3: convert into a fraction

1. The value of k for which equation 9x2 + 8xk+8 = 0 has equal roots is:

Nesterboy [21]

Answer:

Option C

+ or - 3

Step-by-step explanation:

A quadratic equation will have equal roots if its Discriminant is equal to zero.

the discriminant in this case is $b^{2}- 4 ac$

considering the equation,

$9x^{2} + 8xk+8 = 0$

a = 9, b= 8k, c=8

Replacing the variables in the original equation with their respective values, we will have:

$8k^{2}- 4 \times 9 \times 8=0\\64k^{2}=288\\k=\sqrt{288/64} =\sqrt{9/2}$

Note: The values of k are meant to be + or -2.12 as seen from the workings

However, these are not in the options given. the closest choice to it

is + or - 3

8 0

4 years ago

The chart below shows the distribution of the number of books in a library.

Murljashka [212]

Answer:

Yes, it is representative because each type of book was represented in the approximate proportion that exists in the library.

Step-by-step explanation:

Given is a chart, showing the distribution of the number of books in a library.

Also given that Sahira chooses a random sample from the library and records the type of books in the chart below.

Sahira's sample can be said to be representative because given that books are taken at random. So just because literacy books were more we cannot say it is not representative II option is not right, because each book was not chosen uniquely, just random books were drawn

Lastly The Answer is C) Yes, it is representative because each type of book was represented in the approximate proportion that exists in the library is right, because each book selected represents the sample from population of full library books.

5 0

3 years ago

Peyton has 5/8 of pumpkin pie left over from thanksgiving. She eats 1/8 of the pie and her friend joy eats 1/6 of the pie. How m

neonofarm [45]

Answer:

1/3

Step-by-step explanation:

Left over pie=5/8

Payton eats=1/8 of the left over pie

Joy eats =1/6 of the left over pie

Total pie eaten by Payton and joy= 1/8+1/6

To add the fraction,

Find the lowest common multiple of 6 and 8 which is 48

Then,

divide 48 by 8 multiplied by 1 which is 6,

divide 48 by 6 multiplied by 1 which is 8

We have,

=6+8/48

=14/48

=7/24

Total pie eaten by Peyton and joy=7/24

Total pie left(after Peyton and joy share)= Total left over- total pie eaten by Peyton and joy

=5/8-7/24

=15-7/24

=8/24

=1/3

8 0

3 years ago

You are trying to estimate the average amount a family spends on food during a year. In the past the standard deviation of the a

svetoff [14.1K]

Answer:

$n=(\frac{2.58(1000)}{50})^2 =2662.56 \approx 2663$

So the answer for this case would be n=2663 rounded up to the nearest integer

Step-by-step explanation:

We have the following info:

$ME = 50$ margin of error desired

$\sigma = 1000$ the standard deviation for this case

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =50 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance is $\alpha=0.01$ . And for this case would be $z_{\alpha/2}=2.58$ , replacing into formula (b) we got:

$n=(\frac{2.58(1000)}{50})^2 =2662.56 \approx 2663$

So the answer for this case would be n=2663 rounded up to the nearest integer

5 0

3 years ago

A box contains 9 identical glass spheres that are used to make snow globes.

DIA [1.3K]

Uhmmm B I pretty sure

5 0

3 years ago