Harry buys a TV priced at £1200 plus 20% VAT.
He pays £300 deposit and the balance in ten equal monthly payments.
Calculate each monthly payment.

An appropriate hypothesis test to determine whether scores of depression are different pre- and post-treatment would be the paired t-test.

The paired t-test is suitable in this scenario because it compares the mean scores of depression before and after the treatment within the same group of participants.

This test takes into account the paired nature of the data, where each participant is measured twice (pre- and post-treatment).

By conducting a paired t-test, the researchers can assess whether there is a statistically significant difference in depression scores before and after the treatment. This will help determine the effectiveness of the new treatment for depression.

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Answer:

\(\frac{91+129+16}{44}\)

Step-by-step explanation:

Step-by-step explanation:

well i have homework due tommorow an essay due Monday. 2 projects due Sunday. and finals next week

so you know, standard school night

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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Answer:

hope it helps you......................

Answer:

x = 5

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

Here b = 8 and h = 15 , then

A = \(\frac{1}{2}\) × 8 × 15 = 4 × 15 = 60 cm²

The area of the rectangle is also 60 cm² , then

length × breadth = 60 , that is

12x = 60 ( divide both sides by 12 )

x = 5

The equation for the line containing (-8,12) that is perpendicular to the line containing the points (3,2) and (-7,2) is x = -8.

To find the equation of a line perpendicular to another line, we need to consider the relationship between their slopes.

Step 1: Find the slope of the line passing through the points (3,2) and (-7,2).

The slope formula is given by (y2 - y1) / (x2 - x1). Let's substitute the values:

m = (2 - 2) / (-7 - 3) = 0 / -10 = 0

Step 2: Since the line we want to find is perpendicular to the given line, we know that the slopes of the two lines will be negative reciprocals of each other.

In other words, the product of the slopes of two perpendicular lines is -1.

So, the slope of the line we want to find is the negative reciprocal of the slope we found in Step 1. Let's calculate:

m_perpendicular = -1 / m = -1 / 0 = undefined

The slope of the perpendicular line is undefined because it is a vertical line.

Step 3: Now that we know the slope of the perpendicular line is undefined, we can write the equation of the line in the form x = a, where 'a' is the x-coordinate of any point on the line.

Since the line contains the point (-8,12), we can write the equation as:

x = -8

Therefore, the equation for the line containing (-8,12) that is perpendicular to the line containing the points (3,2) and (-7,2) is x = -8.

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The statement "the standard deviation is the square root of the variance" is TRUE.What is the standard deviation?The standard deviation is a statistical measure that calculates the amount of variability or dispersion in a set of data.

It quantifies the distribution's spread by measuring the average distance of each point from the mean. In other words, it's a measure of how much the values in a data set deviate from the mean.What is the variance?Variance is a statistical measure that quantifies the distribution's dispersion.

It is defined as the average of the squared distances of each data point from the mean of the data set. It provides information on how spread out the data is with regard to the mean.Standard Deviation vs VarianceThe variance and standard deviation are two closely related statistical measures.

The variance is computed by squaring the standard deviation. To calculate the standard deviation, take the square root of the variance. In simpler terms, the standard deviation is the square root of the variance.Therefore, the statement "the standard deviation is the square root of the variance" is TRUE.

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Answer:

\(3240^{0}\)

Step-by-step explanation

n = Number of sides

Sum of interior angles of a regular polygon = (n - 2) x \(180^{o}\)

                                                                        = (20 - 2) x  \(180^{o}\)

                                                                        = 18 x \(180^{o}\)

                                                                        = \(3240^{o}\)

Answer:

10.7703296142

Step-by-step explanation:

Using "Desmos" a graphing chart and the hypotenuse formula, i have found the distance diagonally from point (4,7) and (2,2)

The set of expressions that is NOT an example of the associative property is B. (8 - 2) + 3 and 8 + (-2 + 3).

The associative property states that the way you group numbers when adding or multiplying does not change the result. For example, (8 + 2) + 3 is the same as 8 + (2 + 3). However, the associative property does not apply to subtraction or division. Therefore, (8 - 2) + 3 is not the same as 8 + (-2 + 3).

Besides associative property, there are 3 other mathematical properties that only works on adding and multiplying. They are:

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Answer:is that subtraction?

Step-by-step explanation:

The Riemann sum S4,3 is then given by: S4,3 = ∑∑ f(x_i+1, y_j+1) * ΔA= ∑∑ 2xy * Δx * Δy= 60.5 + 80.5 + 100.5 + 90.5 + 120.5 + 150.5 + 12

To compute the Riemann sum S4,3 for the double integral of f(x,y) = 2xy over R=[1,3] x [1,2.5], we need to partition the region R into smaller subrectangles and evaluate the function at the upper-right vertex of each subrectangle, then multiply by the area of the subrectangle and add up all the values.

