A brand of shampoo is Available in two different bottles 900ml for £5.50 400ml for £2.50 work out which offers the best value for money

Answer:

\(x\geq 6\)

Step-by-step explanation:

Assuming you meant the equation was \(y=2\sqrt{x-6}\)

The x-value must be greater than or equal to 6 because you cannot have an imaginary(negative) number underneath the square root.

Option D is correct, the domain of the function is x≥6, or in interval notation, [6, ∞) or 6≤x<∞, Option D is correct.

A relation is a function if it has only One y-value for each x-value.

The domain of the function y=2√(x-6) is the set of all values of x for which the function is defined.

Since the only restriction on x in this function is that the expression inside the square root (x-6) must be non-negative, we have:

x-6 ≥ 0

Solving for x, we get x greater than or equal to six.

x ≥ 6

Therefore, the domain of the function is x≥6, or in interval notation, [6, ∞)., Option D is correct.

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Answer:

The dog will run the 21-mile race in 4.04 hours

Step-by-step explanation:

The first thing we need to do is find out how far he ran the race at the local fair in 1 hour.

To do this, we can set up a simple relationship:

If he ran 10.5 miles in 2 hours,

He will run x miles in 1 hour

Cross multiplying, we have

x = (10.5 X 1)/2 = 5.25 miles in 1 hour.

We can now comfortably say that he runs at the rate of 5.2miles/hr

He now goes to the state fair race, which is 21 miles long.

if he runs at the rate of 5.2 miles in 1 hour,

He will run 21 miles in y hours

y = 21 / 5.2 = 4.04 hours

The dog will run the 21-mile race in 4.04 hours

A) The rate constant is 1.71 × 10⁻⁴ M/s .

B) The initial concentration of the reactant is 7.99 × 10⁻² M .

C) The rate constant is 0.129 s⁻¹ .

D) The rate constant is  0.0140 M⁻¹ s⁻¹ .

Given:

t = 175 s

[A] = 5.00 × 10⁻² M

At t = 350 s

[A] = 2.00 × 10⁻² M.

Substituting the values in the above formula:

5.00 × 10⁻² M = -k (175 s) +  [A₀].........(1)

2.00 × 10⁻² M = -k (350 s) + [A₀].........(2)

Solving for equation 1:

5.00 × 10⁻² M = -k (175 s) +  [A₀]

5.00 × 10⁻² M + 175 s · k = [A₀]............(3)

Using equation 3 in 2:

2.00 × 10⁻² M = -k (350 s) + [A₀]

2.00 × 10⁻² M = -k (350 s) + 5.00 × 10⁻² M + 175 s · k

2.00 × 10⁻² M - 5.00 × 10⁻² M = -350 s · k + 175 s · k

-3.00 × 10⁻² M = -175 s · k

-3.00 × 10⁻² M/ -175 s = k

k = 1.71 × 10⁻⁴ M/s

The rate constant is 1.71 × 10⁻⁴ M/s

B)

The initial reactant concentration will be:

5.00 × 10⁻² M + 175 s · k = [A₀]

5.00 × 10⁻² M + 175 s · 1.71 × 10⁻⁴ M/s = [A₀]

[A₀] = 7.99 × 10⁻² M

The initial concentration of the reactant is 7.99 × 10⁻² M

C) In this case, the equation is the following:

ln[A] = -kt + ln([A₀])

ln(5.30 × 10⁻² M) = -10.0 s · k + ln([A₀])............(4)

ln(7.80 × 10⁻³ M) = -70.0 s · k + ln([A₀])............(5)

Solving for equation 4:

ln(5.30 × 10⁻² M) = -10.0 s · k + ln([A₀])

ln(5.30 × 10⁻² M) + 10.0 s · k = ln([A₀])............(6)

Using equation 6 in 5:

ln(7.80 × 10⁻³ M) = -70.0 s · k + ln([A₀])

ln(7.80 × 10⁻³ M) = -70.0 s · k + ln(5.30 × 10⁻² M) + 10.0 s · k

ln(7.80 × 10⁻³ M) -  ln(5.30 × 10⁻² M) = -70.0 s · k + 10.0 s · k

ln(7.80 × 10⁻³ M) -  ln(5.30 × 10⁻² M) = -60.0 s · k

ln(7.80 × 10⁻³ M) -  ln(5.30 × 10⁻² M) / -60.0 s = k

k = 0.129 s⁻¹

The rate constant is 0.129 s⁻¹

D) For second order the reaction is as follows:

1/[A] = 1/[A₀] + kt

1/ 0.280 M = 1/[A₀] + 265 s · k............(7)

