The function H(t) = −16t2 + 60t + 95 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in the air along a path represented by g(t) = 20 + 38.7t, where g(t) is the height, in feet, of the object from the ground at time t seconds. Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points) (10 points)
We are given the functions:
h(t) = -16t^2 + 60t + 95
g(t) = 20 + 38.7t
Part A. All we have to do is to plug in the value of t = 1 to 4 on the two functions
t h(t) g(t)
1 139 58.7
2 151 97.4
3 131 136.1
4 79 174.8
Looking at
the table, we can say that the time when h(t)=g(t) must be between t=2 and t= 3
seconds
At t=2 seconds h(t) is above g(t), and at t = 3 seconds h(t) is below g(t).
Therefore the two functions must be at the same height in between.
Part B. The solution in Part A gives us the exact time where the two objects have the same height. Further, we can see from the table that h(t) is decreasing meaning the projectile is going down while g(t) is increasing so the other projectile is going up.
Please help a brother out! Thank you!
they are saying x = 3 so you would use the middle equation
so -4x becomes -4(3)
-4 * 3 =-12
What is 2(x+6)=20 pls I need help
Thompson Alberts purchased a pack of 12 pencils for $4.99. What is the unit price per pencil rounded to the nearest tenth of a cent?
divide total coast by number of pieces
4.99/12 = 0.415833
rounded to 0.42
42 cents each
$0.416
This is the correct answer for primavera
$4.99/12=0.4158 Rounded to the nearest tenth of a cent is $0.416
Use the functions a(x) = 3x + 10 and b(x) = 2x − 8 to complete the function operations listed below. Part A: Find (a + b)(x). Show your work. (3 points) Part B: Find (a ⋅ b)(x). Show your work. (3 points) Part C: Find a[b(x)]. Show your work. (4 point
All computers are on sale for 10% off the original price. If x is the original price of the computer, then the function that represents the price after only a 10% discount is: P(x) = x - 0.1x P(x) = 0.9x The function that gives the price, C, if only a $150 coupon is used is: C(x) = x - 150 Choose the composition function that gives the final sale price after a 10% discount is followed by a $150 coupon
We are given the functions:
P (x) = 0.9 x
C (x) = x – 150
We can generate two composition functions from the given two functions in the form of:
P [C (x)] and C [P (x)]
Since the problem states that we are to find for the final price after a 10% discount is followed by a $150 coupon then we should find for:
C [P (x)]
The value of C [P (x)] can obtained by plugging in the value of P (x) into x in the equation of C (x), therefore:
C [P (x)] = [0.9 x] – 150
C [P (x)] = 0.9 x – 150 (ANSWER)
Answer:
A On edge 2020!
Step-by-step explanation:
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If the correlation between two variables is .496, how much of the variance has not been accounted for
If the correlation between two variables is .496, it has 24.6 percent (24.6%) of the variance that has not been accounted for. Hence, correlation is a statistical technique that is used to measure and describe the strength and direction of the relationship between two variables and 24.6% has not been accounted for the two variables which is .496.
Final answer:
About 75.40% of the variance between two variables with a correlation coefficient of .496 is unaccounted for, as it is the complement of the coefficient of determination (24.60%) obtained by squaring the correlation coefficient.
Explanation:
To determine the amount of variance not accounted for by the correlation between two variables with a correlation coefficient of .496, we must use the coefficient of determination. The coefficient of determination is the square of the correlation coefficient (r₂), which represents the proportion of the variance for the dependent variable that's explained by an independent variable in a regression model.
First, we calculate r₂:
.4962 = .246016, or approximately 24.60%. This means that about 24.60% of the variance in the dependent variable is explained by the independent variable.
Next, we find the unexplained variance by subtracting r₂ from 1:
1 - .246016 = .753984, or approximately 75.40%. Therefore, 75.40% of the variance has not been accounted for by the correlation.
Find the length of a line segment with endpoints of 19 and –39. A. –58 B. –20 C. 20 D. 58
Answer:
Option D, 58
Step-by-step explanation:
Line segment having end points are 19 and -39
So total length of line segments having end points of 19 and (-39) = distance from origin to one end at (19) + distance of another end from origin
= 19 + 39
= 58
Option D, 58 is the answer.
3x-4y=-5 y=4x-2 Is (1,2) a solution of the system?
Suzie drew the line of best fit on the scatter plot shown. A graph is shown with scale along x axis from 0 to 10 at increments of 1 and scale along y axis from 0 to 15 at increments of 1. The ordered pairs 0, 3 and 1, 3 and 2, 4 and 3, 7 and 4, 6 and 5, 8 and 6, 10 and 7, 10 and 8, 12 and 9, 14 and 10, 15 are shown on the graph. A straight line joins the ordered pairs 0, 3 and 10, 15. What is the approximate equation of this line of best fit in slope-intercept form?
Answer:
y = 1.2 x + 3
Step-by-step explanation:
Hope this helps
Quadrilateral ABCD is similiar to quadrilateral EFGH The lengths of the three longest sides in quadrilateral ABCD are 24 feet, 16 feet, and 12 feet long. If the two shortest sides of quadrilateral EFGH are 9 feet long and 18 feet long, how long is the 2nd longest side on quadrilateral EFGH
?
Answer:
A.) 24 feet
Step-by-step explanation:
I got it correct on founders edtell!
How can you prove that a constructed line is parallel to a given line? assume that the transversal line is not perpendicular to the other lines?
To prove that a line is parallel to another, one usually shows that two lines cut by a transversal have either congruent corresponding angles or alternate interior angles. In the lack of perpendicular transversal or angle knowledge, projecting lines onto a new coordinate system can show matching slopes to confirm parallelism.
Explanation:In mathematics, proving that a constructed line is parallel to a given line typically involves showing that the lines do not intersect and have the same slope or use a parallel postulate. The most common method is taking two lines l and m and a transversal t. If the corresponding angles or alternate interior angles created by t are congruent, then l and m are parallel.
For example: If line l and line m are cut by a transversal t and the corresponding angles (∠1 and ∠2) are congruent, then lines l and m are parallel. The same can be said if the alternate interior angles are congruent.
In some cases, if the transversal line is not perpendicular and we do not know about corresponding or alternate interior angles, we can establish a different coordinate system, project the lines onto the x-axis and y-axis, and show that they have the same slope which proves them to be parallel.
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What is the volume of the sphere? Round the answer to the nearest cubic unit. Diameter: 22 cm
1) 507 cm^3
2) 1,394 cm^3
3) 5,575 cm^3
4) 16,725 cm^3
The volume of the Sphere is 5,575 cm^3.
What is the volume of the Sphere ?
The volume of the Sphere is the capacity it has. It is the space occupied by the sphere.
Formula used to find volume of the Sphere is :
V = 4/3 × π × r^3
Given : diameter = 22 cm
r = diameter/2
r = 11 cm
So ,
V = 4/3 × π × 11 ^3
⇒ 4/3 × π × 1331
⇒ 1.34 × 4179.34
V = 5575.28 cm^3
The nearest cubic unit is 5,575 cm^3.
Hence , the volume of the Sphere is 5,575 cm^3 .
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I don't understand this at all please help me
4y-y +11 = 38
4y -y = 3y
3y + 11 = 38
3y = 27
y = 27/3 =9
y = 9
answer is 9
Which of the following is a parent function
A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function h=-16t^2+36t+5. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height
1)1.13 s; 27.5 ft
2)2.25 s; 5 ft
3)1.13 s; 25.25 ft
4)1.13 s; 65.75 ft
Answer: 1.13s;25.25ft you welcome
Step-by-step explanation:
The radius of the earth is approximately 3960 miles find the approximate surface area to volume ratio of the earth
Analyze the diagram below and answer the question that follows.
Which of the following best describes triangle GFH?
A.
isosceles triangle
B.
acute triangle
C.
scalene triangle
D.
right triangle
The pie store is having a 15% percent off sale on all of its pies. If the pie you want regularly costs $11 how much would you save with the discount?
10 POINTS PLEAAAAAASE HELP
Help a brother out here! Thank you!!!
7 blue cards
26 total cards
probability = 7/26
Joel is laying pipe for a sprinkler system before he plants his lawn. The lawn is a rectangle, 15 feet long and 8 feet wide. He needs to lay a piece of pipe that will be run along the diagonal of the lawn. It will divide the area of the lawn into two right triangles. What will be the length of that diagonal piece of pipe?
The following graph describes function 1, and the equation below it describes function 2:
Function 1
graph of function f of x equals negative x squared plus 8 multiplied by x minus 15
Function 2
f(x) = −x2 + 2x − 15
Function ____ has the larger maximum.
(Put 1 or 2 in the blank space)
Answer:
The Function __1__ has the larger maximum.
Step-by-step explanation:
The given functions are
Function 1:
[tex]f(x)=-x^2+8x-15[/tex]
Function 2:
[tex]f(x)=-x^2+2x-15[/tex]
Both functions are downward parabola because the leading coefficient is negative. So, the vertex is the point of maxima.
If a function is [tex]f(x)=ax^2+bx+c[/tex], then its vertex is
[tex]Vertex=(\frac{-b}{2a}, f(\frac{-b}{2a}))[/tex]
The vertex of Function 1 is
[tex]Vertex=(\frac{-8}{2(-1)}, f(\frac{-8}{2(-1)}))[/tex]
[tex]Vertex=(4, f(4))[/tex]
The value of f(4) is
[tex]f(4)=-(4)^2+8(4)-15=1[/tex]
The vertex of Function 1 is (4,1). Therefore the maximum value of Function 1 is 1.
The vertex of Function 2 is
[tex]Vertex=(\frac{-2}{2(-1)}, f(\frac{-2}{2(-1)}))[/tex]
[tex]Vertex=(1, f(1))[/tex]
The value of f(1)is
[tex]f(1)=-(1)^2+2(1)-15=-14[/tex]
The vertex of Function 2 is (1,-14). Therefore the maximum value of Function 2 is -14.
Since 1>-14, therefore Function __1__ has the larger maximum.
Solve by factoring: 8p2 - 64p = 0
75% of a number is 4.5 cm
Answer: 6 cm
Step-by-step explanation: 4.5 cm is 75/100
75/100=4.5/x
100*4.5=75*x
450=75x
divide both sides by 75
6=x
The number 4.5 is 75 percent of the number 6.
The given number is 4.5 cm.
Let 75% of x is 4.5 cm.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Here, 75% of x=4.5
[tex]\frac{75}{100} \times x=4.5[/tex]
[tex]\frac{75x}{100}=4.5[/tex]
[tex]75x=4.5\times100[/tex]
[tex]75x=450[/tex]
[tex]x=\frac{450}{75}[/tex]
[tex]x=6[/tex]
Therefore, the number 4.5 is 75 percent of the number 6.
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"Your question is incomplete, probably the complete question/missing part is:"
75% of what number is 4.5 cm.
A 100-foot ramp is tilted at a 45° angle. How high is the top of the ramp from the ground?
5(2x-8) i dont get how to do distributive prop on this
There are values of t so that the equation cos t= 5/3
impossible, the maximum value of either cos(t) or sin(t) is 1; look to the unit circle for proof
Urn A has balls numbered 1 through 6. Urn B has balls numbered 1 through 4. What is the probability that a 4 is drawn from A followed by a 2 from B?
The probability that a 4 is drawn from A followed by a 2 from B is 1/24
Further explanationThe probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation ( Arrangement )Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination ( Selection )Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
Urn A has balls numbered 1 through 6 → Total = 6 ballsThe probability of choosing a 4 ( 1 ball ) from Urn A is:
[tex]P(A) = \boxed{\frac{1}{6}}[/tex]
Urn B has balls numbered 1 through 4 → Total = 4 ballsThe probability of choosing a 2 ( 1 ball ) from Urn B is:
[tex]P(B) = \boxed {\frac{1}{4}}[/tex]
The probability that a 4 is drawn from A followed by a 2 from B is
[tex]P(A \cap B) = P(A) \times P(B)[/tex]
[tex]P(A \cap B) = \frac{1}{6} \times \frac{1}{4}[/tex]
[tex]P(A \cap B) = \boxed {\frac{1}{24}}[/tex]
Learn moreDifferent Birthdays : https://brainly.com/question/7567074Dependent or Independent Events : https://brainly.com/question/12029535Mutually exclusive : https://brainly.com/question/3464581Answer detailsGrade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
Help!!!!! how do i slove this equation