The chord of the sphere is represented by OT.
The geometrical equivalent of a two-dimensional circle in three dimensions is a sphere. The collection of points in three-dimensional space that are all located at the same r distance from one another is known as a sphere.
The line segment connecting any two locations on a circle's circumference is referred to as the chord of the sphere. It should be emphasized that the diameter is the circle's longest chord, which runs through its center.
So, if L, M, and N lie on the surface of a sphere with its center at point O. Point T lies in the interior of the sphere, then OT would connect two points on the circumference of the sphere.
Hence, the chord of the sphere is represented by OT.
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The graph shows a two-dimensional side view of a
satellite dish and the small reflector inside it. The vertex
of the small reflector is 6 in. from focus F₁ and 20 in. from
focus F2. What equation best models the small reflector?
Picture of graph attached !!! please help
The equation is -7x+y=0.
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
Hence, The equation is -7x+y=0.
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An object is dropped from a small plane. As the object falls, its distance, d, above the ground after t seconds, is
given by the formula d = -16² +1,000. Which inequality can be used to find the interval of time taken by the object
to reach the height greater than 300 feet above the ground?
-16² +1,000 <300
-16² +1,000 ≤300
-16² +1,000 ≥ 300
-16f²+1,000 > 300
Answer:
-16²+1,000 > 300 [After an edit in the original expression, as noted below).
Step-by-step explanation:
The equation d = -16² +1,000 tells us the height above ground, d, of the object after t seconds. When t = 0 seconds, the ball has not been dropped yet, but the equation tells us that d = 1,000 at t = 0. That means the object starts at 1,000 feet above ground.
We want the time it takes for the object to reach any height greater than 300 feet above ground. This is a tad (metric for just a tiny bit) unexpected, since even at time of 0 the object is greater than 1,000 feet.
Looking at the answer options, note that the left side of the inequalities is -16^2+100. I will assume the 4th option has a typo: the f^2. It should read the same as the others.
-16^2+100 is the distance, d. So to help us think this through, let's rephrase the answer options in terms of distance, d:
1) d<300
2) d≤300
3) d≥300
4) d>300
The question asks "We want the time it takes for the object to reach any height greater than 300 feet above ground."
Option 4 says d>300, or height greater than 300. That is the inequality that matches the question. [Note: It did not say greater than or equal to (option 3).]
Please help me! A sector has a central angle measure of 90 degrees, and a radius of 8 cm. Which equation shows the correct calculation of the area of the sector?
Therefore , the solution of the given problem of area comes out to be
A = 16 is the equation that accurately depicts how to calculate the sector's area.
What is an area ?Its total size can be determined by figuring out how much space is required to completely cover the outside. The immediate surroundings are taken into consideration when calculating the surface of a trapezoidal shape. The total measurements of something are determined by its surface area. A cuboid's capacity for internal water is determined by the sum of the borders that link all of it's six rectangle edges.
Here,
The formula for calculating a circle's sector's area is:
=> A = (θ/360) x πr²
where A is the sector's area, is its central angle measurement, and r is the circle's radius.
Since the radius is 8 cm and the central angle is 90 degrees in this instance, we can reduce by plugging in these values:
=> A = (90/360) x π(8²)
=> A = (1/4) x π(64)
=> A = π(16)
=> A = 16π
A = 16 is the equation that accurately depicts how to calculate the sector's area.
The answer will be given in radius squared units, in this case, cm2.
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Option D. The correct calculation of the area of the sector is [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]
What is an area of the sector?An area of the sector is the portion of the area of a circle that is enclosed by two radii and an arc. The area of a sector can be found using the formula:
A = (θ/360)πr²
where A is the area of the sector, θ is the central angle of the sector (in degrees), π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
Given, the radius is 8 cm and the central angle is 90° in this instance, put all these values:
[tex]A=(\frac{90}{360}) * \pi (8^{2} )[/tex]
or we can write down, [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]
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The radius of circle B
is 4 centimeters and the circumference of
Circle A is 30 pi
centimeters. Find CD.
Find CD:
Let,
[tex]r_1[/tex] be a radius of Circle A
[tex]r_2[/tex] be a radius of Circle B
Given:
[tex]r=4cm.[/tex]
Circumference: [tex]2\pi r[/tex]
[tex]2\pi r_1=30[/tex]
[tex]r_1=\dfrac{15}{\pi }[/tex]
[tex]CD=D_1+D_2[/tex]
[tex]=2r_1+2rx_2[/tex]
[tex]=2\times(\dfrac{15}{\pi })+2\times4[/tex]
[tex]CD=17.55cm.[/tex]
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
plot the point at 1
Step-by-step explanation:
what is value expression
1.3(X + 2)-(y - 6)
when X= 4 and Y= 2
a 1.1
b 11.8
c 2.6
d 26
The value of the expression 1.3(x + 2) - (y - 6) when x = 4 and y = 2 is Option B: 11.8.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
To find the value of the expression 1.3(x + 2) - (y - 6) when x = 4 and y = 2, we substitute these values into the expression and simplify -
Substitute the values x = 4 and y = 2 into the expression -
1.3(x + 2) - (y - 6)
= 1.3(4 + 2) - (2 - 6)
Apply the addition and subtraction operation -
= 1.3(6) - (-4)
Apply the multiplication operation -
= 7.8 + 4
= 11.8
Therefore, the value of the expression is 11.8.
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Mr Keag's swimming pool is 15 feet long, 12 feet wide and 10 feet deep. How much water would it take to fill it half way to the top
Answer:
900 cubic feet
Step-by-step explanation:
[tex] \frac{1}{2} (15 \times 12 \times 10) = \frac{1}{2} (1800) = 900[/tex]
The 1989 U. S. Open golf tournament was played on the East Course of the Oak Hills Country Club in Rochester, New York. During the second round, four golfers scored a hole in one on the par 3 sixth hole. The odds of a professional golfer making a hole in one are estimated to be 3,708 to 1, so the probability is 1/3,709. There were 175 golfers participating in the second round that day. A. What is the probability that no one gets a hole in one on the sixth hole
The probability that no one gets a hole on the sixth hole is given as follows:
0.9534 = 95.34%.
What is the binomial distribution formula?The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
The mass probability formula is given as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are listed as follows:
n is the number of trials of the experiment.p is the probability of a success on a single independent trial of the experiment.The parameter values for this problem are given as follows:
n = 175 -> number of golfers.p = 1/3709.The holes are independent, hence the probability of no one getting a hole in the sixth hole is P(X = 0), thus:
P(X = 0) = (1 - 1/3709)^175
P(X = 0) = 0.9534 = 95.34%.
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A population has a standard deviation of sigma = 24. a. On average, how much difference should exist between the population mean and the sample mean for n = 4 scores randomly selected from the population? b. On average, how much difference should exist for a sample of n = 9 scores? c. On average, how much difference should exist for a sample of n = 16 scores?
Therefore , the solution of the given problem of standard deviation comes out to be he average difference between the population mean and the sample mean is 6.
What is standard deviation?Variance is a measure of variation used in statistics. The average difference between the gathering and the mean is calculated using the photo of that figure. By comparing each number to the mean, it incorporates those data points into the calculations on their own, in contrast to many other legitimate measures of variable. Variations could result from deliberate errors, unrealistic expectations, or changing economic or commercial circumstances.
Here,
For a group of n = 4, the standard error of the mean (SEM) is as follows:
=> SEM = α/√(n)
=> 24/√(4) = 12
Therefore, for n = 4 scores drawn at random from the population, the average difference between the population mean and the sample mean is 12.
b. The SEM for a group of n = 9 is:
=> α/√(n) = 24/√(9)
=> 8; SEM = α
Therefore, for n = 9 scores drawn at random from the population, the average difference between the population mean and the sample mean is 8.
c. The SEM for a sample of 16 is as follows:
=> α / √(n) = 24 / √(16) = 6;
=> SEM =α
Therefore, for n = 16 scores drawn at random from the population, the average difference between the population mean and the sample mean is 6.
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An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $4500 and her stock in Company B was worth $3900. The stock in Company A has increased 5% since last year and the stock in Company B has increased 11%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
The total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.
To calculate the total percentage increase in the investor's stock account, we first need to calculate the new values of the stocks in Company A and Company B after the increase.
The new value of the stock in Company A is:
[tex]4500 + (5 \times 4500) = $4725[/tex]
The new value of the stock in Company B is:
[tex]3900 + (11 \times 3900) = 4339[/tex]
The total value of the investor's stock account after the increase is:
$4725 + $4339 = $9064
To calculate the percentage increase in the investor's stock account, we need to find the difference between the new total value and the original total value, and then divide that difference by the original total value:
($9064 - $8400) / $8400 = 0.0795
We then multiply this decimal by 100 to get the percentage increase:
0.0795 x 100 = 7.95%
Therefore, the total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).
