The diver is closer to sea level since their distance to sea level (7 ft) is less than the distance of the tour guide to sea level (23 ft).
As we know,
|Tour guide - sea level| < |One diver - sea level|
The distance between the tour guide and sea level is 5 - (-18) = 23 feet.
The distance between one diver and sea level is -11 - (-18) = 7 feet.
Since the absolute value of the difference between the tour guide and the sea level is greater than the absolute value of the difference between one diver and the sea level, we can conclude that the diver is closer to the sea level.
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The path of a ball is given by the rectangular equation . Use the result of Exercise 31 to find the position vector. Then find the speed and direction of the ball at the point at which it has traveled feet horizontally.
The direction of the ball at this point is <1/8, -4, 96/8>
The Position Of The VectorThe position vector of the ball can be found by taking the derivative of the rectangular equation with respect to time:
r(t) = <8t, -16t², 32t³>
To find the speed of the ball at the point where it has traveled 64 feet horizontally, we can use the magnitude of the velocity vector, which is the derivative of the position vector with respect to time:
v(t) = <8, -32t, 96t²>
|v(t)| =√(8² + (-32t)² + 96t⁴) = 8*√(1 + t² + 3t⁴)
We need to find the time t at which the ball has traveled 64 feet horizontally. We know that x = 8t, so we can set x = 64 and solve for t:
8t = 64
t = 8
At t = 8, the speed of the ball is:
|v(8)| = 8√(1 + 8² + 3(8⁴)) = 8√(65) = 8*8 = 64
To find the direction of the ball at this point, we can use the unit vector of the velocity vector:
v(t) = <8, -32t, 96t²> / |v(t)|
v(8) = <8, -256, 6144> / 64 = <1/8, -4, 96/8>
So the direction of the ball at this point is <1/8, -4, 96/8>
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Isabella filled her pool with water at a constant rate.
The table compares the remaining volume of water left to fill the pool (in liters) and the time since Isabella started filling the pool (in minutes)Time Water2 1847 9412 4How fast did Isabella fill her pool?
Isabella fills her pool at a rate of 18 liters per minute as per the given condition.
The slope of the volume can be used to determine how quickly it changes when given Time t in minutes and Volume V in liters. That represents a change in volume relative to a change in time.
m = (v2-v1)/(t2-t1).
selecting the first two points (2, 184) and from the provided data (7, 94).
Volume remains in the pool at what rate =
(94-184)/(7-2) = -90/5 = -18.
Therefore the rate at which Isabella fills her pool is 18 liters/minute as per the given question.
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1) Solve for a
a+6=6 a-5= -8 a x -10= 100 (5+2a) ÷ 17 = 3
2) A rectangular field has an area of 49m. If its not a square field and the dimension is a whole number then
a) What are the dimensions of the field?
b) What is the perimeter of the field?
c) Make an equation that shows how you could find the answer to A
3) The following are the first 5 terms in a patterns: 3,5,7,9,11...
a) Make a T chart of term
b) Come up with a pattern rule relating T and V
1.
a+6=6
Solving for a:
a = 0
a-5= -8
Solving for a:
a = -13
a x -10= 100
Solving for a:
a = -10
(5+2a) ÷ 17 = 3
Solving for a:
a = -4
2.
a) The dimensions of the field are 7m by 7m.
b) The perimeter of the field is 28m.
c) To find the area of the field, you could use the equation: length x width = area. In this case, the length and width are both 7m, so the equation would be 7m x 7m = 49m^23
3.
a) T | V
1 | 3
2 | 5
3 | 7
4 | 9
5 | 11
b) The pattern rule is that the value (V) is 2 greater than the previous value.
Is half and 0.5 same?
Answer: Yes.
Step-by-step explanation:
0.5 is also the same as 1/2
Use the table of values to evaluate the expressions below.
We can use the table to evaluate the compositions of the functions, we will get:
f(g(6)) = 3g(f(0)) = 8f(f(4)) = 4g(g(1)) = 1How to evaluate the expressions below?Here we have a table for functions f(x) and g(x), and we want to use that table to evaluate the compositions of the functions.
