Answer:
The line passing through the given points is:
[tex]y=-\frac{4}{3}x+\frac{1}{3}[/tex]
in its slope-intercept form
Step-by-step explanation:
Start by finding the slope of the segment that joins the two given points using the slope formula:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
which for our case renders:
[tex]slope=\frac{3-(-5)}{-2-4}=\frac{8}{-6} =-\frac{4}{3}[/tex]
Now we can find the y-intercept by using any one of the given points in the general slope-intercept form of a line with this slope:
[tex]y=-\frac{4}{3} x+b\\3=-\frac{4}{3} (-2)+b\\3=\frac{8}{3}+b\\b=3-\frac{8}{3} \\b=\frac{9-8}{3} \\b=\frac{1}{3}[/tex]
Therefore, the equation of the line becomes:
[tex]y=-\frac{4}{3}x+\frac{1}{3}[/tex]
Use the information to answer the question.
A store sells paint sets. Each paint set costs the same amount. During a sale, the store reduces the price of each paint set by $1.50. Logan spends
$13.47 on 3 paint sets at the sale price.
What was the price of 1 paint set before the sale? Enter the answer in the box.
BD bisects ∠ABC. Find m∠ABD and m∠CBD.
Answer:
angle ABD=1/2 angle ABC ,Angle CBD =1/2 angleCBD
Step-by-step explanation:
The measure of angles ∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°.
We have,
BD bisects the angle ABC makes two equal halves angle.
So, < ABD= < CBD.
and ∠ABD= (8x + 35)°
∠CBD= (11x + 23)°
Substituting the values of the angles
(8x + 35)° = (11x + 23)°
35-23 = 11x- 8x
3x= 12
x= 4.
Putting x=4 in (i) we have,
∠ABD= 8(4) + 35
∠ABD= 67°
As ∠ABD = ∠CBD,
∠CBD= 67°
Now, ∠ABC= ∠ABD + ∠CBD
∠ABC= 67° + 67°
∠ABC= 134°.
Hence, the measure of m∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°.
Learn more about Angular bisector here:
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State whether the data described below are discrete or continuous, and explain why. The weights of dogs (in pounds) at a dog show
A. The data are discrete because the data can take on any value in an interval.
B. The data are discrete because the data can only take on specific values.
C. The data are continuous because the data can only take on specific values.
D. The data are continuous because the data can take on any value in an interval.
Answer: D. The data are continuous because the data can take on any value in an interval.
Step-by-step explanation: When distinguishing between quantitative variables, they could be classed as either discreet or continuous. This difference between a discreet and continuous variable lies in whether the variable has a finite number of values or not. When a variable can only take up a certain number of values usually while numbers within a certain interval, then such varibak eis said to be finite. On the other hand variables which can take up any value within an interval are said to be continuous as they can take up an uncountable number of values within an interval. When weight is being recorded, it could take up an infinite number of values including decimal within an interval making it difficult to ascertain the number of possible values within the interval.
Find the maximum rate of change of f(x; y) = 4y p x at the point (4,1) and the direction in which it occur
Answer:
16p
Direction: positive/upward direction
Step-by-step explanation:
First, the function is f(x,y) = 4ypx
At the point where x=4 and y=1, the maximum rate of change of the function f(x,y) is
4(1)p(4) = 16p
The direction in which it occurs is the positive(upward) direction
A car traveled at a constant speed for 4 hours and covered 144.6 miles. It used 12 gallons of gas to travel this distance. How far did the car go in 1 hour? How far did the car travel on 1 gallon of gas? The car traveled miles in 1 hour. The car traveled miles on 1 gallon of gas.
Answer:
36.15 miles, 12.05 miles on one gallon
Step-by-step explanation:
4hours=144.6 miles
1 hour= x
Therefore it traveled 36.15 miles per hour.
12 gallon = 144.6 miles.
1 gallon = x
12.05 miles on one gallon
Write an equivalent expression by distributing the "-−" sign outside the parentheses:
-(4s+8.5)
Answer: -4s-8.5
Step-by-step explanation:
-(4s+8.5)
you need to change all the signs in the parentheses that is after a negative (-) sign.
-4s-8.5
since the signs of 4s and 8.5 are all positive (+), we need to change it to its opposite which is negative (-)
Hope this helps!! :)
Please let me know if you have any question
There are n machines in a factory, each of them has defective rate of 0.01. Some maintainers are hired to help machines working. Using Poisson approximations to answer the following questions and explain why we can use Poisson approximation.
(a) If one maintainer is responsible for 20 machines, what’s the probability that machines go defective and cannot be repaired on time?
(b) If three maintainers are responsible for 80 machines, what’s the probability that machines go defective and cannot be repaired on time?
(c) Assume n=300, then at least how many maintainers are required such that the probability machines cannot be fixed on time is less than 0.01?
Answer:
a) 1 - ∑²⁰ˣ_k=0 ((e^-λ) × λ^k) / k!
b) 1 - ∑^(80x/d)_k=0 ((e^-λ) × λ^k) / k!
c) ∑²⁰ˣ_k=0 (3^k)/k! = 0.99e³
Step-by-step explanation:
Given that;
if n ⇒ ∞
p ⇒ 0
⇒ np = Constant = λ, we can apply poisson approximation
⇒ Here 'p' is small ( p=0.01)
⇒ if (n=large) we can approximate it as prior distribution
⇒ let the number of defective items be d
so p(d) = ((e^-λ) × λ) / d!
NOW
a)
Let there be x number of repairs, So they will repair 20x machines on time. So if the number of defective machine is greater than 20x they can not repair it on time.
λ[n0.01]
p[ d > 20x ] = 1 - [ d ≤ 20x ]
= 1 - ∑²⁰ˣ_k=0 ((e^-λ) × λ^k) / k!
b)
Similarly in this case if number of machines d > 80x/3;
Then it can not be repaired in time
p[ d > 80x/3 ]
1 - ∑^(80x/d)_k=0 ((e^-λ) × λ^k) / k!
c)
n = 300, lets do it for first case i.e;
p [ d > 20x } ≤ 0.01
1 - ∑²⁰ˣ_k=0 ((e^-λ) × λ^k) / k! = 0.01
⇒ ∑²⁰ˣ_k=0 ((e^-λ) × λ^k) / k! = 0.99
⇒ ∑²⁰ˣ_k=0 (λ^k)/k! = 0.99e^λ
∑²⁰ˣ_k=0 (3^k)/k! = 0.99e³
Factor x2 - 8x + 15 Group of answer choices
( x - 3) ( x - 5)
( x + 3) ( x - 5)
( x + 3) ( x + 5)
( x - 2) ( x - 4)
Answer:
(x - 5)(x - 3)
Step-by-step explanation:
Step 1: Write out expression
x² - 8x + 15
Step 2: Factor
(x - 5)(x - 3)
Geometry pls helppp!
) Professor Jin wants to travel from place A to place B without a map. There are four ways lead away from place A. If road I is selected, the probability of arriving place B is 1/8; if road II is selected, the probability of arriving place B is 1/6; if road III is selected, the probability of arriving place B is 1/4; and if road IV is selected,the probability of arriving place B is 9/10. (a) What is the probability that professor will arrive at place B
Complete Question
Professor Jin wants to travel from place A to place B without a map. There are four ways lead away from place A. If road I is selected, the probability of arriving place B is 1/8; if road II is selected, the probability of arriving place B is 1/6; if road III is selected, the probability of arriving place B is 1/4; and if road IV is selected,the probability of arriving place B is 9/10.
(a) What is the probability that professor will arrive at place B?
(b) If Professor Jin arrives at place B, what is the probability that she chooses road IV?
Answer:
a
[tex]P(B) = 0.36[/tex]
b
[tex]P(4 /B) = 0.62[/tex]
Step-by-step explanation:
From the question we are told that
The number of ways from A to B is n = 4
The probability if road 1 is selected is [tex]P(1) = \frac{1}{8}[/tex]
The probability if road 2 is selected is [tex]P(2) = \frac{1}{6}[/tex]
The probability if road 3 is selected is [tex]P(3) = \frac{1}{4}[/tex]
he probability if road 4 is selected is [tex]P(4) = \frac{9}{10}[/tex]
The probability that professor will arrive at place B is mathematically represented as
[tex]P(B) = \frac{1}{n} * P(1) + \frac{1}{n} * P(2) + \frac{1}{n} * P(3)+ \frac{1}{n} * P(4)[/tex]
[tex]P(B) = \frac{1}{4} * \frac{1}{8} + \frac{1}{4} * \frac{1}{6} + \frac{1}{4} * \frac{1}{4} + \frac{1}{4} * \frac{9}{10}[/tex]
[tex]P(B) = 0.36[/tex]
If Professor Jin arrives at place B, what is the probability that she chooses road IV is mathematically represented as
[tex]P(4 /B) = \frac{ \frac{1}{n} * P(4)}{P(B)}[/tex]
=> [tex]P(4 /B) = \frac{ \frac{1}{4} * \frac{9}{10} }{0.36}[/tex]
=> [tex]P(4 /B) = 0.62[/tex]
The label on William's muffin said that one serving provided 11 grams of protein, which is 22% of the recommended daily
amount. What is the total recommended daily amount of protein?
Answer: 50 grams
Step-by-step explanation:
11=0.22 a
A =50
Limit (sin4x-4sinx)/x^3 when x close to zero
[tex]\Large \boxed{\sf \bf \ \ \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}=-10 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
Using Maclaurin series expansion, we can find an equivalent of sin(x) in the neighbourhood of 0.
[tex]sin(x) \sim \left(x-\dfrac{x^3}{3!}\right)\\\\\text{So, in the neighbourhood of 0}\\\\\begin{aligned}(sin(4x)-4sin(x)) &\sim \left( 4x-\dfrac{(4x)^3}{3!}-4x+\dfrac{4x^3}{3!}\right)\\\\&\sim \left(\dfrac{x^3*4*(1-4^2)}{3*2}\right)\\\\&\sim \left(\dfrac{x^3*2*(-15)}{3}\right)\\\\&\sim \left(x^3*2*(-5)\right)\\\\&\sim \left(x^3*(-10)\right)\\\end{aligned}[/tex]
Then,
[tex]\displaystyle \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}\\\\= \lim_{x\rightarrow0} \ {\dfrac{-10*x^3}{x^3}}\\\\=-10[/tex]
Thank you
Answer:
-10
Step-by-step explanation:
L' Hopital's rule can be used to solve it.
We search for lim (f(x)/g(x))
this is the same as lim (f' (x)/g' (x))
this is the same as lim f'' (x)/g'' (x)
so here we have f(x) =sin(4x)-4sin(x)
g(x)=x^3
g'' (x)= 6x
f'' (x)=-16sin(4x)+4sin(x)
so lim f'' (x) / g ''(x) = -16/6 lim sin(4x)/x + 4/6 lim (sin(x)/x)
= -16*4/6+4/6
=(-64+4)/6=-60/6=-10
Pls help fast What is this number's most specific set name √144 A. Natural B. Whole C. Integer D. Rational E. Irrational
Answer:
C. Integer
Step-by-step explanation: Since the square root of 144 could either be -12 or 12, so it is an integer.
b) The following table provides information about production at the XYZ-TV Company. Number of Workers TVs Produced 0 0 1 35 2 68 3 99 4 128 5 155 How many workers will the XYZ-TV Company hire if the going wage for TV production workers is $16,000? Show your calculation in detail.
Answer:
5
Step-by-step explanation:
Given the following :
Number of workers - - TVs produced
0 - - - - - - - - - - - - - - - - - 0
1 - - - - - - - - - - - - - - - - - - 35
2 - - - - - - - - - - - - - - - - - 68
3 - - - - - - - - - - - - - - - - - - 99
4 - - - - - - - - - - - - - - - - - - 128
5 - - - - - - - - - - - - - - - - - - 155
We need to calculate the marginal product :
Workers - - - marginal product - - - value of m/p
0 - - - - - - - - - - - ____ - - - - - - - - - - - - - - __
1 - - - - - - - - - - - 35 (35 - 0) - - - - - - 35000
2 - - - - - - - - - - - - 33 (68 - 35) - - - - 33000
3 - - - - - - - - - - - - 31 (99 - 68) - - - - - 31000
4 - - - - - - - - - - - - 29 (128 - 99) - - - - - 29000
5 - - - - - - - - - - - - 27 (155 - 128) - - - 27000
The marginal product shows the change in output due to one additional unit of a certain input of production, in this case, number of workers. If the going wage of workers is $16,000, the company can afford to hire up to 5 workers and still make profit.
Write an expression to represent the area of the following figure.
X - 12
х
Your answer:
4x - 48
4x - 24
x² - 12
Answer:
[tex] x^2 - 12x [/tex]
Step-by-step explanation:
The given rectangle had a length (l) of (x - 12), and a width (w) of x.
Area of rectangle = [tex] l * w [/tex]
Therefore, the expression representing the are if the given rectangle is:
[tex] Area_{rectangle} = (x - 12)*x [/tex]
[tex] Area_{rectangle} = x*x - 12*x [/tex]
[tex] Area_{rectangle} = x^2 - 12x [/tex]
The expression for the area = [tex] x^2 - 12x [/tex]
Question DEF will be reflected across a line such that all of vertices of triangle D’E’F are in quadrant II. What line of reflection is used to form triangle D’E’F’?
The line of reflection is
A. y = 0
B. x = 0
C. y = x
D. y = -x
Answer:
i think the answer is b by far
Answer:B
Step-by-step explanation : DEF will be reflected across a line such that all of vertices of triangle D’E’F are in there own quadrant ways. The line of reflection is used to form triangle D’E’F’.
The line of reflection is (B. x = 0 )
Classify the groups below. Do they list repeating decimals, terminating decimals, or irrational numbers? 12,1/2, 34.2, and 4/5
Answer:
terminating decimals
Step-by-step explanation:
All of the fractions (4/5, 1/2) can go into 100 so they are all termination
and 34.2 is a terminating decimal.
12 is also terminating
WHAT PROPERTY IS 12.2+18.6+-4.3+(18.6)
Answer:
it has to be 45.1.
Step-by-step explanation:
The reason why its 45.1 is because I added the equation all together including the negative number. I out that one in parentheses right next to the plus sign of 18.6. then added the last 2 numbers. and get 45.1. I'm not really good with stop by step explanations to be honest.
:(
Grace had $51 when she browsed an on-line store, which sells a pair of green earrings for $9.00 each plus a one-time $6.00 shipping charge. How many pairs of green earrings did Grace purchase? Solve the equation for the situation.
Answer:
5 Green earrings
Step-by-step explanation:
Given that:
Total amount held = $51
Cost per pair of green earrings = $9
One time shipping fee = $6
How many pairs of green earrings did grace purchase?
Let the number of green earrings purchased = g
Then,
$9*g + $6 = $51
$9g + $6 = $51
$9g = $51 - $6
$9g = $45
g = $45 / $9
g = 5
Hence, the number of green earrings purchased = 5
b) In a box of 10 oranges, 3 are bad. If two oranges are drawn at random one after the other
without replacement, find the probability that
(i)both are good
(ii)one is good and the other is bad
Answer:
Step-by-step explanation:
Let A,B, and C be the respective events that the first, second, and third drawn orange is good.
Therefore, probability that first drawn orange is good, P(A)=
15
12
The oranges are not replaced.
Therefore, probability of getting second orange good, P(B)=
14
11
Similarly, probability of getting third orange good, P(C)=
13
10
The box is approved for sale if all the three oranges are good.
Thus, probability of getting all the oranges good =
15
12
×
14
11
×
13
10
=
91
44
=0.48
Therefore, the probability that the box is approved for sale is 0.48
Answer:i
i) 7/15
ii) 7/15
Step-by-step explanation:
total: 10
good: 7
bad: 3
i) both are good
p(both good) = 7/10 * 6/9 = 42/90 = 7/15
ii) one good & one bad
p(first good & second bad) = 7/10 * 3/9 = 21/90 = 7/30
p(first bad & second good) = 3/10 * 7/9 = 21/90 = 7/30
p(one good & one bad) = 7/30 + 7/30 = 14/30 = 7/15
Can someone help me with this please anyoneeeeee
Answer:
michelle made more money
Step-by-step explanation:
How many 4-letter permutations can be made from the letters in the word “MATH”?
Answer:
There are 24 different ways using the letters from "math" can be rearranged.
Hopefully this helps! :)
question what is 2√8+√8=
Answer:
6√2Step-by-step explanation:
[tex]2\sqrt{8}+\sqrt{8}\\\\\mathrm{Add\:similar\:elements:}\:2\sqrt{8}+\sqrt{8}=3\sqrt{8}\\\sqrt{8}=2\sqrt{2}\\\\=3\times\:2\sqrt{2}\\\\=6\sqrt{2}[/tex]
Kelsey is going to graph the ordered pairs that are represented by this table on a coordinate plane. x –6 –4 3 5 y –4 –6 –6 0 How many points should appear in Kelsey’s graph? 3 4 6 7
Answer:
The answer is B, don't listen to the dude that said is A... A is wrong
Step-by-step explanation:
De nada :)
There are 4 coordinates which means we can make 4 points on the graph.
4 points is the correct answer.
Given,
Kelsey is going to graph the ordered pairs that are represented by this table on a coordinate plane.
______________
|x| – 6 | –4 | 3 | 5|
|y| –4 | –6 | –6 | 0|
We need to find how many points should appear in Kelsey’s graph.
What are coordinates in a coordinate plane?Coordinates are the points in a given plane.
The plane can be a two-dimensional plane or a three-dimensional plane.
In a two-dimensional plane the coordinates are represented as:
(x, y).
In a three-dimensional plane the coordinates are represented as:
(x, y, z).
Find the coordinates from the given table.
We have,
There are four x values and four y values.
So,
(x, y) = { (-6, -4), (-4, -6), (3, -6), (5, 0) }
We see that we can make 4 coordinates in the coordinate plane.
Thus there are 4 coordinates which means we can make 4 points on the graph.
Learn more about matching the coordinates with the points on the coordinate plane here:
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Which equation shows a slope of -5 and a y-intercept of (0,1) ?
Answer:
y = -5x + 1
Step-by-step explanation:
Y= mx +b
m = slope
b = y-intercept
y = -5x + 1
Answer:
y = -5x + 1
Step-by-step explanation:
Seeing the words "slope" and "y-intercept," I jump immediately to the slope-intercept form of the equation of a straight line: y = mx + b.
Here we have m = -5 and b = 1:
y = -5x + 1
help please and no troll answers for i will report it i also need the explanation to how u get to the answer please, thank you !!
Answer:
the marked choice is correct
Step-by-step explanation:
It usually works well to follow directions: use technology. The attachment shows the use of the technology I like for short regression problems. For longer problems, a spreadsheet program is a good choice.
_____
In this problem, it is easy to eliminate the nonsensical answers, so no real use of technology is necessary.
First of all, the y-value for x=0 needs to be near 48, eliminating the last two choices.
Second, the minimum of the function corresponds to a positive x-value, so the coefficient of the x-term must have opposite sign from the coefficient of the x^2 term. This eliminates the second choice, leaving the marked choice as the only viable one.
How do I solve for (2√5−√3)^2?
Answer:
[tex]23-4\sqrt{15}[/tex]
Step-by-step explanation:
So we want to simplify:
[tex](2\sqrt5-\sqrt3)^2[/tex]
Note that this is in the format:
[tex](a-b)^2[/tex]
And we know that this is the same as:
[tex](a-b)^2=a^2-2ab+b^2[/tex]
Let 2√5 be a and let √3 be b. Thus:
[tex](2\sqrt5-\sqrt3)^2\\=(2\sqrt5)^2-2(2\sqrt5)(\sqrt3)+(\sqrt3)^2[/tex]
Simplify:
[tex]=(4(5))-4(\sqrt5)(\sqrt3)+(3)\\=20-4\sqrt{15}+3\\=23-4\sqrt{15}[/tex]
And this cannot be simplified any further.
Using the information regarding the proportion of work time linguists study a new language, choose the correct conclusion for this hypothesis test. H0:p=0.10 ; Ha:p>0.10 The p-value for this hypothesis test is 0.09. The level of significance is α=0.025 Select the correct answer below: A) There is sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.
B) There is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.
C) There is sufficient evidence to conclude the proportion of work time linguists study a new language is more than 90%.
D) There is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 90%.
Answer:
The correct option is B
Step-by-step explanation:
From the question we are told that
The null hypothesis is [tex]H_o : p = 0.10[/tex]
The alternative hypothesis is [tex]H_a : p > 0.10[/tex]
The p-value is [tex]p-value = 0.09[/tex]
The level of significance is [tex]\alpha = 0.025[/tex]
From the given values [tex]p-value > \alpha[/tex] so we fail to reject the null hypothesis
So there is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.
Translate this phrase into an algebraic expression.
58 decreased by twice Chrissy's score
Use the variable c to represent Chrissy's score.
Answer:
2C - 58
Step-by-step explanation:
Chrissy = C
=> 2C - 58
I wrote 2C - 58 because 58 is decreased from 2 times C
=> 2 times C = 2C
=> 58 decreased = -58
=> 2C - 58
3/5 is what percent less than 5/3?