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3 years ago

VN

Mathematics

1 answer:

navik [9.2K]3 years ago

6 0

Answer:

£2,121.8

Step-by-step explanation:

Given the following;

Principal P = £2000

Rate r = 3%

Time t = 2 years

n = 1 (time of compounding)

Using the compound interest formula;

A = P(1+r)^t

A = 2000(1+0.03)^2

A = 2000(1.03)^2

A = 2000(1.0609)

A = 2,121.8

hence the amount that will be in his account after 2 years is £2,121.8

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Write the equation of a parabola with focus at (1,-4) and a directrix at X=2

konstantin123 [22]

Answer:

The equation of a parabola is

$x = \frac{1}{4(f - h)} (y - k) ^{2} + h$

Step-by-step explanation:

(h,k) is the vertex and (f,k) is the focus.

Thus, f = 1, k = −4.

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix: f - h = h - 2.

Solving the system, we get h = 3/2, k = -4, f = 1.

The standard form is:

$x = - \frac{y ^{2} }{2} - 4y - \frac{13}{2}$

The general form is:

$2x + {y}^{2} + 8y + 13 = 0$

The vertex form is:

$x = - \frac{(y + 4) ^{2} }{2} + \frac{3}{2}$

The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y = -4.

The focal length is the distance between the focus and the vertex: 1/2.

The focal parameter is the distance between the focus and the directrix: 1.

The latus rectum is parallel to the directrix and passes through the focus: x = 1.

The length of the latus rectum is four times the distance between the vertex and the focus: 2.

The eccentricity of a parabola is always 1.

The x-intercepts can be found by setting y = 0 in the equation and solving for x.

x-intercept:

$( - \frac{13}{2} \: ,0)$

The y-intercepts can be found by setting x = 0 in the equation and solving for y.

y-intercepts:

$(0, - 4 - \sqrt{3)}$

$(0, - 4 + \sqrt{3)}$

3 0

3 years ago

A shop sells packs of black pens, packs of red pens and packs of green pens.

olchik [2.2K]

Answer:

85 pens

Step-by-step explanation:

The computation of the number of green pens sold is shown below;

As the number of black pens, red pens, and green pans is 3:5:6

And, the ratio of sold of black pens, red pens, and green pans is 7:3:4

So, the ratio of pens in a number of pens is

= 3 × 7 : 5 × 3 : 4 × 6

= 21: 15 : 24

= 7: 5 : 8

And, the total of 212 pens are sold

So, the number of green pens sold is

= 8 × 212 ÷ (7 + 5 + 8)

= 85 pens

4 0

3 years ago

You are using a recipe for meatloaf that calls for 10 ounces of ground beef: the recipe is for 5 servings but you want to make e

pogonyaev

Answer:

16

Step-by-step explanation:

10 divided by 5 equals 2 (10/5=2)

2 times 8 equals 16 (2 x 8 = 16)

8 0

3 years ago

n HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you tha

Dominik [7]

Answer:

0.321 is the probability that their mean printing speed of the sample is greater than 17.99 ppm.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 17.39 ppm

Standard Deviation, σ = 4.25 ppm

Sample size = 11

We are given that the distribution of printing speed is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

P(printing speed of the sample is greater than 17.99 ppm.)

P(x > 17.99)

$P( x > 17.99) = P( z > \displaystyle\frac{17.99-17.39}{\frac{4.25}{\sqrt{11}}}) = P(z > 0.468229)\\\\P( z > 0.468229) = 1 - P(z < 0.468229)$

Calculating the value from the standard normal table we have,

$1 - 0.679 = 0321= 32.1\%\\P( x > 17.99) = 32.1\%$

Thus, 0.321 is the probability that their mean printing speed of the sample is greater than 17.99 ppm.

8 0

4 years ago

I just don't know it

denis23 [38]

Looking at the question. you'll know that it's a subtraction question so that eliminates C and D. Now look at A and B. It says that 33 stamps were used. So that means the answer is not a negative expression. (B) Is Eliminated.

ANSWER : A

5 0

3 years ago