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Remember: SOH-CAH-TOA

Sine (of an angle!) = opposite / hypotenuse

We're looking at angle M here, to find the sine of M. Looking from angle M, the side that is opposite is NO and the hypotenuse is MO.

sin(M) = NO / MO = NO / 13

We do not know NO, but we can use the Pythagorean theorem to find NO because this is a right triangle.

Pythagorean theorem: a^2 + b^2 = c^2

---a and b are legs of the triangle, c is the hypotenuse

12^2 + b^2 = 13^2

144 + b^2 = 169

b^2 = 25

b = 5

NO = 5

sin(M) = NO / MO = 5 / 13

Answer: sin(M) = 5 / 13

Hope this helps!

Answer:

17.3

Step-by-step explanation:

50 - 32.7 = 17.3

Answer:

[tex]m\angle C=47.07^\circ[/tex]

Step-by-step explanation:

Law of Sines

[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]

Determine angle C given angle A and side "a"

[tex]\frac{sin(118^\circ)}{41}=\frac{sinC}{34}\\ \\34sin(118^\circ)=41sinC\\\\\frac{34sin(118^\circ)}{41}=sinC\\\\C=sin^{-1}(\frac{34sin(118^\circ)}{41})\\\\C\approx47.07^\circ[/tex]

Therefore, [tex]m\angle C=47.07^\circ[/tex]

Answer:

y = - 2x + 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ )  = (1, 4 ) and (x₂, y₂ ) = (2, 2 )

m = [tex]\frac{2-4}{2-1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 2 ) , then

2 = - 4 + c ⇒ c = 2 + 4 = 6

y = - 2x + 6 ← equation of line

Answer:

1/12

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

The answer is B. 16-30!

Step-by-step explanation:

Answer:

1 hour

Step-by-step explanation:

If he totals 5 hours total, and Monday is 2 hours, that would make 3 hours left. So there is 3 hours, and 3 days, which can be simplified to 1 hour in 1 day

Answer:

p = [tex]\frac{3}{32}[/tex]

Step-by-step explanation:

[tex]\frac{\frac{3}{10} }{p}[/tex] = [tex]\frac{\frac{4}{5} }{\frac{1}{4} }[/tex] ( cross- multiply )

[tex]\frac{4}{5}[/tex] p = [tex]\frac{3}{10}[/tex] × [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{40}[/tex]

Multiply both sides by [tex]\frac{5}{4}[/tex] to clear the fraction on left side

p = [tex]\frac{5}{4}[/tex] × [tex]\frac{3}{40}[/tex] = [tex]\frac{1}{4}[/tex] × [tex]\frac{3}{8}[/tex] = [tex]\frac{3}{32}[/tex]

Answer:

2 weekend days and 4 weekday days

Step-by-step explanation:

12 x 2 = 24

7 x 4 = 28

28 + 24 = 52

Answer:

b= (-6,-7)

c= (-6,-2)

d= (0,-2)

e= (4,-7)

Step-by-step explanation:

Answer:

3 groups of 17, or 7-17 groups of 3

Step-by-step explanation:

52 - 1 = 51

3(17) = 51

Answer:

Dee divided her bears into 3 groups of 17 bears, OR 17 groups of 3 bears

Step-by-step explanation:

If Dee had 1 bear left over after she divided her collection, then the number of bears in the groups = 52 - 1 = 51

To find the groups, we need to find the factors of 51.

(a factor is a number that divides another number evenly, with no remainder)

As 51 is an odd number, we can say that all multiples of 2 (even numbers) cannot be a factor.

Factors of 51:

1 and 51

3 and 17

We are told that Dee divided her collection into equal groups (not one group), so we can discard 1 and 51.  Therefore, Dee divided her bears into 3 groups of 17 bears, OR 17 groups of 3 bears (both solutions are correct)

Answer: x=18

Step-by-step explanation:Based on the given conditions, formulate: 122.5+61.5 times x =2331.5

Rearrange unknown terms to the left side of the equation:

Calculate the sum or difference:61.5x=1107

Divide both sides of the equation by the coefficient of variable: x=1107 divided by 61.5

Calculate the product or quotient:x=18

get the result:x=18

Answer:

140ft.^2

Step-by-step explanation:

3.5 x 4 = 14 (the width)

2.5 x 4 = 10 (the length)

- to find the area of the rectangle, you multiply the width and length

14 x 10 = 140

if you need a more detailed explanation i am free to give one!!

Answer:

B)34

Step-by-step explanation:

9+3=12

12+4=16

16+6=22           6+6=12

22+12=34         12+12=24

34+24=58

Answer:

25508

Step-by-step explanation:

Answer:

25508

Step-by-step explanation:

100 x 256 - 468 + 376

100 x 256 = 25600

25600-468= 25132

25132+376 = 25508

Answer:

Given below.

Step-by-step explanation:

1) Hypotenuse

2) Using Pythagoras theorem:

              35² + 12² = c²

                c = √1225+144

                c = √1369

                 c = 37  ....this is the length of missing side.

Here given that opposite is 35 , adjacent is 12 , hypotenuse is 37.

