What is the sum of 1/2+2/4+3/8 write your answer as an improper fraction

The value of cos B in the fraction is 12/37.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

Given:

A right-angled triangle.

The trigonometric identity:

Cos B = Adjacent leg of the triangle/ Hypotenuse of the triangle

Cos B = 12/37

Therefore, Cos B = 12/37.

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The equation Ax = 0 has no free variables, so A has n pivot columns. Since A is square, the pivots must be on the main diagonal, so A is row equivalent to the n x n identity matrix Iₙ.

In order for the equation Ax = 0 to have only the trivial solution, there must be no free variables. This means that the matrix A must have n pivot columns. Since A is square, the n pivot positions must be in different rows, which means that the pivots must be on the main diagonal. This means that A is row equivalent to the n x n identity matrix Iₙ. To make it row equivalent, we can perform elementary row operations, such as adding or subtracting rows, or multiplying or dividing a row by a non-zero constant. Once we have done this, the matrix will be in echelon form and the main diagonal will be composed of all 1s. This means that A is row equivalent to Iₙ.

The  complete question: Suppose A is nˣn and the equation Ax=0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to Iₙ

Choose the correct answer below.

A. Suppose A is nˣn and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nˣn identity matrix,  Iₙ.

B. Suppose A is nˣn and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in A must be on the main diagonal. Hence A is the nˣn identity matrix,  Iₙ.

C. Suppose A is nˣn and the equation Ax=0 has only the trivial solution. Then there are n free variables in this equation, thus A has n pivot columns. Since A is square and then pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nˣn identity matrix,  Iₙ

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The burgundy fabric:1.135 square yards

The yellow fabric: 0.307 square yards

The total yards of fabric will she have to buy 1.442 square yards.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Chelsea needs 1472 square inches of burgundy fabric and 399 square inches of yellow.

As, 1 yards= 36 inches

and, 1 square yards= 1296 inches

Then, 1472 square inches of burgundy fabric

= 1472/ 1296

= 1.135 square yards

and, 399 square inches of yellow.

= 399/ 1296

= 0.307 square yards

Thus, the total yards of fabric will she have to buy

= 1.135 + 0.307

= 1.442 square yards

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Step-by-step explanation:

5 × -8a = -40a

5 × -9 = -45

-40a - 45 = 5(-8a - 9)

5 × -8a = -40a

5 × -9 = -45

-40a - 45 = 5(-8a - 9)

The probability of not selecting a green marble is equal to the total number of non-green marbles in the bag divided by the total number of marbles in the bag.

To calculate the probability: there are three green marbles out of a total of twenty-five marbles, so the probability of selecting a green marble is 3/25.

The likelihood of not selecting a green marble is then 1 - 3/25 = 22/25.

This is equal to 22/25 * 100 = 88% as a percentage.

As a result, P(not green) = 88%

Probability denotes the possibility of something happening. It is a mathematical branch that deals with the onset of a random event. The value ranges from zero to one. Probability has been tried to introduce in mathematics to predict the probability of events occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also used in probability distribution, in which you will learn about the possible outcomes of a random experiment.

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Answer:

u have to put lenght ×weight =volume

Answer:

591.2 kilometers

Step-by-step explanation:

times 295.6 × 2 and you will get 591.2

The correct statement is : The volume of the sphere is approximately equal to the volume of the cube, but the sphere has a greater surface area.

Surface Area of a Sphere. A = 4 π r². The volume of a Sphere. V = (4 ⁄ 3) π r³. Where r is the radius of the circle.

Given here: A sphere with 5 in. radius and a cube with side measuring 8.06 in.

Volume of the sphere is

V=4/3πr³

=4/3·π·5³≈523.59878 in³

Surface area of the sphere is

A=4πr²

=4·π·5²≈314.15927 in²

Now volume of the cube

a³=8.06³

≈523.60662 in³

Surface area of the cube

A=6a²

=6×8.06²

≈389.7816 in²

Thus The volume of the sphere is approximately equal to the volume of the cube, but the sphere has a greater surface area.

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It would take the two boys working together 2.38 hours to clean the pool.

The formula for working out the time it would take two people to complete a job when working together is:

T(combined) = 1 / (1/T1 + 1/T2)

Where T1 is the time it takes one person to complete the job and T2 is the time it takes the other person to complete the job.

In this case, T1 is 4 hours for Kevin and T2 is 6 hours for Jerome.

To solve the equation:

T(combined) = 1 / (1/4 + 1/6)

T(combined) = 1 / (0.25 + 0.17)

T(combined) = 1 / 0.42

T(combined) = 2.38 hours

Therefore, it would take the two boys working together 2.38 hours to clean the pool.

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The value of x is √12.73 when Barrett is aware that the structure measures 32x feet in height, 46x feet in breadth, and 200 feet diagonally.

Definition of Pythagoras Theorem:

The square of the long side of a right-angled triangle is equal to the sum of the squares of the other two sides.

It is stated in this formula:

[tex](side)^2+(side)^2=(hypotenuse)^2[/tex]

Given that,

Barrett is focusing on a rectangle-shaped structure on the school's property. He is aware that the structure measures 32x feet in height, 46x feet in breadth, and 200 feet diagonally.

We must determine what x stands for.

We know that,

The height of building is 32x.

The width is 46x

The diagonal is 200 feet

So we form a triangle

From the Pythagoras theorem,

Hyp² = Side²+ Side²

200² = (32x)² + (46x)²

40000 = 1024x² + 2116x²

3140x² = 40000

x² = 12.73

Square root on both sides

x = √12.73

Therefore, The value of x is √12.73 when Barrett is aware that the structure measures 32x feet in height, 46x feet in breadth, and 200 feet diagonally.

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Answer:

the answer is B) and E)

Step-by-step explanation:

it's not that complicated, just have to subtract 12 from 37

Answer:This is a right triangle.One of the legs has a length of 20.

Step-by-step explanation:

The correct time when the displays on the clocks next agree is 01:00.

Let's assume that one hour on the normal clock is equal to x.

The clock that goes twice as fast takes x/2 hours to show one hour on the normal clock.

And the clock that goes backward takes 24 - x hours to show one hour on the normal clock.

At 13:00, both clocks show the correct time.

So, x/2 + x = 24 - x + x.

Simplifying the equation:

24 = x + x/2

Multiplying both sides by 2:

48 = 2x + x

Subtracting x from both sides:

48 - x = 2x

Solving for x:

x = 24

So, one hour on the normal clock is equal to 24 hours.

The clock that goes twice as fast will show one hour in 24/2 = 12 hours.

And the clock that goes backward will show one hour in 24 - 24 = 0 hours.

So, when the displays on the clock next agree, it will be 12 + 0 = 12 hours after 13:00, which is 01:00.

So the correct time when the displays on the clocks next agree is 01:00.

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Answer:

Step-by-step explanation:

a) Just work backwards!

Instead of adding 4, subtract by 4

Instead of multiplying by 3, divide by 3

22 - 4 / 3 = x

b)

22 - 4 = 18

18 / 3 = 6

Therefore, x = 6

To find f(2) using synthetic division, we set up the synthetic division table with the coefficients of the polynomial:

2 │ 5  -13  4  -2

 │    10 -6 -2

 └───────────

   5  -3 -2  0

The last entry in the bottom row of the table gives the remainder of the division, which is f(2). Therefore, we have:

f(2) = 5(2)³ - 13(2)² + 4(2) - 2 = 40 - 52 + 8 - 2 = -6

So, the value of the function f(x) = 5x³-13x² + 4x-2 at x = 2 is f(2) = -6.

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Answer:that is correct it is 2/9

Step-by-step explanation:

The given expression is polynomial and degree of the polynomial  is 2.

What is polynomials?

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

the expression -10c° – c + 3c²

So the given expression is a polynomial,

The highest degree of the  polynomial will be 2

Hence The given expression is polynomial and degree of the polynomial  is 2.

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Answer: The force on an object is directly proportional to its acceleration, which means that if the force is increased, the acceleration will also increase, and if the force is decreased, the acceleration will decrease. This can be expressed mathematically as:

F = k * a

where F is the force, a is the acceleration, and k is a constant of proportionality.

We can use the given information to find the value of k:

30 N = k * 10 m/s^2

k = 3 N*s^2/m

Now we can use this value of k to find the acceleration when the force is 9 N:

9 N = 3 Ns^2/m * a

a = 3 Ns^2/m / 9 N

a = 1/3 m/s^2

Therefore, the acceleration of the object when the force is 9 N is 1/3 m/s^2.

Answer:

AOC=360-130 = 230

ABC= 230/2=115

Answer:

∠ABC = 115∘

Step-by-step explanation:

∠ABC = 1/2 ∠AOC

(Angle subtended by a chord on major area is half of that subtended on center)

∴ ∠ABC = 1/2 x 130 = 65

ABCD is  a cyclic quadrilateral

Sum of opposite angles = 180∘

∴ ∠ABC + ∠AOC = 180∘

 ∠ABC + 65 = 180∘

 ∠ABC = 115∘

The solution of the inequalities is (0.67, 3.33)

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

y >= 2

x + y <= 4

y <= 2x + 2

Next, we plot the graph of the inequalities

Using the above as a guide, we have the following:

The solution is (0.67, 3.33)

This is so because the lines intersect at (0.67, 3.33) for y >= 2

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Answer:

See the picture

Step-by-step explanation:

The 1 tells us where to start.  This is our y-intercept.  We start when x =0 and y =1.  The y intercept is 1 (0,1).  You see it in green.

From that point (0,1) you go up 1 and 2 to the right.  This is the slope. You see it in pink.

Once you have the begin part in pink.  You join it to the pink points and draw your line.

Answer: 4 is correct

Step-by-step explanation:

A(x) + B(x) = (4x - 1) + (8x - 3)

= 12x - 4

Answer:

[tex]c=2\sqrt{13[/tex]

Step-by-step explanation:

In a right triangle, to find the hypotenuse (c) you use Pythagoras theorem. Which is [tex]a^2+b^2=c^2[/tex]. Once we plug in our variables we get [tex]6^2+4^2=c^2[/tex], then we solve.

[tex]36+16=c^2[/tex]

[tex]52=c^2[/tex]

[tex]\sqrt{c^2} =\sqrt{52}[/tex]

[tex]c=\sqrt{52}[/tex]

If we simplify...

[tex]c=2\sqrt{13}[/tex]

Answer:

16 candy bars

Step-by-step explanation:

We know

Each candy bar cost costs $0.75

Billy buys candy bars for $12.50

How many candy bars did he buy?

We take

$12.50 divided by $0.75 = 16 candy bars

So, he bought 16 candy bars.

Answer:

16 2/3 candy bars.  Usually you cannot buy 2/3 of a candy bar so I am wondering if a number was copied incorrectly.

Step-by-step explanation:

12.50/.75 = 16 2/3 candy bars

16 candy bars would cost $12.00

16 x .75 = 12.00

Answer:

I'd say about a couple

you're welcome

The minimum number of (whole) dictionaries that you need to measure together is s ≤ 7.0 x 10⁻⁷

Measurement is the process of determining the size, amount, or degree of something, usually using an instrument or a tool.

To determine the thickness of one page in a dictionary, you can measure a number of dictionaries together and average the results.

To achieve an uncertainty of only 7.0 x 10-7 inches in your measurement of one page, you need to determine the minimum number of dictionaries that you need to measure together.

Let's assume that you have N dictionaries and the thickness of the i-th dictionary is xi. Then, the average thickness of one page is given by:

(x1 + x2 + x3 + ... + xN) / N = x

The uncertainty in the average thickness of one page is given by:

s = √(∑((xi - x_bar)²)/(N-1)) / √(N) = √(∑((xi - x_bar)²)/N²(N-1))

We want to find the minimum value of N such that the uncertainty in the average thickness, s, is less than or equal to 7.0 x 10⁻⁷ inches.

So, we have:

s <= 7.0 x 10⁻⁷

Complete Question:

1. You have a set of calipers that can measure the thicknesses of a few inches with an uncertainty of + 0.0050 inches. You measure the thickness of one Oxford American Dictionary (2096 pages) and get 2.51 in.

You can improve this result by measuring dictionaries together. If you want to know the thickness of 1 page with an uncertainty of only 7.0 x 10⁻⁷ in., what is the minimum number of (whole) dictionaries that you need to measure together?

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The percent of change from 5/4 to 3/8 is a 70% decrease.

To find the percent of change, we need to determine the difference between the original amount and the new amount, and then divide that difference by the original amount and multiply by 100 to express the answer as a percentage.

Let's first convert both fractions to decimals:

5/4 = 1.25

3/8 = 0.375

Next, let's find the difference between the original amount (1.25) and the new amount (0.375):

1.25 - 0.375 = 0.875

Finally, let's divide the difference by the original amount and multiply by 100 to express the answer as a percentage:

(0.875 / 1.25) * 100 = 70

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