Answer:
a) The factored form of the function Hs= -16s2+96s is Hs = -16(s-3)(s-2).
b) The two factors in the factored form of the function, -16(s-3)(s-2), represent the maximum height of the baseball and the time at which the baseball reaches its maximum height. The first factor, -16, represents the maximum height of the baseball, since a negative value multiplied by the product of two positive values will always be negative. The second factor, (s-3)(s-2), represents the time at which the baseball reaches
or
a) Hs = (-16s + 48)(s - 2)
b) The factor (-16s + 48) represents the initial height of the baseball when it is hit, and the factor (s - 2) represents the time it takes for the baseball to reach its maximum height.
A company loses $75 as a result of a shipping delay. The owners of the company must share the loss equally. Write an expression for the earnings per person. Evaluate the expression.
Expression for the earnings per person = $75/n
What is loss?
The amount of loss on any commodity expressed as a percentage is referred to as the loss percentage. Additionally known as percentage loss. Any time a commodity's selling price is less than its cost price, we consider this to be a loss. The magnitude of this loss may be determined by calculating the difference between the cost price and the selling price. The loss percentage measures the loss as a proportion of the actual cost price.
Given: company loss=$75
no. of owners =n
The loss must be split evenly between the two business owners.
Therefore, we must split the sum of money in order to determine how much each individual receives.
=$75/n
Expression for the earnings per person = $75/numer of owners
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a pool can be filled by one pump in 50 minutes and by another pump in 60 minutes. a third pump can drain the pool in 75 minutes. if all 3 pumps go into operation at the same time, how long will it take to fill the pool?
In 42 6/7 minutes the pool will get filed when all 3 pumps work together.
Given,
Time taken by the pump 1 to fill a pool = 50 minutes
Time taken by pump 2 to fill the same pool = 60 minutes
The time taken by pump 3 to drain the pool = 75 minutes
When all the 3 pumps work together, we have to find the time taken to fill the pool;
Here,
In every minute,
Pump 1 fills 1/50 of pool
Pump 2 fills 1/60 of pool
Pump 3 drains 1/75 of pool
That is,
1/50 + 1/60 - 1/75 = 6/300 + 5/300 - 4/300 = 11 - 4 / 300 = 7/300
The time taken = 300/7 minutes = 42 6/7 minutes
Therefore,
When the 3 pumps work together, it will take 42 6/7 minutes to fill the pool.
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larry's lazertag park charges $50 flat fee for birthday partly rental and $5.50 per person. Sam has no more than $100 to spend on his birthday party. How many friends can he invite without going over his limit?
The maximum number of friends that he can invite without going over his limit is 9.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
As per the given,
Fixed fee = $50
Suppose the number of people is x.
Total fee = 50 + 5.50x
Total fee ≤ budget
50 + 5.50x ≤ 100
5.50x ≤ 50
x ≤ 9.09 thus, x = 9
Hence "The maximum number of friends that he can invite without going over his limit is 9".
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(PLUS 2) Instead suppose the contest always starts with $100 and adds $20 to the pot when people give wrong answers. How many people would have to guess incorrectly for the winner to get $1360? Show your work. (You'll need to know the 'starting value' and 'rate of change' Once you create the equation, substitute the 1360 into the correct position) pelt i
Answer:
63
Step-by-step explanation:
trial and error aint that hard
which represents the lowest degree of certainty? group of answer choices conclusion theory fact hypothesis
Theory is the correct answer, theory represents the lowest degree of certainty.
What is certainty?
The epistemic attribute of beliefs that one cannot rationally reject is certainty, often known as epistemic certainty or objective certainty. Epistemic certainty is commonly defined as a belief being certain if and only if the person holding it could not be wrong in holding it. Other popular definitions of certainty refer to the beliefs' incontrovertibility or describe certainty as a characteristic of those beliefs with the strongest foundation. Although certainty and knowledge are closely related, modern philosophers frequently treat knowledge as having less conditions than certainty.
The rest of the options given in the questions which are conclusion, fact, hypothesis are evidence based and they provides comparatively higher degree of certainty than theory.
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Line A contains the points (2, 6) and (4, 10). Line B contains the
points (-2, 3) and (3, 13).
1. Are the lines parallel? Explain your reasoning.
Answer:
It is not possible to determine whether the lines are parallel based on the information given. To determine whether two lines are parallel, we need to calculate the slope of each line and compare them. The slope is calculated as the change in the y-coordinate divided by the change in the x-coordinate, or (y2-y1)/(x2-x1). Since we only have the coordinates of the endpoints of the lines and not the equations of the lines, we cannot calculate the slope and therefore cannot determine whether the lines are parallel.
Answer: lines are parallel
Step-by-step explanation:
Lines are parallel if they have the same slope
[tex]\boxed {The\ slope\ m=\frac{y_2-y_1}{x_2-x_1} }[/tex]
1) (2,6) (4,10)
x₁=2 x₂=4 y₁=6 y₂=10
Hence,
[tex]\displaystyle\\m=\frac{10-6}{4-2} \\\\m=\frac{4}{2}\\\\m=2[/tex]
2) (-2,3) (3,13)
x₁=-2 x₂=3 y₁=3 y₂=13
Hence,
[tex]\displaystyle\\m_1=\frac{13-3}{3-(-2)} \\\\m_1=\frac{10}{3+2} \\\\m_1=\frac{10}{5}\\\\m_1=2[/tex]
m=m₁=2
Hence, lines are parallel
simplify any fractions……………
The probability that a bike is green given that it has road tyres is 2/3
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
The table of values
From the table of values, we have:
Number of bikes that are green and road tyres = 4
Number of bikes that are road tyres = 6
The probability is then calculated using the following formula
Probability = Number of bikes that are green and road tyres/Number of bikes that are road tyres
Substitute the known values in the above equation, so, we have the following representation
Probability = 4/6
Simplify
Probability = 2/3
Hence, the value of the probability is 2/3
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Find the value of x. A. Square root 3, B.3 square root 2 over 2
The value of x is 3√2/2.
What is a right-angled triangle?A triangle with one angle being a right angle is called a right-angled triangle.
Given a right-angled triangle, with both acute angles equal to 45°
Since, acute angles = 45°
Therefore, both the legs of the triangle are equal.
Applying Pythagoras theorem,
x²+x² = 3²
2x² = 9
x² = 9/2
x = 3/√2
Rationalizing the denominator,
x = 3√2/√2x√2
x = 3√2/2
Hence, The value of x is 3√2/2.
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Part B: Fill out the Problem-Solving boxes to talk yourself through the problem.
Two mountain bikers leave from the same parking lot and head in opposite directions on two different trials. The first rider goes 8km due East, then rides due south for 15km. The second rider goes 8km due West, then changes direction and rides 20 degrees west due North for 15km. (See the picture below.) Both riders have been traveling for 23km, but when they stopped, which one was further away from the parking lot?
Understand & Think (1 point): What is being asked in the problem? What do I know and what does it mean? What plan am I going to try?
Do/Answer (2 points): I will write out my response to the question, explaining my answer and what it means. I will explain why my answer makes sense.
Explanation of my answer why it makes sense:
PLEASE HELP AND TRY NOT TO MAKE IT SOUND SO COMPLICATED… THANKS AND MUCH APPRECIATED!!!
The first rider the displacement is, 17 km.
And the 2nd river the displacement is 20.22 km.
What is right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
It is asked in this problem is who's displacement is greater (not distance) it means that the shortest distance of starting and ending point with direction from start and end.
Here we have two triangle with two arm know for both.
So we have to find the 3rd arm for both triangle.
Now we have for a right triangle
a^2 + b^2 = c^2
For other triangle we know the cosine law of triangle is,
a^2 + b^2 - 2ab cosθ = c^2
θ is the opposite angle of c
For the first rider the displacement is,
c = [tex]c = \sqrt{a^2 + b^2} = \sqrt{8^2 + 15^2} = 17 km\\[/tex]
For the 2nd river the displacement is
[tex]c = \sqrt{a^2-b^2 -2abcosheta}[/tex], θ = 120°
[tex]c = \sqrt{8^2 + 15^2 - 2ab cos(120)} \\c = \sqrt{289 - 240cos(120)} \\c = \sqrt{289 - (-120)} \\c = \sqrt{289 + 120}\\ c = \sqrt{409} \\c = 20.22km[/tex]
Hence, the first rider the displacement is, 17 km.
And the 2nd river the displacement is 20.22 km.
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In triangle def, m∠d = (4x 15)°, m∠e = (5x 32)°, and m∠f = 70°. determine the degree measure of the exterior angle to ∠d. 137° 113° 67° 43°
The degree measure of the exterior angle triangle is ∠D = 137°.
What is Triangle ?Having three vertices and three angles that add up to 180 degrees, a triangle is a three-sided polygon.
given this, the angles D, E, and F in the triangle DEF are (4x + 15), (5x + 32), and 70 respectively.
The sum of the angles of a triangle is now 180°.
Therefore, we may write: m ∠D m∠ E m ∠F = 180
When all the numbers are substituted, we obtain the following results: (9x + 117 = 180) 9x
= 180 -117 (4x + 15) + (5x + 32) + 70
⇒ 9x = 63
⇒ x = 7
As a result, we obtain m∠ D = (4x + 15)°,
m∠ D = (4 x 7 + 15)°,
m ∠D = (28 + 15)°, and m∠ D = (43)°.
Furthermore, m∠ E = (5x + 32)°
m ∠E = (5 x 7 + 32)°
m ∠E = (35 + 32)°
m ∠E = 67°
Since, The measure of the exterior angle to ∠D = m ∠E + m ∠F
= 67° + 70
= 137°
Thus, The measure of the exterior angle ∠D will be 137°.
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Describe and correct the error in solving the
system of linear equations.
y = 3x -8
y = 3x - 12
The lines have the same slope. So, the system
has infinitely many solutions.
Answer:
it’s no solution
Step-by-step explanation:
PLS HELP 15 POINTS!!!!!!
15. What is the solution to the system of equations below?
y=4x+2
y=1/2x-5
A. (2,6)
B (6,2)
C. (-6,-2)
D. (-2,-6)
which suggests that failure to meet a higher-order need may trigger regression to an already fulfilled lower-order need.
According to ERG theory, frustration over not being able to satisfy a higher-order need may cause regression to a lower level.
What is ERG theory?ERG theory is a psychological theory put forth by Clayton Alderfer.
ERG concept, An individual will put more effort into the higher category once needs in the lower category are met. An individual will put more effort into the lower category if needs in the higher category are not met.
Maslow's hierarchy of needs was further developed by Alderfer by being categorised into his ERG theory (Existence, Relatedness and Growth). The necessity of meeting the essential material needs of people falls under the existence category. Concerned in the relatedness category is the desire to uphold significant interpersonal connections.
The desire for personal growth is addressed in the growth category. These include the self-actualization traits and the intrinsic component from Maslow's esteem category.
in a simple manner we define the three stages of ERG theory
1. Existence - what we need from a physiological point of view .
examples- a house , healthcare, etc.
2- Relatedness - our social needs.
examples - friendship, social connectivity, national identity, etc.
3-growth - Self-realization needs.
examples- feelings , success, failure ,etc.
Hence, ERG Theory suggests that failure to meet higher-order need may trigger regression to an already fulfilled lower-order need.
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A hallway has a length of 450 inches (in) and width of 80 inches (in). What are the
dimensions for the hallway in meters (m)? Round to the nearest tenth if necessary.
Answer:
2.5 feet = 30 inches.
Step-by-step explanation:
Let L = length not carpeted
L = 400/30
L = 13.3333333333
L = 13.33 inches
How do you find the range of a quadratic graph?
The range is all real integers bigger than or equal to the range's y-coordinate if a quadratic function opens up. All real integers less than or equal to the range's y-coordinate are in the range if a quadratic function opens downward.
In the given question we have to explain, how we can find the range of a quadratic graph.
Because it is the most fundamental quadratic function, all quadratic functions collectively can be referred to as a family, with this particular function serving as the parent (i.e., not transformed in any way). This function can be used to start broadly generalising the domains and ranges of quadratic functions.
The range is partly determined by the pivotal point, or vertex. The parabola's opening direction is the other. The range is all real integers bigger than or equal to the range's y-coordinate if a quadratic function opens up. All real integers less than or equal to the range's y-coordinate are in the range if a quadratic function opens downward.
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Write an equation of a line
passing through the point
(-6, -3) and perpendicular to JK
with J(-2, -7) and K(6, 5).
A) y = -2/3x – 4 the airport
B) y = -2/3x – 7 the library
C) y = 2/3x + 1 the park
D) y = 2/3x + 9 the zoo
E) y = -3/2x – 4 the police station
The equation of the line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5) is y = -2 / 3x - 7, so option B is correct.
What is line?
An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.
Given:
A line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5)
Calculate the slope of the line,
m = 5 - (-7) / 6 - (-)
m = 12 / 8
m = 3 / 2
The slope of a line perpendicular to JK, M = - 1 / 3 / 2 = -2 / 3
Calculate the equation of the line as shown below,
y - (-3) = -2 / 3[x - (-6)]
y + 3 = -2 / 3x - 4
y = -2 / 3x - 7
Therefore, the equation of the line passing through the point (-6, -3) and perpendicular to JK with J(-2, -7) and K(6, 5) is y = -2 / 3x - 7.
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What are the x- and y- coordinates of point e, which partitions the directed line segment from j to k into a ratio of 1:4? x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–13, –3) (–7, –1) (–5, 0) (17, 11)
Point E's coordinates are (-7, -1).
The formulas for our new x and y are provided to us. We must first establish our points 1 and 2 before applying this formula. Due to the fact that the issue was sole with the point E that divides the line segment "from J to K,"
the following formula: point 1 = point J = (x1, y1)
Points 2 and K are equal (x2, y2)
The partition segments JE and EK take up a certain amount of the original segment, as indicated by the variables m and n. Given that the ratio is 1:1, then
JE = m = 1
EK = n = 4
Consequently, using the above formulas to calculate for x and y:
x = [1 / (1 + 4)] (25 – (-15)) + (-15) (-15)
x = -7
y = [1 / (1 + 4)] (15 – (-5)) + (-5) (-5)
y = -1
Consequently, point E's coordinates are (-7, -1)
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What is the y-intercept of the line on the graph?
b=
Point form: ( , )
The y-intercept of the line on the graph is -60.
How to find y-intercept of a graph?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of a lineb = y-interceptTherefore, the y-intercept is the point where the graph intersects the y-axis. The y-intercept is the value of y when x = 0.
Therefore, on the graph the value of y when x is equals to zero is -60.
Hence,
y-intercept = -60
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Which of the following is an example of discrete data?
a.The volume of the pencil case.
b.The length of the pencil case.
c.The length of the pencil.
d.The number of pencils in a pencil case.
e,The time taken to close the pencil case.
An example of discrete data is the number of pencils in a pencil case. Option D
What is discrete data?Discrete data can be defined as a numerical type of data including concrete or whole numbers with fixed and specific data values determined by counting.
Some features of discrete data are;
They are finiteNumericCountableNon-negative integersExamples of discrete data are;
The number of customers The number of computers in an officeThe number of items bought per weekHence, the correct option is the number of pencils in a pencil case.
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A company find that it advertiing cot increaed from 72000 to 76680 in a year. What wa the rate of increae?
Using the basic percentage change rule, the answer is 6.5%.
What do you mean by percentage?In essence, percentages are fractions with a 100 as the denominator. In order to indicate that a number is a percentage, the percent symbol (%) is placed next to the number.
What is the formula to find percentage change?The required formula is:
[tex]Percentage = \frac {change}{inital} * 100[/tex]
initial=72000
final=76680
change=76680-72000
=4680
% change = 4680 / 72000 * 100
=6.5%
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what is the area of a parallelogram with a base of 8. meters and a height of 12 meters
Answer:
96 m²
Step-by-step explanation:
area = base × height
area = 8 m × 12 m
area = 96 m²
A group of students take a test. The group consists of 8 girls and 12 boys. The mean mark for the girls is 18. The mean mark for the boys is 16. 5. Calculate the mean mark for the whole group.
First, let's calculate the total number of marks for each group:
Girls: 8 students * 18 marks/student = 144 marksBoys: 12 students * 16 marks/student = 192 marksThen, we can calculate the mean mark for the whole group by adding up the total number of marks for each group and dividing by the total number of students:
(144 marks + 192 marks) / (8 students + 12 students) = 336 marks / 20 students = 16.8 marks/student
Therefore, the mean mark for the whole group is 16.8.
The mathematical mean is a measure of central tendency that is calculated by adding up all the values in a data set and dividing by the number of values in the set. It is also commonly known as the "average."
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Answer:
34.5
Step-by-step explanation:
If the speed limit is 50 miles per hour and a speeding ticket is issued for speeds of 10 miles per hour or more over the limit, for what angles should the trooper issue a ticket? The trooper should issue a ticket when the angle is equal to or less
If the speed of the vehicle is greater than or equal to 60 miles per hour, the angle will be greater than or equal to zero and the trooper should issue a ticket.
What is the distance?Distance is defined as the product of speed and time.
If the speed limit is 50 miles per hour and a speeding ticket is issued for speeds of 10 miles per hour or more over the limit, then the trooper should issue a ticket for any speed greater than 50 + 10 = 60 miles per hour.
In general, the speed of a vehicle is given by the formula v = d/t, where v is the speed, d is the distance traveled, and t is the time it takes to travel that distance.
The angle at which a speeding ticket should be issued is determined by the ratio of the speed of the vehicle to the speed limit. If the speed of the vehicle is greater than the speed limit, then the ratio of the speed of the vehicle to the speed limit will be greater than 1.
Therefore, the trooper should issue a ticket for any angle that is equal to or less than 1.
Alternatively, you could also say that the trooper should issue a ticket when the angle is greater than or equal to zero. Since any number divided by 1 is equal to the original number, this means that the angle will be equal to the speed of the vehicle in miles per hour.
Therefore, if the speed of the vehicle is greater than or equal to 60 miles per hour, the angle will be greater than or equal to zero and the trooper should issue a ticket.
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Find the least common multiple of 3, 8 and 12
The least common multiple(LCM) of 3, 8, and 12 is 24.
What is the least common multiple(LCM)?
The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.
We have,
3, 8 and 12
and least common multiple of 3, 8, and 12?
LCM of 3, 8, and 12 is the smallest number among all common multiples of 3, 8, and 12.
The smallest number that can be divisible by 3, 8, and 12 exactly is the LCM.
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, ….
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, …..
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, …..
Hence, the least common multiple(LCM) of 3, 8, and 12 is 24.
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PLEASE HELPPPPPPPPPPPPP
Answer:
0.15- Strong Association
-0.21 - Weak Association
0.71- Strong Association
0.55-Moderate Association
A cramers V value of O = No relationship, 0.2 or less = Weak relationship, from 0.21 to 0.3 = moderate, and above 0.3 = Strong relationship.
Someone help with Literal equations
Solve for R
a=nr2h
[tex]\displaystyle\\Answer:\ r=\sqrt{\frac{a}{nh} }[/tex]
Step-by-step explanation:
a=nr^2h
Divide both parts of the equation by nh:
[tex]\displaystyle\\\frac{a}{nh} =r^2\\[/tex]
Extract the square root of both parts of the equation:
[tex]\displaystyle\\\sqrt{\frac{a}{nh} } =\sqrt{r^2} \\\\\sqrt{\frac{a}{nh} } =r\\\\Thus,\ r=\sqrt{\frac{a}{nh} }[/tex]
The equation y=34x−2 is the slope-intercept form of which equation?
Answer:
The equation y = 34x - 2 is the slope-intercept form of the equation y = 34x + b, where b is the y-intercept, which is the point where the line crosses the y-axis. The value of b in this case is -2, so the equation can be written as y = 34x - 2. This form of the equation makes it easy to find the slope (which is 34 in this case) and the y-intercept (which is -2 in this case) of the line.
What properties are whole numbers closed under?
All the properties of whole numbers are closed under addition and multiplication.
Whole numbers are a set of natural numbers including zero, but the set does not include fractions, decimals, and negative integers. The set of whole numbers is represented by ‘W’={0, 1, 2, 3, 4, 5, …...}
To check if the whole numbers are closed under subtraction or not we will check out the four properties namely, the closure property, the commutative property, the associative property, and the distributive property.
Let us consider each property one by one -
1. The closure property-
let's take two whole numbers say 5 and 3.
now, 5+3=8
and 5 × 3 =15
Thus, whole numbers are closed under addition and multiplication by closure property.
2. The commutative property-
let's take two whole numbers say 5 and 3.
now, 5+3=8 and 3+5=8,
hence, we get 3+5 = 5+3.
Also, 5 × 3 =15 and 3 × 5 =15
hence, we get 5 × 3 = 3 × 5
Thus, whole numbers are closed under addition and multiplication by commutative property.
3. The associative property-
let's take three whole numbers say 5, 3, and 1.
now (5+3)+1 = 9 and 5+(3+1)= 9
hence, we get (5+3)+1 = 5+(3+1).
Also, (5×3)×1 = 15 and 5×(3×1)= 15
hence, we get (5×3)×1 = 5×(3×1).
Thus, whole numbers are closed under addition and multiplication by associative property.
4. The distributive property-
let's take three whole numbers say 1, 6, and 5.
now, 1 × ( 6 + 5 ) = 1 + 6 – 1 × 5 = 1
and 1 × ( 6 – 5 ) = 1 × 1 = 1
Hence, 1=1.
Also, 1 × (6×5)= (1 × 6) × (1 ×5) = 6 × 5 =30
and 1 × (6×5) = 1 × 30 =30
hence, we get 30=30.
Thus, whole numbers are closed under addition and multiplication by distributive property.
Hence, we can conclude that all the properties of whole numbers are closed under addition and multiplication.
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The complete question is-
What properties are whole numbers closed under addition and multiplication?
Andres needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 5. 25 hours and charged him $116 for parts. The total was $719. 75. Which equation could be used to determine cc, the cost of labor per hour?.
Answer:
5.25c + 116 = 719.75
Step-by-step explanation:
Let c = cost of labor per hour
He worked for 5.25 hours, so the part of the cost due to the hourly rate is
5.25c
You must the add the cost of the parts.
5.25c + 116
Now you set the total cost expression equal to the actual total cost.
5.25c + 116 = 719.75
What is the solution to the compound inequality in interval notation?
4(z +1) > -4 or 2z - 4 < -10
Answer:
(-infinity, -2) ∪ (-3, infinity).
Step-by-step explanation:
To solve this compound inequality, we need to first solve each inequality separately. For the first inequality, 4(z+1) > -4, we can distribute the 4 to get 4z + 4 > -4. Then, we can subtract 4 from both sides to get 4z > -8. Finally, we can divide both sides by 4 to get z > -2.
For the second inequality, 2z - 4 < -10, we can add 4 to both sides to get 2z < -6. Then, we can divide both sides by 2 to get z < -3.
Now that we have solved both inequalities, we need to consider their intersection. Since the inequalities are joined by the "or" operator, the solution is the union of the solutions to each inequality. In interval notation, this is represented as the union of the intervals (-infinity, -2) and (-3, infinity).
Therefore, the solution to the compound inequality in interval notation is (-infinity, -2) ∪ (-3, infinity).