Simplify completely and find the restrictions on the variable.
Answer:
[tex]\displaystyle \frac{8}{x - 11}, x \neq 2, 11[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFactoringAlgebra II
DiscontinuitiesDomain RestrictionsStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{8x - 16}{x^2 - 13x + 22}[/tex]
Step 2: Simplify
[Fraction] Factor numerator: [tex]\displaystyle \frac{8(x - 2)}{x^2 - 13x + 22}[/tex][Fraction] Factor denominator: [tex]\displaystyle \frac{8(x - 2)}{(x - 11)(x - 2)}[/tex][Fraction] Divide: [tex]\displaystyle \frac{8}{x - 11}[/tex]We know that x cannot equal 11, because that would give us a divide by 0 error and we know that x cannot equal 2 because it was canceled out when simplifying.
A boat travels 154 miles in 5 hours (with a constant speed). Approximately how much time will it take to travel 455 miles?
Answer:
14.77 hours.
Step-by-step explanation:
154÷5= 30.8
455÷30.8=14.76
a woman spent 3/5 of her weekly salary on rent and 25% of her weekly salary on food. Her food cost $2500. How much did she spend on rent
Answer:
$6,000
Step-by-step explanation:
If her food costed $2500 and was 25%, then she had $10,000 to begin with. 3/5 of $10,000 is $6,000, so her rent costs $6,000.
Answer:
$6,000 on rent
Step-by-step explanation:
Find her weekly salary by dividing 2500 by 0.25
2500/0.25
= 10,000
Now, find how much she spent on rent by multiplying 10,000 by 3/5
10,000(3/5)
= 6,000
So, she spent $6,000 on rent
two numbers have a sum of 527 and a difference of 195
Answer:
y+x = 527- 195
Step-by-step explanation:
correct me if im wrong pls anyone!
Mr. Williams is making wooden toy trucks for a craft show. He has 85 pieces of wood for the trucks
Each truck requires 6 pieces of wood.
Part A
How many toy trucks can Mr. Williams make? Enter your answer in the box.
00:00
Part B
How many pieces of wood will he have left? Enter your answer in the box.
Part A: He could make 14 toy trucks.
Divide 85 by 6.
85/6
14
(don't take any notice to the decimals)
Part B: He would have 1 piece of wood leftover.
6x14=84
Since Mr. Williams has 85 pieces of wood,
he would have 1 leftover.
Hope this helped!
A group of friends wants to go to the amusement park. They have $363 to spend on parking and admission. Parking is $5.50, and tickets cost $35.75 per person, including tax. How many people can go to the amusement park?
Find AC.
B
7x-6
6x +4
answer:
put a picture of the question, it is easier to understand that way.
A train journey is approximately 150 miles.
How many centimetres will it be on a map with a scale of 30 miles = 1 cm?
==========================================================
Explanation:
The jump from 30 miles to 150 miles is "times 5", meaning 30*5 = 150.
So we need to multiply both sides of the equation
30 miles = 1 cm
by 5 and we get
5*(30 miles) = 5*(1 cm)
150 miles = 5 cm
--------------------
Another way to solve:
This involves proportions
Let x be the distance on the paper map that corresponds to 150 miles
(150 miles)/(x cm) = (30 miles)/(1 cm)
150/x = 30/1
150*1 = x*30 .... cross multiply
150 = 30x
30x = 150
30x/30 = 150/30 ... divide both sides by 30
x = 5 cm is the distance on the paper map
100) = +8 what is) when x = 102
Answer:
13
Step-by-step explanation:
10/2=5
5+8=13
Assume that the probability of error-free transmission of a message over a communication channel is p. If a message is not transmitted correctly, a retransmission is initiated. This procedure is repeated until a correct transmission occurs. Such a channel is often called a feedback channel. Assuming that successive transmissions are independent, what is the probability that: a) No retransmission is required. b) Exactly two retransmissions are required
This question is incomplete, the complete question is;
Assume that the probability of error-free transmission of a message over a communication channel is p=0.9. If a message is not transmitted correctly, a retransmission is initiated. This procedure is repeated until a correct transmission occurs. Such a channel is often called a feedback channel. Assuming that successive transmissions are independent, what is the probability that:
a) No retransmission is required.
b) Exactly two retransmissions are required
Answer:
a) probability that No retransmission is required is 0.90
b) the probability that exactly two retransmissions are required is 0.009
Step-by-step explanation:
Given the data in the question;
the probability of error-free transmission of a message over a communication channel is p = 0.9
a) probability that No retransmission is required will be;
Let x represent the error-free transmission of a message
Now, the P( error-free_transmission_of_a_message) = 0.90
so;
P( X=0 ) = 0.90( 1 - 0.90 )⁰
P( X=0 ) = 0.90( 0.1 )⁰
P( X=0 ) = 0.90( 1 )
P( X=0 ) = 0.90
Therefore, probability that No retransmission is required is 0.90
b) Probability that exactly two retransmissions are required will be;
P( X=2 ) = 0.90( 1 - 0.90 )²
P( X=2 ) = 0.90( 0.1 )²
P( X=2 ) = 0.90( 0.01)
P( X=2 ) = 0.009
Therefore, the probability that exactly two retransmissions are required is 0.009
Without writing the equation x^2 + y^2 + 24x – 26y+ 277 = 0 in the standard form, state whether the graph of this equation is a
parabola, circle, ellipse, or hyperbola.
a. parabola
c. hyperbola
b. ellipse
d. circle
Answer:
circle
Step-by-step explanation:
You can see there is a x^2 and y^2 and 24 x and 26 y meaning if you do complete the square you can write it as a circle in standard form
Maria found a circular rug for her floor. The rug has a circumference of 50.24 inches. Which formula should Maria use to help her find the diameter of the rug?
Answer:
She should use the formula [tex]C = \pi d[/tex] to find a diameter of 16 inches.
Step-by-step explanation:
The circunference of a circle is given by:
[tex]C = 2\pi r[/tex]
In which r is the radius, which is half the diameter. So, it can also be given by the following formula:
[tex]C = 2\pi \frac{d}{2} = \pi d[/tex]
In which d is the diameter.
Which formula should Maria use to help her find the diameter of the rug?
She should use this formula:
[tex]C = \pi d[/tex]
Since the circunference is 50.24 inches, the diameter will be of:
[tex]d = \frac{C}{\pi} = \frac{50.24}{\pi} = 16[/tex]
Suppose that the length of research papers is uniformly distributed from 12 to 25 pages. We survey a class in which 55 research papers were turned in to a professor. The 55 research papers are considered a random collection of all papers. We are interested in the average length of the research papers.
A.) Give the distribution of X. (round your standard deviation to two decimal places. X
∼ N (18.5, _____)
B.) Give the distribution of SumX. Round your standard deviation to two decimal places. SumX
∼ (1017.5, _____).
C). Calculate the probability that the professor will need to read a total of more than 1080 pages. _____
Answer:
A.) X ~ N(18.5, 3.75)
B.) SumX ~ N(1017.5,27.8).
C.) 0.0122 = 1.22% probability that the professor will need to read a total of more than 1080 pages.
Step-by-step explanation:
Uniform distribution:
A distribution is called uniform if each outcome has the same probability of happening.
The uniform distributon has two bounds, a and b.
The mean is given by:
[tex]M = \frac{a+b}{2}[/tex]
The standard deviation is given by:
[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The uniform distribution can be approximated to the normal, using its mean and its standard deviation.
Sum of n terms of a normally distributed variable:
The mean of the sum will be:
[tex]\mu_{s} = n\mu[/tex]
The standard deviation of the sum will be:
[tex]\sigma_{s} = \sqrt{n}\sigma[/tex]
Suppose that the length of research papers is uniformly distributed from 12 to 25 pages.
This means that [tex]a = 12, b = 25[/tex]
We survey a class in which 55 research papers were turned in to a professor.
This means that [tex]n = 55[/tex]
A.) Give the distribution of X.
The mean has already been given, and the standard deviation is:
[tex]S = \sqrt{\frac{(25-12)^2}{12}} = 3.75[/tex]
So
X ~ N(18.5, 3.75)
B.) Give the distribution of SumX.
Sum of 55 papers, the standard deviation will be of:
[tex]\sigma_{s} = \sqrt{55}*3.75 = 27.8[/tex]
So
SumX ~ N(1017.5,27.8).
C). Calculate the probability that the professor will need to read a total of more than 1080 pages
This is 1 subtracted by the pvalue of Z when X = 1080. So
[tex]Z = \frac{X - \mu_{s}}{\sigma_{s}}[/tex]
[tex]Z = \frac{1080 - 1017.5}{27.8}[/tex]
[tex]Z = 2.25[/tex]
[tex]Z = 2.25[/tex] has a pvalue of 0.9878
1 - 0.9878 = 0.0122
0.0122 = 1.22% probability that the professor will need to read a total of more than 1080 pages.
WILL GIVE BRAINEST!!! PLEASE HELP
Answer:
1.) The point (24,30) would not be on the line
2.) The point (12,13) would not be on the line either
4.) The slope is a fraction of 2/1
Bonus: y = (2/1)x - 2
Step-by-step explanation:
For question three, I looked at the (6,10) point on the graph and compared it with the (a,8) point. That showed me that the y coordinate always moves by 2. Then I looked at the (6,10) coordinate and the (a,8) coordinate and the (4,b) coordinate and saw that there was one x coordinate between 6 and 4 so it must be five. That means the x coordinate moves by 1.
Let me know if you need more help!
:)
what is 1 x 5555 + -6779 . 55555
Answer:
−376601790
Step-by-step explanation:
1
⋅
5
5
5
5
−
6
7
7
9
⋅
5
5
5
5
5
5
5
5
5
−
6
7
7
9
⋅
5
5
5
5
5
Answer:
it's -1,224.55555
Step-by-step explanation:
1 x 55,555 = 55,555
55,555 + -6779.55555 = -1224.55555
hope this helps...
tell me you love me pls i need sum luv i spents alot of time doing this im doing another one but 100 pts
Answer:
I love you and i'm proud of you :)
I will give you a brainliest if you answer this question 16
Answer:
0.75, 0.5, 0.25, 0.05
Hope it helps!!!
B.)0.75, 0.5,0.25,0.05
0.25
0.52
0.75 greatest
0.05 Least
An examination class of 55% of pupil scored 70% , if 54% scored above 70%. how many scored above 70%.
Answer:
54
Step-by-step explanation:
Let us assume the examination class is of 100 students
Now 55% scored 70% so 55% of 100 is 55
And, the 54% scored above 70% so 54% of 100 is 54
Therefore there are 54 who scored above 70%
Hence, the same would be considered and relevant too
write at least 250 word about a way you have used math outside of school. Use your own word
You look up at a 62 m tall building and find that the angle of elevation from the ground to the top of the building is 51 degrees. How far away from the building's base are you?
Answer:
Step-by-step explanation:
horizontal distance = 62/tan(51°) ≅ 50.2 m
The distance between the building base to a standing point is 50.20 m if the angle of elevation from the ground to the top of the building is 51 degrees.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.
It is given that:
You look up at a 62 m tall building and find that the angle of elevation from the ground to the top of the building is 51 degrees.
The angle = 51 degrees.
The height of the building = 62 m
Applying the tan ratio
tan51 = height of the building/distance between the building base to a standing point
tan51 = 62/x
x = 50.20 m
Thus, the distance between the building base to a standing point is 50.20 m if the angle of elevation from the ground to the top of the building is 51 degrees.
Learn more about trigonometry here:
brainly.com/question/26719838
#SPJ6
Class: How can we graph using slope intercept form?
1/3y=x
Find the perimeter. Simplify your answer.
3t+6
10t+7
6t-2
10t+4
Step-by-step explanation:
Perimeter is the sum of every side
6t-2 + 3t+6 + 10t+7 + 10t+4
= 6t + 3t + 10t + 10t -2 +6 +7 +4
= 29t + 15
What is the value of the Expression
H-20 when h=60?
A:30
B:40
C:80
D:120
Answer:
BBBBBBBB
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
Subtract 60-20 you'll get the answer
(FILL IN THE BLANK)
Analyze the graph of the exponential decay function.
The initial value is _____
The base, or rate of change is _____
The domain is _____
pleaseeeee help ill give brainliest answerrrrr
Answer:
A= 360
Step-by-step explanation:
360
A water-walking ball has a volume of approximately 904.32 cubic feet. What is the radius of the ball? (V = 4/3(pi)r^3)
Make sure you do put the unit with this answer rounded to the tenth if necessary.
Answer:
The radius of the ball is of 6 feet.
Step-by-step explanation:
The radius of the ball in spheric format is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In which r is the radius.
A water-walking ball has a volume of approximately 904.32 cubic feet. What is the radius of the ball?
Volume in cubic feet, so the radius will be in feet. We have to find r for which [tex]V = 904.32[/tex]. So
[tex]V = \frac{4\pi r^3}{3}[/tex]
[tex]904.32 = \frac{4\pi r^3}{3}[/tex]
[tex]r^3 = \frac{904.32*3}{4\pi}[/tex]
[tex]r = \sqrt[3]{\frac{904.32*3}{4\pi}}[/tex]
[tex]r = 6[/tex]
The radius of the ball is of 6 feet.
Whats the square root of 128
Answer:
exact form: 8√2
decimal form: 11.3137
Answer:
i dont know
Step-by-step explanation:
Determine whether m=27 is a solution to 20=m+3
Answer:
No.
Step-by-step explanation:
27+3=30, not 20.
Answer:
Nopeeee it is not
Step-by-step explanation:
20 = 27 + 3 ?
20 = 30 ?
Nope
m = 27 is not a solution
can some please help me to solve this gometry with full process
Answer: x in top right = 90°
x in bottom left = 90°
Step-by-step explanation:
The vertical angle of 110° = 110°. That angle is corresponding to x + 20°
110° - 20° = 90°
We know all of the interior angles of the triangle because:
1. Vertical angle to 20° = 20°
2. Supplementary angle to 110° = 70°
3. Other angle = 180 - 20 - 70 = 90°
The supplement to 90° = 90° , so the x in the bottom left = 90°
I am not a professional, simply using prior knowledge!
Note- It would mean the world to me if you could mark me brainliest!
Simplify completely''''
Answer:
[tex]\displaystyle \frac{2x + 5}{x - 9}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{2x^2 + 13x + 20}{x^2 - 5x - 36}[/tex]
Step 2: Simplify
[Fraction] Factor numerator: [tex]\displaystyle \frac{(x + 4)(2x + 5)}{x^2 - 5x - 36}[/tex][Fraction] Factor denominator: [tex]\displaystyle \frac{(x + 4)(2x + 5)}{(x - 9)(x + 4)}[/tex][Fraction] Divide: [tex]\displaystyle \frac{2x + 5}{x - 9}[/tex]