If [tex]a\ \textless \ b[/tex], there are three ordered pairs of positive integers [tex](a,b)[/tex] that satisfy [tex]a^{2}+b^{2}=10(123)^{2}[/tex] If two of these ordered pairs are [tex](39,387)[/tex] and [tex](201,333)[/tex]. What is the third such ordered pair?
The third ordered pair positive integers that satisfies the equation is (123, 369).
The given parameters;
[tex]a^2 + b^2 = 10(123)^2[/tex]First pair of the equation, = (39, 387)Second pair of the equation = (201, 333)The third ordered pair of the equation can be determined by using general equation of a circle;
[tex]a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}[/tex]
The radius of the circle is calculated as;
[tex]r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96[/tex]
The value of a can be obtained by randomly choosing numbers less than the radius as values of b.
[tex]b < r\\\\b < 388.96[/tex]
[tex]a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)[/tex]
Thus, the third ordered pair positive integers that satisfies the equation is (123, 369).
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The length of a rectangle is times the width. If the perimeter is 32 inches, what is the width of the rectangle
Answer:
11
Step-by-step explanation:
6
0 0 0
TIME RE
44
Jeremiah flies an airplane for 2.7 hours at an average speed of 304.6 miles per hour. How far did Jeremiah fly?
Answer:
112.81 miles
Step-by-step explanation:
304.6 divided by 2.7
Help on this algebra 2 question look at the pic. Is it’s A, B or C
Answer:
A is correct
Step-by-step explanation:
perimeter is twice the sum of the two adjacent sides
p = 2(x + (2x³ - 3x + 4))
p = 2(2x³ - 2x + 4)
p = 4x³ - 4x + 8
Is 0.136 greater or least to 0.23?
Answer: least
Step-by-step explanation: because 0.23 is closer to 1
Least
If you removed the last term from 0.136, it would become 0.13
Compared to 0.25, it is lower.
please help ill mark brainliest
Answer:
it's 11
Step-by-step explanation:
Help help help help math please ASAP
Answer:
I think its 86
Step-by-step explanation:
As the two lines going in the same direction are parallel and angles within parallel lines add to 180.
so 180-94=86
Hogie lizards have tail lengths that are normally distributed with a mean of 22.5 cm and a standard deviation of 3.6 cm. What tail length is at the 40th percentile for these lizards?
A tail length of 23.94 cm is at the 40th percentile for these lizards.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x\ is\ raw\ score, \mu\ is\ mean,\sigma\ is\ standard\ deviation\\\\\\Given\ that:\\\mu=22.5\ cm,\sigma = 3.6\ cm[/tex]
For the 40th percentile, that is z = 40% = 0.4:
[tex]0.4=\frac{x-22.5}{3.6} \\\\x=23.94\ cm[/tex]
A tail length of 23.94 cm is at the 40th percentile for these lizards.
Find out more at: https://brainly.com/question/15016913
11
Y1
0
4
1
12
2
36
3
108
Write an explicit function
56566965577553666645556566667
At a local college, 204 of the male students are smokers and 306 are non-smokers. Of the female students, 180 are smokers and 420 are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are smokers?
Step-by-step explanation:
Male ratio: 204:306 = 2:3 (66%)
Female ratio: 180:420 = 3:7 (42%)
Hope that helps
Answer:
both are non smokers is 0.48.
will give brainly if you help me thx
Answer:
A
Step-by-step explanation:
The answer is A because is it asking for a 3 in the hundredths place of the difference. Difference means subtraction. And you can find the hundredth spot in the second place over from the decimal
(ex. 1.23, hundredth place is a 3)
So then you do the math and find the differences.
14.56-9.33=5.23, which has a 3 in the hundredth place.
Which of the following statements explains the correct method to solve the equation 7x - 8 = 48?
Answer:
Follow the explanation below.
Step-by-step explanation:
7x = 48 - 8
7x = 40
x = 40/7
x = 5.714
What is an equation of the line that passes through the points (8,-4) and (6,-5)?
Answer:
y=1/2x-8
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-5-(-4))/(6-8)
m=(-5+4)/-2
m=-1/-2
m=1/2
y-y1=m(x-x1)
y-(-4)=1/2(x-8)
y+4=1/2(x-8)
y=1/2x-8/2-4
y=1/2x-4-4
y=1/2x-8
Please help me solve this question I'm stuck on
The answer to the question is
D) ($9. 60, $9. 84)
the number obtained on rationalizing the denominator of 1/(√7--2) is
[tex] \frac{1}{ \sqrt{7} -(- 2)} \\ rationalizing \: \: \: the \: \: \: denominator \: \: \: we \: \: \: have \\ = \frac{1}{ \sqrt{7} + 2 } \times \frac{ \sqrt{7} - 2}{ \sqrt{7} - 2} \\ = \frac{ \sqrt{7} - 2}{ {( \sqrt{7} )}^{2} - {(2)}^{2} } \\ = \frac{ \sqrt{7} - 2 }{7 - 4} \\ = \frac{ \sqrt{7} - 2}{3} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Given that:
1/(√7 - 2)
The denominator is (√7-2).
We know
The rationalising factor of (√a-b) is (√a+b)
Therefore, the rationalising factor of √7-2 is √7+2.
On rationalising the denominator them
⇛[1/(√7-2)]×[(√7+2)/(√7+2)]
⇛[1(√7+2)]/[(√7-2)(√7+2)]
Since, (a-b)(a+b) = a²-b²
Where, a = √7 and b = √2.
⇛[1(√7+2)]/[(√7)²-(2)²]
⇛[1(√7+2)]/[(√7*7)-(2*2)]
⇛[1(√7+2)]/[7-4]
⇛[1(√7+2)]/3
⇛(√7+2)/3
Hence, the denominator is rationalised.
also read similar questions:
pls can u help me with this question
Answer:
yes less than a min
Step-by-step explanation:
Simplify.
(2a2−3ab+5b2)−(a2−2ab+3b2)
A.a4−a2b2+2b4
B.3a2−5ab+8b2
C.a2−5ab+2b2
D.a2−ab+2b2
Simplify. (6x−3)−(2x−2)
A.4x2−1
B.4x−1
C.4x−5
D.4x2−5
Answer:
DBStep-by-step explanation:
You may find this easier if you distribute the minus sign first.
1)2a^2 -3ab +5b^2 -a^2 +2ab -3b^2
= (2 -1)a^2 +(-3+2)ab +(5 -3)b^2
= a^2 -ab +2b^2 . . . . . matches choice D
__
2)6x -3 -2x +2
= (6 -2)x +(-3 +2)
= 4x -1 . . . . . matches choice B
Write the ratio 1 1/3 to 3 1/9 as a simplified fraction
Answer:
First ratio:4/3
Second:28/9
The movement of the progress bar may be uneven because questions can be worth more or less (ir
Add: (– 15xz + 4xy) + (20xy - 9yz + 16xz)
O 24x2 y2 – 9yz + x² zº
0 16xyz
0 5xy – 5 yz + 16xz
024xy - 9yz + xz
Your Answer Is : - 31xz + 16xy - 9yz
Subtract 95 800 by 28 766 ?
please please please help!!
Answer: 95,800 - 28,766 = 67,034
Step-by-step explanation: hope this helps :)
How do you know where to place the decimal in a quotient?
Answer:
Step-by-step explanation:Move the decimal point in the divisor and dividend. ...
Place a decimal point in the quotient (the answer) directly above where the decimal point now appears in the dividend.
Divide as usual, being careful to line up the quotient properly so that the decimal point falls into place.
please help!! 100 points
[tex]\\ \tt\bull\rightarrowtail h(x)=1/5(x^2-6)-8[/tex]
[tex]\\ \tt\bull\rightarrowtail h(4)[/tex]
[tex]\\ \tt\bull\rightarrowtail 1/5(4^2-6)-8[/tex]
[tex]\\ \tt\bull\rightarrowtail 1/5(16-6)-8[/tex]
[tex]\\ \tt\bull\rightarrowtail 10/5-8[/tex]
[tex]\\ \tt\bull\rightarrowtail 2-8[/tex]
[tex]\\ \tt\bull\rightarrowtail -6[/tex]
A single die is rolled twice. The 36 equally-likely outcomes are shown to the right.
Find the probability of getting two numbers whose sum exceeds 20.
Answer:
If the die is 6 sided then the likely is none (0)
Step-by-step explanation:
Hope this helps!:)
Help me out Ik you love Algebra as much as I do
Answer:
pop
yes no total
country yes 11 38 49
no 43 8 51
total 54 46 100
Hope you understand this haha
The answer is in the file. Hope it helps.
Solve the proportion
4
x
=
9
6
[tex]\huge\text{\bf Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{4x = 96}}\\\\\large\text{DIVIDE 4 to BOTH SIDES}\\\\\huge\boxed{\mathsf{\dfrac{4x}{4} = \dfrac{96}{4}}}\\\\\large\text{CANCEL out: }\rm{\dfrac{4}{4}}\large\text{ because it gives you 1}\\\large\text{KEEP: }\rm{\dfrac{96}{4}}\large\text{ because it helps solve for the x-value}\\\\\large\text{NEW EQUATION: }\huge\boxed{\rm{x = \dfrac{96}{4}}}\\\\\large\text{SIMPLIFY IT\textbf{!}}\\\\\huge\text{x = \bf 24}\\\\\\\huge\text{Therefore, your answer is: \boxed{\textsf{x = 24}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \&}\\\huge\textbf{enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A random variables X and Y are distributed according to the joint PDF. The value of constant a = _______.f(x,y)=ax if 1<=1x<=y<=2 and 0 otherwise
======================================================
Explanation:
PDF = probability density function
The given joint PDF is
[tex]f(x,y) = \begin{cases}ax \ \ \ \text{ if } 1 \le x \le y \le 2\\0 \ \ \ \ \ \text{ otherwise}\end{cases}[/tex]
Let's focus on the [tex]1 \le x \le y \le 2[/tex]. Specifically the x term for now. Erasing out the y term, we have the inequality [tex]1 \le x \le 2[/tex] which says x is between 1 and 2, inclusive. We have almost the same story for y, but there's another condition attached to it: y must also be equal to or larger than x.
So let's say x = 1.5. This would mean [tex]1.5 \le y \le 2[/tex]. As another example, x = 1.7 leads to [tex]1.7 \le y \le 2[/tex]. In general, we would say [tex]x \le y \le 2[/tex] where x is between 1 and 2.
As x gets bigger, the range of possible y values gets smaller. If x = 2, then y has no choice but to be 2 as well.
-----------------
Based on that, we'll have a double integral that looks like this:
[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\[/tex]
The outer integral handles the x terms that range from 1 to 2, describing [tex]1 \le x \le 2[/tex]. Note the dx on the outside. The order of the dy and dx matters.
On the inside, we have the integral for dy ranging from x to 2 to describe the interval [tex]x \le y \le 2[/tex]
To have f(x,y) be a PDF, the volume under the f(x,y) surface must be 1, where the volume is based on the bounds set up. So we must have V = 1. We'll use this later.
-----------------
Let's simplify the double integral.
We'll start by computing the inner integral with respect to y.
[tex]\displaystyle V = \int_{1}^{2}\int_{x}^{2}f(x,y)dydx\\\\\displaystyle V = \int_{1}^{2}\int_{x}^{2}\left(ax\right)dydx\\\\\displaystyle V = \int_{1}^{2}\left(axy\Bigg|_{x}^{2}\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(ax(2) - ax(x)\right)dx\\\\\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\[/tex]
Then we'll finish it off by integrating with respect to x.
[tex]\displaystyle V = \int_{1}^{2}\left(2ax - ax^2\right)dx\\\\\displaystyle V = \left(ax^2 - \frac{1}{3}ax^3\right)\Bigg|_{1}^{2}\\\\\displaystyle V = \left(a(2)^2 - \frac{1}{3}a(2)^3\right) - \left(a(1)^2 - \frac{1}{3}a(1)^3\right)\\\\\displaystyle V = \left(4a - \frac{8}{3}a\right)-\left(a - \frac{1}{3}a\right)\\\\[/tex]
[tex]\displaystyle V = 4a - \frac{8}{3}a-a + \frac{1}{3}a\\\\\displaystyle V = 3a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9}{3}a - \frac{8}{3}a + \frac{1}{3}a\\\\\displaystyle V = \frac{9-8+1}{3}a\\\\\displaystyle V = \frac{2}{3}a\\\\[/tex]
Side note: We don't have to worry about the "plus C" integration constant when working with definite integrals.
Recall that V = 1. So,
[tex]\displaystyle V = \frac{2}{3}a\\\\\displaystyle \frac{2}{3}a = 1\\\\\displaystyle a = \frac{3}{2} = 1.5\\\\[/tex]
a = 3/2 is the final answer.
Suppose that in a certain state, all automobile license plates have four letters of the 26 English alphabet letters followed by three digits from 0,1,2,3,4,5,6,7,8,9. For example, WCRY-122. How many license plates are possible that begins with A and ends with 1 with NO repetition
Answer:
[tex]993,\!600[/tex].
Step-by-step explanation:
There is one way to choose the first character (has to be an [tex]\verb!A![/tex].)
There is one way to choose the last character (has to be a [tex]\verb!1![/tex].)
Since repetition among the letters is not allowed and the letter [tex]\verb!A![/tex] was already reserved for the first character, there would be [tex](26 - 1) = 25[/tex] English alphabet letters available for the second character.
Likewise, with the first and second characters chosen, the third character could be chosen from [tex](26 - 2) = 24[/tex] letters. There would be [tex](26 - 3) = 23[/tex] choices for the fourth letter.
Repetition of the digits is not allowed, either. With the digit [tex]\verb!1![/tex] already reserved for the last character, there would be [tex](10 - 1) = 9[/tex] ways to choose the fifth character (a digit.) There would then be [tex](10 - 2) = 8[/tex] ways to choose the sixth character (also a digit.)
Overall, the number of unique combinations would be:
[tex]\begin{aligned}& 1 \times 1 \times (25 \times 24 \times 23) \times (9 \times 8) \\ =& \; 993,\!600 \end{aligned}[/tex].
Write and expression for the senqence of operations described below.
raise 6 to the 2nd power, then subtract r from the result
Do not simplify any part of the expression.
Raise [tex]6[/tex] to the second power, [tex]6^{2}[/tex], the subtract r from the result, that should be [tex]6^{2} - r[/tex], since we are not to simplify the expression, that's the answer.
112
121
124
137
147
156
173
189
Find the median revenue.
Answer:
142
Step-by-step explanation:
Median is the MID Number
a sphere has a volume of 2,304 pi mm3. find the diameter of the sphere
Answer:
24
the formula of sphere is
[tex]v = \frac{4}{3} {r}^{3} [/tex]
Since we know the volume, and have to find the diameter (twice the radius), we need to determine the radius first.
Hence, using the given data:
[tex]2304\pi = \frac{4}{3} \pi {r}^{3} [/tex]
We can cancel
We can cancel π from each side.
[tex]2304 = \frac{4}{3} {r}^{3} [/tex]
Multiply both sides by
[tex] \frac{3}{4} [/tex]
hope I help you ☺️❤️
