3 Charlie invests £4000 for 3 years in a savings
account.
She gets 2% per annum compound interest in
the first year, then x% for 2 years.
Charlie has £4228.20 at the end of 3 years,
work out the value of x.

The circle graphs which correctly represents the data in the table is "a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent"

The correct answer choice is option B.

Type of Sandwich Number of Customers

Vegetarian 30

Turkey 20

Ham 35

Chicken 15

Total number of customers = 30 + 20 + 35 + 15

= 100

Percentage of each sandwich:

Vegetarian = 30/100 × 100

= 30%

Turkey = 20/100 × 100

= 20%

Ham = 35/100 × 100

= 35%

Chicken = 15/100 × 100

= 15%

Therefore, a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent represents the table.

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The circumference of circle has the formula 2xPixr

where, r = radius of circle.

The relation between radius (r) and diameter (d) of the circle is d = 2r

Circumference = pi x diameter = 3.14 x 25m = 78.5m

Circumference = 2 x pi x radius = 2 x 3.14 x 4.5cm = 28.26cm

Circumference = 2 x pi x radius = 2 x 3.14 x 28in = 175.84in

Circumference = pi x diameter = 3.14 x 19ft = 59.66ft

Circumference = 2 x pi x radius = 2 x 3.14 x 3mm = 18.84mm

Circumference = 2 x pi x radius = 2 x 3.14 x 35in = 219.8in

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Answer:

1 minute = 1/6

2 minutes = 1/3

3 minutes =1/2

Step-by-step explanation:

one can eat a bag in 15 minutes so in 1 minute this cat can eat 1/15 of a bag

the other cat can eat a bag in 10 minutes so in 1 minute the cat can eat 1/10 of the bag

to find how much they can eat in 1 minute, add 1/10 and 1/15 which gives you 1/6. to find 2 and 3 minutes just multiply by 1/6 by 2 or 3

Answer:

x=4.9

Step-by-step explanation:

using the Pythagorean theorem to find the leg of tringle A:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]y^{2} +3^{2} =7^{2}[/tex]

[tex]y^{2} +9=49\\y^{2} =40\\\sqrt{y^{2} } =\sqrt{40} \\y=\sqrt{40}[/tex]

we know that the hypotenuse for tringle B is [tex]\sqrt{40}[/tex] so, now we can find the value of x:

using the Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]4^{2} +x^{2} =(\sqrt{40} )^{2}[/tex]

[tex]16+x^{2} =40\\x^{2} =24\\\sqrt{x^{2} } =\sqrt{24} \\x=4.9[/tex]

Answer: To solve the problem, we need to use the given time to find Michaela's swimming rate in meters per second, and then use that rate to calculate the distance she will swim in 10 minutes.

1 minute = 60 seconds

4 minutes and 50 seconds = 4 x 60 + 50 = 290 seconds

So, Michaela's rate is:

distance / time = x / 290 seconds

where x is the distance she can swim in 290 seconds.

Simplifying the equation:

x = distance = (time x distance) / time = (290 seconds x distance) / 290 seconds = distance

We know that Michaela can swim 500 meters in 290 seconds:

500 meters / 290 seconds = 1.724 meters per second

Therefore, in 10 minutes (600 seconds), she will swim:

distance = rate x time = 1.724 meters/second x 600 seconds = 1034.4 meters

So, Michaela will swim 1034.4 meters in 10 minutes.

Step-by-step explanation:

The volume of the rectangular prism with the same dimensions as the rectangular pyramid is 300 cubic centimeters.

A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional solid shape with six rectangular faces, where each pair of opposite faces are congruent (i.e., have the same dimensions) and parallel to each other.

The rectangular prism is defined by three dimensions: length, width, and height. The length is the longest dimension of the prism, the width is the second-longest dimension, and the height is the shortest dimension, perpendicular to both length and width. The volume of a rectangular prism is given by the formula: V = l * w * h.

In the given question,

Let's assume that the rectangular pyramid has a rectangular base with length l, width w, and height h. The formula for the volume of a rectangular pyramid is given by:

V_pyramid = (1/3) * base_area * height

where base_area = l * w is the area of the rectangular base of the pyramid.

We know that the volume of the rectangular pyramid is 100 cm^3, so we can write: 100 = (1/3) * l * w * h

Simplifying this equation, we get:

l * w * h = 300

Now, let's find the volume of the rectangular prism with the same dimensions. The formula for the volume of a rectangular prism is given by: V_prism = base_area * height

where base_area = l * w is the area of the rectangular base of the prism.

Since the rectangular prism has the same dimensions as the rectangular base of the pyramid, its volume is given by: V_prism = l * w * h

Substituting the value of l * w * h from the equation we derived earlier, we get: V_prism = 300

Therefore, the volume of the rectangular prism with the same dimensions as the rectangular pyramid is 300 cubic centimeters.

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Answer:

10/63

Step-by-step explanation:

Equation: 2/7 * 5/9

Multiply the numerators: 2*5=10

Multiply the denominators: 7*9=63

Your answer: 10/63

Answer:

1. The graphs of f(x) and h(x) are both quadratic functions with a minimum point. However, the minimum point of f(x) is located at (6,0), while the minimum point of h(x) is located at (2,3).

2. The graphs of g(x) and h(x) both open upwards and are quadratic functions. However, the vertex of g(x) is located at the origin (0,0), while the vertex of h(x) is located at (2,3).

3. The graph of g(x) is a simple parabola that opens upwards, while the graphs of f(x) and h(x) are more complex parabolas with a minimum point and an upward opening. The graph of f(x) is centered at (6,0), while the graph of h(x) is centered at (2,3).

There are 6 ways for the student to select her lunch when she chooses from the given main course selection and chooses between water or tea for her drink selection. 3 × 2 = 6 ways.

The problem is about counting the number of ways that can be possible to select the meal for the student.

The student selects one main course and one drink. The main course consists of one of the following:

beef with broccoli, moo shu pork, or chicken with cashew. She can select water or tea for her drink. Therefore, the total number of ways that can be possible to select her lunch is obtained by multiplying the number of options for each course.For instance, there are three options for main course selection, and two options for drink selection. Therefore, the total number of ways that she can select her lunch

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As a result, in order to make the most money, the widgets must be sold for $15.83, to the nearest cent.

The cost that consumers pay for a single piece of a good is known as the price at which it is sold. For instance, if a company produces lamps, the sales unit price is indeed the cost to customers of a single lamp. We must identify the x value that maximizes the profitability function y = -6x² + 190x - 826 in order to estimate the selling price for widgets that will yield the highest profit.

Calculus can be used in this process. The critical points, or maximum and lowest values of the function, can be found by taking the derivatives of a profitability function in relation to x and setting it to zero. The derivative test can then be used to assess if the crucial point is indeed a maximum or even a minimum. If we take the profit function's derivative with regard to x, we get:

y' = -12x + 190

By setting y' to zero and figuring out x, we obtain:

-12x + 190 = 0

x = 15.83

The critical value of x is therefore 15.83.

We must compute the second derivative of a profit function with respect to x to determine if this critical point is indeed a maximum or a minimum:

y'' = -12

The critical point at x = 15.83 corresponds to the greatest value of the money demand function since y" is negative. In order to optimize the profit, the widgets must be sold for $15.83, to the nearest cent.

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The time that Andrew can use to row his boat in still waters would be = 5.75 hrs.

The speed can be defined as the scalar quantity that shows that amount of distance that is covered with respect to time.

The formula that can be used to calculate speed = distance/time.

The speed of the current in the river = 2 mph

The distance covered downstream = 15miles

The distance covered upstream = 8

average distance = 15+8/2 = 11.5 miles

Given 2 miles = 1 HR

11.5 miles = X

Make X the subject of formula;

X = 11.5×1/2

= 5.75 hrs

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The amount of time Sophie waited for Rana at the finish line can be calculated as 20/r - 20/s, where r is Rana's biking speed in mph and s is Sophie's biking speed in mph.

To find out how long Sophie waited for Rana at the finish line, we need to calculate the time it takes for each of them to complete the 20 mile trip. The time taken can be calculated using the formula: time = distance / speed.

Sophie's time to complete the trip can be calculated as follows:

time taken by Sophie = distance / speed of Sophie

time taken by Sophie = 20 / s

Similarly, Rana's time to complete the trip can be calculated as:

time taken by Rana = distance / speed of Rana

time taken by Rana = 20 / r

Since Sophie waits for Rana at the finish line, she would have to wait for the amount of time it takes for Rana to finish the trip. Therefore, the total waiting time would be the time taken by Rana to complete the trip minus the time taken by Sophie to complete the same trip:

waiting time = time taken by Rana - time taken by Sophie

waiting time = 20/r - 20/s

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If a and b are any odd integers, then a2 + b2 is even.

And the proof for that we can explain as,

 So we have a and b are any odd integers. By definition of odd integer,

           a = 2r + 1 and b = 2r + 1 for any integers r and s.

By definition of odd integer,

          a = 2r + 1 and b = 2s + 1 for some integers r and s.

By substitution and algebra,

      a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 +52) + 2(r + s) + 1]. 2r2 + 2s2.

        Then k is an integer because sums and products of integers are integers. Let k = Thus, a2 + b2 = 2k, where k is an integer.

Proof: 1. Suppose a and b are any odd integers.

Proof:2. By definition of odd integer, a = 2r + 1 and b = 2r + 1 for any integers r and s.

Proof:3. By substitution and algebra, a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 + s2) + 2(r + s) + 1].

Proof:4. Let k = 2(r2 + s2) + 2(r + s) + 1. Then k is an integer because sums and products of integers are integers.

Proof:5. Hence a2 + b2 is even by definition of even.

Proof:6. Thus, a2 + b2 = 2k, where k is an integer.

  Hence we proved that "If a and b are any odd integers, then a2 + b2 is even".

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The centre οf the circle is (-4, -11).

We knοw that the general equatiοn fοr a circle is (x - h)² + (y - k)² = r² with (h, k) representing the centre and r representing the radius. Sο multiply bοth sides by 21 tο get the cοnstant term οn the right side οf the equatiοn. Then, fοr the y terms, cοmplete the square.

Tο write a circle equatiοn in standard fοrm, we must cοmplete the square fοr bοth x and y.

Tο begin, cοnsider the fοllοwing equatiοn: x²+ y² + 8x + 22y + 37 = 0.

Let's separate the terms with x frοm the terms with y:

[tex](x^2 + 8x) + (y^2 + 22y) + 37 = 0[/tex]

We add (8/2)² = 16 tο bοth sides tο cοmplete the square fοr x: (x²+ 8x + 16) + (y² + 22y) + 37 = 16

Simplifying the left side οf the equatiοn and cοmbining cοnstants οn the right:

[tex](x + 4)^2 + (y^2 + 22y + 121) = 16 - 37 - 121\s(x + 4)^2 + (y + 11)^2 = 50[/tex]

The equatiοn can nοw be written in standard fοrm:

[tex](x + 4)^2/50 + (y + 11)^2/50 = 1[/tex]

The circle's centre is (-4, -11).

As a result, the standard fοrm οf the circle's equatiοn is (x + 4)²/50 + (y + 11)²/50 = 1, and the circle's centre is (-4, -11).

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The answer of the given question based on the the number of students using the cafeteria's healthy lunch line can be found by solving the inequality 1/5s - 51 < 20, the correct answer is (1) 142 , (1) or more.

An equation is  mathematical statement that shows  equality of two expressions, typically separated by  equal sign. Equations are used to express relationships between variables and to solve problems in various fields of mathematics, science, and engineering. In essence, an equation is representation of  real-world scenario or problem in mathematical terms.

The variables in equation can take on different values, and  equation remains true regardless of the values chosen for  variables. Solving  equation means finding  values of the variables that make  equation true.

Equations can be linear, quadratic, polynomial, exponential, logarithmic, or trigonometric, among other types. They are fundamental tool in mathematics and have numerous applications in fields like physics, engineering, economics, and finance.

There are 155 students or more students that use this lunch line.

The correct answer is 1. or more.

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Answer: If you end up with a remainder of 0, then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.

Step-by-step explanation:

I hope that this helped! :)

She purchased 4 Paper Lanterns, 12 Bags of Balloons, 11 Garlands, and 4 Banners if she paid $145. 50.

The cost of lanterns is $6.50

Mrs Murphy bought 4 lanterns

Multiply the cost of one lantern ($6.50) by the number of lanterns bought (4) 6.50 multiplied by 4 equals 26

The cost of banners is $5.25

Mrs Murphy bought 4 banners

Multiply the cost of one banner ($5.25) by the number of banners bought (4) 5.25 multiplied by 4 equals 21

Mrs Murphy bought 3 times as many balloons as she did lanterns

So, you multiply the number of lanterns bought (4) by 3

This gives 12

We then multiply the cost of each balloon ($5.00) by the number of balloons bought (12)

5.00 multiplied by 12 equals 60

Mrs Murphy bought 7 more garlands as she did lanterns

So, we add 7 to the number of lanterns bought (4)

7 plus 4 equals 11

To find the cost of the total garlands bought

We multiply the cost of each garland ($3.50) by the number of garlands bought (11)

3.50 multiplied by 11 equals 38.5

Now we can add up the costs of all the items

26+21+60+38.5=145.50

145.50 was the total amount she spent so we know it is the correct answer.

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A smaller sample size can offer a good estimate of the mean. The expressions population of working adults is not too vast to estimate the mean of the entire group using a sample.

An expression in mathematics is a collection of numbers, variables, and complex mathematical (such as addition, subtraction, multiplied, division, multiplications, and so on) that express a quantity or value.

Expressions might be as basic as [tex]"3 + 4"[/tex] or as complicated as [tex]"(3x2 - 2) / (x + 1)"[/tex] . They may also contain functions like "sin(x)" or "log(y)".

Expressions can indeed be evaluated by swapping values for the variables and performing the algebraic calculations in the order specified.

If [tex]x = 2[/tex] , for example, the formula [tex]"3x + 5"[/tex] equals  [tex]3(2) + 5 = 11[/tex] . Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

If Fran chooses a random sample of the working adult population in her town, the mean for that group will most likely be close to the mean for the entire group.

Therefore,  A smaller sample size can offer a good estimate of the mean. The population of working adults is not too vast to estimate the mean of the entire group using a sample.

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Equation A is converted to equation B by multiplying or dividing both parts by a non-zero constant. Thus, option C is correct.  

If a function accepts more than one value, it is said to be nonconstant (if there is more than one element in its range).

As an illustration, a polynomial with real numbers as its domain and codomain becomes nonconstant. Just observing that and means the function accepts at least two distinct values allows us to demonstrate this.

Starting with the variable solely on a single side of the equation, we can start resolving equation A for x:

[tex]x/4 + 1 = -3\sx/4 = -3 - 1\sx/4 = -4[/tex]

We obtain x = -16 by multiplying both of the equation's sides by 4.

Starting with the variable with one of the equation's equations, we can solve equation B for x:

[tex]x + 4 = -12[/tex]

Therefore, We obtain [tex]x = -16[/tex] by deducting  [tex]4[/tex] from both of the equation's components.

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The size of the the matrix B if a matrix A is 5x3 and the product AB is 5x7 is B =[3x7].

Two matrices can only be multiplied if the first matrix has the same number of columns as the second matrix has. If the first matrix has dimensions of a x b and the second matrix has dimensions of c x d, then b = c and their product will have dimensions of a x d.

Let A is a 3 x 5 matrix and B is a 5 x 7 matrix

We know that matrix multiplication of A and B is possible if

Number of columns of A = Number of rows of B

Since in the given problem

Number of columns of A = Number of rows of B = 5

So the product is possible

Now the product AB is a matrix of order 3 × 7

Now the order of the product AB is 3 × 7

If a 3 x 5 matrix is multiplied by a 5 x 7 matrix then their product is a matrix of order 3 × 7.

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The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.

The basic form of a linear equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. Many real-world situations, such as the connection between a product's price and the number of sales, or the relationship between a person's age and height, can be modelled using linear equations.

given

Let t be the number of hours and d be the number of miles that Sebi goes. Since Sebi consistently travels at 10 mph on his bicycle, we can apply the following equation:

Distance is determined by rate and duration.

When we change the numbers, we obtain:

d = 10t

The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.

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Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)

Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.

Peter buys 30 apples at a value of R5.00 every, for a total price of R150.00. He then sells every apple at R7.00, for a complete sales of R210.00.

To calculate his earnings, we subtract his price from his revenue.

profit = revenue - cost

In this case, his income is R210.00 - R150.00 = R60.00. this means that Peter makes a profit of R60.00 from selling 30 apples.

Consequently, Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.

The earnings made with the aid of Peter is the distinction between the sales generated via the income and the price of buying the apples. with the aid of subtracting the cost from the revenue, we are able to see the earnings he has made. This easy calculation can be used by organizations to decide their earnings and to make choices approximately pricing and stock.

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Answer: 52,400

Step-by-step explanation:

We may approximate the sin 165 angles using trigonometric formulas as: tan 165°/(1 + tan2(165°)) (1-cos2(165°))...

Trigonometric identities enable the expression of sin 165° as,

Sin (15°) = sin(180° - 165°)

(-sin 180 + -sin 165) = -sin 345

cos(-75°) = cos(-90° - 165°)

(90 + 165)/255 = -cos 255

Explanation: We know that cos(165) is negative and sin(165) is positive because 165 is in QII. We will use 330 with in half angle formulae because 165=3302.

165 degrees are somewhere between 90 and 180 degrees. Hence, it has an acute angle.

Hence, the 165° angle's addition is 15°. Q. Below are a few angles' measurements.

525 is a positive number of interactions angle, while 195 is a negative coterminal angle.

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Answer:

X

Step-by-step explanation:

We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.

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Answer:

p ≥ 228

Step-by-step explanation:

p ≥ 228

This inequality means the Bowlers have to score at least 228 points to move on.

Hope this helped!

Answer:

d. 32 in.²

Step-by-step explanation:

Bottom face: 6 in. × 0.5 inch

Side faces: 2 × 5 in. × 0.5 in.

Front and back faces: 2 x 6 in. × 4 in. / 2

surface area = 3 in.² + 5 in.² + 24 in.²

surface area = 32 in.²

Answer: We have one km being covered in one minute. So how many km do we cover in one hour? Remember, there are 60 minutes in one hour. Do you think it might be 60 km in one hour? Can you say that a different way, say number of km in one hour? 60 km in one hour. Close. Very good. Now let’s clean up your answer and just say 60 km per hour or 60 ``````````````````````.