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2 years ago

Which of the following accurately compare 15-√105 and 5?

Mathematics

2 answers:

Vlad [161]2 years ago

7 0

The answer is c. I hope that helps

Afina-wow [57]2 years ago

6 0

Answer: The correct option is

(C) $\sqrt{105}$ is slightly greater than 10, so $15-\sqrt{105}$ is less than 5.

Step-by-step explanation: We are given to select the correct statement that accurately compare $15-\sqrt{105}$ and $5$ .

We have

$\sqrt{105}=10.2469,$

so, we get

$15-\sqrt{105}=15-10.2469=4.7531.$

Since 4.7531 < 5, so

$15-\sqrt{105}$

Therefore, $\sqrt{105}$ is slightly greater than 10, so $15-\sqrt{105}$ is less than 5.

Thus, the correct option is (C).

You might be interested in

How many pairs of whole numbers have a sum of 99

alexandr402 [8]

With the sum of 99, we will get 50 pairs whole numbers. Why?

Let’s start with

0+ 99

1 + 98

2 + 97

3 + 96

4 + 95

5 + 94

6 + 93

7 + 92

8 + 91

9 + 90

10 + 89

………

……..

43 + 49

44 + 50

Therefore, if you’re going to count all pairs of whole number, you will get 50 pairs of whole number with the sum of 99.

Hope this helps!

4 0

2 years ago

Read 2 more answers

The points plotted below are on the graph of a polynomial. In what range of x-values must the polynomial have a root?

joja [24]

Actually, I think the question should be, "In what range(s) of x-values must there be a root of the POLYNOMIAL?" Unless you are working with some real strange maths, polynomials are smooth and continuous. If you drew a smooth and continuous line through the points in the graph, where would the line have to cross the x-axis?

6 0

2 years ago

In measuring reaction time, a psychologist estimates that a standard deviation is .05 seconds. How large a sample of measurement

blondinia [14]

Answer:

Step-by-step explanation:

We are asked to find the size of sample to be 95% confident that the error in psychologist estimate of mean reaction time will not exceed 0.01 seconds.

We will use following formula to solve our given problem.

$n\geq (\frac{z_{\alpha/2}\cdot\sigma}{E})^2$ , where,

$\sigma=\text{Standard deviation}=0.05$ ,

$\alpha=\text{Significance level}=1-0.95=0.05$ ,

$z_{\alpha/2}=\text{Critical value}=z_{0.025}=1.96$ .

$E=\text{Margin of error}$

$n=\text{Sample size}$

Substitute given values:

$n\geq (\frac{z_{0.025}\cdot\sigma}{E})^2$

$n\geq (\frac{1.96\cdot0.05}{0.01})^2$

$n\geq (\frac{0.098}{0.01})^2$

$n\geq (9.8)^2$

$n\geq 96.04$

Therefore, the sample size must be 97 in order to be 95% confident that the error in his estimate of mean reaction time will not exceed 0.01 seconds.

5 0

2 years ago

What is the range of the function graphed below?

Xelga [282]

<h2>Answer:</h2>

Option: B is the correct answer.

The range of the function is:

B. 5 < y < ∞

<h2>Step-by-step explanation:</h2>

Range of a function--

The range of a function is the set of all the values that is attained by the function.

By looking at the graph of the function we see that the function tends to 5 when x→ -∞ and the function tends to infinity when x →∞

Also, the function is a strictly increasing function.

This means that the function takes every real value between 5 and ∞ .

i.e. The range of the function is: (5,∞)

Hence, the answer is:

Option: B

8 0

2 years ago

Point b has coordinates (3,-4) and lies on the circle whose equation is x^2 + y^2= 25. If angle is drawn in a standard position

lakkis [162]

<span>Point B has coordinates (3,-4) and lies on the circle. Draw the perpendiculars from point B to the x-axis and y-axis. Denote the points of intersection with x-axis A and with y-axis C. Consider the right triangle ABO (O is the origin), by tha conditions data: AB=4 and AO=3, then by Pythagorean theorem:
</span>
<span> $BO^2=AO^2+AB^2 \\ BO^2=3^2+4^2 \\ BO^2=9+16 \\ BO^2=25 \\ BO=5$ .
</span>
{Note, that BO is a radius of circle and it wasn't necessarily to use Pythagorean theorem to find BO}
<span>The sine of the angle BOA is</span>
$\sin \angle BOA= \dfrac{AB}{BO} = \dfrac{4}{5} =0.8$

Since point B is placed in the IV quadrant, the sine of the angle that is <span> drawn in a standard position with its terminal ray will be </span>
<span /><span>
</span><span>
</span> $\sin \theta=-0.8$ .

3 0

2 years ago