Step 1: Find the cost of 1 pie
1 pie = 4 cups of fruit + 1 pie crust
1 pie = 4(0.75) + 1(2.50)
1 pie = 3 + 2.50
1 pie = 5.50
Step 2: Find the amount of money a baker makes by selling 1 pie
1 pie cost = 5.50
1 pie revenue = 10.25
1 pie profit = 4.75
Step 3: Find the amount of money a baker makes by selling 10 pies
1 pie profit = 4.75
10 pies profit = 47.5
Answer: $47.50
Hope this helps!
This box plot shows scores on a recent math test in a sixth grade class. Identify at least three things that you can infer from the box plot about the distribution’s center, variability, and spread.
The median score, which represents the middle value of the dataset, can be identified by the line inside the box.
The IQR is represented by the length of the box in the box plot.
Based on the provided box plot for the sixth grade math test, we can infer the following information about the distribution's center, variability, and spread:
1. Center: The median score, which represents the middle value of the dataset, can be identified by the line inside the box. This value divides the data into two equal halves and helps to understand the central tendency of the scores.
2. Variability: The Interquartile Range (IQR) represents the variability in the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
The IQR is represented by the length of the box in the box plot and indicates how scores are dispersed around the median.
3. Spread: The range of the dataset can be identified by the distance between the minimum and maximum scores, represented by the whiskers in the box plot.
This shows the overall spread of the scores and indicates the extent of variation within the class.
By analyzing these aspects of the box plot, we can better understand the distribution of math test scores in the sixth grade class.
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This box plot shows scores on a recent math test in a sixth grade class. Identify at least three things that you can infer from the box plot about the distribution’s center, variability, and spread.
The cows on a farm were producing 12.8 liters of milk per cow each day. The farmer bought 60 new cows and began using a new feed for all the cows. Now each of his cows is producing 15 liters of milk each day. How many cows are on the farm now if the farmer gets 1340 more liters of milk per day than he did before any changes were made?
There are now 260 cows on the farm.
Let's start through calculating the amount of milk produced with the aid of the original cows before any modifications were made.
If every of the unique cows was producing 12.8 liters of milk in keeping with day, and there had been "x" cows, then the entire amount of milk produced by means of the original cows could be:
12.8x liters per day
After the adjustments, the farmer has 60 more cows and all cows produce 15 liters of milk per day. So, the full amount of milk produced with the aid of all cows after the modifications would be:
15(x + 60) liters per day
we're told that the new milk production is 1340 liters more according to day than before the changes. So, we can set up an linear equation:
15(x + 60) = 12.8x + 1340
Simplifying the equation, we get:
15x + 900 = 12.8x + 1340
2.2x = 440
x = 200
therefore, there were at first 200 cows on the farm. After the changes, the full number of cows would be:
x + 60 = 200 + 60 = 260 cows
So, there are now 260 cows on the farm.
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A small country emits 103,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 5% per year for the next 14 years. In the first year of the agreement, the country will keep its emissions at 103,000 kilotons and the emissions will decrease 5% in each successive year. How many kilotons of carbon dioxide would the country emit over the course of the 14 year period, ?
The total amount of carbon dioxide emitted over the 14-year period is 879,594.08 kilotons.
The small country emits 103,000 kilotons of carbon dioxide per year and agreed to cut its emissions by 5% per year for the next 14 years, starting with 103,000 kilotons in the first year.
To find the total amount of carbon dioxide emitted over the 14-year period, follow these steps:
1. Determine the initial amount of emissions: 103,000 kilotons in the first year.
2. Calculate the reduction rate per year: 5% or 0.05.
3. Calculate the total emissions for each year using the formula:
Emissions = Initial Emissions * (1 - Reduction Rate)^Year
4. Sum up the emissions for all 14 years.
Hence,
Year 1: 103,000 * (1 - 0.05)^0 = 103,000 kilotons
Year 2: 103,000 * (1 - 0.05)^1 = 97,850 kilotons
Year 3: 103,000 * (1 - 0.05)^2 = 93,057.50 kilotons
...
Year 14: 103,000 * (1 - 0.05)^13 = 56,516.87 kilotons
Now, add up the emissions for all 14 years:
Total Emissions = 103,000 + 97,850 + 93,057.50 + ... + 56,516.87 = 879,594.08 kilotons.
Therefore, the total amount of carbon dioxide emitted over the 14-year period is approximately 879,594.08 kilotons.
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In triangle efg, ef=fg. if m < e = (4x+50), m < f = (2x+60), and m < g = (14x+30), find m < g
In the given isosceles triangle, the measure of angle G is 74 degrees.
In the given problem, we are dealing with an isosceles triangle where angle G measures 74 degrees. It is mentioned that EF and FG are congruent, indicating that triangle EFG is isosceles.
Since EFG is an isosceles triangle, we can conclude that angles E and G are congruent. Therefore, we can set the measure of angle E equal to the measure of angle G and solve for x.
By setting 4x + 50 (measure of angle E) equal to 14x + 30 (measure of angle G), we have the equation 4x + 50 = 14x + 30.
Solving for x, we find that x = 2.
Now that we have the value of x, we can substitute it into each angle measure to determine their values.
The measure of angle E (mE) is given by 4x + 50, which becomes 4(2) + 50 = 58 degrees.
The measure of angle F (mF) is given by 2x + 60, which becomes 2(2) + 60 = 64 degrees.
Finally, the measure of angle G (mG) is already known to be 74 degrees.
Therefore, the measures of the angles in the isosceles triangle are: mE = 58 degrees, mF = 64 degrees, and mG = 74 degrees.
By understanding the properties of isosceles triangles and utilizing algebraic equations, we can determine the measures of the angles in the given triangle.
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In circle M with m \angle LMN= 66m∠LMN=66 and LM=19LM=19 units find area of sector LMN. Round to the nearest hundredth
We can use the formula for the area of a sector to find the area of sector $LMN$
How to find the area of a sector with central angle $\theta$ in a circle with radius $r$?The area of a sector with central angle $\theta$ in a circle with radius $r$ is given by:
$A = \frac{\theta}{360^\circ} \pi r^2$
In this case, we know that $m\angle LMN = 66^\circ$ and $LM = 19$ units, so the radius of circle M is half of the diagonal of the rectangle formed by $LM$ and $MN$. Using the Pythagorean theorem, we can find the length of $MN$:
$MN^2 = LM^2 + LN^2 = LM^2 + LM^2 = 2LM^2$
$MN = \sqrt{2} LM = \sqrt{2} \cdot 19$
So the radius of circle M is $r = \frac{1}{2}MN = \frac{1}{2}\sqrt{2} \cdot 19$
Now we can use the formula for the area of a sector to find the area of sector $LMN$:
$A = \frac{m\angle LMN}{360^\circ} \pi r^2 = \frac{66^\circ}{360^\circ} \pi \left(\frac{1}{2}\sqrt{2} \cdot 19\right)^2 \approx \boxed{90.89}$ square units (rounded to the nearest hundredth).
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For the function f(x)= 4x³ – 36x² +1.
(a) Find the critical numbers of f(if any) (b) Find the open intervals where the function is increasing or decreasing.
(a) The critical numbers are x = 0 and x = 6.
(b) The function is increasing on the interval (0, 6) and decreasing on the intervals (-∞, 0) and (6, ∞).
How to find the critical numbers of f(x)?(a) To find the critical numbers of f(x), we need to find the values of x where f'(x) = 0 or f'(x) does not exist.
f'(x) = 12x² - 72x
Setting f'(x) = 0, we get:
12x² - 72x = 0
12x(x - 6) = 0
So, the critical numbers are x = 0 and x = 6.
How to determine where the function is increasing or decreasing?(b) To determine where the function is increasing or decreasing, we need to examine the sign of f'(x) on different intervals.
For x < 0, f'(x) = 12x² - 72x < 0, which means the function is decreasing on (-∞, 0).
For 0 < x < 6, f'(x) = 12x² - 72x > 0, which means the function is increasing on (0, 6).
For x > 6, f'(x) = 12x² - 72x < 0, which means the function is decreasing on (6, ∞).
So, the function is increasing on the interval (0, 6) and decreasing on the intervals (-∞, 0) and (6, ∞).
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Ted spent 1 hour 21 minutes less than Jared reading last week. Jared spent 52 minutes less than Pete. Pete spent 3 hours reading. How long did Ted spend reading?
Ted spent 67 minutes reading.
Ted spent 1 hour and 21 minutes less Jared reading last week. Jared spent 52 minutes less Pete. Pete spent 3 hours reading. How long did Ted spend reading?
First, let's determine how long Jared spent reading:
Jared = Pete - 52 minutes
Jared = 3 hours * 60 minutes/hour - 52 minutes
Jared = 148 minutes
Now we can use the fact that Ted spent 1 hour 21 minutes less than Jared:
Ted = Jared - 1 hour 21 minutes
Ted = 148 minutes - 81 minutes
Ted = 67 minutes
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The lateral area of a cone is 614cm squared. The radius is 16.2 cm. What is the slant height to the nearest tenth of a cm?
The slant height of the given cone is 16.36 cm.
What is the slant height?The length from the base to the peak along the "center" of a lateral face of an object (like a frustum or pyramid) is its slant height.
It is, in other words, the height of the triangle that a lateral face is a part of (Kern and Bland 1948, p.
So, calculate the slant height as follows:
614π = πr√h²+r²
614 = 16.2√h²+16.2²
614 = 262.44√h²
614/262.44 = h
2.33
Height = 2.33 cm
Then, slant height formula:
s=√(r² + h²)
s=√(16.2² + 2.33²)
s=√267.8689
s=16.36 cm
Therefore, the slant height of the given cone is 16.36 cm.
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Let ⋆ be the binary operation on z (set of integers) defined by
a ⋆ b = 2ab + 5
show that ⋆ is commutative. hint: show that a ⋆ b = b ⋆ a
solution:
show that ⋆ is associative. hint: show that (a ⋆ b) ⋆ c = a ⋆ (b ⋆ c)
solution:
a. let ⋆ be the binary operation on z (set of integers) defined by
a ⋆ b = a + b + ab
1. show that ⋆ is commutative. hint: show that a ⋆ b = b ⋆ a
solution:
2.show that ⋆ is associative. hint: show that (a ⋆ b) ⋆ c = a ⋆ (b ⋆ c)
solution:
Since the expression is the same, we can conclude that the binary operation ⋆ is associative.
To show that the binary operation ⋆ is commutative, we need to demonstrate that a ⋆ b is equal to b ⋆ a for any integers a and b.
Let's start by evaluating a ⋆ b:
a ⋆ b = 2ab + 5.
Now let's evaluate b ⋆ a:
b ⋆ a = 2ba + 5.
By comparing the expressions for a ⋆ b and b ⋆ a, we can see that they are indeed equal:
2ab + 5 = 2ba + 5.
Since the expression is the same, we can conclude that the binary operation ⋆ is commutative.
To show that the binary operation ⋆ is associative, we need to demonstrate that (a ⋆ b) ⋆ c is equal to a ⋆ (b ⋆ c) for any integers a, b, and c.
Let's evaluate (a ⋆ b) ⋆ c:
(a ⋆ b) ⋆ c = (2ab + 5) ⋆ c = 2(2ab + 5)c + 5 = 4abc + 10c + 5.
Now let's evaluate a ⋆ (b ⋆ c):
a ⋆ (b ⋆ c) = a ⋆ (2bc + 5) = 2a(2bc + 5) + 5 = 4abc + 10a + 5.
By comparing the expressions for (a ⋆ b) ⋆ c and a ⋆ (b ⋆ c), we can see that they are indeed equal:
4abc + 10c + 5 = 4abc + 10a + 5.
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David is setting up camp with his friend Xavier. David and Xavier want to place their tents equal distance to the ranch where the mess hall is. A model is shown, where points D and X represent the location
tents and point R represents the ranch. DR = (12.3z + 12.4) meters (m) and XR= (10.5z+34) m.
D
X
R
What is the distance Xavier and David are from the ranch?
Therefore, the distance from both Xavier and David's tents to the ranch is: 151 meters and 159.6 meters.
What is equation?An equation is a mathematical statement that shows the equality of two expressions, often separated by an equal sign (=). The expressions on either side of the equal sign can contain variables, constants, and mathematical operations. Equations are used to solve problems, find unknown values, and represent relationships between quantities in various fields such as mathematics, physics, engineering, and economics.
Here,
The distance from Xavier's tent to the ranch is XR = (10.5z + 34) meters.
The distance from David's tent to the ranch is DR = (12.3z + 12.4) meters.
Since David and Xavier want to place their tents at equal distances from the ranch, we can set these two expressions equal to each other and solve for z:
(10.5z + 34) = (12.3z + 12.4)
Simplifying this equation, we get:
1.8z = 21.6
z = 12
Therefore, the distance from both Xavier and David's tents to the ranch is:
XR = (10.5z + 34)
= (10.5 x 12 + 34)
= 151 meters
DR = (12.3z + 12.4)
= (12.3 x 12 + 12.4)
= 159.6 meters
So both tents are 151 meters away from the ranch.
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A researcher collected the number of letters in each of 200 first names. The data are found to be normally distributed with a mean of 5. 82 and a standard deviation of 1. 43.
What percentage of first names have seven letters or less?
79. 4%
82. 5%
84. 1%
99. 8%
If a researcher collected the number of letters in each of 200 first names, approximately 79.4% of first names have seven letters or less. Therefore, the correct answer is 79.4%.
To find the percentage of first names with seven letters or less, we will use the mean (5.82) and standard deviation (1.43) of the normally distributed data. We will calculate the z-score for a name with seven letters:
z = (7 - 5.82) / 1.43
z ≈ 0.83
Now, using a z-table or a calculator that can compute the cumulative distribution function (CDF) of a standard normal distribution, we find the probability associated with the z-score:
P(z ≤ 0.83) ≈ 79.4%
So, approximately 79.4% of first names have seven letters or less. The correct answer is 79.4%.
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Jocelyn is designing a bed for cactus specimens at a botanical garden. The total area can be
modeled by the expression 2x2 + 7x +3, where x is in feet.
Suppose in one design the length of the cactus bed is 4x, and in another, the length is 2x + 1. What are the widths of
the two designs?
The width of the first design is -2.5 feet and the width of the second design is 0.5 feet.
How to calculate thw widthFor the first design, where the length is 4x, the total area is:
2(4x)² + 7(4x) + 3 = 32x² + 28x + 3
To find the width, we can divide the total area by the length:
width = (32x² + 28x + 3) / 4x
width = 8x + 7 + 3/4x
For the second design, where the length is 2x + 1, the total area is:
2(2x + 1)² + 7(2x + 1) + 3 = 8x² + 23x + 5
width = (8x² + 23x + 5) / (2x + 1)
width = 4x + 2 + 1/(2x + 1)
For the first design:
width = 8(-1/2) + 7 + 3/4(-1/2) = -2.5 feet
For the second design:
width = 4(-1/2) + 2 + 1/(2(-1/2) + 1) = 0.5 feet
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Part A: An angle is two collinear rays with a common endpoint Find an example that contradicts this definition How would you change the delito
accurate? (5 points)
Part B: Give an example of an undefined term and how it pertains to angles (5 points)
PLEASE HELP ME !!
Part A: The given definition states that an angle is two collinear rays with a common endpoint. Part B : A point is an example of an undefined term.In relation to angles, a point is crucial as it serves as the common endpoint of the two rays that form the angle.
Part A : The given definition states that an angle is two collinear rays with a common endpoint. However, this definition is incorrect as it contradicts the correct definition of an angle. In the correct definition, an angle is formed by two non-collinear rays with a common endpoint.
An example that contradicts the given definition is when you have two rays, AB and BC, with B being the common endpoint. If they were collinear, they would lie along the same straight line, and thus, no angle would be formed between them. To make the definition accurate, you would need to change it to: "An angle is formed by two non-collinear rays with a common endpoint."
