2  increases along intervals of (-∞, 3) and decreases along (-3, -2), (-2, ∞) and the function y = 2x - 1 / (x - 1)² has no inflection points but  concave downwards along (-∞, 1) ∪ (1 ,∞)

An extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.

The function given;

y = (e⁻⁽ˣ⁺²⁾) / x + 2

The extrema and intervals of increase or decrease of this function are

(-1, 1.63) and it increases along (-∞, 3) and decreases along (-3, -2), (-2, ∞)

2. The inflection points and intervals of concavity and convexity of the function

y = 2x - 1 / (x - 1)² are

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Answer:

Step-by-step explanation:

You have everything you need to find the area directly

A = 1/2 * b * h

b = 20

h = 15

Area = 1/2 * 20 * 15

Area = 150 m^2

Therefore, the probability that a respondent read a book in the last month and is at least 30 years old is the closest to  is A) 0.33.

Probability is a measure of the likelihood or chance of an event occurring. It is a branch of mathematics that deals with analyzing and quantifying uncertainty in various contexts, such as games of chance, weather forecasting, financial risk management, and scientific experiments. The probability of an event is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. For example, the probability of flipping a fair coin and getting heads is 0.5, since there are two equally likely outcomes (heads and tails) and only one of them corresponds to the desired event.

Here,

To find the probability that a respondent read a book in the last month and is at least 30 years old, we need to find the number of respondents who meet both conditions and divide it by the total number of respondents.

Looking at the contingency table, we can see that the number of respondents who are 30+ and answered "Yes" is 65. Therefore, the probability that a respondent read a book in the last month and is at least 30 years old is:

65 / (76 + 65 + 24 + 35) = 0.33 (rounded to two decimal places)

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Answer:

200

Step-by-step explanation:

Ella's name appears on the table 2/10 times, so we can multiply the denominator to make it 1000.

10x100 = 1000

If we multiply the denominator by 100, we must do the same to the numerator,

2x100=200

In 1000 draws Ella's name can be expected to come about  200 times.

An experiment is a way of determining how things may work.

From small sample space of experiments or models, we can assume the result of a larger sample space or models.

From the given table we observe that Ella's name came 2 times out of 10 random draws.

∴ In (10×100) = 1000 draw Ella's name can be expected to come about

(2×100) = 200 times.

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Answer:

x^5+4x^4+9x is what I would simplify it to.

(a). The Tanakas paid a total of $523,906.40 for the townhome.

(b). The Tanakas paid $206,906.40 in interest on their mortgage over the 15-year period.

Simple interest is the type of interest that is calculated on the principal amount only.

It is a fixed percentage of the principal amount that is charged or earned over a certain period of time, without any compounding of interest.

(a) The total amount they ended up paying for the townhome is the sum of the down payment and the total amount of the mortgage payments.

Down payment = $41,000

Total amount of mortgage payments = monthly payment x number of payments = $2675.04 x 12 months/year x 15 years = $482,906.40

Total amount paid = down payment + total amount of mortgage payments = $41,000 + $482,906.40 = $523,906.40

(b) The amount of interest paid on the mortgage can be calculated by subtracting the principal (the amount borrowed) from the total amount paid.

Principal = Total cost of townhome - Down payment = $358,000 - $41,000 = $317,000

Total interest paid = Total amount paid - Principal = $523,906.40 - $317,000 = $206,906.40

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Answer: B- 0.18. Because the probability is not very small, it is plausible that the 65% claim of the owner is correct.

Step-by-step explanation: