NOT NECESSARILY would a triangle be equilateral if one of its angles is 60 degrees. To be an equilateral triangle (a triangle in which all 3 sides have the same length), all 3 angles of the triangle would have to be 60°-angles; however, the triangle could be a 30°-60°-90° right triangle in which the side opposite the 30 degree angle is one-half as long as the hypotenuse, and the length of the side opposite the 60 degree angle is √3/2 as long as the hypotenuse. Another of possibly many examples would be a triangle with angles of 60°, 40°, and 80° which has opposite sides of lengths 2, 1.4845 (rounded to 4 decimal places), and 2.2743 (rounded to 4 decimal places), respectively, the last two of which were determined by using the Law of Sines: "In any triangle ABC, having sides of length a, b, and c, the following relationships are true: a/sin A = b/sin B = c/sin C."¹
An ecologist is examining whether the number of fish caught in a large river basin has changed since a fire burned some of the surrounding forested area and vegetation along the river. Data in the form of fishing reports was available for a five-year period before the fire. From a random sample of 195 fishing reports before the fire, the mean catch was 6.3 fish with a standard deviation of 1.6. In a random sample of 143 reports three years after the fire, the mean catch was 7.1 fish with a standard deviation of 2.1.
Required:
What represents the standard error of the difference in the mean number of fish caught before and after the fire?
Answer:
The standard error of the difference in the mean number of fish caught before and after the fire is 0.2153.
Step-by-step explanation:
Subtraction of normal variables:
When we subtract two normal variables, the standard deviation is the square root of the sum of variances of each variable.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Sample of 195 fishing reports before the fire, the mean catch was 6.3 fish with a standard deviation of 1.6.
The standard error for this sample is:
[tex]s_b = \frac{1.6}{\sqrt{195}} = 0.1246[/tex]
Sample of 143 reports three years after the fire, the mean catch was 7.1 fish with a standard deviation of 2.1.
The standard deviation for this sample is:
[tex]s_a = \frac{2.1}{\sqrt{143}} = 0.1756[/tex]
What represents the standard error of the difference in the mean number of fish caught before and after the fire?
[tex]s = \sqrt{s_a^2 + s_b^2} = \sqrt{0.1756^2 + 0.1246^2} = 0.2153[/tex]
The standard error of the difference in the mean number of fish caught before and after the fire is 0.2153.
Answer:
sqrt [ (1.6^2)/195 + (2.1^2)/143 ]
what is an outlier number?
Answer:
an outlier is a number that is at least 2 standard deviations away from the mean for example in the set 1,1,1,1,1,1,1,1,1,7,7,7 would be the outlier
Step-by-step explanation:
watashi wa sore ga tadashī koto o negatte imasu
arigatozaimasu!!
Step-by-step explanation:
i have noooo idea but ayyeee
The width of a rectangle is represented by 5 - 2y.
The length is twice as long as the width What is the
perimeter of the rectangle? Select all correct expressions
A45-27
3 65 - 27
C20 -
D30 - 12
Answer:
Perimeter of rectangle = 30 - 12y
Step-by-step explanation:
Given:
Width of rectangle = 5 - 2y
Length of rectangle = 2(width) = 2[5 - 2y] = 10 - 4y
Find:
Perimeter of rectangle
Computation:
Perimeter of rectangle = 2[l + b]
Perimeter of rectangle = 2 [10 - 4y + 5 - 2y]
Perimeter of rectangle = 2[15 - 6y]
Perimeter of rectangle = 30 - 12y
Pls help me
10 12 15 str 220 pls help me
Answer:
which language I cant understand
What are the zeros of the polynomial function f(x) = x3 + 9x2
Hi there!
[tex]\large\boxed{x = -9, 0}[/tex]
Find the zeros using factoring:
f(x) = x³ + 9x²
Factor out the common term, or x²:
f(x) = x²(x + 9)
Set each factor equal to 0:
x² = 0
x = 0
x + 9 = 0
x = -9
The zeroes are -9, 0.
is 3/10 bigger than 2/9
Answer:
2
9
is smaller than
3
10
Step-by-step explanation:
Select all of the terms that apply to the shape.
A) pentagon
B) hexagon
C) heptagon
D) octagon
E) nonagon
F) decagon
G) regular polygon
H) irregular polygon
I) m concave
J) m convex
LOOK AT THE PICTURE!!
Answer:
it is data
Step-by-step explanation:
just look at it and describe its properties
Bye,
Canus Lupus
Intercontinental, Inc., uses a perpetual inventory system. Consider the following information about its inventory: July 1, purchased 10 units for $910 or $91 per unit; July 3, purchased 15 units for $1,590 or $106 per unit; July 14, sold 20 units; July 17, purchased 20 units for $2,300 or $115 per unit; July 28, purchased 10 units for $1,190 or $119 per unit; July 31, sold 23 units.
Using weighted average, the cost of goods sold for the sale of 23 units on July 31 is ____ and the inventory balance at July 31 is _____.
Answer:
Using weighted average, the cost of goods sold for the sale of 23 units on July 31 is $2,504.70, and the inventory balance at July 31 is $ 1,306.90.
Step-by-step explanation:
Since Intercontinental, Inc., uses a perpetual inventory system, and on July 1, purchased 10 units for $ 910 or $ 91 per unit; on July 3, purchased 15 units for $ 1,590 or $ 106 per unit; on July 14, it sold 20 units; on July 17, purchased 20 units for $ 2,300 or $ 115 per unit; on July 28, purchased 10 units for $ 1,190 or $ 119 per unit; and on July 31, sold 23 units, to determine the average costs and the inventory balance as of July 31, the following calculations must be performed:
(910 +1590 + 2300 + 1190) / (10 + 15 + 20 + 10) = X
5990/55 = X
108.90 = X
108.90 x 23 = 2504.7
(55 x 108.9) - (43 x 108.9) = X
5990 - 4683.10 = X
1306.90 = X
Using weighted average, the cost of goods sold for the sale of 23 units on July 31 is $ 2504.70, and the inventory balance at July 31 is $ 1,306.90.
Saundra can write 5 thank-you notes in 15 minutes. She wants to know how many notes she can write in 2 hours if she continues
writing at the same rate.
Mike says that Saundira could write 60 notes in 2 hours.
Is Mike correct? Explain your answer using the drop-down menus.
Mike is not
correct
. Since 15 minutes is of an hour, Saundira is writing at a rate of Choose... notes per hour. That
means Saundra could write 120
notes in 2 hours.
In the similarly transformations of ABC
calculate the actual sales since the sales tax were rung up together. assume sales tax of 6% and total sales of $27,000. What is the actual sales? ( round your answer to the nearest cent.)
Answer:
$25471.7
Step-by-step explanation:
1.06*25471.7=27000.002
Hope this helps
Simplify: 14y+13x+12y÷19x+4
Answer:
13x+14y+12y/19x+4
Step-by-step explanation:
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 3x^4 − 4x^3 − 12x^2 + 1, [−2, 3]
Find the stationary points.
f(x) = 3x ⁴ - 4x ³ - 12x ² + 1
f '(x) = 12x ³ - 12 x ² - 24x
Solve f '(x) = 0.
12x ³ - 12 x ² - 24x = 12x (x ² + x - 2) = 12x (x - 1) (x + 2) = 0
→ x = 0, x = 1, x = -2
Check the value of f at the stationary points.
f (0) = 1
f (1) = -12
f (-2) = 33
Check the value of f at the boundary of the domain.
f (3) = 28
(We've already checked f (-2).)
Then over [-2, 3], we have max(f ) = 33 and min(f ) = -12.
What is radiant energy from the sun called
Answer:
Solar rays
Step-by-step explanation:
Either that or uv rays
Answer:
Electromagnetic Radiation
Step-by-step explanation:
write the equation of the given line in slope intercept form (2,3) (8,6)
Answer:
y = 1/2x + 2
Step-by-step explanation:
slope:
6 - 3 / 8 - 2 = 3 / 6 = 1/2
start by putting it in point slope form and then simplify it to slope intercept form:
y - 3 = 1/2(x - 2)
y - 3 = 1/2x - 1
y = 1/2x + 2
Describe how the graph of the parent function y = StartRoot x EndRoot is transformed when graphing y = negative 3 StartRoot x minus 6 EndRoot
The graph is translated 6 units
Answer: is b- right
Step-by-step explanation:
We want to see how the graph of the parent function compares to the graph of the transformed function.
The transformed function is a reflection across the x-axis, followed by a translation of 6 units to the right, followed by a vertical dilation of scale factor 3 of the parent function.
The parent function is y = √x
The transformed function is y = -3*√(x - 6)
So there are 3 transformations applied to the parent function, let's describe these generally.
Reflection across the x-axis:
For a function f(x), a reflection across the x-axis just changes the sign:
g(x) = -f(x).
Horizontal shift:
For a function f(x), a horizontal shift of N units is written as:
g(x) = f(x + N)
if N is positive, the shift if to the left.if N is negative, the shift is to the right.Vertical dilation:
For a function f(x), a vertical dilation of scale factor K is written as:
g(x) = K*f(x)
Then from the parent function to the transformed function, we have:
A reflection across the x-axis, followed by a translation of 6 units to the right, followed by a vertical dilation of scale factor 3.
If you want to learn more, you can read:
https://brainly.com/question/19046248
Identify the vertex and the y-intercept of the graph translated 1 unit right from the parent function f(x)=x2
Vertex ( ?,?)
y-intercept: ?
Answer:
Step-by-step explanation:
y = (x-1)²
vertex (1,0)
y-intercept = (0-1)² = 1
divide the 240g into the ratio 5:3:4?
5x+ 3x +4x =12x
12x =240
X=20
100:60:80
PLEASE ANSWER ASAP! Triangle ABC has side lengths 8 cm, 17 cm, and x cm. The side length of x is shorter than the longest side. What does the value of x need to be in order for the triangle to be considered a right triangle?
A. 4 cm
B. 9 cm
C. 15 cm
D. 12 cm
which of the following rotational symmetry is applied to the regular not
9514 1404 393
Answer:
yesyesStep-by-step explanation:
A regular nonagon has vertices that are 360°/9 = 40° apart. Any rotation by a multiple of 40° will make the figure indistinguishable from the original.
Rotational symmetry of 40° applies.
Rotational symmetry of 200° applies.
The vertices of APQR are P(-3, 8) Q(-6,-4), and R(1, 1). If you reflect APQR across the x-axis, what will be the coordinates of the vertices of the image AP'Q'R'?
Answer:(-3,-8),(-6,4),(1,-1)
Step-by-step explanation:
Given
Vertices of the triangle are
[tex]P(-3,8), Q(-6,-4),R(1,1)[/tex]
Coordinates (a,b) when reflected about x-axis is given as (a,-b) i.e. Y coordinate changes its sign
[tex]\therefore P\rightarrow P'(-3,-8)\\\Rightarrow Q\rightarrow Q'(-6,4)\\\Rightarrow R\rightarrow R'(1,-1)[/tex]
The graph of g(x) = log(4x) has -
A two x-intercepts and no y-intercept
B one x-intercept and one y-intercept
C no x-intercept or no-y-intercept
D one x-intercept and no y-intercept
estimate each percent: 50% of 39
Answer:
19.5
Step-by-step explanation:
39 x 0.50 = 19.5
What is the probability that Mary will get an "11"?
Answer:
yeaa what
Step-by-step explanation:
What is the solution to the equation below?
0.5x + 20 = 0.6x
A. x = -200
B. x=2
C.x = 20
D.x = 200
Answer:
it's D 200 for sure my answer I correct
Which expression has a value of 7 when x=-2?
A:|3x+5|-4
B:|-3x-3|+10
C:|-4x+6|-7
D:|4x-8|-5
Answer:
DONT PRESS THAT LINK
Step-by-step explanation:
Write a polynomial that represents the area of the large rectangle with side lengths of x+4 and x+3
Answer:
Step-by-step explanation:
First off use algebra tiles, Didax has a good one. So basically x*x is x^2 right? and 4*3 is 12 right? also 4x+3x=7x. So the answer is x^2+7x+12! :)
If you place a 37-foot ladder against the top of a 12-foot building, how many feet will the bottom of the ladder be from the bottom of the building?
The building will be making 90° with the ground/horizontal.
Then we can apply Pythagoras theorem.
(Base)² + (Height)² = (Hypotenuse)²
=> x² + (12 foot)² = (37 foot)²
=> x² = (37 foot)² - (12 foot)²
We can expand LHS using a² - b² = (a + b)(a - b)
=> x² = (37 + 12 foot)(37 - 12 foot)
=> x² = 49 * 25 foot²
=> x² = (7 * 5)² foot²
=> x = 7 * 5 foot
=> x = 35 foot.
This month Joe spent 1/2 of his salary on food and 1/3 on rent. What part of his salary did he spend? Simplify the fraction if possible.
Answer:
the answer is 5/6
Step-by-step explanation:
1/2 + 1/3
1 =3 + 2=1 5
x
-- + --- = ---
2 x 3 = 6