Peter owns a currency conversion shop.


Last Monday, Peter changed a total of £20,160 into a number of different currencies.


He changed


3/10


of the £20,160 into euros.


He changed the rest of the pounds into dollars, rupees and francs in the ratios 9:5:2


Peter changed more pounds into dollars than he changed into francs.


Work out how many more.

Answer:

16

Step-by-step explanation:

4*4

Answer:

Ur answer is B!!!

Step-by-step explanation:

I have no time to explain but trust me ive had this question

The equation \(ax(t) = -(18 m/s^2)cos(33t)\) describes the acceleration of an oscillator. The acceleration varies sinusoidally with time, following a cosine function, and has a maximum value of \(-18 m/s^2\).

The given equation \(ax(t) = -(18 m/s^2)cos(33t)\) represents the acceleration of an oscillator undergoing simple harmonic motion. In this equation, t represents time measured in seconds.

The term cos(33t) indicates that acceleration varies sinusoidally with time. The cosine function has a period of 2π, meaning it completes one full cycle over the interval [0, 2π]. The coefficient 33 in front of t determines the frequency of oscillation. In this case, the oscillator completes approximately 33 cycles per second.

The negative sign indicates that the acceleration is directed opposite to the displacement of the oscillator. As the oscillator moves in one direction, the acceleration pulls it back in the opposite direction, causing it to oscillate around a stable equilibrium position.

The maximum acceleration is given by \(-18 m/s^2\), which represents the amplitude of the oscillation. The acceleration varies between \(-18 m/s^2\) and \(18 m/s^2\), with the maximum magnitude occurring when the cosine function is at its peak value of 1 or -1.

Overall, the equation describes the acceleration of an oscillator undergoing simple harmonic motion, providing information about its amplitude, frequency, and direction of motion.

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The value of the surface integral ∬S​G(x,y,z) dS over the hemisphere x^2 + y^2 + z^2 = 4, z ≥ 0, where G(x,y,z) = 3z^2, is 12π.

the surface integral, we can use a parametric description of the surface. Let's use spherical coordinates to parameterize the hemisphere.

In spherical coordinates, the equation of the hemisphere x^2 + y^2 + z^2 = 4 can be written as ρ = 2, where ρ represents the radial distance from the origin. Since we are considering the hemisphere with z ≥ 0, the spherical coordinates range as follows: 0 ≤ ρ ≤ 2, 0 ≤ θ ≤ 2π, and 0 ≤ φ ≤ π/2.

Now, let's express the function G(x, y, z) = 3z^2 in terms of spherical coordinates. We have z = ρ cos(φ), so G(x, y, z) = 3(ρ cos(φ))^2 = 3ρ^2 cos^2(φ).

The surface area element dS in spherical coordinates is given by dS = ρ^2 sin(φ) dρ dθ. Thus, the surface integral becomes ∬S G(x, y, z) dS = ∫∫ G(ρ, θ, φ) ρ^2 sin(φ) dρ dθ.

Substituting G(ρ, θ, φ) = 3ρ^2 cos^2(φ) and the limits of integration, we have ∬S G(x, y, z) dS = ∫[0,2π]∫[0,π/2] 3ρ^2 cos^2(φ) ρ^2 sin(φ) dφ dθ.

Evaluating this double integral, we get the value of 12π as the result.

Therefore, the value of the surface integral ∬S G(x,y,z) dS over the hemisphere x^2 + y^2 + z^2 = 4, z ≥ 0, using the parametric description, is 12π.

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You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

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This number in scientific notation is 6.2 x 10^-3

The number is given as

0.0062

Multiply by 1

So, we have

0.0062 = 0.0062 * 1

Express 1 as 1000/1000

So, we have

0.0062 = 0.0062 * 1000/1000

This gives

0.0062 = 6.2/1000

This gives

0.0062 = 6.2/10^3

Rewrite as

0.0062 = 6.2 x 10^-3

Hence, this number in scientific notation is 6.2 x 10^-3

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Answer:

124 boxes

Step-by-step explanation:

13*24/2.5

124.8

9514 1404 393

Answer:

  see below (2nd graph)

Step-by-step explanation:

It can be useful to consider the value of f(4).

  f(4) = 1/2√4 -1 = 1/2(2) -1 = 1 -1 = 0

This matches the 2nd graph best.

The probability of exactly 3 of the containers being defective is given as 0.1468

We have to set p as the  probability of container being non- defective

We have p as the  probability of container being defective 50 - 10 = 40

p = 40/50

= 0.8

q = 10/50

= 0.2

P(3) = 8c3 * 0.2² * 0.8⁵

= 0.1468

Hence the probability that the container has exactly 3 defective containers is 0.1468

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Answer:

Step-by-step explanation:

d. the plant management believes that an increase in ambient temperature of 1 degree fahrenheit is associated with an increase in average monthly steam consumption of 10 thousand pounds. do the data support this statement? explain. (hint: perform a hypothesis test.)

Answer:

I don't know itachi bro.You can ask your friend sorry I can't help you.I am in class 7 lol hahahahah

The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

The volume of a cube is 15.625 cubic cm.

What is the volume of a cube?

A cube is a three-dimensional shape having 6 square faces, all the faces are of equal length, breadth, and height.

The volume of the cube is given by side * side * side.

The volume of a cube is given by:

V = a³,

where a is the side length of the cube.

Each side of a cube is 2.5 cm long.

Then, the volume of the cube will be:-

V = (2.5)³,

=  15.625

Hence, the volume of a cube is 15.625 cubic cm.

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Hey there! :)

Answer:

cos²x.

Step-by-step explanation:

Multiply by FOIL:

(1 - sin x)(1 + sin x)

1 + sin x - sin x - sin²x

Simplify:

1 - sin²x

This is a Pythagorean trigonometric identity.

1 - sin²x = cos²x.

The completed matrix represents the system of equations in a convenient format for solving using matrix operations.

The given system of equations has been represented in a matrix form, where the coefficients of the variables x and y and the constant terms are arranged in a matrix. To solve the system of equations, we can use matrix operations to isolate the variables and find their values. The completed matrix shows that the coefficient of x is 700, the coefficient of y is -200, and the constant term is 0 for the first equation. Similarly, the coefficient of x is -75, the coefficient of y is 200, and the constant term is 5000 for the second equation.

To solve this system using matrix operations, we can perform row operations to eliminate one of the variables. For example, we can multiply the first row by 75 and the second row by 200, and then add the two rows to eliminate x. This gives us a new system of equations with only one variable, which we can solve to find the values of x and y.

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Answer:

a - 6%

b - $7.50

Step-by-step explanation:

The answer for a

the only items that had sales tax were $3.00 and $0.50. The total tax for the both was $0.21 so you can find what percent 0.21 is of 3.00 + 0.50 o 3.50. Do this by dividing the percent you are looking for, 0.21, by what it is the percent of 3.50. 0.21 / 3.50 = 0.06. then you multiply the number you got, in this case 0.06 by 100 to find the percentage so it is 6%

The answer for b

Here you can just take the subtotal, $13.00, and subtract all the other prices and you will be left with the price of the top. 13.00 - 3.00 - 2.00 - 0.50 = 7.50. So the answer is $7.50

The estimates that is led from the data from a poll conducted by Travelocity , then the percentages are "computed from a sample"  .

The Data from the poll conducted by Travelocity was computed from a sample of travelers and was used to estimate the proportion of travelers

The travelers have certain habits or behaviors, such as checking work email (44%) taking a cell phone (32%) , or bringing a laptop computer on vacation (26%) .

The sample estimates are used to make inferences about the population.

Therefore , the given percentages are that they were  "computed from a sample" .

The given question is incomplete , the complete question is

Data from a poll conducted by Travelocity led to the following estimates:

Approximately 44% of travelers check work email while on vacation, about 32% take cell phones on vacation in order to stay connected with work, and about 26% bring a laptop computer on vacation.

Are the given percentages "population values" or were they "computed from a sample" ?

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The probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

Given that Edward works as a waiter, where his monthly tip income is normally distributed with a mean of $2,000 and a standard deviation of $350.

The z score formula is given by;`z = (x - μ) / σ`

Where; x is the raw scoreμ the mean of the populationσ is the standard deviation of the population.

The probability that Edward’s monthly tip income exceeds $2,350 is to be found.`z = (x - μ) / σ``z = (2350 - 2000) / 350``z = 1`

The value of z is 1.

To find the area in the right tail, use the standard normal distribution table.

The table value for z = 1.0 is 0.8413.

Therefore, the probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

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The graph of the inequalities x < -8 and x ≥ 3 would be the lines right to 3 in the number line which also includes 3 and the line left to -8 but -8 not included.

Number lines are the graphical representation of numbers on a horizontal straight line where the numbers are placed on equal intervals. We can graph the equations and inequalities of one variable on a number line.

The given inequalities are x < -8 and x ≥ 3.

First let us consider the inequality x < -8.

This means that all the numbers which is less than -8 but does not include -8.

That will be a line tends to left from -8 with an open circle on -8.

Consider the other inequality x ≥ 3.

This includes all the numbers which are greater than 3 and also include the number 3 since the inequality is ≥.

The graph will be a line tends to right from 3 with a closed circle on 3.

Hence the graph of this compound inequality will be a line tends to left with an open circle on -8 and a line tends to right with a closed circle on 3.

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Answer: i did it

Step-by-step explanation: answered the 2nd question aswell, hope this helps someone

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

The cost price of the sales is Birr 774.4

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

Selling Price = Birr 880

Loss = 12%

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

Cost price = Selling Price * (1 - Loss)

Substitute the known values in the above equation, so, we have the following representation

Cost price = 880 * (1 - 12%)

Evaluate

Cost price = 774.4

Hence, the cost price is 774.4

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In addition to finding confidence intervals for population parameters, another type of inferential statistics is a test of significance, also known as hypothesis testing.

Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution.

This assumption is called the null hypothesis and is denoted by \(\text{H}_{\text{o}}\). An alternative hypothesis (denoted \(\text{H}_{\text{a}}\)), which is the opposite of what is stated in the null hypothesis, is then defined. The hypothesis-testing procedure involves using sample data to determine whether or not \(\text{H}_{\text{o}}\) can be rejected. If \(\text{H}_{\text{o}}\) is rejected, the statistical conclusion is that the alternative hypothesis \(\text{H}_{\text{a}}\) is true.

Hence, another type of inferential statistics is a test of significance, also known as hypothesis testing.

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Answer:

the answer would be B -4/3

Step-by-step explanation:

Answer:

First, we need to put the expression into slope-intercept form: y = mx + b, where the m is the slope,

8x + 6y = 12

-8x            -8x

6y = 12 - 8x

y = 2 - 8/6x

y = -8/6x + 2

the slope is B. -4/3

Answer:

B

Step-by-step explanation:

got stuck on it too lol

The graph of an equation intersects the y-axis at some point. Therefore, the coordinates of the intersection indicate is B. the output when the input is zero.

Its the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).

Since sum of side lengths of the triangle of vertices: 3

Area: ½ × base × height

Number of edges: 3

Internal angle: 60° (for equilateral)

The Sum of interior angles is 180°

Therefore, the coordinates of the intersection indicate will be;

B. the output when the input is zero.

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The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Using the formula the curvature. κ(t) = \(\frac{\sqrt{900t^2+6480}}{(5t^2+36)^2}\).

The reciprocal of a curve's radius can be used to compute an object's curvature. It is significant to keep in mind that the curvature varies depending on the kind of curve being evaluated.

From the question vector function

r(t) = <6t, t²/2, t²>

Now we have

r'(t) = (6, t, 2t)

and |r'(t)| = √(6)² + (t)² + (2t)²

|r'(t)| = √36 + t² + 4t²

|r'(t)| = √36 + 5t²

Now the unit tangent T(t) is given as:

T(t) = r'(t)/|r'(t)|

T(t) = (6, t, 2t)/√36 + 5t²

Now T'(t) = \(\left < \frac{-30t}{(36+5t^2)^{1/2}}, \frac{36}{(36+5t^2)^{1/2}},\frac{72}{(36+5t^2)^{1/2}}\right >\)

|T'(t)| = \(\sqrt{\frac{900t^2+6480}{(36+5t^2)^{3}}}\)

Therefore the unit normal N(t) is given by;

N(t) = T'(t)/|T'(t)

N(t) = \(\left < \frac{-30t}{\sqrt{900t^2+6480}}, \frac{36}{\sqrt{900t^2+6480}},\frac{72}{\sqrt{900t^2+6480}}\right >\)

Hence,

κ(t) = |T'(t)|/|r'(t)|

κ(t) = \(\frac{\sqrt{900t^2+6480}}{(5t^2+36)^2}\)

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Answer:Here is the algebraic solution: T is the tens digit O is the ones digit T+O = 14 So

Step-by-step explanation:O = 14 - T <---- this is the first equation

The original number is 10*T + O

If the digits are reversed the original number is increased by 18.

The number if the digits are reversed is:

10*O + T = 10*T + O + 18

10*(14-T) + T = 10*T + (14-T) + 18 <--- substitutes O with 14-T per first equation above in bold

140 - 10T + T = 10T + 14 - T + 18 <--- distributive left side

140 - 9T = 9T + 32

140 = 9T + 9T + 32

140 - 32 = 9T + 9T

108 = 18T

108/18 = T

T= 6

THe tens digit is 6.

The ones digit must be 8.

Reversing 86 - 68 = 18

The original number is 68.

Answer:

Volume: 75.39 ft^3

Surface area: 100.5 ft^2

Step-by-step explanation:

To find volume, you use the formula V=πr^2h (V=3.14*2^2*6)

To find the surface area you use formula A=2πrh+2πr^2 (A=2*3.14*2*6+2*3.14*2^2)