A Ferris wheel at an amusement park is modeled by (x – 100)2 + (y – 75)2 = 4,900, where the measurements are in feet. A slingshot attraction is modeled by y = –3x2 + 48x – 30. Which attraction reaches a greater height, and what does it represent in terms of the context?
The attraction that reaches a greater height and what it represent in terms of the context is:
The slingshot reaches a greater height at 162 ft, which is the vertex of the parabola.The Ferris wheel reaches a greater height at 145 ft, which is the highest point on the circle.HeightFerris wheel
(x – 100)2 + (y – 75)2 = 4,900
y max= 75+70
y max=145 ft
Sling shot
y = –3x² + 48x – 30
dy/dx=-6+48=0
x=48/6
x=8
Hence:
y max = –3(8)² + 48(8) – 30
y max = –3×64+48(8)-30
y max = –192+384-30
y max =162 ft
Therefore slingshot reaches a greater height at 162 ft and Ferris wheel reaches a greater height at 145 ft.
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for the function f(x)=5(x+2) find f (2)
Answer:
20
Step-by-step explanation:
To calculate f(2), just replace x in the equation of f(x) with 2:
[tex]f(x) = 5(x + 2)\\\\f(2) = 5(2+2)\\\\f(2) = 5(4)\\\\f(2) = 20[/tex]
(h+k)(1) is
(k-h)(4) is
(k/h)(3) is
(h•k)(0) is
(k •h)(0) is
(h•k)(3) is
h(k(-2))
Answer:
Step-by-step explanation:
(h+k)(1)=h(1)+k(1)=2+(-1)=2-1=1
(k-h)(4)=k(4)-h(4)=0-(-1)=1
(k/h)(3)[tex]=\frac{k(3)}{h(3)} =\frac{-1}{0} =- \infty[/tex]
(h.k)(0)=h(0).k(0)=3(-2)=-6
(k.h)(0)=k(0).h(0)=-2(3)=-6
(h.k)(3)=h(3).k(3)=0(-1)=0
h(k(-2))=h(-3)=0
A variable is normally distributed with mean 6 and standard 2 deviation .
a. Find the percentage of all possible values of the variable that lie between 5 and 9.
b. Find the percentage of all possible values of the variable that exceed 1.
c. Find the percentage of all possible values of the variable that are less than 4.
The normal distribution is also known as the Gaussian distribution. The percentage of all possible values of the variable that are less than 4 is 15.87%.
What is a normal distribution?
The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
A.) The percentage of all possible values of the variable that lie between 5 and 9.
P(5<X<9) = P(X<9) - P(5<X)
= P(z<1.5) - P(-0.5<z)
= 0.9332 - 0.3085
= 0.6247
= 62.47%
B.) The percentage of all possible values of the variable that exceed 1.
P(X>1) = 1 - P(X<-2.5)
= 1-0.0062
= 0.9938
= 99.38%
C.) The percentage of all possible values of the variable that are less than 4.
P(X<4) = P(X <4)
= P(z<-1)
= 0.1587
= 15.87%
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A farmer has 324 feet of fencing to make three identical adjacent rectangular pens, as shown in the picture. What dimensions of each pen will maximize the total enclosed area?
The dimensions of each pen that will maximize the total enclosed area would be as; Length 81 feet; Width 81 feet.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let the Dimension of each pen
Length = x
Width = y
Area = xy
Perimeter equation
2(x + y) = 324
x + y = 162
Substituting the perimeter equation
Area = x(162 - x)
Area = -x^2 + 162x
If the zeros of the quadratic are 0 and 162, then the median will be at where the maximum area occurs.
162/ 2
= 81
Hence, The dimensions of each pen that will maximize the total enclosed area would be as; Length 81 feet; Width 81 feet.
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three-quarters of a pile of bricks were used for a certain project. when two thirds of the reminder had been used, 50 bricks were left. how many bricks were there in the original pile?
Answer:
sorry I don't know the answer
Please answer this for me
Step-by-step explanation:
all the details see in the attachment.
The graphs below have the same shape. What is the equation of the red graph? g(x) = A. g(x)=2^x+3-2 B. 2^x-3-2 C. 2^x-2-3 D. g(x)=^x+2-3
The equation of the red graph is g(x)=^x+2-3.
Since the upscaling in the y-axis is not the main focus of this equation (being g(x) and not g(y)), the change is not applied to the x-axis.
What is the equation of the graph?
The y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. The slope is the change in y over the change in x.
Hence, we can rule out (-3)^2 and (x+3)^2 since they apply changes to the x-axis.
Finally, since this is an upscaling of the y-value on the y-axis, the answer is x^2 + 3 and not x^2 - 3.
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63, 58, 57, 71, 54, 60 Calculate the coefficient of variation for the following data
Answer:
The coefficient of variation (CV)= 9.83
Step-by-step explanation:
look at the attachment above ☝️
write an exponential expression that shows (10 to the power of 4) to the power of 4 simplified
Answer: it could be
[tex](10^{4} ) ^{4}[/tex]
Step-by-step explanation:
How Do You Answer This Question
No Question, this account was set up in error.
Answer:
is the question no questions question ❓
Find the equation of the line through point
(2, 2) and parallel to y= x+4.
Answer:
The equation of a parallel line is y = x
Step-by-step explanation:
Parallel lines have the same slope
hence the new lines slope is = 1
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
Given:
through point (2, 2) parallel to y = x + 4we need to find b, y = 1x + b
we can plug in the point (2, 2)
2 = 1(2) + b
2 = 2 + b
0 = b
Hence, the equation of the line through point
(2, 2) and parallel to y = x+4 is y = x
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Doug split a pack of cards so that he and his friends each got 6 cards. If there were 24 cards in the pack, how many friends did Doug share his cards with ?
Answer is not 4.
Answer:
3
Step-by-step explanation:
24 divided by 6 is 4, subtract Doug, there were 3 friends
What’s the vertex of this graph??
Answer:
(4, -3)
Step-by-step explanation:
A vertex is just a point where 2 lines going in different directions meet. so the answer is (4, -3)
Samantha is 9 years younger than her brother Maurice. In 10
years, Maurice will be 1.5 times older than his sister. Find their
present ages.
Step-by-step explanation:
hope you can understand
Answer:
Samantha is 8 years and Maurice is 17 years
Step-by-step explanation:
First represent Samantha's brother's age with a variable, x.
Secondly, find Samantha's age. since shes 9 years younger, then it will be her brother's age which is x minus 9
Thirdly, in ten years, they will all age hence 10 will be added to all their ages.
Fourthly, once 10 has been added to their after 10 years, rhen we realise Maurice age will be 1.5 timess Samantha's age... Then you solve the resulting equation.
Which line is perpendicular to a line that has a slope of -5/6?
Answer:
Line LM
Step-by-step explanation:
First, we need to know what the slope is of a line that would be perpendicular to a line with a slope of -5/6. To find this, we take the reciprocal and multiply it by -1. Therefore, the line we are looking for needs to have a slope of 6/5.
Based on the fact that the slope is positive, we can eliminate lines PQ and JK as they have a negative slope. This leaves us with lines LM and NO.
To find out whether or not it is between LM and NO, you could eyeball it by looking at the graph and simply counting which might be faster if you understand how to do that (rise/run), or you can use the pair of coordinates given to you on each line to calculate for slope.
Line LM - [tex]\frac{-3-3}{-5-0}=\frac{-6}{-5}=\frac{6}{5}[/tex]
Line NO - [tex]\frac{-5-0}{-6-0}=\frac{-5}{-6}=\frac{5}{6}[/tex]
Based on this, we know that line LM is perpendicular to a line that has a slope of -5/6.
If you need help on calculating slope from two points, I'd suggest watching this video: https://www.brightstorm.com/math/algebra/linear-equations-and-their-graphs/finding-the-slope-of-a-line-from-2-points-problem-1/#:~:text=Use%20the%20slope%20formula%20to,second%20points%20are%20x2%2C%20y2.
Find equation in slope intercept form of the line passing through the points with given coordinates (-3,-4), (0,-3)
Answer:
Step-by-step explanation:
→ Find the gradient
( -3 --4 ) ÷ ( 0 --3) = 1/3
→ Write into format
y = 1/3x + c
→ Substitute in a coordinate pair
-3 = 0 + c
→ Solve for c
c = -3
→ Write into format
y = 1/3x - 3
Can y’all help me with ! I need correct anwsers ! Please
Answer:
Im pretty sure its B, 1.75. Not exactly sure though
Step-by-step explanation:
vertical angles must : check all that apply
A. be complementary
B. have the same vertex
C. be congruent
D. be acute
Answer: B and C
Step-by-step explanation: For A, vertical angles can be complimentary or supplementary. For D, vertical angles can sometimes be acute but not always.
Which of the following equations is equivalent to the formula for velocity
Six angles of a heptagon have measures of 80°, 90°, 100°, 145°, 165° and 170°. The smallest of all the exterior angles measures ____.
80°
150°
190°
10°
Answer: 10°
Step-by-step explanation:
Since an exterior angle and its corresponding interior angle are supplementary, meaning they have a fixed sum, to minimize the exterior angle, we need to maximize the interior angle.
This means we need to consider the 170° interior angle, so the corresponding exterior angle is 10°.
Which expression is modeled by this arrangement of tiles?
40 positive tiles are broken up into 10 groups of 4 positive tiles.
40 divided by (negative 10)
40 divided by 10
40 divided by 40
40 divided by 40
Answer:
40 divided by 10
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
What is the inverse of f(x)=9x-3
Answer:
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x9+13 f - 1 ( x ) = x 9 + 1 3 is the inverse of f(x)=9x−3 f ( x ) = 9 x - 3
Answer:
y = x + 3/9
Step-by-step explanation:
Change f(x) y = 9x-3Solve for y +3 +3
x+3 = 9y = y=x+3/9
15. Desde la punta de un edificio el hombre araña lanza una tela a 500 metros, de la base del edificio
con un ángulo de depresión de 60°, ¿Qué altura (h) tiene el edificio?
ayudaaaa
Step-by-step explanation:
the correct answer will be 93
A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which equation gives the measure of the central angle, q? 08- 5 O 0-7+5 O e-7-5
The equation gives the measure of the central angle 7/5 times 3 60/2 π.
What is Central angle?An angle with its vertex at the center of a circle and with sides that are radii of the circle.
radius= 5 feet.
Circumference of circle,
= 2πr
=2*3.14*5
= 31.4 feet.
Arc length = 7.
Then, the part of circle 7 feet arc have
=7/31.4
=0.2229
Also, 0.2229 * 360 = 80.244°
In radian,
80.244° = 1.4 radians
Hence, 7/5 times 360/2 π.
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has a bag containing twenty balls. There are twice as many yellow balls than blue balls, but the yellow balls are only a third of the red balls. The green balls are the same number as the blue balls. How many are each of the colour ball?
Answer:
Yellow: 4
blue: 2
red: 12
green: 2
line / is parallel to line m. the slope of line / is 4/9. what is the slope of line m?
Answer: 4/9
Step-by-step explanation:
Parallel lines have equivalent slopes.
As line 'l' and line 'm' are parallel to each other ,then the slope of line 'm' is also 4/9.
Parallel lines have the same slope. The slope of line segments is identical because they are all similarly inclined with respect to the positive x-axis. If 'l', and 'm' are the slopes of two parallel lines,
then l = m
Slope-intercept notation for lines may be expressed as y=mx+b.
In this notation, b denotes the location of the line's y-axis intercept, and slope(m) indicates the slope of the line.
The slope of 'l'=4/9
The slope of the two parallel lines is the same.
Therefore, the slope of the parallel line "m" = 4/9.
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I need help in this problem
Step-by-step explanation:
this is first an arithmetic sequence with the first term A1=3(1)+1=4 And the 12th term A12=3(12)+1=37. Then use this formula
S12=12/2 ×(4+37)
=6×41
=246
5.7y-5.2=y/2.5 how to solve
5.7y-5.2=y/2.5
Add 5.2 to both sides:
5.7y = y/2.5 + 5.2
y/2.5 = 0.4y
5.7y = 0.4y + 5.2
Subtract 0.4y from both sides:
5.3y = 5.2
Divide both sides by 5.3:
y = 5.2/5.3
y = 0.98113
Answer:
y = 0.981
Step-by-step explanation:
Given expression:
5.7y-5.2=y/2.5Solution:
5.7y-5.2=0.4ySubtract 0.4y from both sides:
5.7y-5.2-0.4y=0.4y-0.4y5.3y - 5.2 = 0Add 5.2 to both sides:
5.3y-5.2+5.2 = 0+5.25.3y = 5.2Divide both sides by 5.3:
[tex] \cfrac{5.3y}{5.3} = \cfrac{5.2}{5.3} [/tex][tex]y = 0.981[/tex]Hence, y = 0.981.
