The average weight of an almond is 1,200 milligrams. You buy 65 almonds at the price of $0.10 per gram. How much do you pay for the almonds?

The difference in price of a car is £375 it is due to the rate of VAT increase from 17.5% to 20% and this can be evaluated by the help of unitary method.

Given :

Rate of VAT increased from 17.5% to 20%.

Total price of a car =  £15000 + VAT.

In this problem unitary method can be used to determine the difference in price of a car which is due to the increased rate of VAT.

The price of VAT when its' rate is 17.5% can be:

[tex]= \dfrac{15000}{100} \times 17.5[/tex]

= £ 2625

Therefore, the total price of car when VAT is 17.5% is £17625.

The price of VAT when its' rate is 20% can be:

[tex]= \dfrac{15000}{100} \times 20[/tex]

= £ 3000

Therefore, the total price of car when VAT is 20% is £18000.

So, the difference in price of car = 18000 - 17625 = £375.

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Answer:

Option A- 60°            

Step-by-step explanation:

Given : Function - [tex]4cos^2x-1=0[/tex]

To solve the function

Step 1 - Write the function

[tex]4cos^2x-1=0[/tex]

Step 2- Add 1 both side

[tex]4cos^2x=1[/tex]

Step 3- Divide 4 both side

[tex]cos^2x=\frac{1}{4}[/tex]

Step 4 - Taking root both side

[tex]cosx=\sqrt{\frac{1}{4}}[/tex]

Step 5 - solve

[tex]cosx=\pm{\frac{1}{2}}[/tex]

Either [tex]cosx={\frac{1}{2}}[/tex] or [tex]cosx=-{\frac{1}{2}}[/tex]

When [tex]cosx={\frac{1}{2}}[/tex]

            [tex]\rightarrow cosx={cos\frac{\pi}{3}}[/tex]

            [tex]\rightarrow x={\frac{\pi}{3}} or 60^{\circ}[/tex]

or when  [tex]cosx=-{\frac{1}{2}}[/tex]

               [tex]\rightarrow cosx={cos(\pi-\frac{\pi}{3})}[/tex]

            [tex]\rightarrow x={\frac{2\pi}{3}} or 120^{\circ}[/tex]

Therefore, Option A is correct solution of function is at 60°.

The solution of the given trigonometric ratio for the expression 4cos²x - 1 = 0 is equal to 60°

To find the solutions to the equation 4cos²x - 1 = 0, we first need to isolate the cosine term and then solve for x.

Let's go through the steps,

Add 1 to both sides of the equation:

4cos²x = 1

Divide both sides by 4:

cos²x = 1/4

Take the square root of both sides:

cosx = ±√(1/4)

Now, we have two cases to consider: positive and negative square roots.

Case 1,

cosx = √(1/4)

The cosine of an angle can never be negative when expressed in degrees, so we ignore the negative square root.

cosx = √(1/4) = 1/2

To find the angles for which the cosine is 1/2, we look at the unit circle or use a calculator to find the inverse cosine (arccos) values:

x = arccos(1/2)

The principal angle that satisfies this is x = 60°.

Case 2,

cosx = -√(1/4)

Again, we ignore the negative square root as the cosine is not negative in degrees.

Therefore, the only solution to the equation is:

x = 60°

Therefore, among the given options, the solution to 4cos²x - 1 = 0 is 60°.

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Answer:

d 8 1/3

Step-by-step explanation:

Answer: 193

Step-by-step explanation: an image is included to show you the steps.

From the division of given numbers we get quotient as 193 and the remainder as 0.

The two given numbers are 579 and 3.

Here, 579 divided by 3.

That is, 579/3

3|579|193

  3

_____

 279

 27

_____

  09

  09

_____

  00

So, the quotient is 193 and the remainder is 0.

Therefore, from the division of given numbers we get quotient as 193 and the remainder as 0.

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Answer:

Because it is a rectangle, the area is expressed as A = xy, or length times width.

Step-by-step explanation:

Because it is next to the river, he only needs to fence three sides, so F = x + 2y.

Knowing the amount of fencing available is 7500m, we get:

7500 = x + 2y        solve for x

x = 7500 - 2y         substitute into the area equation

A = (7500 - 2y)y     distribute

A = -2y2 +7500y

You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875

x = 7500 - 2(1875) = 3750

A = 3750(1875)  = 7,031,250 m2

If Farmer Ed has 3,500 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, Then 7,031,250  is the largest area that can be​ enclosed.

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel.

As it is next to the river, he only needs to fence three sides, so F = x + 2y.

Knowing the amount of fencing available is 7500m, we get:

7500 = x + 2y        

solve for x

x = 7500 - 2y        

substitute into the area equation

A = (7500 - 2y)y    

Distribute

A = -2y2 +7500y

You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875

x = 7500 - 2(1875) = 3750

A = 3750(1875)  = 7,031,250 m².

Hence 7031250  is the largest area that can be​ enclosed.

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The value of 'x' will be;

⇒ x = 13/5

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

A triangle has sides with lengths of 5x, 15 and 17.

And, The perimeter of the triangle is 45 meters.

Now,

Since, the perimeter of the triangle is 45 meters.

Hence, We can formulate;

⇒ 5x + 15 + 17 = 45

Solve for x as;

⇒ 5x + 32 = 45

⇒ 5x = 45 - 32

⇒ 5x = 13

⇒ x = 13/5

Thus, The value of 'x' will be;

⇒ x = 13/5

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To find the number of albums Floyd sold last month, we calculate it using the linear equation $644 = $200 + ($12 \u00d7 a), where $644 is the total earnings, $200 is the base rate, and $12 is the amount earned per album. Floyd sold 37 albums last month.

To determine the number of albums Floyd sold last month, we can set up a linear equation based on the information provided. Floyd is paid a base rate of $200 per month, and he earns an additional $12 for every album sold. The total amount Floyd earned last month was $644.

Let's let a represent the number of albums sold. The equation that represents the total earnings for the month would be:

Total Earnings = Base Rate + (Number of Albums Sold × Price per Album)

Based on what has been given, we can express this as:

$644 = $200 + ($12 × a)

To find the number of albums sold, we subtract the base rate from the total earnings, then divide by the additional amount earned per album:

$644 - $200 = $12 × a

$444 = $12 × a

a = $444 / $12

a = 37

So, Floyd sold 37 albums last month.

Final answer:

Point Z is located at 2 on the number line, found by adding the distance YZ=11 to the location of Y at -9.

Explanation:

If Y and Z are points on the number line, YZ=11, and Y lies on -9, to find where Z would be located, you simply add the distance between Y and Z to the point Y. Since the distance YZ=11, and Y is at -9 on the number line, you add 11 to -9 to find Z.

Therefore, the location of point Z will be:

-9 + 11 = 2

So, point Z is located at 2 on the number line.

In the graph, the Front view (FV), Top view (TV), and side view (SV) are given.

The orthographic drawing is the 2-D design of the isometric drawing.

Making an orthographic drawing for the isometric drawing that is the right.

The isometric drawing is the 3-D view of the object.

The graph is given below.

In the graph, the Front view (FV), Top view (TV), and side view (SV) are given.

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Answer:

D). 1,808.64 in2

Step-by-step explanation:

Diameter - 48 in.

Therefore, the radius is half of 48. 48/2 = 24.

Area = 3.14(24) 24 = 1,808.64in2

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