Answers
7.3/2 = 18.25/?
Cross multiply
18.25*2 = 7.3*?
36.5 = 7.3*?
Divide both sides by 7.3
36.5/7.3 = ? (Because 7.3/7.3 is 1 you’re just left with ?)
36.5/7.3 = 5
So 5 hours
Related Questions
Match the following items.
Determine the functions if θ is a first-quadrant angle, and sin = .
1. cosθ √(15)/5
2. tanθ √(10)/2
3. cscθ √(15)/3
4. secθ √6/3
5. cotθ √6/2
Answers
The functions are illustrations of trigonometry ratios
[tex]\mathbf{(a)\ cos\theta = \frac{\sqrt{15}}{5}}[/tex]
The sine of an angle is calculated as follows
[tex]\mathbf{sin\theta = \sqrt{1 - cos^2\theta}}[/tex]
So, we have:
[tex]\mathbf{sin\theta = \sqrt{1 - (\sqrt{15}/5)}}[/tex]
[tex]\mathbf{sin\theta = \sqrt{1 - (15/25)}}[/tex]
Take LCM
[tex]\mathbf{sin\theta = \sqrt{\frac{10}{25}}}[/tex]
[tex]\mathbf{sin\theta = \frac{\sqrt{10}}{5}}[/tex]
[tex]\mathbf{(b)\ tan\theta = \frac{\sqrt{10}}{2}}[/tex]
The tangent of an angle is:
[tex]\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}[/tex]
Using Pythagoras theorem, we have:
[tex]\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}[/tex]
So, we have:
[tex]\mathbf{Hypotenuse^2 = (\sqrt{10})^2 + 2^2}[/tex]
[tex]\mathbf{Hypotenuse^2 = 10 + 4}[/tex]
[tex]\mathbf{Hypotenuse^2 = 14}[/tex]
Take square roots
[tex]\mathbf{Hypotenuse = \sqrt{14}}[/tex]
So, the sine of the angle is:
[tex]\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}[/tex]
[tex]\mathbf{\ sin\theta = \frac{\sqrt{10}}{\sqrt{14}}}[/tex]
Rationalize
[tex]\mathbf{\ sin\theta = \frac{\sqrt{140}}{14}}[/tex]
[tex]\mathbf{(c)\ csc\theta = \frac{\sqrt{15}}{3}}[/tex]
The sine of the angles is:
[tex]\mathbf{sin \theta = \frac{1}{csc\theta}}[/tex]
So, we have:
[tex]\mathbf{sin \theta = \frac{1}{\sqrt{15}/3}}[/tex]
[tex]\mathbf{sin \theta = \frac{3}{\sqrt{15}}}[/tex]
Rationalize
[tex]\mathbf{sin \theta = \frac{3\sqrt{15}}{15}}[/tex]
[tex]\mathbf{sin \theta = \frac{\sqrt{15}}{5}}[/tex]
[tex]\mathbf{(d)\ sec\theta =\frac{\sqrt 6}{3}}}[/tex]
The sine of an angle is calculated as follows
[tex]\mathbf{sin\theta = \sqrt{1 - (1/sec\theta)^2}}[/tex]
So, we have:
[tex]\mathbf{sin\theta = \sqrt{1 - (3/\sqrt 6)^2}}[/tex]
[tex]\mathbf{sin\theta = \sqrt{(1 - 9/6)}}[/tex]
[tex]\mathbf{sin\theta = \sqrt{( - 3/6)}}[/tex]
The sine of the angle does not have a real value
[tex]\mathbf{(e)\ cot\theta = \frac{\sqrt 6}{2}}[/tex]
Start by calculating the tangent of the angle
[tex]\mathbf{tan\theta = \frac{1}{cot\theta}}[/tex]
So, we have:
[tex]\mathbf{tan\theta = \frac{1}{\sqrt 6/2}}[/tex]
[tex]\mathbf{tan\theta = \frac{2}{\sqrt 6}}[/tex]
Rationalize
[tex]\mathbf{tan\theta = \frac{2\sqrt 6}{6}}[/tex]
[tex]\mathbf{tan\theta = \frac{\sqrt 6}{3}}[/tex]
The tangent of an angle is:
[tex]\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}[/tex]
Using Pythagoras theorem, we have:
[tex]\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}[/tex]
So, we have:
