A kite is flying 86 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 56 degrees . Find the length of the string. Round your answer to the nearest tenth.

A fifth-degree polynomial can have at most 4 critical numbers, and hence 4 relative extrema. It can have at most 3 points of inflection.

Explanation:
1. A polynomial function of degree n has (n-1) critical numbers, which are points where the derivative is either zero or undefined. Since a fifth-degree polynomial has a degree of 5, it can have at most (5-1)=4 critical numbers.

2. Relative extrema are local maximum or minimum points of the function. A relative extrema occurs at a critical number where there is a change in the sign of the first derivative (going from positive to negative or negative to positive). Since we have at most 4 critical numbers, there can be at most 4 relative extrema for a fifth-degree polynomial.
3. Points of inflection are points on the graph where the function changes its concavity (from concave up to concave down or vice versa). This occurs when the second derivative of the function changes sign. To find the points of inflection, we need to find the critical numbers of the first derivative, which is a fourth-degree polynomial (one degree less than the original polynomial). A fourth-degree polynomial has at most (4-1)=3 critical numbers.
4. Therefore, a fifth-degree polynomial can have at most 4 relative extrema and 3 points of inflection.

For more questions  on polynomial

https://brainly.com/question/2833285

#SPJ11

Therefore , the solution of the given problem of expressions comes out to be 4/x + 10/y can be expressed as 2(2y + 5x)/xy.

It is preferable to make use of shifting integer values that can be increasing, reducing, or blocking rather than approximations generated at random. They were only able to assist one another by exchanging resources, knowledge, or answers to problems. A declaration of truth equation may include the justifications, components, and mathematical.

Here,

We need to determine a common denominator for the two fractions in order to combine the rational expressions 4/x + 10/y. Here, xy is the common factor.

As a result, 4/x can be rewritten as (4y)/xy and 10/y as (10x)/xy.

We can now combine the two fractions:

=> (10x)/xy + (4y)/xy

=> (4y + 10x)/xy

=> 2(2y + 5x)/xy

As a result, 4/x + 10/y can be expressed as 2(2y + 5x)/xy.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

Step-by-step explanation:

Area of a circle = pi r^2

   44  cm^2      = pi r^2

     r  =    sqrt (44/pi)

     r  = 3.74 cm

Answer:

≈ 3,74 cm

Step-by-step explanation:

Given:

A (area) = 44 cm^2

Find: r (radius) - ?

[tex]a = \pi {r}^{2} [/tex]

[tex]\pi {r}^{2} = 44[/tex]

[tex] {r}^{2} = \frac{44}{\pi} [/tex]

[tex]r = \sqrt{ \frac{44}{\pi} } ≈3.74[/tex]

Step-by-step explanation:

Top floor is x     next floor is 2 x   then the bottom is 4 x

= 7x

7x = 245    x = 35

then  35 ft    70 ft   140 ft   = 245 ft total

By Probability , You expect Stella to remove a apple chew from the bag

 For apple ,  Pₐ = 7/21

    For lime ,  Pi = 2/21

What is probability with and example?

Probability is a measure of how likely or likely-possible something is to happen. For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 potential outcomes overall (a head or tail). P(heads) = 12 is what we write.

Out of 21 times that the experiment was performed

A orange chew was selected 12 times

A orange chew was selected 7 times

A lime chew was selected 2 times

then for the orange ones we have a relative frequency (that can be thought as the probability ) of

          P₀ = 12/21

    For apple ,  Pₐ = 7/21

    For lime ,  Pi = 2/21

Learn more about Probability

brainly.com/question/30034780

#SPJ1

Surface area of rectangular prism is 280/9yd²

A rectangular prism, also known as a rectangular cuboid, is a three-dimensional geometric shape that has six rectangular faces, where each face is perpendicular to the adjacent faces. It is a special type of cuboid where all the faces are rectangles.

The rectangular prism has eight vertices, 12 edges, and six faces, where each face has a pair of congruent and parallel rectangular sides. The opposite faces of the rectangular prism are congruent and parallel, which means that it has a uniform cross-section throughout its length.

