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Keith_Richards [23]

3 years ago

12

A set of data is summarized by the stem and leaf plot below.

1 answer:

AlekseyPX3 years ago

6 0

Answer:

(a) There are <u>12</u> values in the data set which are greater than or equal to 10 and less than or equal to 19.

(b) There are 12 values in the data set which are greater than or equal to 30 and less than or equal to 39.

(c) There are 7 values in the data set which are greater than or equal to 40 and less than or equal to 49.

Step-by-step explanation:

We are given a set of data that is summarized by the stem and leaf plot below;

Steam Leaf

1 0 0 2 4 4 4 7 8 8 8 8 9

2 2 2 5 5 7 8

3 3 4 4 5 5 5 6 6 6 7 9 9

4 3 3 3 5 5 7 9

<u>This shows that the data values are:</u> 10, 10, 12, 14, 14, 14, 17, 18, 18, 18, 18, 19, 22, 22, 25, 25, 27, 28, 33, 34, 34, 35, 35, 35, 36, 36, 36, 37, 39, 39, 43, 43, 43, 45, 45, 47, 49.

(a) From the data above, the number of values in the data set which are greater than or equal to 10 and less than or equal to 19 is 12, i.e; 10, 10, 12, 14, 14, 14, 17, 18, 18, 18, 18, 19.

(b) From the data above, the number of values in the data set which are greater than or equal to 30 and less than or equal to 39 is 12, i.e; 33, 34, 34, 35, 35, 35, 36, 36, 36, 37, 39, 39.

(c) From the data above, the number of values in the data set which are greater than or equal to 40 and less than or equal to 49 is 7, i.e; 43, 43, 43, 45, 45, 47, 49.

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Find the value(s) of k such that 4x² + kx + 4 = 0 has 1 rational solution

Blababa [14]

Answer:

If you mean only one rational solution, the answer is

$k_1 = 8, k_2 = -8$

If you mean at least 1 rational solution, the answer is

$k\in (-\infty, -8]\cup[8, \infty)$

Step-by-step explanation:

$4x^2 + kx + 4 = 0$

Let's calculate the discriminant.

$\Delta = b^2 - 4ac$

$\Delta = k^2 -4 \cdot 4 \cdot 4$

$\Delta = k^2 -64$

Now, remember that:

$\text{If } \Delta > 0 : \text{2 Real solutions}$

$\text{If } \Delta = 0 : \text{1 Real solution}$

$\text{If } \Delta < 0 : \text{No Real solution}$

Therefore, I will just consider the first two cases.

$k^2 - 64 > 0$

and

$k^2 -64 = 0$

$\boxed{\text{For } k^2 - 64 > 0}$

$k^2 > 64 \Longleftrightarrow k>\pm\sqrt{64} \Longleftrightarrow k\in (-\infty, -8)\cup(8, \infty)$

$\boxed{\text{For } k^2 - 64 = 0}$

$k^2 = 64 \Longleftrightarrow k=\pm\sqrt{64} \implies k_1 = 8, k_2 = -8$

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Suppose that cot θ = c and 0 < θ < π 2 . what is a formula for cos θ in terms of c?

loris [4]

Answer:

<h3>cosθ = c/√1+c²</h3>

Step-by-step explanation:

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cotθ = 1/tanθ = c

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cross multiply

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Tanθ = opposite/adjacent = 1/c

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To get the hypotenuse, we will use the pythagoras theorem:

hyp² = opp²+adj²

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