A car is sold for $20,000. After one year, the value of the car is $11,000. Write an exponential function y to determine the value of the car after x years if the rate of decrease is the same each year.

Answer: Suppose there exists a positive rational number r such that r^2 < 2. Then we have 2 - r^2 > 0. Let h = (2 - r^2)/4. Then h > 0 because r^2 < 2.

Consider the number rh = r + h. We have:

(rh)^2 = (r + h)^2 = r^2 + 2rh + h^2 = r^2 + 2(2 - r^2)/2 + (2 - r^2)/16

= r^2 + 2 + (2 - r^2)/16

< 2 + 2 + (2 - 2)/16 = 2.

Thus, for any positive rational number r such that r^2 < 2, there exists a larger positive rational number rh = r + h such that (rh)^2 < 2.

Step-by-step explanation:

Answer:

Look below

Step-by-step explanation:

A. First we need to add up the carbohydrates, protein, and fat:

4+3+2=9

Now we find what percentage is protein...

3/9=1/3=33.33%

B. We know the number 4 represents carbohydrates and the number 2 represents fat, so we can write a ratio:

4:2

We can simplify this down to:

2:1

Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

Answer:

Nate has 8 times more jelly beans than Walt.

Step-by-step explanation:

Nate's quantity:

8 x (12 x 34 x 56)

Walt's quantity:

(12 x 34 x 56)

To find the ratio, we can divide Nate's quantity by Walt's quantity:

Ratio = Nate's quantity / Walt's quantity

Ratio = (8 x (12 x 34 x 56)) / (12 x 34 x 56)

Simplifying the expression:

Ratio = 8

Therefore, Nate has 8 times more jelly beans than Walt.

Answer:

a)0.25

b)0.375

Step-by-step explanation:

Possible outcomes when dice are rolled : 1 ,2 ,3,4,5 ,6

Even= 2,4,6  

Odd = 1 ,3 , 5

Probability of getting even =\(\frac{3}{6}=\frac{1}{2}\)

Probability of getting odd = \(\frac{3}{6}=\frac{1}{2}\)

4 dices are rolled together

a)P(3 even and 1 odd numbers)

P(3 even and 1 odd numbers)=\(^4C_3 (\frac{1}{2})^3 (\frac{1}{2})^1\)

P(3 even and 1 odd numbers)=\(\frac{4!}{3!1!} (\frac{1}{2})^3 (\frac{1}{2})^1 =0.25\)

b)P(2 even and 2 odd numbers)

P(2 even and 2 odd numbers)=\(^4C_2 (\frac{1}{2})^2 (\frac{1}{2})^2\)

P(3 even and 1 odd numbers)=\(\frac{4!}{2!2!} (\frac{1}{2})^2 (\frac{1}{2})^2\)=0.375

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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The unit cost for Cinema A is $5.50 per pass and the unit cost for Cinema B is $5.80 per pass.

To find the unit cost of each movie pack, we need to divide the total cost by the number of passes in each pack.

The unit cost for Cinema A's twelve-pack can be calculated as follows:

unit cost for Cinema A = $66 / 12 passes = $5.50 per pass

The unit cost for Cinema B's five-pack can be calculated as follows:

unit cost for Cinema B = $29 / 5 passes = $5.80 per pass

So, the unit cost for Cinema A is $5.50 per pass and the unit cost for Cinema B is $5.80 per pass.

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The number of routes that Paula can take using graph theory is; E: 4

We will observe that out of the 12 cities, 6 of them possess 3 edges going in/out of them.

The 6 cities are such that there are 2 at the top, 2 at the bottom, and 1 on each side.

In graph theory terms, we can say that they are of degree 3.

Thus, at least 1 edge connecting to each of these cities cannot therefore be used. Furthermore, the same concept applies to the start and end points, due to the fact that we don't want to return to them.

There are 6 + 2 = 8 vertices that we can tell have 1 unused edge, and then we have 17 - 13 = 4 unused edges to work with due to the fact that we have 17 edges in total, and as such must use exactly 13 of them).

Finally, we notice that at each of the 2 cities marked with an O on a path in the image attached, that there are 2 possibilities such that it's either we continue straight and cross back over that same path later, or we will make a left turn, and then turn rightward when we approach the junction again.

