The area of the picture is 144 square inches.
What is Area?The area is a measurement of the extent of a two-dimensional surface or region. It is expressed in square units, such as square inches, square meters, or square feet. The area of a shape is the amount of space it occupies in a plane or on a flat surface. The calculation of area depends on the shape of the object. For example, the area of a circle is calculated by using the formula A = πr², where r is the radius of the circle.
The area of a square with side length s is given by the formula A = s². If the side length of the picture is 12 inches, then we can substitute s = 12 into the formula to get:
A = s² = 12² = 144
Therefore, the area of the picture is 144 square inches.
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The redwood national park is home to some of the largest trees in the world hyperion is the tallest tree in the park with a heigt of approximately 379 feet tom wants to find the height of the tree in yards
Using the unit conversions, the height of the tree in yards is 126.33 yd
Let h be the height of the tree.
It is given that the Height of the tree is 379 feet and we need to find the height of the tree in yards.
From the given statement, Hyperion is the tallest tree in the park, with a height of approximately 379 feet,
We need to convert the height of the tree from feet to yards. So, We divide the height of the tree by three for the yard.
So, for one foot: h = (1/3) yd
For, 379 feet: h = 379/3 yd
= 126.33 yd
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The table shows the travelling time to work for 50 people. Calculate an estimate of the mean travelling time.
With the help of given table of data of travelling time to work for 50 people, the estimated mean travelling time is 24.8 minutes.
To estimate the mean travelling time from the given frequency table, we can use the midpoint method, where we calculate the midpoint of each class interval and multiply it by the frequency of that interval. We then sum up the products and divide by the total frequency to get the estimate of the mean travelling time. The midpoint of each interval can be calculated as the average of the lower and upper bounds of the interval. Using this method, we get:
Class interval 0 < t < 10 | 10 < t < 20 | 20 < t < 30 | 30 < t < 40 | 40 < t < 50
Midpoint (m) 5 15 25 35 45
Frequency (f) 5 15 13 10 7
Midpoint x Frequency 25 225 325 350 315
Total | | 50 | 1240
To estimate the mean travelling time, we can now calculate the sum of the products of the midpoint and frequency for each interval, which is 1240. We then divide this by the total frequency, which is 50. Therefore, the estimate of the mean travelling time for these 50 people is: Mean travelling time = Sum of (midpoint x frequency) / Total frequency
Mean travelling time = 1240 / 50 = 24.8
Thus, the estimated mean travelling time is 24.8 minutes.
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Complete Question
The table shows the travelling time to work of 50 people.
-Travelling time (t) in minutes- -Frequency-
0 <t<10 5
10 < t < 20 15
20 < t < 30 13
30 < t < 40 10
40 < t < 50 7
Calculate an estimate of the mean travelling time
Solve for n: 4^n+3 x 16^n - 8^3n
The expression 4^n+3 x 16^n - 8^3n cannot be solved for n
How to determine the solution of nfrom the question, we have the following parameters that can be used in our computation:
4^n+3 x 16^n - 8^3n
The question implies that we solve for n
This in other words mean that we determine the solution for n
The given parameter is an expression (not an equation or an inequality)
To solve for a variable, the given parameter must be an equation or an inequality
Hence, the value of n cannot be determined or it has infinite many solutions
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A group of hikers walked from Hawk Mt. Shelter to Blood Mt. Shelter along the Appalachian Trail, a total distance of 20.5 mi. It took 2 days for the walk. On the second day, the hikers walked 4.1 mi less than they did on the first day. How far did they walk each day?
They walked 12.3 miles on first day and 8.2 miles on second day. The solution has been obtained by using linear equation.
What is a linear equation?
The linear equation with this degree of one is the largest. This shows that linear equations with exponents greater than one have no variables. Such an equation gives rise to a straight line on the graph.
We are given that a group of hikers walked from Hawk Mt. Shelter to Blood Mt. Shelter along the Appalachian Trail, a total distance of 20.5 mi which took them 2 days.
Let the distance traveled on first day be 'x'.
Since, on the second day, the hikers walked 4.1 mi less than they did on the first day so,
Distance traveled on second day = (x - 4.1)
From this, we get a linear equation as
⇒x + (x - 4.1) = 20.5
⇒2x - 4.1 = 20.5
⇒2x = 24.6
⇒x = 12.3
So, (x - 4.1) = 12.3 - 4.1 = 8.2 miles
Hence, they walked 12.3 miles on first day and 8.2 miles on second day.
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a poll is given, showing 61% are in favor of a new building project. let x be the number of people who favor the new building project when 25 people are chosen at random. what is the distribution of x? x ~ ? (,) please show the following answers to 4 decimal places. what is the probability that exactly 16 people out of 25 favor the new building project? what is the probability that at least 16 people out of 25 favor the new building project? what is the probability that at most 16 people out of 25 favor the new building project? what is the probability that between 12 and 19 (including 12 and 19) people out of 25 favor the new building project?
The probability that exactly 16 people out of 25 favor the new building project is 0.1285.
The probability that at most 16 people out of 25 favor the new building project is 0.3528.
The probability that between 12 and 19 (including 12 and 19) people out of 25 favor the new building project is 0.9088.
A binomial distribution is a probability distribution that describes the number of successes in a fixed number of trials, where each trial has two possible outcomes (success or failure) and the trials are independent.
The distribution of x, the number of people who favor the new building project when 25 people are chosen at random, can be modeled using a binomial distribution.
In this case, the probability of success (favoring the new building project) is 0.61, and the probability of failure (not favoring the project) is 0.39. The number of trials is 25, since we are choosing 25 people at random.
Thus, we can write x ~ Bin(25, 0.61), which means that x follows a binomial distribution with 25 trials and a probability of success of 0.61.
To find the probability that exactly 16 people out of 25 favor the new building project, we can use the binomial probability formula:
[tex]P(X = k) = (^n_k) * p^k * (1 - p)^{n - k}[/tex]
where X is the random variable (in this case, the number of people who favor the project), k is the number of successes we are interested in (in this case, 16), n is the number of trials (25), p is the probability of success (0.61), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.
Plugging in the values, we get:
P(X = 16) = (25 choose 16) * 0.61¹⁶ * 0.39⁹ = 0.1285
Therefore, the probability that exactly 16 people out of 25 favor the new building project is 0.1285.
To find the probability that at least 16 people out of 25 favor the new building project, we need to add up the probabilities of all the events where the number of successes is 16 or greater. We can do this using the cumulative distribution function (CDF) of the binomial distribution, which gives us the probability of X being less than or equal to a certain value.
Using a calculator or a table, we can find that P(X ≥ 16) = 0.3528.
Therefore, the probability that at least 16 people out of 25 favor the new building project is 0.3528.
To find the probability that at most 16 people out of 25 favor the new building project, we can use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of its complement (the event not occurring). In this case, the complement event is the number of people who favor the project being greater than 16.
Using the same CDF, we can find that P(X > 16) = 0.6472. Therefore,
P(X ≤ 16) = 1 - P(X > 16) = 1 - 0.6472 = 0.3528
We can do this using the binomial probability formula for each possible value of k, and then summing the results.
P(12 ≤ X ≤ 19) = P(X = 12) + P(X = 13) + ... + P(X = 19)
Using a calculator or a table, we can find the probabilities for each value of k, and then add them up:
P(12 ≤ X ≤ 19) = 0.0309 + 0.0746 + 0.1322 + 0.1821 + 0.2001 + 0.1821 + 0.1322 + 0.0746 = 0.9088
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jayden measured a pen to be 20 cm long the actual length of the pen is 20.8
The percent error in a measure is given by the formula:
P = 100%*|real value - measure|/real value
Here we know that:
real value = 20.8 cm
measure = 20cm
Replacing that in the formula we will get:
P = 100%*|20.8 cm - 20cm|/20.8cm = 3.8%
That is the percent error.
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Complete question:
Jayden measured a pen to be 20 cm long the actual length of the pen is 20.8 cm, then what is the percentage error?.
Simplify the following expression:
3x − 4y + z − 2z + x − y
2x − 6z
4x − 5y − z
4x − 3y − z
4x − 5y − 3z
Answer:
4x - 5y - z
Step-by-step explanation:
3x − 4y + z − 2z + x − y
Add like terms
= 4x - 5y - z
Answer: 4x-5y-z
Step-by-step explanation: 3x + x -4y-y -2z + z
It becomes a lot easier to simplify if you reorganize the equation so that the same variables are next to each other
Point A is located at (-2,-1) on the coordinate plane. Point A is reflected over the y-axis to create point A. What ordered pair describes the location of A?
Answer:
A' (2, - 1 )
Step-by-step explanation:
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
A (- 2, 1 ) → A' (-(- 2), - 1) → A' (2, - 1 )
two cards are selected at random from a deck of 52. what is the probability that one is a spade and the other is a king
The probability that one card is a spade and the other is a king when two cards are drawn at random from a deck of 52 cards is 0.0196.
To calculate the probability that one card is a spade and the other is a king when two cards are drawn at random from a deck of 52 cards, we need to first determine the total number of possible outcomes, which is the number of ways to select two cards from a deck of 52. This can be calculated using the formula for combinations, which is:
nCr = n! / r!(n-r)!
where n is the total number of objects (52 cards in this case), r is the number of objects to be selected (2 cards), and ! denotes the factorial operation.
So, the total number of possible outcomes is:
52C2 = 52! / 2!(52-2)! = 1326
Next, we need to determine the number of favorable outcomes, which is the number of ways to select one spade and one king from the deck. Since there are 13 spades and 4 kings in a deck, there are 13 x 4 = 52 ways to select one spade and one king.
However, we need to divide this number by 2 to avoid double counting the two possible orders (king-spade or spade-king), which gives us 26 favorable outcomes.
P = favorable outcomes / total outcomes = 26 / 1326 = 0.0196 or about 1.96%
So, there is a very low probability of selecting one spade and one king when two cards are drawn at random from a deck of 52 cards.
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PLEASE HELP ME AS SOON AS POSSIBLE!!
A university purchased two different paintings in one year. The value of Painting A over time is modeled by f(x)=30,000(1.068)^x. The value of Painting B is represented by the graph at the right. Find the average rate of change of the value of each artwork over a -year time period. Which art work's value is increasing more quickly?
Rate of change of Panting A over a year period
2000Rate of change of Panting B over a year period
2500Painting B increases more quickly
How to find the rate of changeRate of change of Panting A over a year period, using the function f(x)=30,000(1.068)^x
at x = 0, f(x) = 30,000
at x = 1, f(x) = 32,040
rate of change = (30 000 - 32 000) / (0 - 1) = -2000 / -1 = 2000
Rate of change of painting B over a year period
= (25 - 27.5) * 1000 / (0 - 1)
= -2.5 * 1000 / -1
= 2500
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What is the radius of a cylinder with a volume of 950 inches to the third power in a height of 10 inches
Answer:
Step-by-step explanation:
Given the volume of a cylinder, V = πr^2h, where r is the radius, h is the height, and π is Pi, we can find the radius by rearranging the equation and solving for r.
V = πr^2h, so r^2 = V / (πh)
Taking the square root of both sides, we have:
r = √(V / (πh))
Substituting the given values:
r = √(950 / (π * 10))
Since Pi is approximately equal to 3.14, we can calculate the approximate value of r:
r = √(950 / (3.14 * 10))
r ≈ 7.46
Therefore, the radius of the cylinder with a volume of 950 cubic inches and a height of 10 inches is approximately 7.46 inches.
Determine whether the underlined number is a statistic or a parameter. A sample of employees is selected and it is found that 45% own a television. a. Statistic because the value is a numerical measurement describing a characteristic of a population. b. Parameter because the value is a numerical measurement describing a characteristic of a sample. c. Statistic because the value is a numerical measurement describing a characteristic of a sample. d. Parameter because the value is a numerical measurement describing a characteristic of a population.
The answer is c. Statistic because the value is a numerical measurement describing a characteristic of a sample.
A statistic is a value that summarizes a characteristic of a sample. In this case, the percentage of employees in the sample who own a television (45%) is a statistic because it summarizes a characteristic of the sample of employees that was selected. A parameter, on the other hand, is a value that summarizes a characteristic of a population. For example, if we were to consider the percentage of all employees in the company who own a television, then the mean or median percentage of television ownership would be a parameter because it would describe a characteristic of the entire population of employees. In summary, statistics are values that describe a characteristic of a sample, while parameters are values that describe a characteristic of a population.
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Are both correct? EXPLAIN your reasoning.
We can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.
What are equations?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
As in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, and others.
Equation: A declaration that two expressions with variables or integers are equal.
In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
So, as we have the equation:
12x + 3 = 3(5x + 9)
Now, as we can see, Sadio took out 3 as common from LHS and RHS and solved the equation.
Which gave her the value of x as -8.
Amir, on the other hand, did not take out anything as common and directly multiply 3 with other terms in the brackets to solve the equation.
He also got -8 as the value of x.
Hence, we can conclude that yes both the ways of solving the equation is correct which is done by Sadio and Amir.
Therefore, we can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.
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Solve for x questions in picture
Answer:
x = 4
Step-by-step explanation:
Move the x to the left-hand side and change its sign
2x - x = 9 - 5
x = 9 - 5
Answer:
x=4
Step-by-step explanation:
Subtract 1x from both sides
Subtract 5 from both sides to isolate the variable
x=4
Which of the following is the correct order when multiplying 2 binomials
A. First, outer, inner, last
B. Inner, first, last, outer
C. Last, inner, outer, first
D. Outer, last, first, inner
Answer:
A. First, outer, inner, last.
Step-by-step explanation:
Number 4: Would the product change if 30 and 5 on the left side of the area model were changed to 20, 10, and 5? Explain.
No, if the figures on the left side of the area model were changed to 20, 10, and 5, the product would retain the same.
Area model multiplication is what?
The area model approach is based on the straightforward equation that may be used to calculate the area of a rectangle: LxW=A. As this anchor chart from Primary Punch illustrates, students typically begin by learning basic arrays for one-digit multiplication. When we multiply each digit of one number by each digit of another number while maintaining the place value of each digit, the resulting numbers are called partial products.
According to the supplied query,
30 and 5 on the left side of the area model are altered to 20,10, and 5
Thus, after multiplying partial products, we obtain:
First row = 20×100+20×20+8×20
= 2000+400+160 = 2560
Second row = 10×100+10×20+10×8
= 1000+200+80 = 1280
Third row = 5×100+5×20+5×8
= 500+100+40 = 640
Adding all the rows we get,
2560+1280+640 = 4480
The item we receive when the dimensions are 30 and 5 is the same as this. In each instance, the area product stays the same.
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y =−4x−3 and y=−2x + 1
The value of x and y is -2 and 5
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.
Using elimination method
y =−4x−3 equation 1
y=−2x + 1 equation 2
subtract equation 1 from 2
0 = 2x +4
collect like terms
2x = -4
x= -4/2
x = -2
substitute -2 for x in equation 1
y = -4(-2)-3
y = 8 -3
y = 5
therefore the value of x and y are -2 and 5 respectively.
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Frank in going to plant b vegetables in one garden and 2b+1 vegetables seeds in a another how many seed is frank going to plant
Answer: Frank is going to plant "b" vegetables in one garden and "2b + 1" vegetables in another garden. So, the total number of seeds he is going to plant is b + (2b + 1) = 3b + 1.
Step-by-step explanation:
A gardener made a scale drawing of a lawn with a scale factor of 1:15. The dimensions of his drawing are 6 inches long by 3 inches wide. his partner plans to make another scale drawing of the lawn, but with a scale factor of 1:5. What are the dimensions of his scale drawing?
A. The length is 1 inch and the width is 2 inch
B. The length is 2 inch and the width is 1 inch
C. The length is 9 inch and the width is 18 inch
D. The length is 18 inch and the width is 9 inch
D. The length is 18 inches and the width is 9 inch
What is a scale factor?
A scale factor resembles a unit scale in several ways. It is a ratio that assesses the relationship between scale and real dimensions. Because it doesn't provide any specified units, it differs.
It is given that the scale factor of the gardener is 1:15.
The dimensions of his drawing are 6 inches long by 3 inches wide.
Therefore the original dimensions are 6*15= 90 inches.
3*15= 45 inches.
The scale of his partner is 1:5.
So, we have to divide the original dimensions by 5.
The dimensions of the scale drawing are 90/5= 18 inches long
45/5=9 inches wide.
Therefore length is 18 inches and the width is 9 inches.
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You have $700 to buy a new carpet for you bedroom write an inequality that represents the cost c per 14 squares for your new carpet
The inequality that represents the cost c per 14 squares for a new carpet with a budget of $700 is: c ≤ 700/14 = 50 Therefore, the answer is:
The inequality is c ≤ 50.
Assuming that the price of the carpet is constant per square foot, we can write the following inequality to represent the cost c per 14 squares:
c/14 ≤ 700
This inequality states that the cost per 14 square feet (c/14) cannot exceed $700, which is the total amount of money available to purchase the carpet.
To write an inequality representing the cost of a new carpet per 14 square feet, we need to first define the cost per square foot. Let's say the cost per square foot is $x. Then, the cost of the carpet for 14 square feet would be 14x.
Since we have a budget of $700, we can write the inequality:
14x ≤ 700
This inequality represents that the cost of the carpet for 14 square feet should be less than or equal to $700. We can solve for x by dividing both sides by 14:
x ≤ 50
This means that the cost per square foot of the carpet should be less than or equal to $50 for it to fit within the budget of $700.
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Determine the correct answer using pi = 3.14 and rounding to the
nearest thousandth if necessary.
Find the surface area of a pyramid with a height of 9.8 meters,
slant height of 10.34 meters, and a square base with a width of
6.7 meters.
What is the weight of a 35. 99-carat diamond in grams and ounces? (1 carat=0. 2 g)
The 35.99-carat diamond weighs approximately 7.198 grams (0.254 ounces).
We can use the conversion factor of 1 carat = 0.2 g to convert carats to grams.
Diamond weight in grams: 35.99 carats x 0.2 g/carat = 7.198 g (rounded to three decimal places)
We can use the conversion factor of 1 ounce = 28.3495 g to convert the weight in grams to ounces.
Diamond weight in ounces: 7.198 g / 28.3495 g/o z = 0.254 o z (rounded to three decimal places)
Carats are now commonly used to measure the weight of gemstones, including diamonds, and are abbreviated as "ct." A 1-carat diamond, for example, weighs 0.2 grams while a 2-carat diamond weighs 0.4 grams.
As a result, the 35.99-carat diamond weighs approximately 7.198 grams (0.254 ounces).
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a 12-ft-by-15-gt rectangular swimming pool has a 3-ft-wide no-slip surface around it. what is the outer preimeter of the no-slip surfaec
If a 12-ft-by-15-gt rectangular swimming pool has a 3-ft-wide no-slip surface around it. The outer perimeter of the no-slip surface around the rectangular swimming pool is 78 feet.
The key idea in this problem is to recognize that the no-slip surface around the pool consists of a rectangular strip of uniform width that runs parallel to the edges of the pool. To find the outer perimeter of this strip, we need to add up the lengths of all four sides of the rectangle formed by the outermost edges of the no-slip surface.
Let's start by finding the length of the no-slip surface that runs along the length of the pool. Since the pool is 12 feet long and the no-slip surface extends 3 feet beyond each end of the pool, the total length of the no-slip surface is:
12 + 2(3) = 18 feet
The "2(3)" term in this equation represents the 3-foot-wide extension on each end of the pool. Next, we need to find the length of the no-slip surface that runs along the width of the pool. Since the pool is 15 feet wide and the no-slip surface extends 3 feet beyond each side of the pool, the total width of the no-slip surface is:
15 + 2(3) = 21 feet
Now we have the lengths of the two parallel sides of the rectangle formed by the outermost edges of the no-slip surface. To find the lengths of the other two sides, we simply add up the lengths of the corresponding sides of the pool.
Therefore, the length of the rectangle is 12 + 2(3) = 18 feet, and the width of the rectangle is 15 + 2(3) = 21 feet.
Finally, we can add up the lengths of all four sides of the rectangle to find the outer perimeter of the no-slip surface:
2(18) + 2(21) = 36 + 42 = 78 feet.
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Use the Angle Addition Postulate to find x
The value of x by using the addition postulate of an acute angle is 36.
What are acute angles?Acute angles are those between 0 and 90 degrees, and those angles are less than 90 degrees. When two rays intersect at a vertex, an angle is created.
An acute angle is one that is smaller than 90 degrees in length and has all internal angles that are less than 90 degrees.
Here, we have an acute angle NCQ that is 70 degrees. Using the addition postulate to determine the value of x, we have:
x + 34 = 70
x = 70 + (-34)
x = 70 - 34
x = 36
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Explain why the denominator 6 in 3/6 is not changed when adding fractions
The denominator 6 in 3/6 is should not be changed when adding fractions if other fractions have a denominator of 6, to make the addition easy because 6 will be the lowest common multiple.
Why are denominators not changed when adding fractions?
One of the reasons why the denominator will always stay the same when adding fraction is because the size of the equal pieces does not change when you combine the two fractions together.
For example say you want to add 3/6 + 1/6 + 2/6,
you will notice that all the fractions have equal denominator, so adding the fractions together will have the following result.
3/6 + 1/6 + 2/6 = (3 + 1 + 2 ) / 6
= 6/6
= 1
So the 6 in 3/6 should not be changed if all other fractions you wish to add to 3/6 have 6 as their denominator, because the 6 is lowest common multiple.
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3.162 corrected to a 2 significant figure
Explanation:
The left-most digits are more significant than digits on the right.
For example, in the very large number 1,234,567 the "1" and "2" are more important than the "6" and "7". We focus on the more important digits when rounding. This would mean 1,234,567 rounds to 1,200,000 = 1.2 million = 1.2*10^6
Going back to 3.162, we have "3" and "1" as the left-most digits. We'll bump 3.1 up to 3.2 because of the digit 6 fits the criteria of "5 or larger".
Put another way: 3.162 is closer to 3.2 than it is to 3.1
This is why 3.2 is the final answer.
2500, 500, 100, ...
Find the next 3 terms of the geometric sequence.
PLEASE GIVE BRAINLIEST!
have a good day ;)
Answer:
2500,500,100, 20, 4, 0.8
Step-by-step explanation:
dividing by 5 every term.
2500/ 5 = 500
500/ 5 = 100
100/ 5 = 20
20/5 = 4
4/5 = 0.8
What number would correctly replace the G?
Answer:
40
Step-by-step explanation:
x is being multiplied by 8 to get y
so 5 x 8 = 40
if ∆DEF ~ ∆ABC, AB/AC =2/3 and DF=6cm then find the length of DE
Answer:
4cm
Step-by-step explanation:
∵∆DEF ~ ∆ABC，AB/AC =2/3，
∴DE/DF=2/3.
∵DF=6cm，
∴DE=6*2/3=4cm.
4.if a man has six different sportshirts and four different pairs of slacks, how many different combinations can he wear?
The man can wear 15 different outfit combinations by mixing and matching his six different sport shirts and four different pairs of slacks.
Combination is a way of counting the number of different groups of items that can be selected from a larger set without regard to the order in which they are selected.
In this case, the man has six different sport shirts and four different pairs of slacks, and he wants to know how many different outfit combinations he can wear. We can use the formula for combinations to calculate the number of possibilities.
The formula for combinations is:
ⁿCₓ = n! / (x! * (n - x)!)
Where n is the total number of items, x is the number of items being selected, and the exclamation mark (!) represents the factorial of a number (i.e., the product of all positive integers up to that number).
Using this formula, we can calculate the number of different combinations the man can wear as follows:
Number of sport shirts (n) = 6
Number of slacks (x) = 4
Number of combinations = ⁶C₄ = 6! / (4! * (6 - 4)!)
= (6 * 5 * 4 * 3 * 2 * 1) / [(4 * 3 * 2 * 1) * (2 * 1)]
= 15
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