Using a regular partition, we can divide the interval [1,3] into 4 subintervals of length 1, and the interval [1,2.5] into 3 subintervals of length 0.5, to get a grid of 4 x 3 = 12 subrectangles. The dimensions of each subrectangle are Δx = 1 and Δy = 0.5.

The upper-right vertex of each subrectangle is given by (x_i+1, y_j+1), where i and j are the indices of the subrectangle in the x and y directions, respectively. So we have:

(x_1, y_1) = (2, 1.5), f(x_1, y_1) = 221.5 = 6

(x_1, y_2) = (2, 2), f(x_1, y_2) = 222 = 8

(x_1, y_3) = (2, 2.5), f(x_1, y_3) = 222.5 = 10

(x_2, y_1) = (3, 1.5), f(x_2, y_1) = 231.5 = 9

(x_2, y_2) = (3, 2), f(x_2, y_2) = 232 = 12

(x_2, y_3) = (3, 2.5), f(x_2, y_3) = 232.5 = 15

(x_3, y_1) = (4, 1.5), f(x_3, y_1) = 241.5 = 12

(x_3, y_2) = (4, 2), f(x_3, y_2) = 242 = 16

(x_3, y_3) = (4, 2.5), f(x_3, y_3) = 242.5 = 20

(x_4, y_1) = (5, 1.5), f(x_4, y_1) = 251.5 = 15

(x_4, y_2) = (5, 2), f(x_4, y_2) = 252 = 20

(x_4, y_3) = (5, 2.5), f(x_4, y_3) = 252.5 = 25

The Riemann sum S4,3 is then given by:

S4,3 = ∑∑ f(x_i+1, y_j+1) * ΔA

= ∑∑ 2xy * Δx * Δy

= 60.5 + 80.5 + 100.5 + 90.5 + 120.5 + 150.5 + 12

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2 units left means x is deducted by 2

5 units down means y is deducted by 5

So the rule is

New coordinates

Answer:

Below in bold.

Step-by-step explanation:

The vertices of the new triangel are:

A' = (3-2, 5-5) = (1, 0).

In the same way:

B' = (2, -4)

C' = -1, -3).

The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.

The chain rule formula can be stated as follows:

If y = f(g(x)), then the derivative of y with respect to x is given by:

dy/dx = (df/dg) * (dg/dx)

In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.

The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:

dy/dx = (df/dg) * (dg/dh) * (dh/dx)

This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.

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Answer:

The factorized form of the given expression is  \(4 [(a-1)^2 - b(a - 1 + \frac{b}{4})]\)

Step-by-step explanation:

Given;

4a² + b²  -  4ab  -  8a +  4b   + 4

This expression is factorized as follows;

(4a²  -  8a  + 4)  +  (b² -  4ab + 4b)

(4a² - 4a - 4a + 4)  + b² - 4b(a - 1)

(4a - 4)(a - 1) + b² - 4b(a - 1)

(4a - 4)(a - 1) -  4b(a - 1) + b²

4(a - 1)(a - 1)   -  4b(a - 1) + b²

4(a - 1)²  - 4b(a - 1 + b/4)

\(4(a- 1)^2 - 4b(a - 1 + \frac{b}{4} )\\\\4 [(a-1)^2 - b(a - 1 + \frac{b}{4})]\)

The average rate of change of the function over the interval 1 ≤ x ≤ 4 is -5/3.

To find the average rate of change of the function g(x) = -x^2 + 6x + 11 over the interval 1 ≤ x ≤ 4, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values.

At x = 1:

g(1) = -(1)^2 + 6(1) + 11 = 16

At x = 4:

g(4) = -(4)^2 + 6(4) + 11 = 11

The difference in the function values is 11 - 16 = -5.

The difference in the x-values is 4 - 1 = 3.

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The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey

Answer:

Step-by-step explanation:

Let the third interior angle be x

Since it's a triangle , all it's interior angles sum up to 180°

To find the third interior angle , add up the two of the equivalent angles that's 34 and subtract it from 180

We have

x + 34 + 34 = 180

x + 68 = 180

x = 180 - 68

We have the final answer as

Hope this helps you

Answer:

The Answer To This Question Would Be 116

Step-by-step explanation:

Step One. 34 + 34 = 68

Since Two Of The Angles Are Each 34 Degrees We Want To Add Them Both Up That Way We Get 68 Which Leads To Another Step To Find The Measure Of The Third Interior Angle.

Step Two. 180 - 68 = 116

We Got 180 Because Every Triangle No Matter What Type It Is It Will Always Equal To 180 Degrees.

With That Being Said, The Answer To This Is 116.

I Hoped I Helped You Today, Have A Amazing Day (:

Answer:

yes

Step-by-step explanation:

it passes the verticle line test which states that if you put a verticle line anywhere on the graph it will only have one point in where the two lines intersect

Answer:

False

Step-by-step explanation:

Dividing integers is opposite operation of multiplication. But the rules for division of integers are same as multiplication rules. Though, it is not always necessary that the quotient will always be an integer.

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1. The height of the cone is equal to

2. You can solve for the slant height, s by applying Pythagorean's theorem.

3. To get from the base of the cone to the top of the hill, an ant has to crawl 29 mm.

In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:

Volume of cone, V = 1/3 × πr²h

Where:

By substituting the given parameters into the formula for the volume of a cone, we have the following;

8792 =  1/3 × 3.14 × 20² × h

26,376 =  3.14 × 400 × h

Height, h = 26,376/1,256

Height, h = 21 mm.

Question 2.

In order to solve for the slant height, s, we would have to apply Pythagorean's theorem since the height of the cone has been calculated above.

Question 3.

By applying Pythagorean's theorem, we have the following:

r² + h² = s²

20² + 21² = s²

400 + 441 = s²

s² = 841

Slant height, s = √841

Slant height, s = 29 mm.

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Answer:

Step-by-step explanation:

Slopes: - \(\frac{7}{3}\) and -x

y- intercepts: 3 and -6

Answer:

\(-\frac{3}{4}\)

Step-by-step explanation:

1.\(\frac{9}{10}\)×\(-\frac{5}{6}\)

2.\(-\frac{3}{4}\)

Answer:

15.5

Step-by-step explanation:

Yes

Answer:

I'm glad you asked!

Step-by-step explanation:

5/18 pounds per person.

he problem already says what to do, we need to divide because that's what Karen is doing, she is spliting or dividing the pounds of candy for 3 people. So, we just need to divide 5/6 by 3,

\(\frac{5}{6} \div 3 = \frac{5}{6} \times \frac{1}{3} =\frac{5}{18}\)

Answer:

8.9 × 10^{4}

Step-by-step explanation:

Calculating scientific notation for a positive integer is simple, as it always follows this notation: a x 10b.

Follow the steps below to see how 89,000 is written in scientific notation.

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 89,000

New Number: 8.9000

Step 2

Now, to find b, count how many places to the right of the decimal.

New Number: 8 . 9 0 0 0

Decimal Count: 1 2 3 4

There are 4 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10b

a = 8.9 (Please notice any zeroes on the end have been removed)

b = 4

Now the whole thing:

8.9 x 10^{4}

Step 4

Check your work:

10^{4} = 10,000 x 8.9 = 89,000

Answer:

72 dogs

Step-by-step explanation:

3 dogs/2 cats = x dogs/48 cats

Cross Multiply

3/2 x x/48

2x=144

x=72

Answer:

72 dogs

Step-by-step explanation:

First turn 3:2 into a fraction:

3/2

Then you can make the equation a proportion question, which is much eaiser to handle.

3/2=x/48  (I recommend writing this out so it will be easier to see)

Then you cross multiply, or multiply by the numerator of the first fraction by the denominator of the second, and the denominator of the first fraction by the numerator of the second.

Multiply 2 by x, which becomes 2x.

Multiply 3 by 48, which is 144

This becomes... 2x=144

You then solve with equation by dividing 144/2 and getting 72.

Meaning x=72 dogs

Therefore, Inequalities represent the following intervals: 1. (-3, -2), 2. (2, 3), 3. (-∞, -3) ∪ (-2, ∞), 4. (-∞, 2) ∪ (3, ∞).

Let's examine each inequality:
1. –3 > n > –2: This means n is greater than -3 and less than -2. In interval notation, it's written as (-3, -2).
2. 2 < n < 3: This means n is greater than 2 and less than 3. In interval notation, it's written as (2, 3).
3. n < –3 or n > –2: This means n is either less than -3 or greater than -2. In interval notation, it's written as (-∞, -3) ∪ (-2, ∞).
4. n < 2 or n > 3: This means n is either less than 2 or greater than 3. In interval notation, it's written as (-∞, 2) ∪ (3, ∞).

Therefore, Inequalities represent the following intervals: 1. (-3, -2), 2. (2, 3), 3. (-∞, -3) ∪ (-2, ∞), 4. (-∞, 2) ∪ (3, ∞).

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