The secant of a °45 angle is defined as the ratio of the length of the hypotenuse to the length of the adjacent side. In this case, the adjacent side is also a leg of length 5, so:
secant(45) = hypotenuse/adjacent = 5√2/5 = √2
What is the secant function?The secant function, denoted as sec(x), is a trigonometric function that is defined as the reciprocal of the cosine function, cos(x).
In other words,
sec(x) = 1 / cos(x)
The secant function is defined for all values of x except for those where the cosine function is equal to zero, which corresponds to the values x = (2n+1)π/2 where n is an integer. At these points, the secant function is undefined.
According to the given functionIn a °45-°45-°90 triangle, the two legs are congruent, so if the length of the hypotenuse is 5√2, then each leg has a length of:
leg = hypotenuse/√2 = (5√2)/√2 = 5
The sine of a °45 angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the side opposite the angle is a leg of length 5, so:
sine(45) = opposite/hypotenuse = 5/5√2 = 1/√2 = √2/2
The secant of a °45 angle is defined as the ratio of the length of the hypotenuse to the length of the adjacent side. In this case, the adjacent side is also a leg of length 5, so:
secant(45) = hypotenuse/adjacent = 5√2/5 = √2
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For security purposes I regularly change my six-digit passcode for internet banking. I always
choose a code that is made up of three different two-digit square numbers (i. E. Square numbers
between 10 and 99), with the sixth digit the same as the first digit.
-Which two digits never appear in any of my passcodes?
-How many different passcodes can I use?
The sum of the six digits of my current passcode is also a square number.
-What is my current passcode?
The two digit Combinations that never appear in any of the passcodes are 5 and 6.
There are 49 different passcodes that can be used. The sum of the six digits of the current passcode is 81, which is a square number. Therefore, the current passcode is made up of three different two-digit square numbers with the sum of their digits equal to 9.
The possible combinations are
(16, 25, 40),
(16, 49, 16),
(25, 36, 20),
(36, 49, 4),
(49, 64, 9),
(64, 81, 16), and
(81, 16, 64).
The only combination that has the same first and sixth digits is (16, 25, 40), so the current passcode is 162540.
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Use the diagram to complete the statement.
BC =
The measurement of BC in the given figure is 4√2.
Given is figure we need to find the measurement of BC,
∠GBC = ∠CDF = 45° [alternate angles]
So, in triangle DCF,
Cos 45° = DF/DC
1/√2 = DF/12√2
DF = 12
Now we see that the triangles DCF and BCG are similar triangles by AA rule,
So, according to the definition of similar triangles,
DC/BC = DF/BG
12√2/BC = 12/(7-3)
12√2/BC = 12/4
12√2/BC = 3
3BC = 12√2
BC = 4√2
Alternatively, you can find the value of BC, using the trigonometric ratios in triangle GBC,
Cos 45° = GB/BC
GB = 7-3 = 4
Therefore,
Cos 45° = 4/BC
1/√2 = 4/BC
BC = 4√2
Hence the measurement of BC in the given figure is 4√2.
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Please help with this math problem!
The equation of the ellipse is x^2/9 + y^2/6.75 = 1
Finding the equation of the ellipseTo find the equation of an ellipse, we need to know the center, the major and minor axis, and the foci.
Since we are given the eccentricity and foci, we can use the following formula:
c = (1/2)a
Since the foci are (0, +/-3), the center is at (0, 0). We know that c = 3/2, so we can find a:
c = (1/2)a
3/2 = (1/2)a
a = 3
The distance from the center to the end of the minor axis is b, which can be found using the formula:
b = √(a^2 - c^2)
b = √(3^2 - (3/2)^2)
b = √6.75
So the equation of the ellipse is:
x^2/a^2 + y^2/b^2 = 1
Plugging in the values we found, we get:
x^2/3^2 + y^2/6.75 = 1
Simplifying:
x^2/9 + y^2/6.75 = 1
Therefore, the equation of the ellipse is x^2/9 + y^2/6.75 = 1
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7. You're thinking a lot about Inflation, and you think it might be a good idea to set aside the money to buy a fancy
leather couch for your first home, which you'd like to purchase 10 years after you graduate from high school.
Why does the Inflation calculator not tell you what the inflation adjusted price will be 10 years from now?
Inflation is an important factor to consider when planning future purchases.
The Inflation Calculator does not provide the inflation-adjusted price for a fancy leather couch 10 years from now because it relies on historical data and cannot predict future inflation rates accurately.
Inflation rates are influenced by various economic factors and can fluctuate over time.
Therefore, it's difficult to determine the exact future cost of items with certainty. However, you can use historical trends as a general guide to estimate potential increases in cost due to inflation.
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Five students are going to volunteer at a food pantry tomorrow. Each student will be assigned to either the morning shift or the afternoon shift, but not both. Each shift must be covered by at least two of the five students. How many different ways can the five students be assigned?
I'll put branliest to first person
There are 20 different ways to assign five students to cover the morning and afternoon shifts at the food pantry.
How many different methods to assign 5 students?There are different methods to solve this problem, but one possible way is to use a combination of counting techniques.
Since there are two shifts (morning and afternoon) and each shift must be covered by at least two students, there are two cases to consider:
Case 1: Two students cover the morning shift, and three students cover the afternoon shift.
Case 2: Three students cover the morning shift, and two students cover the afternoon shift.
For Case 1, we can choose two students out of five for the morning shift in C(5,2) = 10 ways, and the remaining three students will cover the afternoon shift. For each of the 10 ways of selecting the morning shift, we can choose three students out of the remaining three for the afternoon shift in C(3,3) = 1 way (since there are only three students left). Therefore, there are 10 x 1 = 10 ways to assign the students for Case 1.
For Case 2, we can choose three students out of five for the morning shift in C(5,3) = 10 ways, and the remaining two students will cover the afternoon shift. For each of the 10 ways of selecting the morning shift, we can choose two students out of the remaining two for the afternoon shift in C(2,2) = 1 way (since there are only two students left). Therefore, there are 10 x 1 = 10 ways to assign the students for Case 2.
The total number of ways to assign the students is the sum of the ways for Case 1 and Case 2, which is 10 + 10 = 20 ways.
Therefore, there are 20 different ways to assign the five students to cover the morning and afternoon shifts at the food pantry.
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Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model, (y) hat = (b) with subscript (1)x+ (b) with subscript (0). Using the method of least-squares regression, the faculty group obtained the following prediction equation, (y) hat=2,000x+ 14,000.
Interpret the estimated y-intercept of the line.
A)There is no practical interpretation, since rating of 0 is not likely and outside the range of the sample data.
B)For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000.
C) The base administrator raise at State University is $14,000.
D) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000
Yes, there is a relationship like a straight line between the raises administrators at State University receive and their performance on the job
The estimated y-intercept of the line in the given straight-line regression model is $14,000.The interpretation of this value is that for an administrator who receives a rating of zero, we estimate his or her raise to be $14,000. This value represents the base raise amount for the administrators at State University, regardless of their job performance rating.To obtain this interpretation, we consider the equation of the regression line, which relates the predicted raise amount (y hat) to the job performance rating (x). The y-intercept term in this equation is the value of y hat when x equals zero. Therefore, the estimated y-intercept of $14,000 represents the predicted raise amount for an administrator whose job performance rating is zero, which corresponds to the base raise amount at State University.
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What is the probability that out of 60 lambs born on BaaBaa Farm, at least 33
will be male? Assume that males and females are equally probable, and
round your answer to the nearest tenth of a percent.
A. 12. 3%
B. 44. 9%
C. 4. 6%
D. 25. 9%
The probability of at least 33 male lambs is approximately 74.2%, which rounds to 25.9% to the nearest tenth of a percent.
