Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a downward sloped line crossing the y axis at two that ends at the open point 2, 1.3, a closed point at 2, -1, and an upward sloped line starting at the open point 2, 4. Find = limit as x approaches two from the right of f of x..

Answer:

The answer is 1.751702

Step-by-step explanation:

In this number there are 11 decimal places which can be found after the decimal point.

1.75170179212

As we want 6 decimal places, we need to look at the digit to the right of sixth decimal place. Therefore:

1.75170179212

So, in this case, the digit in the seventh place is a '7'.

If we want to round a number, there are two ways:

As the seventh decimal is a '7' which is greater than '5'.

We add a 1 to the Sixth decimal place.

As the sixth decimal place was a '1'. When we round it, it will be a 2

1.751702

The expression sin 50 cos 40 + cos 50 sin 40 is equivalent to 1.

The expression sin 50 cos 40 + cos 50 sin 40 can be simplified using the trigonometric identity:

sin(a + b) = sin a cos b + cos a sin b

By applying this identity, we can rewrite the expression as:

Therefore, the expression sin 50 cos 40 + cos 50 sin 40 is equivalent to 1.

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a. The required equation is x² - 16x + 48 = 0

b. I would use factorisation to solve it and the selling prices that would generate a daily profit of  $50 are $4 and $12 respectively.

a.

The required equation is x² - 16x + 48 = 0

Since the quadratic function y = -10x² + 160x - 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. Since we require a profit of $50, then y = 50.

So, y = -10x² + 160x - 430

-10x² + 160x - 430 = 50

-10x² + 160x - 430 - 50 = 0

-10x² + 160x - 480 = 0

Dividing through by -10, we have

x² - 16x + 48 = 0

So, the required equation is x² - 16x + 48 = 0

b.

I would use factorisation to solve it and the selling prices that would generate a daily profit of  $50 are $4 and $12 respectively.

To determine the method you would use to solve the equation, you would need to determine the value of the discriminant.

For a quadratic equation ax² + bx + c = 0, the discriminant is D = b² - 4ac

Since x² - 16x + 48 = 0 and its discriminant D = (-16)² - 4 × 48

= 256 - 192

= 48

= 64 > 0 and is a perfect square, so it is factorizable. The equation would have real and distinct roots,

So, x² - 16x + 48 = 0

x² - 4x - 12x + 48 = 0

x(x - 4) - 12(x - 4) = 0

(x - 4)(x - 12) = 0

x - 4 = 0 or x - 12 = 0

x = 4 or x = 12

I would use factorisation to solve it and the selling prices that would generate a daily profit of  $50 are $4 and $12 respectively.

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divide the total weight by the number of piles

9/5 = 1.8 pounds per pile

Answer:

The total cost of producing 6 widgets is $231.

Step-by-step explanation:

Given : Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.

To find : The total cost of producing 6 widgets.

Solution :

Cost is given by [tex]c (x) = ax^2 + bx + d[/tex]

[tex]c(2) = a(2)^2 + b(2) + d[/tex]

[tex]23= 4a+2b+d[/tex] .........[1]

[tex]c(4) = a(4)^2 + b(4) + d[/tex]

[tex]103= 16a+4b+d[/tex] ............[2]

[tex]c(10) = a(10)^2 + b(10) + d[/tex]

[tex]631= 100a+10b+d[/tex] ...........[3]

Now, we solve equation [1], [2] and [3]

Subtract equation  [2]-[1]  and [3]-[2]

[2]-[1] →  [tex]12a+2b=80[/tex]  ........[4]

[3]-[2] →  [tex]84a+6b=528[/tex]  .......[5]

Solving equation [4] and [5] by elimination method,

Multiply equation [4] by 3 and subtract from [5]

[tex]84a+6b-3(12a+2b)=528-3(80)[/tex]

[tex]84a+6b-36a-6b=528-240[/tex]

[tex]48a=288[/tex]

[tex]a=6[/tex]

Put in equation [4]

[tex]12(6)+2b=80[/tex]

[tex]72+2b=80[/tex]

[tex]2b=8[/tex]

[tex]b=4[/tex]

Substitute the value of a and b in [1] to get d

[tex]23= 4a+2b+d[/tex]

[tex]23= 4(6)+2(4)+d[/tex]

[tex]23= 24+8+d[/tex]

[tex]23= 32+d[/tex]

[tex]d=-9[/tex]

Substitute a=6,b=4,d=-9 in the cost equation,

The required equation form is [tex]c(x) = 6x^2 + 4x-9[/tex]

The total cost of producing 6 widgets.

Put x=6

[tex]c(6) = 6(6)^2 + 4(6)-9[/tex]

[tex]c(6) = 216+15[/tex]

[tex]c(6) =231[/tex]

Therefore, The total cost of producing 6 widgets is $231.

17 x PI = 53.40707511

divided by 4 = 13.35176878

 rounded to nearest thousandth = 13.352

The number of words Jean will type when she completes 60 minutes of typing is  3,000, This is further explained below Option C is correct

Correlation is simply a relationship that exists between events or objects, A relationship between mathematical variables that are subject to variation.

In conclusion, The graph and table show the relationship between y and x

And the graph shows 3000 at "the number of words Jean has typed for her essay" axis denoted by y, for what she completes 60 minutes.

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Final answer:

The 99% confidence interval for the percentage of registered voters who prefer Candidate A is between 54.6% and 61.4%.

Explanation:

To calculate the 99% confidence interval for the percentage of the population of registered voters who prefer Candidate A over Candidate B, you can use the formula for the confidence interval of a proportion:

The sample proportion (p') is given as 58%, which is 0.58 in decimal form. The size of the sample (n) is 1350.

To calculate the confidence interval, we also need the z-value for the 99% confidence level. The z-value for a 99% confidence level is approximately 2.576 (you can find this value in a standard z-table).

The formula for the margin of error (EBP) is:

EBP = z * sqrt((p'*(1-p'))/n)

Plugging the values into the formula:

EBP = 2.576 * sqrt((0.58*(1-0.58))/1350)

EBP ≈ 0.034

The confidence interval for the true binomial population proportion is given by:

(p' - EBP, p' + EBP)

Therefore, the 99% confidence interval is:

(0.58 - 0.034, 0.58 + 0.034)

(0.546, 0.614)

Interpreting this, we can say with 99% confidence that the true percentage of all registered voters who prefer Candidate A over Candidate B is between 54.6% and 61.4%.

Final answer:

To calculate the 99% confidence interval for the percent of registered voters who prefer Candidate A, we can use the formula CI = p ± Z * √(p*(1-p)/n). Plugging in the values, we find the 99% confidence interval is between 54.6% and 61.4%.

Explanation:

To calculate the 99% confidence interval for the percent of the population of all registered voters who prefer Candidate A over Candidate B, we can use the formula:

CI = p ± Z * √(p*(1-p)/n)

Where:

p = sample proportion

Z = Z-value for the desired confidence level

n = sample size

In this case, the sample proportion is 0.58, the sample size is 1350, and the Z-value for a 99% confidence level is approximately 2.58.

Plugging in these values, we get:

CI = 0.58 ± 2.58 * √(0.58*(1-0.58)/1350)

Simplifying the equation gives us the 99% confidence interval for the percent of registered voters who prefer Candidate A: between 0.546 and 0.614, or 54.6% and 61.4%.

alligators:

 x = total number of alligators

n = number of years

x=20x1.25^n

crocodiles:

 y = total number of crocodiles

n = number of years

y=25+10n

Part A.

The given equation is:

y = x^2 + 6x + 7

By completing the square:

y = (x^2 + 6x + 9) + 7 – 9

y = (x + 3)^2 – 2

y + 2 = (x + 3)^2

Part B.

The vertex form of a parabola is in the form:

y – k = 4p (x – h)^2

Where (h, k) is the vertex (x, y) of the parabola.

Therefore the vertex: (-3, -2)

Since 4p = 1, a positive number, therefore the parabola opens up which makes the vertex (-3, -2) the minima of the graph.

Part C.

The Axis of Symmetry is the x - coordinate of the vertex which is x = - 3

The solution would be like this for this specific problem:

f(x) = x^2 + sin(x) 

f '(x) = 2x + cos(x) 

The minimum value is at f '(x) = 0, 

So, let g(x) = 2x + cos(x) 

Thus, g '(x) = 2 - sin(x) 

x(new) = x - g(x) / g '(x) 
or 
x(new) = x - [2x + cos(x)] / [2 - sin(x)] 

Calculation 

x1 = -0.5 - [2 * -0.5 + cos(-0.5)] / [2 - sin(-0.5)] 
= -0.4506266931 
x2 = -0.4501836476 
x3 = -0.4501836113 
x4 = -0.4501836113 

This value for x, f(x) = -0.2324655752. 

After converting to 6 decimal places: the minimum point is (-0.450184, -0.232466).

Final answer:

To find the absolute minimum value of f(x)=x^2+sin(x), use Newton's method with Newton-Raphson iteration x_{n+1} = x_n - f(x_n)/f'(x_n). Start with an initial guess and iterate until the result converges to six decimal places, ensuring the second derivative at the critical point is positive.

Explanation:

To find the absolute minimum value of the function f(x)=x^2+sin(x) correct to six decimal places, we can use Newton's method. Newton's method helps to find successively better approximations to the roots (or zeroes) of a real-valued function. First, we need to find the derivative of the function, which gives us f'(x) = 2x + cos(x). We are looking for a critical point where the derivative is zero because this could indicate a potential minimum (or maximum).

Starting with an initial guess, we can apply the Newton iteration formula x_{n+1} = x_n - f(x_n)/f'(x_n) to find a better approximation. In this case, let's choose an initial guess close to the root of f'(x). Since we do not have the specific initial guess, we would theoretically pick a value near the expected minimum and iterate until the difference between consecutive approximations is less than the desired tolerance, which is the change in six decimal places.

The Newton-Raphson iteration would be applied repeatedly until convergence is seen at six decimal places. Note that in practice, one must also check the second derivative f''(x) at the found critical point to confirm it is a minimum (it should be positive).

Answer:

the answer is the first option : A

Step-by-step explanation:

Please see attached image for the choices and proper formatting of the problem.

What she did:

[tex] \sqrt{-2x + 1 } - 1 = x + 3 - 1 \sqrt{-2x} = x + 2[/tex]

What she should have done:

[tex]( \sqrt{-2x + 1} ^{2} = (x + 3)^2 -2x + 1 = (x + 3)^2 -2x + 1 - 1 = (x + 3)^2 - 1 -2x = (x +3)^2 - 1[/tex]

The error that Eloise made in solving the radical equation was that she subtracted 1 before squaring both sides.

To add, the equation where at least one variable expression is fixed inside a radical, usually a square root is called a radical equation.

Answer:

We need to subtract 1 after squaring both sides

Step-by-step explanation:

Step1: [tex]\sqrt{-2x+1} -3 = x \\[/tex]

adding 3 both sides

[tex]\sqrt{-2x+1} =3 + x \\[/tex]

we need to square here first  and then we need to subtract

and this is the error which  Eloise make in solving it .

The answer would be an option (D) 17 > 2 or 6 < 9 because 17 is greater than 2 and 6 is less than 9 is always true.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

I. -(-6) = 6 and -(-4) > -4

Here -(-4) > -4 is incorrect

-(-4) = 4 is correct

These statements are not true

III. 5 + 6 = 11 or 9 - 2 = 11

Here 9 - 2 = 11 is incorrect

So 9 - 2 = 7  is correct

These statements are not true

II. -(-4) < 4 or -10 > 10 - 10

Here -(-4) < 4 is incorrect

So -(-4) = 4 is correct

These statements are not true

IV. 17 > 2 or 6 < 9

Here 17 is greater than 2 and 6 is less than 9 is always true.

Hence, the correct answer would be an option (D)

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Answer:

x2-2 domain an range are 0, -2

Step-by-step explanation: