the solution to the equation -16p + 37 = 49 - 21p is p = 12/5. The equation -16p + 37 = 49 - 21p is a simple linear equation with one variable, p.
Linear equations are equations where the highest exponent of the variable is one, and they can be solved using algebraic techniques.
To solve this equation, we need to isolate the variable, p, on one side of the equation. We can start by simplifying the equation by combining like terms. To do this, we can add 21p to both sides of the equation, which gives us:
-16p + 37 + 21p = 49
Next, we can combine the terms -16p and 21p, which gives us 5p. So, the equation becomes:
5p + 37 = 49
We can further simplify the equation by subtracting 37 from both sides, which gives us:
5p = 12
Finally, we can solve for p by dividing both sides of the equation by 5:
p = 12/5
So, the solution to the equation -16p + 37 = 49 - 21p is p = 12/5.
In summary, the given equation is a simple linear equation that can be solved using algebraic techniques. We can isolate the variable, p, on one side of the equation by combining like terms and simplifying the equation. Finally, we can solve for p by dividing both sides of the equation by the coefficient of p.
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Schools have different ways of fund raising. The parents and the SGB of Progress High School agree that each learner should donate an amount to the school. The money is payable during the first month of the year. 1.1 Use TABLE 1 to answer the questions that follow. Write down the donation per leamer. 1.2 TABLE 1: INCOME IN RANDS OF FUND RAISING Number of learners that paid Income (R) 1 200 1.3 1.5 Calculate the missing value A. 10 2 000 20 45 215 4 000 9 000 A [Adapted from original school financial books ] Use TABLE 1 and write down the dependent variable. 1.4 Write the income received from 10 leamers to the income received from 45 learners, in a ratio in its simplest form. (3) (2) (2) (2) have The SGB chairperson claims that if 80% of the leamers paid, the school would raised more than R170 000. There are 1 100 learners enrolled at the school. Verify, by showing ALL calculations, whether his statement is valid. (4)
Answer: 1.1. The donation per learner cannot be determined from the given table.
1.2. TABLE 1: INCOME IN RANDS OF FUNDRAISING
Number of learners that paid Income (R)
1 200
1.3. To calculate the missing value A, we need to add up all the given incomes and subtract it from the total income for 45 learners, which is 45 x A. Then we can solve for A:
Total income = 200 + 150 + 10(2,000) + 20(45) + A + 4,000 + 9,000
Total income = 45A
45A = 25,150
A = 558.89
Therefore, the missing value A is R558.89.
1.4. The dependent variable in the table is the income received from fundraising.
To find the ratio of income received from 10 learners to income received from 45 learners, we need to divide the income received from 10 learners by the income received from 45 learners and simplify the fraction:
Income from 10 learners = R1,100 (since each learner donates R110)
Income from 45 learners = R215
Ratio = Income from 10 learners : Income from 45 learners
= 1,100 : 215
= 20 : 3 (in its simplest form)
The total number of learners enrolled at the school is 1,100. If 80% of the learners paid, then the number of learners who paid is:
80% of 1,100 = 0.8 x 1,100 = 880 learners
The minimum income that the school can raise if 80% of the learners paid is when each of the 880 learners paid the minimum donation, which is R150:
Minimum income = 880 x 150 = R132,000
Since R132,000 is less than R170,000, the SGB chairperson's statement is not valid.
Step-by-step explanation:
Can someone help me with this
Answer:
corn dogs: $1.25fries: $3.50Step-by-step explanation:
You want to know the cost of corn dogs and the cost of chili-cheese fries when 2 dogs and 3 fries cost $13, while 4 dogs and 1 fries cost $8.50.
SetupThe cost of each purchase can be represented by the equations ...
2d +3f = 134d +f = 8.50SolutionSubtracting the second equation from twice the first gives ...
2(2d +3f) -(4d +f) = 2(13) -(8.50)
5f = 17.50 . . . . . . simplify
f = 3.50 . . . . . . . divide by 5
4d = 8.50 -f = 5.00 . . . . use the second equation to find d
d = 1.25 . . . . . . divide by 4
Corn dogs cost $1.25; chili-cheese fries cost $3.50.
__
Additional comments
Many calculators provide a number of methods of solving systems of equations. The use of an augmented matrix of the equation coefficients is perhaps one of the simplest.
The second equation is a good choice for writing an expression for f in terms of d: f = 8.50 -4d. This expression can be substituted into the first equation if you want to solve the system by substitution, rather than elimination. Making that substitution gives 2d +3(8.50 -4d) = 13, and that simplifies to -10d = -12.50 after subtracting 25.50 from both sides.
How does the volume of a square pyramid change if the base edge is multiplied by 6?
[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Lwh}{3} ~~ \begin{cases} L=\stackrel{base's}{length}\\ w=\stackrel{base's}{width}\\ h=height\\[-0.5em] \hrulefill\\ L=6L\\ w=6w \end{cases}\implies V=\cfrac{(6L)(6w)h}{3}\implies \stackrel{ \textit{36 times the volume} }{V=\cfrac{Lwh}{3}(36)}[/tex]
A landscaper needs to mix a 80% pesticide solution with 35 gal of a 30% pesticide solution to obtain a 55% pesticide solution. How many gallons of the 80%
solution must he use?
By answering the question the answer is Therefore, landscapers should equation use 35 gallons of an 80% pesticide solution.
What is equation?In mathematics, an equation is a statement that two expressions are equal. The equation consists of her two sides divided by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of solving an equation is to find the values of the variables to make the equation true. Simple or complex equations, regular or nonlinear, and equations involving one or more factors are all possible. For example, the expression "[tex]x2 + 2x - 3 = 0\\[/tex]" squares the variable x. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
Let's say a landscaper needs to use x gallons of an 80% pesticide solution.
The amount of pesticide for an 80% solution is 0.8 x gallons and the amount of pesticide for a 30% solution is 0.3 (35) = 10.5 gallons.
After mixing the two solutions, the total amount of pesticides in the mixture is 0.8 x + 10.5 gallons and the total volume of the mixture is x + 35 gallons.
Since we need a 55% pesticide solution, we can set the following formula:
[tex]0.8x10.5 0.55(x+35)0.8x10.5 0.55x+19.250.25x = 8.75x = 35[/tex]
Therefore, landscapers should use 35 gallons of an 80% pesticide solution.
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If the angles of a pentagon are xº, x°, 2xº, (2x +
40), (2x+10)º, find the value of the biggest
angle
Answer:
285°
Step-by-step explanation:
x + x + 2x + 2x + 40 + 2x + 10 = (5 - 2)180
8x + 50 = 540
8x = 490
x = 61.25
2x + 40 = 2(61.25) + 40 = 285
Answer:
Step-by-step explanation:
Interior angles in a pentagon equal 540°.
Simplify
x°,x°,2x°, (2x+40) and (2x+10) = 8x+50
Calculate x
8x + 50 = 540
8x = 540 - 50 = 490
x = 490/8
x = 61.25°
Calculate largest angle
2x + 40, where x = 61.25°
=162.5°
Use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. r = 7 cos(20), [0, Phi/4]
The approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis is 67.59 square units.
To solve the question, we can use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. Polar curve is a type of curve that is made up of points that represent polar coordinates (r, θ) instead of Cartesian coordinates.
A polar curve can be represented in parametric form, but it is often more convenient to use the polar equation for a curve. According to the question, r = 7 cos(20), [0, Phi/4] is the polar equation and we need to find the approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis.