This gives us a total of;

2 * 2 = 4 possible different routes

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Answer:

C

Step-by-step explanation:

Miami rainfall:  1.61 +2.24 +2.99 +3.15 +5.35 + 9.68 = 25.02

Tampa rainfall: 2.24 +2.8 +3.03 + 2.05 + 2.09 + 6.69 = 18.9

25.02 - 18.9 = 6.12

Miami gets more rainfall by 6.12 more inches

Have a great day! :)

Answer:

Step-by-step explanation:

H0 = .5 prefer  Democratic candidate

Ha > .5 prefer Democratic candidate

p = .48

z = -1.285179129

0.9006 >= .05 thus we "FAIL TO REJECT THE NULL HYPOTHESES"

Answer: 0

Step-by-step explanation: To make this easier, ignore the addition sign (for this one, at least), so just do 5-5

Answer: 0

Step-by-step explanation:

Gianna is 90 miles far away in 3 hours of driving.

She drove in total of 180 minutes.

The speed can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s.

Given,

Gianna drives 5 miles in 10 minutes

Speed per minute = 5/10 = 0.5 miles/minute

Gianna drove in total for 3 hours

1 hour = 60 minutes

3 hours = 60 × 3 = 180 minutes

Distance Gianna drove in 180 minutes = speed per minute × time

                                                                = 0.5 × 180

                                                                = 90 miles

Hence, Gianna drove 90 miles in 3 hours, 180 minutes is total time she drove.

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Answer:

assuming that was at 2:45 PM they will be there at 3:25AM or if they left at 2:45AM they will be there at 1:25 PM

Step-by-step explanation:

Answer:

91kg

Step-by-step explanation:

weight= mass × gravitational force

910kg = m× 10ms^-2

m= 910÷ 10

m= 91

Answer:

\(\boxed{\sf x=12}\)

Step-by-step explanation:

By applying Similar Triangles Theorem:-

\(\sf \cfrac{x}{6} =\cfrac{6}{3}\)

We'll multiply both sides of the equation by 6, the LCM of 6,3.

\(\sf x=2 \times 6\)

\(\sf x=12\)

Answer:

a-1. See part a-1 of the attached excel file for the time series plot.

a-2. The linear trend is not appropriate

b. The quadratic trend equation is y = -0.1618x^2 + 2.889x + 5.7022

c. Revenue in year 11 is 17.90.

Step-by-step explanation:

a-1. Construct a time series plot. Comment on the appropriateness of a linear trend.

Note: See part a-1 of the attached excel file for the time series plot.

a-2. Comment on the appropriateness of a linear trend.

Note: See part a-2 of the attached excel file for the time series plot with a linear trend.

From the time series plot with a linear trend, it can be seen that the movements of the time series plot and the linear trend are not the same. This implies that the linear trend is not appropriate

b. Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue.

Note: See part b of the attached excel file for the quadratic equation trend.

From the quadratic equation trend, we obtained the following quadratic trend equation that can be used to forecast revenue:

y = -0.1618x^2 + 2.889x + 5.7022 ……………. (1)

Where;

y = Revenue

x = Year

c. Using the trend equation developed in part (b), forecast revenue in year 11.

Substituting x = 11 into equation (1), we have:

y = (-0.1618 * 11^2) + (2.889 * 11) + 5.7022 = 17.90

Therefore, revenue in year 11 is 17.90.

Answer:

  ∆ABC is an isosceles triangle

Step-by-step explanation:

You have a triangle ABC such that the angle bisector of angle B also bisects side AC.

An angle bisector divides the sides of the triangle proportionally. This means the sides BA and BC will have the same ratio as the segments of AC on either side of the point of intersection with the angle bisector.

Since AC is bisected, that means those segments are congruent, hence sides BA and BC are congruent. The triangle is isosceles.

The approximate surface area of the package is approximately 245.05 square inches.

The best model for the package is a cylinder.

To calculate the approximate surface area of the package, we need to find the lateral surface area of the cylinder and the area of the circular base.

The lateral surface area of a cylinder can be calculated using the formula:

Lateral Surface Area = 2πrh

where r is the radius of the base and h is the height.

The area of the circular base can be calculated using the formula:

Area of Base = \(πr^2\)

Given that the diameter of the bottom is 9 inches, the radius (r) would be half of that, which is 4.5 inches.

Using the given height of 13 inches, we can now calculate the surface area:

Lateral Surface Area = 2πrh = 2π(4.5)(13) ≈ 117.81 square inches

Area of Base = \(πr^2 = π(4.5)^2 ≈ 63.62\) square inches

To find the total surface area, we add the lateral surface area and the area of the base:

Total Surface Area = Lateral Surface Area + 2 × Area of Base = 117.81 + (2 × 63.62) ≈ 245.05 square inches

Therefore, the approximate surface area of the package is approximately 245.05 square inches.

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Answer:

90 would be right i think good luck!

Step-by-step explanation:

The value of x is 14 units.

