Law of Cosines Of A Triangle -GIVEN: C (the degree) 20, 22,18 (the base). C is 26.5 degrees.
To solve for the angle C using the law of cosines, we use the formula:
[tex]c^2 = a^2 + b^2[/tex] - 2ab cos(C)
where c is the angle C's opposite side.
Substituting the given values, we get:
[tex]18^2 = 20^2 + 22^2[/tex] - 2(20)(22)cos(C)
324 = 1048 - 880cos(C)
880cos(C) = 724
cos(C) = 724/880
C = [tex]cos^{(-1)}[/tex](724/880)
C ≈ 26.5 degrees
Therefore, the measure of angle C is approximately 26.5 degrees.
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given the following exponential function, identify whether the change represents growth or decay and determine the percentage rate of increase or decrease y=620(0.941)x
the function represents exponential decay with a rate of decrease of 5.9% per unit increase in x.
In the exponential function y = [tex]620(0.941)^x:[/tex]
The base of the exponent is 0.941, which is between 0 and 1.
As x increases, the value of [tex](0.941)^x[/tex]gets smaller and smaller, approaching 0 but never reaching it.
Therefore, the function represents exponential decay.
To determine the percentage rate of decrease, we can use the formula:
rate of decrease = (1 - base) x 100%
In this case, the base is 0.941, so the rate of decrease is:
rate of decrease = (1 - 0.941) x 100% = 5.9%
The exponential function is y = 620(0.941)^x.
To determine whether the function represents growth or decay, we need to look at the base of the exponential function, which is 0.941. Since this base is less than 1, the function represents decay.
To determine the percentage rate of decrease, we can use the formula:
r = (1 - b) x 100%
where r is the percentage rate of decrease, and b is the base of the exponential function.
In this case, b = 0.941, so we have:
r = (1 - 0.941) x 100%
= 0.059 x 100%
= 5.9%
Therefore, the exponential function y = 620(0.941)^x represents decay with a rate of 5.9% per unit of x.
A sort of mathematical function called exponential decay can be used to explain a quantity's decline across time or space. The quantity at any given time will change at a pace that is proportionate to the quantity itself, which is characterised by a decreasing rate of change. In other words, the amount of reduction decreases as time or space grows, but it never decreases to zero.
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=620(0.941)^x y=620(0.941) x
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State the degree of the polynomials
2r^3v + 150r – r^4 v^2
Answer:
11
Step-by-step explanation:
add up the exponents
3+1+1+4+2=11
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what is the equivalent expression of (2x+3)(4x^2-x-5)
Answer:
8x^(3)+10x^(2)-13x-15
Step-by-step explanation:
Determine the total cost of the items if they were not sold to be as a combo if both are sold at R100 and when both sold at R100 you save R37
The total cost of the items if they were not sold as a combo is R137.
Let's assume that the individual prices of the two items are X and Y. Here we have to use the concept of algebraic equation. We have two unknowns (X and Y), and we use the information given about their combined cost and the savings made when sold as a combo to form an equation in terms of X and Y
When the items are sold individually, the total cost would be X + Y.
When the items are sold together as a combo, the cost is R100, and this saves R37 compared to the individual prices. This means:
X + Y - 37 = 100
Simplifying the above equation, we get:
X + Y = 137
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Please help and please hurry
factor the polynomial to find the side length the polynomial is on the picture
Factorization of the given polynomial is: (x - 15)(x - 15).
The length of a side is: x = 15
How to factorize the polynomial?In the case of polynomials in mathematics, the factors of the polynomials are the polynomials which are multiplied to produce the original polynomial. For example, the factors of x² + 5x + 6 is (x + 2) (x + 3).
When we multiply both x + 2 and x +3, then we will see that the original polynomial is generated.
We are given the polynomial as:
A = x² - 30x + 225
This can be broken down into:
A = x² - 15x - 15x + 225
A = x(x - 15) - 15(x - 15)
A = (x - 15)(x - 15)
Thus:
x = 15
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binomial a lottery will be held. from 1000 numbers, one will be chosen as the winner. a lottery ticket is a number between 1 and 1000. how many tickets do you need to buy in order for the probability of winning to be at least 50%?
we need to buy at least 694 tickets to have a probability of winning at least 50%.
We can use the binomial distribution formula to solve this problem. Let X be the number of tickets we need to buy to have a probability of winning at least 50%. Then:
P(X ≥ 1) ≥ 0.5
This means that the probability of winning with at least one ticket is at least 50%. We can find this probability using the complement rule:
P(X ≥ 1) = 1 - P(X = 0)
The probability of not winning with any ticket is:
P(X = 0) = (999/1000)^n
where n is the number of tickets we buy. Therefore:
1 - (999/1000)^n ≥ 0.5
Simplifying this inequality, we get:
(999/1000)^n ≤ 0.5
Taking the logarithm of both sides, we get:
n log(999/1000) ≤ log(0.5)
n ≥ log(0.5) / log(999/1000)
n ≥ 693.15
Therefore, we need to buy at least 694 tickets to have a probability of winning at least 50%.
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SOMEONE PLEASE DO THIS FOR ME I WILL SELL MY SOUL AND A BUNCH OF THE LITTE POINT THINGS
Answer: SORRY THIS TOOK FOREVER ITS SO HARD- THE ANSWER IS F, C, D, H, E, A, G, B!!!
Step-by-step explanation:
THE LEAST TO GREATEST ARE F, C, D, H, E, A, G, B! HOPE IT HELPED!! :D
What’s 3.14 times six?
Answer:
18.84
Step-by-step explanation:
:)
This is parallelograms practice and I don’t get it at all!! Please help me guys
Step-by-step explanation:
p-grams have equal opposite side lengths
soooo
5x+7 = 27
x = 4
then 22x = 22(4) = 88 units ( this is also AB length)
q. what shape is the base? what is the area of the base (b)? multiple choice question. a) rectangle; 60in2 b) rectangle; 32 in2 c) triangle; 6 in2 d) triangle; 12 in2
the correct answer is either (c) or (d), depending on the size of the object. If the object is small, the base is likely to be a triangle with an area of 6in2. If the object is larger, the base is likely to be a triangle with an area of 12in2.
The question asks about the shape and area of the base of an object. The possible answers are a rectangle with an area of 60in2, a rectangle with an area of 32in2, a triangle with an area of 6in2, and a triangle with an area of 12in2.
To determine the correct answer, it is important to understand what the base of an object is. The base is the surface upon which the object rests, and it is often a flat, two-dimensional shape. The area of the base is the measure of the surface area of that shape.
Answer (a) is a rectangle with an area of 60in2. This means that the length and width of the rectangle multiply to give a product of 60. However, we are not given any measurements of the object, so we cannot determine if this is correct.
Answer (b) is a rectangle with an area of 32in2. Again, we are not given any measurements of the object, so we cannot determine if this is correct.
Answer (c) is a triangle with an area of 6in2. This means that the base and height of the triangle multiply to give a product of 12, and then divide by 2 to get an area of 6.
Answer (d) is a triangle with an area of 12in2. This means that the base and height of the triangle multiply to give a product of 24, and then divide by 2 to get an area of 12.
Based on this information, we can see that the correct answer is either (c) or (d), depending on the size of the object. If the object is small, the base is likely to be a triangle with an area of 6in2. If the object is larger, the base is likely to be a triangle with an area of 12in2.
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11. MP Find the Error A student was finding the radius of a sphere with a volume of 4,500 cubic inches. Find his mistakes and correct them. V= πr²³ 4,500T= 4,500 = 4 3 6,000 = ³ πTP³ 3 -p³ r = 2,000
The radius of the sphere with a volume of 4,500π cubic inches is 15 inches, not 2,000 inches as the student had incorrectly calculated.
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The volume of the sphere is given as 4,500π cubic inches.
The formula for volume of the sphere is -
V= 4/3πr³
Substituting the values in the equation -
4,500π = 4/3πr³
4,500 = 4/3r³
The mistake in the student's calculation is in the step where they simplified 4/3πr³ to 4,500.
To correct this, we need to isolate r³ by dividing both sides by 4/3 -
4,500 = (4/3)r³
4,500 ÷ (4/3) = r³
4,500 × 3/4 = r³
3,375 = r³
Then, we can take the cube root of both sides to find r -
r = ∛3,375 = 15
Therefore, the radius of the sphere is 15 inches.
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Geometry help please
As a result, 37.6 is the number of x in the provided diagram as The fact that angles x and z are opposite angles in a parallelogram.
what is triangle ?A triangle is a two-dimensional polygon with three straight edges and three angles in geometry. The most basic polygon, it serves as the foundation for more complicated shapes. Triangles can be categorized based on the lengths of their sides and the angles in their angles. Triangles can be categorized as either equilateral (all three sides are equal) or isosceles (two sides are equal) or scalene (three sides are equal) (all three sides are different lengths). Triangles can be categorized as acute, right, or oblique based on how many angles they have. Acute triangles have three angles that are all less than 90 degrees (one angle is greater than 90 degrees).
given
x + y + z = 180
By replacing y = 3x - 8 we obtain:
x + (3x - 8) + z = 180
When we simplify this solution, we obtain:
4x - 8 + z = 180
8 is added to both parts to arrive at:
4x + z = 188
The fact that angles x and z are opposite angles in a parallelogram, indicating that they are identical, can be used to determine the value of x. As a result, we have:
x = z
The result of adding x = z to the formula 4x + z = 188 is:
5x = 188
When we multiply both sides by 5, we get:
x = 37.6
As a result, 37.6 is the number of x in the provided diagram as The fact that angles x and z are opposite angles in a parallelogram.
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Nora is taking a multiple choice test with a total of 100 points available. Each
question is worth exactly 2 points. What would be Nora's test score (out of 100) if she
got 6 questions wrong? What would be her score if she got x questions wrong?
Score with 6 questions wrong:
Score with a questions wrong:
Submit Answer
attempt 1 out of 2
The score with 6 wrong answers is 88, and with x is modeled by the function:
S(x) = 100 - 2x
What will be her score with 6 questions wrong?We know that the test has a total of 100 points avaible, such that each question is whort 2 points.
So, if she answers 6 questions wrong, she will get a total of 100 points minus 6 times 2 points, this gives:
100 - 6*2 = 100 - 12 = 88 points.
Now, similarly, if she gets x questions wrong, the total score will be 100 minus 2 times x, then we define the linear function:
S(x) = 100 - 2x
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Really appreciated d :) 25points (Reupload)
Answer:
,,,
Step-by-step explanation:
Answer:
Scientifically proven that there is a 60% chance you will get an odd number and a 40% chance you will get an even number.
I hope this helps!!
Use the numbers. Please help
Step-by-step explanation:
A negative divided by a negative gives a positive
If we put the biggest negative divided by the smallest negative, that gives our best chance
[tex] \frac{ - 10}{ - (\frac{2}{5} )} = 25[/tex]
the price of firewood 4 years ago was $140 per cord. today, a cord of wood costs $182. what has been the annual rate of increase in the cost to the nearest tenth of a percent?
Using the formula for compound interest we find that the annual rate of increase in the cost of firewood is approximately 7.8%.
We can use the formula for compound interest to calculate the annual rate of increase:
A = P(1 + r)^n
where A is the final price, P is the initial price, r is the annual rate of increase, and n is the number of years.
We know that P = $140, A = $182, and n = 4, so we can solve for r:
182 = 140(1 + r)^4
(1 + r)^4 = 1.3
1 + r = 1.3^(1/4)
r ≈ 0.0777
The annual rate of increase is approximately 0.0777 or 7.8% to the nearest tenth of a percent.
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calculate the probability of obtaining a sample result of a mean of $470 or more if the true population mean is 460. (use salt. round your answer to four decimal places.)
The probability of obtaining a sample result of a mean of $470 or more if the true population mean is 460 is very low, almost zero.
To calculate the probability of obtaining a sample result of a mean of $470 or more, we need to use the sampling distribution of the mean.
Assuming that the sample size is large enough and that the sample means are normally distributed, we can use the central limit theorem to approximate the sampling distribution of the mean to a normal distribution. We can standardize the sample mean using the formula
z = (x - μ) / σ,
where x is the sample mean, μ is the population mean, and σ is the standard error of the mean.
In our case, we want to find the probability of obtaining a sample mean of $470 or more. We can convert this to a z-score by standardizing it using the formula
z = (470 - 460) / (σ / √n),
where n is the sample size.
If the sample size is 100 and the population standard deviation is 10, then the standard error of the mean is 1. We can then calculate the z-score as
=> z = (470 - 460) / (1 / √100) = 10.
We can look up the probability of obtaining a z-score of 10 or greater in a standard normal distribution table, which is almost zero.
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HELP PLEASE, ASAP, FIRST ANSWER GETS BRAINLIEST!!!
Which of the following tables represents a linear function?
x −4 −1 0 1 2
y −4 2 −4 0 2
x 1 1 1 1 1
y −3 −2 −1 0 1
x −6 −1 0 2 3
y −7 negative sixteen thirds −5 negative thirteen thirds −4
x −2 −1 0 2 4
y −4 negative two thirds −1 two thirds 1
Answer:The first table is linear. The other are not linear.
Step-by-step explanation:
PLEASE HELP An elevator goes down 3 floors, up 5 floors, and finally down 7 floors. Which expression represents the total number of floors the elevator traveled?
*
A | -3 | + | 5 | + | -7 |
B | -3 | - | 5 | + | -7 |
C ( -3 ) + 5 + ( -7 )
D 3 - 5 + 7
Answer:
B is the answer
Step-by-step explanation:
Which is the best estimate of the perimeter of the figure? one side is 6
Option (C) yields the perimeter of the supplied figure, which is 45 feet.
What is the perimeter?In geometry, the perimeter is the overall length of a shape's boundary.
The perimeter of a shape is determined by adding the lengths of all of its edges and sides.
Linear measurements like centimeters, meters, inches, and feet are used to express their dimensions.
So, two circles and one square make up the figure.
A square's perimeter is equal to 4. (side)
The square's side length is 5 feet.
Put the value in the equation as a replacement -
Perimeter of square = 4(5)
Perimeter of square = 20 feet
The circle's radius is equal to 2.5 feet.
A circle's perimeter is equal to 2r.
Put the value in the equation as a replacement -
Perimeter of circle = 2π(2.5)
Perimeter of circle = 5π
Due to the two circles, the circumference is 2 + 5 = 10 ft.
The figure's border measures -
The total perimeter equals the sum of the square and circle perimeters.
Total perimeter = 2.5 + 10π
Total perimeter = 2.5 + 10(3.14)
Total perimeter = 12.5 + 31.4
Total perimeter = 43.9 feet ≈ 45feet
Therefore, option (C) yields the perimeter of the supplied figure, which is 45 feet.
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Correct question:
Which is the best estimate of the perimeter of the figure? Use 3.14 for pie.
a manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 9 inches and standard deviation of 1 inches. if a sample of 50 items are chosen at random, what is the probability the sample's mean length is greater than 9.1 inches? round answer to
If a sample of 50 items are chosen at random. the probability that the sample mean length is greater than 9.1 inches is 0.0571, or 5.71%.
How to find the probability?The sample mean of the 50 items follows a normal distribution with mean equal to the population mean (μ), and standard deviation equal to σ/√n, where n is the sample size.
Substituting the given values, we have:
= μ = 9 inches
= σ/√n = 1/√50 inches
Now, we need to standardize the sample mean distribution to find the corresponding z-score using the formula:
z = (X- μX) / σX
Substituting the given values, we have:
z = (9.1 - 9) / (1/√50) = 1.58
The probability of getting a z-score of 1.58 or less is 0.9429. Therefore, the probability of getting a z-score of 1.58 or greater is:
P(z > 1.58) = 1 - P(z ≤ 1.58) = 1 - 0.9429 = 0.051
Therefore the probability that the sample mean length is greater than 9.1 inches is 0.0571.
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Which of the following statements is true of the Comprehensive Environmental Response, Compensation, and Liability Act?
Cleanups may be carried out by the Environmental Protection Agency or private parties.
The statement "Cleanups may be carried out by the Environmental Protection Agency or private parties" is true of the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), also known as Superfund.
What is the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA)?
The Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), commonly known as Superfund, is a United States federal law aimed at cleaning up sites contaminated with hazardous substances as well as preventing future hazardous waste site contamination.
CERCLA was passed by the United States Congress in December 1980 as a means of counteracting the increasing risk of hazardous waste sites in the United States.
What does CERCLA cover?
CERCLA was enacted to offer a federal "Superfund" to clean up uncontrolled or abandoned hazardous waste sites, as well as responding to oil spills, chemical disasters, and other emergencies that present a threat to the public health and the environment.
Cleanups may be carried out by the Environmental Protection Agency or private parties.
When it comes to financing these cleanups, the law mandates that those responsible for the contamination pay for the cleanup or those who do not take responsibility for the pollution.
The legislation was enacted to provide for the cleanup of the country's most hazardous waste sites and to ensure that businesses that generate hazardous waste are held responsible for their toxic contributions to the environment.
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Solve for x.
10
40
10
X
X
Set up the proportion.
[?]
Enter
Answer:
x = 20
Step-by-step explanation:
If an altitude is drawn to the hypotenuse of a right triangle, then the altitude is the geometric mean between the segments on the hypotenuse.
[tex] \frac{10}{x} = \frac{x}{40} [/tex]
[tex] {x}^{2} = 400[/tex]
[tex]x = 20[/tex]
Answer:
[tex]\frac{10}{x} =\frac{x}{40} \\\\x=20[/tex]
Step-by-step explanation:
The quadratic function of d = 7x^2 + 80 models a ball’s distance, in feet from the bottom of the hill x seconds after the ball is rolled down the hill. I know the answer is (approximately) 3.4, but how do I get to there without a graph
Answer:
3.38
Step-by-step explanation:
Set the equation given equal to 0 and solve for x, this will give you the distance the ball travels. Use the absolute value of the 80 to be able to get a positive number, because time is a positive number.
[tex]0=7x^2+80\\7x^2=-80\\x=\sqrt{\frac{80}{7}\\\\x=3.38062[/tex]
Can someone pls help me (you are the best)
The answer is x=6x +2
Land's Bend sells wide variety of outdoor equipment and clothing: The company sells both through mail order and via the internet: Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale random sample of 17 sales receipts for mail-order sales results in mean sale amount of $70.60 with standard deviation of 521.75. A random sample of 9 sales receipts for internet sales results in mean sale amount of $87.30 with standard deviation of S18.75 . Using this data, find the 99 % confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases: Assume that the population variances are not equal and that the two populations are normally distributed.
Step of 3 : Find the point estimate that should be used in constructing the confidence interval:
16.70Therefore, the point estimate that should be used in constructing the confidence interval is -$16.70.
To find the point estimate that should be used in constructing the confidence interval, the formula for the point estimate can be used. The formula is as follows: Point Estimate = Sample Mean of Mail-Order Sales - Sample Mean of Internet Sales = $70.60 - $87.30 = -$16.70.How to find the point estimate?The point estimate is the best estimate of the unknown population parameter based on a given sample of data. In this case, the unknown population parameter is the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases.
To find the point estimate, we need to calculate the difference between the sample mean of mail-order sales and the sample mean of internet sales .The formula for the point estimate is given by :Point Estimate = Sample Mean of Mail-Order Sales - Sample Mean of Internet Sales= $70.60 - $87.30= -$
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HELP ASAP, 100 POINTS, WILL MARK BRAINLIEST TO FIRST ANSWER!
Which of the following tables represents a linear function?
x −4 −1 0 1 2
y −4 2 −4 0 2
x 1 1 1 1 1
y −3 −2 −1 0 1
x −6 −1 0 2 3
y −7 negative sixteen thirds −5 negative thirteen thirds −4
x −2 −1 0 2 4
y −4 negative two thirds −1 two thirds 1
Answer:
Step-by-step explanation:
Its the 3rd one
Find the general solution of the following nonhomogeneous differential equation: y" (x) + 25 y (x) = 2 tan 5x Use C and D (both capital letters) for any arbitrary constants. y (x) = C sin (5x) + D cos (5x)-(2/25)ln(sec(5x)+tan(5x)) [Solution available after due date]
General solution = CF + PS= c₁ cos 5x + c₂ sin 5x - (2/25) tan 5x= C sin (5x) + D cos (5x) - (2/25) ln(sec(5x) + tan(5x)), where C = c₂ and D = c₁.
Explanation:
The general solution of the given non-homogeneous differential equation: y"(x) + 25y(x) = 2tan 5x isy (x) = C sin (5x) + D cos (5x) - (2/25) ln(sec(5x) + tan(5x)).
First of all, we need to find the complementary function(CF) of the differential equation to find the general solution.To find the complementary function (CF),
we set the non-homogeneous term to 0.y" (x) + 25y (x) = 0T
his is a homogeneous differential equation with the characteristic equation: r² + 25 = 0Solving this quadratic equation gives:r = ± 5i
Hence, the complementary function is given by:CF = c₁ cos 5x + c₂ sin 5xwhere c₁ and c₂ are constants of integration.
Now, we find the particular solution (PS) of the given non-homogeneous differential equation using the method of undetermined coefficients.
Given, y" (x) + 25 y (x) = 2 tan 5x
For PS, we assume that y = A tan 5x + B
where A and B are constants to be determined.Substituting this in the given equation, we get:10A sec² 5x + 25(A tan 5x + B) = 2 tan 5x
Simplifying this equation, we get:10A sec² 5x + 25A tan 5x + 25B = 2 tan 5x⇒ 10A sec² 5x + 23A tan 5x + 25B = 0
Comparing the coefficients of tan 5x and sec² 5x on both sides, we get:A = -2/25 and B = 0
Hence, the particular solution is given by:PS = - (2/25) tan 5xNow, the general solution of the given non-homogeneous differential equation is given by
:GS = CF + PS= c₁ cos 5x + c₂ sin 5x - (2/25) tan 5x= C sin (5x) + D cos (5x) - (2/25) ln(sec(5x) + tan(5x)), where C = c₂ and D = c₁.
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the area of the figure is
The area of the parallelogram above is 490 metres squared.
How to find the area of a parallelogram?A parallelogram is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
The area of a parallelogram can be calculated as follows:
area of a parallelogram = bh
where
b = baseh = heightTherefore,
b = 49 metres
h = 10 metres
Therefore,
area of a parallelogram = 10 × 49
area of a parallelogram = 490 metres squared
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