Answer:
The correct answer is option B
Step-by-step explanation:
Payment done per week [tex]= 35 dollar\\[/tex]
Total number of weeks in a year [tex]= 52 weeks\\[/tex]
Total number of weeks in two year [tex]= 104 weeks\\[/tex]
Total amount paid in two weeks
[tex]= 35 * 104\\=3,640\\[/tex]
The make up rate is basically the amount paid over and above $2400
[tex]=(\frac{3640 - 2400}{2400} ) * 100\\= 51. 7 perecent[/tex]
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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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
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:
Find the length of EF. Round to the nearest hundredth.
to find EF multiply 31 by tan(72)
31 * tan(72) = 95.4082
rounded to nearest hundredth = 95.41
Find all solutions to the equation. cos x = sin x
When asked to factor the trinomial 4x2 + 20x + 25, a student gives the answer (2x - 5)(2x - 5). what is one thing wrong with this answer?
Answer:
The minus signs should be plus signs
The required factor of the given trinomial is (2x+5)(2x + 5).
Given that,
When asked to factor the trinomial 4x² + 20x + 25, a student gives the answer (2x - 5)(2x - 5). the mistakes in the solution is to be justified.
What is the factors?
factors can be defined by splitting the value into multipliable values.
Here,
Given trionomial,
= 4x² + 20x + 25,
= 4x² + 10x + 10x + 25
= 2x(2x + 5) + 5 (2x + 5)
= (2x + 5)(2x + 5)
Thus, the required factor of the given trinomial is (2x+5)(2x + 5).
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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.
Need help please!!!!
I can't see the question...maybe I would be better at helping if I knew what to assist with.
;)
What are the rules for dividing signed numbers
Final answer:
In dividing signed numbers, the answer's sign depends on the signs of the numbers involved: same signs result in a positive answer, different signs yield a negative answer. Additionally, the final answer should have the same number of significant figures as the number with the fewest significant figures in the problem.
Explanation:
Rules for Dividing Signed Numbers
The rules for dividing signed numbers are similar to the rules for multiplication. When dividing numbers, it is important to consider both the sign of the numbers involved as well as the significant figures in the result. Here are the key rules to remember:
When two positive numbers divide, the answer has a positive sign, e.g., 6 ÷ 2 = 3.When two negative numbers divide, the answer also has a positive sign, e.g., (-6) ÷ (-2) = 3.When the numbers being divided have opposite signs, the answer has a negative sign, e.g., (-6) ÷ 2 = -3 or 6 ÷ (-2) = -3.As for the significant figures, the final answer should have the same number of significant figures as the number with the fewest significant figures before the division. For example, if you are dividing 23 by 448, limit the final reported answer to two significant figures.Remember, when performing calculations, significant figures are important for maintaining accuracy based on the precision of the data you start with.
What is the equation in point-slope form of the line passing through (1, 9) and (−1, 11)?
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
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.
Solve the system of equations by substitution. x + y = x + 7y = 8
Answer:
1 and 1
Step-by-step explanation:
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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Andrea can clean a house 4 times as fast as Denise. When they work together, Andrea and Denise can clean a large house in 8 hours. How many hours would it take Denise to clean the house by herself?
20
15
40
5
Answer:
8 hours
Step-by-step explanation:
A&D can clean a house in 8 hours together.
Proportionally, Denise works at x. Andrea works at 4x. There is a total of 5x.
Out of the 5x, Denise accounts for x.
x/5x = 1/5 of the work over 8 hours.
1/5 ( Denise's time for cleaning the whole house) = 8 hours.
Multiply both sides by 5:
5(1/5)(Denise's time for cleaning the whole house) = 5*8
Denise's time for cleaning the whole house = 40 hours
I like this method better...
That means in ONE hour, they get 1/8 of the job done.
Let's say Denise takes x hours to clean the house.
In one hour, she would do 1/x of the job (x can't be 0 hours).
Since Andrea does the house 4 times as fast as Denise, who takes x hours to do the job, Andrea takes x/4 hours.
In one hour, Andrea does 4/x of the job.
In one hour the part of the job Andrea does, plus the part of the job Denise does, must total 1/8.
(4/x) + (1/x) = 1/8
5/x = 1/8
Cross multiply:
x = 40
So it would take Denise 40 hours to clean the house by herself. (She's not really that efficient, or the house was REALLY dirty.
Andrea takes x/4 hours or 40/4 = 10 hours to clean the house by herself.
So with a little help from Denise, Andrea decreases her time to clean the house from the 10 hours it would take by herself to 8 hours.
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
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.
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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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
Newton currently has a balance of $1,716.18 in an account he has held for 29 years. He opened the account with an initial deposit of $784. What is the simple interest rate on the account?
10 points! I will thanks, rate, and give best answer!!
Find the 4th term if the sequend in which a 1 = 2 and a n+1 = -4a n + 2
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.
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?
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)
solve the inequality -5.3≥6.7+4.3+q
The top of a 15-foot ladder touches the edge of the roof of a building, and the base of the ladder is 6 feet from the building. What assumptions are made about the building and the ladder when using the Pythagorean Theorem to solve real world problems like this?
Jessica is baking a cake. the recipe says that she has to mix 96 grams of sugar into the flour. jessica knows that 1 cup of this particular sugar has a mass of 128 grams. she added 1/2 of a cup of sugar into the flour. should jessica add more sugar to make the exact recipe, or did she go over by what amount?
Answer:
she needs to add 32 grams. this is 1/4 cups
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)
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 .