If a ball is thrown in the air with a velocity of 52 ft/s, its height in feet t seconds later is given by y = 52t − 16t2.
Then the average velocity for the time period beginning when t = 2 and lasting for 0.5s,0.1s,0.05s,0.01s will be -20,-13.6,-12.8,-12.16 respectively
y=y(t)=52t-16t²
At t=2, y=52(2)-16(2)² =40
The average velocity between time 2 and 2+h is Vav. = [tex]\frac{y(2+h)-y(2)}{(2+h)-2}[/tex]
=[tex]\frac{-12h-16h^2}{h}[/tex]
= -12-16h
Now finding the average velocity for the period beginning when t = 3 and lasting-
(i)0.5 s is (2,2.5) , Vav. = -20.0 ft/s
(ii)0.1 s is (2,2.1), Vav = -13.6 ft/s
(iii) 0.05s is (2,2.05), Vav. = -12.8ft/s
(iv) 0.01s is (2,2.01) Vav.=-12.16ft/s
And at t=2 , h will approaches to zero so Vav= -12ft/s
Therefore, If a ball is thrown in the air with a velocity of 52 ft/s, its height in feet t seconds later is given by y = 52t − 16t2.
Then the average velocity for the time period beginning when t = 2 and lasting for 0.5s,0.1s,0.05s,0.01s will be -20,-13.6,-12.8,-12.16 respectively.
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Question 7
The cone will fit in 4 times and the volume of the cone is 535.89 in³
Volume of a ConeTo solve this problem, we have to find the volume of the cone and the volume of the sphere.
The formula of volume of a cone is given as;
V = 1/3πr²h
v = volume of the coner = radius of the coneh = height of the coneWe need to calculate the volume of the sphere which is given as
V = 4/3 πr³
The volume of the ball = 4/3 * 3.14 * 8³ = 2143.57in³
The volume of the cone = 1/3 * 3.14 * 8² * 8 = 535.89 in³
The number of times it will fit into will be 2143.57 / 535.89 = 4
It will fit in 4 times
b)
The volume of the cone is 535.89in³
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A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 24 feet across at its opening and 2 feet deep at its center, where should the receiver be placed?
Find the equation of the parabola?
How far above the vertex should the receiver be placed?
Equation of parabola: y =ax² and receiver should be placed 18 feet above vertex.
Explanation:
Considering satellite dish as parabola we can have vertex as origin and concave upward.
So, equation of parabola will be justifying structure of satellite dish i.e
y = ax² -------(1)
Two points other than (0,0) are (-12,2) and (12,2), unit being feet.
This points will satisfy equation of parabola, substituting them in equation 1, we will calculate the value of constant 'a'.
a = [tex]\frac{2}{12^{2} }[/tex]
[tex]\frac{2}{2*6*12}\\ =\frac{1}{72}[/tex]
Substituting value of a = 1/72 in equation 1 we get
72y = x²
As receiver need to be located at focus, so it will be places at a distance of 'p' above the vertex
4p = 72
Dividing both sides by 4, we get
p = 18 feet
So, receiver will be placed at a distance of 18 feet above vertex.
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Solve the system.
2x + y + 3z = 20
X + 2y - z = -11
3x - 2z = -3
Enter your answer as an ordered triple.
The solution to the system, as an ordered triple is: (3, -4, 6).
How to Solve a System of Equations?To solve the following given system of equations:
2x + y + 3z = 20 --> eqn. 1
x + 2y - z = -11 --> eqn. 2
3x - 2z = -3 --> eqn. 3
Multiply equation 1 by 2 to get eqn. 4:
4x + 2y + 6z = 40 --> eqn. 4
Subtract eqn. 4 from eqn. 2:
x + 2y - z = -11 --> eqn. 2
4x + 2y + 6z = 40 --> eqn. 4
-3x - 7z = -51 --> eqn. 5
Add equations 3 and 5 together:
3x - 2z = -3 --> eqn. 3
-3x - 7z = -51 --> eqn. 5
-9z = -54
z = -54/-9
z = 6
Substitute the value of z into equation 5:
-3x - 7(6) = -51 --> eqn. 5
-3x - 42 = -51
-3x = -51 + 42
-3x = -9
-3x/-3 = -9/-3
x = 3
Find the value of y by substituting the values of x and z into equation 1:
2(3) + y + 3(6) = 20 --> eqn. 1
6 + y + 18 = 20
24 + y = 20
y = 20 - 24
y = -4
The solution as an ordered triple is: (3, -4, 6).
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Steve is m years old. His brother, Jack, is n years older than Steve. How old will Jack be in 2 years?
Answer:
n+m+2 years
Step-by-step explanation:
m=Steve's age.
J=Jack's age.
n=Age difference between Steve and Jack
J=n+m
J+2=n+m+2 years
as the class finishes what do you see as the most useful tools or knowledge you will be able to use in the professional world? part two: elaborate on the business research project and what you learned about your topic and about the research process. compose two fully-developed paragraphs that address each area to the fullest.
The business research project was a valuable experience that taught me about the importance of research in the business world and the various methods and techniques that can be used to conduct effective research.
One of the most useful tools or knowledge that I will be able to use in the professional world after completing this class is the ability to analyze and interpret data. This includes the ability to perform statistical analysis and draw meaningful conclusions from data sets. This skill is crucial in today's business world, as data-driven decision-making is becoming increasingly important in all industries.
In the business research project, I learned about the importance of conducting thorough research in order to make informed decisions. I also learned about the various methods of conducting research, such as primary and secondary research, and the pros and cons of each method. I also learned about the importance of using reliable sources and properly citing sources in order to ensure the credibility of my research.
It also helped me to develop my analytical skills and the ability to interpret data in order to draw meaningful conclusions. These skills will be essential in my future professional career as I work to make informed decisions and solve complex business problems.
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Generaly speaking, the amount of gun powder particles found around a bullet hole is ____ to the distance from which the weapon was fired:
The amount of gun powder particles found around a bullet hole is directly related to the distance from which the weapon was fired.
Which two forces are acting on a bullet?
Two major forces are acting on the bullet ,the forward force of the gunshot and the downward force of gravity. The first force is called aerodynamics and the other force is called gravitational.
What does the distribution of gun powder residue around the bullet hole help to determine?
The residue exit the muzzle in a cone shaped and can land on the target objects. The size and density of the residue on the object can vary with distance allowing the fire man examiner to determine proximity of shooter to the target killing when gun is fired.
Therefore, the amount of gun powder particles found around a bullet is directly related to the distance when gun was fired.
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Calculate and then write the reciprocal of your answer.
2/43 of the difference of 3 2/15 and 2 5/12
The reciprocal of 2/43 of the difference between 3 2/15 and 2 5/12 is 30.
Here, we have to subtract 2 mixed fractions i.e
=> (3 2/15) - (2 5/12)
which when converted to a proper fraction is equal to,
=> (47/15) - (29/12)
= 43/60
∵ (3 2/15) - (2 5/12) = 43/60
now, 2/43 of the difference of 3 2/15 and 2 5/12,
=> (2/43) × (43/60) = 1/30............(i)
taking the reciprocal of the value obtained above,
∴ reciprocal of 1/30 = 30.
Thus, The reciprocal of 2/43 of the difference between 3 2/15 and 2 5/12 is 30.
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Please help with attached linear function question. Thank you!!
The graph of cubic equations, a to d and the associated cubic equations are as follows;
Equation (B) ⇒ Graph a
Equation (C) ⇒ Graph b
Equation (D) ⇒ Graph c
Equation (A) ⇒ Graph d
What is a cubic equation?A cubic equation that has only one variable is an equation of the form a·x³ + b·x² + c·x + d, where a ≠ 0.
The evaluation of the graphs are as follows;
Graph a
The y-intercept of the graph a, is 1, and the x-intercept, which is a solution of the equation is x = -1,
Therefore, when x = 0, y = 1, and when y = 0, x = -1
The function in graph a represents the translation of the parent function, y = x³, one unit, upwards, which corresponds with the function;
y = x³ + 1
Therefore, graph a corresponds to cubic equation (B) y = x³ + 1
Graph b
The y-intercept is one (1), and the turning point is at the point x = -1, which represents a shift of one unit to the left, and which can be obtained by the equation; y = (x + 1)³
Therefore, graph b corresponds with the cubic equation (C) y = (x + 1)³
Graph c
The turning point of the graph and the y-intercept is shifted one unit down, which corresponds with the equation; (D) y = x³ - 1
Graph d
The turning point is shifted 1 unit to the right and is located on the x-axis, The y-intercept is located at the point y = 1, therefore, the graph corresponds with the equation y = (x - 1)³
Graph d corresponds to equation (A), y = (x - 1)³
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standard form of (2 ten thousands 7 thousands) divided by 10
Answer:
2,700
Step-by-step explanation:
10,000x2=20,000+7,000=27,000÷10=2,700
Which figure has four sides that are the same length
HELP PLEASE ASAP!!!
The entire graph of the function g is shown in the figure below. Write the domain and range of g as intervals or unions of intervals.
Answer:
D= [-4,-1) U (2,4)
R = [-3,5)
The base of a solid is bounded by the graphs of the given equations. The cross section of the solid taken perpendicular to the y- axis is a square. Write, butt do not evaluate, an integral expression that gives the volume of the solid where
y=x,y=2,x=6
An integral expression that provides the solid's volume at the points y=x, y=2, and x=6 is [tex]\int\limits^{6}_{2} {y^3} \, dy[/tex]
How many areas of space are filled by an object is determined by its volume. The amount of unit cubes required to completely fill the solid serves as the measurement. By counting the solid's unit cubes, the answer can be determined.
A three-dimensional object's volume is typically thought of as its ability to accommodate matter.
According to the question,
The cross section of the solid taken perpendicular to the y- axis is a square.
Solid base equation: y=x, y=2, x=6
Square Volume = (Side3)
Since y = x in the equation and y = 2 as a result, x must equal 2.
So , Limit of x varies from 2 to 6
Volume of solid is [tex]\int\limits^{6}_{2} {y^3} \, dy[/tex]
Hence , , an integral expression that gives the volume of the solid is [tex]\int\limits^{6}_{2} {y^3} \, dy[/tex]
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the model that includes as predictors all independent variables but no quadratic or interaction terms.
When each independent variable is changed by one unit, use linear regression to get the mean change in the dependent variable. Polynomials can be used to simulate curvature as well as to add interaction effects.
An entire second order model is what?
The x1 and x2 linear terms, the x12 and x22 second-degree terms, and the x1x2 interaction term make up the entire second degree polynomial model. As could be used to represent the estimated model.
Which kind of model would you apply to discover the relationship between the dependent and independent variables?
Considering a one-unit change in each independent variable, use linear regression to determine the mean change in a dependent variable. To represent curvature and take interaction effects into account, you may also employ polynomials.
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The complete question is "Consider a regression analysis with three independent variables x1,x2, and x3. Give the equation for the following regression models: a. The model that includes as predictors all independent variables but no quadratic or interaction terms. b. The model that includes as predictors all independent variables and all quadratic terms. c. All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term. d. The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms (the full quadratic model)."
What is the measure of angle I? (number only)
If H is
102°
Answer:<I=78
Step-by-step explanation:
<1 and 102 are supplementary angles so they add to 180 degrees
<1 + 102 = 180
Subtract 102 from each side
<1 + 102 -102 = 180-102
<1 = 78
What is the slope of the line that passes through the points (-1, 2) and (-4, 3)? i need this now
-3
3
1/3
-1/3
Answer:
m = -1/3
Step-by-step explanation:
(-1, 2) and (-4, 3)
m = 3-2/-4+1
m = 1/-3
m = -1/3
finding missing angle of 32 and 17 with trigonometry
missing angle of 28 and 21 with trigonometry
Answer:
Step-by-step explanation:
as suggested, use SOH CAH TOA
we are given the H and O and want an angle
use SOH, b/c it's got the two given pieces of info
Sin(∅) = Opp / Hyp
Sin(x) = 21 / 28
arcSin ( Sin(x)) = arcSin(21/28)
x = 48.59°
what are the first six terms for a₁ = -9, d=8?
a₁ = -9
a₂ = -9 + (2 - 1) * 8 = -9 + 8 = -1
a₃ = -9 + (3 - 1) * 8 = -9 + 16 = 7
a₄ = -9 + (4 - 1) * 8 = -9 + 24 = 15
a₅ = -9 + (5 - 1) * 8 = -9 + 32 = 23
a₆ = -9 + (6 - 1) * 8 = -9 + 40 = 31
4. *
This pattern of squares continues. Which equation below relates the number of squares, n, in a picture to the size number, s ?
Size 1
Size 2
a) n=s+4
b) n=4 s
c) n=4 s+1
d) s=4 n
A
B
c
D
The required equation that following the pattern is n = 4s+1. So the option c is correct.
In the given question, we have to choose which equation below relates the number of squares, n, in a picture to the size number, s.
The given options are:
a) n = s+4
b) n = 4s
c) n = 4s+1
d) s = 4n
We find the pattern we firstly observe the given diagram closely.
As we can see that in first diagram have 5 blocks.
In second diagram have 9 blocks.
In third diagram have 13 blocks.
So, if the number of squares, represent by n, in a picture and the size number, represented by s, so the required equation that following the pattern is n = 4s+1. So the option c is correct.
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Corresponding angles formed by two parallel lines intersected by a transversal are always:
complementary.
congruent.
acute.
obtuse.
supplementary
Answer:
Congruent
Step-by-step explanation:
If you slide the angle down the transversal, it would land perfectly on top of the corresponding angel and you would be able to see that they are congruent.
Read the following prompt and type your response in the space provided.
Sarah has a $30 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card have still have a balance of more than $18?
Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.
Answer:
She will have a balance of more than $18 for up to 6 days
Step-by-step explanation:
Start with $30.
Each day, x, subtract $1.99 from $30.
30 - 1.99x
The amount must be greater than $18.
30 - 1.99x > 18
Subtract 30 from both sides.
-1.99x > -12
Divide both sides by -1.99. Remember than when you multiply or divide both sides of an inequality by a negative number, the inequality sign changes direction.
-1.99x/(-1.99) < -12/(-1.99)
x < 6.03
The number of days must be less than 6.03. Since we deal with whole days, she will have a balance of more than $18 for up to 6 days.
Carli is comparing two phone companies. Big Phone Company charges $0.39 for the connection fee and $0.03 per minute. Little Phone Company charges $0.25 for the connection fee and $0.07 per minute. Which system of equations could be used to determine the total cost, y, for using x minutes?
Answer:
Step-by-step explanation:
I also need help.
Kyra is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve large rooms that can hold 4 people, and small rooms that can hold 3 people. Kyra reserved twice as many large rooms as small rooms, which altogether can accommodate 77 guests. Determine the number of small rooms reserved and the number of large rooms reserved.
Answer:
19 small room and 25 big room
Step-by-step explanation:
3x+5y = 4
Constant?
Change?
4x2 + y = 4
Constant?
Change?
6x + 1 = y
Constant?
Change?
Answer:
Step-by-step explanation:
Question 6 A test of hypothesis was performed to determine, at 5% level of significance, if the majority of the engineering graduates pass the PE exam in their first try. If the computed value of the test statistic Z based on the sample information is z = 2.10, then the p-value for this test is: 0.00895 O 0.05 0.9821 None of these O 0.0179 N • Previous Not saved S
The p-value for the test is 0.9821.
What is hypothesis?
A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters through hypothesis testing.
What is z-score?
You can plot a z-score on a normal distribution curve. The range of Z-scores ranges from -3 standard deviations (which would be on the far left of the normal distribution curve) to +3 standard deviations (which would fall to the far right of the normal distribution curve). You must be aware of the mean and population standard deviation in order to use a z-score.
Given that the test statistic Z based on the sample information is z = 2.10.
z = 2.1 + 0.00
From the z-score table the value of p is 0.9821.
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Question 7
The cone would fit into the beachball two times, and has a volume of 134 in^3. Answers required are:
Blank 1 - two
Blank 2 - 134 in^3.
A beachball has the shape of a sphere, so that its volume can be determined by;
volume of a sphere = 4/3 [tex]\pi r^{3}[/tex]
where r is the radius of the sphere.
Given that the diameter of the beachball is 8 inches, then;
its radius = 8/ 2
= 4 inches
volume of beachball = 4/3 x 22/7 x 4^3
= 268.19 cubic in.
The volume of a cone can be determined by;
volume of a cone = 1/3 [tex]\pi r^{2} h[/tex]
where r is its radius, and h is its height.
Given a cone of radius 4 inches and height 8 inches, then;
its volume = 1/3 x 22/7 x 4^2 x 8
= 134.1cubic inches
Thus,
268.19/ 134.10 = 1.999993
≅ 2.0
Thus the cone would fit into the beachball twice, and its volume is 134.10 in^3.
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PLEASE HELP WILL GIVE 100 POINTS
Answer:
72y
Step-by-step explanation:
Perfect square monomials are in the form:
[tex]x^2+bx+\left(\dfrac{b}{2}\right)^2[/tex]
They factor as:
[tex]\left(x + \dfrac{b}{2}\right)^2[/tex]
To find the middle term of this polynomial, first factor 16 out of the expression.
[tex]16(y^2 \: + \: ?+5.0625)[/tex]
We know that the middle term will be in the form [tex]by[/tex], and the last term will be in the form [tex]\left(\dfrac{b}{2}\right)^2[/tex]. Using this information, we can solve for b.
[tex]5.0625 = \left(\dfrac{b}{2}\right)^2[/tex]
[tex]\sqrt{5.0625} = \dfrac{b}{2}\right[/tex]
[tex]4.5 = b[/tex]
Then, we can substitute that into the term [tex]by[/tex].
[tex]16(y^2 + 4.5y+5.0625)[/tex]
Finally, distribute the 16 and then take the middle term as the answer.
[tex]16y^2 + 72y+81[/tex]
72y
Answer:
72y or -72y-----------------------------
We are given a binomial and need to add a monomial to make it a perfect square.
Recall the identities for a square of a sum or difference of two numbers:
(a ± b)² = a² ± 2ab + b²Analyze the given and compare with the identity above:
16y² + ... + 81Here 16y² = (4y)² and 81 = 9², so a = 4y and b = 9.To complete the square we need to add ± 2ab, which is:
± 2ab = ± 2(4y*9) = ± 72yBy adding this we get:
16y² + 72y + 81 = (4y + 9)²or
16y² + (-72y) + 81 = (4y - 9)²Ian's car can go 165 miles on 5 gallons of gas. During a drive last weekend, Ian used 6 gallons of gas. How far did he drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas he used.
The distance that Ian can drive is 198 miles.
How far did Ian drive?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Here, Ian's car can go 165 miles on 5 gallons of gas. The mile per gallon will be:
= 165 / 5
= 33 miles per gallon.
Therefore, the miles in 6 gallons will be:
= 33 × 6
= 198 miles.
The distance is 198 miles.
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Two researchers are gathering data on hours of video games played by school-aged children and young adults. They each randomly sample different groups of 150 students from the same school. They collect the following data.
Researcher A
Hours Played per Week Frequency Relative Frequency Cumulative Relative Frequency
0-2 26 0.17 0.17
2-4 30 0.20 0.37
4-6 49 0.33 0.70
6-8 25 0.17 0.87
8-10 12 0.08 0.95
10-12 8 0.05 1
Researcher B
Hours Played per Week Frequency Relative Frequency Cumulative Relative Frequency
0-2 48 0.32 0.32
2-4 51 0.34 0.66
4-6 24 0.16 0.82
6-8 12 0.08 0.90
8-10 11 0.07 0.97
10-12 4 0.03 1
Give a reason why the data may differ.
A) The researchers are studying different statistics, so there will be some variation in the data.
B) The researchers are studying different parameters, so there will be some variation in the data.
C) The researchers are studying the same statistic, so there will be some variation in the data.
D) The researchers are studying different samples, so there will be some variation in the data.
E) The researchers are studying the same population, so there will be some variation in the data.
The reason for data variation is that the researchers are studying different samples, so there will be some variation in the data.
What is meant by data?In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.
Write types of data.Qualitative, quantitative, discrete, continuous, primary and secondary are the types of data.
Since researches choose same school but group of 150 people is randomly chosen and different therefore, the reason for data variation is that the researchers are studying different samples, so there will be some variation in the data.
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Find the derivative of f(x) = 3x² + 2x at 3. That is, find f '(3).
Answer:
20
Step-by-step explanation:
To find the derivative of f(x) = 3x² + 2x at x = 3, we can use the power rule:
f'(x) = 2*3x + 2
When x = 3, the derivative of f(x) is:
f'(3) = 2*3(3) + 2
f'(3) = 18 + 2
f'(3) = 20
Therefore, the derivative of f(x) = 3x² + 2x at x = 3 is f'(3) = 20.