In this exercise we want to explain why two more similar functions have different ranges, like this:
the values of the range are different because the domain in which the inverse function exists are different .
In this exercise we know that we are dealing with two distinct functions, like this:
What is the function of sine?The sine function is considered an odd function, as there is a symmetry in the graph with respect to the bisector of the odd quadrants. When a function is considered odd, we have that f (x) = -f (x), that is, sin (-x) = -sin (x).
What is the function of cosine?Cosine is a trigonometric function, used in a right triangle to define the ratio of the side adjacent to and the hypotenuse of this triangle.
So we can see that the reason the two functions have different ranges is associated with them having different domains.
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A student rolls a number cube whose six faces are numbered 1 through 6. What is the sample space for this experiment? S = {2, 4, 6} S = {1, 2, 3, 4, 5, 6} S = {6} S = {1, 2, 3, 4}
HURRY PLEASE HELP
Answer: {1, 2, 3, 4, 5, 6}
Step-by-step explanation:
Sample space is the set of all possible outcomes for a certain experiment.Given : A student rolls a number cube whose six faces are numbered 1 through 6.
Then, the possible outcomes of rolling it = 1, 2, 3, 4, 5, 6
Then , the sample space for this experiment = set of all possible outcomes
= {1, 2, 3, 4, 5, 6}
What is the length of one leg of the triangle
Answer:
Step-by-step explanation:
The length measure of the second leg of the right-angle triangle is 12 units.
What is the measure of the missing leg length of the triangle?Given the parameter:
Hypotenuse = 15 units
Length of leg1 = 9 units
Length of leg2 = x
To determine the measure of the missing side length of the right triangle, we use the Pythagoras theorem.
It is expressed as:
( hypotenuse )² = ( leg 1 )² + ( leg 2 )²
Plug in the given values:
( 15 )² = ( 9 )² + ( leg 2 )²
Simplifying, we get:
225 = 81 + ( leg 2 )²
( leg 2 )² = 225 - 81
( leg 2 )² = 144
Take the square roots:
leg 2 = √144
leg 2 = 12 units
Therefore, the second leg measures 12 units.
The question is not complete, the complete question is:
A right triangle's leg is 9 and the hypotenuse is 15, What is the length of of the other leg of the triangle?
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In a normal distribution, the mean is ____ it's mean and mode
Final answer:
In a normal distribution, the mean, median, and mode are all the same, since it is symmetric around the mean. The standard deviation affects the shape of the distribution, and the empirical rule states that most values lie within two standard deviations of the mean. Differences in symmetry may cause the mean, median, and mode to diverge, with the mean being most affected by skewness.
Explanation:
In a normal distribution, the mean is equal to the median and mode, by definition. This is because the normal distribution, which is also known as the Gaussian distribution, is symmetrically shaped like a bell curve around the mean (μ). The mean indicates the center of the distribution and the point of symmetry, while the median divides the data such that half of the values are above it and half are below. The mode is the most frequently occurring value in the data set, and in a perfect normal distribution, it coincides with the mean and median.
The standard deviation (σ) is a measure of the spread of the distribution. If the standard deviation is increased, the curve becomes wider and flatter, while a decrease in σ makes the distribution steeper and narrower. Additionally, the location of μ on the X-axis can shift the entire graph to the left or right, but the shape of the graph remains the same. The empirical rule helps us understand that approximately 95% of values lie within two standard deviations from the mean.
Drawing from the collaborative exercise provided, by recording the heights and creating histograms with smooth bell-shaped curves, one can calculate the mean and identify how characteristics such as skewness affect the mean, median, and mode, especially in non-symmetric distributions. In these cases, the mean can be influenced by the direction of the skew more than the median, pulling it towards the tail of the distribution.
What is the area of the hexagon? Numerical answer only!
Which of the expressions below can be factor using the difference of squares method
HELPPP PLLLZZZ III BEEEG
For what value of x is the square of the binomial x+1 twenty greater than the square of the binomial x–3?
Answer:
x=3.5 they did nothing wrong but I am pretty sure you meant not twenty but one hundred and twenty for that the answer is x=16
Step-by-step explanation:
Evaluate 0.3 y+\dfrac yz0.3y+zy0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5z, equals, 5.
When [tex]\( y = 10 \) and \( z = 5 \)[/tex], [tex]\( 0.3y + \frac{y}{z} \) equals \( 5 \)[/tex].
Step 1 :To evaluate the expression [tex]\(0.3y + \frac{y}{z}\) when \(y = 10\) and \(z = 5\)[/tex], follow these steps:
1. Substitute the given values of [tex]\(y\) and \(z\)[/tex] into the expression:
[tex]\[0.3 \times 10 + \frac{10}{5}\][/tex]
2. Calculate each term separately:
- [tex]\(0.3 \times 10 = 3\)[/tex]
- [tex]\(\frac{10}{5} = 2\)[/tex]
3. Add the results:
[tex]\[3 + 2 = 5\][/tex]
So, when [tex]\(y = 10\) and \(z = 5\)[/tex], the expression [tex]\(0.3y + \frac{y}{z}\) equals \(5\).[/tex]
Step 2 :1. Multiply 0.3 by 10:
[tex]\[0.3 \times 10 = 3\][/tex]
2. Divide 10 by 5:
[tex]\[\frac{10}{5} = 2\][/tex]
3. Add the results:
[tex]\[3 + 2 = 5\][/tex]
Thus, when [tex]\(y = 10\) and \(z = 5\)[/tex], the expression [tex]\(0.3y + \frac{y}{z}\) equals \(5\).[/tex]
The function given by Upper A left parenthesis t right parenthesis equals 0.0265 t cubed minus 0.444 t squared plus 1.774 t plus 8.76A(t)=0.0265t3−0.444t2+1.774t+8.76, 0 less than or equals t less than or equals 100≤t≤10, can be used to estimate the amount, in billions of dollars, invested by large oil companies in exploration for new reserves t years after 19951995. Find the relative extreme points, and sketch a graph of the function.
How many times is function f called in the code segment below? 25 points?
write the rate as a fraction? 17 meters per second
solve equation (n-1)(n+6)(n+5)=0
Tom and Sonya were comparing their answers on a math problem. It was an order of operations problem, and they each had a different answer. Tom had an answer of 11, and Sonya had an answer of 104. Which student correctly solved the order of operations problem given by the teacher?
(5^2 +6)–(7•4)+8
Which equation represents the general form a circle with a center at (–2, –3) and a diameter of 8 units?
A.) x^2+y^2+4x+6y-51=0
B.) x^2+y^2-4x-6y-51=0
C.) x^2+y^2+4x+6y-3=0
D.) x^2+y^2-4x-6y-3=0
To find the equation, we will form the general equation of a circle and then will find the equation that matches the equation we formed.
General equation of a circleThe general equation of a circle is given as
[tex](x-h)^2+(y-k)^2 = R^2[/tex]
where, the (h, k) are the coordinates of the center of the circle, and R is the radius of the circle.
The correct option is c.
Given to uscircle with a center at (–2, –3) diameter of 8 unitsTo findthe equation of the circle that represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.
Radius of the CircleGiven that the diameter of the circle is 8 units. therefore,
[tex]\rm{ Radius\ of\ the\ circle =\dfrac{Diameter}{2} = \dfrac{8}{2}[/tex]
Equation of a circleThe equation of the circle that represents the general form of a circle with a center at (–2, –3) and a radius of 4 units can be found by substituting the values in the equation of a circle:
[tex](x-h)^2+(y-k)^2 = R^2[/tex]
Substituting the values,
[tex][x-(-2)]^2+[y-(-3)]^2 = 4^2\\\\ (x+2)^2+(y+3)^2 = 16[/tex]
[tex](x+2)^2+(y+3)^2 = 16\\\\ (x^2 + 4 + 4x)+(y^2+9+6y) = 16\\\\ x^2 + 4 + 4x+y^2+9+6y = 16\\\\ x^2 + 4x+y^2+6y = 16-4-9\\\\ x^2 + 4x+y^2+6y = 3\\\\ x^2 + 4x+y^2+6y -3 = 0[/tex]
Therefore, the equation which will be in the above form will be the equation we want. As we can see the above equation is similar to option c.
VerificationTo verify that we will plot the graph. The image given below represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.
Hence, the correct option is c.
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Cecil Green sells golf hats. He knows that most people will not pay more than $20 for a golf hat. Cecil needs a 40% markup on cost. What should Cecil pay for his golf hats? (Round your answer to the nearest cent.) Cecil pays $
Final answer:
Cecil should pay $14.29 for his golf hats.
Explanation:
To determine what Cecil should pay for his golf hats, we need to calculate the cost price and apply the 40% markup. Let's assume the cost price is 'x'. Since Cecil needs a 40% markup on cost, the selling price will be 140% of the cost.
To find the selling price, we can use the equation: 140% of 'x' = $20. Solving this equation, we get: x = $20 / 1.4 = $14.29.
Therefore, Cecil should pay $14.29 for his golf hats.
What are the 3 steps for factoring completely?
2. How did the technique of “Factoring by Grouping” get it’s name?
3. How can you tell if Factoring by Grouping works for a problem?
4. What is a perfect square trinomial?
5. a.) How can you tell if a binomial is the difference of two squares.
b.) What is the factored form of the difference of two squares.
6. How do you find the zero’s of a polynomial function?
Factoring completely involves three steps: identifying the GCF, applying the appropriate factoring method, and checking for additional factors. Factoring by grouping is used when there are four terms in an expression and common factors can be factored out separately. An example is given to illustrate the factoring by grouping process.
Explanation:Factoring Completely:Identify the greatest common factor (GCF) of the terms in the expression and factor it out.Apply the difference of squares, trinomial, or grouping method to factor the remaining expression.Check if there are any additional factors that can be factored further.Factoring By Grouping:This technique is used when there are four terms in an expression and there is a common factor between the first two terms and the last two terms. The common factor is factored out separately from the two pairs, and then the resulting binomials are factored further.
Factoring by Grouping Example:Consider the expression 2x + 3y + 4x + 6y. In this case, we can group the terms as (2x + 3y) + (4x + 6y). Common factors can be factored out separately, resulting in (2x + 3y)(1 + 2).
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Find the x-intercepts (if any) for the graph of the quadratic function.
6x^2 +12x+5=0
Give your answers in exact form. Show your work
which pair of angles are corresponding angles
a. 1 and 2
b. 1 and 5
c. 2 and 7
d. 2 and 5
A school has 18 left-handed students. If 8% of the total number of students in the school are left-handed, what is the total number of students in the school?
Complete the expansion of (a + b)6 with a = 1 and b = 0.3.
(dont add everything together)
(1 + 0.3)^6 = (____)^6 + 6(____)^5(____) + 15(____)^4(____)^2 + 20(____)^3(____)3 + 15(____)^2(____)^4 + 6(___)(___)^5 + (____)^6
Answer:
[tex](1+0.3)^{6}=(1)^6+6(1)^{5}(0.3)+15(1)^{4}(0.3)^{2}+20(1)^{3}(0.3)^{3}+15(1)^{2}(0.3)^{4}+6(1)^{1}(0.3)^{5}+(0.3)^{6}[/tex]
Step-by-step explanation:
This is an expansion of the expression [tex](a+b)^{6}[/tex]. In general you can expand expressions of this form by a formula known as the binomial theorem. This formula establishes that
[tex](a+b)^{n}=\sum_{k=0}^{n} {n\choose k} a^{n-k}b^{k}[/tex]
Where the coeficients [tex]n\choose k[/tex] are called binomial coeficients, and can be computed by the formula
[tex]{n\choose k} =\frac{n!}{(n-k)! k!}[/tex]
where [tex]n!=1\times 2\times 3\times \cdots\times n[/tex].
Find the radius of the circle whose equation is 3x² + 3y² = 75.
Answer: 5 units
Step-by-step explanation:
We know that the general equation of a circle having center at (h,k) and radius r is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Given : The equation of a circle : [tex]3x^2 + 3y^2 = 75[/tex]
Taking 3 as common from the left side of the given equation , we get
[tex]3(x^2 + y^2) = 75[/tex]
Divide 3 on both the sides , we get
[tex]x^2 + y^2 = 25[/tex]
Comparing to the general equation of circle , we get
[tex]r^2 = 25\\\\\Rightarrow\ r=5[/tex]
Hence, the radius of the circle = 5 units
It's 3/5 of the wall is made from brick how do you determine the height of the brick proportion of the wall
To find the height of the brick proportion of a wall, multiply the total wall height by the fraction representing the brick portion. For instance, if the wall is 220 cm high and 3/5 is brick, the brick portion's height would be 132 cm.
To determine the height of the brick proportion of the wall, you would need to know the total height of the wall first. Once you have the total height, you can calculate the height of the brick section by multiplying the total height by the fraction of the wall that is brick. For example, if 3/5 of the wall is made from brick, and the wall is 220 cm high, the calculation would be as follows:
Height of brick portion = Total height of the wall × Fraction of wall that is brick
Height of brick portion = 220 cm × (3/5) = 132 cm
Therefore, the height of the brick proportion of the wall would be 132 cm.
onsider the following pseudocode function. function Crunch(x R) if x ≥ 100 then return x/100 else return x + Crunch(10 · x) (a) Compute Crunch(4). Crunch(4) = (b) What happens if you try to compute Crunch(−23)? What does this suggest about an appropriate precondition for this function?
Which prefix means 1/10 of a unit in the metric system?
A. milli
B. Deci
C. Hecto
D. Centi
-3x = 4y = 8
X and y intercepts of this equations . Then graph line
annual college tuition and fees are 8000$. Books and other charges cost 1000$ per year. If Tony receives a $4500 scholarship each year, how much more will he need to pay for 1 year of college?
What is the mode of the data set?
103, 77, 90, 102, 103, 81, 78, 84, 84, 87, 99, 103, 118
Question 3 options:
84
90
93
103
4z - 7 in terms of z
who is the fastest man alive?
Usain Bolt set world records for the 100-m and 200-m dashes with impressive maximum speeds and accelerations.
Usain Bolt of Jamaica set the world record for the men's 100-m dash in the 2008 Olympic Games in Beijing. He accelerated for 3.00 s to reach his maximum speed and maintained it for the race. Calculating his maximum speed and acceleration involves understanding his performance data.
For the 100-m dash, Bolt's maximum speed was approximately 12.19 m/s and his acceleration was 2.63 m/s². In the 200-m dash, his maximum speed using the same assumptions was 10.36 m/s. This insight into Bolt's remarkable athleticism showcases his exceptional speed and acceleration capabilities on the track.
The manager of a video game store found that 35 of the 140 people who preordered the latest baseball game canceled their orders the day before the game was released. He used that data to create a simulation to predict the probability that future customers will cancel their preorders.
Using the data presented in the problem, you are asked to predict the probability that future customers will cancel their preorders. To find the probability, you have to divide the number of people who cancelled their preorders by the total number of people who preordered.
35 people / 140 people = .25 or 25% probability that the future customers will cancel their preorders.
Answer:
A
Step-by-step explanation:
this math problem is hard