4j-2/2=4j+5
4j minus 2 divided by 2 equals 4j plus 5 ?
The solution to the equation (4j - 2) / 2 = 4j + 5 is j = -3. The equation was simplified by eliminating fractions and isolating the variable j through algebraic steps.
To solve the equation (4j - 2) / 2 = 4j + 5 for the variable j, you can follow these steps:
1. First, simplify both sides of the equation:
(4j - 2) / 2 = 4j + 5
2. Multiply both sides of the equation by 2 to eliminate the fraction:
4j - 2 = 2 * (4j + 5)
3. Distribute the 2 on the right side:
4j - 2 = 8j + 10
4. Move the variable terms to one side of the equation and the constants to the other side. You can do this by subtracting 8j from both sides:
4j - 8j - 2 = 10
5. Combine like terms:
-4j - 2 = 10
6. Add 2 to both sides to isolate the variable term:
-4j = 10 + 2
-4j = 12
7. Finally, divide both sides by -4 to solve for j:
j = 12 / -4
j = -3
So, the solution to the equation is j = -3.
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Find f '(0.3) for f of x equals the integral from 0 to x of the arccosine of t, dt
By the fundamental theorem of calculus,
[tex]\displaystyle\frac{\mathrm d}{\mathrm dx}\int_0^x\cos^{-1}t\,\mathrm dt=\cos^{-1}x[/tex]
so that
[tex]f'(0.3)=\cos^{-1}0.3\approx1.266[/tex]
A stop sign is a regular octagon. Each side of the sign is 12.6 in. long. The area of the stop sign is 770 in.^2. What is the length of the apothem to the nearest whole number?
Final answer:
To determine the length of the apothem of a regular octagonal stop sign given its side length and area, use the formula for the area of a regular polygon, solve for the apothem, and then calculate it to be approximately 15 inches when rounded to the nearest whole number.
Explanation:
The student is asking how to find the length of the apothem of a regular octagonal stop sign with side lengths of 12.6 inches and a total area of 770 square inches. The apothem of a regular polygon is a line from the center to the midpoint of one of its sides and is also the radius of the inscribed circle within the polygon.
To find the apothem's length, we can use the formula for the area of a regular polygon: Area = (1/2) × Perimeter × Apothem. The perimeter (P) of the octagon is the length of one side multiplied by 8 (since an octagon has eight sides). Therefore, the perimeter is 12.6 in × 8 = 100.8 in.
We can rearrange the area formula to solve for the apothem (a): Area = (1/2) × P × a becomes a = Area × 2 / P. Substituting the known values, we get: a = 770 in² × 2 / 100.8 in, which calculates to an apothem length of approximately 15.24 inches. Round this to the nearest whole number to get an apothem length of 15 inches.
A biologist studied the populations of common guppies and Endler's guppies over a 6-year period. the biologist modeled the populations, in tens of thousands, with the following polynomials where x is time, in years.
common guppies: 3.1x^2+6x+0.3
Endler's guppies: 4.2x^2-5.2x+1
what polynomial models the total number of common and Endler's guppies
what polynomial models the total number of common and Endler's guppies
your answer will be:
7.3x^2+0.8+1.3
Step-by-step explanation:
this answer correct for 2022
A certain lottery has 3434 numbers. in how many different ways can 44 of the numbers beâ selected? (assume that order of selection is notâ important.)
Suppose p(x1) = .75 and p(y2 | x1) = .40. what is the joint probability of x1 and y2?
The joint probability of x1 and y2 is P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.
What is the probability about?In the joint probability of x1 and y2 is P (Y₂/X₁ )= P(Y₂ ∩ X₁ )/ P (X₁).
Therefore:
P(Y₂ ∩ X₁ )
=0.40 x 0.75
= 0.3
Therefore by following the law of conditional probability, the outcome of the The joint probability of x1 and y2 is P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.
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The mean of people in the sample of households of 7th-grade students is 4.3. The mean of people in the sample of households for 8th-grade students is 4.5. What might Principal Coleman infer or predict about the entire population based on the data?
Answer:
The mean of something is the "average"
For example, if the mean of people in the households of 7th-grade students is 4.3, this means that if you go to a random house of a 7th-grade student, you can expect around 4 people in there.
Now, for the 7th-grade students, the mean is 4.5, just a 0.2 bigger. (This means that, on average, there is more people in the 8th-grade student's households)
So Principal Coleman can infer that the amount of people in the households of 7th-grade students and 8th-grade students is almost the same, wherein the 8th-grade students there is a small chance of finding more people, but this difference is almost depreciable.
what is the gcf of the numerator and denominator of the rational expression
3x-15/x^2-x-20
A: x-5
B: x+4
C: 4
D: 5
Use the distributive property to create an equivalent expression to 42+6x
The expression 42 + 6x is already in its simplest form and does not have a common factor to apply the distributive property to simplify it. However, factoring out 6 would rewrite it as 6(7 + x), albeit without further simplification.
To create an equivalent expression to 42 + 6x using the distributive property, we need to factor out a common term from both parts of the expression. However, this expression does not have a common factor available in both terms. The distributive property typically comes into play when you have an expression in the form of a(b + c), where you would then distribute a to both b and c. The expression 42 + 6x is simplified as much as possible, given that one term is a constant and one term is a multiple of a variable. There is no factor that can be distributed to simplify the expression further.
However, if we wanted to factor out a number to potentially simplify the expression, we might choose to factor out 6, which would change the expression to 6(7 + x), although this does not simplify it further since the original expression is already in its simplest form.
glenn raced his motorcycle 30 times last season. he finished first 12 times, second 5 times and crashed in 9 races. what percent of races did he crash? set up a proportion and solve.
Final answer:
Glenn crashed in 30% of the races.
Explanation:
To find the percentage of races Glenn crashed, you can set up a proportion. A proportion is an equation that states that two ratios are equivalent. Since Glenn raced 30 times and crashed 9 times, the ratio of crashes to total races is 9 crashes out of 30 races.
You can set up the proportion as follows:
Crashes / Total Races = Percentage of Crashes / 100
Plugging in the known values gives us this:
9 / 30 = Percentage of Crashes / 100
To solve for the percentage of crashes, you multiply both sides of the equation by 100:
(9 / 30)
100 = Percentage of Crashes
Simplifying gives us:
(9/3) 10 = Percentage of Crashes
Hence, the percentage of races that Glenn crashed is 30%.
Ava bought a rectangular rug for her hallway. The rug is 23 yards wide and 234 yards long. What is the area of the rug as a mixed number in simplest form?
The area of Ava's rectangular rug is 5382 square yards, calculated by multiplying the width (23 yards) and the length (234 yards).
To find the area of Ava's rectangular rug, we need to multiply its length and width:
Area = length × width
Using the given dimensions: 23 yards wide and 234 yards long:
Area = 23 × 234
First, let's perform the multiplication:
23 × 234 = 5382 square yards
Thus, the area of the rug is 5382 square yards as an improper fraction, which cannot be simplified further as a mixed number. Since the measurements are whole numbers, converting to a mixed number doesn't apply in this case.
How many possible outcomes exist when Louisa spins the spinner below twice? The spinner is numbered from 1-8.
Answer:
The total number of possible outcomes are:
64
Step-by-step explanation:
It is given that:
Louisa spins the spinner below twice.
The spinner is numbered from 1-8.
Now, on spinning the spinner twice we obtain the sample space as:
(1,1) (1,2)....................(1,8)
(2,1) (2,2)...................(2,8)
(3,1) (3,2)..................(3,8)
(4,1) (4,2)..................(4,8)
(5,1) (5,2)..................(5,8)
(6,1) (6,2)..................(6,8)
(7,1) (7,2)..................(7,8)
(8,1) (8,2)..................(8,8)
Hence, the total number of outcomes is equal to the number of elements in sample space.
Hence, the total number of possible outcomes are:
64
Write a while loop that adjusts uservalue while uservalue is less than 0 or greater than 80. if uservalue is greater than 80, then subtract 5 from uservalue. if uservalue is less than 0, then add 10 to uservalue.
A 'while loop' can be programmed with conditions to adjust a 'user value'. If 'user value' is greater than 80, 5 would be subtracted from it. If it is less than 0, 10 would be added to it. This loop continues until 'user value' does not meet either condition.
Explanation:The question asks for a while loop in programming that modifies a value (user value) based on these conditions: if the user value is less than 0, it should be increased by 10 and if it's greater than 80, it should be decreased by 5. Here's a representative code for that:
while(user value < 0 || user value > 80) {
if(user value > 80) {user value -= 5; } else if(user value < 0) {user valuable += 10;}
This loop will continue to execute until the user value is not less than 0 or greater than 80.
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find d for the arithmetic series with S17=-170 and a1=2
Deposit $400 into an account that pays simple interest at rate of 4% per year how much interest will she be paid in the first 6 years
HELP PLEASE!!!!!!!
Which of the following is equal to 4 and 1 over 2 divided by 2 and 2 over 3?
4 and 1 over 2 times 2 and 3 over 2
9 over 2 times 8 over 3
9 over 2 times 3 over 8
41 over 2 times 3 over 22
a square has 4 right angle corners. give another shape with 4 right angle corners
share 747 pound in the ratio 2:7 betwen tom and ben
Use euler's theorem to find a number x between 0 and 28 with x85 congruent to 6 modulo 35.
To find a number x between 0 and 28 with x ≡ 6 (mod 35) using Euler's theorem, we can use Euler's totient function to find the power x^24 that is congruent to 1 (mod 35). The value x = 1 satisfies the congruence, so it is a possible solution.
Explanation:To use Euler's theorem to find a number x between 0 and 28 with x ≡ 6 (mod 35), we need to find the value of x that satisfies the congruence. Euler's theorem states that if a and n are coprime positive integers, then a^φ(n) ≡ 1 (mod n), where φ(n) is the Euler's totient function of n. In this case, we need to find x such that x^φ(35) ≡ 1 (mod 35). The Euler's totient function of 35 is φ(35) = φ(5) * φ(7) = 4 * 6 = 24. Therefore, we need to find x such that x^24 ≡ 1 (mod 35).
We can start by examining the powers of x modulo 35:
x ≡ x (mod 35)
x2 ≡ x² (mod 35)
x³ ≡ x³ (mod 35)
...
x^24 ≡ 1 (mod 35)
From this, we can see that x = 1 satisfies the congruence x^24 ≡ 1 (mod 35).
Therefore, a possible value of x between 0 and 28 that satisfies x ≡ 6 (mod 35) is x = 1.
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What fraction is equivalent to the fraction 0/6
Fiona is serving iced tea and lemonade at a picnic. She has only 44 cups in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of iced tea she can serve?
Answer:
[tex]x=44-y[/tex]
Step-by-step explanation:
Let x represents the number of glasses of iced tea .
Let y represents the number of glasses of lemonade.
Now we are given that She has only 44 cups in which to serve the drinks
Since y is the number of glasses of lemonade out of 44 glasses
So, remaining glasses = [tex]44-y[/tex]
So, remaining glasses is for iced tea .
So, No. of iced tea glasses = [tex]x=44-y[/tex]
Hence She can serve [tex]x=44-y[/tex] number of glasses of iced tea serve.
What are the solutions of the system? Solve by graphing. y=x2-2x-1 y = -2
for this job , Hayden earns an hourly rate of $30. For each hour he works over 40 hours, he earns 1.5 times his regular hourly rate. In a two-week period, Hayden earns $2175 by working 40 regular hours, plus overtime. How many overtime hours did Hayden work?
Which describes the slope of this line?
Number graph ranging from negative five to five on the x and y axes. A line is drawn on the graph that passes through (zero, negative three) and (two, one).
negative slope
positive slope
undefined slope
zero slope
the number of sentence is an example of which multiplication property
Action wheels manufacturers models of antique cars for collectors. In August , it manufactured 300 model cars. In September, action wheels manufactured 5% fewer model cars than in August . What is the difference in the numbers of cars manufactured in August and September?
The difference in the number of cars manufactured in August and September is 15 cars.
The difference in the number of cars manufactured in August and September can be calculated as follows:
In August, Action Wheels manufactured 300 model cars.In September, they manufactured 5% fewer cars than in August, which means they made 95% of the cars they made in August.Calculating the number of cars manufactured in September: 300 * 0.95 = 285 cars.Therefore, the difference in the numbers of cars manufactured in August and September is 300 - 285 = 15 cars.Matt Miller, age 28, takes out $50,000 of straight-life insurance. His annual premium is $418.20. Using
the tables in the Business Math Handbook that accompanies the course textbook, determine the cash value
of his policy at the end of 20 years.
A. $13,250
B. $26,000
C. $30,000
D. $26,500
In a circle with a radius of 26.9 m, an arc is intercepted by a central angle of 9π5 radians.
What is the arc length?
Use 3.14 for π and round your final answer to the nearest hundredth.
Make sure to show your calculations.
152.04 is right i just took the test
your welcome ;)
It takes 212121 minutes for 555 people to paint 777 walls. How many minutes does it take 333 people to paint 555 walls?
Solution: We are given that:
5 people can paint 7 walls in 21 minutes
Therefore, 1 person can paint 7 walls in [tex] 21 \times 5=105 [/tex] minutes
Which means 1 person can paint 1 wall in [tex] \frac{105}{7} =15 [/tex] minutes
Now, 3 people can paint 1 wall in [tex] \frac{15}{3} =5 [/tex] minutes
Therefore, 3 people can paint 5 walls in [tex] 5 \times 5=25 [/tex] minutes
Answer:
25 :)
Step-by-step explanation:
Make a comparison between the government’s roles in a capitalist economic system versus a socialist or communist economic system.
A capitalist economic system is built on the respect of private property and competition. Hard work and free enterprise benefit citizens more than the government can. For the most part, government intervention is reduced. However, the government does provide security and some basic services, like infrastructure, to its citizens.
Socialist and communist systems endure more government control. Citizens of these economies have a limited amount of freedom by law. The government controls the market place and the production of most goods and services.
^ My answer from Edge