Parts of similar triangles
Find x
In the triangle, x has a value of 18.
Which triangle is on the right?A right triangle is one with a 90 degree inner angle. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The two arms of a right angle are made up of height and base.
We know that the respective sides of the two triangles in the diagram are proportional since they resemble one another. Namely, we have
AB / AE = BC / CD
Inputting the values provided yields:
x / 12 = 9 / 6
Finding x and simplifying results in:
x = 12 * (9/6) = 18
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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.
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:
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?
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
Find the interquartile range.
Answer:
3.7
Step-by-step explanation:
1.5, 2.2, 2.8, 3.4, 5, 5.6, 6.8, 7
Q1 = 2.2+2.8 = 5.0 divided 2 = 2.5
Q3 = 5.6+6.8 = 12.40 divided 2 = 6.2
IQR = 6.2 - 2.5 = 3.7
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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.
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
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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If the tax is $3.36 on a $48 jacket, what is the tax rate?
Answer:
The answer would be $49.01
Step-by-step explanation:
I thought of a number. Seven times the number decreased by 13 equals 5 times the number increased by 5. What was my number?
answer:
The number is 9
Step-by-step explanation:
9 × 7 = 63
63 - 13 = 50
9×5 = 45
45 + 5 = 50
What is the value of angle b?
If f(x)=3x-5, g(x)=7x-3, find (f+g)(x) and (f-g)(x
Answer:
Step-by-step explanation: To find (f+g)(x), we simply add the two functions:
(f+g)(x) = f(x) + g(x)
= (3x - 5) + (7x - 3)
= 10x - 8
Therefore, (f+g)(x) = 10x - 8.
To find (f-g)(x), we subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x)
= (3x - 5) - (7x - 3)
= -4x - 8
Therefore, (f-g)(x) = -4x - 8.
Determine o resultado das perguntas a baixo por favor, pra agora
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}.
A quadratic function passes through the points (-2,5) and (-8,5) and has a graph in the xy-plane that opens downward. Which of these could be the coordinates of the highest point of the graph?
O (5, 1)
O (5, 8)
O (5, 1)
O (5, 8)
The highest point of the quadratic equation that opens down can be (-5, 8)
Which of these could be the coordinates of the highest point of the graph?We have a quadratic equation whose graph opens downwards, and we know that it also passes through the points (-2,5) and (-8, 5).
The highest point will be of the form (x, y).
Such that y is larger than 5, and the value of x is right between the two values above:
x = (-2 - 8)/2
x = -5
So the point is of the form (-5, y) where again y > 5.
From the given options the only of this form is (-5, 8)
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T
A
D
√
5
B
C
Ĉ
X
Figure ABCD is a square. The side lengths are all 1.
Estimate the length of the diagonal.
Submit
Therefore, the estimated length of the diagonal is approximately 1.414 units.
What is square root?The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, the square root of a number "x" is a value "y" such that y multiplied by y equals x. The symbol for square root is √.
For example, the square root of 25 is 5, because 5 multiplied by 5 equals 25. Similarly, the square root of 64 is 8, because 8 multiplied by 8 equals 64. The square root of a negative number is not a real number, as there is no real number that, when squared, equals a negative number.
Using the Pythagorean theorem, we can find the length of the diagonal of the square.
If we draw a diagonal from one corner of the square to the opposite corner, we create a right triangle. The two legs of the right triangle are the sides of the square, which have a length of 1. The hypotenuse, which is the diagonal of the square, is the side we are trying to find.
Using the Pythagorean theorem, we can write:
[tex]d^2 = 1^2 + 1^2[/tex]
where d is the length of the diagonal.
Simplifying, we get:
[tex]d^2 = 2[/tex]
Taking the square root of both sides, we get:
d ≈ 1.414
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bob had 2 apples and he ate 1 how many does he have now?
Answer: He has one left
Step-by-step explanation: 2-1=1
I need this done in 10 mins or less!!!
Answer:
To find the volume of Leah's new planter, we need to multiply the length, width, and height of the container:
V = 15 m x 4 m x 8 m x 11 m x 3 m
V = 11,880 cubic meters
Therefore, the total volume of Leah's new planter is 11,880 cubic meters.
Let's represent the volume of the large box as x cubic inches. Since the total volume of both boxes is 212 cubic inches, we can set up the following equation:
8 x 4 x 2 + x = 212
Simplifying the left side, we get:
64 + x = 212
Subtracting 64 from both sides, we get:
x = 148
Therefore, the volume of the large box is 148 cubic inches.
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)
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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Look at the picture, I'm really confused
Answer:
Option (C)
-0.46 brother
Answer:
Option (C)
-0.46
Step-by-step explanation:
I need this work sheet done in 10 minutes or less!!
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
needed help on this one too
Answer:
1st -pentagon -regular
2nd -hexagon -irregular
3rd -octagon -irregular
i’m begging someone help please i’ll give brainlist
Answer:
a-no for the first triangle, because the total of the inner angles must be 180, the last angle must be 90.
b-yes- a triangle with angles 90, 50, and 40 is possible
c-yes. 65+45+70=180.
Step-by-step explanation:
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.
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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CAN SOMEONE HELP WITH THIS QUESTION?
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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The measure of angle t is 60 degrees. What is the x-coordinate of the point where the terminal side intersects the unit circle?
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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QUICK PLS 30 POINTS
For a quadratic function, f, f(0) = 15.
Which equation could represent f?
A: f(x)=x²-8x+15
B: f(x)=(x-3)(x+5)
C: f(x)=x²+3x+5
D: f(x)=(x-15)²
Answer:
The answer is A
Step-by-step explanation:
You can use a graphing calculator (geogebra) It works
HELP ME PLSSSS!
1. Start in Hawaii on the black dot. Reflect this point over the y-axis. What ocean are you in?
Arctic Ocean
Atlantic Ocean
Indian Ocean
Pacific Ocean
2. Start in Hawaii on the black dot. Reflect this point over the x-axis. What state are you in?
3. Start in Georgia on the black dot. Reflect this point over the x-axis. The cube you are in contains all of the following EXCEPT for which state?
Alabama
Georgia
North Carolina
South Carolina
Tennessee
4. Start in Georgia on the black dot. Reflect this point over the y-axis. What state are you in?
5. Start in Ohio in the square that contains the black dot. What translation would get you to the cube that contains the black dot in Montana?
(x,y) ----> (x+4,y-10)
(x,y) ----> (x-8,y+3)
(x,y) ----> (x+4,y+3)
(x,y) ----> (x-10,y+4)
6. Start in Louisiana on the black dot. Rotate 90 degrees counter-clockwise. What state occupies most of the space of the cube you are now in?
7. Start in New York on the black dot. Translate (x,y) ---> (x-4,y-3). Then, reflect over the x-axis. What state are you in?
8. Start in South Dakota on the black dot. Rotate 270 degrees clockwise. You are at the intersection of which two states?
Arizona and New Mexico
New Mexico and Texas
Minnesota and Wisconsin
Illinois and Wisconsin
9. Start in Kansas on the black dot. Reflect over the y-axis and then translate your cube 6 right and 2 up. What state are you in?
10. Start in New Hampshire on the black dot. Which system of transformations describes a way you could get to any cube in the state of Texas?
Rotate 180 degrees and then translate right 7 and up 3.
Reflect over x-axis and then translate left 2 and up 1.
Reflect over y-axis and then reflect over x-axis.
Rotate 90 clockwise and then reflect over y=x.
11. Start in Idaho on the black dot. Perform the following transformations in order.
(x,y) ----> (x+6,y-3)
(x,y) ----> (-x,y)
What state are you most likely in?
12. Start in Colorado on the black dot. Dilate by a scale factor of 2. What two states could you be in?
New Jersey or Pennsylvania
Indiana or Ohio
Kansas or Oklahoma
Idaho or Oregon
13. Start in North Carolina on the black dot. Reflect over the y-axis. Translate 5 up and 4 right. Reflect over the y-axis. Translate 3 down. Rotate 180 degrees clockwise. What state are you in?
*
It's tough to know for sure what a black dot on the sea might mean without more information. A ship, boat, or other watercraft may occasionally be indicated by a black dot on the water.
What black dot indicate about sea?Depending on the situation, a black dot on the sea could mean a variety of various things. Here are some potential examples:
A black dot on a nautical chart could represent a buoy, beacon, marker, or other navigating aid.
A black dot in the ocean may be the result of a bird, a fish jumping out of the water, or other marine life, depending on your distance.
A black dot may represent the existence of a microscopic organism or particle if you are using a microscope or other scientific equipment to see the ocean.
Therefore, 1. Pacific Ocean 2. South Carolina 3. Georgia 4. Alabama 5. (x,y) ----> (x+4,y-10) 6. Colorado 7. Pennsylvania 8. Minnesota and Wisconsin, 8. Missouri 9. Reflect over y-axis and then reflect over x-axis.
10. Oregon 11. Kansas or Oklahoma, 12. Tennessee
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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!
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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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?
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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Select all the equations where x = 5 is a solution.
x-5=0
11-x=3
1+x=5
10=2x
(1/2)x=10
x^2=25
Answer:
x-5=0
10=2x
(1/2)x=10
x>2=25
Step-by-step explanation:
all of these are x=5
the ones that are wrong are 11-x=3 and 1+x=5
Determine the perimeter of the composite figure.
The perimeter of the figure is approximately 63.6 meters, since the lengths of all the sides add up to the figure's perimeter.
What is perimeter?Perimeter is the total length of the boundary of a closed 2-dimensional shape. In other words, it is the distance around the edge of a shape. The perimeter is usually measured in units such as meters, centimeters, feet, or inches depending on the measurement system used. The perimeter can be calculated by adding up the lengths of all the sides of the shape.
Since opposite sides of a parallelogram are equal in length, the length of the straight side of the first parallelogram is:
Length of first parallelogram = 9m
Similarly, the length of the straight side of the second parallelogram is:
Length of second parallelogram = 11m
Now, let's find the length of the straight side of the semicircle segment. We are given that the other side of each parallelogram gets half of the diameter, which is 17m. Therefore, the length of the straight side of the semicircle segment is:
Length of semicircle segment = 17m / 2 = 8.5m
The lengths of all the sides add up to the figure's perimeter. Let's use P to represent the perimeter. Then:
P = 2 (parallelogram length) + semicircle length
When we replace the values we discovered earlier, we obtain:
P = 2(9m + 11m) + π(17m)/2
= 38m + 8.5πm
≈ 63.6m (using π ≈ 3.14)
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Can somebody help me please asap
Answer:
y = x + 1
Step-by-step explanation:
i dont rlly have an explanation, i mean its just that