Total cost of racquet at Bob's Tennis Racquet Emporium is $192.60 with a 7% sales tax on the original price of $180.00. The price tag on a similar racquet at Tennis Pro, which offers a 10% discount, is $162.00 before tax.
To calculate the total cost of the tennis racquet at Bob's Tennis Racquet Emporium, we need to add the sales tax to the original price.
Sales tax = 7% of $180.00 = 0.07 x $180.00 = $12.60
Total cost = $180.00 + $12.60 = $192.60
Therefore, the total cost of the tennis racquet at Bob's Tennis Racquet Emporium is $192.60.
If Tennis Pro offers a before-tax price that is 10% less than Bob's store for a similar racquet, we can calculate the price tag as follows:
Price at Bob's store = $180.00
Discounted price at Tennis Pro = 10% less than $180.00 = 0.10 x $180.00 = $18.00 discount
Price at Tennis Pro = $180.00 - $18.00 = $162.00
Therefore, the price tag on the similar racquet at Tennis Pro is $162.00 before tax. The sales tax amount will depend on the applicable tax rate in the area where the store is located.
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the total number of goals scored per soccer match in the english premier league (epl) follows a poisson distribution, with mean 2.768. what is the probability that three or more goals will be scored in a game?
The probability of three or more goals being scored in an EPL match is approximately 0.522, or 52.2%.
To find the probability that three or more goals will be scored in a game, we need to calculate the cumulative probability of the Poisson distribution for x = 3, 4, 5, and so on, up to infinity. This can be written as:
P(X ≥ 3) = 1 - P(X < 3)
where X is the random variable representing the number of goals scored in a match.
To calculate P(X < 3), we can use the Poisson distribution formula:
[tex]P(X = x) = (e^{(-\lambda)} \times \lambda^x) / x![/tex]
where e is the mathematical constant approximately equal to 2.71828, and x! represents the factorial of x.
Using this formula, we can calculate the probabilities of scoring 0, 1, and 2 goals:
[tex]P(X = 0) = (e^{(-2.768)} \times 2.768^0) / 0! = 0.063\\\\P(X = 1) = (e^{(-2.768)} \times 2.768^1) / 1! = 0.174\\\\P(X = 2) = (e^{(-2.768)} \times 2.768^2) / 2! = 0.241[/tex]
To find P(X < 3), we add these probabilities:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.063 + 0.174 + 0.241 = 0.478
Finally, we can calculate the probability of scoring three or more goals using the formula we derived earlier:
P(X ≥ 3) = 1 - P(X < 3) = 1 - 0.478 = 0.522 or 52.2%
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8. A rectangular room is shown.
4x - 1
--x
2
3x + 6
A. (4x-1)-2x
B. (3x2+6) + (4x - 1) + x
C. (4-1)-(3x² + 6)
(3x2+6) + 2(4x - 1) + 2x
Door
X
4x - 1
Port A: Which of the following expressions represents the perimeter of the room without th
door?
(3x²+6)+(x-1)x2+²x = (3x²+6) + 2(9x-=
Port B: What is the perimeter of the room without the door in simplest form? Show you
work.
I only need part b
Answer: 14x + 10
Step-by-step explanation: The perimeter of the room without the door can be found by adding up the lengths of all four sides:
Perimeter = 2(4x-1) + 2(3x+6)
Simplifying and combining like terms, we get:
Perimeter = 14x + 10
Therefore, the perimeter of the room without the door in simplest form is 14x + 10.
Ranko bought two dozen eggs at the store. On the way home Ranko dropped the eggs and broke 3/4 of them. How many eggs broke
Answer:
Step-by-step explanation:
9 eggs broke
I Really want this pleaseeeeeeeeeeeeeeeeeee
Answer:
no
Step-by-step explanation:
using Pythagorean theorem:
[tex]26^{2} +42^{2}=50^{2}[/tex]
676+1764=2500
2440=2500
2440<2500
Answer:no
a proof is a step-by-step . (write one word; two possible correct answers.) 2. informal proofs in this class are written in which language? 3. formal proofs that we will soon learn are written in which language? 4. informal proofs should start with the
1. A proof is a step-by-step Argument/Explanation.
2. Informal proofs in this class are written in English language.
3. Formal proofs that we will soon learn are written in Fitch notation language.
4. Informal proofs should start with the word given and end with the word therefore.
1. A proof is used to show that a statement is true or that a given statement follows logically from given assumptions. A proof can be used to prove a theorem, corollary, or lemma, or to solve an equation.
2. Informal proofs in this class are written in English in order to make them easier to understand. The proof should explain the reasoning behind each step and provide clear evidence that the conclusion is valid.
3. Formal proofs that we will soon learn are written in Fitch notation language, which is a language used to represent logical proof structures. Fitch notation consists of lines of logical statements, linked together with arrows that indicate the structure of the proof.
4. Informal type of proof is often used in mathematics as it does not require a formal proof. It is used to explain why a certain statement is true. It usually involves making an assumption and then deriving a logical conclusion from that assumption.
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The complete question is:
1. A proof is a step-by-step ____________ . (Write one word; two possible correct answers.)
2. Informal proofs in this class are written in which language?
3. Formal proofs that we will soon learn are written in which language? _____________
4. Informal proofs should start with the word ______________ and end with the word _________________ .
Find the missing value
73cm
92cm
5cm
?cm
Answer:
6.3cm
Step-by-step explanation:
73/5 = 92/x
cross multiply to get: 73x=460
divide both sides by 73
x=6.3
I need the questions 25,28 and 29
Using the given values, the values of the expression and equations are:
25. -0.8
28. S ≈ 137.22
29. V ≈ 50.94
Evaluating an expressionFrom the question, we are to evaluate each of the expressions for the given values
25.
[-b + √(b² -4ac)]/2a
a = 2, b = 8, c = 5
Substituting the values into the expression
[-b + √(b² -4ac)]/2a
= [-8 + √((8)² - 4(2)(5))]/2(2)
= [-8 + √(64 - 40)]/4
= [-8 + √(24)]/4
= [-8 + 2√6]/4
= -2 + 1/2(√6)
= -0.775
≈ -0.8
28.
S = 2πrh + 2πr²
r = 2.3, h = 7.1 (Take π = 3.14)
Thus,
S = 2(3.14)(2.3)(7.2) + 2(3.14)(2.3)²
S = 103.9968 + 33.2212
S = 137.218
S ≈ 137.22
29.
V = 4/3 πr³
r = 2.3(Take π = 3.14)
V = 4/3 × 3.14 × (2.3)³
V = 50.939
V ≈ 50.94
Hence, the value of V is 50.94
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What is the mean of this data set?
The line graph is titled Amount of Rainfall. The Y axis is labeled inches. The X axis is labeled weeks. Week 1 has a dot at 2 inches. Week 2 has a dot at 3 inches. Week 3 has a dot at 1 inch. Week 4 has a dot at 3 inches. Week 5 has a dot at 5 inches. Week 6 has a dot at 4 inches. The dots are connected one to the next by a line to show a change in the amount of rainfall.
1
2
3
4
Answer: To find the mean of this data set, we need to add up all the amounts of rainfall and divide by the number of weeks. From the line graph, we can estimate the following amounts of rainfall:
Week 1: 2 inches
Week 2: 3 inches
Week 3: 1 inch
Week 4: 3 inches
Week 5: 5 inches
Week 6: 4 inches
To calculate the mean, we need to add up these amounts and divide by 6 (the number of weeks):
(2 + 3 + 1 + 3 + 5 + 4) / 6
= 18 / 6
= 3
Therefore, the mean amount of rainfall in this data set is 3 inches. The answer is (B) 3.
Step-by-step explanation:
An aquarium tank holds 190 liters of water. How much is this in gallons? Use the following conversion: 1 gallon is 3. 8 liters. What is the Answer?
The aquarium tank that holds 190 liters of water equals to 50.15 gallons. Therefore, the answer to the given problem is 50.15 gallons.
Conversion factors are the ratios that describe the numerical relationship between two units of measurement.
The conversion factor of liters to gallons is 1 gallon is 3.8 liters.
Therefore, by multiplying the given value of liters by the conversion factor of liters to gallons, we can convert liters to gallons.
190 liters x 1 gallon/3.8 liters = 50.15 gallons
Thus, the aquarium tank that holds 190 liters of water equals to 50.15 gallons.
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a schools class rings can include a student's initials in an engraved monogram on the ring. How many different monograms are possible form 2 sizes, 5 type styles, and 3 boarder styles?
there are 30 different monograms possible, based on the given choices.
A monogram is a design that uses the initials of a person's name, usually in an artistic or decorative way. In the case of school class rings, the monogram is often engraved onto the surface of the ring. The monogram typically consists of the student's initials, with the first initial on the left, the middle initial (if applicable) in the centre, and the last initial on the right.
In this problem, we are given that there are two sizes of initials (presumably a larger size for the first and last initials, and a smaller size for the middle initial), five different type styles (i.e., different ways the letters can be designed), and three different border styles (i.e., different decorative borders around the monogram).
To calculate the total number of possible monograms, we need to multiply the number of choices for each category. This is known as the multiplication principle of counting.
So, we start by considering the number of choices for the initial sizes. We are given that there are two sizes, so there are two choices. Next, we consider the number of choices for the type styles. We are given that there are five different type styles, so there are five choices. Finally, we consider the number of choices for the border styles. We are given that there are three different border styles, so there are three choices.
To get the total number of possible monograms, we multiply the number of choices for each category together. So we get:
2 (initial sizes) x 5 (type styles) x 3 (border styles) = 30
Therefore, there are 30 different monograms possible, based on the given choices.
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the empirical rule says that 95% of the population is within 2 standard deviations of the mean, but when i find the z-scores that mark off the middle 95% of the standard normal distribution i calculate -1.96 and 1.96. is this a contradiction? why or why not? in other words why are the normal distribution calculators not agreeing with the empirical rule?
The empirical rule states that approximately 95% of the population lies within 2 standard deviations of the mean for a normal distribution, but you found that the z-scores that mark off the middle 95% of the standard normal distribution are -1.96 and 1.96. This does not represent a contradiction, and I will explain why is it so ?
The empirical rule, also known as the 68-95-99.7 rule, is a useful guideline to help us understand the proportions of data in a normal distribution. According to this rule, about 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. However, it is essential to note that the empirical rule is a simplified approximation.
On the other hand, the z-scores that you calculated, -1.96 and 1.96, are more precise values based on the actual standard normal distribution. These values come from a more accurate calculation using the cumulative distribution function (CDF) of the normal distribution, which gives the exact probability for any given range of z-scores.
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Can you solve this with workings out please
Answer:
Eighty biscuits.
Step-by-step explanation:
We need to find the limiting factor. We can do that by comparing ratio of mass of ingredient given to mass of ingredient needed for 20 biscuits
[tex]Butter:\\800:150\\=16:3\\=5.33\\Sugar:\\700:75=28:3\\=9.33\\Flour:\\1000:180\\=50:9\\=5.56\\Chocolate Chips:200:50\\=4:1\\=4\\[/tex]
We can clearly see that the choco. chips are the limiting factor since it has the lowest ratio, basically meaning we will run out of choco chips before anything else.
[tex]Biscuits=4*20=80[/tex]
Since we only have 4 times the choco chips needed to make 20 biscuits, we can only make 80 biscuits. Now you can see, we have other ingredients left, but choco chips have ran out which is why it was the limiting factor.
[tex]Flour:\\1000-4(180) = 280g[/tex]
After making 4 servings we still have 280g of flour left.
Find the number of degrees in an angle which is 120 less than its supplement?
The angle in question measures 60 degrees.
What are supplementary angles?
Supplementary angles are two angles that has sum of 180 degrees. In other words, if you have two angles that are next to each other, and when you add them together, they equal 180 degrees, then those angles are considered to be supplementary.
Let x be the measure of the angle in question.
The supplement of an angle is the angle that, when added to the given angle, results in a sum of 180 degrees. So, the supplement of x is 180 - x.
The problem tells us that the given angle (x) is 120 degrees less than its supplement (180 - x).
Therefore, we can set up the equation:
x = (180 - x) - 120
Simplifying this equation, we get:
x = 60
So, the angle in question measures 60 degrees.
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PLS HELP! WILL MAKE U BRAINLIST
Answer:
(5,2)
Step-by-step explanation:
Let's solve your system by substitution.
[tex]x+y=7{\text{ ; }}x=y+3[/tex]
Step 2: let Solve [tex]$x+y=7$[/tex] for[tex]$x$[/tex]
[tex]x+y=7[/tex]
[tex]x+y +(-x)=7+(-x)[/tex] (Add (-x) on both sides)
[tex]y=-x+7[/tex]
0+(x)=7-x-y+(x) (Add (x) on both sides)
x = -y + 7
x/1 = -y+7/1 (divide through by 1)
x = -y + 7
Substitute -y+7 for x in x = y + 3, then solve for u
(-y + 7) = y + 3
-y + 7 = y + 3 (simplify)
-y+7+(-7) = y + 3 + (-7) (Add (-7) on both sides)
-y=y-4
-y = y-4 (simplify)
-y+(-y)=y-4+(-y) (Add (-y) on both sides)
-2y-=-4
-2y/-2 = -4/-2 (Divide through by -2)
y = 2
Substitute in 2 for y in x = -y + 7
x = -y+7
x = -2+7
x = 5
Answer:
x = 5 and y = 2
Kiki blew up 64 balloons. She separated the balloons into 8 groups. She then added 4 more balloons to each group.
How many balloons are in each group?
Responses
4 balloons
4 balloons
8 balloons
8 balloons
12 balloons
12 balloons
18 balloons
Answer: 12
Step-by-step explanation: if you take the number 64 and devide it by 8 you get 8. then add 4 to eight and you get twelve
at noon, a truck and a car leave the same intersection traveling in the same direction. the truck is traveling at 30 mph and the car is traveling at 42 mph. at what time will they be 9 miles apart?
Considering they left at precise noon, at 12:45 they will be 9 miles apart after they leave the intersection.
Let's call the time it takes for them to be 9 miles apart "t". During this time, the truck will have traveled a distance of 30t, and the car will have traveled a distance of 42t. Since they are traveling in the same direction, we can subtract the distances to find the distance between them:
42t - 30t = 12t
So they are separating at a rate of 12 miles per hour.
To find when they will be 9 miles apart, we can set up the equation:
12t = 9
Solving for t:
t = 9/12
t = 0.75 hours,
To convert 0.75 hours into minutes, we have to multiply it by 60.
= 0.75 × 60
= 45 minutes
So they will be 9 miles apart 45 minutes after they leave the intersection, or at 12:45pm.
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How To Do 387 x 72 In standard algorithm.
Answer: k898
iiii
Step-by-step explanation:
k8ni7mrvnyrt
out of a random sample of 1000 dutch men, how many would we expect to be taller than 190 cm (rounded to the nearest whole number)?
The number of Dutch men taller than 190 cm is approximately 100.
The proportion of men taller than 190 cm is estimated using the normal distribution.
We'll be using a normal distribution, which requires the mean and standard deviation of the height data.
The percentage of Dutch men who are over 190 cm tall can be estimated using a normal distribution model.
We must first determine the mean and standard deviation of the heights.
For the population mean and standard deviation, we use the following values.
μ = 181 cm (the mean of Dutch men's heights)
σ = 7 cm (standard deviation)We may now convert the height of 190 cm to a z-score, which is a standard score that represents the number of standard deviations from the mean of the distribution.
The z-score is calculated using the following formula: Z = (X - μ) / σ
where X is the height of 190 cm,
μ is the population mean,
and σ is the population standard deviation.
Z = (190 - 181) / 7 = 1.2857
We look up the percentage corresponding to this z-score in the standard normal distribution table.
