Answer:
3Solution,
Let the points be A and B
A(7,-1)--->( X1,y1)
B(6,-4)---->(x2,y2)
Now,
[tex] slope = \frac{y2 - y1}{x2 - x1} \\ \: \: \: \: \: \: = \frac{ - 4 - ( - 1)}{6 - 7} \\ \: \: \: \: \: \: = \frac{ - 4 + 1}{ - 1} \\ \: \: \: \: \: = \frac{ - 3}{ - 1} \\ \: \: \: \: = 3[/tex]
Hope this helps..
Good luck on your assignment..
Answer:
-1/3 (given that the first co-ordinate is the initial point)
Step-by-step explanation:
slope of a line is basically the change in y divided by the change in x.
we have the 2 co-ordinates (7,-1) , (6,-4)
lets find the change in x = 7 - 6 (the difference of the x - values of both the coordinates)
change in y = -1 - (-4)
change in x = -1
change in y = 3
now, slope is change in y / change in x
slope = -1/3
The two triangles are similar. What is the value of x? Enter your answer in the box. x =
Answer:
x=1
Step-by-step explanation:
Since the two triangles are similar you want to look at what two dimensions have x included and if they are similar. Both have the same angles and on the bottom they both have x.
In order to figure out the value you need to compare them:
3x + 1 = 4x
1 = 4x-3x
1 = x
x = 1
if there were only three types of music in the world pop,rock and rap and set A equals all the people in the world who prefer pop music,what is A`?
Answer:
people who prefer rock or rap
Step-by-step explanation:
We assume that "silence" is a type of music that is not in this universe. Hence the complement of set A is ...
people who prefer rock or rap
Is the area of this shape approximately 57 6 cm ? If not, give the correct area.
O True
O False
Answer: True
Step-by-step explanation: Taking the triangle from the left and moving it to the right creates a rectangle. From there just do 12.8×4.5.
What are the y-intercepts for each function? What do these y-intercepts represent?
Answer:
In a function that is represented by Y=mx+b b would be the y-intercept
Definition of y-intercept. : the y-coordinate of a point where a line, curve, or surface intersects the y-axis.
1. A fruitseller bought 200 apples for Rs 300.40 of them were rotten and thrown away.
She sold the rest at Rs 2.25 each. Find its gain or loss percent.
253
A Book of Mathematics-8
Answer:
ok I am tellin6 to you
Step-by-step explanation:
ok I will tell to you
Check that your solutions to part (a) and (b) are consistent by substituting the expression for y into your solution for part (a).
9x^2 - y^2 = 1
Answer:
Step-by-step explanation:
The question is incomplete. Find the complete question in the attached file.
a) Given the expression 9x^2 - y^2 = 1
Differentiating implicitly will give;
[tex]18x-2y\frac{dy}{dx} = 0\\[/tex]
We can then make dy/dx the subject of the formula as shown;
[tex]18x = 2y\frac{dy}{dx}\\\frac{dy}{dx} = \frac{18x}{2y} \\\frac{dy}{dx} = \frac{9x}{y} \\y' = \frac{9x}{y}[/tex]
b) In order to solve the question explicitly, we will first have to make x the subject of the formula before differentiating.
[tex]9x^{2} -y^{2} = 1\\9x^{2} = 1+ y^{2}\\y^{2} =9x^{2}- 1\\y^{2} = 9x^{2} - 1\\y = \sqrt{9x^{2}- 1 } \\[/tex]
Using chain rule to solve the equation;
let;
[tex]u = 9x^{2} -1\\ y = u^{1/2}[/tex]
du/dx = 18x
dy/du = [tex]1/2u^{-1/2}[/tex]
dy/dx = dy/du * du/dx
dy/dx = [tex]1/2u^{-1/2} * 18x[/tex]
[tex]\frac{dy}{dx} = \frac{1}{2}({9x^{2}-1 } )^{-1/2} * 18x\\\frac{dy}{dx} = 9x({9x^{2} -1 } )^{-1/2} \\\frac{dy}{dx} = 9 x(\sqrt{{\frac{1}{9x^{2} -1} } }) \\\frac{dy}{dx} = \frac{9x}{\sqrt{9x^{2}-1 } }[/tex]
c) In order to confrim that solutions to part (a) and (b) are consistent, we will substitute [tex]y = \sqrt{9x^{2} - 1 } \\[/tex] into the answer in (a) as shown;
From (a) [tex]\frac{dy}{dx} = \frac{9x}{y} \\[/tex]
[tex]y' = \frac{9x}{ \sqrt{9x^{2} - 1 } \\} } \\}[/tex]
This shows that they are consistent
What is the value of x? The figure contains 2 lines that intersect to form what looks like an x. Two of the 4 angles in the x are labeled. The left angle is labeled open parenthesis 3 x minus 3 close parenthesis degrees. The right angle across from it is labeled open bracket 6 open parenthesis x minus 10 close parenthesis close bracket degrees. Enter your answer in the box. x =
Answer:
[tex]x=38.5^\circ[/tex]
Step-by-step explanation:
Given that the left angle = [tex](3x-3)^\circ[/tex]
The right angle across from it [tex]= 6(x-10)^\circ[/tex]
The other two angles are x and x.
We know that the sum of angles at a point equals 360 degrees.
Therefore,
[tex](3x-3)^\circ+6(x-10)^\circ+x+x=360^\circ\\3x-3+6x-60+2x=360\\11x-63=360\\11x=360+63\\11x=423\\x=38.5^\circ[/tex]
The value of x is approximately 38.5 degrees.
someone help please !
Each line between 0 and 1 is 1/10 ( there are 10 lines)
First arrow is on the 3rd line so would be 3/10
The next arrow is 3 away from that so would be 3/10
The 3rd arrow is 2 away from the 2nd so would be 2/10
3/10 + 3/10 + 2/10 = 8/10
The answer is b
Don glover borrowed $14,000 for 250 days and paid $806.20 in simple interest on the loan. what annual simple interest rate did don pay on the loan?
Simple interest formula = I = PRT where I = interest, P = principal, r = interest rate and t = time.
i = 806.20, p = 14,000 t = 250 days.
Change t to be fraction of a full year: t = 250/365
Now solve for r:
806.20 = 14000 x r x 250/365
Simplify :
806.20 = r x 9589.04
Divide both sides by 9589.04:
r = 806.20 / 9589.04
r = 0.08407
Multiply by 100 to get percent:
r = 8.41% (rounded to nearest hundredth)
Question 1
You can ride a taxi and pay a flat rate of $25 to go anywhere in the city, or you can pay a
base rate of $15 and $1 per mile. For which trip would it make more sense to pay the base
rate and 1$ per mile?
15 mile trip
9 mile trip
25 mile trip
O 12 mile trip
Answer:
9 mile trip
Step-by-step explanation:
$15 + $15 = $30
$15 + $9 = $24
$15 + $25 = $40
$15 + $12 = $27
$30 > $25
$24 < $25
$40 > $25
$27 > $25
Write the fraction in simplest form. (3/6) x (7/10)
Please answer this correctly
Answer:
Option 2
Step-by-step explanation:
The average temperature in January is -1 degrees celsius. Last year, it was 1 degrees celsius higher than the average.
-1 + 1 = 0
Answer:
The second answer.
Step-by-step explanation:
The average temp. is -1C.
'was 1C warmer' = +1
-1+1=0
Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r=0.767, n=25 A. Critical values: r= +0.396, no significant linear correlation B. Critical values: r= +0.487, no significant linear correlation C. Critical values: r = +0.396, significant linear correlation D. Critical values: r = + 0.487, significant linear correlation
Answer:
C. Critical values: r = +0.396
Step-by-step explanation:
Hello!
A linear correlation for two variables X₁ and X₂ was calculated.
For a sample n= 25 the sample correlation coefficient is r= 0.767.
Be the hypotheses:
H₀: ρ = 0
H₁: ρ ≠ 0
α: 0.05
For this hypothesis test, the rejection region is two-tailed, and the degrees of freedom are Df= n-2= 25-2= 23
So using the Pearson product-moment correlation coefficient table of critical values, under the entry for "two tailed tests" you have to cross the level of significance and the degrees of freedom to find the corresponding critical value:
[tex]r_{n-2;\alpha }= r_{23;0.05}= 0.396[/tex]
Since the calculated correlation coefficient is greater than the critical value, you can reject the null hypothesis, this means that the correlation is significant at level 5%
I hope this helps!
Please answer this correctly
Answer:
The first answer.
Step-by-step explanation:
The first answer.
What was the temperature of the air?
'was 2C warmer than the surface of the ice'
warmer than= +2c
Temp. of ice=-2c
-2c+2c=0
Answer:
Option 1
Step-by-step explanation:
The temp. was -2 degrees celsius.
The temp. got 2 degrees celsius warmer.
-2 + 2 = 0
cos3x-3cosx=cos2x+1 {Domain: 0<=x<=360} The solution is 90deg, 180deg, and 270deg, but what are the simplifying steps in between? I know all trig identities.
Step-by-step explanation:
cos(3x) − 3 cos x = cos(2x) + 1
Use triple and double angle formulas.
(4 cos³x − 3 cos x) − 3 cos x = (2 cos²x − 1) + 1
Simplify.
4 cos³x − 6 cos x = 2 cos²x
4 cos³x − 2 cos²x − 6 cos x = 0
2 cos³x − cos²x − 3 cos x = 0
Factor.
cos x (2 cos²x − cos x − 3) = 0
cos x (cos x + 1) (2 cos x − 3) = 0
Solve.
cos x = 0 → x = 90°, 270°
cos x + 1 = 0 → x = 180°
2 cos x − 3 = 0 → no solution
Find the percent of increase. Original Price: $135 Retail Price: $162
20%
Here's a tip: Always start percentage calculating with dividing the current number by 10.
Please help need to do corrections and can't figure out this homework question??
Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which of the following choices is not true?
A. The ACT score gt 17.0 is relatively better than the SAT score of 1490 a relatively better then the SAT score of 1490 .
B. An SAT score of 1490 has a z-score of -0.09
C. The SAT score of 1490 is relatively better than the ACT score of 17.0.
Answer:
The ACT score gt 17.0 is relatively better than the SAT score of 1490 a relatively better then the SAT score of 1490 .
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
A. The ACT score gt 17.0 is relatively better than the SAT score of 1490 a relatively better then the SAT score of 1490.
We find the z-score for each of these options. Whichever has the higher z-score is the better grade.
ACT:
Mean 21.1, standard deviation of 4.8. Score of 17. So [tex]\mu = 21.1, \sigma = 4.8, X = 17[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17 - 21.1}{4.8}[/tex]
[tex]Z = -0.85[/tex]
SAT:
Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Score of 1490. So [tex]\mu = 1518, \sigma = 325, X = 1490[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1490 - 1518}{325}[/tex]
[tex]Z = -0.09[/tex]
The SAT score of 1490 has the higher z-score, so this is the better score, which means that this statement is false and A. is the answer of this question.
B. An SAT score of 1490 has a z-score of -0.09
From A., this is true
C. The SAT score of 1490 is relatively better than the ACT score of 17.0.
From A., this is true.
What is the value of this expression when n approaches infinity?
Answer:
C. Approaches 35
Step-by-step explanation:
If we graph the expression, we see that we have an asymptote at y = 35.
2jenxnwioznxjwhjjjjjhdhwbxnoaowbfnxiw
What is your question?
Answer:
yeah what's your question?
A lumber company has just taken delivery on a shipment of 10,000 2 ✕ 4 boards. Suppose that 10% of these boards (1000) are actually too green to be used in first-quality construction. Two boards are selected at random, one after the other. Let A = {the first board is green} and B = {the second board is green}.
(a) Compute P(A), P(B), and P(A ∩ B) (a tree diagram might help). (Round your answer for P(A ∩ B) to five decimal places.)
(b) With A and B independent and P(A) = P(B) = 0.1, what is P(A ∩ B)?
Answer:
Step-by-step explanation:
Given That:
Let A = {the first board is green} and B = {the second board is green}.
A lumber company has just taken delivery on a shipment of 10,000 2×4 boards.
Suppose that 10% of these boards (1000) are actually too green to be used in first-quality construction. Two boards are selected at random, one after the other.
We are to compute the following probabilities :
P(A)
P(B)
P(A ∩ B)
To start with the probability P(A)
[tex]P(A) = \dfrac{1000}{10000}[/tex]
P(A) = 0.1
[tex]P(B) = P(B|A)*P(A)+P(B|A')*P(A')[/tex]
where;
[tex]P(B|A) = \dfrac{N(B|A)}{N-1}[/tex]
[tex]P(B|A) = \dfrac{999}{9999}[/tex]
[tex]P(B|A) =0.0999[/tex]
[tex]P(B|A') = \dfrac{N(B|A')}{N-1}[/tex]
[tex]P(B|A') = \dfrac{1000}{999}[/tex]
[tex]P(B|A') = 0.10[/tex]
Recall that :
[tex]P(B) = P(B|A)*P(A)+P(B|A')*P(A')[/tex]
[tex]P(B) = 0.0999*0.1+0.10*(1-0.1)[/tex]
[tex]P(B) = 0.00999+0.10*(0.9)[/tex]
[tex]P(B) = 0.00999+0.09[/tex]
[tex]P(B) = 0.0999[/tex]
P(A ∩ B) = P(B|A)B
P(A ∩ B) = 0.0999 × 0.10
P(A ∩ B) = 0.00999
(b)
Given that A and B are independent; Then:
P(A ∩ B) = P(A) × P(B)
0.00999 = 0.1 × 0.09999
0.00999 = 0.00999
As such A and B are independent
However; when P(A ∩ B) = P(A) = P(B) = 0.1
P(A ∩ B) = P(A) × P(B)
P(A ∩ B) = 0.1 × 0.1
P(A ∩ B) = 0.01
Two hot-air balloons, one red and one blue, took off at the same time from different platforms. Each began ascending at a constant rate. The following equation gives the height (in meters) of the red hot-air balloon as a function of time (in seconds). h=1/2t+4 The height (in meters) of the blue hot-air balloon as a function of time (in seconds) is given by the following table of values: (Table is attached) Which balloon started at a greater height? A. The red balloon B. The blue balloon C. They are both the same height
Answer:
1. the red balloon
2.they both ascended at the same rate
Step-by-step explanation:
Answer:
1.red
acended
Step-by
what are the multiples of 5,6,8,9?
What multiplication expression is equal to 3/5÷1/4 out of 3/5×1/4 or 5/3×1/4 or 3/5×1/4 or 3/5×4/1
Answer:
it would be 3/5*4/1
Step-by-step explanation:
To divide you multiply the first number by the reciprocal of the second number. Check and you'll see that the answer is the same. Hope this helps!
Answer:
The answer is 3/5 x 4/1
Step-by-step explanation:
The scheduled arrival time for a daily flight from Boston to New York is 9:30 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:07 am and a late arrival time of 9:57 am.a. After converting the time data to a minute scale, calculate the mean and the standard deviation for the distribution. (Round your answers to 2 decimal places.)Mean:____________________________ minutes Standard deviation: _________________ minutes b. What is the probability that a flight arrives late (later than 9:30 am)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)Probability:________
Answer:
Step-by-step explanation:
Let x be a random variable representing the flight arrival time from Boston to New York.
For a uniform probability distribution, the notation is
X U(a, b) where a is the lowest value of x and b is the lowest value of x
The probability density function, f(x) = 1/(b - a)
Mean, µ = (a + b)/2
Standard deviation, σ = √(b - a)²/12
From the information given, the time difference in minutes is 9:57 - 9:07 = 50 minutes. Therefore,
a = 0
b = 50
µ = (0 + 50)/2 = 25
σ = √(50 - 0)²/12 = 14.43
b) converting to minutes, it is 9:30 - 9:07 = 23 minutes
the probability that a flight arrives late(later than 9:30 am) is expressed as P(x > 23)
f(x) = 1/(50) = 0.02
P(x > 23) = (50 - 23)0.02 = 0.54
A poll found that 5% of teenagers (ages 13 to 17) suffer from arachnophobia and are extremely afraid of spiders. At a summer camp there are 11 teenagers sleeping in each tent. Assume that these 11 teenagers are independent of each other. (Round your answers to four decimal places.)
a) Calculate the probability that at least one of them suffers from arachnophobia. - 0.4312
b) Calculate the probability that exactly 2 of them suffer from arachnophobia? 0.08666
c) Calculate the probability that at most 1 of them suffers from arachnophobia? What is C?
Answer:
a) Calculate the probability that at least one of them suffers from arachnophobia.
x = number of students suffering from arachnophobia
= P(x ≥ 1)
= 1 - P(x = 0)
= 1 - [0.05⁰ x (1 - 0.05)¹¹⁻⁰ ]
= 1 - (0.95)¹¹
= 0.4311999 = 0.4312
b) Calculate the probability that exactly 2 of them suffer from arachnophobia? 0.08666
= P(x = 2)
= (¹¹₂) x (0.05)² x (0.95)⁹
where ¹¹₂ = 11! / (2!9!) = (11 x 10) / (2 x 1) = 55
= 55 x 0.0025 x 0.630249409 = 0.086659293 = 0.0867
c) Calculate the probability that at most 1 of them suffers from arachnophobia?
P(x ≤ 1)
= P(x = 0) + P(x = 1)
= [(¹¹₀) x 0.05⁰ x 0.95¹¹] + [(¹¹₁) x 0.05¹ x 0.95¹⁰]
= (1 x 1 x 0.5688) + (11 x 0.05 x 0.598736939) = 0.5688 + 0.3293 = 0.8981
100
x
x
||
=
8X10
15
||
Answer:
the answer is 6x
Step-by-step explanation:
which one doesn't belong ? please help thx :)
Answer:
THE CURVED ONE
Step-by-step explanation:
THE OTHER ONES R STRAIGHT LINES
THE ONE ON THE TOP RIGHT CORNER IS A PARABOLA
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
When Sam simplified the expression 3.5 - (-4.1), she got -0.6.
What mistake did Sam likely make when she simplified
the expression?
Answer:
She forgot to combine the 2 negative signs and turn it into a positive.
Step-by-step explanation:
When you subtract a negative, you are adding the number. So if we have 3.5 - (-4.1), it would equal 3.5 + 4.1, which is 7.6
Answer:
She subtracted a negative incorrectly by simply subtracting a positive when subtracting a negative means to add a positive.
Step-by-step explanation:
She subtracted 3.5 - 4.1 which is -0.6
The problem is subtracting -4.1 which means to add 4.1
3.5 - (-4.1) = 3.5 + 4.1 = 7.6
She did: 3.5 - (-4.1) = 3.5 - 4.1 = -0.6 which is incorrect.
An auto parts chain asked customers to complete a survey rating the chain's customer service as below average, average, or above average. The frequency distribution below displays the results for the survey. Calculate the relative frequency.
Response Frequency Relative Frequency
Below Average 7
Average 5
above Average 3
Is this categorical or umerical data?
Answer:
(b)Categorical Data
Step-by-step explanation:
The response, frequency, and calculation of the relative frequency of the data is given in the table below.
[tex]\left|\begin{array}{c|c|c}$Response&$Frequency &$Relative Frequency\\---&----&---\\$Below Average& 7&\dfrac{7}{15} \times 100 \approx 47\% \\&&\\$Average&5&\dfrac{5}{15} \times 100 \approx 33\%\\&&\\$Above Average&3&\dfrac{3}{15} \times 100 =20\%\\---&---&---\\$Total&15&100\end{array}\right|[/tex]
(b)
A quick way to determine if a data is categorical or numerical is to determine if the mean of the data can be found.
In this case, we cannot determine the mean of the data, therefore, it is a categorical data.