To select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys , there are 1260 ways.
To find the number of ways to select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys, you can use the formula for combinations:
C(n, k) = n! / (k! * (n - k)!)
where n is the total number of items (9 girls and 5 boys), k is the number of items to be selected (3 boys and 4 girls), and ! represents the factorial function.
So, the number of ways to select 3 boys out of 5 boys is:
C(5, 3) = 5! / (3! * (5 - 3)!) = 5! / (3! * 2!) = 10
And the number of ways to select 4 girls out of 9 girls is:
C(9, 4) = 9! / (4! * (9 - 4)!) = 9! / (4! * 5!) = 126
Finally, the number of ways to select a team of 7 members consisting of 3 boys and 4 girls is:
C(14, 7) = 10 * 126 = 1260
So, there are 1260 ways to select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys.
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Which of the following is the correct answer?
From the given data value of function f ' (- 10) is,
⇒ f ' (- 10) = 0.035
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.
Given that;
Table for the given data is shown.
Now, We have to find the value of f ' (- 10).
Since, - 10 is in between - 11 and - 9.
Hence, The slope given the value of f ' (- 10) as;
⇒ f ' (- 10) = (1.12 - 1.05) / (- 9 - (- 11))
⇒ f ' (- 10) = (0.07/2)
⇒ f ' (- 10) = 0.035
Thus, From the given data value of f ' (- 10) is,
⇒ f ' (- 10) = 0.035
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Two variables, y and x, are inversely proportional.
When x = 12, y = 10.
(a) Find an equation that relates y and x.
(b) Given that x and y are positive integers, find the values of x and y when y=x+7.
I don’t understand this question at all!
Answer:
x = 8, y = 15
Step-by-step explanation:
Part (a)
If x and y are inversely proportional, the relationship can be expressed as
[tex]y \propto \dfrac{1}{x}\\\\\rm{(or \;alternatively\;x \propto \dfrac{1}{y})\\\\}\\\\[/tex]
The above relationship [tex]y \propto \dfrac{1}{x}[/tex] can be written as an equation:
[tex]y = \dfrac{k}{x} \codts\cdots(1)[/tex]
where the constant k is known as the constant of proportionality
Part (b)
We know that when x = 12, y = 10
Plugging this into equation (1):
10 = k/12
k/12 = 10
k = 12 x 10
k = 120
So the proportional equation (1) becomes
y = 120/x
We are now given the equation
y = x + 7
Substitute y = 120/x
120/x = x + 7
Subtract 120/x from both sides
0 = x + 7 - 120/x
Multiply by x both sides;
0 = x² + 7x - 120
Or,
x² + 7x - 120 = 0
This is a quadratic equation which we can solve by factoring. There are various techniques. One of them is to find two factors of 120 and see if their sum or difference can be made -7
Factors of 120 are:
[tex]1,\:2,\:3,\:4,\:5,\:6,\:8,\:10,\:12,\:15,\:20,\:24,\:30,\:40,\:60,\:120[/tex]
Take the two factors, a and b that will add or subtract to -7 and multiply to -120
We see that if we choose a = -15 and b = 8
a + b = -7
and
a x b = -120
The solution to the equation is x = 8 or x = -15
Since we are told that both x and y are positive, we can ignore x = -15 and just state that x = 8 is a solution
If x = 8, substitute this in y = x + 7 to get
y = 8 + 7 = 15
This checks with our original proportionality equation:
y = 120/x = 120/8 = 15
Answer
x = 8, y = 15
Determine the solution to the inequality. one fourth times the absolute value of the quantity x plus 1 end quantity is greater than or equal to 4 x ≥ −1 or x ≥ 17 x ≤ −17 or x ≥ 15 x ≤ −9 or x ≥ 7 x ≤ −2 or x ≥ 0
The solution of the inequality will be x ≥ -1/4.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that inequality is one-fourth time the absolute value of the quantity x plus 1 end quantity.
The given inequality can be solved as below:-
4x ≥ −1
4x ≥ −1
x ≥ -1 / 4
Therefore, the value of x for the inequality is - 1 / 4.
