Round 7905.68466806 to the nearest thousand.

What additional information is needed to prove that triangles are congruent by the SAS Postulate?

Oliga [24]

Answer: Fourth Option AB=AD

Solution:

The SAS (Side Angle Side) Postulate indicates that two triangles are congruent if they have two congruent sides and congruent the angle between these sides.

According with the figure, the triangles ABC and ACD have a congruent side (S) AC, because is a common side between the two triangles.

Additionally they have a congruent angle (A): the angle BAC in triangle ABC is congruent with the angle DAC in triangle ACD (indicated in the figure).

Then we have one congruent side (S) and one congruent angle (A). We need another congruent side to complete the SAS postulate:

The side (S) AB in triangle ABC must be congruent with the side AD in triangle ACD

Answer: Fourth option AB=AD

5 0

2 years ago

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Two con terminal angles 3pi/4 negative and positive answer in radians

son4ous [18]

Answer:

Negative Coterminal: -5π/4

Positive Coterminal: 11π/4

Step-by-step explanation:

The easiest way to find specific (not infinite) coterminal values is to ±2π. When you subtract 2π, you will get a negative coterminal. When you add 2π, you will get a positive coterminal. Keep in mind though that a tan∅ or cot∅ only needs ±π, not ±2π.

8 0

1 year ago

You want to test the effects of water aerobics on resting heart rate. You decide to test two different levels of exercise (water

DochEvi [55]

Answer:

The correct option is;

A). Randomized block design

Step-by-step explanation:

In a randomized block design the experimental units or subjects of the experiment are separated into subgroups known as blocks with the property that the the variability (difference) of the parameters within the blocks are lesser than the variability between block, such that the treatment of the research or experiment are assigned differently to each block

The groups can therefore comprise of the following;

Group 1

15 men and 15 women to perform water aerobics for 30 minutes twice a week

Group 2

15 men and 15 women to perform water aerobics for 60 minutes once a week

Therefore, the effect of the experiment will be much less attributed to gender than to the durations of the water aerobic exercise.

5 0

2 years ago

The quality control manager at a light bulb factory needs to estimate the mean life of a batch (population) of light bulbs. We a

Nadusha1986 [10]

Answer:

a)95% confidence intervals for the population mean of light bulbs in this batch

(325.5 ,374.5)

b)

The calculated value Z = 4 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The manufacturer has not right to take the average life of the light bulbs is 400 hours.

Step-by-step explanation:

Given sample size n = 64

Given mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

The tabulated value Z₀.₉₅ = 1.96

95% confidence intervals for the population mean of light bulbs in this batch

$(x^{-} - Z_{\frac{\alpha }{2} } \frac{S.D}{\sqrt{n} } , x^{-} + Z_{\frac{\alpha }{2} }\frac{S.D}{\sqrt{n} } )$

$(350 - 1.96\frac{100}{\sqrt{64} } , 350 + 1.96\frac{100}{\sqrt{64} } )$

$(350 -24.5, 350 +24.5)$

(325.5 ,374.5)

b)

Explanation:-

Given mean of the Population μ = 400

Given sample size n = 64

Given mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

Null hypothesis : H₀:The manufacturer has right to take the average life of the light bulbs is 400 hours.

μ = 400

Alternative Hypothesis: H₁: μ ≠400

The test statistic

$Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }$

$Z = \frac{350 -400}{\frac{100}{\sqrt{64} } }$

|Z| = |-4|

The tabulated value Z₀.₉₅ = 1.96

The calculated value Z = 4 > 1.96 at 0.05 level of significance

Null hypothesis is rejected.

Conclusion:-

The manufacturer has not right to take the average life of the light bulbs is 400 hours.

5 0

2 years ago

A price was increasing at a rate of 15% per month what is the annual growth rate enter your answer rounded to the nearest tenth

Leokris [45]

Hello there! I can help you! The formula for finding the annual growth rate is (1 + r)^t. In other words, you add the rate in decimal form from 1 and raise it to the t power, depending on how many times it is compounded. 15% is 0.15 in decimal form. 1 + 0.15 is 1.15. We have that number. Now, we are looking for the annual growth rate. It increases monthly, annual has to do with 1 year, and there are 12 months in 1 year. Now, let's raise 1.15 to the 12th power. 1.15^12 is 5.350250105. Don't delete it. We can subtract 1 from that number to get 4.350250105. Now, let's multiply it by 100 to get the answer in percent form. When you do, you get 435.0250105 or 435 when rounded to the nearest tenth, because there is a 0 in the tenths place. We can subtract There. The annual growth rate is about 435%.

7 0

1 year ago

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