To solve the problem, follow these steps: Convert the polar equation to a rectangular equation. The polar equation r = 7 cos(20) is converted to a rectangular equation using the following formulas: x = r cos θ, y = r sin θx = 7 cos (20°) cos θ, y = 7 cos (20°) sin θx = 7 cos (θ - 20°) cos 20°, y = 7 cos (θ - 20°) sin 20°
Sketch the curve in the plane. We can sketch the curve of r = 7 cos(20) by plotting the points (r, θ) and then drawing the curve through these points. Use the polar equation to set up the integral for the volume of the solid of revolution.
The volume of the solid of revolution is given by the formula: V = ∫a b πf2(x) dx where f(x) = r, a = 0, and b = Φ/4.We can find the volume of the solid of revolution using the polar equation: r = 7 cos(20) => r2 = 49 cos2(20) => x2 + y2 = 49 cos2(20)Thus, f(x) = √(49 cos2(20) - x2) = 7 cos(20°) sin(θ - 20°)
So, V = ∫a b πf2(x) dx = ∫0 Φ/4 π(7 cos(20°) sin(θ - 20°))2 dθStep 4: Use a graphing utility to evaluate the integral to two decimal places. Using a graphing utility to evaluate the integral, we get V ≈ 67.59.
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A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze, and the second brand is 60% pure antifreeze. In order to obtain 110 gallons of a mixture that contains 55% pure antifreeze, how many gallons of each brand of antifreeze must be used?
22 gallons of the first brand (35% pure antifreeze) and 88 gallons of the second brand (60% pure antifreeze) to make 110 gallons of a mixture that contains 55% pure antifreeze.
Let x be the number of gallons of the first brand (35% pure antifreeze) needed, and y be the number of gallons of the second brand (60% pure antifreeze) needed to make the desired mixture.
We know that the total volume of the mixture is 110 gallons and the desired concentration of antifreeze is 55%.
We can set up two equations based on the amount of antifreeze and the total volume of the mixture:
0.35x + 0.6y = 0.55(110) (amount of antifreeze)
x + y = 110 (total volume)
Simplifying the first equation, we get:
0.35x + 0.6y = 60.5
Now we can use substitution or elimination to solve for x and y. Here's one way to use substitution method
x + y = 110 (equation 1)
x = 110 - y (solve for x)
0.35x + 0.6y = 60.5 (equation 2, substitute x)
0.35(110 - y) + 0.6y = 60.5 (substitute x into equation 2)
38.5 - 0.35y + 0.6y = 60.5 (distribute 0.35)
0.25y = 22 (combine like terms)
y = 88 (divide both sides by 0.25)
So we need 88 gallons of the second brand (60% pure antifreeze). To find the amount of the first brand (35% pure antifreeze), we can substitute y back into equation 1:
x + y = 110
x + 88 = 110
x = 22 gallons
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Enter the correct answer in the box.
Write this expression in simplest form.
Don’t include any spaces or multiplication symbols between coefficients or variables in your answer.
16h^(10/2) *remove the root sign
16h^5 *simplify the exponent
Answer: 16h^5
Step-by-step explanation: im correct
Simplify (cos^2a - cot^2a)/(sin^2a - tan^2a)
Answer:
The simplified expression is sec^2a
Step-by-step explanation:
We can start by using the trigonometric identities:
cot^2 a + 1 = csc^2 a
tan^2 a + 1 = sec^2 a
Using these identities, we can rewrite the expression as:
(cos^2 a - cot^2 a)/(sin^2 a - tan^2 a)
= (cos^2 a - (csc^2 a - 1))/(sin^2 a - (sec^2 a - 1))
= (cos^2 a - csc^2 a + 1)/(sin^2 a - sec^2 a + 1)
Now we can use the identity:
sin^2 a + cos^2 a = 1
to rewrite the expression further:
= (1/sin^2 a - 1/sin^2 a cos^2 a)/(1/cos^2 a - 1/cos^2 a sin^2 a)
= (1 - cos^2 a)/(sin^2 a - sin^2 a cos^2 a)
= sin^2 a / sin^2 a (1 - cos^2 a)
= 1 / (1 - cos^2 a)
= sec^2 a
Therefore, the simplified expression is sec^2 a.
Radioactive decay tends to follow an exponential distribution; the half-life of an isotope is the time by which there is a 50% probability that decay has occurred. Cobalt-60 has a half-life of 5.27 years. (a) What is the mean time to decay? (b) What is the standard deviation of the decay time? (c) What is the 99th percentile? (d) You are conducting an experiment which first involves obtaining a single cobalt-60 atom, then observing it over time until it decays. You then obtain a second cobalt-60 atom, and observe it until it decays; and then repeat this a third time. What is the mean and standard deviation of the total time the experiment will last?
The exponential distribution is a probability distribution that models the time between events in a Poisson process, where events occur randomly and independently at a constant average rate.
It is commonly used in reliability theory, queuing theory, and other fields to model the failure or waiting times of systems.
(a) The mean time to decay for Cobalt-60 is 5.27 years.
(b) The standard deviation of the decay time is 2.6355 years.
(c) The 99th percentile is 13.6825 years.
(d) The mean time of the experiment is 15.8175 years and the standard deviation is 4.86788 years.
Note: The answers are calculated based on the exponential distribution of radioactive decay with a half-life of 5.27 years for Cobalt-60.
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James have 18 litres of water. He poured unequally into 3 tank
I. Poured three quarter of water from tank one into tank 2
II. Poured half of the water that is now in tank 2 into tank 3
III. Poured one third of water that is now in tank 3 into tank 1
Find how much water is in each tanks
Answer:
ames have 18 litres of water. He poured unequally into 3 tank
I. Poured three quarter of water from tank one into tank 2
II. Poured half of the water that is now in tank 2 into tank 3
III. Poured one third of water that is now in tank 3 into tank 1
Find how much water is in each tanks
Step-by-step explanation:
Let's start with the amount of water in tank 1 as x liters.
I. Poured three quarter of water from tank one into tank 2, so tank 1 now has 1/4 of x liters and tank 2 has 3/4 of x liters.
II. Poured half of the water that is now in tank 2 into tank 3, so tank 2 now has 3/8 of x liters and tank 3 has 3/8 of x liters.
III. Poured one third of water that is now in tank 3 into tank 1, so tank 3 now has 1/3 * 3/8 * x = 1/8 * x liters and tank 1 has 1/4 * x + 1/8 * x = 3/8 * x liters.
We know that James poured 18 liters of water into the three tanks, so the sum of the water in the three tanks must be 18 liters.
3/8 * x + 3/8 * x + 1/8 * x = 18
Simplifying the equation, we get:
7/8 * x = 18
x = 18 * 8 / 7 = 20.57 (rounded to two decimal places)
Therefore, the amount of water in each tank is:
Tank 1: 3/8 * x = 7.71 liters
Tank 2: 3/8 * x = 7.71 liters
Tank 3: 1/8 * x = 2.57 liters
Using the discriminant, how many real solutions does the following quadratic equation have? x^2 +8x+c= 0
The equation has two distinct real roots if 64 - 4c > 0, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.
The discriminant of a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex] is given by [tex]b^2 - 4ac[/tex]. In the given quadratic equation, a = 1, b = 8, and c = c. Therefore, the discriminant is:
[tex]b^2 - 4ac[/tex]
[tex]= 8^2 - 4(1)(c)[/tex]
[tex]= 64 - 4c[/tex]
Now, we can use the discriminant to determine the nature of the solutions of the quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has one real root (a double root). If the discriminant is negative, the equation has no real roots (two complex conjugate roots).
In this case, we do not have enough information about the value of c to determine the nature of the roots of the equation. All we know is that the discriminant is 64 - 4c.
Hence, if 64 - 4c > 0, we can state that the equation has two separate real roots, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.
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a credit risk study found that an individual with good credit score has an average debt of $15,000. if the debt of an individual with good credit score is normally distributed with standard deviation $3,000, determine the shortest interval that contains 95% of the debt values.
The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98
How do we calculate the interval values?Given that a credit risk study found that an individual with good credit score has an average debt of $15,000 and the debt of an individual with good credit score is normally distributed with standard deviation $3,000.
Then the 95% confidence interval can be calculated as follows:
Upper limit: µ + Zσ
Lower limit: µ - Zσ
Where
µ is the mean ($15,000)Z is the z-scoreσ is the standard deviation ($3,000).The z-score corresponding to a 95% confidence interval can be found using the standard normal distribution table.
The area to the left of the z-score is 0.4750 and the area to the right is also 0.4750.
The z-score corresponding to 0.4750 can be found using the standard normal distribution table as follows:z = 1.96Therefore
Upper limit: µ + Zσ= $15,000 + 1.96($3,000) = $20,880
Lower limit: µ - Zσ= $15,000 - 1.96($3,000) = $9,120.02
The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98.
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8hr/2days=28hr/?days
a system of equations is shown below. y=2x+1 and y=x+2 what is the solution to the system? A. (0,1) B. (1,2) C. (1,3) D. (2,4)
Answer:
(1,3)
Step-by-step explanation:
Given system of equations is :-
y = 2x + 1y = x + 2We can solve this by using substitution method by substituting the value of y from equation (1) into equation (2) as ,
2x + 1 = x + 2
Subtract x on both sides,
2x - x + 1 = 2
Simplify,
x = 2 - 1
x = 1
Substitute this value of x into equation (2) as ,
y = 1 + 2
y = 1 + 2
y = 3
Hence the required answer is (1,3) .
and we are done!
(13-12p) × (13+12p)
...
Answer:
169 - 144p²
Step-by-step explanation:
(13 - 12p) × (13 + 12p)
each term in the second factor is multiplied by each term in the first factor
13(13 + 12p) - 12p(13 + 12p) ← distribute parenthesis
= 169 + 156p - 156p - 144p² ← collect like terms
= 169 - 144p²
A circular flower garden has an area of 314m². A sprinkler at the center of the garden can cover an area of 12 m. Will the sprinkler water the entire garden?
Step-by-step explanation:
No,
if the sprinkler covers a distance of 12 m meaning the 12 m is the diameter...then to find the area that it covers we use the formula for the circle since it's circular
A=πr2
A=3.142*36
A=113.112 cm3
Find the missing angle. Round your
answer to the nearest tenth.
tº
11 mi
5 mi
Answer:
24.4 degrees
Step-by-step explanation:
This is a right triangle so you can use trig to solve. If you take the arctan of 5/11 you get 24.4(rounded to the nearest tenth)
successful firms must focus on the quality of the products and services they offer. which of the following factors does not contribute to the quest for quality?
a. Global competition
b. Consumer expectations
c. Technological advances
d. All the answer choices are correct
Among the given factors, global competition does not contribute to the quest for quality. The correct answer is Option A.
Why does a successful firm need to focus on quality?In today's business environment, quality has become an important factor that can make or break a company's success. A successful firm must focus on the quality of the products and services they offer, as this can help them maintain their competitive advantage and ensure customer loyalty.
Quality is important for a variety of reasons, including customer satisfaction, reduced costs, increased productivity, and increased revenue. When firms focus on quality, they can provide better products and services to their customers, which can lead to increased customer loyalty and repeat business. This can help firms build a strong reputation in the market and maintain a competitive advantage.
How does global competition contribute to the quest for quality?Global competition has made it necessary for firms to focus on quality to maintain their competitive advantage. When firms face global competition, they need to ensure that their products and services are of high quality to compete effectively in the global market. High-quality products and services can help firms differentiate themselves from their competitors and gain a competitive advantage. This can help firms increase their market share and revenue.
What are the factors that contribute to the quest for quality?Several factors contribute to the quest for quality. These include:
Consumer expectations: Customers have high expectations when it comes to quality. They expect products and services to be of high quality, and they are willing to pay a premium for quality.Technological advances: Technological advances have made it possible for firms to produce high-quality products and services. Firms can use technology to automate production processes, improve quality control, and reduce defects.Global competition: Global competition has made it necessary for firms to focus on quality to maintain their competitive advantage.Regulations: Regulations require firms to meet certain quality standards. Firms that fail to meet these standards can face legal action and damage to their reputation.Learn more about Global competition here: https://brainly.com/question/29479819
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Select all of the reasons that the range is an appropriate measure of variability to describe the variation in the hours slept by eighth graders.
A double box plot showing hours sleeping. For seventh graders, the left whisker is at 7.5, the left edge of the box is at eight, the line inside the box is at 8.5, the right edge of the box is at nine, and the right whisker is at 9.5. For eighth graders, the left whisker is at seven, the left end of the box is at 7.5, the line inside the box is at eight, the right end of the box is at 8.5, and the right whisker is at nine. Screen reader support enabled.
All of the reasons that the range is an appropriate measure of variability to describe the variation in the hours slept by eighth graders include the following:
A. The data are evenly distributed between 7 hours and 9 hours.
D. There is no outlier in the data.
What is a range?In Mathematics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.
Mathematically, the range of a data set can be calculated by using the following mathematical equation;
Range = Highest number - Lowest number
By critically observing the double box-and-whisker plots or box plot for the variation in the hours slept by eighth graders, we can logically deduce that there is no outlier in the data because they are evenly distributed and centered about the mean.
In conclusion, the box-and-whisker plot or box plot is symmetrical.
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Answer:
Step-by-step explanation:
Yeah what the other guy said
if the area of the quadrilateral ABCS is 924cm^2 and the length of the diagonal AC is 33cm,find the sum of lengths of the perpendicular from points B and D to AC.
please answer with full steps asap
3BE² + 3DF²- (2AC²- AB) is the answer of the following question
The calculation is as follows
Let E and F be the feet of the perpendiculars from B and D, respectively, to AC. We can use the fact that the area of a quadrilateral is equal to half the product of the diagonals multiplied by the sine of the angle between them to find the length of the diagonal BD.
Since ABCS is a quadrilateral, we have:
Area of ABCS = (1/2) * AC * BD * sin(angle between AC and BD)
Substituting the given values, we get:
924 = (1/2) * 33 * BD * sin(angle between AC and BD)
sin(angle between AC and BD) = 924 / (16.5 * BD)
Now, consider triangles ABC and ACD. Using the Pythagorean theorem, we can write:
AB² + BC² = AC² (1)
CD²+ BC² = AC² (2)
Adding equations (1) and (2), we get:
AB² + 2BC²+ CD²= 2AC²
Substituting AC = 33 and rearranging, we get:
BC² = (2AC²- AB² - CD²) / 2
We can also write:
BE²= AB²- AE² (3)
DF² = CD²- CF²(4)
Adding equations (3) and (4), we get:
BE² + DF²= AB²+ CD² - AE²- CF²
Substituting BC²from earlier, we get:
BE²+ DF² = 2AC² - BC²- AE²- CF²
We want to find BE + DF. Squaring both sides of equation (3), we get:
BE²= AB² - AE²
AE²= AB²- BE²
Similarly, squaring both sides of equation (4), we get:
DF²= CD²- CF²
CF²= CD² - DF²
Substituting these expressions into the equation for BE²+ DF², we get:
BE²+ DF² = 2AC² - BC² - (AB² - BE²) - (CD²- DF²)
Simplifying, we get:
BE² + DF²= 2AC² - BC²- AB²- CD² + 2BE² + 2DF²
Collecting like terms, we get:
BE²+ DF²- 2BE² - 2DF²= 2AC²- BC² - AB² - CD²
Simplifying, we get:
BE²- DF² = 2AC²- BC²- AB²- CD²- 2BE² - 2DF²
Substituting the values we know, we get:
BE²- DF²= 2(33)²- BC²- AB² - CD²- 2BE²- 2DF²
Rearranging, we get:
3BE²+ 3DF² - BC²- AB²- CD²= 2(33)² - 924
Substituting BC^2 from earlier, we get:
3BE²+ 3DF² - (2AC²- AB)
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can you give me the answer to this question sin y minus cos (y + 20), sin theta minus cos theta equals to 0 cos theta equals to sin theta - 10
Answer:
can you give me the answer to this question sin y minus cos (y + 20), sin theta minus cos theta equals to 0 cos theta equals to sin theta - 10
Step-by-step explanation:
To solve sin y - cos (y + 20) = 0, we can rearrange it as sin y = cos (y + 20).
Then, we can use the identity sin (90 - x) = cos x to rewrite the right side as cos (y + 20) = sin (70 - y).
Substituting this into the equation, we get sin y = sin (70 - y).
Now, there are two possibilities:
y = 70 - y, which gives y = 35 degrees.
y = 180 - (70 - y), which gives y = 105 degrees.
To solve cos theta = sin theta - 10, we can rearrange it as cos theta - sin theta = -10 and then use the identity cos (x - 90) = sin x to rewrite it as -sin (theta - 90) = -10.
Taking the inverse sine of both
the set of all continuous real-valued functions defined on a closed interval (a, b] in ir is denoted by c[a , b]. this set is a subspace of the vector space of all real-val ued functions defined on [a, b]. a. what facts about continuous functions should be proved in order to demonstrate that c [a , b] is indeed a subspace as claimed? (these facts are usually discussed in a calculus class.) b. show that {fin c[a ,b]: f(a )
Let f be a continuous function in c[a, b] such that f(a) = 200. Then for all real numbers c, the scalar multiple cf is also a continuous function in c[a, b]. Specifically, cf(a) = c(200) = 200c.
To demonstrate that c[a, b] is a subspace, the following facts must be proved:
1. If f and g are both continuous functions in c[a, b], then the sum f + g is also a continuous function in c[a, b].
2. If f is a continuous function in c[a, b], then the scalar multiple cf is also a continuous function in c[a, b], where c is a real number.
3. The zero vector of c[a, b] is the constant zero function.
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A random experiment can result in one of the outcomes {a,b,€,d} with probabilities P({a}) = 0.4, P({b}) = 0.1, P({c}) = 0.3, and P({d}) 0.2. Let A denote the event {a,b}, B the event {b,c,d}, and the event {d} From the previous information , P(A UBUC)= QUESTION 31 A random experiment can result in one of the outcomes {a,b,€,d} with probabilities P({a}) = 0.4, P({b}) = 0.1, P({c}) = 0.3, and P({d}) 0.2. Let A denote the event {a,b}, B the event {b,c,d}, and C the event {d} From the previous information , P(Anenc)=
The data we get from the question is a random experiment can result in one of the outcomes {a,b,c,d} with probabilities from that information, P(A U B U C) = 0.8.
The given probabilities of events and outcomes are:
P({a}) = 0.4,P({b}) = 0.1,P({c}) = 0.3,P({d}) 0.2
So the given events are:
A = {a,b},B = {b,c,d},C = {d}
We have to find P(A U B U C) Using the formula of the probability of the union of two events,
we get:
P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
Now we will find the values of all probabilities:
P(A) = P({a}) + P({b})
= 0.4 + 0.1
= 0.5
P(B) = P({b}) + P({c}) + P({d})
= 0.1 + 0.3 + 0.2
= 0.6
P(C) = P({d})
= 0.2
P(A ∩ B) = P({b})
= 0.1
P(A ∩ C) = P({d})
= 0.2
P(B ∩ C) = P({d})
= 0.2
P(A ∩ B ∩ C) = 0
(No common event) Put all the above values in the formula:
P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) +
P(A ∩ B ∩ C)
= 0.5 + 0.6 + 0.2 - 0.1 - 0.2 - 0.2 + 0
= 0.8
Therefore, P(A U B U C) = 0.8 is the required probability.
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 choose all the shapes with at least one pair of perpendicular sides
According to the image, we can infer that the shapes which have at least 1 pair of perpendicular sides are the top leftmost trapezium and the bottom-center rectangle.
What is the definition of perpendicular sides?Perpendicular sides is a term to refer to a shape with a special characteristic. These shapes have two sides connected through an angle or vertex of 90°. So, to select the correct shapes we have to take into account this feature. According to the above, the correct shapes would be:
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Write the line equation of (5,-12) and (0,-2)
Answer:
To find the equation of the line passing through the points (5,-12) and (0,-2), we first need to find the slope of the line:
slope = (change in y) / (change in x)
slope = (-2 - (-12)) / (0 - 5)
slope = 10 / (-5)
slope = -2
Now that we have the slope, we can use the point-slope form of the line equation to find the equation of the line:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is one of the given points on the line.
Let's use the point (5,-12):
y - (-12) = -2(x - 5)
y + 12 = -2x + 10
y = -2x - 2
Therefore, the equation of the line passing through the points (5,-12) and (0,-2) is y = -2x - 2.
Arrange the steps in the correct order to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm.
a = 55, m = 89
An inverse of a modulo m for a = 55, m = 89 using the Euclidean algorithm is 34.
In order to find an inverse of a modulo for each of the following pairs of relatively prime integers using the Euclidean algorithm can be found by:
Using the Euclidean algorithm to find the greatest common divisor (gcd) of a and m. In this case, we have:
89 = 1 x 55 + 34
The gcd of 55 and 89 is 1.
Using the extended Euclidean algorithm, work backwards up the chain of remainders to express 1 as a linear combination of a and m. In this case, we have: 34 x 55 - 21 x 89
The coefficient of a in the expression from step 3 is the inverse of a modulo m. In this case, the inverse of 55 modulo 89 is 34.
To verify that the inverse is correct, multiply a and its inverse modulo m. The product should be congruent to 1 modulo m. In this case, we have:
55 x 34 = 1870
11 = 1 x 11 + 0
Since the remainder is 0, we know that 55 x 34 is a multiple of 89, so it is congruent to 0 modulo 89. Therefore, we have:
55 x 34 ≡ 0 |89|
Adding 89 to the left-hand side repeatedly until we get a number that is congruent to 1 modulo 89, we find:
55 x 34 ≡ 0 + 89 x 7 ≡ 1 |89|
Therefore, the inverse of 55 modulo 89 is indeed 34.
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are these equivalent
10-2x -2x10
Isosceles Trapezoids: Only one pair of opposite sides are _______
Answer:
equal
Step-by-step explanation:
To make a fruit smoothie, Olivia uses 4 blueberries, 3 strawberries, 1 banana, 5 orange slices, and 2 slices of mango. What is the ratio of blueberries to banana?
Thus, the ratio for the number of blueberries to banana is 4:1.
Define about the ratios of the numbers?A ratio in mathematics is a correlation of at least two numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or integer that is dividing is referred to as the consequent.
A ratio compares two numbers by division. Comparing one quantity to the total, for example the dogs that belong to all the animals in the clinic, is known as a part-to-whole analysis. These kinds of ratios occur considerably more frequently than you might imagine.
The given data for preparing fruit smoothie:
4 blueberries, 3 strawberries, 1 banana, 5 orange slices, and 2 slices of mango.
Then,
ratio of blueberries to banana:
blueberries/banana = 4/1
Thus, the ratio for the number of blueberries to banana is 4:1.
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