Beth took out a loan at an annual

compound interest rate of 30%.

After 2 years, she owes a total of £8112.

What was the original amount that Beth

borrowed?

Give your answer to the nearest £1.

Start

After 1 year

After 2 years

4

£

?

£8112

The correct answer is (e) Between 890,000 and 900,000 people.

To find out how many people from this city will have a monthly income between £2,000 and £2,300, we need to use the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

First, we'll find the z-score for £2,000:

z = (2000 - 2075) / 162 = -0.46

Next, we'll find the z-score for £2,300:

z = (2300 - 2075) / 162 = 1.39

Using a z-table, we can find the corresponding probabilities for these z-scores. The probability for a z-score of -0.46 is 0.3228, and the probability for a z-score of 1.39 is 0.9177.

To find the probability of having a monthly income between £2,000 and £2,300, we need to subtract the smaller probability from the larger probability:

0.9177 - 0.3228 = 0.5949

This means that approximately 59.49% of the population will have a monthly income between £2,000 and £2,300. To find out how many people this represents, we'll multiply the probability by the total population:

0.5949 * 1,500,000 = 892,350

Therefore, the answer is (e) Between 890,000 and 900,000 people.

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Three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°). These points are equivalent because they all have the same magnitude of 7, but their angles differ by multiples of 360°.

In polar form, these points are written as:
- (7,400°) = 7cis(400°)
- (7,-320°) = 7cis(-320°)
- (7,760°) = 7cis(760°)

These points are equivalent because the angle in polar coordinates is measured modulo 360°. This means that any angle that differs by a multiple of 360° will be equivalent. For example, 40° is equivalent to 400° because 400° - 40° = 360°. Similarly, -320° is equivalent to 40° because -320° + 360° = 40°, and 760° is equivalent to 40° because 760° - 720° = 40°.

In conclusion, the three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°), and they are written in polar form as 7cis(400°), 7cis(-320°), and 7cis(760°).

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Answer:

530.66 cm²

Step-by-step explanation:

Pizza has a circle shape

The formula for the area of the circle is

A = π · r²

r = 13 cm

π = 3.14

3.14 x 13² = 3.14 x 169 = 530.66 cm²

So, the area of the pizza is  530.66 cm²

Answer:

530.66cm^2

Step-by-step explanation:

since a pizza is in the shape of a circle, we can use the formula π[tex]r^{2}[/tex] and here the radius is r which is 13cm, and since you asked to use 3.14 as pi's value,

=3.14*(13^2)cm

=3.14*169cm

is approximately = 530.66cm^2

Transformed equation for f(x)-5 is the function h(x)=2x-4.

A functional equation in mathematics is, broadly speaking, an equation that has one or more functions as variable. A functional equation, however, is frequently used in a more narrow sense, where it refers to an equation that connects many values of the same function.

An equation that transforms into another equation and has roots that are the opposite of those in the given equation is said to be a transformation. To grasp the transformation equation, this transformation process must be made easy.

f(x)=2x+1

Transforming the function f(x)-5, we get

h(x)=2x+1-5

h(x)=2x-4

h(x) is a function which is made by shifting f(x) 5 units downward.

Hence, transformed equation for f(x)-5 is h(x)=2x-4.

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[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{20})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{22}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{22}-\stackrel{y1}{20}}}{\underset{\textit{\large run}} {\underset{x_2}{-1}-\underset{x_1}{(-2)}}} \implies \cfrac{2}{-1 +2} \implies \cfrac{ 2 }{ 1 } \implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{20}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-2)}) \implies y -20 = 2 ( x +2) \\\\\\ y-2=2x+4\implies {\Large \begin{array}{llll} \end{array}} y=2x+6\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The cheapest straightedge and compass construction of two perpendicular straight lines will cost you 11¢. This is because each use of the straightedge costs 3¢, and each use of the compass costs 5¢. Therefore, it takes three uses of the straightedge (3 x 3¢ = 9¢) and two uses of the compass (2 x 5¢ = 10¢) to create the two perpendicular straight lines, for a total of 11¢. So it will cost you  11¢

To create the perpendicular lines, first move the straightedge to create a line segment with one endpoint at the origin. Next, place the compass at one endpoint of the line segment and draw an arc with the desired radius, cutting the line segment at another point. Then, repeat this process with the straightedge and compass, but with the compass at the new endpoint and draw a perpendicular arc, intersecting the original arc. This will create the two perpendicular lines.

Each time you move the straightedge or compass, you incur a new charge. As outlined above, it will take three moves of the straightedge and two moves of the compass, for a total of five moves and a cost of 11¢.

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Answer:

See below.

Step-by-step explanation:

We are asked to find the result of the expression.

We have 3 proper fractions, and they don't have a common denominator.

Meaning, that in order to simply subtract the Numerators, we should have the same Denominator for each.

We can find the Denominator simplify by finding the LCM.

The LCM is the smallest multiple that 2 or more numbers share.

We can easily find the LCM by making a list of numbers that adds the number to itself. The previous explanation is simpler, but what really is happening is we're multiplying the number with a number that grows by 1 each time; A common multiple.

The list should look like;

[tex]4; 4 \times 1 ,\ 4 \times 2, \ 4 \times 3, \ 4 \times 4, \ 4 \times 5, \ 4 \times 6, \ 4 \times 7.\\4; 4, 8, 12, 16, 20, 24, 28.[/tex]

Let's find the LCM of 5, 3, and 15:

[tex]5; 5, 10, [15], 20, 25\\3; 3, 6, 9, 12, [15]\\15; [15], 30, 45, 60, 75[/tex]

These numbers share a LCM of 15.

Multiply the fractions by setting up a proportion:

[tex]\frac{4}{5} -\frac{1}{3} -\frac{1}{15} \\\frac{4 \times 3}{5 \times 3} = \frac{12}{15} \checkmark \\\frac{1 \times 5}{3 \times 5} = \frac{5}{15} \checkmark\\\frac{1}{15} \ stays \frac{1}{15} \checkmark[/tex]

Subtract:

[tex]\frac{12}{15} - \frac{5}{15} - \frac{1}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5} .[/tex]

Your final answer is [tex]\frac{2}{5} .[/tex]

The correct answer is c. 7/15.

To find the result of 4/5 - 1/3 - 1/15, you need to first find a common denominator for all three fractions. The smallest common denominator for these fractions is 15.

Next, you need to convert each fraction to an equivalent fraction with a denominator of 15.

4/5 = 12/15
1/3 = 5/15
1/15 = 1/15

Now you can subtract the numerators of each fraction and keep the common denominator of 15.

12/15 - 5/15 - 1/15 = 6/15 - 1/15 = 5/15

Finally, you can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 5.

5/15 = 1/3

So the result of 4/5 - 1/3 - 1/15 is 7/15, which is answer choice c.

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Answer:

no it is not a trick question

The equation of the parabola can be written as

y=-0.16(x+2.0)(x-4.6)

A parabola is a curve made from the conic section whose eccentricity is 1 and is defined by the linear equation,

y=a(x-h)²+k, where a is an arbitrary constant and (h,k) denotes the vertex of the parabola.

According to the Intercept form of a parabola, if two x-intercepts (h1, 0), (h2, 0) are given, then the equation of parabola can be written as,

y=a(x+h1)(x-h2)

In this question,

h1 = 2.0

h2 = 4.6

So, the equation of the parabola would be,

y=a(x+2.0)(x-4.6)

Now, to find the value of the arbitrary constant "a", we can plug the point (0, 1.5) in this equation,

1.5 = a(0+2.0)(0-4.6)

1.5 =  a(-9.2)

a = -0.16

So, the equation of the parabola can be written as,

y=-0.16(x+2.0)(x-4.6)

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The value of x for each rectangle is given as follows:

5) x = 7.

7) x = 10.

The area of a rectangle of base b and height h is given by the multiplication of these two dimensions, as follows:

A = bh.

Hence, for item 5, the value of x is given as follows:

3(5x - 2) = 99

5x - 2 = 33

5x = 35

x = 7.

For item 7, the value of x is obtained as follows:

3(4x - 3) = 111

4x - 3 = 37

4x = 40

x = 40/4

x = 10.

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The solution to the system of equations is [tex]x = -3/4 $ and $ y = -3^{1/2}.[/tex] The solution has been obtained by using substitution method.

What is substitution method?

The substitution approach is one approach of solving equation problems. To use the substitution method, obtain an expression for one variable in terms of the second variable using one equation. Replace that variable with that expression in the second equation after that.

We are given system of equations as:

y = -2x - 5

y = 2x - 2

Now, by using the substitution method, we get

⇒-2x - 5 = 2x - 2

⇒-4x = 3

⇒x = -3 / 4

On substituting the value of x in y = 2x - 2, we get

⇒y = 2(-3/4) - 2

⇒y = (-3/2) - 2

⇒y = -7/2

Hence, the solution to the system of equations is[tex]x = -3/4 $ and $ y = -3^{1/2}.[/tex]

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Step-by-step explanation:

If Kneaders in Lehi sold 4000 rolls last year and expects a 22% increase in sales this year, the number of rolls they will bake this Thanksgiving can be calculated as follows:

Calculate the 22% increase in sales:

22% of 4000 = 0.22 x 4000 = 880

Add the increase to last year's sales to get the total expected sales this year:

4000 + 880 = 4880

Therefore, Kneaders in Lehi will bake approximately 4880 rolls this Thanksgiving rounded to the nearest whole roll.

Answer:

4,880 rolls, see explanation below :)

Step-by-step explanation:

1.22(4000)= 4,880

and you instantly get your answer.

if you don't understand I basically did 1.22 times 4000 and got 4,880.

Formula: X + %increase/decrease x orginal amount/amount sold last year of rolls, (we can assume there is an invisible 1 in front of the x)

Basically Everything Behind This, Kind of (sorry I'm not the best explainer! :( ;

Here in this case 22% as a decimal is 0.22, how we get to a decimal from a percent: 22 divided by a 100= 0.22. and we got the decimal for 22%!

So X + 0.22= 1.22, and remember the X has an invisible 1 in front of it. so 1 + 0.22= 1.22 in other words.

Now the other value we have is 4000, so we multiply it by 1.22 and get 4,880. And this is how we got to our answer.

The required inequality expression is 2 + w ≥ 360.

In mathematics, an inequality is a statement that compares two quantities or expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

An inequality states that one quantity is either less than or greater than the other, but not necessarily equal to it.

Here we have

You get 100 points for playing the game. In addition, you get 50 points for each seven-letter word you make with the ten letters you receive.

Sal wants to break the record, and he needs 18,000 or more points.

Let's assume Sal does 'w' number of seven-letter words

Then total points that Sal will gain = 100 + 50(w)

To break the record Sal wants 18000 points or more

=> 100 + 50w ≥ 18000    

=> 2 + w ≥ 360

Therefore,

The required inequality expression is 2 + w ≥ 360.

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Answer:

4:7

Step-by-step explanation:

We know

A car factory made 24 cars with a sunroof and 18 cars without a sunroof.

What is the ratio of the number of cars with a sunroof to the total number of cars?

We find the total number of cars by taking

24 + 18 = 42 cars

The ratio of the number of cars with a sunroof to the total number of cars is

24:42

Simplify by 6, we get the ratio

4:7

Therefore, the probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 is 0.25, or 25%.

The probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 can be found using the formula:

P(event) = number of favorable outcomes / total number of possible outcomes

In this case, the number of favorable outcomes is 3, since there are 3 preparation stations that we are interested in (6, 7, and 8). The total number of possible outcomes is 12, since there are 12 preparation stations in total.

So, the probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 is:

P(event) = 3 / 12

P(event) = 0.25

Therefore, the probability that a randomly chosen product was prepared on preparation stations 6, 7, and 8 is 0.25, or 25%.

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Answer: a ticket to an amusement park is $100 per person. you have a coupon for $20 off of the admission price. the amusement park is also having a promotion where if you bring an empty pepsi can you can take an additional $4 off of the total admission cost. how much do you have to pay to be admitted to the amusement park after the coupons? (it would be $76)

Step-by-step explanation: my brain thought this up

Answer:

Step-by-step explanation:

Mikes mom gave him 100 dollars to spend and his favorite toy shop. Mike bought a Lego set which cost him 20 dollars. When he bought a lollipop which cost him 4 dollars.

Shawn’s science class takes 1 and half hour.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Shawn’s science class starts at 11:25 a. M.

It ends at 12:45 p. M.

Now, to find the How long is Shawn’s science class we have to find the time difference as

= 12: 45 pm - 11: 25 am

So, From 11:25 am to 12:25 pm it is one hour and additional of 30 minutes or half an hour.

This, the class is 1 and half hour long.

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The equation in slope intercept form for a line that passes through (10,-1) and a y intercept of -6 is y = -1/10x - 6.

Equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two expressions that are separated by an equals sign (=), and the equation is true if and only if both expressions have the same value.
Slope intercept form is a way to express a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y intercept. In this equation, m is equal to -1/10 (the slope of the line between the two given points) and b is equal to -6 (the given y intercept). This equation can be used to describe the line that passes through (10,-1) and has a y intercept of -6.

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Answer:

To find out how many books each member read, we can divide the total number of books by the number of members in the reading group:

168 books ÷ 6 members = 28 books per member

Therefore, each member of Dan's reading group read 28 books this year.

168/6 = 28

28 books per member

The simplified expression is [[3,0,6], [-4,-6,3], [-1,4,0]].

The given expression is [[-2,-2,4],[-6,-2,5],[-5,-1,5]] + [[5,2,2],[2,-4,-2],[4,5,-5]]. To simplify it, add the corresponding elements of each matrix:

[[-2,-2,4] + [5,2,2] = [3,0,6],
[-6,-2,5] + [2,-4,-2] = [-4,-6,3],
[-5,-1,5] + [4,5,-5] = [-1,4,0]]

Therefore, the simplified expression is [[3,0,6], [-4,-6,3], [-1,4,0]].

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The simplified form of the expression ( 1/10 ) - 30 is -299/10 or -29 9/10.

Given the expression in the question;

( 1/10 ) - 30

To solve the expression (1/10) - 30, we need to first find a common denominator for the two terms in the expression.

The common denominator between 1/10 and 30 is 300, so we can rewrite the expression as:

(1/10) - 300/10

Now we can combine the two terms by subtracting the second term from the first:

(1/10) - 300/10 =

(1 - 300 )/10

-299/10

Convert -299/10 to mixed fraction

-29 9/10

Therefore, the solution to (1/10) - 30 is -299/10 or -29 9/10.

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The polynomial 7x^(7)-9x^(5)+3x^(4)+12x+1 has four roots. Roots are the values of x that make the polynomial equal to zero. To find these values, one can use a variety of methods, such as factoring, graphing, and the quadratic formula.

Factoring is the simplest method to use, and it involves breaking the polynomial down into simpler terms. In this case, the polynomial can be broken down into the product of two linear polynomials (7x^(7)-9x^(5) and 3x^(4)+12x+1). By setting each factor equal to zero and solving for x, you can find the roots.

Graphing is also a useful tool for finding the roots of a polynomial. By graphing the polynomial, you can see the x-intercepts, which are the values at which the graph crosses the x-axis. These are the roots.

Finally, the quadratic formula can be used to find the roots of this polynomial. This formula is a general solution for any quadratic equation, and it can be applied to the polynomial by replacing the coefficients of x^2 with those of x^7 and solving for x.

In conclusion, the polynomial 7x^(7)-9x^(5)+3x^(4)+12x+1 has four roots. These can be found using factoring, graphing, or the quadratic formula.

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Answer:

  see attached

Step-by-step explanation:

Given some of the angles in a parallelogram with diagonals shown, you want the measures of missing angles.

The measures of missing angles are found by making use of triangle and parallelogram angle relations:

In the attached diagram, the given angles are shown in red. The requested angles are shown in blue.

  ∠BDC = 40°, congruent to alternate interior angle ABD

  ∠DEA = 78°, supplementary to adjacent angle AEB

  ∠BDA = 70°, congruent to alternate interior angle DBC

  ∠BCD = 70°, supplementary to adjacent angle ABC = 40°+70°.

We can see here that solving the parallelogram, we have:

A parallelogram is a quadrilateral (a polygon with four sides) in which opposite sides are parallel to each other. This means that the opposite sides of a parallelogram have the same slope and will never intersect, even if extended infinitely.

A parallelogram has four sides, four angles, and two pairs of opposite sides that are equal in length. The opposite angles of a parallelogram are also equal in measure.

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The polynomial function is f(x) = (x + 1)³(x - 1)²(x - 3). A polynomial function is a mathematical expression that consists of variables, constants, and exponents that are combined using the operations of addition, subtraction, multiplication, and division.

The zeros of a polynomial function are the values of x that make the function equal to zero. The given polynomial function has a triple zero at x = -1,

double zero at x = 1, and zero at x = 3.

This means that the factors of the polynomial function are (x + 1)³, (x - 1)², and (x - 3).

Multiplying these factors together gives us the polynomial function:f(x) = (x + 1)³(x - 1)²(x - 3).

To find the value of the constant term, we can use the given point (2, 27). Substituting x = 2 and f(x) = 27 into the polynomial function gives us:

27 = (2 + 1)³(2 - 1)²(2 - 3)27

3³(1)²(-1)27 = 27(-1)27

= -27

To make the function pass through the point (2, 27), we need to multiply the polynomial function by -1:

f(x) = -1(x + 1)³(x - 1)²(x - 3)f(x)

= -(x + 1)³(x - 1)²(x - 3)

Therefore, the polynomial function is f(x) = -(x + 1)³(x - 1)²(x - 3).

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200 miles is covered by Keith when the plans have the same price. When both plans have the same price, the cost is $160.

Two rents plans and the costs, the miles traveled by Keith when the two plans cost the same and the cost when the two plans cost the same, quadratic equations will be

Let the total miles covered for each plan be

The cost of the first plan would be

cost of the plan A=40+0.60x

The cost of the second plan would be

Cost of second plan=0.80x

If the two cost is the same, then

[tex]0.80x=40+0.60x[/tex]

Solve for x by collecting like terms

[tex]0.80x-0.60x=40[/tex]

[tex]0.20x=40[/tex]

[tex]x=\frac{40}{0.20}[/tex]

[tex]x=200[/tex]

The cost when the two plans cost the same would be

[tex]0.80x=0.80(200)=160[/tex]

or

[tex]40+0.60x=40+0.60(200)=160[/tex]

Hence, the miles covered when the plans cost the same is 200 miles.

The cost when the two plans cost the same is $160.

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The fourth vertex of the rectangle is obtained as (-5, 4).

A quadrilateral with parallel sides that are equivalent to one another and four equal vertices is known as a rectangle. It is also known as an equiangular rectangle for this reason.

To find the fourth vertex of the rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length.

The given vertices are (1, 4), (1, -4), and (-5, -4).

Apply the midpoint theorem of diagonals of a rectangle -

Midpoint of BD = Midpoint of AC

(x,y) =  , [(1 - 5)/2 , (4 - 4)/2)

(x,y) = (-2, 0)

Now, the fourth vertex of the rectangle is -

(-2,0) = [(x + 1)/2 , (y - 4)/2)

-2 = (x + 1)/2

-4 = x + 1

x = -5

0 = (y - 4)/2

y = 4

So, the fourth vertex of the rectangle is (-5, 4).

Therefore, the points are is (-5, 4).

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To write a C++ program that prints a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5, you can use the following code:

This program will print a table showing the square and square root of x starting from 1 to 5, with an increment of 0.5. The table will display x in one decimal place, its square in 2 decimal places and its square root in 4 decimal places, with all numbers being right justified. The columns of the table will have appropriate headings.

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Question 1
a) The density function of X is given by f(x)= 3x^2/64 for 0 ≤ x ≤ 4 and f(x) = 0 otherwise.
b) The expected value of X is E(X)= 3/2 and the variance of X is Var(X)= 3/8.
c) The mean of the net profit Y is given by E(Y) = 0.1E(X) - 1000 = -950 and the standard deviation is given by σY = 0.1σX = 0.1(√3/2) = 0.1825.

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the complete question in the attached figure

Part 1) find sec (theta)

we know that

sec (theta)=1/ cos (theta)

cos (theta)=adjacent side angle theta/hypotenuse

adjacent side angle theta=5

hypotenuse=13

so

cos (theta)=5/13

sec (theta)=1/(5/13)-------> sec (theta)=13/5

the answer Part 1) is

sec (theta) = 13/5

Part 2)simplify sec(theta)*cos (theta)

sec (theta)=13/5

cos (theta)=5/13

so

sec(theta)*cos (theta)=(13/5)*(5/13)----> 1

the answer part 2) is 1

Part 3)simplify cot(theta)/cos(theta)

cot (theta)=5/12

cos (theta)=5/13

so

cot(theta)/cos(theta)=(5/12)/(5/13)----> 13/12

we know that

sin (theta)=opposite angle theta/hypotenuse

opposite side angle theta=12

hypotenuse=13

sin (theta)=12/13

csc (theta)=1/sin (theta)------> csc (theta)=1/(12/13)----> csc (theta)=13/12

therefore

cot(theta)/cos(theta)=csc (theta)

the answer Part 3) is

csc (theta)

Part 4)simplify cot(theta)*sin(theta)

cot (theta)=5/12

sin (theta)=12/13

so

cot(theta)*sin(theta)=(5/12)*(12/13)----> 5/13

cos (theta) =5/13

therefore

cot(theta)*sin(theta)=cos (theta)

the answer part 4) is

cos (theta)

The quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+1 is x+1 and 2x^2-3, respectively.

To find the quotient and remainder, use long division. First, divide the leading terms of both polynomials. 3x^4 divided by x^3 gives x.

Next, multiply the quotient by the divisor and subtract from the dividend. x(x^3-x^2+1) subtract from 3x^4-x^2 gives x+1.

Finally, divide the remainder by the divisor to get the remainder. x+1 divided by x^3-x^2+1 gives 2x^2-3. Therefore, the quotient and remainder when 3x^(4)-x^(2) is divided by x^(3)-x^(2)+1 is x+1 and 2x^2-3, respectively.

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