the maximum time that he can have in his last race is 23 seconds.
What is the maximum running time, in seconds?
We know that the average can not be greater than 22.8 seconds, then if x represents the time of the last race, the maximum value that x can take is given by the equation:
(23.1 + 23.2 + 22.8 + 21.9 + x)/5 = 22.8
(That is the equation for the mean of the 5 times)
Solving that for x we will get:
(23.1 + 23.2 + 22.8 + 21.9 + x) = 5*22.8
91 + x = 114
x = 114 - 91 = 23
So the maximum time that he can have in his last race is 23 seconds.
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Solve the inequality.
8 + 8(x + 9) ≥ 72
The diagram shows a triangle. What is the value of y?
Answer:
y=61°
Step-by-step explanation:
(y-8°)+(y+15°)+(y-10°)=180°
y-8°+y+15°+y-10°=180°
3y-3°=180°
3y=180°+3°
3y=183°
3y÷3=183°÷3
y=61°
The value of y from the given triangle can be calculated using the angle sum property as 61.
Given that:
A triangle has three angles given.
The measures of the angles are y - 8°, y - 10°, and y + 15°.
The angle sum property of triangles is defined as the property which states that the sum of the angles of the triangle is 180°.
Equating the angle measures:
y - 8 + y - 10 + y + 15 = 180
Add the like terms together.
3y - 3 = 180
Take 3 as common.
3(y - 1) = 180
Divide both sides of the equation by 3.
y - 1 = 60
Add 1 on both sides.
y = 61
Hence, the value of y is 61.
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SAT/ACT Mitsu travels a certain distance at 30 miles per hour and returns the same route at 65 miles per hour. What is his average speed in miles per hour for the round trip?
A 32.5
B 35.0
C 41.0
D 47.5
E 55.3
The average speed in miles per hour for the round trip is (D) 47.5.
What do we mean by average?In layman's terms, an average is a single number chosen to represent a set of numbers, typically the sum of the numbers divided by the number of numbers in the set (the arithmetic mean). The average of the numbers 2, 3, 4, 7, and 9 (summed to 25) is 5, for example. An average could be another statistic, such as the median or mode, depending on the context. For example, the average personal income is frequently given as the median—the number below which 50% of personal incomes fall and above which 50% of personal incomes fall—because the mean would be misleadingly high if a few billionaires' personal incomes were included.To find the average speed:
30 miles + 65 miles = 95Formula: Sum of terms/Number of terms
95/2 = 47.5Therefore, the average speed in miles per hour for the round trip is (D) 47.5.
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Sketch the region bounded by the curves x=y3,x=1, and y=0 then find the volume of the solid generated by revolving this region about the y-axis.
According to the question, the region is bounded by the curve with the given data as [tex]x = y^{3} , x=1, y=0.[/tex]
To compute the volume of the solid, use the disk method. The given object is rotated along the horizontal axis with the disk cross sectional area and the volume can be written as:
[tex]v=\int\limits^a_b {\pi x^{2} } \, dx[/tex]
As per question, when x = 1 then the value of y is: y = 1
Now, substituting calculated values in the expression:
[tex]v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx[/tex]
Substitute the value of the variable 'x':
Therefore, the expression can be written as:
[tex]v=\int\limits^a_b {\pi x^{2} } \, dx=v=\int\limits^0_1 {\pi x^{2} } \, dx=\int\limits^0_1 {\pi (y^{3}) ^{2} } \, dx=\frac{\pi }{7}=0.448[/tex]
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j=g+a solve for a be sure to take into account whether a letter is capitalized or not.
Answer:
a = j - g
Step-by-step explanation:
"solve for a" means to get a all by itself on one side of the equation. You can see the beginning of the answer that is provided on your screen says "a = "
We are starting with:
j = g + a
First, subtract g from both sides of the equation.
j - g = a
Now just trade the left and right sides of the equation.
a = j - g
Fill in your answer in the box: j - g
Simplify
(Show work)
−6(x−2)+5
Answer:
-6x+17Step-by-step explanation:
[tex]−6(x−2)+50\\\\-6x+12+5\\\\\sf{-6x+17}[/tex]
we are done!! ~~
Answer:
-6x + 17
Step-by-step explanation:
We can use algebraic expansion and order of operations to solve for this expression.
