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3 years ago

If one of the acute angles of a right angled triangle is 55 , calculate the remaining angle

Mathematics

1 answer:

lions [1.4K]3 years ago

8 0

Answer:

35 degrees

Step-by-step explanation:

To start off, the term "acute angle" means less than 90 degrees. In this case, the acute angle is 55 degrees.

The type of triangle mentioned in the question is a right-angled triangle, meaning it has a right triangle (90 degrees) along 2 other triangles. A triangle is generally 180 degrees. So now that we know the value of 2 out of 3 angles we do simple math.

Assume the unknown angle is A.

55 + 90 + A = 180

A = 35

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7. These values represent the expected number of paintings a person will produce over the next 10 days. 0, 0, 0, 1, 1, 1, 2, 2,

Natasha_Volkova [10]

The mean of a dataset is the average of the dataset.

The mean is 1.5
The standard deviation is 1.58
The median remains unchanged, the mean increases, and the standard deviation decreases when 5 is increased to a larger value

The given parameters are:

$\mathbf{x = 0, 0, 0, 1, 1, 1, 2, 2, 3, 5}$

(a) Mean and Standard deviation

The mean of the dataset is calculated using:

$\mathbf{\bar x = \frac{\sum x}{n}}$

So, we have:

$\mathbf{\bar x = \frac{0+ 0+ 0+ 1+ 1+ 1+ 2+ 2+ 3+ 5}{10}}$

$\mathbf{\bar x = \frac{15}{10}}$

$\mathbf{\bar x = 1.5}$

Hence, the mean is 1.5

The standard deviation is calculated using:

$\mathbf{\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n - 1}}}}$

So, we have:

$\mathbf{\sigma_x = \sqrt{\frac{(0 - 1.5)^2 + (0- 1.5)^2 + (0- 1.5)^2 + (1- 1.5)^2 + (1- 1.5)^2 + (1- 1.5)^2 + (2- 1.5)^2 + (2- 1.5)^2 + (3- 1.5)^2 + (5- 1.5)^2}{10 - 1}}}$

$\mathbf{\sigma_x = \sqrt{\frac{22.5}{9}}}$

$\mathbf{\sigma_x = \sqrt{2.5}}$

$\mathbf{\sigma_x = 1.58}$

Hence, the standard deviation is 1.58

(b) When 5 is increased to a larger value

When 5 is increased:

The median remains unchanged
The mean increases
The standard deviation decreases

Read more about median, mean, and standard deviation at:

brainly.com/question/12598273

3 0

2 years ago

How many minutes did it take for sammi to finish the race ?

Elina [12.6K]

Answer:

Step-by-step explanation:

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4 0

3 years ago

PLEASE HELP!!! very confused

Leni [432]

Answer:

Step-by-step explanation:

The vertices lie on the x-axis, as is determined by their coordinates. This makes the center of this hyperbola (0, 0) because the center is directly between the vertices. The fact that the foci also lie on the x-axis tells us that this is the main axis. What this also tells us is which way the hyperbola "opens". This one opens to the left and the right as opposed to up and down. The standard form for this hyperbola is:

$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$ and so far we have that h = 0 and k = 0.

By definition, a is the distance between the center and the vertices. So a = 5, and a-squared is 25. So we're getting there. Now here's the tricky part.

The expressions for the foci are (h-c, k) and (h+c, k). Since we know the foci lie at +/-13, we can use that to solve for c:

If h+c = 13 and h = 0, then

0 + c = 13 and c = 13.

We need that c value to help us find b:

$c^2=a^2+b^2$ and

$13^2=5^2+b^2$ and

$169=25+b^2$ and

$144=b^2$ so

b = 12. Now we're ready to fill in the equation:

$\frac{x^2}{25}-\frac{y^2}{144}=1$ and there you go!

3 0

2 years ago

The price of an item has risen to $ 299 today. Yesterday it was $130.

hoa [83]

Answer:

It has risen by $169

Step-by-step explanation:

299

130

----------

169

7 0

2 years ago

The average cost of living for a family of four in twelve different cities was found to be $65,351 with a standard deviation of

Andrej [43]

Answer:

$65,351+/-$3,661.73

= ( $61,689.27, $69,012.73)

Therefore, the 90% confidence interval (a,b) = ( $61,689.27, $69,012.73)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $65,351

Standard deviation r = $7,711

Number of samples n = 12

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

$65,351+/-1.645($7,711/√12)

$65,351+/-1.645($2,225.973962860)

$65,351+/-$3661.727168905

$65,351+/-$3,661.73

= ( $61,689.27, $69,012.73)

Therefore, the 90% confidence interval (a,b) = ( $61,689.27, $69,012.73)

6 0

3 years ago

If one of the acute angles of a right angled triangle is 55 , calculate the remaining angle​

If one of the acute angles of a right angled triangle is 55 , calculate the remaining angle