The function y=20(0.975)ˣmodels the intensity of sunlight beneath the surface of the ocean. The output y represents the percent of surface sunlight intensity that reaches a depth of x feet. The model is accurate from about 20 feet to about 600 feet beneath the surface.
b. Find the percent of sunlight at a depth of 370 feet.
The percent of surface sunlight intensity that reaches a depth of 370 feet is 0.0017%
We have been given the function which models the intensity of sunlight beneath the surface of the ocean which is
y = [tex]20 * (0.975)^{x}[/tex] (1)
where, y = the percent of surface sunlight intensity that reaches a depth of x feet.
x = depth in feet
b) We need to find the percent of sunlight at a depth of 370 feet that is we have been given, x = 370feet.
putting the required values in equation (1) we get
[tex]y = 20*(0.975)^{370}[/tex]
y = 20* 0.000085
y = 0.0017%
Hence 0.0017% of sunlight intensity reaches a depth of 370 feet
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Solve each equation.
x²+7 x-8=0
After solving, the factors of the equation x²+7x-8=0 are:
(x + 8) and (x - 1)What is an equation?A mathematical statement made up of two representations joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value for the variable x as x = 7 after solving this equation.So,
Given equation: x²+7x-8=0Then,
x²+7x-8 = 0x²+x( - )-8 = 0x²+x( 8 - 1 )-8 = 0x²+8x -x -8x(x + 8) -1( x+8)Factors are: (x + 8) and (x - 1)
Therefore, after solving, the factors of the equation x²+7x-8=0 are:
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Which action is an example of someone taking action to accept personal responsibility for eating right? continuing to eat while watching television consuming high-fat foods every day writing down foods consumed at each meal in a day going to the store on an empty stomachWhich action is an example of someone taking action to accept personal responsibility for eating right? continuing to eat while watching television consuming high-fat foods every day writing down foods consumed at each meal in a day going to the store on an empty stomachWhich action is an example of someone taking action to accept personal responsibility for eating right? continuing to eat while watching television consuming high-fat foods every day writing down foods consumed at each meal in a day going to the store on an empty stomach
The action that is an example of someone taking action to accept personal responsibility for eating right is writing down foods consumed at each meal in a day.
How to take responsibility for eating?There are several ways to take responsibility for our eating habits and one of them is to write down the foods that we consume during each meal that we take in a day.
This would enable us to keep track of the calories we consume and therefore give us a better idea of which foods to eat and which to avoid to maintain our recommended dietary intake.
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Answer:
Which action is an example of someone taking action to accept personal responsibility for eating right?
(A.) continuing to eat while watching television
(B.) consuming high-fat foods every day
(C.) writing down foods consumed at each meal in a day
(D.) going to the store on an empty stomach
Step-by-step explanation:
2022-2023 :)
Ryan works as a tutor for $15 an hour and as a waiter for $10 an hour. This month, he worked a combined total of 81 hours at his two jobs.
Let be the number of hours Ryan worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.
An expression for the combined total dollar amount he earned this month:
Total Earning = 15b + P(N - b)
where, b is the total hours worked as a tutor
P is the amount earned by Ryan per hour as a waiter
N is the total number of possible hours Ryan can work in a month
In this question,
Ryan works as a tutor for $15 an hour and as a waiter for $10 an hour. This month, he worked a combined total of 81 hours at his two jobs.
Let the number of hours Ryan works daily as a waiter be x
and the number of hours worked daily as a tutor be y
Ryan earns $15 per hour as tutor.
So, we get an expression for the daily earnings on tutoring = 15y
Let Ryan earns $P per hour as waiter.
so, we get an expression for the daily earning as a waiter = Px
The total possible hours Ryan can work in a month is dependent on conditions not specified.
Assuming 24 working days (6 days weekly for 4 weeks) in a month with maximum approved work hours of 12 hours daily, the total hours Ryan can work will equal 24 x 12 = 288 hours
This 288hrs is an estimate and can change based on applicable hours of work daily and number of working days in a month; it can also be represented as N
If b is the total hours Ryan worked as a tutor this month, the hours Ryan can work as a waiter in a month is equal to 288 - b
So, in a month, Ryan will earn 15b as a tutor and P(288-b) as a waiter or optionally P(N - b)
So, the combined dollar amount earned in a month is:
Total Earning = 15b + P(N - b)
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Gary, the local traffic guy is in his helicopter. He takes off from his base location and notices two car accidents south of him. He measures the angle of depression from the helicopter to the first accident at 63° and the angle of depression from the helicopter to the second accident at 49°. The helicopter is hovering 5000 feet above his base location. He needs to tell emergency services the locations of the accidents based on where he is. What are the distances from his base location to the accidents?
The distances from base location to first and second accident site is 2551 feet and 4347.8 feet.
The angle of depression is 63° and 49°. Also, joining the base location, accident site and position of helicopter, we will get a right angled triangle. Using tangent of given angle we will find the distance between base location and accident site.
Distance of first accident site
tan theta = perpendicular ÷ base
tan 63° = 5000 ÷ base
Base = 5000 ÷ 1.96
Base = 2551 feet
Distance of second accident site
tan 49° = 5000 ÷ base
Base = 5000 ÷ 1.15
Base = 4347.8 feet
Therefore, the distance of base location to first accident site is 2551 feet and distance to second accident site is 4347.8 feet.
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36
8. Kendall is making a shelf for her room.
The length of the shelf is 3.5 times the
width of the shelf. If the width of the
shelf is 1.6 feet, what is the length of
the shelf?
Simplify this expression. Assume that x is nonzero. x^10 x x^3
Answer:
[tex]\sf x^{13}[/tex]
Step-by-step explanation:
Exponent law:If bases are same, add the exponents.
[tex]\sf \boxed{a^m*a^n =a^{m+n}}[/tex]
[tex]\sf x^{10}*x^3} = x^{10+3}\\[/tex]
[tex]\sf = x^{13}\\[/tex]
Hey there!
x^10 * x^3
x^10
= x * x * x * x * x * x * x * x * x * x
x^3
= x * x * x
x * x * x * x * x * x * x * x * x * x + x * x * x
= x^13
Or
10 + 3 = 13
Therefore, your answer should be:
x^13
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
R is inversely proportional to A
R=12
A=1.5
Work out the value of A when R= 9
Answer:
Hi the answer to that question is 2
Write each expression in simplest form. (x⁻¹⁰ / x⁵)²/₅
The radical expression of the term (x⁻¹⁰ / x⁵)²/⁵ is ⁵√(1/x¹⁰)
What is a radical?A radical is a number that is denoted by a root and can be easily identified because before the number is the symbol √, which lets us know that it is a root.
In this case we have an exponential number since it is raised to a number, radicals can be expressed as powers raised to fractions as follows:
√a = a¹/²
We reduce the fraction value
(x⁻¹⁰ / x⁵) = x⁻⁵ = 1/x⁵
If our term is raised to 2/5, it can be expressed as:
(1/x⁵)²/⁵ = ⁵√(1/x⁵)² = ⁵√(1/x¹⁰)
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Use the properties of logarithms to evaluate each expression.
log₆12 + log₆3
Using the properties of logarithm the value of the expression is [tex]log_{6} 12 + log_{6} 3 = 2[/tex]
A logarithm is the power to which a number must be raised in order to get some other number.
According to the question we have been given the logarithmic expression as
= [tex]log_{6} 12 + log_{6} 3[/tex]
The properties of logarithm that we are going to use are :
[tex]log(x*y) = logx + logy[/tex] and [tex]log_{a} a = 1[/tex]
Also we can see that the base are same so we can use the property of logarithm in the given equation.
Now solving it step by step using the properties of logarithm we get
[tex]= log_{6} (12*3)\\= log_{6} 36\\= log_{6} 6^{2} \\= 2* log_{6} 6\\= 2*1\\ = 2[/tex]
Hence using the properties of logarithm the value of the expression is [tex]log_{6} 12 + log_{6} 3 = 2[/tex]
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write the equation for a line perpendicular to y = 3x - 2
The equation of the line is y = -(1/3)x + 5,
What is an equation of a line?The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
We have,
The line is perpendicular to y = 3x - 2 and passes through (3, 4).
The slope of the line and the slope of y = 3x - 2 is:
[tex]m_{1} m_{2}[/tex] = -1
Where [tex]m_{2}[/tex] = 3
[tex]m_{1}[/tex] = -1/3
The equation for the line that passes (3, 4) is given by:
y - 4 = -1/3 ( x - 3)
y = -1/3x + 1 + 4
y = -(1/3)x + 5
Thus the equation of the line is y = -(1/3)x + 5,
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The complete question is:
What is the equation of the line perpendicular to y = 3x − 2 and passes through point (3,4)?
Round 6.1687 to the nearest hundredth
Answer:
6._ _ is the hundreth.
Since the diget after 6 is infact greater than or equal to 5.. (8>5).
We can round up to 6.17
Simplify each rational expression. State any restrictions on the variables.
12-x-x² / x²-8 x+15
The required simplication of rational expression is -(4 + x) / (x - 5).
What is a rational number?
Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.
Simplifying the rational expression, 12 - x - x² / x² - 8x + 15
Given a rational expression,
12 - x - x² / x² - 8x + 15
On simplifying, we get,
For numerator, 12 - x - x²: (3 - x)(4 + x)
For denominator, x² - 8x + 15: (x - 5)(x - 3)
Now, 12 - x - x² / x² - 8x + 15 = (3 - x)(4 + x) / (x - 5)(x - 3)
= -(4 + x) / (x - 5)
Restriction is that the denominator, x - 5 should not be 0.
Hence, the required simplication of rational expression is -(4 + x) / (x - 5)
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Find all the zeros of each function. f(x)=x⁴-16
The required zeros of the polynomial f(x) are 2, -2, and ±√-4.
What are zeros of the polynomial?
All the possible values of x that will make the polynomial zero are called the zeros of the polynomial, p(x). Zeros of a polynomial can either be negative or positive.
Solving for the zeros of a polynomial
f(x)=x⁴ - 16
Let, f(x) = 0
x⁴-- 16 = 0
(x²)² - 4² = 0
(x² + 4) (x² - 4) = 0
(x² + 4)(x - 2)(x + 2) = 0
i.e. x² + 4 = 0, x - 2 = 0, x + 2 = 0
x = 2, -2, ±√-4
Hence, the required zeros of the polynomial f(x) are 2, -2, and ±√-4.
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Psychologists use an exponential model of the learning process, f(t)= c(1-e -kt) , where c is the total number of tasks to be learned, k is the rate of learning, t is time, and f(t) is the number of tasks learned.
a. Suppose you move to a new school, and you want to learn the names of 25 classmates in your homeroom. If your learning rate for new tasks is 20 % per day, how many complete names will you know after 2 days? After 8 days?
We will know 8 complete names after 2 days and 20 complete names after 8 days.
Here, we are given an exponential function: f(t)= c{1- [tex]e^{-kt}[/tex]}
where f(t) = number of tasks learned.
c = total number of tasks to be learned
k = rate of learning
t = time
Now, when we move to a new school, number of names we need to learn ⇒ c = 25
learning rate for new tasks = 20%
⇒ k = 0.2
and time = 2 days
⇒ t = 2
Substituting these values in the given function we get-
f(2) = 25{1- [tex]e^{-0.2 *2}[/tex]}
= 25{1- [tex]e^{-0.4}[/tex]} [tex]e^{-0.4}[/tex]
= 0.67
Thus, f(2) = 25( 1-0.67 )
f(2) = 25(0.33)
f(2) = 8.25
Thus, we will be able to learn 8 complete names in 2 days.
If t = 8f(8) = 25{1- [tex]e^{-0.2 * 8}[/tex]}
= 25{1- [tex]e^{-1.6}[/tex]}
= 25(1- 0.20)= 25(0.80)
= 20
Thus, we will be able to learn 20 complete names in 8 days.
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Write each fraction as a percent 17/20
Answer:
85%
Step-by-step explanation:
[tex]\frac{17}{20} * 100 = 85[/tex]
Answer:
85%
Step-by-step explanation:
See attachment for answers.
Determine the slope of the blue and green line
Answer:
2/-9
Step-by-step explanation:
Brainliest! Please answer quickly! Thank you
How many 5 ounce glasses of milk can you pour from a gallon of milk.? How many ounces of milk will you have left over? A gallon of milk contains 128 ounces.
Show your work.
25 5-ounce-glasses of milk can be poured out from a gallon of milk and 3/5 ounces of milk will be left over
How to find the how many 5 ounce glasses of milk can you pour from a gallon of milkAssuming
1 gallon 4 quarts
1 quart 2 pints
1 pint 2 cups
1 cup = 8 fluid ounces
if 1 quart 2 pints, then 4 quarts will be
= 4 * 2 = 8 pints
if 1 pint 2 cups, then 8 pints will be
= 8 * 2 = 16 cups
if 1 cup is 8 fluid ounces, then 16 pints will be
= 8 * 16 = 128 fluid ounces
solving the amount of 5 ounce glasses of milk in a ballon
= 128 / 5
= 25.6
= 25 3/5
Hence we can say that a gallon of milk will give 25 5-ounce-glasses of milk and 3/5 ounces of milk left over
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Answer:1 gallon 4 quarts
1 quart 2 pints
1 pint 2 cups
1 cup = 8 fluid ounces
if 1 quart 2 pints, then 4 quarts will be
= 4 * 2 = 8 pints
if 1 pint 2 cups, then 8 pints will be
= 8 * 2 = 16 cups
if 1 cup is 8 fluid ounces, then 16 pints will be
= 8 * 16 = 128 fluid ounces
solving the amount of 5 ounce glasses of milk in a ballon
= 128 / 5
= 25.6
= 25 3/5
Hence we can say that a gallon of milk will give 25 5-ounce-glasses of milk and 3/5 ounces of milk left over
Step-by-step explanation:
Which properties can be changed by a transformation? (Check ALL that apply.)
Shape
Size
Position
Color
is 64,96 and 60,90 proportional
The common rate of both expressions are equal, so the expressions 64,96 and 60,90 are proportional
How to determine if the expressions are proportional?The expressions are given as
64,96 and 60,90
Rewrite the expressions as
(x, y) = (64,96) and (60,90)
As a general rule
Proportional expressions have the same constant rate
The constant rate (r) of the expressions is then calculated as
r = y/x
For the expression (64, 96), we have the following computation
r = 96/64
Evaluate the quotient
So, we have
r = 1.5
For the expression (60, 90), we have the following computation
r = 90/60
Evaluate the quotient
So, we have
r = 1.5
The common rate of both expressions are equal i.e. 1.5
Hence, the expressions 64,96 and 60,90 are proportional
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Use the table to answer the table Input: 2, 3, 6.
Output: 6, 9, 18 what ratio is represented in the table?
A: 1:3
B: 1:4
C: 1:5
D: 1:13
Thanks to whoever answers this.
The required ratio of the input value to the output value is 1:3.
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given:
Input Output
2 6
3 9
6 18
Now, the ratio is
2/6 = 1/3
and, 3/9 = 1/3
6/18 = 1/3
Hence, the ratio is 1:3.
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jake rearranges the letters in the word SHREK. How many possible arrangements begin with R?
There are 24 possible arrangements that begin with letter R
What are combinations and permutations?Combinations are used to determine the number of selections of an item within another while permutation is used for arrangements
How to determine the number of arrangement?The arrangements of the digits is an illustration of factorials
The word is given as: SHREK
If the first letter begins with the letter R, then we have the following possible arrangements
First letter: 1 character i.e RSecond letter: Any of the remaining 4 charactersThird letter: Any of the remaining 3 charactersFourth letter: Any of the remaining 2 charactersFifth letter: The last characterThe number of arrangement is the product of the above values
So, we have
Arrangement = 1 * 4 * 3 * 2 * 1
Evaluate
Arrangement = 24
Hence. there are 24 possible arrangements that begin with letter R
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f(x)=2x+5/3x find f-1(x)
please answer quickly!
Answer:I think its 2x-5/3
Step-by-step explanation:
please let me know if I'm wrong.
Work out (9 × 10¹) – (2 × 10³) Give your answer in standard form.
Answer:
Standard notation/form
-1.91 × 10³
Hope this helps.
Find the inverse of each function.
y=log₀.₅x
The inverse of the function y = log₀.₅ x is f⁻¹ (x) = (0.5) ˣ.
We are given the function:
y = log₀.₅ x
We need to find the inverse of the function.
First we will find the value of x in terms of y.
The logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.
We can write it as:
(0.5)^ y = x
x = (0.5) ^ y
now, the inverse of the function will be:
f⁻¹ (x) = (0.5) ˣ
Therefore, the inverse of the function y = log₀.₅ x is f⁻¹ (x) = (0.5) ˣ.
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A car is traveling at a steady speed. It travels 1 3 4 miles in 2 1 3 minutes. How far will it travel in 33 minutes?
The ratio of eds toy cars to petes toy cars was 5:2 after ed gave pete 30 cars te owned a equall amount of cars how many cars did they have all together
Answer:
87
Step-by-step explanation:
5/2 ×30 = 75
2/5× 30=12
75 +12 = 87
Therefore , the total number of cars they altogether is 87
3. TRAILS Caroline and Rodney went on a hike. They
started at the clubhouse, which is located at((-4,-3)
on their map. They hiked on a straight line to the
canoe livery, which is located at (2, 3). They had
3
completed of their hike when they stopped for lunch.
At what coordinates on their map were Caroline and
Rodney when they stopped to eat lunch?
Caroline and Rodney, on their way to the canoe livery, stopped to eat lunch at the point on their map with coordinates of (-2, -1).
What is the coordinate of a point?The coordinates of a point on a two dimensional plane are two numbers that define its location.
The given coordinates of the journey are;
Location of the clubhouse = (-4, -3)Coordinates of the canoe livery = (2, 3)Proportion of the hike completed before they stopped for lunch = (1/3) of the journeyRequired; The coordinates of the map where Caroline and Rodney stopped for lunch.
Solution:
The coordinates of a point (x, y), which is a proportion, t, of the distance between two points (a, b), and (c, d) is given by the formula;
x = a•(1 -t) + c•t
y = b•(1 -t) + d•t
The location where they had lunch is therefore;
x = -4×(1 - (1/3)) + (1/3)×2 = -2
y = -3×(1 - (1/3)) + (1/3)×3 = -1
The points is therefore; (-2, -1)
The coordinates on the map where Caroline and Rodney stopped for lunch is (-2, -1)
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360000/180 in standard form
Answer:
2000
Step-by-step explanation:
what is the multiplicative inverse 23
Answer: 1/23
Step-by-step explanation:
x=multiplicative inverse of 23
23*x=1
23x=1
23x/23=1/23
x=1/23