Nina and Ryan each ran at a constant speed for a 100-meter race. Each runner’s distance for the same section of the race is displayed on the left. Who had a head start, and how big was the head start?
had a head start of
meters.
Answer:
Ryan had a head start of 10 meters
Step-by-step explanation:
Which graph represents the function?
f(x)=x√+1
The graph of the function f(x)=√(x + 1) is in the first option
What is a radical graphA radical graph, also known as a square root graph, represents the graph of a square root function. A square root function is a mathematical function that takes the square root of the input variable.
The general form of a square root function is f(x) = √(ax + b) + c,
where a, b, and c are constants that determine the characteristics of the graph.
In the given function:
a = 1
b = 1
c = 0
The graph is plotted and attached
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The darkness of the print is measured quantitatively using an index. If the index is greater than or
equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and
not acceptable. Assume that the machines print at an average darkness of 2.2 with a standard
deviation of 0.20.
(a) What percentage of printing jobs will be acceptable? (4)
(b) If the mean cannot be adjusted, but the standard deviation can, what must be the new standard
deviation such that a minimum of 95% of jobs will be acceptable?
84.13% of the printing jobs will be acceptable.
The new standard deviation required to achieve a minimum of 95% of jobs acceptable is 0.121.
The darkness of the print is measured quantitatively using an index. If the index is greater than or equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and not acceptable. The machines print at an average darkness of 2.2 with a standard deviation of 0.20.
The mean of the darkness of the print is µ = 2.2 and the standard deviation is σ = 0.20.Therefore, the z-score can be calculated as; `z = (x - µ) / σ`.The index required for acceptable prints is 2.0. Thus, the percentage of prints that are acceptable can be calculated as follows;P(X ≥ 2.0) = P((X - µ)/σ ≥ (2.0 - 2.2) / 0.20)P(Z ≥ -1) = 1 - P(Z < -1)Using the standard normal table, P(Z < -1) = 0.1587P(Z ≥ -1) = 1 - 0.1587= 0.8413.
To find the new standard deviation, we can use the z-score formula.z = (x - µ) / σz = (2.0 - 2.2) / σz = -1Therefore, P(X ≥ 2.0) = 0.95P(Z ≥ -1) = 0.95P(Z < -1) = 0.05Using the standard normal table, the z-score value of -1.645 corresponds to a cumulative probability of 0.05. Hence,z = (2.0 - 2.2) / σ = -1.645σ = (2.0 - 2.2) / -1.645= 0.121.
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Patricia serves the volleyabll to terri with an upward velocity of 19.5 ft/s . The ball is 4.5 feet above the ground when she strikes it. How long does terri have to react before the volleyball hits the ground ? Round your answer to gwo decimal places
Terri have to react 1.42 seconds before the volleyball hits the ground.
What are quadratic equations?Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is:
[tex]\text{ax}^2 + \text{bx} + \text{c} = 0[/tex]
Given data:
Velocity [tex](v_0)[/tex] = 19.5 ft/sHeight [tex](h_0)[/tex] = 4.5 ftThe height can be modeled by a quadratic equation.
[tex]h(t)=-16t^2+v_0t+h_0[/tex]
Where h is the height and t is the time.
[tex]h(t)=-16t^2+19.5t+4.5[/tex]
[tex]-16t^2+19.5t+4.5=0[/tex]
[tex]a = -16, b = 19.5, c = 4.5[/tex]
It looks like a quadratic equation. we can solve it by quadratic formula.
[tex]\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{(-19.5)^2-4\times(-16)(4.5)} }{2(-16)}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{380.25+288} }{-32}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm25.851 }{-32}[/tex]
[tex]\rightarrow t=\dfrac{-19.5-25.851 }{-32}, \ t=\dfrac{-19.5+25.851 }{-32}[/tex]
[tex]\rightarrow t=1.42, \ t=-0.20[/tex]
Time cannot be in negative. So neglect t = –0.235.
Hence, Terri have to react 1.42 seconds before the volleyball hits the ground.
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Using the physics concept of projectile motion and inputting the given values into the appropriate equation, we can determine the time it takes for the volleyball to hit the ground after being served
Explanation:This question is a classic use of physics, more specifically, the concept of projectile motion. Here, the volleyball can be conceived as a projectile. When Patricia serves the ball upward, the ball will first ascend and then descend due to gravity.
Let's use the following equation which is a version of kinematic equations to solve this problem, adjusting for the fact that we're dealing with an initial height of 4.5 ft and an ending height of 0 ft (when the ball hits the ground). The equation y = yo + vot - 0.5gt² , where:
y is the final vertical position (which we'll take to be 0),yo is the initial vertical position (in this case, the 4.5 feet above the ground),vo is the initial vertical velocity, t is the time (which we're trying to find), andg is the acceleration due to gravity, with the value approximately 32.2 feet per second squared.
Setting y=0, yo=4.5 feet, vo=19.5 feet/second, and g=32.2 feet/second², and plug these values into the equation, we'll get a quadratic equation in the form of 0 = 4.5 + 19.5t - 16.1t². Solve that equation for t to find the time it takes for the ball to hit the ground.
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To find the number in a square, add the numbers in the two circles
connected to it.
Fill in the missing numbers.
The missing values in the quantitative reasoning given are : -2, 13 and 9
Given the rule :
square = circle + circleWe can deduce that :
circle = square - circleFor the left circle :
circle = -6 - (-4) = -6 + 4 = -2
For the right circle :
circle = 11 - (-2) = 11 + 2 = 13
For the left square :
square = 13 + (-4)
square = 13 -4 = 9
Therefore, the missing values are : -2, 13 and 9
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Consider a medium with parameters € = 1.2 (10^-10 )F/m , n= 3(10^-3) H/m and sigma=0. Magnetic field intensity in the medium is given as R = 2cos (10^10t- 600x)äz Am.
Use Maxwell's equations to obtain the followings:
1) Magnetic flux density
These questions is circuit theory
Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:
[tex]\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}[/tex],
where [tex]\displaystyle \nabla \times \mathbf{H}[/tex] is the curl of the magnetic field intensity [tex]\displaystyle \mathbf{H}[/tex], [tex]\displaystyle \mathbf{J}[/tex] is the current density, and [tex]\displaystyle \frac{\partial \mathbf{D}}{\partial t}[/tex] is the time derivative of the electric displacement [tex]\displaystyle \mathbf{D}[/tex].
In this problem, there is no current density ([tex]\displaystyle \mathbf{J} =0[/tex]) and no time-varying electric displacement ([tex]\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0[/tex]). Therefore, the equation simplifies to:
[tex]\displaystyle \nabla \times \mathbf{H} =0[/tex].
Taking the curl of the given magnetic field intensity [tex]\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}[/tex]:
[tex]\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}[/tex].
Using the curl identity and applying the chain rule, we can expand the expression:
[tex]\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z[/tex].
Since the magnetic field intensity [tex]\displaystyle \mathbf{R}[/tex] is not dependent on [tex]\displaystyle y[/tex] or [tex]\displaystyle z[/tex], the partial derivatives with respect to [tex]\displaystyle y[/tex] and [tex]\displaystyle z[/tex] are zero. Therefore, the expression further simplifies to:
[tex]\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z[/tex].
Differentiating the cosine function with respect to [tex]\displaystyle x[/tex]:
[tex]\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z[/tex].
Setting this expression equal to zero according to [tex]\displaystyle \nabla \times \mathbf{H} =0[/tex]:
[tex]\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0[/tex].
Since the equation should hold for any arbitrary values of [tex]\displaystyle \mathrm{d} x[/tex], [tex]\displaystyle \mathrm{d} y[/tex], and [tex]\displaystyle \mathrm{d} z[/tex], we can equate the coefficient of each term to zero:
[tex]\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0[/tex].
Simplifying the equation:
[tex]\displaystyle \sin( 10^{10} t-600x) =0[/tex].
The sine function is equal to zero at certain values of [tex]\displaystyle ( 10^{10} t-600x) [/tex]:
[tex]\displaystyle 10^{10} t-600x =n\pi[/tex],
where [tex]\displaystyle n[/tex] is an integer. Rearranging the equation:
[tex]\displaystyle x =\frac{ 10^{10} t-n\pi }{600}[/tex].
The equation provides a relationship between [tex]\displaystyle x[/tex] and [tex]\displaystyle t[/tex], indicating that the magnetic field intensity is constant along lines of constant [tex]\displaystyle x[/tex] and [tex]\displaystyle t[/tex]. Therefore, the magnetic field intensity is uniform in the given medium.
Since the magnetic flux density [tex]\displaystyle B[/tex] is related to the magnetic field intensity [tex]\displaystyle H[/tex] through the equation [tex]\displaystyle B =\mu H[/tex], where [tex]\displaystyle \mu[/tex] is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.
Thus, the correct expression for the magnetic flux density in the given medium is:
[tex]\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}[/tex].
A rocket is fired vertically upward. Its height h(t) in meters above the ground at t seconds is given
by h = -4.9t² +232t + 185.
How high was the rocket when it was initially launched?
meters
How high is the rocket after 9 seconds?
meters
What is the velocity of the rocket after 9 seconds?
m/s
What is the acceleration of the rocket after 9 seconds?
m/s^2
Submit Question
The rocket is at a height of 1876.1 meters after 9 seconds,the velocity of the rocket after 9 seconds is 143.8 m/s and the acceleration of the rocket after 9 seconds is -9.8 m/s².
To find the height of the rocket when it was initially launched, we can plug in t = 0 into the equation h(t) = -4.9t² + 232t + 185.
h(0) = -4.9(0)² + 232(0) + 185
= 0 + 0 + 185
= 185
Therefore, the rocket was initially launched at a height of 185 meters.
To find the height of the rocket after 9 seconds, we can plug in t = 9 into the equation h(t) = -4.9t² + 232t + 185.
h(9) = -4.9(9)² + 232(9) + 185
= -4.9(81) + 2088 + 185
= -396.9 + 2088 + 185
= 1876.1
Therefore, the rocket is at a height of 1876.1 meters after 9 seconds.
To find the velocity of the rocket after 9 seconds, we can take the derivative of the height function h(t) with respect to time (t) and evaluate it at t = 9.
The velocity function v(t) is the derivative of h(t) with respect to t:
v(t) = dh/dt = d/dt(-4.9t² + 232t + 185)
= -9.8t + 232
v(9) = -9.8(9) + 232
= -88.2 + 232
= 143.8
Therefore, the velocity of the rocket after 9 seconds is 143.8 m/s.
To find the acceleration of the rocket after 9 seconds, we can take the derivative of the velocity function v(t) with respect to time (t) and evaluate it at t = 9.
The acceleration function a(t) is the derivative of v(t) with respect to t:
a(t) = dv/dt = d/dt(-9.8t + 232)
= -9.8
a(9) = -9.8
Therefore, the acceleration of the rocket after 9 seconds is -9.8 m/s².
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Bally Manufacturing sent Intel Corporation an invoice for machinery with a $13,100 list price. Bally dated the invoice August 01 with 3/10
EOM terms. Intel receives a 40% trade discount. Intel pays the invoice on August 14. On August 10, Intel Corporation returns $100 of the machinery due to defects. What does Intel pay Bally on August 14?
The Intel pays $7,760 to Bally Manufacturing on August 14.
The first step in calculating what Intel Corporation pays Bally on August 14 is to determine the net price of the machinery after the trade discount and the return of $100 due to defects.
The trade discount of 40% is calculated as follows:
Discount = List price × Discount rate
Discount = $13,100 × 0.40 = $5,240
So the net price of the machinery after the trade discount is:
Net price = List price - Discount
Net price = $13,100 - $5,240 = $7,860
After Intel returns $100 of machinery, the cost of the machinery is further reduced to:
Net price after return = Net price - Return
Net price after return = $7,860 - $100 = $7,760
Since the payment terms are 3/10 EOM (end of month), Intel receives a discount of 3% if payment is made within 10 days. The 10-day period begins on August 1 and ends on August 10 (the payment due date). Since Intel pays the bill on August 14, payment is late and the 3% discount does not apply.
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Like us, mice are warm-blooded creatures. Their bodies must maintain a constant
temperature of 37°C, regardless of the temperature of their environment. Doing so burns
calories. The more severe the temperature difference, the more calories the mouse must
burn to maintain its body temperature. Consulting the research literature, you found the
following model:
C = 0.37219T + 1,560
Where C is the number of calories an idle mouse burns each day and T is the temperature
of its environment in °C. What is the most comfortable temperature for an idle mouse?
(This is the temperature where it burns the least calories per day). How many calories will
it burn each day at that temperature?
At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.
To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.
To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:
dC/dT = 0.37219 = 0
Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.
Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.
For example, if we take a temperature of 20°C, we can calculate the calorie burn:
C = 0.37219 * 20 + 1,560
C = 7.4438 + 1,560
C ≈ 1,567.4438 calories per day
Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.
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what is the y intercept of y=7
Answer:
7
Step-by-step explanation:
The line represented by the equation y = 7 is a horizontal line that passes through the y-axis at 7, so the y intercept of this line is 7
Waiting times (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of data, then compare the variation.
Bank A (single line) Bank B (individual lines)
6.5 4.0
6.6 5.4
6.7 5.9
6.7 6.2
7.1 6.8
7.4 7.7
7.5 7.7
7.7 8.5
7.7 9.4
7.7 9.8
A) The coefficient of variation for the waiting times at Bank A is
(Round to one decimal place as needed.)
B) The coefficient of variation for the waiting times at Bank B is
(Round to one decimal place as needed.)
C)Is there a difference in variation between the two data sets?
The coefficient of variation for Bank A is approximately 8.04%, while the coefficient of variation for Bank B is approximately 25.55%.
To find the coefficient of variation for each set of data, we need to calculate the mean and standard deviation for each set. The coefficient of variation is then calculated by dividing the standard deviation by the mean and multiplying by 100.
Let's calculate the coefficient of variation for each set of data:
Bank A (single line):
Mean: Calculate the mean of the data set.
Mean = (6.5 + 6.6 + 6.7 + 6.7 + 7.1 + 7.4 + 7.5 + 7.7 + 7.7 + 7.7) / 10 = 7.03 minutes
Standard deviation: Calculate the standard deviation of the data set.
Standard deviation = √[(6.5 - 7.03)² + (6.6 - 7.03)² + ... + (7.7 - 7.03)²] / 10 ≈ 0.565 minutes
Coefficient of variation:
Coefficient of variation = (0.565 / 7.03) * 100 ≈ 8.04%
Bank B (individual lines):
Mean: Calculate the mean of the data set.
Mean = (4.0 + 5.4 + 5.9 + 6.2 + 6.8 + 7.7 + 7.7 + 8.5 + 9.4 + 9.8) / 10 = 7.5 minutes
Standard deviation: Calculate the standard deviation of the data set.
Standard deviation = √[(4.0 - 7.5)² + (5.4 - 7.5)² + ... + (9.8 - 7.5)²] / 10 ≈ 1.916 minutes
Coefficient of variation:
Coefficient of variation = (1.916 / 7.5) * 100 ≈ 25.55%
Comparing the variation:
The coefficient of variation for Bank A is approximately 8.04%, while the coefficient of variation for Bank B is approximately 25.55%. Since the coefficient of variation measures the relative variability of the data, we can conclude that the waiting times at Bank B (individual lines) have a higher variation compared to Bank A (single line).
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Write the English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The product of 8 and a number, which is then subtracted from the product of 17 and the number.
The algebraic expression for the given phrase is: 17x - 8x. To simplify this expression, we can combine like terms by subtracting the coefficients of x. The simplified expression is: 9x.
In the given phrase, "The product of 8 and a number" can be represented as 8x, where x represents the number. Similarly, "The product of 17 and the number" can be represented as 17x. Since we are subtracting the product of 8x from the product of 17x, the algebraic expression becomes 17x - 8x.
To simplify the expression, we combine like terms. The coefficients of x are 17 and -8. Since we are subtracting 8x from 17x, we subtract the coefficient of 8x from the coefficient of 17x, resulting in 17x - 8x. Combining like terms gives us 9x.
In conclusion, the simplified expression for the phrase "The product of 8 and a number, which is then subtracted from the product of 17 and the number" is 9x.
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URGENT
The area of a kite is 180 cm^2. The length of one diagonal is 16cm. What is the length of the other diagonal?
SHOW WORK AND ANSWER PLEASE
The length of the other diagonal is 11.25 cm.
What is area?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
In this question, we are given the following:
The area of a kite is 180. One of the diagonals is 16.
What is the length of the other diagonal?
The details of the solution are as follows:
We know that,
The area of a kite is the product of the diagonals divided by 2:
[tex]\text{A} = \dfrac{(\text{d}^1 \times \text{d}^2)}{2}[/tex]
You can substitute what we have:
[tex]180= \dfrac{(16 \times \text{d}^2)}{2}[/tex]
And solve.
[tex]180 = 16 \times \text{d}^2[/tex]
[tex]\text{d}^2=\dfrac{180}{16}[/tex]
[tex]\text{d}^2=\bold{11.25 \ cm}[/tex]
Therefore, the length of the other diagonal = 11.25 cm.
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