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1 year ago

Solve the inequality 4/3 < -8/3y.

Mathematics

2 answers:

Kazeer [188]1 year ago

4 0

Answer:

The answer to this inequality is y < -1/2.

Hope this could help you! (*＾წ＾*)

tensa zangetsu [6.8K]1 year ago

4 0

Answer:

$y$

Step-by-step explanation:

$\frac{4}{3}$

$-\frac{8}{3}y>\frac{4}{3}\\$

$\left(-\frac{8}{3}y\right)\left(-1\right)$

$\frac{8}{3}y$

$3\cdot \frac{8}{3}y$

$8y$

$\frac{8y}{8}$

$y$

Hope this helps!

All the love, Ya boi Fraser :)

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1 year ago

Given the line a and b are parallel angles 1 and5 are congruent because they are

kakasveta [241]

Answer:

Step-by-step explanation:

When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles.

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Vertical angles are always congruent, which means that they are equal.

Adjacent angles are angles that come out of the same vertex. Adjacent angles share a common ray and do not overlap.

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The size of the angle xzy in the picture above is the sum of the angles A and B.

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Two angles are said to be supplementary when the sum of the two angles is 180°.

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If we have two parallel lines and have a third line that crosses them as in the ficture below - the crossing line is called a transversal

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figure55

The eight angles will together form four pairs of corresponding angles. Angles 1 and 5 constitutes one of the pairs. Corresponding angles are congruent. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g. 3 + 7, 4 + 8 and 2 + 6.

Angles that are in the area between the parallel lines like angle 2 and 8 above are called interior angles whereas the angles that are on the outside of the two parallel lines like 1 and 6 are called exterior angles.

Angles that are on the opposite sides of the transversal are called alternate angles e.g. 1 + 8.

All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.

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figure56

The picture above shows two parallel lines with a transversal. The angle 6 is 65°. Is there any other angle that also measures 65°?

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2 years ago

A coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces. A random sample of 15 co

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Answer:

We conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

Step-by-step explanation:

We are given that a coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces.

A random sample of 15 containers were weighed and the mean weight was 31.8 ounces with a sample standard deviation of 0.48 ounces.

Let $\mu$ = mean weight of coffee in its containers.

SO, Null Hypothesis, $H_0$ : $\mu \geq$ 32 ounces {means that the mean weight of coffee in its containers is at least 32 ounces}

Alternate Hypothesis, $H_A$ : $\mu$ < 32 ounces {means that the mean weight of coffee in its containers is less than 32 ounces}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean weight = 31.8 ounces

s = sample standard deviation = 0.48 ounces

n = sample of containers = 15

So, the test statistics = $\frac{31.8 -32}{\frac{0.48}{\sqrt{15} } }$ ~ $t_1_4$

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The value of t test statistics is -1.614.

Now, at 0.01 significance level the t table gives critical value of -2.624 at 14 degree of freedom for left-tailed test.

Since our test statistic is more than the critical value of t as -1.614 > -2.624, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

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