Part B: An undefined term in geometry is a term that cannot be defined using other known geometric terms, but its meaning is generally understood. One example of an undefined term is a point. A point is a basic element in geometry, and it has no size, shape, or dimensions. It is merely a location in space. For instance, when discussing angle ABC, point B is the common endpoint of rays AB and BC.
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Alyssa makes $200 for every 8 hour shift she works as a personal trainer. She graphs the amount of money she earns on the y-axis, and number of hours she works the x-axis. What is the slope of the graph?
The slope of this graph is equal to 25.
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided above, we can reasonably infer and logically deduce that Alyssa made $200 for every 8 hour shift she works as a personal trainer. Additionally, the amount of money Alyssa earned would be plotted on the y-axis while the number of hours she work would be plotted on the x-axis of a graph;
Slope (m) = 200/8
Slope (m) = 25.
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In a discussion between Modise and Benjamin about functions, Benjamin said that the diagram below represents a function, but Modise argued that it does not. Who is right? Motivate your answer. x - Input value 5 8 y-Output value - 2 - S 7 -9
Modise is correct, as the input of 5 is mapped to the outputs of 2 and 9, hence the relation does not represent a function.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
For a point in the standard format (x,y), we have that:
x is the input.y is the output.The meaning is that the input given by the x-coordinate is mapped to the output given by the y-coordinate.For this problem, there are two arrows departing the input of 5, meaning that the input of 5 is mapped to the outputs of 2 and 9, hence the relation is not a function.
Missing InformationThe diagram is given by the image presented at the end of the answer.
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Each theme park charges an entrance fee plus an additional fee per ride. Write a function for each park. (3 points)
a) write a function rule for Big Wave Waterpark
b) write a function rule for Coaster City
c) write a function rule for Virtual Reality Lan
(a) The function rule for Big Wave Waterpark, f(x) = 2.5x + 5. where f(x) is total cost and x is number of slides ridden.
b) The function rule for Coaster City is, f(x) = 5x + 7.50, where x is the number of roller coaster ridden and f(x) is total cost.
c) The function rule for Virtual Reality Lan is, f(x) = 3x + 10, where f(x) is total cost and x is the number reality rides ridden.
(a) Let f(x) = ax +b be the function which represents the total cost of Big Wave Park where x represents the number of taken ride.
We can see that f(2) = 10; f(4) = 15 and f(6) = 20.
Therefore, 2a + b = 10 and 4a + b = 15
So, 2(2a + b) - (4a + b) = 2*10 - 15
4a + 2b - 4a - b = 20 - 15
b = 5
Now, f(6) = 20
6a + b = 20
6a + 5 = 20 [putting the value of 'b']
6a = 20 - 5 = 15
a = 15/6 = 5/2 = 2.5
Hence, the function rule for Big Wave Waterpark is, f(x) = 2.5x + 5.
(b) The function rule for Coaster city is, f(x) = 5x + 7.50, where x is the number of roller coaster ridden.
(c) Let the total cost for Virtual Reality Lan is, f(x) = cx + d, where x is the number reality rides ridden.
From the given graph we can see that, f(10) = 40; f(20) = 70; f(30) = 100.
So, 10c + d= 40 ........... (i)
20c + d = 70 ............... (ii)
Solving (i) and (ii) we get,
2(10c + d) - (20c + d) = 2*40 - 70
20c + 2d - 20c - d = 80 - 70
d = 10
So putting the value d = 10 in f(30) = 100 we get,
30c + 10 = 100
30c = 100 - 10 = 90
c = 90/30 = 3
So the function rule is, f(x) = 3x + 10.
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In a certain high school, a survey revealed the mean amount of bottled water consumed by students each day
was 153 bottles with a standard deviation of 22 bottles. Assuming the survey represented a normal distribution,
what is the range of the number of bottled waters that approximately 68. 2% of the students drink?
The range of the number of bottled waters that approximately 68. 2% of the students drink is between 131 and 175 bottled waters per day.
The range of the number of bottled waters that approximately 68.2% of the students drink can be calculated using the empirical rule, also known as the 68-95-99.7 rule.
According to this rule, for a normal distribution:
Approximately 68.2% of the data falls within one standard deviation of the mean
Approximately 95.4% of the data falls within two standard deviations of the mean
Approximately 99.7% of the data falls within three standard deviations of the mean
falls within a certain number of standard deviations from the mean
Since we are interested in the range of values that approximately 68.2% of the students drink, we can start by calculating one standard deviation from the mean:
One standard deviation = mean ± standard deviation
= 153 ± 22
= 131 to 175
This answer is based on the empirical rule, which is a useful tool for understanding the spread of data in a normal distribution. It tells us that for a normal distribution, a certain percentage of the data
Therefore, approximately 68.2% of the students drink between 131 and 175 bottled waters per day.
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In circle N with \text{m} \angle MQP= 44^{\circ}m∠MQP=44 ∘ , find the angle measure of minor arc \stackrel{\Large \frown}{MP}. MP ⌢. M P N Q
The measure of minor arc MPQ in a circle with central angle <MQP measuring 44 degrees is 316 degrees.
To find the measure of minor arc MPQ, we need to first find the measure of central angle <MNQ that intercepts this arc. Since minor arc MPQ and minor arc MP are adjacent, their sum equals the measure of minor arc MPNQ,
<MPQ+arc MP = <MPNQ
Substituting the measure of minor arc MP as 44 degrees, we get,
ZMPQ+ 44 360
Solving for MPQ, we get,
ZMPQ = 360-44
<MPQ = 316 degrees
Therefore, the measure of minor arc MPQ is 316 degrees.
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Classify the following expression by degree and term: (2 points)x2y − 7xy + xyz + x2nd degree polynomial7th degree polynomial2nd degree trinomial3rd degree polynomial
The given expression x²y − 7xy + xyz is a 3rd degree polynomial.
To classify it by degree and term, let's first determine the degree of each term:
1. x²y: The degree is the sum of the exponents of the variables (x and y). Here, the degree is 2 (from x²) + 1 (from y) = 3.
2. 7xy: The degree is 1 (from x) + 1 (from y) = 2.
3. xyz: The degree is 1 (from x) + 1 (from y) + 1 (from z) = 3.
Now, we can classify the expression:
- Degree: Since the highest degree among the terms is 3, the expression is a 3rd-degree polynomial.
- Term: There are three terms in the expression, so it is a trinomial.
In summary, the given expression, x²y − 7xy + xyz, is a 3rd-degree trinomial.
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A large container has 6 gallons of acid that needs to be dilluted by adding water. define the formula that models the ratio of the number of gallons of acid in the container compared to the total volume of liquid in the container when x gallons of water is added
The formula that models the ratio y is:
y = 6 / (6 + x)
Let y be the ratio of the number of gallons of acid in the container compared to the total volume of liquid in the container, and let x be the number of gallons of water added to the container.
Initially, the container has 6 gallons of acid and 0 gallons of water, for a total volume of 6 gallons. When x gallons of water is added, the total volume of liquid becomes 6 + x gallons, and the amount of acid remains at 6 gallons.
Therefore, the formula that models the ratio y is:
y = 6 / (6 + x)
This formula gives the ratio of the number of gallons of acid in the container compared to the total volume of liquid in the container when x gallons of water is added.
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A wildlife refuge in South America has howler monkeys and spider monkeys. A biologist working there randomly selected eight adults of each type of monkey, weighed them, and recorded their weights in pounds. Show your work.
howler monkey: {16, 17, 18, 18, 18, 20, 22, 23}
spider monkey: {8, 10, 10, 11, 11, 12, 14, 14}
Calculate the meaning and MAD for each type of monkey.
Calculate the means-to-MAD ratio for the two types of monkeys.
What inference can be made about the weight of both types of monkeys? Explain.
Howler monkeys are heavier on average than spider monkeys (17.75 lbs vs. 11.25 lbs).
How to solveCalculate the mean:
Some of the weights divided by the number of monkeys
Calculate the MAD:
Find the absolute deviation (difference) of each weight from the mean
Calculate the average of these deviations
Mean Howler Monkey = (16+17+18+18+18+20+22+23)/8 = 142/8 = 17.75 lbs
Mean Spider Monkey = (8+10+10+11+11+12+14+14)/8 = 90/8 = 11.25 lbs
Now, we calculate the MAD for each type of monkey:
MAD Howler Monkey= 1.875 lbs
MAD Spider Monkey= 1.5625 lbs
we calculate the means-to-MAD ratio for both types of monkeys:
Howler Monkey: Mean/MAD = 17.75/1.875 = 9.466
Spider Monkey: Mean/MAD = 11.25/1.5625 = 7.2
Inference:
Howler monkeys are heavier on average than spider monkeys (17.75 lbs vs. 11.25 lbs).
The means-to-MAD ratio shows that howler monkeys have more consistent weights (9.466) compared to spider monkeys (7.2), as a higher ratio indicates less variability in weights.
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If the table shows the results for spinning the spinner 50 times. What is the relative frequency for the event "spin a 2"
The relative frequency for the event of spin a 2 is P = 0.16
Given data ,
Let the total number of times the event occurs = 50
Now , the number of times the spin of 2 occurs = 8 times
So , the relative frequency is given by
Relative Frequency = Subgroup frequency / Total frequency
P = 8 / 50
P = 0.16
Hence , the relative frequency is 0.16
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The complete question is attached below :
If the table shows the results for spinning the spinner 50 times. What is the relative frequency for the event "spin a 2"
HELP PLEASE I AM STRUGGLING!!!!!!!!!!!!
1. An enclosure at the zoo holds two squirrel monkeys. The floor of the enclosure is a rectangle that has an area of 36 square feet. Then the zoo gets four more squirrel monkeys. The rules say that the zoo must add 9 square feet to the floor area for each additional monkey. What must the area of the floor be for all six monkeys? Explain
To find the area of the floor needed for 6 squirrel monkeys, first calculate the additional area needed for 4 monkeys 4 x 9 = 36 square feet. Add this to the initial area of 36 square feet, to get a total area of 72 square feet. Thus, the floor area for all six monkeys should be 72 square feet.
Let's first find the area of the floor required for the additional 4 monkeys
4 additional monkeys * 9 sq ft per monkey = 36 sq ft
So, to accommodate all 6 monkeys, the total floor area required would be
36 sq ft (original area) + 36 sq ft (additional area) = 72 sq ft
Therefore, the area of the floor for all six monkeys must be 72 square feet.
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The tables represent hat sizes measured in inches for two softball teams.
Pelicans
21.5 25 22
21 22 23
22.5 24 21.5
22 23.5 22
23.5 22 24.5
Falcons
22.5 20 23.5
21 24 22
20.5 21.5 23
23 22.5 21
24 22 24.5
Which team has the largest overall size hat for their playersThe tables represent hat sizes measured in inches for two softball teams.
Pelicans
21.5 25 22
21 22 23
22.5 24 21.5
22 23.5 22
23.5 22 24.5
Falcons
22.5 20 23.5
21 24 22
20.5 21.5 23
23 22.5 21
24 22 24.5
Which team has the largest overall size hat for their players? Determine the best measure of center to compare and explain your answer.
Falcons; they have a larger median value of 22.5 inches
Pelicans; they have a larger median value of 22 inches
Falcons; they have a larger mean value of about 22 inches
Pelicans; they have a larger mean value of about 23 inches? Determine the best measure of center to compare and explain your answer.
Falcons; they have a larger median value of 22.5 inches
Pelicans; they have a larger median value of 22 inches
Falcons; they have a larger mean value of about 22 inches
Pelicans; they have a larger mean value of about 23 inches
When Nabhitha goes bowling, her scores are normally distributed with a mean of 115
and a standard deviation of 11. What percentage of the games that Nabhitha bowls
does she score between 93 and 142, to the nearest tenth?
The percentage of the games that Natasha scores between 93 and 142 is given as follows:
96.9%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation are given as follows:
[tex]\mu = 115, \sigma = 11[/tex]
The proportion of games with scores between 93 and 142 is the p-value of Z when X = 142 subtracted by the p-value of Z when X = 93, hence:
Z = (142 - 115)/11
Z = 2.45
Z = 2.45 has a p-value of 0.992.
Z = (93 - 115)/11
Z = -2
Z = -2 has a p-value of 0.023.
0.992 - 0.023 = 0.969, hence the percentage is of 96.9%.
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15. Given that M ={x:x^2-5x+2x+8=0}
show that
P(A)= (1, 2), (1, 4), (2, 1), (2, 4), (2, 4, 1), (1, 4), (4, 2}, {}.
The powerset of M can be written as P(M) = {(1, 2), (1, 4), (2, 1), (2, 4), (2, 4, 1), (1, 4), (4, 2}, {}}.
Given that, M = {x: x² - 5x + 2x + 8 = 0}
This is a quadratic equation and it can be written in the form of (x - a)(x - b) = 0, where a and b are the roots of the equation.
Substituting x² - 5x + 2x + 8 = 0 in (x - a)(x - b) = 0, we get
(x - a)(x - b) = (x - (-3))(x - 5) = 0
Therefore, the roots of the equation are a = –3 and b = 5.
Now, the powerset of M can be written as P(M) = {(1, 2), (1, 4), (2, 1), (2, 4), (2, 4, 1), (1, 4), (4, 2}, {}}.
Here,
(1, 2) represents the set containing only the root ‘–3’,
(2, 1) represents the set containing only the root ‘5’,
(2, 4) represents the set containing both the roots
Therefore, the powerset of M can be written as P(M) = {(1, 2), (1, 4), (2, 1), (2, 4), (2, 4, 1), (1, 4), (4, 2}, {}}.
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David’s net worth is 45,765. 78 and his assets have a value of 62,784,24 if his assets increase by 2,784. 89 and his liabilities decrease y 3,742. 36 what is his net worth
David's net worth: 86,329.95
To calculate David's new net worth, we need to add the increase in assets and subtract the decrease in liabilities from his current net worth.
New assets value = 62,784.24 + 2,784.89 = 65,569.13
New liabilities value = David's current net worth - his current assets value
New liabilities value = 45,765.78 - 62,784.24 = -17,018.46
Since his liabilities have decreased by 3,742.36, we need to subtract this value from the new liabilities value:
New liabilities value = -17,018.46 - 3,742.36 = -20,760.82
Now we can calculate his new net worth by subtracting his new liabilities value from his new assets value:
New net worth = 65,569.13 - (-20,760.82) = 86,329.95
Therefore, David's new net worth is 86,329.95.
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You estimated that you would need 252 more points to move up a level on your favorite
video game. But after earning just 240more points, you leveled up! What was your percent
error?
(Show all work)
The percent error is 4.76%.
To find the percent error, we first need to calculate the actual error, which is the absolute difference between the estimated points and the actual points:
Actual error = |252 - 240| = 12
Next, we need to calculate the percent error, which is the ratio of the actual error to the estimated value, expressed as a percentage:
Percent error = (actual error / estimated value) x 100%
Percent error = (12 / 252) x 100%
Percent error = 4.76%
Therefore, the percent error is 4.76%.
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State how many terms are in each algebraic expression:
(a) -112y2 ____________________ [1mark]
(b) 7x2 + 5y – 9xy + 3 __________________ [1mark]
(A) There is only one term in the expression:[tex]-112y^2.[/tex]
(B) There are four terms in the expression[tex]: 7x^2, 5y, -9xy, and 3.[/tex]
In A option, There is only one term within the algebraic expression [tex]-112y^2.[/tex]A term is a single numerical or variable expression this is separated from other expressions through addition or subtraction.
In B option, There are 4 terms within the algebraic expression[tex]7x^2 + 5y - 9xy +[/tex] 3. A time period is a single numerical or variable expression that is separated from other expressions through addition or subtraction.
In this situation, the primary term is[tex]7x^2[/tex], the second time period is 5y, the 0.33 time period is -9xy, and the fourth term is 3.
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