Answers
Answer:
[tex]\sin A=\frac{a}{b}[/tex]
[tex]\cos A=\frac{c}{b}[/tex]
[tex]\tan A=\frac{a}{c}[/tex]
[tex]\csc A=\frac{b}{a}[/tex]
[tex]\sec A=\frac{b}{c}[/tex]
[tex]\cot A=\frac{c}{a}[/tex]
Step-by-step explanation:
Here are the definitions of the trig functions listed in the picture
[tex]\sin x=\frac{O}{H}[/tex]
[tex]\cos x=\frac{A}{H}[/tex]
[tex]\tan x=\frac{O}{A}[/tex]
[tex]\csc x=\frac{H}{O}[/tex]
[tex]\sec x=\frac{H}{A}[/tex]
[tex]\cot x=\frac{A}{O}[/tex]
Note:
[tex]A[/tex] = side adjacent to angle
[tex]O[/tex] = side opposite to angle
[tex]H[/tex] = hypotenuse
All 6 questions are about angle A.
The side adjacent to angle A is side c.
The side opposite to angle A is side a.
The hypotenuse is side b.
Therefore we can write
[tex]A=c\\O=a\\H=b[/tex]
Knowing that we can fill out the table.
[tex]\sin A=\frac{a}{b}[/tex]
[tex]\cos A=\frac{c}{b}[/tex]
[tex]\tan A=\frac{a}{c}[/tex]
[tex]\csc A=\frac{b}{a}[/tex]
[tex]\sec A=\frac{b}{c}[/tex]
[tex]\cot A=\frac{c}{a}[/tex]
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Related Questions
The image of a trapezoid is shown.
An isosceles trapezoid with a short base of 3 meters and a height of 5 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.
What is the area of the trapezoid?
70 m2
38 m2
35 m2
19 m2
Answers
Answer: 35m2
Step-by-step explanation:took the test and i got it right
An isosceles trapezoid with a short base of 3 meters and a height of 5 meters then the area of the trapezoid is 35 m²
What is the area of the trapezoid?
To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
We can start by finding the length of the long base. Since the trapezoid is isosceles, we know that the length of the portion of the large base from the left vertex to the perpendicular is equal to the length of the portion from the right vertex to the perpendicular. Let's call the length of the long base "x":
x = 4 + 7 = 11 meters
Now we can use the formula for the area of a trapezoid:
Area = (1/2) * (short base + long base) * height
Substituting the values we have:
Area = (1/2) * (3 + 11) * 5
Area = 7 * 5
Area = 35 m²
Therefore, the area of the trapezoid is 35 m².
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Using the picture below, which trig function can be used to find the length of x?
Answers
The length of the base is approximately 8.71 units.
What is triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
Let's call the two legs of the right triangle a and b, and the hypotenuse c. The hypotenuse is the side opposite the right angle, so in this case, we have c = 29. We also know that one of the acute angles is 71 degrees.
Using trigonometry, we can use the tangent function to find the length of the base:
tan(71) = a/b
We can solve for b by multiplying both sides by b:
b tan(71) = a
Now we can substitute c = 29 and solve for b:
b = c / tan(71)
b = 29 / tan(71)
b ≈ 8.71
Hence, The length of the base is approximately 8.71 units.
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Write the equation of the line that passes through the points (4, -3) and (8,5). Put
your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.
Answers
An equation of the line that passes through the points (4, -3) and (8,5) is y + 3 = 2(x - 4).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data points (4, -3), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-3) = (5 - (-3))/(8 - 4)(x - 4)
y + 3 = 8/4(x - 4)
y + 3 = 2(x - 4)
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sketch a graph for days 0-9
Answers
According to the information in the table, the graph would look like the one in the attached image.
How to graph the information in the table?To graph the information in the table we must carefully observe the information. In this case, the relationship is decreasing because the number of infected is decreasing as time increases. In accordance with the above, the curve that shows this relationship is a decreasing curve.
In this case, we must locate the time on the x axis and the infected on the y axis and mark a point in the areas where the data coincide. Later we must graph a line that joins the points and our graph would be finished.
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HELP ASAP!!
Simplify the expression.
the expression negative one fifth j plus three fourths minus the expression five halves j plus seven eighths
Answers
The simplified expression is given as follows:
-27j/10 - 1/8.
How to simplify the expression?The expression for this problem is defined as follows:
-j/5 + 3/4 - (5j/2 + 7/8).
The negative sign means that every term in the parenthesis has the signal exchanged, hence:
-j/5 + 3/4 - 5j/2 - 7/8.
Then the expression is simplified combining the like terms, as follows:
With j: -j/5 - 5j/2 = -2j/10 - 25j/10 = -27j/10.Constant: 3/4 - 7/8 = 6/8 - 7/8 = -1/8.Meaning that the expression is of:
-27j/10 - 1/8.
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Vector u = (-3, 8), and vector v = (-14, 6). Match each vector operation with the magnitude of its resultant vector
Answers
The magnitude of given operations of vectors are found.
What are Vectors?Quantities with the independent characteristics of magnitude and direction are called vectors.
Given:
u = (-3, 8) and v = (-14, 6)
So, 3u = (-9, 24) and 2v = (-28, 12)
3u - 2v = (-9+28, 24-12)
3u - 2v = (19, 12)
Magnitude of 3u - 2v = √19² + 12² = √505 units
2u = (-6, 16) and 3v = (-42, 18)
2u - 3v = (36, -2)
Magnitude = √36² + (-2)² = √1300 units
u = (-3, 8) and 4v = (-56, 24)
u + 4v = (-59, 32)
Magnitude = √(-59)² + 32² = √4505 units
5u = (-15, 40) and v = (-14, 6)
5u - v = (-1, 34)
Magnitude = √1157 units
7u = (-21, 56) and 2v = (-28, 12)
7u - 2v = (7, 44)
Magnitude = √1985 units.
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Which function is the inverse of g (z) = (²-1)³ — 3?
Of(1) = √2+6+1
Of(1) = 2√2+3+1
O f(1) = 2√1+1+3
O f(1) = √21+2+3
Answers
The inverse of function is f(x) = (x - 4)³/8 + 3
What is inverse function?A function that reverses the results of another function is known as an inverse function. If y = f(x), then x = g(y), then a function g is the opposite of a function f. To put it another way, applying f and then g is equivalent to doing nothing. This can be expressed as g(f(x)) = x in terms of how f and g are made up.
Given g(x) = 2(∛x-3)+4
let g(x) = y
y = 2(∛x-3)+4
change the variables since options are in form of x
x = 2(∛y-3)+4
simplify for y
subtract 4 from both side
x - 4 = 2(∛y-3)+4 - 4
x - 4 = 2(∛y-3)
divide both side by 2
(x - 4)/2 = (2(∛y-3))/2
(x - 4)/2 = (∛y-3)
cube both side
((x - 4)/2)³ = ((∛y-3))³
(x - 4)³/8 = y - 3
(x - 4)³/8 + 3 = y
Hence the value f(x) = (x - 4)³/8 + 3 .
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Figure ABCD is a square. If AC+BD=56, what is the length of AX?
Answers
Figure ABCD is a square. If AC+BD=56, the length of AX is 28.
How did we get the value?Since ABCD is a square, all sides have the same length, let's call it "x".
We know that the sum of the diagonals of a square is equal to twice the length of a side, so AC + BD = 2x.
Therefore, 56 = 2x, and x = 28.
So the length of AX (or any side of the square) is 28 units
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What is 200 Micrograms (mcg) in Milligrams (mg)?
Answers
To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms, 200 micrograms (mcg) is equal to 0.2 milligrams (mg).
When we want to convert a unit of measurement to another unit of measurement, we use conversion factors to make the conversion. In the case of converting micrograms (mcg) to milligrams (mg), we need to know that 1 milligram is equal to 1000 micrograms. This means that to convert any value from micrograms to milligrams, we need to divide by 1000.
To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms.
So, to convert 200 mcg to mg, we divide 200 by 1000:
200 mcg ÷ 1000 = 0.2 mg
Therefore, 200 micrograms (mcg) is equal to 0.2 milligrams (mg)
It is important to understand the concept of unit conversions because it is a crucial aspect of many scientific and engineering calculations. Knowing how to convert units of measurement allows us to work with data that is expressed in different units and compare results from different experiments. In addition, being able to convert units is a valuable skill for everyday life, such as when reading nutrition labels or measuring medication dosages.
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the population of a school is 800 students and is increasing at a rate of 2%per year.
Answers
Answer: Increases by 16 students per year
Step-by-step explanation:
100% = 800
2% = x
So between 100% and 2%, the scale factor would be 50 since 100 / 2 = 50
Then 800 / 50 would be 16
So..
1 Year = 816 students
2 Years = 832 students
3 Years = 848 students
4 Years = 864
And so on..
Erika has a baking company and needs to purchase 17 2/5 pounds of flour for her cakes. The Baking Goods Store sells two different-sized bags of flour. The table shows the amounts of flour in the bag, the number of bags at the store, and the cost per bag of flour.
