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1 month ago

Given angle A, how can you construct an angle whose measure is 1/4 m of angle A?

Mathematics

2 answers:

Inessa [12.3K]1 month ago

8 0

Solution:

Detailed steps:

Given angle A, our objective is to construct an angle whose measure equals one-fourth of angle A.

This means dividing angle A into four equal parts, where each part corresponds to the required angle.

To achieve this, first construct the bisector of angle A, splitting it into two equal angles each measuring half of A. Then bisect one of these halves to create an angle that is one-quarter of A.

The resulting smaller angle is the desired one.

Thus, option A is correct: first bisect angle A, then bisect one of the resulting smaller angles.

lawyer [12.2K]1 month ago

3 0

Suppose angle A measures 80 degrees. Halving it would yield 40 degrees, and bisecting that angle again produces 20 degrees. This 20 degrees angle is exactly one-quarter of 80 degrees, since 20 times 4 equals 80.

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Christie has $200 in her bank account. Every month, she deposits $20 into her account. The equation of the line that models the

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Each month she puts in 20......therefore annually she deposits (20 * 12) = 240 y = 240x + 200

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20 days ago

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A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of awriting

tester [12079]

Answer:

a) Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

b) $p_v =P(t_{17}$

Given that the p-value is lower than the significance threshold in this situation, we have sufficient grounds to reject the null hypothesis.

c) $p_v =P(t_{17}$

In this case, since the p-value exceeds the significance threshold, we have adequate evidence to FAIL to reject the null hypothesis.

d) $p_v =P(t_{17}$

Here again, with the p-value being less than the significance level, we can reject the null hypothesis.

Step-by-step explanation:

1) Provided data and references

$\bar X$ represents the average of the samples

$s$ denotes the standard deviation of the samples

$n=18$ indicates the number of samples

$\mu_o =10$ is the value we are examining

$\alpha$ defines the significance level for the test.

t represents the specific statistic of interest

$p_v$ indicates the p-value relevant to the test (the variable of concern)

Define the null and alternative hypotheses.

To assess if the true mean is at least 10 hours, we must set up a hypothesis:

Part a

Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

If we consider the sample size being less than 30 and the population deviation unknown, it’s more appropriate to use a t-test to compare the actual mean with the reference value, calculated as:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Part b

In this scenario t=-2.3, $\alpha=0.05$

Initially, we need to calculate the degrees of freedom $df=n-1=18-1=17$

Since this is a left-tailed test, the p-value is determined by:

$p_v =P(t_{17}$

In this instance, with the p-value being less than the significance level, we have sufficient evidence to reject the null hypothesis.

Part c

For this situation t=-1.8, $\alpha=0.01$

We need to find the degrees of freedom $df=n-1=18-1=17$

For the left-tailed test, the p-value is given by:

$p_v =P(t_{17}$

In this case, since the p-value is above the significance level, we have enough grounds to FAIL to reject the null hypothesis.

Part d

For this case t=-3.6, $\alpha=0.05$

Firstly, we find the degrees of freedom $df=n-1=18-1=17$

Since we are conducting a left-tailed test, the p-value is calculated as:

$p_v =P(t_{17}$

Here, with the p-value being lower than the significance threshold, we can reject the null hypothesis.

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1 month ago

If p+pq is 4 times p-pq, and pq does not equal to 0, which of the following has exactly one possible value? A)p B)q C)pq D)p+pq

Inessa [12311]

D is the correct option since it represents a combination where neither p nor a equals zero.

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26 days ago

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babunello [11495]

Answer:

Here’s the answer below.

Step-by-step explanation:

Finished Product A 1 2 3 4

Gross Requirements 20 20 50 30

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Planned Delivery 0

Projected on Hand Inventory 30 10 15 40 10

Planned Order Release 0

safety stock 10

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21 day ago

At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately no

Leona [12306]

Answer:

The correct answer is;

A. 0.17

Step-by-step explanation:

Here are the provided details;

The average time taken for a cashier to handle an order, μ = 276 seconds

The deviation from the average, σ = 38 seconds

The z-score for an order processing time of x = 240 seconds can be calculated as follows;

$Z=\dfrac{x-\mu }{\sigma }$

Thus;

$Z=\dfrac{240-276 }{38 } \approx -0.9474$

The resulting probability

P(z = -0.9474) = 0.17361

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1 month ago