Let x be the number of t-shirts and y the number of shorts they sold. Since in total they sold 266 items we have the equation:
[tex]x+y=266[/tex]Now we know that each shirt cost $2 and each short cost $4 and that the total sales were $672 then we have the equation:
[tex]2x+4y=672[/tex]Hence we have the system of equations:
[tex]\begin{gathered} x+y=266 \\ 2x+4y=672 \end{gathered}[/tex]Solving for y from the first equation we have:
[tex]y=266-x[/tex]Plugging this in to the second equation we have:
[tex]\begin{gathered} 2x+4(266-x)=672 \\ 2x+1064-4x=672 \\ -2x=672-1064 \\ -2x=-392 \\ x=\frac{-392}{-2} \\ x=196 \end{gathered}[/tex]Plugging this value in the equation for y we have:
[tex]y=266-196=70[/tex]Therefore the sold 196 shirts and 70 shorts.
Jake throws a rock downward from his deck at time t = 0 and it lands in his yard below.
Which of the following graphs best shows the velocity u of the rock until it hits the ground?
A graph of velocity vs time displays the change in an object's velocity in a straight line with regard to time.
What is meant by Velocity-time graph?A plot between speed and time is called a velocity-time graph. It depicts the motion of an object moving straight ahead. At any given time, the magnitude of velocity equals its instantaneous speed.
A graph of velocity vs time displays the change in an object's velocity in a straight line with regard to time. The x-axis is used to measure time, and the y-axis is used to measure velocity. For an item moving at a constant velocity, the height of the velocity-time graph does not change over time.
We can use a velocity vs. time graph to determine position and a time graph to determine velocity. We are aware that v = d/t. Rearranging the equation with a little mathematics reveals that d = v × t.
The complete question is:
Jack throws a rock downward from his deck at time t = 0 and it lands in his yard below. Make velocity-time graph of the rock until it hits the ground? Assume upward is the positive direction.
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A 50-ω resistor is connected to a 9.0 V battery. How much thermal energy is produced in 7.5 minutes?1.2 102 J1.3 103J3.0 102 J7.3 102 J
The power consumed by the resistor can be expressed as,
[tex]P=\frac{V^2}{R}[/tex]Substitute the given values,
[tex]\begin{gathered} P=\frac{(9.0V)^2}{50\text{ }\Omega}(\frac{1\text{ W}}{1V^2\Omega^{-1}}) \\ =1.62\text{ W} \end{gathered}[/tex]The thermal energy produced in the given time can be expressed as,
[tex]E=Pt[/tex]Plug in the known values,
[tex]\begin{gathered} E=(1.62\text{ W)(7.5 min)(}\frac{60\text{ s}}{1\text{ min}}) \\ =729\text{ J} \\ \approx7.3\times10^2\text{ J} \end{gathered}[/tex]Thus, the thermal energy produced is 7.3*10^2 J which means fourth option is correct.
A net force of 20 Newtons acts on and object of mass 5.0 kilograms for 5.0 seconds. What is the magnitude of the impulse?
The impulse of the objects is N-s.
In physics, the term "impulse" is used to characterize or measure the impact of force operating gradually to alter an object's motion. It is often stated in Newton-seconds or kilograms per second and is denoted by the symbol J.
We are given that,
The net force acted on the object = F = 20 N
The mass of the object = m = 5.0kg
The total time taken = t = 5.0s
Therefore, the impulse of the object can be calculated by the formula,
J = F × t
Where, J is the impulse on the object, F is the force on the object , t is the total time taken ,
J = 20N × 5.0sec
J = 100 N-sec
Thus , the total impulse on the object would be 100N-sec.
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A mosquito was accelerating from rest at a rate of 0.15 m/s'. If she flew for 12 meters, what was her final velocity?
The final velocity of the mosquito if it was accelerating from rest at a rate of 0.15 m/s² and flew for 12 meters, is 1.8 m/s
What is velocity?velocity is a term used to describe how quickly and in what direction a point is moving. A point always moves in a direction that is perpendicular to its path; in the case of a circular path, for instance, its direction is always perpendicular to a line connecting the point to the circle's centre (a radius).
The speed at which a point is moving along a path is measured by the magnitude of the velocity.
When a point moves a specific distance along its path in a predetermined amount of time, the distance travelled divided by the time required represents the point's average speed during that time. For instance, the average speed of a train travelling 100 km in two hours is 50 km/h.
The formula for final velocity is
v² - u² = 2as
where v is the final velocity,
u is initial velocity,
a the acceleration and
s the distance
Assuming initial velocity to be 0
Substituting the values
v² - (0)² = 2(0.15)(12)
v = 1.8
So, The final velocity of the mosquito if it was accelerating from rest at a rate of 0.15 m/s² and flew for 12 meters, is 1.8 m/s.
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number 16part b: what is the speed of the combined vehicles after the collison?
velocity = p/m
p = momentum= 51,000 kgm/s
m = mass = 3,000+2,000= 5,000kg
v= 51,000 kgm/s / 5000 kg = 10.2 m/s
Calculate the resultant displacement for the following 10km left,20 km right,30 km left.polygon method
The resultant displacement of the object is 20 km left.
What is resultant displacement?
The resultant displacement of an object is the net or sum of all the distance travelled by an object in a given direction.
The given position of the object;
first position, = 10 km leftsecond position = 20 km rightthird position = 30 km leftThe resultant displacement is calculated as follows;
D = -10 km + 20 km - 30 km
D = 20 km - 40 km
D = -20 km
Thus, the magnitude and direction of the resultant displacement of the object is 20 km and left respectively.
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A rectangular loop of wire with a cross-sectional area of 0.118 m2 carries a current of 0.679 A. The loop is free to rotate about an axis that is perpendicular to a uniform magnetic field strength of 0.179 T. The plane of the loop is initially at an angle of 22.09o to the direction of the magnetic field. What is the magnitude of the torque on the loop ?
Given:
The area of the rectangular loop is,
[tex]A=0.118\text{ m}^2[/tex]The current in the loop is,
[tex]I=0.679\text{ A}[/tex]The magnetic field is of strength
[tex]B=0.179\text{ T}[/tex]The plane of the loop is at an angle
[tex]\theta=22.09\degree[/tex]To find:
The magnitude of the torque on the loop
Explanation:
The torque on a current-carrying loop is,
[tex]\begin{gathered} \tau=IABsin\theta \\ =0.679\times0.118\times0.179\times sin22.09\degree \\ =5.39\times10^{-3}\text{ N.m} \end{gathered}[/tex]Hence, the torque is
[tex]5.39\times10^{-3}\text{ N.m}[/tex]A box with a mass of 45.0 kg is pushed across a horizontal surface with a force of 19.0 N. What isthe acceleration of the box in meters per second squared?
Given data:
Mass of the box;
[tex]m=45.0\text{ kg}[/tex]Force;
[tex]F=19.0\text{ N}[/tex]The force is given as,
[tex]F=ma[/tex]Here, a is the acceleration of the box.
Rearraning the above equation to get an expression for acceleration,
[tex]a=\frac{F}{m}[/tex]Substituting all known values,
[tex]\begin{gathered} a=\frac{19\text{ N}}{45\text{ kg}} \\ =0.42\text{ m/s}^2 \end{gathered}[/tex]Therefore, the acceleration of the box is 0.42 meters per second squared.
what is scientific knowledge
Answer: Based on evidence
Explanation: Scientific knowledge is based on evidence and is included in scientific theories: consistent and deductively complete sets of propositions around a topic of scientific interest, which describe it and give it a verifiable explanation.
A pitcher claims he can throw a 0.145-kg baseball with as much momentum as a 3.00-g bullet moving with a speed of 1.50 x 103 m/s. What must the baseball’s speed be if the pitcher’s claim is valid?
ANSWER
3.10 x 10⁴ m/s
EXPLANATION
Given:
• The mass of the baseball. m₂ = 0.145 g
,• The mass of the bullet, m₁ = 3.00 g
,• The speed of the bullet, v₁ = 1.50 x 10³ m/s
Find:
• The speed of the ball, v₂, if it has the same momentum as the bullet.
The momentum of an object of mass m moving at a speed v is,
[tex]p=mv[/tex]So, in this problem, if both objects have the same momentum,
[tex]m_1v_1=m_2v_2[/tex]Solving for v₂,
[tex]v_2=\frac{m_1v_1}{m_2}[/tex]Replace the known values and solve,
[tex]v_2=\frac{3.00\text{ }g\cdot1.50\times10^3\text{ }m/s}{0.145\text{ }g}\approx3.10\times10^4m/s[/tex]Hence, the speed of the baseball must be 3.10 x 10⁴ m/s.
This defense mechanism offers self-justifying explanations in place of the real, more threatening, unconscious reasons for one's actions. This is known as:
This defense mechanism offers self-justifying explanations in place of the real, more threatening, unconscious reasons for one's actions. This is known as Rationalization.
According to the question, rationalization is a defense mechanism, and the phrase refers to the act of justifying through the creation of numerous sorts of justifications, explanations, and reasons for any behavior.
A coherent, logically ordered system that also serves to rationalize an individual's unconscious motivation for acting is referred to as a rationalization.
One method of reorganizing a business to improve operational effectiveness and alter organizational policy is rationalization.
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Electronegativity can best be defined as a) relative measure showing how many bonds an atom will formb) a relative measure showing the degree to which electrons can be removed from an atom c) the degree to which an electron will leave an atom d) the degree to which an atom wants to gain more electrons
The electronegativity of an element is the tendency of an atom to attract electrons to itself in a chemical compound.
The electronegativity decreases down the group and increases from left to right across the period.
Therefore, electronegativity can best be defined as the degree to which an atom wants to gain more electrons. Hence, option (d) is the correct choice.
Josh has 12 blue marbles and 7 red marbles. Write the ratio of blue marbles to red marbles.
ANSWER
[tex]12\colon7[/tex]EXPLANATION
Josh has 12 blue marbles and 7 red marbles.
To find the ratio of blue marbles to red marbles, we have to write them in the form:
[tex]a\colon b[/tex]Therefore, the ratio of blue marbles to red marbles is:
[tex]12\colon7[/tex]3. Find for the total resistance of the series-parallel circuit below
In order to find the total resistance, first let's calculate the total resistance between R2 and R3, which are in series, so the total resistance is the sum:
[tex]R23=R2+R3=3+2=5\text{ ohms}[/tex]Now, let's calculate the total resistance between R23 and R1, which are in parallel, so we use the equation below:
[tex]R123=\frac{R23\cdot R1}{R23+R1}=\frac{5\cdot6}{5+6}=\frac{30}{11}=2.727\text{ ohms}[/tex]Finally, we calculate the total resistance between R123 and R4, which are in series:
[tex]RT=R4+R123=3+2.727=5.727\text{ ohms}[/tex]An object of 31.3 kg is at rest. You apply a constant force to this object and the object moves a distance of 103 m in 13 s. find the acceleration produced by your force.
The acceleration produced by your force is determined as 1.22 m/s².
What is the acceleration of the object?
The acceleration of the object is the rate of change of its velocity with time.
Apply the following kinematic equation to solve the acceleration of the object.
s = vt + ¹/₂at²
where;
s is the distance travelled by the objectv is the initial velocity of the object = 0t is the time of motion of the objecta is the acceleration of the objects = ¹/₂at²
103 = ¹/₂a(13)²
103 = 84.5a
a = 103/84.5
a = 1.22 m/s²
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You observe that 34 crests of a water wave pass you each minute. if the wavelength is 12 m, what is the speed of the wave?
ANSWER:
6.8 m/s
STEP-BY-STEP EXPLANATION:
We must calculate the frequency, knowing that per minute (60 seconds) there are 34 crests, therefore:
[tex]f=\frac{34}{60}=0.57\text{ Hz}[/tex]Therefore, the speed of the wave would be:
[tex]\begin{gathered} s=f\cdot w \\ s\text{ =speed} \\ f=\text{ frequency = 0.57 Hz} \\ w\text{ = wavelength = 12 m} \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} s=0.57\cdot12 \\ s=6.8\text{ m/s} \end{gathered}[/tex]The speed of the wave is 6.8 m/s
Question 11 of 16 If a reaction occurs, what will be the products of the unbalanced reaction below? Zn(s) + HCl(aq) The Activity Series of Elements A. ZnH(s) + Cl2(9) OB. No reaction will occur. O C. HZnCl(s) O D. ZnCl2(s) + H2(9)
When zinc reacts with hydrochloric acid, zinc chloride and hydrogen gas will be produced.
i.e.,
[tex]Zn(s)+\text{HCl(aq)}\rightarrow ZnCl_2(s)+H_2(g)[/tex]Hence the correct answer is option D.
8. Climbing a mountain, your water bottle falls and hits the ground. If it is moving at 30m/s upon impact. how far did it fall?
Answer:
45.9 m
Explanation:
FIRST:
vf = a t
30 = 9.81 (t) shows t = 3.06 s
THEN:
df = 1/2 a t^2
= 1/2 ( 9.81)(3.06)^2 = 45.9 m
Julie flew 450 miles to Connecticut to visit her sister and then returned three days later. At the end of the trip, what was her displacement and distance traveled?
a. 450 miles; 0 miles
b. 900 miles; 0 miles
c. 0 miles; 900 miles
d. 450 miles, 450 miles
Submission
VIEW GRADE DETAILS
Julie travelled displacement of 0 miles distance of 900 miles. So the correct answer is option (C) 0 miles; 900 miles.
According to question, Julie travelled from Connecticut to visit her sister is 450 miles and return back to Connecticut .
Here, total journey = distance travelled by Julie = 450 + 450 = 900 miles.
Displacement is shortest distance from point one to other, but here Julie return back to her initial point. So, the displacement is zero.
Distance is the total journey travelled between two points from one point to other. Its magnitude cannot be zero. Its S.I. unit is meter.
Displacement is the shortest distance between two points. Its magnitude may be zero. Its S.I. unit is meter.
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Under a pressure of 14Nm-2, some air has
a volume of 1.5m3. Determine its volume
when its pressure is 10Nm-2. Assuming the
temperature is kept constant
Answer:
2.1 m³
Explanation:
Boyle's Law states:
The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system (Wikipedia) }
We can express this relationship as
[tex]P \propto \dfrac{1}{V}[/tex]
where V is the volume under pressure P
This can be re-written as:
PV = a constant
We are given that [tex]$V = 1.5m^3$[/tex] when [tex]$P = 14N/m^2$[/tex]
So PV = 1.5 x 14 = 21 Nm
At [tex]10 N/m^2[/tex] the PV product must also be 21
So 10V' = 21 where V' = volume at [tex]\displaystyle 10 N/m^2[/tex]
Therefore V' = 21/10 = 2.1 m³
What is the difference and similarity between ∆x & ∆y
The difference between ∆x & ∆y is found say in its position. ∆x refers to the change in the position of the horizontal direction while ∆y refers to the change in the vertical direction.
The similarity between ∆x & ∆y is that both of them has to express same nature of phenomena.
What is position?
Position is described as a place where someone or something is located or has been put.
x and y has been used in all sciences to denote known and unknown variables. ∆x & ∆y deals with the changes in those variables either known or unknown.
X is usually in the horizontal position while Y is in the vertical position.
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in order to you need to apply a force of 1700N to the baseball. How much work done on baseball to hit a distance of 110m? How much power is delivered to the baseball the hitter takes 0.35s to swing the bat?
F = 1700N
Work = ?
mass = 0.14kg
distance = 110m
Work = Force * distance = 1700N * 110 m = 187,000J
Power = Work/ time = 187000J/0.35 = 534,285.7 Watts
ㄱ Question 18 of 25 Studying the solar system helps scientists learn about the universe. Why might a scientist use a model to represent the solar system? O A. The actual solar system is too large. B. The actual solar system is too small. C. The actual solar system is too simple. D. The actual solar system moves too slowly. SUBMIT it's A
A person walks 8 km east, turns and walks 5 km west, then turns back around and walks 3 km, east.
What is the distance traveled of the person from the initial point to ending point?
A person walks 8 km east, turns and walks 5 km west, then turns back around and walks 3 km, east. Total distance traveled of the person from the initial point to ending point will be 16 km
Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
total distance = 8 km + 5 km + 3 km = 16 km
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What’s the magnitud of the force?
F=(557N)i-(611N)j+(468N)k
Answer: 950.05 N
Explanation:
Which of the following statements about treating PTSD is true? a. By focusing on a person’s specific traumatic memory, trauma-focused therapy has been shown to be too narrow in scope to be helpful in treating PTSD. b. The American Psychological Association has issued guidelines to replace psychotropic interventions with trauma-focused therapy. c. The American Psychological Association has issued guidelines to replace cognitive-behavioral therapy with trauma-focused therapy. d. Trauma-focused therapy is gaining support as a first-line treatment showing longer-lasting results than psychotropic medication.
A person with PTSD has trouble bouncing back after experiencing or seeing a traumatic event.
With triggers producing intense emotional and physical reactions as well as memories of the incident, the syndrome can last for months or even years.
Affected individuals may experience nightmares or unwelcome recollections of the trauma, avoid situations that trigger those memories, have heightened reactions, experience anxiety, or experience depression.
Different forms of trauma-focused psychotherapy are utilized in treatment, along with drugs to treat symptoms.
Trauma-focused therapies maintain a constant focus on the trauma and its ensuing repercussions on the patient over the course of therapy. By exposing the patient to reminders of the traumatic incident, this method aids in the correction of incorrect cognitions and the reduction of symptoms.
"Trauma-focused treatment has been demonstrated to be too limited in scope to be effective in treating PTSD since it concentrates on a person's particular traumatic memory."
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A gardener mows a lawn with an old-fashioned push mower. The handle of the i mower makes a 32° angle with the surface of the lawn.
a)If a 68N force is applied along the handle of the 17kg mower, what is the force exerted by the lawn on the mower? b）If the angle between the surface of the lawn and the handle of the mower is increased, does this force increase, decrease, or stay the same? Explain.
The force exerted by the lawn on the mower is 202 N when applied 68N force along the handle.
What is force and how come it be 202 N and how it decreases?Whenever we talk of force we talk of Newton as is discovered by him and so the unit of force is Newton.Force is simply a push or pull but stating it in Newton's way it is the product of mass and acceleration.Here is given that the handle is making a 32 degree angle with the surface of the lawn.Applying 68 N force along the handle of 17 kg mower the force exerted would be 202 N , here we have to encounter the normal force.The normal force would approach the force due to gravity because there is decreased force from the handle.To know more about force visit:
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Please answer 9 only. Simple answer and simple explanation is needed, thanks.
Answer:
a = -493.83 m/s²
Explanation:
The acceleration can be calculated as:
[tex]a=\frac{v_f-v_i}{t}[/tex]Where vf is the final velocity, vi is the initial velocity and t is the time.
Then, we need to convert 320 km/h to m/s as follows:
[tex]320\frac{\operatorname{km}}{h}\times\frac{1000m}{1\operatorname{km}}\times\frac{1h}{3600s}=88.89\text{ m/s}[/tex]Now, we can replace vf by 0 m/s, vi by 88.89 m/s, and t by 0.18 s to get an acceleration equal to:
[tex]\begin{gathered} a=\frac{0-88.89\text{ m/s}}{0.18s}=\frac{-88.89\text{ m/s}}{0.18s}=-493.83m/s^2 \\ \end{gathered}[/tex]Therefore, the acceleration that takes place in this time is equal to -493.83 m/s²
6kg of human blood at a temperature of 65degees celcius is mixed with 4kg of human blood ata temperature of 20 degrees celcius . evaluate the final temperature of the mixture
Answer:
[tex]T_f=47^{\circ}[/tex]Explanation: Two samples of blood that have different masses and temperatures and are mixed, we have to find the final temperature of the mixture. the final temperature can be found using the following formula:
[tex]T_f=\frac{(m_1\cdot T_1+m_2T_2)}{(m_1+m_2)}\Rightarrow(1)[/tex](1) Formula basically tells us that the product of mass and temperature remains constant throughout, so the addition of two products of the two separate blood samples would be equal to the product of final temperature and the total mass of the mixture. Mathematically this means that:
[tex]\mleft(m_1+m_2\mright)T_f=(m_1\cdot T_1)+(m_2T_2)[/tex]Using (1) and plugging in the corresponding values, we get the answer as follows:
[tex]\begin{gathered} T_f=\frac{(m_1\cdot T_1+m_2T_2)}{(m_1+m_2)}\Rightarrow(1) \\ m_1=6\operatorname{kg} \\ m_2=4\operatorname{kg} \\ T_1=65^{\circ} \\ T_2=20^{\circ} \\ \therefore\rightarrow \\ T_f=\frac{(6kg\cdot65^{\circ}+4\operatorname{kg}\cdot20^{\circ})}{(6kg+4\operatorname{kg})}=\frac{(390+80)}{10}=\frac{470}{10}=47^{\circ} \\ \therefore\rightarrow \\ T_f=47^{\circ} \end{gathered}[/tex]An ore cart of mass 1200 kg is rolling at a speed of 12.8 m/s across a flat surface a crane dumps 338 kg of ore into the cart from directly above it how fast does the cart move after being loaded with ore assume that frictional forces with the flat surface are negligible
Given,
The mass of the cart, M=1200 kg
The speed of the cart before the ore is dumped, u=12.8 m/s
The mass of the ore dumped on the cart, m=338 kg
From the law of conservation of momentum, the total momentum of the system of the cart and the ores before and after the ore is dumped into the cart must be equal.
Thus,
[tex]Mu=(M+m)v[/tex]Where vis the speed of the cart after the ore is dumped.
On substituting the known values in the above equation,
[tex]\begin{gathered} 1200\times12.8=(1200+338)v \\ \Rightarrow v=\frac{1200\times12.8}{1200+338} \\ =9.99\text{ m/s} \\ \approx10\text{ m/s} \end{gathered}[/tex]Thus the speed of the loaded cart will be 10 m/s