Answer:
1. Find the GCF of all the terms in the polynomial.
2. Express each term as a product of the GCF and another factor.
3. Use the distributive property to factor out the GCF.
A. 1
B. 9
C. 10
D.1/9
Answer:
B. 9
Step-by-step explanation:
When the line runs( x variation) by 1 , it rises (y variation) by 9
And since unit rate is calculated by Rise/Run, the unit rate is 9/1 or 9
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Seth and Ted can paint a room in 5 hours if they work together. If Ted were to work by himself, it would take him 2 hours longer than it would take Seth working by himself. How long would it take Seth to paint the room by himself if Ted calls in sick?
Answer:
9 hours
Step-by-step explanation:
Let
x = number of hours it would take Seth to work by himself
He would paint 1/x in 1 hour
x + 2 = number of hours it would take Ted to work by himself
He would paint 1/(x + 2) in 1 hour
Seth and Ted = 5 hours
They would paint 1/5 in 1 hour
The equation is this:
1/x + 1/(x + 2) = 1/5
(x + 2)+x/x(x+2) = 1/5
x+2+x / x(x+2) = 1/5
2x + 2 / x(x+2) = 1/5
2x + 2 = x(x + 2)1/5
2x + 2 = (x² + 2x)1/5
5(2x + 2) = x² + 2x
10x + 10 = x² + 2x
x² + 2x - 10x - 10 = 0
x² - 8x - 10 = 0
x = -b ± √b² - 4ac/2a
= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)
= 8 ± √64 - (-40) / 2
= 8 ± √64 + 40) / 2
= 8 ± √104 / 2
= 8 ± 2√26 / 2
= 8/2 ± 2√26/2
= 4 ± √26
= 4 ± 5.0990195135927
= 4 + 5.0990195135927 or 4 - 5.0990195135927
= 9.0990195135927 or -1.Answer:
Step-by-step explanation:
Let
x = number of hours it would take Seth to work by himself
He would paint 1/x in 1 hour
x + 2 = number of hours it would take Ted to work by himself
He would paint 1/(x + 2) in 1 hour
Seth and Ted = 5 hours
They would paint 1/5 in 1 hour
The equation is this:
1/x + 1/(x + 2) = 1/5
(x + 2)+x / x(x+2) = 1/5
x+2+x / x(x+2) = 1/5
2x + 2 / x(x+2) = 1/5
Cross product
2x + 2 = x(x + 2)1/5
2x + 2 = (x² + 2x)1/5
Cross product
5(2x + 2) = x² + 2x
10x + 10 = x² + 2x
x² + 2x - 10x - 10 = 0
x² - 8x - 10 = 0
x = -b ± √b² - 4ac/2a
= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)
= 8 ± √64 - (-40) / 2
= 8 ± √64 + 40) / 2
= 8 ± √104 / 2
= 8 ± 2√26 / 2
= 8/2 ± 2√26/2
= 4 ± √26
= 4 ± 5.0990195135927
= 4 + 5.0990195135927 or 4 - 5.0990195135927
= 9.0990195135927 or -1.0990195135927
Approximately,
x = 9 hours or -1 hour
It can't take Seth negative hours to work
Therefore,
x = number of hours it would take Seth to work by himself = 9 hours
For each of the following variables, identify the type of variable (categorical vs. numeric). (1) Temperature (in Fahrenheit) of an office building (11) Traffic congestion (e.g. light, medium, heavy)
1) (1) Numeric, and (II) Categorical
2) (1) Numeric, and (II) Numeric
3) (1) Categorical, and (II) Numeric
4) There is no correct match.
5) (1) Categorical, and (11) Categorical
Answer:
(a) Temperature: Numerical
(b) Traffic congestion: Categorical
Step-by-step explanation:
Required
Determine the variable type
(a) Temperature
Temperatures are measured in numeric values e.g. 22 degree Fahrenheit, etc.
Hence, the variable is numerical
(b) Traffic congestion
From the question, we understand that the traffic congestion are divided into three categories i.e. light, medium....
Hence, the variable is categorical
solve the system of equation — 3х + бу = 9
5х + 7y = -49
Answer:
y = 64/3
x = -119/3
Step-by-step explanation:
3х + 6у = 9 => 5*3x+5*6у = 9*5 => 15x+30у=45 (1)
5х + 7y = -49 => 3*5x + 3*7y = -49*3 => 15x+21y=-147 (2)
(1)-(2) => 9y = 192 => y = 64/3
x = -119/3
Not sure about the answers I gave
Need help with the others
Answer:
Ask me
Step-by-step explanation:
Tell me dear ask..
8) If 150% of a number is 75, then what is the 80% of that number?
A. 40
B. 50
C. 70
D. 85
Answer:
A. 40
Step-by-step explanation:
Answer:
A. 40
Step-by-step explanation:
75 ÷ 1.5 = 50 = original number
80% of 50 = 50 × 0.8 = 40
The lengths of pregnancies are normally distributed with a mean of days and a standard deviation of days. a. Find the probability of a pregnancy lasting days or longer. b. If the length of pregnancy is in the lowest %, then the baby is premature. Find the length that separates premature babies from those who are not premature.
Answer:
a) The probability of a pregnancy lasting X days or longer is given by 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
b) We have to find X when Z has a p-value of [tex]\frac{a}{100}[/tex], and X is given by: [tex]X = \mu - Z\sigma[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]
a. Find the probability of a pregnancy lasting X days or longer.
The probability of a pregnancy lasting X days or longer is given by 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
b. If the length of pregnancy is in the lowest a%, then the baby is premature. Find the length that separates premature babies from those who are not premature.
We have to find X when Z has a p-value of [tex]\frac{a}{100}[/tex], and X is given by: [tex]X = \mu - Z\sigma[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
Which choice is equivalent to the expression below?
V -100
O A. 110;
B. 101
C. -10
O D. 10
O E. - V10
Answer:
C. -10Step-by-step explanation:
[tex]hope \: it \: helps[/tex]
CarryOnLearning
Matthew participates in a study that is looking at how confident students at SUNY Albany are. The mean score on the scale is 50. The distribution has a standard deviation of 10 and is normally distributed. Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale
Answer:
The percentage of people that could be expected to score the same as Matthew or higher on this scale is:
= 93.3%.
Step-by-step explanation:
a) Data and Calculations:
Mean score on the scale, μ = 50
Distribution's standard deviation, σ = 10
Matthew scores, x = 65
Calculating the Z-score:
Z-score = (x – μ) / σ
= (65-50)/10
= 1.5
The probability based on a Z-score of 1.5 is 0.93319
Therefore, the percentage of people that could be expected to score the same as Matthew or higher on this scale is 93.3%.
How do I solve this. Y=f(x)+a moves the function
Answer:
up
Step-by-step explanation:
for linear functions, adding a constant will increase the y value by two and shift the line up two units on the graph.
Answer: It moves the function 'a' units up if a > 0. Or it moves the function |a| units down if a < 0.
Explanation:
Consider an example like y = f(x)+2. This shifts the f(x) curve 2 units up because we're adding 2 to each y or f(x) output. A point like (5,7) shifts up to (5,9).
As another example, y = f(x)-5 moves the curve 5 units down.
In the first example, we had a > 0 which moved the function 'a' units up (a = 2 in that case). The second example had a = -5 which means a < 0, so that's why we shifted |a| = |-5| = 5 units down.
At a coffee shop, the first 100 customers'
orders were as follows.
Medium Large
Small
Hot
5
48
22
Cold
8
12
5
What is the probability that a customer ordered
a small given that he or she ordered a hot
drink?
Rounded to the nearest percent, [? ]%
Well formatted distribution table is attached below :
Answer:
7%
Step-by-step explanation:
The probability that a customer ordered a small Given that he or she ordered a hot drink ;
This is a conditional probability and will be represented as :
Let :
P(small drink) = P(S)
P(hot drink) = P(H)
Hence, the conditional probability is written as :
P(S|H) = P(SnH) / P(H) = 5 / (5+48+22) = 5/75 = 0.0666 = 0.0666 * 100% = 6.67%
Compare the subtraction problems (6/8-5/8=1/8) and (6/9-7/9=-1/9) why is the answer to the first problem positive nad the answer to the second problem negative select all that apply
6/9 - 7/9 = -1/9
is a negative number.
Solve by graphing. Round each answer to the nearest tenth.
6x2 = −19x − 15
a: −2, 1.7
b: −1.7, −1.5
c: −1.5, 1.5
d: −1.5, 1.7
9514 1404 393
Answer:
b: -1.7, -1.5
Step-by-step explanation:
The graph is shown below. We have annotated the x-intercepts for the equivalent equation ...
6x^2 +19x +15 = 0
A statewide real estate sales agency, Farm Associates, specializes in selling farm property in the state of Nebraska. Its records indicate that the mean selling time of farm property is 90 days. Because of recent drought conditions, the agency believes that the mean selling time is now greater than 90 days. A statewide survey of 100 recently sold farms revealed a mean selling time of 94 days, with a standard deviation of 22 days.
At the 0.10 significance level, has there been an increase in selling time?
a. What is the decision rule? (Round your answer to 3 decimal places.)
b. Compute the value of the test statistic. (Round your answer to 2 decimal places.)
c. What is your decision regarding H0?
Answer:
Test statistic = 1.818
Reject H0
Step-by-step explanation:
H0 : μ = 90
H1 : μ > 90
xbar = 94 ; s = 22 ; n = 100
The test statistic : (xbar - μ) ÷ (s/√(n))
Test statistic = (94 - 90) ÷ (22/√100)
Test statistic = 4 ÷ 2.2
T = 1.818
The critical value :
At α = 0.10
Degree of freedom = n - 1 = 100 - 1 = 99
Tcritical(0.10, 99) = 1.290
Decison region :
Reject H0 if Test statistic > |Tcritical |
1.818 > 1.290
We reject H0
Find the missing term in the following pattern.
1984, 992, 496, blank space, 124, 62
Answer:
248
Step-by-step explanation:
common ratio for two consecutive terms is 2/1
for eg: 1984÷992 =2
992÷ 496 = 2
124÷ 62 = 2
that means 124 ×2 = 248 Answer
write 16.76 correct to the nearest whole number
Answer:
17
Step-by-step explanation:
because they are both above 5 so add 1
the complement of guessing 5 correct answers on a 5 question true or false examination is
Answer:
Guessing at least one incorrect answer
Step-by-step explanation:
The complement of guessing 5 correct answers on a 5-question true/false exam is-
Guessing at least one incorrect answer because, when 1 or more questions are incorrectly guessed, the event of 5 correct answers can not occur.
1.A multiple choice exam has five possible answers per question. Only one of those five answers is the correct answer. A student, who did not prepare for the test,answers the exam randomly and in order,starting from the first question. a.What is the probability that the first question he answered correctly is the second question
Answer:
Step-by-step explanation:
P(answers correctly)=1/5
P(answers incorrectly)=1-1/5=4/5
P( answers correctly second question)=4/5 ×1/5=4/25
g In the year 2005, the age-adjusted death rate per 100,000 Americans for heart disease was 222.3. In the year 2009, the age-adjusted death rate per 100,000 Americans for heart disease had changed to 213.4. a) Find an exponential model for this data, where t
This question is incomplete, the complete question is;
In the year 2005, the age-adjusted death rate per 100,000 Americans for heart disease was 222.3. In the year 2009, the age-adjusted death rate per 100,000 Americans for heart disease had changed to 213.4.
a) Find an exponential model for this data, where t = 0 corresponds to 1999
Answer:
the exponential model for this data will be; y = 222.3( 0.9898 )^t
Step-by-step explanation:
Given the data in the question;
{ 2005 }, at t = 0, death rate was 222.3
In 2009, { 2009 - 2005 = 4 }, at t = 4 death rate was 213.4
Now, let the exponential equation be;
y = ab^(t)
so at t = 0
222.3 = a × b^(0)
222.3 = a × 1
a = 222.3
at t = 4
213.4 = a × b^(4)
213.4 = 222.3 × b^(4)
b⁴ = 213.4 / 222.3
b = ( 213.4 / 222.3 )^(1/4)
b = 0.9898
y = ab^(t)
Hence, the exponential model for this data will be; y = 222.3( 0.9898 )^t
Find the area enclosed by y1 = (x - 1)3 and y2 = x -1.
I wanted to double check the answer. The professor got something completely different.
Find area between two curves
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Answer:
0.5
Step-by-step explanation:
The "enclosed area" can be taken to mean different things. Here, we consider it to mean the finite area bounded between the two curves, regardless of which curve is higher value than the other.
The area is bounded on the interval [0, 2]. On half that interval y1 > y2; on the other half, y2 > y1. This means the integral of the area between the curves will be different for one part of the interval than for the other. (The curves are symmetric about the point (1, 0).)
The area on the interval [0, 1] is given by the integral ...
[tex]\displaystyle\int_0^1{(y_1-y_2)}\,dx=\int_0^1{((x-1)^3-(x-1))}\,dx\\\\=\int^1_0{(x(x-1)(x -2))}\,dx=\left.(\frac{x^4}{4}-x^3+x^2)\right|^1_0=\boxed{\frac{1}{4}}[/tex]
The area on the interval [1, 2] is the integral of the opposite integrand, but has the same value.
The positive area over the whole interval from 0 to 2 is 1/4+1/4 = 1/2.
If you simply integrate y2-y1 or y1-y2 over that interval, the result is 0.
98 POINTS!!!
Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Consider the graph of f(x) = 5x + 1. Explain how to find the average rate of change between x = 0 and x = 4. What is the average rate of change?
Answer:
The average rate of change is 5.
Step-by-step explanation:
First plug in the x values.
y=5x+1
=(0)5+1
=1
y=5x+1
=(4)5+1
=21
Average rate of change = the change in the output divided by the change in the input.
Output change: 21-1=20
Input change: 4-0=4
20/4=5
Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power series expansion. Do not show that Rn(x)→0 . f(x)=lnx, a=
Answer:
Here we just want to find the Taylor series for f(x) = ln(x), centered at the value of a (which we do not know).
Remember that the general Taylor expansion is:
[tex]f(x) = f(a) + f'(a)*(x - a) + \frac{1}{2!}*f''(a)(x -a)^2 + ...[/tex]
for our function we have:
f'(x) = 1/x
f''(x) = -1/x^2
f'''(x) = (1/2)*(1/x^3)
this is enough, now just let's write the series:
[tex]f(x) = ln(a) + \frac{1}{a} *(x - a) - \frac{1}{2!} *\frac{1}{a^2} *(x - a)^2 + \frac{1}{3!} *\frac{1}{2*a^3} *(x - a)^3 + ....[/tex]
This is the Taylor series to 3rd degree, you just need to change the value of a for the required value.
What is the following product? Assume x>0 and y>0 v5x^8y^2•v10^3•v12y
Answer:
[tex]10x^{5}y \sqrt{6xy}[/tex]
Step-by-step explanation:
Create a quadratic equation in one variable of the form ax^2+bx+c=0 that meets the following criteria. A=1, b=0 , c=-100. 20 points.
Answer:
Equation is x^2-100=0
Step-by-step explanation:
I'm assuming everything is in standard form. Just plug in the values.
1(x)^2+(0)x+(-100)=0
0 times x is 0, so it simplifies to
x^2-100=0
What does y equal in the solution of the system of equations below? 5y-3x-4z=22 2z-2x=-6 2z+3x=-6
9514 1404 393
Answer:
y = 2
Step-by-step explanation:
Subtracting the second equation from the third gives ...
(2z +3x) -(2z -2x) = (-6) -(-6)
5x = 0
x = 0
Using this in the third equation, we have ...
2z +0 = -6
z = -3
And substituting these values into the first equation, we have ...
5y -3(0) -4(-3) = 22
5y = 10 . . . . . subtract 12
y = 2
__
The solution to the system is (x, y, z) = (0, 2, -3).
answer please don't skip plz answer
What is the value of x^2
-2xy+y^2
if x-y = 4 ?
please answer
Answer:
16
Step-by-step explanation:
[tex]x^2 - 2xy + y^2 = (x -y)^2 \\[/tex]
[tex]= 4^2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ given : x - y= 4 \ ]\\\\= 16[/tex]
The value of x^2-2xy+y^2
will be 16 .
Explanation is in the attachment .
hope it is helpful to you ☺️
If someone can pls give me the answer the would be greatly appreciated :)
Step-by-step explanation:
The Answer Is Provided Below ➳
(2²)² = 2⁴/2⁴ = 2⁰ × 2⁰ = 2⁰/2⁰
What piece of information is needed to prove
the triangles are congruent through ASA?
Answer:
B. <B is congruent to the <Z
OPTION B is the correct answer
T=3 and t=5 to determine if the expression 4(t+3) and 4 t+12 are equivalent
An employee at a shoe store has observed that taller customers have larger shoe sizes than customers who are shorter. She knows that shoe sizes are based on foot length, so she hypothesizes: Compared with shorter people, taller people have longer feet.
Question attachment below
Answer and explanation:
Data patterns are repeated data occurrences in a certain way that is recognizable.
In the example below, the data pattern shows taller people require larger shoe sizes(the taller the person the larger the shoe size) but does make some exceptions. Example: while Denver is taller and requires a larger shoe size, Eduardo is shorter than Tim and still requires a larger shoe size than Tim.