First, we want to get f(g(6))
Using the table, we can see that g(6) = 0, then:
f(g(6)) = f(0)
And using the table we can see that f(0) = 3, then:
f(g(6)) = 3
The second composition is:
g(f(0))
We know that f(0) = 3
g(f(0)) = g(3)
And using the table g(3)= 8, then:
g(f(0)) = 8
The third one is:
f(f(4))
We can see that f(4) = 7
So: f(f(4)) = f(7)
And again, you can find f(7) on the table to see that f(7) = 4
Then:
f(f(4)) = 4
The last composition is:
g(g(1))
You can see that g(1) = 1
Then:
g(g(1)) = g(1) = 1
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military radar and missile detection systems are designed to warn a country of enemy attacks. a reliability question deals with the ability of the detection system to identify an attack and issue the warning. assume that a particular detection system has a 0.91 probability of detecting a missile attack. answer the following questions using the binomial probability distribution: what is the probability that one detection system will detect an attack? if required, round your answer to two decimal places. fill in the blank 1 if two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack? if required, round your answer to two decimal places. fill in the blank 2 if 3 systems are installed, what is the probability that at least one of the systems will detect the attack? if required, round your answer to four decimal places. fill in the blank 3 would you recommend that multiple detection systems be operated? explain. the input in the box below will not be graded, but may be reviewed and considered by your instructor.
A detection system has a probability of 0.91 to detect a missile attack. It is recommended to have multiple detection systems as it increases the overall probability of detecting an attack and allows for redundancy in case one system fails.
The probability that one detection system will detect an attack is: 0.91If two detection systems are installed in the same area and operate independently, the probability that at least one of the systems will detect the attack is: 1 - (0.09)² = 0.9801If 3 systems are installed, the probability that at least one of the systems will detect the attack is: 1 - (0.09)³ = 0.99291Yes, it is recommended to have multiple detection systems as it increases the overall probability of detecting an attack. It allows for redundancy in case one system fails and increases the chances of detecting an attack even if one system is not functioning properly.To learn more about the probability, visit:
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Answer the screenshot
The domain of the given function f(x) = √(x⁴ - 1) include the following: C. {x|x ≤ -1 or x ≥ 1}.
What is a domain?In Mathematics, a domain simply refers to the set of all real numbers for which a particular function is defined. Additionally, the horizontal extent of a graph represents all domain values (input values) and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Next, we would use an online graphing calculator to plot the graph of the given function f(x) = √(x⁴ - 1). By critically observing the graph of this function shown in the image attached below, we can reasonably and logically deduce the following domain:
Domain = (-∞, 1) U (1, ∞)
By using set builder notation, the domain of this function f(x) = √(x⁴ - 1) can be re-written as follows;
Domain = {x|x ≤ -1 or x ≥ 1}.
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There are 270 students in year 7
each student studies one of french or german or spanish.
of these 270 students
2
study french
9
the number who study french : the number who study spanish = 3:7
42 boys study german
of the students who study german, what percentage are boys?
you must show your working.
Answer is 60 % is the percentage of boys studying German .
So, for this one, you must first determine the number of French students.
Simple method:
[tex]\frac{1}{9}[/tex] is 270 divided by 9, which equals 30, hence [tex]\frac{2}{9}[/tex]of 270 is 60. The result of multiplying [tex]\frac{1}{9}[/tex] by 2 to get [tex]\frac{2}{9}[/tex] is 60.
French is being studied by 60.
When you apply this to the French to Spanish ratio of 3:7, you get 3 and 60 on the same side. In order to get to 60, you must multiply 3 by 20. (or divide 60 by 20 to get 3).
Therefore, 20 is the number you use to apply the same formula to the other side of the ratio.
To reach 140, multiply 7 by 20 (or 7 by 10, then multiply that number by 2).
Spanish is being studied by 140.
After subtracting the French and Spanish from the overall number, you are left with 70 German speakers at 270-140-60.
42 of these 70 are males. 28 females are produced by 70-42. The percentage of males studying German is [tex]\frac{42}{70}[/tex]. This is equivalent to [tex]\frac{6}{10}[/tex], and you multiply a fraction by 10 to convert it to a percentage ([tex]\frac{60}{100}[/tex] in this case).
Additionally, 60% is equal to [tex]\frac{60}{100}[/tex] .
Your response is thus 60%.
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Suppose a ball was dropped from a TV tower 2120 feet high. The time it takes an object to free-fall from the top of this tower to the ground can be represented by the equation s = - 16t^2 + 2120, where s is the distance from the ground in feet and t is the time in seconds. Approximately how long would it take the object to reach the ground? Round your answer to the nearest tenth.
it would take the object approximately 11.51 seconds to reach the ground.
What is time?Generally, Time is a concept used to describe the progression of events, or the duration of those events. It is often measured in units such as seconds, minutes, hours, days, and years.
Time can also be described as a continuum, with past events on one end and future events on the other.
Time is a fundamental aspect of the universe and is closely related to concepts such as causation, change, and entropy.
The time it would take the object to reach the ground can be found by setting the distance from the ground, s, to 0 and solving for t.
0 = -16t^2 + 2120
t^2 = (2120/16)
t = [tex]\sqrt{(2120/16)}[/tex]
t = approximately 11.51 seconds
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The aquarium has 10 more red fish than blue fish. 60% of the fish are red. How many blue fish are in the aquarium? Show your work.
Answer:
20 blue fish
Step-by-step explanation:
r=red fish, b=blue fish. r = 10+b. 60%r=r+b. (10+b)= 0.6(r+b); 10+b = 0.6(2b+10); 10+b=1.2b+6; 4=0.2b; b=20.
How do you find the absolute value of positive and negative numbers?
The absolute value of a negative number will always be a positive number.
As discussed above, regarding the absolute number, therefore, the absolute value of a negative number will always be a positive number.
for example, |-24| = 24
The absolute value of any number will always be a positive number.
As discussed above, regarding the absolute number, therefore, the absolute value of any number will always be a positive number.
for example, |-24| = 24
Positive numbers will always have a higher absolute value than negative numbers.
As discussed above, regarding the absolute number. therefore, the absolute value of any number will always be a positive number, which will be equal in value.
for example, |-24| = 24
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A gas occupies 4.23 l at 2.25 atm. What is the volume at 3.46 atm?
a. 1.84 l
b. 2.75 l
c. 6.50 l
d. 32.9 l
e. 0.364 l
A gas occupies 4.23 l at 2.25 atm. 2.75 L is the volume at 3.46 atm. This can be solved using the concept of Boyle's law.
What is Boyle's law?Boyle's law gives the relationship between pressure and volume of gas.
It states that at constant temperature pressure in inversely proportional to volume.
PV = k
where P - pressure V - volume and k - constant
P₁V₁ = P₂V₂
Given that,
initial pressure (P₁) = 2.25 atm
final pressure (P₂) = 3.46 atm
initial volume (V₁) = 4.23 L
final volume (V₂) = ?
where parameters for the first instance are on the left side and parameters for the second instance are on the right side of the equation
substituting the values in the equation
2.25 atm x 4.23 L = 3.46 atm x V
V = 2.75 L
Thus, the final volume is 2.75 L
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(PLS HELP!!!!)
What are the degree and leading coefficient of the polynomial?
-6u+u²-23u-3
Degree:
Leading coefficient:
Degree: 2
Leading coefficient: -1 (The leading coefficient is the coefficient of the term with the highest degree in the polynomial, in this case, the coefficient of u², which is -1)
A car costs £12000 when bought. It's value depreciates by 10% of the previous years value for 1 year and then at 7.2% for the next 10 years. How much will the car be worth in 5 years time?
Therefore ,on solving the provided question we can say that - Simple Interest after 5 year the car value is £7,689.6
what is interest ?Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it.
here,
rate = 10%
Time = 1 year
Principle = 12000
=>SI = PRT/100
=> SI = 10*1*12000/100
=> SI = 1200
and
=> After 1 year = 12000 -1200 = 10800
and
for five years
=> SI = PRT/100
=> SI = 10800 * 7.2 * 4 / 100
=> SI = 3110.4
After 5 year = 10800 - 3110.4 = 7,689.6
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Find all the zeros of each equation.
[tex]7x^2-144=-x^4[/tex]
The equation 7x² - 144 = -x⁴ has the 4 solutions below:
x = ±3
x = ±4i
How to find the zeros of the equation?
