All categories

2 years ago

The segments shown below could form a triangle.

Mathematics

1 answer:

Rina8888 [55]2 years ago

5 0

Answer:

A. True

Step-by-step explanation:

The Triangle Inequality Theorem says that the sum of any two sides must be greater than the third side. Let's see if this is true.

a + b

9 + 1 = 10>9

a + c

9 + 9 = 18>1

c + b

9 + 1 = 10>9

You might be interested in

a(0.3−y)+1.1+2.4x (y−1.2) =0 =−1.2(x−0.5) Consider the system of equations above, where aaa is a constant. For which value o

Veseljchak [2.6K]

Answer:

For a = 1.22 there is one solution where y = 1.3

Step-by-step explanation:

Hi there!

Let´s write the system of equations:

a(0.3 - y) + 1.1 +2.4x(y-1.2) = 0

-1.2(x-0.5) = 0

Let´s solve the second equation for x:

-1.2(x-0.5) = 0

x- 0.5 = 0

x = 0.5

Now let´s repalce x = 0.5 and y = 1.3 in the first equation and solve it for a:

a(0.3 - y) + 1.1 +2.4x(y-1.2) = 0

a(0.3 - 1.3) + 1.1 + 2.4(0.5)(1.3 -1.2) = 0

a(-1) + 1.1 + 1.2(0.1) = 0

-a + 1.22 = 0

-a = -1.22

a = 1.22

Let´s check the solution and solve the system of equations with a = 1.22. Let´s solve the first equation for y:

1.22(0.3 - y) + 1.1 +2.4(0.5)(y-1.2) = 0

0.366 - 1.22y + 1.1 + 1.2 y - 1.44 = 0

-0.02y +0.026 = 0

-0.02y = -0.026

y = -0.026 / -0.02

y = 1.3

Then, the answer is correct.

Have a nice day!

4 0

2 years ago

A scientist poured 1.6 x 103 milliliters of water into a container that already had 2.8 x 104 milliliters of salt water and 9.4

Tomtit [17]

This question is incomplete

Complete Question

A scientist poured 1.6 x 10³ milliliters of water into a container that already had 2.8 x 10⁴ milliliters of salt water and 9.4 x 10³ milliliters of sugar water. How many milliliters of liquid were in the container?

A.1.7 x 10⁴ milliliters

B.3.58 x 10⁴ milliliters

C.3.74 x 10⁴ milliliters

D.3.9 x 10⁴ milliliters

Answer:

C. 3.74 x 10⁴ milliliters

Step-by-step explanation:

The milliliters of liquid that WERE in the container = The milliliters of liquid that were in the container before adding 1.6 x 10³ milliliters of water

This equals to:

2.8 x 10⁴ milliliters of salt water and 9.4 x 10³ milliliters of sugar water.

Hence:

2.8 x 10⁴ milliliters of salt water + 9.4 x 10³ milliliters of sugar water

= (2.8 × 10⁴) + (9.4 × 10³)

= 37400

= 3.74 x 10⁴ milliliters

Therefore, option C is correct

4 0

2 years ago

"Majesty Video Production Inc. wants the mean length of its advertisements to be 30 seconds. Assume the distribution of ad lengt

Westkost [7]

Answer:

a) $\bar X \sim N(\mu=30, \frac{2}{\sqrt{16}})$

b) $Se=\frac{\sigma}{\sqrt{n}}=\frac{2}{\sqrt{16}}=0.5$

c) $P(\bar X >31.25)=0.006=0.6\%$

d) $P(\bar X >28.25)=0.9997=99.97\%$

e) $P(28.25$

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variabl length of advertisements produced by Majesty Video Production Inc. We know from the problem that the distribution for the random variable X is given by:

$X\sim N(\mu =30,\sigma =2)$

We take a sample of n=16 . That represent the sample size.

a. What can we say about the shape of the distribution of the sample mean time?

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is also normal and is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar X \sim N(\mu=30, \frac{2}{\sqrt{16}})$

b. What is the standard error of the mean time?

The standard error is given by this formula:

$Se=\frac{\sigma}{\sqrt{n}}=\frac{2}{\sqrt{16}}=0.5$

c. What percent of the sample means will be greater than 31.25 seconds?

In order to answer this question we can use the z score in order to find the probabilities, the formula given by:

$z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}$

And we want to find this probability:

$P(\bar X >31.25)=1-P(\bar X$

d. What percent of the sample means will be greater than 28.25 seconds?

In order to answer this question we can use the z score in order to find the probabilities, the formula is given by:

$z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}$

And we want to find this probability:

$P(\bar X >28.25)=1-P(\bar X$

e. What percent of the sample means will be greater than 28.25 but less than 31.25 seconds?"

We want this probability:

$P(28.25$

3 0

2 years ago

On this graph, 4:00 p.m. occurs at 16 hours after midnight, and 6:00 p.m. occurs at 18 hours after midnight. Which statements ar

KatRina [158]

Answer:

TRUE OPTIONS ARE:

"The temperature increased until 4:00 p.m. "

"The temperature decreased after 6:00 p.m. "

"The temperature increased more quickly between 12:00 p.m. and 4:00 p.m. than before 12:00 p.m."

Step-by-step explanation:

graph attached and complete question below:

Which statements are true about the temperatures Luis recorded on the graph? Check all that apply.

The temperature increased until 4:00 p.m.
The temperature was not recorded between 4:00 p.m. and 6:00 p.m.
The temperature decreased after 6:00 p.m.
The temperature increased and then decreased before holding constant.
The temperature increased more quickly between 12:00 p.m. and 4:00 p.m. than before 12:00 p.m.

Until 1600 hours, the graph increases, so we can say temperature increased until 4.00 pm (FIRST OPTION TRUE).

From 1600 to 1800 hours (4 - 6pm), the temperature stayed same (horizontal line). This doesn't mean the temperature wasn't recorded. (2nd OPTION FALSE).

After 1800 hours (6pm), the line goes downward, so temperature decreased after 6 pm. (3rd OPTION TRUE).

If you look at the temperature graph, we can see temperature increased, then increased more, then constant, then decreased. Thus the 4th option isnt true. (4th OPTION FALSE).

Before 12, the increase isn't as sharp as after 12. After 12 temperature increase has more slope, so this increase is more. (5th OPTION TRUE).

7 0

2 years ago

Read 2 more answers

if all 10 players scored the same number of points,how many would each player have to score for a totel of 230

PIT_PIT [208]

23 points for each player :)

5 0

2 years ago