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3 years ago

Each side of an equilateral triangle measures 30cm. Find the length of an altitude, a , of the triangle?

Mathematics

1 answer:

Archy [21]3 years ago

6 0

Answer:

$X=25.98cm$

Step-by-step explanation:

From the question we are told that:

Length of each side $l=30cm$

Let the triangle be divide by two form a right angle triangle with base angles as $90 \textdegree$ (angle of perpendicularity) and $60 \textdegree$ (angle on each vertices of an equilateral triangle)

Generally the equation for the Altitude X is mathematically given by

Trigonometric Rule

$X=30sin60$

$X=15\sqrt{3}$

$X=25.98cm$

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the height of a cone-shaped statue is 9ft, and the diameter is 12 ft. what is the approximate volume of the statue? Use 3.14 to

Lady bird [3.3K]

Answer:

1017.36

Step-by-step explanation:

9times 36=324

324 times pi =1017.36

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3 years ago

Read 2 more answers

Hi .. I really need help on this one

IgorLugansk [536]

Answer:

LCM of 3 and 2 is 6

so, firstly we had to make the denominator same:-

$\frac{2(2a + 1) + 3(3a - 1)} {6}$

$\frac{4a + 2 + 9a - 3}{6}$

$\frac{13a - 1}{6}$

Step-by-step explanation:

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2 years ago

Pls help if you actually can

Setler79 [48]

The triangles that are similar would be ΔGCB and ΔPEB due to Angle, Angle, Angle similarity theorem.

<h3>How to identify similar triangles?</h3>

From the image attached, we see that we are given the Parallelogram GRPC. Thus;

A. The triangles that are similar would be ΔGCB and ΔPEB due to Angle, Angle, Angle similarity theorem.

B. The proof of the fact that ΔGCB and ΔPEB are similar pairs of triangles is as follow;

∠CGB ≅ ∠PEB (Alternate Interior Angles)

∠BPE ≅ ∠BCG (Alternate Interior Angles)

∠GBC ≅ ∠EBP (Vertical Angles)

C. To find the distance from B to E and from P to E, we will first find PE and then BE by proportion;

225/325 = PE/375

PE = 260 ft

BE/425 = 225/325

BE = 294 ft

Read more about Similar Triangles at; brainly.com/question/14285697

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5 0

2 years ago

How many times must we toss a coin to ensure that a 0.95-confidence interval for the probability of heads on a single toss has l

musickatia [10]

Answer:

(1) 97

(2) 385

(3) 9604

Step-by-step explanation:

The (1 - α) % confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The margin of error in this interval is:

$MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The formula to compute the sample size is:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}$

(1)

Given:

$\hat p = 0.50\\MOE=0.1\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use the z-table for the critical value.

Compute the value of n as follows:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.1^{2}}\\=96.04\\\approx97$

Thus, the minimum sample size required is 97.

(2)

Given:

$\hat p = 0.50\\MOE=0.05\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use the z-table for the critical value.

Compute the value of n as follows:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.05^{2}}\\=384.16\\\approx385$

Thus, the minimum sample size required is 385.

(3)

Given:

$\hat p = 0.50\\MOE=0.01\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use the z-table for the critical value.

Compute the value of n as follows:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.01^{2}}\\=9604$

Thus, the minimum sample size required is 9604.

8 0

3 years ago

The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.372 minute. The winning ca

Fed [463]

Answer:

Sam had a finish time with a z-score of -2.93.

Karen had a finish time with a z-score -1.91.

Sam had the more convincing victory.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Sam:

The mean finish time for a yearly amateur auto race was 186.94 minutes with a standard deviation of 0.372 minute. The winning car, driven by Sam, finished in 185.85 minutes.

So $\mu = 186.94, \mu = 0.372, X = 185.85$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{185.85 - 186.94}{0.372}$

$Z = -2.93$

Sam finishing time was 2.93 standard deviations below the mean.

Sam had a finish time with a z-score of -2.93.

Karen:

The previous year's race had a mean finishing time of 110.7 with a standard deviation of 0.115 minute. The winning car that year, driven by Karen, finished in 110.48 minutes.

So $\mu = 110.7, \sigma = 0.115, X = 110.48$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{110.48 - 110.7}{0.115}$

$Z = -1.91$

Karen finishing time was 1.91 standard deviations below the mean.

Karen had a finish time with a z-score -1.91.

Who had the more convincing victory?

Sam finishing time was 2.93 standard deviations below the mean.

Karen finishing time was 1.91 standard deviations below the mean.

Sam finished more standard deviations below the mean than Karen, that is, he was faster relative to his competition than Karen.

So Sam had the more convincing victory.

8 0

3 years ago