Here we want to solve the equation below:
7x² - 144 = -x⁴
We can redefine the variable:
y = x²
Replacing that we will get:
7y - 144 = -y²
y² + 7y - 144 = 0
So we have a quadratic equation now, the using the quadratic formula we will get:
[tex]y = \frac{-7 \pm \sqrt{7^2 - 4*1*144} }{2} \\\\y = \frac{-7 \pm 25 }{2}[/tex]
Then the two solutions are:
y = (-7 + 25)/2 = 9
y = (-7 - 25)/2 = -16
And we know that:
y = x²
Then:
x = ±√9 = ±3
x = ±√-16 = ±4i
These are the 4 solutions.
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f(-5) = 2,ƒ(7) = - 4
Please help
Answer:
f(x) = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
f(x) = mx + c ( m is the slope and c the y- intercept )
given f(- 5) = 2, that is when x = - 5 , y = 2
f(7) = - 4, that is x = 7, y = - 4
the 2points (- 5, 2 ) and (7, - 4 ) lie on the line
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 2 ) and (x₂, y₂ ) = (7, - 4 )
m = [tex]\frac{-4-2}{7-(-5)}[/tex] = [tex]\frac{-6}{7+5}[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex] , then
f(x) = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the line
to find c substitute either of the 2 points into the partial equation
using (- 5, 2 ) , then
2 = - [tex]\frac{1}{2}[/tex] (- 5) + c = [tex]\frac{5}{2}[/tex] + c ( subtract [tex]\frac{5}{2}[/tex] from both sides )
- [tex]\frac{1}{2}[/tex] = c
f(x) = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex] ← equation of line
Keilantra has $660 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $488.20.
She buys 2 bicycle reflectors for $11.17 each and a pair of bike gloves for $19.05.
She plans to spend some or all of the money she has left to buy new biking outfits for $37.26 each.
Write and solve an inequality which can be used to determine
x
x, the number of outfits Keilantra can purchase while staying within her budget.
Answer:
We know that Keilantra has $660 to spend, she has already spent $488.20 on a bicycle, $11.17 on two reflectors and $19.05 on a pair of gloves.
We can represent the amount spent on reflectors as 2 * $11.17 = $22.34
So the total amount spent so far is:
$488.20 + $22.34 + $19.05 = $529.59
We can represent the remaining amount of money she has to spend on outfits as:
$660 - $529.59 = $130.41
We can use this remaining amount to find out the number of outfits she can purchase by dividing the remaining amount by the cost of each outfit:
$130.41 / $37.26 = 3.5
The inequality that represents this situation is:
x <= 3.5
Where x is the number of outfits Keilantra can purchase while staying within her budget.
This inequality tells us that Keilantra can purchase at most 3.5 biking outfits while staying within her budget.
However, since the number of outfits has to be a whole number, the greatest number of outfits that Keilantra can buy is 3.
a 6-foot man is running away from the base of a streetlight that is feet high. if he moves at the rate of feet per second, how fast is the length of his shadow changing?
As per the unitary method, the length of his shadow changing is 30 feet.
The term unitary method is known as a process of finding the value of a single unit, and based on this value.
Here we have given that a 6-foot man is running away from the base of a streetlight that is feet high.
Then let us consider that the man be x feet away from the street light and his shadow length be y,
Here we have also consider that let the tip of the shadow be l feet away from the light is written as
=> l = x + y
Here we are given that,
=> dx/dt=2
Then as per the concept of similar triangles, we can write it as,
=> x/5 = 6x+6/31
=> 31x = 30x + 30
=> x = 30
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X-N(5.7, 0.61). Find the z - score corresponding to an observation of 4.7. a. 1.64 b. -1.64 c. 1.02 d. -1.02
The Z-score is (b) -1.64.
Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.
To find the z-score corresponding to an observation of 4.7, we can use the formula:
z = (x - mu) / sigma
where x is the observation, mu is the mean, and sigma is the standard deviation.
Given that X-N(5.7, 0.61) we can substitute
z = (4.7 - 5.7) / 0.61 = -1.64
So the answer is (b) -1.64.
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(WILL GIVE BRAINIEST) A collage artist makes art out of real-life objects. She has three pieces of bamboo that measure 4 inches, 5 inches and 7 inches. If she makes a triangle out of the pieces will it be right, acute or obtuse triangle?
