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7nadin3 [17]
2 years ago
10

The ratio of math teachers to choir teachers is 3:2 respectively. There are 12 math teachers. How many math and choir teachers a

re there all together?
Mathematics
2 answers:
marysya [2.9K]2 years ago
8 0

Answer:

30

Step-by-step explanation:

3 + 2 = 5 \\  \frac{2}{5}  \times x = 12 \\   \\  \frac{2x}{5}   = 12 \\ cross \: mutiply \\ 2x = 60 \\ divde \:both \: sides \: by \: 2 \\ x = 30

IrinaK [193]2 years ago
8 0

Answer:

30

Step-by-step explanation:

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A car is traveling at a steady speed. It travels 2 1/2 miles in 3 1/3 minutes. How far will it travel in 45 minutes ?
Oksana_A [137]

Answer: The car will travel 30 2/3 miles in 45 minutes.

7 0
2 years ago
Read 2 more answers
Can someone help (Its a photo) ill give brain list
Savatey [412]

Answer:

this is the order

-14/5, -11/5, -3/2, -2/3, 6/5, 4/2, 11/5, 16/5

8 0
3 years ago
Use the given information to find (a) sin(s+t), (b) tan(s+t), and (c) the quadrant of s+t. cos s = - 12/13 and sin t = 4/5, s an
Anton [14]

Answer:

Part a) sin(s + t) =-\frac{63}{65}    

Part b) tan(s + t) = -\frac{63}{16}

Part c) (s+t) lie on Quadrant IV

Step-by-step explanation:

[Part a) Find sin(s+t)

we know that

sin(s + t) = sin(s) cos(t) + sin(t)cos(s)

step 1

Find sin(s)

sin^{2}(s)+cos^{2}(s)=1

we have

cos(s)=-\frac{12}{13}

substitute

sin^{2}(s)+(-\frac{12}{13})^{2}=1

sin^{2}(s)+(\frac{144}{169})=1

sin^{2}(s)=1-(\frac{144}{169})

sin^{2}(s)=(\frac{25}{169})

sin(s)=\frac{5}{13} ---> is positive because s lie on II Quadrant

step 2

Find cos(t)

sin^{2}(t)+cos^{2}(t)=1

we have

sin(t)=\frac{4}{5}

substitute

(\frac{4}{5})^{2}+cos^{2}(t)=1

(\frac{16}{25})+cos^{2}(t)=1

cos^{2}(t)=1-(\frac{16}{25})

cos^{2}(t)=\frac{9}{25}

cos(t)=-\frac{3}{5} is negative because t lie on II Quadrant

step 3

Find sin(s+t)

sin(s + t) = sin(s) cos(t) + sin(t)cos(s)

we have

sin(s)=\frac{5}{13}

cos(t)=-\frac{3}{5}

sin(t)=\frac{4}{5}

cos(s)=-\frac{12}{13}

substitute the values

sin(s + t) = (\frac{5}{13})(-\frac{3}{5}) + (\frac{4}{5})(-\frac{12}{13})

sin(s + t) = -(\frac{15}{65}) -(\frac{48}{65})

sin(s + t) =-\frac{63}{65}

Part b) Find tan(s+t)

we know that

tex]tan(s + t) = (tan(s) + tan(t))/(1 - tan(s)tan(t))[/tex]

we have

sin(s)=\frac{5}{13}

cos(t)=-\frac{3}{5}

sin(t)=\frac{4}{5}

cos(s)=-\frac{12}{13}

step 1

Find tan(s)

tan(s)=sin(s)/cos(s)

substitute

tan(s)=(\frac{5}{13})/(-\frac{12}{13})=-\frac{5}{12}

step 2

Find tan(t)

tan(t)=sin(t)/cos(t)

substitute

tan(t)=(\frac{4}{5})/(-\frac{3}{5})=-\frac{4}{3}

step 3

Find tan(s+t)

tan(s + t) = (tan(s) + tan(t))/(1 - tan(s)tan(t))

substitute the values

tan(s + t) = (-\frac{5}{12} -\frac{4}{3})/(1 - (-\frac{5}{12})(-\frac{4}{3}))

tan(s + t) = (-\frac{21}{12})/(1 - \frac{20}{36})

tan(s + t) = (-\frac{21}{12})/(\frac{16}{36})

tan(s + t) = -\frac{63}{16}

Part c) Quadrant of s+t

we know that

sin(s + t) =negative  ----> (s+t) could be in III or IV quadrant

tan(s + t) =negative ----> (s+t) could be in III or IV quadrant

Find the value of cos(s+t)

cos(s+t) = cos(s) cos(t) -sin (s) sin(t)

we have

sin(s)=\frac{5}{13}

cos(t)=-\frac{3}{5}

sin(t)=\frac{4}{5}

cos(s)=-\frac{12}{13}

substitute

cos(s+t) = (-\frac{12}{13})(-\frac{3}{5})-(\frac{5}{13})(\frac{4}{5})

cos(s+t) = (\frac{36}{65})-(\frac{20}{65})

cos(s+t) =\frac{16}{65}

we have that

cos(s+t)=positive -----> (s+t) could be in I or IV quadrant

sin(s + t) =negative  ----> (s+t) could be in III or IV quadrant

tan(s + t) =negative ----> (s+t) could be in III or IV quadrant

therefore

(s+t) lie on Quadrant IV

4 0
3 years ago
You earn 60 dollars for mowing 5 lawns how much do you earn for mowing 15 lawns
Nookie1986 [14]

well 60/5=12

so you get $12 per yard

12*15=180

or you could notice that 5 goes into 15 3 times and then multiply 60*3 any way the answer is 180

4 0
3 years ago
Read 2 more answers
Denzel earned $8.50 moving along and six dollars raking the leaves. How much total money did he earn
Stels [109]

Answer:

$14.50

Step-by-step explanation:

8.50+6= 14.50

7 0
2 years ago
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