Using the table, we can see that the percentage of individuals with a z-score greater than 1.2857 is 0.1003.
We will use this percentage to estimate the number of Dutch men over 190 cm tall in a random sample of 1000 men.0.1003 * 1000 = 100.3
The number of Dutch men taller than 190 cm is approximately 100.
To the nearest whole number, we round this up, and the expected number of men taller than 190 cm in a random sample of 1000 Dutch men is 101.
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Two numbers add to 90 degrees. The larger angle is 54 more than twice the smaller. How many degrees are in each angle?
Answer:
12 and 78
Step-by-step explanation:
x + 2x+54 = 90 2x+54=2(12)+54
24+54
78
3x + 54 = 90
3x = 36
x=12
12 and 78
2sin(2x+π÷3)≥√3
[tex]2 \sin(2x + \frac{\pi}{3} ) \geqslant \sqrt{3} [/tex]
with steps
The solution to the inequality 2sin(2x+π/3)≥√3 is:
x ∈ [-π/6, π/3]
What is inequality?
An inequality is a mathematical statement that compares two values or expressions using symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to). Inequalities are used to express relationships between quantities that are not necessarily equal.
To solve the inequality 2sin(2x+π/3)≥√3, we can follow these steps:
Step 1: Subtract π/3 from both sides to get rid of the constant term on the right-hand side:
2sin(2x+π/3) - π/3 ≥ √3 - π/3
Step 2: Divide both sides by 2 to isolate sin(2x+π/3):
sin(2x+π/3) ≥ (√3 - π/3)/2
Step 3: Use the fact that sin(x) is positive in the first and second quadrants of the unit circle to find the interval of x that satisfies the inequality. To do this, we need to find the angles α and β such that sin(α) = (√3 - π/3)/2 and sin(β) = - (√3 + π/3)/2. Then, the solution interval will be:
α/2 - π/6 ≤ x ≤ β/2 + π/6
To find α and β, we can use the inverse sine function on a calculator or look them up in a table. We get:
α ≈ 0.4636 radians
β ≈ 2.6779 radians
Substituting these values into the solution interval, we get:
0.2318 - π/6 ≤ x ≤ 1.3389 + π/6
Simplifying, we get:
-π/6 ≤ x ≤ π/3
Therefore, the solution to the inequality 2sin(2x+π/3)≥√3 is:
x ∈ [-π/6, π/3]
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which events are independent? check all that apply.each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. sarah picks a number less than 5, keeps it, and then picks an odd number.
The events that are independent are,
1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.
2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.
3) Olivia choosing an ace and the dart hitting the bull's-eye
The events that are independent are:1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.
2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.
3) Olivia choosing an ace and the dart hitting the bull's-eye.
The other events are dependent because the outcome of the first event affects the outcome of the second event. Specifically
1) Sarah picking a number less than 5 and then picking an odd number. The second event depends on the outcome of the first event.
2) A number cube being rolled and a spinner being spun. The two events are independent of each other, but the outcomes of each event are not independent.
3) Two cards being randomly chosen from a standard deck, and Eliza choosing a jack, replacing it, and then choosing a black card. The outcome of the second event depends on the outcome of the first event, and the outcome of the first event affects the composition of the deck for the second event.
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The given question is incomplete, the complete question is:
Which events are independent? Check all that apply. Each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. Sarah picks a number less than 5, keeps it, and then picks an odd number. A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner. Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card. Two pairs of socks are randomly chosen from a drawer. Hayden chooses a black pair of socks, puts them on, and then chooses another black pair. A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull’s-eye.
the height of a parallelogram is 10 feet more than the length of the base. if the area of the parallelogram is 1200 square feet, find the length of the base and the height.
The length of the base of a parallelogram is 30 feet and the height is 40 feet.
Given that the height of a parallelogram is 10 feet more than the length of the base, and the area of the parallelogram is 1200 square feet. We have to find the length of the base and the height. Let the length of the base of a parallelogram be x. Then, the height of the parallelogram = x + 10.
We know that the area of a parallelogram is given by; A = base × height1200 = x(x + 10). Simplify the equation1200 = x² + 10x. Rearrange the equationx² + 10x - 1200 = 0. On solving this quadratic equation, we get; x = 30 and x = -40.
Since the length of the base cannot be negative, therefore, the length of the base is 30 feet. So, the height of the parallelogram is 30 + 10 = 40 feet. Therefore, the length of the base of a parallelogram is 30 feet and the height is 40 feet.
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on monday, cody bought 41 4141 cherries. on tuesday, cody ate 19 1919 cherries. now, she wants to divide the remaining cherries into bags of 4 44 cherries each. estimate how many bags of 4 44 cherries cody can make.
we're estimating, we can round down to the nearest whole number to get an answer of 50. This means Cody can make approximately 50 bags of 4 44 cherries with the cherries she has left.
To estimate the number of bags of 4 44 cherries that Cody can make, we first need to calculate how many cherries she has left after eating 19 1919 cherries on Tuesday.
The number of cherries left will be:
41 4141 - 19 1919 = 22 2222 cherries.
Now, to estimate the number of bags of 4 44 cherries Cody can make, we divide the remaining cherries by 4 44 cherries per bag:
22 2222 ÷ 4 44 ≈ 50.225
Since we're estimating, we can round down to the nearest whole number to get an answer of 50. This means Cody can make approximately 50 bags of 4 44 cherries with the cherries she has left.
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when changes in one variable tend to be accompanied by specific changesin another, the two variables are said to .
The two variables are said to have a correlation.
Correlation is a statistical measure of the relationship between two variables. When two variables are correlated, changes in one will be associated with changes in the other. For example, as the temperature increases, ice cream sales will also increase.
The correlation coefficient is a measure of the strength of the relationship between two variables. If the coefficient is close to +1, there is a strong positive correlation.
This means that as one variable increases, the other also increases. If the coefficient is close to -1, there is a strong negative correlation. This means that as one variable increases, the other decreases. If the coefficient is close to zero, the variables are said to have no correlation.
Correlation does not necessarily imply causation. It only indicates that two variables are related and does not necessarily explain why.
For example, two variables can be correlated because of a third variable. Therefore, correlation does not always indicate a causal relationship between two variables.
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S.
5.
You may be surprised to learn that prime
numbers are used for sending information
securely over the internet. The internet uses
computers, so they do this by multiplying two
huge prime numbers. It is hard work. Here is
a challenge for you. The number 51 is the
product of two prime numbers. What are the
two prime numbers?
The prime factors or the prime numbers whose product is 51 are 3 and 17.
What is the operation of prime numbers?
The operation of prime numbers refers to the various mathematical operations that can be performed using prime numbers. Prime numbers are positive integers that have exactly two divisors, 1 and the number itself. Some of the important operations involving prime numbers include:
Prime factorizationGCD and LCMModular arithmeticPrimality testingCryptographyNow,
If you meant to ask for the prime factors of 51, then they are 3 and 17.
because 51 is divisible by 3 because 5+1=6
and after dividing 51/3=17 which is also a prime number.
Hence,
the prime factors of 51 are 3 and 17.
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In a free throw shooting contest, the winner is randomly given one of 5 prizes. How can you simulate the winner being given a certain prize?
After answering the provided question, we can conclude that You can expression run this code several times to simulate the winner receiving different prizes at random.
what is expression ?In mathematics, an expression is a group of representations, digits, and conglomerates that resemble a statistical correlation or regimen. An expression can be a real number, a mutable, or a combination of the two. Addition, subtraction, rapid spread, division, and exponentiation are examples of mathematical operators. Arithmetic, mathematics, and shape all make extensive use of expressions. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.
To simulate the winner receiving a prize at random, use a random number generator to generate a number between 1 and 5, with each number representing a prize. Here's some Python code to help you out:
# create a list of prizes
prizes = ['prize A', 'prize B', 'prize C', 'prize D', 'prize E']
# simulate the winner being given a prize
winner_prize = random.choice(prizes)
print('The winner has been given', winner_prize)
In this case, the random.choice() function chooses one prize at random from a list of prizes and assigns it to the winner prize variable. The code's output will be a message displaying the prize awarded to the winner. You can run this code several times to simulate the winner receiving different prizes at random.
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[tex] \frac{cos9 + \sin9 }{cos9 - sin9} = tan54[/tex]
Prove the above question
To Prove :
[tex] \sf \dfrac{\cos9\degree + \sin9\degree }{\cos9\degree- \sin9\degree} = \tan54\degree \\ \\ [/tex]
[tex] \sf LHS = \dfrac{\cos9\degree + \sin9\degree }{\cos9\degree- \sin9\degree} \\ \\ [/tex]
[tex] \sf RHS = \tan54\degree \\ \\ [/tex]
Solving for LHS :
Divide numerator and denominator by cos9°
[tex]\longrightarrow \: \: \sf\dfrac { \dfrac{ \cos9\degree}{ \cos9\degree} + { \dfrac{\sin9}{ \cos9} }}{ \dfrac{ \cos9\degree }{ \cos9\degree} - { \dfrac{ \sin9\degree}{ \cos9\degree}}} \\ \\ [/tex]
[tex] \longrightarrow \: \: \sf\dfrac{1 + { \dfrac {\sin9\degree}{ \cos9\degree}} }{1 - { \dfrac{ \sin9\degree}{ \cos9\degree} }} \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf \dfrac{1 + \tan9\degree}{1 - \tan9\degree} \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf{ \dfrac{ \tan45 \degree + \tan9\degree}{1 - \tan45 \degree \tan9 \degree}} \: \: \: \: \: \: \: \sf \red{\bigg( \tan(A + B) = \dfrac{ \tan A + \tan B}{1 - \tan A \tan B} \bigg)} \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf \tan(45\degree + 9\degree) \\ \\ [/tex]
[tex]\longrightarrow \: \: \sf \tan54 \degree[/tex]
LHS = RHS
Hence, proved!!two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. find the probability that both marbles are red.
The probability that both marbles are red is 2/14 or 1/7.
This is because there are only two red marbles in the box, so the probability of the first being drawn is 2/14 (or 1/7). Since the first marble is not replaced, the probability of the second being drawn is also 2/14 (or 1/7). Mathematically, this can be expressed as: P(Both Red) = P(Red 1) x P(Red 2) = (2/14) x (2/14) = 1/7
In general, when dealing with probability questions involving drawing multiple objects from a box, the probability of drawing one object followed by another is calculated by multiplying the probability of drawing each individual object.
In the case of two marbles being drawn without replacement, the probability of both marbles being the same color is calculated by multiplying the probability of the first marble being of that color by the probability of the second marble being of that color.
The probability of the second marble being of the same color is lower than the probability of the first marble being of that color since it is drawn from a reduced set (the original set minus the first marble).
In this case, the probability of the second marble being of the same color as the first is 2/14, or 1/7. In conclusion, the probability of both marbles being red is 2/14, or 1/7.
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what is the difference between the lowest price in store 1 and the lowest price in store 2 the highest prices?.
The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store, with both stores having the same price.
What is difference?The difference between the two terms is that "difference" refers to the way in which two or more things are not the same, whereas "difference" is more of a comparison between two or more things.
The difference between the lowest price in store 1 and the lowest price in store 2 is the difference between the first digit of each store's key. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1.
The difference between the highest prices in store 1 and store 2 is the difference between the last digit of each store's key. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0.
The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1. This difference is reflected in the lowest prices of each store, with store 1 having a lower price than store 2.
The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0. This difference is reflected in the highest prices of each store, with both stores having the same price.
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decrease 144 in the ratio 4:3
Answer:
If you want to decrease 144 in the ratio of 4:3, you can do so by first finding the difference between the two parts of the ratio (4-3=1) and then dividing 144 by this difference (144/1=144). This gives you the value of one part of the ratio. You can then multiply this value by 3 to find how much you need to decrease 144 by: 144 * 3 = 432. So if you decrease 144 by 432, it will be in the ratio of 4:3.
Step-by-step explanation: