Answer: A right triangle with acute angles measuring 45° and 45°
Step-by-step explanation:
This question is related to the criteria of congruence for triangles.
The criteria are:
SSS (you know the 3 sides)
SAS (you know two sides, and the angle between those two sides)
ASA (you know two angles, and the side between those two angles)
AAS (you know two angles, and one side).
So for the given examples, the only one that does not reach any of those criteria is the last option, where we only have the angles:
45°, 45° and 90°.
This means that we can craft multiple triangles with this data:
this is a triangle rectangle where the length of the cathetus is the same, that is the only restriction.
For example we can have lengths:
1, 1 and √2
or 2, 2 and √(2^2 + 2^2) = √8
Answer:
A right triangle with acute angles measuring 45° and 45°
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
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:
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!
What methods does the textbook present for solving recurrences by guessing a bound and using mathematical induction to prove accuracy
Answer:
The correct answer is - Substitution method
Step-by-step explanation:
substitution method or strategy where an individual solve for one variable first and afterward substitute that articulation into the other equation. The significant thing here is that you are consistently substituting values that are the same.
Steps :
- Comprehend or solve one of the variables and make an equation.
- Substitute (module) this articulation into the other equation and comprehend.
- Resubstitute the value into the first equation to find the value of other variable.
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
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
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.
In the diagram below, if AD= 100 and AC = 34, find CD.
A 59
B 76
C 45
D 66
Answer:
D. 66
Step-by-step explanation:
Well if AD is 100 and AC is 34 that leaves CD so we can just subtraction 34 from 100 and get 66.
Answer:
D. 66
Step-by-step explanation:
AD = 100
AC = 34
The whole line is 100. A part of the line is 34. The other part will be 66.
100 - 34 = 66
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
How do you write 0.00609 in scientific notation? ____× 10^_____
Answer:
6.09 * 10 ^-3
Step-by-step explanation:
We want one non zero digit to the left of the decimal
Move the decimal 3 places to the right
6.09
The exponent is 3 and it is negative since we move to the right
6.09 * 10 ^-3
Answer:
6.09(10⁻³)
Step-by-step explanation:
Step 1: Put number into proper scientific decimal form
6.09
Step 2: Figure out how many decimals places it moves
Since it moves to the left 3, our exponent would be -3
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
by which number -7 /25 should be divided to get -1/15?
Answer:
21/5
Step-by-step explanation:
if a/b = c, then b=a/c
in other words:
divide -7/25 by -1/15 to get the answer
It also helps to use the fact that a/b / c/d = a/b * d/c
-7/25 / -1/15 = -7/25 * -15/1
= 105 / 25
= 21 / 5
Answer:
[tex]4 \frac{1}{5} [/tex]
Step-by-step explanation:
[tex] \frac{ - 7}{25} \div x = \frac{ - 1}{15} [/tex]
[tex]x = \frac{ - 7}{25} \div \frac{ - 1}{15} [/tex]
[tex] = \frac{7}{25} \times \frac{15}{1} [/tex]
[tex] = \frac{21}{5} = 4 \frac{1}{5} [/tex]
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.
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.
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
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.
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
A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 4% margin of error at a 99% confidence level, what size of sample is needed? Give your answer in whole people.
Answer:
Step-by-step explanation:
Hello!
The variable of interest is:
X: Number of people that support the candidate.
You need to calculate the sample size to estimate the population proportion of supporters given a confidence level of 99% and a margin of error of 4%
The margin of error of the confidence level for the population proportion is
d= [tex]Z_{1-\alpha /2}[/tex] * [tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
From this formula you have to clear the value of n:
[tex]\frac{d}{Z_{1-\alpha /2}}[/tex]= [tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
[tex](\frac{d}{Z_{1-\alpha /2}})^2[/tex]= [tex]\frac{p'(1-p')}{n}[/tex]
[tex]n*(\frac{d}{Z_{1-\alpha /2}})^2[/tex]= [tex]p'(1-p')[/tex]
n= [tex]p'(1-p') * (\frac{Z_{1-\alpha/2}}{d} )^2[/tex]
[tex]Z_{1-\alpha/2}= Z_{0.995}= 2.586[/tex]
sample proportion "p'" since there is no sample information, nor any previous information is known, you have to consider it as the "worse case scenario" and use the value of p'= 0.50
d= 0.04
[tex]n= p'(1-p') * (\frac{Z_{1-\alpha/2}}{d} )^2= 0.5*0.5*(\frac{2.586}{0.04} )^2= 1044.9= 1045[/tex]
She has to take a sample of 1045 people to estimate the population proportion of her supporters with a confidence level of 99% and a margin of error of 4%
I hope this helps!
On a normally distributed anxiety test with mean 48 and standard deviation 4, approximately what anxiety test score would put someone in the top 5 percent? Group of answer choices
Answer:
Anxiety score close to 54.58.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
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.
In this question:
[tex]\mu = 48, \sigma = 4[/tex]
Approximately what anxiety test score would put someone in the top 5 percent?
We have to find the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 48}{4}[/tex]
[tex]X - 48 = 1.645*4[/tex]
[tex]X = 54.58[/tex]
Anxiety score close to 54.58.
Find the product of: 1.(6a²+2b³) and -4ab²
Answer:
[tex]-24a^3b^2 -8ab^5\\[/tex]
Step-by-step explanation:
Given the two expression (6a²+2b³) and -4ab², to find their product, the following steps are valid;
[tex]= (6a^2+2b^3) *-4ab^2\\= (6a^2+2b^3)(-4ab^2)\\= (6a^2)(-4ab^2)+(2b^3)(-4ab^2) \\= -24a^3b^2 + (-8ab^5)\\= -24a^3b^2 -8ab^5\\[/tex]
The final expression gives the required product
what are the multiples of 5,6,8,9?
Find an equation of the tangent line to the curve at the given point.
y = √ (x) , (16, 4)
Answer: y=1/8*x+2
Step-by-step explanation:
The equation of any tangent line is y=a*x+b (1)
To the equation of the tangent line we have to find the coefficients a and b and the to substitute them to equation (1).
As we know a=y'(x0) ( where x0=16)
So y'(x)= (√ (x) )' = 1/(2*√x)
a=y'(x0)= 1/(2*√16)=1/(2*4)=1/8
So lets substitute a in equation (1):
y=1/8 *x+b
Now we have to find b
We know that the point (16, 4) belongs to the tangent line.
That means
4=1/8*16+b => 4=2+b => b=2
SO the equation of the tangent line is y=1/8*x+2
Write the fraction in simplest form. (3/6) x (7/10)
What pages will be favored for the given search? Search terms: Michael OR Jordan A. Pages about Michael Jordan B. Pages about Michael, plus pages about OR, plus pages about Jordan C. Pages about Michael, plus pages about Jordan D. Pages about Michael, plus pages about Jordan, plus pages about both
Answer:
A. Pages about Michael Jordan.
Step-by-step explanation:
Michael Jordan, MJ, is a great basketball player, and has achieved one the best records in his career. He is a National Basketball Association (NBA) player with great skills and energy.
From the search item, the two names Michael OR Jordan is for one person, Michael Jordan. The search would combine the two names because it is a well known one and give an output on Michael Jordan. Thus, the pages that would be favored are pages about Michael Jordan.
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)
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
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.
what is the answer pls help me
Answer:
D.
Step-by-step explanation:
It is D. because there are lines on top of the letters meaning that the points PQ, QR, and PR are lines/sides.
You chose the answer already!
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.