Work out the percentage change when a price of £40 is decreased to £38.
pls give simple working out :)

In linear equation, the store will get $468.72 from the sale of the couch.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

a.

Commission can be referred to as the reward given by the company on goods for the employee to sell products in order to make more sales and more money.

Commission is calculated as follows:

Total commission = Total Sales * Commission Percentage

Given

Total Sales = $495

Commission Percentage = 5½%

Substitute in, the above values

Total Commission = $496 * 5½%

Total Commission = $496 * 5.5%

Total Commission = $496 * 0.055

Total Commission = $27.28

Hence, the total commission is calculated as $27.28

b. The amount remitted to the store is calculated as

Amount = Total Sales - Total Commission

Where Total Sales = $496

Total Commission = $27.28

Amount = $496 - $27.28

Amount = $468.72

Hence, the store will get $468.72 from the sale of the couch.

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The complete question is -

Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5½% of the selling price.

A.How much commission will the salesperson earn by selling a couch for $495?

B.How much money will the store get from the sale of the couch?

Answer:

a. The total commission is $27.28

b. The store will get $468.72 from the sale of the couch

Answer:

degree is 2

standard form is

-x^2+2x-8

classification is trinomial

leading coeff is -1

hope i helped

Step-by-step explanation:

Answer: A and D

Step-by-step explanation:

This is the REAL correct answer.

Answer: B. The environment of the zoo may cause the lions to behave

differently than they would in a natural habitat.  

                                         and

D. The presence of the researchers may affect the lions' behavior.

Step-by-step explanation:  Studying lion behavior in zoos has limitations. The artificial environment of a zoo can affect how lions behave compared to their behavior in the wild.  Additionally, the presence of researchers may influence the lions' behavior, making it difficult to observe and understand their natural interactions.

B. The environment of the zoo may cause the lions to behave differently than they would in a natural habitat.

In a zoo, lions are confined to a limited space and are provided with a controlled environment.  This artificial setting may not accurately reflect their natural habitat and can influence their behavior.  For example, the availability of food, different social dynamics, and reduced hunting opportunities in a zoo can lead to altered behaviors that may not be representative of how lions behave in the wild.

D. The presence of the researchers may affect the lions' behavior.

When researchers observe animals in a zoo, their presence can influence the behavior of the lions.  The presence of unfamiliar humans can cause the animals to become more cautious, stressed, or exhibit abnormal behavior.  This could potentially alter the social interactions and dynamics observed by the researchers, making it challenging to accurately understand and interpret natural lion behavior.

Answer:

x = 1/10

Step-by-step explanation:

3x - 4/5 = -1/2

-1/2 + 4/5 =

-5/10 + 8/10 =

3/10

3x = 3/10

x = 1/10

The significance level is an factor in hypothesis testing and helps us determine the likelihood of making a Type I error.

A significance level is a critical value in hypothesis testing that determines the probability of making a Type I error, which is rejecting a null hypothesis when it is actually true.

To test whether a specific slope coefficient is equal to one, we can perform a t-test to see if the estimated slope coefficient is significantly different from one at a certain significance level.

The null hypothesis for this test is that the slope coefficient is equal to one, and the alternative hypothesis is that it is not equal to one.

We can use the t-statistic to determine the level of significance for the estimated slope coefficient. The t-statistic is calculated by dividing the estimated slope coefficient minus one by the standard error of the slope coefficient.

The resulting t-value is then compared to the critical t-value from a t-distribution table with the appropriate degrees of freedom.

If the t-value is less than the critical t-value, we fail to reject the null hypothesis and conclude that the estimated slope coefficient is not significantly different from one at the 5% significance level.

On the other hand, if the t-value is greater than the critical t-value, we reject the null hypothesis and conclude that the estimated slope coefficient is significantly different from one at the 5% significance level.

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Answer: 1: -8x+6

Step-by-step explanation:

Therefore , the solution of the given problem of angle comes out to be  x value is 3.

An angle in Euclidean space is a shape made up of two poles that divide at the centre, or apex, of the structure. These beams are referred to as the sides or loops. When two rays are combined, there may be an inclination inside this surface where they are situated. Angles can also be created by combining two surfaces. Dihedral angles are what these are known as. Two-dimensional designs can be created by arranging two line beams at their ends in a variety of ways.

Here,

Give :

=> GH is tangent to ⨀F.

According to angle sum property of triangle :

=> ∠HGJ+ ∠JHG + ∠HJG= 180

=> 8x + 9 + 58 + 90 = 180

=> 8x = 24

=> x = 24/8 = 3

Thus , x value is 3.

Therefore , the solution of the given problem of angle comes out to be  x value is 3.

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Solving a system of equations we will see that they sold 184 adult tickets.

We know that the theater sells two types of tickets:

adult tickets for $8 and child tickets for $4.

The variables that we will use are:

x = number of adult tickets sold.

y = number of child tickets sold.

Then we can write the cost revenue equation as:

8x + 4y = 1900

And the total number of tickets sold is 291, then:

x + y = 291

Then we have a system of equations:

8x + 4y = 1900

x + y = 291

We can isolate y on the second equation to get:

y = 291 - x

Replacing that on the other equation we will get:

8x + 4*(291 - x) =1900

4x + 1164 = 1900

4x = 1900 - 1164 =736

x = 736/4 = 184

They sold 184 adult tickets.

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Answer:

7%

Step-by-step explanation:

To find the percentage of grape tomatoes among all plants, we can multiply the percentage of tomato plants by the percentage of grape tomatoes among tomato plants:

(35%) * (20%) = 7%

So, 7% of the plants in the greenhouse are grape tomato plants.

Answer: im not sure how but i hope you can get ut

Step-by-step explanation:

The distance between the points is given by the equation D = 17 units

Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )

The distance from A to B is the same as the distance from B to A

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

This formula is used to find the distance between any two points on a coordinate plane or x-y plane

Given data ,

Let the distance between the points be D

Now , the equation will be

Let the first point be P ( 1 , 0 )

Let the second point be Q ( 9 , 15  )

Now , Distance between two points is the length of the line segment that connects the two points in a plane.  

And , D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( ( 9 - 1 )² + ( 15 - 0 )² )

D = √ ( 8 )² + ( 15 )²

D = √ ( 64 + 225 )

D = √289

D = 17 units

Hence , the distance is 17 units

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There are 30 dogs in the store, and 12 cats.

Let's call the number of dogs in the store "x".

Since the sum of the number of dogs and cats is 42, we know that:

x + (x - 18) = 42

Expanding and solving for x:

2x - 18 = 42

2x = 60

x = 30

So there are 30 dogs in the store, and (30 - 18) = 12 cats.

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The correct statement regarding the solution to the system of equations is given as follows:

A. There are no solutions.

The system of equations for this problem is defined as follows:

Multiplying the first equation by 3, we have that:

1.5x - y = 5.

Substituting the second equation into the first, the solution for y is obtained as follows:

3/2(2y/3 + 10) - y = 5.

y + 15 - y = 5

0y = -10

y = -10/0.

Division by zero is not possible, hence the system of equations has zero solutions.

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Answer:

[tex]2\sqrt{14}[/tex]

D.

Step-by-step explanation:

10 in half is 5

[tex]b = \sqrt{c^{2} - a^{2} }[/tex]

b = [tex]\sqrt{81 - 25}[/tex] = [tex]\sqrt{56}[/tex] = [tex]2\sqrt{14}[/tex]

Set up as a system of equations,

Let x represent the number of 4 credit courses and y represent the 3 credit courses.

The total number of courses the student took was 15. So we can say[tex]x+y=15[/tex]

The total credits earned was 54. So we can say, [tex]4x+3y=54[/tex]

Now we have the following system of equations, solve for the value of x.

[tex]\left \{ {{x+y=15} \atop {4x+3y=54}} \right.[/tex]

Take the top equation and solving for y. We get,

=> [tex]x+y=15[/tex]

=>[tex]y=15-x[/tex]

Take the value of y above and plug it into the second equation.

=> [tex]4x+3y=54[/tex]

=> [tex]4x+3(15-x)=54[/tex]

=> [tex]4x+45-3x=54[/tex]

=> [tex]x+45=54[/tex]

=> [tex]x=54-45[/tex]

=> [tex]x=9[/tex]

Thus, the student took 9, 4 credit classes.

Lee estimated he would need a total number of ten bags of sand, which is 25% more than the eight bags he actually used.

Lee estimated he would need 10 bags of sand.

To calculate how many number of bags of sand Lee estimated he would need, we must first find 25% of 8 bags.

25% of 8 is 2, so Lee estimated he would need 8 + 2 = 10 bags of sand.

