Final answer:
The probability of rolling a prime number on a six-sided die is 1/2 or 50%, since there are three prime numbers (2, 3, 5) out of six possible outcomes.
Explanation:
The probability of rolling a prime number on a six-sided cube labeled with the numbers 1 through 6 can be determined by identifying which numbers on the cube are prime. Prime numbers are numbers that are only divisible by 1 and themselves. On a six-sided die, the prime numbers are 2, 3, and 5.
Since there are 6 faces on the die, the total number of possible outcomes when you roll it once is 6. The event of rolling a prime number includes three outcomes: rolling a 2, rolling a 3, or rolling a 5. So, the probability, P, of rolling a prime number is determined by dividing the number of favorable outcomes (rolling a 2, 3, or 5) by the total number of possible outcomes.
The calculation for the probability is therefore P(Prime) = Number of prime faces / Total number of faces = 3/6. This simplifies to 1/2, which means that the probability of rolling a prime number is 1/2, or 50%.
We can conclude that if you roll the die only a few times, the law of large numbers may not hold, and the experimental probability may not closely align with the theoretical probability of 1/2, but over many rolls, it would generally converge to this value.
Marta bought new fish for her home aquarium. She bought 3 guppies and 2 platies for a total of $13.95. Hank also bought guppies and platies for his aquarium. He bought 3 guppies and 4 platies for a total of $18.33. Find the price of a guppy and the price of a platy.
The price of a guppy and the price of a platy are $3.19 and $2.19 respectively.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions. Equation: A declaration that two expressions with variables or integers are equal.
Given:
Marta bought 3 guppies and 2 platies for a total of $13.95,
Hank bought 3 guppies and 4 platies for a total of $18.33,
Write the equation of the above statements as shown below,
3g + 2p = 13.95
3g + 4p = 18.33
Here, g is the price of guppies and p is the price of platies,
Solve the above equation by elimination as shown below,
3g + 2p - (3g + 4p) = 13.95 - 18.33 (Subtract equation from each other)
3g + 2p - 3g - 4p = -4.38
- 2p = -4.38
p = 4.38 / 2
p = $2.19 and,
3g = 18.33 - 4 × 2.19
3g = 9.57
g = 9.57 / 3
g = $3.19
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Jessie set up a lemonade stand for three days. On Saturday she sold 10 and 2/3 gallons of lemonade. On Sunday she sold 3 and 1/3 gallons mor3 than she sold on Saturday. On Monday she sold 2 and 2/3 gallons less than she sold on Sunday. How many gallons of lemonade did jessie sell on Monday
Jessie set up a lemonade stand for three days.
On Saturday she sold 10 and 2/3 gallons of lemonade = 10+2/3 = 32/3 gallons
On Sunday she sold 3 and 1/3 gallons more than she sold on Saturday
Lemonade sold on Sunday = 32/3 + 3 and 1/3 gallons
= 32/3 + 10/3 = 42/3 gallons = 14 gallons
On Monday she sold 2 and 2/3 gallons less than she sold on Sunday
Lemonade sold on Monday = 14 - 2 and 2/3 gallons
= 42/3 - 8/3 = 34/3 gallons
Therefore, Jessica sold 11 and 1/3 gallons of lemonade on Monday
Kaylie had $1250 in her saving account. She withdrew $82 each month in order to pay for a summer vacation. How much did Kaylie have in he account at the end of eight months?
A rectangle has a perimeter of 48 feet and a length of 14 ft which equation can you solve to find the width
Answer: 2n + 28 = 48
Step-by-step explanation: Got it right on TTM
Melanie eats 1.5 pounds of cereal each week. Which model below best represents the number of pounds of cereal she eats in .5 weeks?
To see how costly it would be for other people to complete a similar cycling tour, you decide to work out two averages and compare.
Group A
Person 1: $500
Person 2: $600
Person 3: $900
Person 4: $450
The average amount spent by members of cycle group A was $
Group B
Person 1: $700
Person 2: $500
Person 3: $680
Person 4: $500
The average amount spent by members of cycle group B was $
What is 6x – 8 = 4 written as a system?
A. y = 6x – 8
y = –4
B. y = 6x – 8
y = 4
C. y = –6x + 8
y = 4
6x – 8 = 4 written as a system y = 6x – 8, y = 4. So, option B) is correct.
An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given,
6x-8=4
For A) Given system
y = 6x – 8.....................1
y = –4.....................2
Substituting y=-4 in eq 1
-4=6x – 8
6x – 8=-4, which is not the same as the given equation.
For B) Given system
y = 6x – 8.....................3
y = 4.....................4
Substituting y=4 in eq 3
4=6x – 8
6x – 8=4, which is the same as the given equation.
For C) Given system
y = -6x +8.....................5
y = 4.....................6
Substituting y=4 in eq 5
4=-6x + 8
-6x +8=4, which is the same as the given equation.
Thus, 6x – 8 = 4 written as a system y = 6x – 8, y = 4. So, option B) is correct.
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Richard caught f fish two weeks ago and 32 fish last week.
How many fish has Richard caught these last two weeks combined?
Write your answer as an expression.
Answer:
The answer is f+32
Step-by-step explanation:
The expression which represents the total fish caught by Richard is
f + 32.
What is expression?A set of variables, constants, and mathematical operations forms an algebraic expression.
According to the given question.
The number of fishes caught by Richard two weeks ago = f
And the fish caught by Richard last week = 32
Therefore,
The expression for the total fish caught by Richard these last two weeks
= f + 32
Hence, the expression which represents the total fish caught by Richard is f + 32.
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Write an inequality to represent this situation: Nina wants to take at least $15 to the movies. How did you decide which inequality symbol to use?
mathew is 2 yards tall how many inches tall is he.
What is the y intercept of y = 6x + 32?
Question 4 options:
6
6x
32
0
The y-intercept of y = 6x + 32 is 32.
Explanation:The y-intercept of a linear equation is the point where the graph of the equation intersects the y-axis. In the equation y = 6x + 32, the y-intercept is the value of y when x is equal to 0. To find it, substitute 0 for x in the equation: y = 6(0) + 32. Simplify the equation to find that the y-intercept is 32.
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A bear cub weighed 64 oz in March. After three months, it weighed 31 lbs. How many lbs did the cub weigh in March?
what is between 3/8 in a number line
Thomas wrote the equation y equals 3x + 3/4 when Sandra her equation they discovered that her equation had all the same Solutions at Thomas's equation which equation could be Sandra's
What is the value of x in this number sentence?
32 = 17 + x
Anyone please help solving this maths problems not sure if I did it right. Thanks.
How many different triangles can be constructed with three angles, each measuring 30°?
Anthony ‘s family went out to dinner. They left at the. Time 5:05 pm any they returned home at 6:52p.m
How long was Anthony ‘s family gone
what is the solution to this equation x-16=-8
The solution to the equation x - 16 = -8 is x = 8.
We have,
To solve the equation x - 16 = -8, we want to isolate the variable x on one side of the equation.
First, let's add 16 to both sides of the equation:
x - 16 + 16 = -8 + 16
This simplifies to:
x = 8
Therefore,
The solution to the equation x - 16 = -8 is x = 8.
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He height of a triangle is 9 m less than is base the area is 56 m^2 what is the length of the base?
Your doctor told you to eat 25 grams of fiber each day.
You had 4 grams of fiber for breakfast.
What percent of the 25 grams of fiber have you eaten so far?
A ladder is placed 7 feet from the base of a building and reaches a point on the building that is 24 feet above the ground.Find the length of the ladder?
The length of the hypotenuse or the ladder is 25 feet.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know in right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, A ladder is placed 7 feet from the base of a building and reaches a point on the building that is 24 feet above the ground.
So, The base is 7 feet and the height is 24 feet.
Therefore,
Hypotenuse² = Base² + Height².
Hypotenuse = [tex]\sqrt{49 + 576}[/tex].
Hypotenuse = [tex]\sqrt{625}[/tex].
Hypotenuse = 25 feet.
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Kit bought a soft drink and a sandwich for $9.00. What was the price of each if the sandwich cost 3.5 times much as the soft drink?
