Alex, Cameron and Sam are all taking part in a 400 m race.
They are each running at a different constant speed.
Alex is running 12% faster than Cameron, whilst Sam is running 2% slower than Cameron.
When Alex crosses the finish line, how many metres is Sam from the finish line?
Answer:
A= C + 12%C = 1.12C
S=.C -2%C = .98C
A,C and S are the speeds of Alex, Cameron and Sam
400 meter race
how far is Sam from the finish line when Alex crosses the finish line?
distance = speed times time
400 = AT where T=Alex' finish time
400=1.12T
400=CU where U = Cameron's finish time
400=SV where V = Sam's finish time
T<U<V
Alex' finish time is less than Cameron's finish time is less than Sam's finish time
if Cameron runs at 20 meters per second, finishing in 20 seconds
then Sam is about 50 meters from the finish line when Alex finishes
sorry if i´m too late, hope this helps!
Find the values of x and y that maximize the objective function
Answer: D
Step-by-step explanation:
A. [tex]P=2(4)-3=5[/tex]
B. [tex]P=2(0)-3=-3[/tex]
C. [tex]P=2(0)-0=0[/tex]
D. [tex]P=2(4)-0=8[/tex]
1. How many ways can you flip a coin and roll four-sided tetrahedron dice?
Draw the tree diagram in the space provided below.
Answer:
Step-by-step explanation: I cant do the tree Diagram, however, I will help if you flip a coin (Heads or tails) The chances of it landing on heads will divide by 2 every time its heads or tails again and vise versa .
Form a polynomial whose zeros and degree are given.
Zeros: -7, multiplicity 1; -2, multiplicity 2; degree 3
MODE
Type a polynomial with integer coefficients and a leading coefficient of
f(x) = (Simplify your answer.)
Let p(x) be the required polynomial.
we are given that p(x) has a zero 1 with multiplicity 2
in other word, this means that (x-1) occurs twice as a factor of p(x).
How Do Polynomial Functions Work?Expressions with polynomial functions include variables with various degrees, non-zero coefficients, positive exponents (of variables), and constants. A polynomial in "b" of degree 2 is, for instance, f(b) = 4b2 - 6.
Likewise, (x-3) appears as a factor of p(x) once.
we are also given that the degree of p(x) is 3.
So, p(x) can not have more than 3 linear factors.
Altogether,
p(x) = k(x-1)^2 (x-3), where constant k ∈ R - {0}.
We may take k = 1 and get the desired polynomial,
p(x) = ( x-1)^2 ( x-3) = x^3 - 5x^2 +7x -3
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hi helpppppppppppppppppppppppppppppppppppp
Answer:
with what?
Step-by-step explanation:
The personal assets and liabilities of a carpenter are listed below.
What is the carpenter's net worth?
$139,450
$145,228
$281,313
$284,678
$139,450
==========================================================
Explanation:
asset = an item that is either cash or can be turned into cash
liability = something that needs to be paid back (eg: truck loan)
A = total assets
A = (homeValue) + (workEquipment) + (carValue) + (investments)
A = ( $175,742 ) + ($3,365) + ($44,346) + ($61,225)
A = $284,678
B = total liabilities
B = (mortgage)+(credit card balance)+(truck loan)
B = ($76,765)+($2,055)+($66,408)
B = $145,228
C = net worth
C = A - B
C = ($284,678) - ($145,228)
C = $139,450 which points us to choice A as the final answer.
The net worth of the carpenter is $144,633.
Given that, Home value = $175,742, Mortgage = $76,765, Credit card balance = $2,055, Owned work equipment = $3,365 and Car value = $44,346.
What is the net worth?Net worth is the value of all the non-financial and financial assets owned by an individual or institution minus the value of all its outstanding liabilities.
Here,
Net worth = Financial assets - Liabilities
= (175,742+3,365+44,346) - (76,765+2,055)
= 223,453 - 78,820
= $144,633
Therefore, the net worth of the carpenter is $144,633.
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Please help. quickly
The total surface area of the triangular prism is 756 meter²
Given,
A triangular prism and its net.
We have to find the surface area of the triangular prism.
First we can consider the right angled triangle.
Height = 9 meter
Base = 12 meter
Hypotenuse = 15 meter
Area of the right angled triangle = (1/2 bh)
Here,
Area = 2 × (1/2 bh) = 2 × (1/2 × 12 × 9) = 2 × 6 × 9 = 108 meter²
Now, area of right rectangle.
Area of rectangle = length × breadth
Here, the breadth of the rectangle is the height of the triangle = 9 meter
Length = 18 meter
Area = length × breadth = 9 × 18 = 162 meter²
Then, area of middle rectangle.
Length = 18 meter
Breadth = 12 meter
Area = length × breadth = 18 × 12 = 216 meter²
Next, area of left rectangle.
Length = 18 meter
Breadth = Hypotenuse of the triangle = 15 meter
Area = length × breadth = 18 × 15 = 270 meter²
Now, lets calculate the total surface area of the triangular prism.
Surface Area of triangular prism = 108 + 162 + 216 + 270 = 756 meter²
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Provide the missing reasons for the following proof:
(In the picture)
Options
- Transitive Property of
Congruence
- Subtraction Property of
Equality
- Vertical Angles Theorem
(VAT)
- Division Property of
Equality
- Given
- Angle Congruence
Postulate
- Substitution Property of
Equality
The missing reasons are for the given two triangles VXW and VYZ are found.
What is defined as the congruent triangles?The assessments of the sides and angles of two or so more triangles determine their congruence. A triangle's size is determined by its three sides, and its shape is determined by its three angles. Two triangles have been shown to be congruent if the pairs of their corresponding angles and sides are equal. They are the same size and shape.The missing reasons for the following proof are -
∠XVW ≅ ∠W ; - Given∠XVW ≅ ∠ZVY ; Vertical Angles Theorem (VAT)m ∠ZVY ≅ ∠W ; Transitive Property of Congruence80x + 13 = 75x + 28 ; Angle Congruence Postulate5x = 15 ; Substitution Property of Equalityx = 3 ; Division Property of EqualityThus, the missing reasons are for the given two triangles VXW and VYZ are found.
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Evaluate (-3)^8 and (-3)^9
The evaluation of the numbers (-3)^8 and (-3)^9 will be (-3)^17.
How to calculate the value?Based on the information given, it should be noted that this illustrates that the numbers are raised to power.
In this case, it should be noted that we want to multiply the powers, this illustrates that we gave to add the powers. This will be:
Evaluate (-3)^8 × (-3)^9
Note that 8 + 9 = 17. Therefore,
Evaluate (-3)^8 and (-3)^9
= -3^17.
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Evaluate (-3)^8 × (-3)^9
State the transformation performed on the parent function.
What is the equation of the line that passes through the point (8, 1) and has a slope of -3/4?
Answer:
y-1= -(3/4)(x-8)
Step-by-step explanation:
y -1 =(-3/4)(x-8)
Distribute
y -1= (-3/4)x+6
Get rid of -1 by adding 1 to both sides
y=(-3/4)x+7
Hope this helps :)
1. consider a lottery with three possible outcomes: $125 will be received with probability 0.25, $100 will be received with probability 0.3 and $50 will be received with probability 0.45. a. what is the expected value of the lottery? b. what is the variance of the outcome? c. what would a risk-neutral person pay (at most) to play the lottery?
The lottery's anticipated worth is $80.
Given that,
The probability of receiving $125 is 0.25; the likelihood of receiving $100 is 0.3; and the likelihood of receiving $50 is 0.45.
A) EV=125*.2+100*.3+50*.5=$80
The lottery's anticipated worth is $80.
The expected value is obtained by multiplying each result by its likelihood.
The expected value of the lottery is then calculated by adding up all of these.
This is what we have: ;;
125(0.2) + 100(0.3) + 50(0.5) (0.5)
= 25 + 30 + 25 = $80
B) This is the formula for variance is shown in figure :
So, we can calculate the variance as follows:
.2*(125-80)^2+.3*(100-80)^2+.5*(50-80)^2=975
C) A risk-neutral person would pay $80 or less to play the lottery.
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Answer:
Step-by-step explanation:
Expected value of the lottery is $83.75.
Variance of the outcome is 909.6.
A risk-neutral person would pay $83.75 or less to play the lottery.
a) The expected value is obtained by multiplying each result by its likelihood.
The expected value of the lottery is then calculated by adding up all of these.
This is,
125(0.25) + 100(0.3) + 50(0.45)
= $83.75
b) we can calculate the variance as follows:
Variance=.25*(125-83.75)^2+.3*(100-83.75)^2+.45*(50-80)^2=909.6
c) A risk-neutral person would pay $83.75 or less to play the lottery.
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A sequence is defined by f(0) = -3, f(n) = f(n-1) + 0.5 for n ≥ 1.
1.
Write the first five terms of this sequence, starting with term 0.
2.
Write the nth term definition of this sequence.
Answer:
1.
f(0) = -3
f(1) = f(0) + 0.5 = -3 + 0.5 = -2.5
f(2) = f(1) + 0.5 = -2.5 + 0.5 = -2
f(3) = f(2) + 0.5 = -2 + 0.5 = -1.5
f(4) = f(3) + 0.5 = -1.5 + 0.5 = -1
2.
f(n) = 0.5n - 3
This function is linear.
En una circunferencia señalamos diez puntos. ¿Cuál es la diferencia entre el número de heptágonos y el de triángulos cuyos vértices son algunos de esos puntos?
Answer:
ok wirrudi 123 alf8 434 21 3dis w
Write the equation for the line that passes through the given point and is perpendicular to the given line (1,7); x - 4y = 8
The equation for the line that passes through the given point and is perpendicular to the given line is x - 4y = 3
Given : x - 4y = 8
4y = x- 8
On dividing by 4 we get;
y= x/4 - 2
This is of the form y = mx + c
Thus m in this case on comparing we get m= 1/4
We know the formula of the slope ;
y - y₁ =m ( x - x₁ )
y - 1 = 1/4 ( x- 7)
On cross multiplying we get ;
x- 4y = 3
Thus the equation for the line that passes through the given point and is perpendicular to the given line is x - 4y = 3 .
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A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels at this speed in t hours.
a. What does the 65 tell us in this situation?
The car travels
miles in 1 hour.
b. How many miles does the car travel in 1.5 hours?
The car travels
miles in 1.5 hours.
c. How long does it take the car to travel 26 miles at this speed?
It takes the car
hours to travel 26 miles.
(a) 65 means the car will travel 65 miles in 1 hour .
(b) The car will travel 97.5 miles in 1.5 hours .
(c) The car will take 0.4 hours to travel 26 miles at his speed .
In the question ,
it is given that
the car is traveling down a highway at a constant speed
and the equation representing is d =65*t
Part(a)
On comparing , the given equation with the equation of speed , time and distance
which is , distance = speed × time
on comparing both the equations , we get speed = 65 mph .
hence , 65 means the car will travel 65 miles in 1 hour .
Part(b)
substituting the value t = 1.5 hours in the given equation , we get
d = 65×1.5
= 97.5
hence , The car will travel 97.5 miles in 1.5 hours
Part(c)
Substituting the value of d = 26 miles in the given equation , we get
26 = 65×t
t = 26/65
t = 0.4 hours
hence , It takes the car 0.4 hours to travel 26 miles.
Therefore , (a) 65 means the car will travel 65 miles in 1 hour .
(b) The car will travel 97.5 miles in 1.5 hours .
(c) The car will take 0.4 hours to travel 26 miles at his speed .
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Springfield Mini Golf offers its customers a
25-round pass for $84, or they can pay
$3.25 per round. Which option has the
lesser price per round?
1) Work out the area and the perimeter of the shape below.
10 cm
12 cm
4 cm
Diagram NOT
accurately dr
Answer: 10 cm
Step-by-step explanation: because i am alwauys right about your mom
write a real world situation for which the rate of change is -15
The most appropriate choice for velocity and accleration will be given by- Deacceleration of a car of 15 [tex]m/s^2[/tex] is a real world situation for which the rate of change is -15
What is velocity and acceleration?
Velocity
The distance travelled by a body per unit interval of time where the direction of the motion of a body is taken into account is known as velocity.
Velocity is a vector quantity as direction of motion of body is taken into account.
If d is the displacement of body and t is the time,
Velocity = [tex]\frac{d}{t}[/tex]
Acceleration
The rate of change of velocity of a body is called acceleration.
Acceleration is a vector quantity as direction of motion of a body is taken into account.
If [tex]\Delta[/tex]v is the change of velocity and t is the time,
Acceleration = [tex]\frac{\Delta v}{t}[/tex]
If velocity decreases then it is called Deacceleration
Here
Deacceleration of a car is 15 [tex]m/s^2[/tex]
That means rate of change of velocity of a car is -15 [tex]m/s^2[/tex]
This is a real world situation for which the rate of change is -15
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The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons is 9 to 11. There are 55 gallons of gasoline. How many ounces of oil are there?
Given:
Ratio of ounces of oil to gallons of gasoline = 9 : 11
Gallons of gasoline = 55 gallons
Let's find the ounces of oil.
To find the ounces of oil, we have the equation:
[tex]\begin{gathered} \frac{\text{Ratio of ounces of oil}}{Ratios\text{ of gallons of gasoline}}=\frac{\text{Ounces of oil}}{\text{Gallons of gasoline}} \\ \\ \end{gathered}[/tex]Thus, we have:
[tex]\frac{9}{11}=\frac{x}{55}[/tex]Let x represent the ounces of oil.
Cross multiply:
[tex]\begin{gathered} 11x=9(55) \\ \\ 11x=495 \\ \\ \text{Divide both sides by 11:} \\ \frac{11x}{11}=\frac{495}{11} \\ \\ x=45 \end{gathered}[/tex]Therefore, there are 45 ounces of oil.
ANSWER:
45 ounces of oil
Find the height, if area is 24cm2 and the base is 6cm.
Answer:
4cm..............................
Step-by-step explanation:
24/6=4
4x6=24
100 times my number is 12.6 more than 5,000.
Answer:
50.126
Step-by-step explanation:
hope this helps
The solution is 50.126
What is Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
100 times my number is 12.6 more than 5000
Let the number be x
100 times the number = 100x
Now, 100x is 12.6 more than 5000
100x = 5000 + 12.6
100x = 5012.6
Divide by 100 on both sides , we get
x = 50.126
Hence , the solution is 50.126
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is (0,-4) a solution to the equation y = -10x + -4?
Yes, it is a solution
Explanation:y = -10x + - 4
The given point: (0, -4)
To know if it is a solution, we need to replace the y and x with the points given.
If the result on the left hand side is the same as the right hand side then, it is a solution
x =0, y = -4
-4 = -10(0) + -4
-4 = 0 + (-4)
Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
-4 = 0 - 4
-4 = -4
The left hand side is the same as the right hand side. Hence, it is a solution
Answer:
Yes it is a solution
Step-by-step explanation:
y = -10x + - 4
Point: (0, -4)
a. Solve a³ = 11.
b. Solve c² = 27.
Answer: a = 2.2
C = 5.1,-5.1
Write an equation of the line passing through the point (2, -9) that is perpendicular to the line y=x+6.
Answer:
y = -x - 7
Step-by-step explanation:
Perpendicular to the slope m = 1 is the slope -1/m = -1.
y = m * (x - Px) + Py
y = -1 * (x - 2) + (-9)
y = -x + 2 - 9
y = -x - 7
Plot the intercepts to graph the equation
8x-3y=-24
Answer:
Step-by-step explanation:
Find the surface area and volume of the following solids , a cylinder with radius 5 m and height 0.5 m
The radius of the cylinder is 5 m and the height is 0.5 m.
Then, the total surface area is
[tex]\begin{gathered} A=2\pi r(r+h) \\ =2\pi(5)(5+0.5) \\ =55\pi\text{ squared meter} \end{gathered}[/tex]So, the surface area is
[tex]55\pi=172.79\text{ squared meter}[/tex]Now, the volume is
[tex]\begin{gathered} V=\pi(r^2)h \\ =\pi(5)^2(0.5) \\ =39.27\text{ cubic meter} \end{gathered}[/tex]So, the volume of the cylinder is 39.27 cubic meters.
The product of 8 and n decreased by 5 is _________________ 25. less than greater than less than or equal to greater than or equal to
The statement that represents the given inequality is:
The product of 8 and n decreased by 5 is less than 25.
Which sentence represents the inequality?The inequality is defined as follows:
8(n - 5) < 25.
The meaning of the expression n - 5 is given as follows:
n decreased by 5. (n is an unknown number).
The meaning of the expression 8(n - 5) is given as follows:
The product of 8 and n decreased by 5. (multiplication of two numbers is also called product).
The symbol of the inequality is given as follows:
<
Which represents the expression less than.
Considering the 25 on the other side of the inequality, the complete sentence is given as follows:
The product of 8 and n decreased by 5 is less than 25.
Missing informationThe complete problem is:
Sal wrote the statement below to represent the inequality 8(n - 5) < 25. Which words should Sal use to complete the verbal statement? The product of 8 and n decreased by 5 is ___________
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Explore Part 2
Drag the number cards to create three points that represent a proportional relationship.
Use the sketch tool if it helps you with your thinking.
Please help I give 10 pt
Answer:
Step-by-step explanation:
1,3 2,6 4,8
I hope it helps, thank you!
I don’t get it I have to find the exterior angle (t+20)
Answer:
110
Step-by-step explanation:
To find the measure of the exterior angle we first need to find the value of t.
The sum of interior angles in a triangle is equal to 180° so we can write the following equation:
t + 10 + t + t + 20 = 180 add like terms
3t + 30 = 180 subtract 30 from both sides
3t = 150 divide both sides by 3
t = 50
The exterior angles and the angle represented with t + 20 make a straight line
and they are supplementary angles so their sum is equal to 180
t + 20 = 70 to complete this to 180 we need 110