Which symbol should be used here?

1 __ -1


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≤


=

Divide the numerator by the denominator to create a mixed number from an incorrect fraction. The mixed number is created after the division in such a way that the achieved quotient becomes the whole number, the leftover becomes the new numerator, and the denominator stays the same.

A mixed number is one that combines both a proper fraction and a full number. Mixed fractions are another name for mixed numbers.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. "Top-heavy" fractions are sometimes used to describe improper fractions.

Follow these procedures to convert a mixed number to an incorrect fraction:

1. Divide the entire number by the numerator.

2. Increase the numerator by that sum.

3. Add that total to the denominator from the previous step.

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Answer:

if the marble slab is 1 cm³ in volume the mass is 2.7 g but u did not put a volume

The graph that best shows the line of best fit is graph (c)

A graph that shows the appropriate line of best fit has the following properties:

The graph that satisfies the above highlights is the graph (c)

Hence, the graph that best shows the line of best fit is graph (c)

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Answer:

c

Step-by-step explanation:

Answer:

The answer is explained below

Step-by-step explanation:

Given that The volume of air inside a rubber ball with radius r can be found using the function V(r) = \(\frac{4}{3}\pi r^3\), this means that the volume of the air inside the rubber ball is a function of the radius of the rubber ball, that is as the radius of the rubber ball changes, also the volume of the ball changes.

As seen from the function, the radius is directly proportional to the volume of the ball, if the radius increases, the volume also increases.

\(V(\frac{5}{7} )\) is equal to the volume of the ball when the radius of the ball is \(\frac{5}{7}\). Therefore:

\(V(\frac{5}{7} )=\frac{4}{3} \pi *(\frac{5}{7} )^3=1.53\ unit^3\)

It provides character details that indicate Mrs. This function Faxon's interaction with this character serve in the given excerpt. Therefore, the correct option is option A.

An excerpt is indeed a quotation from that other resource that the author introduces with fresh language in a sentence. This phrase is taken from Thomas Jefferson's 1801 inaugural speech: As he warned his audience, "I may often go wrong by defect of judgement," Jefferson admitted the fallibility of human nature. "I shall frequently err through lack of judgement" is the excerpt. It provides character details that indicate Mrs. This function Faxon's interaction with this character serve.

Therefore, the correct option is option A.

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Let B be a basis for U1 ∩ U2. We will extend B to bases for U1 and U2 and show that the union of these bases is a basis for U1 + U2.

Since U1 and U2 are subspaces of V, they both contain the zero vector. Therefore, B contains the zero vector, and we can extend it to a basis B1 for U1 by adding vectors from U1 that are not in U1 ∩ U2 until we have a basis of U1. Similarly, we can extend B to a basis B2 for U2.

Let B' = B1 ∪ B2. We claim that B' is a basis for U1 + U2.

To prove this, we will show that B' is a linearly independent set that spans U1 + U2.

First, we will show that B' is linearly independent. Suppose that a linear combination of vectors in B' equals the zero vector:

c1v1 + c2v2 + ... + ckvk = 0,

where ci is a scalar and vi is a vector in B'. We need to show that all the ci are zero.

Without loss of generality, assume that v1 is in B1 and v2 is in B2. Since B is a basis for U1 ∩ U2, we can write v1 and v2 as linear combinations of vectors in B:

v1 = a1b1 + a2b2 + ... + ambm,

v2 = b1' + b2' + ... + bn'',

where ai, bi, and bi' are scalars and b1, b2, ..., bm, b1', b2', ..., bn'' are vectors in B.

Therefore, we have:

c1(a1b1 + a2b2 + ... + ambm) + c2(b1' + b2' + ... + bn'') + ... + ckvk = 0.

Since U1 and U2 are subspaces, they are closed under scalar multiplication and vector addition. Thus, the left-hand side of the equation can be rewritten as a linear combination of vectors in B1 and B2:

(c1a1)b1 + (c1a2)b2 + ... + (c2)b1' + (c2)b2' + ... + (ck)vk.

Since B1 and B2 are both bases, they are linearly independent sets. Therefore, all the coefficients in this linear combination must be zero:

c1a1 = 0, c1a2 = 0, ..., c2 = 0, ..., ck = 0.

Since B is linearly independent, we know that a1, a2, ..., am, b1', b2', ..., bn'' are not all zero. Therefore, we must have c1 = c2 = ... = ck = 0, which shows that B' is linearly independent.

Next, we will show that B' spans U1 + U2. Let u be an arbitrary vector in U1 + U2. Then u can be written as a sum of a vector in U1 and a vector in U2:

u = u1 + u2,

where u1 is in U1 and u2 is in U2. Since B1 is a basis for U1, we can write u1 as a linear combination of vectors in B1:

u1 = a1b1 + a2b2 + ... + ambm,

where ai are scalars and b1, b2, ..., bm are vectors in B1. Similarly, we can write u2 as a linear combination of vectors in B2:

u2 = b1' + b2' + ... + bn'',

where bi' are scalars and b1', b2', ..., bn'' are vectors in B2.

Therefore, we have:

u = (a1b1 + a2b2 + ... + ambm) + (b1' + b2' + ... + bn'').

Since U1 and U2 are subspaces, they are closed under vector addition and scalar multiplication. Therefore, the right-hand side of this equation is a linear combination of vectors in B':

u = a1b1 + a2b2 + ... + ambm + b1' + b2' + ... + bn''.

This shows that every vector in U1 + U2 can be expressed as a linear combination of vectors in B'. Therefore, B' spans U1 + U2.

Since we have shown that B' is both linearly independent and spans U1 + U2, it is a basis for U1 + U2. Therefore, we have:

dim(U1 + U2) = |B'| = |B1 ∪ B2|.

To finish the proof, we need to express the dimension of U1 + U2 in terms of the dimensions of U1 and U2 and the dimension of U1 ∩ U2.

Since B is a basis for U1 ∩ U2, it has |B| vectors. We extended B to a basis B1 for U1 by adding |B1| - |B| vectors, and to a basis B2 for U2 by adding |B2| - |B| vectors. Therefore:

|B1| = |B2| = |B| + |B1 ∩ B2|,

where |B1 ∩ B2| is the number of vectors we added to extend B to bases for U1 and U2.

Using this equation, we have:

|B1 ∪ B2| = |B1| + |B2| - |B1 ∩ B2|

= (|B| + |B1 ∩ B2|) + (|B| + |B1 ∩ B2|) - |B1 ∩ B2|

= 2|B| + 2|B1 ∩ B2| - |B1 ∩ B2|

= 2|B| + |B1 ∩ B2|.

Therefore, we have:

dim(U1 + U2) = |B1 ∪ B2| = 2|B| + |B1 ∩ B2|

= 2(dim(U1 ∩ U2)) + dim(U1) - |B| + 2(dim(U1 ∩ U2)) + dim(U2) - |B|

= dim(U1) + dim(U2) - dim(U1 ∩ U2),

as required.

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Answer:

median<mode

Step-by-step explanation:

median is 18

mode is 19

so median<mode

plz mark as brainliest

a) The Probability density function of given uniform distribution example is

F(x) = 1/3.5 for 8.5 < x< 12

Uniform distribution in Statistics is a type of probability distribution in which all possible outcomes have equally likely chance to occur. It is generally represented by U(x,y) where

x ---> minimum value and y---> maximum value

Probability density function is a probability function which defines the density of continuous random variable lying between specified range

values. It is denoted by f( a<X<b)

Probability density function for uniform distribution is F(x) = 1/(b-a) for a<x<b where a and b are parameters of uniform distribution.

We have following informations,

weigh of mini iPad = 11 ounces or 50% lighter than standard iPad.

Assume that the battery of iPad is uniformly distributed between 8.5 hours to 12 hours.

this implies a = 8.5 , b = 12

F(x) = 1/(12 - 8.5) = 1/3.5 for 8.5<x<12

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#Complete Qestion :

In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal. Assume that the battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

a) What is the probability that the battery life for an iPad Mini will be 10 hours or less?

The charge on the capacitor after a long time in the LRC-series circuit is 1 Coulomb.

To find the charge on the capacitor after a long time in an LRC-series circuit, we need to consider the behavior of the circuit as it reaches a steady state. In a steady state, the circuit reaches a balance where the inductor, resistor, and capacitor have settled into their respective behaviors.

Given the values:

L = 21 H (inductance)

R = 10 Ω (resistance)

C = 0.01 F (capacitance)

E(t) = 150 V (voltage source)

q(0) = 1 C (initial charge on the capacitor)

i(0) = 0 A (initial current)

To find the charge on the capacitor after a long time, we need to find the steady-state value of the charge. In a steady state, the capacitor acts as an open circuit, and the current through the circuit becomes zero.

As the time approaches infinity, the current through the circuit becomes negligible, and the capacitor becomes fully charged. Therefore, the charge on the capacitor after a long time is equal to the initial charge, q(0) = 1 C.

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Answer:

D. 6 feet

Step-by-step explanation:

The volume of a rectangular prism can be found by using L * W * H, or B * H

-> The length (L) times the width (W) is equal to the base (B)

V = B * H

528 = 88H

6 = H

The value of  variable x in the equation is 16.

The equation represented as follows:

x + 14 + x³ = 78

The value x is the variable.

A variable is number represented with a letter in an equation.

Therefore,

x + 14 + 3x = 78

subtract 14 from both sides of the equation

x + 3x + 14 - 14 = 78 - 14

x + 3x = 64

Therefore,

4x = 64

divide both sides by 4

4x / 4 = 64 / 4

x = 16

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The angle 1 can be named as follows:

∠RST

∠TSR

∠S

There are various ways to name an angles. You can name an angle by its vertex, by the three points of the angle (the middle point must be the vertex), or by a letter or number written within the opening of the angle.

Therefore, let's name the angle 1 indicated on the diagram as follows:

Hence, the different ways to name the angle 1 is as follows:

∠RST or ∠TSR

Or

∠S

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Answer:

Third one

Step-by-step explanation:

The only equation that is even true is the third one.

If the cube of a number is x, then cube root of x is that number.

So the cube of 7^(1/3) is (7^(1/3))^3.

By law of exponents, we have (7^(1/3))^3=7^(1/3×3)=7^1=7.

So the cube of 7^(1/3) is 7, so the cube root of 7 is 7^(1/3).

log 8 + log 3

log ((8)(3)) (Using the product rule of logarithms)

log (24) (Multiplying)

The answer is log(24)

Answer:

Step-by-step explanation:

In linear equation, x−y = 18x+6y=29 system of equations represents this situation.

What are instances of linear equations?

given,

     Ham costs $8 per pound.

      Cheese costs $6 per pound.

so, according to question

let You buy x pounds of ham.

Hence, you spend 8 * x = $8x on ham.

Cheese costs $6 per pound.

You bay y pounds of cheese.

Hence, you spend 6 x y = $6y on cheese.

The difference on the spending on ham and cheese is:

8x - 6y = 29

Hence, x−y = 18x + 6y=29 is system of equations represents this situation.

The cost of 1.5 pounds of ham = 1.5 * 4.48 = 6.72

the cost of 0.75 pounds of cheese = 0.75 * 6.36 = 4.77

  6.72 - 4.77 = $1.95

you pay $1.95 more for ham .

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39/4

its mixed from is 9 3/4

Answer:   1 is c)   2 is c)    3 is a)   4 is

Step-by-step explanation:

z-value is -1.9599

To find the value z such that the area to the left of z under the standard normal curve is 0.025, you can use the qnorm() function in R as follows:

The output will be the z-value you are looking for. To round your answer to 4 digits after the decimal point, you can use the round() function in R:

The output will be the rounded z-value, which should be approximately -1.9599.

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Answer: 1053.7225

Step-by-step explanation:

Answer:

63°

Step-by-step explanation:

a = 27°

b = 180° - (a + 27°)

b = 180° - (27° + 27°)

b = 180° - 54°

b = 126°

By inscribed angle theorem:

c = 1/2 b = 1/2 * 126°

c = 63°

The standard deviation of a data is given by:

the summation is over all the elements of the data and μ is the mean of the data, n is the number of elements.

Calculate the mean μ as follow:

Next, replace the values of the parameters into the formula for the standard deviation and simplify:

Hence, the standard deviation of the given data is approximately 5.06

After rounding off the numbers product of the given numbers is 27000.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

The given number are 88 and 304.

Rounding each number to the nearest 10

That is, 88 to 90 and 304 to 300

Now, 88×304 can be written as

90×300

= 27000

Therefore, after rounding off the numbers product of the given numbers is 27000.

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When a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

It's important to note that pressure increases as depth increases under water. The pressure in pounds per square foot, P, at a depth of d feet is given by the equation:

P = 0.433d + 14.7 where 0.433 is a constant for water, and 14.7 is the pressure at the surface.

In order to find the depth at which the pressure is 159 pounds per square foot, we need to solve the equation for

d.P = 0.433d + 14.7

Substitute P = 159 and solve for

d.159 = 0.433d + 14.7

Subtract 14.7 from both sides.

144.3 = 0.433d

Divide both sides by 0.433 to isolate d.

d ≈ 333.06

Hence, when a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

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After using the method of cylindrical shells, the integral that calculates the volume of the solid formed when the region is rotated around the line y = 3 is 4π.

To calculate the volume of the solid formed when the region bounded by the graph of y = x^2, y = 0, and x = 2 is rotated around the line y = 3, we can use the method of cylindrical shells.

The integral that calculates the volume in this case is given by:

V = ∫[a, b] 2π * x * h(x) dx

where [a, b] are the limits of integration and h(x) represents the height of the cylindrical shell at a given x-value.

Since we are rotating the region around the line y = 3, the height of each cylindrical shell is the difference between the y-coordinate of the line y = 3 and the y-coordinate of the curve y = x^2.

The equation of the line y = 3 is a constant, so its y-coordinate is always 3. The y-coordinate of the curve y = x^2 is given by h(x) = x^2.

Therefore, the integral that calculates the volume becomes:

V = ∫[0, 2] 2π * x * (3 - x^2) dx

Simplifying the equation, we have:

V = 2π ∫[0, 2] (3x - x^3) dx

To evaluate the integral, we integrate term by term:

V = 2π * [(3/2)x^2 - (1/4)x^4] evaluated from 0 to 2

V = 2π * [(3/2)(2)^2 - (1/4)(2)^4] - [(3/2)(0)^2 - (1/4)(0)^4]

V = 2π * [(3/2)(4) - (1/4)(16)] - 0

V = 2π * (6 - 4) - 0

V = 2π * 2

V = 4π

Therefore, the integral that calculates the volume of the solid formed when the region is rotated around the line y = 3 is 4π.

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Answer:

Below

Step-by-step explanation:

The corners are the vertices of the rectangle

So to Kick the ball from the corner to the opposite one the player must kick far enough to cross all the width.

The width is 54 m

Then the distance needed is 54 m at least if the ball goes straight.

Answer:

He will kick is 90 m

Step-by-step explanation:

We can use the Pythagorean theorem to solve

a^2 + b^2 = c^2

72^2 + 54^2 = c^2

5184+2916=c^2

8100 = c^2

Take the square root of each side

sqrt(8100) = sqrt(c^2)

90 = c

He will kick is 90 m

Answer:

Part A. Mary has 2 3/4 cups of sugar to make cookies. The recipe requires 1/8 cup of sugar for one portion of cookies. How many portions of cookies can Mary make?

Part B.

 portions.

Part C. The quotient is 22 and this number represents the amount of portions of cookies that Mary can make.

Step-by-step explanation:

To find the slope of the tangent line to the parabola y=4x²+7x+2 at the point (-5,67), we need to find the derivative of the function y=4x²+7x+2, and evaluate it at x=-5.

The derivative of the function y=4x²+7x+2 can be found by applying the power rule and the constant multiple rule of differentiation. Thus, we have:

y' = d/dx (4x²+7x+2) = 8x+7

To find the slope of the tangent line at the point (-5,67), we evaluate the derivative at x=-5:

y'(-5) = 8(-5)+7 = -33

Therefore, the slope of the tangent line is -33. To find the y-intercept of the line, we substitute the point (-5,67) and the slope (-33) into the equation y=mx+ b and solve for b:

67 = (-33)(-5) + b

b = -202

Therefore, the equation of the tangent line is y=-33x-202.

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Jack spent 40 minutes on his algebra quiz.

Let's call the time it took Jack to complete his algebra quiz "a".

According to the problem, it took Jack 10 minutes longer to complete his biology quiz than his algebra quiz, so the time it took for his biology quiz would be "a + 10".

We know that Jack spent a total of 1.5 hours taking quizzes, which is equal to 90 minutes.

Therefore, we can write an equation based on this information:

a + (a + 10) = 90

Simplifying this equation, we get:

2a + 10 = 90

Subtracting 10 from both sides, we get:

2a = 80

Dividing both sides by 2, we get:

a = 40

Therefore, Jack spent 40 minutes on his algebra quiz.

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