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Sarah earns €8 per hour working in the local shop. How much does she get paid for working 2 3 hours?

The exponential equation of ln x = 3 is: x = e^3.

The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

The logarithmic function can be written in exponential form as follows:

x = logb(a) ⇔ a = b^x

The two functions can be written in an equivalent form.

The given logarithmic function is ln x = 3.

The exponential equation of ln x = 3 is:

x = e^3

Hence, The exponential equation of ln x = 3 is: x = e^3.

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The best and most restrictive description of that quadrilateral is Rhombus.

The line segment joining the parallelogram's non-adjacent vertices is known as the diagonal. A parallelogram has two diagonals, and depending on the parameters and dimensions given, it is possible to determine the length of the diagonals using a variety of formulas. In this post, let's learn more about a parallelogram's diagonals.

Given: if the diagonals of a parallelogram are perpendicular then what would be the best and most restrictive description of that quadrilateral?

ABCD is Parallelogram . E is midpoint

As Since the diagonals of the parallelogram bisect each other.

BE and DE are congruent.

We have given that all four angles at E are 90 degrees. So, they are congruent.

Therefore, triangle ABE and ADE are congruent by side-angle-side.

Therefore, AB and AD are congruent.

Since opposite sides of the parallelogram are congruent.

AD and BC are congruent and AB and CD are congruent.

So, all four sides are congruent.

Hence,  The best and most restrictive description of that quadrilateral is Rhombus

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Given:

The equation of polynomial is

\(2x^3-5x^2+1=0\)

To find:

All rational roots of the polynomial.

Solution:

According to the rational root theorem, all the possible rational roots of a polynomial are defined as

\(x=\dfrac{p}{q}\)

where, p is a factor of constant term and q is factor of leading coefficient.

We have,

\(2x^3-5x^2+1=0\)

Here, leading coefficient is 2 and constant term is 1.

Factors of 1 are ±1.

Factors of 2 are ±1, ±2.

Using rational root theorem, we get

\(x=\pm \dfrac{1}{1},\pm \dfrac{1}{2}\)

\(x=\pm 1,\pm \dfrac{1}{2}\)

Therefore, all possible rational roots of the given polynomial are \(\pm 1,\pm \dfrac{1}{2}\).

Answer:

4y-13/5

Step-by-step explanation:

-

1/5(20y-13)
Use the distributive property to multiply 1/5 by 20y−13.

Result: 1/5*20y+1/5(-13)

Now, multiply 1/5 and 20 to get 20/5.

Result: 20/5y+1/5(-13)

Divide 20 by 5 to get 4.

Result: 4y+1/5(-13).

Multiply 1/5​ and −13 to get -13/5.

4y+-13/5

4y-13/5.

Step-by-step explanation:

The triangle is equilateral (OPTION D) because any triangle that has 3 equal side lengths is an equilateral triangle.

We have to say if 9,953 is divisible by 2, 3, 4, 5, 9 or 10 and justify each one:

• Is no divisible by 2 becuase the number is odd.

• Is not divisible by 3 becuase the sum of the digits is 26 that is not divisible by 3.

• Is not divisible by 4 becuase the last two digits form a number that is not divisible by 4.

• Is not divisible by 5 because the last digit is not 0 or 5.

• Is not divisible 9 becuase the sum of the digits is 26 that is not divisible by 9.

• Is not divisible by 10 because the last digit is not 0,

The graph of the given problem is shown below.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

Given that,

Distance travelled by airplane from Chicago to Los Angeles in 2 minutes = 15 miles.

In return,

The airplane covers distance in 3 minutes = 25 miles.

The formula for equation of line between two points (x₁, y₁) and (x₂, y₂) is,

(y - y₁) = {(y₂ - y₁)/(x₂ - x₁)} (x - x₁)

The linear equation for the given distance and time can be written as,

y - 15 = {(25 - 15)/(3 - 2)}(x-2)

y - 15 = 10 (x - 2)

y - 15 = 10x - 20

10x - y - 5 = 0

The graph for the equation 10x - y - 5 = 0 is shown below.

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Answer:d

Step-by-step explanation:

The answer is d. None of the above is true.

To calculate velocity, we need to use the equation:

Velocity = M * P / Y

Given:

M = 1,000

P = 2.25

Y = 2,000

Plugging in the values:

Velocity = 1,000 * 2.25 / 2,000

Simplifying:

Velocity = 2.25 / 2

The result is:

Velocity = 1.125

Therefore, the correct answer is: d. None of the above is true.

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The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

When two lines meet at a point, an angle is created. An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians. Angles are a common occurrence in daily life. Angles are used by engineers and architects to create highways, structures, and sports venues.

When two rays are linked at their ends, they create an angle in geometry.

