Liam bought 11/8 cups of carrots. If Liam eats 2/8 cup in a serving, how many servings did Liam buy

Answer: y= 3/2x - 6

Step-by-step explanation:

The equation is y=mx + b

The y-intercept is when x = 0, so on the table y-intercept = -6

The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2

to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}\)

now, the y-intercept occurs when x = 0, recheck the picture below.

Step-by-step explanation:

to answer that we need to know what irrational and what whole numbers are.

whole numbers are all positive numbers with only 0s after the decimal point. in other words positive integers incl. 0.

they do not include any fragments of numbers.

e.g. 1, 2, 3, 34865, ...

e.g. 5.83, 7.333333333... are NOT whole numbers.

irrational numbers are all numbers with infinite digits after the decimal point, that do not have any repeating patterns.

in the example above, 5.83 is NOT irrational, because it has a finite number of digits after the decimal point.

7.3333333... is NOT irrational either, as it has a clear pattern in its digits after the decimal point. it is in fact 22/3 and therefore a rational number.

examples for irrational numbers :

pi, e, sqrt(2), ...

so, the fourth (bottom right) answer is correct.

these two sets of numbers have no element in common.

whole numbers are completely a part of the rational numbers.

but rational and irrational numbers have no elements in common (together they are the real numbers). and therefore, also whole numbers and irrational numbers have no elements in common.

Answer:

B

left side results in 42 and right side results in 42

Torsion refers to the twisting of a structural member due to the application of torque. Pure torsion occurs when a structural member is subjected to torsional loading only. It is analyzed using assumptions such as linear elasticity, circular cross-sections, and small deformations. The torsion equation relates the applied torque, the polar moment of inertia, and the twist angle of the member. However, this formula has limitations in cases of non-circular cross-sections, material non-linearity, and large deformations.

Torsion is the deformation that occurs in a structural member when torque is applied, causing it to twist. In pure torsion, the member experiences torsional loading without any other external forces or moments acting on it. This idealized scenario allows for simplified analysis and calculations. The assumptions made in pure torsion analysis include linear elasticity, which assumes the material behaves elastically, circular cross-sections, which simplifies the geometry, and small deformations, where the twist angle remains small enough for linear relationships to hold.

To analyze pure torsion, engineers use the torsion equation, also known as the Saint-Venant's torsion equation. This equation relates the applied torque (T), the polar moment of inertia (J), and the twist angle (θ) of the member. The torsion equation is given as T = G * J * (dθ/dr), where G is the shear modulus of elasticity, J is the polar moment of inertia of the cross-section, and (dθ/dr) represents the rate of twist along the length of the member.

However, the torsion equation has its limitations. It assumes circular cross-sections, which may not accurately represent the geometry of some structural members. Non-circular cross-sections require more complex calculations using numerical methods or specialized formulas. Additionally, the torsion equation assumes linear elasticity, disregarding material non-linearity, such as plastic deformation. It also assumes small deformations, neglecting cases where the twist angle becomes significant, requiring the consideration of non-linear relationships. Therefore, in practical applications involving non-circular cross-sections, material non-linearity, or large deformations, more advanced analysis techniques and formulas must be employed.

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Step-by-step explanation:

I don't know what the 3rd fruit is. let's call it an apple.

so,

1 apple + 3 cherries = 3 bananas

1 apple = 3 bananas - 3 cherries

1 banana + 2 cherries = 1 apple = 3 bananas - 3 cherries

5 cherries = 2 bananas

1 apple + 1 banana = (1 banana + 2 cherries) + 1 banana =

= 2 bananas + 2 cherries =

= 5 cherries + 2 cherries =

= 7 cherries

the numbers did not help, as they were wrong.

e.g. if you assume the apple = 5, a cherry = 1 and a banana = 2, you would get 8 = 6 on the first scale.

if you change the apple to a 3, that would make the first scale true (6 = 6), but the second scale wrong (4 = 3).

funny enough, the other answer got 7 nevertheless (but the wrong way - actually 2 mistakes balanced each other out).

it is 7 cherries, though !

the actual numbers would be e.g.

a cherry = 1

then

1 banana = 5/2 = 2.5

1 apple = 3×5/2 - 3 = 15/2 - 6/2 = 9/2 = 4.5

to get whole numbers, we could multiply all by 2 :

cherry = 2

banana = 5

apple = 9

and then the first balance :

9 + 3×2 = 3×5

9 + 6 = 15

15 = 15 correct

the second balance

5 + 2×2 = 9

9 = 9 correct.

Answer:

w = ±3

Step-by-step explanation:

(w - 1) (w + 1) = 8

FOIL the left hand side.

w^2 -w+w-1 = 8

w^2 -1 =8

Add 1 to each side.

w^2 -1+1 = 8+1

w^2 = 9

Take the square root of each side.

sqrt(w^2) = sqrt(9)

w = ±3

Answer:

A. 2 cups for $0.90

C. 8 cups for $3.60

E. 19 cups for $8.55

Step-by-step explanation:

I just did it , hope I helped ! :)

Answer:

The person above me is correct!!

Step-by-step explanation:

Answer:

84+6x=y or it can be 78+6x=y

Step-by-step explanation:

To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:

ρ(r) = ρ₀(1 - r/R) for r ≤ R,

ρ(r) = 0 for r > R,

where ρ₀ = 3Q/πR³.

To find the total charge, we integrate ρ(r) over the volume:

Q = ∫ρ(r) dV,

where dV represents the volume element.

Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.

The integral becomes:

Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.

Evaluating this integral gives:

Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.

Simplifying further, we get:

Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].

Simplifying the expression inside the parentheses:

Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].

Simplifying once more:

Q = ρ₀ * π * (R³ - R³/3),

Q = ρ₀ * π * (2R³/3),

Q = (3Q/πR³) * π * (2R³/3),

Q = 2Q.

Therefore, the total charge contained in the charge distribution is Q.

To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.

By Gauss's law, the electric field through a closed surface is given by:

∮E · dA = (1/ε₀) * Qenc,

where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.

Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.

For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q,

Simplifying:

E = Q / (4πε₀r²).

This is the same expression as the electric field created by a point charge Q at the origin (r = 0).

To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.

The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.

By Gauss's law, we have:

∮E · dA = (1/ε₀) * Qenc.

Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q.

Simplifying:

E = Q / (4πε₀r²).

This expression represents the electric field inside the charge distribution for r ≤ R.

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Answer:

1/12 a mile

Step-by-step explanation:

Answer:

B. 1/12 is the right answer because you have to times the fraction by the reciprocal because you can't divide a fraction. So, you do 1/3 *1/4 = 1/12

Step-by-step explanation:

have a good day/night

may i please have a branlliest

Answer:

1.2 rolls

Step-by-step explanation:

6 rolls=5 dresses

1.2 rolls             =1 dress

hope i helped:)

The ratio of the number of female attendants to the number of male attendants is 21/17

let

900 = 1200x + 800y / (x + y)

900x + 900y = 1200x + 800y

900x + 1200x = 800y + 900y

2100x = 1700y

x : y = 2100 / 1700

x : y = 21 ; 17

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Answer:

The major field of anthroplogy and evolutionary and paleo anthropological perspectives on the origin of humankind

The equation after the transformation is y = -5x - 1

From the question, we have the following parameters that can be used in our computation:

Equation: 5x - y = 15

Make y the subject

So, we have

y = 5x + 15

The rule of reflection across the y-axis is

(x, y) = (-x, y)

So, we have the following equation

y = -5x + 15

The rule of translation by (3 -1) is

(x, y) = (x + 3, y - 1)

So, we have the following equation

y = -5(x + 3) + 15 - 1

Expand

y = -5x - 15 + 15 - 1

So, we have

y = -5x - 1

Hence, the equation is y = -5x - 1

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Answer:

To break-even, Zorah needs to play for 8 hours.

Step-by-step explanation:

To calculate the break-even point in hours, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 120 / (25 - 10)

Break-even point in units= 8 hours

To break-even, Zorah needs to play for 8 hours.

Answer:

19/3 (6 1/3)

Step-by-step explanation:

If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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Step-by-step explanation:

elimination means that we multiply one or both equations by certain numbers, so that the sum of terms of the same variable across both equations is 0.

then the sum of both equations is one equation in one variable.

with the solution of that we go into any of the original equations to solve for the second variable.

I suggest in our case to multiply the first equation by -4. and then x add both equations.

-4x - 16y = -88

4x + y = 13

----------------------

0 - 15y = -75

y = -75/-15 = 5

with this y = 5 we go e.g. into the second original equation.

4x + 5 = 13

4x = 8

x = 8/4 = 2

The value of the given expression of subtraction 0.75–0.5, in simplest fractional form is 1/4.

Use the concept of subtraction defined as:

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

The given expression is:

0.75–0.5

After removing the decimal it can be written as,

75/100 - 5/10

Now simplifying it, we get

(75-50)/100 = 25/100

Now convert 25/100 in their simplest form:

Since 25x4 = 100

Therefore,

25/100 = 1/4

Hence,

The simplest fractional value of 0.75–0.5 is 1/4.

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The probability that the entire batch of 6500 write-rewrite CDs will be accepted, given that 170 are defective and 6 are randomly selected for testing, is approximately 0.859 or 85.9%.

To find the probability that the entire batch of 6500 write-rewrite CDs will be accepted using acceptance sampling, we need to consider the number of defective CDs in the batch and the number of CDs selected for testing.

Given that the batch consists of 6500 CDs and 170 of them are defective, we know that the remaining 6500 - 170 = 6330 CDs are non-defective.

Now, if we randomly select 6 CDs for testing, we want to determine the probability that all 6 CDs are non-defective. To calculate this probability, we need to use the hypergeometric distribution.

The hypergeometric distribution calculates the probability of obtaining a specific number of successes (in this case, non-defective CDs) from a finite population (the entire batch) without replacement.

Using the hypergeometric distribution formula, the probability of selecting 6 non-defective CDs can be calculated as follows:

P(X = 6) = (C(6330, 6) * C(170, 0)) / C(6500, 6)

where C(n, r) represents the number of combinations of selecting r items from a set of n items.

Evaluating this expression, we find:

P(X = 6) = (C(6330, 6) * C(170, 0)) / C(6500, 6) ≈ 0.859

Therefore, the probability that the entire batch of CDs will be accepted is approximately 0.859, or 85.9%.

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The work done in stretching the spring from its natural length to 10 in. beyond its natural length is 5 ft-lb.

Work is a physical quantity that measures the amount of energy transferred or expended in the process of performing a task or causing a displacement. It is defined as the product of force and displacement, where the force acts in the direction of the displacement.

In the context of the given problem, the work done in stretching the spring refers to the energy expended in extending the spring from its natural length to a certain displacement. The work done can be calculated by multiplying the force applied to stretch the spring by the distance the spring is stretched.

To find the work done in stretching the spring, we can use the formula:

W = (1/2)k(x2² - x1²)

Where W is the work done, k is the spring constant, x2 is the final displacement, and x1 is the initial displacement.

Given that a force of 20 lb is required to hold the spring stretched 8 in. beyond its natural length, we can use Hooke's Law to find the spring constant:

F = kx

20 lb = k * 8 in.

k = 20 lb / 8 in.

Now we can calculate the work done in stretching the spring from its natural length to 10 in. beyond its natural length:

W = (1/2)(20 lb / 8 in.)(10 in.² - 8 in.²)

W = (1/2)(20 lb / 8 in.)(2 in.²)

W = (1/2)(20 lb / 8 in.)(4 in.²)

W = (1/2)(20 lb)(0.5 ft²)

W = 5 lb-ft

Therefore, the work done in stretching the spring from its natural length to 10 in. beyond its natural length is 5 ft-lb.

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Answer:

If you owe your friend 10 dollars that would be -10 on a number line and then you borrow 5 dollars which means you owe that money too and you would continue to move left on the number line 5 spaces.

Step-by-step explanation:

if () is not defined for non-integer values of d, then f (3.5) would not make sense.

In mathematics, an inequality is a statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). The values being compared can be numbers, variables, or expressions.

by the question.

a. At the beginning of the epidemic, the number of days since the epidemic began is 0. Therefore, substituting d = 0 in the equation f(d) = 50- () gives f (0) = 50 - 0 = 50. So, there were 50 people with the flu at the beginning of the epidemic.

b. The rate at which the flu is spreading can be determined by examining the coefficient of d in the equation f(d) = 50- (). Specifically, if the coefficient is positive, then the flu is spreading at an increasing rate, and if the coefficient is negative, then the flu is spreading at a decreasing rate. Additionally, the magnitude of the coefficient gives an indication of how quickly the flu is spreading. However, since the expression in the parentheses is not given in the question, it is not possible to determine the rate at which the flu is spreading.

c. f(1) represents the number of people with the flu after one day since the epidemic began. Substituting d = 1 in the equation f(d) = 50- (), we get f(1) = 50 - (). Therefore, f (1) depends on the value of ().

d. It is not possible to determine whether f(3.5) makes sense in this situation without knowing the value of (). If () is defined for non-integer values of d, then f(3.5) would make sense and represent the number of people with the flu after 3.5 days since the epidemic began.

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The new dimensions of the pictures are 2.5 inches by 3.5 inches.

Chris did image resizing of Career Week, which originally measured 5 inches by 7 inches, by a factor of 1/2. This means that he reduced each dimension of the pictures by half of its original size.

To calculate the new dimensions, he multiplied each original dimension by the scaling factor of 1/2.  

If the pictures were resized by a factor of 1/2, it means that each dimension was reduced to half of its original size.

The original dimensions of the pictures were 5 inches by 7 inches.

Resizing each dimension by a factor of 1/2 gives:

5 inches x 1/2 = 2.5 inches

7 inches x 1/2 = 3.5 inches

Therefore, the new dimensions of the pictures are 2.5 inches by 3.5 inches.

This means that the new pictures are significantly smaller than the original ones, which may affect their resolution and quality.

However, depending on the intended use of the pictures, a smaller size may be suitable or even desirable.

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The observed change in beak characteristics can be explained through the concepts of competition, survival of the fittest, and inheritance.

In an environment with limited resources, birds with different beak shapes compete for food. This competition leads to the survival of the fittest, where only individuals with beak shapes best suited for accessing available food sources will survive and reproduce.

This advantageous trait (the suitable beak shape) is then inherited by their offspring, ensuring the continuation of the successful trait in future generations. Over time, this process results in the prevalence of the advantageous beak shape within the population.

The observed change in beak characteristics can be explained by the concepts of competition, survival of the fittest, and inheritance.

As a result of competition for limited resources such as food, birds with beaks that were better suited to their environment were more likely to survive and reproduce. This is known as survival of the fittest. Over time, these advantageous beak characteristics were inherited by their offspring, leading to a shift in the overall beak characteristics of the population.

Therefore, the observed change in beak characteristics is a result of natural selection acting on inherited traits that allowed for better survival and reproduction in a competitive environment.

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Answer:

10x -6 +4x & -6 + 14x are equivalent to the algebraic Expression : 2(5x -3) + 4x

Step-by-step explanation:

First, you should Simplify the expression.

2(5x -3) + 4x = 10x -6 +4x <-- Here we distributed. We see this expression is an option, so you would choose that.

We Contiue:

10x -6 + 4x =  -6 + 14x <-- here we added the like terms, 10x and 4 x

Next:

-6x + 14 = -2.3. <-- here we got our answer, but our choices are only expressions, so this is just an extra step.

Answer

-6 + 14x

10x - 6+ 4x

Step-by-step explanation:

First, we need to find the coordinates of each vertex of triangle ABC. Let's assume that A is located at (a,b), B is located at (c,d), and C is located at (e,f). Since we know the measures of the angles, we can also determine the slopes of the lines connecting the vertices:

The slope of line AB is (d-b)/(c-a), which is equal to tan(55°).

The slope of line BC is (f-d)/(e-c), which is equal to tan(80°).

The slope of line AC is (f-b)/(e-a), which is equal to tan(55°-45°) = tan(10°).

Using these slopes, we can find the equations of the three lines and solve for the coordinates of the vertices:

Line AB: y-b = tan(55°)(x-a)

Line BC: y-d = tan(80°)(x-c)

Line AC: y-b = tan(10°)(x-a)

Solving these equations simultaneously, we get:

A = (b + (c-a)tan(55°), b + (c-a)tan(55°-45°))

B = (c + (f-d)/tan(80°), d + (f-d))

C = (e + (b-f)/tan(10°), f + (e-a)tan(10°))

Next, we need to apply the rotation and reflection to these vertices to find the corresponding vertices of triangle XYZ. The rotation by 90° counterclockwise about the origin transforms a point (x,y) into (-y,x), while the reflection across the line y=x transforms a point (x,y) into (y,x). So:

Vertex A of ABC is mapped to vertex X of XYZ: (a,b) → (-b,a) → (a,-b)

Vertex B of ABC is mapped to vertex Y of XYZ: (c,d) → (-d,c) → (c,d)

Vertex C of ABC is mapped to vertex Z of XYZ: (e,f) → (-f,e) → (e,f)

Now we need to find the measure of angle Y. Since we don't know the exact coordinates of the vertices of XYZ, we'll use the fact that the rotation by 90° counterclockwise about the origin preserves angles and the reflection across the line y=x changes the orientation of angles but not their measure. Therefore:

m∠Y = m∠ZOX, where O is the origin

m∠ZOX = 90° - m∠XOZ

m∠XOZ = m∠COA = 55° + 45° = 100°

Therefore, m∠Y = 90° - 100° = -10°, but since angles can't have negative measures, we add 360° to get m∠Y = 350°.

So the measure of angle Y in triangle XYZ is 350°.

Question 1

1/1

Triangle ABC

maps to triangle XYZ

by a rotation of 90∘

counterclockwise about the origin followed by a reflection across the line y=x.

In triangle ABC,

m∠A=45∘,

m∠B=55∘,

and m∠C=80∘.

What is the measure of ∠Y?

Enter your answer as the correct value, like this: 42

55 is the answer I'm not joking try it lol

Answer:

(10,85)

Step-by-step explanation:

x=10

y=85