Lee estimated he would need a total of ten bags of sand, which is 25% more than the eight bags he actually used.

Lee was filling a new sandbox and he used his best judgement to estimate how many bags of sand he would need. He thought that he would need 25% more than the amount of sand he actually used, which was 8 bags. To calculate the amount of sand he estimated he would need, we must first find 25% of 8 bags. 25% of 8 is 2, so Lee estimated he would need 8 + 2 = 10 bags of sand to fill the sandbox. Thus, Lee estimated he would need a total of ten bags of sand, which is 25% more than the eight bags he actually used.

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5 : 3  is the ratio of cooking times for the rice to pasta .

What does a math ratio mean?

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A percentage is an equation in which two ratios are made equal to one another.

                                    You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

Rice takes 20 minutes to cook

pasta takes 12

the ratio of cooking times for the rice to pasta = 20  :  12

                                                                            = 5 : 3

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Answer:

b = 10

Step-by-step explanation:

substitute x = 10 into the equation

b = [tex]\frac{2(10)^2(10-5)}{10(10)}[/tex]

  = [tex]\frac{2(100)(5)}{100}[/tex] ← cancel 100 on numerator/ denominator

 = 2(5)

 = 10

The expression equivalent to given expression is -1/(4x²+9x+5).

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 4/(4x+5) -1/(x+1)

Here, 4(x+1)-(4x+5)/(4x+5)(x+1)

= (4x+4-4x-5)/(4x²+5x+4x+5)

= -1/(4x²+9x+5)

Therefore, the expression equivalent to given expression is -1/(4x²+9x+5).

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The value of the given factorial expression is 10! - 6! will be 3,628,800.

The factor of n is given as the production of the number n, (n - 1), (n - 2)... and 1. Then the factorial of n is given as

n! = n x (n - 1) x (n - 2) x ... 3 x 2 x 1

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 10! - 6!

Simplify the expression, then we have

⇒ 10! - 6!

⇒ 10 x 9 x 8 x 7 x 6! - 6!

⇒ 6! (10 x 9 x 8 x 7 - 1 )

⇒ 6 x 5 x 4 x 3 x 2 x 1 x (5040 - 1 )

⇒ 6 x 5 x 4 x 3 x 2 x 1 x 5039

⇒ 3,628,800

The value of the given factorial expression is 10! - 6! will be 3,628,800.

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Answer:

(0,-6), (2,0), and (1,-3)

Step-by-step explanation:

We are given the equation of the line, and are then asked to find points on that line that correspond to values of x and y (x,y).  We can either graph the line and look for the points, or we can solve the equation using the given value of x or y, to find the other value of y or x.  Let's do both.

Graph

See the attached graph.  The line is drawn and then the three points are located using the provided value of x or y.  

We find:

    (0,-6)

    (2,0), and

    (1,-3)

Solve

Fun, but we could also put the one given value in the equation and then solve for the other:

y = 3x - 6

----------

1.  (0,__)

y = 3x - 6

y = 3*(0) - 6

y = -6

The point is (0,-6)

2.  (__,0)

y = 3x - 6

0 = 3x - 6

-3x = -5

x = 2

The point is (2,0).

3.  (1,__)

y = 3x - 6

y=3*(1)-6

y= -3

The point is (1,-3)

(a) To find the product of 1/2x-1/4 and 5x^2-2x+6, we can use the distributive property of multiplication:

(1/2x - 1/4)(5x^2 - 2x + 6)

= (1/2x)(5x^2) + (1/2x)(-2x) + (1/2x)(6) - (1/4)(5x^2) + (1/4)(2x) - (1/4)(6)

= (5/2)x^2 - x + 3 - (5/4)x + (1/2)x - (3/2)

= (5/2)x^2 - (3/4)x + 3/2

Therefore, the product of 1/2x-1/4 and 5x^2-2x+6 is (5/2)x^2 - (3/4)x + 3/2.

(b) No, the product of 1/2x-1/4 and 5x^2-2x+6 is not equal to the product of 1/4x-1/2 and 5x^2-2x+6. This is because when we expand both products using the distributive property, we get different expressions:

(1/2x - 1/4)(5x^2 - 2x + 6) = (5/2)x^2 - (3/4)x + 3/2

(1/4x - 1/2)(5x^2 - 2x + 6) = (5/4)x^2 - (7/4)x + 3

So the coefficients of the x^2 and x terms in the two products are different. Therefore, the two products are not equal.