Sides of rectangular prism are

l=3yd

b=1 1/3yd=4/3yd

h=2 2/3yd=8/3yd

Surface area of rectangular prism=2(lb+bh+lh)

=2(3×4/3+4/3×8/3+8/3×3)

=2(4+8+32/9)

=280/9yd²

To know more about rectangle, visit:

https://brainly.com/question/29085356

#SPJ1

If a 25 bag-sample has mean of 415 grams and variance of 400, then the p-value of test statistic is 0.0169.

To test whether the bag filling machine is working correctly at the 424 gram setting, we use one-sample t-test.

The null hypothesis is that mean weight of the bags filled by machine is 424 grams, and

The Alternative hypothesis is that the mean weight is less than 424 grams.

The test statistic "t" :

⇒ t = (415 - 424)/√(400/25)) = -2.25,

The degrees of freedom for this test is = 25-1=24.

To find the p-value of the test statistic, we need to determine the probability of observing a t-value less than or equal to -2.25,

Using a t-distribution table with 24 degrees of freedom, the p-value corresponding to t = -2.25 is approximately 0.0169.

Therefore, the p-value of the test statistic is 0.0169.

Learn more about P-Value here

https://brainly.com/question/17087896

#SPJ4

Step-by-step explanation:

no calculator at hand ?

-1963 - x = -9512

-x = -9512 + 1963 = -7549

x = 7549

so, 7549 has to be subtracted.

Answer: The transformation is a reflection.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

According to the puzzle the specified values are;

1. TU = 156.15m    

2. Area of rectangle = 12335.85 m²

3. GH = 182.33m

4. Area of triangle = 8934.17 m²

Three line segments meet at three non-collinear points to form a triangle, a geometric shape. The three points where the line segments meet are referred to as the vertices of the triangle, while the three line segments themselves are referred to as the sides of the triangle.

1. Given triangle TUV apply Pythagoras theorem,

175² = 79² + TU²   after simplification,

TU = 156.15m                   (option A is correct)

2. Area of rectangle = length × width

Area of rectangle = TU × UV  =  156.15 × 79  

Area of rectangle = 12335.85 m² (option G is correct)

3. Given triangle GHI apply Pythagoras theorem,

207² = 98² + GH²   after simplification,

GH = 182.33m    (option I is correct)

4. Area of triangle = [tex]\frac{1}{2}[/tex]  × base × height

Area of triangle =  [tex]\frac{1}{2}[/tex]  × HI × GH

Area of triangle =  [tex]\frac{1}{2}[/tex]  × 98m × 182.33m

Area of triangle = 8934.17 m²

To know more about triangle, visit:

https://brainly.com/question/17815056

#SPJ1

Answer:

Step-by-step explanation:

dock is 12 ft tall

boat is 16 ft from dock

how long is the rope?

The dimensions form a right tringle.

Use Pythagorean,

a² + b² = c²

12²  +  16² = c²

144 +  256 = c²

400 = c²

√400 = √c²

20 = c

The rope is 20 ft long.

The length of the rope connecting the boat to the dock is approximately 20 feet. This can be answered by the concept of Pythagorean theorem.

To calculate the length of the rope, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the rope is the hypotenuse, and the distance between the boat and the dock (16 feet) and the height of the dock (12 feet) are the other two sides. So we have:

Rope length² = 16² + 12²

Rope length² = 256 + 144

Rope length² = 400

Rope length = √400 = 20 feet

Therefore, the length of the rope connecting the boat to the dock is approximately 20 feet

To learn more about Pythagorean theorem. here:

brainly.com/question/14930619#

#SPJ11

The measures of the angles in the unit circles are 53 degrees, 138 degrees, 300 degrees and 214 degrees

The question is an illustration of unit circles and the angles would be solved using

(x, y) = (cos(∅), sin(∅))

Figure (a)

Here, we have

(x, y) = (3, 4)

This means that

tan(∅) = y/x

So, we have

tan(∅) = 4/3

Take the arc tan of both sides

∅ = 53 degrees

Figure (b)

Here, we have

(x, y) = (-√5, 2)

This means that

tan(∅) = y/x

So, we have

tan(∅) = 2/-√5

Take the arc tan of both sides

∅ = 138 degrees

Figure (c)

Here, we have

(x, y) = (1, -√3)

This means that

tan(∅) = y/x

So, we have

tan(∅) = -√3/1

Take the arc tan of both sides

∅ = 300 degrees

Figure (d)

Here, we have

(x, y) = (-3, -2)

This means that

tan(∅) = y/x

So, we have

tan(∅) = -2/-3

Take the arc tan of both sides

∅ = 214 degrees

Read more about unit cirlce at

https://brainly.com/question/26284611

#SPJ1

The statement that is not correct is in marketing research, the null hypothesis is formulated in such a way that rejection leads to the acceptance of the desired conclusion.

The null hypothesis (often denoted H0)[1] is the claim that no relationship exists between two sets of data or variables

being analyzed. The null hypothesis is that any experimentally observed difference is due to chance alone, and an

underlying causative relationship does not exist, hence the term "null". In addition to the null hypothesis, an alternative

hypothesis is also developed, which claims that a relationship does exist between two variables.

The null hypothesis is the actual hypothesis being tested and it can never be accepted based on a single statistical

test. Failing to reject the null hypothesis will not lead to any changes in opinions or action.

The statement that is not correct is in marketing research, the null hypothesis is formulated in such a way that rejection

leads to the acceptance of the desired conclusion.

for such more question on marketing research

https://brainly.com/question/24906199

#SPJ11

The normally distributed with mean 2.4 and standard deviation 0.8:

a) fraction of the students will possess a GPS is 0.4648.

b) probability that all three will possess a gpa in excess of 3.0 is 0.2266.

c) percentage of the students will be dropped is 19.08%.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence. With it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

we have, μ = 2.4, σ = 0.8

(a) z1 = (x1 - μ)/σ = (2 - 2.4)/0.8 = -0.5

z2 = (x2 - μ)/σ = (3 - 2.4)/0.8 = 0.75

P(2 < x < 3) = P(-0.5 < z < 0.75) = 0.4648

(b) P(x > 3) = P(z > 0.75) = 0.2266

(c) z = (1.7 - 2.4)/0.8 = -0.875

P(x < 1.7) = P(z < -0.875) = 0.1908, which is 19.08%.

Learn more about Probability:

https://brainly.com/question/15106212

#SPJ4

Complete question:

The grade point averages (GPAs) of a large population of college students are approximately normally distributed with mean 2.4 and standard deviation 0.8. What fraction of the students will have GPAs between 2.0 and 3.0? What fraction of students will possess a GPA in excess of 3.0? If students possessing a GPA less than 1.7 are dropped from college, what percentage of the students will be dropped?

an organized list representing the sample space of drawing one letter tile and one number tile: {(A, 1), (A, 2), (A, 3), (B, 1), (B, 2), (B, 3), (C, 1), (C, 2), (C, 3)}

In probability theory, sample space refers to the set of all possible outcomes of a random experiment.

For example, if we toss a coin, the sample space would consist of two possible outcomes, heads or tails. Similarly, if we roll a die, the sample space would consist of six possible outcomes, the numbers 1 through 6.

The sample space is an important concept because it allows us to define the probabilities of events. In order to calculate the probability of an event, we divide the number of outcomes that are favorable to the event by the total number of possible outcomes in the sample space.

To know more about outcomes, visit:

https://brainly.com/question/17238771

#SPJ1

The complete question is;

The bag contains tiles labeled with the letters A, B,

and C. The box contains tiles labeled with the

numbers 1, 2, and 3. June draws one letter tile and

one number tile. Represent the sample space using

either a table or an organized list.

B

B

A

2

3

after 5 years with different compounding frequencies: a. Monthly: $13,952.19 b. Daily: $14,059.89 c. Quarterly: $13,784.98 d. Weekly: $14,001.84

How to solve the question ?

To calculate the balance after 5 years with compound interest, we can use the formula:

A = P (1 + r/n) in power nt

where A is the balance after t years, P is the principal balance, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

For this problem, P = $10,000 and r = 6.92%. To find the balance after 5 years with different compounding frequencies, we can use the following values for n:

a. Monthly: n = 12 A = $10,000 (1 + 0.0692/12)¹²*⁵ = $13,952.19

b. Daily: n = 365 A = $10,000 (1 + 0.0692/365)³⁶⁵*⁵ = $14,059.89

c. Quarterly: n = 4 A = $10,000 (1 + 0.0692/4)⁴*⁵= $13,784.98

d. Weekly: n = 52 A = $10,000 (1 + 0.0692/52)⁵²*⁵ = $14,001.84

Therefore, after 5 years with different compounding frequencies: a. Monthly: $13,952.19 b. Daily: $14,059.89 c. Quarterly: $13,784.98 d. Weekly: $14,001.84

To know more about compound interest visit :-

https://brainly.com/question/28020457

#SPJ1

Answer:

I believe it is is A

Step-by-step explanation:

The total mass in tones of the 2500 books is 1.75 tones

A proportion is defined as an equation having two ratios that are set equal to each other.

From the information given, we have that;

There are 2500 books

But then, a book weighs 700 grams

So, we have;

1 book = 700 grams

then, 2500 books = x grams

cross multiply

x = 1, 750, 000 grams

Let's convert the grams to tones , we get;

I gram = 10⁻⁶

Then 1. 75 ×  10⁻⁶ = x

cross multiply

x = 1. 75 tones

Learn about proportions at: https://brainly.com/question/1781657

#SPJ1

The coordinate of point S given the midpoint is 1, 5)

To find the coordinates of S, we first need to use the midpoint formula to find the coordinates of M.

The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

We are given that the midpoint of ST is M = (4, -3), and we know the coordinates of T are T = (7, -11).

Using the midpoint formula, we can write:

M = ((x1 + 7)/2, (y1 - 11)/2)

Solving for x1 and y1, we get:

x1 + 7 = 2 * 4 = 8

y1 - 11 = 2 * (-3) = -6

x1 = 8 - 7 = 1

y1 = -6 + 11 = 5

Therefore, the coordinates of S are S = (1, 5).

Read more about midpoint at

https://brainly.com/question/25886396

#SPJ1

The area of the square ABCD is approximately 420/π cm².

To find the area of the square, follow these steps:
1. Calculate the radius of the circle:
Since the area of the circle is 105 cm², you can use the formula for the area of a circle,

which is A = πr²,

where A is the area and r is the radius.
105 = πr²
Divide both sides by π:
r² = 105/π
Take the square root of both sides:
r = √(105/π)
2. Calculate the side length of the square:
Since the circle touches all 4 sides of the square, the diameter of the circle is equal to the side length of the square. The diameter is twice the radius (d = 2r), so:
d = 2√(105/π)
3. Calculate the area of the square:
Now, use the formula for the area of a square, which is A = s²,

where A is the area and s is the side length. In this case, s = d:
A = (2√(105/π))²
A = 4 * (105/π)
4. Multiply to find the area:
A = 420/π cm².

For similar question on area.

https://brainly.com/question/21947163

#SPJ11

Answer:

see explanation

Step-by-step explanation:

(a)

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 7 , then

sum = 180° × (7 - 2) = 180° × 5 = 900°

(b)

since the polygon is regular then the 7 interior angles are congruent

each interior angle = 900° ÷ 7 ≈ 128.6° ( to 1 decimal place )

(c)

the sum of the exterior angles of a polygon is 360°

since the polygon is regular then the 7 exterior angles are congruent

each exterior angle = 360° ÷ 7 ≈ 51.4° ( to 1 decimal place )

Answer:

a) 900°

b) ≈ 128,6°

c) ≈ 51,4°

Step-by-step explanation:

a) s = (n - 2) × 180°

n - the number of sides (in this case, it's 7)

s - the sum of interior angles

s = (7 - 2) × 180° = 5 × 180° = 900°

.

b) In order to find the size of each angle, we have to divide the sum by the number of sides:

900° / 7 ≈ 128,6°

.

c) Since the sum of exterior angles of a polygon is 360°, we can find the size of one exterior angle by dividing this sum by the number of sides:

360° / 7 ≈ 51,4°

The true statements about the image △A'B'C' include the following:

A. AB is parallel to A'B'.

B. [tex]D_{O, \frac{1}{2} }[/tex] (x, y) = (1/2x, 1/2y)

C. The distance from A' to the origin is half the distance from A to the origin.

In Mathematics and Geometry, a dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

This ultimately implies that, the size of the geometric shape would be increased (stretched or enlarged) or decreased (compressed or reduced) based on the scale factor applied.

Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 0.5 centered at the origin as follows:

Ordered pair A (-4, 3) → Ordered pair A' (-4 × 1/2, 3 × 1/2) = Ordered pair B' (-2, 1.5).

Ordered pair B (4, 4) → Ordered pair B' (4 × 1/2, 4 × 1/2) = Ordered pair B' (2, 2).

Read more on dilation and scale factor here: https://brainly.com/question/4421026

#SPJ1

y = (46.5 - (0.5b / 58))x + b This equation allows us to plug in any value for x (the number of miles driven) and calculate Kristen's total pay for that month.

To write an equation in slope intercept form to find Kristen's total pay, we need to first determine the variable values for the equation. In this case, we know that Kristen is paid the same salary each month, so we can assign a constant value to represent her base pay. Let's call this value "b" for simplicity.

Next, we need to determine the relationship between the number of miles Kristen drives and the extra pay she receives. We can do this by calculating the rate at which she is paid per mile. To do this, we can use the formula:

Pay per mile = (Total pay - Base pay) / Number of miles driven

Using the values given in the problem, we can calculate the pay per mile for March and April as follows:

March:

Pay per mile = ($7,748.00 - b) / 58 miles

April:

Pay per mile = ($8,532.00 - b) / 72 miles

To find the overall slope of the equation, we can calculate the difference in pay per mile between March and April:

Slope = (Pay per mile for April - Pay per mile for March) / (Number of miles driven in April - Number of miles driven in March)

Slope = (($8,532.00 - b) / 72 miles) - (($7,748.00 - b) / 58 miles)) / (72 miles - 58 miles)

Simplify the equation and solve for the slope:

Slope = 46.5 - (0.5b / 58)

Now that we have the value of the slope, we can write the equation in slope intercept form:

y = mx + b

y represents Kristen's total pay, m represents the slope we just calculated, x represents the number of miles she drives, and b represents her base pay.

Putting it all together, the final equation for Kristen's total pay in a month given the number of miles she drives is:

y = (46.5 - (0.5b / 58))x + b

This equation allows us to plug in any value for x (the number of miles driven) and calculate Kristen's total pay for that month.

To know more about slope intercept form click here:

brainly.com/question/29146348

#SPJ1

The three different counterclockwise angles the wheel of radian 1 can rotate-

5π/6 ,     7π/6   ,     11π/6

Angles are measured in terms of radians. It is described as the angle subtended from a circle's center that intercepts an arc with a length equal to the circle's radius1. A radian is equivalent to roughly 57.3 degrees

Here is a wheel with a one-foot radius. There are 12 equal pie-shaped segments cut out of the circular. On the y-axis, below the origin, Point Q is located outside the circle.

The following angles, measured in radians, can be used to determine three different anticlockwise rotational angles that the wheel can take to get from point P to position Q:

- 5π/6

- 7π/6

- 11π/6

For any one of these angles, the wheel rolls a distance of /6 feet

To know more about radian visit:

brainly.com/question/7721249

#SPJ1

Answer: y = 18000(0.89)^x, where x represents the number of years in the future.

Step-by-step explanation:

Answer:

Y= 18,000 X (0.11x)

Step-by-step explanation:

x being years y being car

6 Students can arrange themselves in 720 different ways to sit in the front row of an auditorium.

To determine the number of ways 6 students can arrange themselves to sit in the 6 seats in the front row, you can use

the concept of permutations.

There are 6 seats, so for the first seat, there are 6 choices of students who can sit there.

For the second seat, 5 students remain, so there are 5 choices.

For the third seat, 4 students remain, so there are 4 choices.

For the fourth seat, 3 students remain, so there are 3 choices.

For the fifth seat, 2 students remain, so there are 2 choices.

For the last seat, only 1 student remains, so there is 1 choice.

Now, multiply the number of choices for each seat together to find the total number of arrangements:

6 × 5 × 4 × 3 × 2 × 1 = 720 ways.

So, 6 students can arrange themselves in 720 different ways to sit in the front row of an auditorium.

for such more question on permutations.

https://brainly.com/question/1216161

#SPJ11