To find the time for Car X to be 5 laps ahead of Car Y, we calculate the difference in laps completed per minute (0.25 laps) and divide the target difference (5 laps) by this rate, which gives us 20 minutes.
Explanation:The question asks how long it will take for Car X to be 5 laps ahead of Car Y if Car X makes one lap every 60 seconds and Car Y every 80 seconds. To solve this, we need to find the difference in laps completed by the two cars over time, until Car X is 5 laps ahead. Since Car X is the faster car, it takes one lap less time than Car Y to complete a lap.
First, we find out how many laps Car X completes more than Car Y in one minute:
Laps per minute for Car X: 1 lap/60 seconds = 1/60 laps per second * 60 seconds = 1 lapLaps per minute for Car Y: 1 lap/80 seconds = 1/80 laps per seconds * 60 seconds = 0.75 lapsThe difference in the number of laps per minute is 1 lap - 0.75 laps = 0.25 laps per minute for Car X compared to Car Y.
Next, we calculate the time it will take for Car X to be 5 laps ahead:
5 laps / 0.25 laps per minute = 20 minutesTherefore, it will take 20 minutes for Car X to be 5 laps ahead of Car Y.
Need Answer NOW!!! Solve for the following equation step by step and justify your steps when using an exponential property.
Answer:
x = 5/7
Step-by-step explanation:
(7^x)^4) = 7^2 * 7^3 / 7^3x
1. Simplify the expression
(7^x)^4) becomes 7^4x
7^2 * 7^3 becomes 7^5
7^5/7^3x becomes 7^5 - 7^3x
Your new equation: 7^4x = 7^5 - 7^3x
2. Since the bases(7) are the same set the exponents equal to each other
4x = 5 - 3x
3. Combine like terms
4x + 3x = 5
7x = 5
4. Divide both sides by 7 to get x by itself
x = 5/7
Answer:
x = [tex]\frac{5}{7}[/tex]
Step-by-step explanation:
[tex](7^{x})^{4}=\frac{7^{2}\times 7^{3}}{7^{3x}}[/tex]
[tex](7^{x})^{4}=\frac{7^{(2+3)}}{7^{3x}}[/tex] [Since [tex]a^{b}\times a^{c}=a^{b+c}[/tex] ]
[tex]7^{4x}=\frac{7^{5}}{7^{3x}}[/tex] [since [tex](a^{b})^{c}=a^{bc}[/tex] ]
[tex]7^{4x}={7^{5}\times{7^{-3x}}[/tex] [ [tex]\frac{1}{a}=a^{-1}[/tex] ]
[tex]7^{4x}=7^{(5-3x)}[/tex]
4x = 5 - 3x
[tex]4x+3x=5[/tex] ⇒ 7x = 5
x = [tex]\frac{5}{7}[/tex]
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Answer:
In Step 4, Daryl multiplied 12 and 100 incorrectly.
Step-by-step explanation:
12 x 100 = 1200, not 120
Simplify using the distributive property. 1/4 (4x + 8)
Answer:
1x+2
Step-by-step explanation:
1/4*4x=1x
1/4*8=2
1x+2
Answer:
x+2
Step-by-step explanation:
1/4 (4x + 8)
Multiply each term inside the parentheses by 1/4
1/4*4x + 1/4*8
x+2
What is the probability of not drawing a blue marble?
The probability of not drawing a blue marble from a bag containing four blue and three white marbles is calculated as the number of white marbles divided by the total number of marbles, resulting in 3/7. The marble is replaced after the first draw, so the total number of marbles stays the same for the second draw.
Explanation:The question is about calculating the probability of not drawing a blue marble from a bag which contains a certain number of blue and white marbles. The probability of an event is calculated as:
P(event) = The number of ways the event can occur / Total number of outcomes
In the given example, there are four blue marbles and three white marbles in the bag, making a total of seven marbles. If James draws one marble, the probability of not drawing a blue marble i.e., drawing a white marble, is the number of white marbles divided by the total number of marbles. Thus:
P(Not Blue) = P(White) = Number of White Marbles / Total Marbles = 3 / 7
It's important to note that the probability is calculated this way because James replaces the marble after drawing it the first time. So, the total number of marbles remains the same for the second draw, keeping the probability the same. This concept is related to probability in Geometric Distribution scenarios.
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The probability is 9/12 which can simplify to D: 3/4
When you draw a marble, there are 12 possible marbles you can draw. There are 3 blue marbles and 9 non-blue marbles. Therefore, the probability of drawing a non-blue marble is 9/12. This can simplify to 3/4.
Another way to solve this problem is to use the concept of complements. The complement of event A is the event that does not occur. In this case, the event A is drawing a blue marble and the complement of event A is not drawing a blue marble.
The probability of event A is 1 - the probability of the complement of event A.
The probability of not drawing a blue marble is 1 - 3/12 = 9/12 = 3/4.
Therefore, the answer is D: 3/4.
Which exponential function goes through the points (1,32) and (4,2048)
Answer:
y=8*4^x
Step-by-step explanation:
Let the exponential function be of the form y=A*B^x
We want to find constant A and B.
So I'm going to use (1,32) giving me 32=A*B
I'm going to use (4,2048) giving me 2048=A*B^4
2048/32=64
A*B^4/A*B=B^3
So If you divide the equation 2048=A*B^4 by 32=A*B
we get 64=B^3
which gives us B=4
Since 32=A*B and B=4 then A=8
So the answer is y=8*4^x
1. Mr. McClellan has a board game that requires the use of two 4-sided dice. According to his rules, you can only start the game if you roll a 2 on at least one of the dice.
(a) Make a list of all the different possible outcomes when two 4-sided dice are rolled.
(b) What is the probability of a favorable outcome
(c) Suppose you rolled the two 4-sided dice 100 times, would you expect at least one 2 more or less than 28 times? Explain.
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Sam is applying for a single year life insurance policy worth $25,700.00. If the actuarial tables determine that he will survive the next year with probability 0.99, what is his expected value for the life insurance policy if the premium is $362.00?
Answer:
-261.85
Step-by-step explanation:
If she lives with probability .996, it cost her - 334.
If she dies with probability .004, the value is 71150 - 334
.996*(-334) + .001*(71150 - 334) = -261.85
Final answer:
Sam's expected value from the life insurance policy is calculated by considering both the probability of survival and death. The probability-adjusted outcomes are summed, showing that Sam would, on average, lose $105 with this policy over a year.
Explanation:
Sam is interested in purchasing a single year life insurance policy that has a value of $25,700. According to actuarial tables, the probability of Sam surviving the next year is 0.99. We calculate the expected value of the life insurance policy for him by taking into account both outcomes: survival and death within the next year.
The expected value (EV) is calculated by multiplying the value of the potential outcomes by their respective probabilities and then summing these products together.
To calculate Sam's expected value from the life insurance policy, we account for both scenarios:
If Sam survives (which has a 0.99 probability), he receives nothing from the policy and only loses the premium paid, which is $362.00.
If Sam dies (which has a 0.01 probability), his estate receives the policy worth of $25,700.
Expected Value = (Probability of Surviving) * (Value if Survive) + (Probability of Dying) * (Value if Die) - (Cost of Insurance Premium)
So for Sam's case, it would be:
Expected Value = (0.99 * $0) + (0.01 * $25,700) - $362
Expected Value = ($0) + ($257) - $362
Expected Value = $257 - $362
Expected Value = -$105
Therefore, the expected value of the life insurance policy for Sam is a negative $105, meaning that, on average, Sam would lose $105 over the one year term of the policy.
Helpppppp helpppppppp plssssssssss
Answer:
Scales-No equal sides
Isosceles- 2 Equal
Equilateral-
Right-90 degree
Obtuse- Obtuse Angle
If the graph of the following parabola is shifted four units right and three units down, what is the resulting equation in vertex form? x=4y^2
ANSWER
The resulting parabola in vertex form is:
[tex](x - 4) = 4( {y + 3)}^{2}[/tex]
EXPLANATION
The original equation of the parabola is given as
[tex]x = 4 {y}^{2} [/tex]
This parabola has its vertex at the origin.
If the graph of this parabola is shifted four units right and three units down, then the new equation is:
[tex](x - 4) = 4( {y + 3)}^{2}[/tex]
This the equation of the transformed parabola.
Its vertex is now at (4,-3).
Answer:
(x-4)=4(y+3)^2
Step-by-step explanation:
What is the distance between the points (3,_5) (-2,7) ?
Answer:
The distance between (3,5) (-2,7) is 29 blocks or squares
Step-by-step explanation:
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the captain of a boat knows that the lighthouse on the coast is 200 feet tall. he measures the angle of elevation to the top of the lighthouse to be 2 degrees. how far is the boat from the coast? round to the nearest hundredth of a foot.
Answer:
The boat is 5727.25ft far from the coast
Step-by-step explanation:
Refer the figure given.
We need to find how far is the boat from the coast = AB
Angle of elevation = 2°
The lighthouse on the coast is 200 feet tall, AC = 200 ft
We have
[tex]tan2=\frac{AC}{AB}=\frac{200}{AB}\\\\AB=\frac{200}{tan2}=5727.25ft[/tex]
The boat is 5727.25ft far from the coast
Answer:
The boat is 5727.25ft far from the coast
3z + 4x – d = 4d + e
Answer: 3z+4x-5d-e=0
Step-by-step explanation:
I’m assuming you were asked to simplify or combine like terms...
I moved the 4d over to combine with -d by changing the sign and I did the same for e
Answer:
[tex]z = \frac{5d}{3} + \frac{e}{3} - \frac{4x}{3} [/tex]
Name the type of angles shown. Check all that apply.
Answer:
B, D
Step-by-step explanation:
The types of angles are:
Right angle
Straight angle
Complementary angles
Options A< B< and D are the correct answer.
We have,
The right angle is a 90-degree angle.
When two angles add up to 180 degrees, the angles are called complementary angles.
A straight angle is a 180-degree angle.
Now,
From the figure,
∠JLK = 90
∠KLM = 90
These are 90-degree angles.
And,
∠JLM = ∠JLK + ∠JLM
= 90 + 90
= 180
This can be termed as:
- straight angle (∠JLM)
- complementary angle (∠JLK and ∠JLM)
Thus,
The types of angles are:
Right angle
Straight angle
Complementary angles
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If f (x) =2x+2 and g (x) =³, what is (g°f) (2)? Enter the correct answer
Answer:
∴ (g ο f)(2) = 216
Step-by-step explanation:
* Lets revise at first the meaning of f of g (composite function)
- A composite function is a function that depends on another function
- A composite function is created when one function is substituted into
another function
- Example:
# (g ο f)(x) is the composite function that is formed when f(x) is
substituted for x in g(x).
* Now lets solve the problem
∵ f(x) = 2x + 2
∵ g(x) = x³
- We need to find (g ο f)(2), so we will substitute x by f(x) in g(x)
∴ (g ο f)(x) = (2x + 2)³
- Now substitute x by 2
∴ (g ο f)(2) = [2(2) + 2]³ = [4 + 2]³ = [6]³ = 216
* * (g ο f)(2) = 216
# Another way
- We can find f(2) at first and then substitute the x by the answer
in g(x)
∵ f(x) = 2x + 2
∴ f(2) = 2(2) + 2 = 4 + 2 = 6
∵ g(x) = x³
∴ g(6) = (6)³ = 216
* (g ο f)(2) = 216
Classify the statements based on whether they are represented by +3 or -3.
Deposit of $3 3 F Below 0 F 3 floors Below ground level 3 feet above sea level 3 F above 0 F Loss of $3
Answer
Step-by-step explanation:
If you deposit money, your bank account shows it as +3
3 degrees below zero = - 3 o F which is darn cold.
3 floors below ground level = - 3 floors below ground level
3 feet above sea level = +3 feet
3 degrees about 0 = + 3
3 dollars lost = -3 dollars.
Which of the following are remote interior angles of 1? Check all that apply.
Answer:
A and BStep-by-step explanation:
Remote interior angles are defined as the two angles that are inside the triangle and opposite from the exterior angle.
In this case, [tex]\angle 3[/tex] and [tex]\angle 2[/tex] are remote interior angles of 1, because they are opposite to it, which is the exterior angle.
Therefore, the right choices are A and B.
The remote interior angles of 1 are -90°, -60°, and -30°.
Explanation:Remote interior angles are angles formed by two lines and a transversal where the interior angles are not adjacent or consecutive. In the given options, the remote interior angles of 1 are:
-90°-60°-30°These angles are considered remote interior angles because they are not adjacent or consecutive to 1°.
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The perimeter of a rectangle is 42 inches. If the width of the rectangle is 6 inches, what is the length
Answer:
Length = 15 inches
Step-by-step explanation:
Here we are given the width and the perimeter of the rectangle and we are required to find out our length. We will use the formula of perimeter in order to find the length.
The formula for perimeter
P=2(l+b)
where
l is length
b is width = 6
P is perimeter = 42
substituting them in formula we get
42=2(l+6)
dividing both sides by 2 we get
21 = l + 6
subtracting 6 from both sides we get
15 = l
Hence length is 15 inches
Answer: 15 inches
Step-by-step explanation: It is 15 inches i had this question and did all the steps and got 15 then i answered 15 and it was correct
-4w(w+2) can someone help me find the answer to this please ;c
Answer:
-4w^2- 8w
Step-by-step explanation:
-4w(w+2), use distributive property, (-4w x w)+(-4w x 2)= (-4w^2)+-8w
What is the inverse of the function f(x) = 2x – 10?
h(x) = 2x - 5
h(x) = 2x + 5
"
h(x)=2x-5
o ncx) = {x+5
Answer:
see explanation
Step-by-step explanation:
let y = f(x) then rearrange making x the subject
y = 2x - 10 ( add 10 to both sides )
y + 10 = 2x ( divide both sides by 2 )
[tex]\frac{y+10}{2}[/tex] = x
Change y back into terms of x
[tex]f^{-1}[/tex] (x) = [tex]\frac{x+10}{2}[/tex]
How much would $400 be worth after 11 years, if it were invested at 4% interest compounded monthly? (Use the formula below and round your answer to the nearest cent.)
The formula for compound interest is: A = P(1 +r/n)^nt
Where P is the principal ( starting value)
r is the interest rate
n is the number of compounds
and t is the number of years.
Fill in the letters with the given information:
A = 400(1+0.04/12)^(12*11)
A = 400(1.00333)^132
A = 400*1.551557
A = 620.63
The answer is $620.63
What equation of a line that has a y-value that increases by 4 for every x that increases by 1 and also crosses the y-axis at -2
Answer: y = 4(x + 1) - 2
Step-by-step explanation:
" increases by 4 for every x + 1" means the slope is 4 and the value inside the parentheses with x is +1
"crosses the y-axis at -2" means the y-intercept is -2
Input those values into the formula: y = m(x) + b where
m is the slopeb is the y-interceptPLEASE HURRY AND ANSWER THIS!
Circle X with a radius of 6 units and circle Y with a radius of 2 units are shown
Which steps would prove the circles similar?
Translate the circles so they share a common center
point, and dilate circle Y by a scale factor of 4.
Translate the circles so the center of one circle rests on
the edge of the other circle, and dilate circle Y by a scale
factor of 4.
Translate the circles so they share a common center
point, and dilate circle Y by a scale factor of 3.
Translate the circles so the center of one circle rests on
the edge of the other circle, and dilate circle Y by a scale
factor of 3
Answer:
Translate the circles so they share a common center
point, and dilate circle Y by a scale factor of 3.
Step-by-step explanation:
^^^
Answer:
C) Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.
Step-by-step explanation:
factorise 2x(a-2b)+3y(2b-a)
[tex]2x(a-2b)+3y(2b-a)=2x(a-2b)-3y(a-2b)=(2x-3y)(a-2b)[/tex]
Solve for x: 2/3+1/3x=2x
Answer:
x=2/5 or
x=0.4
Step-by-step explanation:
Answer:
[tex]\frac{2}{5}[/tex] or 0.4.
Step-by-step explanation:
[tex]\frac{2}{3}[/tex]+[tex]\frac{1x}{3}[/tex]=2x
[tex]\frac{2}{3}[/tex]=2x-[tex]\frac{1x}{3}[/tex]
[tex]\frac{2}{3}[/tex]=[tex]\frac{6x-x}{3}[/tex]
[tex]\frac{2}{3}[/tex]=[tex]\frac{5x}{3}[/tex]
x=[tex]\frac{2}{5}[/tex]
or
x=0.4
Solve for L: P = 2L + 2W
[tex]P = 2L + 2W\\2L=P-2W\\L=\dfrac{P-2W}{2}[/tex]
What is the slope of the line represented by the equation y = –x + ? – –
Step-by-step answer:
Assuming the equation is y=-x+k,
where k is a constant, such as 5, pi, 10/7, etc.
then the slope is the coefficient of the term containing x, namely
-1 (since -x is a shorthand for (-1)*x ).
For this case we have by definition, that the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut point with the "y" axis
We have, according to the data provided, that the line is of the form:
[tex]y = -x + b[/tex]
That means that the slope is -1.
ANswer:
[tex]m = -1[/tex]
Choose the correct simplification of (3x3y4z4)(2x3y4z2).
Answer:
6x^6y^8z^6
Step-by-step explanation:
(3x^3y^4z^4)(2x^3y^4z^2)
= 6x^(3+3) y^(4+4) z^(4+2)
= 6x^6y^8z^6
Answer:
The simplified form of given expression is [tex]6x^6y^8z^6[/tex].
Step-by-step explanation:
The given expression is
[tex](3x^3y^4z^4)(2x^3y^4z^2)[/tex]
On multiplication of constants, we get
[tex](3\times 2)(x^3y^4z^4)(x^3y^4z^2)[/tex]
[tex]6(x^3y^4z^4)(x^3y^4z^2)[/tex]
It can be written as
[tex]6(x^3x^3)(y^4y^4)(z^4z^2)[/tex]
Using product property of exponent, we get
[tex]6x^{3+3}y^{4+4}z^{4+2}[/tex] [tex][\becuase a^ma^n=a^{m+n}][/tex]
[tex]6x^6y^8z^6[/tex]
Therefore the simplified form of given expression is [tex]6x^6y^8z^6[/tex].
What is the solution to this system of linear equations?
3x – 2y = 14
5x + y = 32
0 (3,5)
0 (6,2)
0 (8.-1)
(14.-18)
Answer:
C) (6,2)
Step-by-step explanation:
To solve the system of equations, solve one of the equations for y, then plug the result into the other equation to get the value of x. When you get x, substitute it back into one of the original equations to find the value of y, which is 2.
To find the solution to the system of linear equations, we can use the method of substitution or elimination. Let's use the method of substitution and solve for x and y. The solution is (6, 2).
Explanation:To find the solution to the system of linear equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From the second equation, we can isolate y by subtracting 5x from both sides: y = 32 - 5x
Substitute this expression for y in the first equation: 3x - 2(32 - 5x) = 14
Simplify and solve for x: 3x - 64 + 10x = 14, 13x - 64 = 14, 13x = 78, x = 6
Now substitute the value of x back into one of the original equations and solve for y: 5(6) + y = 32, 30 + y = 32, y = 2
Therefore, the solution to the system of linear equations is x = 6 and y = 2, which can be written as (6, 2).
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Four students were discussing how to find the unit rate for a proportional relationship. Which method is valid?
Answer:
“Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.”
“Look at the graph of the relationship. Count the number of units up and the number of units to the right one must move to arrive at the next point on the graph. Write these two numbers as a fraction.”
“Look at the graph of the relationship. Find the x-value of the point that corresponds to y = 2. That value is the unit rate.”
“Look at the graph of the relationship. Find two points which have y-values that are one unit apart. The unit rate is the difference in the corresponding x-values.”
Step-by-step explanation:
Answer: A. “Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.”
find f(-3) if f(x) =x^2
-9
-6
6
9
Answer:
9Step-by-step explanation:
[tex]f(x)=x^2\\\\f(-3)\to\text{put x = -3 to the equation of the function}\\\\f(-3)=(-3)^2=(-3)(-3)=9[/tex]