What is the value of sin(−θ) ?Let cos(−θ)=−3/5 and tanθ>0 .

A. -4/5
B. 4/3
C. -3/5
D. 4/5


Answer 1



Step-by-step explanation:

The cosine of a right triangle is the adjacent over the hypotenuse. If the cosine is -3/5 then it must be a right triangle with sides 3, 4, & 5 since this is a Pythagorean triple. This means the sin will be -4/5. We know its negative because the tangent is positive so this is the 3rd quadrant where both Sine and Cosine are negative.

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A local doctor’s office logged the number of patients seen in one day by the doctor for ten days. Find the means, median, range, and midrange of the patients seem in 10 days. 27 31 27 35 35 25 28 35 33 24



Mean = 30, Median = 29.5, Range = 9 and Mid-range = 29.5.

Step-by-step explanation:

We are given that a local doctor’s office logged the number of patients seen in one day by the doctor for ten days.

Arranging the given data in ascending order we get;

24, 25, 27, 27, 28, 31, 33, 35, 35, 35.

(a) Mean is calculated by using the following formula;

         Mean, \bar X  =  \frac{\text{Sum of all values}}{\text{Total number of observations}}

                          =  (27+ 31+ 27+ 35+ 35+ 25+ 28+ 35+ 33+ 24)/(10)

                          =  (300)/(10)  = 30

So, the mean of the given data is 30.

(b) For calculating the median, we have to first have to observe that the number of observations (n) in the data is even or odd.

  • If n is odd, then the formula for calculating median is given by;

                     Median  =  ((n+1)/(2))^(th) \text{ obs.}

  • If n is even, then the formula for calculating median is given by;

                     Median  =  \frac{((n)/(2))^(th) \text{ obs.}+ ((n)/(2)+1)^(th) \text{ obs.} }{2}

Here, the number of observations is even, i.e. n = 10.

So,  Median  =  \frac{((n)/(2))^(th) \text{ obs.}+ ((n)/(2)+1)^(th) \text{ obs.} }{2}

                     =  \frac{((10)/(2))^(th) \text{ obs.}+ ((10)/(2)+1)^(th) \text{ obs.} }{2}

                     =  \frac{(5)^(th) \text{ obs.}+ (6)^(th) \text{ obs.} }{2}

                     =  (28+31)/(2)

                     =  (59)/(2)  =  29.5

So, the median of the data is 29.5.

(c) The range of the data is given by = Highest value - Lowest value

                                                        = 35 - 24 = 9

So, the range of the data is 9.

(d) Mid-range of the data is given by the following formula;

                   Mid-range  =  \frac{\text{Highest value}+\text{Lowest value}}{2}

                                      =  (35+24)/(2) = 29.5

Final answer:

The mean of the patients seen in 10 days is 30, the median is 29.5, the range is 11, and the midrange is 29.5.


To find the mean, median, range, and midrange of the numbers, we first need to understand what these terms mean. The mean is the average, the median is the middle number in a sorted set, the range is the difference between the highest and lowest values, and the midrange is the average of the highest and lowest values.

First, let's sort the numbers: 24 25 27 27 28 31 33 35 35 35.

To calculate the mean, add all the numbers and divide by the count (10): (24+25+27+27+28+31+33+35+35+35)/10 = 30.

The median is the average of the two middle numbers (which are 28 and 31 in this case): (28 + 31) / 2 = 29.5.

The range is the highest number minus the lowest number: 35 - 24 = 11.

The midrange is the average of the highest and lowest values: (35 + 24) / 2 = 29.5.

Learn more about Mean, Median, Range



WILL GIVE BRAINLIESTThe graph below represents which system of inequalities? (attachment below)

A. y ≤ −2x + 3
y ≤ x + 3

B. y ≥ −2x + 3
y ≥ x + 3

C. y ≤ −3x + 2
y ≤ −x + 2

D. y > −2x + 3
y > x + 3


The answer is A.
We can first eliminate D since it uses these (<, >) signs and the lines are shaded, indicating the points on those lines are solutions.
We can also eliminate C because the y intercept in C’s lines is 2, while in the graph, they are both 3.
Finally, we can look at both inequalities on the graph and see that the shaded areas are both underneath the line. This means that y is less than the equation for the line, eliminating B
So, the answer is A
Hope this made sense!!

if a line with an angle of inclination 120⁰ and passes trough (√3,1),then what is the equation of a line​



The equation of a line, having inclination 120° with positive direction of x-axis, .of x-axis, which is at a distance of 3 units from the origin is​. 1. See answer ... where α is the angle with the positive X-axis, made by the perpendicular line drawn Now, from equation  the equation of the straight line will be.

Step-by-step explanation:

Find the area of the combined figure. A figure is made up of a triangle and a rectangle. The triangle has a height of 8.5 inches and a base of 10 inches. The rectangle has dimensions of 9 inches x 10 inches. What is the area of the figure? a 102.5 square inches b 132.5 square inches C 110.2 square inches d 140.2 square inches​




Step-by-step explanation:

for the triangle 8.5 * 10 / 2 = 42.5

the rectangle 9 * 10 = 90

42.5 + 90 = 132.5

The sum of x and -15 is 23


Answer: x=38

Step-by-step explanation:



+15  +15


When there is a positive and negative sign the negative sign cancels the positive sign.



Step-by-step explanation:

23+15=38 because in order to get 23 from -15 a negative number you need to have 38 to silence the -15.

Find the measure of angle b ​



49 degrees

Step-by-step explanation:

You just subtract 41 degrees from 90 degrees because it's a right angle.