Answers
Answer:
[tex]A_{total} = 16\ cm^2[/tex]
Step-by-step explanation:
Step 1: Determine the area of the top rectangle
We can tell that the total shape seems like two rectangles glued together. We can separate the top rectangle and determine the area of it and then determine the area of the bottom rectangle and combine them. Lets first solve the left rectangle.
[tex]A=l*w[/tex]
[tex]A_{top\ rectangle}=6\ cm * 2\ cm[/tex]
[tex]A_{top\ rectangle}=12\ cm^2[/tex]
Step 2: Determine the area of the bottom rectangle
[tex]A=l*w[/tex]
[tex]A_{bottom\ rectangle}=2\ cm * 2\ cm[/tex]
[tex]A_{bottom\ rectangle}=4\ cm^2[/tex]
Step 3: Determine the total area
[tex]A_{total}=A_{top\ rectangle}+A_{bottom\ rectangle}[/tex]
[tex]A_{total}=12\ cm^2+4\ cm^2[/tex]
[tex]A_{total} = 16\ cm^2[/tex]
Answer: [tex]A_{total} = 16\ cm^2[/tex]
Break in middle horizontally
For square (Below)
Area =Side²=2²=4cm²For rectangle
Area =LB=6(2)=12cm²Total area
12+416cm²Related Questions
solve the equation 1/x+3/x=16
Answers
[tex] \frac{1}{x} + \frac{3}{x} = 16 \\ [/tex]
[tex] \frac{4}{x} = 16 \\ [/tex]
[tex]16x = 4[/tex]
[tex]x = \frac{4}{16} \\ [/tex]
[tex]x = \frac{1}{4} \\ [/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ \frac{1}{x} + \frac{3}{x} = 16} \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ \frac{4}{x } = 16 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \large\implies\sf{ x = 16 \times 4 } \\ \end{gathered}[/tex]
[tex] \begin{gathered}\\ \implies \orange{\underline{\boxed{\large\frak \pink{x = 64 }}}} \\ \end{gathered}[/tex]
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Jeff sells shirts at a store in the mall. Which group should he survey to determine which color of shirt will have the greatest number sold?
Female customers
customers who are wearing blue
200 random customers
10 friends at work
Answers
The 200 random customers is the group in which he surveys to determine which colour of shirt will have the greatest number sold, option third is correct.
What is a survey?A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.
We have:
Jeff sells shirts at a store in the mall.
The selecting the colour of the shirts is subjective.
It also depends on that how many colours that store sell.
Female customers cannot be an option because men also buy shirts and affect the result of the survey.
Customers who are wearing blue data only tells that how many blue shirts sold.
200 random customers. 200 is a sample from a population, so it will give appropriate results about the colour of shirt will have the greatest number sold
Thus, the 200 random customers is the group in which he surveys to determine which colour of shirt will have the greatest number sold, option third is correct.
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1. What is the volume of this composite figure?
i6m
16 m
10 m
4 m
5 m
Answers
Answer:
560
Step-by-step explanation:
16 times 5 times 4=320
6 times 16 divide 2 then multiple 5
PLEASE HELP ME
Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level a.
n=11, a = 0.01
A r=+0.735
B r=+0.602
C r= 0.765
D r= 0.735
Answers
The reason for why the answer is not “A” is due to the fact that we’re finding all of the possible r values, we are not a evaluating r to see whether or not it is significant.
Triangle ABC is congruent to triangle DEF. Angle B is a right angle, and m∠C = 34°. What is m∠D?
56°
34°
64°
46°
Answers
Answer: 56°
Step-by-step explanation:
At Frosty Freeze, 14 of the last 18 sundaes sold had nuts. What is the experimental probability that the next sundae sold will have nuts?
Answers
Answer:
The correct answer is:
P(nuts)=7/9
Step-by-step explanation:
The experimental probability that the next sundae sold will have nuts is
7/9
What is experimental probability?Experimental probability calculates the probability of some event from the results of experiments.
For an event E, we get the experimental probability of that event
[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]
where, [tex]P_e(E)[/tex] is denoting the experimental probability of occurrence of E.
We are given that At Frosty Freeze, 14 of the last 18 sundaes sold had nuts.
Therefore,
Probability that the next sundae has nuts is 14/18 = 7/9.
Thus, Probability that the next sundae does not have nuts = 2/9
P(nuts)=7/9
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Find the HEIGHT of a cylinder if the volume is 160 and the radius is 4
Answers
Step-by-step explanation:
this is the answer
hope it help
1: solve the following pair of equations simultaneously using the method stated.
a) 2x-3y = 5 and 3x+4y = 6 (elimination method)
b) 4x-y = 9 and 3xy = -6 (substitution method)
c) y=x^2 - 2x and y = 2x -3 (substitution method)
Answers
Answer:
Your answers are below ↓
Step-by-step explanation:
Given ↓
A) 2x-3y = 5 and 3x+4y = 6 ( The method this has to be solved in is the elimination method. )
Now using these,
(1)×3 - (2)×2 = 6x + 9y - 6x - 8y = 15 - 12
therefore,
y = 3
putting the value of y in eqn. (1)
2x + 6 = 5
therefore,
x = -1/2
B) y=x^2 - 2x and y = 2x -3 ( The method this has to be solved in is the substitution method. )
Reduce the greatest common factor on both sides of the equation:
[tex]\left \{ {{4x-y=9} \atop {xy=-2}} \right.[/tex]
Rearrange like terms to the same side of the equation:
[tex]\left \{ {{-y=9-4x} \atop {xy=-2}} \right.[/tex]
Divide both sides of the equation by the coefficient of the variable:
[tex]\left \{ {{y=-9+4x} \atop {xy=-2}} \right.[/tex]
Substitute the unknown quantity into the elimination:
[tex]x(-9+4x)=-2[/tex]
Apply Multiplication Distribution Law:
[tex]-9x+4x^2=-2[/tex]
Reorder the equation:
[tex]4x^2-9x=-2[/tex]
Divide the equation by the coefficient of the quadratic term:
[tex]\frac{1}{4}(4x^2)+\frac{1}{4}(-9x)=\frac{1}{4}*(-2)\\[/tex]
Calculate:
[tex]x^2-\frac{9x}{4}=-\frac{1}{2}[/tex]
Add one term in order to complete the square:
[tex]x^2-\frac{9x}{4}+(\frac{9}{4}*\frac{1}{2})^2=-\frac{1}{2}+(\frac{9}{4}*\frac{1}{2})^2[/tex]
Calculate:
[tex]x^2-\frac{9x}{4}+(\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]
Factor the expression using [tex]a^2$\pm$2ab+b^2=(a$\pm$b)^2[/tex]:
[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2[/tex]
Simplify using exponent rule with the same exponent rule: [tex](ab)^n=a^n*b^n[/tex]
[tex](x-\frac{9}{8} )^2=-\frac{1}{2} +\frac{9^2}{8^2}[/tex]
Calculate the power:
[tex](x-\frac{9}{8} )^2=-\frac{1}{2}+\frac{81}{64}[/tex]
Find common denominator and write the numerators above the denominator:
[tex](x-\frac{9}{8} )^2=\frac{-32+81}{64}[/tex]
Calculate the first two terms:
[tex](x-\frac{9}{8} )^2=\frac{49}{64}[/tex]
Rewrite as a system of equations:
[tex]x-\frac{9}{8} =\sqrt{\frac{49}{64} }[/tex] or [tex]x-\frac{9}{8} =-\sqrt{\frac{49}{64} }[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]x=\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]
Rewrite the expression using [tex]\sqrt[n]{ab} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:
[tex]x=\frac{\sqrt{49} }{\sqrt{64} } +\frac{9}{8}[/tex]
Factor and rewrite the radicand in exponential form:
[tex]x=\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]
Simplify the radical expression:
[tex]x=\frac{7}{8} +\frac{9}{8}[/tex]
Write the numerators over the common denominator:
[tex]x=\frac{7+9}{8}[/tex]
Calculate the first two terms:
[tex]x=\frac{16}{8}[/tex]
Reduce fraction to the lowest term by canceling the greatest common factor:
[tex]x=2[/tex]
Rearrange unknown terms to the left side of the equation:
[tex]x=-\sqrt{\frac{49}{64} } +\frac{9}{8}[/tex]
Rewrite the expression using [tex]\sqrt[n]{a} =\sqrt[n]{a} *\sqrt[n]{b}[/tex]:
[tex]x=-\frac{\sqrt{49} }{\sqrt{64} }+\frac{9}{8}[/tex]
Factor and rewrite the radicand in exponential form:
[tex]x=-\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}[/tex]
Simplify the radical expression:
[tex]x=-\frac{7}{8} +\frac{9}{8}[/tex]
Write the numerators over common denominator:
[tex]x=\frac{-7+9}{8}[/tex]
Calculate the first two terms:
[tex]x=\frac{2}{8}[/tex]
Reduce fraction to the lowest term by canceling the greatest common factor:
[tex]x=\frac{1}{4}[/tex]
Find the union of solutions:
[tex]x=2[/tex] or [tex]x=\frac{1}{4}[/tex]
Substitute the unknown quantity into the elimination:
[tex]y=-9+4*2[/tex]
Calculate the first two terms:
[tex]y=-9+8[/tex]
Calculate the first two terms:
[tex]y=-1[/tex]
Substitute the unknown quantity into the elimination:
[tex]y=-9+4*\frac{1}{4 }[/tex]
Reduce the expression to the lowest term:
[tex]y=-9+1[/tex]
Calculate the first two terms:
[tex]y=-8[/tex]
Write the solution set of equations:
[tex]\left \{ {{x=2} \atop {y=-1}} \right.[/tex] or [tex]\left \{ {{x=\frac{1}{4} } \atop {y=-8}} \right.[/tex] -------> Answer
C) y=x^2 - 2x and y = 2x -3 ( This method this has to be solved in is the substitution method. )
Step 1: We start off by Isolating y in y = 2x - 3
y=2x-3 ----------> ( Simplify )
y+(-y)=2x-3+(-y) ---- > ( Add (-y)on both sides)
0=-3+2x-y
y/1 = 2x-3/1 --------> (Divide through by 1)
y = 2x - 3
We substitute the resulting values of y = 2x - 3 and y = x^2 - 2x
(2 * x - 3) = x^2 - 2x ⇒ 2x -3 = x^2 - 2x ----> ↓
(Substituting 2x - 3 for y in y = x^2 -2x )
Next: Solve (2x - 3 = x^2 - 2x) for x using the quadratic formular method
2x - 3 = x^2 - 2x
x = -b±b^2-4ac/2a Step 1: We use the quadratic formula with ↓
a = -1,b=4,c= - 3
x = -4±(4)^2-4(-1)(-3)/2(-1) Step 2: Substitute the values into the Quadratic Formular
x = -4± 4/ - 2 x = 1 or x = 3 Step 3: Simplify the Expression & Separate Roots
x = 1 or x = 3 ------- ANSWER
Substitute 1 in for x in y = 2x - 3 then solve for y
y = 2x - 3
y = 2 · (1) - 3 (Substituting)
y = -1 (Simplify)
Substitute 3 for in y = 2x - 3 then solve for y
y = 2x - 3
y = 2 · (3) - 3 (Substituting)
y = 3 (Simplify)
Therefore, the final solutions for y = x^2 -2x; y = 2x - 3 are
x₁ = 1, y₁ = -1
x₂ = 3, y₂ = 3
4x+3y=6
-4x+2y=14
Solve the system of equations.
A. x= 1/2, y=3
B. x=3, y =1/2
C. x=4, y = -3/2
D. x=-3/2, y = 4
Answers
Answer:
D
Step-by-step explanation:
4x + 3y = 6
-4x + 2y = 14
0 + 5y / 5 = 20/ 5 = 4 = y
4x + 3(4) = 6
4x + 12 - 12 = 6 - 12
4x / 4 = -6 / 4 = -3 / 2 =x
Stan pays a 10% deposit to put a pool table on lay-by.
If the pool table costs $1590, how much does he have left to pay?
Answers
Answer:
$1431
Step-by-step explanation:
If Stan pays a 10% deposit, he pays $159. 10% of $1590 is simply 0.1 * 1590 = 159. Assuming this is the only amount he pays, he then simply needs to pay the full price minus $159. We can find this by simply subtracting 159 from 1590 to get 1431. Stan still needs to pay $1431.
simplify. 5ab/15a+10a²
Answers
Answer this volume based Question. I will make uh brainliest + 50 points
Answers
Answer:
[tex]\huge{\purple {r= 2\times\sqrt[3]3}}[/tex]
[tex]\huge 2\times \sqrt [3]3 = 2.88[/tex]
Step-by-step explanation:
For solid iron sphere:radius (r) = 2 cm (Given)Formula for [tex]V_{sphere} [/tex] is given as:[tex]V_{sphere} =\frac{4}{3}\pi r^3[/tex][tex]\implies V_{sphere} =\frac{4}{3}\pi (2)^3[/tex][tex]\implies V_{sphere} =\frac{32}{3}\pi \:cm^3[/tex]For cone:r : h = 3 : 4 (Given)Let r = 3x & h = 4xFormula for [tex]V_{cone} [/tex] is given as:[tex]V_{cone} =\frac{1}{3}\pi r^2h[/tex][tex]\implies V_{cone} =\frac{1}{3}\pi (3x)^2(4x)[/tex][tex]\implies V_{cone} =\frac{1}{3}\pi (36x^3)[/tex][tex]\implies V_{cone} =12\pi x^3\: cm^3[/tex]It is given that: iron sphere is melted and recasted in a solid right circular cone of same volume[tex]\implies V_{cone} = V_{sphere}[/tex][tex]\implies 12\cancel{\pi} x^3= \frac{32}{3}\cancel{\pi}[/tex][tex]\implies 12x^3= \frac{32}{3}[/tex][tex]\implies x^3= \frac{32}{36}[/tex][tex]\implies x^3= \frac{8}{9}[/tex][tex]\implies x= \sqrt[3]{\frac{8}{3^2}}[/tex][tex]\implies x={\frac{2}{ \sqrt[3]{3^2}}}[/tex][tex]\because r = 3x [/tex][tex]\implies r=3\times {\frac{2}{ \sqrt[3]{3^2}}}[/tex][tex]\implies r=3\times 2(3)^{-\frac{2}{3}}[/tex][tex]\implies r= 2\times (3)^{1-\frac{2}{3}}[/tex][tex]\implies r= 2\times (3)^{\frac{1}{3}}[/tex][tex]\implies \huge{\purple {r= 2\times\sqrt[3]3}}[/tex]Assuming log on both sides, we find:[tex]log r = log (2\times \sqrt [3]3)[/tex][tex]log r = log (2\times 3^{\frac{1}{3}})[/tex][tex]log r = log 2+ log 3^{\frac{1}{3}}[/tex][tex]log r = log 2+ \frac{1}{3}log 3[/tex][tex]log r = 0.4600704139[/tex]Taking antilog on both sides, we find:[tex]antilog(log r )= antilog(0.4600704139)[/tex][tex]\implies r = 2.8844991406[/tex][tex]\implies \huge \red{r = 2.88\: cm}[/tex][tex]\implies 2\times \sqrt [3]3 = 2.88[/tex]Please help me. I don’t understand at all.
Answers
Answer:
Option 2
Step-by-step explanation:
Evaluating the options :
Option 1
2 |x - 5| - 4 < -82 |x - 5| < -4|x - 5| < -2Empty set as modulus cannot be less than 0Option 2
|2x - 1| - 7 < -6|2x - 1| < 1x < 1There is a solution set other than empty setOption 2 is the right answer.
Can someone please just check my answers over to make sure I got them right. Thank you so much!
Let me know if you need a close up on any of the pictures!
Answers
Answer: they are all correct congrats!
Step-by-step explanation:
use a formula to find the surface area of the cylinder use 3.14 for pi
Answers
Answer:
376.8 cm²
Step-by-step explanation:
Given:
Radius of circular base: 4 cmHeight of cylinder: 11 cmSurface area = 2πrh + 2πr²
[Where "r" and "h" represents the radius and the height respectively]
Let's substitute the height and the radius in the formula and simplify it.
[tex]\implies 2\pi rh + 2\pi ^{2}[/tex]
[tex]\implies 2\pi (4)(11) + 2\pi (4)^{2}[/tex]
[tex]\implies 2\pi (44) + 2\pi (16)[/tex]
[tex]\implies 88\pi + 32\pi[/tex]
We can factor π out of the expression. Therefore, we get:
[tex]\implies 88\pi + 32\pi[/tex]
[tex]\implies \pi (88 + 32)[/tex]
Now, simplify the expression inside the parentheses.
[tex]\implies \pi (88 + 32)[/tex]
[tex]\implies \pi (120)[/tex]
The value of π, we are given, is 3.14. When substituted, we get:
[tex]\implies \pi (120)[/tex]
[tex]\implies 3.14(120) = 31.4(12) = \boxed{376.8 \ \text{cm}^{2} }[/tex]
Therefore, the surface area of the cylinder is 376.8 cm².
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The area of a triangle is 7.5 . The base of the triangle is 5 cm .what is the height of this triangle.
Answers
Answer:
3 cm
Step-by-step explanation:
Formula :
Area = 1/2 x Base x HeightGiven :
Area = 7.5 cmBase = 5 cmSolving :
Height = 7.5/5 x 2Height = 3 cmFind X
A = 49
B = 27
C = 98
D = 76
Answers
Answer:
C=98°
Step-by-step explanation:
125°- 27°
=98°
Use the graph to determine the function’s DOMAIN and RANGE
Answers
Answer:
Domain = x ≥ 0
Range = f( x ) ≥ 1
Step-by-step explanation:
The graph starts from 0 in the x - axis and 1 in the y hence the given domain and range.
What are the coordinates of the focus of the parabola?
y=−0.25x2+6
Answers
What is the median of the data represented by the box plot?
Answers
Answer: 20
Step-by-step explanation:
Box plots give us the median just by looking at them. See attached.
the coefficients corresponding to k=0,1,2….,5 in the expansion of (x+y)^5 are
Answers
Answer:
1, 5, 10, 10, 5, 1
Step-by-step explanation:
The coefficients for the expansion of the 5th power of a binomial are found on the 5th row of Pascal's triangle. They are ...
1, 5, 10, 10, 5, 1
__
Algebraically, they are computed using the formula for 5 things taken k at a time:
5!/(k!(5-k)!)
If h(x)=(0,-9),(5,2)(8,-3),(10,11) which set of ordered pairs represents the inverse of h(x)
Answers
Set of ordered pairs is {(-9,0),(2,5)(-3,8),(11,10)
What is ordered pair?
An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.
Given:
h(x)=(0,-9),(5,2)(8,-3),(10,11)
The inverse of anything interchange the position of variables or numbers or etc.
In ordered set the inverse will be x- coordinate become y- coordinate and y- coordinate become x- axis.
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Six people want to share five boxes of raisins. How many boxes of raisins will each person get?
Answers
5/6 or 0.83 boxes of raisins
On his third math quiz of the semester, Cooper answered 28 questions correctly and got 7 wrong. What is the ratio of the number of questions he got right on the quiz to the total number of questions?
Answers
Step-by-step explanation:
Given that Cooper answered 28 questions correctly and 7 incorrect answers, If the total number of questions is x,
let total number of questions be X,therefore X = 28+7
= 35
ratio of right answered questions to the total questions, R isR =
[tex] \frac{28}{35} [/tex]
=
[tex] \frac{4}{5} [/tex]
therefore, the ratio is 4:5
please answer this question
Answers
Answer:
[tex]a_n=3n-2[/tex]
Step-by-step explanation:
General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth term[tex]a[/tex] is the first term[tex]d[/tex] is the common difference between termsCreate expressions for the 4th and 6th terms:
[tex]\implies a_4=a+(4-1)d=a+3d[/tex]
[tex]\implies a_6=a+(6-1)d=a+5d[/tex]
The ratio of the 4th term to the 6th term is 5:8, therefore:
[tex]\implies \dfrac{a_4}{a_6}=\dfrac{5}{8}[/tex]
[tex]\implies \dfrac{a+3d}{a+5d}=\dfrac{5}{8}[/tex]
[tex]\implies 8(a+3d)=5(a+5d)[/tex]
[tex]\implies 8a+24d=5a+25d[/tex]
[tex]\implies 8a-5a=25d-24d[/tex]
[tex]\implies 3a=d \quad \leftarrow \textsf{Equation 1}[/tex]
Sum of the first n terms of an arithmetic series:
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
The sum of the first 7 terms of an arithmetic progression is 70:
[tex]\implies S_7=70[/tex]
[tex]\implies \dfrac{7}{2}[2a+(7-1)d]=70[/tex]
[tex]\implies 2a+6d=20[/tex]
[tex]\implies a+3d=10 \quad \leftarrow \textsf{Equation 2}[/tex]
Substitute Equation 1 into Equation 2 and solve for [tex]a[/tex]:
[tex]\implies a+3(3a)=10[/tex]
[tex]\implies a+9a=10[/tex]
[tex]\implies 10a=10[/tex]
[tex]\implies a=1[/tex]
Substitute found value of [tex]a[/tex] into Equation 1 and solve for [tex]d[/tex]:
[tex]\implies 3(1)=d[/tex]
[tex]\implies d=3[/tex]
Finally, substitute found values of [tex]a[/tex] and [tex]d[/tex] into the general form of the arithmetic sequence:
[tex]\implies a_n=1+(n-1)3[/tex]
[tex]\implies a_n=1+3n-3[/tex]
[tex]\implies a_n=3n-2[/tex]
Wyatt bought $40 worth of materials to make braided keychains. If Wyatt Sells his keychains for $2.50
each, how many keychains must he sell to earn a profit?
Answers
Inequalities help us to compare two unequal expressions. Wyatt needs to sell at least 17 keychains.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Given Wyatt bought $40 worth of materials to make braided keychains. Also, it is given that Wyatt Sells his keychains for $2.50 each. Therefore, the minimum number of keychains he should sell to make a profit are,
Number of keychains>(40/2.50)
Number of keychains > 16
Thus, Wyatt needs to sell at least 17 keychains.
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Answer:
Step-by-step explanation:
17
Solve for x. Round to the nearest tenth.
Answers
Answer:
x = 25.84
Step-by-step explanation:
Secx = hyp /adj
Secx = 30/27
x = ArcSec(30/27)
x = 25.84
A triangle has a base of 4 m and a height of 3 m.
What is the area of the triangle?
Enter your answer in the box.
m²
Answers
Answer:
Area of the triangle is 6
Step-by-step explanation:
The formula for the area of a triangle is the base x height / 2. This means we can just plug in the variables and solve
A = b x h/2
A= 4 x 3/2
A= 12/2
A= 6
Answer: 6
Step-by-step explanation:
I really need a help, help help helppp Helpppppp please
Answers
Answer:
I am clueless. Take care though.
Step-by-step explanation:
Which of the following statements is true?
A. The experimental probability of an outcome is always the same as the theoretical probability of the outcome
B. The experimental probability of an outcome is never the same as the theoretical probability of the outcome.
C. As the number of trials of a random process decreases, the experimental probability of an outcome approaches the theoretical probability of the outcome
D. As the number of trials of a random process increases, the experimental probability of an outcome approaches the theoretical probability of the outcome
Answers
Answer:
B
Step-by-step explanation:
first of all articles are perfect and there is . sign at the last of the sentence