The approximate value of the correlation coefficient for the given graph is D. -1.
The correlation coefficient is a statistical measure that indicates the strength and direction of the linear relationship between two variables. A correlation coefficient of -1 indicates a perfect negative linear relationship, meaning that as the value of one variable increases, the value of the other variable decreases at a constant rate. In this case, as the number of years increases, the price of the car decreases, so the correlation coefficient is negative.
According to the NCAA, 3. 9% of female high school basketball players go onto play basketball in the NCAA. Of these players, 0. 9% are drafted into the WNBA. If you randomly select one female high school basketball player, what is the probability she will be drafted by a WNBA team?
The probability that a randomly selected female high school basketball player will be drafted by a WNBA team is 0.000351 or approximately 0.04%.
The probability of a female high school basketball player being drafted into the WNBA can be taken as a combination of two probabilities.
The probability that she will play basketball in the NCAA, which is equal to 3.9%, and the probability that she will be drafted into the WNBA given that she plays in the NCAA, which is equal to 0.9%, are both equal.
The probability can be calculated by using the formula:
P(WNBA draft) = P(NCAA) × P(WNBA draft | NCAA)
Where, P(NCAA) = 3.9 ÷ 100 which is equal to 0.039
and, P(WNBA draft | NCAA) = 0.9 ÷ 100 which is equal to 0.009
Hence, by substituting the values in the equation we get
P(WNBA draft) = 0.039 × 0.009
Which is equal to 0.000351 or approximately 0.04%
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Aliza needs to run at a rate faster than 8.2 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:
He concludes that she is not running fast enough to exceed her fastest time.
What errors did the coach make?
The coach made a mistake in converting the average rate from miles per hour to feet per second. To convert miles per hour to feet per second, the formula is (miles per hour) x (5280 feet/mile) / (60 minutes/hour) = (feet per second).
However, the coach used a different conversion factor, which resulted in an incorrect value. This incorrect value led the coach to conclude that Aliza was not running fast enough, when in reality, the actual rate could be higher than 8.2 feet per second.
Therefore, the coach made an error in the conversion factor used and in the conclusion based on the incorrect converted value.
Find The Area Of The Region Under The Given Curve From 1 To 2. Y = 3 X3 + 4x
The area under the curve y = 3x³ + 4x from x = 1 to x = 2 is 4 square units.
What do you mean by curve?A curve is a continuous, smooth, and often repeating shape in the plane or in space. It is a geometric object that can be described mathematically by an equation or a set of points.
In mathematics, curves are used to model real-world phenomena and to study geometric and mathematical properties. For example, curves can be used to describe the shape of objects, the path of moving objects, or the graph of a mathematical function.
There are many types of curves, including lines, circles, ellipses, parabolas, hyperbolas, and spirals, among others. Each type of curve has unique properties and characteristics, and they are studied and used in different ways in different fields of mathematics and science.
In physics, curves are used to describe the motion of objects and the behavior of physical systems. For example, the trajectory of a projectile can be modeled by a parabolic curve, while the path of a planet around the sun can be modeled by an elliptical curve.
To find the area under the curve y = 3x^3 + 4x from x = 1 to x = 2, we can use the definite integral:
∫[1,2] (3x^3 + 4x) dx
To evaluate this integral, we can use the power rule for integration: ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration.
Using this rule, we get:
∫ (3x³ + 4x) dx = ∫ 3x³ dx + ∫ 4x dx = x^4/4 + 2x² + C
Evaluating this definite integral from x = 1 to x = 2, we get:
[tex][x^{\frac{4}{4}+2x^{2} } ]2-[x^{\frac{4}{4}+2x^{2} } ]1=(2^{\frac{4}{4} }+22^{2} ) -(1^{\frac{4}{4} } +21^{2} )=\frac{21}{4}-\frac{16}{4}=4[/tex]
So the area under the curve y = 3x^3 + 4x from x = 1 to x = 2 is 4 square units.
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In the figure ABCD is a cyclic find the measure of each angles
The angle relations in a cyclic quadrilateral are discussed above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that ABCD is a cyclic quadrilateral.
A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.
Each vertex of the quadrilateral lies on the circumference of the circle and is connected by four chords.
The opposite angles of a cyclic quadrilateral have a total of 180°.
For a cyclic quadrilateral with successive sides a, b, c, d, semi - perimeter s, and angle A between sides a and d, the angle relations for a cyclic quadrilateral as -
Cosine {A} : [tex]${\displaystyle \cos A={\frac {a^{2}-b^{2}-c^{2}+d^{2}}{2(ad+bc)}}}[/tex]Sine (A) : [tex]$\sin A={\frac {2{\sqrt {(s-a)(s-b)(s-c)(s-d)}}}{(ad+bc)}}[/tex]tan (A/2) : [tex]$\tan {\frac {A}{2}}={\sqrt {\frac {(s-a)(s-d)}{(s-b)(s-c)}}}.[/tex]The angle θ between the diagonals that is opposite sides a and c satisfies -[tex]$\tan {\frac {\theta }{2}}={\sqrt {\frac {(s-b)(s-d)}{(s-a)(s-c)}}}.[/tex]
If the extensions of opposite sides a and c intersect at an angle φ, then -[tex]${\displaystyle \cos {\frac {\varphi }{2}}={\sqrt {\frac {(s-b)(s-d)(b+d)^{2}}{(ab+cd)(ad+bc)}}}}[/tex]
Therefore, the angle relations in a cyclic quadrilateral are discussed above.
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Sixty students of a school are randomly selected and asked about their favorite ice cream flavor. Eighteen of the students sampled chose chocolate as their favorite ice cream flavor. How many students are expected to choose chocolate as their favorite ice cream flavor if there are 700 students in the school?
answers:
• 200
• 640
• 21
• 210
There are 640 students are expected to choose chocolate as their favorite ice cream.
How many students are expected to choose chocolate as their favorite ice cream flavor if there are 700 students in the school?
Total number of student =700
no of students are expected to choose chocolate as their favorite ice cream be x
school are randomly selected and asked about their favorite ice cream flavor =60
60+x=700
x=700-60=640
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In how many ways can 8 persons be seated at a round table if 2 particular persons must not sit next to each other?A 40320B 5040C 3600D 720
The total number of arrangements possible if A and B must not sit together:
= 3600
Now, According to the question:
The no. of circular arrangements of n distinct items = (n-1)!
If A,B,C,D,E,F,G and H are the 8 persons to be seated around the table and A,B the 2
particular persons who must not sit together.
The total no.of circular arrangements for 8 persons = (8-1)! = 7! = 5040 --(1)
The no. of circular arrangements possible if A and B were to sit together = 6! (considering A and B as a single pair).
But, A and B can interchange their positions.
Hence, the no. of arrangements =6!×2=720×2=1440−−−−>(2)
So, the total number of arrangements possible if A and B must not sit together, = (1) - (2)
= 5040-1440
= 3600
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Evaluate the integral.I = ∫ √3 9 arctan( 1 x) dx.
the integral value of = ∫ √3 9 arctan( 1 x) dx is: 9 {√3x/6 - π/4 + 1/2 ln 2}
What is integration?Integration in mathematics is a technique for integrating or adding up the parts to get the total. By breaking down the functions into their component pieces, differentiation is carried out in reverse. The summation under a broad scale is found using this approach. The process of combining smaller parts or information from various subsystems into a single operational unit is known as integration. By breaking down the functions into their component pieces, differentiation is carried out in reverse. The summation under a broad scale is found using this approach.
Given that,
= [tex]\int\limits^{\sqrt{3}}_1{9arc\tan(1/x)} \, dx[/tex]
= [tex]9\int\limits^{\sqrt{3}}_1{tan^{-1}(1/x)} \, dx[/tex]
= [tex]9\int\limits^{\sqrt{3}}_1{cot^{-1}(x)} \, dx[/tex]
[As here we use tan⁻¹(1/x) = cot⁻¹x]
We integrate cot⁻¹x by parts by taking cot⁻¹x as I function.
= [tex]9{[cot^{-1}(x)\int\limits\, dx]{^\sqrt{3}} _1 - \int\limits^\sqrt{3}} _1 {d/dx (cot^{-1}x \int\limits\, dx }[/tex]
= 9 {√3x/6 - π/4 + 1/2 ln 2}
Thus, the integral value of = ∫ √3 9 arctan( 1 x) dx is: 9 {√3x/6 - π/4 + 1/2 ln 2}.
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EASY POINTS, WILL GIVE BRAINLIEST TO FIRST ANSWER
Which equation represents the graph?
A. y equals negative one third times x minus 1
B. y = −3x − 1
C. y equals negative one third times x plus one third
D. y equals negative 3 times x plus one third
Answer:
B. y = -3x -1
Step-by-step explanation:
Is this one because of the part of maths that studies the way in which words and the groups they form are combined to express meanings, as well as the relationships that are established between all these units. A set of rules defining the correct sequences of the elements of a programming science and maths formulas.
A' certain state legislature has senators and representatives. The combined number of senators and representatives is 290. The difference of the numbers is 180. There are more representatives than senators.
How many senators and how many representatives are in this state's legislature?
There are 55 senators and 235 representatives are in this state's legislature.
What do you mean by equation?An equation is a mathematical statement that shows the equality of two expressions. Equations can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
For example, the equation 2x + 3 = 7 is an equation that states that the expression on the left side (2x + 3) is equal to the expression on the right side (7). The goal is to find the value of the variable x that satisfies the equation. In this case, x = 2 is a solution to the equation.
Let's call the number of senators in the state legislature "s" and the number of representatives "r". We know the following:
s + r = 290 (the combined number of senators and representatives is 290)
r - s = 180 (the difference of the numbers is 180)
We can use the first equation to solve for one of the variables in terms of the other:
r = 290 - s
Next, we can substitute this expression for r into the second equation:
290 - s - s = 180
Simplifying the left-hand side:
290 - 2s = 180
Adding 2s to both sides:
290 = 180 + 2s
Subtracting 180 from both sides:
110 = 2s
Dividing both sides by 2:
s = 55
So there are 55 senators in the state legislature. To find the number of representatives, we can use the first equation:
r = 290 - s = 290 - 55 = 235
So there are 235 representatives in the state legislature.
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problem 8. (10 pts) for the function find the gradient of at ; find the rate of increase of at the point in the direction ; find the direction of maximum rate of increase at . what is the rate of increase in this direction?
The given function is [tex]f(x,y) = x^2 + y^2[/tex].
To find the gradient of f at the point (x0, y0), we take the partial derivatives of f with respect to x and y:
[tex]$$\nabla f(x0,y0) = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}\right) = \left(2x0, 2y0\right)$$[/tex]
The rate of increase of $f$ at the point (x0, y0) in the direction (u,v) is given by the dot product of the gradient and the direction vector:
[tex]$$\nabla f(x0,y0) \cdot (u,v) = 2x0u + 2y0v$$[/tex]
The direction of maximum rate of increase at (x0, y0) is the direction of the gradient, which is (2x0,2y0). The rate of increase in this direction is the length of the gradient vector, which is given by:
[tex]$$||\nabla f(x0,y0)|| = \sqrt{(2x0)^2 + (2y0)^2} = 2\sqrt{x0^2 + y0^2}$$[/tex]
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Evaluate ∫∫D^y^dA where d is the set of points (x,y) such that 0 ≤ 2x/ π ≤ y, y ≤ sinx.
The value of the double integral is [tex]$-\frac{\pi}{12}$[/tex].
We are given that;
∫∫D^y^dA where d is the set of points (x, y)
0 ≤ 2x/ π ≤ y, y ≤ sin x
Now,
We can see that x varies from 0 to [tex]\pi[/tex], and for each fixed x, y varies from [tex]\frac{2x}{\pi} to \sin x[/tex]. Therefore, we can write the double integral as:
[tex]$$\iint_D y \, dA = \int_0^\pi \int_{\frac{2x}{\pi}}^{\sin x} y \, dy \, dx$$[/tex]
Now we can evaluate the inner integral with respect to y:
[tex]$$\int_{\frac{2x}{\pi}}^{\sin x} y \, dy = \frac{y^2}{2} \bigg|_{\frac{2x}{\pi}}^{\sin x} = \frac{\sin^2 x}{2} - \frac{2x^2}{\pi^2}$$[/tex]
Plugging this result into the outer integral, we get:
[tex]$$\iint_D y \, dA = \int_0^\pi \left( \frac{\sin^2 x}{2} - \frac{2x^2}{\pi^2} \right) dx = \frac{1}{4} \int_0^\pi (1 - \cos 2x) dx - \frac{2}{\pi^2} \int_0^\pi x^2 dx$$[/tex]
Using the antiderivatives of [tex]\cos 2x[/tex] and x^2, we get:
[tex]$$\iint_D y \, dA = \frac{1}{4} (x - \frac{1}{2} \sin 2x) \bigg|_0^\pi - \frac{2}{\pi^2} (\frac{x^3}{3}) \bigg|_0^\pi =\frac{\pi}{4} - 0 - 0 + 0 - \frac{2}{\pi^2} (\frac{\pi^3}{3}) + 0 =\frac{\pi}{4} - \frac{2\pi}{3} =-\frac{\pi}{12}$$[/tex]
Therefore, by integral the answer will be [tex]$-\frac{\pi}{12}$[/tex].
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How To Convert 36.4 °C to °F
The Fahrenheit value is 97.52
How To Convert 36.4 °C to °F?
Normal body temperature ranges from 97.5°F to 98.9°F (36.4°C to 37.2°C). It tends to be lower in the morning and higher in the evening. Most healthcare providers consider a fever to be 100.4°F (38°C) or higher.To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.You probably have a fever if your temperature is 38°C or higher. A normal temperature is around 36-37°C, although it depends on your age, what you've been doing, the time of day and how you take the measurement. A high temperature can be caused by: viral respiratory infections, like colds and flu and COVID-19.To learn more about Fahrenheit refers to:
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Find the slope of a line parallel to the line whose equation is x + 2y = -14. Fully
simplify your answer.
Answer:
So first solve the equation given
X+2y=-14
-x -x
-----------------
2y=-x-14
---- ---------
2 2
y=- 1/2x-7
this would be your parallel line equation because y=-1/2x-7
Parallel lines have the same slope
Perpendicular lines have a negative reciprocal slope (so -2 would be positive 1/2)
Hope this helps!
Please leave a comment if I made a mistake, I will correct it!
How to convert cups to pounds?
To convert cups to pounds, you can use the following conversion factor 1 cup = 0.5 pounds
How to convert cups to pounds?A cup is a unit of volume commonly used in cooking and baking recipes, while a pound is a unit of weight.To convert from cups to pounds, you need to know the density of the substance you are measuring.The conversion factor of 1 cup to 0.5 pounds assumes that you are measuring a substance with a density of 8 ounces per cup. This is a commonly used conversion factor for substances such as sugar, flour, or butter.If you are measuring a different substance with a different density, the conversion factor may be different.To convert from cups to pounds, simply multiply the number of cups by the conversion factor of 0.5.For example, 2 cups of sugar is equal to 2 x 0.5 = 1 pound of sugar.It's important to keep in mind that this conversion is an approximation and may not be completely accurate for all substances.If you need a more precise conversion, it's best to consult a reference or use a conversion calculator.To learn more about cups and pounds refer:
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Which would cause a shift in the supply curve?
The supply curve shifts as a result of every factor but a change in market price. The movement along the supply curve and the change in price are correlated.
What is meant by supply curve?The supply curve can change depending on a number of variables, such as shifts in production costs (such as raw material and labor prices), advancements in technology, the level of competition and the number of sellers/producers, as well as the regulatory and tax environment.
Although a shift in the quantity supplied or along the supply curve for a given commodity or service is frequently brought about by a change in price, the supply curve itself does not alter as a result.
Input prices, weather conditions, technological advancements, as well as governmental taxes, regulations, and subsidies, can all modify the supply curve for goods and services, resulting in a different quantity being delivered for a given price.
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If I paid $625 interest on $5000 that I borrowed at 5%, how many years did I borrow it? *Remember, I = P x R x T help fast
Does anybody know how to do this with the work pls
Answer:
Below
Step-by-step explanation:
See diagram below solve the angles in order 1-2-3-4-5-6
as shown in the diagram:
Answer:
85 degrees
Step-by-step explanation:
Okay, let's have a look at the triangle on the left.
We can see an exterior angle of 115 degrees, adjacent to the interior angle.
Thus, as they both form a line (180 degrees), Interior angle = 180 - 115
= 65 degrees
We know that all the angles of the triangle equal 180.
Now to find the remaining angle of the triangle on the left,
180 - (85 + 65) = 30 degrees
Moving towards the center, we have our interior triangle angle (30 degree), a 90 degree angle and an interior angle of the triangle on the right. So, as they all form a line, the interior angle of the triangle on the right will be
180 - (90 + 30) = 60 degrees
Also, on top of the triangle on the right, we have a 115 degree exterior angle again.
Repeating our first step, the interior angle would be 65 degree
Now to find the remaining angle of the triangle on the right,
180 - (30 + 65) = 95 degrees
This angle forms a line with another angle exterior to this one, so again,
180 - 95 = 85 degrees
Hope this helps
Ahmed ell boxe of pen ($8) and rubber band ($4). Leona ordered a total of 30 carton for $220. How many boxe of pen did Leona order?
By applying the algebra concept, it can be concluded that Leona ordered 25 boxes of pens.
Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.
We have this information:
The price of a box of pens = $8
The price of a box of rubber bands = $4
Total order = 30 boxes
Total payment = $220
Let p symbolize the number of pens and r symbolize the number of rubber bands. Now we have the following equations:
p + r = 30 ....................... (1)
8p + 4r = 220 ............... (2)
To find the value of p and r, we can do it by simplifying the first equation as follows:
p + r = 30
r = 30 - p
Then we can substitute this value into the second equation:
8p + 4r = 220
8p + 4(30 - p) = 220
8p + 120 - 4p = 220
4p = 220 - 120
= 100
p = 100/4
= 25 boxes of pens
So we can calculate the value of r as well:
r = 30 - p
= 30 - 25
= 5 boxes of rubber bands
Thus, it can be concluded that Leona ordered 25 boxes of pens.
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Malachi asks students in his class, “How long does it take you to get to school?” The histogram shows the data. How many students answered Malachi's question?
The number of students that answered Malachi's question is 20 students.
What is the histogram?A histogram is a graphical representation of data that shows the frequency distribution of a set of continuous or discrete data. It is a bar graph that displays the number of data points within specified ranges or bins, allowing for the observation of patterns, trends, and anomalies in the data.
The height of each bar in the histogram represents the frequency of data within the corresponding bin or range, providing a visual representation of the distribution of the data.
In this case, we have that the number of students that answered the question are;
1 + 4 + 10 + 4 + 1 = 20 students
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Answer:
20
Step-by-step explanation:
i got it correcttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Zach’s car travels 21 miles on 1 gallon of gas. Write an equation to represent the relationship between the gas Zach’s car uses and the distance he travels. Then solve the equation to see how far Zach travels on a trip if he uses 16 gallons of gas
The equation to see how far Zach travels is y = 21x and Zach traveled 336 miles using 16 gallons of gas.
What is the equation to see how far Zach travels on a trip?Number of miles traveled Zach's car traveled= 21 miles
Quantity of gallons used = 1 gallon
y = kx
Where,
x = total gallons used
k = unit rate of miles per gallon
y = Number of miles traveled
So,
21 = k × 1
21 = k
y = 21x
Hence,
if he uses 16 gallons of gas
y = kx
y = 21 × 16
y = 336 miles
In conclusion, Zach's car traveled 336 miles.
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don't quite understand. can someone explain pls?
The two column proof showing that m∠AKG = m∠HKB is as below and explained.
How to interpret two column proof?A two-column proof is defined as a geometric proof consists of a list of statements, and the reasons that we know those statements are true.
The two column proof showing the vertical angles are explained below.
Statement 1: Segment GH Intersects Segment AB at K
Reason 1: Given
Statement 2: m∠AKG + m∠GKB = 180°
m∠GKB + m∠HKB = 180°
Reason 2: Definition of supplementary angles
Statement 3: m∠AKG + m∠GKB = m∠GKB + m∠HKB
Reason 3: Substitution property
Statement 4: m∠AKG = m∠HKB
Reason 4: Subtraction property
Now, supplementary angles are defined as angles that sum up to 180 degrees and that is why m∠AKG + m∠GKB = 180° and m∠GKB + m∠HKB = 180°
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The ratio of the circumference of the sun to the earth is given as 109:1. What will be the ratio of the diameter of the earth to the sun?
a. Data insufficient
b. 1:109
c. 40:3
d. 109:1
The Sun's diameter is 864,000 miles. 864,000 x 108 = 93,000,000 kilometers separate the earth from the sun. This is equivalent to 109 times the size of Earth.
What is the Sun's diameter in relation to the Earth's diameter?The Sun's diameter is 1,391,000 kilometers, or 864,400 miles. This is equivalent to 109 times the size of Earth. About 333,000 times as much as Earth's weight is that of the Sun.The diameter of 108 Earths is equivalent to the diameter of the Sun. The Sun's diameter is 864,000 miles. 864,000 x 108 = 93,000,000 kilometers separate the earth from the sun. This is equivalent to 109 times the size of Earth.The Sun's diameter is 864,000 miles. 864,000 x 108 = 93,000,000 kilometers separate the earth from the sun. This is equivalent to 109 times the size of Earth.The Sun's diameter is 1,391,000 kilometers, or 864,400 miles. This is equivalent to 109 times the size of Earth.To learn more about Sun's diameter refer to:
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Option is not mentioned, The ratio of the diameter of the earth to the sun is di = 1.8 × 10-3m.
What is the ratio of the Sun's diameter to that of the Earth's?The Sun is 1,391,000 kilometres (864,400 miles) across. It is the same as Earth being 109 times its size. The Sun's mass is roughly 333,000 times that of the Earth.
The Sun's diameter is equal to the diameter of 108 Earths. The Sun is 864,000 kilometres across. The earth is 93,000,000 kilometres from the sun, or 864,000 times 108 kilometres. It is the same as Earth being 109 times its size.
The Sun is 864,000 kilometres across. The earth is 93,000,000 kilometres from the sun, or 864,000 times 108 kilometres. It is the same as Earth being 109 times its size.
The Sun is 1,391,000 kilometres (864,400 miles) across. This is the same as 109 times the size of Earth. .
The angle of reflection is θ.
D is the distance between the mirror's centre and the sun's centre, where d is the sun's diameter. d/D the equation is equal to 0.009
Angle of incidence = angle of reflection according to the rules of reflection. Consequently, θ2 = θ, = θ, d D The ratio tan θ;=0.009 tan θ =0.009 is another option.
We will assume that because the sun is far away from the mirror, the image will form at the mirror's focus. Therefore, distance OB = f, where f is the concave mirror's focal length
The focal length of a spherical concave mirror is equal to half of its radius of curvature. Given that the radius of the curveturer is 0.4 m, f= 42 = 0.4 m 2 = 0.2 m.
Taking into account the image's diameter as d2, tan 0, di f tan 0 di 0.2 = Taking the value of tan from above, 0.009 di 0.2 = di 0.009 x 0.2 = As a result, the image's diameter is d; = 0.0018m di = 1.8 × 10-3m.
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what is the slope indicated in the table below
Answer:
Step-by-step explanation:
Take any two pairs of coordinates to find the slope.
The forumla for slope is (y2-y1)/(x2-x1)
Wil will choose the points (2,10) and (4,20)
Therefore:
m = (20-10)/(4-2)
m = 5
you can determine if the inverse of a polynomial function is a function by using the ____ line test on the inverse.
You can determine if the inverse of a polynomial function is a function by using the Horizontal Line Test on the inverse.
The Horizontal Line Test is a graphical method that can be used to determine whether a given function is one-to-one, meaning that for each output value, there is at most one input value that maps to it.
If the inverse of a polynomial function is a function, it must pass the Horizontal Line Test, meaning that no horizontal line intersects the graph of the inverse more than once.
In other words, if the inverse of a polynomial function passes the Horizontal Line Test, it is guaranteed to have an inverse, which will be a function itself. If the Horizontal Line Test fails, then the inverse is not a function and does not have an inverse.
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write an equation that represents the kims and her sisters age combined, where k represents kims age, and x represents her sisters age
An equation that represents the Kim's and her sister's age combined is,
x + k = n.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Let k represents Kim's age, and x represents her sister's age.
Let the combined age is n.
Then,
an equation that represents the Kim's and her sister's age combined is,
x + k = n.
Therefore, the equation is x + k = n.
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What is 0.03 divided by 18? Step by step
a rectangle is formed by placing two identical squares side by side the perimeter of each square is 24 cm what is the area of the entire rectangle
The area of the rectangle is 72 cm^2.
How to determine the area of the rectangleLet's call the side length of each square s.
Since the perimeter of each square is 24 cm, then each side measures 24 cm / 4 = 6 cm.
So the length of the rectangle is 2s = 2 * 6 cm = 12 cm.
And the width of the rectangle is s = 6 cm.
Therefore, the area of the rectangle is A = l * w = 12 cm * 6 cm = 72 cm^2.
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The area of the rectangle is 72 square centimeters.
How to find the area of the rectangle?The rectangle is formed by placing two identical squares side by side the perimeter of each square is 24 cm.
Remember that for a square of sidelength S, the perimeter is P = 4*S
Then the sidelength of the squares is
24cm = 4*S
24cm/4 = 6cm = S
When we place these two squares together, we will have a rectangle of 6cm by 12cm, and the area is the product of the dimensions, then the area is:
A = 6cm*12cm = 72cm²
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Suppose x and y are inversely proportional.
(A) If x^p and y^q are also inversely proportional, then how must p and q be related?
(B) If x^p and y^q are directly proportional, then how must p and q be related?
We can see that p-q = 1, which implies that p and q are directly related.
(a) If x and y are inversely prοpοrtiοnal, then we knοw that xy = k fοr sοme cοnstant k.
If [tex]x^p[/tex] and [tex]y^q[/tex] are alsο inversely prοpοrtiοnal, then we can write [tex](x^p)(y^q) = k'[/tex] fοr sοme cοnstant k'. Using the inverse prοpοrtiοnality relatiοn, we get:
[tex](x^p)(y^q) = k'[/tex]
[tex](xy)^pq = k'[/tex]
[tex](k)^pq = k'[/tex]
[tex]k^(pq-1) = k'[/tex]
Frοm this equatiοn, we can see that pq-1 = 0, which implies that pq = 1. Therefοre, p and q are inversely related.
(b) If x and y are inversely prοpοrtiοnal, then we knοw that xy = k fοr sοme cοnstant k.
If [tex]x^p[/tex] and [tex]y^q[/tex] are directly prοpοrtiοnal, then we can write [tex](x^p) = k'(y^q)[/tex] fοr sοme cοnstant k'. Using the direct prοpοrtiοnality relatiοn, we get:
[tex](x^p) = k'(y^q)[/tex]
[tex](xy)^p = k'(y^q)(k)[/tex]
[tex]k^p = k'(y^{(q-1)})[/tex]
[tex]k^{(p-q)} = k'[/tex]
Frοm this equatiοn, we can see that p-q = 1, which implies that p and q are directly related.
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I NEED HELP ASAP!! (20 PTS)
An 8-pack of granola bars costs $7.04. What is the unit price?
Answer:
Step-by-step explanation: just / the $7.04 by 8 since there is 8 bars then boom
Select the correct answer from each drop-down menu. Use the system of equations and graphs below to complete the sentence. Set of 4 graphs are represented. Graph A shows two lines plotted on a coordinate plane. A line goes through (minus 1, 0) and (2, minus 1). Another line goes through (4, minus 2) and (minus 3, minus 3). The graph that correctly represents the given system of equations is graph , and the solution to the system is ( , ). Reset Next
The two equations are y = - 1 and y = (1/5)x - 12/5 and the solution to the system is (7, - 1).
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The first line passes through (- 1, 0) and (2, - 1).
Slope(m) = (- 1 + 1)/(2 - 0).
Slope(m) = 0.
- 1 = 0(2) + b.
b = - 1.
y = - 1.
A horizontal line at y = - 1.
The second line passes through (4, - 2) and (- 3, - 3).
Slope(m) = (- 3 + 2)/(- 3 - 4).
Slope(m) = - 1/- 5.
Slope(m) = 1/5.
- 3 = (1/5)(- 3) + b.
b = 3/5 - 3.
b = (3 - 15)/5.
b = - 12/5.
y = (1/5)x - 12/5.
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