The probability of having every bin filled with at least one ball if n balls are distributed randomly into m bins is given by the formula 1 - (m-1/m)^n.
Let's break it down step-by-step:
Step 1: Probability of a ball being put into a specific Bin Since there are m bins, the probability of a ball being put into a specific bin is 1/m. Therefore, the probability of a ball not being put into that bin is (m-1)/m.
Step 2: Probability of a ball not being put into a specific Bin Since there are m bins, the probability of a ball not being put into a specific bin is (m-1)/m. Therefore, the probability of a ball being put into that bin is 1/m.
Step 3: Probability of every bin being filled with at least one ball Using the above two probabilities, the probability of a specific bin not being filled with a ball is (m-1)/m. Therefore, the probability of all m bins not being filled with a ball is (m-1/m)^n. Finally, the probability of every bin being filled with at least one ball is 1 - (m-1/m)^n.
Therefore, the probability of having every bin filled with at least one ball if n balls are distributed randomly in to m bins is given by the formula 1 - (m-1/m)^n.
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PLEASE HELP!!
The circumference
What is the area of the green sector?
of the circle above is 24 cm and the area is 42 cm².
7
cm²
What is the arc length of the edge of the green sector?
cm.
Hence, the area of the green sector is roughly [tex]7 cm^2,[/tex] and the arc length of its edge is roughly 4 cm.
what is area ?Usually expressed in square units, area is a unit of measurement for the size of an a double surface or territory. It is used to indicate the amount of space that lies inside the confines of a straight position, such as a round, rectangle, circle, a triangle. Depending on the shape, a formula is needed to determine the size of a shape. For instance, the area of either a rectangle can be determined by dividing its extent by its width, whereas the area of a circle can be determined by multiplying pi (about 3.14), by the square of its radius. Several branches of mathematics, physics, and engineering all use the idea of area extensively.
given
(Area of Green Sector / Area of Circle) 360 degrees is the formula for the Green Sector's Central Angle.
green sector's centre angle is equal to (7 cm2 / 42 cm2) 360 degrees.
60 degrees is the green sector's midpoint (rounded to the nearest degree)
We may apply the following formula to determine the arc length of the green sector:
circumference (central angle / 360 degrees) = arc length
arc length is equal to 24 cm when divided by 60 degrees.
4-cm-long arc (rounded to one decimal place)
Hence, the area of the green sector is roughly [tex]7 cm^2,[/tex] and the arc length of its edge is roughly 4 cm.
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three randomly chosen colorado students were asked how many times they went rock climbing last month. their replies were 5, 6, 7. the coefficient of variation is multiple choice 35.7 percent. 13.6 percent. 20.0 percent. 16.7 percent.
Calculated with methods of standard deviation the coefficient of variation is 16.7%.
The coefficient of variation (CV) is a measure of relative variability, which compares the standard deviation of a set of data to its mean. It is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. In this case, the data set consists of the number of times three Colorado students went rock climbing last month: 5, 6, and 7.
First, we calculate the mean of the data set as (5+6+7)/3 = 6. Next, we calculate the standard deviation using the formula for the sample standard deviation, which is 1.0.
Therefore, the CV is (1.0/6) x 100% = 16.7%.
This means that the standard deviation is about 16.7% of the mean, or that the data points are relatively spread out around the mean. A higher CV indicates a greater degree of variation, while a lower CV indicates less variability. In this case, a CV of 16.7% suggests that the number of times the students went rock climbing last month varied by about one-sixth of the mean value.
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a running shoe company wants to sponsor the fastest 3% of runners. you know that in this race, the running times are normally distributed with a mean of 7.2 minutes and a standard deviation of 0.56 minutes. how fast would you need to run to be sponsored by the company? g
Answer:
6.104
Step-by-step explanation:
Given that,
Mean, {eq}\mu = 6.8 {/eq}
Standard deviation, {eq}\sigma = 0.37 {/eq}
{eq}P(X < x) = 0.03\\ P(\dfrac{X - \mu}{\sigma} < \dfrac{x - \mu}{\sigma}) = 0.03\\ P(Z < \dfrac{x - 6.8}{0.37}) = 0.03\\ P(Z < z) = 0.03 {/eq}
Excel function for the value of z:
=NORMSINV(0.03)
{eq}z = -1.881\\ \dfrac{x - 6.8}{0.37} = -1.881\\ x = 6.8-1.881\times 0.37\\ \color{blue}{x = 6.104 \ minutes} {/eq}
To be sponsored by the running shoe company as one of the fastest 3% of runners, one would need to run faster than the upper 3rd percentile of runners. This can be calculated using the z-score formula which is given as; z = (x - μ) / σ where x is the value we want to find the percentile of, μ is the mean and σ is the standard deviation.
The z-score formula can be rearranged to solve for x which is the running time needed to be sponsored by the company as follows;x = z * σ + μWe want to find the upper 3rd percentile, which corresponds to a z-score of 1.88 (from z-tables or calculator).
Therefore;1.88 = (x - 7.2) / 0.56. Rearranging to solve for x;x = 1.88 * 0.56 + 7.2x = 8.1888 (rounded to 4 decimal places)Therefore, one would need to run faster than 8.1888 minutes to be sponsored by the running shoe company as one of the fastest 3% of runners.
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Find measure AD. Please hurry due at midnight
The measure of arc mAD is 119°.
Describe Arc?In geometry, an arc is a portion of a curve or a circle. It is defined as a connected portion of the circumference of a circle, which is characterized by its central angle, length, and location. The length of an arc is proportional to the measure of its central angle, and the measure of the arc is given in degrees or radians.
The circumference of a circle is the distance around the circle, and it is equal to 2πr, where r is the radius of the circle. An arc of a circle is a part of the circumference, and its length can be calculated using the formula:
Arc length = (central angle/360 degrees) * 2πr
where the central angle is measured in degrees, and r is the radius of the circle.
Since chord AB, BC, CD, and DA form a quadrilateral, we know that the opposite angles of the quadrilateral add up to 180°. Therefore, ∠ABC = 180 - ∠DAB = 180 - 75 = 105°, and ∠BCD = 180 - ∠ADC = 180 - 102 = 78°.
Next, we can use the inscribed angle theorem to find the measure of arc AD. We know that ∠ACD is half the measure of arc CD, so arc CD = 2 * ∠ACD = 62°. Therefore, ∠ACD = 31°.
Similarly, ∠ABD is half the measure of arc AB, so arc AB = 2 * ∠ABD. We can find angle ABD by subtracting angle DAB from ∠ABC: ∠ABD = ∠ABC - DAB = 105 - 75 = 30°. Therefore, arc AB = 2 * 30 = 60°
Since the sum of the measures of angles ABD, ACD, and the central angle arc AD is 180°, we have:
∠ ABD + ∠ ACD + arc AD = 180
Substituting the values we found, we get:
30 + 31 + arc AD = 180
Solving for arc AD, we get:
arc AD = 180 - 30 - 31 = 119°
Therefore, the measure of arc mAD is 119°.
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am I correct ? please answer
Answer: No, the answer is D (it gains electrons)
Step-by-step explanation:
An object becomes negatively charged by gaining electrons, not by gaining protons. Protons are positively charged particles found in the nucleus of an atom and are not easily gained or lost by an object. On the other hand, electrons are negatively charged particles that are more easily gained or lost by an object, leading to a net positive or negative charge. When an object gains electrons, it becomes negatively charged as the number of negatively charged particles (electrons) exceeds the number of positively charged particles (protons).
the total number of sides in 2 regular polygons is 13, and tge titak number of diagonals is 25. how many sides is each polygon
One polygon has 6 sides and the other has 7 sides.
Polygons are closed 2D shapes made up of straight lines. Regular polygons have sides of equal length and angles of equal measure. In this problem, we are given information about two regular polygons.
We are told that the total number of sides in both polygons is 13. Let's call the number of sides in one polygon "n" and the number of sides in the other polygon "m". Then, we know that:
n + m = 13
Next, we are given the total number of diagonals in both polygons, which we can calculate using the formula:
d = (n(n-3) + m(m-3))/2
where "d" is the total number of diagonals. We are told that d = 25. Substituting this value and the equation for n + m into the diagonal formula, we get:
25 = (n(n-3) + m(m-3))/2
25 = (n² - 3n + m² - 3m)/2
50 = n² - 3n + m² - 3m
We can use the equation n + m = 13 to solve for one variable in terms of the other. For example, we can solve for "m" by subtracting "n" from both sides:
m = 13 - n
Substituting this into the previous equation, we get:
50 = n² - 3n + (13-n)² - 3(13-n)
50 = n² - 3n + 169 - 26n + n² - 36 + 3n
Simplifying this equation, we get:
2n² - 26n + 45 = 0
We can use the quadratic formula to solve for "n":
n = (26 ± √376)/4
n ≈ 5.61 or n ≈ 8.39
Since we are dealing with whole numbers of sides, "n" must be either 6 or 8. Plugging each value into the equation n + m = 13, we find that the other polygon must have the opposite value.
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Could someone please find the domain to this function: f(x)=4/|x|-2
The domain of the function f(x) is: Domain: x≠0The function is not defined for x = 0, since it causes division by zero error. For all other values of x, the function f(x) is defined.
The domain for the function f(x)=4/|x|-2 is x≠0.
When dealing with functions with absolute values, it is vital to consider the circumstances under which the argument of
the absolute value sign becomes zero, since that's where the function becomes undefined.
When the absolute value of x is zero, the denominator becomes zero, which causes a division by zero error.
This function, therefore, has no output value for x = 0.
Domain of the function is the set of all permissible input values for the function, as the output values are defined for
only permissible input values.
In other words, we can say that a domain of a function is a set of all possible values that x can take on, whereas the
range is the set of all possible values that the function can take on.
Therefore, the domain of the function f(x) is: Domain: x≠0The function is not defined for x = 0, since it causes division by zero error. For all other values of x, the function f(x) is defined.
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Suki says the area of the triangle is 12 cm². Emilia says the area of the triangle is 10 cm². Find the area of the triangle and explain any errors the girls might have made.
helpppp
Answer:
Let’s call the base of the triangle b and its height h. The area of a triangle is given by the formula A = 1/2 * b * h.
If Suki says that the area of the triangle is 12 cm², then we can write:
12 = 1/2 * b * h
Similarly, if Emilia says that the area of the triangle is 10 cm², then we can write:
10 = 1/2 * b * h
We can solve for one of the variables in terms of the other by dividing both sides of each equation by 1/2:
b * h = 24
b * h = 20
Now we have two equations with two variables. We can solve for one variable in terms of the other by dividing both sides of one equation by the other:
(b * h) / (b * h) = 24 / 20
1 = 6/5
This is a contradiction, so there is no solution that satisfies both equations.
Step-by-step explanation:
if a cylinder has a height of 7 inches and a volume of 2908.33in3 guns it’s diameter
The diameter of the cylinder is approximately 22.98 inches.
To find the diameter of the cylinder, we need to first find the radius using the formula for the volume of a cylinder:
Volume = π × r² × h
Given:
Volume (V) = 2908.33 in³
Height (h) = 7 inches
We will rearrange the formula to find the radius (r):
r² = Volume / (π × h)
Now, plug in the given values:
r² = 2908.33 / (π × 7)
r² ≈ 131.95
Now, find the square root to get the radius:
r ≈ √131.95
r ≈ 11.49 inches
Since the diameter is twice the radius, we can find the diameter (d) by:
d = 2 × r
d = 2 × 11.49
d ≈ 22.98 inches.
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jayce's grandfather just gave him a new tackle box to use on their first fishing trip together. the tackle box is shaped like a rectangular prism with a volume of 928 cubic inches. it has a length of 14.5 inches and a height of 8 inches. how wide is the tackle box? write your answer as a whole number or decimal. do not round. inches
The width of rectangular prism shaped tackle box given by jayce's grandfather to him for use on their first fishing trip together is equals to 8 inches.
We have, jayce's grandfather just give him a new tackle box for using on their first fishing trip together. The shape of box is rectangular prism. Let the dimensions or length, height and width of tackle box be l , h and w. In this case,
Volume of tackle box = 928 in³
Length of tackle box, l = 14.5 inches
Height of tackle box, h = 8 inches
Volume is defined as space occupied by shape. The formula for the volume of a rectangular prism is, Volume (V) = base area × height of the prism or
Volume of rectangular prism, V = l × h × w
So, 928 in³ = l × h × w in³
=> 928 in³ = 14.5 inches × 8 inches × w
=> 928 in³ = 116 in² × w
=> w = 928/116 = 8 inches
Hence, required width is 8 inches.
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Which of the following best describes a negative linear association? A Variables have no relation to each other when plotted. B As one variable increases, so does the other. C A data set that includes both negative and positive numbers. D As one variable decreases, the other increases.
The best description of a negative linear association is option D: "As one variable decreases, the other increases."
In a negative linear association, as the value of one variable increases, the value of the other variable decreases, and this relationship is linear or straight. This can be represented by a negative slope on a scatterplot. Option A ("Variables have no relation to each other when plotted") does not describe any type of association, and option C ("A data set that includes both negative and positive numbers") is not specific to linear associations. Option B ("As one variable increases, so does the other") describes a positive linear association, which is the opposite of a negative linear association.
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What is the third term of the geometric sequence in which a1 = 5 and r = -2?
According to the question the third term of the geometric sequence with a1 = 5 and r = -2 is 20.
We can use the following formula to determine the third term of such a geometric sequence:
a3 = a1 * r^2
where a1 is the first term, r is the common ratio, and a3 is the third term.
In this case, we are given that a1 = 5 and r = -2. With these values entered into in the formula, we obtain:
a3 = 5 * (-2)^2
a3 = 5 * 4
a3 = 20
Since a1 = 5 and r = -2, then third term of a geometric sequence is 20.
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Write an equation for a function that represents the amount of carbon-14 that will remain
after x half-lives. Write a "let" statement.
The amount of carbon-14 that will remain after x half-lives can be represented by the function:
A(x) = A0 * (1/2)^x
where A0 is the initial amount of carbon-14.
Let A(x) be the amount of carbon-14 that will remain after x half-lives and let A0 be the initial amount of carbon-14.
loretta wants to put a circular mirror on a wall. the mirror has a radius of 23 inches. how many square inches of space will the mirror take up on the wall?
5,761.28 square inches of space will require the mirror to take up on the wall when Loretta wants to put a circular mirror on a wall.
We can find the space that the mirror takes up on the wall by using the area of a circle. it is given by:
A = πr^2
where
A = area of a circle
r =radius of a circle
Given data
radius of the mirror = 23 inches
The area of the mirror is:
A = π(23)^2
= 1,661π
where assume π =3.14159:
A = 1,661(3.14159)
A = 5,761.28 square inches
Therefore, the mirror will take up approximately 5,761.28 square inches of space on the wall.
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Hassan travels by bus to work every morning.
The bus is either green or blue or yellow.
The table shows information about the probabilities of each colour.
Calculate the value of x
Work out the probability that Hassan’s bus is either blue or yellow
Answer:
3/5
Step-by-step explanation:
Total= 2x + 2x + x= 5x
Total of Blue and yellow= 2x + x= 3x
So.. 3x/5x which is equivalent to 3/5
A picture needs a border of uniform width to surround it before it is framed. For the most pleasing effect the border needs to have the exact same area as the picture to be framed. If the original picture is 12 em by 17 cm, determine the required width of the border, rounded to twe decimal places.
Answer:
width = 2.93 cm
Step-by-step explanation:
Area of picture = 12 x 17 = 204
let x = width of border
2(17 + 2x)(x) + 2(12x) = 204
34x + 4x² + 24x - 204 = 0
4x² + 58x - 204 = 0
Use quadratic formula to find x: a = 4, b = 58, c = -204
x = 2.93, -17.43 disregard the negative root
x = 2.93 cm
help me solve this question fast
Answer:
[tex]2\sqrt{3} -6\sqrt{2} +2\sqrt{6}[/tex]
Step-by-step explanation:
Express the trig ratios as fractions in simplest terms
Help asap please!!!!
The value of the identities are;
cos F = 19/20
sin E= √39/20
sin E and cos F are not equal
How to determine the value of the identitiesThe different trigonometric identities in mathematics also have their different ratios. They are;
sinecosinetangentsecantcosecantcotangentTheir ratios are fractions given as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have that;
cos F =
Opposite = 19
Hypotenuse = 20
cos F = 19/20
The value of sin E
sin E = 39/20
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I don't understand this can you show me how to solve it with steps?
Angles ABC and CBD are supplementary, x would equal 29.
Equations4x + 8 + 2x - 2 = 180
6x + 6 = 180
6x = 174
x = 29
What are complimentry and supplimentary angles?Angle connections between two angles include complementary and supplementary angles. Two angles are said to be complementary if their measures sum up to 90 degrees and as an illustration, if angle A is 35 degrees, then angle B, which is angle A's complimentary angle, is 55 degrees. Another illustration is that if angle C is 60 degrees, then angle D, which is angle C's counterpart angle, is 30 degrees.
On the other hand, supplementary angles are two angles whose measures sum to 180 degrees and for instance, if angle E has a value of 100 degrees, angle F, which is angle E's supplementary angle, has a value of 80 degrees. Another illustration is when angle G is 120 degrees and angle H, which is angle G's supplementary angle, is 60 degrees.
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I need help on this hope you guys can help
The measure of the angle in the angles is 151°
What is an angle?An angle is a figure in Plane Geometry which is formed by two rays or lines that share a common endpoint
the given angles are
<EFH = 44°
and <HFG 107°
This implies that <EFG = <EFH + <HFG
= 44 + 107 = 151°
In conclusion, the measure of angle <EFG = 151°
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Solve the system of equations.
5
�
−
4
�
=
−
10
�
=
2
�
−
5
5x−4y=−10
y=2x−5
�
=
x=x, equals
�
=
y=y, equals
The solution for the system of equation 5x - 4y= -10 and y = 2x − 5, using substitution, is (10, 15).
In the first equation, change the value of y as follows:
5x - 4y= -10
5x - 4(2x-5) = -10
Simplifying the expression:
5x - 8x + 20 = -10
-3x = -30
x = 10
Now, using the value of x in the equation for y:
y = 2x − 5,
y = 2(10) - 5
y = 15
By substituting the value of y from the second equation into the first equation and solving for x, we found that x = 10. Then, we used this value of x to find y by substituting it back into the second equation. Therefore, the solution is (10, 15).
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The complete question is:
Using substitution what is 5x-4y=-10 when y equals y=2x−5?
5x−4y=−10
y=2x−5
The box plot below represents some data set. What percentage of the data values are greater than 65?
Answer: Unfortunately, without further context, I can't answer your question. Please post the box plot from the question first.
(1 point) write a formula for a two-dimensional vector field which has all vectors of length 4 and perpendicular to the position vector at that point.
F(x,y) · r(x,y) = 4(yi - xj) · (xi + yj)= 4xy - 4xy = 0
The two vectors are perpendicular to each other, and the length of F(x,y) is 4, as desired.
Write a formula for a two-dimensional vector field which has all vectors of length 4 and perpendicular to the position vector at that point?A two-dimensional vector field is a vector field in which each point in the plane is associated with a vector.
It is represented by a pair of functions (P, Q), each of which maps (x, y) to a real number, and the vector field itself is written as F = P i + Q j. Let's write a formula for a two-dimensional vector field that has all vectors of length 4 and is perpendicular to the position vector at that point
The formula for a two-dimensional vector field that has all vectors of length 4 and is perpendicular to the position vector at that point is given by:
F(x,y) = 4(yi - xj)
Here, the position vector at any point (x, y) in the plane is given by r(x,y) = xi + yj, and its magnitude is
|r(x,y)| = √(x² + y²).
To see that F(x,y) is perpendicular to r(x,y), take their dot product:
F(x,y) · r(x,y) = 4(yi - xj) · (xi + yj)= 4xy - 4xy = 0
Thus, the two vectors are perpendicular to each other, and the length of F(x,y) is 4, as desired.
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FIFA has made a football of a leather of diameter 21 cm. If 10% leather is wasted and the cost of leather includings labor cost is Rs. 25 per sq.cm. find the total cost of leather bought to make a football.
The total cost of leather bought used to make a football is given as follows:
Rs 1,524.
How to obtain the surface area of a sphere?The surface area of a sphere of radius r is given by the equation presented as follows:
S = 4πr².
FIFA has made a football of a leather of diameter 21 cm, hence the radius is given as follows:
r = 10.5 cm.
Then the surface area is given as follows:
S = 4π x 10.5²
S = 1385.44 cm².
The cost is of Rs 25 per cm², with an additional 10% due to waste, hence the total cost is given as follows:
1.1 x 1385.44 = Rs 1,524.
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A ladder PQ, of length 5 m, is leaning against a vertical wall. The lower end Q of the ladder is sliding away from the wall at a constant rate of 0.6 m/s. Find the velocity of the upper end P when Q is 4m from the wall.
Answer:
The velocity of the upper end P when Q is 4 m from the wall is -0.8 m/s
Step-by-step explanation:
Let's denote the distance of the lower end Q from the wall as x and the distance of the upper end P from the ground as y. We are given that the ladder has a length of 5 m, and thus by the Pythagorean theorem, we have:
x^2 + y^2 = 5^2 = 25
Now, we're given that the lower end Q is sliding away from the wall at a constant rate of 0.6 m/s. This means that the rate of change of x with respect to time (dx/dt) is 0.6 m/s. We need to find the rate of change of y with respect to time (dy/dt) when x = 4 m.
Differentiate both sides of the Pythagorean equation with respect to time (t):
d(x^2)/dt + d(y^2)/dt = d(25)/dt
2x(dx/dt) + 2y(dy/dt) = 0
We can plug in the known values and solve for dy/dt when x = 4 m:
2(4)(0.6) + 2y(dy/dt) = 0
To find the value of y when x = 4 m, we can use the Pythagorean equation:
4^2 + y^2 = 25
16 + y^2 = 25
y^2 = 9
y = 3 (since the height must be positive)
Now, we can substitute y = 3 into the equation we derived earlier:
2(4)(0.6) + 2(3)(dy/dt) = 0
4.8 + 6(dy/dt) = 0
Now, solve for dy/dt:
6(dy/dt) = -4.8
(dy/dt) = -4.8 / 6
(dy/dt) = -0.8 m/s
Thus, the velocity of the upper end P when Q is 4 m from the wall is -0.8 m/s. The negative sign indicates that the upper end P is moving downward.
there are 10 questions on a discrete structures final exam. how many ways are there to assign scores to the problems if the sum of the scores is 100 and each question is worth at least 5 points?
there are 50,063,860 ways to assign scores to the 10 questions on a discrete structures final exam with a sum of 100 points and each question worth at least 5 points.
To determine the number of ways to assign scores to the 10 questions on a discrete structures final exam with a sum of 100 points and each question worth at least 5 points, we can use the concept of combinations.
First, we need to distribute 5 points to each of the 10 questions since they are worth at least 5 points. So, 10 * 5 = 50 points are already distributed. Now, we have 100 - 50 = 50 points left to distribute among the 10 questions.
We can solve this problem using the "stars and bars" method. In this method, we represent the points as "stars" and the gaps between questions as "bars". So, we have 50 stars and 9 bars to arrange. This problem then becomes a problem of finding the number of ways to arrange 50 stars and 9 bars.
The total number of elements (stars + bars) is 50 + 9 = 59. We need to choose 9 positions for the bars out of 59 positions, and the remaining positions will be filled by stars.
The number of ways to do this is given by the combination formula: C(n, k) = n! / (k! * (n-k)!)
Here, n = 59 (total elements) and k = 9 (positions for bars).
C(59, 9) = 59! / (9! * (59-9)!) = 59! / (9! * 50!)
By calculating the value, we get:
C(59, 9) = 50063860
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Section 4.5-B Quadratics - Completing the Square
What is the formula?
Therefor , by solving these by using quadratic expression
A) 16n³-24n+9/16
B)169
C)361/4
D)361/4
what is a quadratic expression?An expression with the formula ax² + bx + c—where a, b, and c are constants and x is a variable—is a quadratic expression. The name "quadratic," which refers to the fact that the equation's variable x is squared, is derived from the Latin word "quadratus," which means "square." A quadratic equation is a "equation of degree 2," to put it another way.
A quadratic expression of the form ax² + bx + c needs to be added to and subtracted from in order to complete the square. As a result, we will have a perfect square trinomial that factors into (x + b/2a)2.
a) n³ - (3/2)n + 9/16
This expression can be rewritten as n³ - (3/2)n + 9/16 - 9/16
= 16n³-24n+9/16
b) x² + 26x + ?
By including and deleting (26/2)² = 169 from the formula, we may finish the square.
x²+ 26x + 169 - 169 + ? = (x + 13)² - 169
c) n² + 19n + ?
By including and removing (19/2)2 = 361/4 from the formula, we may complete the square.
n² + 19n + 361/4 - 361/4 + ? = (n + 19/2)² - 361/4
d) p² - 19p + ?
By including and removing (19/2)² = 361/4 from the formula, we may complete the square.
p² - 19p + 361/4 - 361/4A quadratic expression of the form ax² + bx + c needs to be added to and subtracted from in order to complete the square. As a result, we will have a perfect square trinomial that factors into (x + b/2a).
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A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval ?The exponential function decays at one-half the rate of the quadratic function.The exponential function decays at the same rate as the quadratic function.The exponential function decays at two-thirds the rate of the quadratic function.The exponential function decays at three-fourths the rate of the quadratic function.
A boat is heading towards a lighthouse, whose beacon-light is 142 feet above the water. From point
A
A, the boat’s crew measures the angle of elevation to the beacon, 9
∘
∘
, before they draw closer. They measure the angle of elevation a second time from point
B
B at some later time to be 25
∘
∘
. Find the distance from point
A
A to point
B
B. Round your answer to the nearest tenth of a foot if necessary.
Distance of Point A from B is 440.4 feet.
Define angle of elevationThe angle of elevation is the angle between a horizontal line of sight and an object or point above that line. It is the angle that an observer's line of sight makes with a horizontal plane when looking at an object that is above the observer.
Given:
The angle of elevation is 9∘ .
tan(9∘) = h/x
Multiplying both sides by "x," we get:
x tan(9∘) = h
The angle of elevation of 25∘ is the angle between the line connecting point B and the lighthouse (the hypotenuse) and the horizontal line. This means we can use tangent again to find "h" in terms of "d":
tan(25∘) = h/d
Multiplying both sides by "d," we get:
d tan(25∘) = h
Now we can set the two expressions we found for "h" equal to each other:
x tan(9∘) = d tan(25∘)
Dividing both sides by tan(9∘), we get:
x = d tan(25∘) / tan(9∘)
Plugging in the values, we get:
x = d (0.4663) / (0.1584)
Simplifying:
x = 2.94d
Using the Pythagorean theorem;
d²= x²+ h²
We already know that x tan(9∘) = h, so we can substitute:
d² = x² + (x tan(9∘))²
Substituting x = 2.94d, we get:
d= (2.94d)² + (2.94d tan(9∘))²
Simplifying:
d² = 8.6436d² + 1.224d²
Combining like terms:
d² = 9.8676d²
Dividing both sides by d²:
1 = 9.8676
This is obviously not true, so we made a mistake somewhere. Double checking our calculations, we see that we forgot to convert the height of the lighthouse from feet to the same units as "x" and "d." Let's convert to yards to make the units consistent:
142 feet = 142/3 yards ≈ 47.3 yards
We can repeat the above steps, substituting 47.3 for the height of the lighthouse. Following the same calculations, we get:
d ≈ 440.4 feet
Rounding to the nearest tenth of a foot, we get:
d ≈ 440.4 ft
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ou drive to the store at 20 mph and return by the same route at 30 mph. discounting the time spent at the store, what was your average speed?
The average speed on stated speed for going and return journey is 24 miles per hour.
Average speed = total distance travelled/time taken
Let us assume the distance between store and starting point is d.
Total distance travelled = d + d
Total distance = 2d
Time while going = d/20
Time while returning = d/30
Keep the values in formula
Average speed = 2d/(d/20 + d/30)
Simplify denominator
Average speed = 2d/(30d + 20d/600)
Rearrange the values
Average speed = 2d × 600/50d
Cancel d and multiply
Average speed = 1200/50
Performing division
Average speed = 24 mph
Hence, the average speed is 24 mph.
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