Answers
3y^2 - 5y - 2 = 0 so we solve for y
Δ = b^2 - 4ac (a=3 b=-5 c=-2)
Δ = 25 + 24 = 49
y1 = (5 + 7) / 6 = 12/6 = 2
y2 = (5 - 7) / 6 = -2/6 = -1/3
since tan is positive in the first and third quadrant and according to the question x belongs somewhere in the first two quadrants the following is true
for y1 = tanx = 2 only applies for the first quadrant ( from 0° to 90°) while for y2 = tanx = -1/3 it can only apply for the second quadrant (from 90° to 180°). i hope this made sense because english is not my first language.
Related Questions
Find the geometric mean between each pair of numbers 8 and 12
Answers
Step-by-step explanation:
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An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. Assume that the population standard deviation for Compound 1 is 4414 miles, while the population standard deviation for Compound 2 is 2368 miles. Determine the 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.
Answers
Answer:
The margin of error is of 623.2016.
The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem, and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. The population standard deviation for Compound 1 is 4414 miles.
This means that [tex]\mu_1 = 37866, s_1 = \frac{4414}{\sqrt{243}} = 283.16[/tex]
A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. The population standard deviation for Compound 2 is 2368 miles.
This means that [tex]\mu_2 = 45789, s_2 = \frac{2368}{\sqrt{268}} = 144.65[/tex]
Distribution of the difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
The mean is:
[tex]\mu = \mu_1 - \mu_2 = 37866 - 45789 = -7923[/tex]
The standard deviation is:
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{283.16^2 + 144.64^2} = 317.96[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.96*317.96 = 623.2016[/tex]
The margin of error is of 623.2016.
The lower end of the interval is the sample mean subtracted by M. So it is -7923 - 623.2016 = -8546.2016
The upper end of the interval is the sample mean added to M. So it is -7923 + 623.2016 = -7299.7984
The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).
Help ASAP 6x - 3(2 – 3x)
Answers
Answer:
First: we expand
6x-(6-9x)
Then we simplify
6x-6+9x
Collect like terms
(6x+9x)-6
Simplify:
15x-6
The answer is 15x-6
Write an equation that you can use to find the value of x.
The perimeter of the triangle: 16 in.
Answers
Answer:
This question seems incomplete
Use the picture below and determine which of the lines or line segments 20 points
is/are a diameter
mA
VE
Line m
Line Segment BC
Ο Ο Ο Ο Ο
Line Sesnent AB or AC
Line Segment DE
Line 1
Answers
Simplify 25a/8 x 2a/5
Answers
Answer:
If the slashes mean divisions and the x means multiplication, the answer would be 25a²/4/5
You determine that you can make 72 donuts in 2 hours. At that rate, how
many donuts can you make in 8 hours?
Answers
Answer:
576
Step-by-step explanation:
A triangle has side lengths 8, 7, 4. In a similar triangle the smallest side is represented by x + 5 and the longest side is represented by x - 3. What is the value of x?
Answers
Answer:
x = 11
Step-by-step explanation:
8/4 = (x+5)/(x-3)
cross-multiply:
8(x-3) = 4(x+5)
8x - 24 = 4x + 20
4x = 44
x = 11
Answer:
Step-by-step explanation:
X=11
The longest known is double than samallest known
2(x-3) = x+5
2x-6 = x+5
x= 11
11-3 = 8
11+5 = 16
Sides of the known triangle 8,7,4 (side 8 double than side 4)
Sides of the similar triangle 16,14,8 (side 16 double than side 8 )
Stock in Macy's costs $25.75 per share. Hector buys 200 shares of Macy's
through his broker who charges a commission of $25.75. How much did George
pay in total to purchase the stock?
Answers
Answer: $5175.75
Step-by-step explanation:
The amount that is paid in total to buy the stock will be gotten through the addition of the cost of the shares and the commission paid. This will be:
= (200 × $25.75) + $25.75
= $5150 + $25.75
= $5175.75
Therefore, the total amount that is paid to buy the stock will be $5175.75.
the sum of the first four terms of an A.p is 62.if the difference between 4 terms and 2nd terms is 14. find the first term and common difference
Answers
Answer:
-2 -4 -6 -8
Step-by-step explanation:
I got the answer off of khan academy
(05.03 LC) What is the equation of a horizontal line passing through the point (2, 10)? (5 points)
Answers
Answer:
y=10
Step-by-step explanation: a horizontal line has no slope
What is -13 decreased by 9
Answers
Answer:
-4
Step-by-step explanation:
Answer:
-22
Step-by-step explanation:
-13 - 9
When both the numbers have the same sign, we add them. After adding we put the same sign of the numbers to the answer
-13-9 = -22(50 points) please help! no links, brainliest, extra points.
I understand if you need points, you can go to my old questions and answer them for points, please only answer if your 100% sure you're correct. I've redone this over 20 times, asked over 50, and failed all those times. thank uu.
Students were asked to find the median of this data set.
Darcy said, "The median is the number in the middle of the list. So, the median is 21."
Darcy made a mistake.
Her mistake is that she did not _____
A) choose the data point that is in the data set most often
B) order the data points from least to greatest before finding the middle data point
C) ignore the data points that repeat in the data set
D) divide the middle data point by the total number of data points
,
The correct median of the data set is ___
A) 14
B) 16
C) 15
D) 14.5
E) 15.5
Answers
Answer:
The answer is B. The correct median of the data set is C, 15.
Step-by-step explanation:
To do a quick recap:
Mode is the average value that is found by adding up all the values and dividing them by the number of values you used.
Median is the number found in the very middle, so Darcy is correct about what a median is.
Mode is the number that appears most.
Notice that the numbers are not arranged in numerical order from least to greatest. She just took the number that she saw in the middle, without considering where it would stand if the numbers were ranked from least to most.
Here's a ranking of all the numbers from least to greatest:
8, 9, 9, 12, 13, 14, 15, 15, 16, 16, 16, 17, 21
From this ranking, we can see that there are a total of 13 numbers. Therefore, the 7th number is the median, which means that the median is 15.
Answer:
as the person before me said, it is b and 15.
Step-by-step explanation:
i know study island can be hard but keep going, you can do it!
Can I please get help with this math problem? Thanks in advance.
Answers
Answer:
answer: scale factor is 3
Hope this helps
Answer:
ans :; scale factor is 3
this is the correct ans.
GIVING EVERYTHING IF CORRECT. No fake answers, you will be reported.
Answers
Answer:
283.5
Step-by-step explanation:
please help me here im begging you it won't let me just skip it
Answers
Answer:
ABCD in statement and the other in reasoning
Step-by-step explanation:
14. The Manilow family paid their electric bill using balanced billing all last year. The monthly
payment was m dollars. At the end of the year, the electric company told them they used more
electricity than they were billed for, and they owed d dollars. Express the value of the electricity
used by the Manilows last year algebraically.
Z
Answers
Answer:
12mx
Step-by-step explanation:
Given that
The monthly payment was m dollars
And, they used more electricity
We need to determine the value that should be expressed in algebraically
The Monthly payment is m dollars
Using balance billing, it would be mx dollars
So, the equation is
= mx × 12
= 12mx
hence, the same would be relevant and considered too
Can someone here please help me out?
Answers
Answer:
hope you can now substitute and find y
Sandy is getting ready for the day. She can wear either a balck or white shirt and then either pants, shorts, or a skirt. Create a tree diagram or label all the combinations she can make. How many are there total?
Answers
Black shirt and shorts
Black shirt and skirt
White shirt and pants
White shirt and shorts
White shirt and skirt
6 COMBINATIONS TOTAL
What is the volume of a rectangular prism with a length of 2 1/2 inch width of 4 inches, and a height of 3 inches? * 21: 36 cu, in O 30 cu in 9.5 cu in 0 26 cu.in
Answers
Answer:
30 cubic inch
Step-by-step explanation:
expanded form :32,456
Answers
Answer:
30,000 + 2,000 + 400 + 50 + 6
Step-by-step explanation:
[tex]\text{The expanded form of 32,456 would be 30,000 + 2,000 + 4,000 + 50 + 6.}[/tex]
[tex]\text{We would have to identify what each number stands for.}[/tex]
[tex]\text{For example, 3 in 32,456 stands for 30,000.}[/tex]
[tex]\text{Hence, following this rule, we can conclude that the answer above is correct.}[/tex]
[tex]\text{I hope I helped you suceed!}[/tex]
can someone help, please :)
Answers
What type of correlation is shown in the graph?
Answers
Answer:
no correlation
Step-by-step explanation:
it shows no trend or a line thing
also i think your pic is upside down haha
Should we take care of useless equipment and avoid the "trash pile" that is growing in space?
Answers
I personally think yes.
What are the answers
Answers
Answer:
3. 5cm
[tex]4. \: {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Step-by-step explanation:
3. the hypotenuse C squared = side A squared + side B squared. So 3 × 3=9 and 4 × 4 =16 therefore 9 + 16 =25 and the square root of 25 = 5.
4. In mathematics, the Pythagorean theorem, or Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
Hope it is helpful....PLEASE HELP ME TO ANSWER THIS QUESTION.
A right pyramid PQRST has a rectangular base QRST. Given
that W is the midpoint of QS and RT, the lengths of QT = 8 cm,
TS = 6 cm and point P is vertically above point W, calculate
(a) PT, in cm, if PW = 12 cm
(b) the value of < PTR [angle PTR]
THANK YOU!!!
Answers
Answer:
(a) PT = 13 cm
(b) <PTR = [tex]39.7^{o}[/tex]
Step-by-step explanation:
(a) Applying the Pythagoras theorem to QST, we have;
[tex]QS^{2}[/tex] = [tex]ST^{2}[/tex] + [tex]QT^{2}[/tex]
= [tex]6^{2}[/tex] + [tex]8^{2}[/tex]
[tex]QS^{2}[/tex] = 36 + 64
100
QS = [tex]\sqrt{100}[/tex]
= 10
QS = 10 cm
Since QS = TR, then;
WT = [tex]\frac{1}{2}[/tex] TR
= [tex]\frac{1}{2}[/tex] x 10
WT = 5 cm
Thus, applying Pathagoras theorem to PWT;
[tex]PT^{2}[/tex] = [tex]PW^{2}[/tex] + [tex]WT^{2}[/tex]
= [tex]12^{2}[/tex] + [tex]5^{2}[/tex]
= 144 + 25
[tex]PT^{2}[/tex] = 169
PT = [tex]\sqrt{169}[/tex]
= 13
PT = 13 cm
(b) To determine <PTR, TR = 10 cm. Apply the required trigonometric function;
Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
Cos θ = [tex]\frac{10}{13}[/tex]
= 0.7692
θ = [tex]Cos^{-1}[/tex] 0.7692
= 39.7179
θ = [tex]39.7^{o}[/tex]
Therefore, <PTR = [tex]39.7^{o}[/tex]
Write equivalent fractions for 1 2/3 and 1 7/8 using 24 as the common denominator 2 24 7 1 0
Answers
Answer:
2×8=16
7×3=21
2/3 + 7/8 = 16/24 + 21/24
What is 1/3 of $4.89 dollars
Answers
Answer:
im pretty sure its 1.63
Step-by-step explanation:
lmk if im wrong
Can somebody tell me which one of these options do I put? (I need to put two)
Answers
Answer:
B D and E
Step-by-step explanation:
Expressions do not contain equal signs
Determine the median of the following numbers: 8, 11, 11, 12, 13, 15, 16, 16, 18, 21
Answers
Order the numbers from least to greatest
Since median means middle mark off a number on each side until there is one left. That will be your answer
If it is an even amount of numbers than take the middle two numbers and find the average (mean)
To do so add the numbers and divide by two
Answer:
The median of the following numbers is 14
Step-by-step explanation: