5. Angela earns £35 240 a year.
She has to pay income tax.
She is allowed to earn £6475 before paying tax.
She pays 20% tax on the rest.
Her employer deducts the income tax each month.
Work out how much income tax Angela gets deducted each month

18 pounds of candy costing $1.05 and 12 pounds of candy costing $1.35 are needed to be mixed to get a 30 pounds of mixture costing $1.17

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the amount of candy costing $1.05, y represent the candy costing $1.35.

The mixture is worth $1.17 a pound and is about 30 pounds. Hence:

1.05x + 1.35x = 1.17(30)    (1)

Also:

x + y = 30    (2)

From both equations:

x = 18, y = 12

18 pounds and 12 pounds of candy are needed to be mixed

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Answer:

4x + y = 15

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 4 , then

y = - 4x + c ← is the partial equation

to find c substitute (2, 7 ) into the partial equation

7 = - 4(2) + c = - 8 + c ( add 8 to both sides )

15 = c

y = - 4x + 15

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

then

y = - 4x + 15 ( add 4x to both sides )

4x + y = 15 ← in standard form

The scale of figure A to Figure B is given by 9 : 5 and option C is the correct answer.

Shapes in various dimensions can be scaled using the Scale Factor. In geometry, we study many geometrical forms that exist in both two- and three-dimensions. The scale factor is a way to compare figures with similar appearances but differing scales or measurements. Consider two circles that resemble one another but may have different radii.

The scaling factor indicates how much a figure has increased or decreased from its initial value.

The scale of figure A to Figure B is given by:

Scale factor = Segment of figure A / segment of figure B

SF = 36 / 20

SF = 9 / 5

Hence, the scale of figure A to Figure B is given by 9 : 5 and option C is the correct answer.

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Answer:

Below

Step-by-step explanation:

Slope-intercept form of a line  is   y = mx + b     m is slope    b is intercept

so it is just   y = -3/4 x -4

According to the information, it can be inferred that the balance after 3 months is that we have made interest payments for $107.6 of interest and $264.39.

To calculate the payment balance for the car loan we must take into account the following information:

According to the above, we must find how much the interest is equal to:

So, we must divide the result in the 12 months of the year

and later multiply it by the three months that are being asked.

Additionally, we must calculate how much the installment payment would be.

So we would pay 371.79 for the 3 months.

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The radius of the circle with the same vertex is 6 and the height of the triangle is 10.39 and the area of the triangle is 62.34.

Since the arc divides the triangle into two regions of equal area, it follows that half of the circle's area is equal to the area of the triangle. The area of a triangle with sides 12 and 12√3 and a 60-degree angle can be found using the formula for the area of a triangle, which is 0.5bh.

The height of the triangle can be found using trigonometry, as the sine of 60 degrees is 0.8660. Thus, the height of the triangle is 10.39 and the area of the triangle is 62.34.

Since half of the circle's area is equal to the area of the triangle, the radius of the circle can be found by taking the square root of the area of the triangle and dividing it by pi. Thus, the radius of the circle is 6.

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A triangle has a 60-degree angle, and the two adjacent ide are 12 and 12 roots 3. Find the radius of a circle with the same vertex a center, if the arc inside the triangle divides it into two regions of equal area

Answer: 3/4 * 1/2 = 3/8 = 0.375

hope this helpes

[tex] = \frac{3}{4} \times 8 \frac{1}{2} \\ [/tex]

[tex] = \frac{3}{4} \times \frac{8 \times 2 + 1}{2} \\ [/tex]

[tex] = \frac{3}{4} \times \frac{17}{2} \\ [/tex]

[tex] = \frac{51}{8} \\ [/tex]

Answer:

If the pet store had 1/9 of a bag of cat food, and they want to divide it equally between 4 cats, then each cat would get 1/9 of the bag divided by 4.

So, each cat would get:

1/9 ÷ 4 = 1/9 * 1/4 = 1/36

So, each cat would get 1/36 of the bag of cat food.

Answer:

Below

Step-by-step explanation:

this is the same as [tex]\sqrt[4]{64}[/tex]      and   is   [tex]\sqrt[4]{16*4}[/tex]     and this equals 2 [tex]\sqrt[4]{4}[/tex]

A right-skewed histogram has a peak that is left of center and a more gradual tapering to the right side of the graph. This is a unimodal data set, with the mode closer to the left of the graph and smaller than either the mean or the median.

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The distance from a to the line passing through b and c is 7/5.

To find the distance from a point to a line, you can use the cross product and the dot product.

First, find the vector pointing from a to b and the vector pointing from b to c:

u = b - a = (3, -5, 0) - (0, 3, -5) = (3, -8, 5)

v = c - b = (3, 0, -5) - (3, -5, 0) = (0, 5, -5)

Next, find the cross product of these two vectors, which gives a vector orthogonal to the plane defined by the line:

n = u x v = (-40, 0, 40)

Finally, find the dot product of n and a - b, which gives the magnitude of the projection of a - b onto n:

d = |n . (a - b)| / |n| = |(-40, 0, 40) . (-3, -8, -5)| / |(-40, 0, 40)| = 57 / √(40^2 + 40^2) = 57 / √1600 = 57 / 40 = 7/5

Therefore, the distance from a to the line passing through b and c is 7/5.

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Answer: X=3

Step-by-step explanation: Since it’s a vertical line the Y value is 0 making the line x=3 bc it’s on the 3 for the x-axis

When a plane is inclined at a 45-degree angle and intersects a cylinder's base along its diameter with radius "r," it results in the division of the cylinder into two identical right circular cones.

Imagine a cylinder with a radius "r."

The plane passes through the cylinder's base, creating a line that bisects the circular base into two equal halves.

This intersection between the inclined plane and the cylinder forms a cross-section that resembles an isosceles right triangle.

By symmetrically splitting the cylinder along its central axis, the inclined plane generates two congruent right circular cones, each with a 45-degree angle at its apex. The curved line formed by the intersection represents the boundary between the two cone halves.

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Answer:

After 4 years, the computer will be worth approximately $576. Since the computer loses 20% of its value each year, the total amount lost after 4 years is 80%. This means that the computer's original value of $1200 will be reduced to $576.

Step-by-step explanation:

Answer: I’d say that Saul’s generalization is more valid because even though he interviewed less people, he interviewed girls as well as boys, and Richie only interviewed the boys.

Answer:Given that Saul spoke with both boys and females, his generalization is accurate

Step-by-step explanation:?A generalization is a kind of abstraction where the general traits of specific cases are articulated as overarching concepts or claims. Generalizations presuppose a domain or collection of elements, as well as one or more shared characteristics.Why is being general useful?Generalization is the capacity to do an action, engage in an activity, or display a behavior in a variety of situations, with a variety of people, and at a variety of times. Our ability to complete routine tasks in a variety of contexts and settings is due to the fact that we have "generalized" the necessary skills.

Answer:

12: A = 40 and C = 32

13: A = 45 , C=72 and D=72

Step-by-step explanation:

Angles inscribed by the same arc are equal.

1 gallon equal to  3.785411784 liter.

The gallon is a unit of volume in imperial units and United States customary units. Three different versions are in current use:

The imperial gallon (imp gal), defined as 4.54609 litres, which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand and some Caribbean countries.

The US gallon (US gal), defined as 3.785411784 L, (231 cubic inches) which is used in the US and some latin American and Caribbean countries.

The US dry gallon ("usdrygal"), defined as 1/8 US bushel (exactly 4.4.0388377086 L)

By using the above formula to convert US gallons to litres.

Solution: Inserting the value of a gallon in the above formula we will get:

Litre =1×3.785411784 =3.785411784

Hence 1 gallons are equal to 3.785411784 liter.

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The linear regression equation for estimating tip amount is y = 0.174x + 1.971, where x is the total bill amount and y is the estimated tip amount.

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The area of the region bounded by f(x)=(x-8)^2, g(x)=-x-2 and the x-axis is the definite integral of f(x)-g(x) from -2 to 8.

The area of the region bounded by f(x)=(x-8)^2, g(x)=-x-2 and the x-axis is given by the definite integral of f(x)-g(x) from -2 to 8. First, expand f(x) and g(x) to get f(x)=x^2-16x+64 and g(x)=-x-2. Then, subtract g(x) from f(x) to get f(x)-g(x)=x^2-16x+66. This is the equation of the area of the region. To calculate the area, use the definite integral of f(x)-g(x) from -2 to 8. This is equivalent to the integral from -2 to 8 of x^2-16x+66 dx. After integrating, the area is given by the expression (x^3/3)-8x^2+66x from -2 to 8, which is equal to 1176/3 units^2. Therefore, the area of the region bounded by f(x), g(x) and the x-axis is 1176/3 units^2.

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Answer: 15kg is equivalent to 33.0693 or 33, for short.

Step-by-step explanation:

33.0693 kilograms, or 33, are equal to 15 kilograms.

A pound is about equivalent to 0.45359237 kilograms. By dividing the specified pound value by 0.45359237, one can convert a pound to kilograms. Remember that 1 kg equals 2.2046 lbs when converting weights.

The weight of a kilogram (kg) is said to be 2.2 times that of a pound. Thus, 2.26 pounds are equal to one kilogram of mass. In light of this, we shall now examine some of the primary variations between the pound and the kilogram. A pound is an imperial unit used to measure bulk or weight.

A weight of 500 pounds exceeds a weight of 200 kilograms because 227 kilograms is greater than 200 kilograms.

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Answer:

central angle

Step-by-step explanation:

an angle with a vertex on the center of a circle and slides that are radii of that circle is called a central angle

Central angle has a vertex on the center of the circle and sides that are radii of that circle .

What does central angle mean?

A right angle, which has sides that are the radii of the circle, and a vertex that is at the center of the circle Given that it intercepts an arc with a length equal to the circle's radius, a central angle has radian measure [Math Processing Error].