[tex]\mathbf{Hypotenuse^2 = (\sqrt{6})^2 + 3^2}[/tex]
[tex]\mathbf{Hypotenuse^2 = 6 + 9}[/tex]
[tex]\mathbf{Hypotenuse^2 = 15}[/tex]
Take square roots
[tex]\mathbf{Hypotenuse = \sqrt{15}}[/tex]
So, the sine of the angle is:
[tex]\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}[/tex]
[tex]\mathbf{\ sin\theta = \frac{\sqrt{6}}{\sqrt{15}}}[/tex]
Rationalize
[tex]\mathbf{\ sin\theta = \frac{\sqrt{90}}{15}}[/tex]
Rewrite as:
[tex]\mathbf{\ sin\theta = \frac{3\sqrt{10}}{15}}[/tex]
[tex]\mathbf{\ sin\theta = \frac{\sqrt{10}}{5}}[/tex]
Read more about trigonometry ratios at:
https://brainly.com/question/24888715
A company makes pens. They sell each pen for $9. Their revenue is represented by R = 9 x. The cost to make the pens is $3 each with a one time start up cost of $6500. Their cost is represented by C = 3 x + 6500. a) Find the profit, P, (P = R - C) when the company sells 1000 pens. 15500 0-500 O 9000 0-3500 0-9000
Answers
Answer:
-$500
Step-by-step explanation:
C = 3(1000) + 6500
C = 3000 + 6500
C = 9500
R = 9(1000)
R = 9000
P = 9000 - 9500
P = -500
if y varies inversely as x, when y=20 and x=2 find the equation for y. then, find y when x=4
Answers
Answer:
the equation for y=20=1/2
Step-by-step explanation:
y=1/4
y=0.25
An academy requires there to be 3 teachers for every 72 students and 5 tutors for every 60 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 132 students?
Answers
Pls help can’t figure it out
Answers
Y = 20
Let me know if you want me to show my work (:
__% of 4 is 7
Please answer its due today
Answers
Answer:
175%
hope that helps. :)
What is the largest multiple of 9 whose negation is greater than -100?
Answers
Answer:
99
Step-by-step explanation:
Its negation is greater than -100. Hope this helps!
~Just a joyful teen
[tex]SilentNature[/tex]
Answer:
99
Step-by-step explanation:
what is the approximate length of segment PR?
25
11
125
18
Answers
Answer:
18
correct me if I'm wrong❌
Solve pls branliest!
Answers
Answer:
1 23 then 70 .2 corrected
B) is the second choice 2+(-8)
X-6y=6 find an ordered pair
Answers
Answer:
(6,0) or (0,-1)
Step-by-step explanation:
X-6y=6
X=6+6y
X/6=1+y
X/6-1=y
y=X/6-1
We'll use substitution to solve the ordered pair. Let's say Y = 0. We'll insert it back into our equation.
0=X/6-1
1=X/6
6=X
(6,0)
We can also start with X being = 0.
y=0/6 -1
y=-1
(0,-1)
I've attached what that would look like as a graph.
At a diving competition, Allison scored 78.5 on her first dive. Hannah's score on her first dive was 74.65. How many more points did Allison score on her first dive than Hannah? SHOW YOUR WORK.
Answers
pls help meeeee
pls....
Answers
Answer:
1→10
Step-by-step explanation:
12
27
45
105/4
49/2
2/15
2/9
22/45
7/12
1/3
And then simplify the final answer
Eg: 3/10 * 4/9 = 12/90 = 2/15
What is the area of this trapezoid?
Enter your answer in the box.
= cm²
Answers
A = 440
answer...
A
=
a
+
b
2
h
=
25
+
19
2
·
20
=
440
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answers
unit rate = 45
so $45 per person
85 guests x 45 = 3825
I hope this helps!
I’m doing my math homework and I don’t understand it all. I did most of it in class but I don’t get it still so here’s the question
Question:
-4/3(3q -10)
Answers
Answer:
-4q+ 40/3
Step-by-step explanation:
How to find the Smallest value?
3/8
3/4
1/2
7/8
5/6
Answers
Answer:
Make all fractions have the same common denominator, and you will find that 3/8 is the smallest value.
Step-by-step explanation:
Which problem could the bar diagram represent
Answers
ANSWER: is there a picture for the question?
Step-by-step explanation:
A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If the height of the bounce follows geometric progression, find the general term that represent the situation in term of k. [2 marks] Hence, if the ball dropped from a height of 235ft, determine i. the highest height achieved by the ball after six bounces ii. the total distance travelled by the ball when it strikes the ground for 12th time [2 marks] [3 marks b) The number of cell double after each process of cell division every 2 hours. If there are 120 bacteria initially, how many bacteria will be there after one and half day? [4 marks]
Answers
The movement of the ping pong ball follows a exponential progression.
The expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]The height after the 6th bounce is 41.82 ftThe total distance after the 12th bounce is 1584.84ft.There will be 31457280 bacteria after a day and a half.1. Ping pong ball
The given parameters are:
[tex]\mathbf{a = 235}[/tex] --- the initial height
[tex]\mathbf{r = 75\%}[/tex] --- the common ratio
(a) The expression after bouncing k times
To do this, we make use of
[tex]\mathbf{T_n = a \times r^n}[/tex]
So, we have:
[tex]\mathbf{T_n = 235 \times (0.75)^n}[/tex]
In this case; k = n.
So, the equation becomes
[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
Hence, the expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
(b) The height after bouncing 6 times
This means that k = 6.
So, we have:
[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
[tex]\mathbf{T_6 = 235 \times (0.75)^6}[/tex]
[tex]\mathbf{T_6 = 41.82}[/tex]
Hence, the height after the 6th bounce is 41.82 ft
(c) The total distance after the 12th bounce
First, we calculate the total height after the 12th bounce using:
[tex]\mathbf{S_k = \frac{a(1 - r^k)}{1 - r}}[/tex]
So, we have:
[tex]\mathbf{S_k = \frac{235 \times (1 - 0.75^{12})}{1 - 0.75}}[/tex]
[tex]\mathbf{S_k = \frac{235 \times (0.968)}{0.25}}[/tex]
[tex]\mathbf{S_k = 909.92}[/tex]
So, the total distance is:
[tex]\mathbf{Distance = 2 \times S_k - a}[/tex]
[tex]\mathbf{Distance = 2 \times 909.92 - 235}[/tex]
[tex]\mathbf{Distance = 1584.84}[/tex]
Hence, the total distance after the 12th bounce is 1584.84ft.
(2) Cell division
The given parameters are:
[tex]\mathbf{r = 2/2hr}[/tex] --- rate
[tex]\mathbf{a = 120}[/tex] --- initial number of cells
[tex]\mathbf{t = 18}[/tex] --- number of 2 hours is a day and a half
So, the number of bacteria is:
[tex]\mathbf{T_t = ar^t}[/tex]
This gives
[tex]\mathbf{T_t = 120 \times 2^{18}}[/tex]
[tex]\mathbf{T_t = 31457280}[/tex]
Hence, there will be 31457280 bacteria after a day and a half.
Read more about exponential functions at:
https://brainly.com/question/11487261
help with 14 please!!! please also explain!!
Answers
Answer:
f = ab/(a + b)Step-by-step explanation:
#14Given:
1/f = 1/a + 1/bSolving for f:
1/f = b/ab + a/ab1/f = (a + b)/ab cross - multiplyf(a + b) = ab divide by (a + b)f = ab/(a + b)Show how to use a power of 10 to write 42.66 / 2.97 as an equivalent expression with a whole number divisor
PLEASE HELP DUE TONIGHT!!
WILL MARK BRAINLIEST!!
Answers
Expressing the given equation as a power of 10 with the divisor expressed as an whole number can be written as [tex] \frac{42.66 \times 10^{2}}{297}[/tex]
Given the expression :
42.66/2.97Expressing the numbers as a power of 10 :
Dividend = 42.66 Divisor = 2.97To convert the divisor to a whole number :
Multiply both by 100
Dividend = 42.66 × 100Divisor = 2.97 × 100 = 297Expressing dividend as a power of 10 :
Dividend = 42.66 × 100 = 42.66 × 10²Hence, the equivalent equation would be : [tex] \frac{42.66 \times 10^{2}}{297}[/tex]
Learn more : https://brainly.com/question/18796573
help #2 #4 #6 #8 #10 #12
Answers
Aashi buys
2 packets of bread rolls costing £1.40 for each packet
1 bottle of ketchup costing £1.80
3 packets of sausages
Aashi pays with a £10 note.
She gets 45p change.
Work out the price in pounds (£) of one pack of sausages.
(you will get brainliest) !! :D
Answers
Ketchup = K
Sausages = S
2BR +1K + 3S = £10 - 45p
2BR + 1K + 3S = £9.55
2BR = 1.40 x 2 = £2.80
1K = £1.80
£2.80 + £1.80 + 3S = £9.55
3S = £9.55 - £2.80 - £1.80
3S = £4.95
£4.95 / 3 = BR
S = £1.65
The answer is £1.65 for one pack of sausages
Price of one unit Sausage = 1.65
Sum ( Price x Quantity) = Total Expenditure
Price of Bread x Quantity of Bread + Price of Ketchup x Quantity of Ketchup + Price of Sausage x Quantity of Sausage
Total Expenditure Value = 10 - 0.45 = 9.55
Let price of sausage = P
Therefore, 2 (1.40) + 1 (1.80) + 3 P = 9.55
2.80 + 1.80 + 3 Ps = 9.55
4.6 + 3 P = 9.55
3P = 9.55 - 4.60 = 4.95
P = 4.95 / 3 = 1.65
To learn more, refer https://brainly.com/question/16910784?referrer=searchResults
2. Mack buys a gourmet pizza for $50. The shop increases its purchase price by 50%? What is the new price of the pizza?
Answers
Answer:
$75
Step-by-step explanation:
50% is half of the total, meaning that we can take half of $50, then add it to 50. Half of 50 is 25, so 50 + 25 = 75 dollars.
Find the volume of the composite solid.
Answers
Answer:
volume________
7 ft 8 ft 7.5 ft 7 ftWrite the equation in function form:
8x + 4y = 20
Answers
Function form means just replace y with f(x).
So given 8x + 4y = 20:
Subtract 8x
4y = 20 - 8x
Divide both sides by 4
y = 5 - 2x
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
should be 40
1.6[3(5(2))-5]
1.6[30-5]
1.6[25]
40
See the question
Help
I’ll give a brainliest
1 , 2 , 3 , or 4 ?
Answers
Answer:
the answer is 3 I think if not than 2
evaluate f(m-5) and simplify if f(x)=5x-9
Answers
Answer:
f(m-5) = 5m-34
Step-by-step explanation:
f(x)=5x-9
Replace x with m-5
f(m-5) = 5(m-5) -9
Distribute
= 5m-25 -9
= 5m-34
Answer:
answer is 5m - 34
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!
Camille is 7 years older than Donny, and Donny is 4 years younger than Tommy.
Write an expression for the total ages of the three people, in simplest form.
Answers
11
Step-by-step explanation:
first you add seven plus four and then you get your answer that is eleven
(Pre calc) I only need to do part A i would love to have some help I will make it 120 Points
Answers
Answer:
The domain should be X
Step-by-step explanation:
I'm a bit unsure but I think it's correct