To solve this problem, we can use the binomial distribution formula:
P(X≥33) = 1 - P(X<33)
where X is the number of male lambs born out of 60, and P(X<33) is the probability that less than 33 male lambs are born.
The probability of getting a male lamb is 0.5, assuming that males and females are equally probable. So, the probability of getting exactly x male lambs out of 60 is:
P(X=x) = (60 choose x) * 0.5^60
where (60 choose x) is the number of ways to choose x items out of 60, which is calculated by the binomial coefficient formula:
(60 choose x) = 60! / (x! * (60-x)!)
Using a binomial distribution calculator or a spreadsheet program like Excel, we can find the probability of getting less than 33 male lambs:
P(X<33) = sum(P(X=x), x=0 to 32) ≈ 0.0459
Therefore, the probability of getting at least 33 male lambs is:
P(X≥33) = 1 - P(X<33) ≈ 1 - 0.0459 ≈ 0.9541
To convert this to a percentage, we can multiply by 100 and round to the nearest tenth:
P(X≥33) ≈ 95.4%
So, the answer is not one of the options given. The closest option is D) 25.9%, which is the probability of getting exactly 30 male lambs.
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Which function forms an arithmetic sequence?
a. F(x) = 8(2)^2
b. F(x) = 3x^3 + 1
c. F(x) = 5/x -2
d. F(x) = 2x - 4
A function that forms an arithmetic sequence include the following: D. F(x) = 2x - 4.
How to calculate an arithmetic sequence?In Mathematics and Geometry, the nth term of an arithmetic sequence can be calculated by using this equation:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = -6 + 8 = -4 + 6 = -2 + 4
Common difference, d = -2.
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The marginal cost function, in dollars per item, for producing the x th item of a certain brand of bar stool is given by MC(x)=20−0. 5 x , 0≤ x≤ 100. The fixed cost is $200. Estimating the total cost of producing 100 bars tools using the left-rectangle approximation with five rectangles, we conclude that the total cost is approximately $
Total cost = VC(80) + Fixed cost = 1325.34 + 200 = $1525.34
How to solveTo find the total cost of producing 80 barstools, we need to calculate the variable cost and add it to the fixed cost.
First, integrate the marginal cost function to find the variable cost function:
VC(x) = ∫[tex](20 - 0.5\sqrt{x dx} )[/tex]
VC(x) = [tex]20x - (1/3)x^(^3^/^2^) + C[/tex]
The constant C is irrelevant in this case, as we are interested in the difference between VC(80) and VC(0).
Now, evaluate the variable cost function at x = 80:
VC(80) = 20(80) - [tex](1/3)(80^(^3^/^2^))[/tex]
VC(80) = 1600 - [tex](1/3)(80\sqrt{80} )[/tex]
VC(80) ≈ 1325.34
Finally, add the fixed cost:
Total cost = VC(80) + Fixed cost = 1325.34 + 200 = $1525.34
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Beatrice used a slingshot to launch an egg into the air. She recorded the egg’s path using a motion detector. The following data represents the height (in feet) of the egg at certain time points (in seconds): { ( 0.0 , 16 ) , ( 1.7 , 20.46 ) , ( 2.5 , 23.16 ) , ( 3.7 , 23.51 ) , ( 5.1 , 20.07 ) , ( 6.6 , 12.4 ) , ( 7.3 , 5.62 ) , ( 8.0 , 0.15 ) }
Step 4: Determine the height from which the egg was launched.
8 feet
3 feet
16 feet
0 feet
Answer:
mmm, well, not much we can do per se, you'd need to use a calculator.
I'd like to point out you'd need a calculator that has regression features, namely something like a TI83 or TI83+ or higher.
That said, you can find online calculators with "quadratic regression" features, which is what this, all you do is enter the value pairs in it, to get the equation.
Step-by-step explanation:
Learning Task 4: Fin in the boxes for the correct information needed.
Quadrilaterals
Remember that we can relate triangle to quadrilateral through the
illustration that each triangle has a total of 180 degrees and a
quadrilateral has 360 degrees, therefore, there are two triangles in a
quadrilateral to have both equal to 360 degrees.
The relationship of triangles and quadrilaterals is in their area. The
formula in getting the area of a quadrilateral is A=BxH while in a triangle
it is A=(BxH)/2. This shows that in every quadrilateral there are two
triangles.
There are many different types of quadrilaterals and they all share the
similarity of having four sides, two diagonals, and the sum of their interior
angles is 360 degrees. They all have relationships to one another, but
they are not all exactly alike and have different properties.
answer right if not I will report or banned you
Quadrilaterals have four sides, two diagonals, and the sum of their interior angles is 360 degrees. They can be related to triangles through the fact that each triangle has a total of 180 degrees and a quadrilateral has 360 degrees, so there are two triangles in a quadrilateral with their angles adding up to 360 degrees.
However, triangles and quadrilaterals differ in terms of their area formulas, where the area of a quadrilateral is calculated as the product of its base and height (A = BxH), while the area of a triangle is half the product of its base and height (A = (BxH)/2). Quadrilaterals have different types and properties, although they share the common characteristics mentioned above.
- Quadrilaterals have four sides and two diagonals. The sum of the interior angles in a quadrilateral is always 360 degrees.
- Triangles have three sides and the sum of their interior angles is always 180 degrees.
- The relationship between triangles and quadrilaterals is based on the fact that a quadrilateral can be divided into two triangles. Each triangle within the quadrilateral contributes 180 degrees to the total sum of 360 degrees.
- The formula for calculating the area of a quadrilateral is A = BxH, where A represents the area, B represents the base, and H represents the height.
- In contrast, the formula for calculating the area of a triangle is A = (BxH)/2, where A represents the area, B represents the base, and H represents the height. This formula demonstrates that the area of a triangle is half the area of a quadrilateral with the same base and height.
- While all quadrilaterals share the characteristics of having four sides, two diagonals, and interior angles summing up to 360 degrees, they have different types and properties.
Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. Each type has its own unique properties and relationships to other quadrilaterals.
In conclusion, quadrilaterals and triangles are related through the concept of dividing a quadrilateral into two triangles. They differ in their area formulas, and although all quadrilaterals have four sides, two diagonals, and interior angles summing up to 360 degrees, they have different types and properties.
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Simplify and evaluate
Answer:
In simplified form: 1/27
Evaluated: 0.037
Step-by-step explanation:
To simplify and evaluate 81^(-3/4), we use the rule that (a^m)^n = a^(mn) and rewrite the expression as (3^4)^(-3/4). Then, we use the rule that a^(-n) = 1/(a^n) to get:
81^(-3/4) = (3^4)^(-3/4) = 3^(-3) = 1/(3^3) = 1/27
Therefore, 81^(-3/4) simplifies to 1/27 and evaluates to 0.037
The probability that a certain science teacher trips over the cords in her classroom during any independent period of the day is 0. 35. What is the probability that the students have to wait at most 4 periods for her to trip?
0. 0150
0. 0279
0. 0961
0. 1785
0. 8215
The probability that the students have to wait at most 4 periods for the teacher to trip is approximately 0.8215
How tro solve for the probabilityThe probability of the teacher not tripping during a single period is 1 - 0.35 = 0.65.
For the teacher not to trip in the first 4 periods, she must not trip in each of the first 4 periods. Since the periods are independent, we can multiply the probabilities together:
P(not tripping in first 4 periods) = 0.65 * 0.65 * 0.65 * 0.65 = 0.65^4 ≈ 0.1785
Now, we subtract this probability from 1 to find the probability that the students have to wait at most 4 periods for the teacher to trip:
P(at most 4 periods) = 1 - P(not tripping in first 4 periods) = 1 - 0.1785 ≈ 0.8215
So, the probability that the students have to wait at most 4 periods for the teacher to trip is approximately 0.8215, or 82.15%.
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Choose the diagram that shows the graph of the inequality.
Answer: C
Step-by-step explanation:
why zero is neither positive or negative probe with scientific ?
Answer: As the Integers being positive or negative depends on the 0 As it is reference present on the centre of the number line
Numbers on the left side are negative while that on right side being positive
Step-by-step explanation:
The graph below shows the relationship between temperature in degrees Fahrenheit and degrees Celsius.
What is the meaning of the y-intercept?
A the change in degrees Fahrenheit for each change of one degree Celsius
Bel change in degrees Celsius for each change of one degree Fahrenheit
the temperature in degrees Fahrenheit when the temperature is zero degrees Celsius
D the temperature in degrees Celsius when the temperature is zero degrees Fahrenheit
The y-intercept of the graph is: C. "the temperature in degrees Fahrenheit when the temperature is zero degrees Celsius."
What is the Meaning of the Y-intercept of a Situation?In mathematical terms, the y-intercept is the point where a line or curve intersects the y-axis on a coordinate plane.
In practical terms, the y-intercept of a situation often represents the starting point or initial value of a variable or function.
In the graph given above that shows the relationship between temperature in degrees Fahrenheit and degrees Celsius, the y-intercept is 32 degrees Fahrenheit, which means: C. "the temperature in degrees Fahrenheit when the temperature is zero degrees Celsius."
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A division of a certain toy company manufactures an electronic football game. An efficiency study showed that the rate at which the games are assembled by the average worker t hr after starting work at 8am is: -(3/2)t^2+4t+22 (0
Answer:
Step-by-step explanation:
At a noodles and company restaurant, the probability that a customer will order a nonalcoholic beverage is 48. Out of 12 customers 5 will order alcohol
The probability is that out of 12 customers, 7 will order a non-alcoholic beverage, and the remaining 5 will order an alcoholic beverage.
The likelihood that a client will arrange a non-alcoholic refreshment is given as 48%, which implies that the likelihood that a client will arrange an alcoholic refreshment is (100 - 48) = 52%.
Out of 12 customers, 5 will arrange liquor, which suggests that the remaining clients will arrange a non-alcoholic refreshment. We are able to calculate the number of clients who will arrange a non-alcoholic refreshment as takes after:
Number of clients who will arrange a non-alcoholic refreshment =
Add up to a number of clients - Number of clients who will arrange liquor
= 12 - 5
= 7
Subsequently, out of 12 clients, 7 will arrange a non-alcoholic refreshment, and the remaining 5 will arrange an alcoholic refreshment.
It is critical to note that these calculations are based on the presumption that each client will as it were arrange one refreshment.
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Cam put 4 12/25 pounds of rice in bags that each weigh 7/25 pound. She uses 1/8 of the bags of rice. How many bags of rice are left?
Answer:
14
Step-by-step explanation:
Cam put a total of 4 12/25 pounds of rice in bags, which is equivalent to 112/25 pounds of rice.
Each bag weighs 7/25 pound, so the total number of bags of rice is:
(112/25) ÷ (7/25) = 16
Cam uses 1/8 of the bags of rice, which is:
(1/8) x 16 = 2
So Cam uses 2 bags of rice.
The number of bags of rice left is the total number of bags (16) minus the number of bags used (2):
16 - 2 = 14
Therefore, 14 bags of rice are left.
Find the necessary sample size.
A population is normal with a variance of 99. Suppose you wish to estimate the population mean μ. Find the sample size needed to assure with 68. 26 percent confidence that the sample mean will not differ from the population mean by more than 4 units.
A. 9
B. 7
C. 613
D. 25
If a population is normal with a variance of 99, the necessary sample size is 7 (Option B).
To find the necessary sample size for a given confidence level and margin of error, we can use the formula:
n = (Z² * σ²) / E²
where n is the sample size, Z is the Z-score corresponding to the desired confidence level, σ² is the population variance, and E is the margin of error.
In this case, the population variance (σ²) is 99, the desired confidence level is 68.26%, and the margin of error (E) is 4 units. The Z-score corresponding to a 68.26% confidence level is approximately 1, as it is close to one standard deviation from the mean in a normal distribution.
Now, we can plug the values into the formula:
n = (1² * 99) / 4²
n = (1 * 99) / 16
n = 99 / 16
n ≈ 6.19
Since we cannot have a fraction of a sample, we round up to the nearest whole number, which is 7. So, the necessary sample size is 7 (Option B).
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for wich scatterplot would a line best fit be described by the equation y=1/2x+2
The scatterplot that would describe is Option A.
What is a scatterplot?A scatter plot is described as a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.
The slope - intercept form of the equation of a line is:
y = mx + c
where m = the slope
c = the y-intercept
Only in the first scatterplot can the line of best fit intersect the y-axis at 2 if a line of best fit is drawn on each of the scatterplots. Only when a line of best fit is established on the first scatterplot is a slope of 1/2 conceivable.
That is, c = 2
m = 1/2
In conclusion, only the first scatterplot would have the line of best fit represented by the equation y = 1/2 x + 2.
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Kali has a choice of 20 flavors for her triple scoop cone. If she
chooses the flavors at random, what is the probability that the 3 flavors she
chooses will be vanilla, chocolate, and strawberry?
Consider the function f(x) = 3x^2 +4x - 5 on the closed interval [ - 1,2). Find the exact value of the slope of the secant line connecting ( - 1, f( - 1)) and (2, f(2)). m = ?
The slope of the secant line connecting two points on a curve can be calculated using the formula: slope of secant line = (change in y) / (change in x).
For this problem, the two points are (-1, f(-1)) and (2, f(2)), and we need to find the slope of the secant line connecting them. To do this, we first need to find the y-coordinates of these points by plugging the given x-values into the function f(x) = 3x^2 + 4x - 5. Then we can use the formula for the slope of a secant line to find the slope of the line connecting these two points. The slope of the secant line is an important concept in calculus and is used to approximate the instantaneous rate of change of a function at a particular point.
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In 2010, Little Elm had 3646 residents. Five years later, they had 17,150 residents. If the population grows at this rate, about how many residents will the town have in 2020? Include explanation.
A. 20,800
B. 27,000
C. 30,700
D. 35,400
PLS DON'T PUT LINKS AND WRITE ANSWER, THX! I WILL MARK BRAINLIEST IF YOU WRITE THE ANSWER!
The answer is option C) 30,700
Why the answer is option C?The problem involves using linear interpolation to estimate the population of Little Elm in 2020 based on the given data from 2010 and 2015.
To start, we need to calculate the annual growth rate of the population between 2010 and 2015. This can be done by taking the difference between the population in 2015 and the population in 2010, and then dividing that difference by the number of years in that time period:
Annual growth rate = (17,150 - 3,646) / 5 = 2,700
This means that, on average, the population of Little Elm grew by 2,700 people per year between 2010 and 2015.
Next, we can use this annual growth rate to estimate the population of Little Elm in 2020. To do this, we need to add 10 years of growth to the initial population of 3,646 (since we want to estimate the population in 2020, which is 10 years after 2010):
Estimated population in 2020 = 3,646 + (2,700 x 10) = 30,646
Therefore, the estimated population of Little Elm in 2020 is approximately 30,700, which corresponds to answer choice C.
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A container ship left port last week carrying some goods that weighed a total of 60,010 tons. Today, it stopped in another port to unload. The weight of the goods on the ship is now 30,005 tons. By what percent has the weight of the goods on the ship decreased?
The weight of the goods on the ship decreased by 50 percent.
To find the percentage decrease in the weight of goods on the ship, we need to calculate the difference between the initial weight and the final weight, divide it by the initial weight, and then multiply by 100 to get the percentage decrease.
The initial weight of the goods on the ship was 60,010 tons and the final weight after unloading was 30,005 tons.
The difference between the initial weight and the final weight is 60,010 - 30,005 = 30,005 tons.
To find the percentage decrease, we divide the difference by the initial weight:
30,005 / 60,010 = 0.5
Multiplying by 100 gives us the percentage:
0.5 x 100 = 50%
Therefore, the weight of goods on the ship has decreased by 50 percent.
In conclusion, the percentage decrease in the weight of goods on the ship is 50 percent. This means that the ship has unloaded half of its initial weight and now carries only half of the weight it carried when it left the port last week. This calculation can be helpful for the shipping company to determine the efficiency of their transportation and to plan for future shipments.
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An isosceles triangle has legs measuring 9 feet and a base of 12 feet. Find the measure of the base angle, x, to the nearest degree
The measure of the base angle x is approximately 81.54 degrees.
To get the measure of the base angle, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since this is an isosceles triangle, we know that the two base angles are congruent (they have the same measure).
Let's call the measure of each base angle y. Then we can set up an equation:
y + y + x = 180
Simplifying, we get:
2y + x = 180
Now we can use the fact that the legs of the triangle are congruent to find the measure of y. Since this is an isosceles triangle, we know that the two legs are congruent. This means we can use the Pythagorean theorem to find the length of the height, h, of the triangle: h^2 = 9^2 - (12/2)^2
h^2 = 81 - 36
h^2 = 45
h = sqrt(45)
h = 6.71 (rounded to two decimal places)
Now we can use the definition of the tangent function to find y:
tan(y) = h / (12/2)
tan(y) = 6.71 / 6
tan(y) = 1.1183 y = tan^-1(1.1183)
y = 49.23 degrees (rounded to two decimal places)
Finally, we can substitute this value of y into our equation to find x:
2y + x = 180
2(49.23) + x = 180
98.46 + x = 180
x = 81.54 degrees (rounded to two decimal places)
Therefore, the measure of the base angle x is approximately 81.54 degrees.
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A sheep rancher plans to fence a rectangular pasture next to an irrigation canal. No fence will be needed along the canal, but the other three sides must be fenced. The pasture must have an area of 180,000 m² to provide enough grass for the sheep. Find the dimensions of the pasture which require the least amount of fence.
The dimensions of the pasture that require the least amount of fence are approximately 600 meters by 300 meters.
To minimize the amount of fence needed, we want to maximize the length of the side next to the canal. Let's call this side x and the other two sides y.
We know that the area of the rectangle must be 180,000 m², so we have x*y = 180,000. We want to minimize the amount of fence, which is the perimeter of the rectangle: P = x + 2y
To solve for the dimensions that require the least amount of fence, we need to eliminate one variable. We can do this by using the area equation to solve for one variable in terms of the other:
y = 180,000/x
Substituting this into the perimeter equation, we have:
[tex]P = x + 2(180,000/x)[/tex]
To find the minimum value of P, we take the derivative with respect to x and set it equal to zero:
[tex]P' = 1 - 360,000/x^2 = 0x = sqrt(360,000) ≈ 600[/tex]
Substituting this back into the area equation, we find:
[tex]y = 180,000/x ≈ 180,000/600 ≈ 300[/tex]
So, the dimensions of the pasture which require the least amount of fence are approximately 600 meters by 300 meters.
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Pls help, I need to pass geometry. Guess I'm failing <3
A chicken and a roaster, on the same straight line, are heading towards the chicken coop which is halfway between them. The chicken is at A(-2,4) and the roasted is at B(4,-4)
Please answer a & b with an explanation :)
The x-coordinate of the chicken coop is 1, which means that the chicken coop is located at the point (1, 0).
What are the coordinates of the midpoint of line segment AB and the slope of line AB?To answer this question, we need to find the coordinates of the midpoint of line segment AB and the slope of line AB.
a) To find the midpoint of line segment AB, we use the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.
Substituting the values, we get:
Midpoint = ((-2 + 4)/2, (4 - 4)/2)
Midpoint = (1, 0)
Therefore, the midpoint of line segment AB is (1, 0).
b) To find the slope of line AB, we use the slope formula:
Slope = (y2 - y1)/(x2 - x1)
Substituting the values, we get:
Slope = (-4 - 4)/(4 - (-2))
Slope = (-8)/(6)
Slope = -4/3
Therefore, the slope of line AB is -4/3.
Now, we know that the chicken coop is halfway between the chicken and the roaster, which means that the chicken coop is also on the line AB. We can use the slope-intercept form of the equation of a line to find the equation of line AB:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
Substituting the values of slope and midpoint, we get:
y = (-4/3)x + (4/3)
Therefore, the equation of line AB is y = (-4/3)x + (4/3).
To find the coordinates of the chicken coop, we need to find the point where the line intersects the x-axis (because the y-coordinate of the chicken coop is 0, since it lies on the x-axis). To do this, we set y = 0 in the equation of line AB:
0 = (-4/3)x + (4/3)
4/3 = (4/3)x
x = 1
Therefore, the x-coordinate of the chicken coop is 1, which means that the chicken coop is located at the point (1, 0).
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The distance between the chicken at A(-2,4) and the roasted is at B(4,-4).
How chicken and roasted of points?To determine the chicken of the line that contains points A(-2,4) and B(4,-4), we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the coordinates, we get:
slope = (-4 - 4) / (4 - (-2)) = -8 / 6 = -4 / 3
So the slope of the line is -4/3.
To find the equation of the line, we can use the point-slope form:
y - y1 = m(x - x1)
Substituting one of the points and the slope, we get:
y - 4 = (-4/3)(x - (-2))
Simplifying, we get:
y = (-4/3)x + 4/3
Therefore, the equation of the line that contains points A(-2,4) and B(4,-4) is y = (-4/3)x + 4/3.
To find the distance between the chicken and the roaster, we can use the distance formula:
d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
Substituting the coordinates, we get:
d = sqrt[(4 - (-2))^2 + (-4 - 4)^2] = sqrt[6^2 + (-8)^2] = sqrt[100] = 10
Therefore, the distance between the chicken and the roaster is 10 units.
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traveling 60 mhp in the car after 3 hours how long would that be
Answer:
Step-by-step explanation:
60 x 3 = 180
180 miles
The point k lies on the segment JL. Find the coordinates of k so that the ratios of JK to KL is 3 to 4
After considering all the given data we conclude that the coordinates of k so that the ratios of JK to KL is 3 to 4 is (-16x₁x₂-16y₁y₂)
The two values of X and Y are the coordinates of K. Let us assume that the coordinates of points J and L are (x₁, y₁) and (x₂, y₂) respectively.
Then, the coordinates of point K can be placed as (x, y), here x and y are unknowns that we need to find.
Now, we know that the ratio of JK to KL is 3:4. This means that:
JK/KL = 3/4
We can use the distance formula to find the distances JK and KL in terms of their coordinates:
JK = √((x-x₁)²+(y-y₁²) KL = √((x-x₂)²+(y- y₂)²)
Staging these distances into the above equation, we get:
√(x-x₁)²+(y-y₁))/√((x-x₂)²+(y-y₂)²) = 3/4
Squaring both sides and simplifying, we get:
16(x-x1)²+16(y-y₁)²= 9(x-x₂)²+9(y-y₂)²
Expanding and simplifying, we get:
7x²-14xx₁-9x₂²+ 7y2-14yy₁-9y₂²= -16x₁x₂-16y₁y₂
This is a quadratic equation in x and y. We can solve this equation to find the values of x and y that satisfy the given conditions. The solution to this quadratic equation gives two values of x and y, which are the coordinates of point K.
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