Where can I find the center angle?

The angle that the arc at the center of a circle occupies is known as the central angle. The arms of the angle are created by the radius vectors. The formula for calculating a central angle is: Central Angle = Arc length(AB) / Radius(OA) = (s 360°) / 2r, where s denotes the length of the arc and r denotes the radius of the circle.

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Step-by-step explanation:

12/10.1

16.85/13

21.61/15

The best way, in my opinion, is to divide each price by it's respective inches. Doing that you will see the cost per inch. the cheapest one is the best deal.

[tex]small = \frac{12}{10.1} = 1.19[/tex]

[tex]medium = \frac{16.85}{13} = 1.30[/tex]

[tex]large = \frac{21.61}{15} = 1.44[/tex]

Seeing these 3, the cheapest was $1.19, making the small pizza the best deal because you get the best price per inch

Answer:

For the first question:

A) -9.7 > -18.2

For the second:

A) The temperature is warmer in Minnesota than South Dakota.

Step-by-step explanation:

Hope it helps! =D

The first three terms are all 0 since they are constants. The last term is [tex]15x2y4[/tex]. Therefore, the partial derivative of J with respect to y is [tex]40 + 15x2y4.[/tex]

Partial Derivative of J with Respect to[tex]x: 50 - 6x2y5[/tex]

Partial Derivative of J with Respect to[tex]y: 40 + 15x2y4[/tex]

To find the partial derivatives of J with respect to x and y, we need to use the chain rule. The partial derivative of J with respect to x is the derivative of 5000 with respect to x plus the derivative of 10x with respect to x plus the derivative of 40y with respect to x plus the derivative of [tex]3x2y5[/tex] with respect to x. The first three terms are all 0 since they are constants. The last term is [tex]6x2y5[/tex]. Therefore, the partial derivative of J with respect to x is [tex]50 - 6x2y5[/tex]. The partial derivative of J with respect to y is the derivative of 5000 with respect to y plus the derivative of 10x with respect to y plus the derivative of 40y with respect to y plus the derivative of [tex]3x2y5[/tex] with respect to y. The first three terms are all 0 since they are constants. The last term is [tex]15x2y4.[/tex]Therefore, the partial derivative of J with respect to y is [tex]40 + 15x2y4[/tex].

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Answer:

C. - 8

Step-by-step explanation:

substitute - 4 for x value

-4 + (2×-4) - (-4)

= -4 + (-8) + 4

= -12 +4

= -8

The cost of downloading 10 songs for Johnny is $30.

The cost of downloading music for Johnny can be represented by the expression 1.5x + 15, where x is the number of songs downloaded. To find the cost of downloading 10 songs, we can plug in x = 10 into the expression:

1.5 * 10 + 15 = 15 + 15 = 30

So, it will cost Johnny $30 to download 10 songs. This expression represents the total cost as the sum of a $30 $30 ($15 monthly fee) and a variable cost ($1.50 per song fee).

The fixed cost remains constant regardless of the number of songs downloaded, while the variable cost increases as more songs are downloaded.

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7000 is the 3 period moving average forecast for week 6.

Using a moving average, a data set's general trend may be determined. The sales volume from the company's historical data is the data set used in operations management. For predicting recent trends, this method is quite helpful. Simply said, it is the average across a range of times.

The most basic method for predicting is a simple moving average (SMA). The data from the previous 'n' periods are added up, and the sum is divided by 'n' to create a simple moving average. So the projection for the following period is based on the moving average value.

3-period weighted moving forecast for week 6:

= (Demand for Period 3 + Demand for Period 4 + Demand for Period 5) / 3 = (8000 + 7000 + 6000) / 3

= 7000

3-period weighted moving forecast for week 6 = 7000

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The complete question is as follows:

Answer:

i agree good job mate I'm not zooded while doing homework

Step-by-step explanation:

I didn't clear a then another then two more

For the given vectors the sum of u is  (-44/10,-6/10).

Vectors are mathematical objects that have both magnitude and direction.

The projection of u onto v is equal to the dot product of u and the unit vector of v divided by the magnitude of v.

The unit vector of v can be found by dividing v by its magnitude. Once we have the unit vector, we can multiply it by the dot product and add it to the initial point of v to find p.

Since u = (-4,-1) and v = (1,3), the magnitude of v is √(1^2 + 3^2) = √10 and the unit vector of v is (1/√10, 3/√10).

The dot product of u and the unit vector of v is

=> (-4)(1/√10) + (-1)(3/√10)

=> -4/√10 - 3/√10.

Thus,

=> p = (-4/√10 - 3/√10)(1/√10, 3/√10) + (1,3)

=> p = (-4/10 - 3/10, -1/10 + 3/10) + (1,3)

=> p =  (7/10 + 3/10, 2/10 + 3/10) = (10/10, 5/10).

To find n vector, we subtract p from u.

Finally,

=> n = u - p = (-4,-1) - (10/10, 5/10)

=> (-4 - 10/10, -1 - 5/10) = (-44/10,-6/10).

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