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Answer:
The answer Is B) x ≤ −17 or x ≥ 15
Step-by-step explanation:
What is 16.15549442 rounded to the nearest 10th
Answer:
Below
Step-by-step explanation:
16.15549442 rounded to the nearest 10th is 16.2
Answer:
16.2
Step-by-step explanation:
Find the number in the tenth place 1 and look one place to the right for the rounding digit 5. Round up if this number is greater than or equal to 5 and round down if it is less than 5
Where are the asymptotes for the following function located?
f (x) = StartFraction 14 Over (x minus 5) (x + 1) EndFraction
x = –1 and x = 5
x = –1 and x = 14
x = 1 and x = –5
x = 14 and x = 5
The asymptotes for the function are:
x = 5 and x = -1.
Option A is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
There are three types of asymptotes.
1) Horizontal asymptotes
2) Vertical asymptotes
3) Oblique asymptotes
Now,
Horizontal asymptotes.
f(x) = 14 / (x - 5)(x + 1)
f(x) = 14/(x² + x - 5x - 5)
f(x) = 14 / (x² - 4x - 5)
The degree of the numerator is less than the denominator.
So,
Horizontal asymptotes.
y = 0
i.e
The x-axis.
Now,
Vertical asymptotes
f(x) = 14 / (x - 5)(x + 1)
Simplify in its lowest term.
Now,
Set the denominator to zero.
So,
(x - 5) ( x + 1) = 0
x - 5 = 0
x = 5
And,
x + 1 = 0
x = -1
Now,
Since there is a horizontal asymptote there are no oblique asymptotes.
Thus,
The asymptotes for the function are:
x = 5 and x = -1.
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Answer:
A. x = -1 and x = 5Step-by-step explanation:
Using Pythagorean Theorem
calculate the diagonal
distance from point
(-2,12) to (2,2)
Answer:
10.8 units or [tex]2\sqrt{29}[/tex] units
Step-by-step explanation:
The line drawn connecting two points on a graph is known as a line segment.
The formula used to calculate the length of a line segment is derived from the Pythagorean Theorem
Length of a line segment: [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} -y_{1})^{2}}[/tex]
= [tex]\sqrt{[2-(-2)]^{2} + (2-12)^{2} }[/tex]
= [tex]\sqrt{(2+2)^{2} +(-10)^{2} }[/tex]
= [tex]\sqrt{4^{2} + 100}[/tex]
= [tex]\sqrt{16 +100}[/tex]
= [tex]\sqrt{116}[/tex]
= [tex]\sqrt{4}[/tex]×[tex]\sqrt{29}[/tex]
= [tex]2\sqrt{29}[/tex] units
Diagonal distance = 10.8 units (Rounded to 3 significant figures)
A women is 159 1/4 cm tall and her son is 147 6/8 cm how taller is the women
Answer: 11 1/2 cm or 11.5 cm
Step-by-step explanation:
To see how much taller the woman is than her son, we will subtract the son's height from the woman's height. We can convert these fractions into decimals to make it easier to subtract.
159 1/4 - 147 6/8 = 159.25 - 147.75 = 11.5 = 11 1/2 cm
Find the distance between the points (3, 8, 2)and (3,8,2)
The solution is, the distance between the points (3, 8, 2)and (3,8,2) is 0.
What is Distance Formula?The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 3 dimensional plane, the distance between points (X1, Y1, Z1) and (X2, Y2, Z2) is given by:
d=√(x2−x1)2+(y2−y1)2+(z2−z1)2
here, we have,
the given points are,
(3, 8, 2)and (3,8,2)
so, distance = √(x2−x1)2+(y2−y1)2+(z2−z1)2
solving we get,
d= 0
as the points are same.
Hence, The solution is, the distance between the points (3, 8, 2)and (3,8,2) is 0.
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Please help, I’m not good at math
Step-by-step explanation:
a regular function finds the functional result y to a given x value.
the inverse function finds the original x to a given y value.
g^-1(1) is therefore the x-value, so that g(x) = 1.
so, we look through the value pairs. where do we find y = 1 ? ah, in the pair (9, 1).
x = 9 lead to the functional result y = 1.
therefore, g^-1(1) = 9
h(x) = y = -3x - 14
in other words, h(x) expresses y in terms of x.
h^-1(x) expresses x in terms of y.
so, we want to transform the functional equation, so that it says "x = ...." :
y = -3x - 14
y + 14 = -3x
x = (y + 14)/-3
and to turn it into regular function notation, we rename x to y and y to x :
y = h^-1(x) = (x + 14)/-3 = (-1/3)(x + 14)
(h○h^-1)(x) = x
always.
in that process we find first what original input value for h lead to the value of x. and then we use that as input value for h. and, of course, we have to get x as result.
to check here in our case
(h○h^-1)(-5) = -5
h^-1(-5) = (-5 + 14)/-3 = 9/-3 = -3
h(-3) = -3×-3 - 14 = 9 - 14 = -5
there you have it.
