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2 years ago

How many integers n satisfy the inequality 3n² - 4≤44?

Mathematics

1 answer:

Margaret [11]2 years ago

7 0

Answer:

The possible values of n for n ≤ +4 = (-∞,+4]

The possible values of n for n ≤ -4 = (-∞,-4]

Step-by-step explanation:

Here, the given inequality is:

$3n^2 - 4 \leq 44$

Firstly, let us solve the given inequality for the desirable value of n.

$3n^2 - 4 \leq 44$

Adding 4 on both sides, we get:

$3n^2 - 4 + 4 \leq 44 + 4$

$3n^2 \leq 48$

or, $n^2 \leq \frac{48}{3}\implies n^2 \leq 16\\$

⇒ n ≤ +4 or n ≤ -4

So, the possible values of n for n ≤ +4 = (-∞,+4]

And, the possible values of n for n ≤ -4 = (-∞,-4]

So, we can pick any of the integer values from the both defined sets.

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1. The side view of Mrs. Marigold's roof on her house

Ostrovityanka [42]

Answer:

The height of Mrs. Marigold's roof is 10 feet.

Step-by-step explanation:

Given that,

Base of the given triangle = 48 ft

Hypotenuse = 26 ft

Half of the base = 24 ft

Using Pythagoras theorem,

$h=\sqrt{26^2-24^2}\\\\h=10\ ft$

So, the height of Mrs. Marigold's roof is 10 feet.

7 0

2 years ago

How to create a pattern with the rule n 3?

SCORPION-xisa [38]

If you copied the "n 3" part, it's very likely that your job was to create a pattern with either the rule n^3 or n*3.

In the case of the former, we can start with the initial number of 1 and increase by 1.
In that way, using the rule n^3 would create this pattern of numbers: 1, 8, 27, 64, and so on. Or stated in another way 1*1*1, 2*2*2, 3*3*3, 4*4*4 ...

In the case of the latter, we can start with the initial number of 1 and increase it by 1.
In this way, using the rule of n*3 would create this pattern of numbers: 3, 6, 9, 12, 15, 18 and o son. Or stated in another way 1*3, 2*3, 3*3, 4*3, 5*3 ...

5 0

3 years ago

Can anyone help solve this for me ASAP. Thanks!

Anuta_ua [19.1K]

Answer:

x = 20

y = 26

Step-by-step explanation:

40 and 2x are vertical angles, so they're equal to each other.

40 = 2x

Divide both sides by 2

x = 20

We see that 40 and 5y + 10 are a linear pair, which means they add up to 180.

5y + 10 + 40 = 180

5y + 50 = 180

5y = 130

y = 26

8 0

2 years ago

In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equa

arlik [135]

Answer:

Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Step-by-step explanation:

The question is incomplete:

The significance level is 0.05.

The data is:

Brand X: 91, 100, 88, 89

Brand Y: 99, 96, 94, 99

Brand Z: 83, 88, 89, 76

We have to check if there is a significant difference between the absorbency rating of each brand.

Null hypothesis: all means are equal

$H_0:\mu_x=\mu_y=\mu_z$

Alternative hypothesis: the means are not equal

$H_a: \mu_x\neq\mu_y\neq\mu_z$

We have to apply a one-way ANOVA

We start by calculating the standard deviation for each brand:

$s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33$

Then, we calculate the mean standard error (MSE):

$MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78$

Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:

$M_x=92,\,\,M_y=97,\,\,M_z=84\\\\M=(92+97+84)/3=91$

The MSB is then:

$s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172$