Answer:
D
Step-by-step explanation:
The Triangle Inequality states that the sum of the two largest side lengths of a triangle must be greater than the length of the largest side. Let's check these answers.
A: Since 18 + 26 > 46 is a false statement, A is not the answer.
B: Since 18 + 26 > 49 is false, B is not the answer.
C: Since 18 + 6 > 26 is false, C is not the answer.
D: Since 18 + 26 > 32 is false, D is the answer.
Answer:
since ab=18 and bc= 26 and if u draw out the shape and write them down u would mostly get d but I not too sure is d that the best I can do
Step-by-step explanation:
An instructor asks students to rate their anxiety level on a scale of 1 to 100 (1 being low anxiety and 100 being high anxiety) just before the students take their final exam. The responses are shown below. Construct a relative frequency table for the instructor using five classes. Use the minimum value from the data set as the lower class limit for the first row, and use the lowest possible whole-number class width that will allow the table to account for all of the responses. Use integers or decimals for all answers.
48,50,71,58,56,55,53,70,63,74,64,33,34,39,49,60,65,84,54,58
Provide your answer below:
Lower Class Limit Upper Class Limit Relative Frequency
Answer:
The frequency table is shown below.
Step-by-step explanation:
The data set arranged ascending order is:
S = {33 , 34 , 39 , 48 , 49 , 50 , 53 , 54 , 55 , 56 , 58 , 58, 60 , 63 , 64 , 65 , 70 , 71 , 74 , 84}
It is asked to use the minimum value from the data set as the lower class limit for the first row.
So, the lower class limit for the first class interval is 33.
To determine the class width compute the range as follows:
[tex]\text{Range}=\text{Maximum}-\text{Minimum}[/tex]
[tex]=84-33\\=51[/tex]
The number of classes requires is 5.
The class width is:
[tex]\text{Class width}=\frac{Range}{5}=\frac{51}{2}=10.2\approx 10[/tex]
So, the class width is 10.
The classes are:
33 - 42
43 - 52
53 - 62
63 - 72
73 - 82
83 - 92
Compute the frequencies of each class as follows:
Class Interval Values Frequency
33 - 42 33 , 34 , 39 3
43 - 52 48 , 49 , 50 3
53 - 62 53 , 54 , 55 , 56 , 58 , 58, 60 7
63 - 72 63 , 64 , 65 , 70 , 71 5
73 - 82 74 1
83 - 92 84 1
TOTAL 20
Compute the relative frequencies as follows:
Class Interval Frequency Relative Frequency
33 - 42 3 [tex]\frac{3}{20}\times 100\%=15\%[/tex]
43 - 52 3 [tex]\frac{3}{20}\times 100\%=15\%[/tex]
53 - 62 7 [tex]\frac{7}{20}\times 100\%=35\%[/tex]
63 - 72 5 [tex]\frac{5}{20}\times 100\%=25\%[/tex]
73 - 82 1 [tex]\frac{1}{20}\times 100\%=5\%[/tex]
83 - 92 1 [tex]\frac{1}{20}\times 100\%=5\%[/tex]
TOTAL 20 100%
The Marine Corps is ordering hats for all the new recruits for the entire next year. Since they do not know the exact hat sizes they will use statistics to calculate the necessary numbers. This is the data from a sample of the previous recruits: 7.2, 6.8, 6, 6.9, 7.8, 6.2, 6.4, 7.2, 7.4, 6.8, 6.7, 6, 6.4, 7, 7, 7.6, 7.6, 6, 6.8, 6.4 a. Display the data in a line plot and stem-and-leaf plot. (These plots don’t need to be pretty; just make sure I can make sense of your plots.) Describe what the plots tell you about the data. b. Find the mean, median, mode, and range. c. Is it appropriate to use a normal distribution to model this data? d. Suppose that the Marine Corps does know that the heights of new recruits are approximately normally distributed with a mean of 70.5 inches and a standard deviation of 1.5 inches. Use the mean and standard deviation to fit the new recruit heights to a normal distribution and estimate the following percentages. d1. What percent of new recruits would be taller than 72 inches? d2. What percent of new recruits would be shorter than 67.5 inches? d3. What percent of new recruits would be between 69 and 72 inches? d4. Between what two heights would capture 95% of new recruits?? By using statistics are the numbers changed to whole numbers?
Answer:
60-|||
61-
62-||
62
64-|||
65
66
67-|
68-|||
69-|
70-||
71
72-||
73
74-||
75
76-||
77
78-|
This is a stem and leaf plot.
mean is 138.2/20=6.91
median of 20 is half way between 10th and 11th or an ordered plot. The 10th and the 11th are both 6.8, so that is the median.
6.4 and 6.8 are modes, but they are so minimal I would say there isn't a clear mode.
The range is 1.8, the largest-the smallest
This is not a normal distribution.
z=(x-mean) sd
a.(72-70.5)/1.5=1 so z>1 is the probability or 0.1587.
b.shorter than 67.5 inches is (67.5-70.5)/1.5 or z < = -2, and probability is 0.0228.
c.Between 69 and 72 inches is +/- 1 sd or 0.6826.
95% is 1.96 sd s on either side or +/- 1.96*1.5=+/- 2.94 interval on either side of 70.5
(67.56, 73.44)units in inches
Step-by-step explanation:
if a varies inversely as the cube root of b and a=1 when b=64, find b
Answer:
b = 64/a³
Step-by-step explanation:
Using the given information, we can only find a relation between a and b. We cannot find any specific value for b.
Since a varies inversely as the cube root of b, we have ...
a = k/∛b
Multiplying by ∛b lets us find the value of k:
k = a·∛b = 1·∛64 = 4
Taking the cube of this equation gives ...
64 = a³b
b = 64/a³ . . . . . divide by a³
The value of b is ...
b = 64/a³
Find the length of UC
Answer: 25 units
Step-by-step explanation:
Simply do 40(UN)-15(CN) to get 25(UC)
Hope it helps <3
Answer:
25Option D is the correct option
Solution,
Here,
UN = 40
CN = 15
Now,
UN = UC + CN
plugging the values,
40 = UC + 15
-UC = 15 - 40
-UC = -25
The difference sign (-) will be cancelled in both sides:
UC = 25
hope this helps...
Good luck on your assignment..
The dimensions of a closed rectangular box are measured as 96 cm, 58 cm, and 48 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.
Answer:
161.6 cm²Step-by-step explanation:
Surface Area of the rectangular box = 2(LW+LH+WH)
L is the length of the box
W is the width of the box
H is the height of the box
let dL, dW and dH be the possible error in the dimensions L, W and H respectively.
Since there is a possible error of 0.2cm in each dimension, then dL = dW = dH = 0.2cm
The surface Area of the rectangular box using the differentials is expressed as shown;
S = 2{(LdW+WdL)+(LdH+HdL)+(WdH+HdW)]
Also given L = 96cm W = 58cm and H = 48cm, on substituting this given values and the differential error, we will have;
S = 2{(96*0.2+58*0.2) + (96*0.2+48*0.2)+(58*0.2+48*0.2)}
S = 2{19.2+11.6+19.2+9.6+11.6+9.6}
S = 2(80.8)
S = 161.6 cm²
Hence, the surface area of the box is 161.6 cm²
In a survey, 205 people indicated they prefer cats, 160 indicated they prefer dots, and 40 indicated they don’t enjoy either pet. Find the probability that if a person is chosen at random, they prefer cats
Answer: probability = 0.506
Step-by-step explanation:
The data we have is:
Total people: 205 + 160 + 40 = 405
prefer cats: 205
prefer dogs: 160
neither: 40
The probability that a person chosen at random prefers cats is equal to the number of people that prefer cats divided the total number of people:
p = 205/405 = 0.506
in percent form, this is 50.6%
1. Growth of Functions (11 points) (1) (4 points) Determine whether each of these functions is O(x 2 ). Proof is not required but it may be good to try to justify it (a) 100x + 1000 (b) 100x 2 + 1000
Answer:
See explanation
Step-by-step explanation:
To determine whether each of these functions is [tex]O(x^2)[/tex], we apply these theorems:
A polynomial is always O(the term containing the highest power of n)Any O(x) function is always [tex]O(x^2)[/tex].(a)Given the function: f(x)=100x+1000
The highest power of n is 1.
Therefore f(x) is O(x).
Since any O(x) function is always [tex]O(x^2)[/tex], 100x+1000 is [tex]O(x^2)[/tex].
[tex](b) f(x)=100x^ 2 + 1000[/tex]
The highest power of n is 2.
Therefore the function is [tex]O(x^2)[/tex].
Answer:
i think its 2000
Step-by-step explanation:
Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year. Which of the following choices is the correct function? a p(s) = 114000• 0.985x b p(s) = 114000x c p(s) = 114000x + 0.985 d None of these choices are correct.
Answer: D
Step-by-step explanation:
According to the question, Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year
The initial population Po = 114000
Rate = 1.5% = 0.015
The declining population formula will be:
P = Po( 1 - R%)x^2
The decay formula
Since the population is decreasing, take away 0.015 from 1
1 - 0.015 = 0.985
Substitutes all the parameters into the formula
P(s) = 114000(0.985)x^2
P(s) = 114000× 0985x^2
The correct answer is written above.
Since option A does not have square of x, we can therefore conclude that the answer is D - non of the choices is correct.
Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing? f(x) = x2 + 36x + 12 f(x) = x2 – 36x – 12 f(x) = –x2 + 12x + 36 f(x) = –x2 – 12x – 36
Answer:
f(x) = –x^2 – 12x – 36
Step-by-step explanation:
The parent function, x^2, touches the x-axis at x=0. Translating it 6 units left replaces x with x-(-6) = x+6, so the function is ...
f(x) = (x+6)^2 = x^2 +12x +36
Reflecting the graph across the x-axis doesn't change the x-intercept, so Heather could be writing ...
f(x) = -x^2 -12x -36
It's D.
I have to have at least 20 characters.
The problem is: On a Map, 3 inches represents 40 miles, How many inches represents 480 miles?
the ellipse is centered at the origin, has axes of lengths 8 and 4, its major axis is horizontal. how do you write an equation for this ellipse?
Answer:
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
Step-by-step explanation:
The standard equation of the ellipse is described by the following expression:
[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1[/tex]
Where [tex]a[/tex] and [tex]b[/tex] are the horizontal and vertical semi-axes, respectively. Given that major semi-axis is horizontal, [tex]a > b[/tex]. Then, the equation for this ellipse is written in this way: (a = 8, b = 4)
[tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex]
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
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━━━━━━━☆☆━━━━━━━
▹ Answer
0.25 = 1/4 because 25/100 = 1/4
▹ Step-by-Step Explanation
0.25 to a fraction → 25/100
25/100 = 1/4
Therefore, this statement is true. (0.25 = 1/4 because 25/100 = 1/4)
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Simplify the expression (5j+5) – (5j+5)
Answer:
0
Step-by-step explanation:
multiply the negative thru the right part of the equation so, 5j+5-5j-5. The 5j and the 5 than cancel out with each other. Hope this helps!
Answer:
0
Explanation:
step 1 - remove the parenthesis from the expression
(5j + 5) - (5j + 5)
5j + 5 - 5j - 5
step 2 - combine like terms
5j + 5 - 5j - 5
5j - 5j + 5 - 5
0 + 0
0
therefore, the simplified form of the given expression is 0.
Given a right triangle with a hypotenuse length of radical 26 and base length of 3. Find the length of the other leg (which is also the height).
Answer:
√17
Step-by-step explanation:
The Pythagorean theorem can be used for the purpose.
hypotenuse² = base² +height²
(√26)² = 3² +height²
26 -9 = height²
height = √17
The length of the other leg is √17.
A right triangle is shown. The length of the hypotenuse is 4 centimeters and the lengths of the other 2 sides are congruent. The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle? 2 cm 2 StartRoot 2 EndRoot cm 4 cm 4 StartRoot 2 EndRoot cm
Answer:
The leg measures 2 I believe
Step-by-step explanation:
Since the squares of the legs equal C ([tex]A^{2} +B^{2} = C^{2}[/tex]) the square root of 16 would be 4.
The Pythagorean theorem is a basic relationship between the three sides of a right triangle. The length of one leg of the triangle is 2√2 cm.
What is the Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]
Let the length of the perpendicular be x.
Given the length of the hypotenuse is 4 centimeters, while the length of the other two sides is the same, therefore, the length of the other two sides is x. Therefore, using the Pythagorus theorem we can write,
[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]
[tex]4^2 = x^2+x^2\\\\16=2x^2\\\\8=x^2\\\\x= 2\sqrt2[/tex]
Hence, the length of one leg of the triangle is 2√2 cm.
Learn more about Pythagoras Theorem:
https://brainly.com/question/14461977
#SPJ2
The additive inverse of x/y is
Answer
The additive inverse is
-x/-y
That is equal to x/y
hope this may help you
You spend 6,380.00 a year for rent. This is 22% of your income. What is your income?
Answer: 29,000.00
Step-by-step explanation:
Let the income=x. 22%=0.22.
So 6380/x=0.22
x=6380/0.22=29,000.00
[!] Urgent [!] Find the domain of the graphed function.
Which proportion would convert 18 ounces into pounds?
Answer:
16 ounces = 1 pound
Step-by-step explanation:
You would just do 18/16 = 1.125 pounds. There are always 16 ounces in a pound, so it always works like this
Legal descriptions tend to prefer neat straight lines from point to point, regardless of describing a square, rectangle, triangle or even a smooth circle. When might a property boundary end up being a squiggly line?
Answer:
When describing a property line drawn down the center of a creek bed
a) Al usar un microscopio el microscopio se amplía una célula 400 veces. Escribe el factor de ampliación como cociente o como escala.
b) La imagen de una célula usando dicho microscopio mide 1,5 mm ¿ Cuánto mide la célula en la realidad?
Answer:
x = 0,00375 mm
Step-by-step explanation:
a) El factor de ampliación es 400/1 es decir el tamaño real se verá ampliado 400 veces mediante el uso del microscopio
b) De acuerdo a lo establecido en la respuesta a la pregunta referida en a (anterior) podemos establecer una regla de tres, según:
Si al microscopio el tamaño de la célula es 1,5 mm, cual será el tamaño verdadero ( que es reducido 400 en relación al que veo en el microscopio)
Es decir 1,5 mm ⇒ 400
x (mm) ⇒ 1 (tamaño real de la célula)
Entonces
x = 1,5 /400
x = 0,00375 mm
The lengths of adult males' hands are normally distributed with mean 190 mm and standard deviation is 7.4 mm. Suppose that 45 individuals are randomly chosen. Round all answers to 4 where possible.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For the group of 45, find the probability that the average hand length is less than 189.
Find the third quartile for the average adult male hand length for this sample size.
For part b), is the assumption that the distribution is normal necessary?
Answer:
a. The distribution of the sample means is normal with mean 190 mm and standard deviation 1.1031 mm.
b. The probability that the average hand length is less than 189 is P(M<189)=0.1823.
c. The third quartile for the average adult male hand length for this sample size is M_75=190.7440.
d. The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
Step-by-step explanation:
We have a normal distribution, with mean 190 and standard deviation 7.4.
We take samples of size n=45 from this population.
Then, the sample means will have a distribution with the following parameters:
[tex]\mu_s=\mu=190\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{7.4}{\sqrt{45}}=\dfrac{7.4}{6.7082}=1.1031[/tex]
The probability that the sample mean is less than 189 can be calculated as:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{189-190}{7.4/\sqrt{45}}=\dfrac{-1}{1.1031}=-0.9065\\\\\\P(M<189)=P(z<-0.9065)=0.1823[/tex]
The third quartile represents the value of the sample where 75% of the data is to the left of this value. It means that:
[tex]P(M<M^*)=0.75[/tex]
The third quartile corresponds to a z-value of z*=0.6745.
[tex]P(z<z^*)=0.75[/tex]
Then, we can calculate the sample mean for the third quartile as:
[tex]M=\mu_s+z^*\sigma_s=190+0.6745\cdot 1.1031=190+0.7440=190.7440[/tex]
The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
Jeremy makes $57,852 per year at his accounting firm. How much is Jeremy’s monthly salary? (There are 12 months in a year.) How much is Jeremy’s weekly salary? (There are 52 weeks in a year.)
Answer:
Monthly: $4,821
Weekly: $1112.54
Step-by-step explanation:
Monthly
A monthly salary can be found by dividing the yearly salary by the number of months.
salary / months
His salary is $57,852 and there are 12 months in a year.
$57,852/ 12 months
Divide
$4,821 / month
Jeremy makes $4,821 per month.
Weekly
To find the weekly salary, divide the yearly salary by the number of weeks.
salary / weeks
He makes $57,852 each year and there are 52 weeks in one year.
$57,852 / 52 weeks
Divide
$1112.53846 / week
Round to the nearest cent. The 8 in the thousandth place tells use to round the 3 up to a 4 in the hundredth place.
$1112.54 / week
Jeremy makes $1112.54 per week
Suppose 150 students are randomly sampled from a population of college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 99% confidence interval for the average IQ of college students? Possible Answers: 1) A) E =1.21 B) E = 1.25 C) E =2.52 D) E = 2.11 2) A) 112.48 < μ < 117.52 B) 113.79 < μ < 116.21 C) 112.9 < μ < 117.10 D) 113.75 < μ < 116.3
Answer:
99% confidence interval for the mean of college students
A) 112.48 < μ < 117.52
Step-by-step explanation:
step(i):-
Given sample size 'n' =150
mean of the sample = 115
Standard deviation of the sample = 10
99% confidence interval for the mean of college students are determined by
[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]
Step(ii):-
Degrees of freedom
ν = n-1 = 150-1 =149
t₁₄₉,₀.₀₁ = 2.8494
99% confidence interval for the mean of college students are determined by
[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]
on calculation , we get
(115 - 2.326 , 115 +2.326 )
(112.67 , 117.326)
The width of a casing for a door is normally distributed with a mean of 24 inches and a standard deviation of 1/8 inch. The width of a door is normally distributed with a mean of 23 7/8 inches and a standard deviation of 1/16 inch. Assume independence. a. Determine the mean and standard deviation of the difference between the width of the casing and the width of the door. b. What is the probability that the width of the casing minus the width of the door exceeds 1/4 inch? c. What is the probability that the door does not fit in the casing?
Answer:
a) Mean = 0.125 inch
Standard deviation = 0.13975 inch
b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25) = 0.18673
c) Probability that the door does not fit in the casing = P(X < 0) = 0.18673
Step-by-step explanation:
Let the distribution of the width of the casing be X₁ (μ₁, σ₁²)
Let the distribution of the width of the door be X₂ (μ₂, σ₂²)
The distribution of the difference between the width of the casing and the width of the door = X = X₁ - X₂
when two independent normal distributions are combined in any manner, the resulting distribution is also a normal distribution with
Mean = Σλᵢμᵢ
λᵢ = coefficient of each disteibution in the manner that they are combined
μᵢ = Mean of each distribution
Combined variance = σ² = Σλᵢ²σᵢ²
λ₁ = 1, λ₂ = -1
μ₁ = 24 inches
μ₂ = 23 7/8 inches = 23.875 inches
σ₁² = (1/8)² = (1/64) = 0.015625
σ₂ ² = (1/16)² = (1/256) = 0.00390625
Combined mean = μ = 24 - 23.875 = 0.125 inch
Combined variance = σ² = (1² × 0.015625) + [(-1)² × 0.00390625] = 0.01953125
Standard deviation = √(Variance) = √(0.01953125) = 0.1397542486 = 0.13975 inch
b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25)
This is a normal distribution problem
Mean = μ = 0.125 inch
Standard deviation = σ = 0.13975 inch
We first normalize/standardize 0.25 inch
The standardized score of any value is that value minus the mean divided by the standard deviation.
z = (x - μ)/σ = (0.25 - 0.125)/0.13975 = 0.89
P(X > 0.25) = P(z > 0.89)
Checking the tables
P(x > 0.25) = P(z > 0.89) = 1 - P(z ≤ 0.89) = 1 - 0.81327 = 0.18673
c) Probability that the door does not fit in the casing
If X₂ > X₁, X < 0
P(X < 0)
We first normalize/standardize 0 inch
z = (x - μ)/σ = (0 - 0.125)/0.13975 = -0.89
P(X < 0) = P(z < -0.89)
Checking the tables
P(X < 0) = P(z < -0.89) = 0.18673
Hope this Helps!!!
The following data represent the miles per gallon for a particular make and model car for six randomly selected vehicles. Compute the mean, median, and mode miles per gallon 24.2. 22.2. 37.8, 22.7. 35 4. 31.61. Compute the mean miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean mileage per gallon is _______B. The mean does not exist 2. Compute the median miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The median mileage per gallon is __________B. The median does not exist. 3. Compute the mode miles per gallon. Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. The mode is _________B. The mode does not exist.
Answer:
A. The mean mileage per gallon is _____ 28.99__
A. The median mileage per gallon is _____27.905_____
B. The mode does not exist.
Step-by-step explanation:
Mean= Sum of values/ No of Values
Mean = 24.2 + 22.2+ 37.8+ 22.7 + 35.4 +31.61/ 6
Mean = 173.91/6= 28.985 ≅ 28.99
The median is the middle value of an ordered data which divides the data into two equal halves. For an even data the median is the average of n/2 and n+1/2 value where n is the number of values.
Rearranging the above data
22.2 , 22.7 , 24.2 , 31.61 , 35.4, 37.8
Third and fourth values are =24.2 + 31.61 = 55.81
Average of third and fourth values is = 55.81/2= 27.905
Mode is the values which is occurs repeatedly.
In this data there is no mode.
Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 116 meters
Answer:
Length = 29 m
Width = 29 m
Step-by-step explanation:
Let x and y be the length and width of the rectangle, respectively.
The area and perimeter are given by:
[tex]A=xy\\p=116=2x+2y\\y=58-x[/tex]
Rewriting the area as a function of x:
[tex]A(x) = x(58-x)\\A(x) = 58x-x^2[/tex]
The value of x for which the derivate of the area function is zero, is the length that maximizes the area:
[tex]A(x) = 58x-x^2\\\frac{dA}{dx}=0=58-2x\\ x=29\ m[/tex]
The value of y is:
[tex]y = 58-29\\y=29\ m[/tex]
Length = 29 m
Width = 29 m
¿Cuál serie numérica tiene como regla general Xn = 2n +1?
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
Answer:
The series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
Step-by-step explanation:
We are given with the following series options below;
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].
For this, we will put the values of n in the above expression and then will see which series is obtained as a result.
So, the given expression is ; [tex]X_n=2n+1[/tex]
If we put n = 1, then;
[tex]X_1=(2\times 1)+1[/tex]
[tex]X_1 = 2+1 = 3[/tex]
If we put n = 2, then;
[tex]X_2=(2\times 2)+1[/tex]
[tex]X_2 = 4+1 = 5[/tex]
If we put n = 3, then;
[tex]X_3=(2\times 3)+1[/tex]
[tex]X_3 = 6+1 = 7[/tex]
If we put n = 4, then;
[tex]X_4=(2\times 4)+1[/tex]
[tex]X_4 = 8+1 = 9[/tex]
Hence, the series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
4
The equation of a circle is x2 + y2 + x + Dy+ E= 0. If the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients CD,
and E affected?
O A CD, and E are unchanged.
Answer:
Step-by-step explanation:
in x²+y²+2gx+2fy+c=0
center=(-g,-f)
radius=√((-g)²+(-f)²-c)
if center is not changed ,then c will change .
Here only coefficients of E will change.
The length of a rectangle is 5M more than twice the width and the area of the rectangle is 63M to find the dimension of the rectangle
Answer:
width = 4.5 m
length = 14 m
Step-by-step explanation:
okay so first you right down that L = 5 + 2w
then as you know that Area = length * width so you replace the length with 5 + 2w
so it's A = (5 +2w) * w = 63
then 2 w^2 + 5w - 63 =0
so we solve for w which equals 4.5 after that you solve for length : 5+ 2*4.5 = 14