Stoplight A changes color every 42 seconds and Stoplight B changes color every 30 seconds. Both stoplights changed color 10 seconds ago. After how many seconds will the stoplights change color at the same time again
Answers
Related Questions
Please answer this my grade depends on it, also I have other problems like these so please feel free to answer them if you would like.
Answers
Answer:
-4,-3 and 4,5
Step-by-step explanation:
solve the quadratic equation by completing the square \( {x}^{2} + 12x + 2 = 0\)
Answers
To complete the square you add and subtract the next to the equation:
\((\frac{b}{2})^2\)For the given equation:
\(x^2+12x+2=0\)\((\frac{b}{2})^2=(\frac{12}{2})^2=6^2\)Add and subtract 6 squared as follow:
\(x^2+12x+6^2+2-6^2=0\)Simplify:
\(\begin{gathered} (a^2+2ab+b^2)=(a+b)^2 \\ \\ x^2+12x+6^2=(x+6)^2 \\ \\ \\ \\ (x+6)^2+2-6^2=0 \\ (x+6)^2+2-36=0 \\ (x+6)^2-34=0 \end{gathered}\)Solve x by taking square roots:
\(\begin{gathered} (x+6)^2-34+34=0+34 \\ (x+6)^2=34 \\ \\ \sqrt[]{(x+6)^2}=\sqrt[]{34} \\ \\ x+6=\pm\sqrt[]{34} \\ x+6-6=\pm\sqrt[]{34}-6 \\ \\ x_1=\sqrt[]{34}-6 \\ x_2=-\sqrt[]{34}-6 \end{gathered}\)Then, the solutions for the given quadratic equation are:\(\begin{gathered} x_1=\sqrt[]{34}-6 \\ x_2=-\sqrt[]{34}-6 \end{gathered}\)10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
Answers
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
For more questions on prime number
https://brainly.com/question/145452
#SPJ8
3 A system of two linear equations is graphed on a coordinate plane. If the system of
equations has infinitely many solutions, which statement must be true?
a. On the graph, there are no points (x, y) that satisfy both equations.
b. On the graph, there is exactly one point (x, y) that satisfies both equations.
c. On the graph, any point (x, y) that satisfies one of the equations cannot satisfy the
other equation.
d.
On the graph, any point (x, y) that satisfies one of the equations must also satisfy
the other equation.
Answers
Answer:
d. On the graph, any point (x, y) that satisfies one of the equations must also satisfy the other equation.----------------------
If the system of linear equations has infinitely many solutions, it means the two lines overlap.
In other words, each point of one of the lines also belongs to the second line.
Choices a, b, c give us one or no solutions and therefore not the answer.
Choice d is reflecting the infinitely many solutions and hence is the correct one.
Someone please help I’m having trouble
Answers
do you need the work?
two similar triangles have a ratio of sides of 3:4 if one side of the small triange is 9 inches long how long is the corresponding side of the larger triange
Answers
Answer:
The answer to the question is Sixteen.
Solve the inequality 1/2x<10
Answers
Answer: x is less than 20
Step-by-step explanation:
We need to get x by itself, we can do that by multiplying 1/2 by its reciprocal, 2/1. What we do to one side we have to do to the other, so we need to multiply 10 (2/1)
Now we have our answer, x is less than 20
We can check our work by substituting x for anything less than 20.
Step-by-step explanation:
the equation 1/2×<10
2×1/2×<2×10
x<20
Question 13 FUNDRAISER Owen is organizing a fundraiser. The proceeds will be split between a charity and the expenses from the fundraiser. Owen would like the cost of the fundraiser to be 15% of the proceeds. If the fundraiser will cost $500, how much money do they need to raise at the fundraiser?
Answers
Answer:
The amount to be raised at the fund raiser is $3,333.33
Step-by-step explanation:
Here, we want to know the amount of money needed to be raised for the fundraiser
Let the amount raised be $x
Thus;
15% of $x = $500
$500 is the cost of the fund raiser
15/100 * x = 500
15x/100 = 500
15x = (100 * 500)
x = (100 * 500)/15
x = 3,333.33
PLEASE HELP! What is 2 x 2!
I cannot figure this out!
Answers
Answer:
4
Step-by-step explanation:
2*2=4
Hope this helps!
:)
Answer: Monke.
Step-by-step explanation:
get good.
Don’t mind the work but can someone please help fast I’m stuck!! I also need to show work
Answers
Answer:
The answer for this problem is at the bottom of picture.
A moving company charges a flat rate of $150, and an additional $5 for each box. if a taxi service would charge no flat rate and $15 for each box, how many boxes would you need for it to be cheaper to use the moving company? (do not label your answer)
Answers
Answer:
16 boxes
Step-by-step explanation:
16x5=80+150=230>15x16=240
Kellen is having friends over for dinner and needs to buy chicken. He is looking for the best deal. There are three package options for the chicken.
3 lbs. for $15.39
2 lbs. for $9.19
1 lb. for $7.05
Answers
Answer:
But the 2lbs.
Step-by-step explanation:
Divide $9.19 by 2 and you get 4.595 which would be the cheapest option out of the 3 because the 1lb is $7.05 and the 3lb is $5.13.
You're welcome.
Find the value of: i) (4/3)³ x (3/5)-² (2/5)-²
Answers
Answer:
Step-by-step explanation: 10000/243
Use long hand division to determine if (x-1) is a factor of 4x^4 + 7x^2 - 5x + 1
Answers
Answer:
\( \bold{quotient } = {4x}^{3} + {4x}^{2} + 13x + 8 \\ \bold {remainder} = 9\)
Step-by-step explanation:
See the attached image.
help pls!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
y = -3x - 1
hope this helps!
income from operations of $231,000. In addition, it received interest income of $23,100 and received dividend income of $29,700 from another corporation. Finally, it paid $11,000 of interest income to its bondholders and paid $45,000 of dividends to its common stockholders. The firm's federal tax rate is 21%. What is the firm's federal income tax? Do not round intermediate calculations. Round your answer to the nearest dollar.
Answers
The firm's federal income tax is $57,168.
To calculate the firm's federal income tax, we need to determine its taxable income first. Taxable income is calculated by subtracting deductions from the firm's total income.
In this case, the firm's total income consists of income from operations, interest income, and dividend income.
Total income:
Income from operations = $231,000
Interest income = $23,100
Dividend income = $29,700
Total income = $231,000 + $23,100 + $29,700 = $283,800
Next, we deduct expenses from the total income. In this case, the only relevant expense is the interest paid to bondholders:
Total expenses = Interest paid to bondholders = $11,000
Taxable income = Total income - Total expenses = $283,800 - $11,000 = $272,800
Now, we can calculate the federal income tax by applying the federal tax rate of 21% to the taxable income:
Federal income tax = Taxable income * Federal tax rate
Federal income tax = $272,800 * 0.21 = $57,168
Therefore, the firm's federal income tax is $57,168.
For more such questions on tax,click on
https://brainly.com/question/28414951
#SPJ8
A 12-ounce sports drink costs $0.99, and a 16-ounce sports drink costs $1.19. Which size is the best buy?
Answers
Answer:
The best buy is the 16-ounce drink
Step-by-step explanation:
here, we see that,
12 ounce = 3/4 (16 ounce)
So, the price should reflect that,
i.e,
price of 12 ounce drink = 3/4 (price of 16 ounce drink)
By this metric,
Price of 12 ounce drink = 3/4 ( 1.19)
Price of 12 ounce drink = $0.8925
So, 12-ounce drink should cost $0.8925 but the actual drink costs $0.99,
So, it is more expensive than it should be,
So, the best buy is the 16-ounce drink
PLZ HELPPP will give BRAINLIEST
Answers
Explanation: If a graph is proportional, it means that but the x coordinate and the y coordinate have the same rate of change
Answer:
True
Step-by-step explanation:
Saying the graph is proportional means that the line crosses through the origin which is (0,0).
A randomized telephone survey of adults in the United States determines that a certain number out of 504 respondents have one or more pets. They use p^ to construct a 95% confidence interval to estimate the proportion p of American adults who have pets to be (0.56137,0.60529).
How many respondents said they have one or more pets?
283
294
305
290
Answers
Answer:
\( \hat p=\frac{0.56137+0.60529}{2}= 0.58333\)
The critical value for 95% of confidence is \(z_{\alpha/2}=1.96\)
And since we know the total and the proportion is defined as:
\( \hat p=\frac{X}{n}\)
If we solve for X (number of people who say yes) we got:
\( X= 0.58333* 504= 293.998 \approx 294\)
And the best answer would be:
294
Step-by-step explanation:
We know that the confidence interval for the proportion is given by:
\( \hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\)
The margin of error for the proportion interval is given by this formula:
\( ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}\) (a)
The margin of error can be calculated with this formula:
\( ME=\frac{0.60529- 0.56137}{2}= 0.02196\)
And the estimation for the true proportion is:
\( \hat p=\frac{0.56137+0.60529}{2}= 0.58333\)
The critical value for 95% of confidence is \(z_{\alpha/2}=1.96\)
And since we know the total and the proportion is defined as:
\( \hat p=\frac{X}{n}\)
If we solve for X (number of people who say yes) we got:
\( X= 0.58333* 504= 293.998 \approx 294\)
And the best answer would be:
294
\(4√3\)what is equivalent to 4 sqrt 3
Answers
The equivalent expression to 4√3 is √48 or 6.928.
What is the equivalent expression?
An equivalent expression is an expression that has equal value to the original given expression.
From the given expression, we can determine its equivalent expression as follows;
The given expression = 4√3
We can square 4 and multiply it by 3 and enclose all with the square root.
4√3 = √(4² x 3 )
= √ ( 16 x 3 )
= √ ( 48 )
= 6.928
Learn more about equivalent expression here: https://brainly.com/question/22365614
#SPJ1
o
A toy rocket is shot vertically into the air from a launching pad 8 feet above the ground with an initial velocity of 72 feet per
second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function
h(t) = - 1612 + 72t + 8. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)
Answers
Answer:
1845 totaly i help yo to up grade
Step-by-step explanation:
im help :)
The price of a phone is decreased by 19% and now is $319.14. Find the original price
Answers
The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.
what is percentage ?In arithmetic, a percentile is a number or statistic that is given as a fraction of 100. Occasionally, the acronyms "pct.," "pct," nor "pc" are also used. But it is broadly classified into the following by the cent sign, "%." The % amount has no characteristics. Percentages are essentially integers when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it close to it. For instance, you score a 75% if you properly answer 75 so out 25 pages on a test (75/100). Divide the money by the whole and multiply the results by 100 you compute percentages. The formula for calculating the percentage is (value/total) x 100%.
given
Put this together using the conditions given: 319.14 / (1- 19%)
Determine the total or difference: 319.14 / 0.81
Diminish the fraction: 394
Response: 394
The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.
To know more about percentage visit:
https://brainly.com/question/28269290
#SPJ1
DF and GI are parallel lines.
Which angles are alternate interior angles?
Answers
Answer:
The answer is D.
Step-by-step explanation:
An equilateral triangle was rotated to create this figure. What is true about the axis of rotation?
Answers
The true statement about the axis of rotation is the option;
It is parallel to a side of the equilateral triangle, but is separate from the equilateral triangle.
What is an axis of rotation?The axis of rotation is a straight line around which all points on a rotating body rotates.
The diagram shows a figure with a hollow cylindrical cross section and triangular cross section on the left and right, which indicates that the figure is created by the rotation of the equilateral triangle about height of the cylinder, such that the axis of rotation is a vertical line through the center of the hollow cylinder. Therefore, the axis of rotation is parallel to the height of the cylinder, and therefore, it is parallel to the base of the equilateral triangle, but it it seperate from walls of the cylinder, and therefore, separate from the equilateral triangle
Learn more on the rotation of plane figures here: https://brainly.com/question/12688268
#SPJ1
The front lawn of NPHS has a roped off area of 2x^2 - 11x + 15. What are the
possible dimensions of the roped off area?
Answers
Answer:
\(x-3\) by \(2x-5\) units
Step-by-step explanation:
Use the slide-and-divide method to factor the polynomial:
\(2x^2-11x+15\)
\(x^2-11x+30\)
\((x-6)(x-5)\)
\((x-3)(2x-5)\)
Therefore, the dimensions are \(x-3\) by \(2x-5\) units
. If two of the angles in a scalene triangle are 54° and 87°, what is the other angle?
Answers
The answer is:
⇨ x = 39°Work/explanation:
Bear in mind that the sum of all the angles in a triangle is 180°.
Given two angles, we can easily find the third one.
Let's call it x.
Next, we set up an equation:
\(\sf{54+87+x=180}\)
\(\sf{141+x=180}\)
Subtract 141 on each side.
\(\sf{x=180-141}\)
\(\sf{x=39}\)
Hence, the other angle is 39°.can someone help me on my math pls
Answers
Answer:
22
Step-by-step explanation:
Plugging the numbers into the equation, we get 10^2+20^2=c^2
10^2 is 100, and 20^2 is 400
400 + 100 is 500
find the square root of that, which is exactly 22.36068 but the problem says to round to the nearest whole number, so the answer is 22.
Answer:
22 ft
Step-by-step explanation:
a² + b² = c²
10²+20²= c²
c= (square root of) 100+ 400
c= 22.36
The wheel on a scooter completes 124 revolutions and travels 22.4 meters. What is the diameter of the wheel in mm? Use 3.14 for pi and round to the nearest whole millimeter.
Answers
If wheel on a scooter completes 124 revolutions and travels 22.4 meters then diameter of the wheel is 57 mm
Each revolution of the wheel covers a distance equal to the circumference of the wheel.
The diameter of the wheel "d".
The distance covered in 124 revolutions is:
distance = 124 x circumference
= 124 x pi x d
= 124 x 3.14 x d
We know that this distance is equal to 22.4 meters, so we can set up an equation:
124 x 3.14 x d = 22.4
Simplifying and solving for d:
d = 22.4 / (124 x 3.14)
d = 0.057 meters
As we know that 1 meter is equal to thousand millimeters so multiply by 1000 to get in millimeters
d = 57 millimeters
Therefore, the diameter of the wheel is approximately 57 mm.
To learn more on Circles click:
https://brainly.com/question/11833983
#SPJ1
Solve for w.
3w+2w= 10
Simplify your answer as much as possible.
W =
Answers
Answer:
3w+2w= 10
5w= 10
w = 10/5
w = 2
Answer:
w = 2
Step-by-step explanation:
3w+2w= 10
Combine like terms
5w = 10
Divide each side by 5
5w/5 = 10/5
w = 2
15n^2-27n-6
step by step plsss
Answers
Step-by-step explanation:
Factor the trinomial with the GCF.
The GCF of all of the terms is 3.
Using the GCF:
\(3(5n^2-9n-2)\)
Using 2 binomials to factor:
\(3(5n+1)(n-2)\)
When unfactorized, the expression will equal \(15n^2-27n-6\).