Answer:
1/8 or 0.125
Step-by-step explanation:
1/2×1/8
multiply the numerators 1×1=1 and multiply the denominators 2×4=8
Final answer =1/8 or 0.125
Please help this is AP calculus. Please answer all parts due in 2 hours
a) The velocity of the particle is described by v(t) = - 3 · t² + 12 · t - 9.
b) The particle is at rest when t = 1 s. and t = 3 s.
c) The particle changes its direction when t = 1 s. and t = 3 s.
d) The particle is moving right when 0 s < t < 1 s and t > 3 s and left when 1 s < t < 3 s.
e) The acceleration of the particle is described by a(t) = a(t) = - 6 · t + 12.
f) The velocity increases at t = 1 s.
g) The particle has a total distance of 54 meters.
How to analyze the kinematics of a particle
In the statement we find the function of a particle that describes its position (y), measured in meters, in time (t), in seconds. Herein we shall analyze the function to determine all important features.
a) The velocity of the particle (v), in meters per second, is the first derivative of the function position:
v(t) = - 3 · t² + 12 · t - 9
b) The particle is at rest when v(t) = 0. Now we proceed to determine the roots of the resulting polynomial:
- 3 · t² + 12 · t - 9 = 0
t = 3 s. or t = 1 s.
c) The particle changes its direction when v(t) = 0. Then, this change happens in t = 1 s and t = 3 s.
d) The particle is moving right when v(t) > 0, then:
(t - 1) · (t - 3) > 0
There are two possible intervals: (i) 0 s < t < 1 s, (ii) t > 3 s. The particle is moving left when 1 s < t < 3 s.
e) The acceleration is the second derivative of function position, thus:
a(t) = - 6 · t + 12
f) The velocity increases when a(t) > 0. Then, the acceleration at t = 1 s is:
a(1) = - 6 · 1 + 12
a(1) = 6
The velocity is increasing at t = 1 s.
g) The total distance (s), in meters, traveled is determined by the following expression:
s = |x(1) - x(0)| + |x(3) - x(1)| + |x(6) - x(3)|
s = |7 - 11| + |11 - 7| + |- 43 - 11|
s = |- 4| + |4| + |- 54|
s = 54
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The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 274 people entered the park, and the admission fees collected totaled 836.00 dollars. How many adults were admitted?
a. 209
b.170
c.104
Therefore in this question the solution of particular equation is 108 children and 175 adults in the amusement park on that particular day.
What is Equation ?When two expressions' values are set to be equal by a mathematical statement, that statement is known as an equation. To put it another way, it is a mathematical expression that means "this is equivalent to that." An equal sign, a mathematical expression, and a mathematical expression can all be seen on the left side of the symbol. The right ride of the equation frequently contains zero.
Let's first configure our system by giving x and y meaningful definitions. Let x be the total number of kids and y be the total number of adults.
Children cost $1.50, while adults cost $4.00. The number of kids, x, is multiplied by 1.5 to determine how much money a group of kids will cost. The 1.5x symbol stands for this. We will use 4y for adults, who must pay $4 to enter. On the specified day, $862 in total revenue was earned. We must add 1.5x and 4y to get at this sum.
1.5x + 4y = 862 equation required
Second equation: The total number of individuals present on the day is 283. X and Y, or the number of children and adults, must be added together to arrive at this figure.
x + y = 283
System of equations:
1.5x + 4y = 862
x + y = 283
Thus,
x + y = 283
y = 283 - x
Substitute y = 283 - x
862=1.5x + 4 (283 - x)
1.5x + 1132 - 4x = 862
1132 - 2.5x = 862
-2.5x = -270
x = 108
Substitute x =108 back into y = 283 - x
y = 283 - 108 = 175
Therefore there were 108 children and 175 adults in the amusement park on that particular day.
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which inequality is less than the quadratic function with zero -7 and 1 and includes the point (2,27/2) on the boundary?
The second inequality, y < (3/2)x² + 9x -21/2, is less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).
What is a quadratic equation?The equation of the form ax² + bx +c is known as a quadratic equation.
Given that, the zeros of the quadratic function are -7 and 1 and include the point (2,27/2).
Substitute x = 1 into the given inequality to check whether any of them becomes less than 0 or not:
From the first inequality:
y < -3/2 + 9 + 21/2
y < 18
From the second inequality:
y < 3/2 + 9 -21/2
y < 0
Since the inequality is less than 0, it is also less than the quadratic function at x = 1.
