Therefore , the solution of the given problem of inequality comes out to be Paul can drive at most 208 more miles before he will have to refill the tank.
What does inequality mean ?A connection or collection of variables without the equal sign is a mathematical inequality. Equilibrium is typically followed by equity. Inequality happens when two values are not equal. Differences exist between equality and inequality. It was decided to utilize the most factors symbol because the quantities are not identical or equivalent (). Any discrepancy, regardless of how small or large, can be used to compare values.
Here,
Let x be the number of miles Paul can drive before he will have to refill the tank.
Since Paul's car can go at most 375 miles on one tank of gas, and he has already driven 167 miles, we can write the inequality:
x ≤ 375 - 167
Simplifying, we get:
x ≤ 208
Therefore, Paul can drive at most 208 more miles before he will have to refill the tank.
Interpretation: If Paul drives more than 208 miles, he will not have enough gas to complete the journey and will need to refill the tank.
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2. Cornerstone High School has 1860 students.
45% of the students bike or walk to school.
372 students drive to school.
• The remaining students travel to school by bus.
●
How many students travel to school by bus?
a.651
b.837
c.1209
d.1443
The number of students who travel to school by bus will be equal to 651. Hence, option "a" is correct.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
here, we have,
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the information given in the question,
Total students in the school = 1860
Percentage of students who come by bike or walk = 45%
So,
(1860 × 45)/100 = 837
Number of students who drive to school = 372
So, the number of students traveling by school bus will be,
1860 - (837 + 372).
= 1860 - 1209
= 651
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How to convert 750 ml is how many ounces?
The value of volume 750 ml after converting to ounces is 25.36 ounces.
To convert 750 ml to ounces, we need to use a conversion factor. Knowing how to convert between ml and oz can help you accurately measure and mix ingredients for cooking, baking, or creating cocktails.
One fluid ounce is equal to 29.5735 milliliters. Therefore, we can multiply 750 ml by the conversion factor of 1/29.5735 to get the equivalent amount in ounces.
750 ml x (1/29.5735) = 25.36 oz
So, 750 ml is equal to 25.36 ounces.
This is a common conversion that you may encounter when dealing with liquids, especially in the United States, where ounces are the standard unit of measurement for volume.
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Bella and Justin opened new bank accounts. Bella opens an account that has a $3 monthly service fee and charges $1.50 each time she makes a withdrawal with her bank card. Justin opens an account that does not have a monthly service fee, but charges $2 each time he makes a withdrawal with his bank card. Which system of equations could be used to determine how many withdrawals, w, Bella and Justin must make so that the monthly cost, C, of the accounts is the same?
Multiple choice question.
A)
C=1.50w+2C=3w
cross out
B)
C=1.50w+3C=2w
cross out
C)
C=2w+1.50C=3w
D)
C=3w+1.50C=2w
Answer:
Option B
Step-by-step explanation:
Let:
w = number of withdrawals
C = Monthly cost
For Bella:
$3 = Fixed monthly charge
$1.50 × w = Amount charged for every withdrawal she makes
∴Linear equation describing her monthly cost:
C = 3 + 1.5w
For Justin:
$0 = Fixed monthly charge
$2 × w = Amount charged for every withdrawal he makes
∴Linear equation describing his monthly cost:
C = 2w
∴System of equations:
C = 3 + 1.5w
C = 2w
∴Option B
how many groups of 1/4 are in 1
Answer:
1...
Step-by-step explanation:
hope this helps
how to convert 2.75 inches to mm?
2.75 inches is equal to 69.85 millimeter
To convert 2.75 inches to millimeter, we can use the following formula:
1 inch = 25.4 millimeter
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The length in feet = conversion factor × The length in meter
Substitute the values in the equation
2.75 inches = 25.4 × 2.75
Multiply the numbers
= 69.85 millimeter
Therefore, 2.75 inches is 69.85 millimeter
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What is bell shape distribution?
The bell shaped distribution is the continuous probability distribution with a specific shape resembling a symmetrical
Bell-shaped distribution is a statistical term that describes a continuous probability distribution with a specific shape resembling a symmetrical, bell-shaped curve. This distribution is also known as the normal distribution or Gaussian distribution.
The bell-shaped distribution is characterized by its mean, which is the center of the curve, and its standard deviation, which measures the spread of the distribution. The curve is symmetric, meaning that the probabilities of values to the left and right of the mean are equal.
In a bell-shaped distribution, the majority of data points cluster around the mean, with fewer points as you move further away from the mean. The tails of the distribution extend infinitely in both directions, although the probability of observing values far from the mean becomes increasingly small.
The normal distribution is used in many fields, including science, engineering, and finance, to model real-world phenomena that are influenced by many small, random factors.
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the senior classes at high school A and high school B planned separate trips to Yellowstone national park. the senior class at high school A rented and filled 3 vans and 7 buses with 263 students High school B rented 12 vans and 3 buses with 177 students. every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?
The number of students in the van are 6 and in the bus are 35.
What are system of equations?A system of equations is a combination of equations with a common solution pair.
Given is that the senior class at high school A rented and filled 3 vans and 7 buses with 263 students. High school B rented 12 vans and 3 buses with 177 students. every van had the same number of students in it as did the buses.
Assume that there are {x} students in each van and {y} students in each bus. We can write the system of equations as -
3x + 7y = 263
12x + 3y = 177
Now, we can write -
3x + 7y = 263
3x = 263 - 7y
4 x 3x = 4(263 - 7y)
12x = 1052 - 28y
So -
1052 - 28y + 3y = 177
25y = 1052 - 177
25y = 875
y = 35 ... { 1 }
and
3x + 7 x 35 = 263
3x = 18
x = 6 ... { 2 }
Therefore, the number of students in the van are 6 and in the bus are 35.
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The dimensions of a cone are shown in the diagram.
Which measurement is closest to the volume of the sugar cone in cubic inches?
the volume of the sugar cone is closest to 14.14 cubic inches.
How to determine?
The volume of a cone can be calculated using the formula V = (1/3)πr²2h, where r is the radius of the base, h is the height of the cone, and π is approximately 3.14.
In this case, the diameter of the cone is 3 inches, which means the radius, r, is half of that or 1.5 inches. The height of the cone is given as 6 inches.
Plugging these values into the formula, we get:
V = (1/3)π(1.5²2)(6)
V ≈ 14.14 cubic inches
Therefore, the volume of the sugar cone is closest to 14.14 cubic inches.
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Ambers dinner bill is $36. 00 if amber leaves a 17% tip, how much tip will amber leave?
Answer:
$42.12
Step-by-step explanation:
if tip is 17% then she should pay 117% (this is 1.17)
$36 * 1.17 = $42.12
It is assumed that approximately 15% of adults in the US. are left-handed. Consider the probability that among 100 adults selected in the U.S., there are at least 30 who are left-handed. Given that the adults surveyed were selected without replacement, can the probability be found by using the binomial probability formula with x counting the number who are left-handed? Why or why not? Choose the correct answer below ○ A. O B. Yes, because the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent. No, because the 30 adults represent more than 5% of the sample size, the trials are dependent No, because the 100 adults were selected without replacement, the selections are dependent. No, because the probability of being right-handed is greater, x must count the number of right-handed adults. C. O D.
D. No, because the probability of being left-handed is greater, x must count the number of left-handed adults.
The binomial probability formula can be used to calculate the probability of a certain number of successes (or left-handed individuals) in a given number of trials (100 adults). In order for the binomial probability formula to be used, the trials must be independent, meaning that the selection of one person does not affect the selection of the next one. Since the probability of being left-handed is greater, the binomial probability formula cannot be used in this case and x must count the number of left-handed adults.