Answers
The number of small ball bags she will need is 7 small bags, the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given that;
Need of flour for cakes= 17 2/5 pounds
Now,
There are 4 large bags, and each one has 4 pounds.
She buys all of the large bags, she already has;
4x4=16
16 pounds. So, she only needs
17 2/5 -16= 1 2/5
=5/5+2/5
=7/5
1 2/5 pounds more, this fraction is equals to 7/5 pounds.
The small bags only contains 1/5 pounds of flour so,
7/5/1/5
=7*5/1*5
=7
Therefore, by algebra the answer will be 7 bags
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The complete question is;
Erika has a baking company and needs to purchase 17 pounds of flour for her cakes. The Baking Goods Store sells two different-sized bags of flour. The table shows the amounts of flour in the bag, the number of bags at the store, and the cost per bag of flour. Size Pounds 1 Bags for Sale 75 Cost per Bag Small $0.84 5 Large 4 4 $16.80 If Erika buys all of the large bags, how many small bags will she need? A. 7 small bags B. 12 small bags C. 28 small bags D. 71 small bags
how to tell if an integral is convergent or divergent
Answers
Convergent - If the limit exists and is a finite number it is a “improper integral convergent” / “convergent”
Divergent - If the limit is positive infinity (+♾️) or doesn’t exist it is a “ improper integral divergent” / “divergent”
Simplifier chacune des expressions suivantes et identifier la nature du nombre obtenu.
= 2 +
2
3
; =
2
5
+ 7; = (√3 + 1)(√3 − 1) ; = (√5 + 1)²
Answers
Answer:its 5
Step-by-step explanation: cuz
A student is walking to school and sees a mirror on the ground.
She stops a short distance from the mirror to practice her Geometry.
She knows her own height and the height of the school. She also knows the distance from the mirror to the school from previous Geometry activity. She would like to calculate the distance she is standing from the mirror.
The height of the school is 30 ft.
The distance from the school to the mirror is 50 ft.
The height of the student is 6.3 ft.
What is the distance d between the student and the mirror?
Answers
The distance d between the student and the mirror is given by the similar triangles are d = 10.5 feet
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the triangles be represented as ΔABC and ΔCDE
Now , they are similar triangles
The measure of AB = height of the school = 30 feet
The measure of BC = distance from the school to the mirror = 50 feet
And ,
The measure of DE = height of the student = 6.3 feet
The measure of CD = distance d between the student and the mirror
So , the corresponding sides of similar triangles are in the same ratio
On simplifying the equation , we get
BC / AB = CD / DE
And , 50 / 30 = d / 6.3
Multiply by 6.3 on both sides , we get
d = ( 5/3 ) x 6.3
d = 31.5 / 3
d = 10.5 feet
Hence , the distance d between the student and the mirror is 10.5 feet
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By rounding to one significant figure estimate the answer to 59 divided by 25
Answers
Answer:2
Step-by-step explanation:
59 to 1 sig. fig= 60
25 to 1 sig fig = 30
Therefore, 60/30 =2
Hope this helps :)
Answer:
2
Step-by-step explanation:
divide the numbers. then find the left furthest critical number.
count to the rifht by desired sig fig. use decimal to mark a place of significant zeros.
Write an equation in slope-intercept form for the line that passes through the points (0, 5) and (1, 3)?
Answers
Answer:
Step-by-step explanation:
y= -2x + 5
Write the following ratio in simplest form: 32 min : 36 min (1 point) a. 8 : 9 b. 8 : 36 c. 32 : 9 d. 128 : 144
Answers
The simplest form of the given ratio 32 min : 36 min is equal to
option a. 8 : 9.
Ratio is equal to
32 min : 36 min
Factors of 32 are = 1, 2, 4, 8, 16, 32
Factors of 36 are = 1, 2, 3, 4, 6, 9, 12, 18, 36
Greatest common factor of 32 and 36 is equal to 4
Simplest form of the given ratio is equal to
32 min : 36 min
= ( 8 × 4 ) min : ( 9 × 4 ) min
'4' get cancelled with other we get,
= 8 min : 9 min
Therefore, the simplest form of the given ratio by taking out common factors is equal to option a. 8 : 9 .
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∠A and ∠B are vertical angles. If m∠A=(7x−18) ∘ and m∠B=(6x−8) ∘ , then find the measure of ∠A.
Answers
The measure of angle A is 52 degree.
What is the measure of angle A?Vertical angles are angles that are opposite of each other when two lines crosses, they are congruent.
