A shop has a sale of 10% off all items in stock.
If the original price of a dress is £70 what would be its sale price?

Answer:

C

Step-by-step explanation:

Mae, Elsa, Rodley, Cristina, Christian

The first step to solve this problem is to solve the substraction between the first two fractions:

Answer:

6 dollars on lunch because 36 divided by 6 is 6 lol and you should multiply 1/3 to 2/6 to have an even number so it would be 12 on music and 6 on lunch so 18 total spent and 18 saved

18 total saved

Step-by-step explanation:

Answer:

$3

Step-by-step explanation:

12$-(12$:4+12$:2)=12$-(3$+6$)=12$-9$=3$ Hope this helped!

Answer:

0.2 repeating

Step-by-step explanation:

Answer:

Point A is at (0, –4).

Point B is at (–8, –7).

Step-by-step explanation:

point A is 4 units down : y = –4

Point B is 8 units to the left : x = –8

and 7 units down: y = –7

A : (0, –4)

B : ( –8, –7)

The statements that are true are:

A. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6).

C. f(-1) = 6

To determine the truth of each statement, we need to analyze the given table of values for the function f(x).

A. The domain for f(x) is the set {-2, -1, 0, 1, 2, 3, 4, 5, 6).

The x-values listed in the table are -2, -1, 0, 1, 2, 3, 4, 5, and 6. These are the inputs for the function, and therefore, they represent the domain of f(x). Thus, statement A is true.

B. The range for f(x) is all real numbers.

Looking at the y-values listed in the table for f(x), we can see that the range of f(x) is from 5 to 13. It does not include all real numbers, so statement B is false.

C. f(-1) = 6

From the table, we can see that when x = -1, f(x) = 6. Thus, statement C is true.

D. f(5) = -2

There is no entry in the table for f(5), so we cannot determine the value of f(5) from the given information. Therefore, statement D is false.

In conclusion, the true statements are A and C.

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The difference between the dining set cost using the hire purchase method of payment is $37400.

It should be noted that when the hire purchase is used and there is a deposit of $37000 and 24 equal monthly installments of $4600 each.

The total amount will be:

= $37000 + ($4600 × 24)

= $37000 + $110400

= $147400

On the other hand, the dinner set can be bought for $110000 cash.

Therefore, the difference will be:

= Hire purchase - Cash.

= $147400 - $110000.

= $37400

Therefore, the difference between the dining set cost using the hire purchase method of payment is $37400.

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Answer:

11/15 7/10 4/5 2/3

Step-by-step explanation:

the bigger the fraction the smaller the number

The unit rate of lime is 0.25 dollars.

Limes are on sale.

The sale price is 8 limes for 2 dollars.

The unit rate of lime can be calculated as follows:

A rate is a ratio that compares quantities in different units.

A unit rate is a rate where the second quantity is one unit, such as $80 per pound, 25 km per hour, 80 naira per Ghana cedi's, etc.

Therefore,

8 limes = 2 dollars

1  lime = ?

cross multiply

Hence,

unit rate = 2 × 1 / 8

unit rate = 2 / 8

unit rate = 1 / 4

unit rate of lime = 0.25

Therefore, the unit rate of lime is 0.25 dollars.

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The required number of general admissions is 76 and the number of admission with student id is 108.

Here,
let the number of general admissions be x and the number of the admission with student id be y
Using arithmetic operations
According to the question,
x + y = 184  
x = 184 - y  - - -  -(1)
5x + 4y = 812  - - - - (2)
From equation (1)
5 (184 - y) + 4y = 812
920 - 5y + 4y = 812
-y = 812 - 920
-y = 108
y = 108
Put y in equation 1
x = 184 - 108
x = 76

Thus, the required number of general admission is 76, and the number of admission with student id is 108.

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Answer:

the distance covered by a car at a constant speed

Answer:

- 0.118

Step-by-step explanation:

Formula : -

log n x/y = log n x - log n y

Here,

n = b

x = 8

y = 9

So,

log b 8/9 = log b 8 - log b 9

Given,

log b 8 = 2.079

log b 9 = 2.197

log b 8/9

= log b 8 - log b 9

= 2.079 - 2.197

= - 0.118

Answer:

  2 +4√2

Step-by-step explanation:

Perhaps you want the simplified form of (6-√8)/(√2 -1).

The denominator can be rationalized by multiplying numerator and denominator by the conjugate of the denominator:

  \(\dfrac{6-\sqrt{8}}{\sqrt{2}-1}=\dfrac{(6-\sqrt{8})(\sqrt{2}+1)}{(\sqrt{2}-1)(\sqrt{2}+1)}=\dfrac{6\sqrt{2}+6-\sqrt{16}-\sqrt{8}}{2-1}=\boxed{2+4\sqrt{2}}\)

__

Additional comment

The conjugate of the denominator is the same pair of terms with the sign between them changed. The product of the binomial and its conjugate is then the difference of squares. Since the square of a square root eliminates the radical, multiplying by the conjugate has the effect of removing the radical from the denominator.

The same "difference of squares" relation can be used to remove a complex number from the denominator.

  (a -b)(a +b) = a² -b²

In general, the differences of terms of the same power can be factored. This means that denominators with this form can be "rationalized" by taking advantage of that factoring.

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Answer:

-----------------------

Simplify the expression in steps:

\(\cfrac{6-\sqrt{8} }{\sqrt{2}-1 } =\)

\(\cfrac{6-2\sqrt{2} }{\sqrt{2}-1 } =\)

\(\cfrac{2(3-\sqrt{2} )(\sqrt{2} +1)}{(\sqrt{2}-1)(\sqrt{2}+1) } =\)

\(\cfrac{2(3\sqrt{2}+3-(\sqrt{2}^2) -\sqrt{2} )}{(\sqrt{2})^2-1 } =\)

\(\cfrac{2(2\sqrt{2}+3-2) }{2-1} =\)

\(\cfrac{2(2\sqrt{2}+1) }{1} =\)

\(4\sqrt{2}+2\)

Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

The evaluation of the statements with regards to the graph of a function are;

A function maps an input value to an output based on a definition or rule.

First part of the statement;

The graph of a non-vertical straight line has a range of values for the slope, m, of 0 ≤ m < ∞

The equation of a straight line function is of the form; y = m·x + c

Therefore;

The graph of a non-vertical straight line can be represented by the equation, y = m·x + c, where y has possible values of; -∞ < y < ∞, which indicates that as x increases or decreases, y increases (or decreases), such that each value of x maps unto only one value of y, which indicates that the graph is a function. The statement is therefore true.

Second part of the statement.

The graph of the quadratic function; y = a·x² + b·x + c has a shape of a parabola, therefore, the statement, the graph of a function is not always a straight line is true also.

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The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.

First, the rate of change

= (483 - 210) / (23 - 10)

= 273 / 13

= 21

So, the equation for the relationship between the number of bracelets made and the number of beads used.

(y - 210) = 21 (x-  10)

y - 210 = 21x - 210

y = 21x

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Answer:

141°

Step-by-step explanation:

  The angle given is 39°;

Since this problem deals with angles in a transversal, it is easy to solve.

Now;

       Angle given is a corresponding angle to the angle a;

  Corresponding angles are equal; so angle a  = 39°

Also,

   angle a is corresponding to angle b;

         angle b  = 39°

So, angle b and x are on a straight line;

           b  + x  = 180

                  x = 180 - 39  = 141°

Answer:

Its 15 because 3 times 5 = 15.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Product means multiply.

-300

The value of the variable 'A' which is a consecutive digit in the card is: 6

What is consecutive digits?

In mathematics, the consecutive digits are those digits whose difference between the two terms are constant. And the pattern of the terms should be continuous. It is used for the calculation based problems.

According to the question, the given data states that the 14 digits of a credit card has sum of the three consecutive digits is 18.

Therefore, at the end the blank box between 8 and 4 can be written as:

8 + m + 4 = 18 ⇒ m = 18 - 12 = 6 ⇒ m =6

Now, the pattern for the last three digits be: 864.

The pattern is repeating and the whole IN  number is 64864864864864.

Hence, the value of the variable 'A' which is a consecutive digit in the card is: 6

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You have to find the slope .

How?

Take 2points

\(\\ \rm\Rrightarrow \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Step-by-step explanation:

What the Slope Means A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y also decreases. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises.

Answer:

\(6 + 5 = 11 + 3 = 14 + 2 = 16\)

\(6 \div 5 \div 3 \div 2 = 0.2\)

\( 6 \times 5 \times 3 \times 2 = 180\)

Step-by-step explanation:

If its addition add them, multiplication multiply them, division divided them.

Answer:

Step-by-step explanation:

i need help sorry no answer got u

we have the expression

(9x+7)+(x+3)

step 1

Group terms

(9x+x)+(7+3)

step 2

Combine like terms

10x+10

the answer is (10x+10)

Answer:

the percent error in the student's measurement is 4.65%.

Step-by-step explanation:

The percent error can be calculated using the formula:

| (measured value - actual value) / actual value | * 100%

In this case, the measured value is 2.7 grams and the actual value is 2.58 grams. Substituting these values into the formula, we get:

| (2.7 - 2.58) / 2.58 | * 100% = 4.65%

Rounding this to the nearest hundredth of a percent, we get a percent error of 4.65%.

Therefore, the percent error in the student's measurement is 4.65%.

3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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The first quantity (45g) as 60 percentage of second (75g).

A part of whole expressed in Hundredth. Percentage is a fraction of a number out of 100%. It can be in fraction or in decimal.

To convert the given percentage value in decimal, divide the given value by 100.

For example:

1. 50% in decimal or fraction will be 50/100 = 0.5.

2. 20% in decimal or fraction will be 20/100 = 0.2.

1. Finding the total amount from which we need to find the percent.

2. Dividing the required amount to find the percentage by total amount.

3. Multiply it by 100.

For example:

1. It rained 10 of the 30 days in April.

Percentage will be 10/30 = (1/3) x 100

Percentage = 33.33%

Here, we have given that:

Total amount = 75g

Required amount for percent = 45g

Now, to find the percentage:

Percentage = 45/75

Percentage = 0.6 x 100

Percentage = 60%

Hence,

The first quantity (45g) as 60 percentage of second (75g).

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The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:12 gallons

Step-by-step explanation: It is enough to fill 40

The number of gallons in 40 quarts will be 10 gallons. Then the one that contains 12 gallons of oil.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

A motor oil retailer needs to fill 40 one-quart bottles.

We know that in 1 gallon, there are 4 quarts. Then the number of gallons in 40 quarts will be given as,

⇒ 40 / 4

⇒ 10 gallons

The number of gallons in 40 quarts will be 10 gallons. Then the one that contains 12 gallons of oil.

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Answer:

The number of computers that must be surveyed is 1681.

Step-by-step explanation:

The formula to find the sample size is given by:-

\(n=p(1-p)(\frac{\frac{z_{\alpha } }{2} }{E} )^{2}\)

where p = prior population proportion,

\(\frac{z_{\alpha }}{2}\)= Two-tailed z-value for ∝

E= Margin of error.

As per the given, we have

Confidence level :

1 - ∝ = 0.90

⇒∝= 1 - 0.90= 0.10

Two -tailed z-value for ∝= 0.10 : \(\frac{z_{\alpha }}{2}\) = 1.64

E= 2%=0.02

We assume that nothing is known about the percentage of computers with new operating systems.

Let us take p=0.5  [we take p= 0.5 if the prior estimate of proportion is unknown.]

The required sample size will be:-

\(n= 0.5(1-0.5)(\frac{1.64}{0.02} )^{2}\)

=> \(0.25(82)^{2}\)

=> 1681

Hence, the number of the computer must be surveyed = 1681

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