Aiden's tennis ball will reach the ground 0.65 seconds than Mason's tennis ball
How to determine the time difference in reaching the groundThe function of time with respect to distance is given as
(sqrt(d)/(4))
Rewrite the function properly
This is represented as follows
√d/4
It can also be written as
t = 1/4√d
From the question, we have
Aiden = 50 meters
Mason = 20 meters
The time difference is then calculated as
T = t₁ - t₂
So, we have
T = 1/4√d₁ - 1/4√d₂
The equation becomes
T = 1/4√50 - 1/4√20
This gives
T = 1/4(√50 - √20)
Evaluate
T = 0.65
Hence, the time difference is 0.65 seconds
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Given f(x)=x+2 and g(x)=4-x^2 find the following (g o f)(x)
Given functions are
[tex]\begin{gathered} f(x)=x+2 \\ g(x)=4-x^2 \end{gathered}[/tex]Then,
[tex]\begin{gathered} (g\circ f)(x)=g(f(x)) \\ =g(x+2) \\ =4-(x+2)^2 \\ =4-(x^2+4x+4) \\ =4-x^2-4x-4 \\ =-(x^2+4x) \end{gathered}[/tex]Thus,
[tex](g\circ f)(x)=-(x^2+4x)[/tex]Scientists are studying the temperature on a distant planet. They find that the surface temperature at one location is 45 ° Celsius. They also find that the temperature decreases by 7 ° Celsius for each kilometer you go up from the surface. Let T represent the temperature (in Celsius), and let H be the height above the surface (in kilometers). Write an equation relating T to H , and then graph your equation using the axes below.
The equation relating T to H is H = 45 - 7T.
What is temperature?Temperature simply means the degree of hotness and coldness in a body.
In this case, they find that the surface temperature at one location is 45 ° Celsius. They also find that the temperature decreases by 7 ° Celsius for each kilometer you go up from the surface.
Let T = the temperature (in Celsius).
Let H = the height above the surface (in kilometers).
The equation will be:
H = 45 - (7 × T)
H = 45 - 7T
The axes aren't given and can't be graphed.
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a recipe uses 1 aubergine for every 3 people. how many aubergines should you buy for 10 people
Answer:
3 1/3 I am assuming that you cannot by 1/3 of an aubergines, so you would need to buy 4. if you can buy a partial one then it would be 3 1/3
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] = [tex]\frac{a}{10}[/tex] Set up a proportion and then cross multiply and solve for a
3a = 10 Divide both sides by 3
a = [tex]\frac{10}{3}[/tex] = 3 1/3
24. Anna went bowling. She spent less than or equal to $30, but spent more
than $25. Create a number line that shows all the possible amounts that
Anna may have spent at the bowling alley.
All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.
What is a number line?In mathematics, a numbered line is a straight line with numbers organized at regular intervals or sections throughout its breadth. The beginning of period is frequently shown laterally and may be shifted in any position.
Anna visited a bowling alley. She did not spend less than or equal to $30, but she did spend more than $25.
The inequality is given as,
$25 < x ≤ $30
All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.
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Let g be a group with normal subgroups m and n. furthermore, assume n is a subste of m. use the first isomorphic theorem to prove that (g/n)/(m/n) is isomorphic to g/m.
The proof of (g/n)/(g/m) isomorphic to g/m from the first isomorphism theorem is as shown below.
Let a group g with normal subgroups m and n. Furthermore, n is a subset of m.
Proof: We have to prove (g/n)/(m/n) ≅ g/m (1)
g/m and g/n are valid because m and n are normal in g. As normality satisfies the intermediate subgroup condition, n is normal in m. because normality is image-closed m/n is a normal subgroup in g/n. Under the quotient map by n, the normal subgroup m of g is sent to a normal subgroup m/n of g/n. Thus the L.H.S of the statement to prove makes sense.
To describe the isomorphism from the left side to the right side
φ: g/n \to g/m
ψ(gn) = gm
So, a coset of n is taken by the map and it gives the corresponding coset of m. This is well-defined, because if h∈ n, thus h∈ m, hence (gh)m = g(hm) = gm.