Write a function rule for "The output is one more than twice the input x ."
The function rule for "The output is one more than twice the input x ." is y= 2x+ 1.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.given:
"The output is one more than twice the input x ."
let the output by y.
Then, the mathematical expression for the above statement is
= 1+ 2x
Thus, the output is, y= 2x+ 1.
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the last me Else ved Adventure Island, she rode her favorite roller coaster, Maximum Velocity, d times Maxmum Velocity has ride time of 145 seconds. Write on sixpression that shows how many seconds Elise spn riding Maximum city the last time she visited Adventure island.
The total time Elise spent riding Maximum Velocity on her last visit to Adventure Island can be expressed as: 145d seconds.
What is expression?In mathematics, an expression is a combination of numbers, symbols, and/or variables that can be evaluated to produce a value. Expressions can also include functions, such as sin(x) or log(y), as well as operators like multiplication (*), division (/), and exponentiation (^). Expressions can be used to represent mathematical formulas, equations, and relationships in a concise and symbolic way, making them easier to work with and manipulate using mathematical tools and techniques.
Here,
If we know the value of d, we can calculate the total time Elise spent riding Maximum Velocity by simply multiplying the ride time by the number of rides.
For example, if Elise rode Maximum Velocity 3 times, the total time she spent on the ride would be:
145 seconds/ride x 3 rides = 435 seconds
So, using the expression from the previous answer, we can substitute the value of d to get the actual calculation:
Total time = 145d seconds
For instance, if Elise rode Maximum Velocity 5 times during her last visit, the total time spent on the ride would be:
Total time = 145 x 5 = 725 seconds
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The proportional relationship between the number of sweaters a clothing store buys and sells, s, and the profit, in dollars and cents, that it makes off those sweaters, can be represented by the equation p=23sp=23s. What is the profit in dollars and cents that the store makes per sweater?
The profit in dollars cent that the store makes per sweater is $23.
In general, the profit is defined as the amount gained by selling a product, which should be more than the cost price of the product. It is the gain amount from any kind of business activity. In short, if the selling price (SP) of the product is more than the cost price (CP) of a product, then it is considered as a gain or profit. It describes the financial benefit obtained if the revenue from the business activity exceeds the taxes, expenses, and so on, which are involved in sustaining business activities.
Through this information, we can calculate.
[tex]\because p=23 \mathrm{~s} \text {. }[/tex]
when S=1, we could get:
[tex]\therefore P=23 \times 1=23$ \{Operation\}.[/tex]
Therefore, the profit in dollars cent that the store makes per sweater is $23.
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how can you find a 30% increase of some thing which started at 50? 
increase=(30/100)*50
=15
so,
value after increase
=50+15
=65
There is an antenna on the top of a building. From a location 319 feet from the base of the building, the angle of elevation to the top of the building is measured to be 7°. From the same location, the angle of elevation to the top of the antenna is measured to be 5° more than the angle of elevation to the building. Find the height of the antenna. Round the height to the nearest 10th of a foot. No units necessary.
Answer:
Step-by-step explanation:
Let's call the height of the building "h", and the height of the antenna "a". From the given information, we have:
Angle of elevation to the top of the building = 7°
Angle of elevation to the top of the antenna = 7° + 5° = 12°
We can use tangent to find the height of the building and the height of the antenna. The tangent of an angle is equal to the height divided by the distance, so we have:
tan(7°) = h / 319
And
tan(12°) = (a + h) / 319
We can use the first equation to solve for h:
h = 319 * tan(7°)
And use the second equation to solve for a:
a = 319 * tan(12°) - h
Now that we have expressions for h and a, we can use the tangent function to find the values for h and a. We can use a calculator or look up the values in a table of tangent values.
Rounding the height of the antenna to the nearest 10th of a foot, we find:
a = 319 * tan(12°) - h = approximately 69.9 feet.
5,8,11,14
What term comes next?
What formula can we use?
What is the 10th term?
What formula can we use to find the 10th term?
Answer:
(1) 17 (2) +3 every new term (5+3) or 8+3) or 5+x*3
we can use this as to find 2nd number (1) as its first one to be found 5+3(1) 5+3=8
(3) 5+9*3=5+27 , 32
(4) 5+9*3 ,
we can test this out by counting
starter: 5
1 -> 8
2-> 11
3-> 14
4 -> 17
5 -> 20
6 -> 23
7 -> 26
8 -> 29
9 -> 32 (realisticly it is still the 10th but it's the 9th after the 1st.)
Step-by-step explanation:
To solve for the lengths of the right triangle sides, which equation is correct?
According to the Pythagorean theorem [tex]c^{2} = a^{2} + b^{2},[/tex] Option D is accurate since[tex](2x-10)^{2} + x^{2} = (3x)^{2}.[/tex]
The Pythagorean Theorem: What is it?The Pythagorean Theorem, also known as the Equation, is the fundamental Cartesian geometry relationship between a right triangle's three sides.
The Pythagorean Theorem states that the sum of the squares that thus span the angles of a right triangle is equal to the number that crosses the right triangle's rectangular prism opposite any right angle. Sometimes it is expressed using the general geometric notation [tex]a^{2} + b^{2} = c^{2}[/tex]
Given,
according to the diagram
in right triangle
[tex](base )^{2} + (perpendicular) ^{2} = (hypotenuse)^{2}[/tex]
[tex](2x-10 )^{2} + x^{2} = (3x)^{2}[/tex]
According to the Pythagorean theorem [tex]c^{2} = a^{2} + b^{2}[/tex],
Option D is accurate since [tex](2x-10)^{2} + x^{2} = (3x)^{2}.[/tex]
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I need help with this question(Divide.
Express your answer as a decimal.
51
÷
6
=
51÷6) the first person answer get 10 points thanks for the help!
Answer:
Below
Step-by-step explanation:
51÷6= 51/6 = 8 3/6 = 8 1/2 = 8.5
6
Explain the process and the properties you have to use to solve the logarithmic equation: log_3(x) + log_3(4) - 2log_3(3) = 2
The solution to the logarithmic equation is; x = 81/4
How to solve Logarithmic Equations?We want to solve the logarithmic equation;
log₃x + log₃4 - 2log3 = 2
From property of logarithms, we know that;
logₐ4 = log 4/log a
Similarly we know that;
log a + log b = log (ab)
log a - log b = log (a/b)
Thus;
log₃x + log₃4 - 2log₃3 = 2 is;
(log₃4x) - 2log₃3 = 2
(log₃4x) - log₃3² = 2
log₃(4x/3² ) = 2
3² = 4x/9
4x = 9 * 9
4x = 81
x = 81/4
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the sum of three fractions is 6.if 18/7 and5/6 are two of the fractionsfind the third fraction
A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
First, we need to solve for a common denominator.
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
To get the common denominator between [tex]\frac{18}{7}[/tex] and [tex]\frac{5}{6}[/tex], we multiply their denominators.
7 × 6 = 42Now, we know the fractions would look like this:
[tex]\frac{?}{42} \frac{?}{42}[/tex]To solve for the numerators, we can use these equations:
18 × 6 = 1085 × 7 = 35Now, the fractions look like this:
[tex]\frac{108}{42}[/tex] and [tex]\frac{35}{42}[/tex]Adding them together:
[tex]\frac{108}{42} +\frac{35}{42} = \frac{143}{42}[/tex]Now, we can convert this into a mixed number.
[tex]\frac{143}{42} = 3\frac{17}{42}[/tex]Now that we have this, we can subtract that from 6 to get the missing value.
[tex]6 - 3\frac{17}{42}[/tex][tex]=2\frac{25}{42}[/tex]Therefore, the third fraction is [tex]2\frac{25}{42}[/tex].
Can you please find the perimeter of the blueprint room in feet? And could you find the area of the blueprint room in sqaure feet.
2 of the walls are 11 and 11, there's 3 more walls to find. Break thr room into rectangles and then do Base × height then add both rectangles together.
Based on the information in the graph, it can be inferred that the perimeter of the room is 44 feet.
How to find the perimeter of the room in the graph?To find the perimeter of the room in the graph we must apply the following formula:
Perimeter = base + upper base + left side + right sideAccording to the above, if each of the sides is 11 feet long we have two alternatives
perimeter = 4 * 11perimeter = 11 + 11 + 11 + 11In both operations the result would be 44.
Based on the above, the perimeter of the room would be 44 feet.
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PLEASE PLEASE PLEASE HELP ME!!!!
A plane, 50 miles away from its
destination, is flying toward the airport at
an altitude of 30,500 feet. Later, this same
plane is 20 miles from the airport and has
descended to an altitude of 18,000 ft.
How far has the plane flown?
Answer:
Below
Step-by-step explanation:
The plane's distance is the hypotenuse of a right triangle with legs of
(50 -20)mi = 30 miles and 30500 - 18000 = 12500 ft
for consistent units 12500ft/5280ft/mile = 2.36742 miles
Now just use Pythagorean theorem
Hypotenuse^2 = leg1^2 + leg2^2
h^2 = 30^2 + 2.36742^2
h = ~ miles 30.093 miles ( note that the vertical descent distance does not matter much)
(this is 158 892 feet)
Suppose that C and D are points on the number line.
If CD=6 and D lies at 4, where could C be located?
If there is more than one location, separate them with commas.
On the number line if CD = 6 then the point C lied either on -2 or 10.
What is a number line?A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, the whole number is a collection of numbers that contains both zero (0) and all counting numbers (1, 2, 3,4,5,6), whereas the natural number is a collection of all counting numbers (1, 2, 3,4, 5, 6).
Given that, CD = 6 and D lies at 4.
Then C would lie either on the left or right side of the point D.
On left the point C would be:
4 - 6 = -2
On right the point C would be at:
4 + 6 = 10
Hence, on the number line if CD = 6 then the point C lied either on -2 or 10.
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This graph represents one of the following descriptions. Which one?
a. A phone loses 80% (20% left) of its value every year after purchase: the relationship between the number of years since purchasing the phone and the value of the phone.
b. The number of stores a company triples approximately every 5 years: the relationship between the number of years and the number of stores.
c. A camera loses 40% (60% left) of its value every year after purchase: the relationship between the number of years since purchasing the camera and the value of the camera.
Which equation is graphed here?
A. y+5=-3/2(x-4)
B. y-5=-2/3(x+4)
C. y-5=-3/2(x+4)
D. y-4=-3/2(x+5)
The equation of the graphed line is expressed as: A. y + 5 = -3/2(x - 4).
How to Write the Equation of a Line?The equation that represents a line can be written in point-slope form as y - b = m(x - a), where a point on the line is (a, b) and the slope is m.
Slope (m) = rise/run = -3/2
Substitute a point on the line (a, b) = (4, -5) and m = -3/2 into y - b = m(x - a):
y + 5 = -3/2(x - 4)
The equation is: A. y + 5 = -3/2(x - 4).
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Find the ratios of the side lengths of ΔHIJ to the corresponding side lengths of ΔEFG. Then determine the ratio of the area of ΔHIJ to the area of ΔEFG.
The ratio of the sides are 1:2 and the ratio of the areas is 1:4
What is similarity?Two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other, this is called similarity.
Since, the side lengths of the triangles are not given, let us consider,
Δ HIJ =
HI = 12, IJ = 14, HJ = 16
And,
Δ EFG =
EF = 24, FG = 28, EG = 32
Therefore, the ratios of the side lengths of Δ HIJ to the corresponding side lengths of Δ EFG are;
HI / EF = 12/24 = 1/2
IJ / FG = 14/28 = 1/2
HJ / EG = 16/32 = 1/2
Since, we get all the ratios equal, therefore, the Δ HIJ is similar to Δ EFG
With a scale factor of 1/2,
The ratio of area is found by squaring the scale factor for length.
Therefore,
ar(Δ HIJ) / ar(Δ EFG) = (1/2)² = 1/4
Hence, the ratio of the sides are 1:2 and the ratio of the areas is 1:4
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When Carmen leaves school at the end of the day, she walks to soccer practice at the park and then to the hobby shop before walking home. How many blocks does Carmen walk after school in all?
Since 1 unit on the map represents 1 block, Carmen walks 22 blocks after school.
To find the total distance Carmen walks, we need to find the distance between each of the four locations: school, park, hobby shop, and home.
