Answer:
The function is
[tex]f(x)=0.5x^3-3x^2+5.5x-2[/tex]
The graph is attached.
Step-by-step explanation:
We have a function g(x) and we need to graph a new function that is function of g(x).
The final function is
[tex]f(x)=0.5\cdot g(x-2)+1[/tex]
We start by calculating g(x-2):
[tex]g(x-2)=(x-2)^3-(x-2)\\\\g(x-2)=(x^3-6x^2+12x-8)-(x-2)\\\\g(x-2)=x^3-6x^2+11x-6[/tex]
Then, we can calculate f(x) as:
[tex]f(x)=0.5\cdot g(x-2)+1\\\\g(x-2)=x^3-6x^2+11x-6\\\\\\f(x)=0.5(x^3-6x^2+11x-6)+1\\\\f(x)=0.5x^3-3x^2+5.5x-3+1\\\\\\f(x)=0.5x^3-3x^2+5.5x-2[/tex]
5/8 of the staff are male. 5/12 of the staff works part time at the aquarium.What fraction of the staff is female?
Answer:
3/8
Step-by-step explanation:
If 5/8 of the staff is male, then 8/8 is the total number of staff.
8/8 - 5/8 = 3/8
3/8 of the staff is female.
Hope this has helped. If the question has more to it, then please specify.
PLEASEEE HELP JUST THE ANSWER I don’t to explain !!!
Find the measure of one exterior angle for the following regular polygon.
Answer:
72º
Step-by-step explanation:
Hey there!
Well the interior of a pentagon's angle is 108º,
so we do,
180 - 108 = 72º
Hope this helps :)
Answer:
72°
Step-by-step explanation:
→ First find the measure of all interior angle, utilise the formula (n-2) × 180° where n is the number of sides
(n-2) × 180° ⇔ (5-2) × 180° ⇔ 3 × 180° ⇔ 540°
→ 540° is the total sum of the angles in the pentagon, divide this by 5 to get one of the interior angles
540° ÷ 5 = 108°
→ Now, remember the fact that 1 interior + 1 exterior angle = 180°
180 - ( 1 interior angle ) → 180 - (108) = 72°
30. A rectangular prism has a volume of
285.6 cubic feet. The prism is
12 feet long and 3.4 feet wide. What is
the height of the prism?
A 7 ft
C 19 ft
B 15 ft
D 22 ft
Answer:
The answer is a
Step-by-step explanation:
my brother is very smart
An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 150 miles from the point and has a speed of 300 miles per hour. The other is 200 miles from the point and has a speed of 400 miles per hour.
(a) At what rate is the distances between the planes decreasing?
(b) How much time does the air traffic controller have to get one of the planes on a different flight path?
Answer:
(a) D(t) = 250t -500 miles
(b) Controller has 2 hours, but including time for pilots to divert course or altitude.
Step-by-step explanation:
Given:
two planes at same altitude heading in a collision course.
Plane A at 400 miles from collision point at 200 mph
Plane B at 300 miles from collision point at 150 mph.
Theoretical collision happens in
t = 400/200 = 300/150 = 2 hours
Distance ya of plane A from collision point as a function of time in hours
ya(t) = 400 -200t
Distance yb of plane B from collision point as a function of time in hours
yb(t) = 300-150t
(a) Distance between two planes,
Since the two planes are on courses perpendicular to each other, will need using pythagorean theorem
D(t) = sqrt(ya(t)^2+yb(t)^2)
= sqrt((400-200t)^2+(300-150t)^2)
= 250(t-2)
D(t) = 250t -500 miles
b. time available
Time until D(t) = 0
solve D(t) = 0
D(t) = 0
250(t-2) = 0
t = 2 (two hours)
Answer:
a) -500 mph
b) 1/2 h
Step-by-step explanation:
a)[tex]\frac{ (150(-300))+(200(-400))}{\sqrt{150x^{2} +200^{2} } }[/tex]
b) [tex]\frac{\sqrt{150^{2}+200^{2} } }{500}[/tex]
Please answer this question now
Answer:
469.4ft²
Step-by-step explanation:
We have Triangle WXY
In the question, we are given already
Angle W = 27°
Angle X = ?
Angle Y = 40°
Side w =?
Side x = ?
Side y = 38ft
Area of the triangle= ?
Step 1
We find the third angle = Angle X
Sum of angles in a triangle = 180°
Third angle = Angle X= 180° - (27 + 40)°
= 180° - 67°
Angle X = 113°
Step 2
Find the sides w and x
We find these sides using the sine rule
Sine rule or Rule of Sines =
a/ sin A = b/ Sin B
Hence for triangle WXY
w/ sin W = x/ sin X = y/ sin Y
We have the following values
Angle W = 27°
Angle X = 113°
Angle Y = 40°
We are given side y = 38ft
Finding side w
w/ sin W= y/ sin Y
w/sin 27 = 38/sin 40
Cross Multiply
sin 27 × 38 = w × sin 40
w = sin 27 × 38/sin 40
w = 26.83879ft
w = 26.84ft
Finding side x
x / sin X= y/ sin Y
x/ sin 113 = 38/sin 40
Cross Multiply
sin 113 × 38 = x × sin 40
x = sin 113 × 38/sin 40
x = 54.41795ft
x = 54.42ft
To find the area of triangle WXY
We use heron formula
= √s(s - w) (s - x) (s - y)
Where S = w + x + y/ 2
s = (38 + 26.84 + 54.42)/2
s = 59.63
Area of the triangle = √59.63× (59.63 - 38) × (59.63 - 26.84 ) × (59.63 - 54.42)
Area of the triangle = √
Area of the triangle = 469.40772706541ft²
Approximately to the nearest tenth =469.4yd²
Find the length of a cube with a surface area of 850cm^2 rounded to the nearest tenth. I need a step by step solution pleaseeee:)
Answer:
11.9 cm.
Step-by-step explanation:
A cube has a SURFACE AREA of 850 cm^2.
A cube has six congruent sides. That means that each side measures 850 / 6 = 141.666666667 cm^2.
Since a side measures 141.66667 cm^2, a side length will be the square root of that (the area of a square is a side length times the side length, and they are the same).
[tex]\sqrt{141.666666666667}[/tex]
= 11.90238071
So, the side length of the cube is 11.9 cm.
Hope this helps!
TRUE OF FALSE : -4 <-2
Answer: false but not sure
A bag contains 5 red, 6 green, 7 yellow, and 8 blue jelly beans. A jelly bean is selected at random. What is the probability that it is blue?
Answer:
4/13 is the probability does a blue Jelly Bean is selected
Step-by-step explanation:
sample space = sum of all the jelly beans in the bag
sample space =5+6+7+8
sample space =26
probability = Jelly Bean selected / sample space
probability =8/26
probability =4/13
write the expression in radical form. (88c)^2/3
Answer:
[tex]\sqrt[3]{88c^{2} }[/tex]
Step-by-step explanation:
If we have a term to a fractional power, that’s the same as finding the denominator root of the number - if the numerator of the fraction isn’t 1, then the term itself inside the root sign becomes the term to the numerator power.
So - since the denominator of this fraction is 3, we find the cube root of 88c. Since the numerator is 2, we square 88c.
[tex]\sqrt[3]{88c^{2} }[/tex].
Hope this helped! (By the way, this was my 100th answer!)
Round Ed to the nearthest tenth and answer now question
Answer:
[tex] y = 9.1 [/tex]
Step-by-step explanation:
y can be found using the Law of sines as explained below:
m < Y = 106°
m < X = 58°
WY = x = 8
WX = y = ?
Thus,
[tex] \frac{x}{sin(X)} = \frac{y}{sin(Y)} [/tex]
[tex] \frac{8}{sin(58)} = \frac{y}{sin(106)} [/tex]
[tex] \frac{8}{0.848} = \frac{y}{0.961} [/tex]
Multiply both sides by 0.961 to solve for y
[tex] \frac{8}{0.848}*0.961 = \frac{y}{0.961}*0.961 [/tex]
[tex] \frac{8*0.961}{0.848} = y [/tex]
[tex] \frac{8*0.961}{0.848}*0.961 = y [/tex]
[tex] 9.07 = y [/tex]
[tex] y = 9.1 [/tex] (to the nearest tenth)
if cos 0=2/3, what are the values of sin 0 and tan 0?
Answer:
Below
Step-by-step explanation:
● cos O = 2/3
We khow that:
● cos^2(O) + sin^2(O) =1
So : sin^2 (O)= 1-cos^2(O)
● sin^2(O) = 1 -(2/3)^2 = 1-4/9 = 9/9-4/9 = 5/9
● sin O = √(5)/3 or sin O = -√(5)/3
So we deduce that tan O will have two values since we don't khow the size of O.
■■■■■■■■■■■■■■■■■■■■■■■■■
●Tan (O) = sin(O)/cos(O)
● tan (O) = (√(5)/3)÷(2/3) or tan(O) = (-√(5)/3)÷(2/3)
● tan (O) = √(5)/2 or tan(O) = -√(5)/2
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the weights in pounds of 11 players randomly selected from the roster of a championship sports team. Are the results likely to be representative of all players in that sport's league? 293 255 264 240 190 295 199 184 293 205 199
Answer:
A.) Mean = 237.9
B.) Median = 240
C.) Mode = 199
D.) Midrange = 239.5
Step-by-step explanation:
The given data are :
293 255 264 240 190 295 199 184 293 205 199
The mean = (sum of X) / f
Where frequency f = 11
X = 293 + 255 + 264 + 240 + 190 + 295 + 199 + 184 + 293 + 205 + 199
X = 2617
Substitute X and f into the formula
Mean = 2617/11
Mean = 237.9 approximately
B.) To get the median, you need to first rearrange the data, then pick the middle number.
184 190 199 199 205 240 255 264 293 293 295
The median = 240
C.) The mode is the highest frequency. That is the most occuring number
Mode = the two most occuring numbers are 199 and 293
D.) Range = highest number - lowest number
But midrange = (highest number + lowest number ) ÷ 2
Highest number = 295
Lowest number = 184
Substitute into the formula
Midrange = (295 + 184)/2
Midrange = 479/2
Midrange = 239.5
A company has determined that its weekly profit is a function of the number of items that it sells. Which equation could represent the weekly profit in thousands of dollars, y, when the company sells x items? y squared = 4 x squared minus 100 y = negative x squared + 50 x minus 300 x = negative y squared minus 400 x squared = negative 6 y squared + 200
Answer:
B. y= -x^2 + 50x - 300
Step-by-step explanation:
Options given
A. y^2=4x^2 - 100
B. y= -x^2 + 50x - 300
C. x= -y^2 - 400
D. x^2= -6y^2 + 200
We are to find profits (y) function in thousands of dollars if the company sells x items.
We will use elimination method to eliminate the wrong options above in order to find the correct answer
Option A. y^2= 4x^2 - 100 is used to find the square of the profit function
Option B. y= -x^2 + 50x - 300 is used to calculate profit (y) function
Option C. x= -y^2 - 400 is for the calculation of the items x sold
Option D. x^2= -6y^2 + 200 is to find items x sold squared.
Since, we are required to find the profit (y) function, option A, C and D will be eliminated.
We are left with option B which is the correct answer to the question.
The weekly profits (y) function in thousands of dollars when the company sells x items is
B. y= -x^2 + 50x - 300
Answer:
B.
Step-by-step explanation:
I just took the quiz on edge
What's the correct answer to this..? Please help
Answer:
D. {x:-8≤x<-5}
Step-by-step explanation:
x≥-8
x={-8,-7,-6,-5,-4,-3,-2,-1,0...}
x<-5
x={-6,-7,-8,-9,-0...}
Numbers equal to or less than -8 are also less than -5
Hope it helps ;) ❤❤❤
Answer:
The answer is "D"
how would you solve #81?
Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was three eighths the size of the brand name. If the generic television set is 12 inches by 24 inches, what are the dimensions of the brand name television
Answer:
32 inches by 64 inches
Step-by-step explanation:
Since the generic television is [tex]\frac{3}{8}[/tex] the size of the brand name.
Then the brand name is [tex]\frac{8}{3}[/tex] the size of the generic, thus
[tex]\frac{8}{3}[/tex] × 12 = 32
[tex]\frac{8}{3}[/tex] × 24 = 64
Thus dimensions are 32 inches by 64 inches
Answer:
The dimensions are 32 inches by 64 inches
Explain how to solve the equation |2x-3| = x^2 graphically. Using a graphing calculator to find all real number solutions to the equation.
Answer:
x = -3 , x = 1
Step-by-step explanation:
Hello,
you need to draw the graph of the two functions and then find the intersection points.
please see below
So the solution is the two points A and B
(-3,9) and (1,1)
Hope this helps
the mapping diagram shows a function S(x).
Which mapping diagram shows the inverse of S(x)?
Answer:
Again the domain consists of the pre-images and the range the images.
When we are looking for the f(x) we just look at the number it is pointing to in the range (when we have a diagram), and when we are looking for x when f(x)=y we look at the number that has a line pointed to y.
So the f(4)=
f(x)=4 when x is 8
The pentagon ABCDE is dilated to the image A'B'C'D'E' with the center of the dilation at the origin.
Select all true statements
The scale factor of the dilation is 1/4
The line EA is parallel to the E’A’ because EA passes through the center of the dilation
Since the line C’D’ falls on the line CD, the scale factor is. It applied on the line CD
The scale factor of the dilation is 1/2
The line CD is not parallel to the line C’D’ because CD passes through the center of the dilation
Now I’m no genius but I‘m pretty sure the answers are “c” and “d”
Ya’ll have a good day or night, whichever one!
The true statement for the Pentagon in the given graph is
The scale factor of the dilation is 1/2 with the center at the origin(0,0).
Dilation:Dilation implies resize of any object.
It may increase or decrease the object by a particular value.The particular value is called the scale factor. Properties of Dilation of figure:Parallel lines in the dilated figure remain the same as in the original figure.The dilation of any figure does not vary from each angle of the figure.The midpoints of the dilated figure remain the same as that of the original figure.True statement:The scale factor of the dilation of the pentagon is 1/2.
Reason:The pentagon with vertices A(0.5,4.5), B(2,3), C(1,0), D(-2,0), E(-3,3) when multiplied by 1/2 we get The vertices of the dilated pentagon as A'(0.25,2.25), B'(1,1.5), C'(0.5,0), D'(-1,0), E(-1.5,1.5). When we plot the points A'B'C'D'E' in the graph, obtain the dilated pentagon with a center at the origin. Wrong statement with Reasons:The scale factor of the dilation is not 1/4 because when we multiply the vertices of pentagon ABCDE by 1/4 we are not getting the dilated points as in the graph.The line EA is parallel to E'A' but,1. The line EA does not passes through the center of the dilation
at origin(0,0), which can be clearly seen from the given graph.
2. For two lines to be parallel it is not necessary for one of the
lines to pass through the origin.
The line C'D' is parallel to CD as we should see the figure in a 3-dimensional way and it also follows the properties of dilation of a figure.Hence the scale factor of the given pentagon is 1/2.
To learn more about the Dilation of polygons:
https://brainly.com/question/3020085?referrer=searchResults
#SPJ2
What is the simplified form of -9x+3x
Answer:
-6x
Step-by-step explanation:
you can combine numbers with the same coefficient like any other number
Answer:
-6x
Step-by-step explanation:
It would be doing the same thing as -9 + 3, but without a variable.
The solution to an inequality is given in set-builder notation as {x l x > two-thirds}. What is another way to represent this solution set?
Answer:
[tex](\frac{2}{3},\infty)[/tex]
Step-by-step explanation:
Set builder notation is a mathematical notation used to write the elements of a set stating the conditions that the elements of the set must satisfy. A solution set is also a way of defining solutions to equations and inequalities. A solution set contains a set of all variables for which the equation is true.
The notation {x l x > two-thirds} is a set of all real numbers greater than 2/3, it can also be represented as:
[tex](\frac{2}{3},\infty)[/tex]
Answer:
c) (two-thirds, ∞)
Step-by-step explanation:
edg2020
How does the graph of g(x) = (x + 2)3 − 7 compare to the parent function of f(x) = x3? g(x) is shifted 2 units to the right and 7 units down. g(x) is shifted 7 units to the right and 2 units up. g(x) is shifted 2 units to the left and 7 units down. g(x) is shifted 7 units to the left and 2 units down
Answer: g(x) is shifted 2 units to the left and 7 units down.
Step-by-step explanation:
The original function f(x) becomes f(x+c), if it is shifted c units to the left.The original function f(x) becomes f(x-c), if it is shifted c units to the right.Also, if it is shifted d units down, then the function becomes f(x)-d.If it is shifted d units up, then the function becomes f(x)+d.Here, if we compare the graph of [tex]g(x) = (x + 2)^3 -7[/tex] compare to the parent function of [tex]f(x) = x^3[/tex].
We can observe that f(x) is shifted 2 units to the left and 7 units down.
So, the correct statement is "g(x) is shifted 2 units to the left and 7 units down".
Answer:
g(x) is shifted 2 units to the left and 7 units down.
Step-by-step explanation:
I took it and got it correct.
Select the correct answer. An inverse variation includes the point (2,12). Which point would also belong in this inverse variation? A. (3,-8) B. (-8,-3) C. (1,6) D. (-6,1)
Answer:
d
Step-by-step explanation:
An annual salary is $45000. His tax free allowances total $13000. He has to pay a tax of 20% on his taxable income.
The tax payable is?
Answer:
6400
Step-by-step explanation:
Taxable amount=45000-13000=32000
tax=32000*20/100
=6400
4 ft
8 ft
3 ft
2 ft
6 ft
What is the volume of the composite figure
Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of a
apples
Answer:
40 apples
Step-by-step explanation:
2 apples= [tex]\frac{1}{5}[/tex] grams
x apples= 4 grams
8/[tex]\frac{1}{5}[/tex] = 8 x 5/1=40
Answer:
40
Step-by-step explanation:
edu instruction correct
Which of the following statements is true
A. The relationship is a function because there are no two y-values corresponding to the same x-value
B. The relationship is not a function because there is more than one x value corresponding to y=2
C. The relationship is not a function because there are values of y that have no corresponding x- value
D. The relationship is not a function because each y has a corresponding x-value
Suppose you computed a 95% confidence interval for the difference in mean weight between two species of snakes in a large nature reserve (species #1 – species #2), and your interval is –3.6 to 61.6 ounces. What can you conclude?
Answer:
1. In a situation were we are willing to use 90% confidence, this means we could say that the observed difference that we have in the sample means tend to represents a real difference in the population means.
2. We cannot actually say because even with 95% confidence, that is the observed difference in sample means tend to as well represents a real difference in the population means.
3. Because the interval extends further in the positive direction than the negative direction this means that the evidence suggests that species #1 tend to weighs more than species #2 on average, but we can't actually say for sure.
Step-by-step explanation:
The following are what I will conclude about based on the information given in the question.
1. In a situation were we are willing to use 90% confidence, this means we could say that the observed difference that we have in the sample means tend to represents a real difference in the population means.
2. We cannot actually say because even with 95% confidence, that is the observed difference in sample means tend to as well represents a real difference in the population means.
3. Because the interval extends further in the positive direction than the negative direction this means that the evidence suggests that species #1 tend to weighs more than species #2 on average, but we can't actually say for sure.
Write the equations after translating the graph of y = |x|:
one unit up,
Answer:
y = | x | + 1
Step-by-step explanation:
Given y then y + c represents a vertical translation of y
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here the shift is 1 unit up, thus
y = | x | + 1