Consider right angle triangle ABC, right angled at B. If AC=17 units and BC+8 units determine all the trigonometric ratios of angle C

Answer:

64

Step-by-step explanation:

Answer:

225

Step-by-step explanation:

All you have to do is plug in the numbers, it will look like this

(2(2)^2 * -1^3)^2

It looks weird but trust me

Ok so first you have to mutiply 2*2 whitch is 4

(4^2 * -1^3)^2

now what is the 1 with the exponet of 3? It will stay at -1

(4^2 * -1) ^2

what is 4^2? it is the same a 4*4

whitch is 16

(16-1)^2

16-1?

(15)^2, same thing as 15*15

whitch is 225

makingn 255 your answer

The height of a TV screen with a diagonal length of 156cm and an angle of 37 degrees in the top corner can be calculated using trigonometry. The height is approximately 109.5cm.

To find the height of the TV screen, we can use the properties of a right triangle and trigonometry. In this case, the diagonal of the TV screen forms the hypotenuse of the right triangle, and the angle in the top corner is given as 37 degrees.

Let's label the height of the TV screen as "h" and the length of the diagonal as "d." According to trigonometry, the sine of an angle is equal to the opposite side divided by the hypotenuse. In this case, the opposite side is the height (h) and the hypotenuse is the diagonal (d). Therefore, we can set up the equation: sin(37 degrees) = h/d.

We can rearrange this equation to solve for the height: h = d * sin(37 degrees). Plugging in the given diagonal length of 156cm and the angle of 37 degrees, we get: h = 156cm * sin(37 degrees). Using a calculator, we find that sin(37 degrees) is approximately 0.6018. Multiplying this value by the diagonal length, we find that the height of the TV screen is approximately 109.5cm.

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Answer: To find the equation of a line passing through two points, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1, y1) are the coordinates of one of the points, and m is the slope of the line.

To find the slope, we can use the formula:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

So, let's plug in the values we have:

m = (-8 - 3)/(-8 - (-10)) = (-8 - 3)/2 = -11/2

Now we can use either point to find the equation. Let's use (-10, 3):

y - 3 = (-11/2)(x - (-10))

y - 3 = (-11/2)x - 55/2

y = (-11/2)x - 49/2

So the equation of the line through (-10, 3) and (-8, -8) is:

y = (-11/2)x - 49/2.

We would expect to find the middle 68% of the average amounts of nicotine in a sample of size 41 to be between approximately 0.901 g and 0.991 g by using properties of the normal distribution.

To find the range in which you would expect to find the middle 68% of amounts of nicotine in these cigarettes, we can use the properties of the normal distribution.

Given:
Mean (μ) = 0.946 g
Standard deviation (σ) = 0.289 g

For a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Therefore, we can expect the middle 68% of amounts of nicotine to fall within the range:

μ ± σ

Substituting the given values:

0.946 ± 0.289

To calculate the range, we have:

Lower bound = 0.946 - 0.289 ≈ 0.657 g
Upper bound = 0.946 + 0.289 ≈ 1.235 g

Therefore, we can expect to find the middle 68% of amounts of nicotine in these cigarettes to be between approximately 0.657 g and 1.235 g.

Now, if we were to draw samples of size 41 from this population, the standard deviation of the sample mean (also known as the standard error) can be calculated as:

Standard error (SE) = σ / √n

where σ is the population standard deviation and n is the sample size.

Substituting the given values:

SE = 0.289 / √41 ≈ 0.045 g

To find the range in which we would expect to find the middle 68% of the sample means, we multiply the standard error by 1 to capture approximately 68% of the data, giving us:

Lower bound = μ - SE ≈ 0.946 - 0.045 ≈ 0.901 g
Upper bound = μ + SE ≈ 0.946 + 0.045 ≈ 0.991 g

Therefore, we would expect to find the middle 68% of the average amounts of nicotine in a sample of size 41 to be between approximately 0.901 g and 0.991 g.

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The sum of all the angles of a triangle is equal to 180°. The value of x is 12.

The sum of all the angles of a triangle is equal to 180°.

The Exterior Angle is the angle formed by either of a shape's sides and a line drawn from the opposite side.

We know that in a triangle the sum of the exterior angle and the interior angle is 180°. Therefore, the following angles of the triangle can be written as,

\(\angle H=180-(9x+6)\)

\(\angle G=180-(10x-1)\)

\(\angle J=180-(10x+7)\)

Now, the sum of all the angles of the triangle is 180°, therefore, the sum can be written as,

\(\angle H+\angle G+\angle J=180^o\\\\180-(9x+6) + 180-(10x-1) + 180-(10x+7) = 180\\\\540-(9x+6)-(10x-1)-(10x+7)=180\\\\540-180 = (9x+6)+(10x-1)+(10x+7)\\\\360=9x+6+10x-1+10x+7\\\\360=29x+12\\\\360-12=27x\\\\x = 12\)

Hence, the value of x is 12.

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Answer:

12

Step-by-step explanation:

According to the problem the mass of the prism is 207.875 g.

The measure of an object's matter content is its mass. It is typically measured in kilograms, grams, pounds, or ounces. Mass is related to weight, which is the measure of the force of gravity on an object, but the two terms are not interchangeable.

The mass of the prism can be calculated using the formula mass = density x volume. To calculate the volume of the prism, we can first calculate the area of the faces using the formula area = length x width. The area of the faces of the prism is 7.8 cm x 2.5 cm = 19.5 cm2. The volume of the prism is the area of the faces multiplied by the height, which is 2.5 cm. The volume of the prism is then 19.5 cm2 x 2.5 cm = 48.75 cm3. The mass of the prism is then density x volume, which is 4.3 g/cm3 x 48.75 cm3 = 207.875 g. Therefore, the mass of the prism is 207.875 g.

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Answer:

false

Step-by-step explanation:

Hope it helps!

Answer:

The missing side is X=4

Step-by-step explanation:

Since the triangles are similar to eachother, they will have the same ratio.

One way to solve is dividing 8 by 2. Since 12 divided by 2 is 6,

we can expect 8 divided by 2 to be the missing side we are looking for.

Hope that helps!

Answer:

x = 4

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{x}{8}\) = \(\frac{6}{12}\) ( cross- multiply )

12x = 48 ( divide both sides by 12 )

x = 4

Answer:

c

Step-by-step explanation:

in order for it to be a triangle the smaller sides have to add up to be greater than the longest side

for a 5+14=19 so that is not a triangle because the  side dont add up to be greater than 19

for b 14+8=22 so that is also not a triangle because the sides dont add up to be greater than 24

for c 5+15=20 so that is a triangle because to 2 shorter sides added are greater than the longest side

for d 14+9=23 so that is not a triangle because the two smaller sides dont add up to be greater than 24

Answer:

it would be A

Step-by-step explanation:

places are capitalized, an the first letter of a sentence is always capitalized

Answer:

2/3 or 0.6

Step-by-step explanation:

\((m)/(3)\times (n)/(2)-:(mn)/(4)\)=2/3

Hope it helped you brainiest plz and thank you!!!!!!!!

Answer:

A. the study had no control group

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

Answer:

20 gallons.

Step-by-step explanation:

The given points (2, 44) and (5, 80) represent two points on the linear function that relates the total amount of water in the pool to the time since Jabari turns on the hose. We can use these points to find the equation of the function in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Using the two given points, we get:

m = (80 - 44) / (5 - 2)

m = 12

To find the y-intercept, we can use the point-slope form of the equation and substitute one of the given points, say (2, 44), for x and y, and the slope we just found for m:

y - y1 = m(x - x1)

y - 44 = 12(x - 2)

y - 44 = 12x - 24

y = 12x + 20

So the equation of the function that relates the total amount of water in the pool to the time since Jabari turns on the hose is:

y = 12x + 20

When Jabari turns on the hose, the time since he turns on the hose is 0 minutes. Substituting a = 0 into the equation we just found, we get:

y = 12(0) + 20

y = 20

Therefore, when Jabari turns on the hose, there is already 20 gallons of water in the pool.

If P, Q and R are the angles of triangle PQR, then cosec((P+R)/2) = sec(Q/2)

Since P, Q and R are the angles of triangle, then they hold the relation

P + Q + R = 180° .....(i)

Rearranging this equation, we get

P + R = 180° - Q ---(ii)

Using the lhs of the equation,

cosec((P+R)/2)

Substituting (P+R) from (ii), we get

cosec((180°-Q)/2)

=> cosec((180/2)°- (Q/2))

=> cosec(90°- (Q/2))

We know that cosec(90°- A) = sec(A). Using this in the above relation, we get

=> sec(Q/2)

which equates to the rhs of the equation given the question.

Therefore, cosec((P+R)/2) = sec(Q/2)

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Answer:

1 1/4 hours=60+15 minutes =75 minutes

hence, 75 divided by 5 = 15 five minutes intervals:)

Ans: 15 five minutes intervals

Answer:

There are 15 five minute intervals

Step-by-step explanation:

60 minutes is 1 hour

1/4 hours is 15 minutes

1 1/4 hour is 60+15 = 75 minutes

75 minutes / 5 minutes =15

There are 15 five minute intervals

The value of x is d. None of above

From the information given, we have that the fraction is;

7/3 + 35 / 18 + 54 / 20  = x

Note that fractions are described as expression used to represent the part of a whole number or a whole variable.

The different types of fractions are;

Find the LCM

420 + 350 + 486 /180 = x

add the values

180x = 1256

Divide the values, we have;

x = 1256/180

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The equation of the line that passes through the point (2, 1) and has a slope of -5/2 is y=(-5/2)*x+6.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=3x+4. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=3 and b=4.

The question gives:

Point : (2,1) , where x=2 and y=1

Slope= -5/2

From the  standard form of the linear equation ( y= mx+b) and the given point and the slope, you can write:

y=mx+b

1=-5/2*(2)+b , thus you can find b.

1=-5+b

-b=-5-1

-b=-6

b=6

If b=6 and m=-5/2, you can write the linear equation:

y=mx+b

y=(-5/2)*x+6

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The equation of line that models this is y = -5/2x + 6

The equation of a line is typically written in slope-intercept form, which is y = mx + b, where m is the slope of the line, and b is the y-intercept.

The slope (m) is a measure of how steep the line is, and it can be calculated using the formula:

y = mx + c

In the given question, the slope is -5/2 and the points are (2, 1)

Substituting the values into the formula of equation of line;

y = mx + c

1 = -5/2(2) + c

1 = -5 + c

c = 1 + 5

c = 6

The equation is y = -5/2 + 6

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Cindy's average tax rate is approximately 13.59%.

To calculate Cindy's average tax rate, we divide the total tax paid by her taxable income and then multiply by 100 to express it as a percentage.

Average tax rate = (Total tax paid / Taxable income) * 100

In this case, Cindy's taxable income is $65,500, and she has calculated that she will owe $8,902 in taxes.

Average tax rate = (8,902 / 65,500) * 100

Average tax rate ≈ 13.59%

Therefore, Cindy's average tax rate is approximately 13.59%.

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Cindy is projecting her earnings to be $90,000, a taxable income of $65,500, and has calculated that she will owe $8,902. Her average tax rate is 13.60%.

How to find the average tax rate?

The average tax rate is determined by dividing the total tax paid by the total income earned. The average tax rate is calculated by dividing the total amount of tax paid by the total taxable income.

Average Tax Rate = Total Tax Paid / Taxable Income Cindy's

The average tax rate can be found as follows:

Average tax rate = (Total tax paid ÷ Taxable income) × 100%

Average tax rate = ($8,902 ÷ $65,500) × 100%

Average tax rate = 0.135994 × 100% ≈ 13.60%

Therefore, Cindy's average tax rate is 13.60%.

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The average burnout time of a large number of bulbs has a sampling distribution that is close to the normal is known as central limit theorem states.

The Population Distribution is a form of a probability distribution that measures the frequency with which the items or variables that make up the population are drawn or expected to be drawn for a given research study.

In statistics, the frequency (or absolute frequency) of an event can be said as the number of times the observation has occurred/recorded in an experiment or study.

Probability in statistics denotes the possibility of the outcome of any random event. The term means to check the extent to which any event is likely to happen.

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Answer:

you would put a full dot on 7 and make an arrow going to the left

Step-by-step explanation:

Answer:

A solid dot over the 8 with the arrow going to the left

Step-by-step explanation:

56/8=7

30 % of the measurements are found below the 30th percentile. 70 % of the measurements are found above the 30th percentile.

Percentile is a comparison score between a particular score and the scores of the rest of a group.  

Percentile = percentage of people who scored below you / Total percentage of  people who gave the exam.

For example, 99 percentile means 99 percentage of people are below the person who scored 99 percentile.

Hence, 30 % of the measurements are found below the 30th percentile and 70 % of the measurements are found above the 30th percentile.

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We can calculate the number of people suffering malnutrition in the world by using the Rule of three:

If 200 is the total population, then 28 suffer from malnutrition.

Then, if the total population is 6.9 billion people, x suffer from malnutrition:

Answer: The number of people of the world's population that suffer from malnutrition is 0.97 billion.

Step-by-step explanation:

I hope this answer is helpful ):

Answer:  \(5\sqrt{5} \ \text{ feet}\)

Work Shown:

\(a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{5^2+10^2}\\\\c = \sqrt{125}\\\\c = \sqrt{25*5}\\\\c = \sqrt{25}*\sqrt{5}\\\\c = 5\sqrt{5}\\\\\)

For more information, search out "pythagorean theorem".

Answer:

2 inches

Step-by-step explanation:

Since his actual height was 4 feet and 2 inches, instead of the estimate of 4 feet, the difference was 2 inches.

This means the error in inches was also 2 inches, since the estimated height was 2 inches lower than the one at the doctor's office.

So, the error is 2 inches