The map is a homomorphism. So we observe that it maps the identity element to the identity element, keeps group multiplication preserved, and also preserves the inverse map.
Also, the map is surjective because any coset gm is present as the image of gn under ψ.
Lastly, we need to find the kernel of the map which is given by the set of gn such that gm = m. This is those cosets of n that are in m, and this is the same as the coset space m/n. Thus the kernel of the map is exactly g/m. Thus, the surjective homomorphism ψ: g/n → g/m has kernel m/n. And now by the first isomorphism theorem
(g/n)/(m/n)≅g/m where ≅ shows isomorphism
another problem to prove whether f is an isomorphism:
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The perimeter of a square can be found using p=n+n+n+n
Answer: Well, yes. It's more like p = s + s + s + s. "S" = side. "P" = perimeter.
So, this is theoretically true if your variable for a side just happened to be "n".
You also put, "The perimeter of a square", A simpler way to put this is
P = s4 or in your case P = n4.
Because this shape is a square all side lengths and angles will be congruent, and therefore will all be the same (which is why we are able to multiply one side by four.)
Hope this helps. :)
in professional tennis, the length of time that the strings of a tennis racquet last is distributed uniformly anywhere from 5 to 30 days. given that the strings are still not broken on day 15 since they were strung, what is the probability that the strings will not break for at least another 10 days? round your answer to 2 digits after the decimal.
Eli has 12 eggs. He uses his grandpa's recipe to bake 4 loaves of challah. Find how many eggs are left over if Eli uses 2 eggs for each loaf of challah?
Answer:
4 Eggs are left since he uses 2 eggs per 1 loaf so 2x4=8
Step-by-step explanation:
if tan 1/3 and cos is less than 0 was in the sin of x
Answer:
[tex] \frac{1}{ \sqrt{10} } [/tex]
A fair coin is flipped 10 times. Each flip is independent.
What is the probability of getting exactly eight heads?
Answer:
8 out of 10.
Step-by-step explanation:
if you flip a coin independent then it doesn't matter what the other outcomes are. So if it's a one out of two chance every time then it's 8 /10.
Find the slope of the line that passes through the following points: (-4,-2) and (-3,5)
PLEASE HELP ASAPPP!!!!!!!!!!!!!!!!!!!!!
PLEASE HELP ASAP!!!!
The quadratic function f(x) has roots of −4 and 2 and point (1, −5) lies on f(x). What is the equation of f(x)?
f(x) = (x − 2)(x + 4)
f(x) = (x − 2)(x − 4)
f(x) = 4(x − 2)(x + 4)
f(x) = 4(x − 2)(x − 4)
The function has an equation of f(x) = (x + 4)(x - 2)
How to determine the equation of f(x)?The given parameters in the question are
Roots = -4 and 2
Point = (1, -5)
The above parameters can be rewritten as
Roots: x = -4 and x = 2
Point: (x, y) = (1, -5)
A quadratic equation can be represented as
f(x) = a * (x - Roots)
Where Roots: x = -4 and x = 2
The above parameters imply that we have the following equation
y = a(x + 4)(x - 2)
From the question, we have
(x, y) = (1, -5)
This gives
-5 = a(1 + 4)(1 - 2)
Divide
a = 1
Substitute a = 1 in y = a(x + 4)(x - 2)
y = (x + 4)(x - 2)
Hence, the equation of the quadratic function f(x) is f(x) = (x + 4)(x - 2)
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Answer: The answer would be A: f(x) = (x − 2)(x + 4)
Step-by-step explanation: I got it right on my test
The line containing the points (14, 15) and (20, 24) crosses the y-axis at what point?
The linear equation that passes through the points (14, 15) and (20, 24) crosses the y-axis at y = -6.
How to get the y-intercept?
A general linear equation can be written as:
y = m*x + b
Where m is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
m = (y₂ - y₁)/(x₂ - x₁).
In this case the line passes through (14, 15) and (20, 24) so the slope is:
m = (24 - 15)/(20 - 14) = 9/6 = 3/2
y = (3/2)*x + b
To find the y-intercept we can replace the values of one of the points, like (14, 15)
15 = (3/2)*14 + b
15 = 3*7 + b
15 = 21 + b
15 - 21 = b
-6 = b
The y-intercept is -6.
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an industrial manufacturing company uses an inverted conical (cone-shaped) tank to dispense liquid into containers. the tank measure 24 inches with a base radius of 48 inches. if the liquid flows out of the tank at a rate of 40 cubic inches per minute, at what rate is the height of the liquid falling when the height of the liquid is 10 inches deep?
If the liquid flows out of the tank at a rate of 40 cubic inches per minute, the height of the liquid will decrease at rate 0.0318 in./minute
Referring to the attached picture, the two triangles in a cone are similar. Hence,
r/h = 48/24
or
r = 2h.
The volume of the liquid is given by:
V = 1/3 . πr²h
Substitute r = 2h,
V = 1/3 . π(2h)²h = 4/3 . πh³
Take the derivative with respect to t
dV/dt = 4/3 . 3πh² . dh/dt
dV/dt = 4 . πh² . dh/dt
Substitute dV/dt = -40 and h = 10
-40 = 4 . π(10)² . dh/dt
dh/dt = - 0.0318 in./minute
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Part A Write the multiplication expression shown by the model. Do not solve the problem. Part B
Explain the expression written in Part A. Include the final product and how it is shown with the model.
The multiplication expression is given as L × w
The expression is given as N = r+ g + w + b
The final product of the expression is 200 boxes
How to determine the expressionNote that the formula determining the area of a rectangle is expressed as;
Area = lw
Where;
l denotes the length of the rectanglew denotes the width of the rectangleThe area of the figure can be calculated by multiplying the length and the width and then addition of the number of boxes.
This is given as;
10( 4 + 5 + 4 + 7)
Also
L × w = r + g + w + b
The expression L×w is a multiplication expression.
Total number of boxes vertically is the length = 20
Total number of boxes horizontally is the width = 10
Total area = L×w = 20 × 10 = 200
Number of the red boxes = 46Number of the green boxes = 46Number of the blue boxes = 46Number of the white boxes = 62Then,
N= r + g + w + b
We have;
L×B = 3r + w
Hence, a multiplication expression is expression having variables that are multiplied.
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Simplify: 2.4 x 10−4 0.00024 0.000024 −0.000024 −2.4000
Answer:
0.00067
Step-by-step explanation:
You always want the period to the right of the first number meaning you’ll start from there counting backwards because it is negative.
Solve the given linear equation.14x + 4 = 8x + 23x =
We have to solve this linear equation for x:
[tex]\begin{gathered} 14x+4=8x+23 \\ 14x-8x+4-4=8x-8x+23-4 \\ 6x+0=0x+19 \\ 6x=19 \\ x=\frac{19}{6} \\ x\approx3.16\ldots \end{gathered}[/tex]The answer is x=19/6
Mid point of -2,11 and 18,-1
The midpoint of (-2, 11) and (18, -1) is:
[tex]\begin{gathered} \bar{x}=\frac{-2+18}{2}\rightarrow\bar{x}=8 \\ \\ \bar{y}=\frac{11-1}{2}\rightarrow\bar{y}=5 \end{gathered}[/tex]Point (8,5)
What is the exchange rate? Show your work.
1 US dollar = _________ euro.
The exchange rate is 1 USD = 0.992714 EURO
What is Conversion of unit?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
We need to convert between units in order to ensure accuracy and prevent measurement misinterpretation. For example, we do not measure a pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm).
Given:
1 US dollar = _________ euro.
As, the exchange rate between US dollar to Euros
1 USD = 0.992714 EURO
1 USD = 1 EURO
So, if we have to find 5 US dollar into EURO then
5 US dollar = 5.02 EURO = 5 EURO
Hence, the exchange rate is 1 USD = 0.992714 EURO
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Find the ordered pair $(x,y)$ if
\begin{align*}
x+y&=(3-x)+(3-y),\\
x-y &=(x-2)+(y-2).
\end{align*}
Thanks
In accordance with the system of linear equations, the ordered pair is (x, y) = (1, 2).
How to find the values associated to an ordered pair
Ordered pairs are constructions characterized by two components, typically real numbers. The most common form of notation is (x, y). In this problem we need to resolve a system of linear equations to obtain the needed values. We find a system of two equations and two variables:
x + y = (3 - x) + (3 - y)
x - y = (x - 2) + (y - 2)
First, simplify each expression of the system:
First equation:
x + y = 6 - x - y
2 · x + 2 · y = 6
x + y = 3
Second equation:
x - y = (x - 2) + (y - 2)
x - y = x + y - 4
- 2 · y = - 4
y = 2
Second, substitute in the first equation:
x + 2 = 3
x = 1
The ordered pair is (x, y) = (1, 2).
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Two companies are competing for a contract to make the programs for middle school gymnastics meets. Nadia’s Printing charges a $19.99 fee for printing and $0.25 for each program printed. Simone’s Stylish Print charges a $29.99 fee for printing and $0.10 for each program printed. For the most recent meet, Nadia’s Printing charged more than Simone’s Stylish Print.
Which inequality models this situation?
Answer:
the second answer
Step-by-step explanation:
Evaluate without any table 3log2 +log20 - log 1.6
The value of 3log2 +log20 - log 1.6 is 2.
What is logarithm?
A logarithm is defined as the power to which a number must be raised to get some other values. It is the most convenient way to express large numbers. or
logarithm is the exponent or power to which the base must be raised to be raised to yield a given number.
Given,
3log2 +log20 - log 1.6
we can write it as
log[tex]2^{3}[/tex]+log20 - (log 1.6)
= log 8+ log20 - (log 1.6) (property of logarithm)
= log (8×20/1.6)
=log 100
=2
Hence, the value of 3log2 +log20 - log 1.6 = 2
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which of the following coordinates represent a point on the Y - axis choose all that apply
Question 7:
The y-axis on a graph is the vertical line on a graph, it represents the dependent variable.
Any point on the y-axis of a graph, has an x-value of zero.
Therefore, from the list given, any coordinate with an x-value of zero is on the y-axis.
Apply the point form: (x, y)
The following coordinates represent a point y-axis:
(x, y) ==> (0, -4)
(x, y) ==> (0, 3)
ANSWER:
(0, -4)
(0, 3)
Martha has 4 different colored pens in her bag. After she uses a pen she just throws it back into bag. If she does this 5 day a week, how many different ways can she use the pens for the week?.
By likelihood, she can utilize the pens in 1024 distinct ways during the week.
Probability is the study of possible outcomes of events, together with the probabilities and distributions of those occurrences.
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
To calculate probability, divide the total number of outcomes by the total number of possible possibilities. There are differences between probability and odds.
Odds are computed by dividing the likelihood that an event will occur by the likelihood that it won't.
From the stated circumstance,
Total ways = [tex]4^{5}[/tex]= 1024
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insert parentheses to make the expression true
4×2+3×2=32
Answer:
4 * ( 2 + 3 * 2) = 32
Step-by-step explanation:
The strategy I used in this question is generally trial and error. The most important thing here to remember is to follow the order of operations. If you think a little out of the box, then you will see the answer. To solve, first multiply 3*2, then add two, which should result in 8. 4*8 is 32, which makes the equation true.
To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?
First equation:
Second equation:
The first equation should be multiplied by 3 and the second equation by -5.
The first equation should be multiplied by 3 and the second equation by 5.
The first equation should be multiplied by 7 and the second equation by -6.
The first equation should be multiplied by 7 and the second equation by 6.
Answer: the answer is c)The first equation should be multiplied by 7 and the second equation by -6.
Step-by-step explanation:edge 2022
Answer:
C
Step-by-step explanation: -6
Solve for X round to nearest tenth
Answer:
the answer for this question is 35.0
Parallel and transversals
I was in a rush so I couldn't write fown the steps. If you need the explanations for how they were gotten, please say.
explain how you got the answer
Slope - 2/3
y - intercept : (0,3)
x | y
0 | 3
3 | 1
Use the order of operations to evaluate.[tex]16.5 + ({62 }^{2} - 15.6) - 2[/tex]
Thus, the final answer is 34.9.
2.
[tex]16.5+(6^2-15.6)-3=16.5+(36-15.6)-3[/tex]