As per the unitary method, Jackson needs 64 tablespoons of lemonade mix to make 4 quarts of lemonade. (option D).
First, we need to convert the 4 quarts of lemonade into ounces since we know the ratio in terms of ounces. One quart is equal to 32 ounces (8 oz per cup and 4 cups per quart). So, 4 quarts would be equal to 128 ounces (32 oz x 4).
Next, we need to determine how much lemonade mix is needed for every 6 ounces of water.
Therefore, the ratio of lemonade mix to water is 3 tablespoons/6 ounces.
Now that we have the ratio, we can use it to find out how much lemonade mix is needed for 128 ounces of water (4 quarts). We can set up a proportion using the ratio we just found:
3 tbsp / 6 oz = x tbsp / 128 oz
We want to solve for x, which represents the amount of lemonade mix needed for 128 ounces of water. To solve for x, we can cross-multiply and simplify:
3 tbsp x 128 oz = 6 oz x
384 tbsp oz = 6x
x = 64 tbsp
So the answer is D) 64 tbsp.
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GIVING BRAINLIEST FOR RIGHT ANSWER (provide proof please i need to know how you got the answer)
Answer:
x>7
Step-by-step explanation:
The circle is open so seven is not included which eliminates the second and fourth choice.
x<7 means x is less than seven which is wrong.
x> means x is greater than seven.
Answer:
x > 7
Step-by-step explanation:
We see that the arrow is going to the right, signaling greater than.
We know that it is not greater than or equal to, since the dot is not shaded.
So, the answer is x > 7.
The associative property works with expressions that use
A
division and subtraction. B
addition and subtraction. C
multiplication and division. D
multiplication and addition
The associative property works with expressions that use multiplication and addition. The correct option is (D).
The associative property is a rule in mathematics that allows us to change the grouping of the numbers or variables in an expression without changing the result. This property only applies to addition and multiplication, and not to subtraction and division.
The associative property of addition tells us that we can add a group of numbers in any order, and the result will be the same. For example, (2 + 3) + 4 is the same as 2 + (3 + 4). The associative property of multiplication tells us that we can multiply a group of numbers in any order, and the result will be the same. For example, (2 × 3) × 4 is the same as 2 × (3 × 4).
However, the associative property does not work with subtraction and division. For example, (10 - 3) - 2 is not the same as 10 - (3 - 2). Similarly, (12 ÷ 2) ÷ 3 is not the same as 12 ÷ (2 ÷ 3). Therefore, the correct answer to the question is D - the associative property works with expressions that use multiplication and addition.
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the high school dropout rate in the united states is greater than 25 percent. c. wright mills would classify this situation as
The high school dropout rate in the United States is greater than 25 percent. C. Wright Mills would classify this situation as a societal issue.
This is because societal issues are matters of public concern that affect large numbers of people and require collective action to resolve. The high school dropout rate in the United States is an example of a societal issue because it has widespread implications for both individuals and society as a whole.
According to Mills, a societal issue is one that cannot be attributed solely to the actions of individuals. Instead, it is the result of social structures and processes that operate at a broader level.
For example, the high school dropout rate in the United States is influenced by a variety of factors such as poverty, race, and family background. These factors are not solely determined by the actions of individual students but are instead shaped by broader social forces such as economic inequality and institutional racism.
To address the high school dropout rate, therefore, requires collective action at the societal level. This may involve policy changes, community-based initiatives, or other forms of collective action aimed at addressing the underlying social factors that contribute to the problem.
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scores on an iq test are normally distributed with a mean of 100 and a standard deviation of 15. what is the z-score for an iq score of 122?
The z-score for an IQ score of 122 is 2.
This is calculated by subtracting the mean (100) from the score (122) and dividing by the standard deviation (15). So, 122-100=22, 22/15=2.
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the purchasing agent at a local hardware store noticed a sale on hammers. the original price of the hammers was $12 each. with the discount, he could get each hammer for $9.50. what percentage was the discount (rounded to nearest whole percentage)?
The percentage discount on the hammers is about 21%.
The discount is the difference between the original price and the discounted price.
Discount = $12 - $9.50
subtract the numbers
= $2.50
To find the percentage discount, we divide the discount by the original price and multiply by 100
Percentage discount = ( Discount / Original price ) x 100
Substitute the values in the equation and find the percentage discount
Percentage discount = ( $2.50 / $12 ) x 100
Do the arithmetic operation
Percentage discount = 20.83%
Rounding to the nearest whole percentage, the discount is approximately equal to 21%.
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please help me and I will give a branlist.
The vertices of the image of QRTW for a dilation with center (0, 0) and a scale factor of 1/4 include the following:
Q' (-0.5, 0.75).
R' (-0.75, 0.25).
T' (0.5, -0.25).
W' (0.25, 1).
What is dilation?In Mathematics and Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin (0, 0) as follows:
Ordered pair Q (-2, 3) → Ordered pair Q' (-2 × 1/4, 3 × 1/4) = (-0.5, 0.75).
Ordered pair R (-3, 1) → Ordered pair R' (-3 × 1/4, 1 × 1/4) = (-0.75, 0.25).
Ordered pair T (2, -1) → Ordered pair T' (2 × 1/4, -1 × 1/4) = (0.5, -0.25).
Ordered pair W (2, 4) → Ordered pair W' (2 × 1/4, 4 × 1/4) = (0.25, 1).
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exponents and powers
express the number 729 in exponential form
Step-by-step explanation:
729 = 9³ = (3²)³ = 3⁶
I hour that is what you needed.
An empty shipping box has a mass of 2. 75 kilograms. An electronics store is packing 5 identical laptops in the shipping box. Each laptop has a mass of 1. 65 kg. The cost to ship the box was $40. 00 for the first 5 kg and $3. 15 for each kilogram over 5 kg. What was the cost to ship the packed box?
The cost to ship a box containing 5 laptops, weighing a total of 11 kg (including the empty box), is $58.90, with a cost of $40.00 for the first 5 kg and $3.15 for each additional kilogram.
The total mass of the packed shipping box can be found by adding the mass of the laptops (5 * 1.65 kg = 8.25 kg) to the mass of the empty box (2.75 kg) for a total mass of 11 kg.
Since the cost to ship the box is $40.00 for the first 5 kg and $3.15 for each additional kilogram over 5 kg, we can split the total mass into two parts: the first 5 kg and the additional weight above 5 kg.
The cost to ship the first 5 kg is $40.00, and the remaining weight is 11 kg - 5 kg = 6 kg.
The cost to ship the additional 6 kg is $3.15 per kilogram, so the total cost to ship the packed box is:
$40.00 + $3.15 * 6 kg = $58.90
Therefore, the cost to ship the packed box is $58.90.
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A system of linear equations and a reduced matrix for the system are given. 1 0 Nm 1 x - y + z = 3 3x + 2z = 7 (x - 4y + 2z = 5 0 1 0 1 Use the reduced matrix to find the general solution of the system, if one exists. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (x, y, z) = ( (x, y, z) = *) (b) If multiple solutions exist, find two specific solutions. (Enter your answers as a comma-separated list of ordered triples. If there is no solution, enter NO SOLUTION.) (x, y, z) =
a) General solution of the system is (x, y, z) = (2, 0, 1).
b) There are no multiple solutions, and we cannot find two specific solutions.
How to evaluate each part of the question?The given system of linear equations is:
1) x - y + z = 3
2) 3x + 2z = 7
3) x - 4y + 2z = 5
The reduced matrix for this system is:
1 0 1
0 1 0
0 0 1
Using the reduced matrix, we can rewrite the system of linear equations as:
1) x + z = 3
2) y = 0
3) z = 1
Now we can solve the system step by step:
From equation (3), we know that z = 1.
Next, we can use the value of z in equation (1) to find x:
x + 1 = 3
x = 3 - 1
x = 2
Finally, from equation (2), we know that y = 0.
So, the general solution of the system is (x, y, z) = (2, 0, 1).
(b) Since there is only one solution to this system, there are no multiple solutions, and we cannot find two specific solutions.
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Complete the table and graph the corresponding ordered pairs. Draw the line defined by the points to
represent all solutions to the equation: 4x + 2y = 8
Plot the x-intercept of (-0.5,0) Plot the y-intercept of (0,-2) Draw a line passing through both intercepts.
To graph 4x + 2y = 8, we'll first look at the x-intercept and y-intercept.
The x-intercept occurs when y is zero, and the y-intercept occurs when x is zero.
0 = 4x + 2y => x = -0.5y = 4x + 2(0) => y = -2
From the two equations, we get the ordered pairs(-2,0), and (-0.5,0) as our intercepts.
The line defined by these two points and that represent all solutions to the equation is:
y = -2x + 4
The table would show different values of x for different values of y, but since there are no specific values to solve, you
just have to use the slope-intercept formula to determine the points on the graph.
Here's how to plot the ordered pairs on a graph:
Plot the x-intercept of (-0.5,0)
Plot the y-intercept of (0,-2)
Draw a line passing through both intercepts.
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How do you put fractions in order from least to greatest?
To put fractions in order from least to greatest, you need to compare their values by finding the common denominator.
Here are the steps to follow:Step 1: Find a common denominator for all the fractions.
Step 2: Convert each fraction to an equivalent fraction with the common denominator.
Step 3: Compare the numerators of the equivalent fractions. The fraction with the smallest numerator is the smallest fraction, and the fraction with the largest numerator is the largest fraction.
Step 4: If two or more fractions have the same numerator, compare their denominators. The fraction with the smallest denominator is the smallest fraction, and the fraction with the largest denominator is the largest fraction.
Step 5: Write the fractions in order from least to greatest.
For example, let's say you need to put the fractions 1/3, 2/5, and 3/8 in order from least to greatest.
Step 1: The common denominator for 3, 5, and 8 is 120.
Step 2: Convert each fraction to an equivalent fraction with a denominator of 120.
1/3 = 40/120
2/5 = 48/120
3/8 = 45/120
Step 3: Compare the numerators of the equivalent fractions: 40 < 45 < 48
Step 4: Since 40 is not equal to 45 or 48, we don't need to compare the denominators.
Step 5: Write the fractions in order from least to greatest: 1/3 < 3/8 < 2/5.
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Find the area of a 2.5-by-2.5 square by splitting it into unit squares.
The area of 2.5 by 2.5 square is given as follows:
6.25 square units.
How to obtain the area of a square?The area of a square of side length s is given by the square of the side length, as follows:
A = s².
For this problem, we have 2.5 by 2.5 square, hence the side lengths are given as follows:
s = 2.5.
Then the area of 2.5 by 2.5 square is obtained applying the formula as follows:
A = 2.5²
A = 6.25 square units.
This means that the entire 2.5-by-2.5 square can be divided into 6.25 unit squares, in which each of them would have a side length of one unit.
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Exercise 3-23A (Algo) Using ratio analysis to assess financial risk LO 3-5
The following information was drawn from the balance sheets of two companies. Company Assets = Liabilities + Equity
East 206,000 91,000 115,000
West 603,000 169,000 434,000
Required
a. Compute the debt-to-assets ratio to measure the level of financial risk of both companies. B. Compare the two ratios computed in requirement a to identify which company has the higher level of financial risk
The answer based on debt to assets ratio for east and west company are,
East company debt to assets ratio is equal to 0.44.
West company debt to assets ratio is equal to 0.28.
After comparing both the company debt to assets ratio East company is at higher level of financial risk.
Assets = Liabilities + Equity
For East company,
206,000 = 91,000 + 115,000
Assets = 206,000
liabilities = 91,000
Equity = 115,000
For West company,
603,000 = 169,000 + 434,000
Assets = 603,000
liabilities = 169,000
Equity = 434,000
Debt-to-assets ratio = Total liabilities divided by the total assets.
Debt-to-assets ratio for East
= 91,000 / 206,000
= 0.44
Debt-to-assets ratio for West
= 169,000 / 603,000
= 0.28
Comparing the two ratios,
0.44 > 0.28
This implies,
Company East has a higher debt-to-assets ratio is greater than the compared to Company West.
This represents that Company East has a higher level of financial risk.
As larger proportion of their assets are financed through debt.
This shows it is difficult to repay if the company experiences financial difficulties.
Company West has a lower level of financial risk as smaller proportion of their assets are financed through debt.
Therefore, the answer of the following questions are,
Debt to asset ratio of east company = 0.44
Debt to asset ratio of west company = 0.28
Company east has a higher financial risk level .
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find the measure in degrees of the angle
Answer:
120°
Step-by-step explanation:
We know that the exterior angle of a triangle is equal to the sum of the interior opposite angles.
Let the unknown angle be x.
Accordingly,
70° + 50° = x
120° = x
helppppppppp plsssssssssssssssssss
to begin a bacteria study, a petri dish had 2800 bacteria cells. each hour since, the number of cells has increased by 3.3%. let t be the number of hours since the start of the study. let y be the number of bacteria cells. write an exponential function showing the relationship between y and t.
[tex]y = 2800(1.033)^t[/tex] is the exponential function for starting population of 2800 bacterium cells that is shown to multiply exponentially over time using this function, increasing by a factor of 1.033 every hour.
We can use an exponential function of the type y = abt to simulate the development of bacteria cells over time, where y stands for the number of cells, t for the number of hours, and a and b for constants that we must establish.
Since we now know there are 2800 bacterium cells, we can enter this number into the equation to obtain:
[tex]2800 = ab^0[/tex]
By simplifying this equation, we obtain a = 2800, which informs us that there are 2800 bacterium cells in the initial population.
We must use the knowledge that the number of cells rises by 3.3% every hour to get the value of b. By dividing this percentage growth by 100, we can convert it to a decimal, yielding a growth rate of 0.033. The value of b can then be obtained by multiplying this growth rate by 1:
b = 1 + 0.033 = 1.033
These values of a and b are what we obtain when we enter them into our exponential function:
[tex]y = 2800(1.033)^t[/tex]
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i need this paper finished within 2 hours to stay in honors math. help? (2 attachments for 50 points)
Answers:
Q.1 B. 6.88.
Q2. Sorry Not clearly visible its blurred
Q3. The closest answer choice is C. 4.9
Q4. 2.94
Q5. Set B
Q6. C
Step-by-step explanation:
Q1.
To find the mean absolute deviation, we first need to find the mean of the data set
Data: 32, 43, 38, 28, 51
Mean = (32 + 43 + 38 + 28 + 51) / 5 = 38.4
Next, we need to find the absolute deviations of each number from the mean
|32 - 38.4| = 6.4
|43 - 38.4| = 4.6
|38 - 38.4| = 0.4
|28 - 38.4| = 10.4
|51 - 38.4| = 12.6
To find the mean absolute deviation, we need to take the average of these absolute deviations
Mean Absolute Deviation = (6.4 + 4.6 + 0.4 + 10.4 + 12.6) / 5 = 6.88
Therefore, the answer is B. 6.88.
Q3.
To find the mean absolute deviation, we first need to find the mean of the data set
Data: 12.7, 22, 23.5, 24, 11, 22
Mean = (12.7 + 22 + 23.5 + 24 + 11 + 22) / 6= 18.2
Next, we need to find the absolute deviations of each number from the mean
|12.7 - 18.2| = 5.5
|22 - 18.2| = 3.8
|23.5 - 18.2| = 5.3
|24 - 18.2| = 5.8
|11 - 18.2| = 7.2
|22 - 18.2| = 3.8
To find the mean absolute deviation, we need to take the average of these absolute deviations
Mean Absolute Deviation = (5.5 + 3.8 + 5.3 + 5.8 + 7.2 + 3.8) / 6 = 5.9
Therefore, the closest answer choice is C. 4.9. However, this answer is not correct as the calculated value is 5.9.
Q4.
To find the average distance of these points from the mean of the data, we need to first find the mean of the data.
The mean of the data can be found by adding up all the values and dividing by the total number of values:
Mean = (-8 + 6.2 + 2.5 + 12 - 2 - 1.3 + 15 - 2 + 0 + 7) / 10
= 29.4 / 10
= 2.94
The average distance from the mean is found by taking the absolute value of the difference between each value and the mean, adding them up, and dividing by the total number of values:
Average Distance from Mean = (|(-8) - 2.94| + |6.2 - 2.94| + |2.5 - 2.94| + |12 - 2.94| + |-2 - 2.94| + |-1.3 - 2.94| + |15 - 2.94| + |-2 - 2.94| + |0 - 2.94| + |7 - 2.94|) / 10
= (10.94 + 3.26 + 0.44 + 9.06 + 4.94 + 4.24 + 12.06 + 4.94 + 2.94 + 4.06) / 10
= 5.688
Therefore, the average distance of these points from the mean of the data is 5.688, which is option D.
Q5.
o find out if the mean and median are equal in a set of data, we need to calculate both the mean and median and compare them.
Mean is calculated by adding up all the values and dividing by the total number of values.
Median is the middle value of the data when it is arranged in order.
Let's calculate the mean and median of both data sets:
A. (5, 3, 5, 8, 2, 5)
Mean = (5 + 3 + 5 + 8 + 2 + 5) / 6
= 4.6667
To calculate the median, we first need to arrange the data in order:
2, 3, 5, 5, 5, 8
Since the data set has an even number of values, the median is the average of the middle two values:
Median = (5 + 5) / 2
= 5
Since the mean and median of set A are not equal (4.6667 ≠ 5), set A is not the correct answer.
B. (7, 3, 5, 11, 5, 3)
Mean = (7 + 3 + 5 + 11 + 5 + 3) / 6
= 5.8333
To calculate the median, we first need to arrange the data in order:
3, 3, 5, 5, 7, 11
Since the data set has an even number of values, the median is the average of the middle two values:
Median = (5 + 5) / 2
= 5
Since the mean and median of set B are equal (5.8333 ≈ 5), set B is the correct answer.
Therefore, the set of data in which the mean and median are equal is set B: (7, 3, 5, 11, 5, 3). Answer: B.
Q6.
To answer this question, we need to first find the mean, median, and range of the data:
Data: 10, 23, 52, 18, 5, 60, 35
Mean = (10 + 23 + 52 + 18 + 5 + 60 + 35) / 7
= 28.57
Median = 23
To find the range, we need to subtract the smallest value from the largest value:
Range = 60 - 5
= 55
Now, let's evaluate each statement:
A. The mean is greater than the range.
- 28.57 > 55
- This statement is false.
B. The range is 50.
- The range is 55, not 50.
- This statement is false.
C. The median is less than the mean.
- The median is 23 and the mean is 28.57
- This statement is true.
D. The median is greater than the range.
- 23 > 55
- This statement is false.
Therefore, the statement that is true is C. The median is less than the mean.
My bed is 3 inches by 2 2/3 by 1/3 what is the volume of my bed.
Answer:
2 [tex]\frac{2}{3}[/tex] [tex]in^{2}[/tex]
Step-by-step explanation:
Factor 6y–42z
Write your answer as a product with a whole number greater than 1.
6(y - 7z) This is a product with a whole number greater than 1 (6), since we factored out a 6 from the original expression.
What is a factor?A factor is an expression or number that evenly divides another expression or number without leaving a remainder.
According to question:To factor the expression 6y - 42z, we need to find the greatest common factor (GCF) of the two terms.
The GCF of 6y and 42z is 6, since both terms are divisible by 6. We can factor out the 6 from both terms, leaving:
6(y - 7z)
Notice that the term inside the parentheses (y - 7z) cannot be factored any further, since there is no common factor other than 1. Therefore, the fully factored form of 6y - 42z is:
6(y - 7z)
This is a product with a whole number greater than 1 (6), since we factored out a 6 from the original expression.
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which of the following conditions must be met to conduct a two-proportion significance test? the populations are independent. the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population. the sample sizes are greater than 30.
The following conditions must be met to conduct a two-proportion significance test:
the populations are independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.
The two-proportion significance test is a hypothesis test that compares the proportions of two independent populations.
To conduct the two-proportion significance test, the following conditions must be met:
Populations must be independent.
Sample sizes are greater than 30.
The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.
The sample size should be large enough so that the sampling distribution of the sample proportion is nearly normal. The sample sizes should be large enough so that the central limit theorem can be applied.
In short, to conduct a two-proportion significance test, the populations must be independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.
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Put the items below into order of length, from shortest to longest. Car Mobile phone Football pitch Tennis racket Paper clip S
Answer:
Paper clip, Mobile phone, S, Tennis racket, Car, Football pitch.
A tortoise is walking in the desert. It walks for 6.4 meters at a speed of 4 meters per minute. For how many minutes does it walk?
Answer:
1.6 minutes
Step-by-step explanation:
6.4 meters/4 speed
the feasible corner points are (48,84), (0,120), (0,0), and (90,0). what is the maximum possible value for the objective function?
In linear programming, the feasible region is the set of all feasible solutions that satisfy the constraints of the problem. The feasible corner points are the extreme points of the feasible region, which represent the optimal solutions to the problem. In this case, we have four feasible corner points: (48,84), (0,120), (0,0), and (90,0).
To find the maximum possible value for the objective function, we need to evaluate the objective function at each of the feasible corner points and select the one that gives the highest value. The objective function is a linear combination of the decision variables and represents the quantity that we are trying to maximize or minimize.
Assuming that the objective function is in the form of z = ax + by, where x and y are the decision variables and a and b are constants, we can evaluate the objective function at each of the feasible corner points:
At (48,84): z = a(48) + b(84)
At (0,120): z = a(0) + b(120)
At (0,0): z = a(0) + b(0)
At (90,0): z = a(90) + b(0)
Since we don't have the values of a and b, we cannot calculate the maximum possible value of the objective function. However, we can compare the values of the objective function at each of the feasible corner points and select the one that gives the highest value.
Therefore, we can conclude that the maximum possible value for the objective function will be obtained at one of the feasible corner points: (48,84), (0,120), (0,0), or (90,0).
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In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Khloe sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
95 visitors purchased no costume.
288 visitors purchased exactly one costume.
13 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth.
In linear equation, 0.76 will purchase one or more costumes as a decimal to the nearest hundredth.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
from the given information
the probability that the next person will purchase one or more costumes
= 288 + 13/288 + 13 + 95
≈ 0.76
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a particular triangle has sides of length 14 cm, 8 cm and 9 cm. in centimeters, what is the perimeter of the triangle?
Answer:
31cm
Step-by-step explanation:
14 + 8 + 9 = 31
Make sure to add the cm on the end!
The perimeter of the triangle is 31cm.
The perimeter of the triangle with sides of length 14 cm, 8 cm and 9 cm is 31 cm. This can be calculated by simply adding up the length of each side. To explain, the perimeter of a triangle is the sum of the lengths of all three sides.
In this particular triangle, the length of side 1 is 14 cm, the length of side 2 is 8 cm and the length of side 3 is 9 cm. When we add these three lengths, we get the perimeter of the triangle: 14 cm + 8 cm + 9 cm = 31 cm.
In general, to calculate the perimeter of any triangle, we first have to identify the lengths of all three sides. Then, we simply add these lengths together to get the perimeter.
For example, if the triangle had sides of lengths 4 cm, 5 cm and 6 cm, then the perimeter would be 4 cm + 5 cm + 6 cm = 15 cm.
In conclusion, the perimeter of any triangle can be calculated by adding together the length of each side. In the case of the particular triangle in question, the perimeter is 31 cm.
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what extraneous solution arises when solving for the point of intersection of the line f(x)=-1/2x+6 and the square root function f(x)= √x-4
The extraneous solution which arises when solving for the point of intersection of the line and the square root function is 20.
What is an extraneous solution?
An extraneous solution in mathematics is a solution that develops during the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
We are given two equations as f(x) = [tex]\frac{-1}{2}[/tex]x + 6 and f(x) = √x - 4.
Now, on equating both the equations, we get
⇒ [tex]\frac{-1}{2}[/tex]x + 6 = √x - 4
On squaring both sides, we get,
⇒ [tex](\frac{-1}{2}x + 6)^{2}[/tex]= x - 4
⇒ [tex]\frac{1}{4}x^{2}[/tex] + 36 - 6x = x - 4
⇒ [tex]\frac{1}{4}x^{2}[/tex] + 40 = 7x
⇒ [tex]\frac{1}{4}x^{2}[/tex] -7x + 40 = 0
⇒ [tex]x^{2}[/tex] -28x + 160 = 0
⇒ x = 20 , 8
For point of intersection, we will substitute x = 20 in both the equations.
So, we get
⇒ f(x) = [tex]\frac{-1}{2}[/tex] (20) + 6
⇒ f(x) = -10 + 6
⇒ f(x) = -4
Similarly,
⇒ f(x) = √20 - 4
⇒ f(x) = √16
⇒ f(x) = 4
Since both the solutions are not same so this is an extraneous solution.
Hence, the extraneous solution which arises is 10.
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Determine the surface area of a square pyramid that has a perimeter of 32 cm
and a slant height of 15 cm
Given that the perimeter of the square base is 32 cm, The surface area of the square pyramid is 304 cm².
The surface area of a square pyramid can be calculated using the formula: SA = B + (1/2)Pl, where B is the area of the base, P is the perimeter of the base, l is the slant height, and SA is the total surface area.
Given that the perimeter of the square base is 32 cm, we can divide it by 4 to find the length of each side: 32 cm / 4 = 8 cm.
Now, we can calculate the area of the base by squaring the length of a side: B = (8 cm)² = 64 cm²
Using the given slant height of 15 cm, we can plug in the values into the formula for SA: SA = 64 cm² + (1/2)(32 cm)(15 cm) = 64 cm² + 240 cm² = 304 cm².
Therefore, the surface area of the square pyramid is 304 cm².
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What most likely happened in the game below when analyzing the win probability chart?
Group of answer choices
TB started as the favorite, then fell behind most of the game, and then had a last minute comeback
TB led the entire game and ended up winning
NO started as the favorite and then had a comeback at the end of the game
This shows that TB did not have a game-long advantage but rather needed to recover from a deficit to triumph.
what is probability ?A subfield of mathematics known as probability studies random events and the possibility that they will occur. It entails calculating the probability of an event happening and expressing it as a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty. The possibility of a coin landing heads-up, the chances of winning a game, or the likelihood of a disease spreading throughout a population are just a few examples of real-world occurrences that may be studied and understood using probability.
given
It is most likely that option 1 happened, according to the victory probability chart in the illustration provided: TB came out as the favourite, trailed for the majority of the game, then made a late comeback.
The graph demonstrates that the victory probability for TB initially increased before sharply declining as NO seized the lead and kept it for the most of the game.
The dramatic increase in the win probability for TB towards the end of the chart, however, shows that TB came back and won in the final few minutes of the game.
This shows that TB did not have a game-long advantage but rather needed to recover from a deficit to triumph.
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Suppose the demand d, in units sold, for a company's jeans at price x, in dollars, is d(x) = 400 - 4x.
a. If revenue = price x demand, write the rule for the
function r(x), which represents the company's
expected revenue in jean sales. Then state the
domain of this function.
b. If the price is $40, how much revenue will the
company earn?
Revenue
Price
a. The revenue function, r(x), is given by the product of the price x and the demand function d(x):
[tex] \sf r(x) = x \times d(x) = x \times (400 - 4x) = 400x - 4x^2[/tex]
The domain of this function is the set of possible prices that can be charged for the jeans, which is typically a positive real number, or in interval notation: (0, infinity).
b. If the price is $40, we can find the revenue by plugging in x = 40 into the revenue function:
[tex] \sf r(40) = 400(40) - 4(40)^2 = 16,000 - 6,400 = 9,600[/tex]
Therefore, the company will earn $9,600 in revenue if they sell their jeans at a price of 40
if the dental director wanted to analyze the data collected from the cpi, which type of descriptive statistics should be used to measure central tendencies?
To measure central tendencies in the data collected from the Consumer Price Index (CPI), the dental director should use measures of central tendency, such as the mean, median, and mode.
The mean is the average of a set of numbers and is calculated by adding all the numbers together and then dividing by the total number of numbers. The median is the middle number when the numbers are placed in order from least to greatest. The mode is the number that appears most often in a set of numbers.
Using these measures of central tendency will allow the dental director to gain a better understanding of the CPI data, as they will be able to identify the center point of the data and also see how frequently particular values appear. This can help in making informed decisions about policies and other changes.
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