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3 years ago

Can someone please answer. There is a picture. It is only one question. Thank you so much!

Mathematics

1 answer:

Charra [1.4K]3 years ago

6 0

We can check each of these using the Pythagorean Theorem, $a^2 + b^2 = c^2$
Option A:
$.5^2 + 1.2^2 = 1.3^2

$
.25 + 1.44 = 1.691.69 = 1.69
This option works
Option B
$1^2 + 2^2 = 3^2$
1 + 4 = 9
5 ≠ 9
This option does not work, but let's check the others to make sure
Option C:
$6^2 + 8^2 = 10^2$
36 + 64 = 100
100 = 100
This option works
Option D:
$3^2 + 4^2 = 5^2$
9 + 16 = 25
25 = 25
This option works

So, after doing the calculations, we see that option B does not work

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Which pair of equations represents two perpendicular lines? <br>answers shown in picture.

kolezko [41]

Answer:

y =1/2x+6

y = -2x+2

Step-by-step explanation:

Perpendicular line have slopes that multiply to -1

The slopes are negative reciprocals

-4*4 = 16 not perpendicular

1/2 * -2 = -1 perpendicular

1/5 *5 = 1 not perpendicular

2/3 * 2/3 = 4/9 not perpendicular

3 0

3 years ago

An oxygen tank contained 212 12/3 liters of oxygen before 27 1/3 liters were used. If the tank can hold 240 3/8 liters, how much

lukranit [14]

So, initially 240 $\frac{3}{8}$ -212 $\frac{12}{3}$ were empty:

this is :

$240 \frac{3}{8} - 212 \frac{12}{3} = 240 \frac{3}{8} - 212 +4 = 240 \frac{3}{8} - 216= 24 \frac{3}{8}$

12/4 is 4 so that's why i substituted it with 4.

now, later 27 1/3 were used so we add this tho the original empty space

$24 \frac{3}{8}+ 27 \frac{1}{3}$ = $24 \frac{9}{24}+ 27 \frac{8}{24}$ = $51 \frac{17}{24}$

which is the result!

5 0

3 years ago

The value 5pi/24 is a solution for the equation 4 cos^2 (4x)-3=0. True or false

Margaret [11]

Let's check.

x = 5π/24

4x = 5π/6

cos 4x = cos(5π/6) = cos 150° = -√3/2

cos² 4x = (-√3/2)^2 = 3/4

4 cos² 4x -3 = 4 (3/4) - 3 = 0

Answer: TRUE

5 0

3 years ago

Assume that the population of human body temperatures has a mean of 98.6 degrees F and a standard deviation of 0.62 degrees F. I

dimulka [17.4K]

Answer:

0% probability of getting a mean temperature of 98.2 degrees F or lower.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 98.6, \sigma = 0.62, n = 106, s = \frac{0.62}{\sqrt{106}} = 0.06$