An 8-sided number cube is rolled 4000 times. The number 2 appeared 200 times. Determine the theoretical and experimental probability of rolling a 2 in order to determine the fairness of the number cube. Drag values or words to the boxes to correctly complete the statements.
Theoretical Probability of rolling a 2= 1/20
Experimental Probability of rolling a 2 = 1/20
Theoretical probability of rolling a 2:
The theoretical probability of an event is the ratio of the number of favourable outcomes to the total number of possible outcomes. Since there are 8 sides to the cube, the total number of possible outcomes is 8. Since the number 2 appeared 200 times out of 4000 rolls, the number of favorable outcomes is 200. Therefore, the theoretical probability of rolling a 2 is:
Theoretical Probability of rolling a 2 = Number of favourable outcomes / Total number of possible outcomes = 200/4000 = 1/20
Experimental probability of rolling a 2:
The experimental probability of an event is the ratio of the number of times the event occurred to the total number of trials. In this case, the event is rolling a 2, which occurred 200 times out of 4000 rolls.
Therefore, the experimental probability of rolling a 2 is:
Experimental Probability of rolling a 2 = Number of times the event occurred / Total number of trials = 200/4000 = 1/20
Comparing theoretical and experimental probability:
If the cube is fair, we would expect the theoretical probability and the experimental probability to be similar. In this case, both probabilities are 1/20, which means that the cube appears to be fair. However, we would need to conduct more trials to be more confident in our conclusion.
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50 Points!!!!!! Triangle ABC is given.
Angle A is labeled two x degrees. Angle B is labeled forty degrees. Angle C is labeled three x degrees.
What is the measure, in degrees, of ∠A?
Enter your answer in the box.
All 3 angles add up to 180 degrees.
so 40 + 2x + 3x = 180
40 + 5x = 180
5x = 140
x = 28
So angle A = 2x = 2(28) = 56 degrees.
Answer: 56°
Step-by-step explanation:
We know that a triangle's angles add up to 180 degrees. We will create an equation to help us solve for x using this information.
Given:
2x + 3x + 40 = 180
Combine like terms:
5x + 40 = 180
Subtract 40 from both sides of the equation:
5x = 140
Divide both sides of the equation by 5:
x = 28
Next, we will substitute this value of x into the expression for ∠A.
∠A = 2x = 2(28) = 56°
At a run festival, 5/7 of the runners are women. If there are 1050 runners, how many are women?
There are 750 women runners at the festival out of 1050 runners.
What is the arithmatic calcaltion?
Arithmetic is a branch of mathematics that deals with the manipulation of numbers and the properties of operations such as addition, subtraction, multiplication, and division. It is often referred to as "elementary mathematics" or "number theory" and is one of the oldest and most basic branches of mathematics.
If 5/7 of the runners at the festival are women, we can use this information to find how many runners are women.
Let's call the number of women runners W. We know that 5/7 of the runners are women, so we can set up the following proportion:
W / 1050 = 5/7
To find the value of W, we can cross-multiply and then solve for W:
W * 7 = 5 * 1050
W = 750
Hence, there are 750 women runners at the festival out of 1050 runners.
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Find y.
I will give Brainliest to correct answer !
Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: \(g(x) = -\sqrt{9(x - 1)} + 2\)
What is a square root function?In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;
f(x) = √x
g(x) = -√9(x - 1) + 2
\(g(x) = -\sqrt{9(x - 1)} + 2\)
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Which equation represents a line which is parallel to the line y = -4/5x+3
Answer: y = \(y=-\frac{4}{5} x+3\)
Step-by-step explanation:
When it is parallel, the slope stays the same.
Answer:
y=45x-3
Step-by-step explanation:
y
=
4
5
x
−
3
Using the slope-intercept form, the slope is
4
5
.
m
=
4
5
All lines that are parallel to
y
=
4
5
x
−
3
have the same slope of
4
5
.
m
parallel
=
4
5
What is 1,987 rounded to the nearest thousand?
Answer: 2000 hope this helps. Can u give me brainliest
Step-by-step explanation:
Answer:
2,000
Step-by-step explanation:
Since there's a 9 before the 1 you would round up the 1,987 to 2,000
Maya purchased a boat for $18,340. Its value depreciated by 15% in the first year she owned it. What was her boat worth at the end of this first year?
Answer:
$15,589
Step-by-step explanation:
Since it deteriorated 15%, it is now worth 85% of the original.
18340 * .85 = 15589
a like that includes the points (s,-3) and (-8,-4) has a slope of 1/4.
The value of s in the point (s,-3) after using slope formula is -4.
What is slope?
Slope is a term used to define how steep a line is. The rise of a line over the run of a line, or the change in the vertical direction (y) over the change in the horizontal direction, is the definition of slope (x). The slope is the angle at which one is moving forward or backward when skiing down a hill or climbing a mountain. Depending on what it is, the slope may occasionally be fairly flat or extremely steep. The slope of an object indicates how steep it is. Slope knowledge is crucial for daily decision-making.
Using slope formula,
=> slope m = \(\frac{y_2-y_1}{x_2-x_1}\)
Now the given point is ,
\((x_1,y_1)=(s,-3) \\(x_2,y_2)=(-8,-4)\)
=> slope m= 1/4
=> \(\frac{1}{4}= \frac{-4+3}{-8-s}\)
=> \(\frac{1}{4} = \frac{-1}{-8-s}\)
=> -8-s=-4
=>-s=-4+8
=> -s=4
=> s =-4.
Hence the value of s is -4.
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In a data distribution that is skewed left.
The median will be greater than the mean in a left-skewed distribution
We have,
In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.
A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.
When the data is skewed left, it means that the distribution is being pulled towards the left side.
This is because there are a few extreme values on the left side that are pulling the mean in that direction.
In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.
For a left-skewed distribution,
The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.
In a data distribution that is skewed left, the mean will be less than the median.
This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.
Therefore,
The median will be greater than the mean in a left-skewed distribution
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URGENT DUE IN FEW MINS6th grade math Calculate to TOTAL Surface Area.
Do NOT count the surface under the pyramid.
The surface area of the solid is 281 ft².
Given that, a solid figure made of a rectangular prism and a square pyramid,
We need to find its surface area,
To find the same, we will find the lateral surface area of square pyramid, and total surface area of rectangular prism,
So,
Surface area = 2×side×slant height + 2(length·width+width·height+height·length)-base area of the square pyramid,
= 2×5×5 + 2(4·12+12·5+4·5)-5²
= 50+256-25
= 281 ft²
Hence the surface area of the solid is 281 ft².
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Consider the statement n2 + 1 ≥ 2n where n is an integer in [1, 4].
Identify the n values for which the equation is to be verified in order to prove the given statement.
(You must provide an answer before moving to the next part.)
Consider the statement that min(a, min(b, c)) = min(min(a, b), c) whenever a, b, and c are real numbers.
Click and drag the steps to prove min(a, min(b, c)) = min(min(a, b), c) whenever a, b, and c are real numbers. Assume a is the smallest real number.
The statement n² + 1 ≥ 2ⁿ, where n is an integer in [1, 4] is true statement.
The statement that min(a, min(b, c)) = min(min(a, b), c) whenever a, b, and c are real numbers is also true statement in all possible cases.
We have provide two statements and we have to prove them .
a) Consider the statement n² + 1 ≥ 2ⁿ where n is an integer in [1, 4].
For n= 1, we have n²+ 1 = 1 + 1= 2 and 2ⁿ = 2¹ = 1 so, 2≥ 2 then n² + 1 ≥ 2ⁿ.
For n = 2, we have n²+ 1 = 4+1 = 5 and 2ⁿ = 2² = 4 , so 5 > 4 then n² + 1 ≥ 2ⁿ.
For n = 3, we have n² + 1 = 9 + 1= 10 ≥ 8 =2³ =2ⁿ, then n² + 1 ≥ 2ⁿ.
For n = 4, we have, n²+1 = 16 + 1 = 17 > 16 = 2⁴ = 2ⁿ, so n² + 1 ≥ 2ⁿ.
In each case, we see n² +1 ≥ 2ⁿ Hence, the statement is proved.
b) Consider the statement that min(a, min(b, c)) = min(min(a, b), c) whenever a, b, and c are real numbers. Proof it by cases :
Case 1 : min (a, min (b, c)) = a."a" is the minimum element if a is smaller than or equal to the other elements within the minimum statement: a ≤ min(b, c) or in other words a ≤b and a ≤ c.
The minimum of a and b then has to be equal to a (due to a ≤ b), min(a, b) = a
The minimum of a and c has to be equal to a (due to a ≤ c), min(min(a, b), c)
= min(a, c) = a
Thus we have shown in this case min(a. min (b.c))= min (min(a,b). c).
Case 2: min (a, min (b, c)) = b,b is the minimum if b is smaller than or equal to the elements within minimum statement: b≤a and b≤min(b, c)
b is smaller than or equal to the minimum, if b is smaller than or equal to both of the terms expressed in the minimum.
b≤ b and b≤c
The minimum of a and b then has to be equal to b (due to b ≤ a), min(a,b) = b
The minimum of b and c has to be equal to b (due to b≤ c)
min(min(a, b), c) = min (b, c) = b
Thus we have shown in this case min(a, min (b, c)) = min (min(a,b), c).
Case 3 : min (a, min (b, c)) = c,c is the minimum if c is smaller than or equal to the elements within the minimum statement: c≤a and c< min(b, c)
c is smaller than or equal to the minimum, if c is smaller than or equal to both of the terms expressed in the minimum, c≤ b
c≤ c. Since c<a and c≤ b, c then also has to be smaller than or equal to the minimum of a and b, c≤ min(a, b). The minimum of min (a, b) and c has to be equal to c (due to c<min(a, b)), min(min(a, b), c) = c. Thus we have shown in this case min(a, min (b, c)) = min (min(a, b), c).
Conclusion : Since min(a, min(b, c)) = min (min(a, b), c) is true for all three possible cases, the statement is always true.
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(-x^2 -2) + (2x^2 + -1)
Answer:36
Step-by-step explanation:
x2 - 10x + 25 = 0 2x2 - 2x - 5 = 0 x2 - 16x = 36. This problem has been solved!
Randy is 20 years old. He has a resting heart rate of 79 bpm. What is his target heart rate range(this should be 2 numbers spanning a range)? For example 70-170 bpm.
Answer:
100-170 bpm
Step-by-step explanation:
А
x cm
12 cm
B
6 cm
C
Answer:
Please help quickly
Answer:
trigonometry
Step-by-step explanation:
Josh used 3 packages of spaghetti to make dinner for 19 guests. How much did
each guest have?
Answer:
6.3
Step-by-step explanation:
19/3=6.3 repeating so i just shortened it to 6.3.
final answer: 6.3
Can someone help explain this? Im stuck!
Determine if the two figures are congruent and explain your answer
Answer:
The two figures are congruent. This is because all of the side lengths are equal/the same. The slope from A to B and E to F are congruent. The slope from B to C and F to G are also congruent, and so on.
Step-by-step explanation:
hope this helped :))
Standard form:simplify the expression into fewer terms for each problem (a)-(g), write an expression in standard form
find the sum of -3x and 8x
Answer:
Step-by-step explanation:
To find the sum of -3x and 8x, you can add the two terms together using the commutative property of addition, which states that the order in which you add numbers does not affect the sum. This gives you the following:
-3x + 8x = (-3 + 8)x = 5x
So the sum of -3x and 8x is 5x. This expression is already in standard form, as it consists of a single term.
A cyclist rode 3.85 miles in 0.7 hours. How fast was she going in miles per hour?
A. 3.85 miles per hour
B. 0.18 miles per hour
C. 5.5 miles per hour
D. 1.4 miles per hour
5p-10=2p+4
find the value of p
5p-10= 2p+4
5p-2p= 10+4
3p = 14
\(p = \frac{14}{3} = 4 \frac{2}{3} \)
Answer: 14/3 or 4.7
Step-by-step explanation: 5p-10=2p+4
add 10 to both sides -10+10=0 and 4+10=14 so 5p=2p+14.
now subtract 2p from both sides. 5p -2p =2p-2p =3p
3p=14, now isolate the variable. 3p/3 and 14/3 =4.66666666667 rounded is 4.7.
so you can have your answer as a fraction 14 over 3, or a mixed fraction 4 and 2/3 or into a decimal 4.7
which expression is equivalent to -8m-8+3m-6?
-11m-2 -5m-2
-5m-14 or -16m-3
I need help!!!!
If g(x)= 3x-5 and h(x)= 2x–4 then (goh)(x)=?
Answer:
(g o h)(x) = 6x - 17
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Composite FunctionsStep-by-step explanation:
Step 1: Define
g(x) = 3x - 5
h(x) = 2x - 4
(g o h)(x) is g(h(x))
Step 2: Find
Substitute: (g o h)(x) = 3(2x - 4) - 5Distribute 3: (g o h)(x) = 6x - 12 - 5Combine like terms: (g o h)(x) = 6x - 17And we have our final answer!
Tomas used 3 \(\frac{1}{2}\) of flour and now has 1 and two-thirds cups left. Which equation can he use to find f, the number of cups of flour he had to begin with?
f + 3 and one-third = 1 and two-thirds
f minus 3 and one-third = 1 and two-thirds
3 and one-third f = 1 and two-thirds
f divided by 3 and one-third = 1 and two-thirds
Answer:
B
Step-by-step explanation:
Answer:
I think It's b or a
Step-by-step explanation:
did this like 4 weeks ago.
Elena receives $95 per year in simple interest from three investments totaling $2100 . Part is invested at 3%, part at 4%, and part at 5%. There is $1000 more invested at 5% than at 4%. Find the amount invested at each rate.
The amount invested at 3% is $
the amount invested at 4% is $
and the amount invested at 5% is $
The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.
Let's assume the amount invested at 4% is x dollars.
According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.
So, the amount invested at 5% is (x + $1000).
The total amount invested is the sum of the amounts invested at each rate, which is $2100.
Therefore, we can write the equation:
x + (x + $1000) + (amount invested at 3%) = $2100
Now, we can calculate the amount invested at 3%.
We subtract the sum of the amounts invested at 4% and 5% from the total investment:
(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)
Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:
Simple Interest = Principal × Interest Rate
The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.
According to the problem, the total interest earned is $95.
So we can write the equation:
(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95
Now we can substitute the expression for (amount invested at 3%) and solve for x.
Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.
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75.5% of the students at Sarasota Community College are from in state. If 24,950 students are from in state, how many students attend the college?
Answer:
33046 students
Step-by-step explanation:
Find how many students attend the college by dividing 24,950 by 0.755
24,950 / 0.755
= 33046.36
Round down, since the answer has to be a whole number:
33046.36
= 33046
So, approximately 33046 students attend the college
If a bus is typically 10 yds long, how many inches would it be? (1yd = 3ft) (1ft = 12in)
Answer:
360
Step-by-step explanation:
(1yd = 3ft) (1ft = 12in)
12 x 3 = 36
36 x 10 = 360
Copy and complete the statement.
1. If HG = HK, then ____ = ____
2. If KHJ = KJH, then ____ = ____
Please add explanation as to why
Answer:
If HG = HK, then HG = HK. This statement is true by definition, as both sides of the equation are equal to the same value.
If KHJ = KJH, then KHJ = KJH. This statement is also true by definition, as both sides of the equation are equal to the same combination of letters.
HELP PLS ASAP!! ILL GIVE 10 BRAINLEST THINGYS !!!
Explain how to find the slope of the function without using technology.
2x + 3y = 12
Answer: The slope is −2/3
Step-by-step explanation:
2 x + 3 y = 12 is the standard form for a linear equation. To determine the slope, solve the equation for y in order to convert to the slope-intercept form y = m x + b , where m is the slope and b is the y-intercept.
2 x + 3 y = 12
Subtract 2 x from both sides.
3 y = − 2 x + 12
Divide both sides by
3 . y = − 2 /3 x + 12 /3 =
y = − 2 /3 x + 4
The slope is
− 2 /3
The total cost of 5 kg rice and 6 kg sugar is Rs 940. If the
rate of rice increases by 20% and the rate of sugar decreases
by 10%, the total cost of 4 kg rice and 3 kg sugar will be
Rs 627. By what percent the cost of 1 kg rice is more or less
than the cost of 1 kg sugar. Find it.
The percent cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.
What is percent increase?We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage.
Let the cost price of rice is R and cost price of sugar is S.
Case 1 : total cost of 5 kg rice and 6 kg sugar is Rs. 940.
5R + 6S = 940 ...(1)
Case 2 : rate of rice increased by 20% and the rate of sugar decreased by 10%.
The new cost price of rice = R + 20% of R = 1.2R
The new cost price of sugar = S - 10% of S = 0.9S
So, the total cost of 4 kg rice and 3 kg sugar will be Rs. 627.
Thus,
4 × 1.2R + 3 × 0.9S = 4.8R + 2.7S = 627 ..(2)
From equations (1) and (2) we have,
(5R + 6S)/(4.8R + 2.7R) = 940/627
R/S = 8/9
Hence, if the price of rice is 8 then the price of sugar is 9.
It is clear that the price of sugar is more than that of rice.
The percent cost by which cost of rice is less than sugar is:
(9 - 8)/ 9 (100) = 11 1/9%.
Hence, the cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.
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Stephanie has a spinner with sections labelled 1, 2 and 3.
She spun it 100 times and recorded how many times it landed on each section in
the table below.
Work out the relative frequency of landing on an odd number, giving your answer
as
a) a fraction in its simplest form.
b) a decimal.
Section
1
Frequency 17
2
20
3
63
Answer:
\(\frac{4}{5}\)
0.8
Step-by-step explanation:
Happy to help:)
At Davis's Hat Store around the block, they have a total of 300 hats in the store. 14% of the hats are white.
How many of the hats in the store are white?
Answer:
42.
Step-by-step explanation:
14% of 300 is 42.
hope this helped