The distance traveled by the ping-pong ball as it rolls forward 6 meters and bounces backward 3 meters is 3 meters.
Distance is a concept that is important to understand in physics and mathematics. It refers to the amount of space between two points. In this scenario, we will be discussing the distance traveled by a ping-pong ball as it rolls forward and bounces backward.
When the ping-pong ball rolls forward, it covers a distance of 6 meters. This can be represented mathematically as d1 = 6 meters.
When the ball bounces backward, it covers a distance of 3 meters. This can be represented as d2 = -3 meters which means the negative sign indicates that it is moving in the opposite direction.
The total distance traveled by the ball can be found by adding the distance traveled in each direction. This can be represented as
=> d = d1 + d2 = 6 + (-3) = 3 meters.
In other words, the total distance traveled by the ball is 3 meters, which is the net distance covered after taking into account both the forward and backward movements.
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Determine the, LCM, of the following three terms: 3st,4s2,5t2
60 s²t² is the lowest common multiple of 3st, 4s^2, 5t^2
Finding the LCM of expressionsLCM is known as the lowest common multiple. This is the smallest number that is a multiple of both of two numbers is called the least common multiple.
Given the terms 3st, 4s^2, 5t^2
Find the factors
3st = 3 * s * t
4s² = 4 * s * s
5t² = 5 * t * t
The LCM is calculated as thus:
LCM = (3*4*5) * s²t²
LCM = 60 s²t²
Hence the LCM of the terms 3st, 4s^2, 5t^2 is 60 s²t²
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calculate 0.069 x 7000
Answer:
483
Step-by-step explanation:
Answer:483
Step-by-step explanation:
69*7=483
The box plots shows the number of books read by students in Mrs. Long's class
this summer. What is the median number of books read in Mrs. Long's class?
O 3 books
O 6 books
O 8 books
O 9 books
Answer:
8 books
Step-by-step explanation:
On a box plot, there is a line in the middle that says where the median is. In this situation, the median is 8.
At Santorini's Shakes, a regular milkshake costs $3.50. A larger milkshake can be purchased for an additional $0.40 per ounce above the regular size.
If x represents the number of ounces above the regular size, which inequality shows how much can be added to the regular size for a milkshake that costs under $5.00?
Answer:
5=0.40x+3.50
He can get 3 extra ounces
Step-by-step explanation:
5.00-3.50=1.50 so an extra $1.50 to spend on extra ounces
1.50/0.40=3
0.40(3)+3.50= $4.70
So the most ounces he can get is 3
He will have $0.30 left
The table below represents a linear function for the cost of a gym membership based on the number of months of membership.
Time (month) Cost
1 $105
3 $165
5 $225
7 $285
What is the slope and y-intercept of the linear function?
The slope is ____ and the y-intercept is ___.
Answer:
The slope is 30, and the y-intercept is 75.
Step-by-step explanation:
Use two points from the table, and find the equation of a line given two points.
Point 1: (1, 105)
Point 2: (3, 165)
y = mx + b
slope = m = (y_1 - y_1)/(x_2 - x_1)
m = (165 - 105)/(3 - 1) = 60/2 = 30
y = 30x + b
Use point (1, 105) for x and y.
105 = 30(1) + b
105 = 30 + b
b = 75
y = 30x + 75
The slope is 30, and the y-intercept is 75.
Karen drove 335 miles in 5 hours.
At the same rate, how many miles would she drive in 11 hours?
Answer: 737 miles
Step-by-step explanation: 335/5=x/11.
Cross Multiply and divide to get x=737
A. x = 80 degrees
B. x = 60 degrees
C. Cannot be determined
D. x = 30 degrees
The measure of the angle is 60 degrees. Option B
How to determine the value of the variableIt is important to value of the angle, we have to take note of the following;
The sum of angles on a straight line is equivalent to 180 degreesThe pair of angles are also supplementary to each otherFrom the information given, we have that;
The angles 80,690 and x are on a straight line, that is, the sum of the angles is 180
This is represented as;
60 + 80 + x = 180
collect like terms
x = 180 - 140
substract the like terms
x = 60 degrees
Hence, the value is 60 degrees
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An airplane takes 7 hours to fly 2800 kilometers against the wind. The return trip with the wind takes only 4 hours. What is the speed, in kilometers per hour, of the airplane in still air?
Answer: Let's call the speed of the airplane in still air "x".
Since the airplane takes 7 hours to fly 2800 kilometers against the wind, its speed against the wind is 2800/7 = 400 km/hr.
Since the return trip with the wind takes only 4 hours, the speed of the wind must be 400 - x.
The total speed of the airplane on the return trip is x + (400 - x) = 400 km/hr.
So, we have:
400 = x + (400 - x)
Expanding the right side:
400 = 400
Therefore, x = 400 km/hr, which is the speed of the airplane in still air.
Step-by-step explanation:
For any given event, the probability of that event and the probability of the _______ of the event must sum to one.
For any given event, the probability of that event and the probability of the non-occurrence of the event must sum to one.
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The probability of occurrence formula, also known to some as the “probability of occurrence formula PMP” is a tool for determining the chance that a given risk will occur. The formula requires two data points: number of favourable events possible and the total number of events possible.
Non occurrence patterns identifies the absence of events when detecting a pattern.
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10. Find the distance of the line segment RS with R(-2, 3) and S(4, 5) in simplest radical form.
The distance between the points in simplest radical form is equal to 2√10 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given parameters into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(4 - (-2))² + (5 - 3)²]
Distance = √[6² + 2²]
Distance = √[36 + 4]
Distance = √40
Distance = 2√10 units.
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When the car reaches point (A), it has a speed of 25 m/s. If the breaks are applied, its speed is reduced by at= (-1/4t^1/2)m/s^2. Determine the magnitude of acceleration of the car just before it reaches point C
The magnitude of acceleration of the car just before it reaches point C is -0.79 m/s^2.
About magnitude of accelerationThe magnitude of acceleration of the car just before it reaches point C can be calculated using the given formula for acceleration, at= (-1/4t^1/2)m/s^2.
First, we need to determine the time it takes for the car to travel from point A to point C.
Since the speed of the car at point A is 25 m/s, and the speed at point C is 0 m/s, we can use the formula for speed, v=at, to find the time it takes for the car to travel from point A to point C.
Rearranging the formula, we get t=v/a.
Substituting the values for speed and acceleration, we get t=25/(-1/4t^1/2).
Solving for t, we get t^3/2 = -100.
Taking the square root of both sides, we get t=10 seconds.
Now, we can substitute the value of t back into the formula for acceleration to find the magnitude of acceleration just before the car reaches point C.
at= (-1/4t^1/2)m/s^2
= (-1/4)(10^1/2)m/s^2
= (-1/4)(3.16)m/s^2
= -0.79 m/s^2
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x^-5y^3 negative exponents
The solution is x^-5y^3 = y^3/x^5.
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
given that,
x^-5×y^3
[ as, the power of x is negative 5, so, we make it positive 5 by dividing}
=1/x^5 * y^3
=y^3/x^5
Hence, The solution is x^-5y^3 = y^3/x^5.
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Round 29.675 to
the hundredths place.
Answer:
29.68
Step-by-step explanation:
If you are rounding to the hundredth place, you take the number in the hundredth place and round it. If it is less than five, for example, if you were rounding 29.674 then it would be 29.67 because 4 is not 5 or more. With 29.675 you will round to 29.68. A saying to remember is, five or above, give it a shove.
The position of a ball after it is thrown is modeled with the
function f(x) = -2(x - 1)² + 7 in vertex form, where y is
the height, in feet, above the ground and x is the horizontal
distance, in feet, of the ball from where it is thrown.
A. Write the function in standard form.
B. What is the height of the ball when it is thrown?
C. What is the horizontal distance from the point where the ball is thrown to the highest point that the ball reaches?
(a) The function in standard form is f(x) = -2x² + 4x + 5.
(b) The height of the ball when it is thrown is 5 feet.
(c) The horizontal distance from the point where the ball is thrown to the highest point that the ball reaches is 1 foot.
What is the function of ball's motion?
To write the function in standard form, we need to expand the square and simplify the expression:
f(x) = -2(x - 1)² + 7
f(x) = -2(x² - 2x + 1) + 7
f(x) = -2x² + 4x - 2 + 7
f(x) = -2x² + 4x + 5
B. The height of the ball when it is thrown is the y-intercept of the function, which occurs when x = 0. So we can find the height by plugging x = 0 into the function:
f(0) = -2(0)² + 4(0) + 5
f(0) = 5
C. The highest point that the ball reaches is the vertex of the parabola, which occurs at x = 1 (from the given vertex form). To find the height of this point, we can plug x = 1 into the vertex form of the function:
f(1) = -2(1 - 1)² + 7
f(1) = -2(0) + 7
f(1) = 7
Therefore, the highest point that the ball reaches is 7 feet above the ground. The horizontal distance from the point where the ball is thrown to this point is the distance between the point (0,5) and the vertex (1,7), which is 1 unit.
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What are the domain and range of this linear function? f(x)=2x-5
Answer:
The Domain : {(−∞,∞), {x/x∈R} and Range : {(−∞,∞), {y/y∈R} of the function f(x)=2x-5
What is a function?
A relation is a function if it has only One y-value for each x-value.
We have to find the domain and range of f(x)=2x-5
The domain of the expression is all real numbers except where the expression is undefined.
In this case, there is no real number that makes the expression undefined.
Interval Notation:(−∞,∞)
The range is the set of all valid y values.
Domain : {(−∞,∞), {x/x∈R}
Range : {(−∞,∞), {y/y∈R}
Hence, the Domain : {(−∞,∞), {x/x∈R} and Range : {(−∞,∞), {y/y∈R} of the function f(x)=2x-5
Have a wonderful day! :-)
Which graph matches the equation y+6=3/4 (x+4)?
Answer: The equation y + 6 = 3/4 (x + 4) can be solved for y to find the corresponding graph:
First, isolate x by subtracting 4 from both sides:
y + 6 - 6 = 3/4 (x + 4) - 6
y = -6 + 3/4 (x + 4)
Next, isolate y by dividing both sides by 3/4:
y = -6 + 3/4 (x + 4) ÷ (3/4)
y = -6 + (x + 4)
y = x - 2 + 10
This equation represents a line with a slope of 1 and a y-intercept of 10 - 2 = 8. The graph of this line is a line that passes through the points (0, 8) and (1, 9).
Step-by-step explanation:
Find the value of X so that the expression X(4-2Y) is equivalent to 2/3 - 1/3Y.
The equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).
The given expression is c² - 64.
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
1) The factorization of c² - 64 is as follows:
Now, factors of c² - 64 is c² - 8²=(c-8)(c+8)
2) 12y² -75 = 3 (4y²-25)
= 3((2y)²-5²)
= 3 (2y+5)(2y-5) (∵ a²-b²=(a-b)(a + b))
3) 9y²-36 = 9(y²-4)
= 9(y²-2²)
= 9(y-2)(y+2) (∵ a²-b²=(a-b)(a + b))
4) -x²+5x-4
= x²-5x+4
= x²-4x-x+4
= x(x-4)-1(x-4) (∵ a²-b²=(a-b)(a + b))
= (x-4)(x-1)
5) ab²-b
=b(ab-1)
Therefore, the equivalent expression for the given expression -x²+5x-4 is (x-4)(x-1).
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The line passing through the points ( -4, 6) and ( b, 2) has a gradient 1 /2 . Find the value of b.
Answer:
b = - 12
Step-by-step explanation:
calculate the slope of the line passing through the 2 points and equate to [tex]\frac{1}{2}[/tex]
calculate the slope ( gradient ) m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 6 ) and (x₂, y₂ ) = (b, 2 )
m = [tex]\frac{2-6}{b-(-4)}[/tex] = [tex]\frac{-4}{b+4}[/tex]
equating gives
[tex]\frac{-4}{b+4}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
b + 4 = - 8 ( subtract 4 from both sides )
b = - 12
The September price of a computer was $1000. Later, an October price was obtained by raising the September price by 20%. Then a November price was obtained by lowering the October price by 20%. What was the November price in dollars?
Answer:
Step-by-step explanation:
1200
Answer:
$960
Step-by-step explanation:
September = 1000
20% * 1000 = 200
1000+200 = 1200
October = 1200
20% * 1200 = 240
1200-240 = 960
November = 960
On a coordinate plane, a curved line with a minimum value of (negative 1, negative 2), crosses the x-axis at (negative 2, 0) and the y-axis at (0, 0).
Determine the x-intercepts of the function. Check all that apply.
(–2, 0)
(–1, –2)
(0, 0)
(1, 0)
(2, 0)
x-intercepts of the curved line are (-2,0) and (0,0)
What is intercept ?The points where a line or curve intersects the chart's axes are called intercepts. When a point intersects the x-axis it is called the x-intercept. When a point intersects the y-axis, it is called the y-intercept.
A line intercept is a point where it intersects the x-axis or the y-axis. If no axis is specified, the y-axis is normally considered. It is usually represented by the letter 'b'.
Given,
A curved line with a minimum value of (-1 , -2)
it crosses x-axis at (-2,0) and y-axis at (0,0)
We know that, x-intercept is the point where line crosses x-axis, y-coordinate = 0
x-intercepts are (-2,0) and (0,0)
Hence, (-2.0) and (0,0) are x-intercepts of the curved line.
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Answer: (–2, 0), (0, 0)
Step-by-step explanation:
Say you have a single pair of pants and a single shirt. In this case you'd only have 1 outfit option.
If you have 2 pairs of pants and 2 shirts, you now have 4 unique outfit options.
How many pairs of pants and shirts would you need in order to have a unique outfit for each day of the week?
What if you wanted a unique outfit each day for a month? for a year? for your whole life
To have a unique outfit for each day of the week, you would need at 3 pairs of pants and 3 shirts.
To have a unique outfit for a month you would need at 6 pairs of pants and 5 shirts.
To have a unique outfit for each day of the year, you would need 26 pairs of pants and 15 pairs of shirts.
How to find the unique outfits ?To find the unique outfits, you need to have enough clothes to have a unique outfit made from those clothes.
There are 7 days in a week. If you had 3 pairs of pants and 3 shirts, the unique outfits would be :
= 3 x 3
= 9 unique outfits
For a month :
= 6 x 5
= 30 unique outfits
For a year :
= 26 x 15
= 390 unique outfits for 365 days
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Which shapes from the Clade Race would be considered autoapomorphic?a. Arrow b. Circle c. Moon d. Triangle e. Square f. Crossg. Star h. Heati. Hexagon
Answer:
Step-by-step explanation:
f
Neron Co. Has two derivatives related to two different financial instruments, instrument A and instrument B, both of which are debt instruments. The derivative related to instrument A is a fair value hedge, and the derivative related to instrument B is a cash flow hedge. Neron experienced gains in the value of instruments A and B due to a change in interest rates. Which of the gains should be reported by Neron in its income statement?Gain in value of debt instrument A Gain in value of debt instrument BYes YesYes NoNo YesNo No
Only the gains from the fair value hedge related to instrument A should be reported by Neron in its income statement.
About the reportNeron Co. should report the gains from the fair value hedge related to instrument A in its income statement. This is because fair value hedges are used to offset changes in the fair value of a financial instrument, and any gains or losses from these hedges are recognized in income.
On the other hand, gains from the cash flow hedge related to instrument B should be reported in other comprehensive income, not in the income statement.
This is because cash flow hedges are used to offset changes in the cash flows of a financial instrument, and any gains or losses from these hedges are recognized in other comprehensive income until the hedged item affects income.
Therefore, only the gains from the fair value hedge related to instrument A should be reported by Neron in its income statement.
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Today hugo got a new credit card, and he made a purchase of $1400. The card offers an introductory apr of 0% for the first 5 months and a standard apr of 30. 8% thereafter. If the card compounds interest monthly, how much money will the introductory apr save hugo in interest over the first 5 months? (assume that hugo will make no payments or additional purchases during the first 5 months, and ignore any possible late payment fees. ).
$189.13
That's the correct answer On Ax
Answer:
$189.13
Step-by-step explanation:
You want to know the interest saved if interest at 30.8% compounded monthly on a balance of $1400 is waived for 5 months.
Compound interestThe balance with interest compounded would be ...
A = P(1 +r/12)^n
where P is the principal earning interest at annual rate r for n months.
The amount of interest earned in that time is ...
I = P((1 +r/12)^n -1) = $1400(1 +0.308/12)^5 -1) ≈ $189.13
Hugo will save $189.13 in interest charges for the first 5 months.
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Select the equation that should be used to solve for x. Responses 8x−14+2x+10=90 8 x minus 14 plus 2 x plus 10 is equal to 90 8x−14+2x+10=180 8 x minus 14 plus 2 x plus 10 is equal to 180 8x−14=2x+10 8 x minus 14 is equal to 2 x plus 10 8x−14+2x+10=360 8 x minus 14 plus 2 x plus 10 is equal to 360
The value of x is 9.4 in the equation 8x−14+2x+10=90.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 8x−14+2x+10=90
Eight times of x minus forteen plus two times of x plus ten equal to ninety.
