The function d =
45t gives the distance d Juan traveled in miles after t hours.

is this discrete or continuous data?

Answer:

tge answer is

A. x-4y=-4

3x+4y=36

The evaluated function values are g(-3) = 11, g(5) = 11, g(a) = 11 and g(a+h) = 11

A composite function is a function that results from combining two or more functions. It is created by using the output of one function as the input of another function.

The function g(x) is defined as g(x) = 11, which means that the output of the function is always 11, no matter what value of x is inputted.

i.e. the function g(x) = 11 always returns the value 11, regardless of the input.

Therefore, we have:

g(-3) = 11

g(5) = 11

g(a) = 11

g(a+h) = 11

So, regardless of the value of a or h, the function g(x) will always return 11.

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The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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Answer:

23 ft

Step-by-step explanation:

a yard is 3 feet multiply it by 7 and you get 21 add 2 and you get 23. 23ft is your answer

Answer:

Step-by-step explanation:

Answer:

y=1/6x-3-2

Step-by-step explanation:

rises 2 runs 12

equals rise 1 run 6

1/6x

10, 6 -2 from x =10, 4

Answer:

the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:

Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.

Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.

Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).

In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

6.26

Step-by-step explanation:

Integer Part: 6

Fractional Part: 258

If the last digit in the fractional part of 6.258 is less than 5, then simply remove the last the digit of the fractional part.

If the last digit in the fractional part of 6.258 is 5 or more and the second digit in the fractional part is less than 9, then add 1 to the second digit of the fractional part and remove the third digit.

If the last digit in the fractional part of 6.258 is 5 or more and the second digit in the fractional part is 9, and the first digit in the fractional part is less than 9, then add 1 to the first digit in fractional part and make the second digit in fractional part 0. Then remove the third digit.

If the last digit in the fractional part of 6.258 is 5 or more and the second digit in the fractional part is 9, and the first digit in the fractional part is 9, then add 1 to the integer part and make the fractional part 00.

With 6.258, rule B applies and 6.258 rounded to the nearest hundredth is 2.26

Answer:

0.0001 = 0.01% probability of the Celtics winning eight straight championships.

Step-by-step explanation:

For each year, there are only two possible outcomes. Either the Celtics are the champions, or they are not. Each year is independent of other years. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

What would be the probability of the Celtics winning eight straight championships?

Each year, we have that \(p = 0.32\)

Eight straight championships: \(P(X = 8)\) when n = 8. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 8) = C_{8,8}.(0.32)^{8}.(0.68)^{0} = 0.0001\)

0.0001 = 0.01% probability of the Celtics winning eight straight championships.

For X ≤ 15, n = 20, π = .70 ; compound event probability is approximately 0.0008 .

For X > 8, n = 11, π = .65 ; compound event probability is  approximately 0.9198.

For X ≤ 1, n = 13, π = .40 ; compound event probability is  approximately 0.6646 .

a. To calculate the probability of the event X ≤ 15, n = 20, π = .70, we will use the binomial distribution formula:

P(X ≤ 15)

=  ∑_(k=0)¹⁵〖(20Ck)(0.70)^k (0.30)^(20-k) 〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.0008 (rounded to 4 decimal places).

b. To calculate the probability of the event X > 8, n = 11, π = .65, we will first find the probability of X ≤ 8, and then subtract this value from 1 to find the complement probability:

P(X > 8) = 1 - P(X ≤ 8)

= 1 - ∑_(k=0)⁸〖(11Ck)(0.65)^k (0.35)^(11-k)〗

Using a binomial distribution calculator, we can find the probability of X ≤ 8 to be approximately 0.0802.

Therefore, the probability of X > 8 is approximately 0.9198 (rounded to 4 decimal places).

c. To calculate the probability of the event X ≤ 1, n = 13, π = .40, we will use the binomial distribution formula:

P(X ≤ 1)

= ∑_(k=0)¹〖(13Ck)(0.40)^k (0.60)^(13-k)〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.6646 (rounded to 4 decimal places).

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Answer:

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

Formula for area of a rectangle with dimensions l and w is:

Substitute 10 for l and 4 for w:

The space shuttle travels about 6713 miles per hour. Rounded to the nearest mile, this is approximately 6713 miles per hour.

What is a radius ?

In mathematics, the radius is a term used to describe the distance from the center of a circle or a sphere to any point on its surface. It is denoted by the letter "r".

The orbit of the space shuttle is circular, so the distance it travels in one orbit is equal to the circumference of the circle with a radius of 275 + 4000 = 4275 miles (275 miles above the Earth's 4000 mile radius).

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π is the mathematical constant pi (approximately 3.14). Therefore, the distance traveled by the shuttle in one orbit is:

C = 2π(4275) ≈ 26851 miles

Since the shuttle orbits once every 4 hours, its average speed is:

distance/time = 26851/4 ≈ 6713 miles per hour

Therefore, the space shuttle travels about 6713 miles per hour. Rounded to the nearest mile, this is approximately 6713 miles per hour.

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Answer:

x=12

Step-by-step explanation:

3x-4=2x+8

-2 +4 -2 +4

x =12

The answer is 23 becuase 15+8=23

The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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A left the work after 3 days was solved by using work formula.

An algebraic equation is a mathematical statement that asserts that two expressions are equal. These expressions can contain variables, which are represented by letters, and the equation states that the values of the expressions are equal for some particular values of the variables.

The work formula is a mathematical concept used to determine how long it will take two or more workers to complete a job together. The formula is based on the idea that the amount of work done is directly proportional to the time spent working.

In the given question,

Let's assume that A worked for x days, and therefore he left the work unfinished for (15 - x) days. During this time, B finished the remaining work in 7 days.

According to the work formula, the amount of work done by A and B together in one day is:

1/15 + 1/18 = 11/90

This means that in one day, they can complete 11/90th of the work together.

During the x days when A worked, the amount of work he did is:

x * (11/90)

And during the remaining (15 - x) days, the amount of work left undone is:

(15 - x) * (11/90)

When A left, B completed the remaining work in 7 days, so we can set up an equation:

(11/90) * 7 = (15 - x) * (11/90)

Simplifying and solving for x, we get:

x = 3

Therefore, A left the work after 3 days.

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Answer:

4.8

Step-by-step explanation:

\( V_{sphere} = \frac{4}{3} \pi r^3 \)

\( 144\pi= \frac{4}{3} \pi r^3 \)

\(r^3 = \frac {3 \times 144\pi}{4\pi}\)

\(r^3 = 3 \times 36\)

\(r^3 = 108\)

\(r = \sqrt[3]{108} \\ \\ r = 4.7622031559 \\ \\ r \approx \: 4.8 \: \)

Question: Find the value of t in the given equation h = 2 + 9t - 5t^2 given the height of the ball is 3m.

Solution:

*

Answer:

7k + 6

Steps:

Subtract the numbers 20+6k-14k+k

6+6k+k

Combine the terms:

6+6k+k

6+7k

Rearange terms:

6+7k

7k+6

Answer:

8

Step-by-step explanation:

Look at the graph and notice when h hits 6, y turns out to be 8

Answer:4

Step-by-step explanation:

Answer:

30% of total students chose snowboarding as their favorite sport.

Step-by-step explanation:

We know that;

=> Total people = 500

=> Snowboarding people = 105

=> Percentage = unknown, so we can say it as x

So we can set up the equation;

x% · 500 = 105

\(\frac{x}{100}\) · 500 = 105

x · 5 = 105

x = 105/5

x = 30

So 30% of total students chose snowboarding as their favorite sport.

Hope this helps!

Answer:

13

Step-by-step explanation:

Cuz the factor of y is angle to the 115° is to the Y value

Answer:

40

you add a 0 to the four and boom

If you are really asking, then the answer is still 4

Answer:

4 is the correct answer

hope it is helpful to you

In general, the simple interest formula is

Where t is given in years.

And the interest is given by

Let B the initial amount Lisa invested in the 10% interest account and C the amount she invested in the 8% account.

Therefore,

Expanding the second equation,

The system of equations becomes

From the first equation, B=30000-C. Substitute into the second equation as shown below

And

Therefore, she invested $12000 in the 10% account and $18000 in the 8% account.

The unit of the rate of change is (b) dollars per month

From the question, we have the following parameters that can be used in our computation:

The table of values

Where we have

y = total amount in dollars

x = number of months

The rate of change is calculated as

Rate  = y/x

substitute the known values in the above equation, so, we have the following representation

Rate = total amount in dollars/number of months

So, we have

Unit = dollars per month

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Answer:

Option B

Step-by-step explanation:

Use the formula

\(x = \frac{-b\±\sqrt{b^{2}-4ac } }{2a}\)

now input the values. In equation \(x^{2} - 5x + 7 = 0\), a = 1, b = -5 & c = 7

By taking positive sign we get,

\(x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}\)

⇒\(x = \frac{-(-5)+\sqrt{(-5)^{2}-4.1.7 } }{2.1}\)

⇒\(x = \frac{5+\sqrt{25-28 } }{2}\)

⇒\(x = \frac{5+\sqrt{-3 } }{2}\)

In the same way, by taking minus sign, we get \(x = \frac{5-\sqrt{-3 } }{2}\)

The inverse of f(x) = x^(7/9) using exponential notation is f(x) = x^(9/7)

An inverse function in mathematics is a function that "undoes" another function.

In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.

An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

The given function is of the form

f(x) = x^(7/9), this is equivalent to ⁹√x⁷

say f(x) = y, then

f(x) = y = x^(7/9)

y = x^(7/9)

solving for the inverse, of y = x^(7/9)

y = x^(7/9)

y^(9/7) = x

interchanging the letters

y = x^(9/7)

hence the inverse function is solved to be f⁻¹(x) = x^(9/7)

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