The mean number of web-enabled devices for the 5 students is 3.8.

Before, solving this question the

The mean, or average, of the data is the sum of all the values divided by the number of values.

In this case, the mean for the data can be calculated as the sum of the number of devices for all 5 students divided by the number of students.

The calculation is as:

mean = (4 + 3 + 5 + 5 + 2) / 5

= 19 / 5

= 3.8

So, the mean number of web-enabled devices for the 5 students is 3.8. This gives an estimate of the average number of devices that students have.

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Answer:

The expression 7/8 + x = 3/8 for x = 3/8 can be solved as follows:

7/8 + 3/8 = 10/8

Therefore, the value of the expression 7/8 + x = 3/8 for x = 3/8 is 10/8, which is equal to 1 1/8 or 1.125 when expressed as a whole or mixed number.

Step-by-step explanation:

The expression 7/8 + x = 3/8 can be solved as follows:

7/8 + x = 3/8

Replace x with 3/8

7/8 + 3/8 = 10/8

Therefore, the value of the expression 7/8 + x = 3/8 for x = 3/8 is 10/8, which is equal to 1 1/8 or 1.125 when expressed as a whole or mixed number.

A graph of XY with endpoints X(-3, 1) and Y(4,-5) and its image after the set of transformations (compositions) is shown in the image attached below.

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

By applying a rotation of 180° to the ordered pairs of points X and Y, the coordinates of its image (X′Y′) can be calculated as follows:

(x, y)                                                   →               (-x, -y)

Ordered pair X = (-3, 1)    →     Ordered pair X' = (-(-3), -(1)) = (3, -1).

Ordered pair Y = (4, -5)    →     Ordered pair Y' = (-(4), -(-5)) = (-4, 5).

Next, we would apply a translation based on this transformation rule:

           (x, y)                    →           (x − 1, y + 1)

Ordered pair X' (3, -1)     →         (3 − 1, -1 + 1)   = X" (2, 0).

Ordered pair Y' (-4, 5)    →        (-4 − 1, 5 + 1) = Y" (-5, 6).

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Lastly, the 7 does not need to be multiplied so it remains at 7. After expanding and grouping like terms, we are left with 8h^3 - 32h^2 + 73h - 27.To solve the given equation, we first need to expand the terms in the parentheses and group like terms together.

= 8h^3 - 32h^2 + 73h - 27

To solve the given equation, we first need to expand the terms in the parentheses and group like terms together. We start by expanding the first term (8h - 4) which gives us 8h + -4. Then, we move on to the second term (4h^3 - 8h^2 + 9h + 7). We start by multiplying the 4h to the third power, which gives us 4h^3. Then, we multiply the 8h squared, which gives us -8h^2. Then, we multiply the 9h, which gives us 9h. Lastly, the 7 does not need to be multiplied so it remains at 7. After expanding and grouping like terms, we are left with 8h^3 - 32h^2 + 73h - 27.

The complete question is :

Simplify the expression : 8h - 4 + (4h to the third power - 8h squared + 9h + 7)

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The exponent expression that is used to express 75 as sum of the powers of 8 is [tex]8^0+8^1+8^2+8^\frac{1}{3}[/tex].

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The integer 75 is written as -

[tex]2^0+2^1+2^2+2^6[/tex]

75 is expressed as sum of the powers of 2, with whole number exponents.

To find 75 expressed as sum of the powers of 8, divide the integer by 8 -

[tex]8^0=1[/tex]

[tex]8^1=8[/tex]

[tex]8^2=64[/tex]

Only one integer 2 is left to complete the sum as 75.

To find what the power value is use the equation -

[tex]8^x=2\\x=\frac{2}{8} \\x=\frac{1}{3}[/tex]

So, the last exponent is [tex]8^{\frac{1}3} }[/tex].

So the expression is [tex]8^0+8^1+8^2+8^\frac{1}{3} =75[/tex].

Therefore, the exponent expression is [tex]8^0+8^1+8^2+8^\frac{1}{3}[/tex].

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Answer:

Below

Step-by-step explanation:

Equivalent interest rate in decimal form will be   ( 1+i)^n - 1    

   where i = periodic interest in decimal = .05/4     n = periods = 4  per year  

(1+ .05/4)^4 -1 = 5.09 % equivalent interest per year

.05 / 4 = .0125    or    1.25%   16 times   ( 4 times per year x 4 years)