Answer:
-8/5Step-by-step explanation:
Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same
Let's get the slope of both equation. For the first equation;
y=(3a+2)x-2
We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2
Similarly for the second line;
2y=(a-4)x+2
Re-writing in the standard format we will have;
y = (a-4)x/2+2/2
y = (a-4)x/2 + 1
The slope of the second line is (a-4)/2
On equating the slope of both lines to get the value of 'a' we will have;
3a+2 = (a-4)/2
Cross multiplying
2(3a+2) = a-4
6a+4 = a-4
Collecting like terms;
6a-a = -4-4
5a = -8
a = -8/5
Hence the value of a is -8/5
find the coordinates of the vertices of the triangle after a reflection across the line y = -1 and then across the line x = -2
Answer: A) N'=(-2, 2) M'=(-1, 0) L'=(-5, -2)
Step-by-step explanation:
N = (-2, -4) M = (-3, -2) L = (1, 0)
Reflection over y = -1
N' = (-2, 2) M' = (-3, 0) L' = (1, -2)
Reflection over x = -2
N'' = (-2, 2) M'' = (-1, 0) L'' = (-5, -2)
The average weight of a person is 160.5 pounds with a standard deviation of 10.4 pounds. 1. What is the probability a person weighs more than 150.2 pounds
Answer:
0.8390
Step-by-step explanation:
From the question,
Z score = (Value-mean)/standard deviation
Z score = (150.2-160.5)/10.4
Z score = -0.9904.
P(x>Z) = 1- P(x<Z)
From the Z table,
P(x<Z) = 0.16099
Therefore,
P(x>Z) = 1-0.16099
P(x>Z) = 0.8390
Hence the probability that a person weighs more than 150.2 pounds = 0.8390
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
The complete question is;
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
(a) less than 10 minutes
(b) longer than 5 minutes
(c) between 8 and 15 minutes
Answer:
A) P (x < 10) = 0.6700
B) P (x > 5 ) = 0.9406
C) P (8.0000 < x < 15.0000) = 0.6332
Step-by-step explanation:
A) we are given;
Mean;μ = 8.9 minutes
Standard deviation;σ = 2.5 minutes
Normal random variable;x = 10
So to find;P(x < 10) we will use the Z-score formula;
z = (x - μ)/σ
z = (10 - 8.9)/2.5 = 0.44
From z-distribution table and Z-score calculator as attached, we have;
P (x < 10) = P (z < 0.44) = 0.6700
B) similarly;
z = (x - μ)/σ =
z = (5 - 8.9)/2.5
z = -1.56
From z-distribution table and Z-score calculator as attached, we have;
P (x > 5 ) = P (z > -1.56) = 0.9406
C)between 8 and 15 minutes
For 8 minutes;
z = (8 - 8.9)/2.5 = -0.36
For 15 minutes;
z = (15 - 8.9)/2.5 = 2.44
From z-distribution table and Z-score calculator as attached, we have;
P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332
Please answer this correctly without making mistakes.Please simplify the correct answer
Answer:
19/70 of NASA shuttle missions were carried out by Discovery.
9/140 of NASA shuttle missions were carried out by Challenger.
17/70 of NASA shuttle missions were carried out by Endeavour.
Step-by-step explanation:
Adding the number of missions carried out by NASA gives us 140 in total.
Discovery's total amount of missions simplified is 19/70.
Challenger's total amount of missions is already in the simplest form.
Endeavour's total amount of missions simplified is 17/70.
Answer:
81/140
Step-by-step explanation:
Well to find the fraction we first need to total amount of NASA missions.
38 + 32 = 70
70 + 34 = 104
104 + 27 = 131
131 + 9 = 140
Now we need to find out the amount of Discovery, Challenger, and Endeavour missions.
38 + 9 + 34 = 81
Now we can make the following fraction,
81/140
This is already in simplest form.
Thus,
the answer is 81/140.
Hope this helps :)
Find the measure of the indicated angle to the nearest degree.
PLEASE HELP ASAP
Answers
A. 26
B. 42
C. 64
D. 48
Answer:
The answer is option C
Step-by-step explanation:
To find the indicated angle we use sine
sin ∅ = opposite / hypotenuse
From the question
The opposite is 37
The hypotenuse is 41
So we have
sin ? = 37/41
? = sin-¹ 37/41
? = 64.4805
? = 64° to the nearest degreeHope this helps you
Answer:
C.) 64
Step-by-step explanation:
I got it correct on founders edtell
The same bedroom furniture set costs $1,500 in both Florida and Alabama. The table gives a breakdown of the taxes someone would pay when purchasing the furniture set in either state. Alabama Florida State of Alabama: 4.225% County Tax: 1.375% City Tax: 3.0% State of Florida: 6.5% County Tax: 1% City Tax: 1.625% Which statement is true? A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations.
Answer:
A: True
B, C and D: False
Step-by-step explanation:
We have a total sales tax for Alabama that is:
[tex]T_A=4.225+1.375+3=8.6[/tex]
The total sales tax for Florida is:
[tex]T_F=6.5+1+1.625=9.125[/tex]
The total sales tax is greater in Florida than in Alabama.
A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE
The sales tax difference in this purchase can be calculated as:
[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]
B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)
C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)
The amount of sales tax in Alabama is:
[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]
D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).
Explain how the interquartile range of a data set can be used to identify outliers. The interquartile range (IQR) of a data set can be used to identify outliers because data values that are ▼ less than equal to greater than ▼ IQR Upper Q 3 minus 1.5 (IQR )Upper Q 3 plus IQR Upper Q 3 plus 1.5 (IQR )or ▼ less than equal to greater than ▼ IQR Upper Q 1 plus 1.5 (IQR )Upper Q 1 minus IQR Upper Q 1 minus 1.5 (IQR )are considered outliers.
Answer:
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Step-by-step explanation:
To identify outliers the interquartile range of the dataset can be used
Outliers can be identified as data values that are
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Using the interquartile range concept, it is found that:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
----------------------------
The interquartile range of a data-set is composed by values between the 25th percentile(Q1) and the 75th percentile(Q3).It's length is: [tex]IQR = Q3 - Q1[/tex]Values that are more than 1.5IQR from the quartiles are considered outliers, that is:[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]
Thus:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
A similar problem is given at https://brainly.com/question/14683936
Part A Each time you press F9 on your keyboard, you see an alternate life for Jacob, with his status for each age range shown as either alive or dead. If the dead were first to appear for the age range of 75 to 76, for example, this would mean that Jacob died between the ages of 75 and 76, or that he lived to be 75 years old. Press F9 on your keyboard five times and see how long Jacob lives in each of his alternate lives. How long did Jacob live each time? Part B The rest of the potential clients are similar to Jacob, but since they’ve already lived parts of their lives, their status will always be alive for the age ranges that they’ve already lived. For example, Carol is 44 years old, so no matter how many times you press F9 on your keyboard, Carol’s status will always be alive for all the age ranges up to 43–44. Starting with the age range of 44–45, however, there is the possibility that Carol’s status will be dead. Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at least 44 years old, since she is already 44 years old. How long did Carol live each time? Part C Now you will find the percent survival of each of your eight clients to the end of his or her policy using the simulation in the spreadsheet. For each potential client, you will see whether he or she would be alive at the end of his or her policy. The cells in the spreadsheet that you should look at to determine this are highlighted in yellow. Next, go to the worksheet labeled Task 2b and record either alive or dead for the first trial. Once you do this, the All column will say yes if all the clients were alive at the end of their policies or no if all the clients were not alive at the end of their policies. Were all the clients alive at the end of their policies in the first trial? Part D Next, go back to the Task 2a worksheet, press F9, and repeat this process until you have recorded 20 trials in the Task 2b worksheet. In the Percent Survived row at the bottom of the table on the Task 2b worksheet, it will show the percentage of times each client survived to the end of his or her policy, and it will also show the percentage of times that all of the clients survived to the end of their respective policies. Check to see whether these percentages are in line with the probabilities that you calculated in questions 1 through 9 in Task 1. Now save your spreadsheet and submit it to your teacher using the drop box. Are your probabilities from the simulation close to the probabilities you originally calculated?
Step-by-step explanation:
brain list me please......
Answer:
Jacob:
Alive 69-70
alive 79-80
alive 62-63
alive 73-74
alive 78-Died 79
Carol:
alive 88-89
alive 67-68
alive 99-100
alive 73-74
alive 94- Died 95
Step-by-step explanation:
Noah tried to prove that cos(θ)=sin(θ) using the following diagram. His proof is not correct.
Answer:
The first statement is incorrect. They have to be complementary.
Step-by-step explanation:
You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.
You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.
The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.
Answer:
[tex]\boxed{\sf A}[/tex]
Step-by-step explanation:
The first statement is incorrect. The angle B is not equal to theta θ. The two acute angles in the right triangle can be different, if the triangle was an isosceles right triangle then angle B would be equal to theta θ.
A recipe for 1 batch of muffins used 2/3 of blueberries. Amir made 2 1/2 batches of muffins. How many cups of blueberries did he use? A. 1 4/6 B. 1 5/6 C. 2 2/6 D. 3 1/6. Please show your work.
Answer:
A. 1 4/6 cups of blueberries
Step-by-step explanation:
1 -- 2/3
Proportion, Batches to Blueberries
1*(2 1/2) -- (2/3)( 2 1/2)
Because we are now multiplying the 1 batch to 2 1/2 batches. So to keep the proportion balanced/equal we are using the same operation on the right side of the proportion
2 1/2 -- (2/3)( 5/2 )
2 1/2 -- 5/3
2 1/2 -- 1 2/3
Simplify
On the right side shows the blueberries for 2 1/2 batches. 1 2/3 = 1 4/6
Hope that helps! Tell me if you need more info
Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The negative root of ex = 4 − x2
Answer:
x = -1.964636
Step-by-step explanation:
Given equation;
eˣ = 4 - x²
This can be re-written as;
eˣ - 4 + x² = 0
Let
f(x) = eˣ - 4 + x² -----------(i)
To use Newton's method, we need to get the first derivative of the above equation as follows;
f¹(x) = eˣ - 0 + 2x
f¹(x) = eˣ + 2x -----------(ii)
The graph of f(x) has been attached to this response.
As shown in the graph, the curve intersects the x-axis twice - around x = -2 and x = 1. These are the approximate roots of the equation.
Since the question requires that we use the negative root, then we start using the Newton's law with a guess of x₀ = -2 at n=0
From Newton's method,
[tex]x_{n+1} = x_n + \frac{f(x_{n})}{f^1(x_{n})}[/tex]
=> When n=0, the equation becomes;
[tex]x_{1} = x_0 - \frac{f(x_{0})}{f^1(x_{0})}[/tex]
[tex]x_{1} = -2 - \frac{f(-2)}{f^1(-2)}[/tex]
Where f(-2) and f¹(-2) are found by plugging x = -2 into equations (i) and (ii) as follows;
f(-2) = e⁻² - 4 + (-2)²
f(-2) = e⁻² = 0.13533528323
And;
f¹(2) = e⁻² + 2(-2)
f¹(2) = e⁻² - 4 = -3.8646647167
Therefore
[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]
[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]
[tex]x_{1} = -2 - -0.03501863503[/tex]
[tex]x_{1} = -2 + 0.03501863503[/tex]
[tex]x_{1} = -1.9649813649[/tex]
[tex]x_{1} = -1.96498136[/tex] [to 8 decimal places]
=> When n=1, the equation becomes;
[tex]x_{2} = x_1 - \frac{f(x_{1})}{f^1(x_{1})}[/tex]
[tex]x_{2} = -1.96498136 - \frac{f(-1.9649813)}{f^1(-1.9649813)}[/tex]
Following the same procedure as above we have
[tex]x_{2} = -1.96463563[/tex]
=> When n=2, the equation becomes;
[tex]x_{3} = x_2 - \frac{f(x_{2})}{f^1(x_{2})}[/tex]
[tex]x_{3} = -1.96463563- \frac{f( -1.96463563)}{f^1( -1.96463563)}[/tex]
Following the same procedure as above we have
[tex]x_{3} = -1.96463560[/tex]
From the values of [tex]x_2[/tex] and [tex]x_3[/tex], it can be seen that there is no change in the first 6 decimal places, therefore, it is safe to say that the value of the negative root of the equation is approximately -1.964636 to 6 decimal places.
Newton's method of approximation is one of the several ways of estimating values.
The approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]
The equation is given as:
[tex]\mathbf{e^x = 4 - x^2}[/tex]
Equate to 0
[tex]\mathbf{4 - x^2 = 0}[/tex]
So, we have:
[tex]\mathbf{x^2 = 4}[/tex]
Take square roots of both sides
[tex]\mathbf{ x= \pm 2}[/tex]
So, the negative root is:
[tex]\mathbf{x = -2}[/tex]
[tex]\mathbf{e^x = 4 - x^2}[/tex] becomes [tex]\mathbf{f(x) = e^x - 4 + x^2 }[/tex]
Differentiate
[tex]\mathbf{f'(x) = e^x +2x }[/tex]
Using Newton's method of approximation, we have:
[tex]\mathbf{x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}}[/tex]
When x = -2, we have:
[tex]\mathbf{f'(-2) = e^{(-2)} +2(-2) = -3.86466471676}[/tex]
[tex]\mathbf{f(-2) = e^{-2} - 4 + (-2)^2 = 0.13533528323}[/tex]
So, we have:
[tex]\mathbf{x_{1} = -2 - \frac{0.13533528323}{-3.86466471676}}[/tex]
[tex]\mathbf{x_{1} = -2 + \frac{0.13533528323}{3.86466471676}}[/tex]
[tex]\mathbf{x_{1} = -1.96498136}[/tex]
Repeat the above process for repeated x values.
We have:
[tex]\mathbf{x_{2} = -1.96463563}[/tex]
[tex]\mathbf{x_{3} = -1.96463560}[/tex]
Up till the 6th decimal places,
[tex]\mathbf{x_2 = x_3}[/tex]
Hence, the approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]
Read more about Newton approximation at:
https://brainly.com/question/14279052
Translate and solve: 3x less than two times the sum of 2X and one is equal to the sum of 2 and 5
Answer:
The answer is x = 5Step-by-step explanation:
The statement
3x less than two times the sum of 2X and one is written as
2( 2x + 1) - 3x
the sum of 2 and 5 is written as
2 + 5
Equate the two statements
We have
2( 2x + 1) - 3x = 2+5
Expand
4x + 2 - 3x = 7
Simplify
4x - 3x = 7 - 2
We have the final answer as
x = 5Hope this helps you
The area of a triangle is 14 square inches. The base is 28 inches. What is the height in inches? Do not include units in your answer.
Answer:
Hey there!
A=1/2bh
14=1/2(28)h
14=14h
h=1
Hope this helps :)
Answer:
the height is 1 inchStep-by-step explanation:
Area of a triangle is
[tex] \frac{1}{2} \times b \times h[/tex]
where b is the base
h is the height
From the question
Area = 14in²
b = 14 inches
So we have
[tex]14 = \frac{1}{2} \times 28 \times h[/tex]
which is
[tex]14 = 14h[/tex]
Divide both sides by 14
That's
[tex] \frac{14}{14} = \frac{14h}{14} [/tex]
We have the final answer as
h = 1
Therefore the height is 1 inch
Hope this helps you
Connor has a collection of dimes and quarters with a total value of $6.30. The number of dimes is 14 more than the number of quarters. How many of each coin does he have?
Answer:
14 Quarters and 28 dimes
Step-by-step explanation: 14 quarters $3.50
28 dimes is $2.80 total is $6.30
a lottery game has balls numbered 1 through 19. what is the probability selected ball is an even numbered ball or a 4 g
Answer:
Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19
Step-by-step explanation:
Given:
Number of balls = 1 to 19
Find:
Probability ball is an even numbered ball or a 4
Computation:
Total even number = 2, 4, 6, 8, 10, 12, 14, 16, 18
Probability to get even number P(A) = 9 / 19
Probability to get 4 number P(B) = 1 / 19
P(A and B) = 1 / 19 (4 common)
Probability ball is an even numbered ball or a 4 [P(A or B)]
P(A or B) = P(A) + P(B) -P(A and B)
P(A or B) = [9 / 19] + [1 / 19] - [1 / 19]
Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19
A bag of marbles contains 4 green marbles, 3 blue marbles, 2 red marbles, and 5 yellow marbles. How many total possible outcomes are there when choosing a marble from the bag?
Answer:
its 14/C
Step-by-step explanation:
i got i right on edg U^U
Answer:
16
Step-by-step explanation:
i did edge test yea dont be imma fake :***
Question 16 (5 points)
Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
i think its b
???
Step-by-step explanation:
im sorry if im wrong im not very confident on my answer :(
Answer:
D
Step-by-step explanation:
Most logical looking if you look at the formula, the last number has to be smaller than the one before, so.
Please help. I’ll mark you as brainliest if correct!
Answer:
CDs: $30,000bonds: $90,000stocks: $50,000Step-by-step explanation:
You can let c, b, s represent the investments in CDs, bonds, and stocks, respectively.
c + b + s = 170000 . . . . . . total invested
0.0325c +0.038b +0.067s = 7745 . . . . . . . annual income
-c + b = 60000
You can solve this set of equations using any of a number of methods, including on-line calculators, graphing calculators, scientific calculators, Cramer's Rule, substitution, elimination, and more. The solution is ...
c = 30,000
b = 90,000
s = 50,000
Maricopa's Success invested $30,000 in CDs, $90,000 in bonds, and $50,000 in stocks.
Yesterday at 1:00 P.M., Maria’s train was 42 miles north of Gull’s Beach, traveling north at an average speed of 90 mph. At the same time on the adjacent track, Elena’s train was 6 miles north of Gull’s Beach, traveling north at an average speed of 101 mph. To the nearest hundredth of an hour, after how much time will the trains meet up? 0.23 hours 0.31 hours 3.27 hours 4.36 hours
Answer:
3.27 hours
Step-by-step explanation:
Calculate the difference in speed and distance between the trains.
The relative speed:
101 - 90 = 11 mph
Difference in distance:
42 - 6 = 36 miles
[tex]time=\frac{distance}{speed}[/tex]
[tex]t=\frac{36}{11}[/tex]
[tex]t = 3.27[/tex]
Answer:
yeah she is correct
Step-by-step explanation:
write and equation to represent the following statement 28 is 12 less thank K. solve for K K =
Answer:
K = 40
Step-by-step explanation:
As they said that 28 is 12 less than K , it means that you've to add them to get the answer. So , 28 + 12 = 40 which is represented by the variable "K"
Hope it helps and pls mark as brainliest : )
Answer:
Equation : 28 = k - 12K = 40Step-by-step explanation:
28 is 12 less than k
Let's create an equation:
[tex]28 = k - 12[/tex]
Now, let's solve:
[tex]28 = k - 12[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] - k = - 12 - 28[/tex]
Calculate the difference
[tex] - k = - 40[/tex]
Change the signs on both sides of the equation
[tex]k = 40[/tex]
Hope this helps...
Best regards!!
in the number 23.45 the digit 5 is in ?
Answer: hundredths place
Step-by-step explanation:
Question 10 of 10
Which set of polar coordinates are plotted in the graph below?
Answer:
(-2, -(2pi)/3)
Step-by-step explanation:
a p ex
In da pic :)))))))))
Harry is trying to complete his hill walking scouts badge. He is using a map with a scale of 1 cm : 2 km. To earn the badge he needs to walk 14 km. What is the distance he needs to walk on the map?
Answer:
7 cm
Step-by-step explanation:
14 / 2 = 7 cm
7cm is the distance Harry needs to walk on the map?
What is Distance?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.
Given that,
Harry is trying to complete his hill walking scouts badge.
He is using a map with a scale of 1 cm : 2 km.
To earn the badge he needs to walk 14 km.
Let the distance he needs to walk on the map is x.
By given data we write an equation
1/2=x/14
Apply Cross Multiplication
14/2=x
7=x
Hence, 7cm is the distance he needs to walk on the map.
To learn more on Distance click:
https://brainly.com/question/15172156
#SPJ5
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 8% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 4% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
a. What percentage of the employees will experience lost-time accidents in both years?
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?
Answer:
a) percentage of the employees that will experience lost-time accidents in both years = 1.2%
b) percentage of the employees that will suffer at least one lost-time accident over the two-year period = 10.8%
Step-by-step explanation:
given
percentage of lost time accident last year
P(L) = 8% = 0.08 of the employees
percentage of lost time accident current year
P(C) = 4% = 0.04 of the employees
P(C/L) = 15% = 0.15
using the probability
P(L ∩ C) = P(C/L) × P(L)
= 0.08 × 0.15 = 0.012 = 1.2%
percentage of the employees will experience lost-time accidents in both years = 1.2%
b) Using the probability of the event
P(L ∪ C) = P(L) + P(C) - P(L ∩ C)
= 0.08 + 0.04 -0.012 = 0.108 = 10.8%
percentage of the employees will suffer at least one lost-time accident over the two-year period = 10.8%
The total cost of a sweater and a jacket was $71.55 If the price of the sweater was $3.19 less than the jacket, what was the price of the sweater? Express your answer as a simplified fraction or a decimal rounded to two places.
Answer: $34.18
Step-by-step explanation:
Let the cost of the Jacket = $x and
The cost of the sweater. = $y
Now total price. = $71.55.
So, $x + $y. = $71.55 -- 1
From the second statements, the price of the sweater was $3.19 less than the price of the jacket. Transforming that into equation
y = ( x - $3.19 )
Now substitute for y in the equation (1) above.
x + ( x - 3.19 ) = 71.55
Now solve the equation
x + x - 3.19 = 71.55
2x - 3.19. = 71.55
2x = 71.55 + 3.19
2x. = 74.74
x = 74.74/2
= $37.37. cost of the jacket
Now to determine the cost of the sweater,
$71.55 - $37.37 = $34.18
The cost of the sweater = $34.18.
What is the next term of the geometric sequence? 1, 2, 4, 8, 16,
Answer: 32
Step-by-step explanation:
and click Submit
By visual inspection, determine the best fitting regression model for the
scatterplot.
O A Quadratic
O B. Linear
OC Exponential
OD. No pattern
Answer:
quadratic
Step-by-step explanation:
This graph has a parabola form wich is a propertie for qaudratic functions
Answer:
A
Step-by-step explanation:
For each of the following, state the equation of a perpendicular line that passes through (0, 0). Then using the slope of the new equation, find x if the point P(x, 4) lies on the new line. y=3x-1 y=1/4 x+2
Answer:
The answer is below
Step-by-step explanation:
a) y=3x-1
The standard equation of a line is given by:
y = mx + c
Where m is the slope of the line and c is the intercept on the y axis.
Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:
3 × d = -1
d = -1/3
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12[/tex]
b) y=1/4 x+2
Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:
1/4 × f = -1
f = -4
To find the equation of the perpendicular line passing through (0,0), we use:
[tex]y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x[/tex]
To find x if the point P(x, 4) lies on the new line, insert y = 4 and find x:
[tex]y=-4}x\\ 4=-4x\\x=-1[/tex]
Which Graph represents the solution to the compound inequality 4x +8< -16 or 4x + 8 > 4
Answer:
option 3
Step-by-step explanation:
4x+8<-16
x<-6
4x+8_>-16
x_>-1
(it's more and equal .so the circle has to be shaded and move to the right of -1)
Answer:C
Step-by-step explanation:
help plsssssssssssss
Answer:
[tex]z = \frac{x}{y} [/tex]
Step-by-step explanation:
Let x be the price of carton of ice cream
Let y be the number of grams in carton
Let z be price per gram.
[tex]z = \frac{x}{y} [/tex]
Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.
Hope this helps ;) ❤❤❤