Answer:
The value of x that corresponds to a y value of 56 is 30.
Step-by-step explanation:
To solve for the value of x that corresponds to a y value of 56, we can plug in 56 for y in the equation y=1.5x+11:
56 = 1.5x + 11
Simplifying this equation, we can subtract 11 from both sides:
45 = 1.5x
Then, we can divide both sides by 1.5 to solve for x:
x = 30
Therefore, the value of x that corresponds to a y value of 56 is 30.
Angie has $1062 in her savings account. If the bank pays 4% simple interest on savings, how much interest does she earn in 3 years
Angie earns $127.44 in interest over the 3-year period.
Angie has $1,062 in her savings account, and the bank pays 4% simple interest on savings. To calculate the interest she earns in 3 years, we need to use the simple interest formula, which is:
Simple Interest = Principal × Rate × Time
In this case, the principal (initial amount) is $1,062, the rate is 4% (or 0.04 as a decimal), and the time is 3 years. Plugging these values into the formula, we get:
Simple Interest = $1,062 × 0.04 × 3
Next, we can calculate the interest:
Simple Interest = $1,062 × 0.04 × 3 = $127.44
So, Angie earns $127.44 in interest over the 3-year period.
In summary, when calculating simple interest, you multiply the principal (initial amount) by the interest rate and the length of time (in years) the money is in the account. In Angie's case, with $1,062 in her account and a 4% interest rate, she earns $127.44 in interest over 3 years.
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Mrs. marcum made 10 baskets out of 48 attempts. what percent of the attempts were baskets?
Approximately 20.83% of the attempts were baskets.
To find the percentage of successful attempts (baskets) out of the total attempts, we can use the following formula:
Percentage = (Number of Successful Attempts / Total Attempts) * 100
In this case, Mrs. Marcum made 10 baskets out of 48 attempts. Plugging these values into the formula:
Percentage = (10 / 48) * 100
Calculating the percentage:
Percentage = 0.208333... * 100 ≈ 20.83%
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If Ella rolls a standard six-sided die until she rolls the same number on consecutive rolls, what is the probability that her 10th roll is her last roll
The probability that Ella's 10th roll is her last roll is 31/108, or approximately 0.2870.
To find the probability that Ella's 10th roll is her last roll, we need to consider the following:
The last roll must be a repeat of the previous roll, so the previous roll cannot be the first roll or the 6th roll, because there is no previous roll in those cases.
Ella must not have rolled the same number on consecutive rolls before her 10th roll.
The probability of rolling the same number on consecutive rolls is 1/6, so the probability of not rolling the same number on consecutive rolls is 5/6.
Let's break down the probability of Ella's 10th roll being her last roll by considering the different cases:
Case 1: Ella's 8th roll is the first roll of a pair, and her 9th roll is the second roll of that pair.
In this case, Ella cannot roll the same number on consecutive rolls, so the probability of her 10th roll being her last roll is simply 1/6.
Case 2: Ella's 8th roll is the first roll of a pair, but her 9th roll is not the second roll of that pair.
In this case, Ella must roll a number different from her 9th roll, and then roll the same number as her 9th roll on her 10th roll.
The probability of rolling a different number on her 9th roll is 5/6, and the probability of rolling the same number on her 10th roll is 1/6.
Therefore, the probability of her 10th roll being her last roll in this case is (5/6)*(1/6) = 5/36.
Case 3: Ella's 8th roll is not the first roll of a pair, but her 9th roll is the second roll of a pair.
In this case, Ella must roll a number different from her 8th roll, and then roll the same number as her 8th roll on her 9th roll.
The probability of rolling a different number on her 8th roll is 5/6, and the probability of rolling the same number on her 9th roll is 1/6.
Therefore, the probability of her 10th roll being her last roll in this case is (5/6)*(1/6) = 5/36.
Case 4: Ella's 8th roll is not the first roll of a pair, and her 9th roll is not the second roll of a pair.
In this case, Ella must roll a number different from both her 8th and 9th rolls, and then roll the same number as her 9th roll on her 10th roll.
The probability of rolling a different number on her 8th roll is 5/6, the probability of rolling a different number on her 9th roll, given her 8th roll, is 4/6, and the probability of rolling the same number as her 9th roll on her 10th roll is 1/6.
Therefore, the probability of her 10th roll being her last roll in this case is (5/6)(4/6)(1/6) = 5/54.
To find the total probability, we need to sum the probabilities from each case:
1/6 + 5/36 + 5/36 + 5/54 = 31/108.
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A construction worker needs to put a rectangular window in the side of a
building. He knows from measuring that the top and bottom of the window
have a width of 5 feet and the sides have a length of 12 feet. He also
measured one diagonal to be 13 feet. What is the length of the other
diagonal?
OA. 5 feet
OB. 13 feet
O C. 17 feet
OD. 12 feet
The length of the other diagonal of the rectangular window, would be B. 13 feet
How to find the length ?The window, which is a rectangle, has the same measure for both diagonals. The diagonal portion cuts the shape into two congruent right triangles in which it acts as the hypotenuse and the width and length of the sides are seen as the legs.
In these particular conditions, we get a Pythagorean triple (5, 12, 13), signifying that this triangle is indeed a right one with a hypotenuse of 13 feet, as well as legs of 5 and 12 feet.
Remaining true to the fact that both of the rectangles' diagonals are frequently equal, its other diagonal must also have a measurement of 13 feet.
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i don’t understand this can someone pls help thx!
Jada's median 20 is lower than Diego's which is 22.5, indicating that on average, Diego practices longer than Jada.
What is the medianThe median is a measure of central tendency that represents the middle value of a data set when the values are arranged in ascending or descending order.
Jada's data in ascending order:
8, 10, 10, 15, 15, 20, 20, 20, 25, 25, 25, 35, 40
median = 20
Diego's data in ascending order:
10, 15, 15, 20, 20, 25, 25, 30, 30, 45
median = (20 + 25)/2
median = 45/2
median = 22.5
In conclusion, Jada's median 20 is lower than Diego's which is 22.5, which implies that on average, Diego practices longer than Jada.
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how do you factor completely:
4x^2 + 20x + 200 = 0
it’s a quadratic equation..
the 4x is squared
The quadratic expression 4x^2 + 20x + 200 = 0 cannot be factored completely
How to factor the expression completelyFrom the question, we have the following parameters that can be used in our computation:
4x^2 + 20x + 200 = 0
Divide through the terms by 5
So, we have
x^2 + 5x + 50 = 0
Next, we check if the above expression has real roots using
D = b^2 - 4ac
So, we have
D = 5^2 - 4 * 1 * 50
Evaluate
D = -175
The above disciminant value is less than 0
This means that the equation has no real root and as such the equation cannot be factored
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Can someone please help me ASAP? It’s due today!! I will give brainliest if it’s all correct
Please do part a, b, and c
Part A: Zachary Used Systematic Sampling
Part B: the percentage of the red car from each sample are:
Sample 1 - Red - 15% Black - 30%
Sample 2- Red - 20% Black - 20%
Sample 3 - Red - 10% Black - 20%
Sample 4 - Red - 15% Black - 25%
Sample 5 Red - 10% Black - 25
In general, sampling allows researchers to collect enough data to address the study question(s) without having to poll the whole population, which saves time and money.
Part A: Based on the image, Zachary used systematic sampling method, and he must have recorded the color of every fifth car that was known to traveled north.
Part B: To know the percentage of red cars and black cars from all of sample, we have to calculate the total number of cars in all sample first and it is done below:
Sample 1:
Total cars = 3 + 5 + 3 + 6 + 3 = 20
The Percentage of red cars = (3/20) x 100%
= 15%
The Percentage of black cars = (6/20) x 100%
= 30%
Sample 2:
Total cars = 4 + 7 + 3 + 4 + 2 = 20
The percentage of red cars = (4/20) x 100%
= 20%
The percentage of black cars = (4/20) x 100%
= 20%
Sample 3:
Total cars = 2 + 6 + 3 + 4 + 5
= 20
The percentage of red cars = (2/20) x 100%
= 10%
The percentage of black cars = (4/20) x 100%
= 20%
Sample 4:
Total cars = 3 + 4 + 4 + 5 + 4 = 20
The percentage of red cars = (3/20) x 100%
= 15%
The percentage of black cars = (5/20) x 100%
= 25%
Sample 5:
Total cars = 2 + 4 + 3 + 5 + 6
= 20
The percentage of red cars = (2/20) x 100%
= 10%
The percentage of black cars = (5/20) x 100%
= 25%
Part C:
From the finding in B above, we can easily conclude that the number of black cars observed were more than those of the red.
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Full Question
All changes saved Zachary took five random samples of cars that passed through the intersection near his school. He recorded the color of every fifth car that traveled north, and the results of his samples are organized in the table below.
Sample 1 Sample 2 Sample 3 Sample 4 Sample5
red 3 4 2 3 2
white 5 7 6 4 4
blue 3 3 3 4 3
black 6 4 4 5 5
gray 3 2 5 4 6
Part A: What sampling method did Zachary use to gather his data?
Part B: Determine the percentage of red cars from each sample and the percentage of black cars from each sample.
Part C: Draw two conclusions about your findings from Part B.
What is the distance on the
coordinate plane between the
points (-2, 16) and (-2,-5)?
the distance on the
coordinate plane between the
points (-2, 16) and (-2,-5) is 21
can someone pretty pleaseee find the volume?
Answer: Your answer is 64 m³
Hope it helped :D
why couldn't Pythagoras use the pythagorean theorem as we know it?
Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.
It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.
He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.
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When it opened for the day, a cafe had seven gallons of lemonade how many quarts of lemonade did the cafe have?
Answer:
The cafe had 28 quarts of lemonade
4 quarts make 1 gallon so multiply number of quarts by number of gallons
Please help hurry I’ll mark brainly
a) The person that starts out with more money is: Julie.
b) Both people are depositing the same amount each month.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.George's amount starts out at $125, and increases by $50 each month, hence the function is:
G(x) = 125 + 50x.
Julie's amount starts out at $175, and increases by $50 each month, hence the function is:
G(x) = 175 + 50x.
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Suppose the competing hypotheses for a test are H0: μ ≤ 10 versus Ha: μ >10. If the p-value is 0.0139 and the level of significance is 5%, what is the correct conclusion?
The correct conclusion is to reject the null hypothesis (H0) and accept the alternative hypothesis (Ha) since the p-value (0.0139) is less than the level of significance (5%).
What is the conclusion for a hypothesis test with H0: μ ≤ 10 and Ha?In hypothesis testing, the p-value is a measure of the strength of evidence against the null hypothesis.
In this case, the p-value is 0.0139, which means that the probability of observing a test statistic as extreme as the one obtained or more extreme, assuming the null hypothesis is true, is only 0.0139.
Since this value is less than the significance level of 5%, we reject the null hypothesis and accept the alternative hypothesis.
Therefore, we conclude that there is enough evidence to suggest that the true mean is greater than 10.
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Jason has $4000 in the bank. If every three months he has to pay $300 for
rent on a storage locker, how much will he have spent on rent after
three years?
5/2g +5 (-5g + 3/2)
Answer asap
Determine the distance between the points (−2, −4) and (−7, −12).
Answer:
To find the distance between two points, we can use the distance formula:
distance = √[(x2 - x1)² + (y2 - y1)²]
Let's plug in the given values:
distance = √[(-7 - (-2))² + (-12 - (-4))²]
distance = √[(-7 + 2)² + (-12 + 4)²]
distance = √[-5² + (-8)²]
distance = √[25 + 64]
distance = √89
So the distance between the points (-2, -4) and (-7, -12) is approximately 9.43 units (rounded to two decimal places).
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you work at dave's donut shop. dave has asked you to determine how much each box of a dozen donuts should cost. there are 12 donuts in one dozen. you determine that it costs $0.32 to make each donut. each dozen is sold in the box shown. each box costs $0.18 per square foot of cardboard. there are 144 square inches in 1 square foot. in this task, you will answer some questions to help you determine the price to charge for each dozen donuts. Each box contains one dozen donuts. The total cost for one dozen donuts includes the cost to make the donuts and the cost of the box. create an expression to model the total cost for one dozen donuts, where t represents the total surface area of the box in square feet.
The expression to model the total cost for one dozen donuts, where t represents the total surface area of the box in square feet, is $3.84 + $0.18t
The cost to make one donut is $0.32.
Therefore, the cost to make one dozen donuts (12 donuts) is:
12 x $0.32 = $3.84
The cost of the cardboard for one box is $0.18 per square foot. Therefore, the cost of the cardboard for a box with surface area t (in square feet) is:
$0.18t
The total cost for one dozen donuts includes the cost to make the donuts and the cost of the box.
So, the expression to model the total cost for one dozen donuts, where t represents the total surface area of the box in square feet, is $3.84 + $0.18t
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The following numerically ordered sequence of numbers has a mean of 17 and a median of 18. 7, a, 12, 15, 17, b, 20, 22,24, 25. What are the values of a and b
The values of a and b in the sequence are 18 and 10, respectively.
To find the values of a and b in the sequence given, we can use the fact that the median is 18 and the mean is 17.
Since the median is 18, we know that a and b must be two numbers that are greater than or equal to 18. Since the sequence is numerically ordered, we can see that a must be 18 or greater.
We can also use the fact that the mean is 17 to find the sum of all the numbers in the sequence. We know that the sum of all the numbers in the sequence divided by the number of terms in the sequence must be equal to the mean. Since there are 10 terms in the sequence, we can write:
(7 + a + 12 + 15 + 17 + b + 20 + 22 + 24 + 25) / 10 = 17
Simplifying this expression, we get:
(142 + a + b) / 10 = 17
Multiplying both sides by 10, we get:
142 + a + b = 170
Subtracting 142 from both sides, we get:
a + b = 28
Now we know that a and b are two numbers greater than or equal to 18 that add up to 28. The only two numbers that satisfy this condition are 18 and 10.
Since the sequence is numerically ordered, we know that a must be greater than or equal to 18. Therefore, a = 18 and b = 10.
So, the values of a and b in the sequence are 18 and 10, respectively.
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The rectangle and square both have the same perimeter.
The value of x is 4cm and the breadth of the rectangle is 11cm and the side of the square is 9cm.
Let's begin by using the formula for the perimeter of a rectangle:
Perimeter of a rectangle = 2 * (length + breadth)
For the rectangle given in the problem, the length is 7 cm and the breadth is x+7 cm. Therefore, the perimeter of the rectangle can be expressed as:
2 * (7 cm + (x+7) cm) = 2 * (x+14) cm = 2x + 28 cm
For the square, the side length is x+5 cm. Therefore, the perimeter of the square can be expressed as:
4 * (x+5) cm = 4x + 20 cm
We are given that the perimeter of both shapes is the same. Therefore:
2x + 28 cm = 4x + 20 cm
Simplifying the equation by subtracting 2x from both sides, we get:
28 cm = 2x + 20 cm
Subtracting 20 cm from both sides, we get:
8 cm = 2x
Dividing both sides by 2, we get:
x = 4 cm
Therefore, the value of x is 4 cm.
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Carly got a model train set for her birthday, and it came with 200 assorted pieces of train track. She randomly picks some pieces of track out of the box. So far, she has picked 8 straight, 7 curved, 4 cross, and 5 switch tracks.
Based on the data, what is the probability that the next piece of track Carly picks will be straight?
Write your answer as a fraction or whole number.
The likelihood that the next piece of music Carly selects will be straight is one-third or 0.3333.
The probability of picking a straight piece of track can be found by dividing the number of straight pieces by the total number of pieces:
P(straight) = number of straight pieces / total number of pieces
The total number of pieces Carly has is the sum of the straight, curved, cross, and switch pieces:
total number of pieces = 8 + 7 + 4 + 5 = 24
Therefore, the probability that the next piece of track Carly picks will be straight is:
P(straight) = 8 / 24 = 1/3
So the probability of the next piece of track Carly picks being straight is 1/3 or 0.3333
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A Farmer has 2400 feet of fencing and wants to fence off a rectangular field that boarders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area
The dimensions of the rectangular field with the largest area are w = 600 feet and L = 1200 feet.
Let's denote the width of the rectangular field by w and its length by L.
Since the field borders a straight river, we only need to fence three sides of the rectangle, which gives us:
2w + L = 2400
Solving this equation for L, we get:
L = 2400 - 2w
Now, we want to find the dimensions of the field that will give us the largest possible area.
The area of a rectangle is given by A = wL. Substituting the expression for L from above, we get:
A = w(2400 - 2w)
= 2400w - 2[tex]w^2[/tex]
To find the maximum value of this function, we can take its derivative with respect to w and set it equal to zero:
dA/dw = 2400 - 4w = 0
Solving for w, we get w = 600.
Substituting this value back into the equation for L, we get:
L = 2400 - 2w = 1200
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a(n) ? is a shorthand method for writing a mathematical rule.
a. Equal sign (=)
b. Equation
c. Formula
d. Math problem
The correct answer is c. Formula. A formula is a shorthand method for writing a mathematical rule that expresses a relationship between variables and constants. It allows us to express complex mathematical concepts in a concise and easy-to-understand way.
A formula is a shorthand method for writing a mathematical rule. The correct answer is Formula. A formula is a shorthand method for writing a mathematical rule that expresses a relationship between variables and constants. It allows us to express complex mathematical concepts in a concise and easy-to-understand way.A formula is a mathematical rule or relationship that uses letters to represent amounts which can be changed –these are called variables.In mathematics, a formula generally refers to an identity which equates one mathematical expression to another, with the most important ones being mathematical theorems. Syntactically, a formula (often referred to as a well-formed formula) is an entity which is constructed using the symbols and formation rules of a given logical language
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O is the center of the regular pentagon below. Find its perimeter. Round to the nearest tenth if necessary.
Answer:
P= 29.389 ~ 29.4
Step-by-step explanation:
P= ns = 2rn sin(180/n)...... formula to find perimeter
p= 2(5)(5)sin(36)
p= 2(5)(5)sin(36)P= 50 ×0.5877
p= 2(5)(5)sin(36)P= 50 ×0.5877 P= 29.389 approximate to 29.4
Pete is standing 5 feet away from a mirror on the ground. Pete is 4 feet tall and can just see the top of the tree in the mirror from where he is standing. The two triangles formed in the picture above are similar.
If the mirror is 25 feet away from the base of the tree, how tall is the tree?
Pete is standing 4 feet away from a mirror on the ground, if mirror is 20 feet away from the base of the tree the height of tree is 30 feet.
Here,
let,
Pete is standing 4 feet away from a mirror on the ground.
Pete is 6 feet tall and can just see the top of the tree in the mirror from where he is standing.
We can say two triangles are formed are similar,
So if the mirror is 20 feet away from the base of the tree
After talkig the similarity theorem we get,
So x = 6*5
x = 30 feet.
The height of the mirror is 30 feet.
Height is a measurement of vertical distance, or how high something or someone is (how tall they are) (how "high" a point is).
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complete question:
Pete is standing 4 feet away from a mirror on the ground. Pete is 6 feet tall and can just see the top of the tree in the mirror from where he is standing. The two triangles formed are similar.
If the mirror is 20 feet away from the base of the tree
A.
22 feet
B.
19 feet
C.
13 feet
D.
30 feet
2. Jane is now four times as old as Rita.
In 6 years, Jane will be only twice as
old as Rita at that time. Find their
present ages.
Answer:
Rita's age = 3 years
Jane's age = 12 years
Step-by-step explanation:
Framing algebraic equations and solving:
Let the age of Rita = x years
Age of Jane = 4 times of Rita's age
= 4*x
= 4x
After 6 years,
Jane's age = 4x + 6
Rita's age = x + 6
Jane's age = twice of Rita's age
4x + 6 = 2* (x + 6)
4x + 6 = 2x + 12 {Distributive property}
Subtract 6 from both sides,
4x = 2x + 12 - 6
4x = 2x + 6
Subtract '2x' from both sides,
4x - 2x = 6
2x = 6
Divide both sides by 2,
x = 6 ÷ 2
x = 3
Rita's age = 3 years
Jane's age = 4 * 3
= 12 years
What is the length of side AC, to the nearest tenth of a unit?
- 13.5 units
- 6.6 units
- 16.7 units
- 30.8 units
Answer :
13.5 unitsStep-by-step explanation:
In the given figure,
AB (Hypotenuse) = 15 units AC (Perpendicular) = ?We know that,
[tex] : \implies \rm\dfrac{P}{H}= sin \theta \\ [/tex]
where,
P is perpendicular (AC)
H is Hypotenuse (AB)
[tex]\theta[/tex] is 64°
Substituting the values,
[tex] : \implies \sf \dfrac{AC}{15} = sin \: 65\degree[/tex]
sin 65 = 0.9063 (approximately)
[tex]:\implies \sf \dfrac{AC}{15} = 0.9063 \\ [/tex]
[tex]:\implies \sf AC = 0.9063 \times 15 \\ [/tex]
[tex]:\implies \sf AC \approx 13.59 \\ [/tex]
Therefore, the length of side AC is 13.5 units
mmon Core Algebra I - MA3109 B-IC
Activity
Vertical Stretches and Shrinks of Exponential Functions
Assignment Active
Identifying a Function
Which is a stretch of an exponential decay function?
◎m=²[
Of(x) = -(5)
Of(x) = 5(²)
O fix) = 5(5)*
The stretch of an exponential decay function is y = 2(1/5)ˣ
Which is a stretch of an exponential decay function?From the question, we have the following parameters that can be used in our computation:
The list of exponential functions
An exponential function is represented as
y = abˣ
Where
a = initial valueb = growth/decay factorIn this case, the exponential function is a decay function
This means that
The value of b is less than 1
An example of this is, from the list of option is
y = 2(1/5)ˣ
Hence, the exponential decay function is y = 2(1/5)ˣ
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Complete question
Which is a stretch of an exponential decay function?
Of(x) = -(5)ˣ
Of(x) = 5(2)ˣ
O fix) = 2(1/5)ˣ
what is the circumfrence of a circle with a diameter of 36 inches in terms of pie
------------------------------------------
Show that the numbers are all rational by writing each number as a ratio of integers.
3/5 + 2/3
We have expressed 3/5 + 2/3 as the ratio of two integers, 19 and 15. Since it can be expressed as a ratio of integers, we can conclude that it is rational.
To show that 3/5 + 2/3 is rational, we need to find a way to write it as a ratio of integers. To do this, we first need to find a common denominator for the two fractions. The least common multiple of 5 and 3 is 15, so we can rewrite the fractions as follows:
3/5 = 9/15
2/3 = 10/15
Now we can add the two fractions:
3/5 + 2/3 = 9/15 + 10/15
Combining the numerators, we get:
3/5 + 2/3 = 19/15
Therefore, we have expressed 3/5 + 2/3 as the ratio of two integers, 19 and 15.
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How many five-digit natural numbers are there such that the leftmost digit is odd, the second digit is even, and all five digits are different
There are 6,720 five-digit natural numbers that satisfy the given conditions.
First, we need to choose the leftmost digit which can be any odd digit from 1,3,5,7,9. This can be done in 5 ways.
Then we need to choose the second digit, which can be any even digit from 0,2,4,6,8, except the digit we already chose for the first place. This can be done in 4 ways.
For the third digit, we have 8 remaining digits (since we have used 2 digits already), out of which we can choose any one, giving us 8 choices.
Similarly, for the fourth digit, we have 7 remaining digits to choose from, and for the last digit, we have 6 remaining digits.
Therefore, the total number of such five-digit numbers is given by:
5 × 4 × 8 × 7 × 6 = 6,720
So there are 6,720 five-digit natural numbers that satisfy the given conditions.
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