Find a generating function for the number of integer solutions of 2x+3y+7z=r

Answer:

f(x)=39.59

(1.09)

After 12 years: 111

After 35 years: 808

The exponential function models the data would be f(x) = 39.59 (1.09). After 12 years, the home’s value will be about $111 thousand and After 35 years, it will be about $808 thousand.

A function is defined as a relation between the set of inputs having exactly one output each.

Elias purchases a home for $38,900.

Let x be the number of years since the purchase. The function f(x) =()x models the data.

f(x) = 39.59 (1.09)

by using the model to predict the home’s value.

After 12 years, the home’s value will be about $

111 thousand.

After 35 years, the home’s value will be about $

808 thousand.

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To find the volume of the cylinder-shaped juice can, calculate using the formula V = π r² h with the radius being half of the can's width and the given height. The volume is found to be approximately 1804 cm³ when rounded to the nearest whole number.

Calculating the Volume of a Cylinder:

To calculate the volume of a cylinder, you should use the formula V = π r² h. First, we need to determine the radius of the juice can. Since it is given that the can is 12 centimeters wide, that means the diameter is 12 centimeters, and therefore, the radius (r) is half of that, which is 6 centimeters. We also have the height (h) of the can, which is 16 centimeters. Plugging these values into the formula gives us:

V = 3.14 × 6² × 16

Now, we calculate:

V = 3.14 × 36 × 16

V = 3.14 × 576

V = 1803.84 centimeters cubed (cm³)

When we round this to the nearest whole number, the volume of the juice can is approximately 1804 cm³.

The solution of the inequality 5x + 13 ≥ − 37 will be greater than or equal to negative 10.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

5x + 13 ≥ − 37

Simplify the inequality for 'x', then we have

5x + 13 ≥ − 37

5x ≥ − 50

x ≥ − 10

The solution of the inequality 5x + 13 ≥ − 37 will be greater than or equal to negative 10.

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Angle F will have the same measure as angle D, which is 53°, because they are vertical angles and thus congruent.

The question asks about the measure of angle F given that it is a vertical angle to angle D, which measures 53°. In geometry, vertical angles (also known as opposite angles) are pairs of non-adjacent angles formed when two lines intersect. Vertical angles are congruent, which means they have the same measure. Therefore, since angle D is 53°, angle F, being its vertical angle, will also have a measure of 53°.

Angle D and angle F are vertical angles, which means they are congruent. If angle D measures 53°, then angle F will also measure 53°. This is because vertical angles are equal in measure.

Answer:

Given is :

∠M≅∠X

∠N≅∠Y

YO≅NZ

We have to prove that ΔMNO≅ΔXYZ

Using segment addition postulate we get YZ=YO+OZ and ON=NZ+OZ and YO=NZ is already given. Using substitution of YO for NZ; we get ON=YO+OZ

Now substituting YZ for YO+OZ we get ON=YZ and also YZ=YO+OZ.

Now applying AAS we get ΔMNO is congruent to ΔXYZ because of angle-angle-side theorem as we have already proved that two sides are congruent and a non-included angle in each triangle is congruent.

Find factors of x^2 and 72, that, when combined, will give you 17x

x ^2 + 17x + 72

x 9

x 8

(x + 9)(x + 8) is your factor.

hope this helps

As per the inverse of a function, the value of [tex]f^{-1}(3)[/tex] is 13.

"An inverse function is defined as a function, which can reverse into another function."

The given function is

[tex]f(x) = \frac{2x+1}{x-4}[/tex]

⇒ [tex]y = f(x) = \frac{2x+1}{x-4}[/tex]

⇒ [tex]xy - 4y = 2x + 1[/tex]

⇒ [tex]xy - 2x = 4y + 1[/tex]

⇒ [tex]x(y - 2)= 4y + 1[/tex]

⇒ [tex]x = \frac{4y+1}{y-2}[/tex]

⇒ [tex]f^{-1}(x) = \frac{4y+1}{y-2}[/tex]

Now, [tex]f^{-1}(3) = \frac{4(3)+1}{3-2} = (12+1) = 13[/tex]

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The speed of the train is 40 km/h, and the speed of the plane is 180 km/h.

To solve the word problem regarding the speeds of a train and a plane, we first let the speed of the train be x km/h. According to the problem, the plane's speed is 20 km/h less than 5 times the speed of the train, which can be expressed as 5x - 20 km/h. Since they both travel the same amount of time, we can set up an equation based on their speeds and distances traveled:

Time taken by the train = Distance / Speed of the train = 160 / x

Time taken by the plane = Distance / Speed of the plane = 720 / (5x - 20)

Since the time is the same for both:

160 / x = 720 / (5x - 20)

Cross-multiply to solve for x:

160(5x - 20) = 720x

800x - 3200 = 720x

80x = 3200

x = 40

Following are the calculation to the given question:

Given:

salesperson sells[tex]\bold{= \frac{3}{4}}[/tex]

acre= 80,000

To find:

price per square foot rounded to two decimal spaces=?

Solution:

Therefore

[tex]1 \ acre=43560\ foot \\\\ \frac{3}{4}\ acre=32670\ foot[/tex]

Calculation

[tex]32670 \ sq \ foot = \$80,000 \\\\1 \ sq \ foot =? \\\\[/tex]

Calculating the price:

[tex]=\frac{80,000}{32670}=2.4487 \approx 2.45[/tex]

Therefore, the final answer is "$2.45".

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The pattern that can be created with the rule n x 2 + 1 is 1, 3, 5, 7, 9, 11

Given:

n × 2 + 1

= 2n + 1

where

n = number of terms

when n = 0

2(0) + 1

0 + 1

= 1

when n = 1

2(1) + 1

= 2 + 1

= 3

when n = 2

2(2) + 1

4 + 1

= 5

when n = 3

2(3) + 1

6 + 1

= 7

when n = 4

2(4) + 1

8 + 1

= 9

Therefore, the pattern that can be created with the rule n x 2 + 1 is 1, 3, 5, 7, 9, 11

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You can arrange the games side by side on a​ shelf in "3628800" ways.

According to the question,

Number of video games,

Now,

The amount of possible ways could you place the games side by side on some kind of shelf will be:

= [tex]10![/tex]

= [tex]10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1[/tex]

= [tex]3628800[/tex]

Thus the response above is appropriate.

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General Idea:

We need to make use of the below formula to find the present value.

[tex] PV=\frac{FV}{(1+\frac{r}{n})^{nt}} \\ \\ Where:\\ FV \; is \; Future\; Value\; of \; money\\ r \; is\; Annual\; rate\; of\; interest\\ t\; is\; number\; of\; years\\ n\; is\; Number\; of\; periods\; based\; on\; compounding \; frequency [/tex]

Applying the Concept:

We are given the below information:

[tex] FV= \$11,500\\ \\ t=5\; years\\ \\ r=4.5 \%\\ \\ n=2\; (because\; given\; compounded\; semi-annually) [/tex]

We need to substitute the above information in the formula to find the Present value.

[tex] PV=\frac{11500}{(1+\frac{0.045}{2})^{2 \times 5}} =\frac{11500}{(1+0.0225)^{10}} =\frac{11500}{1.0225^{10}} \\ \\ PV \approx \$9206 [/tex]

CONCLUSION:

The present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually is approximately 9206 dollars

Final answer:

The probability of flipping a coin six times and getting exactly three heads and three tails is calculated using the binomial formula and is found to be 31.25%.

Explanation:

The probability of flipping a coin six times and getting exactly three heads and three tails can be calculated using the binomial probability formula, which is P(x; n, p) = (n choose x) * p^x * (1-p)^(n-x), where 'n' is the number of trials, 'x' is the number of successes, and 'p' is the probability of success on any given trial.

In this instance, since we are flipping a fair coin, the probability 'p' of getting heads (success) on any single flip is 0.5. We want to find the likelihood of getting 'x' = 3 heads out of 'n' = 6 flips. Therefore, the equation becomes:

P(3; 6, 0.5) = (6 choose 3) * 0.5^3 * 0.5^(6-3)

The combination (6 choose 3) calculates the number of ways to choose 3 successes (heads) from 6 trials, which is 20. Plugging these values into the equation gives:

P(3; 6, 0.5) = 20 * (0.5^3) * (0.5^3) = 20 * (0.125) * (0.125) = 20 * 0.015625

This results in a probability of 0.3125, or 31.25%.

Therefore, the chance of flipping a coin six times and getting three heads and three tails is 31.25%.