Option A is the correct option for determining the total number of possible outcomes when selecting a day of the week and a month of the year, which is 84.
To find the total number of outcomes for picking a day of the week and a month of the year, you need to multiply the number of options for each category. There are 7 days in a week, so there are 7 options for picking a day. There are 12 months in a year, so there are 12 options for picking a month. To find the total number of outcomes, you multiply the number of options for each category: 7 x 12 = 84. Therefore, the total number of outcomes for picking a day of the week and a month of the year is 84. Option A is the correct answer.
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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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A triangle has one side with length 9 and another side with length 6. The angle opposite the side of length 6 measures 40. what is the measure of the angle opposite the side of length 9?
Answer: the angle opposite the side length 9 is 74.62 degrees I think .
Step-by-step explanation:
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]
HURRY PLS
From midnight to 8:00 am, the temperature rose 1. 51. 5°C each hour. If the temperature at midnight was -3−3°C, what was the temperature at 8:00 am?
the temperature at 8:00 am is 9°C This means that every hour from midnight to 8:00 am, the temperature increased by 1.5°C, resulting in a total increase of 12°C over the 8 hour period.
To solve this problem, we need to use the formula for calculating the final temperature based on the initial temperature and the rate of change per hour.
The formula for this is:
Final Temperature = Initial Temperature + (Rate of Change per Hour x Number of Hours)
In this case, the initial temperature is -3°C, the rate of change per hour is 1.5°C, and the number of hours is 8.
Plugging these values into the formula, we get:
Final Temperature = -3 + (1.5 x 8)
Final Temperature = -3 + 12
Final Temperature = 9°C
Therefore, the temperature at 8:00 am is 9°C.
This means that every hour from midnight to 8:00 am, the temperature increased by 1.5°C, resulting in a total increase of 12°C over the 8 hour period.
It's important to note that this problem assumes that the rate of change per hour remains constant throughout the 8 hour period. In reality, the temperature may fluctuate based on various factors, such as wind, cloud cover, and humidity. However, for the purposes of this problem, we can assume that the rate of change per hour remains constant.
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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.
(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
Stephanie puts thirty cubes in a box. The cubes are 1\2 inches on each side. The box holds 2 layers with 15 cubes in each layer. What is the volume of the box?
If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.
To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.
Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:
30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches
The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.
The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.
Now, we can calculate the volume of the box by multiplying its length, width, and height:
Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.
In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.
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50 POINTS
A bathroom heater uses 10.5 A of current when connected to a 120. V potential difference. How much power does this heater dissipate?
Remember to identify all data (givens and unknowns), list equations used, show all your work, and include units and the proper number of significant digits to receive full credit
The power dissipated by the heater is 1260 watts (W).
What is a polynomial?
A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.
Given:
Current (I) = 10.5 A
Potential Difference (V) = 120 V
Unknown:
Power (P) = ?
The formula to calculate the power is:
P = VI
Substituting the given values:
P = 120 V × 10.5 A
P = 1260 W
It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:
P = 1260 W (rounded to three significant digits).
Therefore, the power dissipated by the heater is 1260 watts (W).
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the chance of a blizzard tommorrow is 5%. write the complement of this event
Answer:
the chance of a blizzard tommorrow is 5%. write the complement of this event
Step-by-step explanation:
The complement of an event is the event that it does not happen, so the complement of a blizzard occurring tomorrow with a 5% chance is that a blizzard does not occur tomorrow with a probability of:
100% - 5% = 95%
Therefore, the complement event is that there is a 95% chance that a blizzard does not occur tomorrow.
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:
Isosceles Trapezoids: Only one pair of opposite sides are _______
Answer:
equal
Step-by-step explanation:
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)
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
5. {MCC.6.RP.A.3B} How long will it take you to ski a distance of 24 miles at a speed of 6 miles per 30 minutes?
*
1 point
Answer:
Step-by-step explanation:
It will take you 8 hours to ski a distance of 24 miles at a speed of 6 miles per 30 minutes. This is because you will have to travel the 24 miles at a rate of 6 miles every 30 minutes, so you will need to travel for 4 hours at this rate to cover the full distance. Thus, it will take you 8 hours to ski the full 24 miles at a rate of 6 miles per 30 minutes.
Answer:
120 minutes / 2 hours
Step-by-step explanation:
time = distance / velocity
[tex]time = \frac{24}{(6/30)} \\time = 120 minutes[/tex]
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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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
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°
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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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 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!
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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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
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
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 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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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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are these equivalent
10-2x -2x10
if (20x+10) and (10x+50) are altenative interior angle then find x
Answer:
x = 4
Step-by-step explanation:
Alternative interior angles means these angles are equal in magnitude and sign
[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]
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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