the average time of each runner is 12.36
Answer:
12.36 seconds
Step-by-step explanation:
Total time = 49.44 seconds
Students = 4
Average = 49.44/4 = 12.36 seconds
Answered by GAUTHMATH
YOU THE REAL OG
IF YOU CAN DO THIS FOR ME
YES IT IS HAIKU
How much would you need to deposit in an account each month in order to have $50,000 in the account in 8 years? Assume the account earns 4% annual interest compounded monthly.
THANK YOU TO ANY OG WHO CAN SOLVE THIS , BRAINLIEST GUARANTEE TO ANYONE WHO REALLY TRIES
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Answer:
$442.80
Step-by-step explanation:
The formula for the amount of an ordinary annuity is ...
A = P(12/r)((1 +r/12)^(12t) -1)
where payment P is made n times per year and interest is accrued at annual rate r.
Filling in the given values, we want ...
50,000 = P(12/0.04)(1 +0.04/12)^(12·8) -1) = 112.91854P
P = 50,000/112.91854 ≈ 442.80
You would need to deposit $442.80 each month for 8 years.
Answer by formula please
Answer:
Step-by-step explanation:
I honestly have no idea what you mean by answer by formula, but I'm going to give it my best. I began by squaring both sides to get:
(a² - b²) tan²θ = b² and then distributed to get:
a² tan²θ - b² tan²θ = b² and then got the b terms on the side to get:
a² tan²θ = b² + b² tan²θ and then changed the tans to sin/cos to get:
[tex]\frac{a^2sin^2\theta}{cos^2\theta}=b^2+\frac{b^2sin^2\theta}{cos^2\theta}[/tex] and isolated the sin-squared on the left to get:
[tex]a^2sin^2\theta=cos^2\theta(b^2+\frac{b^2sin^2\theta}{cos^2\theta})[/tex] and distributed to get:
***[tex]a^2sin^2\theta=b^2cos^2\theta+b^2sin^2\theta[/tex]*** and factored the right side to get:
[tex]a^2sin^2\theta=b^2(sin^2\theta+cos^2\theta)[/tex] and utilized a trig Pythagorean identity to get:
[tex]a^2sin^2\theta=b^2(1)[/tex] and then solved for sinθ in the following way:
[tex]sin^2\theta=\frac{b^2}{a^2}[/tex] so
[tex]sin\theta=\frac{b}{a}[/tex] This, along with the *** expression above will be important. I'm picking up at the *** to solve for cosθ:
[tex]a^2sin^2\theta=b^2cos^2\theta+b^2sin^2\theta[/tex] and get the cos²θ alone on the right by subtracting to get:
[tex]a^2sin^2\theta-b^2sin^2\theta=b^2cos^2\theta[/tex] and divide by b² to get:
[tex]\frac{a^2sin^2\theta}{b^2}-sin^2\theta=cos^2\theta[/tex] and factor on the left to get:
[tex]sin^2\theta(\frac{a^2}{b^2}-1)=cos^2\theta[/tex] and take the square root of both sides to get:
[tex]\sqrt{sin^2\theta(\frac{a^2}{b^2}-1) }=cos\theta[/tex] and simplify to get:
[tex]\frac{sin\theta}{b}\sqrt{a^2-b^2}=cos\theta[/tex] and go back to the identity we found for sinθ and sub it in to get:
[tex]\frac{\frac{b}{a} }{b}\sqrt{a^2-b^2}=cos\theta[/tex] and simplifying a bit gives us:
[tex]\frac{1}{a}\sqrt{a^2-b^2}=cos\theta[/tex]
That's my spin on things....not sure if it's what you were looking for. If not.....YIKES
What is the 21st term of the sequence with a1 = -6 and d = 4?
a) 70
b) 74
c) -40
d) 78
Answer:
74
Step-by-step explanation:
for this question you have to use the formula of the nth term which is Tn=a+(n-1)d,
T21=-6+(21-1)4
=-6+(20)4
=-6+80
=74
I hope this helps
what’s the value of x? and what’s the measure of angel JHK?
Answer:
x = 14
JHK = 21
Step-by-step explanation:
The angles are vertical angles and vertical angles are equal
3x-21 = x+7
Subtract x from each side
3x-x -21 = x+7-x
2x-21 = 7
Add 21 to each side
2x-21+21 = 7+21
2x = 28
Divide by 2
2x/2 =28/2
x = 14
JHK = 3x-21 = 3(14) -21 = 42-21 = 21
Answer:
Because ∠GHI and ∠JHK are vertical angles, they're congruent. Therefore, set their angle measures equal to each other & solve for x.
[tex]x+7=3x-21\\x-3x=-7-21\\-2x=-28\\x=\frac{-28}{-2} =14\°[/tex]
Substitute in the value of x to find ∠JHK:
[tex]3x-21=3(14)-21=42-21=21\°[/tex]
Mrs. Gomez has two kinds of flowers in her garden. The ratio of lilies to daisies in the garden is 5:2
If there are 20 lilies, what is the total number of flowers in her garden?
Answer:
28
Step-by-step explanation:
5 : 2
since this is a simplified ratio, they have a common factor. let's say it is 'x'
so now :
5x : 2x
we know that 5x is lilies, and we also know that she has 20 lilies, so:
5x = 20
x = 4
the daisies would be 2x so 2*4 = 8
total flowers is 20 + 8
28
find the value of the trigonometric ratio. make sure to simplify the fraction if needed.
Answer:
36/39
Step-by-step explanation:
Cos(theta) = Base/Hypotenuse
Cos(X) = 36/39
Only the top runners in the world can finish a marathon in close to 2 hours. This graph
shows the pace that one such runner followed in a race. What is the unit rate?
Marathon Pace
N
28
24
20
Distance (mi)
10
12
B
8
A
4
0
0 20 40 60 80 100120140
Time (min)
Answer:
the unit rate is 4mi per minute.
Step-by-step explanation:
if you find the slope between point A and point B, you see that the line rises at 4 mi (distance) per minute (time). thus the unit rate is 4mi per minute. please correct me if I'm wrong, I hope this answer helps.
Will give brainliest answer
what is an example of a quintic bionomial?
Is interquartile range a measure of center or a measure of variation?
Answer:
The interquartile range is the middle half of the data that is in between the upper and lower quartiles. ... The interquartile range is a robust measure of variability in a similar manner that the median is a robust measure of central tendency.
Oscar has 1/5 of a jar of mustard. He puts equal amounts of the mustard onto 7 sandwiches and uses all of the mustard. What fraction of a jar of mustard does each sandwich have?
Answer:
1/35 jar of mustard yuh yuh
what is the decimal equivalent of 7/20
3^x= 3*2^x
solve this equation
Answer:
[tex] {3}^{x} = 3 \times {2}^{x} \\ x = \frac{ln(3)}{ln(3) -ln(2) } = \frac{1.09}{1.09 - 0.69} \\ x = 2.7[/tex]
I hope I helped you^_^
Find TAN
Instructions: Find the value of the trigonometric ratio. Make
sure to simplify the fraction if needed.
please mark this answer as brainlist
Scientists have steadily increased the amount of grain that farms can produce each year. The yield for farms in France is given by y=−2.73x2+11000x−11000000 where x is the year and y is the grain yield in kilograms per hectare (kg/ha).
What does the y-intercept of this function represent?
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Answer:
the yield in year 0
Step-by-step explanation:
The y-value is the yield for farms in France in year x. The y-value when x=0 is the yield for farms in France in year 0.
_____
Additional comment
The reasonable domain for this function is approximately 1843 ≤ x ≤ 2186. The function is effectively undefined for values of x outside this domain, so the y-intercept is meaningless by itself.
Find the missing length indicated
Answer:
x = 960
Step-by-step explanation:
x=√{576×(576+1024)}
or, x = √(576×1600)
or, x = √576×√1600
or, x = 24×40
or, x = 960
Answered by GAUTHMATH
Answer:
Step-by-step explanation:
If a and b are positive numbers, find the maximum value of f(x) = x^a(2 − x)^b on the interval 0 ≤ x ≤ 2.
Answer:
The maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0[/tex]
And we want to find the maximum value of f(x) on the interval [0, 2].
First, let's evaluate the endpoints of the interval:
[tex]\displaystyle f(0) = (0)^a(2-(0))^b = 0[/tex]
And:
[tex]\displaystyle f(2) = (2)^a(2-(2))^b = 0[/tex]
Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:
[tex]\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right][/tex]
By the Product Rule:
[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}[/tex]
Set the derivative equal to zero and solve for x:
[tex]\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right][/tex]
By the Zero Product Property:
[tex]\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0[/tex]
The solutions to the first equation are x = 0 and x = 2.
First, for the second equation, note that it is undefined when x = 0 and x = 2.
To solve for x, we can multiply both sides by the denominators.
[tex]\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))[/tex]
Simplify:
[tex]\displaystyle a(2-x) - b(x) = 0[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}[/tex]
So, our critical points are:
[tex]\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}[/tex]
We already know that f(0) = f(2) = 0.
For the third point, we can see that:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b[/tex]
This can be simplified to:
[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.
To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:
[tex]\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)[/tex]
The critical point will be at:
[tex]\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8[/tex]
Testing x = 0.5 and x = 1 yields that:
[tex]\displaystyle f'(0.5) >0\text{ and } f'(1) <0[/tex]
Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.
Therefore, the maximum value of f(x) occurs at:
[tex]\displaystyle x = \frac{2a}{a+b}[/tex]
And is given by:
[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]
please explain it step by step
What is the distance between (-5,-5) and (-9,-2)
Answer:
A (5)
Step-by-step explanation:
The distance is the slope/gradientIn the pythogaras theorem [tex]c^{2} = a^{2} + b^{2}[/tex],c represents the slope and a and b represent the two shorter sides of the right angled triangle ( x,y)
x = -9 - (-5 ) = -9 +5 = -4y = -2 - (-5) = -2 +5 = 3[tex]c^{2}[/tex] = [tex]-4^{2} + 3^{2}[/tex]
= 16 + 9
= 25,
therefore [tex]\sqrt{c^{2} }[/tex] = [tex]\sqrt{25}[/tex]
c = 5
could anyone help me solve this? I’ve had several questions like this and I don’t understand how to solve it. I’ll give brainliest:)
Answer:
-2, - 1, - 2 and - 3
Step-by-step explanation:
As the graph depicts an odd function, it will follow the rule f(-x) = - f(x)
Find 2
x
y у
30°
4√3
OA. 4/2
OB.22
0.8
D.4
Answer:
8
Step-by-step explanation:
The given is a special right triangle with angle measures
90-60-30 and side lengths represented by
2a-a[tex]\sqrt{3}[/tex]-a
x is the side length that sees angle measure 90 degrees so it's represented by 2a
and 4[tex]\sqrt{3}[/tex] is the side length that sees angle measure that sees 60 degrees so the value of a is 4
therefore x = 2*4 = 8
What is the measure of 7 shown in the diagram below?
110°
O A. 74.5°
B. 32°
X
O C. 71°
Z
D. 35.5°
Answer:
c
Step-by-step explanation:
Answer:
the correct choice is B
Step-by-step explanation:
It is estimated that t months from now, the population of a certain town will be changing at the rate of 4+ 5t^2/3 people per month. If the current population is 10,000, what will the population be 8 months from now?
Answer:
240000
Step-by-step explanation:
Represent the exponential equation.
[tex]10000 (5 {t}^{ \frac{2}{3} } + 4) = [/tex]
Replace 8 with t
[tex]10000(5(8) {}^{ \frac{2}{3} } + 4)[/tex]
[tex]10000(5 \times 4 + 4) [/tex]
[tex]10000(24) = 240000[/tex]
The population of the town after 8 month will be 2,40,000.
What is exponential growth?
Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Let P be the population of the town after 8 months
According to the given question
The current population of the town = 10,000.
Also, the population of the town is changing at the rate of [tex]4+5t^{\frac{2}{3} }[/tex].
Therefore, the population of the town after 8 month is given by the exponential function
[tex]P = 10000(4+5t^{\frac{2}{3} } )[/tex]
Substitute t =8 in the above equation
⇒[tex]P = 10000(4 + 5(8)^{\frac{2}{3} } )[/tex]
⇒[tex]P = 10000(4 + 5(2^{3}) ^{\frac{2}{3} } )[/tex]
⇒[tex]P = 10000(4+5(4))[/tex]
⇒[tex]P = 10000(24)[/tex]
⇒[tex]P = 240000[/tex]
Hence, the population of the town after 8 month will be 2,40,000.
Find out more information about exponential growth here:
https://brainly.com/question/11487261
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Three numbers are in the ratio of 1:2:4. If 3 is added to the first and 8 is subtracted from the third, the new numbers will be the first and third terms of an A.P., whose second term is the second number. Find the original numbers.
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Answer:
5, 10, 20
Step-by-step explanation:
Suppose the three numbers are x, 2x, and 4x. Then they have the required ratios. After the transformation, we have ...
((x+3) +(4x -8))/2 = 2x . . . . . 2nd term is average of 1st and 3rd
5x -5 = 4x ⇒ x = 5
The original numbers are 5, 10, 20.
_____
After the adjustment, the arithmetic sequence is 8, 10, 12.
I need to know the answer please
Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.
g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]
Option C
Hope this helps!
If two bags of popcorn and three drinks cost $14,
and four bags of popcorn and one drink costs
$18, how much does a drink cost?
Answer:
2dollars
Step-by-step explanation:
one bag of popcorn is 4 dollars so 4 bags of popcorn is 16 plus 1 drink which is 2 dollars equal 18.
The cost of each popcorn is $4 and the cost of each drink will be $2.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
If two bags of popcorn and three drinks cost $14, and four bags of popcorn and one drink costs $18.
Let the cost of each popcorn be 'x' and the cost of each drink be 'y'. Then the equations are given as,
2x + 3y = 14 ...1
4x + y = 18 ...2
From equations 1 and 2, then we have
2x + 3(18 - 4x) = 14
2x + 54 - 12x = 14
10x = 40
x = $4
Then the value of the variable 'y' is calculated as,
y = 18 - 4(4)
y = 18 - 16
y = $2
The cost of each popcorn is $4 and the cost of each drink will be $2.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
Gant Accounting performs two types of services, Audit and Tax. Gant’s overhead costs consist of computer support, $267000; and legal support, $133500. Information on the two services is:
(See screenshot)
Answer:
$240,300
Step-by-step explanation:
Given :
Overhead cost :
Computer support = $267000
legal support = $133500
Overheads applied to audit services = (Number of CPU minutes used by Audit services * activity rate per CPU minute)
+
(number of legal hours used by Audit services * activity rate per legal hour)
The overhead applied to audit is thus :
40,000 * (267,000 / (40,000 + 10,000)) +
200 * (133500 / (200 + 800)
(40000 * 5.34) + (200 * 133.5)
= $240,300
Write the quadratic equation whose roots are 2 and -4 and whose leading coefficient is 2
Answer:
2x^2+4x-16
Step-by-step explanation:
The quadratic can be written as
f(x) = a(x-z1)(x-z2) where z1 and z2 are the roots
f(x) = a (x-2)(x- -4)
a is the leading coefficient
f(x) = 2(x-2)(x+4)
= 2(x^2 -2x+4x-8)
= 2(x^2 +2x-8)
= 2x^2 +4x-16
Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms. At one point in the game, you have narrowed the possibilities down to 44 people, 55 weapons, and 77 rooms. What is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices, and the guess being correct
Answer:
The probability of making a correct random guess is 0.00053%.
Step-by-step explanation:
Since Clue is a board game in which you must deduce three details surrounding a murder, and in the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms, and at one point in the game, you have narrowed the possibilities down to 44 people, 55 weapons, and 77 rooms, to determine what is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices , and the guess being correct, the following calculation must be performed:
(1 / (44x55x77)) x 100 = X
(1 / 186,340) x 100 = X
0.0005366 = X
Therefore, the probability of making a correct random guess is 0.00053%.
A bird that was perched atop a 15-foot tree dives down six feet to a branch below. How
the bird's new location?
Answer:
I will b you and your 5AM 88feet
