please need answers ASAP. ​

The intensity of the smallest detectable signal is 1.36 x 10⁻¹⁰ W / m².

The intensity of the smallest detectable signal is calculated by applying formula relating electric field amplitude and the intensity of light.

Mathematically, the formula relating electric field amplitude and the intensity of light is given as;

I = ¹/₂ ε₀E²₀c

where;

The intensity of the smallest detectable signal is calculated as follows;

I = ¹/₂ ε₀E²₀c

Given;

I = ¹/₂ ( 8.85 x 10⁻¹² ) (320 x 10⁻⁶)² ( 3 x 10⁸ )

I = 1.36 x 10⁻¹⁰ W / m²

Thus, the intensity of the smallest detectable signal is a function of the electric field amplitude and speed of light.

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Answer:

13

Explanation:

im rhe smartest person on the erth i j knos jts 13

(a) The diver’s speed 5.70 m above the water’s surface is 9.6 m/s.

(b) The diver’s speed just before striking the water is 14.28 m/s.

(c) The diver's speed when striking the water at the given initial velocity is 14.59 m/s.

The diver’s speed 5.70 m above the water’s surface is calculated by applying the principle of conservation of energy as shown below.

v = √ ( 2gh )

where;

h = 10.4 m - 5.7 m = 4.7 m

v = √ ( 2 x 9.8 x 4.7  )

v = 9.6 m/s

The diver's speed just before striking the water is calculated as follows;

v = √ ( 2gh )

where;

v = √ ( 2 x 9.8 x 10.4 )

v = 14.28 m/s

The diver's speed when striking the water at the given initial velocity is calculated as;

v² = u² + 2gh

where;

v² = (3)² + 2(9.8)(10.4)

v² = 212.84

v = √ (212.84)

v = 14.59 m/s

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365541.022 N   is   the force necessary to accelerate a 20,000-lbm rocket vertically upward at a rate of 100  [tex]\frac{ft}{sec^{2} }[/tex]  .

20000 lbm = 9071 . 8474 kg

100 [tex]\frac{ft}{sec^{2} }[/tex] = 30.48 [tex]\frac{mts}{sec^{2} }[/tex]

and g = 9.814  [tex]\frac{mts}{sec^{2} }[/tex]

force required = mass * (acceleration of  rocket + g)

= 9071.84748*(30.48+9.814)

= 365541.022 N

A force in physics is an impact that has the ability to change an object's motion. As a linear momentum, a force is one with both magnitude and direction. The force exerted on an object is equal to its mass times its acceleration, or Newton's second law, which is sometimes expressed as F=ma (a). Therefore, more force is required to accelerate an object with higher mass. Additionally, an item accelerates more quickly the more force it is under.

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Answer:

acceleration an velocity are two different types of hate for each individual to choose from my favorite ones and not just one for me like you said you would have to pay for the person you want and you will need to pay for your business.

Explanation:

no exceptions

Answer:

Heavy clothes

Explanation:

If you were to hang out in the thermosphere, though, you would be very cold because there aren’t enough gas molecules to transfer the heat to you. This also means there aren’t enough molecules for sound waves to travel through.

Cocaine is a tropane alkaloid that has both local anesthetic and stimulant effects on the central nervous system (CNS).

Cocaine inhibits the re-uptake of dopamine, serotonin, and norepinephrine into pre-synaptic neurons by binding to the transport proteins for these neurotransmitters. As a result, the synaptic cleft accumulates more of the relevant neurotransmitters, which may boost postsynaptic receptor activation. Cocaine works by binding to and blocking the voltage-gated sodium channels in the membrane of neuronal cells to produce local anesthetic effects. Cocaine causes a reversible lack of feeling by stabilizing neuronal membranes, which prevents the start and conduction of nerve impulses. A benzoic acid ester, cocaine was first employed as a local anesthetic.

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The article "Sunrise, Sunset...or Not?" by ReadWorks has a more formal tone compared to "The Ever-Changing Sky" by Megan McGibney.

In "Sunrise, Sunset...or Not?" the author uses scientific and technical terms such as "counterclockwise," "Arctic Circle," and "phenomenon," and provides a detailed explanation of the scientific reasoning behind the rising and setting of the sun.

In contrast, "The Ever-Changing Sky" by Megan McGibney has a more casual tone, using more colloquial language such as "clear day," "bright and shiny," and "People have always looked up at the sky with wonder." The author also uses phrases like "guess how long" and "right!" which implies that the author is addressing a less formal audience and is being conversational.

In all, "Sunrise, Sunset...or Not?" has a more formal tone because of its use of technical language, explanation of scientific concepts, and a generally informative and explanatory writing style.

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Sunrise, Sunset...or Not?

by ReadWorks

The sun is a wonderful thing for Earth. It is a star that heats the planet and makes life on

Earth possible. In addition, its light shines onto the planet. It is Earth's ultimate source of

energy.

Summer days may be longer than winter days, but for most people, the sun seems to do the

same thing each day: it appears to come up in the east for the day, and it appears to go down

in the west for the night. The sun looks like it rises in the east and sets in the west because of

how the earth spins in space. It spins toward the east, or counterclockwise. This means that

when most people look at the sky in the morning, the sun will first appear in the east.

The earth takes 24 hours to complete one turn. For most places on Earth, there is a daytime

and nighttime every 24 hours. But in some places for many days at a time, the sun might stay

up in the sky, or it might not even come up above the horizon.

In some parts of the world, the sun can be up in the sky for months. During part of the spring

and summer in Earth's Northern Hemisphere, the Northern Hemisphere is tilted towards the

sun so much that the sun in northern Alaska, which is located in the Arctic Circle, never goes

below the horizon. The Arctic Circle is an area at the top of the earth. In Barrow, Alaska, the

sun doesn't set for almost three months! This phenomenon is called the midnight sun, when

the sun has not set at midnight. Try sleeping through that!

During parts of the fall and winter in Earth's Northern Hemisphere, the Northern Hemisphere

is tilted in such a way that the sun doesn't come over the horizon in northern Alaska for a little

over two months. Therefore, nights last more than 24 hours. This phenomenon is called the

polar night. Although the sun never rises above the horizon during parts of the fall and winter

in the Arctic Circle, enough light often shines so that people who live there don't need

The Ever-Changing Sky

The Ever-Changing Sky

by Megan McGibney

Look up at the sky on a clear day. You will see the sun. It is bright and shiny, warming much of

what its light touches. Look up at the sky again at night. You may see the stars. They are also

bright and shiny, glimmering in the dark sky. You may also see the moon. It looks bright and

shiny, reflecting light from the sun. People have always looked up at the sky with wonder.

Some have even studied the sun, moon, and stars. These people, called astronomers, have

learned that those objects in the sky do not stay in the same place all the time.

The Ever-Changing Sky

extra quarter of a day.

Let's take a closer look at the moon. The earth does not revolve around the moon. Instead,

the moon revolves around the earth. It takes the moon about four weeks to complete a

revolution around the earth. The portion of the moon we, here on Earth, see changes over

this period of about four weeks as the moon's position around the earth changes. The

moonlight we see at night is the moon's reflection of sunlight onto Earth. The different ways

the moon appears to us are known as the moon's phases. The moon's phases depend on the

moon's position in relation to the earth and the sun.

The four-week period starts and ends with the new moon. The new moon cannot be seen

because the side of the moon lit by the sun is facing away from the earth.

Use the articles "The Ever-Changing Sky" and "Sunrise, Sunset...or Not?" to answer

questions 6.

6. Which article has a more formal tone? Support your answer with details from both texts.

Answers will vary.

If the numerical value of the equilibrium constant increases as the temperature increases then, ∆S₀ < 0. (option C)

The equilibrium constant, K, is a measure of the relative concentrations of reactants and products at equilibrium. It is related to the standard Gibbs free energy change, ∆G₀, by the equation: ∆G₀ = -RT ln K, where,

Important points:

In conclusion, as the temperature increases, the numerical value of the equilibrium constant increases, and ∆S₀ < 0.

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We know the Logistic Equation is dP/dt = r·P(1-P/K) . So twist the given derivative to the logistic form: dy/dt = 10·y(1-y/600) . Then we could see the K = 600 , which is the limit, the Carrying capacity.

To model population growth using a differential equation, we first need to introduce some variables and relevant terms. The variable  t

will represent time. The units of time can be hours, days, weeks, months, or even years. Any given problem must specify the units used in that particular problem. The variable  P will represent population. Since the population varies over time, it is understood to be a function of time. Therefore we use the notation  P(t)

 for the population as a function of time. If  P(t)

 is a differentiable function, then the first derivative  dPdt

 represents the instantaneous rate of change of the population as a function of time.

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The angle between the two beams in the glass to be 42.98°.

Angle is a two-dimensional shape formed by two rays that start from the same point (called the vertex). Angles are measured in degrees, with a full circle being 360 degrees. The size of an angle can range from 0° (no angle) to 180° (a straight line). Angles that measure more than 180° are called reflex angles.

To solve this question, we must use Snell's law. Snell's law states that the ratio of the sine of the incidence angle to the sine of the refraction angle is equal to the ratio of the refractive indices. By applying this formula, we can calculate the angle between the two beams in the glass to be 42.98°.

To calculate this angle, we must first calculate the refraction angle for the blue and red beams. To do this, we can set up the following equations:

Sin (50°) / Sin (θb) = 1.680 / 1

Sin (50°) / Sin (θr) = 1.621 / 1

By solving for θb and θr, we can find that the refraction angles for the blue and red beams are 36.51° and 34.47°, respectively.

Now that we have the refraction angles for the blue and red beams, we can use the law of cosines to calculate the angle between them in the glass. The law of cosines states that the square of the angle between two sides of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides multiplied by the cosine of the angle between them.

We can set up the following equation to calculate the angle between the blue and red beams in the glass:

Cos (θ) = (36.51^2 + 34.47^2 - 50^2) / (2 * 36.51 * 34.47)

By solving for θ, we can find that the angle between the two beams in the glass is 42.98°.

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According to the given statement The angle between the two beams in the glass to be 42.98°.

Angle is a two-dimensional shape formed by two rays that start from the same point (called the vertex). Angles are measured in degrees, with a full circle being 360 degrees. The size of an angle can range from 0° (no angle) to 180° (a straight line). Angles that measure more than 180° are called reflex angles.

To solve this question, we must use Snell's law. Snell's law states that the ratio of the sine of the incidence angle to the sine of the refraction angle is equal to the ratio of the refractive indices. By applying this formula, we can calculate the angle between the two beams in the glass to be 42.98°.

To calculate this angle, we must first calculate the refraction angle for the blue and red beams. To do this, we can set up the following equations:

Sin (50°) / Sin (θb) = 1.680 / 1

Sin (50°) / Sin (θr) = 1.621 / 1

By solving for θb and θr, we can find that the refraction angles for the blue and red beams are 36.51° and 34.47°, respectively.

Now that we have the refraction angles for the blue and red beams, we can use the law of cosines to calculate the angle between them in the glass. The law of cosines states that the square of the angle between two sides of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides multiplied by the cosine of the angle between them.

We can set up the following equation to calculate the angle between the blue and red beams in the glass:

Cos (θ) = (36.51^2 + 34.47^2 - 50^2) / (2 * 36.51 * 34.47)

By solving for θ, we can find that the angle between the two beams in the glass is 42.98°.

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The figure shows the polarization of light in the image.

We have to note that light is the form of energy that we can be able to see by the use of the optical eyes that we have. There are several propoerties of light that are also the properties of waves.

We should know that light is an electromagnetic wave and the polarization of waves can only occur in an electromagnetic wave. From A to B in the figure that have been shown, we can see the polarization of waves.

Thus the light waves are polarized.

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Yes,  the structure has the same moment of inertia about the three axes show below because these axes are equidistant from the structure's center of mass.

What does the moment of inertia mean?

A body's moment of inertia, or resistance to having its speed of rotation about an axis changed by the application of a torque, is a quantifiable measurement of its rotational inertia (turning force). The axis may or may not be fixed, and it may or may not be internal or external.

The direction of the axis usually affects an object's moment of inertia, and the angle between the axis and the center of mass is always a factor. In these instances, the moment of inertia will always be the same if two or more distinct axes are equally spaced from the center of mass.

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Option A is correct. It has been hypothesized that variations in solar output could have an impact on our climate, both directly by altering the pace.

Earth and atmosphere are heated by the sun and indirectly by altering cloud formation processes. Mid-latitude temperate regions exhibit larger seasonal variations in surface temperature than the poles or the tropics; from summer to winter, temperate zones see temperature changes of 8 to 15 degrees Celsius, compared to just 2 degrees Celsius in polar and tropical regions. Energy emitted from the sun in all directions is known as solar radiation. Solar radiation is not the energy that the planet emits. Cosmic rays are any radiation that is sent into space at random. Our seasons are more intense the more tilted Earth is because each hemisphere experiences more solar radiation during its summer.

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The forces in the magnetic field is attractive in nature. Force of attraction is a force that pulls body near due to its attraction.

There are number of attractive forces prevailing in nature and some of them are magnetic force, electric force, electrostatic force and gravitational force.

Magnetic force, is attraction or repulsion that arises between electrically charged particles because of their motion. Magnetic forces are non contact forces as they pull or push on objects without touching the and magnets are only attracted to few 'magnetic' metals.

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Although the human eye has a focal length of approximately 22 mm.

Focal length is defined as the distance between the point of convergence of lens and the sensor that recording the image. The focal length of the digital camera lens indicates how much of the image your camera will be able to capture.

This is deceptive because the back of our eyes is curved, the periphery of our optical field contains progressively less particularly than the center, and the scene we discern is the combined result of both eyes. The cornea and eye lens have focal lengths of 2.3 and 6.4 cm, subsequently.

The eye has a nominal focal length of roughly 17mm, but it varies with housing. The nature of human binocular vision, which uses two lenses rather than a single one,

So we can conclude that A person having a myopic eye uses a hollow lens of focal length 50cm.

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The energy stored in the capacitor dus to 10C charge and 40V potential difference is 200 Joules.

Firstly we will need to calculate the capacitance of the capacitor. It will further help in calculation of stored energy. The formula to be used for each of the following is -

Q = CV and E = 1/2CV², where Q represents charge, E represents energy, C is capacitance and V is voltage.

Keep the values in formula -

C = 10/40

Performing division

C = 1/4

E = 1/2×1/4×40²

Taking square

E = 1/2×1/4×1600

Performing multiplication and division

E = 200 J

Hence, the stored energy is 200 Joules.

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When they are held 0.75 meters apart and have a charge of 2.6E-6 C and a charge of 2.2E-7 C, the electrical force between them is 0.0366 N.

A force is an influence in physics that can change the motion of an object. A force can cause a mass object to change its velocity, or accelerate. Intuitively, force can be described as a push or a pull. A force is a vector quantity because it has both magnitude and direction. Force is an external agent that can change the state of rest or motion of a body. It has a magnitude as well as a direction. The direction of the force is the point where force is applied, and the application of force is the point where force is applied.

Here,

Qa=2.6*10^-6 C

Qb=2.2*10^-6 C

k=9*10^9

r=0.75/2

=0.375 m

F=k*Qa*Qb/r²

=9*2.6*2.2*10^-4/(0.375)²

=0.0366 N

The electrical force between them when each are held 0.75 meters apart and has a charge of 2.6E-6 C and a charge of 2.2E-7 C is 0.0366 N.

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According to the law of reflection, the incident light ray, the reflected light ray, and the normal between them may or may not lie in the same plane. option (b) is correct.

What is law of reflection ?

The law of reflection is the idea that when light rays hit a smooth surface, their angles of incidence and reflection are equal. Additionally, the planes of the incident ray, the reflected ray, and the normal to the surface are all in alignment.

What is incident ray ?

The rectilinear light ray known as an incident ray is one that strikes a surface (surface). Angle of incidence is the angular relationship between this beam and the normal or perpendicular to the surface.

Therefore, according to the law of reflection, the incident light ray, the reflected light ray, and the normal between them may or may not lie in the same plane. option (b) is correct.

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The tension force on both strings is the same. The tension is 3.9 N 10 N 3.3 N S,0 N if each string is at a 40-degree angle to the vertical. launching the video player.

T = (m g) + (m a), where "g" denotes the acceleration caused by gravity of any objects the rope is supporting and "a" denotes any additional acceleration on any such objects, can be used to represent the tension in a given rope.

The force transferred through a rope, string, or wire when pushed by forces acting from opposite sides is referred to as tension. The tension force is applied along the entire length of the wire and exerts an equal amount of strain on the bodies at each end.

You can write it down as FC = mv2 /r. The centripetal force is equal to the total of the object's weight (in grammes) and the tension in the string when an object attached to a string is moving in a vertical circular motion.

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The distance from lens 1 to the final image for the system is -5.4 cm.

The height of an image divided by the height of an object is known as the magnification of a lens. Additionally, it is provided in terms of object and image distance. It is equivalent to the proportion of object distance to image distance. m = h ′ h = v u. m is the magnifying factor.

focal length of lens : f1 = -7cm ; f2 = 14cm

distance from the object : d1 = 24cm : d2= 35 cm

      => 1/f1 = 1/d1 + 1/di

       =>1/-7 = 1/24 + 1/di

di=> -5.4 cm

Magnification of image = focal length/ (object distance - focal length).

The distance between the object and the thin lines is known as the image distance. The image distance is the separation between the picture and the narrow lens. A feature of a narrow lens is its focal length, which specifies the distance at which parallel rays come into focus.

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On a block A free-body diagram for a given figure, there would be 4 force vectors displayed. As an object with both magnitude and direction, a vector is defined.

As an object with both magnitude and direction, a vector is defined as. Moving an object from one position to another is described by a vector. By using a directed line segment, vector mathematics can be geometrically represented. Generally speaking, the term "magnitude" refers to a size or distance. We can relate the magnitude of a movement to an object's size and motion speed. A thing or an amount's magnitude is determined by its size. A automobile moves more quickly than a motorcycle, just like in terms of speed. Vector and scalar quantities both frequently employ magnitude as a factor.

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Explanation: A projectile motion is characterized by a motion whose path is alike to that of an arc. It already has its derived equations. For the maximum height H and the maximum range R, the equations are:

H = v₀²sin²θ/2g       ;       R = v₀²sin(2θ)/g

As you can observe, they are almost alike. Since they both contain v₀²/g, let's isolate this term for both equations:

v₀²/g = 2H/sin²θ

v₀²/g = R/sin (2θ)

Equating both equations:

2H/sin²θ = R/sin (2θ)

H = Rsin²θ/2sin(2θ)

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(1) There are zero fewer electrons than protons.

(2) If you paired them up, the fraction of the protons that would have no electrons is zero.

The of number of electrons present is calculated as follows;

pq -  eq = q (net)

where;

eq = pq - q (net)

e = ( pq - q(net) ) / q

e = ( 3.5 x 10¹⁶ x 1.6 x 10⁻¹⁹   -   1.1 x 10⁻¹² ) / ( 1.6 x 10⁻¹⁹ )

e = 3.5 x 10¹⁶

The number of fewer electrons than the proton = 3.5 x 10¹⁶ - 3.5 x 10¹⁶ = 0

Thus, if you pair them up, all the protons will have electrons.

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Option C is the correct answer .

What is velocity ?

Velocity, a quantity that indicates the speed and direction in which a point moves. Points always move tangent to the path. For example, for a circular path, its direction is always perpendicular to the line (radius) from the point to the center of the circle. The velocity magnitude (velocity) is the fraction of time a point moves along its trajectory.

If a point travels a certain distance along a path in a certain time interval, the average speed during that interval is equal to the distance traveled divided by the time taken. For example, the average speed of a train traveling 100 km in 2 hours is 50 km/h

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The ball's speed when it rolls around a horizontal circle at height y inside the cone is a/h√gy.

Given the height of cone = h

The radius of cone base = a

The ball is at a height of = y inside the cone

Let the speed of ball = v

From the free body diagram of cone we can see that along x axis the force acting is Rcosθ and along y axis the force acting upward is Rsinθ and downwards is mg where g is gravitational acceleration.

Rsinθ = mg

Rcosθ = Fc is centripetal force = mv^2/r here r is radius of base

Rsinθ/Rcosθ = mg/mv^2/r

tanθ = rg/v^2

From the diagram y/r = h/a. r = ya/h and tanθ = h/a

h/a = ay/h x g/v^2

v^2  = ayg/h x a/h

v^2 = a^2 yg/h^2

v = a√yg/h

Hence the speed of ball is a√yg/h.

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O contains 3.93 x 10^22 atoms. In the case of a mass (in grammes) of 2.50 10 2 mol of CdS. To three significant digits, convert the mass to grammes. In 66.6 g of this substance, the amount of NH4Cl in moles (n).

One of a body's fundamental characteristics is mass. Before the discovery of the atom and particle physics, it was widely considered to be connected to the amount of matter in a physical body. Different atoms and elementary particles were found to have different mass numbers (2.50102 mol CdS x 144.4760 g CdS/mol) = 3.61 g CdS (66.6 g NH4Cl / 53.4915 g NH4Cl/mol) = 1.25 mol NH4Cl (8.497102 mol) x (6.022 x 1023 molecules/mol) = 5.117 10

9.1 atoms of oxygen for 1 molecule of Al(NO3)3 (7.25103 mol) x (6.022 x 1023 molecules/mol) x (6.022 x 1023 molecules/mol) = 3.93 10^22.

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The complete question is -

Mass (in grams) of 2.50×10−2 mol of CdS. Express the mass in grams to three significant digits. Number of moles (n) of NH4Cl in 66.6 g of this substance. Express the amount in moles to three significant digits. Number of molecules in 8.497×10−2 mol C6H6. Express the amount in molecules to four significant digits. Number of O atoms in 7.25×10−3 mol Al(NO3)3. Express the amount in atoms to three significant digits.

The heat engine follows the cycle shown in the figure, and the thermal efficiency is calculated to be 35.6%. For process 1-2, WS = -7.14 J, Q = -20.04 J, delta Eth = -12.90 J; for process 2-3, WS = -7.14 J, Q = -7.14 J, delta Eth = -12.90 J; for process 3-1, WS = 7.14 J, Q = 13.21 J, delta Eth = 5.07 J.

Part A: WS = -7.14 J, Q = -20.04 J, delta Eth = -12.90 J

Part B: WS = -7.14 J, Q = -7.14 J, delta Eth = -12.90 J

Part C: WS = 7.14 J, Q = 13.21 J, delta Eth = 5.07 J

Part D: Thermal Efficiency = 35.6%

Part A: WS = -7.14 J, Q = -20.04 J, delta Eth = -12.90 J

To calculate WS, Q and delta Eth for process 1-2, we need to calculate the change in internal energy between the two states. The internal energy of a monatomic gas is given by U = 3/2*n*R*T, where n is the number of moles of the gas, R is the ideal gas constant and T is the temperature.

For process 1-2:

U2 - U1 = -12.90J

To calculate Q, the equation Q = U2 - U1 can be used.

Q = U2 - U1 = -12.90J

To calculate WS, the equation WS = Q - (U2 - U1) can be used.

WS = Q - (U2 - U1) = -20.04J - (-12.90J) = -7.14J

Part B: WS = -7.14 J, Q = -7.14 J, delta Eth = -12.90 J

To calculate WS, Q and delta Eth for process 2-3, we need to calculate the change in internal energy between the two states. The internal energy of a monatomic gas is given by U = 3/2*n*R*T, where n is the number of moles of the gas, R is the ideal gas constant and T is the temperature.

For process 2-3:

U3 - U2 = -12.90J

To calculate Q, the equation Q = U3 - U2 can be used.

Q = U3 - U2 = -12.90J

To calculate WS, the equation WS = Q - (U3 - U2) can be used.

WS = Q - (U3 - U2) = -12.90J - (-12.90J) = -7.14J

Part C: WS = 7.14 J, Q = 13.21 J, delta Eth = 5.07 J

To calculate WS, Q and delta Eth for process 3-1, we need to calculate the change in internal energy between the two states. The internal energy of a monatomic gas is given by U = 3/2*n*R*T, where n is the number of moles of the gas, R is the ideal gas constant and T is the temperature.

For process 3-1:

U1 - U3 = 5.07J

To calculate Q, the equation Q = U1 - U3 can be used.

Q = U1 - U3 = 5.07J

To calculate WS, the equation WS = Q - (U1 - U3) can be used.

WS = Q - (U1 - U3) = 5.07J - (-5.07J) = 7.14

Part D: Thermal Efficiency = 35.6%

The thermal efficiency of a heat engine is given by the equation η = (Wnet/Qh) x 100, where Wnet is the net work output of the engine and Qh is the heat input to the engine.

For this heat engine, Wnet = WS1 + WS2 + WS3 = 7.14J + (-7.14J) + (-7.14J) = -7.14J and Qh = Q1 + Q2 + Q3 = -20.04J + (-7.14J) + 13

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