When handling and dealing with difficulties involving the measurement of length and angles of a right-angled triangle, trigonometric values of ratios such as sine, cos, tan, cosec, cot, and secant come in handy. The trigonometric function is widely used to solve trigonometric issues at 0°, 30°, 45°, 60°, and 90°.

We know for angle of 30° the base is 7 and perpendicular is x

then

sin30° = 7/x

      \(\frac{1}{2} =\frac{7}{x}\)

       x = 7

hence, the value of x = 14 units

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Answer:

about 8 hours

Step-by-step explanation:

8 hours. It is Five hours plus Three hours.

The function of the given graph is;  \(f(x) = \frac{5}{6} (x+2)^2 (x-1) (x-3)\)

A polynomial graph is a graph of a polynomial function. A polynomial function is a mathematical function that is defined as a sum of terms, where each term is a constant multiple of a variable raised to a non-negative integer power.

For example, the function f(x) = 3x² - 2x + 1 is a polynomial function of degree 2.

According the graph below we can see here,

Multiplicity of the root -2 is 2, and it is equivalent to the number \((x+2)^2\)

Multiplicity of the root 1 is 1, and it is equivalent to the factor (x-1)

Multiplicity of the root 3 is 1, and it is equivalent to the factor (x-3)

Therefore,

f(x) = a (x+2)² (x-1) (x-3)

for find the value of a, put x=0;

f(0) = a  (0+2)² (0-1) (0-3)

10 = a  (2)² × (-1) × (-3)     (from the graph f(0) = 10; y= 10 while x=0)

\(a = \frac{5}{6}\)

Therefore, the function will be;

\(f(x) = \frac{5}{6} (x+2)^2 (x-1) (x-3)\)

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Complete question graph-

The given graph's purpose is: \(f(x)=\frac{5}{6}\ (x+2)^{2} (x-1)(x-3)\)

A graph of a polynomial function is known as a polynomial graph. A polynomial function is an abstract mathematical concept that is described as the sum of terms, each of which is a constant multiple of a variable that is raised to a non-negative integer power.

For example, the function f(x) = 3x² - 2x + 1 is a polynomial function of degree 2.

As may be seen on the graph below,

Root -2 has the multiplication factor of 2, which is equal to (x+2)².

The root of 1 has a multiplicity of 1, which is equal to the factor (x-1)

The multiplicity of the third root is one, which is equal to the factor (x-3)

f(x) = a (x+2)² (x-1) (x-3)

for find the value of a, put x=0;

f(0) = a  (0+2)² (0-1) (0-3)

10 = a  (2)² × (-1) × (-3)     (from the graph f(0) = 10; y= 10 while x=0)

a = 5/6

Therefore, the function will be;

\(f(x)=\frac{5}{6}\ (x+2)^{2} (x-1)(x-3)\)

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The complete question is attached below,

The value of x in the similar triangle is 6 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, let's use the similarity ratio to find the value of x in the similar triangle as follows:

Hence,

5 / 40 = x / 48

48 × 5 = 40x

240 = 40x

divide both sides by 40

x = 240 / 40

x = 6

Therefore,

x = 6

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Answer: 6/32 or .1875

Step-by-step explanation:

There are 6 numbers between 2 and 33 that are either squares or cubes

Square 4,9,16,25

Cube 8,27

Therefore the probability of getting a squared or cubed number is 6/32 or 0.1875

Answer:

the answer is a

Step-by-step explanation:

Answer:

\(\frac{x^2+x-2}{x^3-x^2+2x-2}\\=\frac{x^2+(2-1)x-2}{x^2(x-1)+2(x-1)}\\=\frac{x^2+2x-x-2}{(x-1)(x^2+2)}\\=\frac{x(x+2)-1(x+2)}{(x-1)(x^2+2)}\\=\frac{(x-1)(x+2)}{(x-1)(x^2+2)} \\=\frac{x+2}{x^2+2}\\So, ~last~option~is~the~correct~answer.\)

The simplest form of the provided expression is (x + 2)/(x² + 2) option (D) is correct.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

\(\rm \dfrac{\left(x^2+x-2\right)}{x^3-x^2+2x-2}\)

\(\rm =\dfrac{\left(x-1\right)\left(x+2\right)}{x^3-x^2+2x-2}\)

\(\rm =\dfrac{\left(x-1\right)\left(x+2\right)}{\left(x-1\right)\left(x^2+2\right)}\)

= (x + 2)/(x² + 2)

Thus, the simplest form of the provided expression is (x + 2)/(x² + 2) option (D) is correct.

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Answer:

a = 4.5

Step-by-step explanation:

In easy way you can understand by this simple way

if 4m half is 2m

so, 9m half is 4.5

in simple way answer