Brenda and Sam are going to stay at the hotel for one night. It costs a total of £84 to stay at the hotel for one night. Brenda pays a deposit of £20 towards the total cost. Brenda says to Sam, 'We will share the total cost equally.' How much does each person have left to pay?​

Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

Answer:

2/6

1/3 simplified

Rise over run

choose any two points on the graph and do rise over run

Answer:

y-intercept=2

Step-by-step explanation:

2y=-3x+4

divide both sides by 2

y=-1.5x+2

y=mx+c

'c' is the y-intercept so '2' is the answer.

Answer:

= -3/2

Step-by-step explanation:

The equation of the line = 2y = -3x + 4

2y = -3x + 4

2y = -3x + 4

2 2 2

y intercept of the line = -3/2.

Answer:

$20 after the applied coupon

Step-by-step explanation:

The required sale price of the shirt after getting  1/3 off is $20.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
A $30 shirt is marked, "Get 1/3 off.
The sale price of the shirt,
= 30 - 1 / 3×30
= 30 - 10
= $ 20

Thus, the required sale price of the shirt after getting  1/3 off is $20.

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Answer:

7: 63

8: 73

arithmetic sequence

y = 10x - 7

or f(n) = 10x -7

or

\(a_{n}\) = 3 + (n-1)10

Step-by-step explanation:

the output increases by 10 every time that the input increases by 1.  That gives us our common difference or slope.  The y intercept is -7. That is the value is you worked backwards until you get to n = 0.  The initial value  is 3.  That is when n is 1.

When n is 3, f(n) is 23

When n is 2, f(n) is 13

When n is 1, f(n) is 3

When n is 0, f(n) is -7

I am not sure if this is clear.  I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence.  If my explanation is confusing it is me and not you.

Answer:

a. 63,73

b. Arithmetic sequence

c.t(n)=10n-7

Explanation:

a. Here is the completed table:

n | t(n)

4 | 33

5 | 43

6 | 53

7 | 63

8 | 73

b.

The type of sequence is arithmetic.

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.

In this case, the difference between any two consecutive terms is 10.

c.

The equation for the arithmetic sequence is:

t(n)=a+(n-1)d

where:

For Question:

Now

equation becomes:

t(4) = a+(4-1)10

33=a+30

a=33-30

a=3

Now, the Equation becomes

t(n) = 3+(n-1)10

t(n) = 3+10n-10

t(n)=10n-7

The regression equation for this data is y = -6+5x.

Using this regression equation, the value of predicted Y when X=3 is 9.

In the given question, a researcher conducted a number of descriptive statistics for two variables X and Y.

We have to find the regression equation for this data.

Then using this regression equation, we have to find the value of predicted Y when X=3.

We have given that

SP = 15

SSx = 3

My = 4

Mx = 2

B1 = Sp / SSx

B1 = 15/3=5

B0 = My-^B1Mx

B0 = 4-5*2=-6

So, the regression equation for this data is:

y = -6+5x

For x=3, the predicted value of y is

y = -6+5*3

y(predict) = 9

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The write question is given below:

According to the given statement;

a sloth go 600 units in 90 minutes

A fraction is used to denote a piece or component of a whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

According to the given values;

A sloth may move in one hour = 250÷5/8.

let us simplify 250÷5/8 first.

Division sign can be convert into multiplication sign and flip the right side fraction 5/8 to 8/5.

250×8/5

Dividing 250 by 5, we get

= 50 × 8

Multiplying 50 and 8,  we get

= 400.

So, we could say, a sloth may move in one hour = 400 units.

We need to find distance covered in 90 minutes.

Let us convert 90 minutes into hours.

60 minute = 1 hour.

1 minute = 1/60 th of an hour.

and 90 minutes = 90 * 1/60 = 90/60 = 9/6 = 1.5 hours.

a Sloth may move in one hour = 400 units.

Therefore, in 1.5 hours Sloth can move = 1.5 × 400 = 600 units.

So, a sloth go 600 units in 90 minutes

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Answer:

Diagnols of a rectangle are always congruent.

Step-by-step explanation:

Answer:

Volume V = 18.735 m3

Step-by-step explanation:

hope this helps

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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An ordered pair (x, y) that is a solution to the equation include the following: (x, y) = (-3, 0).

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of the given function, we would plot its equation by using an online graphing calculator and then read all the ordered pairs that lie on the line.

By critically observing the graph of the given function (see attachment), the required solutions are include following;

Ordered pair = (0.75, 0).

Ordered pair = (-3, 0).

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The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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The formula substituted into the equation I = P(1 + t)^t - P is 730 = 180,000(1 + 0.08)^0.08 - 180,000

I = P(1 + t)^t - P

where,

I = $1,000 - $270

= $730

P = $180,000

r = 4%

t = 30 days to years

= 1/12

= 0.08333333333333 years

I = P(1 + t)^t - P

730 = 180,000(1 + 0.08)^0.08 - 180,000

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Answer:

not proportional

Step-by-step explanation:

0.2/2.6 is 1:13

0.3/3.6 is 1:12

Using the coordinate geometry formula, the exact area of triangle DEF is: B. 18 square units.

The coordinate geometry formula is used to find the rea of a triangle with given coordinates of its vertices. It is given as: the absolute value of [Dx(Ey - Fy) + Ex(Fy - Dy) + Fx(Dy - Ey)]/2.

Dx = -3

Dy = 4

Ex = 3

Ey =-2

Fx = 3

Fy = 4

Plug in the values:

[-3(-2 - 4) + 3(4 - 4) + 3(4 - (-2))]/2.

[-3(-6) + 3(0) + 3(6)]/2.

[18 + 0 + 18]/2.

36/2

= 18 units²

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The simplified form of 7 log3x + 4 log3z - 6 log3y is log3(x^7 z^4 / y^6).

We can simplify the expression using the following logarithmic rule:

log a + log b = log ab (product rule)

log a - log b = log(a/b) (quotient rule)

c log a = log a^c (power rule)

Using these rules, we can simplify 7 log3x + 4 log3z - 6 log3y as follows:

7 log3x + 4 log3z - 6 log3y

= log3x^7 + log3z^4 - log3y^6 (using the power rule)

= log3(x^7 z^4 / y^6) (using the quotient rule)

Therefore, the simplified form of 7 log3x + 4 log3z - 6 log3y is log3(x^7 z^4 / y^6).

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Answer:

-4-5

Step-by-step explanation:

The temp was at -4 and if it dropped that means you subtract another 5 from it which is -4-5

Answer:

The correct answer is -4 - 5.

Step-by-step explanation:

The original temperature is -4 degrees.  Then, the temperature falls by 5 degrees.  The temperature "falling" means that it is getting colder or that the temperature is getting lower.  This lets us know that we need to use subtraction.  The final answer is -4 - 5, which would give us the temperature of -9 degrees as the new temperature.

Hope this helps!

Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

To write a quadratic function to represent the height h of the acrobat t seconds after the jump, we can use the following formula:

\(h(t) = -16t^2 + vt + h0\)

Where h0 is the initial height of the acrobat, which is 25 feet, and v is the initial vertical velocity, which is 4 ft/s. Plugging in these values, we get:

\(h(t) = -16t^2 + 4t + 25\)

To find how long it will take for her to land safely on the net, we need to find the time at which h(t) = 5. In other words, we need to solve the equation:

\(-16t^2 + 4t + 25 = 5\)

Simplifying this equation, we get:

\(-16t^2 + 4t + 20 = 0\)

Dividing both sides by -4, we get:

\(4t^2 - t - 5 = 0\)

Now we can use the quadratic formula to solve for t:

\(t = (-b ± \sqrt(b^2 - 4ac)) / 2a\)

Where a = 4, b = -1, and c = -5. Plugging in these values, we get:

\(t = (1 ± \sqrt(1 + 4(4)(5))) / 8\)

Simplifying this equation, we get:

\(t = (1 ± 9) / 8\)

So, the two solutions are:

\(t = 1 and t = -5/4\)

Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

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We want to solve the following equation:

First, let's expand the parenthesis by using the distributive property.

Now, let's subtract 6 from both sides of the equation.

Now, let's subtract 9d from both sides.

And finally. let's divide both sides by 3.

d = -12.

It is proved that m = √n.

To prove that given a nonnegative integer n, there is a unique nonnegative integer m, we just need to take the square root of the given equation:

m^2 ≤ n < (m + 1)^2.

So, after taking the square root, it will be:

m ≤ √n < m + 1

From that we can see m = √n is the unique m.

A nonnegative integer is an integer which is either positive or zero. It is the union of the natural numbers and the number zero. Occasionally, it is referred to as Z*, and it can be described as the set {0, 1, 2, 3, 4, 5, …}. In other words, nonnegative integers are integers that are not negative.

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Although part of your question is missing, you might be referring to this full question: Prove that given a nonnegative integer n, there is a unique nonnegative integer m such that m^2 ≤ n < (m+1)^2.

The number of hours he worked walking dogs last week is 6 Hrs

What is problem-solving?

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

Calculation:-

lifeguarding X = $13 per hour

walking doge Y = $10 per hour

last week Jordan earned = $177

13X + 10Y = 177

X = 9 ( lifeguarding)

Y = 6 (walking dog)

Hence, The number of hours he worked walking dogs last week is 6 Hrs

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Answer:

9 hours LIfegarding 6 hours walkng dogs

Step-by-step explanation:

Answer: y = 3x^2 -x + 2

Step-by-step explanation:

A: The linear equations are x + y = 125 and x = y + 45.

B: Everyday Angela spends 40 minutes in playing golf.

C: No, it is not possible for Angela to spend 80 minutes playing soccer every day.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Part A:

Let x be the number of minutes Angela plays soccer every day

Let y be the number of minutes Angela plays golf every day

According to the problem statement the linear equations are -

x + y = 125 (total time playing both sports is 125 minutes)

x = y + 45 (Angela plays 45 more minutes of soccer than golf)

Part B:

Substitute x = y + 45 into the first equation -

(y + 45) + y = 125

Use the addition operation -

2y + 45 = 125

2y = 80

y = 40

Angela spends 40 minutes playing golf every day.

Part C:

If Angela spends 80 minutes playing soccer every day, then

x = 80

y + 45 = 80 (using the equation x = y + 45)

y = 35

But this would mean that she plays golf for 35 minutes and soccer for 80 minutes, which adds up to a total of 115 minutes.

This is not possible since the problem states that Angela plays both sports for a total of 125 minutes every day.

Therefore, it is not possible for Angela to have spent 80 minutes playing soccer every day.

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Answer:

0, -1, 0, 1/6, 0

Step-by-step explanation:

f(x) = sin(x), f'(x) = cos(x), f''(x) = -sin(x), f'''(x) = -cos(x), f''''(x) = sin(x)

evaluated at pi/2 they are 0, -1, 0, 1, 0, respectively

but we have to divide each term by their respective factorials, which turns them into 0/(0!), -1/(1!), 0/(2!), 1/(3!), 0/(4!) = 0, -1, 0, 1/6, 0

if you're wondering why here's a great vid by khan academy

https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-11/v/maclaurin-and-taylor-series-intuition

gl on your homework :)

Answer:

The measure of the reference angle = 30°

Step-by-step explanation:

Convert 11\(\pi\)/6 (radians) to degrees by multiplying by 180 and dividing by \(\pi\):

11\(\pi\)/6 (radians) = 330\(\pi\)/\(\pi\) = 330°

Therefore, reference angle = 360 - 330 = 30°

First convert to degree from radian .

\(\\ \tt\hookrightarrow \dfrac{11\pi}{6}\times \dfrac{180}{\pi}\)

\(\\ \tt\hookrightarrow \dfrac{1980}{6}=330°\)

Find reference angle=360-330=30°

Last option is correct

9514 1404 393

Answer:

Step-by-step explanation:

I find it easiest to match the patterns. You could also work this by finding inverse functions.

1.

  \(y=u^{-1/2}\\\\y=\dfrac{1}{\sqrt{u}}=\dfrac{1}{\sqrt{x+14}}\\\\u=x+14 \qquad\text{match radical contents}\)

__

2.

  \(y=8\tan{u}=8\tan{(\pi x^5)}\\\\u=\pi x^5 \qquad\text{match tangent arguments}\)