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3 years ago

How to solve the inequality 8x + 10 ≤ 60

Mathematics

1 answer:

harina [27]3 years ago

6 0

Answer:

x ≤ 6.25

Step-by-step explanation:

8x + 10 ≤ 60

Subtract 10 from both sides

8x ≤ 50

Divide both side by 8

x ≤ 6.25

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andrew-mc [135]

1) Parallel lines have the same slope, so the answer is 1/2

2) Perpendicular lines have slopes that are negative reciprocals, so the answer is -2

3) The equation of the perpendicular is y = -2x - 6, so a point is (0, -6)

7 0

2 years ago

Test the null hypothesis Upper H 0 : (mu 1 minus mu 2 )equals 0H0: μ1−μ2=0 versus the alternative hypothesis Upper H Subscript a

Law Incorporation [45]

Answer:

The test statistic t is t=2.9037.

The null hypothesis is rejected.

For a significance level of 0.05, there is enough evidence to support the alternative hypothesis.

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>The sample 1, of size n1=25 has a mean of 1.15 and a standard deviation of 0.31. </em>

<em>The sample 2, of size n2=25 has a mean of 0.95 and a standard deviation of 0.15. </em>

This is a hypothesis test for the difference between populations means.

The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

The significance level is α=0.05.

The difference between sample means is Md=0.2.

$M_d=M_1-M_2=1.15-0.95=0.2$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{0.31^2+0.15^2}{25}}\\\\\\s_{M_d}=\sqrt{\dfrac{0.119}{25}}=\sqrt{0.005}=0.069$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.069}=\dfrac{0.2}{0.069}=2.9037$

The degrees of freedom for this test are:

$df=n_1+n_2-1=25+25-2=48$

This test is a two-tailed test, with 48 degrees of freedom and t=2.9037, so the P-value for this test is calculated as (using a t-table):

$P-value=2\cdot P(t>2.9037)=0.0056$

As the P-value (0.0056) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

8 0

3 years ago

Rewrite the function by completing the square.

ddd [48]

Answer:

f(x) = (x -6)² +14

Step-by-step explanation:

Completing the square involves writing part of the function as a perfect square trinomial.

<h3>Perfect square trinomial</h3>

The square of a binomial results in a perfect square trinomial:

(x -h)² = x² -2hx +h²

The constant term (h²) in this trinomial is the square of half the coefficient of the linear term: h² = ((-2h)/2)².

<h3>Completing the square</h3>

One way to "complete the square" is to add and subtract the constant necessary to make a perfect square trinomial from the variable terms.

Here, we recognize the coefficient of the linear term is -12, so the necessary constant is (-12/2)² = 36. Adding and subtracting this, we have ...

f(x) = x² -12x +36 +50 -36

Rearranging into the desired form, this is ...

f(x) = (x -6)² +14

<em>Additional comment</em>

Another way to achieve the same effect is to split the given constant into two parts, one of which is the constant necessary to complete the square.

f(x) = x² -12x +(36 +14)

f(x) = (x² -12x +36) +14

f(x) = (x -6)² +14

6 0

2 years ago

The amounts of paper waste generated in a region during two years were 41,300,000 tons and 50,500,000 tons. What was the total p

kipiarov [429]

That would be 9.18x10^5

4 0

3 years ago

A colony of 900,000 bacteria doubles

shusha [124]

255 hours / 85 hours = 3.

This means that the bacteria will double in size 3 times.

900,000 × 2 = 1,800,000

1,800,000 × 2 = 3,600,000

3,600,000 × 2 = 7,200,000

After 255 hours, the colony of bacteria will be 7,200,000

5 0

3 years ago

Read 2 more answers