Similarly, checking the third inequality also gives y < 0, but the fourth doesn't.
Now, from the second and the third inequality, check which one is less than 27/2 for x = 2:
From the second inequality:
y < 6 + 18 -21/2
y < 27/2
From the third inequality:
y < -6-9+21/2
y < -27/2
Since the second inequality, y < (3/2)x² + 9x -21/2, is less than 0 at x =1 and less than 27/2 at x=2, it is also less than the quadratic function whose zeros are -7 and 1 and includes the point (2,27/2).
Hence, the second inequality, y < (3/2)x² + 9x -21/2, is less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).
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Answer:
it’s B took the test
Step-by-step explanation:
Question Divide. 27÷655 Enter your answer by filling in the boxes. R
100 points and FREE BRAINLYEST IF YOU ANSWER WRONG I WILL ASK A ADIMIN TO DELETE YOUR ANSWER
Answer: 24. The remainder is 7
Step-by-step explanation:
Which is a strict inequality?
A. y>4
B. y≤4x+2
C. y≥x
D. y=−8x+3
The option that is a strict inequality is A. y>4
How can you tell if an inequality is strict?It should be noted that inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.
Inequalities involving < or ">" are considered "strict inequalities," whereas those involving "" or "" are not. If you "switch" the two sides of an inequality, you must then reverse the inequality symbol's direction. For example, because 4 5 is true, it follows that 5 > 4.
In conclusion, the correct option is A.
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Find the slope Y intercept in the equation for the data in the table and in the graph
Answer:
slope 6
y intercept 4
y = 6x + 4
Step-by-step explanation:
The slope is the change in y over the change in x.
Look at he two points (0,4) and (1,10)
The y started at 4 and went up to 10. That is a distance of 6.
AT the same time, the x changes from 0 tp 1 (0,4) (1,10). That is a distance of 1.
6/1 = 6
The y intercept is where the line crosses the y axis. It crosses at (0,4). 4 is the y intercept
y = mx + b Put the slope is for m and the y intercept for b
y = 6x + 4
A street light is mounted at the top of a 6-meter-tall pole. A man 2 m tall walks away from the pole with a speed of 1.4 m/s along a straight path. How fast (in m/s) is the tip of his shadow moving when he is 15 m from the pole?
2.1m/s is the tip of his shadow moving when he is 15 m from the pole
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole. i assume the man and pole are standing straight up, which means the 2 triangles are similar.
(y-x)/y=2/6
(y-x)/y=1/3
Apply cross multiplication
3(y-x)=y
3y-3x=y
2y=3x
y=3/2x
differentiate both sides with respect to t or time.
dy/dt=3/2dx/dt
By given dx/dt=1.4m/s
dy/dt=3/2×1.4
dy/dt=2.1m/s
Hence, 2.1m/s is the tip of his shadow moving when he is 15 m from the pole
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which postulate
ASA
SSS
AAS
HL
Answer:
asa
Step-by-step explanation:
there Is angle
there is side
there is angle but not shown
Help me pls i need help
Answer:
Step-by-step explanation:
oh wow
[tex]\frac{1}{10} +\frac{7}{10}[/tex]
Answer given in the screenshot below. ↓
determine the sum of all the multiples of the first integer from the last problem or the second integer from the last problem - below 1000
The total of all multiples of either the first or second integer from the previous issue that are below 1000 will be 233168.
What is multiples of integer?Manifold is the fundamental definition of multiplicity. A multiple in mathematics refers to the outcome of multiplying two numbers together. In mathematics, multiples are the results of multiplying an integer by a given number. A number that is produced by multiplying a given integer by a natural number is referred to as a multiple of that number. The factors of 20, for instance, are 1, 2, 4, 5, 10, and 20. The multiples of 20 include, for instance, 20, 40, 60, 80, 100, etc.
Here,
The statement of the problem is to sum the multiples of 3 and 5 below 1000, not up to and equal 1000.
The equation is attached in image,
166833+99500−33165=233168
The sum of all the multiples of the first integer from the last problem or the second integer from the last problem - below 1000 will be 233168.
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PLEASE HELPED I"M TIMED I WILL GIVE BRAINLIST
Answer:
Below
Step-by-step explanation:
Angle 2 or angle HFE
Vertex is F
GF and FE are the sides of angle 1
How much simple interest is made on an investment of $800 for 7 years at 6%
Answer:
$1,136
Step-by-step explanation:
The simple interest equation is A = P(1 + rt)Use the following function rule to find f(11).
f(x)=12|x+8|
f(11)=____
Answer:
f(11) = 228
Step-by-step explanation:
Solve for a
2x-2=-3x+13
X =
To solve for x, we need to isolate x on one side of the equation. To do this, we can first move all the terms that do not contain x to the right side of the equation by adding 3x and 2 to both sides:
2x - 2 + 3x + 2 = -3x + 13 + 3x + 2
5x = -3x + 15
8x = 15
Dividing both sides by 8, we get:
x = 15/8
= 1.875
Therefore, the value of x is approximately 1.875.
The value of x in equation 2x-2= -3x+13 is 3
To solve this equation we need to find the value of x so that all x terms should be one side and all constants should be at ones side:
2x+3x=13+2
5x=15
Now divide both side with 5 then, we get:
5x/5=15/5
x=3
Therefore, the value of x is 3
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In a sample of 4972 car owners, 2326 said that they would seriously consider purchasing an electric-powered vehicle. What is the point estimate for the proportion of all car owners who would seriously consider purchasing an electric-powered vehicle?
The point estimate proportion that they would seriously consider purchasing an electric-powered vehicle is 0.468.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
let y be 2326 said that they would seriously consider purchasing an electric-powered vehicle and x be the sample of 4972 car owners.
∴ The point estimate proportions is y = px.
2326 = 4972p.
p = 2326/4972.
p = 0.468.
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Which of the following statements is TRUE?
a. If f(x) and g(x) are differentiable functions defined on the closed interval [a, b], and f(x) attains its global maximum at x = c and g(x) d, then the function f(x) · g(x) attains its global maximum at x = attains its global maximum on [a, b] at x = c · ·d. b. The critical points of f' (x) are same as the critical points of f(x) c. The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint. d. All of the statements are false. e. Every local maximum a global maximum
The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint is correct. Statement C.
What is a critical value of a function?The critical value is the value of x for which the double derivative of the function f(x) becomes zero.
When double derivative becomes zero, the graph of the function is neither increasing nor decreasing and hence, the the function attains either
a maxima or a minima.
Hence, he global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint.
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hi!! if someone could help me out and find the answer for number 17 i would appreciate it sm:) 100 points im just trying to get some of my work done by tomorrow
Answer: y=−2x+16
Step-by-step explanation:
Substitutions this equation
8x-y=-6
2x-3y=4
would appreciate help on this percentage question, its grade 7 level.
a) The percentage reduction in the price of the television each time is as follows:
First time = 10.42%Second time = 11.63%.b) The absolute change after the two reductions amounting to $100 is that the price of the television is now $380.
c) The overall percentage decrease in the price of the television is 20.83%.
What is the percentage?The percentage is the ratio.
The percentage is computed as the quotient of the smaller value (numerator) over the larger value (denominator), between two values.
Percentages are depicted using the percentage sign (%) to show that the value is expressed over 100.
Price of the television = $480
First price reduction = $50
New price after the first price reduction = $430 ($480 - $50)
Percentage reduction in price = 10.42% ($50/$480 x 100)
Second price reduction = $50
New price after the second price reduction = $380 ($430 - $50)
Percentage reduction in price = 11.63% ($50/$430 x 100)
Overall percentage decrease = 20.83% ($100/$480 x 100)
Thus, overall, the price of this television decreased by 20.83 percent.
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The classroom outside bag had 5 frisbees in it. If 25% of the outside toys are frisbees, then how many total toys are in the bag?
AB of rhombus ABCD passes through the point (6, 6) and is perpendicular to the graph of y=3/4x-11. CD is parallel to AB and passes through the point (-6, 10). Select the equation in slope-intercept form of the line that includes CD.
A. y=4/3x+2
B. y=-4/3x+2
C. y=-3/4x+2
D. y=3/4x+2
Answer: [tex]y=-\frac{4}{3}x+2[/tex]
Step-by-step explanation:
The slope of [tex]AB[/tex] is [tex]-4/3[/tex]. Thus, the slope of [tex]CD[/tex] is also [tex]-4/3[/tex].
Thus, the equation of [tex]CD[/tex] can be found as follows:
[tex]y-10=-\frac{4}{3}(x+6)\\\\y-10=-\frac{4}{3}x-8\\\\y=-\frac{4}{3}x+2[/tex]
Sue and her brother wanted to buy 25 pieces of candy for their family's stockings. They chose to buy Kit Kats and Skittles. After shopping they spent $ 20.70. Skittles
cost 80 cents each and kit kats cost 90 cents each. How many of each candy did they get at the store? Let s-skittles and k=kit kats.
Which systems of equations represents this situation?
Answer:
18 Skittles and 7 Kit Kats
Linear system of equations in two variables
Step-by-step explanation:
We a linear system of two equations which can be solved simultaneously
Total pieces of candy equation
s + k = 25 [1]
Total cost equation
0.8s + 0.9k = 20.70 [2]
Multiply [1] by 0.80
0.80s + 0.80k = 20 [3]
Subtract [3] from [2]
0.80s + 0.90k = 20.70
[tex]-[/tex]
0.80s + 0.80k = 20
[tex]\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots[/tex]
0.1k = 0.70
k = 0.70/0.10 = 7
In [1]
[tex]s + 7 = 25\\\\s = 25-7\\\\s = 18\\\\[/tex]
Answer: 18 Skittles and 7 Kit Kats
The pattern below has been created by placing toothpicks together a) Find an expression for the total number of toothpicks in any set up b) How many toothpicks should there be in the 45th set up? Show your work.
For 45th set up 140 toothpicks are required.
What is Arithmetic Progression?A progression of numbers in which the difference between any two succeeding numbers is always a fixed amount is known as arithmetic progression (AP). It also goes by the name Arithmetic Sequence.
given:
For First Figure, 8 toothpicks are used
For Second Figure, 11 toothpicks are used
For Third Figure, 14 toothpicks are used
So, we get the series 8, 11, 14, ...
Now, for n= 45
Using Arithmetic Progression
[tex]a_{45} = a+ (45- 1) d[/tex]
= 8 + 44(3)
= 140
Hence, for 45th set up 140 toothpicks are required.
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Which equation represents the volume of the box
The equation represents the volume of the box as V = - 4s³ + 250s².
The correct option is option A
What is volume?The volume of any object is the capacity. How much it can hold.
What is the formula of volume?The formula of volume is a product of length, breadth and height.
Volume = L × B × H
Given:
The perimeter of the square base of side s plus height h = 250cm
as per the given question,
The perimeter of the square base of side s plus height h = 250cm
2( s + s ) + h = 250
2 (2s) + h = 250
4s + h = 250
We can express h in the terms of s as,
h= 250 - 4s
Volume = length X breadth X height
Volume = s × s × h
V = s² × h
V = s² × (250 - 4s)
V = 250s² - 4s³
The equation represents the volume of the box as V = - 4s³ + 250s².
The correct option is option A
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opinions: y= -3x + 5, y = - 1/5x + 3, y= 1/3x + 1/5, y=1/3x + 5, y= 3x + 1/5
The required matches for the given equation of line are explain below.
Explain general equation of line.The general equation of a straight line is y = mx + c, where m is the inclination, and y = c is the worth where the line cuts the y-hub. This number c is known as the block on the y-pivot. The condition of a straight line with slope m and block c on the y-hub is y = mx + c.
According to question:We will find the graph, by using general form of equation
y = -3x + 5
Its y-intercept is 5,and angle is negative,So graph(3) is matches
similarly,
y = - 1/5x + 3
Its y-intercept is 3,So graph(1) is matches
y=1/3x + 5
Its y-intercept is 5,and angle is Positive,So graph(4) is matches
y= 3x + 1/5
Its y-intercept is 1/5,and angle is more than one,So graph(2) is matches
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Find the domain and solve 2*4^(sqrt(5x^2-8x)+1)+4=33*2^(sqrt5x^2-8x)
To find the domain of the expression 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)), we need to consider the values of x for which the expression is defined.
First, we need to consider the square root term, sqrt(5x^2-8x). The square root of a number is only defined for nonnegative values, so we need to find the values of x for which 5x^2-8x is nonnegative. We can do this by setting 5x^2-8x equal to 0 and solving for x:
5x^2-8x=0
5x(x-8)=0
We can see that x=0 and x=8 are the solutions to this equation. Since the square root of a negative number is not defined, the expression 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)) is only defined for x values that are greater than or equal to 0 and less than or equal to 8. This means that the domain of the expression is x ∈ [0, 8].
To solve the equation 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)), we can start by isolating one of the exponential terms on one side of the equation. Let's isolate the term 2^(sqrt(5x^2-8x)):
24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x))
22^(2sqrt(5x^2-8x)+1)=332^(sqrt(5x^2-8x))
2^(2sqrt(5x^2-8x)+1)=16.52^(sqrt(5x^2-8x))
2sqrt(5x^2-8x)+1=4.5+sqrt(5x^2-8x)
sqrt(5x^2-8x)=3.5
5x^2-8x=12.25
5x^2-8x-12.25=0
We can use the quadratic formula to solve this equation for x:
x = (-(-8) ± sqrt((-8)^2 - 45(-12.25))) / (2*5)
x = (8 ± sqrt(64 + 97)) / 10
x = (8 ± sqrt(161)) / 10
x = (8 ± sqrt(289)) / 10
x = (8 ± 17) / 10
x = -9/10 or 25/10
Since x must be greater than or equal to 0 and less than or equal to 8, the only solution that is within the domain of the expression is x=25/10, or x=2.5.
Therefore, the solution to the equation 24^(sqrt(5x^2-8x)+1)+4=332^(sqrt(5x^2-8x)) is x=2.5.
what do you mean by domain of a function?
The domain of a function is the set of all input values for which the function is defined. In other words, it is the set of all values that can be plugged into the function as an argument, or input, and produce a valid output
For example, consider the function f(x) = x^2. The domain of this function is all real numbers, since the function is defined for any value of x. However, some functions may not be defined for certain values of x. For example, the function g(x) = 1/x is not defined for x=0 because division by zero is not allowed. In this case, the domain of the function g(x) would be all real numbers except for x=0.
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Justin, age 52, wants to pay no more than $800 a year in life insurance. If the annual life insurance premium rate (per $1000 of face value) is $5.38, what is the largest 15-year term policy be can
buy without spending more than $800 annually?
O $80,700
O $148,700
O $538,000
O $800,000
The largest 15-year term policy he can buy without spending more than $800 per annum is $148,699.
What is insurance?
An agreement to pay compensation to another party in the event of a specific loss, damage, or injury is known as insurance, and it is a way to protect against financial loss. It is a type of risk management that is mostly applied to protect against the risk of a potential or unforeseen loss.
The terms "insurer," "insurance company," "insurance carrier," and "underwriter" all refer to organizations that offer insurance.
Given: Justin, age 52, wants to pay no more than $800 a year in life insurance. If the annual life insurance premium rate (per $1000 of face value) is $5.38.
Annual life insurance premium rate = $5.38 per $1000 of the face value.
Largest 15-year term policy possible
= [tex]\frac{800}{5.38}*1000 = 148,698. 885 = 148, 699[/tex]
Therefore, the largest 15-year term policy he can buy without spending more than $800 per annum is $148,699.
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Simplify (m^6n)^3.
mn^21
m^9n^3
m^18n
m^18n^3
After solving the given expression, the value obtained is [tex](m^1^8^n)[/tex]. Hence, option C is correct.
What is Simplification?To streamline a phrase, one must use many techniques to make it shorter and simpler. The actions needed to reduce things are carried out in a predetermined sequence known as BODMAS.
Minimize a fraction to its simplest form to make it simpler. A fraction is said to be in its simplest form if both its numerator and denominator only include the integer.
As per the given information in the question,
The expression is,
[tex](m^6^n)^3[/tex]
= [tex](m^1^8^n)[/tex]
Therefore, option C is correct.
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Sketch a cone with diameter of 16 feet and height of 10 feet, then find the volume. If needed, round to the nearest hundredth.
The volume is 2679.46ft^3.
What is volume?
Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.
We know that
The volume of the cone is equal to
[tex]V=\frac{1}{3} \pi r^2 h[/tex]
where
r is the radius of the circular base of the cone [tex]$\mathrm{h}$[/tex] is the height of the cone
we have
[tex]$$\begin{aligned}& r=16 f t \\& h=10 f \mathrm{t}\end{aligned}$$[/tex]
assume
[tex]\pi=3.14[/tex]
substitute the values
[tex]$$\begin{aligned}& V=\frac{1}{3}(3.14)(16)^2(10) \\& V=2679.46 f t^3\end{aligned}$$[/tex]
The drawing in the attached figure
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