The distance between two points (x1, y1) and (x2, y2) in a plane can be calculated using the Pythagorean theorem:
d = √((x2 - x1)² + (y2 - y1)²)
First, let's find the distance between the school and the park:
d = √((-5 - (-5))² + (4 - (-3))²) = √((0)² + (7)²) = √(49) = 7
Next, let's find the distance between the park and the hobby shop:
d = √((3 - (-5))² + (-3 - (-3))²) = √((8)² + (0)²) = √(64) = 8
Then, let's find the distance between the hobby shop and home:
d = √((3 - 3)² + (-3 - 4)²) = √((0)² + (7)²) = √(49) = 7
Finally, the total distance Carmen walks after school is the sum of the distances between the four locations:
d = 7 + 8 + 7 = 22
Since 1 unit on the map represents 1 block, Carmen walks 22 blocks after school.
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If 42 push ups can be done in 3 minutes how many push ups in 5 minutes
Answer:
Step-by-step explanation:
3 divided by 42 = 14 so 14 times 5 = 70
Answer: 70
Step-by-step explanation:
Since 42 push-ups can be done in 3 minutes, then you would divide
42 by 3 and get 14.
Once you get that, you would need to Multiply 14 by 5 and get as your final answer, 70
Find the first 5 terms of each sum and compute S5.
The total of all S5 terms, the first five terms, and the two different types of mathematical advancement equal 105.5.
what is arithmetic progression ?An arithmetic progression whenever there is a steady difference amongst terms that follows to each other in a series. For instance, following new number 5, 7, 9, 11, 13, and 15 is an example of an exponential function with a limitation of two. A progress with a set tolerance among any two consecutive numbers generally referred to as a "arithmetic progression" (A.P.). Two types of mathematical progress are possible: series in arithmetic with a finite length A finite mathematical progression is a progression with a finite number of terms. The soon, late, allowance, and quantity of terms may all be calculated using the entries in the series.
given
The geometric sequence 8,12,18,27,81/2's
first five partial sums, S1,S2,S3,S4, and S5, must be found in order.
S1=8
S2=8+12=20
S3=8+12+18=38
S4=8+12+18+27=65
S5=8+12+18+27+81/2=105.5 as a result.
The total of all S5 terms, the first five terms, and the two different types of mathematical advancement equal 105.5.
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what are the excluded values?
After divide, the solution of the expression is,
⇒ x (x + 2y) / 5
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
⇒ (x² - 4y²) ÷ (5x - 10y) / x
Now, We an simplify as;
⇒ (x² - 4y²) ÷ (5x - 10y) / x
⇒ (x² - (2y)²) ÷ (5x - 10y) / x
⇒ (x - 2y) (x + 2y) ÷ 5(x - 2y) / x
⇒ (x - 2y) (x + 2y) × x/ 5 (x - 2y)
⇒ x (x + 2y) / 5
Thus, The solution of the expression is,
⇒ x (x + 2y) / 5
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A punter for a football team is trying to determine the optimal angle for striking the football off his foot—this is called the launch angle. Using video, his coach records a number of punts kicked using different launch angles and the height in feet for each punt. Using computer software, the coach achieves a linear model by taking the log of each launch angle and plotting against the log of each height.
A graph titled log (height) versus log (launch angle) has log (launch angle) on the x-axis, and log (height) on the y-axis. The points increase in a line with positive slope.
A graph titled residuals versus log (launch angle) has log (launch angle) on the x-axis, and residual on the y-axis. The points curve down, and then up.
Based on the scatterplot and residual plot, which type of model would best summarize the relationship between launch angle and punt height?
A linear model is appropriate because the residual plot shows a random scatter.
A logarithmic model is appropriate because logarithms were used to transform the data sets.
A power model is appropriate because the scatterplot of log angle and log height is roughly linear.
An exponential model is appropriate because the scatterplot of log angle and log height is roughly linear.
Correct answer is: A power model is appropriate because the scatter plot of log angle and log height is roughly linear.
What is Scatter plot?The graphs known as scatter plots show how two variables within a data collection relate to one another. Both a two-dimensional plane and the Cartesian system are used to represent the data points. The Y-axis is used to plot the dependent variable, while the X-axis is used to represent the independent variable or characteristic. Data points are shown on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.
According to Scatter plot, the relation between log(height) and log(launch angle) is linear.
Let, us consider log(height) = m log(launch angle) + b
Height = [tex]10^{(log(launch angle))}[/tex] + b
Height = [tex](launch angle)^{m}[/tex] + 10ᵇ
Height = (10)ᵇ + [tex](launch angle)^{m}[/tex]
Thus, the relation of height and launch angle is in power mode.
Correct answer is: A power model is appropriate because the scatter plot of log angle and log height is roughly linear.
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