Answer:
x = 2
Step-by-step explanation:
2x - 3 = 9 - 4x
6x - 3 = 9 (added 4x to both sides)
6x = 12 (added 3 to both sides)
x = 2 (divided 12 by 6)
hope this helps :)
Can we conclude that x - 5 is a factor of the polynomial
x^3 − x^2 − 17x − 15
How do you know?
Answer:
use synthetic division
Step-by-step explanation:
use synthetic division to solve [tex]\frac{x^{3}-x^{2} -17x-15}{x-5}[/tex].
if solved correctly, you should get [tex]x^{2} +4x+3[/tex] with no remainder.
because there is no remainder, x-5 is a factor of the polynomial given.
[tex](x-5)[/tex] is a factor of the given polynomial because the value of the polynomial is [tex]0[/tex] at [tex]x=5[/tex].
Given:
The given polynomial is [tex]x^3-x^2-17x-15[/tex].
Explanation:
We know that, [tex](x-c)[/tex] is a factor of [tex]P(x)[/tex] if and only if [tex]f(c)=0[/tex].
We have,
[tex]P(x)=x^3-x^2-17x-15[/tex]
Substituting [tex]x=5[/tex] in the above polynomial, we get
[tex]P(5)=(5)^3-(5)^2-17(5)-15[/tex]
[tex]P(5)=125-25-85-15[/tex]
[tex]P(5)=0[/tex]
Since [tex]P(5)=0[/tex], therefore [tex](x-5)[/tex] is a factor of the given polynomial.
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solve for x 4x-7=2(x+3)+9 i need explanation
Answer:
x=11 :)
Step-by-step explanation:
Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at the University of Texas Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. According to HR, "if you have this tendency, consider using a normal distribution—10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable." Suppose you are rating an employee’s performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 50 and a standard deviation of 15.
a. What is the lowest rating you should give to an "exemplary" employee if you follow the University of Texas HR guidelines?
b. What is the lowest rating you should give to a "competent" employee if you follow the University of Texas HR guidelines?
Answer and Step-by-step explanation:
Solution:
Given:
µ = 50
∂ = 15
Lowest rating given to exemplary.
The top 10 %of the employees are related exemplary:
P(x > L) = 10 % =0.10
The average probability table in the appendix contains the only probability of the form.
P (0 < x< L ) = p ( x > 0 ) – P ( x > L )
= 0.5 -0.10
= 0.40
z- Score in the normal probability table in the appendix corresponding to a probability of 0.40 or the closest probability.
Z = 1.28
The standardized score is the value x decreased by the mean and then divided by the standard deviation.
Z = x - µ / σ
L = x = µ +z0
= 50 + 1.28(15)
= 69.2
Lowest rating giving to competent:
The lower boundary of competent is boundary of bottom 30%
P(x < L ) = 30% = 0.30
The normal probability table contains only probability of the form p( 0≤z≤z0)
P( 0< x < -L) = P(L < x < 0)
= p(x < 0) – p(x < L)
=0.5 – 0.30
= 0.20
Z score in normal probability corresponding to the probability of 0.20
-z = 0.52
Z= - 0.52
Value x decreased by the mean and divide by standard deviation:
Z = x - µ / ∂
L = x = µ + zo
= 50 – 0.52(15)
= 42.2
Triangle ABC is similar to triangle DEF solve for r?
Answer:
send a picture too understand it
Step-by-step explanation:
we dont have enough information
there are 8 teachers in in a school when a 35 year old teacher was transferred and another teacher join the average age was increased by 2 years how old is the new teacher
Answer:51
Step-by-step explanation:
Algebraic expression of 4x
Use the graph of the function. Determine over what interval(s) the function is positive or negative.
Answer:
The function is positive
Step-by-step explanation:
As you can see, the line makes a U shape aiming for the positive side of the graph.
The function in which the function is positive is (- 2, -1] ∪ [1, 2) and negative is [-1 to 1].
We have a graph of a function f(x).
We have to determine over what interval the function is positive or negative.
Define Function.A function from a set X to a set Y is an assignment of an element of Y to each element of X. The set X is called the domain of the function and the set Y is called the codomain of the function. For example - shown below is a piecewise function -
[tex]f(x) = \left\{ \begin{array}{ll} x^2 \quad x > 0 \\ 0 \quad \text{else} \end{array} \right.[/tex]
According to the question, we have a graph.
It can be seen in graph that the function f(x) is '+' in ranges : - 2 to -1 and 1 to 2.
The interval in which f(x) is positive is → (- 2, -1] ∪ [1, 2).
In the interval of : -1 to 1, the function has a negative value.
The interval is → [-1 to 1]
Hence, the function in which the function is positive is (- 2, -1] ∪ [1, 2) and negative is [-1 to 1].
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1. You work for a mortgage lender that really encourages you to sell ARM loans to your clients. In fact, if 75% of the loans you close each month are ARM loans, you receive a very nice bonus. You have a customer on the phone that you don’t feel understands ARM loans very well despite all your efforts. He tells you repeatedly that he would be better off with a 30-year fixed rate mortgage. You proceed to take his application and send all the required documentation to him for a 5/1 ARM. He signs the documents and returns them to you. You process his loan and close it 30 days later.
A. Do you feel you ethically assisted your borrower with this loan?
B. What could you have done differently?
2. You have a co-worker at work that you are also friends with. One day, a borrower comes in and meets with him. You overhear the borrower tell your co-worker that he has a loan with his mom and dad for about $10,000 that he pays $300 a month. Your co-worker proceeds as if he didn’t hear your borrower at all. Once he has taken the application, he tells the borrower that he qualifies for maximum financing for a $250,000 home. However, that does not take into consideration the $300 a month the borrower pays his parents for the loan.
A. Did your coworker do anything unethical in this transaction?
B. Assuming you feel this was an unethical situation, how do you handle this?
Answer:
A
Well in this case i don't feel i have ethically assisted by borrower because the type of loan my costumer requested from me is the 30-year fixed rate mortgage but because of the bonus i will gain from closing ARM loan i sent him/her the documentation to him for a 5/1 ARM loan even though he has told me repeatedly that he would be better off with the 30-year fixed rate mortgage
B
What i would have done differently was to be more patient and explain him the benefits of the ARM loan and the if he / she insists that he still want the 30-year fixed rate mortgage, then i would have sent him /her the documentation for the 30-year fixed rate mortgage.
2
A
Yes my co-worker acted in an unethical manner by not recognizing the fact that the costumer is servicing another loan with $300 a month and then proceeding to qualify him/her for a maximum financing of $250,000 which will would increase the risk in the current transaction
B
Since i feel this is unethical, the next step i will take is to call my co-worker aside and bring to his notice the fact that the borrower is servicing another loan with $300 per month , and then i will ask my co-worker to bring this fact into consideration when determine his maximum financing which in this case he has to reduce , then if my co-worker does not agree with my advice then in order to ensure that the company does not loss funds i will call in a higher authority in the company.
Step-by-step explanation:
You may have polarized sunglasses that eliminate glare by polarizing the light. When light is polarized, all of the waves are traveling in parallel planes. Suppose vertically polarized light with intensity Io strikes a polarized filter with its axis at an angle of θ with the vertical. The intensity of the transmitted light It and θ are related by the equation Cosθ= √ Io/It. If θ, write It as a function of Io,
Answer:
lt = lo/cos²θStep-by-step explanation:
Given the intensity of the transmitted light It and θ are related by the equation Cosθ= √ Io/It, we are to write lt as a function of lo
Given the equation
Cosθ= √ Io/It
Let us make lt the subject of the formula;
square both sides of the equation
(Cosθ)²= (√ Io/It)²
cos²θ = lo/lt
cross multiply
ltcos²θ = lo
divide both sides by cos²θ
ltcos²θ/ cos²θ= lo/cos²θ
lt = lo/cos²θ
Hence the expression of lt as a function of lo is lt = lo/cos²θ
The accompanying data represent the actual amount (in mL) poured into a short, wide glass for individuals asked to pour 44.3 mL (1.5 ounces).
89.3 68.6 32.7 37.3 39.7 46.7 66.1 79.4 66.4 52.1 47.3
64.4 53.7 63.4 46.2 63.0 92.1 57.6
A) Calculate the values of the mean and standard deviation (in mL).
mean 59.222 mL
standard deviation 16.725 mL
Interpret the values of the mean and standard deviation.
A typical amount poured into a short, wide glass is 19.7 mL. A typical deviation from the mean amount poured is_____mL.
B) The mean amount poured into a tall, slender glass for individuals asked to pour 44.3 mL (1.5 ounces) was 51.283 mL. What do the values of the means for the two types of glasses suggest about the shape of glasses used?
The mean amount for a short, wide glass is greater than the mean amount for a tall, slender glass. This suggests that bartenders tend to pour more into a short, wide glass compared to a tall, slender glass.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data below :
x : 89.3 68.6 32.7 37.3 39.7 46.7 66.1 79.4 66.4 52.1 47.3 64.4 53.7 63.4 46.2 63.0 92.1 57.6
Mean(m) = ΣX / n
ΣX = 1066 ; n = number of observations = 18
Mean(m) = 1066 / 18
Mean = 59.22
Standard deviation (σ) :
Using the online standard deviation calculator :
σ = √(Σ(x - m)²/n-1)
σ = √264.198395
σ = 16.72
The mean amount poured into a glass for the 18 samples is 59.22 while the variation in the data samples from the mean value is 16.72.
typical amount poured into a short, wide glass is 19.7 mL. A typical deviation from the mean amount poured is_____mL.
(59.22 - 19.7) mL = 39.52mL
Mean amount poured into a tall slender glass = 51.283
Mean (short wide glass) = 59.22mL
Mean (tall slender glass) = 51.283mL
Short wide glass > tall slender glass
The population of Canada is 34,482 thousand people. If the world population is 7 billion people, then what percentage of the worlds population ilives in Canada.
Answer:
About
Explanation:
To find a percent, divide the numerator, 34,482 by 7 billion to get your percent. I rounded it to the nearest whole. the actual percent is actually 4.92%. Hope it helped!
Find −914+27. Write your answer as a fraction in simplest form.
Answer:
- +=_
914-27=887
887 answer this fraction
helppp pls, I cant seem to place them..
PLEASE HELP WOULD BE APPRECIATED!!!
Mary is saving money for college expenses. She saves the same amount each month.
The table shows the amount of money Mary has saved after 4 and 7 months.
Answer: a, c, and d
Step-by-step explanation: hard to explain
hope this helped :)
PROBLEM I: On Monday the temperature was 70° F. On Tuesday the temperature dropped 10°,
followed by a 5º decrease on Wednesday. On Thursday, the temperature increased 7 degrees followed by a
decrease of 2 degrees on Friday. What was the final temperature on Friday?
Number Sentence:
Solution:
Answer:
Answer 60 degrees
Step-by-step explanation:
70-10 60-5 55+7 62-2 60
how to solve 33 times 32
Answer:
1056
Step-by-step explanation:
33*32= 1056
(33*30)+(33*2)= (990)+(66)=1056
6x-2y=24 what's the slope and Y intercept?
An airline makes 200 reservations for a flight who holds 185 passengers. The probability that a passenger arrives for the flight is 0.9 and the passengers are assumed to be independent. Use the normal approximation of Binomial distribution to answer the following questions.
(a) Approximate the probability that all the passengers who arrives can be seated.
(b) Approximate the probability that there are empty seats.
(c) Approximate the number of reservations that the airline should make so that the probability that everyone who arrives can be seated is 0.95 [Hints: since the number of reservations must be integers, please approximate your answer to an integer.]
Answer:
A=0.9
B=0.855
C=198
Step-by-step explanation:
Let X be the binomial random variation with parameters given bellow as
n=200
p=1-0.9=0.1
Note that the value of Z is approximate standard random normal variable with the values of Ф gotten from table
Kindly find attached a detailed solution of the problem with the right annotation and symbols
Which of the following led the church in the Byzantine empire ?
Answer:
Constantine
Step-by-step explanation:
In 330 A.D., Roman Emperor Constantine I chose Byzantium as the site of a “New Rome” with an eponymous capital city, Constantinople. Five years earlier, at the Council of Nicaea, Constantine had established Christianity — once an obscure Jewish sect — as Rome's official religion.
CIO and MAP are
supplementary MAP measures five times the other angle. What is the complement of the smaller anglo?
Provide the equation to solve for the unknown angle
Measure of Angle CIO
MAP
Complement of smaller angle
Answer:
Measure of CIO = 30°
Measure of MAP = 150°
Complement of smaller angle = 60°
Step-by-step explanation:
Given that <CIO and <MAP are supplementary, therefore:
m<CIO + m<MAP = 180°
Let x be m<CIO
m<MAP = 5x
Thus:
x + 5x = 180
Solve for x
6x = 180
Divide both sides by 6
x = 30°
The smaller angle = m<CIO = x = 30°
The bigger angle = m<MAP) = 5x = 5(30) = 150°
Complement of the smaller angle = 90 - 30 = 60°
I’m doing a midterm and I’m really not doing too hot. can someone help?
What is the range of the relation shown ir the table
Answer:
The answer is C.
Step-by-step explanation:
The range means the values of y.
a 14 inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 4 times as long as the first piece find the length of the pieces
Answer:
the first is 2 inches the 2nd one 4 inches and the 3rd is 8 inches
Step-by-step explanation:
The length of the piece is 2, 4 and 8.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a 14 inch board is to be cut into three pieces
Let first piece be x.
The second piece is twice as long as the first piece
Second piece is 2x
The third piece is 4 times as long as the first piece.
Third piece is 4x
x+2x+4x=14
7x=14
Divide both sides by 7
x=2
Hence, the length of the piece is 2, 4 and 8.
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Mari swims every 4 days and runs every 6 days. In how many days will she both swim and run on the same day?
Answer:
12
Step-by-step explanation:
We find the LCM which is simply 12.
Patric decided to run every day to keep himself healthy. He ended up running 3/5 of a kilometer everyday. How much did he run in a week
Find all solutions n to the equation
$$6^{2n+1}+6^2=6^n+6^{n+3}.$$
9514 1404 393
Answer:
n = -1 or 2
Step-by-step explanation:
The equation can be rewritten using x = 6^n. Then we can solve the quadratic.
[tex]6^{2n+1}+6^2=6^n+6^{n+3}\\\\6\cdot(6^n)^2+6^2=6^n+6^3\cdot6^n\\\\6x^2+6^2=x(1+6^3)\\\\6x^2-6^3x-x+6^2=0\qquad\text{subtract $x(1+6^3)$}\\\\6x(x-6^2)-1(x-6^2)=0\\\\(6x-1)(x-6^2)=0\\\\x=6^n=6^{-1}\quad\text{or}\quad x=6^n=6^2\\\\\boxed{n=-1\text{ or }2}[/tex]
_____
A graphing calculator can find the zeros of the exponential function ...
y = 6^(2n+1) +6^2 -6^n -6^(n+3) . . . . . right side subtracted
Within a company is a (micro)economy that is monitored by the accounting procedures. In terms of the accounts, the various departments "produce" costs, some of which are internal and some of which are direct costs. This problem shows how an open Leontief model can be used to determine departmental costs.
The sales department of an auto dealership charges 10% of its total monthly costs to the service department, and the service department charges 20% of its total monthly costs to the sales department. During a given month, the direct costs are $88,200 for sales and $29,400 for service. Find the total costs (in dollars) of each department. (Round your answers to the nearest whole number.)
sales department
service department
Answer:
The total cost of sales department is [tex]a = \$ 84,000[/tex]
The total cost of services department is [tex]b = \$ 21,000[/tex]
Step-by-step explanation:
From the question we are told that
The direct for sales cost is [tex]SC = \$88,200[/tex]
The direct cost for service department is [tex] SV = \$29,400[/tex]
Given that the sales department charges 10% of its total monthly costs to the service department
The indirect cost of service department is 10% of a = 0.10 a
Here a is the total cost of sales
Given that the service department charges 20% of its total monthly costs to the sales department
The indirect cost of sales department is 20% of b = 0.20 b
Here b is the total cost for service department
Generally the direct cost of sales can be mathematically represented as
[tex]SC = a + 0.20b [/tex]
=> [tex]88200 = a + 0.20b[/tex]
=> [tex]a = 88200-0.20b[/tex]
Generally the direct cost of services can be mathematically represented as
[tex]SV = b + 0.10a [/tex]
=> [tex]29400 = b + 0.10a[/tex]
substituting for a in the above equation
=> [tex]29400 = b + 0.10 [88200-0.20b][/tex]
=> [tex]b = \$ 21,000[/tex]
substituting this value into the equation for a
[tex]a = 88200-0.20 (21000)[/tex]
=> [tex]a = \$ 84000[/tex]
9. Verizon offers a cell phone plan that includes a flat fee of $85 per month for the first phone and $7.50 a
month for each additional phone. If Maria's phone bill was $115, how many extra phone lines does she
have?
Answer:
4 phones
Step-by-step explanation:
Answer:15
Step-by-step explanation:
You multiply the dimensions of Triangle A by 3 to create Triangle B. Select the conclusion(s)
that you can make about the similar triangles.
The ratio of the perimeters (Triangle A to
Triangle B) is :
The ratio of the perimeters (Triangle B to
Triangle A) is 1 to 3.
The ratio of the areas (Triangle B to Triangle A)
is 9:1.
The ratio of the areas (Triangle A to Triangle B)
is 1 to 6.
There is not enough information to make any
of the conclusions above.
Answer:There is not enough information to make any of the conclusions above
Step-by-step explanation:
find the GCF of 28 and 30
Answer:
4
Step-by-step explanation:
The biggest number that you can divide 28 and 30 is 4.
Answer:
Greatest common factor (GCF) of 28 and 30 is 2.
Step-by-step explanation:
You find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28 and 30.
Simplify.
i68
help plz
the answer is 1 ;-; ;-; ;-; ;-;