y=4x^2-56x is the equation of a curve.

by completing the square, show that the co-ordinates of the turning point are (7,-196)

After 10 years, the investment of £200 at 9% compound interest per annum would be worth approximately £432.97.

The amount of money that would be obtained after 10 years can be calculated using the formula for compound interest:

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

Where:

A = final amount

P = initial principal (£200)

r = interest rate (9%)

n = number of times compounded per year

t = number of years invested (10)

For an interest rate compounded annually, n = 1. Plugging in the values into the formula, we have:

A = £200 * (1 + 0.09/1)^(1 * 10)

A = £200 * (1.09)^10

A = £200 * 2.1669

A = £433.38

Therefore, £433.38 would be obtained after 10 years of investing £200 at 9% compound interest per annum.

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The total amount paid for a credit card purchase of $756.25 at an annual rate of 24.5% and monthly repayment of $100, until the balance is paid off, is $829.79.

The total amount paid by the car owner can be determined using an online finance calculator, setting the following parameters.

The total amount paid includes the principal and the interest for the credit.

The payment period will last for 8 months and some days.

I/Y (Interest per year) = 24.5%

PV (Present Value) = $756.25

PMT (Periodic Payment) $-100

Results:

N = 8.298

Sum of all periodic payments = $829.79

Total Interest = $73.54

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Based on the given ratio, the number of teachers at Still Bay Middle School, who have earned their master's degrees, is 18.

The ratio is the relative size of a value compared to another.

Ratios are depicted as percentages, fractions, or decimals, to show that they are fractional values, representing a portion of a whole.

The ratio of teachers who have earned their master's = 3/5

The total number of teachers at the school = 30

The number of teachers with masters = 18 (30 x 3/5)

The number of teachers without masters = 2/5 (1 - 3/5)

= 12 (30 x 2/5)

Thus, since 3 out of 5 teachers at Still Bay Middle School have earned their master's degrees, the number is 18 if there are 30 teachers at the school.

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The pie chart for this problem is given by the image presented at the end of the answer.

A pie chart is constructed in pizza format, considering the percentages of each input data in the problem.

A percentage is calculated as the division of the number of desired outcomes by the number of total outcomes, and then multiplied by 100%.

The percentages for the data-set in this problem is given as follows:

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The system of equations will be:-

6y=4x-18

9y=6x-27

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

For a system to have an infinite number of solutions, the slopes and y-intercepts of the slope must be the same.

We have that one of the equations of the system is 3y = 2x – 9.

We generate another equation that has the same slope and y-intercept by just multiplying through by a non-zero constant.

Let us multiply by 2.

2(3y = 2x – 9)---->6y=4x-18

Or multiply through by 4 to get:

3(3y = 2x – 9)----->9y=6x-27

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The answer is option (C) increases. If a stimulus plus a response results in a satisfying outcome, the probability of that response occurring again increases.

This is called the law of effect, which states that behaviors with positive outcomes are more likely to be repeated in the future.

When a response is followed by a satisfactory outcome, the person is more likely to associate that response with a positive outcome and is more likely to repeat that response in future situations.

This law is based on the concept of reinforcement, ie when an environmental stimulus favors the repetition of a behavior. This law was first proposed by psychologist Edward Thorndike in the early 20th century.

Full question:

If a stimulus plus a response results in a satisfying outcome, the probability of that response occurring again ________.

A. decreases.

B. depends on the CS-UCS relationship.

C. increases.

D. is not affected.

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a. The real annual interest rate is 1.6%

b. He made $14871 after 25 years in account.

What is the interest rate?

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

Here, we have

Given: A taxpayer who pays 22%  in taxes each year has these two accounts. Account 1: $10000 is placed in a tax-deferred account that pays 2.1%  interest compounded annually for 25 years. Account 2:  $10000 is placed in a taxable account that pays 3.1%  interest compounded annually for 25 years.

b. His real annual interest rate is the interest rate decreased by the product of the interest rate and the tax rate.

Actual annual interest rate = 2.1% - (22% × 2.1%)

= 1.6%

Hence, the real annual interest rate is 1.6%

c. P = $10000 , n= 25, r = 1.6%

Compound interest = p(1+(r/100))ⁿ

= 10000(1+(1.6/100))²⁵

= $14871

Hence, he made $14871 after 25 years in account.

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Answer:

Step-by-step explanation:

We know that

[tex]sin^2a+cos^2a = 1[/tex],
so if we rearrange that and solve for [tex]cosa[/tex] then we get
[tex]cosa[/tex] = ± [tex]\sqrt{1-sin^2a}[/tex]

Answer:

True

Step-by-step explanation:

Take the square of 3, for example. The answer is 9. If you find its square root, the square root is 3, showing it is true.

Answer: True.

Step-by-step explanation: One thing to be careful of though is when solving equations. When you square values and square root them later, you are opening the door for extraneous solutions. But yes, Squaring and square rooting a value will undo the process and result in the original number.

