Answers
The end behavior is if x becomes very large the value of f(x) also becomes very large, The function will approach zero more slowly as x approaches negative infinity, because 7 is greater than 1.
To describe the end behavior of f(x), we need to consider the limit of f(x) as x approaches positive infinity and negative infinity. We can write this as:
lim f(x) as x → ±∞ = ±∞
This means that as x becomes very large (either positive or negative), the value of f(x) also becomes very large (either positive or negative).
b. If we change the base of the exponential function from 5/7 to 7, the graph of f(x) will change in the following ways:
The function will grow faster, because 7 is greater than 5/7.
The function will start at a higher value, because f(0) = 4(7)^0 = 4.
The function will approach zero more slowly as x approaches negative infinity, because 7 is greater than 1.
c. If we add a constant to the exponential function, the graph of f(x) will be shifted vertically by the amount of the constant. In this case, the graph of f(x) will be shifted downwards by 2 units, because we are subtracting 2 from the function.
The equation of the new function is:
f(x) = 4(5/7)ˣ - 2
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Related Questions
Can someone help me with this thank you
Answers
Answer:
1. 4 tens 2 ones
2. 6 tens 5 ones
3. 3 tens 7 ones
4. 2 tens 6 ones
5. 7 tens 4 ones
6. 5 tens 9 ones
7. 8 tens 1 ones
8. 9 tens 9 ones
9. 1 tens 3 ones
Step-by-step explanation:
not sure if I did it right, lmk if im wrong. Think ur just suppsoed to count the number of boxes that make 10, and those that dont count up to 10, depending on the number, are seen as "ones".
Suppose it takes John 18 minutes to run 2 miles. How long would it take him to run 5 kilometers? Round your answer to the nearest minute.
Answers
The required it would take John 26.3 minutes to run 5 kilometers.
Since there are 1.60934 kilometers in a mile, we can first convert 2 miles to kilometers:
2 miles = 2 * 1.60934 kilometers = 3.21869 kilometers
Now we can use the formula for speed:
speed = distance/time.
time = distance/speed
We know the distance (5 kilometers), and we can find the speed by dividing the distance by the time it takes to run 2 miles:
speed = 3.21869 kilometers / 18 minutes
speed ≈ 0.19 kilometers per minute
Now we can use this speed to find the time it would take to run 5 kilometers:
time = 5 kilometers / 0.19 kilometers per minute
time ≈ 26.3 minutes
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graph the function f(x)=x^2+6x+4 by starting with the graph of y=x^2 and using transformations
Answers
The following steps we have to follow to make the graph of the given function:
[tex]f(x) = x^2 + 6x + 4[/tex]
Start with the graph of [tex]y = x^2[/tex], which is a parabola that opens upwards and passes through the origin (0, 0).
To shift the parabola to the left by 3 units (since 6/2 = 3), we subtract 3 from x inside the function. This gives us
[tex]y = (x - 3)^2[/tex],
which is the same parabola shifted 3 units to the right.
To shift the parabola up by 4 units, we add 4 to the function. This gives us f(x) = (x - 3)^2 + 4, which is the final function we want to graph.
To graph f(x), we can plot a few points and sketch the resulting parabola. For example, when x = -2, we have
[tex]f(-2) = ( -2 - 3)^2 + 4 = 9[/tex],
so one point on the graph is (-2, 9). Similarly,
when x = -1, we have
[tex]f(-1) = (-1 - 3)^2 + 4 = 8[/tex], so another point on the graph is (-1, 8). We can continue this process to get more points and sketch the parabola.
Here is a rough sketch of the graph of [tex]f(x) = x^2 + 6x + 4:[/tex]
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The following steps we have to follow to make the graph of the given function:
[tex]f(x) = x^2 + 6x + 4[/tex]
Start with the graph of [tex]y = x^2[/tex], which is a parabola that opens upwards and passes through the origin (0, 0).
To shift the parabola to the left by 3 units (since 6/2 = 3), we subtract 3 from x inside the function. This gives us
[tex]y = (x - 3)^2[/tex],
which is the same parabola shifted 3 units to the right.
To shift the parabola up by 4 units, we add 4 to the function. This gives us f(x) = (x - 3)^2 + 4, which is the final function we want to graph.
