Answer:
≈0.52
Step-by-step explanation:
The value of the quantity after 8.7 decades is 0.521.
What is Exponential Growth and Decay?Exponential growth is the increase of rate of change and thus results in the increase of the final quantity.
Exponential decay is the decrease in rate of change and hence results in the decrease of the final quantity.
Given that,
Initial value of the quantity = 230
Rate of decay = 7% per year = 0.07
Time = 8.7 decades = 87 years
The formula for exponential decay is,
A = P e^(-k t)
Here A is the final value of the quantity
P is the initial value of the quantity
k is the decay rate
t is the time.
Substituting the given values,
A = 230 × e^(-0.07 × 87)
A = 230 × e^(-6.09)
= 0.521
Hence the final quantity after 8.7 decades is 0.521.
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Answer: All expect cos of theta=17/8
Step-by-step explanation: Fist, let find a equal cos equation. let use the idenitiy([tex]cos^{2}[/tex]Ф+[tex]sin^{2}[/tex]Ф=1. [tex]cos^{2}[/tex]+15/17^2=1, [tex]cos^{2}[/tex]=1-225/289. [tex]cos^{2}[/tex]=289/289-225/289. [tex]cos^{2}[/tex]=64/289. sqr root of [tex]cos^{2}[/tex]= 8/17.
Using Other Formulas, Since secant is the reciprocal of cosine. sec(theta)=17/8. since cosecant is the inverse of sin. csc(theta)=17/15.
Using the formula sin x/cos x= tan x , [tex]\frac{15}{17}[/tex]=[tex]\frac{8}{17}[/tex] =15/8.
Cos 315°=what?????????????
Answer:
√2/2 or 0.70710678118
Step-by-step explanation:
The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.
11
12
What is that fraction decimal
Answer:
0.91666666666...
f(x) = 16x^3- 20х^2 - 4х + 15
Answer:
hopes this helps
Step-by-step explanation:
HELP PLZ WILL GIVE BRAINLIEST
The answer is True
hope this helps
Answer:
Step-by-step explanation:
False
Can someone help, marking Brainly ! Thank you if you do help .
Answer:
in order
y=0
y=1
y=2
y=3
y=4
y=5
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 160 engines and the mean pressure was 5.3 pounds/square inch (psi). Assume the population standard deviation is 0.6. The engineer designed the valve such that it would produce a mean pressure of 5.4 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.1 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
Test statistic Z = 2.1097
Step-by-step explanation:
Step(i):-
Given that size of the sample 'n' = 160
Given that mean of the Population(μ) = 5.3pounds/square inch
The Standard deviation of the population(σ) = 0.6
Mean of the sample(x⁻) = 5.4
Level of significance =0.1
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{5.4-5.3}{\frac{0.6}{\sqrt{160} } }[/tex]
Z = 2.1097
Final answer:-
Test statistic Z = 2.1097
A restaurant offers a catering service which costs $25.00 per person with a $119.50 service charge. For parties of 50 or more people, a group discount applies, and the cost is $20.00 per person along with the service charge dropping to $59.00. (a) Write a piecewise-defined linear function which calculates the total cost T of the catering service which serves n people.
Answer:
T1(n) = 25n +119.50 where n belongs to [tex]1 \leq n <50[/tex].
T2(n) = 20n + 59 where n belongs to [tex]50\leq n[/tex].
Step-by-step explanation:
We are given two situations first is for normal days and the other is for days when 50 or more people are going to this restaurant for the party.
Let the number of person going for this restaurant be "n"
For normal day, we are given
catering service = $25 per person
service charge = $119.50
Let the total cost of the restaurant be T
Cost for this case will be T1
T1(n) = 25n +119.50 where n belongs to [tex]1 \leq n <50[/tex]
similarly for the case when 50 or more than that goes to this restaurant for party.
cost after discount
Catering service = $20.00 per person
service charge = $59.00
now the cost of this case will be T2
T2(n) = 20n + 59 where n belongs to [tex]50\leq n[/tex].
Therefore the two piecewise linear functions represents the total cost of the restaurant for serving n people.
Part 1. How did you compute sums of dollar amounts that were not whole numbers? For example, how did you compute the sum of $5.89 and $1.45? Use this example to explain your strategy.
Part 2. How did you compute products of dollar amounts that were not whole numbers? For example, how did you compute the cost of 4 pounds of beef at $5.89 per pound? Use this example to explain your strategy.
Answer:
The answer is below
Step-by-step explanation:
1) When you are computing the sums of numbers, you do not round up. You have to be exact.
Summing numbers involves you adding the numbers together as well as their decimals. Therefore:
$5.89 + $1.45 = $7.34
2) When you are computing the product of numbers, you do not round up. You have to be exact.
The product of numbers involves you multiplying the numbers together. Therefore:
$5.89 per pound * 4 pounds of beef = $23.56
When the expression
10x^2/2x^6
is simpified what is the value left in the denominator?
Let LaTeX: x = \text{-}\frac {11} 8x = - 11 8 and LaTeX: y = \text{-}\frac {11} 4y = - 11 4.
Which expression has a negative value?
Group of answer choices
LaTeX: x + yx + y
LaTeX: x - yx − y
LaTeX: x \cdot yx ⋅ y
LaTeX: \frac x y
Answer:
This makes no sense
Step-by-step explanation:
Solve g(x) = 22 + 12x – 5. Submit the sum of your solutions
Answer:
-17/11
Step-by-step explanation:
A small orchestra has 3 stringed instruments. What is the ratio of violins to cellos?
A. 5/15
B. 6/11
C. 5/6
D. 6/5
Violin to Celio.
Violin : Celio
Violin = 6
Celio = 5
6:5
D. 6/5
2
In the diagram, AB Is parallel to DE Also, DE is drawn such that the length of DE is half the length of AB If sin A = 0,5, then what is sin E?
Answer:
than we know that DE parallel AB => m<A = m<E so in this way sin A = sin E
knowed that sin A = 0,5 so sin E = 0,5 too
hope helped
Step-by-step explanation:
For which shape is 45 degrees the smallest angle of rotational symmetry?
Answer:
Step-by-step explanation:
You want the external angle to be 45°.
If n = number of sides, the external angles are each 360°/n = 45°
n = 360/45 = 8
The shape is a regular octagon.
Answer:
the sun
Step-by-step explanation:
truss lebro
Need help on question hurry
Answer: C
Step-by-step explanation: it is c trust me
Please need help on this please
108x25^2divided by
2^6 x 5^2
Answer:
108 x 25² divided by 2⁶ x 5² is equal to [tex]42\frac{3}{16}[/tex]
Step-by-step explanation:
Given;
108 x 25² divided by 2⁶ x 5²
The expression is simplified as follows;
[tex]\frac{108\times 25^2}{2^6 \times 5^2} = \frac{108\times 625}{64\times25} =\frac{675}{16} = 42\frac{3}{16}[/tex]
Therefore, 108 x 25² divided by 2⁶ x 5² is equal to [tex]42\frac{3}{16}[/tex]
Which expression represents the phrase: 8 less than the product of 6 and a number, x?
Answer:
6x-8
Step-by-step explanation:
Answer:
6x - 8
Step-by-step explanation:
Simplify
3/4a - 2/3 - 1/2a + 5/6= ????
Answer:
3a + 2
——————
12
Step-by-step explanation:
Do Now
The ratio of girls to boys in a classroom is 3.1. How many boys are there in the classroom if
it has 12 girlS
Answer: 4
Step-by-step explanation:
To find out how many boys are in the classroom you must divide 12 from 3 to find the rate of change. 12/3= 4 so then you multiply 1*4 to find out how many boys are in the classroom. 1*4=4
Hope this helps ;)
Answer:
4 boys
Step-by-step explanation:
3:1 is the ratio of girls to boys
Lets girls be g and boys be b
G=3
B=1
G=12 12/3=4 and what you do to one side you do to the other it is multiplied by 4 so
B=1 time 4 =4
Is 4/10 equal to 2/3
Answer:
no, its not
Step-by-step explanation:
you can find the decimals by dividing the numerator and the denominator
4/10 = 0.4
2/3 = 0.6666666......
so the values are obviously different
the ratio of marks age to reeta's age is 3:5 marks age is 24 work out reeta's age
Answer:
40
Step-by-step explanation:
Set up a ratio. Solve for x.