Given that;
Angle A = ( 7x - 18 )∘Angle B = ( 6x - 8)∘Since vertical angles are congruent,
Angle A = Angle B
Plug in the given values
( 7x - 18 ) = ( 6x - 8)
Solve for x
7x - 18 = 6x - 8
7x - 6x = -8 + 18
x = -8 + 18
x = 10
Hence, angle A will be;
Angle A = 7x - 18
Plug in x = 10
Angle A = 7( 10 ) - 18
Angle A = 70 - 18
Angle A = 52°
Therefore, angle A is 52 degree.
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A global denim brand announced in 2010 that it is launching a new collection of jeans which are made with reduced consumption of water during the manufacturing process. While usual manufacturing of a pair of jeans requires approximately 42 litres of water, this collection would reduce the water usage by a minimum of 28%. Do you think this initiative by the company is beneficial for water conservation? How much water can be conserved in litres, on a pair of jeans?
Answers
The number of liters of water that can be conserved will be 11.76 liters. The initiative by the company is beneficial for water conservation.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The number of liters of water that can be conserved is given as,
⇒ 28% of 42
⇒ 0.28 x 42
⇒ 11.76 liters
The number of liters of water that can be conserved will be 11.76 liters. The initiative by the company is beneficial for water conservation.
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HELP ME PLEASE!!!!! FAST ASAP HELP
PICTURE ATTACHED
A company logo is made up of a desire and two identical triangles as shown in this image
What is the area of the logo
Answers
The area of the logo is given as 139 cm
How to solve for the areaIn order to get the area of the shape, i would have to get the area of the triangles first
area of a triangle = 1/2 b * h
base = 9 / 2 = 4.5
h = 6
area = 1/2 * 9 * 6
= 27
Area of 2 triangle = 2 x 27
= 58
The are aof the square = a * a
= 9 * 9
= 81
The total area of the logo is given as 81 + 58
= 139 cm
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What is the simplest form of the radical expression?
√2+√5/√2-√5
Answers
What is 20% off 250000 ?
Answers
From the given information provided, 20% off 250000 is 50000, and the discounted price is 200000.
The formula for calculating percentage is:
percentage = (part/whole) x 100
Here's an example:
Let's say you got 35 out of 50 questions correct on a test. To calculate the percentage of questions you answered correctly, you would use the formula as follows:
percentage = (35/50) x 100
percentage = 0.7 x 100
percentage = 70%
To calculate 20% off 250000, you can multiply 250000 by 20% (which is 0.20 in decimal form) and then subtract the result from 250000:
250000 - (0.20 x 250000) = 250000 - 50000 = 200000
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can yall help me with this question immediately pls?
Answers
The diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.
What is diameter?Diameter is the line jwhich passes through the center of a circle and joins two points on the circumference of the circle.
To find the diameter of the Ferris wheel which is a circle, we see that the grpah gives the height of a passenger on the Ferris wheel as a function of the number of complete cycles since the ride started.
Now, the diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.
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: CC> Chapter 9: Mean> Section Exercises 9.2 > Exercise 13
13
Complete these two different sets of data so that they each have six values and a mean of 21.
20, 20.5, 20.5, 21.5, 21.5,
20, 21, 21, 21, 21,
Answers
Answer:
To complete the first set of data so that it has six values and a mean of 21, you can add the following values: 20, 20.5, 20.5, 21.5, 21.5, 21.
The mean of this set is calculated as follows: (20 + 20.5 + 20.5 + 21.5 + 21.5 + 21) / 6 = 21.
To complete the second set of data so that it has six values and a mean of 21, you can add the following values: 20, 21, 21, 21, 21, 22.
The mean of this set is calculated as follows: (20 + 21 + 21 + 21 + 21 + 22) / 6 = 21.
Use the drop-down menus to order the decimals from greatest to least.
8.31, 8.296, 8.06, 8.3
Answers
Answer:
8.31, 8.3, 8.296, 8.06
Step-by-step explanation:
8.31, 8.296, 8.06, 8.3
The order of decimals from greatest to least is
8.31, 8.3, 8.296, 8.06
A student is walking to school and sees a mirror on the ground.
She stops a short distance from the mirror to practice her Geometry.
She knows her own height and the height of the school. She also knows
the distance from the mirror to the school from a previous Geometry activity.
She would like to calculate the distance she is standing from the mirror.
The height of the school is 30 ft.
The distance from the school to the mirror is 50 ft.
The height of the student is 5.1 ft.
What is the distance d between the student and the mirror?
Show all your work
Answers
The distance between the student and the mirror is apprοximately 29.41 feet.
What do you mean by Distance?Distance is a numerical measurement of hοw far apart or how far away objects or lοcations are from each other. It is a physical quantity that is usually expressed in units such as meters, kilοmeters, miles, οr feet. Distance is a scalar quantity, meaning it οnly has magnitude and nο direction.
To sοlve the problem, we can use the similar triangles prοperty of geometry. Let's denοte the distance between the student and the mirrοr as d. Then, we can set up the follοwing proportion:
(student height + height of mirrοr) / distance frοm student to mirror = height of schοol / distance from mirrοr to school
Plugging in the given values, we get:
(5.1 + 0) / d = 30 / (50 + d)
Simplifying and sοlving for d, we get:
5.1d + 0 = 150
d = 29.41
Therefοre, the distance between the student and the mirrοr is apprοximately 29.41 feet.
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A 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association, so some suggested that having male pattern baldness might somehow cause a person to have a severe reaction to COVID-19 (since they had been bald before catching COVID-19, so that the disease could not have caused their baldness). Which option below was most likely a lurking variable?
Age
Diet
Height
Weight
Answers
If a 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association: A. Age is the most likely lurking variable in this scenario.
What is a lurking variable?In this case, the relationship between male pattern baldness and severe COVID-19 reactions may be influenced by age, as older individuals are more likely to experience both male pattern baldness and severe COVID-19 symptoms.
Age could also affect other factors such as overall health and immune system function, which may contribute to the severity of COVID-19 symptoms.
Diet, height, and weight may also be related to overall health and immune system function, but they are less likely to be related specifically to male pattern baldness
Therefore, age is the most likely lurking variable in this scenario.
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Analyze the linear inequalities and determine if the solution set is the shaded region above or below the boundary
line.
Warm-Up
y> -1.4x +7
y> 3x-2
y <19-5x
y>-x-42
y < 3x
y<-3.5x+2.8
Solution Set Shaded Above
Solution Set Shaded Below
Answers
Answer:
The graph in the attached figure
we have
----> inequality A
The solution of the inequality A is the shaded area below the dashed line
The slope of the dashed line A is positive m=2
The y-intercept of the dashed line A is (0,-5)
The x-intercept of the dashed line A is (2.5,0)
----> inequality B
The solution of the inequality B is the shaded area above the dashed line
The slope of the dashed line B is negative m=-3
The y-intercept of the dashed line B is (0,1)
The x-intercept of the dashed line B is (1/3,0)
The solution of the system of inequalities is the shaded area between the two dashed lines
using a graphing tool
The graph in the attached figure
GIVE ME BRAINLIEST IF IM CORRECT :)
select the statement which is true about the functions over the interval [1,2]
Answers
The true statement is (b) Function 2 has the lowest average rate
How to determine the true statementWe start by calculating the average rates of each function
The interval is given as [1, 2]
For Function 1
We have
f(1) = -3
f(2) = 3
The average rate is then calculated as
Average rate = [f(2) - f(1)]/[2 - 1]
Average rate = (3 + 3)/1
Average rate = 6
For Function 2
We have
f(1) = (1/4)^1 + 4 = 4.25
f(2) = (1/4)^2 + 4 = 4.0625
The average rate is then calculated as
Average rate = [f(2) - f(1)]/[2 - 1]
Average rate = (4.0625 - 4.25)/1
Average rate =-0.1875
For Function 2
We have
f(1) = -2
f(2) = 0
The average rate is then calculated as
Average rate = [f(2) - f(1)]/[2 - 1]
Average rate = (0 + 2)/1
Average rate = 2
The lowest average rate is -0.1875 for function 2
Hence, function 2 has the least rate
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what is the probability of three or fewer heads on four flips of a fair coin. enter the answer to four decimal places?
Answers
The probability of three or fewer heads on four flips of a fair coin is 0.375. This can be determined by calculating the probability of zero, one, two and three heads, which are 0.0625, 0.25, 0.375 and 0.25 respectively. The total of these probabilities is 0.375.
The probability of zero heads on four flips of a fair coin is 0.0625 (1/16).
The probability of one head on four flips of a fair coin is 0.25 (4/16).
The probability of two heads on four flips of a fair coin is 0.375 (6/16).
The probability of three heads on four flips of a fair coin is 0.25 (4/16).
The total probability of three or fewer heads on four flips of a fair coin is 0.375 (1/4).The probability of three or fewer heads on four flips of a fair coin is 0.375. This can be calculated by determining the probability of zero, one, two and three heads. The probability of zero heads is 0.0625, the probability of one head is 0.25, the probability of two heads is 0.375, and the probability of three heads is 0.25. When these probabilities are added together, the total probability of three or fewer heads on four flips is 0.375. This means that the probability of getting three or fewer heads on four flips of a fair coin is 0.375.
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