Using the Pythagoras theorem, the height of the tree from the reflection pond is obtained as 27.3 m.
What is the height of the tree?We know that the height of the tree can be obtained from the formula for the Pythagoras's theorem and looking at the theorem, we are going to have that;
C^2 = A^2 + B^2
Where A is the height, in meters, of the tree.
Then we have that;
30.24^ = A^2 + 12.96^2
A^2 = 30.24^2 - 12.96^2
A =27.3 m
This is the length of the tree that have been measured from the ground to the given height as we have bene shown in the question above.
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Mr. Ramiriz i making pie to ell at the local farmer’ market. It cot her $5 to make each pie, plu a one-time cot of $30 for baking upplie. She plan to ell the pie for $12 each. Which equation can be ued to find the number of pie he need to ell to break even?
5x – 12x = 30
5x 12x = 30
5x 30 = 12x
12x 30 = 5x
The equation can be used to find the number of pie he need to sell to break event.
c. 5x + 30 = 12x
Given :Mrs. Ramirez is making pies to sell at the local farmer’s market. It costs her $5 to make each pie, plus a one-time cost of $30 for baking supplies. She plans to sell the pies for $12 each.
To Find: Which equation can be used to find the number of pies she needs to sell to break even.
Solution:
Let no. of pies be x
It cost her $5 to make each pie
So, cost of making x pies = 5x
Since there is a one-time cost of $30 for baking supplies.
So, total cost for her is 5x+30
If she sells each pie for $12
Then cost of pies = 12x
Now,
The equation can be used to find the number of pies she needs to sell to break even:
c) 5x+30=12x
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Eight friends went on a hiking trip they took 40 bottles of water and iced tea each friend carried the same number of bottles they each carried 2 bottles of iced tea how many water bottles did each friend carry
Answer: they each carried 5 water bottles.
Step-by-step explanation: 8x5 equals 40
Answer: 5
Step-by-step explanation:
40 divided by 8
1. find the value of 3x 4y - 10 if x = 3 and y =5
2. find the value a cubed + 5a if a = 2
3. 6ab + 4bc - 2ac if a = 1, b = 2, c = 3
4. subtract 2x squared + 3x - 2 from 5x squared - 9x + 11
5. find the difference of 2x squared + 4xy squared 5xsquared y - 2
-x squared 4xy squared 3xsquared y - 10
Step-by-step explanation:
3×4(5)-10
12(5)-10
60-10
50
Work out the value of x
Answer:
3
Step-by-step explanation:
trust lil bru
jimmy pays 3.69 for every gallon of gas he puts in car. draw a graph which models the change in amount of money Jimmy has.
Therefore , the solution of the given problem of equation comes out to be 3.69x = y.
What is the equation?Equ is the translation of the Latin word for equivalent. Latin roots can be found in the base words of many English language words that are subject to modification, such as adequate, moderate, and equality. As both sides of either an equation are, in essence, "same" to one another, the Latin root term equ enters our variable quite easily.
Here,
Given : Jimmy spends $3.69 per gallon of fuel he puts in his vehicle.
Thus,
To find the equation for the amount of money:
Let x be the number of times he refuel his gallon of fuel:
So,
Here y represents the total amount of money.
3.69x = y
Therefore , the solution of the given problem of equation comes out to be 3.69x = y.
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HELPP PLEASE. What is the equation of the line that passes through the point (-6,-3) and had a slope of -1/6?
Evaluate each expression.
(Examples)
4 7. |10|= ?
Therefore , the solution to the given problem of mean comes out to be the sample size yields the equivalent number of households is 30.
What is mean?Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the total number of values in the dataset by the total number of values in the dataset. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the numbers in a set of data and dividing the total by the total number of numbers.
Mean = 2 Four pets are two standard deviations away from the mean, and one standard deviation equals one pet.