If the artist makes a triangle from three pieces of bamboo that measure 4 inches, 5 inches and 7 inches. The triangle will not be a right triangle because the values are not Pythagorean triple
What is Pythagorean triple?Pythagorean triples are b² + a² = c² where b, a and c are all positive integers.
These triples are represented as (b, a, c).
Here, b is perpendicular (or right angel) to a, a is the base and the hypotenuse of the right - angled triangle is labeled .
The most known and smallest triplets are (3, 4, 5).
In the problem, the values 4 inches, 5 inches and 7 inches cannot make a Pythagorean triple since
c² = 4² + 5²
c² = 16 + 25
c² = 41
c = √41 ≠ 7
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The temperature in Williamstown was 38°F. Then a winter storm came through and the temperature dropped 24°F overnight. Which expression represents the change in temperature?
|−24| − |38|
|−24| + |38|
|38| − |−24|
|38| + |−24|
Answer:The temperature dropped 24°F overnight, so the change in temperature would be represented by the expression |-24|, which is the absolute value of -24.
You can also represent it by |38| - |-24| which is equal to 38 - (-24) = 38 + 24 = 62°F.
Step-by-step explanation:
A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one-quarter of
the second number and 5. The situation can be represented by using the graph below, where x represents the second
number.
46-
14-
42-
10+
8-
6
2-
2-
246
8 10 12 14 16 x
Which equations represent the situation?
Mark this and return
Save and Exit
Next
Submit
Answer:
First number 7
Step-by-step explanation:
First, let's make the first number y and the second number x
Next, we write our equations which are y=1/2x+3 and y=1/4x+5
Then, we set those two equations equal to each other and then solve for x
The first step of the equation is to add/subtract like terms, I subtracted 5 on each side of the equation, our new equation is 1/4x=1/2x-2, I then subtracted 1/2x on each side so now our equation is -1/4x=-2. We then multiply 1/4 by its reciprocal on each side. Its reciprocal is -4.
Now that we know x is equal to 8 now we can fill x into the original equations which were y=1/2x+3 and y=1/4x+5 you don't have to solve both, just one of your choosing.
Therefore your answer! .
Pablo is considering two housekeeping services. Premier housekeeping charges $25 for travel to Pablo's house and $65 per hour for cleaning his house. Best house care does not have a travel fee, but charges $75 per hour for cleaning. PART A: write a system of equations that represents the housekeeping services. PART B: without solving the system of equations, explain what the solution represents.
The solution represents the number of hours of cleaning and cost of two housekeeping services, Premier and Best House Care.
What is algebraic equation ?
An algebraic equation is a mathematical expression containing one or more variables and an equal sign, where the goal is to find the value(s) of the variable(s) that make the equation true. The equation is formed by combining numbers, variables.
PART A:
Let x be the number of hours of cleaning that Premier Housekeeping provides, and let y be the number of hours of cleaning that Best House Care provides. The system of equations representing the housekeeping services is:
Premier Housekeeping: 25 + 65x = cost in dollars
Best House Care: 75y = cost in dollars
PART B:
The solution of this system of equations represents the point (x,y) in the coordinate plane, where x represents the number of hours of cleaning that Premier Housekeeping provides and y represents the number of hours of cleaning that Best House Care provides. The cost in dollars of each service will be given by the corresponding equation: the cost of Premier Housekeeping will be 25 + 65x, while the cost of Best House Care will be 75y.
The solution represents the number of hours of cleaning and cost of two housekeeping services, Premier and Best House Care.
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The difference of 2 times a number and -19 is -5. Find the number.
PLS HELP IMMEDIATELY!!
Answer:
56 adult tickets were sold that day
Step-by-step explanation:
let a represent number of adult tickets sold and c number of child tickets sold , then
a + c = 122 → (1)
9.1a + 5.7c = 885.8 → (2)
from (1) subtract c from both sides
c = 122 - a
substitute c = 122 - a into (2)
9.1a + 5.7(122 - a) = 885.8
9.1a + 695.4 - 5.7a = 885.8
3.4a + 695.4 = 885.8 ( subtract 695.4 from both sides )
3.4a = 190.4 ( divide both sides by 3.4 )
a = 56
that is 56 adult tickets were sold that day.
Convert a pressure of 1379 torr to atm
Conversion of pressure of 1379 torr to atm= 1.814474
What are unit Conversion ?Unit conversion is a multi-step procedure that involves adding, subtracting, multiplying, or dividing by a conversion factor.
Additionally, choosing the right number of significant digits and rounding may be necessary during the process.
The multi-step process of unit conversion involves multiplying or dividing by a numerical factor.
Weight, distance, and temperature can all be measured in a variety of ways.
Temperature is expressed in degrees Celsius, weight is expressed in kilos, and distance is measured in kilometers.
Imagine you are on vacation in India and are informed that the two cities are 100 kilometers apart.
Hence, Conversion of pressure of 1379 torr to atm= 1.814474
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y=6\left(2\right)^{x-4}-1
y = 6(2)^(x-4)-1 is an exponential function with a base of 2 and an exponent of x-4. The coefficient of the base, 6, is called the leading coefficient. The constant term, -1, is the y-intercept, the point where the graph of the function crosses the y-axis. The function is also a shifted version of the basic exponential function y= a*b^x, where a is the leading coefficient and b is the base of the function.
Since the base of the function is 2, the graph of the function will increase or decrease at an increasing rate. The leading coefficient of 6 will affect the steepness of the graph, making it steeper than the basic exponential function y=2^x. The horizontal shift of the graph is 4 units to the left, as the exponent has x-4 instead of x.
In terms of symmetry, the graph of this function has no symmetry.
The function has no rotational symmetry because it is not repeated after any rotation around the origin.
B) El tamaño de las pantallas de televisión viene dado por la longitud en pulgadas de la diagonal de la pantalla. Si un televisor mide 40 pulgadas y tiene 95 cm de base, ¿Cuál será su altura? Recuerda que la pulgada tiene 2,54cm.
Answer: english please so I can answer it
Step-by-step explanation:
Answer:
√80 pulgada
Step-by-step explanation:
Convirtiendo 95 cm a pulgadas,
95/2,54 = 37,40 pulgadas
Ahora, la diagonal dada es de 40 pulgadas
Usando el teorema de Pitágoras, (40)²=(37,4)² + h² (Suponiendo h como altura)
h² = 40² - 37,4²
= 80
o h = √80 pulgada
e wants a green paint that requires 3 parts blue paint to 2 parts yellow paint. if he needs a total of 10 gallons to paint the whole house, how many gallons of blue paint does he need?
The gallons of blue paint he needs to make the green paint is 6 gallons.
This is a problem in ratios. Let's look into what we know.
Volume of green paint needed = 10 gallons
Parts of blue paint needed = 3
Parts of yellow paint needed = 2
Total number of parts = parts of blue paint + parts of yellow paint
3 + 2 = 5
So fraction of blue paint needed = parts of blue paint / total parts
= 3/5
Volume of blue paint needed = [tex]\frac{3}{5}[/tex] × 10
= 6 gallons
Volume of yellow paint needed = [tex]\frac{2}{5}[/tex] ×10
= 4 gallons.
So we need 6 gallons of blue paint and 4 gallons of yellow paint to make 10 gallons of green paint.
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There were 640 gallons of water in a 1600-gallon pool. Water is being pumped into the pool at a rate of 320 gallons per hour. Write and solve an equation to find how many hours it will take to fill the pool.
Word problems aren't my strong suit, they always get me confused.
Answer:
Let's call the number of hours it takes to fill the pool "h".
We know that the initial amount of water in the pool is 640 gallons, and water is being added at a rate of 320 gallons per hour. To find out how many hours it will take to fill the pool to 1600 gallons, we can set up the following equation:
640 + (320h) = 1600
To solve for h, we'll subtract 640 from both sides of the equation:
320h = 960
Then divide both sides by 320:
h = 3
So it will take 3 hours to fill the pool with water.
It will take 3 hours to fill the pool.
Amount of water that can fit in the pool= 1600 gallons.
The amount of water already present= 640 gallons.
Therefore, the amount of water required to fill the pool= 1600-640 = 960 gallons
The rate at which the water is being pumped= 320 gallons/ hour
Therefore, the time needed to fill the pool= the quantity to be supplied/ the rate at which the water is being pumped
=> 960/ 320
=> 3 hours.
Therefore, the time required to fill the pool completely is 3 hours.
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