There is a traffic light at the intersection of Walnut Street and Lawrence Avenue. The traffic light on Walnut Street follows a cycle. It is green for 50 seconds, yellow for 10 seconds, and red for 30 seconds. As you travel along Walnut and approach the intersection, what is the probability that the first color you see is red?
1/5
1/3
3/5
1/2
Given the points A (3,2) and B (-21,0) determine:
a. the slope of line AB
b. the length of AB
c. the midpoint of AB
d. an equation of AB
Julio is playing a trivia game .on his first turn ,he lost 100 points on his second turn ,he lost 75 points . On his third, he lost 85 points. Write a sum of three nagative integer that models the change to julio score after his first three turns
Solve the system of equations by substitution. x + y = x + 7y = 8
Answer:
1 and 1
Step-by-step explanation:
After John worked at a job for 10 years, his salary doubled. If he started at $ x , his salary after 10 years is _____.
$ x
$ x + 2
$ x - 2
$2 x
If you apply the changes below to the absolute value parent function, F(x)=|x|, what is the equation of the new function? Shift 8 units left, shift 3 units down.
A. G(x)=|x-3|-8
B. G(x)=|x-3|+8
C. G(x)=|x-8|-3
G(x)=|x+8|-3
Find an equation of the vertical line that passes through (x, y) = (5, 11).
Geometry please help !!
what should be the first step in solving the equation 1.2 W -3.8 equals 12.4
Answer:
Step 1 would be to add 3.8 on both sides.
Step-by-step explanation:
The Equation mentioned in the question is a simple Algebra Equation. We need to solve for W. To do so, we need to get the variable W alone on one side.
Initial Equation: [tex]1.2W-3.8 = 12.4[/tex]
Step 1: Add 3.8 on both sides. [tex]1.2W = 16.2[/tex]
Step 2: Divide 1.2 on both sides. [tex]W = 13.5[/tex]
This gives us the answer of W = 13.5.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6. Applying Newton's cooling model, the temperature of the tea after 2 hours will be ºF
Answer:
T = 109 degrees f
Step-by-step explanation:
The sum of the first three terms of a convergent geometric series is 19. the sum of the series is 27. find the first term and the common ratio.
A quadratic equation is shown below: 4x2 − 12x + 9 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 9x2 − 30x + 25 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Find the area of a regular hexagon whose side length is 16 in. and the apothem is 8 square root 3
The area of a regular hexagon is mathematically given as
A=665.1 sq units
What is the area of a regular hexagon whose side length is 16 in.?Question Parameter(s):
a regular hexagon whose side length is 16 in.
and the apothem is 8 square root 3
Generally, the equation for the area is mathematically given as
A=(3√3)/2 *a^2
Therefore
A = 6*(0.5*16*8√3)
A= 384√3 sq units
A=665.1 sq units
In conclusion, the area of a regular hexagon
A=665.1 sq units
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Please help me answer this math question.
all 3 angles in a triangle need to equal 180 degrees
62 +73 = 135 degrees are known
180-135 = 45
so angle B = 45 degrees
What is the equation in point-slope form of the line passing through (1, 9) and (−1, 11)?
Which of the following shows the graph of a line through (-2,2) and (2,4)
Answer:
Attachment for graph.
Step-by-step explanation:
Given: (-2,2) and (2,4)
Two points are given and to find the equation of line passing through the points.
First we find the slope of the line.
[tex]\text{Slope }=\dfrac{4-2}{2+2}[/tex]
[tex]=\dfrac{1}{2}[/tex]
Point: (2,4)
using point slope form:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-4=\dfrac{1}{2}(x-2)[/tex]
[tex]y=\dfrac{1}{2}x+3[/tex]
Now, we draw the graph using two given points. Plot the points on graph and join them.
Please find the attachment for graph.
ASAP!!
Shortly before a 1992 mayoral election, a local radio station conducted a Internet survey of voters. Based on the results of the survey, the magazine predicted that the Democratic candidate would beat the Republican candidate by a landslide. In fact, exactly the opposite happened. The trouble with the survey was that the radio station was a largely liberal station and few Republicans visited its Web site. This is a classic example of an error in which phase of inferential statistics?
A.Data gathering
B.Data analysis
C.Probability-based inference
D.Data organization
This is a classic example of an error in data gathering phase of inferential statistics.
What is data gathering?Data gathering is the process of collection and measuring information on variables of interest, in an established systematic fashion that enables one to answer stated research questions, test hypotheses, and evaluate outcomes.
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Find four consecutive positive integers such that the product of the first and fourth is four less than twice the first multiplied by the fourth.
True or false the opposite angles of a quadrilateral in a circumscribed circle are always complementary
Answer: This statement is false.
Step-by-step explanation:
False, the opposite angles of a quadrilateral in a circumscribed circle is not complementary.
As we know that the sum of opposite angles of a cyclic quadrilateral ( quadrilateral circumscribed circle ) is always supplementary.
So, Sum of opposite angles is 180° .
Hence, this statement is false.
Answer:
False
Step-by-step explanation:
We are given that
Opposite angles of a quadrilateral in a circumscribed circle are always complementary.
We have to find that this statement is true or not.
We know that
When a quadrilateral in a circumscribed circle is called cyclic quadrilateral.
We know that
Sum of opposite angles of cyclic quadrilateral is always 180 degrees.
When sum of two angle is equal to 180 degrees then , the angles are called supplementary.
Hence, the sum of opposite angles of cyclic quadrilateral is always supplementary.
Therefore, the given statement is false.
The slope of the line passing through the points (6, -1) and (7, -2) is
You cut a 90 cm long rope into two pieces. the longer piece is 2 times as long as the shorter piece. what is length of the longer piece and the shorter piece respectively?
If 1/3 of an office staff is on vacation and 1/4 of those not on vacation are out sick, what fraction of the staff is in the office
a rectangle has a perimeter of 182 in and length of 52 in. What is the width?
which point of the following ordered pairs is represented by a point located on the y- axis
a. (1,1)
b. (-2,0)
c. (4,-4)
d. (0,3)
The dot plot shows the number of words students spelled correctly on a pre-test. Which statement best describes the shape of the graph?
A.) The graph is skewed right.
B.) The graph is nearly symmetrical.
C.) The graph is skewed left.
D.) The graph is perfectly symmetrical.
Let's think of this problem easily by looking at it instead of going through rigorous mathematics.
When a graph is skewed right, most of the values are to the left side.
When a graph is skewed left, most of the values are to the right side.
Perfectly symmetrical is that both sides, with respect to the median, are same. Here mean and median is equal.
Nearly symmetrical would really close to perfect symmetry, only varying a bit on both sides. Mean would be approximately equal to median.
Now counting the dots as well as looking closely, we can rule out skewed right and skewed left. Now, is the graph perfectly symmetrical? No! So the correct answer is "nearly symmetrical". Correct choice is B.
ANSWER: B
Answer:
The answer is neary symmetrical or answer B
Step-by-step explanation:
If you cut the graph in half exactly, both side would almost line up perfectly.
Which of the following shows the extraneous solution(s) to the logarithmic equation? log4 (x) + log4(x - 3) = log4 (-7x + 21)
A. x= -7
B. x= -3
C. x= 3 and x= -7
D. x=7 and x= -3
Answer: The correct option is C, i.e., x=3 and x=-7.
Explanation:
The given equation is,
[tex]log_4(x)+log_4(x-3)=log_4(-7x+21)[/tex]
Using product property of logarithm [tex]log_a(mn)=log_am+log_an[/tex]
[tex]log_4(x(x-3))=log_4(-7x+21)[/tex]
[tex]log_4(x^2-3x)=log_4(-7x+21)[/tex]
On comparing both sides,
[tex]x^2-3x=-7x+21[/tex]
[tex]x^2-3x+7x-21=0[/tex]
[tex]x^2+4x-21=0[/tex]
Using grouping method 4x can be written as (7x-3x). Because the product of 7 and -3 is equal to the constant term -21 and the addition of 7 and -3 is equal to the coefficient of x.
[tex]x^2+7x-3x-21=0[/tex]
[tex]x(x+7)-3(x+7)=0[/tex]
[tex](x-3)(x+7)=0[/tex]
Equate each factor equal to 0.
The value of x is 3 and -7. Therefore, the option C is correct.
The extraneous solutions are x=3 or x=−7.
We have the equation; log4 (x) + log4(x - 3) = log4 (-7x + 21) we can write;
log4[x(x - 3)] = log4 (-7x + 21)
log4 can be cancelled out from both sides and we have;
x^2 - 3x = -7x + 21
To have a proper quadratic equation;
x^2 + 4x -21 = 0
The solutions of the quadratic equation therefore are x=3 or x=−7.
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Need help please!!!!
I can't see the question...maybe I would be better at helping if I knew what to assist with.
;)
Solve for x: 8x + 10 - 5x = 15.
8x+10-5x = 15
3x+10 = 15
3x = 5
x = 5/3
Jennifer has been saving for college for 57 months. The first month, she saved $11. She was able to save more money each month than the month before. She ended up saving $19,779.00. How much more did she save each month? (2 points)
19779 - 57(11) = 19779 - 627 = 19152
m = 19152*2/(56*57)
m = 12
she saved $12 more every month
A projectile is thrown upward so that it's distance above the ground after t seconds is h=-16t^2 +672t. After how many seconds does it reach its maximum height?
Answer: 21 seconds
Step-by-step explanation:
We know that a parabola with equation [tex]y=ax^2+bx+c[/tex] attains its maximum height at :-
[tex]x=\dfrac{-b}{2a}[/tex]
The given function: [tex]h=-16t^2 +672t[/tex]
It will attain its maximum height at :
[tex]t=\dfrac{-672}{2(-16)}=21[/tex]
Hence , after 21 seconds the projectile will reach its maximum height .