The sides or arms of the angle are what are known as these rays. Read on to learn about the various components of an angle.

Hence, The intersection of two curves is important because it marks the spot where the values of the two curves coincide. There are numerous applications for this.

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A Poisson random variable represents the number of occurrences of an event in a fixed interval of time or space. It is a discrete random variable, which means that it can only take on integer values, starting from zero. Therefore, the smallest numerical value that a Poisson random variable can be is zero.

This means that there is a possibility that the event will not occur at all during the given interval. For example, if we are counting the number of customers who visit a store in an hour, it is possible that no customers show up during that hour, resulting in a Poisson random variable of zero.

However, the probability of this occurring depends on the average rate of the event occurring, which is denoted by the parameter λ in the Poisson distribution. The larger the value of λ, the smaller the probability of a Poisson random variable being zero.

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74100

170000

36000

I believe this is right!

The Laplace transform of the solution is Y(s) = (5 + e^(-5s)) / (s + 1).

To find the Laplace transform of the solution, we first take the Laplace transform of the given differential equation. Applying the Laplace transform to both sides of the equation and using the properties of the Laplace transform, we obtain:

sY(s) - y(0) + Y(s) = 5 + e^(-5s)

Substituting y(0) = 0, we simplify the equation to:

(s + 1)Y(s) = 5 + e^(-5s)

Dividing both sides by (s + 1), we get:

Y(s) = (5 + e^(-5s)) / (s + 1)

Therefore, the Laplace transform of the solution is Y(s) = (5 + e^(-5s)) / (s + 1).

The solution y(t) is y(t) = 5e^(-t) + h(t-5), where h(t) is the Heaviside step function.

To obtain the solution in the time domain, we need to take the inverse Laplace transform of Y(s). Using the properties and inverse Laplace transform table, we find:

L^(-1) [Y(s)] = L^(-1) [(5 + e^(-5s)) / (s + 1)] = 5e^(-t) + L^(-1) [1 / (s + 1)]

The inverse Laplace transform of 1 / (s + 1) is the Heaviside step function, h(t), which is defined as 1 for t ≥ 0 and 0 for t < 0. Therefore, the solution y(t) is given by:

y(t) = 5e^(-t) + h(t-5)

The solution can be expressed as a piecewise defined function:

y(t) = 5e^(-t) for 0 ≤ t < 5

y(t) = 5e^(-t) + 1 for t ≥ 5

If t = 5, the value of y(t) is given by the second piece of the piecewise function, which is 5e^(-5) + 1. At t = 5, the graph of the solution experiences a sudden jump or discontinuity, increasing by a value of 1.

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Answer:

A function in terms of t that represents the situation is:

\(\:y\:=\:10,000\left(1.65\right)^t\)

Step-by-step explanation:

We know that the exponential growth function is of the form

\(y\:=\:a\:\left(1\:+\:r\right)^t\)

Here:

As the sales of $10,000 represent an initial condition. Thus,  

a = 10,000

Given that sales are increased by 65% every year.

r = 65% = 0.65

now substituting a = 10,000 and r = 0.65 in the function

\(y\:=\:10,000\left(1\:+\:0.65\right)^t\)

\(\:y\:=\:10,000\left(1.65\right)^t\)

Therefore, a function in terms of t that represents the situation is:

\(\:y\:=\:10,000\left(1.65\right)^t\)

Answer:

x=42

Step-by-step explanation:

x/6+21=28

28-21=x/6

7=x/6

x=7*6

x=42

Answer:

42

Step-by-step explanation:

Solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

\(\frac{15}{10}\)  and \(\frac{3}{10}\)

 \(\frac{15}{10} -\frac{12}{10} = \frac{3}{10}\)

Step-by-step explanation:

Given

       \(\frac{3}{2} - \frac{6}{5}\)

Now the L.C.M = 10

 =  \(\frac{15-12}{10}\)

 =  \(\frac{15}{10} -\frac{12}{10} = \frac{3}{10}\)

The length of IKE is 2x - 12.

A condition on a variable that is true for just one value of the variable is called an equation.

Since KITE is a kite, we know that KT = IT and KE = IE. Let's call the length of these diagonals d. Then we have:

KT + TI = d

KE + EI = d

Substituting in the given values, we get:

x + 6 + 2x = d

2x + IE = d

Solving for d in the first equation, we get:

3x + 6 = d

Substituting this into the second equation, we get:

2x + IE = 3x + 6

Solving for IE, we get:

IE = x + 6

Therefore, IKE is equal to:

IKE = IT - IE

IKE = (d - KT) - (x + 6)

IKE = (3x + 6 - x - 6) - (x + 6)

IKE = 2x - 12

So, the length of IKE is 2x - 12.

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Given, the function is f(x) = x⁴ and the domain of x is 0 ≤ x ≤ 1.The lent lies approximation of the function g(t) = a₀ + a₂x is to be found out. Using the orthogonal system θ = {1, √3(2x - 1)} in the interval [0, 1].

The formula for the lent lies approximation is given by, `a₀ = (1/L) ∫ f(x)w₀(x)dx and a₂

= (1/L) ∫ f(x)w₁(x)dx`.Where, `w₀(x)

= 1/L ∫ f(x)dx - [1/L ∫ xf(x)dx] * t₀(x) and w₁(x)

= 1/L ∫ f(x)dx - [1/L ∫ xf(x)dx] * t₁(x)`Let's calculate the values of `w₀(x)` and `w₁(x)` respectively.Using integration by substitution, ∫ f(x) dx = (1/5)x⁵ + c₀where c₀ is the constant of integration.Using integration by substitution, ∫ xf(x) dx

= (1/5)x⁵/5 + c₁where c₁ is the constant of integration.Now, L

= ∫ w₀²(x)dx + ∫ w₁²(x)dxLet's find `a₀` and `a₂` now.`a₀

= (1/L) ∫ f(x)w₀(x)dx`Substituting the values, we get,`a₀

= 0.1572` (approx)`a₂

= (1/L) ∫ f(x)w₁(x)dx`Substituting the values, we get,`a₂

= 0.4714` (approx)Therefore, the lent lies approximation of the function `f(x)

= x⁴` using the orthogonal system θ

= {1, √3(2x - 1)} in the interval [0, 1] is `g(t)

= 0.1572 + 0.4714(2x - 1)`.

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On solving the provided question, we can say that equation Therefore, dz/du = 0 when u=-1 and v=0.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical terms. For instance, in the equation 3x + 5 = 14, a equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logos and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

x = 3u² + v²

y = 3uv

Now we can write z as a function of u and v:

z = sin(xy) + xsin(y)

= sin(3uvu) + (3u² + v²)*sin(3uv)

To find dz/du, we need to differentiate z with respect to u while treating v as a constant:

dz/du = d/dx[sin(xy)] * dx/du + d/dx[xsin(y)] * dx/du

= cos(xy) * d/dx[xy] * dx/du + sin(y) * dx/du

= cos(3uvu) * (y + xd/dx[y]) * d/dx[x] + sin(3uv) * d/dx[x] * d/dx[y] * dy/du

= cos(3uvu) * (3uv + (3u²+v²)3v) * 6u + sin(3uv) * (3v)

= 18uv(cos(3uvu) + sin(3uv))

Now we can substitute u=-1 and v=0 into the expression for dz/du to get the final answer:

dz/du = 18uv(cos(3uvu) + sin(3uv))

= 18(0)(cos(3(-1)(0)) + sin(30))

= 0

Therefore, dz/du = 0 when u=-1 and v=0.

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Answer:

C

Step-by-step explanation:

given:

m= -2 and (3, -1)

point-slope form: y-y1= m(x-x1)

y - (-1) = -2(x-3)

y + 1 = -2(x-3)

Answer:

C.

Step-by-step explanation:

A.) y - 1 = -2(x - 3)

y - 1 = -2x + 6

y = -2x + 6 + 1

y = -2x + 7

B.) y - 1 = -2(x + 3)

y - 1 = -2x - 6

y = -2x - 6 + 1

y = -2x - 5

C.) y + 1 = -2(x - 3)

y + 1 = -2x + 6

y = -2x + 6 - 1

y = -2x + 5

D.) y + 1 = -2(x + 3)

y + 1 = -2x - 6

y = -2x - 6 - 1

y = -2x - 7

Answer:

y=1343

Step-by-step explanation:

when you plug in 21 for x the equation would be 3(21)^2+20 solve using the order of operations and you get 1343

Answer:

The most expensive she can buy is the soccerball

Step-by-step explanation:

Given

\(Total =\$29.00\)

\(T\ Shirt = \$15.32\)

\(Soccer\ Ball= \$12.87\)

\(Baseball\ Cap = \$8.39\)

\(Shin\ Guards = \$14.98\)

\(Water\ Bottle = \$5.93\)

Required

Using \(\$15.32 + c = \$29.00\), what is the most expensive she can buy?

\(\$15.32 + c = \$29.00\)

Subtract $15.32 from both sides

\(\$15.32 - \$15.32 + c = \$29.00 - \$15.32\)

\(\$15.32 - \$15.32 + c = \$13.68\)

\(c = \$13.68\)

This means that she can not afford items that cost more than $13.68

i.e. the shin guards which costs $14.98

The items she can afford and their prices are:

\(Soccer\ Ball= \$12.87\)

\(Baseball\ Cap = \$8.39\)

\(Water\ Bottle = \$5.93\)

The most expensive of them all is:

\(Soccer\ Ball= \$12.87\)

Answer:

urmom

Step-by-step explanation:

GAY

The given information is as follows:A random sample of 150 teachers in an​ inner-city school district found that​ 72% of them had volunteered time to a local charitable cause within the past 12 months.

The formula for calculating the standard error of sample proportion is given as:$$Standard\(\ error=\frac{\sqrt{pq}}{n}$$\)where:p = proportion of success in the sampleq = proportion of failure in the samplen = sample sizeGiven:Sample proportion, p = 72% or 0.72Sample size, n = 150

The proportion of failure in the sample can be calculated as:q = 1 - p= 1 - 0.72= 0.28Substituting the known values in the above formula, we get:\($$Standard \ error=\frac{\sqrt{pq}}{n}$$$$=\frac{\sqrt{0.72(0.28)}}{150}$$$$=0.0372$$\)Rounding off to the nearest thousandth, we get the standard error of sample proportion as 0.037

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In order to increase the likelihood that a blue marble would be drawn at random to 3/4, we must thus add 32 more blue marbles.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

Here,

Let the number of blue marbles added be x,

Probability=3/4

Total marbles=20

Number of blue marbles=7

(7+x)/(20+x)=3/4

4(7+x)=3(20+x)

28+4x=60+3x

x=60-28

x=32

So, we need to add 32 more blue marbles to make the probability of randomly drawing a blue marble be 3/4.

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The slope of the tangent line to the curve defined by 9xy + xy = 10 at the point (1, 1) is -1.

To find the slope of the tangent line to the curve defined by the equation 9xy + xy = 10 at the point (1, 1), we can use implicit differentiation.

Let's start by differentiating both sides of the equation with respect to x.

Differentiating the left side of the equation:

d/dx(9xy + xy) = d/dx(10)

Using the product rule for differentiation, we differentiate each term separately:

d/dx(9xy) + d/dx(xy) = 0

Now, let's calculate the derivatives of each term:

For the first term, 9xy:

Using the product rule, we have:

d/dx(9xy) = 9y * dx/dx + 9x * dy/dx

= 9y + 9x * dy/dx

For the second term, xy:

Using the product rule again, we have:

d/dx(xy) = y * dx/dx + x * dy/dx

= y + x * dy/dx

Substituting these results back into our equation, we get:

9y + 9x * dy/dx + y + x * dy/dx = 0

Combining like terms, we have:

10y + 10x * dy/dx = 0

Now, let's find the value of dy/dx at the point (1, 1). We substitute x = 1 and y = 1 into the equation:

10(1) + 10(1) * dy/dx = 0

Simplifying further:

10 + 10 * dy/dx = 0

Dividing both sides by 10:

1 + dy/dx = 0

Finally, subtracting 1 from both sides:

dy/dx = -1

Therefore, the slope of the tangent line to the curve defined by 9xy + xy = 10 at the point (1, 1) is -1.

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Question 1

Question 2

The volume of the given cylinders.

\(\huge\boxed{Formula: V=\pi{r}^{2}h}\)

\(\huge\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}\)

Let's solve!

Substitute the values according to the formula.

\(V=3.14×{3}^{2}×9\)

\(\large\boxed{V= 254.34 \: {ft}^{3}}\)

Let's work on question 2

Substitute the values according to the formula.

\(V=3.14×{13}^{2}×8\)

\(\large\boxed{V= 4245.28 \: {yd}^{3}}\)

1) If u is a column vector and v is a row vector, then uv^T is a matrix in R^(n x n), while if v is a column vector and u is a row vector, then vu^T is also a matrix in R^(n x n).

2) uv^T and vu^T are generally not equal, unless u and v are scalar multiples of each other, in which case they are both equal to k^2 times the identity matrix in R^(n x n).

If u and v are vectors in R^n, then u^T v is the dot product of u and v, which is a scalar. Similarly, v^T u is also the dot product of u and v and is therefore equal to u^T v. Thus, u^T v and v^T u are equal.

If u is a column vector in R^n and v is a row vector in R^n, then uv^T is a matrix in R^(n x n). Similarly, if v is a column vector in R^n and u is a row vector in R^n, then vu^T is also a matrix in R^(n x n).

However, uv^T and vu^T are not generally equal. In fact, they are only equal if u and v are scalar multiples of each other (i.e., u = kv for some scalar k). In this case, uv^T and vu^T are both equal to k^2 times the identity matrix in R^(n x n). Otherwise, uv^T and vu^T are different matrices.

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The given question is incomplete, the complete question is:

If U And V Are In R^n, How Are U^T v And V^T u Related? How Are. Uv^T And Vu^T Related?