In the given equation x is the variable
Plus and minus are the operators.
Add the like terms
Ten times of x minus four equal to ninety
10x-4=90
Add 4 on both sides to cancel four on the left hand side.
10x-4+4=90+4
10x=94
Divide both sides by 10
x=94/10
Divide numerator and denominator by 10.
x=9.4
Hence, the value of x is 9.4 in the equation 8x−14+2x+10=90.
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The complete question
Solve the equation 8x−14+2x+10=90
There were 175
spectators at a concert. The box office sold 10
more adult tickets than twice the number of discounted student tickets.
How many more adults than students bought tickets to the concert?
There were 65 more adults than students who bought tickets to the concert.
How to find the number of hamburgers sold on Saturday?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Let the number of discounted student tickets sold be x.
Then the number of adult tickets sold is 10 more than twice x, which is 2x+10.
The total number of tickets sold is the sum of the student and adult tickets, which is x + (2x+10) = 3x+10.
We know that the total number of tickets sold is 175, so:
3x+10 = 175
Subtracting 10 from both sides gives:
3x = 165
Dividing by 3 gives:
x = 55
Thus, the number of discounted student tickets sold is 55, and the number of adult tickets sold is:
2x+10 = 2(55) + 10 = 120.
The number of adults who bought tickets is 120, and the number of students who bought tickets is 55.
difference = 120 - 55 = 65
Therefore, there were 65 more adults than students who bought tickets to the concert.
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If the vertex of the graph of y = −1(x − 2)2 + 3 is (a,b) what is the value of b?
Answer:
the value of b is 3.
Step-by-step explanation:
The vertex of the graph of a parabola in the form y = a(x - h)^2 + k is given by (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
So in this case, the vertex of the graph of y = -1(x - 2)^2 + 3 is (2, 3), and the value of b is 3.
Answer:
b=3
Step-by-step explanation:
[tex]y=a(x-h)^2+k\\y=-1(x-2)^2+3[/tex]
If we compare the vertex-form equation of a parabola to our given function, we can see the vertex is [tex](2,3)[/tex], which means that b=3.
what a unit of measurement equal to one thousand meters?
A unit of measurement equal to one thousand meters is called a kilometer.
The prefix "kilo" means one thousand, so a kilometer is a unit of length in the metric system that is equal to 1000 meters. Kilometers are commonly used to measure longer distances, such as the distance between cities or countries, or the length of a marathon race. In contrast, smaller distances may be measured in meters, centimeters, or millimeters, which are all smaller units of length in the metric system.
a metric measurement of length that is equal to 1,760 yards or 5,280 feet. A thousandth of a liter is the same as a metric unit of capacity. a length measurement in meters that is one-thousandth of a meter. a time interval that is frequently used and equates to 60 seconds and 1/60 of an hour.
The complete question is:-
What word goes with a unit of measurement equal to one thousand meters?
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What is the value of 350f in c?
The temperature 350°F is equivalent to 176.667°C. This is because the temperature in Fahrenheit can be converted to Celsius using the formula, °C = (°F - 32) / 1.8. Using this formula, 350°F - 32 = 318 and 318/1.8 = 176.667°C.
The relationship between Fahrenheit and Celsius scales is a linear one, meaning that for every degree increase in Fahrenheit, there is a corresponding increase of 1.8 degrees in Celsius. This means that if the temperature increases from 350°F to 351°F, then the corresponding temperature in Celsius would increase from 176.667°C to 178.472°C. The same formula can be used to convert Celsius to Fahrenheit, with the formula °F = (°C x 1.8) + 32. In this case, 176.667°C x 1.8 = 319.2 and 319.2 + 32 = 351.2°F, which is a close approximation of the original temperature of 350°F..
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What are the three components of research questions?
A research question is an inquiry that a study or research project aims to resolve. Quantitative and Qualitative research questions are the components of questions.
Descriptive research questions are used to determine how the population of the study will react to one or more variables or to describe the factors that the study will evaluate. These questions typically begin with "what."
Comparative research questions aim to identify differences between two or more groups for an outcome variable. These inquiries could possibly be the cause. A comparison between two groups, one in which a certain variable is present and the other in which it is not, may be made, for instance.
Relationship research themes aim to find patterns and interactions between two or more variables. The phrases "association" and "trends," as well as dependent and independent variables, are commonly used in these enquiries.
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