Let the cost of the soft drink = C then the price of the sandwich was 3.5 times as much = 3.5C
And
C + 3.5C = Total Cost
C + 3.5C = 9
4.5C = 9 divide both sides by 4.5
C = 9/4.5 = $2.00 for the soft drink
And 3.5C = 3.5(2.00) = $7.00 cost of the sandwich
If Kit bought a soft drink and a sandwich for $9.00 and the sandwich cost 3.5 times much as the soft drink the price of the sandwich and soft drinks will be $7.00 and $2.00 respectively.
What are arithmetic operations?The study of numbers and their operations, which are relevant to all other fields of mathematics, is part of the discipline of arithmetic operations. Addition, subtraction, multiplication, and division are the basic operations that make up this system.
It is given that, Kit spent $9.00 on a soft drink and a sandwich, with the food being 3.5 times as expensive as the soft drink.
Suppose the cost of the soft drink is x as a result the price of the sandwich will be 3.5x.
Total cost = $9
x+3.5x=9
4.5x=9
x=9/4.5
x= $2.00
The price of the sandwich obtained as,
=3.5x
=3.5× $2.00
=$7
Thus, if Kit bought a soft drink and a sandwich for $9.00 and the sandwich cost 3.5 times much as the soft drink the price of the sandwich and soft drinks will be $7.00 and $2.00 respectively.
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how do you solve each absolute value by graphing
Jasmine has 50 shares of a stock. The value of each share went down by $2 today. Express the total change in value of Jasmines shares as an integer calculation.
The half-life of a radioactive substance is the average amount of time it takes for half of its atoms to disintegrate. Suppose you started with 200 grams of a substance with a half-life of 3 minutes. How many minutes have passed if 25 grams now remain? Explain your reasoning.
Answer:
It would take 9 minutes for 25 grams of the substance to remain.
Step-by-step explanation:
Radioactive substance degenerate to release particles and lot of energy. The time required for a radioactive substance to degenerate into half of its original size is termed half life. The substance continues the stages of degeneration with respect to the half life.
The given substance would have 3 stages of degeneration to achieve a mass of 25 grams with respect to the half life.
1st stage, it would degenerate to half of its original size;
= [tex]\frac{200}{2}[/tex]
= 100 grams
This occurs in 3 minutes.
2nd stage, it would degenerate to half of its previous size;
= [tex]\frac{100}{2}[/tex]
= 50 grams
This also occurs in 3 minutes.
3rd stage, it would degenerate to half of it previous size;
= [tex]\frac{50}{2}[/tex]
= 25 grams
This also occurs in 3 minutes.
We stop here due to the restriction in the question for 25 grams.
So, the total time taken for the substance to reach a mass of 25 grams
= 3 + 3 + 3
= 9 minutes
It would take 9 minutes for 25 grams of the substance to remain.
Three girls collected geodes in the desert. Corinne collected 11 1/8 pounds, Ellen collected 4 5/8 pounds, and Leonda collected 3 3/4 pounds. How much did Corinne collected than the other two girls?
Answer:
2 3/4
Step-by-step explanation:
8n+3n-n+3n+5n I need help with this
Help help help plz give me the right answer
A rectangular prism has a length of 112 meters, a width of 3 meters, and a height of 512 meters.
Enter the volume of the prism as a mixed number in simplest form in the box.
Answer:
[tex]Volume=24\frac{3}{4}m^3[/tex]
Step-by-step explanation:
The volume of a rectangular prism is calculated using the formula;
[tex]Volume=l \times w\times h[/tex]
where [tex]l=1\frac{1}{2}m[/tex] is the length, [tex]w=3m[/tex], is the width and [tex]h=5\frac{1}{2} m[/tex] is the height of the rectangular prism.
We substitute all these values into the formula to obtain
[tex]Volume=1\frac{1}{2} \times 3\times 5\frac{1}{2}[/tex]
Convert to improper fractions to get;
[tex]Volume=\frac{3}{2}\times 3\times \frac{11}{2}[/tex]
[tex]Volume=\frac{99}{4}[/tex]
[tex]Volume=24\frac{3}{4}m^3[/tex]