1/8.30 × 10⁻² M = 1/[A₀] + 870 s · k..........(8)

Solving for equation 7:

1/ 0.280 M = 1/[A₀] + 265 s · k

1/ 0.280 M - 265 s · k = 1/[A₀]...........(9(

Using equation 9 in 8:

1/8.30 × 10⁻² M = 1/[A₀] + 870 s · k

1/8.30 × 10⁻² M = 1/ 0.280 M - 265 s · k + 870 s · k

1/8.30 × 10⁻² M - 1/ 0.280 M = - 265 s · k + 870 s · k

1/8.30 × 10⁻² M - 1/ 0.280 M = 605 s · k

(1/8.30 × 10⁻² M - 1/ 0.280 M)/ 605 s = k

k = 0.0140 M⁻¹ s⁻¹

The rate constant is 0.0140 M⁻¹ s⁻¹.

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465 is the cost of the cash price will she pay overall for the car.

What is cost ?

25 % of cash price 4500 ×  25%  = 1125

12 monthly    320 ×  12  = 3840

All 1125 + 3840  =  4965

more than  4965  -  4500  = 465

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Answer:

1) Pr(all three) = 0.064

2) Pr(none) = 0.216

3) Independent event

Step-by-step explanation:

Let Probability of homes constructed in the Quail Creek area with a security system = Pr (security)

Where Pr = probability

This is a binomial distribution problem. There ate only two outcomes in this distribution: a success and a failure

Where p = success, q = failure

For n trials,

Pr(X = x) = n!/[(n-x)!x!] × p^x × q^(n-x)

Pr (security) = 40% = 0.4

p = 0.4

q = 1-p = 1-0.4 = 0.6

Numbers selected at random = n = 3

See attachment for more details on the workings.

1) Probability all three of the selected homes have a security system = Pr(all three)

Pr(all three) = 1× (0.4)³ (0.6)^0 = 0.4³

= 0.4×0.4×0.4

Pr(all three) = 0.064

2) Probability none of the three selected homes have a security system

= Pr(none)

Pr(none) = 1 × (0.4)^0 × (0.6)³

= 0.6³ = 0.6×0.6×0.6

Pr(none) = 0.216

3) The events were assumed to be independent as the selection of one house doesn't affect the outcome of the selection of another.

Answer: 2$ a pound

Step-by-step explanation:

10$ divided by 5lb = 2$ a pound

Answer:

15095.39

Step-by-step explanation:

\(13000(1+(0.03)/4)^{(4)(5)} \approx 15095.39\)

Answer:

Explanation:

Given the equation:

we want to make c the subject of formula;

let us divide both sides by h;

Then let us subtract b from both sides;

Therefore, making c the subject of formula we have;

Answer:

two of the points are (0,5) and (2.5,0)

Answer:

Place one dot at y = 5 x = 0. This represents the y intercept or the "5" in the equation.

Then place dots at:

(-3,10)

(-2,9)

(-1,7)

(1,3)

(2,1)

(3,-1)

(4,-3)

(5, -5)

(6, -7)

(7, -9)

The slope is -2x which makes the line slope downward, and the points above are the points on the line. Starting at the y intercept we can use the rise over run method to plot the points.

I hope this helps!!

- Kay :)

Answer: 30 straps for 66 is better

Step-by-step explanation:

If its 9 straps for 20.25, then one strap costs 2.25

If its 30 traps for 66, one strap costs 2.2

Therefore, if you buy 30 straps for 66, its a better buy.

Answer:

1. 2.25

2. 2.20

3. 1.02

4. 30 straps

Step-by-step explanation:

1. Divide 20.25 by 9

2. Divide 66 by 30

3. Divide 2.25 by 2.20

Answer:

\(\boxed{3^5}\)

Step-by-step explanation:

Hey there!

Look at the image below↓

By looking at the image we can tell the PR expression is \(3^5\).

Hope this helps :)

Answer:

Below in bold.

Step-by-step explanation:

Dividing  by primes:

3 ) 243

3 )  81

3 )  27

3)     9

        3.

So the prime factors of 243 are 3 * 3 * 3 * 3 * 3  or  3^5.

The difference between 141.2 and 79.83 is as follows:141.2 - 79.83 = 61.37The sum of 141.2 and 79.83 is:141.2 + 79.83 = 221.03The product of 141.2 and 79.83 is:141.2 × 79.83 = 11250.996 The quotient when 141.2 is divided by 79.83 is:141.2 ÷ 79.83 = 1.7696655174 (approx. 1.77)

Thus, the sum of 141.2 and 79.83 is 221.03. The difference between 141.2 and 79.83 is 61.37. The product of 141.2 and 79.83 is 11250.996. The quotient when 141.2 is divided by 79.83 is approximately 1.77.Thus, the solution can be summarized as follows: Given the two numbers 141.2 and 79.83, we are to find their sum, difference, product, and quotient.

After performing the necessary arithmetic operations, we get that their sum is 221.03, their difference is 61.37, their product is 11250.996, and their quotient is approximately 1.77.

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In parallelogram lonm, om is 34.

What is parallelogram?

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.

First we have OQ =QM,

So 2x+3=3x-4,

x =7.

Hence OM =2(17)=34.

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Answer: D) 34

Step-by-step explanation:

edge 2023

Answer:

y = -1/4x+2

Step-by-step explanation:

The SIF (slope intercept form) is pretty easy once you get it down. the slope is the interger before x, and the y-intercept is b. so, if you input each number into it's spot, it would become y = -1/4x + 2.

Answer:

12xy - 4x - 2y

Step-by-step explanation:

9xy - 4x + 3yx - 2y

3yx can be written as 3xy so we have:

12xy - 4x - 2y

Input = ?

Output = 1.2

y = x - 0.4

x = y + 0.4

x = 1.2 + 0.4

x = 1.6

(A) The x and y components of the vector A are approximately 50 N and 86.6 N, respectively.

(B) The x and y components of the vector B are 0 N and -50 N, respectively.

(C) The x and y components of the vector C are -10 m and 0 m, respectively.

(D) The x and y components of the vector D are 0 m and -30 m, respectively.

To find the x and y components of the given vectors, we need to use trigonometry.

The x component is the projection of the vector onto the x-axis, and the y component is the projection of the vector onto the y-axis.

(A.) 100 N, 30 degree west of north:

The vector is in the second quadrant and is making an angle of 30° with the y-axis. We need to find the x and y components of this vector.

The y component of the vector is given by:

100\sin 30° = 50 N

The x component of the vector is given by:

100\cos 30° = 86.6 N west

(B.) 50 N south

The vector is pointing towards the south direction, so the y component of this vector is -50 N, and the x component is 0. Negative sign indicates the direction towards south.

(C.) 10 m to the left

The vector is pointing towards the left direction, so the x component of this vector is -10 m, and the y component is 0. Negative sign indicates the direction towards left.

(D.) 30 m going down

The vector is pointing downwards, so the y component of this vector is -30 m, and the x component is 0. Negative sign indicates the direction towards down.

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The possible whole-number values of 'a' that satisfy the triangle inequality are 2, 3, 4, 5, and 6.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

To create a triangle with sides a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side. This can be represented by the triangle inequality:

a + b > c

a + 6 > 7 (substituting the given values for b and c)

a > 1

b + c > a

6 + 7 > a

13 > a

a + c > b

a + 7 > 6

a > -1

Since the length of a cannot be negative, the inequality can be simplified to:

a > 1

Therefore, to create a triangle with side lengths of 7, 6, and some whole number value for a, a must be greater than 1. The possible whole-number values of 'a' that satisfy the triangle inequality are 2, 3, 4, 5, and 6.

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Answer:

y = 2x

y = x + 3

Step-by-step explanation:

Substitute 3 for x and 6 for y and see if you get a true statement

y = 2x

6 = 2(3)

6 = 6  checks

y = x + 3

6 = 3 + 3

6 = 6  checks

Answer: y=x+3 includes (3,6)

Step-by-step explanation:

this graph shows the (3,6) but not others.

The given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].

To express the limit as a definite integral, we can rewrite the sum as a Riemann sum and take the limit as n approaches infinity.

The given sum can be written as:

lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi],

where Δxi = (b - a) / n is the width of each subinterval, xi is a sample point in the i-th subinterval, and [a, b] is the interval [3π, 5π].

To express the limit as a definite integral, we can rewrite the sum using the definite integral notation:

lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi] = ∫[3π, 5π] cos(x) dx,

where dx represents an infinitesimally small change in x. By taking the limit as n approaches infinity, the sum converges to the definite integral.

Therefore, the given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].

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X.509 certificates are widely used in public key infrastructure (PKI) systems to verify the authenticity and integrity of digital identities. Therefore, among the given options, D) Owner's symmetric key is the item that does not apply to an X.509 certificate.

X.509 certificates are widely used in public key infrastructure (PKI) systems to verify the authenticity and integrity of digital identities. They contain various information related to the certificate itself and the entity it represents. Let's examine the options to determine which one does not apply to an X.509 certificate:

A) Certificate version: X.509 certificates include a version number to indicate the format and features of the certificate.

B) The issuer of the certificate: X.509 certificates specify the entity or authority that issued the certificate, which is crucial for validating the certificate's trustworthiness.

C) Public Key Information: X.509 certificates contain public key information, such as the public key itself and related parameters, to facilitate secure communication and cryptographic operations.

D) Owner's symmetric key: X.509 certificates do not typically include the owner's symmetric key. They primarily focus on the public key infrastructure and asymmetric key cryptography.

Therefore, among the given options, D) Owner's symmetric key is the item that does not apply to an X.509 certificate.

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Answer:

60

Step-by-step explanation:

Think of 25% as 1/4, multiply 15 by 4, getting you 60.

Answer:

15 is equal to 25% of 60

Step-by-step explanation:

25x/100 = 15

25x = 15 * 100

25x = 1500

x = 1500/25

 = 60

hope this helps :)

- Span{v1, v2, v3, 0} is equal to the span of {v1, v2, v3}.
- Span{v1, v1-v2, v3} is equal to the span of {v1, v2, v3}.
- Span{v1, v2} is NOT equal to the span of {v1, v2, v3}.

Let's analyze each of the sets of vectors to determine if they are equal to the span of {v1, v2, v3}:
1. Span{v1, v2, v3, 0}:
This set is equal to the span of {v1, v2, v3} because adding the zero vector (0) does not affect the linear independence or the span of the other vectors.

A span is the set of all possible linear combinations of the vectors, and since the zero vector does not change the linear combinations, the span remains the same.
2. Span{v1, v1-v2, v3}:
This set is also equal to the span of {v1, v2, v3}.

The reason is that the vector (v1-v2) can be written as a linear combination of v1 and v2: (v1-v2) = 1*v1 + (-1)*v2.

Since all vectors in this set can be expressed as linear combinations of {v1, v2, v3}, the span remains the same.
3. Span{v1, v2}:
This set is NOT equal to the span of {v1, v2, v3} because it is missing the vector v3.

Since v1, v2, and v3 are linearly independent, removing one of them (v3 in this case) means that the set cannot span the same space as {v1, v2, v3}.

It has a lower dimension, and therefore, the span is different.

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Answer:

Step-by-step explanation:

Answer:

Answer is q = 2

Step-by-step explanation:

First make the equation with a constant so p=k/q

then substitute q to 6 and p to 23.

Then you have 23=k/6 and to find k multiply both sides to get k=138

next substitute p as 69=138/q then multiply q on both sides to get 69xq=138 and then divide 69 to 138 go get q which is 2

Like if it helped!

Two questions about systems aaa and bbb, the given system is:

System aaa: x = -1/3 and y = -7/3
System bbb: x = -1/3 and y = -7/3

To answer two questions about systems aaa and bbb, let's first clarify the given system:

System aaa:
x - 4y = 9

System bbb:
2x + y = -3

Question 1: Solve system aaa.
To solve system aaa, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the first equation in system aaa, we can isolate x:
x = 4y + 9

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for x in the second equation of system aaa:
2(4y + 9) + y = -3

Step 3: Simplify and solve for y.
8y + 18 + y = -3
9y + 18 = -3
9y = -3 - 18
9y = -21
y = -21/9
y = -7/3

Step 4: Substitute the value of y into the expression for x.
Using the first equation in system aaa:
x - 4(-7/3) = 9
x + 28/3 = 9
x = 9 - 28/3
x = (27 - 28)/3
x = -1/3

Therefore, the solution to system aaa is x = -1/3 and y = -7/3.

Question 2: Solve system bbb.
To solve system bbb, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the second equation in system bbb, we can isolate y:
y = -2x - 3

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for y in the first equation of system bbb:
x - 4(-2x - 3) = 9

Step 3: Simplify and solve for x.
x + 8x + 12 = 9
9x + 12 = 9
9x = 9 - 12
9x = -3
x = -3/9
x = -1/3

Step 4: Substitute the value of x into the expression for y.
Using the second equation in system bbb:
y = -2(-1/3) - 3
y = 2/3 - 3
y = 2/3 - 9/3
y = -7/3

Therefore, the solution to system bbb is x = -1/3 and y = -7/3.

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The required length of the hypotenuse of the triangle is √19.

To find the required length of the hypotenuse of the triangle:

Legs in the right triangle refer to the perpendicular and base.

Hypotenuse:

\(= \sqrt{perpendicular^{2}+base^{2} } \\= \sqrt{3^{2}+\sqrt{10^{2} } } \\=\sqrt{19}\)

Therefore, the required length of the hypotenuse of the triangle is √19.

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=======================================================

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

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

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees