Please help me!!!! x2+ (y-4/x2)2=1

Answer:

50 miles

Step-by-step explanation:

This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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Answer:

162 metres

Step-by-step explanation:

Since h is proportional to the square of v, we know that their ratio must be constant, so \(v_1^2/h_1 = v_2^2/h_2\) where v1 and v2 are velocities and h1 and h2 are their respective heights.

Since we are given that v = 10 and h = 8, we can set v1 = 10 and h1 = 8 and since we are trying to find the height for v = 45, we can set v2 = 45. Inputting these values into the equation and solving, we get

10^2/8 = 45^2/h2

h2 = 45^2/(10^2/8) = 162 metres

I hope this helps!

Answer: y= x + 4

Step-by-step explanation:

Answer:

-160

Step-by-step explanation:

All you have to do is substitute -2 for all values of x!

Is that last x raised to the power of 4 (looks like \(x^4\))?

If so, the equation is:

\(f(-2)=2(-2-3)(-2)^4\)

2(-5)(16)

-10(16)

-160

Answer:

$31.88

Step-by-step explanation:

Given

Consumer charges = 2530.16cents

Consumer charges in dollars = $25.3016

Interest rate per day = 0.042%

Interest gotten per day = 0.042×25.3016

Interest per day = $1.06266

Interest in 30 days = ,30×1.06266

Interest in 30 days = $31.88

Answer:

c pls mark barliest

Step-by-step explanation:

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

The probability that the two pets selected are of the same species  is 0.2426   .

In the question ,

it is given that ,

the number of puppies in the pet store = 6

the number of kittens in the pet store = 9

the number of lizards in the pet store = 4

the number of snakes in the pet store = 5

total animals = 24

the probability of selecting 2 puppies = ⁶C₂/²⁴C₂

the probability of selecting 2 kittens = ⁹C₂/²⁴C₂

the probability of selecting 2 lizards = ⁴C₂/²⁴C₂

the probability of selecting 2 snakes = ⁵C₂/²⁴C₂

So , the required probability is

= ⁶C₂/²⁴C₂  + ⁹C₂/²⁴C₂ + ⁴C₂/²⁴C₂  + ⁵C₂/²⁴C₂  

Simplifying further ,

we get ,

= 5/92 + 3/23 + 1/46 + 5/138

= 0.0543 + 0.1304 + 0.0217 + 0.0362

= 0.2426

Therefore , the required probability is 0.2426   .

The given question is incomplete , the complete question is

The pet store has 6 puppies , 9 kittens , 4 lizards and 5 snakes . if you select two pets from the store randomly, what is the probability that they are both the same species ?

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Answer:

I think it Belen

Step-by-step explanation:

Sorry if wrong

Answer:

Molly

Step-by-step explanation:

Mode is the number that appears most often in a data set.

So what you want to do is to find the mode of each student's grade, which means to find the number that appears the most in each of the student's grades.

Ashlee: both 70 and 94 appeared twice, so there's two modes

Belen: 79 appeared the most

Molly: 98 appeared the most

Sofia: All numbers appear in equal proportions, so no mode

When you compare all of the numbers, 98 is the highest mode, therefore Molly could use the mode to show that she is doing better than the other three students.

Answer:

rectangle

Step-by-step explanation:

If you place those points on a grid, you would obtain a rectangle as the slopes are opposite reciprocals when forming lines showing perpendicular and parallel lines that are seen in a rectangle

To find the mass of the copper wire, we need to integrate the density function over the length of the wire.

m = ∫₀¹.₇₅ p(x) dx  (converting 1.75 feet to decimal places, which is 0.5833 feet)

m = ∫₀¹.₇₅ (3x² + 2x) dx

m = [x³ + x²] from x=0 to x=0.5833

m = (0.5833)³ + (0.5833)² - 0

m = 0.2516 lb (rounded to two decimal places)

Therefore, the mass of the thin copper wire is 0.25 lb.
To find the mass of the copper wire, we need to integrate the density function p(x) over the length of the wire (from x = 0 to x = 1.75 ft). We can do this using the definite integral.

1. Set up the integral: ∫(3x² + 2x) dx from x = 0 to x = 1.75.
2. Integrate the function: (3/3)x³ + (2/2)x² = x³ + x².
3. Evaluate the integral at the bounds:
  a. Plug in x = 1.75: (1.75³) + (1.75²) = 5.359375 + 3.0625 = 8.421875.
  b. Plug in x = 0: (0³) + (0²) = 0.
4. Subtract the values: 8.421875 - 0 = 8.421875.
5. Round the result to two decimal places: 8.42 lb.

The mass of the copper wire is approximately 8.42 lb.

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Answer:

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

Step-by-step explanation:

For the first one, in any triangle, we have the sum of two sides is greater than the third side. Hence, we have 3 inequalities: \(4x+3>2x+1, 5x+1>x+3, 3x+4>3x\), which give us \(x>-1, x>\frac{1}{2},4>0\). We conclude that \(x>\frac{1}{2}\).

For the second question, we have \(AB<BP+AP=2x\), and similarly we can show that \(AC, BC<2x\). Hence, \(AB+BC+AC<6x\).

The third question is not very clear.

Answer:

see explanation

Step-by-step explanation:

There are 2 possible approaches to differentiating these.

Expand the factors and differentiate term by term, or

Use the product rule for differentiation.

I feel they are looking for use of product rule.

Given

y = f(x). g(x) , then

\(\frac{dy}{dx}\) = f(x).g'(x) + g(x).f'(x) ← product rule

(a)

y = (2x - 1)(x + 4)²

f(x) = 2x - 1 ⇒ f'(x) = 2

g(x) = (x + 4)²

g'(x) = 2(x + 4) × \(\frac{d}{dx}\) (x + 4) ← chain rule

       = 2(x + 4) × 1

        = 2(x + 4)

Then

\(\frac{dy}{dx}\) = (2x - 1). 2(x + 4) + (x + 4)². 2

    = 2(2x - 1)(x + 4) + 2(x + 4)² ← factor out 2(x + 4) from each term

    = 2(x + 4) (2x - 1 + x + 4)

    = 2(x + 4)(3x + 3) ← factor out 3

    = 6(x + 4)(x + 1)

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

(b)

y =  x(x² - 1)³

f(x) = x ⇒ f'(x) = 1

g(x) = (x² - 1)³

g'(x) = 3(x² - 1)² × \(\frac{d}{dx}\) (x² - 1) ← chain rule

        = 3(x² - 1)² × 2x

        = 6x(x² - 1)²

Then

\(\frac{dy}{dx}\) = x. 6x(x² - 1)² + (x² - 1)³. 1

    = 6x²(x² - 1)² + (x² - 1)³ ← factor out (x² - 1)²

    = (x² - 1)² (6x² + x² - 1)

     = (x² - 1)²(7x² - 1)

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

(c)

y = (x² - 1)(x³ + 1)

f(x) = x² - 1 ⇒ f'(x) = 2x

g(x) = (x³ + 1) ⇒ g'(x) = 3x²

Then

\(\frac{dy}{dx}\) = (x² - 1). 3x² + (x³ + 1), 2x

   = 3x²(x² - 1) + 2x(x³ + 1) ← factor out x

   = x[3x(x² - 1) + 2(x³ + 1) ]

   = x(3x³ - 3x + 2x³ + 2)

   = x(5x³ - 3x + 2) ← distribute

    = 5\(x^{4}\) - 3x² + 2x

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

(d)

y = 3x³(x² + 4)²

f(x) = 3x³ ⇒ f'(x) = 9x²

g(x) = (x² + 4)²

g'(x) = 2(x² + 4) × \(\frac{d}{dx}\)(x² + 4) ← chain rule

       = 2(x² + 4) × 2x

       = 4x(x² + 4)

Then

\(\frac{dy}{dx}\) = 3x³. 4x(x² + 4) + (x² + 4)². 9x²

    = 12\(x^{4}\)(x² + 4) + 9x²(x² + 4)² ← factor out 3x²(x² + 4)

    = 3x²(x² + 4) [ 4x² + 3(x² + 4) ]

    = 3x²(x² + 4)(4x² + 3x² + 12)

    = 3x²(x² + 4)(7x² + 12)

Answer:

No they aren't equal.....

Answer:

x = -10, 0

Step-by-step explanation:

Step 1: Write quadratic

x² + 10x = 0

Step 2: Complete the Square

x² + 10x + 25 = 25

(x + 5)² = 25

Step 3: Square root both sides

x + 5 = ±5

Step 4: Subtract 5 on both sides

x = -5 ± 5

x = -10, 0

Step-by-step explanation:

one second 12345678910

To bisect a segment, Jessica should place the compass on one endpoint, open it to a width larger than half of the segment, draw two intersecting arcs with the compass, and draw a straight line through the intersection points to bisect the segment.

To bisect a segment, Jessica should first place the compass on one endpoint of the segment and open it to a width larger than half of the segment. She should then draw an arc that intersects the segment at two points. Next, she should place the compass on the other endpoint of the segment and draw a similar arc that intersects the first arc she drew.

Finally, she should draw a straight line through the two points where the arcs intersect to bisect the segment into two equal parts. This method is based on the concept of congruent triangles, as the two arcs create two congruent triangles with the segment as their base.

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Answer:

I believe it is:

C) -3

:)

The cost of a package containing x comic books and a poster is given by the equation y = 0.91x + 7.08.

Let's start by using the information given to form two equations. Let x be the number of comic books and let y be the cost of package.

From the first sentence, we can form the equation:

y = 7.99 + 2x

From the second sentence, we can form the equation:

y = 16.99 + 11x

Now we can use these equations to find the linear function rule that models the cost of a package containing any number of comic books.

First, we can set the two equations equal to each other since they both represent the cost of a package:

7.99 + 2x = 16.99 + 11x

Solving for x, we get:

9x = 9

x = 1

Now that we know that 1 comic book costs $4, we can substitute that value into either of the original equations to find the cost of a package with a poster and 1 comic book:

y = 7.99 + 2(1) = 9.99

So a package with a poster and 1 comic book costs $9.99.

Finally, we can use the slope of the line to find the linear function rule that models the cost of a package containing any number of comic books. We know that the slope is the change in y over the change in x, or:

m = (16.99 - 7.99)/(11 - 2) = 0.91

So the linear function rule is:

y = 0.91x + 7.08

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The given question is incomplete, the complete question is:

A store sells packages of comic books with a poster. A poster and 2 comics cost ​$7.99. A poster and 11 comics cost ​$16.99. Write a linear function rule that models the cost y of a package containing any number x of comic books.

Answer:

Step-by-step explanation:

Since mean is the average number of students, the formula for calculating the mean attendance of students is expressed as;

Mean = total number of student/sample size

\(\overline x = \frac{\sum Xi}{N}\)

Given mean = 20

Since the question talks about the first four meetings, the sample size = 4

\(20 = \frac{\sum Xi}{4}\\ \\\sum Xi = 20 * 4\\\\\sum Xi = 80\)

Since the sum total of students for the first four meetings is 80, hence the number of students who attended the meeting is greater than 20

Answer:

Step-by-step explanation:

The slope is:

The y-intercept is:

The line is:

A. The x-Intercept of the graph of k is 8.

B. The slope of the graph of k is 2.

C. The graph of k passes through (-1, -8).

D. The zero of k is 3.

The slope of the graph of k is 2.

The correct statement is B.

Given that the graph of linear function k passes through the points (-3, 0) and (1, 8).

We need to check which option is correct.

To determine the correct statement, let's first find the equation of the linear function k using the given points (-3, 0) and (1, 8).

The slope of a linear function is given by:

slope = (change in y) / (change in x)

Using the points (-3, 0) and (1, 8):

slope = (8 - 0) / (1 - (-3))

slope = 8 / 4

slope = 2

So, the slope of the graph of k is 2.

Now we can write the equation of the linear function using the slope-intercept form: y = mx + b, where m is the slope, and b is the y-intercept.

Using the point (1, 8):

8 = 2 × 1 + b

8 = 2 + b

b = 8 - 2

b = 6

Now, the equation of the linear function k is:

y = 2x + 6

Now, let's evaluate the given statements:

A. The x-Intercept of the graph of k is 8.

To find the x-intercept, we set y = 0 and solve for x:

0 = 2x + 6

2x = -6

x = -3

The x-intercept is -3, not 8. So statement A is false.

B. The slope of the graph of k is 2.

We already found earlier that the slope of k is 2. So statement B is true.

C. The graph of k passes through (-1, -8).

Let's check if (-1, -8) satisfies the equation of k:

-8 = 2 × (-1) + 6

-8 = -2 + 6

-8 = 4

The equation is not satisfied, so statement C is false.

D. The zero of k is 3.

To find the zero of k (the x-value where y = 0), we set y = 0 and solve for x:

0 = 2x + 6

2x = -6

x = -3

The zero of k is -3, not 3. So statement D is false.

In conclusion:

Statement A is false.

Statement B is true.

Statement C is false.

Statement D is false.

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The value of x in the triangle is 2√13.

We have,

There are two similar triangles.

So,

The ratio of the corresponding sides is equal.

Now,

4/x = x/(9 + 4)

4/x = x / 13

4 x 13 = x²

x² = 4 x 13

x = √(4 x 13)

x = 2√13

Thus,

The value of x in the triangle is 2√13.

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The probability that Dan buys a sandwich and gets the bus will be 0.16.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

The probability that Dan buys a sandwich is 0.2.

The probability that Dan gets the bus is 0.8.

Assuming the events are independent.

Then the probability that Dan buys a sandwich and gets the bus will be

P = 0.2 × 0.8

P = 0.16

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Answer:

Step-by-step explanation:

X = 152 -90 = 62 degree

The value of the contour surface passing through the point (1, 0, 2) is ψ(1, 0, 2) = 1^2 + 2e^0 = 1 + 2 = 3.

To find the points on the curve where the tangent is horizontal, we need to determine the values of t that satisfy the condition for a horizontal tangent, which is when the derivative of y with respect to t is equal to 0.

Given the parametric equations:

x = 2t^3 + 3t^2 - 12t

y = 2t^3 + 3t^2 + 1

Taking the derivative of y with respect to t:

dy/dt = 6t^2 + 6t

Setting dy/dt equal to 0 and solving for t:

6t^2 + 6t = 0

t(6t + 6) = 0

From this equation, we have two possible solutions:

t = 0

6t + 6 = 0, which gives t = -1.

Therefore, the points on the curve where the tangent is horizontal are (0, y(0)) and (-1, y(-1)). To find the corresponding y-values, substitute the values of t into the equation for y:

For t = 0:

y(0) = 2(0)^3 + 3(0)^2 + 1 = 1

For t = -1:

y(-1) = 2(-1)^3 + 3(-1)^2 + 1 = -2 + 3 + 1 = 2

Hence, the points on the curve where the tangent is horizontal are (0, 1) and (-1, 2).

To find the points on the curve where the tangent is vertical, we need to determine the values of t that satisfy the condition for a vertical tangent, which is when the derivative of x with respect to t is equal to 0.

Taking the derivative of x with respect to t:

dx/dt = 6t^2 + 6t - 12

Setting dx/dt equal to 0 and solving for t:

6t^2 + 6t - 12 = 0

t^2 + t - 2 = 0

(t + 2)(t - 1) = 0

From this equation, we have two possible solutions:

t + 2 = 0, which gives t = -2

t - 1 = 0, which gives t = 1.

Therefore, the points on the curve where the tangent is vertical are (x(-2), y(-2)) and (x(1), y(1)). To find the corresponding x-values and y-values, substitute the values of t into the equations for x and y:

For t = -2:

x(-2) = 2(-2)^3 + 3(-2)^2 - 12(-2) = -16 + 12 + 24 = 20

y(-2) = 2(-2)^3 + 3(-2)^2 + 1 = -16 + 12 + 1 = -3

For t = 1:

x(1) = 2(1)^3 + 3(1)^2 - 12(1) = 2 + 3 - 12 = -7

y(1) = 2(1)^3 + 3(1)^2 + 1 = 2 + 3 + 1 = 6

Hence, the points on the curve where the tangent is vertical are (20, -3) and (-7, 6).

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Answer:

r

Step-by-step explanation:

r

There exists a value c = 2 such that f'(c) = 0 according to Rolle's Theorem.

To find the value of C:

Let f(x) = (x^2 - 4x)e^z on [0,4].

We are asked to find c such that f'(c) = 0 according to Rolle's Theorem, or if it does not apply, enter DNE.

First, let's verify if Rolle's Theorem applies.

The conditions for Rolle's Theorem are:
1. The function is continuous on the closed interval [0, 4].
2. The function is differentiable on the open interval (0, 4).
3. f(0) = f(4).

Since f(x) = (x^2 - 4x)e^z is a product of a polynomial and an exponential function,

it is continuous and differentiable on its entire domain.

Thus, conditions 1 and 2 are satisfied.

Now, let's check condition 3:
f(0) = (0^2 - 4*0)e^z = 0
f(4) = (4^2 - 4*4)e^z = (16 - 16)e^z = 0

Since f(0) = f(4), all conditions for Rolle's Theorem are satisfied.

Now, we need to find f'(x) and set it equal to 0.

Step 1: Differentiate f(x) using the product rule, which states that (uv)' = u'v + uv'.
u = x^2 - 4x
v = e^z
u' = 2x - 4
v' = 0 (since z is a constant)
f'(x) = (2x - 4)e^z + (x^2 - 4x)*0 = (2x - 4)e^z

Step 2: Set f'(x) equal to 0 and solve for x.
(2x - 4)e^z = 0
2x - 4 = 0
2x = 4
x = 2

Thus, there exists a value c = 2 such that f'(c) = 0 according to Rolle's Theorem.

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