Answer:

See below

Step-by-step explanation:

What is margin of error?

Since it is impossible to predict results of a statistical survey on a sample population  with 100% accuracy, scientists often include an error in estimation along with the calculated proportion

This margin of error tells you how many percentage points your results will differ from the real population value

Answer:

16.8

Step-by-step explanation:

First, plug in the values given.

(0.7*15) - (2.1*3)
From there, it's simple math. Multiply what is in the parentheses first,

10.5 + 6.3

then add together the sums

16.8.

Answer:

it could be 20 and 20 or 0 and 40

Answer:

31.3 m/s

Step-by-step explanation:

v² = v₀² + 2aΔx

v² = 0 + 2(9.8 m/s²)(50 m)

v² = 980 m²/s²

v = √ 980 m²/s² = 31.3 m/s

Notes:  ball starts from rest, so v₀ = 0; ball is in free fall, so a = g = 9.8 m/s²; objects in free fall accelerate at the same rate, g, independent of mass.

The height of the wall is 3.10 meters

It is important to note the six types of trigonometric identities, they are;

From the information given, we have that;

θ = 15 degrees

Hypotenuse= 12 meters

Opposite side = top of the wall

Let's use the sine identity;

sin 15 = x/12

cross multiply

Find the value

0. 2588(12) = x

Multiply the values

x = 3.10 meter

Hence, the value is 3.10 meters

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Based on their sharing ratio of 4:3, when Mike gets £ 75 less than Harvey, the total amount of money shared is $525.

The total amount being shared between Harvey and Mike is determined using the arithmetic of ratios.

Firstly, we determine the sum of ratios as 7.  Since Mike's share is 3/7, which is less by £75 than Harvey's share, which is 4/7, we find the difference as 1/7 and equate it to £75.

Proportionately, if 1/7 equals £75, the total sum being shared will be equal to $525 (£75 x 7/1)

Sharing ratio between Harvey and Mike = 4:3

Sum of ratios = 7

Let the amount Harvey gets = x

x = 4/7

Let the amount Mike gets = x - 75

x - 75 = 3/7

4/7 - 3/7 = 1/7

1/7 = £75

7 = £525 (£75 x 7/1)

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Answer:

BELOW

Step-by-step explanation:

For RIGHT TRIANGLES   sin (L ) = opposite LEG / Hypotenuse

sin (L ) = 21/35 = 3/5

The length of the model is 3.33 feet and the wingspan is 1.87 feet, which are reasonable and manageable sizes for a model of this type.

What is scale conversion?

Scale conversion is the process of determining the size of a model based on the size of the original object being modeled.

One way to determine a reasonable scale for the model is to consider the desired size of the model relative to the actual size of the plane. For example, if we want the model to be 1/30th the size of the actual plane, we can use the following formula to find the length and wingspan of the model:

Model length = Actual length ÷ Scale factor

Model wingspan = Actual wingspan ÷ Scale factor

Using these formulas, the length of the model would be:

Model length = 96 feet + 8 inches ÷ 30 = 3 feet 4 inches ÷ 30 = 3.33 feet

And the wingspan of the model would be:

Model wingspan = 56 feet ÷ 30 = 1.87 feet

The reason for choosing a 1/30th scale factor is that it results in a model that is relatively small but still large enough to show the details of the design. It also provides a good balance between size and detail, allowing the model to be easily handled and displayed while still showcasing the key features of the actual plane.

Using this scale, the length of the model is 3.33 feet and the wingspan is 1.87 feet, which are reasonable and manageable sizes for a model of this type.

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The distance between the points (-3, -2) and (-6, 5) is 7.62 units.

We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √( (x₁ - x₂)² + (y₂ - y₁)²)

So here, the distance between (-3, -2) and (-6, 5) will be:

d = √( (-3 + 6)² + (-2 - 5)²)

d = √( 58) = 7.62

The distance between the points  X(−3,−2) and Y(−6,5) is 7.62 units.

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The volume of the cone is 60 ft³ when the base area is 12 ft² and the height is 6 ft.

Let the constant of variation be k. We know that the volume of a cone is given by the formula:

V = (1/3)πr²h

where r is the radius of the base and h is the height. Since the base area is given by πr², we can write:

V = (1/3)Bh

where B is the base area. From the given information, we know that:

12.5 = (1/3) * 15 * (2(1)/(2))

Solving for k, we get:

k = 12.5 / (15 * (2(1)/(2))) = (12.5 * 2) / 15 = 5/3

Now that we have found the variation constant, we can use it to find the volume when the base area is 12ft² and the height is 6ft:

V = (5/3) * 12 * 6 = 60 ft³

So the volume of the cone is 60 ft³ when the base area is 12 ft² and the height is 6 ft.

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Answer:

55 x 9091 = 500,005

Step-by-step explanation:

This checks with a calculator

A polygon with the given area is given below.

Polygons are closed figures which has at least three set of line segments joined together.

The polygon with least number of sides is triangle.

We have to draw a triangle of area 15 unit².

Area of the triangle = [tex]\frac{1}{2}[/tex] × Base × Height

[tex]\frac{1}{2}[/tex] × Base × Height = 15

Base × Height = 30

Let base = 6 units, height = 5 units

We can draw a right triangle this way as shown below.

If we are starting from the point A(0, 0), a length of base of 6 units will be a line segment from A(0, 0) to B(6, 0).

If the height is 5 units, draw a line segment from B(6, 0) to C(6, 5).

Join A to C.

Hence the required triangle is shown below.

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Answer:

10 packages

Step-by-step explanation:

To find the number of 4 yard packages for the fencing, we need to find the perimeter of the fence.

Perimeter = 2*(20 + 40)

Perimeter = 2*60 = 120 feet

*It is important to note that the perimeter is in feet and the packages are in yards*

4 yards = 12 feet

120 / 12 = 10 packages

45 kg of one nut and 45 kg of another nut should be mixed in order to get 60 kg of a mixture worth $4.80kg.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

One nut = x kg

Cost = $5

Other nuts = y kg

Cost = $4.20

Now,

From the given statement we can make two equations.

x + y = 60

x = 60 - y

Substituting here,

5x + 4.20y = 4.80

5 (60 - y) + 4.20y = 4.80 x 60

300 - 5y + 4.20y = 288

300 - 288 = 5y - 4.20y

12 = 0.8y

y = 12/0.8

y = 15

Now,

x = 60 - 15

x = 45

Thus,

45 kg of one nut and 45 kg of another nut.

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Answer:26

Step-by-step explanation: Base one plus Base 2 divided by 2

The point at which the graphs of the equations would intersect is given as follows:

(-2, -1).

The point at which the two functions would intersect is the solution to the system of equations in this problem.

The equations are given as follows:

Multiplying the first equation by 2, we have that:

Adding the two equations, the solution for y is obtained as follows:

-3y = 3

3y = -3

y = -1.

Hence the solution for x is obtained as follows:

3x - 4(-1) = -2

3x + 4 = -2

3x = -6

x = -2.

Hence the point is:

(-2, -1).

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Answer:8750

Step-by-step explanation:

I did 5000 times .25(1/4 as a decimal) which equals 1250. Then 1250 times 3(year) equals 3750. 5000 plus 3750 is 8750

The polynomial f(x) = x⁷ - x⁵ + 5x - 1 has 4 terms and the highest degree is 7

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using only addition, subtraction, and multiplication.

Term: A term in a polynomial is a single expression that can be added or subtracted to the other terms in the polynomial. A term consists of a coefficient multiplied by one or more variables raised to a power. For example, the term "3x^2" in the polynomial 3x^2 + 2x + 1 is a single term.

Coefficient: A coefficient in a polynomial is a numerical value that multiplies a variable or a set of variables in a term. In the example "3x^2", the coefficient is 3. A coefficient can be a constant value, such as 2 in the term 2x, or a variable, such as x in the term x^2. The coefficient in a polynomial determines the magnitude and the sign of each term in the polynomial.

In the polynomial given;

f(x) = x⁷ - x⁵ + 5x - 1

The term in the polynomial is 4 and the degree of the polynomial is 7 while the leading coefficient is 1

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The number of different ways that 7 guests can be seated is 720 and 5 guests can be seated is 24.

In mathematics, Placing the elements of a set into a certain sequence or order is known as permutation. In other terms, the process of permuting is reordering of the elements of a set if the set is already ordered.

In the case of a round table, the formula for the number of ways that 'n' elements can be arranged is (n - 1)!

Here we have

There are 7 guests and a round table.

By the given formula,  

No of different ways that 7 guests can be seated = (7 - 1)! = 6!

= 6 × 5 × 4 × 3 × 2 × 1  

= 720  

If they are only 5 people

No of different ways that 5 guests can be seated = (5 - 1)! = 4!

= 4 × 3 × 2 × 1  

= 24

Therefore,

The number of different ways that 7 guests can be seated is 720 and 5 guests can be seated is 24.

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Answer:

$36.55

Step-by-step explanation:

$33.75 x 2 = $67.50

$67.50 (two shirts) + $45.95 (pair of trousers) = $113.45 (the amount of money spent)

Subtract that from the budget of $150...

$150-$113.45= $36.55 left bro

Answer:

$36.55

Step-by-step explanation:

$33.75 x 2 = $67.50

$67.50 + $45.95 = $113.5

$150-$113.45= $36.55

The answer is $36.55

Hope this Helped! Have a GOOD DAY!!!!!

Answer:

x= 8

Step-by-step explanation:

17x+14+4x-2= 180

21x= 168

x= 8