What is 4.5 divided by 12.5....I AM SO CONFUSED
can you please show me step by step and please show and don't explain..
THANK YOU

Answer:

x=3.5, h=12.5

Step-by-step explanation:

[tex]x=\frac{1}{4} *14=\frac{7}{2} =3.5\\\\\\\\h^{2}=13^{2}-3.5^{2} \\h^{2} =156.75\\h=12.519....\\h=12.5[/tex]

The height of the triangle is 5.2 and the part of the base which is the base of the right angle triangle formed by h and side with measurement 13 is 13.

The Pythagorean theorem states that the square of the hypotenuse (the longest side of a right triangle) is equal to the sum of the squares of the other two sides.

The easiest way to find h and x is to use the Pythagorean theorem.

14² = 13²  + h²

We can solve this equation for h:

h²  = 14²  - 13²

h = √(14²  - 13² )

h = 5.2

We can also calculate x using the Pythagorean theorem.

x² = 14² - h²

x = √(14² - h²)

x = √(14² - 5.2²)

x = 12.99

x = 13

Therefore, the height of the triangle is 5.2 and x is 13.

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An expression that shows what jasper spent and had left: 4.5 - x = 2.21

Let us assume that x represents the amount of money Jasper s[ent on the rock.

t represents the bill amount,

and m represents the amount of money he  spent  with tax on plants for his fish tank.

Jasper had a $10 bill.

⇒ t = 10

He spent $5. 50 with tax on plants for his fish tank.

m = $5.50

So, the remaining amount is:

t - m = 10 - 5.5

       = 4.5 dollars

After he spent x dollars on the rock, he had $2. 21 in change.

So, we get an expression 4.5 - x = 2.21

Therefore, the required expression is: 4.5 - x = 2.21

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The simplified form of the expression 2(x+1)-2 is 2x, and when x is 5, the answer is 10.

The given expression is 2(x+1)-2. In mathematical terms, this expression can be written as 2x+2-2. This expression can be simplified by combining the like terms. Since 2 and -2 are both like terms, they can be combined. When combining like terms, the answer is 2x. Therefore, the simplified form of the expression is 2x.

In terms of calculation, if the value of x is 5, then the expression 2(x+1)-2 can be written as 2(5+1)-2. This can then be simplified to 2(6)-2, which can be further simplified to 12-2. The The simplified form of the expression 2(x+1)-2 is 2x When combining the like terms, the answer is 10. Therefore, when the value of x is 5, the answer to the expression 2(x+1)-2 is 10.

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As we have shown that

(a) if A and B are diagonal matrices, their sum is also diagonal.

(b) if A and B are symmetric matrices, their sum is also symmetric.

(a) If A and B are diagonal, prove that A + B is diagonal.

To prove this, we need to show that all the non-diagonal elements of A + B are zero. Let's assume that A and B are diagonal matrices of size n x n. Then, the diagonal elements of A are a11, a22, ..., ann, and the diagonal elements of B are b11, b22, ..., bnn.

The sum of A and B is (A + B) = [aij + bij]n x n. Since A and B are diagonal matrices, all the non-diagonal elements of A and B are zero. Therefore, the non-diagonal elements of A + B are also zero. Thus, we have proved that A + B is diagonal.

(b) If A and B are symmetric, prove that A + B is symmetric.

To prove this, we need to show that[tex](A + B)^T[/tex] = A + B. Let's assume that A and B are symmetric matrices of size n x n. Then, we have A = [tex]A^T[/tex] and B = [tex]B^T.[/tex]

Now, the transpose of A + B is [tex](A + B)^T = A^T + B^T[/tex]. Since A and B are symmetric matrices, [tex]A^T[/tex] = A and [tex]B^T[/tex]= B. Therefore, [tex](A + B)^T[/tex] = A + B. Hence, we have proved that A + B is symmetric.

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Our assumption that the negation of the original statement is true is false.

So the original statement is true. therefore, there exists a real number x such that for all real numbers y, xy = 1.

The given statement is that "there exists a real number x such that for all real numbers y,

xy = 1."

(i)The negation of the given statement is: It is not true that there exists a real number x such that for all real numbers y, xy = 1.

Therefore, it can be written as ∀x ∈ R, ∃y ∈ R such that xy ≠ 1.Using proof by contradiction,

let's assume that the given statement is true.

Then there exists a real number x such that for all real numbers y,

xy = 1.

Now we need to prove that the negation of this statement is false,

meaning that the negation of the original statement is not true.

So we need to prove that

∀x ∈ R, ∃y ∈ R such that xy ≠ 1.

Let's assume that the negation of the original statement is true.

Then for all real numbers x, there exists a real number y such that xy ≠ 1.

Consider a specific value of x, say x = 0.

Then, for this value of x, there exists a real number y such that xy ≠ 1.

Since xy = 0 for all values of y, xy ≠ 1 is true.

But the original statement states that for all real numbers y, xy = 1.

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The values of a and b that satisfy the given condition are a = ±n and b = ±n, where n is any non-negative integer.

To see why this is true, note that the Laplacian of u(x,y) is given by:

∇^2 u = (∂^2u/∂x^2) + (∂^2u/∂y^2) = -a^2 sin(ax) exp(by) - b^2 sin(ax) exp(by)

Since u(x,y) satisfies Laplace's equation, this expression must be equal to zero. Factoring out sin(ax) exp(by), we get:

sin(ax) exp(by) (-a^2 - b^2) = 0

For sin(ax) exp(by) to be non-zero, we must have a^2 + b^2 ≠ 0. Therefore, we can conclude that a^2 + b^2 = n^2 for some non-negative integer n. This means that a and b must both be integers (positive, negative, or zero), and satisfy the equation a^2 + b^2 = n^2.

The solutions to this equation are given by all possible combinations of a and b that satisfy the condition a^2 + b^2 = n^2 for some non-negative integer n. Therefore, the values of a and b that satisfy the given condition are a = ±n and b = ±n, where n is any non-negative integer.

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6, 7, 8, 9 all have the longest interval on which this problem has a unique twice-differentiable solution is (-∞,∞)

A function and one or more of its derivatives are connected by a differential equation, which is a mathematical equation.

Let's consider each problem separately:

6. equation, ty"+3y = t at y(1) = 1, y'(1) = 2

After solution of differential equation we get:

y(t) =  [tex]\frac{1}{3} t - \frac{1}{9} +\frac{1}{9}*e^{(-\frac{t^2}{6} )[/tex]

Since this function is a polynomial plus an exponential function, it is infinitely differentiable everywhere. Therefore, the longest interval on which this problem has a unique twice-differentiable solution is (-∞,∞).

7. Equation, t (t-4) y"+ 3t y' + 4y = 2 ; y(3) = 0, y'(3) = -1

Using the method of undetermined coefficients, the homogeneous equation to get:

y(t) = [tex]c_1 e^{(-2t)} + c_2 e^{(t/2)} + y_p(t)[/tex]

Therefore, the solution is:

y(t) = [tex]\frac{33}{32} e^{\frac{t}{2}} - \frac{5}{32} e^{(-2t)} + \frac{1}{4} -\frac{1}{8} t[/tex]

The longest interval on which this problem has a unique twice-differentiable solution is (-∞,∞).

8. Equation, [tex]y"+ (cos\ t) y' + 3 (ln\ |t|) y = 0[/tex] ; y(2)=3, y'(2)=1

This is a Cauchy-Euler equation, which can be solved by assuming a solution of the form y(t) = [tex]t^r[/tex]. Substituting this into the equation, we get the characteristic equation:

r (r-1) + cos(t) r + 3 ㏑ |t| = 0

This equation has complex roots, so the general solution involves complex exponential functions. Therefore, the function is infinitely differentiable everywhere, and the longest interval on which the problem has a unique twice-differentiable solution is (-∞,∞).

9. Equation, (x-2)y" + y'+ (x-2) (tan x) y = 0 ; y(3) = 1, y'(3) = 2

After solution of differential equation using power series,

y(x) = ∑[n≥0] [tex]a_{n} (x-3)^{(n+1)}[/tex]

where aₙ satisfies the recurrence relation:

[tex]a_{n+2} = - \frac{a_n}{[(n+2)(n+3)]} - \frac{tan (3)}{3} a_{n+1}[/tex]

The function is infinitely differentiable everywhere, and the longest interval on which the problem has a unique twice-differentiable solution is (-∞,∞).

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Complete and clear question-

Answer:

To rewrite a complex fraction as a division problem that reads left to right, we need to simplify the numerator and denominator separately and then divide the numerator by the denominator.

For example, if we have the complex fraction:

(3/4) / (5/6)

We can simplify the numerator and denominator separately:

Numerator: (3/4) = 0.75

Denominator: (5/6) = 0.8333...

Now we can divide the numerator by the denominator:

0.75 ÷ 0.8333... = 0.9

So the complex fraction (3/4) / (5/6) can be rewritten as 0.9.

The rewritten complex fraction as a division problem that reads left to right is 0.07 = 7/100.

The complex fraction is:

(3 + 4)/(2 * 5)

To rewrite this as a division problem that reads left to right, we can do the following:

Rewrite the numerator and denominator as single fractions.

Multiply the numerator and denominator by the reciprocal of the denominator.

Simplify the fraction.

The steps are shown below:

Rewrite the numerator and denominator as single fractions:

(3 + 4) = (7)

(2 * 5) = (10)

Multiply the numerator and denominator by the reciprocal of the denominator:

(7) / (10) * (1/10) = (7/100)

Simplify the fraction:

(7/100) = 0.07

Therefore, the complex fraction can be rewritten as the division problem:

0.07 = 7/100

The division problem reads left to right, and the answer is 0.07.

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Answer:                     8

Step-by-step explanation: because you need to remove the all numbers and then it will leave you 1 which is in the middle

Answer:

2

Step-by-step explanation:

please mark as brainliest

the correct answer is

2

When the horizontal line crosses the y axis.

Answer:

Step-by-step explanation:

45:45:90 Triangle

x:x:2[tex]\sqrt{x}[/tex]

x:x:[tex]\sqrt{11}[/tex]

(2[tex]\sqrt{x}[/tex]=[tex]\sqrt{11\\[/tex])^2

2^2x=11

4x=11

x=11/4

x=2.75

Answer:

C is correct

Step-by-step explanation:

Answer: 2.55 as a mixed number is 51/20

The total height of the Washington Monument is approximately 266.6 feet.

We can use trigonometry to determine the total height of the Washington Monument. We know that Noelle is standing 50 feet away from the monument and her line of sight is 84.8° above ground level.

Six fundamental trigonometric functions—sine, cosine, tangent, cosecant, secant, and cotangent—form the basis of trigonometry. These formulas link the angles and side lengths of a right triangle. For instance, the sine of an angle is determined by dividing the length of the hypotenuse by the length of the side opposite the angle (the longest side of the triangle).

In a similar manner, the cosine of an angle is determined by dividing the length of the hypotenuse by the length of the adjacent side, which is the side that faces the angle.

The diagram shows that Washington Monument's height (x) is equal to the sum of monument's height from ground up (h) and Noelle's height (5 ft). The tangent function can be used to determine h:

[tex]tan(84.8) = h / 50\\h = 50 * tan(84.8)[/tex]

h = 261.6 ft

Hence, the Washington Monument's (x) overall height is

x = h + 5

x ≈ 266.6 ft

The Washington Monument is therefore approximately 266.6 feet tall overall.

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The probability of Jennifer's mom taking exactly 6 vitamins a day is 0.20 rounded to the nearest hundredth.

To determine the probability that Jennifer's mom took exactly 6 vitamins a day, we need to count the number of dots that correspond to days when she took 6 vitamins and divide it by the total number of dots in the plot.

Upon careful observation, we can see that there are 4 dots that correspond to days when Jennifer's mom took 6 vitamins. 20 is the total number of dots in the plot.

Therefore, the probability of Jennifer's mom taking exactly 6 vitamins a day is:

Probability = Number of dots corresponding to 6 vitamins / Total number of dots

Probability = 4 / 20

Probability = 0.2

Rounded to the nearest hundredth, the probability is 0.20.

To round the probability to the nearest hundredth, we look at the third decimal place. If it is 5 or greater, we round up the second decimal place; otherwise, we leave it as it is. In this case, the third decimal place is 0, so we do not need to round up the second decimal place. Therefore, the probability rounded to the nearest hundredth is 0.20.

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The T(V) using the follwing properties is:D. x

To find T(v), where T is a linear transformation from P₂ (polynomials of degree 2 or less) to P₃ (polynomials of degree 3 or less), we can use the properties given:

T(x²) = x³

T(x + 1) = 0

T(x - 1) = x

First, we can express the polynomial v = x² + x + 1 in the standard basis for P₂, which is {1, x, x²}. We can write v as a linear combination of the standard basis polynomials:

v = 1 * 1 + 1 * x + 1 * x²

Now, we can apply the linear transformation T to each term separately, using the given properties:

T(1) = 0 (since T(x + 1) = 0)

T(x) = T(x - 1 + 1) = T(x - 1) + T(1) = x + 0 (using T(x - 1) = x and T(1) = 0)

T(x²) = x³ (using T(x²) = x³)

So, we can write T(v) as:

T(v) = 0 + x + x³ = x + x³

Therefore, the correct choice for T(v) is (d) x.

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The probability that fifth storm uses last of the stocks is none as more supply will eventually get provided.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

Here, it is anticipated that once the initial supply of salt runs out, the city will import more salt for consumption, and the transition matrix will then follow the same pattern.

Moreover, it is presumable that the time domain is discrete and comprises of moments in time when storms occur in the metropolis, leading to the creation of salt passages.

The inventory of the salt will last as they will bring more salt after the consumption.

The probability that fifth storm uses last of the stocks is none as more supply will eventually get provided.

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The section of TV that applies the segment inside circle postulate has a length of 25 units.

A line's endpoints, which are two points, and any other points along the line between them are referred to as segments.

It is widely used to denote the distance between two objects as well as the length, height, or width of an object.

It is given a name based on the labels of its endpoints.

Now in the question given here,

VU = 8

TU = 5x -1

VW = 9

QW = 15

According to the segment's concept,

VU × TU = VW × QW

⇒ 8×(5x-1) = 9×15

⇒ 40x - 8 = 135

⇒ 40x = 143

⇒ x = 143/40

⇒ x = 3.57

Now the value of TV = VU + TU

TV = 8 + 5×3.57 -1

= 8 + 17.85 -1

= 24.85

≈ 25 units.

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A and C are the two true statements.

This means that X could be equal to 1, 2, 3, or 4 distinct birthdays.

The random variable X represents the number of distinct birthdays among four persons selected uniformly at random.

The range of X is {1, 2, 3, 4}. This means that X could be equal to 1, 2, 3, or 4 distinct birthdays.

For example, if Alice, Bob, Raul, and Yi-Fei were all born on January 1st, X would equal 1.

If Alice and Bob were born on Jan 1st, but Raul and Yi-Fei were born on July 23rd, X would equal 2.

If Alice was born on Jan 1st, but Bob, Raul, and Yi-Fei were born on July 23rd, X would equal 2.

If Alice and Bob were born on Jan 1st, Raul was born on July 3rd, and Yi-Fei was born on Dec 4th, X would equal 3.

And if all four were born on different days, X would equal 4.

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Answer:

Step-by-step explanation:

First, we determine the hourly wage he gained by dividing $429 by 39 hours.

$429 / 39 = $11 / hour

It is said that this wage (his true wage) is $3 more than what is written in the stub. It must be shown in the stub that he earns only $8 / hour.

Hope it helped! :D

An equation of the plane through the point (−4, 6, 10) and perpendicular to the line x = 4 t, y = 2t, z = 4 − 4t is 12x − 8y + 8z + 72 = 0.

The equation of a plane can be found by using the point-normal form, which is the equation of the form
Ax + By + Cz + D = 0.
To find the equation of the plane, we first need to find a normal vector for the given line.

This normal vector can be calculated using the cross-product of two vectors in the line.

The two vectors in the line are (4,2,−4) and (1,0,−1). Thus, the normal vector is the cross product of these two vectors, which is (12, −8, 8).
Now, we can use the point-normal form to calculate the equation of the plane.

We need to plug in the normal vector and the given point, (−4,6,10).

Thus, the equation of the plane is
12x − 8y + 8z + D = 0
To find the value of D, we can plug in the given point (−4, 6, 10) into the equation,
12(-4) − 8(6) + 8(10) + D = 0
⇒ −48 − 48 + 80 + D = 0
⇒ D = 72
Therefore, the equation of the plane is 12x − 8y + 8z + 72 = 0.

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the range in the number of votes predicted for Alyssa by these four polls is 15 to 200.

To determine the range in the number of votes for Alyssa predicted by these four polls, we need to analyze the minimum and maximum number of votes predicted for Alyssa in each of the four polls.

In poll 1, 16 students planned to vote for Alyssa, while 9 students planned to vote for James. Therefore, the minimum number of votes predicted for Alyssa in this poll is 16.

In poll 2, 12 students planned to vote for Alyssa, while 13 students planned to vote for James. Therefore, the minimum number of votes predicted for Alyssa in this poll is 12.

In poll 3, 14 students planned to vote for Alyssa, while 11 students planned to vote for James. Therefore, the minimum number of votes predicted for Alyssa in this poll is 14.

In poll 4, 15 students planned to vote for Alyssa, while 10 students planned to vote for James. Therefore, the minimum number of votes predicted for Alyssa in this poll is 15.

To determine the maximum number of votes predicted for Alyssa, we need to add up the number of students planning to vote for Alyssa in each of the four polls.

The total number of students planning to vote for Alyssa is 16+12+14+15 = 57.

Since there are a total of 200 students who will vote in the election, the maximum number of votes Alyssa can receive is 200, assuming every student who planned to vote for her actually does so.

Therefore, the range in the number of votes predicted for Alyssa by these four polls is 15 to 200.

It's worth noting that while these four polls can provide a general idea of who might win the election, they are not necessarily representative of the entire student population. Other factors, such as campaign strategies, endorsements, and current events, can also influence the outcome of the election.

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The maximum error in the calculated area of the rectangle is at most 7.62 square centimeters.

Using the partial derivative dA/dl = w, we can estimate the change in area (dA) due to this error in length:

dA = (dA/dl) x dl

dA = w x 0.1

Therefore, we can estimate the maximum possible value of dA:

dA <= 28.1 x 0.1 = 2.81

This means that the error in the calculated area due to the error in length measurement is at most 2.81 square centimeters.

Using the partial derivative dA/dw = l, we can estimate the change in area (dA) due to this error in width:

dA = (dA/dw) x dw

dA = l x 0.1

We don't know the exact value of l, since it could be anywhere between 47.9 cm and 48.1 cm, but we do know that it is less than or equal to 48.1 cm. Therefore, we can estimate the maximum possible value of dA:

dA <= 48.1 x 0.1 = 4.81

This means that the error in the calculated area due to the error in width measurement is at most 4.81 square centimeters.

Since the errors due to the length and width measurements are independent, we can add them together to get the total maximum error in the calculated area:

total maximum error in area = error due to length + error due to width

total maximum error in area <= 2.81 + 4.81

total maximum error in area <= 7.62

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The volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis is (43/4)π.

The volume V of the solid obtained by rotating the region bounded by the given curves about the specified line can be found by using the disk method. The disk method involves integrating the area of a series of disks that make up the solid.

First, we need to find the radius of each disk. The radius of each disk is the distance from the x-axis to the curve y = 4 - (3/2)x. This distance is simply the value of y at each x value.

The volume of each disk is πr^2, so the volume of the solid is the integral of πr^2 from x = 0 to x = 1.

V = ∫[0,1] πr^2 dx = ∫[0,1] π(4 - (3/2)x)^2 dx

We can simplify the integrand and then integrate:

V = ∫[0,1] π(16 - 12x + (9/4)x^2) dx = π[16x - 6x^2 + (3/4)x^3] from x = 0 to x = 1

V = π[(16 - 6 + 3/4) - (0 - 0 + 0)] = π(10 + 3/4) = (43/4)π

Therefore, the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis is (43/4)π.

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It cannot be determined from the information given that how many scores are in the population. The given information is not sufficient to determine the total number of scores in the population.

What is a population?The term population is used in statistics to refer to the whole set of observations or scores of interest that have something in common. The population is the complete collection of data of all possible observations or scores that satisfy some given conditions.

The given information about the population is insufficient, since we are not aware of the total number of scores in the population .A population with a mean of μ = 6 has ∑X = 42 implies that the total sum of all scores is 42. Since the sum of all scores is equal to the sum of individual scores, we cannot say how many scores are in the population.

In fact, we can have different numbers of scores in the population with a sum of 42.For example, if we have 7 scores in the population, the sum of all scores will be 42. That is, 6+6+6+6+6+6+6=42. However, if we have 14 scores in the population, then the sum of all scores will be 42. That is, 3+3+3+3+3+3+3+3+3+3+3+3+3+3=42. Therefore, it is impossible to determine the number of scores in the population with only the given information.

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The average longer piece will be 160 cm long, and the shorter piece will be 105 cm long.

Let x = length of the shorter piece

The longer piece would then be 2x + 5 cm

320 cm = x + (2x + 5)

320 = 3x + 5

3x = 315

x = 105 cm

In order to solve this problem, we need to use basic algebraic equations. The total length of the lumber is 320 cm, and we know that the longer piece will be 5 cm longer than twice the length of the shorter piece. This can be expressed as a mathematical equation: x + 2x + 5 = 320, where x represents the length of the shorter piece. Solving this equation for x will give us the length of the shorter piece. When we solve this equation, we get x = 155, which means that the shorter piece will be 155 cm long. We can then use this information to calculate the length of the longer piece. Since we know that the longer piece will be 5 cm longer than twice the length of the shorter piece, we can add 5 cm to twice the length of the shorter piece (2 x 155 = 310). This gives us a total length of 315 cm for the longer piece. Since we know the total length of the lumber is 320 cm, we can subtract 315 cm from 320 cm, which gives us a length of 160 cm for the longer piece. Therefore, the longer piece will be 160 cm long, and the shorter piece will be 105 cm long.

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Answer:

3.76. Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

4

Step-by-step explanation:

Open bracket

(173/346)¯² =(1/2)¯²

To solve the separable differential equation dudt = e3u + 5t, with the initial condition u(0) = 2, we can use the method of DUDT, or "Divide, Integrate, and Check."

First, we divide both sides of the equation by e3u, giving us:

dudt / e3u = 1 + 5t/e3u

Next, we integrate both sides with respect to t, to get:

∫ dudt / e3u dt = ∫ (1 + 5t/e3u)dt

We can evaluate the left side using the formula for U=U (the indefinite integral of a function and its derivative):

U = e3u + c, where c is an arbitrary constant

For the right side, we get:

t + c2e-3u, where c2 is another arbitrary constant

Evaluating the initial condition u(0) = 2, we can solve for c and c2 to get:

e3u + c = 2

t + c2e-3u = 0

Therefore, our solution is:

e3u = 2 - c

t = -c2e-3u

Finally, plugging the values of c and c2 into the original equation, we get:

dudt = e3u + 5t = 2 + 5(-c2e-3u)

dudt = e3u - 5c2e-3u

This is the solution to the separable differential equation, dudt = e3u + 5t, with the initial condition u(0) = 2.

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