[tex] - 6(x - 2) + 5 \\ = - 6x + 12 + 5 \\ = - 6x + 17[/tex]
Given f(x)= 2x2+4, find the value of f(−1)
Answer:
f(- 1) = 6
Step-by-step explanation:
substitute x = - 1 into f(x)
f(- 1) = 2(- 1)² + 4 = 2(1) + 4 = 2 + 4 = 6
Find the distance between each pair of parallel lines with the given equations.
y=4 x
y=4 x-17
The distance between the given parallel lines is
In the given statement is :
The equations of the pair of each parallel lines is:
y = 4x and y = 4x - 17
To find the distance between each pair of parallel lines.
Two lines a₁x +b₁y + c₁=0 and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.
As we know that distance between the parallel lines (d) is given as:-
d = [tex]\frac{c_{2} -c_{1} }{\sqrt{a^{2} +b^{2} } }[/tex]
Parallel lines equation as:
y - 4x = 0
y - 4x + 17 = 0
Here,
a = -4 , b = 1, c1 = 0, c2 = 17
Therefore, putting the values
d = [tex]\frac{17 -0}{\sqrt{-4^{2}+1^{2} } }[/tex]
d = [tex]\frac{17}{\sqrt{17} }[/tex]
d = root 17
d = 4.12 units
Hence, The distance between the given parallel lines is 4.12 units
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The perimeter, P, of a rectangle is found using the formula P = 2l + 2w, where l is the length of the rectangle and w is the width of the rectangle.
Solution:
The formula for the perimeter of a rectangle is, P = length + breadth + length + breadth.
As you stated the formula of a rectangle is P (perimeter) = 2W (the two widths added together) + 2L (the two lengths added together).
To solve this algebraically you need to define your variable, or unknown, which in this case is the width or "W".
Now set this same equation with any symbol you wish, "x" is often used, and solve for x. You could keep W instead of X also if it makes it easier to work on the problem.
P= 2x + 2L
isolate the 2x by subtracting 2L from both sides.
P-2L=2x
Now isolate the x by dividing both sides by 2 and you have
P-2L/2=x
x will be W. Just put in the numbers P and L and you will have solved for W.
One More Solution :
The perimeter of a rectangle is given by the following formula:
P = 2W + 2L
To solve this formula for W, the goal is to isolate this variable to one side of the equation such that the width of the rectangle (W) can be solved when given its perimeter (P) and length (L).
P = 2W + 2L
subtract 2L from both sides of the equation
P - 2L = 2W + 2L - 2L
P - 2L = 2W
divide both sides of the equation by 2
(P - 2L)/2 = (2W)/2
(P - 2L)/2 = (2/2)W
(P - 2L)/2 = (1)W
(P - 2L)/2 = W
Thus, given that the perimeter (P) of a rectangle is defined by P = 2W + 2L ,
then its width (W) is given by W = (P - 2L)/2
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The cost of tennis lessons varies directly with
the number of lessons given. Gustavo spends
$260 on four lessons. What would be the cost
for nine tennis lessons?
Answer:
solve this
Step-by-step explanation:
260*9/4
Write a two-column proof of the Alternate Exterior Angles Theorem. (Theorem 3.3)
According to the Alternate Exterior Angles Theorem, when two parallel lines are severed by a transversal, the resultant alternate exterior angles are congruent if and only if the transversal is itself parallel to the two parallel lines.
So, in the figure below, if k ∥ l then
∠1 ≅ ∠7 and ∠4 ≅ ∠6.
Proof.
Since k ∥ l by the Corresponding Angles Postulate,
∠1 ≅ ∠5.
Also, by the Vertical Angles Theorem,
∠5 ≅ ∠7
Then, by the Transitive Property of Congruence,
∠1 ≅ ∠7
You may use the same strategy to demonstrate that ∠4 and ∠6 are equivalent to establish that they are congruent.
It should also be noted that the opposite of this theorem is true; more specifically, if two lines, k, and l, are sliced by a transversal in such a way that the alternative exterior angles are congruent, then k∥l.
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If bean bags are tossed towards a circle. what is the probability a bean bag lands closer to the center of the circle than to the edge of the circle?
0.25 is the probability a bean bag lands closer to the center of the circle than to the edge of the circle.
What is the probability in simple terms?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.Let the radius of the circle be r.
Now the distsnce of the edge of the circle from the center is r units.
Now for any point lying in the circle, the sum of the distance of that point
from the center and from the nearest edge of the circle is r.
Thus, the bag will land closer to the circle if it lies within r/2 distance from the center.
Now, the area of the inner circle with radius r/2 is = [tex]\pi (\frac{r}{2})^{2} = \pi \frac{r^{2} }{4}[/tex]
The area of the actual circle = πr²
Thus, the bean bag will land closer to the center if it lies within the inner circle of area = π r²/4
Hence, the required probability = [tex]\pi r^{2} /4/ \pi r^{2}[/tex] = 1/4 = 0.25
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Please help with this question. It’s over similar triangles, what do I do and what is the answer?
In the similar triangles given, the sum of AB and BD is: B. 4⅓.
How to Find the Side Lengths of Similar Triangles?The corresponding side lengths of two triangles that are similar to each other have equal ratio, that is, they are proportional in size.
Find AC:
AB/CD = AE/(8 - AC) [proportional sides of similar triangles]
AB = 3
CD = 2
AE = 8
Substitute
3/2 = 8/(8 - AC)
3(8 - AC) = 2(8)
24 - 3AC = 16
24 - 16 = 3AC
8 = 3AC
8/3 = AC
AC = 2⅔
Find BD:
AB/CD = BE/(5 - BD) [proportional sides of similar triangles]
BE = 5
AB = 3
CD = 2
Substitute
3/2 = 5/(5 - BD)
3(5 - BD) = 2(5)
15 - 3BD = 10
15 - 10 = 3BD
5 = 3BD
5/3 = BD
BD = 1⅔
AB + BD = 8/3 + 5/3
AB + BD = (8 + 5)/3
AB + BD = 13/3
AB + BD = 4⅓
Thus, in the similar triangles given, the sum of AB and BD is: B. 4⅓.
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what is the step by step solution: if 3
Answer:
write your full question.
Help please this is due soon
Answer:
The dimensions of the rectangular plot of the land is 17 × 12 square units.
Step-by-step explanation:
What is perimeter? The perimeter of a shape is the distance around the shape. It is the total length of the shape's sides.
What is the formula for the perimeter of rectangle?
Perimeter of rectangle = 2( length + width)
What is area?
The area can be defined as the space occupied by a flat shape or the surface of an object.
What is formula for the area of rectangle?
Area of rectangle = length × width
Can y’all please help me
Answer:
B
Step-by-step explanation:
Can someone help pls fast
Answer:
b(x) = 4x + 1
Step-by-step explanation:
If x starts from 1, we can give the equation as follows:
b(x) = 4x + 1
Let's check it, for the first one
x = 1, b(x) = 5
for the second, x = 2, b(x) = 4(2)+1 =9
NEED HELP ASAP! will rate 5 stars!!
The answer is C cause it makes ore sense against the other answers
Find a₁ for a geometric sequence with the given terms. a₉ = 1/2 and a₁₂ = 1/16
The first term of the given sequence is a(1) = 128
The formula for the nth term of a geometric sequence is:
a(n) = a(1) . rⁿ⁻¹
In the above formula, a(1) refers to the first term while r refers to the common ratio.
Information from the problem.
a(9) = 1/2 and a(12) = 1/16
Substitute n = 9 into the formula, we get:
a(9) = a(1) . r⁸
1/2 = a(1) . r⁸
Substitute n = 12 into the formula, we get:
a(12) = a(1) . r¹¹
1/16 = a(1) . r¹¹
Divide a(12) by a(9):
1/16 : 1/2 = ( a(1) . r¹¹ ) : (a(1) . r⁸ )
Since a(1) terms are cancelled out, we have:
2 : 16 = r¹¹ : r⁸
1/8 = r³
r = 1/2
Substitute r = 1/2 into a(9) :
a(9) = a(1) . r⁸
1/2 = a(1) . (1/2)⁸
a(1) = 1/2 : (1/2)⁸ = (1/2)¹⁻⁸
= (1/2)⁻⁷ = 2⁷
= 128
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what is 36 divided by 7.2
Answer:
36÷7.2=5
So this is the answer
What are the values of x and y? x = 10 m, y = 1 m x = 10 m, y = 2 m x = 11 m, y = 1 m x = 11 m, y = 2 m
Answer:
o na ain't no one answering that
Answer: D. Have a great day :3
Step-by-step explanation:
rational form of 0.412
The rational form of 0.412 is 103/250.
According to the question, to write the rational expression for the given link by removing the decimal. When the decimal is removed from the numerator then that many zeros will come in the denominator.
Therefore, the rational expression can be written as:
Required expression = 0.412 = 412/1000 = 103/250
Hence, the correct answer for this expression is 103/250.
What is rational expression?
The rational expression can be represented in the form of ratios which has two polynomials in the numerator as well as in the denominator. The value of the denominator term should never be zero.
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a measuring tool captures rain falling at a constant.The table shows the height of rainwater in the measuring tool and the number of minutes it rains.what is the constant of proportionality for the realationship of millimeters of rainwater to time in hours
The constant of proportionality for the relationship of millimeters of rainwater to time in hours is 48 millimeter/hour.
Given that the measuring tool captures rain falling at a constant.The table shows the height of rainwater in the measuring tool and the number of minutes it rains as shown in attached image.
A ratio is a mathematical comparison between two numbers. In proportion, if two given sets of numbers increase or decrease by the same ratio then the given ratios are said to be proportional.
Now we will calculate the proportion by using the formula
Ratio=(r₂-r₁)/(t₂-t₁)
Here, r₁=4, r₂=8, t₁=5, t₂=10
So, r₂-r₁=8-4=4 and
t₂-t₁=10-5=5
Now, we will convert the time from min to hour by dividing it with 60, we get
t₂-t₁=5/60
Substitute this value in above equation, we get
Ratio=4/(5/60)
Ratio=(4×60)/5
Ratio=4×12
Ratio=48 mm/hr
Hence, the constant of proportionality for the relationship of millimeters of rainwater to time in hours by using the given table is 48 mm/hr.
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Simplify the given expression’s
( )
And
( )
Answer:
1. p^10
2. p^24
Step-by-step explanation:
p^6 x p^4=p^(6+4)=p^10
(p^6)^4=p^(6x4)=p^24
Find at least three different sequences beginning with the terms 3, 5, 7 whose terms are generated by a simple formula or rule.
Answer:
3 5,7,9,11,13,16,17 19,21,23,25,27,29
Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10? Select two options.
The steps that could be part of the process of algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10 are
d) 0 = x2 – 9x + 20e) One x-value of a solution to the system is 4.What is an algebraic equation?An algebraic equation is a mathematical statement that sets two expressions equal using variables, coefficients, and constants.
Algebraic equations are represented by the equal symbol (=).
Data and Calculations:y + 5x = x² + 10 and y = 4x – 10
Substitute y = 4x - 10:
4x – 10 + 5x = x² + 10
4x - 10 = x² – 5x + 10
Add 10 to both sides:
4x - 10 + 10 = x² - 5x + 20
4x = x² - 5x + 20
Subtract 4x from both sides:
4x - 4x = x² - 5x - 4x + 20
0 = x² - 9x + 20
Solving, if x = 4:
x² - 9x + 20 = 0
4² - 9 (4) + 20 = 0
16 - 36 + 20 = 0
-20 + 20 = 0
Thus, the steps for algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10 are Options D and E.
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Question Completion with Answer Options:a) y = x2 + 5x + 10
b) y + 5x = x2 + 10 + 4x – 10
c) 0 = x2 – 9x
d) 0 = x2 – 9x + 20
e) One x-value of a solution to the system is 4.
Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample. If a and b are negative, then a + b is also negative.\
Answer:
The conditional statement is true.
Step-by-step explanation:
If a and b are negative, it doesn't matter what numbers they are; the sum will always be negative.
CA=√(d-e²)=d-e
7. (√1+d²)² + (√²+1)'. =?
(1 + ²) + (e²+1)
8.
9.-1 MABMBC
=
2
2+d²+e² =
2 =
-1 = de
OA. -2de
OB. (A + B)2
OC. A²+ B²
OD. (d-e)2
d²2de + e²
d²2de + e²
-2de
Which expression is missing from step 7?
Pythagorean theorem
simplify
substitution property of equality
Answer: [tex]A^{2} + B^{2}[/tex] correct answer.
Step-by-step explanation:
What is Pythagorean Theorem?
Image result for Pythagorean theorem
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation.
[tex]A^{2} + B^{2} + C^{2}[/tex]
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be expressed as, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle.
So, We can write,
Consider the triangle given above:
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
[tex]Hypotenuse^{2}[/tex] = [tex]Perpendicular^{2}[/tex] + [tex]Base^{2}[/tex]
[tex]C^{2} = A^{2} + B^{2}[/tex]
Hence,
[tex]A^{2} + B^{2}[/tex] correct answer.
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you rent a bicycle for 4 days. The bike store charges $20 for the first day and $15 for each additional day. Write and graph a step function that represents the relationship between the number x of days and the total cost y (in dollars) of renting the bicycle.
The relationship between the number x of days and the total cost represent as piecewise function.
f(x) = -x < 0
= x if x ≥ 0
The bike store charges $20 for the first day and $15 for each additional day. The relationship between the number x of days and the total cost represent as:
f(x) = 20 , if 0 < x ≤ 1
= 35, if 1 < x ≤ 2
= 50, if 2 < x ≤ 3
= 65, if 3 < x ≤ 4
The absolute value function f(x) = |x| can be written as a piecewise function.
f(x) = -x < 0
= x if x ≥ 0
Piecewise functions: A piecewise function is made up of two or more functions, each defined on a specific domain. Piecewise functions follow the following format:
f(x) ⇒ -x, x < 0
⇒ 0, x = 0
⇒ x, x > 0
The piecewise function above is the absolute value function. As you can see, piecewise functions include:
A curly bracket to indicate that the function is comprised of more than one subfunction
The subfunctions that make up the piecewise function
The subdomains corresponding to each subfunction
The domains of the subfunctions cannot overlap, but one function can end where another starts. If different functions were part of the same domain, the piecewise function would not be a function anymore!
To graph a piecewise function, graph each subfunction at the indicated domain. Be wary of the inequality symbols (< , ≤ , > , ≥) and whether they include or exclude the end of the subdomain. If they include the domain, draw a point and fill it in. If they exclude the domain, draw a point but do not fill it in.
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Solve each system by elimination.
20x + 5y = 120 , 10x + 7.5y = 80
By elimination, the solution of the system of equations, 20x + 5y = 120 and 10x + 7.5y = 80, is (5 , 4).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
Multiply first equation 2 by 2.
10x + 7.5y = 80 (equation 2)
20x + 15y = 160
Subtracting the two equations will eliminate the variable x.
20x + 15y = 160 (equation 2)
20x + 5y = 120 (equation 1)
0x + 10y = 40
y = 4
Substitute the value of y to any of the two equations and solve for x.
20x + 5y = 120 (equation 1)
20x + 5(4) = 120
20x = 120 - 20
20x = 100
x = 5
Hence, the solution of the system of equations is (5 , 4).
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