Answers
In this question, f is a one-to-one function and f(0)=7. Thus, f⁻¹(7)=0.
As we already know that f(0)=7,
then (f(0))⁻¹ = f⁻¹(7)=0.
Thus, (f(0))⁻¹=0.
What is one-to-one function?These are important as they can be used to show the existence of an inverse function. A one-to-one function is a type of mathematical function that maps one element of its domain to exactly one element of its codomain. This means that for every element of the domain, there is a unique element of the codomain.
f⁻¹(7)=0
The inverse of a one-to-one function f is denoted by f⁻¹, and it is defined as the inverse of the function f.
In this question, f is a one-to-one function and f(0)=7.
This means that the inverse of f, f⁻¹, maps 7 to 0.
Thus, f⁻¹(7)=0.
(f(0))⁻¹=0
Since the inverse of a one-to-one function f is denoted by f⁻¹, then (f(0))⁻¹ is the inverse of f(0).
As we already know that f(0)=7, then (f(0))⁻¹ = f⁻¹(7)=0.
Thus, (f(0))⁻¹=0.
To summarize, f⁻¹(7)=0 and (f(0))⁻¹=0 since f is a one-to-one function and f(0)=7.
This is because the inverse of a one-to-one function f is denoted by f⁻¹ and it maps 7 to 0.
Thus, f⁻¹(7)=0 and (f(0))⁻¹=0.
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Related Questions
The measure of angle t is 60 degrees. What is the x-coordinate of the point where the terminal side intersects the unit circle?
Answers
Therefore, the x-coordinate is 1/2.
What is coordinate?A coordinate is a value that represents a point's position in a given system of reference. In two-dimensional (2D) space, coordinates typically consist of two values, x and y, that represent the point's position along the horizontal and vertical axes, respectively.
Given by the question.
To find the x-coordinate of the point where the terminal side intersects the unit circle, we first need to determine the quadrant in which the terminal side lies based on the angle measure of 60 degrees.
Since 60 degrees is in the first quadrant (0 to 90 degrees), the x-coordinate will be positive.
Next, we can use the fact that the terminal side intersects the unit circle, which means its distance from the origin is 1.
Since the angle measure is 60 degrees, we can construct a right triangle with the terminal side as the hypotenuse, and one leg parallel to the x-axis.
The opposite side to the angle t will be sin (60), and the adjacent side to the angle t will be cos (60).
Using the trigonometric identity cos (60) = 1/2, we can see that the x-coordinate of the point where the terminal side intersects the unit circle is: cos (60) = 1/2.
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EL TRIPLE DE X MENOS CINCO DIVIDIDO ENTRE EL PRODUCTO DE SEIS Y X CUAL ES LA EXPRECION EQUIVALENTE?
Answers
Answer:
Step-by-step explanation:
Answer:
= 3x - 5/(6x)
Step-by-step explanation:
El triple de x es: 3x
La expresión es:
3x - 5/(6x)
Perry's patio is 6 meters long and 53 meters wide. What is the area of his patio?
Answers
You have to multiply 6 and 53 to get 318 as your area, which then you would put into the unit states in the question, so your answer is 318 m^2.
A woman weighing 130 lbs drinks 2 mixed drinks (2 oz of liquor mixed with soda) with
dinner between 7-8 pm. At 10 pm she had a glass of wine.What was her BAC at 8 pm?
Answers
Answer:
Step-by-step explanation:
The BAC (Blood Alcohol Concentration) of a person depends on several factors, such as the amount of alcohol consumed, the time over which the alcohol was consumed, and the weight and gender of the person. For this problem, we will assume that the woman has a normal metabolism and that the alcohol is completely absorbed into her bloodstream.
To calculate the BAC at 8 pm, we need to know the amount of alcohol that the woman consumed and the time over which she consumed it. We are given that she had 2 mixed drinks between 7-8 pm, which contained a total of 2 ounces of liquor. We are also given that she had a glass of wine at 10 pm, but we don't need to consider this for the BAC at 8 pm.
Using the Widmark formula, we can calculate the BAC at 8 pm:
BAC = (Alcohol consumed / (Body weight x r)) - (0.015 x Hours since first drink)
where r is the gender constant (0.55 for females) and 0.015 is the rate at which the liver metabolizes alcohol.
Plugging in the values we know, we get:
BAC = (2 oz / (130 lbs x 0.55)) - (0.015 x 1 hour)
BAC = 0.0208 - 0.015
BAC = 0.0058
Therefore, the woman's BAC at 8 pm was approximately 0.0058, which is below the legal limit for driving in most states in the US.
Please helpppp I need helppp please
Answers
The value of x in the rectangle is 36.
How to find the angle of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
All angles measure 90∘ in a rectangle. The sum of angles in a rectangle is 360 degrees.
Therefore, let's find the value of x in the angles.
Hence,
∠2 = x + 30
∠5 = 2x - 48
Therefore,
∠2 + ∠5 = 90°
x + 30 + 2x - 48 = 90
3x - 18 = 90
3x = 90 + 18
3x = 108
divide both sides by 3
x = 108 / 3
x = 36
Therefore,
x = 36
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Need help pleaaasseee
Answers
By using chi-squared test, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.
What is chi-squared test?
To perform a chi-squared test for independence between breed and milk yield, we need to set up the hypotheses:
Null hypothesis: There is no association between breed and milk yield.
Alternative hypothesis: There is an association between breed and milk yield.
We will use a significance level of 0.05.
To calculate the expected counts for each cell, we will use the formula: (row total x column total) / grand total.
The observed counts and expected counts are:
The grand total is 100.
The degrees of freedom for the test are (number of rows - 1) x (number of columns - 1) = (2 - 1) x (3 - 1) = 2.
Using a chi-squared distribution table or calculator, we find the critical value for a chi-squared test with 2 degrees of freedom and a 0.05 significance level to be 5.99.
To calculate the test statistic, we use the formula:
chi-squared = [tex]sum((observed\ count - expected\ count)^2 / expected\ count)[/tex]
The calculated value of chi-squared is:
[tex]chi-squared = ((32-25.76)^2 / 25.76) + ((20-19.04)^2 / 19.04) + ((16-13.20)^2 / 13.20) + ((10-16.24)^2 / 16.24) + ((18-18.96)^2 / 18.96) + ((4-4.80)^2 / 4.80) = 10.92[/tex]
The degrees of freedom for the test are 2, and the critical value is 5.99.
Since the calculated value of chi-squared (10.92) is greater than the critical value (5.99), we reject the null hypothesis.
Therefore, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.
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If lines, KI and LY, intersect at point A and m/KAY=4x+39, m/LAI=12x-9, what is m/YAI?
Answers
Answer:
0 degrees
Step-by-step explanation:
To find m/YAI, we need to first find the measure of angle KAI, which is the sum of angles KAY and LAI. Then, we can find the measure of angle YAI by subtracting the measure of angle KAI from 180 degrees.
Using the angle addition postulate, we know that:
m/KAY + m/LAI = m/KAI
Substituting the given values, we get:
4x + 39 + 12x - 9 = m/KAI
Simplifying the expression, we get:
16x + 30 = m/KAI
Now, we need to solve for x. To do this, we can use the fact that angles KAY and LAI are supplementary (add up to 180 degrees) since they form a straight line. Thus:
m/KAY + m/LAI = 180
Substituting the given values, we get:
4x + 39 + 12x - 9 = 180
Simplifying the expression, we get:
16x + 30 = 180
Subtracting 30 from both sides, we get:
16x = 150
Dividing both sides by 16, we get:
x = 9.375
Now that we know x, we can substitute it back into the equation we found earlier:
16x + 30 = m/KAI
16(9.375) + 30 = m/KAI
150 + 30 = m/KAI
m/KAI = 180
So, we know that angle KAI measures 180 degrees. To find m/YAI, we need to subtract the measure of angle KAI from 180 degrees:
m/YAI = 180 - m/KAI
m/YAI = 180 - 180
m/YAI = 0
Therefore, we can conclude that the measure of angle YAI is 0 degrees. This means that YAI is not an angle, but a line segment, and it does not have a measure in degrees.
Henderson's Hardware has an ROA of 12%, a 8% profit margin, and an ROE of 19%. What is its total assets turnover? Do not round intermediate calculations. Round your answer to two decimal places. What is its equity multiplier? Do not round intermediate calculations. Round your answer to two decimal places.
Answers
Answer: We can use the DuPont Model to calculate the total assets turnover and equity multiplier:
ROE = ROA × Equity Multiplier
Equity Multiplier = Total Assets / Total Equity
Profit Margin = Net Income / Sales
Total Assets Turnover = Sales / Total Assets
Given:
ROA = 12%
Profit Margin = 8%
ROE = 19%
To find the Total Assets Turnover:
Profit Margin = Net Income / Sales
0.08 = Net Income / Sales
Net Income = 0.08 x Sales
ROA = 12%
ROA = Net Income / Total Assets
0.12 = 0.08 x Sales / Total Assets
Total Assets Turnover = Sales / Total Assets = 0.08 / 0.12 = 0.67
Therefore, the total assets turnover is 0.67.
To find the Equity Multiplier:
ROE = ROA x Equity Multiplier
0.19 = 0.12 x Equity Multiplier
Equity Multiplier = 0.19 / 0.12 = 1.58
Therefore, the equity multiplier is 1.58.
Note: The total assets turnover and equity multiplier are related to each other through the DuPont model. The product of these two ratios should be equal to the ROE. In this case, 0.67 x 1.58 = 1.06, which is approximately equal to 1.9 (ROE in decimal form). This confirms that our calculations are correct.
Step-by-step explanation:
Which graph represents the function f(x) = −|x − 2| − 1?
A.
B.
C.
D.
Answers
In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
Answers
Answer:
This should be a permutation
Step-by-step explanation:
P (n, r) = n!/(n-r)!
P (12,5) = 12!/(12-5)!
P (12,5) = 12!/7!
P(12,5) = 95040
|a+5|=-5-a For what values of a are the following expressions true?
Answers
The expression is true for all values of a between 0 and -5 (inclusive)
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
The expression is given as:
|a+5|= -5–a
The absolute value expression is always positive.
So, we have:
a +5 = -5 -a or -5 - a = -5 - a
For the expression a +5 = -5 -a we have:
a + a = -5 - 5
Evaluate like terms
2a =- 10
Divide both sides by 2
a = -5
For the expression -5 - a = -5 - a, we have:
0 = 0
So, we have:
0 = 0 or a = -5
This means that, the expression is true for all values of a between 0 and -5 (inclusive)
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Question 7
Suppose the graph represents the scale drawing for a fence that Tara is building for a new city dog park. Each unit on the graph represents 12 yards. After studying the scale drawing, Tara decides to build a fence that encloses a smaller area. If Tara dilates rectangle ABCD by a scale factor of 0.75, and fencing costs $6.39 per yard, how much will she spend on fencing?
Answers
The total cost to fence the rectangular yard is given as follows:
$1,610.28.
How to obtain the perimeter of a triangle?The perimeter of a rectangle is the total distance around its outer boundary. To find the perimeter of a rectangle, you need to add up the lengths of all four sides.
If a rectangle has length l and width w, then its perimeter P is given by the equation presented as follows:
P = 2l + 2w
Considering the scale factor of 0.75, the distance represented by each unit on the graph is given as follows:
0.75 x 12 = 9 yards.
Hence the dimensions of the rectangle are given as follows:
Length of 8 x 9 = 72 yards.Width of 6 x 9 = 54 yards.The perimeter of the fence is then given as follows:
2 x (72 + 54) = 252 yards.
It costs $6.39 per yard, hence the total cost to fence the yard is given as follows:
252 x 6.39 = $1,610.28.
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ASAP !
[tex]2 \frac{3}{6} - \frac{1}{3} [/tex]
Answers
The mathematical expression to be evaluated is:
[tex]2 \frac{3}{6} - \frac{1}{3}[/tex]
To simplify the expression, we first convert the mixed fraction to an improper fraction:
[tex]2 \frac{3}{6} = \frac{(2 \times 6) + 3}{6} = \frac{15}{6}[/tex]
Substituting this value back into the original expression, we get:
[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{15}{6} - \frac{1}{3}[/tex]
Now we need to find a common denominator for the two fractions:
[tex]\frac{15}{6} - \frac{1}{3} = \frac{15}{6} \times \frac{2}{2} - \frac{1}{3} \times \frac{2}{2} = \frac{30}{12} - \frac{2}{6}[/tex]
We can simplify the second fraction:
[tex]\frac{30}{12} - \frac{2}{6} = \frac{30}{12} - \frac{4}{12} = \frac{26}{12}[/tex]
Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
[tex]\frac{26}{12} = \frac{13}{6}[/tex]
Therefore, the simplified value of the mathematical expression is:
[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{13}{6}[/tex]
Answer:
[tex]2\frac{1}{6}[/tex]
Step-by-step explanation:
First, write the fractions as improper fractions.
[tex]\sf2\frac{3}{6} -\frac{1}{3} \\\\\sf\frac{15}{6} -\frac{1}{3}[/tex]
To, subtract the fractions make the denominators the same.
For that, multiply both sides of 1/3 by 2.
[tex]\sf\frac{15}{6} -\frac{1*2}{3*2} \\\\\sf\frac{15}{6} -\frac{2}{6}[/tex]
Subtract.
[tex]\frac{13}{6}[/tex]
Write it as a mixed number.
[tex]2\frac{1}{6}[/tex]
Determine o resultado das perguntas a baixo por favor, pra agora
Answers
1. {0, 1, 3, 4, 6}; 2. {4, 6}.
Step-by-step explanation:
1. А={0, 1, 2, 3}, B={2, 4, 5, 6}, C={2, 5, 7, 9}; (A∪B)-(B∩C)-?
a) A∪B⇔{0, 1, 2, 3, 4, 5, 6};
b) B∩C⇔{2, 5};
c) (A∪B)-(B∩C)⇒{0, 1, 3, 4, 6}.
2. A={4, 6, 8, 10}, B={4, 6, 8}, C={1, 2, 3, 4, 7}, D={3, 5, 6, 7}; A∩(D∪(B∩C))=?
a) B∩C⇔{4};
b) D∪(B∩C)⇔{3, 4, 5, 6, 7};
c) A∩(D∪(B∩C))⇒{4, 6}.
Solve for x. Round to the nearest tenth.
x =
(30 points)
Answers
The value of x round to the nearest 10th is 28.
One of the most significant areas of mathematics is trigonometry, which has numerous applications. The study of the relationship between the sides and angles of the right-angle triangle is the main objective of the branch of mathematics known as "trigonometry." Trigonometric identities, functions, and formulas can be used to determine the angles or sides of a right triangle that are unknown or missing. Angles can be expressed in trigonometry as either degrees or radians. The five most frequently used trigonometric angles in calculations are 0°, 30°, 45°, 60°, and 90°.
In the given right-angled triangle the angle is 41 degrees and the altitude is 32 units.
So, the trigonometry ratio is -
[tex]tan \theta=\frac{32}{x}\\\\x= 32 tan41\\\\x=28[/tex]
the value of x=28
The complete question is'
Find the value of x in a given triangle, and round to the nearest tenth,
image of the triangle is attached,
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I need this work sheet done in 10 minutes or less!!
Answers
Answer:
3. 216 cm^3
4a. A = 5 ft, B = 4 ft.
4b. 88 ft^3
Step-by-step explanation:
3. Separate into two rectangular prisms:
Volume of first one: 4cm*2cm*3cm = 24cm^3
Volume of second one: 4cm*12cm*4cm = 192cm^3
Add them together: 24 + 192 = 216cm^3
4a.
Length A = 8-3 = 5ft.
Width B = 8-4 = 4ft.
4b. Separate into two rectangular prisms:
Volume of first one: 2ft*3ft*4ft = 24ft^3
Volume of second one: 8ft*4ft*2ft = 64ft^3
Add them together: 24 + 64 = 88ft^3
CAN SOMEONE HELP WITH THIS QUESTION?
Answers
The volume of the pyramid is V = (1/3) (3²) (5) = 45 cm³ thus the rate at which the water level is rising when the water level is 3 cm is 45 cm³/sec.
What is volume?Volume is a measure of the amount of space that an object occupies or contains. It is measured in terms of cubic units, such as cubic metres or cubic centimetres. Volume is a three dimensional measure, which means it takes into account the length, width and height of an object.
The rate at which the water level is rising when the water level is 3 cm can be calculated using the formula for the volume of a pyramid. The formula for the volume of a pyramid is V = (1/3) bh², where b is the area of the base and h is the height. In this case, the base is a square with sides of length 3 cm and the height is 5 cm. Therefore, the volume of the pyramid is V = (1/3) (3²) (5) = 45 cm³.
Since the water is being filled at a constant rate of 45 cm³/sec, then the rate at which the water level is rising when the water level is 3 cm is 45 cm³/sec. This is because the water level is rising at the same rate at which the water is being filled, and since the water is being filled at a rate of 45 cm³/sec, the water level is also rising at the same rate. This is why the rate at which the water level is rising when the water level is 3 cm is 45 cm³/sec.
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A company's sales in Seattle were $410,000 in 2012, while their sales in Portland were $255,000 for the same year. Complete the following statements:
a. Seattle's sales were ___% larger than Portland's.
b. Portland sales were ___ % smaller than Seattle's.
c. Portland sales were ___ % of Seattle's.
Give answers accurate to at least one decimal place.
Answers
In 2012, a company made $410,000 in sales in Seattle but only making $255,000 in sales in Portland. Fulfill each of the following claims:
a. Seattle outsold Portland in sales by 60.78%.
b. Portland's sales lagged Seattle's by 60.78%.
c. Sales in Portland were 62.2% of those in Seattle.
a. Seattle's sales were ___% larger than Portland's.
To calculate the percentage difference between the two sales figures, we can use the following formula:
Percentage difference = ((larger value - smaller value) / smaller value) x 100%
Substituting the values, we get:
Percentage difference = ((410,000 - 255,000) / 255,000) x 100%
Percentage difference = 155,000 / 255,000 x 100%
Percentage difference = 0.6078 x 100%
Percentage difference = 60.78%
Therefore, Seattle's sales were 60.78% larger than Portland's.
b. The sales in Portland were ___% less than those in Seattle.
Since Portland's sales were smaller than Seattle's, we can simply use the percentage difference we calculated above to find the percentage by which Portland's sales were smaller:
Portland sales were 60.78% smaller than Seattle's.
c. Portland sales were ___ % of Seattle's.
To calculate the percentage of Seattle's sales that Portland's sales represent, we can use the following formula:
Percentage = (smaller value / larger value) x 100%
Percentage = 0.62195 x 100%
Substituting the values, we get:
Percentage = (255,000 / 410,000) x 100%
Percentage = 62.2%
Therefore, Portland's sales were 62.2% of Seattle's.
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COMM 291C Applications of Statistics in Business
Winter 2023
Assignment 07
1. A fish tank is filled with the fish of three different species, and each fish comes in three sizes. The
counts of all the fish are summarized in the following contingency table:
Small Medium Large Total
Goldfish 48 45 19 112
Guppy 70 42 19 131
Gourami 40 9 10 59
Total 158 96 48 302
a. If I randomly catch any one fish from this tank, what is the probability that the caught
fish is medium-sized? Show your calculations. (1)
b. If I randomly catch one fish from this tank, what is the probability that the caught fish is a
medium-sized guppy? Show your calculations. (1)
c. If I randomly catch one medium-sized fish from this tank, what is the probability that the
caught fish is a guppy? Show your calculations. (1)
d. If I randomly catch one guppy from this tank, what is the probability that the caught fish
is medium-sized? Show your calculations. (1)
e. If I randomly catch one fish from this tank, what is the probability that the caught fish is a
not a goldfish? Show your calculations. (1)
f. Are two events, randomly catching a guppy and randomly catching a medium-sized fish,
independent? Explain how you know. (2)
Answers
a) If I randomly catch any one fish from this tank, the probability of catching a medium-sized fish from the tank is 0.3182.
b) the probability of catching a medium-sized guppy from the tank is 0.1391.
c) the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.
d) the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.
e) the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.
f) 0.1384 is not equal to 0.1391, which indicates that the two events are not independent
Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.
The explanation to the above probability answer are given below:
a)
From the contingency table, we can see that the total number of medium-sized fish is 96. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized fish is:
Probability of catching a medium-sized fish = Total number of medium-sized fish / Total number of fish
Probability of catching a medium-sized fish = 96 / 302
Probability of catching a medium-sized fish = 0.3182
Therefore, the probability of catching a medium-sized fish from the tank is 0.3182
b)
From the contingency table, we can see that the total number of medium-sized guppies is 42. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized guppy is:
Probability of catching a medium-sized guppy = Total number of medium-sized guppies / Total number of fish
Probability of catching a medium-sized guppy = 42 / 302
Probability of catching a medium-sized guppy = 0.1391
Therefore, the probability of catching a medium-sized guppy from the tank is 0.1391.
c)
From the contingency table, we can see that the number of medium-sized guppies is 42, and the number of medium-sized fish is 96. Therefore, the probability of catching a guppy if we randomly select a medium-sized fish is:
Probability of catching a guppy given a medium-sized fish = Number of medium-sized guppies / Total number of medium-sized fish
Probability of catching a guppy given a medium-sized fish = 42 / 96
Probability of catching a guppy given a medium-sized fish = 0.4375
Therefore, the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.
d)
To calculate the probability of catching a medium-sized guppy if we randomly select a guppy from the tank, we need to find the number of medium-sized guppies in the tank and divide it by the total number of guppies in the tank.
From the contingency table, we can see that the number of medium-sized guppies is 42, and the total number of guppies is 131. Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is:
Probability of catching a medium-sized guppy given a guppy = Number of medium-sized guppies / Total number of guppies
Probability of catching a medium-sized guppy given a guppy = 42 / 131
Probability of catching a medium-sized guppy given a guppy = 0.3206
Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.
e)
From the contingency table, we can see that the total number of non-goldfish is 190 (45 medium goldfish + 70 small guppy + 42 medium guppy + 9 medium gourami + 10 large gourami + 14 small gourami). The total number of fish in the tank is 302. Therefore, the probability of catching a fish that is not a goldfish is:
Probability of catching a fish that is not a goldfish = Total number of non-goldfish / Total number of fish
Probability of catching a fish that is not a goldfish = 190 / 302
Probability of catching a fish that is not a goldfish = 0.6291
Therefore, the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.
f)
From the contingency table, we can see that the probability of randomly catching a guppy is 131/302, which is approximately 0.4344. Similarly, the probability of randomly catching a medium-sized fish is 96/302, which is approximately 0.3182.
Now, let's consider the joint probability of randomly catching a medium-sized guppy, which we calculated earlier to be 42/302, or approximately 0.1391. To determine if the events are independent, we need to compare the product of the probabilities of the individual events (catching a guppy and catching a medium-sized fish) to the joint probability of the events occurring together.
If the events are independent, then the product of their individual probabilities should be equal to the joint probability:
P(catching a guppy) x P(catching a medium-sized fish)
= P(catching a medium-sized guppy)
0.4344 x 0.3182 = 0.1391
0.1384 is not equal to 0.1391, which indicates that the two events are not independent.
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The equation P=7h gives the amount of pay (P) you earn for working h hours. Identify the independent and dependent variables. How my do you earn after 8 hours of work?
Answers
Earn 56 units of currency after 8 hours of work.
What is independent variable?
The independent variable is the variable that you change and control in your experiment.
The independent variable is the number of hours worked, h. The dependent variable is the amount of pay earned, P.
To find how much you earn after 8 hours of work, we can simply substitute h = 8 into the equation and evaluate:
P = 7h
P = 7(8)
P = 56
So you would earn 56 units of currency after 8 hours of work.
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The demand equation for a popular brand of fruit drink is given by the equation:
Qx=10-5px+0.001M + 10Py
where:
Qx= monthly consumption per family in liters
Px= price perlite of the fruit drink =$2.00
M= median annual family income =$20,000
Py= price per liter of a competing brand of fruit drink = $2.50.
1. Interpret parameter estimates.
2. Calculate the monthly consumptioliterslitres) of the fruit.
3. Suppose that the median annual family income increased to ¢30,000. How does this change your answer to part (b)?
4. Determine the demand function and the inverse demand function.
Answers
Answer:
Parameter estimates
The coefficient for Px (-5) suggests that there is an inverse relationship between the price of the fruit drink and the quantity demanded. In other words, as the price of the drink increases, the quantity demanded decreases.
The coefficient for M (0.001) suggests that there is a positive relationship between the median annual family income and the quantity demanded. In other words, as the median income increases, the quantity demanded also increases.
The coefficient for Py (10) suggests that there is a positive relationship between the price of the competing brand of fruit drink and the quantity demanded for this brand. In other words, as the price of the competing brand increases, the quantity demanded for this brand also increases.
Step-by-step explanation:
To calculate the monthly consumption of the fruit drink, we plug in the given values into the demand equation,
Qx = 10 - 5(2) + 0.001(20,000) + 10(2.5)
Qx = 10 - 10 + 20 + 25
Qx = 45 liters per family per month.
Therefore, the monthly consumption of the fruit drink per family is 45 liters.
If the median annual family income increased to $30,000, then the new monthly consumption of the fruit drink per family can be calculated as follows,
Qx = 10 - 5(2) + 0.001(30,000) + 10(2.5)
Qx = 10 - 10 + 30 + 25
Qx = 55 liters per family per month.
Therefore, the monthly consumption of the fruit drink per family would increase from 45 liters to 55 liters per family per month.
To determine the demand function, we need to solve for Qx in terms of the other variables,
Qx = 10 - 5Px + 0.001M + 10Py
Qx - 10Py = 10 - 5Px + 0.001M
Qx = (10 - 5Px + 0.001M) / 10Py
Therefore, the demand function is:
Qx = (10 - 5Px + 0.001M) / 10Py
To find the inverse demand function, we need to solve for Px in terms of Qx.
Qx = 10 - 5Px + 0.001M + 10Py
5Px = 10 - Qx - 0.001M - 10Py
Px = (10 - Qx - 0.001M - 10Py) / 5
Therefore, the inverse demand function is,
Px = (10 - Qx - 0.001M - 10Py) / 5
HELP ME PLEASE
THIS IS AN Emergency
Answers
The correct graph of the inequality -0.4x - 2 < - 1.2 is option 2.
What is an inequality?Equation containing a relational operator and a linear expression is known as a linear inequality. In a coordinate plane or space, regions that satisfy a linear inequality are defined. A linear inequality defines a half-plane in two dimensions, which, depending on the inequality, can be either above or below a line. A linear inequality defines a half-space in three dimensions, which, depending on the inequality, is either above or below a plane. The goal of optimization problems is to determine the maximum or minimum value of a linear function under a set of constraints, which are typically represented by linear inequalities.
The given inequality is -0.4x - 2 < - 1.2.
-0.4x - 2 < - 1.2
Adding 2 on both sides of the equation we have:
-0.4x < -1.2 + 2
-0.4x < 0.8
-x < 2
x > -2
Hence, the correct graph of the inequality is option 2.
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Can somebody help me please asap
Answers
Answer:
y = x + 1
Step-by-step explanation:
i dont rlly have an explanation, i mean its just that
Emilio wants to create a vegetable garden with the shape shown
below. On the diagram below, write the numbers in the boxes to
show the missing dimensions.
7 ft
3 ft
5 ft
ft
8 ft
Draw a line on the diagram to divide it into two rectangles. Find
the total area of the garden. Write your answer below.
square feet
feet
Find the perimeter of the garden. Write your answer below.
Answers
The total area of the garden is 56 square feet and the perimeter of the garden is 30 feet
Finding the total area of the gardenGiven the diagram of a rectangle
The opposite sides of a rectangle are equal
So, the values that complete the missing dimensions are
3 ft and 5 ft
Also, we have the area to be
Area = Sum of area of each garden
This gives
Area = 7 * 3 + 7 * 5
Area = 56
The perimeter is the sum of the lengths
So, we have
Perimeter = 7 + 5 + 3 + 7 + 3 + 5
Evaluate
Perimeter = 30
Hence, the perimeter is 30 feet
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A young sumo wrestler decided to go on a special diet to gain weight rapidly. He gained weight at a constant rate.
The table compares the wrestler's weight (in kilograms) and the time since he started his diet (in months).
Time (months) Weight (kilograms)
1.5
1.51, point, 5
85.8
85.885, point, 8
3.0
3.03, point, 0
93.6
93.693, point, 6
4.5
4.54, point, 5
101.4
101.4101, point, 4
What was the wrestler's weight before he went on his diet?
Answers
The wrestler's weight before he went on his diet was 78.0 kilograms.
What is y-intercept?
In the context of a graph of a function, the y-intercept is the point where the graph intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is zero. Geometrically, the y-intercept is the value of the function at the point where it crosses the y-axis.
To determine the wrestler's weight before he went on his diet, we need to find the y-intercept of the linear function that represents his weight gain over time. This is because the y-intercept corresponds to the initial weight of the wrestler, i.e., his weight before he started his diet.
We can use the two data points where the time is 0 (i.e., at the start of the diet) to find the slope of the linear function:
(1.5, 85.8) and (3.0, 93.6)
The change in weight over the time interval of 1.5 to 3.0 months is:
93.6 - 85.8 = 7.8
The change in time over that interval is:
3.0 - 1.5 = 1.5
So the slope of the linear function is:
7.8 / 1.5 = 5.2
Now we can use the point-slope form of a linear function to write an equation for the wrestler's weight gain over time:
y - 85.8 = 5.2(x - 1.5)
where y represents the wrestler's weight and x represents the time in months.
To find the wrestler's weight before he went on his diet, we need to evaluate this equation at x = 0:
y - 85.8 = 5.2(0 - 1.5)
y - 85.8 = -7.8
y = 78.0
Therefore, the wrestler's weight before he went on his diet was 78.0 kilograms.
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If the tax is $3.36 on a $48 jacket, what is the tax rate?
Answers
Answer:
The answer would be $49.01
Step-by-step explanation:
ABCD is a square. P and D are points on the y-axis. A is a point on the x-axis. PAB is a straight line. The equation of the line that passes through the points A and D is y=-2x+6. Find the length of PD.
Answers
The length of the segment PD obtained using the relationship between similar right triangles is; PD = 7.5 units
What is a right triangle?A right triangle is a triangle that has an interior angle of 90° (a right angle) and the side opposite the right angle (90°) interior angle is known as the hypotenuse side, while the other two sides of the triangle are the legs of the right triangle.
The possible drawing in the question, obtained from a similar online question, created with MS Word is attached.
The equation of the line that passes through the points A and D, y = -2·x + 6, indicates;
The coordinates of the y-intercept of the line of the equation, is; (0, 6)
The y-intercept indicates that OD = 6 units
The x-intercept coordinates of the graph of the equation, can therefore be obtained as follows; 0 = -2·x + 6
2·x = 6
x = 6/2 = 3
x = 3
The x-intercept is; (0, 3)
The x-intercept indicates that OA = 3 units
The length of the side of the square, s, is therefore;
s = √(s²) = √(6² + 3²) = 3·√5
OA = The length of the x-intercept of ; y = -2·x + 6
The ∠DAO ≅ ∠OPA, and m∠DOA = m∠POA = 90°
Therefore;
∠DOA ≅ ∠POA
ΔOPA is similar to ΔOAD, by Angle-Angle similarity postulate
The ratio of corresponding sides of similar triangles indicates;
OP/OA = OA/OD
Therefore;
OP/OA = OA/OD
OP/3 = 3/6
OP = 3 × 3/6 = 1.5
PD = OP + OD (Segment addition postulate)
PD = 1.5 + 6 = 7.5
The length of segment PD is 7.5 unitsPlease find attached the possible drawing in the question, created with MS Word, obtained from a similar question posted online.
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5. Find the volume of the cylinder. Leave your
answer in terms of t.
8 cm.
8 cm.
Answers
The volume of the cylinder in terms of π is 128π centimetres³.
How to find the volume of a cylinder?The cylinder below has a height of 8 centimetres and a diameter of 8 centimetres. Therefore, the volume of the cylinder can be found as follows:
volume of the cylinder = πr²h
where
r = radiush = height of the cylinderTherefore,
r = 8 / 2 = 4 centimetres
h = 8 centimetres
volume of the cylinder = π × 4² × 8
volume of the cylinder = 128π centimetres³
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A rectangle with side lengths of 3 cm and 1 cm 5 mm was made from two equal squares. Draw a rectangle and divide it into two equal squares! Calculate the perimeter of the rectangle and each square!
Answers
Therefore, each square has a side length of 1.5 cm. The perimeter of each square is 6 cm.
What is perimeter?Perimeter is the distance around the outside of a two-dimensional shape, such as a polygon or a circle. It is the sum of the lengths of all the sides of the shape.
Here,
To calculate the perimeter of the rectangle, we need to first convert the side lengths to the same units. 1 cm 5 mm is equal to 1.5 cm, so the rectangle has dimensions 3 cm by 1.5 cm.
The perimeter of the rectangle is then:
P = 2(3 cm) + 2(1.5 cm)
= 9 cm
To divide the rectangle into two equal squares, we need to find the side length of each square.
The area of the rectangle is:
A = (3 cm)(1.5 cm)
= 4.5 cm²
Since the two squares are equal, each square has area:
A/2 = 2.25 cm²
The side length of each square can be found by taking the square root of the area:
s = √(2.25 cm²)
= 1.5 cm
The perimeter of each square is:
P = 4s
= 6 cm
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Help with math problems
Answers
The inequality can be solved to get 2 > x, and the graph on the number line can be seen in the image at the end.
How to solve the inequality?Here we have an inequality and we want to sole it, to do so, we just need to isolate the variable in the inequality.
Here we have:
10 > 5x
To isolate the variable we can divide both sides of the inequality by 5, then we will get:
10/5 > 5x/5
2 > x
So x is the set of all values smaller than 2.
That is the inequality solved, to graph this, drawn an open circle at x = 2 and a line that goes to the left. The graph is the one you can see in the image below.
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