3/5 = 24/x
3x = 120
x = 40
Reeta is 40 years old.
Answer:
40
Step-by-step explanation:
For every three years mark has, reeta has five.
Find out how many 'three years' mark has: 24/3 = 8
For every 'three years' he has, reeta has five. 5*8=40
Find the Area and Perimeter
Answer: a) Perimeter: 7n-7; Area: 12n^2-23n+10; b) Perimeter: 8n-2 ; Area: 12n^2-16n-3
Step-by-step explanation:
Area Formula:l*w Perimeter formula: l+w
Martin has read 40% of a book. He has 30 more pages to finish. How many pages are there in the book?
Answer:
75
Step-by-step explanation:
Answer:
There are 50 pages in the book.
Step-by-step explanation:
Given that:
Martin has read 40% of the book.
Remaining percent = (100 - 40)% = 60%
Number of pages left to finish = 30
Let,
x be the total number of pages in the book.
60% of x = 30
[tex]\frac{60}{100}x=30[/tex]
0.6x = 30
Dividing both sides by 0.6
[tex]\frac{0.6x}{0.6}=\frac{30}{0.6}\\x= 50[/tex]
Hence,
There are 50 pages in the book.
Which situation can be represented by 10x + 45 = 25x?
A.Ten times the sum of a number and 45 cents is the same as 25 times the number. What is the number, x?
B.A coin collection contains the same number of quarters as dimes. The value of the quarters increased by 45 cents is the same as the value of the dimes. How many quarters or dimes, x, are in the collection?
C.Twenty-five times a number is the same as 45 times the number increased by 10. What is the number?
D.The value of x dimes increased by 45 cents is the same as the value of x quarters. What is the value of x?
Answer:
its A.
Step-by-step explanation:
Answer: A. .Ten times the sum of a number and 45 cents is the same as 25 times the number. What is the number, x?
Step-by-step explanation:
10x + 45 = 25x can be written = its 10 times (x) + 45 is the sum of 25 times (x) the number
Hope this helps :)
HELP QUICK ILL GIVE YOU BRAINLIEST
What is the surface area?
Answer:
25 ft if i am right than u plss mark me as brainliest
Can someone please help me out?
9514 1404 393
Answer:
64°
Step-by-step explanation:
y° and the angle marked 64° are "alternate interior angles", so are congruent.
y° = 64°
6) A sample of water is being cooled according to the formula is given by
C(t)= 80 – 2t, where t represents the number of minutes the water is cooled,
and C measures the corresponding temperature in degrees Centigrade. The
cooling period ends when the water freezes (0°). Determine the relevant
domain and range for this function.
Determine the relevant Domain and relevant Range for this function. Use
interval notation.
Answer:
Relevant domain: [0 40]
Relevant range: [0 80]
Step-by-step explanation:
We have the following function:
[tex]C(t) = 80 - 2t[/tex]
In which C(t) is the water temperature.
t is the time.
The colling period ends when the water freezes (0°).
So it freezes after t minutes, and t is found when C(t) = 0. So
[tex]C(t) = 80 - 2t[/tex]
[tex]80 - 2t = 0[/tex]
[tex]2t = 80[/tex]
[tex]t = \frac{80}{2}[/tex]
[tex]t = 40[/tex]
Relevant domain:
Input value of the function, which is in minutes. So between 0(initial) and 40(when the water freezes).
Relevant range:
Initial temperature, which is C(0) = 80, until it freezes, 0. So from 0 to 80.
The points (2, -12) and (4, r) lie on a line with slope 4. Find the missing coordinate r.