3) sin(θ) = opposite/hypotenuse

   sin(θ) = 35/37

4) cos(θ) = adjacent/ hypotenuse

    cos(θ) = 12/37

5) tan(θ) = opposite/adjacent

      tan(θ) = 35/12

#1

#2

Apply Pythagorean theorem

[tex]\\ \tt\hookrightarrow H^2=25^2+12^2=1225+144=1369[/tex]

[tex]\\ \tt\hookrightarrow H=37[/tex]

#3

[tex]\\ \tt\hookrightarrow Sin\theta=\dfrac{35}{37}[/tex]

#4

[tex]\\ \tt\hookrightarrow cos\theta=\dfrac{12}{37}[/tex]

#5

[tex]\\ \tt\hookrightarrow tan\theta=\dfrac{35}{12}[/tex]

Answer:

  $2076.30

Step-by-step explanation:

In the n-th year, the rent will be ...

  an = a1·r^(n-1) . . . . . . . . . r is the year on year ratio: 1+rate of increase

  an = 1100·(1.095^(n-1))

Then the rent in the 8th year is ...

  a8 = 1100·(1.095^(8-1)) ≈ 2076.30

The rent in the 8th year would be $2076.30.

The rent of the apartment during the 8th year of living would be approximately $2233.9.

To find the rent of the apartment during the 8th year, we need to calculate the rent for each year and then apply the 9.5% increase for 7 years (since we start from the first year).

Given that the initial rent is $1100, and the rent increases by 9.5% per year, the formula for the rent in the nth year can be expressed as:

Rentₙ = Initial Rent * (1 + Rate)ⁿ

Where:

Initial Rent = $1100

Rate = 9.5% = 0.095 (decimal form)

n = year number

For the 8th year (n = 8):

Rent₈ = 1100 * (1 + 0.095)⁸

Rent₈ = 1100 * 2.03079945171

Rent₈ ≈ 2233.87939688

Rounding to the nearest tenth:

Rent₈ ≈ $2233.9

So, the rent of the apartment during the 8th year of living would be approximately $2233.9.

To know more about initial rent:

https://brainly.com/question/898897

#SPJ3

The range is (0-5) and the mean is 2.1.

Mean is simply defined as the average of the given set of numbers. The mean is considered as one of the measures of central tendencies in statistics. The mean is said to be an arithmetic mean. It is the ratio of the sum of the observation to the total number of observations.

Given

Summer Camp Attendance 3, 1 ,0 ,4 ,1 ,4, 2, 3, 0, 5, 0, 1, 1, 2 , 0, 4, 1, 4, 4, 2, 3, 2, 0, 1, 4.

The range of the values for the sample means.

Range = Minimum to Maximum

Range = [0 and 5]

Mean is given by

[tex]\rm Mean = \dfrac{sum\ of\ the\ observation}{number\ of\ the\ observation}[/tex]

Then the mean will be

[tex]\rm Mean = \dfrac{ 3+1+4+1+4+2+3+5+1+1+2+4+1+4+4+2+3+1+4 }{25}\\\\Mean = \dfrac{52}{25}\\\\Mean = 2.08 \approx 2.1[/tex]

Thus the range is (0-5) and the mean is 2.1.

More about the mean link is given below.

https://brainly.com/question/12322912

Answer:

Step-by-step explanation:

2 on edge

Answer:

1. Make imporper franctions: 2 1/2 = 5/2    1 2/5 = 7/5

2. Find common denominater: using 10

5/2 =  25/10       7/5 = 14/10

3. Simplify.

25/10 -  14/10 = 11/10

=  1 1/10

Step-by-step explanation:

11 4/10

eleven and four tenths

i hope this is correct.

Answer:

11 4/10

Step-by-step explanation:

first you have to plus 4+6-=10 and then add 6/10 + 8/10=14/10, 14/10 is a improper fraction, 14/10=11 4/10

Answer

20 would be $30

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

Answer:

$7.45

Step-by-step explanation:

If it's constant , divide the amount he earns by the amount of hours. It should be the same every time.

44.70 divided by 6=7.45

and so on

rate of change is slope:-

[tex]\\ \tt\hookrightarrow m=\dfrac{59.60-44.70}{8-6}[/tex]

[tex]\\ \tt\hookrightarrow m=\dfrac{14.9}{2}=7.45[/tex]

He is wrong

Answer:

1) 64 yd²    2) 3801.3 mm³    3)  56.55 ft³

Step-by-step explanation:

Surface area of rectangular prism: Area =2(wl+hl+hw)

                                                                  = 2(4*2+4*2+4*4)

                                                                   = 64 yd²

Volume of cylinder = πr²h

                                = π*11²*10

                                = 1210π or 3801.3 mm³

Volume of cone = [tex]\frac{1}{3} \pi r^{2}h[/tex]

                           = 1/3 *π*3²*6

                           = 18π or 56.55 ft³

Answer:

Below!

Step-by-step explanation:

We know that:

Solution (Surface area of rectangular prism):

Solution (Volume of cylinder):

Solution (Volume of cone):

Answer:

75

Step-by-step explanation:

Answer:

2077.875

Step-by-step explanation: