Answers
Answer:
Domain is all real numbers; Range is all numbers less than or equal to 0
Step-by-step explanation:
Domain covers x values, range covers y values. The domain of an x^2 parabola, which is what this is, has a domain of all real numbers. Meaning that while the branches of the function keep going up and up and up or down and down and down, the values of x will never stop growing.
The range here is indicative of the lowest y value to the highest that the function covers. In this case, since the parabola is upside down, we have the highest to the lowest. The highest that the function goes up the y axis is right at the origin, where y = 0. Then it drops down into forever. So the range is all values of y less than or equal to 0
The Domain of [tex]f(x)[/tex] is all the real numbers, and
The Range of [tex]f(x)[/tex] is [tex]y\le0[/tex] or [tex]f(x)\le0[/tex]
The diagram shows the graph of the quadratic function
[tex]f(x)=-x^2[/tex]
The domain of [tex]f(x)[/tex] is all the real numbers, since the function has defined values for all real values of [tex]x[/tex].
The range of [tex]f(x)[/tex] is the set of values that [tex]f(x)[/tex] can assume. The square function has a range
[tex]\{y \text{ }|\text{ }y=x^2\text{ and }y\ge0\}[/tex] or the half-open interval [tex][0,\infty)[/tex].
This means that the negative of the square function will have the range
[tex]\{y \text{ }|\text{ }y=-x^2\text{ and }y\le0\}[/tex] or the half-open interval [tex](-\infty,0][/tex].
So, the domain of [tex]f(x)[/tex] is the open interval [tex](-\infty,\infty)[/tex] (all the real numbers), and the range of [tex]f(x)[/tex] is the half-open interval [tex](-\infty,0][/tex] (or, [tex]y\le0[/tex])
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Related Questions
You are getting ready to watch a fireworks display and are sitting about 300 feet away from the launch pad. The angle for you to see the fireworks is about 35°. If the fireworks are launched vertically into the sky, what is the height of the fireworks when they explode?
Answers
Answer:
210.06 feet
Step-by-step explanation:
This is a classic right triangle trig problem. The distance from the launch pad is the measure of the base of the right triangle. The angle of elevation, 35, is the base angle (not the right angle). How high the fireworks go up is the height of the triangle. You have the reference angle of 35, the side adjacent to it, 300, and you're looking for the side length across from it, y. The trig ratio that relates a reference angle to the sides opposite it and adjacent to it is the tangent ratio. Setting that up:
[tex]tan(35)=\frac{y}{300}[/tex]
Solving for y:
y = 300 tan(35)
On your calculator in degree mode find y to be 210.06 feet.
By using basic trigonometry, specifically the tangent of the viewing angle, we can determine that the height of the fireworks when they explode is approximately 210 feet.
Explanation:You are asking how to use trigonometry to find the height of the fireworks when they explode. If we combine your conditions that the launch was vertical and the viewing angle was 35°, we can use the tangent of that angle to find the height of the fireworks. The tangent of an angle in a right triangle is the opposite side (height in this case) divided by the adjacent side (distance from the launch, 300 feet in this case). So setting up the equation, we have: tan(35°) = height / 300. Solving for 'height', we get: height = 300 * tan(35°). Using a calculator, we find that tan(35°) is roughly 0.70021. Multiplying that by 300, we find that the height of the fireworks when they explode is approximately 210 feet.
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19. Heather invests $4,900 in an account with a 3.5% interest rate, making no other deposits or withdrawals. What will Heather’s account balance be after 5 years if the interest is compounded 2 times each year?
Answers
Answer:
[tex]\$5,828.28[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=5\ years\\ P=\$4,900\\ r=0.035\\n=2[/tex]
substitute in the formula above
[tex]A=\$4,900(1+\frac{0.035}{2})^{2*5}[/tex]
[tex]A=\$4,900(1.0175)^{10}=\$5,828.28[/tex]
Answer:
5,828.28
Step-by-step explanation:
Express the product as a sum containing only sines or cosines. 64) sin (5θ) cos (2θ)
Answers
[tex]\bf \textit{Product to Sum Identities} \\\\sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(5\theta )cos(2\theta )\implies \cfrac{1}{2}[sin(5\theta +2\theta )+sin(5\theta -2\theta )]\implies \cfrac{sin(7\theta )+sin(3\theta )}{2}[/tex]
The required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.
What is the product to sum Identities?The product-to-sum formulae are used to represent the sum of the sine and cosine functions. These are generated from trigonometry's sum and difference formulae.
sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]
The trigonometry expression is given in the question
sin (5θ) cos (2θ)
According to the product to sum Identities
sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]
Here A = 5θ and B = 2θ
sin (5θ) cos (2θ) = (1/2) [sin(5θ + 2θ) + sin(5θ - 2θ)]
sin (5θ) cos (2θ) = (1/2) [sin(7θ) + sin(3θ)]
sin (5θ) cos (2θ) = [sin(7θ) + sin(3θ)] / 2
Thus, the required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.
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The table below shows the values for the function y = f(x).
| x | y |
-4 7
-1 -2
0 3
3 -4
6 5
Complete the table for the function y = f(1/5x).
Answers
Answer:
(x, y) = (-20, 7), (-5, -2), (0, 3), (15, -4), (30, 5)
Step-by-step explanation:
You want 1/5x to match the x-value in the given table. To make that happen, multiply the given x by 5.
Example: when (1/5x) = -4, f(1/5x) = 7, so x = -4·5 = -20 for y = 7.
The transformation f(1/5x) is a horizontal expansion by a factor of 5, so each point of f(x) is now 5 times farther from the y-axis than it was.
The completed table for the function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex] is as follows:
x
−4
−1
0
3
6
y
3
−2
3
7
5
To complete the table for the function [tex]\(y = f\left(\frac{1}{5}x\right)\),[/tex] we need to substitute the given \(x\) values into the function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex] and calculate the corresponding \(y\) values.
The function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex]implies that we are scaling the input \(x\) by a factor of 5. This means the \(x\) values in the original table need to be multiplied by 5 to find the corresponding values for the new function. Let's calculate the values step by step:
1. For [tex]\(x = -4\):[/tex]
[tex]\[y = f\left(\frac{1}{5}(-4)\right) = f(-0.8)\][/tex]
Looking at the original table, when [tex]\(x = -0.8\), \(y = 3\).[/tex]
2. For [tex]\(x = -1\):[/tex]
[tex]\[y = f\left(\frac{1}{5}(-1)\right) = f(-0.2)\][/tex]
When [tex]\(x = -0.2\), \(y = -2\).[/tex]
3. For [tex]\(x = 0\):[/tex]
[tex]\[y = f\left(\frac{1}{5}(0)\right) = f(0)\][/tex]
When [tex]\(x = 0\), \(y = 3\).[/tex]
4. For [tex]\(x = 3\):[/tex]
[tex]\[y = f\left(\frac{1}{5}(3)\right) = f(0.6)\][/tex]
When [tex]\(x = 0.6\), \(y = 7\).[/tex]
5. For [tex]\(x = 6\):[/tex]
[tex]\[y = f\left(\frac{1}{5}(6)\right) = f(1.2)\][/tex]
When [tex]\(x = 1.2\), \(y = 5\).[/tex]
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Can someone show me the steps to do this :( please
Answers
Answer:
Step-by-step explanation:
Use the sum of angle formula:
cos(a+b) = cos(a)cos(b) -sin(a)sin(b)
This gives you ...
cos(x)cos(-π/6) -sin(x)sin(-π/6) = 1 + cos(x)cos(π/6) -sin(x)sin(π/6)
Subtracting the right-side trig function terms and factoring, we have ...
cos(x)(cos(-π/6) -cos(π/6)) -sin(x)(sin(-π/6) -sin(π/6)) = 1
Since the cosine is an even function, cos(-π/6) = cos(π/6). Since the sine is an odd function, sin(-π/6) = -sin(π/6). This gives us ...
cos(x)·0 -sin(x)(-2sin(π/6)) = 1
sin(x) = 1/(2·sin(π/6)) = 1/(2·1/2) = 1
x = arcsin(1)
x = π/2
_____
When solving these by using a graphing calculator, it is convenient to subtract one side of the equation so you have a function of x that you want to find the zeros of. Here, we subtracted the right side. The graph shows the result is zero for x=π/2, as we know.
An object moves along a circular path with radius 10 inches and makes 5 revolutions in 1 minute. What is the linear velocity, in inches per minute, of a point on the edge of the wheel?
10π
20π
50π
100π
Answers
Answer:
100π
Step-by-step explanation:
step 1
Find the circumference
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=10\ in[/tex]
substitute
[tex]C=2\pi (10)[/tex]
[tex]C=20\pi\ in[/tex]
step 2
we know that
An object moves along a circular path and makes 5 revolutions in 1 minute
Remember that
[tex]1\ rev=2\pi r[/tex] ----> circumference of the circle
therefore
[tex]5\ rev=5(20\pi)=100\pi\frac{in}{minute} [/tex]
What will happen to the mean if the outlier is removed?
4, 5, 5, 7, 9, 17
It will not change.
It will be the same as the median.
It will decrease.
It will increase.
Answers
The mean is the average. The outlier is a number way bigger or smaller than the rest of the data. The outlier here would be 17. If you remove 17 and then find the average again, it will be smaller because all the numbers left are around the same range.
Answer: It will decrease
What is the solution to sqrt 17-x=x+3? Show your work.
Answers
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
Remember:
[tex](\sqrt[n]{a})^n=a\\\\(a+b)=a^2+2ab+b^2[/tex]
Given the equation [tex]\sqrt{17-x}=x+3[/tex], you need to solve for the variable "x" to find its value.
You need to square both sides of the equation:
[tex](\sqrt{17-x})^2=(x+3)^2[/tex]
[tex]17-x=(x+3)^2[/tex]
Simplifying, you get:
[tex]17-x=x^2+2(x)(3)+3^2\\\\17-x=x^2+6x+9\\\\x^2+6x+9+x-17=0\\\\x^2+7x-8=0[/tex]
Factor the quadratic equation. Find two numbers whose sum be 7 and whose product be -8. These are: -1 and 8:
[tex](x-1)(x+8)=0[/tex]
Then:
[tex]x_1=1\\x_2=-8[/tex]
Let's check if the first solution is correct:
[tex]\sqrt{17-(1)}=(1)+3[/tex]
[tex]4=4[/tex] (It checks)
Let's check if the second solution is correct:
[tex]\sqrt{17-(-8)}=(-8)+3[/tex]
[tex]5\neq-5[/tex] (It does not checks)
Therefore, the solution is:
[tex]x=1[/tex]
the only solution is x = 1.
To solve the equation sqrt(17-x) = x+3, we first eliminate the square root by squaring both sides of the equation. Doing so yields:
17 - x = (x + 3)2
17 - x = x2 + 6x + 9
Next, we rearrange the equation to set it equal to zero, thus forming a quadratic equation:
x2 + 6x + 9 + x - 17 = 0
x2 + 7x - 8 = 0
Now, we factor the quadratic:
(x + 8)(x - 1) = 0
Hence, the solutions are:
x = -8
x = 1
To verify that these solutions satisfy the original equation, we perform a check by substituting them back into the original equation. However, we notice that the solution x = -8 does not work because it would result in taking the square root of a negative number, which is not possible in real numbers. So the only solution is x = 1.
Please Help!!
Which function has zeroes at npi, where n is an integer? Select 2.
y=cos x
y=cot x
y=csc x
y=sec x
y=sin x
y=tan x
Answers
ANSWER
[tex]y = \sin(x) [/tex]
EXPLANATION
The trigonometric function that is zero at integral values is the sine function.
That is;
[tex]y = \sin(x) [/tex]
has x-intercepts at
[tex] n\pi[/tex]
where n is an integer.
In other words, the solution to the equation:
[tex] \sin(x) = 0[/tex]
is
[tex]x = n\pi[/tex]
where n is an integer.
Answer:
y=sin x
y=tan x
these are correct....
Please help me out please
Answers
Answer:
20°
Step-by-step explanation:
40=2x,x=20°
I have SAT's tomorrow and need help with math...
Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3 hours per week to complete the remainder of her volunteer hours. If w is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?
Answers
Answer:
3w + 52 ≥ 90
Step-by-step explanation:
If she volunteers 3 hours per week for w weeks, then the number of hours from tutoring is 3w. Add the 52 hours from her summer volunteering, and her total hours is 3w + 52. This needs to be at least 90 hours for her to graduate, so:
3w + 52 ≥ 90
Please answer this correctly
Answers
The answer is 8......
Answer:
The answer is 8
Step-by-step explanation:
Just add the rest of the numbers and then subtract from the answer
Identify the value of x and the length of each chord. HELP ASAP!!
Answers
Answer:
First option
x = 9.1, AB = 16.5, CD = 14.1
Step-by-step explanation:
5 * x = 13 * 3.5
5x = 45.5
x = 9.1
AB = 3.5 + 13 = 16.5
CD = 5 + 9.1 = 14.1
The value of x and the length of each chord is x = 9.1, AB = 16.5, CD = 14.1. Thus first option is correct.
What is the relation between line perpendicular to chord from the center of circle?If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.
Or
|AC| = |CB|
Let x be the measure of the length of ED.
[tex]5 \times x = 13 \times3.5\\5x = 45.5\\x = 9.1[/tex]
Therefore,
AB = 3.5 + 13 = 16.5
CD = 5 + 9.1 = 14.1
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Jon has 15 coins in nickels and dimes.he has 3 more dimes than nickels.how many nickels and dimes dose he have
Answers
Answer: 6 nickels and 9 dimes
Step-by-step explanation:
15 coins - 3 extra dimes = 12
12 / 2 = 6
6 nickels
6 + 3 = 9 dimes
Our basketball team has 10 players. we need to divide into two teams of 5 for an intra-squad scrimmage. in how many ways can we do this without restriction?
Answers
There are 252 ways to divide the 10 players into two teams of 5 without any restriction.
To determine the number of ways you can divide 10 players into two teams of 5 without any restriction,
Using the formula, C(n, k) = [tex]\frac{n!}{k!(n-k)!}[/tex]
By finding the number of ways to choose 5 players out of 10, which is the same as choosing the other 5 players who are not on the first team.
Where n = 10
k = 5
C(10, 5) = [tex]\frac{10!}{5!(10-5)!}[/tex]
C(10, 5) = [tex]\frac{10!}{5!(5)!}[/tex]
C(10, 5) = 10*9*8*7*6*5*4*3*2*1/5*4*3*2*1(5*4*3*2*1)
C(10, 5) = 30240/5*4*3*2*1
C(10, 5) = 252 ways
Therefore, there are 252 ways to divide the 10 players into two teams of 5 without any restriction.
What is the sum of all the positive two-digit integers divisible by both the sum and product of their digits?
Answers
Answer:
72
Step-by-step explanation:
Exhaustive search shows the numbers to be 12, 24, 36. The sum of these three numbers is 72.
Yvonne is a salesperson who earns a fixed amount of $1,850 per month. She also earns a commission of 4% on the amount of goods that she sells. If she wants to earn more than $2,300 in one month, how many dollars (x) in goods must she sell?
Answers
Answer: $11,250
1850 + (4/100)x = 1850 + 0.04x.
1850 + 0.04x > 2300
0.04x > 2300 - 1850
0.04x > 450
x > 450 / 0.04
x > $11,250
Answer
x> 11,250
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What else would need to be congruent to show that STU is congruent to JKL by SAS? tysm! :)
Answers
Answer:
Choice C.
Step-by-step explanation:
You already have two sides and two angles. Now you need the other two sides that include the angle. Choice C is correct.
Answer: C. [tex]\overline{SU}\cong\overline{JL}[/tex]
Step-by-step explanation:
SAS congruence postulate tells that if two sides and the included angle of a triangle are congruent to corresponding two sides and the included angle of other triangle, then the triangles are congruent.In the given picture , we have two triangles ΔSTU and Δ JKL , in which we have
[tex]\overline{ST}\cong\overline{JK}[/tex]
[tex]\angle{S}\cong\angle{J}[/tex]
To prove ΔSTU is congruent to Δ JKL, we need [tex]\overline{SU}\cong\overline{JL}[/tex] such that [tex]\angle{S}\text{ and }\angle{J}[/tex] becomes congruent the included angles between pair of congruent sides.
Hence, C is the right option.
(99 POINTS AND BRAINLIEST NEED HELP ASAP)
A prism and two nets are shown below:
Part A: Which is the correct net for the prism? Explain your answer.
Part B: Write the measurements of Sides AB, BC, and CD of the correct net.
Part C: What is the surface area of the prism? Show your work.
Answers
I know that the answer is A, however I can not answer the rest
please help me with this geometry question
image attached
Answers
15/17. The value (ratio) of cos A is 15/17.
The trigonometric ratios of an acute angle are, basically, the sine, the cosine and the tangent. They are defined from an acute angle, α, of a right triangle, whose elements are the hypotenuse, the leg contiguous to the angle, and the leg opposite the angle.
-The sine of the angle is the opposite leg divided by the hypotenuse.
-The cosine of the angle is the adjacent leg divided by the hypotenuse.
-The tangent of the angle is the opposite leg divided by the adjacent leg or, which is the same, the sine of the angle divided by the cosine of the angle.
cos A = adjacent leg/hypothenuse = BC/AC = 15/17
A bag contains 40 marble ,4 of which are blue , 10 are red ,25 are green , and 1 purple Shawna takes a marble out of the bag, records the color and returns it to the bag . How many green marbles should she exepect after 400 trials
Answers
She should expect 250 green marbles.
She has a 25 out of 40 chance of selecting a green marble each time since she is putting it back in the bag each time. 25/40 reduces to 5/8. Multiply 5/8 by 400 and you get 2000/8. Reduce the fraction to 250/1 or 250.
For what value of y must QRST be a parallelogram?
A: 1
B: 2
C: 3
D: 0.5
Answers
Answer:
A
Step-by-step explanation:
Diagonals of a parallelogram bisect each other.
3x = 3
x = 1
y = x
y = 1
In a parallelogram, the parts in which each diagonal cuts the other are congruent.
This means that we must have
[tex]\begin{cases}3=3x\\x=y\end{cases}[/tex]
From the first equation we can deduce x=1, and thus y=x=1.
The person at (0, 1) needs a bottled water. He moved to the right on a slope of -4. Where can you find him to give him the water he ordered
Answers
Final answer:
To locate the person who moved from (0, 1) with a slope of -4, we need to know the specific horizontal distance they moved. Without this, we can only say they moved downward 4 units for every 1 unit they moved to the right.
Explanation:
The student's question involves determining the position of a person who has moved along a slope on a coordinate plane. Since the individual started at the point (0, 1) and moved to the right with a slope of -4, we can assume they are moving in the negative y-direction (downward), as the negative slope indicates a decrease in y for every increase in x. The specific horizontal distance isn't given, so we cannot provide an exact new coordinate without more information. However, if we had a specific horizontal distance the person moved, we could calculate the new position using the slope (-4), which means for every 1 unit moved horizontally to the right, the person would move 4 units down.
Kylie started basketball practice at 2:30 p.m and finished at 6:00 p.m how long was kylie at basketball practice
Answers
Answer:
3 hours and 30 minutes
Step-by-step explanation:
Since both of these times are in the P.M., each hour has 60 minutes and 2:30 is half, add 30 minutes to get 3:00 P.M. and then add 3 hours to get 6:00 P.M. . 3 hours and 30 minutes added to 2:30 P.M. equals 6:00 P.M. :)
Answer:
3 hours and 30 minutes
Step-by-step explanation:
Kylie started basketball practice at 2:30
Kylie finished basketball practice at 6:00
Time duration = 3 hours and 30 minutes
2 : 30 → 3 : 00
( 30 minutes )
3 : 00 → 6 : 00
( 3 hours )
3 hours + 30 minutes = 3 hours and 30 minutes
A coal car on a train weighs 30 tons plus 1 ton per cubic yard of coal x that it carries. The total weight of a coal car is: f(x) = x + 30. How will the graph of this function change if the coal car weight is changed to 26 tons?
Answers
Answer:
every point will be 4 tons lower than it was
Step-by-step explanation:
26 is 4 less than 30, so the new function g(x) is ...
g(x) = f(x) -4
It is shifted down 4 units (tons) from the original function.
You pick a card at random, put it back, and then pick another card at random. 3 4 5 What is the probability of picking a number greater than 3 and then picking an even number?
Answers
Final answer:
To find the probability of drawing a four and then a five from a standard deck with replacement, multiply the probabilities of the independent events: (1/13) × (1/13) = 1/169.
Explanation:
The question involves calculating the probability of two independent events when drawing cards from a standard deck. The first event (A) is drawing a card that is a four, and the second event (B) is drawing a card that is a five. The probability of each of these events is calculated separately since the card is replaced after each draw, making the draws independent of each other.
The probability of drawing a four (P(A)) from a standard deck is 1/13, as there are four fours in a 52-card deck. Similarly, the probability of drawing a five (P(B)) is also 1/13. Since the events are independent, the combined probability is the product of the two probabilities: P(A) × P(B) = (1/13) × (1/13) = 1/169.
Please help me out!?????
Answers
Answer
[tex]\frac{121}{4} \pi mm^2[/tex]
Explanation
Find the radius
11/2 = 5.5
The formula to find the area of a circle is [tex]\pi r^2[/tex]
[tex]\pi 5.5^2[/tex] = [tex]30.25\pi[/tex]
Convert number into fraction.
[tex]30.25 \rightarrow \frac{121}{4} \pi[/tex]
Area = [tex]\frac{121}{4} \pi mm^2[/tex]
Answer:
30.25π mm²
Step-by-step explanation:
The area (A) of a circle is calculated using the formula
A = πr² ← r is the radius
here diameter = 11 and radius is half of the diameter. thus
r = 5.5
A = π × 5.5² = 30.25π mm²
Find the value of the indicated angles. PLEASE HELP!!
Answers
Answer:
Part 1) The measure of the angle is 47°
Part 2) The measure of the angle is 52°
Step-by-step explanation:
Part 1)
we know that
The inscribed angle is half that of the arc it comprises.
we have that
(12y-1)°=(9y+11)° ----> because the arc that the inscribed angles comprise is the same
Solve for y
12y-9y=11+1
3y=12
y=4°
Find the measure of the angle
(12y-1)°=12(4)-1=47°
Part 2)
we know that
The inscribed angle is half that of the arc it comprises.
we have that
2(3m+2)°=(4m+20)° ----> because the arc that the inscribed angles comprise is the same
Solve for m
6m+4=4m+20
6m-4m=20-4
2m=16
m=8
Find the measure of the angle
(4m+20)°=4(8)+20=52°
Please help me with these 2
explain the step plz
thanks
Answers
1)when we know x+y=90* the sine of x is equal to cosine of y , so the solution of the first is 0.6 again!
Answer:
Left diagram cos(y) = 0.6
Right diagram x = 5 makes the equation true.
Step-by-step explanation:
Left diagram
Both the sin(x) and the Cos(y) use the same side as the non hypotenuse side.
Therefore they most be equal.
So if sin(x) = 0.6, then cos(y) = 0.6
=========================
Right diagram
You can factor this to get the answer.
From the first 2 terms, take out x^2. From terms 3 and 4 take out 2.
x^2(x - 5) + 2(x - 5) = 0
Take out the common factor of (x - 5)
(x^2 +2)(x - 5)
x^2 + 2 yields a complex answer (which doesn't matter for this question)
x - 5 = 0
x = 5
use an appropriate technology to simulate 35 rolls of a six sided number cube according to this data,what is the experimental probability of a roll of 3? what is the theoretical probability that a roll of the number cube will yield a result of 3? explain any differences between the theoretical probability and the experimental probability.
Answers
Explanation of experimental and theoretical probability of rolling a 3 on a six-sided number cube.
The experimental probability of rolling a 3:
Simulate 35 rolls of a six-sided number cube to get results.
Count the number of times a 3 is rolled and calculate the experimental probability by dividing the number of 3s rolled by 35.
The theoretical probability of rolling a 3:
Theoretical probability = Number of favorable outcomes / Total number of outcomes = 1/6 (since there is 1 favorable outcome out of 6 possible outcomes).
Differences between theoretical and experimental probabilities:
Theoretical probability is based on calculations and assumptions, while experimental probability is based on actual observations. Discrepancies between the two can occur due to sample size, random variations, or errors in the simulation.