We can determine that at least
100 (1-1k2)% = 100 (1-1/4)% = 75%
is within 2 standard deviations of the mean using Chebyshev's Rule with
k = 2. The percentage times the sample size yields the equivalent number of households:
75% x 40 = 30 Therefore , the solution to the given problem of mean comes out to be the sample size yields the equivalent number of households is 30.
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On solving the provided question, we can say that the expression, we have here is 4 7. |10|= 470 or -470
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
the expression, we have here is
4 7. |10|= 470 or -470
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Can you please answer the question o in this image ?
Answer:
-4 x^3 y^2 thus: # 4
Step-by-step explanation:
Simplify the following:
(24 x^6 y^3)/(-6 x^3 y)
The gcd of 24 and -6 is 6, so (24 x^6 y^3)/(-6 x^3 y) = ((6×4) x^6 y^3)/((6 (-1)) x^3 y) = 6/6×(4 x^6 y^3)/(-x^3 y) = (4 x^6 y^3)/(-x^3 y):
(4 x^6 y^3)/(-1 x^3 y)
Combine powers. (4 x^6 y^3)/(-x^3 y) = (4 x^(6 - 3) y^(3 - 1))/(1 (-1)):
(4 x^(6 - 3) y^(3 - 1))/(-1)
6 - 3 = 3:
(4 x^3 y^(3 - 1))/(-1)
3 - 1 = 2:
(4 x^3 y^2)/(-1)
Multiply numerator and denominator of (4 x^3 y^2)/(-1) by -1:
Answer: -4 x^3 y^2
Answer: #4
Step-by-step explanation:
You would divide 24 by -6, leaving u with -4 then u would subtract the powers x to the power of 6 from x to the power of 3 leaving you with x to the power of 3 and then you would subtract y to the power of 3 by y leaving you with y squared.
-4x to the power of 3 y to the power of 2.
Are multiples of 2 prime numbers?
No, not all the multiples of 2 are not prime numbers only 2 itself is prime number other multiples of 2 are composite numbers.
As given in the question,
Given number is equal to :
2
Prime numbers are defined as the number which represents only two factors one and the number itself.
Multiples are defined as the given number when multiply by any integer.
Multiples of 2 are as follow :
2 × 1 = 2
2 × 2 = 4
2 × 3 = 6
2 × 4 = 8
2 × 5 = 10 ................ so on.
2 × n = 2n where 'n' belongs to any integer.
Only 2 has two factors.
other multiples of two has more than two factors.
Minimum number of factors of other multiples are :
One, two , and the number itself.
Other multiples represents composite number.
Only 2 is representing the prime number.
Therefore, in the multiple of 2 only 2 is the prime number other are composite number.
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What is another name for ∠ XYZ?
This means that the solution to the triangle issue is ABC, which is equivalent to XYZ.
What's the triangle all about?Any shape with 3 sides and three points is a polygon. The fundamental form of geometry is this. The corners of the triangular Triangle ABC are A, B, and C. When four parts are not collinear in a geometric shape, a single plane plus triangle are produced. As triangles have three sides as well as a top right corner, they are included in polygons.
Here.
Thus,
To prove : ABC and XYZ are similar
hence ∠A = ∠X.
The definition of ∠B and ∠Y is the same.
Because ∠Z = ∠C,
Similar to xy, line ab shares the same value.
There is no difference between lines bc and yz.
XZ corresponds to line ac.
To come up with a solution, Cpct was used.
Triangle segments that match each other are congruent.
The solution to the triangle problem is ABC is proportional with XYZ as a result.
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Answer: it's Y because i took the test, also when doing this type of math problem you wouldn't start from X or Z because they are starting points
Step-by-step explanation: I TOOK the test
Is △fhk similar to △ghj? if so, which postulate or theorem proves these two triangles are similar? responses △fhk is similar to △ghj by the sss similarity theorem. , , triangle f h k, , , , is similar to , , , , triangle g h j, , , , by the , , , , s s s similarity theorem, , . △fhk is similar to △ghj by the ssa similarity theorem. , , triangle f h k, , , , is similar to , , , , triangle g h j, , , , by the , , s s a similarity theorem, , . △fhk is similar to △ghj by the sas similarity theorem. , , triangle f h k, , , , is similar to , , , , triangle g h j, , , , by the , , , , , , s a s theorem, , . △fhk is not similar to △ghj.
No, they are not similar. There is no postulate or theorem that can prove these two triangles are similar since they are not similar.
Similar triangles are triangles that have the same angle measures and the same side lengths. In order to determine if two triangles are similar, it is necessary to compare the sides and angles of the triangles.
In this case, the sides and angles of △fhk and △ghj are not the same, so they are not similar. Therefore, there is no postulate or theorem that can prove these two triangles are similar. No, they are not similar. There is no postulate or theorem that can prove these two triangles are similar since they are not similar.
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The expression 4 square root of 3 times 3 square root of 3^5 is equivalent to
The given expression is equivalent to 486√3
What are expressions?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, √4 of 3√3 of 3⁵
√4 of 3√3 of 3⁵ = 2×3√3×243
= 486√3
Hence, the given expression is equivalent to 486√3
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URGENT!
Prove that in the isosceles triangle the heights removed from the vertices of the base on the side edges are congruent
Therefore ,consider that the divided congruent triangle corresponding bases are equivalent as proof.
How do triangles work?Given that it contains three sides & three vertices, a triangle qualifies as a polygon. It is a fundamental characteristic in geometry. Triangle ABC is the name given to a triangle with vertices A, B, & C. When the three components are not collinear, Euclidean geometry reveals an unique plane and triangle. The polygonal shape of a triangle has 3 components and three corners. The points where three sides touch each other end to end are referred to as the triangle's corners. The sum of the three triangle angles is 180 degrees.
Here,
Given :
This RHS theorem can be employed to demonstrate the equality of the respective.
bases of all those split congruents as well as the congruency of two independents that are produced by the altitude of such an isosceles from every given vertex.
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Evaluate the following integral : Integral of x^3 + 1/x^0.5 dx
The value of the integration of the expression [tex]$$\int x^3+\frac{1}{x^{0.5}} d x$$[/tex] will be [tex]\frac{1}{4} x^4+2 x^{0.5}+C[/tex]
[tex]$$\int x^3+\frac{1}{x^{0.5}} d x$$[/tex]
Split the single integral into multiple integrals.
We will get: [tex]$$\int x^3 d x+\int \frac{1}{x^{0.5}} d x$$[/tex]
By the Power Rule, the integral of x^3 with respect to x is (1/4)x^4.
[tex]\frac{1}{4} x^4+C+\int \frac{1}{x^{0.5}} d x[/tex]
Let u=x^{0.5}.
Then [tex]d u=\frac{0.5}{x^{0.5}} d x[/tex],
So [tex]$\frac{x^{0.5}}{0.5} d u=d x$[/tex].
Now, we will rewrite the above using u and du.
Let u=x^{0.5}.
Finding the value of (du/dx)
Differentiate x^{0.5}.
[tex]\frac{d}{d x}\left[x^{0.5}\right][/tex]
Differentiate using the Power Rule which states that [tex]$\frac{d}{d x}\left[x^n\right]$[/tex] is n x^{n-1} where n=0.5.
We will get: 0.5 x^{-0.5}
Simplify.
Rewrite the expression using the negative exponent rule
[tex]b^{-n}=\frac{1}{b^n}\\0.5 \frac{1}{x^{0.5}}[/tex]
Combine 0.5 and [tex]\frac{1}{x^{0.5}}[/tex] we will get [tex]\frac{0.5}{x^{0.5}}[/tex]
Rewrite the problem using u and du.
We will get it as:
[tex]\frac{1}{4} x^4+C+\int 2 d u[/tex]
Apply the constant rule, we will get: [tex]\frac{1}{4} x^4+C+2 u+C[/tex]
Simplifying we will get it as: [tex]\frac{1}{4} x^4+2 u+C[/tex]
Replace all occurrences of u with x^{0.5}.
We will get it as: [tex]\frac{1}{4} x^4+2 x^{0.5}+C[/tex]
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Given the equations `9x + (3)/(4)y = 6` and `2x + (1)/(2)y = 9`, by what factor would you multiply the second equation to eliminate y and solve the system through linear combinations?.
We multiply by -3/2 to get rid of y and figure out the system of equations.
What are equations?A mathematical assertion that has an "equal to" symbol between two expressions with equivalent values is called an equation.
As in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including straight, quadratic, cubic, and others.
So, we have:
9x+3/4y=6 and 2x+1/2y=9
By removing y, we must solve a system of equations.
Therefore, we will first make the y-coefficient equal but with the opposite sign.
In the first equation, the y-coefficient is 3/4
The coefficient of y in equation two is half.
LCM: 3/4 and 1/2 = 3/2
To maintain the same coefficient of y, multiply the second equation by -3/2.
-3/2*2x-3/2*1/2y = -3/2*9
-3x-3/4y = -27/2
9x+3/4y = 6
Combine the two equations and get rid of the y variable.
-3x+9x = -27/2+6
6x = -15/2
x = -5/4
Therefore, we multiply by -3/2 to get rid of y and figure out the system of equations.
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Complete question:
Given the equations 9x+3/4y=6 and 2x+1/2y=9, by what factor the equation to eliminate y and solve the system through linea would you multiply the second equation to eliminate y and solve the system through linear combinations?
Options;
A.) -4/3
B.) -3/4
C.) -3/2
D.) -7/2
The scale on map indicates that 3/4 of an inch represents 3
miles. If the distance between two points on its map is 2
inches, how far apart are two locations?
A map uses scaled drawings. The distance between the two considered cities on that specified map is 6.25 inches
How are scale drawings formed?
For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.
Then it means
1ft : s/k in.
All feet measurements will then we multiplied by s/k to get the drawing's corresponding lengths.
For this case, it is specified that the map uses scaling such that:
3/4 of an inch on map = 3 miles in reality.
Dividing both the quantities by 3, we get:
1 mile in reality = 3/4 / 3 inches on map = 1/4 inches on map
Multiplying both the quantities by 25, we get:
25 miles in reality = 25/4 = 6.25 in map
Since 25 miles is the distance between those two considered cities.
Therefore, the distance between those two cities on map would be of 6.25 inches.
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Is a triangle possible with length of the sides as 10.2 cm 6.8 cm and 4.6 cm?
It is not possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm because the sum of two sides are greater than the third sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.
To check this we firstly add the 10.2 and 6.8
10.2 + 6.8 > 4.6
17 > 4.6
Now we add 10.2 and 4.6
10.2 + 4.6 > 6.8
14.8 > 6.8
Now we add 6.8 and 4.6
6.8 + 4.6 > 10.2
11.4 > 10.2
It is possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm because the sum of two sides are greater than the third sides.
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In what quadrant-14 -5i located on the complex plane
Third quadrant the complex plane is where the number -14 - 5i is situated.
-14-5i is located in which quadrant?Based on the common knowledge, the complex number's real and imaginary components are considered as the x- and y- coordinates of an ordered pair in a 2-D plane.
first quadrant a+bi =(a,b)
second quadrant -a+bi= (-a,b)
third quadrant -a-bi=(-a,-b)
fourth quadrant a,-b=(a,-b)
According to the question,-14-5i is located in third quadrant(-14,-5)
As a result, the complex plane's third quadrant is where the number -14 - 5i is situated.
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If a quadratic function has a turning point of (-3, 2)
then where does the quadratic function defined by
g(x) = 2f(x-4) + 5.
a) Describe the transformations(s).
b) State the turning point of g(x).
a) The quadratic function g(x) = 2f(x-4) + 5 is defined as a transformed version of the original quadratic function f(x). The transformation applied to f(x) is a horizontal shift of 4 units to the left and a vertical shift of 5 units upward. This can be observed from the fact that x is replaced with (x-4) in the function g(x). The function is also scaled by a factor of 2.
How does a quadratic function work?
f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.
b) The turning point of the quadratic function f(x) is (-3, 2). To find the turning point of g(x), we must first apply the horizontal shift of 4 units to the left to the x-coordinate, and then apply the vertical shift of 5 units upward to the y-coordinate.
The turning point of g(x) is (-3+4, 2+5) = (1,7)
So, the turning point of the transformed function g(x) is (1,7)
We can see that the transformation of g(x) moves the turning point of f(x) to the right and up, as expected from the transformation.
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13) AMNP-ARST
a) Find the value of x if MN = 5x + 10, MP-5, RT-4, RS= 6x-8, and ST-42.
b) What is the length of MN, RS, and NP?
MN =
RS=
= 80
x=
NP =
what is number 13
When MN = 5x + 10, the lengths of MN, RS, and NP are 410, 400, and 320, respectively in this triangle .
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
given
as AMNP-ARST
the x = 80
so MN = 5 * 80 + 10
= 410
RS = 6* 80 - 8
= 400
When MN = 5x + 10, the lengths of MN, RS, and NP are 410, 400, and 320, respectively in this triangle .
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Which of the following ordered pair is a solution of 2x +3y ≤ 6?A. 1-1,4) B. (-21) C. 11,2) D. (3.3)
(0,2) and (3,0) are the required two solutions of the given equation in an ordered pairs .
The given equation is 2x+3y<=6.
When, x=0,y=2
When, y=0,x=3
Hence,
(0,2) and (3,0) are the two solutions of the given equation
in order to determine the x x and y y values to form the ordered pair.
An ordered pair, is a pair of elements in which it have a specific importance for the order of their required placements. Ordered pairs are mainly used in coordinate geometry in order to represent a point on a coordinate plane and it is also used to represent elements of a relation .
An ordered pair is defined as pair formed by two elements which are separated by a comma and written inside the parentheses. example, (x, y) represents an ordered pair, where 'x' is called the first element and 'y' is called the second element of the ordered pair. These elements which have specific names according to that context they are being used and that can be either variables or constants. The order of the elements which has a certain importance in an ordered pair. It means that (x, y) may not be equal to (y, x)at all the time.
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Brooklyn had math and reading homework tonight. Brooklyn can solve each math
problem in 2 minutes and she can read each page in 3 minutes. The number of math
problems Brooklyn solved is twice the number of pages she read and it took her 70
minutes to complete all of her homework. Write a system of equations that could be
used to determine the number of math problems Brooklyn solved and the number of
pages
she read. Define the variables that you use to write the system.
Let
Let
System of Equations:
Brooklyn could calculate how many arithmetic problems she completed and how many pages she read using the equations x = 2y and 2x + 3y = 70.
What is meant by mathematical equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.let
number of math problems Brooklyn solved = x
number of pages she read = y
Time to solve each math = 2 minutes
Time to read each page = 3 minutes
Brooklyn read twice as many pages as there were arithmetic problems to be done.
x = 2y
2x + 3y = 70
Substitute x = 2y into
2x + 3y = 70
2(2y) + 3y = 70
4y + 3y = 70
7y = 70
divide both sides by 7
y = 70/7
y = 10
Recall,
x = 2y
x = 2(10)
x = 20
Therefore, Brooklyn completed 20 math problems and read 10 pages, which equals 20 math problems and 10 pages, respectively.
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Determine which of the lines,if any are parallel. Explain
PLEASE HELP GEOMETRY FINAL
What is the sequence of transformations that maps A ABC to
A A'B'C'?
Select from the drop-down menus to correctly identify each step.
Step 1: Choose…
rotate 90° clockwise about the origin.
reflect across the line y = x
reflect across the Y axis.
rotate 180° about the origin.
Step 2: Choose..
translate 1 unit right.
Translate 2 units right.
Translate 4 Units down.
Reflect across the x-axis.
Answer:
I believe… ( it might be wrong… )
Reflect across the line y = x.
translate 1 unit right.
Step-by-step explanation:
i took the same test before but i believe i had a question just like this and got it right soooo….. ye
Can someone help me with these pls
Answer:
9) 17 miles/hr
10) 7.14 miles
Step-by-step explanation:
See the attached worksheet. Note the use of conversion factors. In question 9 we want to convert minutes to hours. We know there are 60 minutes/hr. So we can set up a conversion factor in one of 2 ways: (60 minutes/1 hr) or (1 hr/60 minutes). Both are valid, and both are = 1, since the numerator and denominator are both equivalent. This means we can invert a conversion factor and it is still = 1. Since conversion facots are equal to 1, we can multiply them times anything, and the result is numerically the same (anything times 1 = anything) and only the units have changed. For question 9, we want to convert miles/min to miles/hr. I'll choose the conversion factor (60 min/1 hr), mostly because I like multiplication over division. Note how the units cancel in the attachment, resulting in 17 miles/hr. One may also use the factor (1hr/60min), but then a division is required. Perfectly fine, but not my preferred route.
The same approach is used to answer question 10. Again, note how he units cancel, leaving a number wth just the units desired,
A baseball player gets 15 hits in 45 at bats. Distinguish what the experimental probability is of the player getting a hit.
Show all of your work.
Answer:
Below
Step-by-step explanation:
This IS basically an experiment with 15 hits out of 45 at-bats
15/45 = .333 or 33.3 % experimental probability
Answer:
The experimental probability is of the player getting a hit is 1/3 or 33.33%--------------------------------------
Given:
Number of attempts = 45,Number of hits = 15.Find the experimental probability.
Probability of getting a hit is:
P(hit) = hits / attempts,P(hit) = 15/45 = 1/3 ≈ 33.33%.true or false? i need help
g-9=24;g=35 is this true or false
Answer: no
Step-by-step explanation:
35 -9 = 26
you add 1+1 =2
then you look at the equal and that is your answer
What is the domain of the function f/x )= 4 x?
The domain of the function f/x = 4x is all real numbers.
The domain of a function is the et of all values that can be plugged into the equation and produce a valid output. Since any real number, positive, negative, or zero, can be plugged into the equation and produce a valid output, the domain of the function f/x = 4x is all real numbers.
The domain of a function is the set of values that can be plugged into the equation and produce a valid output. In the case of the function f/x = 4x, the domain is all real numbers; that is, any value, positive or negative, can be plugged into the equation and produce a valid output. This means that the domain of the function f/x = 4x includes all real numbers, from the smallest negative number to the largest positive number, as well as zero.
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How do you find the value of N example?
N! also called N factorial is the product of all positive non-integers equal to or less than N or simply is the product of the Nth integer and all integers below it.
N! is represented as 1x2x3x4.......x n which is also equivalent to n x (n-1_x(n-2w)x(n-3)......x1. Therefore the formula for N factorial is N! = n × (n - 1)!. For whole numbers, the factorial is a product of natural numbers till 1 of the values is equal to or less than whole numbers.
N is also used to represent the set of natural numbers up to infinity. Natural numbers include the values from till infinity, they can be represented like N=[1,2,3,4,5,6........].
Examples of N! are:-
4!= 4x3x2x1=24 here we take the product of values equal to or less than 4 upto 112= 12x11x10x9x...... x2x1=479001600 here we calculate the product of 12 and lesser natural numbers(N+3)!= (N-3)X(N+2)X(N+1)X......X1To know more about factorials visit:
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write a new equation 6x+2y=12