Answer:
Step-by-step explanation:
The function is:
x - 5
f(x) = ---------------
x^2 - 1
Horizontal asymptote: observe that as x grows towards infinity, the function (and graph) approaches y = 0. This is the horizontal asymptote.
Vertical asymptote: These occur whenever the denominator of a rational function becomes zero. Here the vertical asymptotes are x = ± 1.
5. The number of service calls received by a local fire department is between 0 and 5. The probabilities are 0.10, 0.15, 0.30, 0.20, 0.15, 0.10, respectively. a. Write the probability distribution for the number of service calls in a given day. b. What is the expected number of service calls per day in this fire department
Answer:
2.45
Step-by-step explanation:
1. Probability distribution shows us sample space(number of calls) and their probabilities
Number of calls. Probability
0. 0.10
1. 0.15
2. 0.30
3. 0.20
4. 0.15
5. 0.19
2. We are to find expected number of calls
(0x0.1) + (1x0.15) + (2x0.30) + (3x0.20) + (4x0.15) + (5x0.10)
E(X) = 0 +0.15 + 0.6 + 0.6 + 0.6 + 0.5
= 2.45
The expected number of Service calls per day is 2.45
Thank you!
Rectangle EFGH has verticles at E(7,7), F(1,5), G(2,2), and H(8,4). How many units is the perimeter of rectangle EFGH. Answer choices: A. 20 B. 10√13 C. 5√10 D. 6√10
Answer:
D. 6√10Step-by-step explanation:
Given the vertices of a rectangle EFGH as E(7,7), F(1,5), G(2,2), and H(8,4), the perimeter if the rectangle will be the sum total of all the sides of the rectangle.
Using the expression Perimeter of rectangle EFGH = EF+FG+GH+EH
Taking the distance between adjacent vertices to get the length of each segment using the formula;
D = √(x₂-x₁)²+(y₂-y₁)²
For segment EF with vertices E(7,7), F(1,5);
EF = √(1-7)²+(5-7)²
EF = √(-6)²+(-2)²
EF = √36+4
EF = √40
EF = 2√10
For segment FG with vertices F(1,5) and G(2,2);
FG = √(2-1)²+(2-5)²
FG = √(1)²+(-3)²
FG = √1+9
FG = √10
For segment GH with vertices G(2,2), and H(8,4)
GH = √(8-2)²+(4-2)²
GH = √(6)²+(2)²
GH = √36+4
GH = √40
GH = 2√10
For segment EH with vertices E(7,7), and H(8,4)
EH = √(8-7)²+(4-7)²
EH = √(1)²+(-3)²
EH = √1+9
EH = √10
Since perimeter of rectangle EFGH = EF+FG+GH+EH
Perimeter of rectangle EFGH = 2√10+√10+2√10+√10
Perimeter of rectangle EFGH = 6√10
An online test of English spelling looked at how well people spelled difficult words. The bar graph to the right shows how many people per 100 spelled each word correctly. a. Estimate the number of people per 100 who spelled weird correctly Round to the nearest 5 b. In a group consisting of 8719 randomly selected people estimate how many more people can correctly spell weird than inoculate a. The approximate number of people per 100 who spelled were correcily is (Type a whole number
Answer:
60 ; 5220
Step-by-step explanation:
A) From the horizontal bar chart provided, it could be inferred that 85 people spell the word 'weird' correctly. The graph is scaled on a fixed interval of 10. Hence, the midpoint of 10 = 5
(80 + 5) = 85
B) In a group consisting of 8719 randomly selected people estimate how many more people can correctly spell weird than inoculate
From the graph :
85 per 100 could spell weird correctly while,
About 25 per 100 could spell inoculate correctly.
Difference In number per 100 people
(85 - 25) = 60 people per 100
We could round 8719 to the nearest 100 = 8700
Number of 100's in 8700 = 8700/100 = 87
(87 × 60) = 5,220 people
Find x for the angles please!!! 20pts!
Answer:
X=53. X=38
Step-by-step explanation:
46+81+x=180
X=180-127
X=53 degrees
31+112+x=180
X=180-143
X=37 degrees
PLEASE HELP! Simplify radical square root -100
Answer: OPTION 3 10i
Step-by-step explanation:
First of all, you need to know about imaginary number, or i.
i (imaginary number)= √-1
---------------------------------------------------------
√-100=√100 × √-1 ⇔ This splitting up √-100 to make it easier for you to understand.
√-1=i ⇔ As mentioned before of the concept of imaginary number
√100= 10 ⇔ It is a perfect square
√-100=√100 × √-1
√-100=10 × i
√-100=10i
Hope this helps!! :)
Please let me know if you have any question
simplify (8 ^2/3) ^4
Answer:
[tex]8^{\frac{8}{3}}[/tex]
Step-by-step explanation:
Rule of Exponents: [tex](r^n)^m=r^{m(n)}[/tex]
Simply multiply the powers together:
2/3(4) = 8/3
[tex]8^{\frac{8}{3}}[/tex]
Answer:
Its 8 and eight-thirds
Step-by-step explanation:
The number 35 is decreased to 33. What is the percentage by which the number was decreased, to the nearest tenth of a percent?
Answer:
The answer is
[tex]5.7 \: \%[/tex]Step-by-step explanation:
To find the percentage at which the number decreased we use the formula
[tex]Percentage \: change (\%) = \frac{change}{original \: quantity} \times 100\% \\ [/tex]From the question
The original number is 35
To find the change subtract the smaller number from the larger number
That's
Change = 35 - 33 = 2
Substitute the values into the above formula and solve.
That's
[tex]\% \: change = \frac{2}{35} \times 100 \\ = 5.714285[/tex]We have the final answer as
5.7 % to the nearest tenthTherefore the number decreased by 5.7%
Hope this helps you
Answer:5.7
Step-by-step explanation:
Hope that helps
Helpppp ASAP
PLEASEDEEEE
Answer: Between 12 and 13
Step-by-step explanation: When put into the calculator to solve the answer comes up as 12.846325...
Solve for j.
J + 22/8 =8
Answer:
j=5.25
Step-by-step explanation:
j+22/8=8
j=8/1-22/8
j=64-22/8
j=5.25
Proof:
5.25+22/8=8
525/100+22/8=8
4200+2200/800=8
6400/800=8
8=8
What is the rectangle's height and base?
Answer:
Base = 16cm
Height = 7cm
Answer:
base = 16 cm
height = 7 cm
Step-by-step explanation:
area of a rectangle = base (b) x height (h)
base (b) = 9 + h
area = 112 cm²
plug in values:
112 = (9 + h) * h
112 = 9h + h²
h² + 9h - 112 = 0
h can be solved using quadratic equation
-9 ± √ (9² - 4 (1) (-112))
h = --------------------------------------
2
-9 ± √529
h = ----------------
2
h = 7 ; h = -16
therefore the height of a rectangle (h) = 7 cm
solve for base (b)
base (b) = 9 + h
base (b) = 9 + 7
base (b) = 16 cm
proof:
area of a rectangle = base (b) x height (h)
112 = 16 * 7
112 = 112 ---- ok
Which describes changes to the graph of w(x), when applying the transformation w(x – 19)?
Answer:
A point (r, s) on the graph of w(x) moves to (r + 19, s).
Step-by-step explanation:
May be wrong, haven’t checked yet
Find the three trigonometric function values for the angle ø shown.
sin ø =
cos ø =
tan ø =
Answer:
at ∠A sin Ф = 180 + (2 / [tex]\sqrt{22}[/tex] )
at ∠B cos Ф = 180 + (3[tex]\sqrt{2}[/tex] / [tex]\sqrt{22}[/tex] )
at ∠C tan Ф = 180 + (2 / 3[tex]\sqrt{2}[/tex] )
Step-by-step explanation:
let (a) = 3[tex]\sqrt{2}[/tex]
let (b) = 2
let (c) = r
to get the value of hypotenuse (r) use pythagorean theorem
a² + b² = c²
2² + (3[tex]\sqrt{2}[/tex] )² = c²
c = [tex]\sqrt{22}[/tex]
use the law of sines to get the value of angle A (point origin)
sin Ф = opp / hyp
cos Ф = adj / hyp
tan Ф = opp / adj
at ∠A
sin Ф = 180 + (2 / [tex]\sqrt{22}[/tex] )
at ∠B
cos Ф = 180 + (3[tex]\sqrt{2}[/tex] / [tex]\sqrt{22}[/tex] )
at ∠C
tan Ф = 180 + (2 / 3[tex]\sqrt{2}[/tex] )
what number makes the equation true ÷3=6
Answer:2
Step-by-step explanation:
you just do 6 divided by 3 and get 2
Select the correct name for the following line.
The answer would be A!
The reason it's A is because you have two arrors on the number line! Hope this helps with your odyssey ware work!
[tex]\overline{AB}[/tex] is the correct name for the given line.
What are are different names of a line ?A line is called a line segment when it has two endpoints.
A line is called a ray when it has one initial point and the other end is denoted by an arrow stating it can be extended in one direction.
A line with two arrows can be extended in both directions generally called a line.
According to the question we have been given a diagram and we have to determine the correct name of the line AB with two points.
We know that when a line has two end points it is called a line segment.
∴ The correct name is [tex]\overline{AB}[/tex]
Learn more about lines here :
https://brainly.com/question/11689511
#SPJ2
The definition of a circle uses the undefined term _______
Answer:
plane because i know what it is
Answer: plane
Step-by-step explanation: I just did it
Isolate x: 1 + Ax-B=0
Answer:
x=(-1+B)/A
Step-by-step explanation:
1+Ax-B=0
Ax-B=0-1
Ax=0-1+B
x=(0-1+B)/A or 0/A-1/A+B/A
:)
If the candidate only wants a 0.2% margin of error at a 95% confidence level, what size of sample is needed?
Answer:
n = 22
Step-by-step explanation:
Using
n = p(1-p)(Zc/E)²
From table E = 0.2 while p= 0.37
So substituting
We have n= 22.4
Thats a sample size of approximately 22
Help me with #4
It’s about limits for calculus class
Show steps
Your help is much appreciated!
Step-by-step explanation:
a. lim(x→2) [g(x) + h(x)]
Use additive property of limits.
= lim(x→2) g(x) + lim(x→2) h(x)
= 0 + 5
= 5
b. lim(x→2) [3 h(x)]
Use multiplication property of limits.
= [lim(x→2) 3] [lim(x→2) h(x)]
= 3 lim(x→2) h(x)
= 3 (5)
= 15
c. lim(x→2) [g(x) h(x)]
Use multiplication property of limits.
= [lim(x→2) g(x)] [lim(x→2) h(x)]
= (0) (5)
= 0
a companies division registered a loss of -$2480 while producing 80 identical parts what was the last per part
Answer:
the loss per part was - $31
Step-by-step explanation:
If the total of losses was $2480 for 80 identical parts, then the loss per part is the division of $2480 by 80:
$2480/80 = $31
So the loss per each part was $31
which normally will be given with a negative sign in front indicating loss:
- $31
My friend makes $7.50 an hour and a combined total of $1500 dollars has made up all of her income from that job. She's curious how much she would have if she was making $8.50 but doesn't wanna go recount her hours herself. Any quick/easy way to find out?
Answer:
use conects thats the best for any math problem including word problems
Answer:
$1500/$7.50 = 200 hours
Step-by-step explanation:
Divide the amount she made by how much she makes an hour.
[tex]\frac{1500}{7.50}[/tex] = 200 hours
Suppose your parents are traveling on a work-related trip for a whole week. They left you P10,000 as allowance for the week to be divided fairly among you and your two younger siblings. How would you divide the money, assuming that the amounts should be in whole pesos and with no spare change? Explain how you came up with your division in one sentence.
Answer:
The divison would be:
My two yonger siblings: P3000 Each
Me: P4000.
This idea came about due to the fact that, the eldest an the youngest siblings are not meant to receive equal amount of anything when it is shared among them.
Step-by-step explanation:
This is the only logical way in which the P10,000 can be shared between me and my younger siblings in-order to obtain a whole pesos division and with no fractions. Anything aside this, would give room to involve spare change.
The amount each person gets from P10,000 in whole pesos and with no spare change is P4,000, P,3000 and P3,000 respectively.
Total amount given as allowance = P10,000
Number of people to share it = 3
1 older and 2 younger siblings
Let
the older sibling get P4,000
Each younger sibling gets P3,000
Each person gets a whole value of pesos without a remainder in the total allowance given.
Therefore, the amount each person gets from P10,000 is P4,000, P,3000 and P3,000
Read more:
https://brainly.com/question/11553378
3. If tangents PA and PB from a point P to a circle with centre O are inclined to each other
at angle of 80°, then Z POA is equal to
Answer:
∠POA= ∠POB = 50°
Step-by-step explanation:
The diagram of the given question has been drawn in the attachment.
From the diagram
Δ PAO is congruent to Δ PBO.
as PO is common in Δ
∠ PAO = ∠PBO = 90°
PA =PB [ tangent from an external point]
⇒∠POA= ∠POB
Also, ∠APB+ ∠AOB = 180°
⇒ 80° + ∠AOB = 180°
⇒∠AOB = 100°
⇒ ∠POA= ∠POB = 50°
Brian needs to start planning for an upcoming move. He is choosing two different size boxes to pack the majority of his stuff. The volume of the first is 1,728 in³ and the second is 13,824 in³. What is the ratio of the surface areas? Given that the boxes are cubes, what is the surface area of the larger of the two boxes?
Solution:
Given,
Volume of the-
First cube box=1728 in³
Second cube box=13824in³
We know that volume of cube =a³
So for the first box
a³= 1728 in³
a= 12 in
Now, surface area of the first box
6a²= 6×(12)²
= 864 in²
and for the second box
b³= 13824 in³
b= 24 in
Now, the surface area of the second box
6b²= 6×(24)²
= 3456 in²
Now, the ratio of the surface area of first box to the second box will be
864:3456
=1:4
The surface area of the larger of two boxes is
3456 in²
Using your understanding of analytic and synthetic geometry, which of the following figures does not belong?
Answer:
Pyramid
Step-by-step explanation:
Figures in the diagram:
Triangle formed by 3 line segmentsPlane (intersecting the prism)PyramidThe first two have two dimensions and the third one has three dimensions
Therefore pyramid does not belong
A data set that includes the years in which your hometown team won championships would be classified as what type of data
Answer:
Interval
Step-by-step explanation:
The interval scale is guageable and data following this scale can be added and subtracted.
Years are values we can either subtract or minus so they fall under the interval scale.
Also, they have no absolute zero, which is a characteristic of the interval scale.
16.103 in expanded form
Answer:
1 ten
6 ones
1 tenth
0 hundredths
3 thousandths
I'm sorry if I misunderstood.
Good luck though! :)
Please add Brainliest if you'd like, not that it matters.
Find the domain and range of following using interval notation
Answer:
Domain: [- ∞, 4.5],
Range: [0.5, ∞]
Step-by-step explanation:
One approach is a graphical representation to solving the problem, which you can see as the two attachment's below. Clearly the domain would be on the interval [- ∞, 4.5] and the range would be on the interval [0.5, ∞]. There is another approach to this though,
We can determine the domain by finding what value for p makes the function undefined
Given : h(p) = (p + 3) / (2p - 9),
Value for p where denominator = 0 :
2p - 9 = 0,
2p = 9,
p = 9 / 2 = 4.5
And to determine the range we have to determine the set of values that corresponds with the domain. In this case it's p = 0.5.
Which rigid motion verifies the triangles are congruent by SAS?
Answer: Reflection.
Step-by-step explanation:
In the image, we can see that the right angles share a common side. In this common side, we can see that the right angles of the triangles are next to each other (because we have a straight line cut by a perpendicular one) and the same case for the top angle.
Then if we do a reflection over this common line of one of the triangles, the result will be the other triangle.
Then the correct option is a reflection
The rigid motion that verifies the triangles are congruent by SAS is reflection.
The angle of reflection simply means the angle that's formed between the normal ray and the reflected ray. It's the line that's perpendicular to the resulting surface at the point of incidence.
According to the law of reflection, the angle of reflection must be equal to the angle of incidence. Therefore, the rigid motion that verifies the triangles are congruent by SAS is reflection.
Read related link on:
https://brainly.com/question/17296106
How is the product of 3 and –2 shown using integer tiles?
Answer:
-6
Step-by-step explanation:
you multiply (3)x(-2). a negative times a positive is a negative. so you get -6
I don't get this pls help
Answer:
d, e
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^-b = 1/a^b
__
In this case, it means the product is ...
(6^1)(6^0)(6^-3) = 6^(1+0-3) = 6^-2 = 1/6^2 = 1/36
__
The 6 without an exponent is equivalent to 6^1, an exponent of 1.
The sum of the exponents is -2.
Add the exponents to simplify the expression.
The value of the expression is 1/36.
An equivalent is any expression that results in 6^-2. One such is (6^5)(6^-7).
__
Only the last two choices, d and e, apply.