2^-4 times how much is 2^-1

Answer:

£15 and £22

Step-by-step explanation:

let,the cost of one shirt be X and one jumper be y.Then according to question,

5x+4y=163-----(1)

also,

3x+2y=89------(2)

Now, multiplying eqn (2) by 2 and then subtracting from (1),we get

5x+4y=163

6x+4y=178

- - -

_________

-x=-15

:.x=15

Putting value of X in eqn (1),

5×15+4y=163

or,4y=163-75

or,y=88/4

:.y=22

Hence cost of one shirt is £15 and one jumper is £22.

Answer:

$30.21

Step-by-step explanation:

100% -25%= 75%

Discounted price of the book

= 75% ×$38

= $28.50

Since the customer must pay an additional 6% of the discounted price,

percentage of discounted price paid

= 100% +6%

= 106%

Total amount paid

= 106% × $28.50

= $30.21

_________________________________

Alternative working:

Original selling price= $38

Since the book is discounted 25%,

100% ----- $38

1% ----- $0.38

75% ----- 75 ×$0.38= $28.50

Since the sales tax is based on the discounted price, we let the discounted price be 100%.

100% ----- $28.50

1% ----- $0.285

106% ----- 106 ×$0.285= $30.21

∴ The total amount the customer pays for the discounted book is $30.21.

I'm going to try my best to explain 90° rotation:

So, you know that if you rotate something 180°, it's completely flipped (think about spinning around half-way).

Or if you spin something 360°, you spin around the whole way and end up in the same spot that you did when you started.

Notice how 90 is actually 1/4 of 360.

So imagine spinning instead of 180, spinning half of that. so you barely rotate. That's exactly what you're doing to this shape here. and if you do it about the origin counterclockwise, the origin is (0,0) so I drew it in Quadrant III, as you can see in my attachment.

You can see that every point has been moved by 90°, I put all of the variables there so you could visualize it better!

I hope this helped, let me know if you have any questions! :)

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Question:

Express each vector as a product of its length and direction.

\(\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k\)

Answer:

\(\frac{1}{\sqrt{2}}\) \((\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)\)

Step-by-step explanation:

A vector v can be expressed as a product of its length and direction as follows;

v = |v| u

Where;

|v| = length/magnitude of v

u = unit vector in the direction of v

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

Let the given vector be v, i.e

\(v = \frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k\)

(i) The length/magnitude |v| of vector v is therefore,

|v| = \(\sqrt{(\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2\)

|v| = \(\sqrt{(\frac{1}{6}) + (\frac{1}{6}) + (\frac{1}{6})\)

|v| = \(\sqrt{(\frac{3}{6})\)

|v| = \(\sqrt{(\frac{1}{2})\)

|v| = \(\frac{1}{\sqrt{2}}\)

(ii) The unit vector u in the direction of vector v, is therefore,

u = \(\frac{v}{|v|}\)

\(u = \frac{\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k}{\frac{1}{\sqrt{2}}}\)

\(u = \sqrt{2}(\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k)\)

\(u = (\frac{\sqrt{2}}{\sqrt{6}}i - \frac{\sqrt{2}}{\sqrt{6}}j - \frac{\sqrt{2}}{\sqrt{6}}k)\)

\(u = (\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)\)

Therefore, the vector can be expressed as a product of its length and direction as:

|v| u = \(\frac{1}{\sqrt{2}}\) \((\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)\)

Answer:

Since f(-1) = 0 and f(-2) = 0, we can set up two equations:

(-1)³ + p(-1)² - q(-1) - 4 = 0

(-2)³ + p(-2)² - q(-2) - 4 = 0

Simplifying each equation, we get:

-1 + p - q - 4 = 0

-8 + 4p - 2q - 4 = 0

Simplifying further, we get:

p - q = 5

2p - q = 6

Solving for p and q, we can add the two equations together to eliminate q:

p - q + 2p - q = 5 + 6

3p - 2q = 11

Then, we can substitute the value of q from the first equation into this equation to solve for p:

3p - 2(q + 5) = 11

3p - 2q - 10 = 11

3p - 2q = 21

3p - 2(5 + p) = 21

p - 10 = 7

p = 17

Substituting this value of p into either equation for q, we get:

q = p - 5 = 12

Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:

-1 | 1 17 -12 -4

|__ -1 -16 28

1 1 12

This gives us the factorization:

f(x) = (x + 1)(x² + x + 12)

To find the solutions, we can use the quadratic formula on the quadratic factor:

x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)

x = (-1 ± sqrt(1 - 48)) / 2

x = (-1 ± sqrt(-47)) / 2

x1 = (-1 + i(sqrt(47))) / 2

x2 = (-1 - i(sqrt(47))) / 2

Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.

Step-by-step explanation:

give me thanks for more! your welcome bud!

Since then, it has spread to other rivers, colonized them, clogged the water intake pipes, and competed with local species for food. Zebra mussels are the method for removing a lot of plankton from the water column.

Here, we have,

The Caspian Sea in Asia is where zebra mussels, or Driessen polymorph, are found naturally.

They arrived in the Great Lakes region in the late 1980s via ballast water from a transatlantic ship.

The Great Lakes, Mississippi, Tennessee, Hudson, and Ohio river basins were all overrun by these mussels within ten years.

The lake's brilliant blue hue is a result of Tahoe's clean air and water.

There is more to this phenomenon than just the fact that Lake Tahoe's surface reflects the sky, which contributes to its blue color.

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complete question:

As you respond to Part A, Part B, and Part C, follow the directions below.

​

​Address all of the instructions in each prompt.

​Use evidence from the information provided and your own knowledge of science to support your responses.

Part A

​

Describe one way scientists near Lake Tahoe can detect if the lake has been impacted by zebra mussels.

Answer:

(2,-1)

Step-by-step explanation:

hope i helped <3

Answer:

(2,-1)

Step-by-step explanation:

That is the answer becasue the x-axis is 2 and the y-axis is -1

Answer:

6 =h

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

12 = 1/2 (4) h

12 =2h

Divide each side by 2

12/2 = 2h/2

6 =h

Answer:

  D)  undefined

Step-by-step explanation:

The tangent function is undefined for odd multiples of pi/2.

__

Additional comment

The terminal point on the unit circle of the ray at angle 3π/2 is (0, -1). The tangent is the ratio of the y-coordinate to the x-coordinate: y/x = -1/0. It is undefined at that point.

It looks like you're given

\(f(x) = 1012x^{101} - 72x^{75} + \pi x^2 - e^{2x} + 100346\)

and are asked to find the 102nd derivative of f(x).

Recall the power rule: for integer n,

\(\displaystyle \left(x^n\right)' = nx^{n-1}\)

This means that the power of x reduces to 0 after differentiating n times, and you're left with a constant coefficient n! :

• after differentiating 2 times,

\(\left(x^n\right)'' = \left(nx^{n-1}\right)' = n(n-1)x^{n-2}\)

• after differentiating 3 times,

\(\left(x^n\right)^{(3)} = \left(n(n-1)x^{n-2}\right)' = n(n-1)(n-2)x^{n-3}\)

• and so on, up to the n-th time, which yields

\(\left(x^n\right)^{(n)} = n(n-1)(n-2)\cdots\times2\times1x^{n-n} = n!\)

As soon as you have a constant, the next derivative will be 0. This means that after differentiating 102 times, the first 3 terms of f(x), as well as the constant term, will vanish.

Recall the chain rule:

\(\bigg(f(g(x))\bigg)' = f'(g(x)) \times g'(x)\)

Then the first few derivatives of the exponential term are

\(\left(e^{2x}\right)' = e^{2x} \times (2x)' = 2e^{2x}\)

\(\left(e^{2x}\right)'' = 2\left(e^{2x}\right)' = 2^2e^{2x}\)

\(\left(e^{2x}\right)^{(3)} = 2^2\left(e^{2x}\right)' = 2^3e^{2x}\)

and so on, with n-th derivative

\(\left(e^{2x}\right)^{(n)} = 2^ne^{2x}\)

Putting everything together, we have

\(\boxed{f^{(102)}(x) = -2^{102}e^{2x}}\)

Answer:

58

Step-by-step explanation:

Answer:

\(\boxed {\boxed {\sf m=\frac{5}{2}}}\)

Step-by-step explanation:

The slope formula is the change in y over the change in x, or:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Where (x₁,y₁) and (x₂, y₂) are the points the line passes through.

The points given are (0,1) and (2,6). Therefore:

\(x_1=0\\y_1=1\\x_2=2\\y_2=6\)

Substitute the values into the formula.

\(m=\frac{6-1}{2-0}\)

Solve the numerator.

\(m=\frac{5}{2-0}\)

Solve the denominator.

\(m=\frac{5}{2}\)

This fraction can not be simplified further, so it is our answer.

The slope of the line is 5/2

Answer:

m=5/2

Step-by-step explanation:

We know that,

\(Slope\ (m)=\frac{Rise}{Run}\\Slope\ (m)=\frac{y_2-y_1}{x_2-x_1} \\As here,\\x_1=0, x_2=2\\y_1=1, y_2=6\\Hence,\\Slope(m)\ of\ the\ following\ line\ =\frac{6-1}{2} =2.5\)

PRICES COUNTS COSTS

8 e 8e

10 420-e-t 10(420-e-t)

12 t 12t

420 3920

system%28e%2B420-e-t=5t%2C8e%2B10%28420-e-t%29%2B12t=3920%29

First equation gives highlight%28t=70%29.

Second equation simplifies to e-t=140.

Substitution gives highlight%28e=210%29.

Quantity of $10 tickets by difference, highlight%28140%29

Answer:

(4)

Step-by-step explanation:

Let's make the smaller number equal to x. Since they are consecutive odd numbers, the larger number is x+2.

Twice the smaller number is 2x. Three times the larger number is 3(x+2). If twice the smaller is subtracted from three times the larger, then the expression should be: 3(x+2) - 2x

Then, since the result of this is four more than the smaller, this expression is x+4.

Finally, we put it all together, so we get: 3(x+2) - 2x = x + 4. Option 4 is our correct answer.

Hence, the option (4) is correct.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger, the result is four more than the smaller.

Let us assume the smaller number is \(x\).

The larger number is  \((x+2)\).

Two numbers are consecutive odd integers. If twice the smaller is subtracted from three times the larger than it is

\(3(x+2)-2x\)

So, the result is four more than the smaller.

i.e., \(3(x+2)-2x=x+4\)

Hence, the option (4) is correct.

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Answer:

\(\cos(W) = \frac{9}{41}\)

Step-by-step explanation:

Given

\(\angle Y = 90^o\)

\(YX = 40; XW = 41; WY = 9\)

Required

Determine \(\cos(W)\)

The question is illustrated with the attached image.

So:

\(\cos(W) = \frac{Adajacent}{Hypotenuse}\)

\(\cos(W) = \frac{WY}{XW}\)

This gives:

\(\cos(W) = \frac{9}{41}\)

Answer:

z = 99

Step-by-step explanation:

\(\frac{z}{9}\) + 4 = 15 ( subtract 4 from both sides )

\(\frac{z}{9}\) = 11 ( multiply both sides by 9 to clear the fraction )

z = 99

The answer of the given question based on the right triangular prism is , the surface area of the prism is option (D) 2.6 + 12 + 8 + 8 = 30.

A right triangular prism is a three-dimensional solid that has two congruent, parallel triangular faces (also known as bases) and three rectangular faces that connect the bases at right angles. The perpendicular distance between the two bases is called the height of the prism.

To find the surface area of the prism, we need to calculate the area of each of its faces and then add them up.

The prism has two congruent triangular faces and three rectangular faces.

The area of each triangular face is equal to one-half the product of the base and height, which gives:

1/2 * 3 * 12 = 18

The area of each rectangular face is equal to the product of its length and width, which gives:

8 * 3 = 24 (two of these faces)

12 * 8 = 96 (one of these faces)

Therefore, total surface area of  prism is given by:

2 * 18 + 2 * 24 + 96 = 60 + 96 = 156

So the correct expression that represents the surface area of the prism is option (D) 2.6 + 12 + 8 + 8 = 30.

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9514 1404 393

Answer:

  33.5 minutes

Step-by-step explanation:

There are many ways you can look at this problem. One is to write equations for the amount in each can, and solve for the time that makes those amounts equal. Another is to consider how much time it takes to reduce the volume by half.

Using the first method, we have ...

  335 -5t = 5t

  335 = 10t

  335/10 = 33.5 = t

It takes 33.5 minutes for the cans to have the same amount.

Given: cost of CAYMAN sleep couch with VAT is R2 699

cost without VAT is R1 999

2.1  To calculate the original price of the couch excluding VAT, we can use the following formula:

Price including VAT / 1 + (VAT rate / 100) = Price excluding VAT

In this case, the VAT rate is 15% (since it is included in the original price), so the formula is:

R2,699 / 1 + (15 / 100) = R2,346.96

2.2  To calculate the expected price of the couch including VAT at the sale price, we can use the following formula:

Price excluding VAT * (1 + (VAT rate / 100)) = Price including VAT

In this case, the VAT rate is still 15% and the sale price is R1,999 (excluding VAT), so the formula is:

R1,999 * (1 + (15 / 100)) = R2,299

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Answer:

27

Step-by-step explanation:

Evaulate 9÷3[(20-7) -2to the power of 2]

9÷3[(20-7) - 2²]

9 ÷ 3 = 3

[(20-7) - 2²] = (13 - 4) = 9

Hence ;

9÷3[(20-7) - 2²]

3(9)

= 27

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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a. The meaning of the variables are:

b. Evaluating 2w-60 when w =140. d = 220 mg

c.  Evaluate 2w-60 when w= 175, d = 290 mg

d. Evaluate 2w-60 when w = 25. d = -10 mg

e. Evaluate 2w-60 when d = 260 mg

Given data

d=2w-60

where:

w = weight

d = dosage

a. label the meaning of the variables

w = weight

d = dosage

b. Evaluate 2w-60 when w = 140,

d=2w-60

d = 2 * 140 - 60

d = 220

c.  Evaluate 2w-60 when w= 175

d=2w-60

d = 2 * 175 - 60

d = 290

This means that for a weight of 175 pounds the dosage is 290 mg

d. Evaluate 2w-60 when w = 25

d=2w-60

d = 2 * 25 - 60

d = -10

Explanation: This means the drug is not recommended for patients weighing 25

e. Evaluate 2w-60 when d = 260

260 = 2w - 60

2w = 260 + 60

2w = 320

w = 160

At the time of prescription the patient was weighing 160 pounds

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Answer:

y = 3.75x + 300

Step-by-step explanation:

hope it was in time :)

Answer:

56

Step-by-step explanation:

56

Answer:

6=a23

8=a35

2=a32

Step-by-step explanation:

Answer:

11/18

Step-by-step explanation:

4/9 + 1/6

Get a common denominator of 18

4/9 * 2/2 = 8/18

1/6 * 3/3 = 3/18

8/18+3/18

11/18

Answer:

11/18

4/9 + 1/6

Get a common denominator of 18

4/9 * 2/2 = 8/18

1/6 * 3/3 = 3/18

8/18+3/18

11/18

ez

Step-by-step explanation: