4x-5y=20 substitute 0 for x, then solve for y

Answer:

4

Step-by-step explanation:

The seat is 99 feet off the ground when it is at the top of the Ferris

wheel.

The height of a seat on a Ferris wheel can be modeled by the function H(t) = 47 sin((π/30)t + (3π/2)) + 52, where t is the time in seconds and H(t) is the height in feet.

To find how far off the ground the seat is when it is at the top of the Ferris wheel, we need to find the maximum value of the function. We know that the sine function has a maximum value of 1, which occurs when the input to the function is (π/2) + kπ, where k is an integer.

Since the input to our function is ((π/30)t + (3π/2)), we need to solve for t when this expression is equal to (π/2) + kπ.

((π/30)t + (3π/2)) = (π/2) + kπ

Multiplying both sides by 30, we get:

πt + 45π = 15π + 30kπ

Subtracting 15π from both sides and simplifying, we get:

t = 30k - 30

This means that the function H(t) will have a maximum value every 30 seconds. To find the maximum height, we can substitute t = 30k - 30 into the function:

H(30k - 30) = 47 sin((π/30)(30k - 30) + (3π/2)) + 52

Simplifying, we get:

H(30k - 30) = 47 sin(kπ - π/2) + 52

Since sin(kπ - π/2) =\((-1)^k\), we can write:

H(30k - 30) =\(52 - 47(-1)^k\)

When k is even, H(30k - 30) is at its maximum height of 99 feet (52 + 47).

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The annual dividend per share of Exxon Mobil (XOM) is $3.60 and the annual yield is 4.15%. Multiply the result by 100 to get the annual yield in percentage: 0.0415 x 100 = 4.15%

Annual dividend per share: $3.60

Annual yield: 4.15%

1. To find the annual dividend per share, divide the increase in shares (1.6) by the number of shares owned before the reinvestment (400).

1.6/400 = 0.004

2. Multiply the result by the current share price of XOM ($86.40):

0.004 x 86.40 = $3.60

3. To find the annual yield, divide the annual dividend per share by the current share price of XOM ($86.40):

3.60/86.40 = 0.0415

4. Multiply the result by 100 to get the annual yield in percentage:

0.0415 x 100 = 4.15%

The annual dividend per share of Exxon Mobil (XOM) is $3.60 and the annual yield is 4.15%.

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Answer:

1536

Step-by-step explanation:

12 x 8 x 4 x 4

(might be wrong)

The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:

log₂(x - 1) = x³ - 4x

Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.

For the point (2, 0):

log₂(2 - 1) = 2³ - 4(2)

log₂(1) = 8 - 8

0 = 0

The equation holds true for the point (2, 0), so (2, 0) is one solution.

For the point (1.1187, -3.075):

log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)

log₂(0.1187) = 1.4013 - 4.4748

-3.075 = -3.0735 (approx.)

The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.

Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

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The smallest possible value of x is the value less than 2/3

Given the series \($\frac{1}{2} + \frac{1}{3} + \ldots +\frac{1}{x} > 1\frac{1}{2}$\)

We need to find the smallest possible value of x as shown:

\(\frac{1}{x} > 1\frac{1}{2}\\ \frac{1}{x} > \frac{3}{2}\\\)

Reciprocate both sides

\(x < \frac{2}{3}\)

Hence the smallest possible value of x is the value less than 2/3

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Answer:x=7

Step-by-step explanation:

Joy can choose to ride the bus, the subway, or take the taxi to travel to work on Monday and Tuesday. The possible outcomes of the day for both days are that Joy can ride any of the three methods of travel distance to her destination.

Monday: Joy can choose to ride the bus, the subway, or take the taxi to travel to work on Monday. If she chooses the bus, she can take the bus to her destination. If she chooses the subway, she can take the subway to her destination. If she chooses the taxi, she can take the taxi to her destination.

Tuesday: On Tuesday, Joy can also choose to ride the bus, the subway, or take the taxi to travel to work. If she chooses the bus, she can take the bus to her destination. If she chooses the subway, she can take the subway to her destination. If she chooses the taxi, she can take the taxi to her destination.

The possible outcomes of the day for Monday and Tuesday are that Joy can ride the bus, the subway, or take the taxi to travel to work. Each day she can choose a different method of travel distance to her destination.

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Answer:no

Step-by-step explanation:

using the Pythagorean theorem:

a^2+b^2=c^2

42^2+26^2=50^2

1764+676=2500

2440=2500

2440<2500

So the answer is no

Answer:

\(69y+23\)

Step-by-step explanation:

The area of a rectangle will always be length times width or width times length, doesn't matter which way.

In this case, the width is \(3y+1\) miles and the length is \(23\) miles. So, the area is \(23(3y+1)=23*3*y+23*1=69*y+23\).

So, the area is \(\boxed{69y+23}\) and we're done.

Answer:

16

Step-by-step explanation:

The equation of parabola is x² = 12y and the endpoints of the latus rectum are (-6, 3) and (6, 3).

Hence the correct option is (C).

We know that for parabola, any point on parabola is equidistance from the directrix and the focus.

Given that the focus of the required parabola is = (0, 3)

The directrix is y = -3.

Let the locus of the point on parabola be (h, k).

The distance between (h, k) and (0, 3) = √((h - 0)² + (k - 3)²) = √(h² + (k - 3)²)

The distance of the point (h, k) from y = -3 is = k + 3.

According to properties,

k + 3 = √(h² + (k - 3)²)

(k + 3)² = h² + (k - 3)²

k² + 6k + 9 = h² + k² - 6k + 9

h² = 12k

Since (h, k) is an arbitrary point.

So the equation of the parabola is, x² = 12y

We know that the endpoints of the latus rectum of parabola x² = 4ay are given by (2a, a) and (-2a, a).

Here a = 3.

So the endpoints of the latus rectum are (6, 3) and (-6, 3).

Hence the correct option is (C).

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the ninth term of the geometric sequence is 781250.

To find the ninth term of a geometric sequence, we need to determine the common ratio (r) of the sequence first.

Given:

Second term (a₂) = 10

Fifth term (a₅) = 1250

We can use the formula for the nth term of a geometric sequence:

aₙ = a₁ * r^(n-1)

Since we are given the second term, we can express it using the formula:

a₂ = a₁ * r^(2-1)

10 = a₁ * r

Similarly, we can express the fifth term:

a₅ = a₁ * r^(5-1)

1250 = a₁ * r^4

Now we have a system of equations:

10 = a₁ * r

1250 = a₁ * r^4

Dividing the second equation by the first equation, we get:

1250/10 = (a₁ * r^4) / (a₁ * r)

125 = r^3

Taking the cube root of both sides, we find:

r = ∛125

r = 5

Now that we have the common ratio (r = 5), we can find the first term (a₁) by substituting it into either of the equations:

10 = a₁ * 5

a₁ = 10/5

a₁ = 2

Finally, we can find the ninth term (a₉) using the formula:

a₉ = a₁ * r^(9-1)

a₉ = 2 * 5^8

a₉ = 2 * 390625

a₉ = 781250

Therefore, the ninth term of the geometric sequence is 781250.

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The graph is a downward-opening parabola opening downward with its vertex at (2,0). Therefore, the correct option is C.

The equation y = -16t^2 + 64t + 16 represents the path of a projectile launched from a 16-ft-tall tower. To determine the correct graph, we can analyze the equation. The coefficient of t^2 (-16) is negative, indicating a downward-opening parabola. The coefficient of t (64) determines the horizontal shift of the graph, and in this case, t = 4 represents the maximum height of the projectile. The constant term (16) represents the initial height of the tower.

Considering these factors, we find that the correct graph of the equation is option C. It depicts a downward-opening parabola with its vertex at (2,0). The parabola starts at an initial height of 16 ft (the tower's height) and descends symmetrically from its vertex.

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Answer:

2

Step-by-step explanation:2

Answer:

$50 = 5 days

$40 = 4 days

$30 = 3 days

$20 = 2 days

$10 = 1 day

Step-by-step explanation:

hope this helps = )

Answer: F,B,D

Hope this helps : )

Step-by-step explanation:

Answer:

B, C, F

Step-by-step explanation:

B, C, and F are the only correct statements

Draw the 2 triangles, correctly labeled, and compare them.  This makes it easy to visualize which choices are true vs. false.

Answer:

For every x feet of rope purchased, the total cost(y) increases by $6.85.

Step-by-step explanation:

the criteria used when deciding upon the inclusion of a variable are A - Theory, B - t-statistic, C - Bias, and D - Adjusted R^2.

When deciding upon the inclusion of a variable, the following criteria are commonly used:

A - Theory: Theoretical justification is often considered to include a variable in a model. It involves assessing whether the variable is relevant and aligns with the underlying theory or conceptual framework.

B - t-statistic: The t-statistic is used to determine the statistical significance of a variable. A variable with a significant t-statistic suggests that it has a meaningful relationship with the dependent variable and may be included in the model.

C - Bias: Bias refers to the presence of systematic errors in the estimation of model parameters. It is important to consider the potential bias introduced by including or excluding a variable and assess whether it aligns with the research objectives.

D - Adjusted R^2: Adjusted R^2 is a measure of the goodness of fit of a regression model. It considers the trade-off between the number of variables included and the overall fit of the model. Adjusted R^2 helps in assessing whether the inclusion of a variable improves the model's explanatory power.

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The domain of e(h) is given as C. the real numbers from 0 to 24

The domain of e(h) should be the set of values that h can take on. Since h represents the number of hours of light per day that the chickens are exposed.,

Therefore, the domain would be the real numbers from 0 to 24. So, the correct answer is: C. the real numbers from 0 to 24

With this in mind, it can be seen that the correct answer is option C

Real numbers encompass all logical and irrational figures, visible on a numerical graph with three values: positive, negative, or zero.

These numbers offer pertinent traits as they allow their arithmetic to undergo operations like adding, subtracting, multiplying, and dividing without loss of significance.

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Answer:

8

Step-by-step explanation:

2/3·12=24/3=8

There are 12 cells or groups in a 3 × 4 ANOVA design.

So, the answer is option B.

This design involves three levels of one independent variable and four levels of another independent variable, resulting in 12 unique combinations or cells.

Each cell represents a specific condition or treatment group in the study, and the dependent variable is measured for each group.

ANOVA, or analysis of variance, is a statistical method used to compare means between groups to determine if there are significant differences. Understanding the number of cells or groups in the design is important for planning the study and interpreting the results accurately.

Hence,the correct answer is B.

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The test statistic-z or z-score will be 1.635.

What is test statistic-z?

A z-score, also known as a z-statistic, is a number that represents how many standard deviations above or below the mean population a z-test score is. It is essentially a numerical measurement that describes the relationship of a value to the mean of a collection of values. A z-score of 0 implies that the data point's score is the same as the mean score. A z-score of 1.0 indicates that the result is one standard deviation from the mean. Z-scores can be positive or negative, with a positive number indicating that the score is higher than the mean and a negative value indicating that it is lower than the mean.

Let p indicate the proportion of customers who are satisfied.

P=0.64

n=number of customers surveyed =125

x=number of satisfied consumers in the survey=89

p=89/125=0.71

The test statistic-z is calculated using the following formula,

z=(p-P)/√(P(1-P)/n)

=(0.71-0.64)/√0.64(1-0.64)/125

=0.07/√0.00184

=0.07/0.0428

=1.635

The test statistic-z is 1.635

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Answer:

C

Step-by-step explanation:

(f + g)(x) = f(x) + g(x) , thus

f(x) + g(x)

= 2x + 1 + x² - 7 ← collect like terms

= x² + 2x - 6 → C

The value of m for the given equation is 18. The solution has been obtained by solving the linear equation.

What is a linear equation?

A linear equation is the one with the highest degree of one. This demonstrates that there are no variables in a linear equation with an exponent bigger than one. On the graph, such an equation yields a straight line.

We are given an equation as 2 = m/2 - 7

On solving the equation for m, we get

⇒2 = m/2 - 7

⇒2 = (m - 14)/2

⇒2*2 = (m - 14)

⇒4 = m - 14

⇒m = 18

Hence, the value of m for the given equation is 18.

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Answer:

Step-by-step explanation:

Perimeter of rectangle = 52 cm

2*(length + width) = 52

2*(l + 42/5) = 52

\(l +\frac{42}{5}=\frac{52}{2}\\\\l+\frac{42}{5}=26\\\\ l = 26 - \frac{42}{5}\\\\ l = \frac{26*5}{1*5}-\frac{42}{5}\\\\l = \frac{130}{5}-\frac{42}{5}\\\\l=\frac{130-42}{5}\\l= \frac{88}{5}\\\\\)

Answer:

A to B for y: -6

A to B for x: 2

Step-by-step explanation:

to figure out y, you subtract the first “y” from the second “y”

0-6= -6

to figure out x, you subtract the first “x” from the second “x”

3-1=2

Answer:

60 feet

Step-by-step explanation:

The easiest way to do this is to go answer by answer with the triangle area formula :)

Formula: A=hb/2

H = height

B: base

Now lets solve this :)

Choice 1: 50 feet

50 x 20 = 1000

1000/2 = 500

Choice 2: 40 feet

Since 40 feet is smaller than the 50, we know this will not be correct :)

Choice 3: 120 feet

120 x 20 = 2400

2400/2 = 1200

Choice 4: 60 feet

60 x 20 = 1200

1200/2 = 600

The correct answer is 4, 60 feet :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

375

Step-by-step explanation:

Applying,

Total surface area of the triangular prism = 3×Area of the rectangular surface + 2×area of the triangular  surface

Assuming the triangular base is an equilateral triangle

A = 3A'+2B.................... Equation 1

Where A = Total  surface area of the prism, A' = Area of the rectangular surface, B = Area of the triangular base.

From the question,

IF  A' = 2B,

Given: A = 3000

Substitute these values into equation 1

3000 = 3(2B)+2B

3000 = 6B+2B

3000 = 8B

8B = 3000

B = 3000/8

B = 375

Answer:

FEED

Explanation:

Notes on the lines = E G B D F (from bottom to top)

Notes in between the lines = F A C E (from bottom to top)

little help:

you can remember the notes on the line by making a sentence with the letters

ex:

E = every

G = good

B = boy

D = deserves

F = fun

The function checks if the result for the current inputs has already been computed and stored in the `memo` cache. If so, it returns the cached result, otherwise it calculates the result using the recursive definition of the Bessel polynomials and stores the result in the `memo` cache for future use.

Memoization is a technique where we store the results of expensive function calls and return the cached result when the same inputs occur again. Here's a recursive function that uses memoization to calculate the n-th Bessel polynomial at x:

```
memo = {}  # Memoization cache

def B(n, x):
   if n == 0:
       return 1
   elif n == 1:
       return x + 1
   elif (n, x) in memo:
       return memo[(n, x)]
   else:
       result = (2 * n - 1) * x * B(n - 1, x) + B(n - 2, x)
       memo[(n, x)] = result
       return result
```

The function checks if the result for the current inputs has already been computed and stored in the `memo` cache. If so, it returns the cached result, otherwise it calculates the result using the recursive definition of the Bessel polynomials and stores the result in the `memo` cache for future use. This approach avoids redundant calculations and can significantly speed up the computation of Bessel polynomials for large values of n.

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