ANSWER:
EXPLANATION:
A simple random sample of size has mean and standard deviation. Construct a confidence interval for the population mean. The parameter is the population The correct method to find the confidence interval is the method.
The sample size is not given. Mean and Standard Deviation are not given.
To construct a confidence interval for the population mean, first find out the margin of error of the sample mean. This is why you need a confidence interval. If you are 90% confident that the population mean lies somewhere around the sample mean then you construct a 90% confidence interval.
This is equivalent to an alpha level of 0.10
If you are 95% sure that the population mean lies somewhere around the sample mean, your alpha level will be 0.05
In summary, get the values for sample size (n), sample mean, and sample standard deviation.
Make use of a degrees of freedom of (n-1).
What is the value of the angle marked with xxx?
Answer:
Here you go!! :)
Step-by-step explanation:
Given that the sides of the quadrilateral are 3.3
The measure of one angle is 116°
We need to determine the value of x.
Value of x:
Since, the given quadrilateral is a rhombus because it has all four sides equal.
We know the property that the opposite sides of the rhombus are equal.
The measure of the opposite angle is 116°
x = measure of opposite angle
x = 116°
Then, the value of x is 116°
Therefore, the value of x is 116°
Answer:
In the diagram, the measurement of x is 87°
Step-by-step explanation:
In this diagram, this shape is a quadrilateral. This quadrilateral in this picture is known as rhombus. In a rhombus, the consecutive angles are supplementary meaning they have a sum of 180°. Consecutive means the angles are beside each other. So, we will subtract 93 from 180 to find the value of x.
180 - 93 = 87
The measurement of x is 87°
Express it in slope-intercept form
Answer:
Step-by-step explanation:
Can u help me
Answer:
cant see the picture
Step-by-step explanation:
The time X(mins) for Ayesha to prepare breakfast for her family is believed to have a uniform
distribution with A=25 and B=35.
a) Determine the pdf of X and draw its density curve.
b) What is the probability that time taken by Ayesha to prepare breakfast exceeds 33 mins?
c) What is the probability that cooking or preparation time is within 2 mins of the mean time?
(Hint: Identify mean from the graph of f(x))
Answer:
(c) [tex]f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.[/tex]
(b) The probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.
(c) The probability that cooking or preparation time is within 2 mins of the mean time is 0.40.
Step-by-step explanation:
The random variable X follows a Uniform (25, 35).
(a)
The probability density function of an Uniform distribution is:
[tex]f_{X}(x)=\left \{ {{\frac{1}{B-A};\ A<X<B} \atop {0;\ Otherwise}} \right.[/tex]
Then the probability density function of the random variable X is:
[tex]f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.[/tex]
(b)
Compute the value of P (X > 33) as follows:
[tex]P(X>33)=\int\limits^{35}_{33} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{35}_{33} {1} \, dx \\\\=\frac{1}{10}\times [x]^{35}_{33}\\\\=\frac{35-33}{10}\\\\=\frac{2}{10}\\\\=0.20[/tex]
Thus, the probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.
(c)
Compute the mean of X as follows:
[tex]\mu=\frac{A+B}{2}=\frac{25+35}{2}=30[/tex]
Compute the probability that cooking or preparation time is within 2 mins of the mean time as follows:
[tex]P(30-2<X<30+2)=P(28<X<32)[/tex]
[tex]=\int\limits^{32}_{28} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{32}_{28}{1} \, dx \\\\=\frac{1}{10}\times [x]^{32}_{28}\\\\=\frac{32-28}{10}\\\\=\frac{4}{10}\\\\=0.40[/tex]
Thus, the probability that cooking or preparation time is within 2 mins of the mean time is 0.40.
Juan y maria mezclan cafe de colombia, cafe de brazil, cafe de guinea y cafe de venezuela en paquetes de un kilo. Observa la fraccion de kilo que utilizan de cada tipo de cafe y calcula la fraccion de kilo que representa el cafe de colombia
Answer:
Step-by-step explanation:
Ya que mezclan café colombiano, brasileño, guineano y venezolano en un paquete de un kilo. Igualmente deben agregar los cafés juntos.
Para encontrar la cantidad igual para cada café en 1 kilo, divida 1 kilo y los 4 cafés. Entonces la cantidad sería 1/4 (o 0.25) de café por kilo. La respuesta significa que cada uno de los cuatro cafés pesa 1/4 kilo.
Como cada café representa 1/4 kilo, el café colombiano representa 1/4 kilo.
Si necesita ayuda adicional, comente a continuación.
Making handcrafted pottery generally takes two major steps: wheel throwing and firing. The time of wheel throwing and the time of firing are normally distributed random variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively. Assume the time of wheel throwing and time of firing are independent random variables. (d) What is the probability that a piece of pottery will be finished within 95 minutes
Answer:
The probability that a piece of pottery will be finished within 95 minutes is 0.0823.
Step-by-step explanation:
We are given that the time of wheel throwing and the time of firing are normally distributed variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively.
Let X = time of wheel throwing
So, X ~ Normal([tex]\mu_x=40 \text{ min}, \sigma^{2}_x = 2^{2} \text{ min}[/tex])
where, [tex]\mu_x[/tex] = mean time of wheel throwing
[tex]\sigma_x[/tex] = standard deviation of wheel throwing
Similarly, let Y = time of firing
So, Y ~ Normal([tex]\mu_y=60 \text{ min}, \sigma^{2}_y = 3^{2} \text{ min}[/tex])
where, [tex]\mu_y[/tex] = mean time of firing
[tex]\sigma_y[/tex] = standard deviation of firing
Now, let P = a random variable that involves both the steps of throwing and firing of wheel
SO, P = X + Y
Mean of P, E(P) = E(X) + E(Y)
[tex]\mu_p=\mu_x+\mu_y[/tex]
= 40 + 60 = 100 minutes
Variance of P, V(P) = V(X + Y)
= V(X) + V(Y) - Cov(X,Y)
= [tex]2^{2} +3^{2}-0[/tex]
{Here Cov(X,Y) = 0 because the time of wheel throwing and time of firing are independent random variables}
SO, V(P) = 4 + 9 = 13
which means Standard deviation(P), [tex]\sigma_p[/tex] = [tex]\sqrt{13}[/tex]
Hence, P ~ Normal([tex]\mu_p=100, \sigma_p^{2} = (\sqrt{13})^{2}[/tex])
The z-score probability distribution of the normal distribution is given by;
Z = [tex]\frac{P- \mu_p}{\sigma_p}[/tex] ~ N(0,1)
where, [tex]\mu_p[/tex] = mean time in making pottery = 100 minutes
[tex]\sigma_p[/tex] = standard deviation = [tex]\sqrt{13}[/tex] minutes
Now, the probability that a piece of pottery will be finished within 95 minutes is given by = P(P [tex]\leq[/tex] 95 min)
P(P [tex]\leq[/tex] 95 min) = P( [tex]\frac{P- \mu_p}{\sigma_p}[/tex] [tex]\leq[/tex] [tex]\frac{95-100}{\sqrt{13} }[/tex] ) = P(Z [tex]\leq[/tex] -1.39) = 1 - P(Z < 1.39)
= 1 - 0.9177 = 0.0823
The above probability is calculated by looking at the value of x = 1.39 in the z table which has an area of 0.9177.
On a Cartesian coordinate plane, points $(2,1)$ and $(3, 4)$ are adjacent points on a square. What is the area of the square?
Hey there! :)
Answer:
A = 10 units².
Step-by-step explanation:
To solve this, we need to find the distance between the two points to derive the side-lengths of the square. Use the distance formula:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Plug in points into the formula to find the distance:
[tex]d = \sqrt{(3 - 2)^2 + (4-1)^2}[/tex]
Simplify:
[tex]d = \sqrt{(1)^2 + (3)^2}[/tex]
[tex]d = \sqrt{(1) + (9)}[/tex]
[tex]d = \sqrt{10}[/tex]
Find the area of the square using the formula A = s² where s = √10:
A = (√10)²
A = 10 units².
Answer:
10
Step-by-step explanation:
We use the distance formula to find the distance between the two points, which is the side length of the square.. Therefore, the area of the square is 10.
what is 3(C - 5) = 48
Answer:
c=21
Step-by-step explanation:
[tex]3(c-5)=48\\3c-15=48\\3c=48+15\\3c=63\\c=63/3\\c=21[/tex]
Hope this helps,
plx give brainliest
Answer:
c=21
Step-by-step explanation:
3(c−5)=48
Divide both sides by 3.
c-5=48/3
Divide 48 by 3 to get 16.
c−5=16
Add 5 to both sides.
c=16+5
Add 16 and 5 to get 21.
c=21
vertex form of x^2+6x+3
Answer:
y = (x + 3)^2 - 6.
Step-by-step explanation:
The vertex formula is Y = a(x - h)^2 + k.
To find the vertex formula, we need to find h and k, by finding the vertex of x^2 + 6x + 3.
h = -b/2a
a = 1, b = 6.
h = -6 / 2 * 1 = -6 / 2 = -3
k = (-3)^2 + 6(-3) + 3 = 9 - 18 + 3 = -9 + 3 = -6
So far, we have Y = a(x - (-3))^2 + -6, so y = a(x + 3)^2 - 6.
In this case, the coefficient of x^2 of the given formula is 1, which means that a will be 1.
The vertex form of x^2 + 6x + 3 is y = (x + 3)^2 - 6.
To check our work...
y = (x + 3)^2 - 6
= x^2 + 3x + 3x + 9 - 6
= x^2 + 6x + 3
Hope this helps!
One positive number is
6 more than twice another. If their product is
1736, find the numbers.
Answer:
[tex]\Large \boxed{\sf \ \ 28 \ \text{ and } \ 62 \ \ }[/tex]
Step-by-step explanation:
Hello, let's note a and b the two numbers.
We can write that
a = 6 + 2b
ab = 1736
So
[tex](6+2b)b=1736\\\\ \text{***Subtract 1736*** } <=> 2b^2+6b-1736=0\\\\ \text{***Divide by 2 } <=> b^2+3b-868=0 \\ \\ \text{***factorize*** } <=> b^2 +31b-28b-868=0 \\ \\ <=> b(b+31) -28(b+31)=0 \\ \\ <=> (b+31)(b-28) =0 \\ \\ <=> b = 28 \ \ or \ \ b = -31[/tex]
We are looking for positive numbers so the solution is b = 28
and then a = 6 +2*28 = 62
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 25 hours and the mean lifetime of a bulb is 510 hours. Find the probability of a bulb lasting for at most 552 hours.
Answer:
The probability of a bulb lasting for at most 552 hours.
P(x>552) = 0.0515
Step-by-step explanation:
Step(i):-
Given mean of the life time of a bulb = 510 hours
Standard deviation of the lifetime of a bulb = 25 hours
Let 'X' be the random variable in normal distribution
Let 'x' = 552
[tex]Z = \frac{x-mean}{S.D} = \frac{552-510}{25} =1.628[/tex]
Step(ii):-
The probability of a bulb lasting for at most 552 hours.
P(x>552) = P(Z>1.63)
= 1- P( Z< 1.63)
= 1 - ( 0.5 + A(1.63)
= 1- 0.5 - A(1.63)
= 0.5 -A(1.63)
= 0.5 -0.4485
= 0.0515
Conclusion:-
The probability of a bulb lasting for at most 552 hours.
P(x>552) = 0.0515
Gwen has $20, $10, and $5 bills in her purse worth a total of $220. She has 15 bills in all. There are 3 more $20 bills than there are $10 bills. How many of each does she have?
Answer:
x = 8 ( 20$ bills)
y = 5 ( 10 $ bills)
z = 2 ( 5 $ bills)
Step-by-step explanation:
Let call x, y, and z the number of bill of 20, 10, and 5 $ respectively
then according to problem statement, we can write
20*x + 10*y + 5*z = 220 (1)
We also know the total number of bills (15), then
x + y + z = 15 (2)
And that quantity of 20 $ bill is equal to
x = 3 + y (3)
Now we got a three equation system we have to solve for x, y, and z for which we can use any valid procedure.
As x = 3 + y by substitution in equation (2) and (1)
( 3 + y ) + y + z = 15 ⇒ 3 + 2*y + z = 15 ⇒ 2*y + z = 12
20* ( 3 + y ) + 10*y + 5*z = 220 ⇒ 60 + 20*y + 10*y + 5*z = 220
30*y + 5*z = 160 (a)
Now we have only 2 equations
2*y + z = 12 ⇒ z = 12 - 2*y
30*y + 5*z = 160 30*y + 5* ( 12 - 2*y) = 160
30*y + 60 - 10*y = 160
20*y = 100
y = 100/20 y = 5 Then by substitution in (a)
30*y + 5*z = 160
30*5 + 5*z = 160
150 + 5*z = 160 ⇒ 5*z = 10 z = 10/5 z = 2
And x
x + y + z = 15
x + 5 + 2 = 15
x = 8
Answer:
x=8 y=5 x=2
Step-by-step explanation:
Which of the following is the
graph of
(x - 3)2 + (y - 1)2 = 9 ?
Answer:
Answer is A
Step-by-step explanation:
The equation (x - 3)² + (y - 1)² = 9, is represented by the second graph as its center is at point (3, 1) and its radius is 3 units, both similar to the equation. Thus, option B is the right choice.
What does the equation of a circle represent?The general equation of a circle is of the form (x - h)² + (y - k)² = r², where (h, k) is the point where the center of the given circle lies, and r is the radius of this given circle.
How to solve the question?In the question, we are asked to find the graph from the given options which represents the equation (x - 3)² + (y - 1)² = 9.
Comparing the given equation, (x - 3)² + (y - 1)² = 9, to the general equation, (x - h)² + (y - k)² = r², we can say that h = 3, k = 1, and r = 3.
Thus the center of the given circle lies at the point (3, 1) and its radius is 3 units.
Now we check the options to find the matching circle:
Option A: The center is at the point (3, -1), which is different from (3, 1) of the equation (x - 3)² + (y - 1)² = 9. Thus, this is not the right choice.Option B: The center is at the point (3, 1), and the radius is 3 units, which is similar to the equation (x - 3)² + (y - 1)² = 9. Thus, this is the right choice.Option C: The center is at the point (-3, 1), which is different from (3, 1) of the equation (x - 3)² + (y - 1)² = 9. Thus, this is not the right choice.Therefore, the equation (x - 3)² + (y - 1)² = 9, is represented by the second graph as its center is at point (3, 1) and its radius is 3 units, both similar to the equation. Thus, option B is the right choice.
Learn more about circles at
https://brainly.com/question/1559324
#SPJ2
If 3x + 9y = 21 , find the value of 4(x + 3y)
Answer:
25
Step-by-step explanation:
The method that should be used is substitution:
Do this by taking 3x+9y=21 and transforming it to be [tex]y=-\frac{1}{2} x+\frac{7}{3}[/tex]
Once you have this, substitute the value of y that we just found into 3x+9y=21 to find the value of x: [tex]3x+9(-\frac{1}{2} +\frac{7}{3} ) =21[/tex]
Solve for x. You should get 1.5
Once you have this, Plug in 1.5 for the value of x into the y= equation that we found in the beginning: [tex]y=-\frac{1}{2} (1.5)+\frac{7}{3}[/tex]
Solve for y. You should get 1.583 (19/12)
Plug in the values of x and y that we found into the last equation to find its value: 4(1.5+3(1.583))
can I get some help please?
━━━━━━━☆☆━━━━━━━
▹ Answer
2,013 cartons
▹ Step-by-Step Explanation
72,468 ÷ 36 = 2,013 cartons
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
72,468 eggs divided by 36 eggs per carton=2,013 cartons
Step-by-step explanation:
the depth D, in inches, od wsnow in my yard t hours after it started snowing this morning is given by D=1.5t + 4. if the depth of the snow is 7 inches now, what will be the depth one hour from now?
Answer:
8.5 inches
Step-by-step explanation:
First let's find the time t when the depth of the snow is 7 inches.
To do this, we just need to use the value of D = 7 then find the value of t:
[tex]7 = 1.5t + 4[/tex]
[tex]1.5t = 3[/tex]
[tex]t = 2\ hours[/tex]
We want to find the depth of snow one hour from now, so we just need to use the value of t = 3 to calculate D:
[tex]D = 1.5*3 + 4[/tex]
[tex]D = 4.5 + 4 = 8.5\ inches[/tex]
The depth of snow one hour from now will be 8.5 inches.
The depth of the snow one hour from now is 8.5 inches.
Let D represent the depth of snow in inches at time t. It is given by the relationship:
D=1.5t + 4
Since the depth of the snow is 7 inches now, hence, the time now is:
7 = 1.5t + 4
1.5t = 3
t = 2 hours
One hour from now, the time would be t = 2 + 1 = 3 hours. Hence the depth at this time is:
D = 1.5(3) + 4 = 8.5 inches
Therefore the depth of the snow one hour from now is 8.5 inches.
Find out more at: https://brainly.com/question/13911928
-12
Natural
Whole
Integers
Rationals
Irrationals
Real
Answer:
the answer is integers if helpful please give 5 star
Which of the following statements are true? I. The sampling distribution of ¯ x x¯ has standard deviation σ √ n σn even if the population is not normally distributed. II. The sampling distribution of ¯ x x¯ is normal if the population has a normal distribution. III. When n n is large, the sampling distribution of ¯ x x¯ is approximately normal even if the the population is not normally distributed. I and II I and III II and III I, II, and III None of the above gives the complete set of true responses.
Complete Question
Which of the following statements are true?
I. The sampling distribution of [tex]\= x[/tex] has standard deviation [tex]\frac{\sigma}{\sqrt{n} }[/tex] even if the population is not normally distributed.
II. The sampling distribution of [tex]\= x[/tex] is normal if the population has a normal distribution.
III. When n is large, the sampling distribution of [tex]\= x[/tex] is approximately normal even if the the population is not normally distributed.
A I and II
B I and III
C II and III
D I, II, and III
None of the above gives the complete set of true responses.
Answer:
The correct option is D
Step-by-step explanation:
Generally the mathematically equation for evaluating the standard deviation of the mean([tex]\= x[/tex]) of samples is [tex]\frac{\sigma}{\sqrt{n} }[/tex] hence the the first statement is correct
Generally the second statement is true, that is the sampling distribution of the mean ([tex]\= x[/tex]) is normal given that the population distribution is normal
Now according to central limiting theorem given that the sample size is large the distribution of the mean ([tex]\= x[/tex]) is approximately normal notwithstanding the distribution of the population
Please answer this correctly
Answer:
1/8
Step-by-step explanation:
Total cards = 8
Card with 4 = 1
P(4) = 1/8
replace each star with a digit to make the problem true.Is there only one answer to each problem? ****-***=2
Answer: We have two solutions:
1000 - 998 = 2
1001 - 999 = 2
Step-by-step explanation:
So we have the problem:
****-*** = 2
where each star is a different digit, so in this case, we have a 4 digit number minus a 3 digit number, and the difference is 2.
we know that if we have a number like 99*, we can add a number between 1 and 9 and we will have a 4-digit as a result:
So we could write this as:
1000 - 998 = 2
now, if we add one to each number, the difference will be the same, and the number of digits in each number will remain equal:
1000 - 998 + 1 - 1 = 2
(1000 + 1) - (998 + 1) = 2
1001 - 999 = 2
now, there is a trivial case where we can find other solutions where the digits can be zero, like:
0004 - 0002 = 2
But this is trivial, so we can ignore this case.
Then we have two different solutions.
Write an equation that represents the relationship.Please help!
Answer:
n = r - 2.5
Step-by-step explanation:
We have the following data:
7 4.5
8 5.5
10 7.5
12 9.5
Now, what we will do is what happens if we subtract each one:
7 - 4.5 = 2.5
8 - 5.5 = 2.5
10 - 7.5 = 2.5
12 - 9.5 = 2.5
The difference is always kept constant, therefore the equation would be:
n = r - 2.5
If ∠1 and ∠2 are complementary and m∠1 = 17º, what is m∠2
Answer:
m<2 = 73
Step-by-step explanation:
Since <1 and <2 are complementary (which means that they equal 90), all you have to do is subtract 17 from 90 to find your answer:
90 - 17 = 73
thus, m<2 = 73
Answer:
73
Step-by-step explanation:
Which algebraic expression represents the phrase below? five times the sum of a number and eleven, divided by three times the sum of the number and eight 5(x + 11) + 3(x + 8) 5 x + 11 Over 3 x + 8 Start Fraction 5 (x + 11) Over 3 (x + 8) 5x + 11 + 3x + 8
Answer:
85
Step-by-step explanation:
im new↑∵∴∵∴∞
Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a function of x { x ( t ) = 5 √ t y ( t ) = 7 t + 4
Answer:
y(x) = (7/25)x^2 + 4
Step-by-step explanation:
Given:
x = 5*sqrt(t) .............(1)
y = 7*t+4 ..................(2)
solution:
square (1) on both sides
x^2 = 25t
solve for t
t = x^2 / 25 .........(3)
substitute (3) in (2)
y = 7*(x^2/25) +4
y= (7/25)x^2 + 4
Please answer this correctly
Answer:
[tex] \frac{1}{6} [/tex]
Step-by-step explanation:
the ways of choosing 2 cards out of 4, is calculator by
[tex] \binom{4}{2} = 6[/tex]
so, 6 ways to select 2 cards.
but in only one way we can have 2 even cards. thus, the answer is
[tex] \frac{1}{6} [/tex]
What does 0 = 0 indicate about the solutions of the system?
Answer:
it indicates that it is infinitely many solutions
Several terms of a sequence StartSet a Subscript n EndSet Subscript n equals 1 Superscript infinity are given below. {1, negative 5, 25, negative 125, 625, ...} a. Find the next two terms of the sequence. b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term of the sequence). c. Find an explicit formula for the general nth term of the sequence.
Answer:
(a) -3125, 15625
(b)
[tex]a_n=-5a_{n-1}, \\n\geq 2 \\a_1=1[/tex]
(c)[tex]a_n=(-5)^{n-1}[/tex]
Step-by-step explanation:
The sequence [tex]a_n$ _{n=1}^\infty[/tex] is given as:
[tex]\{1,-5,25,-125,625,\cdots\}[/tex]
(a)The next two terms of the sequence are:
625 X -5 = - 3125
-3125 X -5 =15625
(b)Recurrence Relation
The recurrence relation that generates the sequence is:
[tex]a_n=-5a_{n-1}, \\n\geq 2 \\a_1=1[/tex]
(c)Explicit Formula
The sequence is an alternating geometric sequence where:
Common Ratio, r=-5First Term, a=1Therefore, an explicit formula for the sequence is:
[tex]a_n=1\times (-5)^{n-1}\\a_n=(-5)^{n-1}[/tex]
Reed made a lasagna for dinner. That night, he ate1/4
% of the lasagna. His brother and sister ate 2/3 of
the lasagna. How much of the lasagna did they eat
in all?
Answer: 11/12
Step-by-step explanation:
First find the LCM of 4 and 3(12). Then make the denominator of both fractions 12(3/12 and 8/12). Then add the fractions to get that they ate 11/2 of the lasagna.
Hope it helps <3
Select the correct answer from each drop-down menu.
The given equation has been solved in the table.
Answer: a) additive inverse (addition)
b) multiplicative inverse (division)
Step-by-step explanation:
Step 2: 6 is being added to both sides
Step 4: (3/4) is being divided from both sides
It is difficult to know what options are provided in the drop-down menu without seeing them. If I was to complete a proof and justify each step, then the following justifications would be used:
Step 2: Addition Property of Equality
Step 4: Division Property of Equality
Please help me !!!!!
Answer:
11.5
Step-by-step explanation:
Put the numbers in order from smallest to largest
2,2,6,9,9,11,11,12,32,43,46,54,54,59
The median is the middle number
There are 14 numbers so the middle is between 7 and 8
2,2,6,9,9,11,11, 12,32,43,46,54,54,59
Take the average of the 7th and 8th numbers
(11+12)/2 = 11.5
The median is 11.5
Answer: 11.5
Step-by-step explanation:
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
2 2 6 9 9 11 11 12 32 43 46 54 54 59
As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:
Median= 11+12/2=11.5
Find the magnitudes of sides x and y.
Answer:
x ≈ 13.8 units
y ≈ 22.0 units
Step-by-step explanation:
We must use trigonometry to address this problem.
First, we know that y is the side opposite to the labelled angle, and x is the side adjacent to the labelled angle. 26 is the length of the hypotenuse.
We use cosine to find x (because cosine = adjacent / hypotenuse) and sine to find y (because sine = opposite / hypotenuse).
cos(58) = x/26
x = 26 * cos(58) ≈ 13.8
sin(58) = y/26
y = 26 * sin(58) ≈ 22.0
Thus, x ≈ 13.8 units and y ≈ 22.0 units.
~ an aesthetics lover