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Admission to Overjoy Amusement Park is $20 $ 20 per visit. However, with a season pass, which costs $40 $ 40 , each admission is $12 $ 12 . Complete the table and write a system of equations to represent the admission costs, where a is the number of admissions and c is the total cost. CLEAR CHECK Complete the table. Cost of Admission($ $ ) Number of Admissions Amount Spent on Season Pass($ $ ) Total Cost With season pass a c Without season pass a c Write a system of equations to represent this problem. With a season pass: Without a season pass:
Total cost with pass = $20a
Total cost without pass = $12a + 40
According to the information
We can write a system of equations for this problem,
Equation 1:
Cost with season pass = 12a + 40
Equation 2:
Cost without season pass = 20a
Therefore,
The system of equations that represents this problem is:
12a + 40 = c ...(i)
20a = c ...(ii)
Now making table for it:
Cost Number Amount Spent Total Cost With Total Cost Without
Ad. Ad. Pass ($) Season Pass Season Pass
20 a 0 20a + 0 20a
12 a 40 12a + 40 12a + 40
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Volume of a cylinder with polynomials radius is x+3 and height is x+11
Answer:
The formula for the volume of a cylinder is:
V = πr^2h
where r is the radius of the cylinder and h is its height.
In this case, the radius is x+3 and the height is x+11, so we can substitute these values into the formula:
V = π(x+3)^2(x+11)
Simplifying this expression, we have:
V = π(x^2 + 6x + 9)(x+11)
V = π(x^3 + 17x^2 + 69x + 99)
Therefore, the volume of the cylinder with radius x+3 and height x+11 is π(x^3 + 17x^2 + 69x + 99) cubic units.
A cylinder has a radius of 12 m and a height of 9 m. what is the exact volume of the cylinder? responses 108π m³ 108 pi, m³ 216π m³ 216 pi, m³ 972π m³ 972 pi, m³ 1296π m³
The volume of cylinder based on the dimensions of radius and height is 1296π m³.
The volume of cylinder can be calculated by the formula -
V = πr²h, where V refers to volume of the cylinder, r is the radius of the cylinder and h is the height of the cylinder.
Now, keeping the value of the dimensions in the formula to find the volume of cylinder.
V = π × 12² × 9
Taking square and performing multiplication on Right Hand Side of the equation
V = 1296π m³
Note that we have not kept the value of π in the formula to find the exact correct answer. Thus, the volume of 1296π m³.
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Quadrilateral hgfj is a rhombus. gf=16 cm and m∠ghk=42°. what is jf and m∠kgh? enter your answers in the boxes.
The value of JF = 16 cm and m ∠KGH = 48° in quadrilateral HGFJ which is a rhombus.
What is a rhombus?A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus. Rhombi or rhombuses are the plural forms of rhombus.
Quadrilateral HGFJ is a rhombus.
GF=16 cm and m∠GHK=42°.
The diagonals of the rhombus bisect each other at the right angle.
So,
m ∠KGH = 180 - 90 - 42
m ∠KGH = 48°.
And JF = GF = 16 cm.
m ∠KGH = 48°.
And JF = GF = 16 cm.
Hence, the value of JF = 16 cm and m ∠KGH = 48° in quadrilateral HGFJ which is a rhombus.
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Complete the equations. 95x10^3= ,95x 10^4= , 95x10^5=
The following equation after completion gives us the result which are given below :
95 x 10³= 9500095 x 10⁴= 95000095 x 10⁵= 9500000An equation is made up of two expressions joined by an equal sign ("="). The two expressions on each side of the equals sign are referred to as the equation's "left" and "right" sides. The right-hand side of an equation is usually assumed to be zero. This will not limit generality since we can balance it by subtracting the right-hand side expression from the expressions on both sides.
Algebra examines two major groups of equations: polynomial equations and linear equations. P(x) = 0, where P is a polynomial and axe + b = 0 is the generic form of linear equations, can be used to write polynomial equations with one variable. a and b are parameters in this case. To solve these equations, we can use geometric or computational approaches from linear algebra or mathematical analysis. There are also several sorts of equations, such as:
Linear equationsQuadratic equationsCubic equationsQuartic equationsDifferential equationsParametric equationsLearn more about Equations:
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The graph linear function is shown on the coordinate grid what is the y-intercept of the graph of this function 4,8 -5 -7
The y-intercept of a linear function is the point at which the graph of the function crosses the y-axis. This point is represented by the coordinate (0, b), where b is the y-intercept.
In the given graph, we can see that the graph of the linear function crosses the y-axis at the point (0, -5). Therefore, the y-intercept of the graph of this function is -5.
To summarize, the y-intercept of the graph of this function is -5.
Answer: -5
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A survey asked a group of adults and youths if they prefer reading books printed on paper or electronic books.
Book Preference
Print Electronic Total
Youths 27 40 67
Adults 29 27 56
Total 56 67 123
What percent of the adults surveyed prefer reading electronic books? Round your answer to the nearest tenth of a percent.
Percentage
48.21% approximately 50%
We got the answer by dividing the number of adults that read electronic books by the total adults
27/56 = 0.4821
we then multiply by 100 to get the percentage of needed. this gives us a decimal
48.21
which when rounded off to the nearest tenth is 50%
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What is the slope of a line perpendicular to a line with a slope of five
Answer: It is undefined
Step-by-step explanation:
Hope this helps-just had a test on this!
What is the conversion of 30 celsius to fahrenheit ?
The conversion value of Celsius to Fahrenheit for the value 30 Celsius is equal to 86 Fahrenheit.
Standard units used for measuring the temperature is named as Celsius and Fahrenheit.Relation to convert the temperature from Celsius to Fahrenheit is equal to :
°F = 9 /5 ( ° C ) + 32.
Convert 30 Celsius to Fahrenheit by substituting the value in the formula :
= 9 /5 ( 30° ) + 32
= 9 (6° ) + 32
= 54° + 32
= 86°F
Therefore, the converted values for the 30Celsius to Fahrenheit is given by 86 Fahrenheit.
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Mario & Luigi decide to invest in a Mushroom business, Mario invests $500,000 whilst Luigi invests $350,000. After their first year of business, they agree to split the profits within the same ratio of their initial investments. If the business made $3 million in profits, how much will Luigi receive?
a) a day
b) an hour
Amount Luigi received per day is $3,384.4 and Amount Luigi received per hour is about $141
What is Profit?Profit is the difference between the revenue that an economic entity has received from its outputs and the total cost of its inputs.
The amount Mario invests = $500,000
Amount Luigi invests = $350,000
The ratio in which the profit was split after their first year = Within the same ratio of their initial investments
The amount of profit made by the business = $3 million
The ratio of their initial investment = 500,000 : 350,000 = 10 : 7
Therefore, the ratio in which the profit is split = 10 : 7
The amount Luigi received in a year = (7/(10 + 7)) × 3 = 1235294 2/17
The time unit conversion from year to day is presented as follows;
Number of days in a year = 365 days
The amount Luigi received per day = (1235294 2/17)/365 = 3384 456/1241
= 3384.4
The amount Luigi received per day = $3,384.4
b) The number of hours in a day = 24 hours
Amount Luigi received per hour = (3384 456/1241)/24 = 141 19/1241
141 19/1241 = 141
The amount Luigi received per hour is about $141
Hence, amount Luigi received per day is $3,384.4
Amount Luigi received per hour is about $141
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An average American consumes 75 liters of icecream in a year how many millimeters will 50 Americans consume in one week
I think I might have an answer to your question!
To convert liters to millimeters, we need to know the density of ice cream. The density of ice cream can vary depending on the type and composition of the ice cream.
According to a source, the density of ice cream is around 0.6 g/mL on average. Therefore, 1 liter of ice cream would weigh around 600 grams or 600,000 milligrams.
With this information, we can calculate the total amount of ice cream consumed by 50 Americans in one week as follows:First, we need to convert the annual consumption from liters to milliliters:
75 liters/year * 1000 milliliters/liter = 75,000 milliliters/year
Next, we need to calculate the amount consumed in one week by one American:
75,000 milliliters/year / 52 weeks/year / 1 American = 1,442 milliliters/week/American
Finally, we can calculate the amount consumed by 50 Americans in one week:
1,442 milliliters/week/American * 50 Americans = 72,100 milliliters/weekTherefore, 50 Americans will consume 72,100 milliliters of ice cream in one week.
Brody and his children went into a movie theater and he bought $44.50 worth of
drinks and pretzels. Each drink costs $6 and each pretzel costs $3.25. He bought a
total of 12 drinks and pretzels altogether. Determine the number of drinks and the
number of pretzels that Brody bought.
Answer:
10 pretzels and 2 drinks
Step-by-step explanation:
2 drinks are 12
10 pretzels are 32.50
Answer:
2 drinks, 10 pretzels
Step-by-step explanation:
d = # of drinks
p = # of pretzels
1) d + p = 12
2) $6d + $3.25p = $44.50
solve equation 1 for d: d = 12 - p substitute this into equation 2 and solve for p
6(12 - p) + 3.25p = 44.50
72 - 6p + 3.25p = 44.50
-2.75p = 44.50 - 72
-2.75p = -27.50
p = -27.50/-2.75 = 10 plug this into equation 1 and solve for d
d = 12 - 10 = 2
double check the answers: 6(2) + 3.25(10) = 44.50 correct!
when can a correlation coefficient based on an observational study be used to support a claim of cause and effect?NeverWhen the correlation coefficient is close to -1 or +1.When the correlation coefficient is equal to -1 or +1.When the scatterplot of the data has little vertical variation.
A correlation between 0 and -1 or 0 and 1 indicates a weaker correlation, but still a statistically significant one.
A correlation coefficient based on an observational study can be used to support a claim of cause and effect when the correlation coefficient is statistically significant. This means that the correlation coefficient is so strong that it is unlikely to have happened by chance, and that there is likely a causal relationship between the two variables.
Mathematically, correlation coefficients are expressed as a number between -1 and 1.
A correlation coefficient of -1 indicates a perfectly negative correlation, where as one variable increases, the other decreases, and vice versa.
A correlation coefficient of 1 indicates a perfectly positive correlation where both variables move in the same direction.
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Which of the following is NOT a key feature of the function h(x)?
h of x equals the quantity x minus 5 end quantity squared when 0 is less than or equal to x is less than or equal to 4 and negative log base 4 of x plus 6 when x is greater than 4.
The domain of h(x) is [0, ∞).
The x-intercept of h(x) is (5, 0)
The y-intercept of h(x) is (0, 25).
The end behavior of h(x) is as x → ∞, h(x) → –∞.
The key feature that is NOT present in the function h(x) is "The x-intercept of h(x) is (5, 0)".
To find the x-intercept of a function, we need to set the y-value to 0 and solve for x. In the case of h(x), we have two different equations for different ranges of x:
h(x) = (x - 5)² when 0 ≤ x ≤ 4
h(x) = -log₄(x + 6) when x > 4
Setting the first equation to 0 and solving for x, we get:
0 = (x - 5)²
0 = x - 5
x = 5
However, this value of x does not fall within the range of 0 ≤ x ≤ 4, so it is not a valid x-intercept for this equation.
Setting the second equation to 0 and solving for x, we get:
0 = -log₄(x + 6)
log₄(x + 6) = 0
4⁰ = x + 6
1 = x + 6
x = -5
This value of x also does not fall within the range of x > 4, so it is not a valid x-intercept for this equation either.
Therefore, the function h(x) does not have an x-intercept of (5, 0), and this is the key feature that is NOT present in the function.
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A high school principal asks a physical education teacher and football coach to obtain a sample of 20 student each to compare times in physical activity each week. the physical education teacher randomly selects 20 students from her classes and the football coach randomly selects 20 students from football teams. Do you expect the comparison to be fair.
No, the comparison is not expected to be fair. The two groups being compared are not selected randomly from the same population
Describe Population?A population is a group of organisms of the same species that live in the same geographic area and are capable of interbreeding. The term "population" can refer to a group of animals, plants, bacteria, or any other type of living organism.
Populations can vary in size from just a few individuals to millions or even billions. The size of a population can be influenced by a number of factors, including birth rates, death rates, immigration, and emigration.
Populations also have characteristics that define their genetic makeup, such as the frequency of particular alleles or genes. This genetic diversity can influence the ability of a population to adapt to changes in its environment or to recover from disturbances, such as disease outbreaks or natural disasters.
Understanding population dynamics is important for fields such as ecology, conservation biology, and public health, as it can help us to better manage and protect populations of organisms, including our own.
No, the comparison is not expected to be fair. The two groups being compared are not selected randomly from the same population, as the physical education teacher's sample only includes students from her classes, while the football coach's sample only includes students from the football team. This could lead to potential biases and differences between the groups that may not accurately reflect the general population of students at the high school. To ensure a fair comparison, both samples should be selected randomly from the same population.
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what is definition of accuracy?
Answer: The fact of being correct and without any mistakes:
Step-by-step explanation: Hope this helps!
Janet created a list of numbers on the board in order from greatest to least. Which list is the one that Janet could have created?
In this list, 10 is the largest number and -1 is the smallest number, so it is also ordered from greatest to least.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Without a list of options to choose from, it is difficult to determine which list Janet could have created. However, generally speaking, a list of numbers in order from greatest to least would start with the largest number and end with the smallest number.
For example:
10, 8, 5, 3, 1
In this list, 10 is the largest number and 1 is the smallest number, so it is ordered from greatest to least. Other examples could include:
-1, 2, 4, 7, 10
Therefore, In this list, 10 is the largest number and -1 is the smallest number, so it is also ordered from greatest to least.
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what teh awnser is plssssssssss
Interest earned on the cash balance in the bank is recorded by the bank as an increase in the depositor’s bank account.
What is the impact of interest earned?A savings account is a type of account that can be opened with a bank. Savings account earn interest based on the amount of money in their account at the end of the month.
here. we have.
The interest that is earned depends on the number of withdraws, interest rate paid on deposits and the amount deposited in the account. Deposits are recorded as a liability in the balance sheet of a bank. A liability is an obligation that has to be paid at sometime in the future.
This means that at the end of the month, the value of the money in the depositor's saving account increases by the value of interest paid.
For example, if the interest paid by a bank on deposits in a savings account is 10%. If an account has $1000 in the account, the value of the amount at the end of the month is 1,100 (1000 x 1.1).
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Select the correct answer.
Find the quotient of
O A.
B.
O c.
(5+21) (6-4)
(2+1)
36-38
36 +38
68-54
D. 68 +5
and express it in the simplest form.
Reset
Next
The quotient of (5+21) (6-4) and (2+1) is 13/3, expressed in its simplest form
The quotient of two numbers is a way of expressing the ratio of their values. It is the result of dividing one number by the other, and can be written as a fraction or as a decimal.
The quotient of 4 and 8 is 0.5, since 4 divided by 8 is 0.5.
The quotient of (5+21) (6-4) and (2+1) can be expressed as follows:
First, we need to solve each parenthesis separately. The first parenthesis is (5+21), which equals 26. The second parenthesis is (6-4), which equals 2. Therefore, the quotient of (5+21) (6-4) is 26/2, which can be simplified to 13/1.
Now, we need to divide 26/2 by (2+1). The result is 13/3, which is the final quotient.
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pls help me
probability
2) The probability that in a cricket match, a batswoman did not hit a boundary, when she hits it 6 times out of 30 balls played, is 80%.
3) The probability of a family having:
i) 2 girls = 31.67%
ii) 1 girl = 54.27%
iii) No girl = 14.06%
iv) The sum of the probabilities = 1 or 100%
What is the probability?The probability refers to the likelihood that an expected event or outcome occurs when there are many possible outcomes.
We compute probability as the quotient of the the expected success and the total number of successes.
Probability lies between zero and one and is usually expressed as a decimal, fraction, or percentage.
2) Cricket Match:The number of boundary hits = 6
The total number of balls the batswoman played = 30
The probability that the batswoman did not hit a boundary = 1 - 6/30
= 0.8 or 80%.
The chance that the batswoman hit a boundary = 6/30 = 0.2 or 20%.
3) Girls in the Family:The total number of families with 2 children = 1,500
The number of families with 2 girls = 475
The number of families with 1 girl = 814
The number of families with 0 girl = 211
The probability of a family having:
i) 2 girls = 475/1,500 = 0.3167 or 31.67%
ii) 1 girl = 814/1,500 = 0.5427 or 54.27%
iii) No girl = 211/1,500 = 0.1406 = 14.06%
iv) The sum of the probabilities = 1 or 100%
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