Answer:
(x - 7)² + (y - 4)² = 49
Step-by-step explanation:
Given
Equation: x² + y² = 49
Required:
New Equation when translated 7 units right and 4 units up
Taking it one step at a time.
When the equation is translated 7 units right, this implies a negative unit along the x axis.
The equation becomes
(x - 7)² + y² = 49
When the equation is translated 4 units up, this implies a negative unit along the y axis.
(x - 7)² + (y - 4)² = 49
The expression can be further simplified but it's best left in the form of
(x - 7)² + (y - 4)² = 49
Solve this quadratic equation.
6x2 - 2x = 7
Answer:
x₁ = (1 + √43)/6
x₂ = (1 - √43)/6
Step-by-step explanation:
6x² - 2x = 7
6x² - 2x - 7 = 0
Formula
ax² + bx + c = 0
a = 6 ; b = - 2 ; c = - 7
x₁/₂ = [-b ± √(b²- 4ac)]/2a
x₁/₂ = (2 ± √4 + 4×6×-7)/12
x₁/₂ = (2 ± √172)/12
x₁/₂ = (2 ± 2√43)/12
x₁/₂ = 2(1 ± √43)/12
x₁/₂ = (1 ± √43)/6
x₁ = (1 + √43)/6
x₂ = (1 - √43)/6
you have 12 monkey but 5 were taken away how much do you have
Answer:
12-5=7
unless it's not a prank or a joke question
Answer:
7
Step-by-step explanation:
Original number of monkeys = 12
Number taken away = 5
So, number left = 12-5 = 7.
Hope this helps.
I promise I will mark as brainiest if a speed of a car increase its average speed in a journey of 200 miles by 5 mile/hour the journey will end with a difference of one hour less, so what is the original speed of the car ?
Answer:
[tex]\large \boxed{\sf \ \ \ \dfrac{\sqrt{4025}-5}{2}=29.22144... \ \ \ }[/tex]
Step-by-step explanation:
Hello
Let's note the original speed of the car v
it means that in 1 hour he is going v miles
so to go 200 miles it takes ( in hour)
[tex]\dfrac{200}{v}[/tex]
If the speed of the car is v+5 than to go 200 miles it takes (in hour)
[tex]\dfrac{200}{v+5}[/tex]
and this time is one hour less so we can write
[tex]\boxed{\sf \ \ \dfrac{200}{v+5}=\dfrac{200}{v}-1 \ \ }[/tex]
We can multiply by v(v+5) both parts of the equation so
[tex]200v=200(v+5)-v(v+5)\\\\<=>200v=200v+1000-v^2-5v\\\\<=>v^2+5v-1000=0[/tex]
[tex]\Delta=b^2-4ac=5^2+4*1000=4025\\\\ \text{There are potential solutions }\\\\\ \ \ \ \ x_1=\dfrac{-5-\sqrt{4025}}{2}\\\\\ \ \ \ \ x_2=\dfrac{-5+\sqrt{4025}}{2}[/tex]
Only one is positive and this is is
[tex]x_1=\dfrac{\sqrt{4025}-5}{2}=29.22144...[/tex]
So the original speed is 29.22144... mph
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
what is the lengthy of side s of the square below
Answer:
D. 4√2
Step-by-step explanation:
A triangle with 45°, 45°, and 90° is a special right triangle.
hypotenuse = √2 · leg
1. Set up the equation
8 = √2 · x
2. Divide by √2 and solve
x = [tex]\frac{8}{\sqrt{2} }[/tex] · [tex]\frac{\sqrt{2} }{\sqrt{2}}[/tex] = [tex]\frac{8\sqrt{2} }{2}[/tex] = 4√2
Find SP when CP=Rs.400 and profit%=4%
Answer:
Rs 416Step-by-step explanation:
Given,
Cost Price ( CP ) = Rs 400
Profit % = 4 %
Selling price ( SP ) = ?
now, Let's find the value of SP:
SP = [tex] \frac{CP \: (100 + \: profit percent \: )}{100} [/tex]
Plug the values
[tex] = \frac{400(100 + 4)}{100} [/tex]
Add the numbers
[tex] = \frac{400 \times 104}{100} [/tex]
Multiply the numbers
[tex] = \frac{41600}{100} [/tex]
Divide
= Rs [tex]416[/tex]
Selling price ( SP ) = Rs 416
Hope this helps...
Best regards!!
Which expressions are equivalent to -6n+(-12)+4n−6n+(−12)+4nminus, 6, n, plus, left parenthesis, minus, 12, right parenthesis, plus, 4, n ? Choose all answers that apply: Choose all answers that apply: (Choice A) A 4(n-3) -6n4(n−3)−6n4, left parenthesis, n, minus, 3, right parenthesis, minus, 6, n (Choice B) B 2(2n-6)2(2n−6)2, left parenthesis, 2, n, minus, 6, right parenthesis (Choice C) C None of the above
Answer:
The correct option is;
Choice A 4·(n - 3) - 6·n
Step-by-step explanation:
The given expression is
Which gives;-6·n+(-12)+4·n
- 12 + 4·n-6·n = -2·n - 12 = - (2·n + 12)
The options given are Choice A and/or Choice B;
(Choice A) 4·(n - 3) - 6·n
Which can be simplified as follows;
4·(n - 3) - 6·n = 4·n - 12 - 6·n
Which gives;
4·n - 12 - 6·n = 4·n - 6·n- 12 = -2·n - 12 = -(2·n + 12)
Therefore, 4·(n - 3) - 6·n is equivalent to -6·n+(-12)+4·n
For choice B, we have;
2·(2·n - 6) which gives;
2·(2·n - 6) = 4·n - 12
Therefore, 2·(2·n - 6) is not equivalent to -6·n+(-12)+4·n
Which gives the correct option as Choice A.
4(n-3)-6n
Khan academy I got this right
what is the product of (-a+3)(a+4)?
[tex](-a+3)(a+4)=-a^2-a+12[/tex].
Hope this helps.
Answer:
-a²-a+12
Step-by-step explanation:
-a²+3a-4a+12
-a²-a+12
Suppose a geyser has a mean time between eruptions of 72 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 23 minutes. Complete parts (a) through (e) below.
(a) What is the probability that a randomly selected time interval between eruptions is longer than 82minutes? The probability that a randomly selected time interval is longer than 82 minutes is approximately nothing. (Round to four decimal places as needed.)
(b) What is the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes? The probability that the mean of a random sample of 13 time intervals is more than 82 minutes is approximately nothing. (Round to four decimal places as needed.)
(c) What is the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes? The probability that the mean of a random sample of 34 time intervals is more than 82 minutes is approximately nothing. (Round to four decimal places as needed.)
(d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. Fill in the blanks below. If the population mean is less than 82 minutes, then the probability that the sample mean of the time between eruptions is greater than 82 minutes ▼ increases decreases because the variability in the sample mean ▼ decreases increases as the sample size ▼ decreases. increases.
(e) What might you conclude if a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes? Select all that apply.
A. The population mean may be less than 72.
B. The population mean must be more than 72, since the probability is so low.
C. The population mean cannot be 72, since the probability is so low.
D. The population mean is 72, and this is just a rare sampling.
E. The population mean may be greater than 72.
F. The population mean is 72, and this is an example of a typical sampling result.
G. The population mean must be less than 72, since the probability is so low.
Answer:
(a) The probability that a randomly selected time interval between eruptions is longer than 82 minutes is 0.3336.
(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 minutes is 0.0582.
(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is 0.0055.
(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.
(e) The population mean must be more than 72, since the probability is so low.
Step-by-step explanation:
We are given that a geyser has a mean time between eruptions of 72 minutes.
Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.
(a) Let X = the interval of time between the eruptions
So, X ~ N([tex]\mu=72, \sigma^{2} =23^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 72 minutes
[tex]\sigma[/tex] = standard deviation = 23 minutes
Now, the probability that a randomly selected time interval between eruptions is longer than 82 minutes is given by = P(X > 82 min)
P(X > 82 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{82-72}{23}[/tex] ) = P(Z > 0.43) = 1 - P(Z [tex]\leq[/tex] 0.43)
= 1 - 0.6664 = 0.3336
The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.
(b) Let [tex]\bar X[/tex] = sample mean time between the eruptions
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 72 minutes
[tex]\sigma[/tex] = standard deviation = 23 minutes
n = sample of time intervals = 13
Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes is given by = P([tex]\bar X[/tex] > 82 min)
P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{13} } }[/tex] ) = P(Z > 1.57) = 1 - P(Z [tex]\leq[/tex] 1.57)
= 1 - 0.9418 = 0.0582
The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.
(c) Let [tex]\bar X[/tex] = sample mean time between the eruptions
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 72 minutes
[tex]\sigma[/tex] = standard deviation = 23 minutes
n = sample of time intervals = 34
Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is given by = P([tex]\bar X[/tex] > 82 min)
P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{34} } }[/tex] ) = P(Z > 2.54) = 1 - P(Z [tex]\leq[/tex] 2.54)
= 1 - 0.9945 = 0.0055
The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.
(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.
(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 minutes, then we conclude that the population mean must be more than 72, since the probability is so low.
Answer:
The probability that a randomly selected time interval between eruptions is longer than 82minutes = [tex]0.3336[/tex]The probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes = [tex]0.0594[/tex]The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes = [tex]0.0057[/tex]Step-by-step explanation:
From the given data
mean, u = 72
Standard deviation [tex]\rho[/tex] = 23
A) Probability that a randomly selected time interval between eruptions is longer than 82minutes
[tex]P (x > 82) = P[\frac{x-u}{\rho} > \frac{82-72}{23}]\\\\P (x > 82) = P[z > 0.43]\\\\P (x > 82) = 0.3336[/tex]
B)
[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{13}}}]\\\\P (x > 82) = P[z > 1.5676]\\\\P (x > 82) = 0.0594[/tex]
C)
[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{34}}}]\\\\P (x > 82) = P[z > 2.5351]\\\\P (x > 82) = 0.0057\\\\[/tex]
D) If the mean is less than 82minutes, then the probability that the sample mean of the time between eruptions is greater than 83 minutes decrease because the variability in the sample mean decrease as the sample size increases
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If x and y are positive integers and x+y+xy=54, then x+y equals what
Answer:
x+y = 14
Step-by-step explanation:
x+y+xy = 54
1+x+y+xy = 55
(1+x)(1+y) = 55
(1+x)(1+y) = 5*11
If x and y are integers,
1+x = 5 => x = 4
1+y = 11 => y = 10
or
1+x = 11 => x = 10
1+y = 5 => y = 4
In either case, x+y = 14
The solution to this system is [tex]x = 4[/tex] and [tex]y = 10[/tex]. Then, [tex]x+y = 14[/tex].
Let be [tex]x + y + x\cdot y = 54[/tex], then we proceed to modify the expression by algebraic means:
[tex]x + y + x\cdot y = 54[/tex] Given[tex]x+y+x\cdot y + 1 = 55[/tex] Compatibility with addition/Definition of addition[tex](x+1)+(y+x\cdot y) = 55[/tex] Commutative property/Associative property [tex](x+1) + y\cdot (x + 1) = 55[/tex] Distributive property/Commutative property[tex](x+1)\cdot (y +1) = 55[/tex] Distributive propertyThe only divisors of 55 is 5 and 11, respectively. Hence, we have the following system of linear equations:
[tex]x + 1 = 5[/tex] (1)
[tex]y + 1 = 11[/tex] (2)
The solution to this system is [tex]x = 4[/tex] and [tex]y = 10[/tex]. Then, [tex]x+y = 14[/tex].
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Simplify this expression.
275(13 +2)
O 2765 + 2/10
O 25+277
O 2665 + 2/10
O 2675 +2V10
Hurrryyy
Answer:
2675 +2V10
Step-by-step explanation:
Answer:
D :)
Step-by-step explanation:
did on edge 2021
How many 5 digit numbers have five distinct digits?
Answer:3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
(Mathematics) Please Help (SOS) House Insurance 50 per 4100 Contents Insurance 25 per $100 The above shows the rates charged by an insurance company. How much will a person pay for his insurance, if his house is valued at $50,000, and the content at $10,000? a) $225 b)$275 c)$450 d)$500
Answer: B.) $275
Step-by-step explanation:
Insurance cost :
Housing insurance - - - 50c per $100
Content insurance - - - 25c per $100
House valuation = $50,000
50c = $0.5
Therefore insurance cost on House:
Valuation × insurance cost
($50,000 / $100) * $0.5
$500 × $0.5 = $250
25c = $0.25
Insurance cost on content :
($10,000 / $100) × $0.25
$100 × $0.25 = $25
Total insurance cost :
$250 + $25 = $275
If x is an even number, the function fX) = 2x - 1 gives an odd number. Identify the set of odd numbers corresponding to this set of even
numbers: {0, 2, 4, 6, 8)
Answer:
{-1, 3, 7, 11, 15}
Step-by-step explanation:
we just substitute the set of even numbers in the function f(x) given to get our corresponding set of odds numbers
for 0
2(0)-1=0-1=-1
for 2
2(2)-1=4-1=3
for 4
2(4)-1=8-1=7
for 6
2(6)-1=12-1=11
for 8
2(8)-1=16-1=15
Answer this question
Answer:
9120(b)
Step-by-step explanation:
95×96
(90+5)×(90+6)
(90×90)+(5+6) (90)+(5)(6)
(90) square+(5+6) (90)+(5)(6)
I am using identity 4
=8100+990+30=9120
Winter temperatures tend to be cold in the city of Johnstown. The table of values represents the temperature of Johnstown during one winter week.
t | f(x)
(days)| (°F)
____|_____________
1 | 6
2 | 5
3 | 1
4 | -2
5 | -1
6 | 0
7 | -3
Part A
Use the table to approximate the key features of the function. Find the extrema, zeros, end behavior, increasing and decreasing intervals, and positive and negative intervals.
Part B
Interpret the key features from part A in the context of the problem.
Part C
Interpret the domain and the range of the function in the context of the problem.
Answer:
Part A Part B Part C explained
Step-by-step explanation:
PART A: Extrema: relative minimums (4,-2) and maybe (7,-3) (uncertain because it’s an endpoint), relative maximums (6,0) and maybe (1,6) (uncertain because it’s an endpoint)
Zeros: (6,0), somewhere between t = 3 and t = 4 since the graph changes from positive to negative, and somewhere possibly between t = 6 and t = 7 unless the graph hits (6,0) and stays negative.
End behavior: We can guess that as x approaches infinity, the functions approaches negative infinity, and as x approaches negative infinity, the function approaches infinity.
Intervals of increase and decrease: Increasing on (4, 6), decreasing on (1, 4) and (6, 7)
PART B: The relative minimums indicate that the two lowest temperatures occurred on day 4 at -2°F and day 7 at -3°F. The relative maximums indicate that the weekly highs were day 1 at 6°F and day 6 at 0°F.
The zeros of the function represent when the temperature in Johnstown was 0°F. This happened sometime between days 3 and 4 and on day 6.
In the context of the problem, it doesn’t make sense to go an infinite number of degrees below zero. And, the end behavior is ignored because of the restricted range.
The intervals of increase indicate when the temperature is rising, and the intervals of decrease indicate when the temperature is dropping. The intervals where the values are positive indicate when the temperature is above 0°F. The intervals where the values are negative indicate when the temperature is below 0°F.
PART C: The domain is restricted to the number of days the town recorded the temperature. So, the domain is [1, 7].
The range represents the range of temperatures of Johnstown over the course of one week. So, the range is [-3, 6].
Answer:
Part A was missing the last so this is the correct answer.
Extrema: relative minimums (4,-2) and maybe (7,-3) (uncertain because it’s an endpoint), relative maximums (6,0) and maybe (1,6) (uncertain because it’s an endpoint)
Zeros: (6,0), somewhere between t = 3 and t = 4 since the graph changes from positive to negative, and somewhere possibly between t = 6 and t = 7 unless the graph hits (6,0) and stays negative.
End behavior: We can guess that as x approaches infinity, the functions approach negative infinity, and as x approaches negative infinity, the function approaches infinity.
Intervals of increase and decrease: Increasing on (4, 6), decreasing on (1, 4) and (6, 7)
Positive and negative intervals: Positive from 1 to somewhere between t = 3 and t = 4, and negative from somewhere between t = 3 and t = 4 to t = 6, and from some point after t = 6 to t = 7.
But other than that everything else was correct and thank you.
Step-by-step explanation:
Please help this is a new topic for me.
Answer:
last answer
Step-by-step explanation:
P' (2, -4)
Q' (-2, -5)
R' (1, -8)
Answer:
C. P'(2, -4) Q'(-2, -5) R'(1, -8)
Step-by-step explanation:
When you reflect something across the y-axis you change (x,y) to (-x,y).
For each point, change the x to a negative x.
P(-2, -4) --> P'(2, -4)
Q(2, -5) --> Q'(-2, -5)
R(-1, -8) --> R'(1, -8)
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
What is the value of x? Enter your answer, as an exact value, in the box.
Answer:
x = 4.2
Step-by-step explanation:
To calculate for the value of x, we must first calculate the value of y as shown in the attached photo.
The value of y can be obtained as follow:
Angle θ = 30°
Opposite = y
Hypothenus = 6
Sine θ = Opposite /Hypothenus
Sine 30° = y/6
Cross multiply
y = 6 × Sine 30°
y = 3
Therefore, the value of y is 3.
Now, we can obtain the value of x as follow:
Angle θ = 45°
Adjacent = y = 3
Hypothenus = x
Cos θ = Adjacent /Hypothenus
Cos 45° = 3/x
Cross multiply
x × Cos 45° = 3
Divide both side by Cos 45°
x = 3/Cos 45°
x = 4.2
Therefore, the value of x is 4.2
what is the length of arc S? angle in radians
Answer:
Length of the arc = π/50 cm
Step-by-step explanation:
Hello,
The diagram above is a circle and the to find the length of the arc, we need to know the formula for that.
Length of an arc = θ/360 ×2πr
θ = 3π/5
radius (r) = 6cm
Substitute the values into the equation
[(3π/5) / 360] × 2πr
Length of an arc = 3π/5 × ¹/₃₆₀ × 2π(6)
Length of an arc = (3π x 12π) / (5×360)
Length of an arc = 36π/1800
Length of an arc = π/50cm
The length of the arc is π/50cm
find the exact value of tan165°.
Answer:
the answer would be
[tex] - 2 + \sqrt{3} [/tex]
but if you want it in decimal form it would be -0.26794919
Answer:
tan 165 = -0.2679491924
Step-by-step explanation:
Carrington used 3/4 of the 1/2 of an hour allotted for an exam to do the first 3 problems. How much time does he have left for tKiley had a piece of bamboo skewer that measured 14 3/5 inches long. She wanted to cut it into toothpicks that were each 3 1/5 inches long. How many toothpicks can she make?He remaining part of the exam?
Answer:
a. 7.5 minutes
b. 4 and one-half toothpicks
Step-by-step explanation:
a. an hour = 60 minutes
Allotted time for the exam = 1/2 hour = 1/2 * 60 = 30 minutes
He used 3/4 of this time, so the time left in fraction would be 1-3/4 = 1/4
So the time left in minutes is 1/4 * 30 = 7.5 minutes
b. The total length he has here is 14 3/5 inches
Now he wants to cut toothpicks of 3 1/5
To know the number of toothpicks he can cut, we simply divide the total length by the length of each toothpick
14 3/5 divided by 3 1/5
= 73/5 divided by 16/5
= 73/5 * 5/16 = 73/16 = 4.5625
which is closer to 4 and one-half toothpicks
Using appropriate properties of rational numbers, find the sum 34+421+78+57
easy.This answer is 590
what is 2.267676767 as a fraction
Answer:
2267676767/1000000000
Step-by-step explanation:
To write 2.267676767 as a fraction you have to write 2.267676767 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
2.267676767 = 2.267676767/1 = 22.67676767/10 = 226.7676767/100 = 2267.676767/1000 = 22676.76767/10000 = 226767.6767/100000 = 2267676.767/1000000 = 22676767.67/10000000 = 226767676.7/100000000 = 2267676767/1000000000
And finally we have:
2.267676767 as a fraction equals 2267676767/1000000000
Hope it helps.. If yes mark me BRAINLIEST!!
TYSM!
Answer:
2267676767/1000000000
Step-by-step explanation:
when converting a decimal to fraction,
write down the decimal divided by 1 and than add as many zeros as the digits after the decimal point.
since we have nine digits after the decimal point nine zeros are put after the '1'
For 100 births, P(exactly girls) and P( or more girls). Is girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question? Consider a number of girls to be significantly high if the appropriate probability is 0.05 or less.
Answer;
The relevant probability is 0.136 so the value of 56 girls in 100 births is not a significantly high number of girls because the relevant probability is greater than 0.05
Step-by-step explanation:
The complete question is as follows;
For 100 births, P(exactly 56 girls = 0.0390 and P 56 or more girls = 0.136. Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question? Consider a number of girls to be significantly high if the appropriate probability is 0.05 or less V so 56 girls in 100 birthsa significantly high number of girls because the relevant probability is The relevant probability is 0.05
Solution is as follows;
Here. we want to know which of the probabilities is relevant to answering the question and also if 56 out of a total of 100 is sufficient enough to provide answer to the question.
Now, to answer this question, it would be best to reach a conclusion or let’s say draw a conclusion from the given information.
The relevant probability is 0.136 so the value of 56 girls in 100 births is not a significantly high number of girls because the relevant probability is greater than 0.05
Consider the construction of a pen to enclose an area. You have 500 ft of fencing to make a pen for hogs. If you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area
Answer:
The dimensions of the rectangular pen that maximize the area are [tex]w = 125\,ft[/tex] and [tex]l = 250\,ft[/tex].
Step-by-step explanation:
Let suppose that one side of the rectangular area to be fence coincides with the contour of the river, so that only three sides are needed to be enclosed. The equations of perimeter ([tex]p[/tex]) and area ([tex]A[/tex]), measured in feet and square feet, are introduced below:
[tex]p = 2\cdot w + l[/tex]
[tex]A = w\cdot l[/tex]
Where [tex]w[/tex] and [tex]l[/tex] are the length and width of the rectangle, measured in feet.
Besides, let suppose that perimeter is equal to the given amount of fencing, that is, [tex]p = 500\,ft[/tex]. The system of equations is:
[tex]2\cdot w + l = 500\,ft[/tex]
[tex]A = w\cdot l[/tex]
Let is clear the length of the rectangle and expand the area formula:
[tex]l = 500\,ft-2\cdot w[/tex]
[tex]A = w\cdot (500\,ft-2\cdot w)[/tex]
[tex]A = 500\cdot w -2\cdot w^{2}[/tex]
To determine the maximum area that can be enclosed, first and second derivatives to obtain the critical values that follow to an absolute maximum.
First derivative
[tex]A' = 500 - 4\cdot w[/tex]
Second derivative
[tex]A'' = -4[/tex]
Now, let equalize the first derivative to zero, the only critical value is:
[tex]500-4\cdot w = 0[/tex]
[tex]4\cdot w = 500[/tex]
[tex]w = 125\,ft[/tex]
Since the second derivative is a negative constant function, then, the previous outcome follows to an absolute maximum. The length of the rectangular area is: ([tex]w = 125\,ft[/tex])
[tex]l = 500\,ft - 2\cdot (125\,ft)[/tex]
[tex]l = 250\,ft[/tex]
The dimensions of the rectangular pen that maximize the area are [tex]w = 125\,ft[/tex] and [tex]l = 250\,ft[/tex].
HELP ME PLS ILL BE SO GRATEFUL AND GIVE BRAINLIEST
1. A wine store conducted a study. It showed that a customer does not tend to buy more or fewer bottles when more samples are offered. What can we conclude?
>There is no correlation between number of bottles bought and number of samples offered.
>There is a correlation between number of bottles bought and number of samples offered. However, there is no causation. This is because there is probably an increase in the number of bottles bought with an increase in the number of samples offered.
>There is a correlation between number of bottles bought and number of samples offered. There may or may not be causation. Further studies would have to be done to determine this.
2. Felipe compared the player statistics from his team's soccer season. He determined that having less playing time implies that a player scores fewer goals. What should he say based on his findings?
>There is no correlation between playing time and number of goals.
>There is a correlation between playing time and number of goals. There may or may not be causation. Further studies would have to be done to determine this.
>There is a correlation between playing time and number of goals. However, there is no causation. This is because there is a decrease in the number of goals with a decrease in playing time.
Answer:
>There is a correlation between number of bottles bought and number of samples offered. However, there is no causation. This is because there is probably an increase in the number of bottles bought with an increase in the number of samples offered.
>There is no correlation between playing time and number of goals.
Hope this helps....
Have a nice day!!!!
K here’s another one please help
Answer:
Both the relations are functions, the correct answer is a.
Step-by-step explanation:
In order to solve this problem we will first find the inverse relation as shown below:
[tex]y = 3x^2 + 5\\x = 3y^2 + 5\\3y^2 = x - 5\\y^2 = \frac{x - 5}{3}\\y = \sqrt{\frac{x - 5}{3}} = \frac{\sqrt{x - 5}}{\sqrt{3}}\\y = \frac{\sqrt{x - 5}\sqrt{3}}{\sqrt{3}\sqrt{3}} = \frac{\sqrt{3x - 15}}{3}[/tex]
Functions are relations between two groups of numbers, for which the input must generate only one output. Using this definition we can classify both the relation and its inverse as a function, therefore the correct answer is a.
Write coordinates of a point whose abscissa is -2 and ordinate is -3.
Answer:
(-2,-3)
Step-by-step explanation:
abscissa is always know as the x axis
ordinate is known as y axis
therefore
it lies in the fourth quadrant
Which function is increasing?
A. f(x)=(1/6)
B.f(x) = (0.6).
C. f(x)=(1/60)
D. f(x)=6
Answer:
Option D. f(x) = 6^x
Step-by-step explanation:
To know which of the function is increasing, let us obtain f(1) and f(2) for each function.
This is illustrated below:
f(x) = (1/6)^x
f(1) = (1/6)¹ = 1/6
f(2) = (1/6)² = 1/36
Therefore, f(x) = (1/6)^x is decreasing.
f(x) = (0.6)^x
f(1) = (0.6)¹ = 0.6
f(2) = (0.6)² = 0.36
Therefore, f(x) = (0.6)^x is decreasing.
f(x) = (1/60)^x
f(1) = (1/60)¹ = 1/60
f(2) = (1/60)² = 1/3600
Therefore, f(x) = (1/60)^x is decreasing.
f(x) = 6^x
f(1) = 6¹ = 6
f(2) = 6² = 36
Therefore, f(x) = 6^x is increasing.
Answer:
Option D
Step-by-step explanation:
The reason why it is D is because if it was something below 1, such as 0.6, it would be decreasing. That is why 6 is the answer.
What is the value of n in the equation 3n + 2(n + 2) = 9n + 12? −4 −2 2 4
Answer:
-2
Step-by-step explanation:
3n+2n+4=9n+12
5n+4=9n+12
5n-9n=-4+12
-4n=8
n=8/-4
n= -2
Answer:
-2
Step-by-step explanation:
I got this right in my assignment.
Find the Equation of the Parallel Line
2
of
Instructions: Find the equation of the line through point (-7,2) and parallel to
= x - 1. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 1).
Y=
y =
Answer:
y = 2/5x + 4/5
Step-by-step explanation:
We'll begin by calculating the slope of the equation: y = 2/5x – 1/2
The slope of the above equation can be obtained as follow:
y = mx + c
Where m is the slope.
c is the y-intercept.
y and x are the coordinate.
Comparing:
y = 2/5x – 1/2 with y = mx + c
The slope of y = 2/5x – 1/2 is 2/5.
Now, let us determine the equation parallel to y = 2/5x – 1/2.
This is illustrated below:
The coordinate of the line => (–7, 2)
x1 = –7
y1 = 2
Slope (m) = 2/5 => Since the lines are parallel, their slope are equal.
y – y1 = m (x – x1)
y – 2 = 2/5(x – –7)
y – 2 = 2/5(x + 7)
Clear bracket
y – 2 = 2/5x + 14/5
Rearrange
y = 2/5x + 14/5 + 2
y = 2/5x + 4/5
Therefore, the equation is:
y = 2/5x + 4/5