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The mass of a sheet of metal varies jointly with it's area and it's thickness. A sheet of metal of area 250cm and thickness 1mm has a mass of 200g
The mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.
The mass of a sheet of metal is directly related to its area and thickness. This means that the mass of a sheet of metal is proportional to the product of its area and its thickness. Mathematically, this can be expressed as the formula M = kAT, where M is the mass, k is a constant, A is the area and T is the thickness.In the given example of a sheet of metal with an area of 250 cm and a thickness of 1mm, we can calculate the mass of the sheet by substituting the given values into the formula: M = k(250)(1) = 200g. The constant k in this example is equal to 0.8 g/cm*mm.Therefore, the mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.
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What is the mass of a sheet of metal with an area of 250cm and a thickness of 1mm?
A catapult launches a pumpkin from the base of a hill. The hill follows an incline with the
height in meters, y, in terms of horizontal distance in meters, x, given by the equation
y=0. 9x. The height of the pumpkin, as it is launched uphill, is given by the function
y = -0. 1x² +4. 9x
What is the height, in meters, where the pumpkin lands on the hill?
The height, in meters, where the pumpkin lands on the hill is 4.9 meters.The equation for the height of the hill is y = 0.9x.
This equation can be rearranged to solve for x, giving x = y/0.9. The equation for the height of the pumpkin is y = -0.1x² + 4.9x. Substituting the x value from the previous equation into the equation for the height of the pumpkin gives y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying this equation gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill.
The equation for the height of the hill is y = 0.9x, which describes the incline of the hill. This equation can be rearranged to solve for x, giving x = y/0.9. This equation can then be used to substitute into the equation for the height of the pumpkin, which is y = -0.1x² + 4.9x. When the x value from the previous equation is substituted into the equation for the height of the pumpkin, the equation simplifies to y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying further gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill. This can be verified by substituting 4.9 for y in the equation for the height of the hill, which gives x = 4.9/0.9 = 5.4. This value can be substituted into the equation for the height of the pumpkin, which gives y = -0.1(5.4)² + 4.9(5.4) = 4.9, verifying the result.
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A screen door spring has a spring constant of 188 N/m, and stretches 0. 292 m when the door is opened. What force does it exert?
(Unit = N)
If the screen door spring has a spring constant of 188 N/m, then the force it exert is 54.9 N .
The force exerted by the screen door spring can be calculated using Hooke's law,
The Hooke's Law states that the force exerted by a spring is directly proportional to its spring constant and the amount it is stretched.
The formula for "Hooke's-law" is ⇒ F = kx
Where F is = force exerted by spring, k is = spring constant, and x is = amount spring is stretched.
In this case , the spring constant(k) = 188 , the distance stretched(x) = 292m ;
Substituting the values,
We get,
⇒ F = (188 N/m)(0.292 m)
⇒ F = 54.896 N
⇒ F ≈ 54.9N
Therefore, The force exerted by the screen door spring is approximately 54.9 N.
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please show work!!!!!!!
Answer:
J. 56
Step-by-step explanation:
The picture in this question can be a little deceiving. Each rectangular glass pane is 3 by 10 inches. This means that the picture of the 4 panes overlapping, leaves the center square open. The open area has your inner edges. The question asks for the sum of the inner and outer edges.
Every pane is 10 inches long, so the out perimeter of the figure is 40 inches because the figure has four sides. The rectangles overlap, creating 3 by 3 inch square. 3 inches off either side of a pane leaves 4 inches as the length for the edge of the inner square. Therefore, the perimeter of the inner square is 16 inches.
Outer Perimeter + Inner Perimeter = 40 + 16 = 56 inches
A bookstore sells 7 books for $89.25. Which table represents the relationship between number of books and the total price?
Answer: C is our answer.
The first thing that we can do is divide the known number of books into the price that they sold for.
Our equation would be 89.25 divided by 7, which is 12.75. This means that one single book is 12.75. We can look at the charts and point out where one book is 12.75, that is both A and D. While Chart B and C have 7 books for 89.25 which we know is correct.
Lets look at chart D.The next part we can solve is the price of 2 books. 12.75 x 2 is 25.50, so we can mark question B incorrect since two books are 25.50 not 13.75.Chart B is incorrect because 14 books is double 7, so it should be twice as much as 89.25, which we should know 90 dollars is not two times as much 80. Chart A is incorrect because 11 x 12.75 is 140.25, while the chart reads as 22.75.
Now lets look at chart C. Next we can solve the price of 8 books. 8 x 12.75 is 102. Then we solve for 9 books. 12.75 x 9 is 114.75, which means that C is correct.
I hope this helped & Good Luck <3!!
A bakery sells apple pies for $12.85. if the pie has a diameter of 10 inches, what is the approximate cost per square inch of the apple pie? round to the nearest hundredth. a. $0.04 b. $0.16 c. $0.32 d. $0.65
The cost per square inch of the apple pie is $ 0.16.
Given that,
The diameter of the pie = 10 in
The radius of the pie = 10/2
= 5 inches.
Area of the pie = [tex]\pi r^{2}[/tex]
= 3.14 × 5²
= 3.14 × 25
= 78.5 in²
The cost of the apple pie = $ 12.85.
Therefore, the cost per square inch of the pie = 12.85 ÷ 78.5
= $ 0.16.
Hence, the cost per square inch of the apple pie is $ 0.16.
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write an equation in slope-intercept form of the line that passes through the given points
[tex]\left[\begin{array}{ccc}x&y\\-4&9\\-2&4\\0&-1\\2&-6\end{array}\right][/tex]
Answer:
y = - [tex]\frac{5}{2}[/tex] x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 9) and (x₂, y₂ ) = (2, - 6) ← 2 ordered pairs from the table
m = [tex]\frac{-6-9}{2-(-4)}[/tex] = [tex]\frac{-15}{2+4}[/tex] = [tex]\frac{-15}{6}[/tex] = - [tex]\frac{5}{2}[/tex]
the line crosses the y- axis at point (0, - 1 ), ordered pair from table, then
c = - 1
y = - [tex]\frac{5}{2}[/tex] x - 1 ← equation of line
I need help on this!
Answer:
He is now selling only one product and making less money because he is not selling other TVs.
Step-by-step explanation:
So if you read the paragraph, you get to the point where he says only making and selling the television model that makes the most money. If you think about it if they only sell one product, the other products they used to sell aren't being sold and they are making less money. I hope this helps!
The diameter of a circle is 17 ft. Find its area to the nearest whole number.
Answer:
[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the area of a circle.}[/tex]
[tex]\textsf{First, we should identify the formula for the area of a circle.}[/tex]
[tex]\large\underline{\textsf{Formula:}}[/tex]
[tex]\mathtt{Area = \pi (radius)^{2}}[/tex]
[tex]\textsf{The radius is \underline{half} of the diameter.}[/tex]
[tex]\mathtt{\frac{17}{2} = 8.5ft.}[/tex]
[tex]\textsf{Let's begin solving for the area.}[/tex]
[tex]\large\underline{\textsf{Substitute:}}[/tex]
[tex]\mathtt{Area = \pi (8.5)^{2}}[/tex]
[tex]\mathtt{Area = 72.25 \pi}[/tex]
[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]
A. What is the magnitude of an earthquake with amplitude 100,000? How
do you know?
The magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale
What do you mean by Magnitude and amplitude in term of Earthquake ?Magnitude: The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. It is typically determined using a logarithmic scale called the Richter scale or other similar scales like the moment magnitude scale (MMS), surface wave magnitude (Ms), or body wave magnitude (Mb). The Richter scale is based on the amplitude of the largest seismic wave recorded on a seismographs, and each increase of one unit on the scale corresponds to a ten-fold increase in the amplitude of the seismic waves and a 32-fold increase in the amount of energy released.
Amplitude: The amplitude of an earthquake is the size of the seismic waves that are generated by the earthquake. It is measured in microns (millionths of a meter) and is recorded on a seismographs. The amplitude of seismic waves can vary greatly depending on the distance from the earthquake's epicenter and the geological structure of the surrounding area.
The magnitude of an earthquake is a measure of the amount of energy released during the earthquake, and is typically determined using a logarithmic scale called the Richter scale.
The formula for calculating the magnitude of an earthquake based on its amplitude is:
Magnitude = log10 (Amplitude) - 3
where the amplitude is measured in microns.
Assuming the amplitude of the earthquake is 100,000 microns, we can calculate its magnitude as:
Magnitude = log10 (100,000) - 3
Magnitude = 5 - 3
Magnitude = 2
Therefore, the magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale.
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A grocer has two kinds of candy, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
Answer:The quantity of grocer of price $1.40 is 45 pounds
The quantity of grocer of price 40 cents is 55 pounds
Step-by-step explanation:
Let The quantity of one grocer = x pound
Let The quantity of other grocer = y pound
The selling price of x grocer = 40 cents per pound
The selling price of y grocer = $ 1.40 per pound = 1.40 × 100 = 140 cents
Total quantity = 100 pounds
Total price of both grocer = 85 cents
According to question
x + y = 100 .........A
And
40 × x + 140 y = 85 × 100
Or, 40 x + 140 y = 8500 ........B
Solving eq A and eq b
(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100
Or, (40 x - 40 x) + (140 y - 40 y) = 8500 - 4000
or, 0 + 100 y = 4500
∴ y =
i.e y = 45 pounds
So, The quantity of grocer of price $1.40 = y = 45 pounds
Again
Put the vaue of y in eq A
x + y = 100
i.e x = 100 - y
or, x = 100 - 45
∴ x = 55 pounds
So, The quantity of grocer of price 40 cents = x = 55 pounds
Hence, The quantity of grocer of price $1.40 is 45 pounds
And The quantity of grocer of price 40 cents is 55 pounds Answer
When asked to draw a quadrilateral with all four sides measuring 5 cm, Jada drew a square.
5 cm
15 cm
5 cm
1. Do you agree with Jada's answer?
2. Is there a different shape Jada could have drawn that would answer the question? Explain your
reasoning
Absolutely, Jada's response is right. A square is a quadrilateral with four equal-length sides. A quadrilateral is a square if all four sides measure 5 cm.
Unfortunately, there is no alternative form Jada could have drawn that meets the requirement of all four sides measuring 5 cm. Every other quadrilateral with four equal-length sides is likewise a square. If Jada had drawn a quadrilateral with one or more sides of varying lengths, the specified criterion would not have been met. As a result, the only design Jada could have sketched that meets the requirement of having all four sides measure 5 cm is a square. It is worthwhile to investigate the properties of quadrilaterals and how they connect to the conditions presented in the problem. A quadrilateral is a four-sided polygon. Quadrilaterals come in a variety of shapes, including squares, rectangles, parallelograms, trapezoids, and kites. Certain quadrilaterals have unique qualities, such as opposing sides that are parallel or all angles that are right angles. The criterion in the provided problem is that all four sides of the quadrilateral measure 5 cm.
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An iPhone costs £800 in London, €880 in Paris and $850 in New York. Using £1 = €1.16 and £1 = $1.41, state the lowest price of the iPhone in £. Give your answer to 2 dp.
Answer:
£602.84 in New York
Step-by-step explanation:
London Cost:
Converting pound to dollars:
£800 * 1.41 = $1128
Paris cost:
Converting euro to pounds:
€880/1.16 = £759
Converting pound to dollars again:
£759 * 1.41 = $1070
New york cost:
$850
The lowest price is in new york which is:
$850/1.41 = £602.84
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Cumulative distribution function for a continuous random variable x
The cumulative distribution function gives us the probability that the random variable is less than or equal to a given value.
The cumulative distribution function (CDF) of a continuous random variable x is a function which gives the probability that the random variable x is less than or equal to a given value x. Mathematically it is expressed as:
[tex]F(x) = P(X ≤ x)[/tex]
The calculation of the cumulative distribution function is done by integrating the probability density function (PDF) from the lower limit to the given value x. Thus,
[tex]F(x) = ∫-∞ x f(u) du[/tex]
Where f(u) is the probability density function.
For example, if we have a continuous random variable x with probability density function f(x) = x2, then the cumulative distribution function [tex]F(x) = ∫-∞ x x2 du = 1/3x3 + c.[/tex]
Thus, It is a powerful tool for analysing the probability distribution of a continuous random variable.
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Complete question:
What is the cumulative distribution function for a continuous random variable x?
what is the result of substituting for y in the bottom equation?
Answer:
A. y=(x-3)^2+2(x-3)-4
B. x-3=x^2+2x-4
C. y=x^2+2x-4-(x-3)
D. (x-3)=x^2
Optiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 =x² + 2x - 4.
What is the equivalent expression?Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.
Tο substitute fοr y in the secοnd equatiοn, we can replace y with its equivalent expressiοn in terms οf x frοm the first equatiοn, which gives us:
x - 3 = x² + 2x - 4
This is option B.
Optiοn A is incοrrect because it substitutes y fοr its expressiοn in terms οf x in the wrοng equatiοn.
Optiοn C is incοrrect because it subtracts (x-3) instead οf adding it tο the secοnd equatiοn.
Optiοn D is incοrrect because it sets the expressiοn fοr y in the first equatiοn equal tο x² instead οf the expressiοn fοr y in the secοnd equatiοn.
Hence, οptiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 = x² + 2x - 4.
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Complete question:
What is result of substituting for y in the bottom equation?
y = x – 3,
y = x² + 2x – 4
A. y=(x-3)²+2(x-3)-4
B. x-3=x²+2x-4
C. y=x²+2x-4-(x-3)
D. (x-3)=x²
What is the equation of the graph below?
On a coordinate plane, a curve crosses the y-axis at (0, negative 1). It has a minimum of negative 1 and a maximum of 1. It goes through 1 cycle at 2 pi.
y = cosine (x + StartFraction pi Over 2 EndFraction)
y = cosine (x + 2 pi)
y = cosine (x + StartFraction pi Over 3 EndFraction)
y = cosine (x + pi)
The equation of the given graph is: y = cosine (x + pi)
Equation of cosine graphsBy convention, the cosine function like most other trigonometric functions has a period of 2π.
Since, the parental function is y = cos x, which has y-intercept at y = 1, and x-intercept at π/2.
From observation, the function showed in the graph attached has y-intercept at y = -1 and x-intercept at π/2.
This can be interpreted to mean that the function has been translated leftwards π units.
Ultimately, the function that belongs to this graph is; y = cosine (x + pi)
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Answer: D. y = cosine (x + pi)
Step-by-step explanation:
How long is the base of a parallelogram if it has an area of 60 square feet and a height of 10 feet? 6 feet 50 feet 60 feet
Answer:6 feet
Step-by-step explanation:
The formula for the area of a parallelogram is:
Area = base x height
We know that the area is 60 square feet and the height is 10 feet, so we can plug these values into the formula and solve for the base:
60 square feet = base x 10 feet
Dividing both sides by 10 feet gives:
6 feet = base
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Triangle PQR with coordinates P(-3,4). Q(-6,1), and R(-6,6) is reflected over the x-axis. List the coordinates of the new image
Answer:
P(0,2), Q(3,5), R(3,0)
Step-by-step explanation:
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The intensity of sound from the stands of a football game is 30 times as great when the home team scores a touchdown as it is when the away team scores. Find the difference in the loudness of the sound when the two teams score. Round your answer to the nearest hundredth.
The difference in the loudness of sound is about _______ decibels
The difference in the loudness of sound when the two teams score is about 14.77 decibels
What is sound intensity ?Sound intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.
We can use the fact that the loudness of sound is measured in decibels (dB) and that the dB scale is logarithmic.
Let's assume that the loudness of the sound when the away team scores is x decibels. Then the loudness of the sound when the home team scores a touchdown is 30 times as great, which means it is 30x decibels.
The difference in loudness between the two scenarios is given by the difference in decibels:
difference in decibels = 10 log (30x/x) = 10 log 30 = 14.77
Therefore, the difference in the loudness of sound when the two teams score is about 14.77 decibels
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A cylindrical soup can is 6 cm in diameter and 12 cm tall.
A. If the diameter is 6 cm, what is the radius?
B. We use the formula to find the surface area of a cylinder (with r = radius & h = height).
C. Plug your "r", "h", and " 3.14 for n" into the formula.
Show your work and label your final answer to find the surface area of the soup can.
Please only help me if your going to help
Answer:
A. If the diameter is 6 cm, then the radius is half of that:
radius = 6 cm / 2 = 3 cm
B. The formula for the surface area of a cylinder is:
S.A. = 2πr^2 + 2πrh
C. Plugging in the values for r, h, and π:
S.A. = 2π(3 cm)^2 + 2π(3 cm)(12 cm)
S.A. = 2π(9 cm^2) + 2π(36 cm^2)
S.A. = 18π cm^2 + 72π cm^2
S.A. = 90π cm^2
Therefore, the surface area of the soup can is 90π square centimeters. This can be simplified to approximately 282.74 square centimeters by using the value 3.14 for π.