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2 years ago

Find two numbers if their ratio is 9:11 and their difference is 6.

Mathematics

2 answers:

erastova [34]2 years ago

8 0

Answer:

Step-by-step explanation:

27,33

9*3 is 27

11*3 is 33

33-27 is 6

i only have one, sorry!

svlad2 [7]2 years ago

3 0

Answer:

Step-by-step explanation:

Let the larger number = y

Let the smaller number = x

x/y = 9/11

y - x = 6

Add x to both sides of the second equation

y = 6 + x

Substitute into the first equation

x/(x + 6) = 9/11

Cross multiply

11x = 9(x + 6)

Remove the brackets

11x = 9x + 54

Subtract 9x from both sides.

2x = 54

x = 54/2

x = 27

y = 27 + 6

y = 33

(27,33)

The way I've done it, there isn't a second pair.

I suppose you could do it this way.

9/11 = -27/-33

-27 - - 33 = 6

So the second pair could be

(-27, - 33)

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A research group needs to determine a 90% confidence interval for the mean repair cost for all car insurance small claims. From

lutik1710 [3]

Answer:

a) $z = 1.645$

b) The should sample at least 293 small claims.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$ , which means that the answer of question a is z = 1.645.

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

(b) If the group wants their estimate to have a maximum error of $12, how many small claims should they sample?

They should sample at least n small claims, in which n is found when

$M = 12, \sigma = 124.88$ . So

$M = z*\frac{\sigma}{\sqrt{n}}$

$12 = 1.645*\frac{124.88}{\sqrt{n}}$

$12\sqrt{n} = 205.43$

$\sqrt{n} = \frac{205.43}{12}$

$\sqrt{n} = 17.12$

$\sqrt{n}^{2} = (17.12)^{2}$

$n = 293$

The should sample at least 293 small claims.

8 0

2 years ago

If C is between A and B, then answer the following if AB=40, AC= 2x+10, CB= 3x-5

Marat540 [252]

If C is between A and B, then, we can write the equation

$AB = AC + CB$

Substitute the value of AB and the expressions for AC and CB in terms of x.

$40 = (2x+10)+(3x-5)$

We can now solve for x.

$40-10+5= 2x+3x$

$35=5x$

Dividing by 5.

$7=x$

$AB=40$

$AC=2(7)+10$

$AC=14+10$

$AC=24$

$BC=3(7)-5$

$BC=21-5$

$BC=16$

6 0

3 years ago

What are the two solutions of 2x^2=-x^2-5x-1

hammer [34]

Answer:

x = 5/-6 + (√13)/-6

x = 5/-6 -(√13)/-6

Step-by-step explanation:

2x^2 = -x^2 - 5x - 1. Subtract 2x^2 from both sides.

-3x^2 - 5x - 1. Do the quadratic formula.

That gives you:

-5/6 ± (√13)/-6.

3 0

3 years ago

Read 2 more answers

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JulsSmile [24]

Answer:

2sin50 cos20

Step-by-step explanation:

We need to write sin (70) + sin(30) as a product. The formula used here is :

$\sin A+\sin B=2\sin (\dfrac{A+B}{2})\cos(\dfrac{a-b}{2})$

Here, A = 70 and B = 30

So,

$\sin 70+\sin 30=2\sin (\dfrac{70+30}{2})\cos(\dfrac{70-30}{2})\\\\\sin 70+\sin 30=2\sin 50\cos20$

So, the value of sin (70) + sin(30) is 2sin50 cos20. Hence, the correct option is (c).

7 0

3 years ago

Which expression is equivalent to \left(3^{-6}\times 3^{3}\right)^{-1}\normalsize?(3 −6 ×3 3 ) −1 ? 3^{-19}3 −19 3^{18}3 18 3^{-

mars1129 [50]

Answer:

Step-by-step explanation:

Given the expression

$\left(3^{-6}\times 3^{3}\right)^{-1}\\$

According to law of indices, this can be written as;

$\left(3^{-6+3})^{-1}\\\\= (3^{-3})^{-1}\\\\= 3^{-3*-1}\\\\= 3^3\\\\= 27$

Hence the required answer is 27

5 0

2 years ago