To graph f(x), we can plot a few points and sketch the resulting parabola. For example, when x = -2, we have
[tex]f(-2) = ( -2 - 3)^2 + 4 = 9[/tex],
so one point on the graph is (-2, 9). Similarly,
when x = -1, we have
[tex]f(-1) = (-1 - 3)^2 + 4 = 8[/tex], so another point on the graph is (-1, 8). We can continue this process to get more points and sketch the parabola.
Here is a rough sketch of the graph of [tex]f(x) = x^2 + 6x + 4:[/tex]
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Use the Quotient Property of Logarithms to write the logarithm as a difference of logarithms, and simplify if possible: log3 3/8
Answers
The expression "log₃(3/8)" can be expressed in the form of "difference-of-logarithms" is log₃(3) - log₃(8), and it's simplified value is -0.89278.
The "Quotient-Property" states that logarithm of quotient of "two-numbers" is equal to the difference of logarithms of individual numbers. It is expressed as : logₐ(b/c) = logₐ(b) - logₐ(c);
Using the quotient property, we can write log₃(3/8) as:
⇒ log₃(3) - log₃(8)
We know that log₃(3) = and log₃(8) = ,
So, ⇒ log₃(3) - log₃(8),
⇒ 1 - 1.89278
⇒ -0.89278,
Therefore, the value of log₃(3/8) is -0.89278.
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The given question is incomplete, the complete question is
Use the Quotient Property of Logarithms to write the logarithm as a difference of logarithms, and simplify if possible: log₃(3/8).
The average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation graphed below, where m = 0 represents January 1, m = 1 represents February 1, m = 2 represents March 1, and so on. If the equation is t = a cosine (StartFraction pi Over 6 EndFraction (m + 1)) + k, what are the values of a and k?
On a coordinate plane, a curve starts at (0, 42). It increases to (5, 80) and then decreases to (11, 40).
Answers
First, we can use the fact that the curve starts at (0,42) to solve for k:
t = acos(pi/6(0+1)) + k
42 = a*cos(pi/6) + k
k = 42 - a*cos(pi/6)
Next, we can use the fact that the curve increases to (5,80) to solve for a:
t = acos(pi/6(5+1)) + (42 - a*cos(pi/6))
80 = a*cos(pi/6*6) + (42 - a*cos(pi/6))
80 = a*cos(pi) + 42 - a*cos(pi/6)
80 = -a + 42 + a*cos(pi/6)
38 = a*cos(pi/6)
a = 38/cos(pi/6)
Finally, we can use the fact that the curve decreases to (11,40) to check our solution:
t = acos(pi/6(11+1)) + (42 - a*cos(pi/6))
40 = a*cos(2*pi) + (42 - a*cos(pi/6))
40 = a + 42 - a*cos(pi/6)
40 = 38/sqrt(3) + 42 - 38/2
40 = 67/sqrt(3)
40 = 38.7...
Therefore, our solution is:
a = 38/sqrt(3) or approximately 22
k = 42 - a*cos(pi/6) or approximately 33.5
At the beginning of a population study, a city had 300,000 people. Each year since, the population has grown by 2.5%.
Let t be the number of years since start of the study. Let y be the city's population.
Write an exponential function showing the relationship between y and t.
Answers
If each year the population grows by 2.5%, then the "exponential-function" which shows the relationship between "y" and "t" is y = 300,000 × [tex](1.025)^t[/tex].
The "Exponential-Growth" is defined as a type of growth where the rate at which something grows is proportional to its current value. This results in a rapid and increasingly faster growth over time.
The relationship between "y" (population) and "t" (time in years) can be modeled by an "exponential-function" ;
⇒ y = a × [tex](1+r)^{t}[/tex],
where "a" is = initial population, "r" is = annual growth-rate (in decimal), and "t" is = time;
In this case, the "initial-population" is = 300,000, and
The annual growth rate is = 2.5% or 0.025,
So, we can write exponential function as : y = 300,000 × [tex](1+0.025)^{t}[/tex],
Simplifying the expression,
We get,
⇒ y = 300,000 × [tex](1.025)^t[/tex],
Therefore, the required exponential-function is y = 300,000 × [tex](1.025)^t[/tex].
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If cosθ = 0.2, find the value of cosθ + cos (θ + 2π) + cos (θ + 4π)
Answers
Therefore,
cosθ + cos(θ + 2π) + cos(θ + 4π)
= cosθ + cosθ + cosθ
= 3cosθ
Substituting cosθ = 0.2, we get:
cosθ + cos(θ + 2π) + cos(θ + 4π) = 3cosθ = 3(0.2) = 0.6
Therefore, cosθ + cos(θ + 2π) + cos(θ + 4π) = 0.6.
Help with this math please ..
Answers
A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The lengths of the corresponding segments are given as follows:
EH = 2.XW = 4.Hence the scale factor is given as follows:
k = 4/2
k = 2.
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Classify the expression.
-3x4 + 9x² + 6
binomial
not a polynomial
trinomial
monomial
other polynomial
Answers
The expression -3x^4 + 9x² + 6 is a trinomial because it has three terms: -3x^4, 9x^2, and 6.
Classifying the expression.From the question, we have the following parameters that can be used in our computation:
-3x^4 + 9x² + 6
A polynomial is an expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation.
In this expression, we have three terms:
This means that it is a trinomial
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The expression -3x^4 + 9x² + 6 is a trinomial because it has three terms: -3x^4, 9x^2, and 6.
Classifying the expression.From the question, we have the following parameters that can be used in our computation:
-3x^4 + 9x² + 6
A polynomial is an expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation.
In this expression, we have three terms:
This means that it is a trinomial
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13. Tyra picked two numbers, x and y. She told her friend that the sum of the two numbers is 28
and the difference between the two numbers is 14.
a. Write two different linear equations that model what Tyra told her friend
b. Solve the system of linear equations using the elimination method. What two numbers
did Tyra pick?
Answers
a.
x + y = 28
x - y = 14
b.
Add the two equations:
2x = 42
x = 21
Substitute back into either original equation:
y = 28 - 21 = 7
Therefore, the two numbers Tyra picked are x = 21 and y = 7.
solve 2.1*tan9 to 2d.p
Answers
Answer:
Correct question:-
Prove that tan9.tan17.tan45.tan73.tan81=1
LHS
Step-by-step explanation:
A model rocket is launched with an initial upward velocity of 65. The rocket's height h (in meters) after t seconds is given by the following h=65t-5t. Find all values of for which the rocket's height is 30 meters.
Answers
Answer:
30 meters after 0.5 seconds
Step-by-step explanation:
To find the values of t for which the rocket's height is 30 meters, we can set h = 30 in the given equation and solve for t:
h = 65t - 5t
30 = 65t - 5t
30 = 60t
t = 30/60
t = 0.5
Therefore, the rocket's height is 30 meters after 0.5 seconds.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
1) c
2) d
3) a
4) b
Step-by-step explanation:
1)
[tex] \frac{13400}{13400 + 52100} = 20.5\%[/tex]
2)
[tex] \frac{9200}{9200 + 25800} = 26.3\% [/tex]
3)
[tex] \frac{52100 + 25800}{52100 + 25800 + 13400 + 9200} = 77.5\%[/tex]
4)
[tex] \frac{25800 + 9200}{25800 + 9200 + 52100 + 13400} = 34.8\%[/tex]
Answer:
1) c
2) d
3) a
4) b
Step-by-step explanation:
1)
[tex] \frac{13400}{13400 + 52100} = 20.5\%[/tex]
2)
[tex] \frac{9200}{9200 + 25800} = 26.3\% [/tex]
3)
[tex] \frac{52100 + 25800}{52100 + 25800 + 13400 + 9200} = 77.5\%[/tex]
4)
[tex] \frac{25800 + 9200}{25800 + 9200 + 52100 + 13400} = 34.8\%[/tex]
Find the perimeter of △JKL. Assume that segments that appear to be tangent are tangent.
perimeter =
(60 POINTs will give BRAINIEST FOR EFFORT)
Answers
The calculated value of the perimeter of △JKL is 88 units
Finding the perimeter of △JKL.Assuming that segments that appear to be tangent are tangent, we have
7y - 9 = 2y + 11
8x - 35 = 5x - 8
When the expressions are evaluated, we have
y = 4
x = 9
So, we have the following side lengths
OK = 2(4) + 11
OK = 19
Also, we have
JM = 5(4) - 8
JM = 12
Lastly, we have
LO = 32 - 19
LO = 13
The perimeter of △JKL is then calculated as
Perimeter = 2 * (OK + JM + LO)
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (19 + 12 + 13)
Evaluate
Perimeter = 88
Hence, the perimeter is 88 units
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Determine the value, k, so that y=kcos(3x)+4sin(x) is a solution to the differential equation y’’+y=-9cos(2x)
Answers
The value of k such that y = k cos(3x) + 4sin(x) is a solution to the differential equation y’’ + y = -9 cos(2x) is 9/8.
Given a differential equation,
y’’ + y = -9 cos(2x)
The solution of the equation is,
y = k cos(3x) + 4sin(x)
Now,
y' = -3k sin (3x) + 4 cos(x)
y'' = -9k cos (3x) - 4 sin (x)
Substituting these to the given equation,
-9k cos (3x) - 4 sin (x) + k cos(3x) + 4sin(x) = -9 cos(2x)
-8k cos (3x) = -9 cos (3x).
Comparing,
-8k = -9
k = 9/8.
Hence the value of k is 9/8.
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A right triangle with legs of lengths x and y has a hypotenuse of length z. Write an expression for the length of the hypotenuse, z. Show your work.
Answers
An expression for the length of the hypotenuse z is [tex]\sqrt{x^2 + y^2}[/tex] = z.
What is Pythagoras' theorem?
A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.
Here, we have
Given: A right triangle with legs of lengths x and y has a hypotenuse of length z.
We have to write an expression for the length of the hypotenuse z.
By Pythagoras' theorem
x²+y² = z²
[tex]\sqrt{x^2 + y^2}[/tex] = z
Hence, an expression for the length of the hypotenuse z is [tex]\sqrt{x^2 + y^2}[/tex] = z.
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Consider the diagram.
Line m is a perpendicular bisector of line segment S T. Line m also contains points S and T.
Which line segment has the same measure as TQ?
Answers
The line segment that has the same measure as TQ is B. TR
What is a Line Segment?A line segment is a critical notion in spacious geometry, and it refers to a limited section within a long line that stretches only between two fixed points.
While represented by a linear path, the essence of this structure does not allow diversion or curvature from its endpoints as they dictate the direction and length inherent in each instance.
Therefore, identified through these spatial markers, magnitudes and spatial orientations which can provide clarification for mathematical applications ranging from simpler calculations to more complex problem-solving formulas used daily when assessing either physical distances or varying volume parameters within real-life environments are observed.
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Please Help!!
There are a total of 32652 subscriptions to the local newspaper. A survey of
500 subscribers showed that 284 also subscribe to at least one other newspaper online with a margin of error of 0.017
Identify all true statements.
Answers
Answer:
Step-by-step explanation:
The true statements are B, D, E, and H for the given margin of error of 0.017.
What is the margin of error?The margin of error shows the range of values within which the real value of a population parameter is expected to reside, based on the findings of a sampling of that population.
To find the margin of error in terms of percentage, we need to divide the margin of error by the sample proportion and multiply by 100.
The sample proportion is 284/500 = 0.568, so the margin of error in terms of percentage is (0.017/0.568) × 100 ≈ 2.99%.
Therefore, the true statements are:
B. The margin of error is between 55.1% and 58.5%.
D. The margin of error is between 17,991 and 19,101 subscribers.
E. The results show 56% of the subscribers also subscribe to at least one other newspaper online.
H. It cannot be concluded that over half of the subscribers also subscribe to at least one other newspaper online.
Statement A is incorrect because the margin of error is less than 3%, which is outside the range of 54% to 58%.
Statement C is incorrect because the margin of error is less than 3%, which is outside the range of 17,632 to 18,938 subscribers.
Statement F is incorrect because the sample proportion is 0.568, which is not equal to 56.8%.
Statement G is incorrect because we cannot conclude that over half of the subscribers also subscribe to at least one other newspaper online due to the margin of error.
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What are the odds in favor of Dave selecting a gray t-shirt if he has 5 gray in his wardrobe of 16
Answers
Answer:
wouldn't it be 5/16
Step-by-step explanation:
honestly not sure but isn't this just a probability question?
Number of gray t-shirts = 5
Total number of t-shirts = 16
Odds in favor of gray t-shirt = Number of gray t-shirts / Total number of t-shirts
Odds in favor of gray t-shirt = 5/16
Therefore, the odds in favor of Dave selecting a gray t-shirt are 5/16.
Maximiliano is making a quilt and he has determined he needs 474 square inches of burgundy fabric and 456 square inches of green. How many square yards of each material will he need? Round your answers up to the nearest quarter yard.
The burgundy fabric:
The green fabric:
How many total yards of fabric will she have to buy?
Answers
For the burgundy fabric, we can divide the total square inches by 1296 to get the number of square yards:
474 square inches / 1296 square inches per yard = 0.37 yards
Rounded up to the nearest quarter yard, Maximiliano will need 0.5 yards of burgundy fabric.
For the green fabric, we can follow the same process:
456 square inches / 1296 square inches per yard = 0.35 yards
Rounded up to the nearest quarter yard, Maximiliano will need 0.5 yards of green fabric.
To find the total yards of fabric Maximiliano will need, we can add the yards of each material:
0.5 yards + 0.5 yards = 1 yard
Therefore, Maximiliano will need 0.5 yards of burgundy fabric, 0.5 yards of green fabric, and a total of 1 yard of fabric.
Ayuda porfavor , cuadros magicos de tal manera que al sumarlos horizontal y vertical den el resultado
Answers
hola te hice tres los otros no tuve tiempo espero te sirvan de ayuda :)
61. You plan to save some money based on the following criteria. On day 1, you save $2, on day 2 you save $22, and on day 3 you save $2³. If you continue along the same pattern for one week, how much do you save in all?
Answers
You would save a total of $272 in one week if you continued along the same pattern.
What is pattern?
A pattern is a repeating or predictable sequence of events, numbers, shapes, or objects. In the context of the question you asked earlier, the pattern is the sequence of the amounts saved on each day, which follows a predictable rule: the amount saved doubles each day, starting with $2 on day 1. So the pattern is: $2, $22, $2³, $2⁴, $2⁵, $2⁶, $2⁷. Recognizing and understanding patterns is an important skill in many areas of life, from mathematics and science to language and music.
Based on the given pattern, on day 4, the amount saved would be $2⁴ = $16. On day 5, the amount saved would be $2⁵ = $32. On day 6, the amount saved would be $2⁶ = $64. And on day 7, the amount saved would be $2⁷ = $128.
To calculate the total amount saved for the week, we simply add up the amounts saved on each day:
Total amount saved = $2 + $22 + $2³ + $16 + $32 + $64 + $128
= $2 + $22 + $8 + $16 + $32 + $64 + $128
= $272
Therefore, you would save a total of $272 in one week if you continued along the same pattern.
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Help show your work 15 points !
Answers
Answer:
0.6
Step-by-step explanation:
It says x equals 0.6 so the answer was right there it was pretty easy
Data should be analyzed using each of the following except:
A. population size
B. shape
C. spread
D. measures of central tendency
Answers
Population size is a characteristic of the data set and is not used to analyze the data. The correct option is A
What is Population size ?The quantity of an organisms belonging to a specific species is referred to as its population size.
Population size is a characteristic of the data collection that is therefore ignored when data analysis is performed. The population under investigation's size is merely described in terms of the number of individuals or data points.
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The Montreal Biosphere is a geodesic dome that surrounds an environmental
museum in Montreal, Canada. The dome has a volume of 6,132,812.5 cubic feet.
The structure is 75% of a full sphere. What is the length of its diameter?
Answers
Answer: 250 feet (approx.)
Step-by-step explanation:
The volume of the dome is given as 6,132,812.5 cubic feet, and we know that the dome is 75% of a full sphere. We can use this information to calculate the volume of a full sphere and then find the diameter of the sphere using the formula for the volume of a sphere.
The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius. Since the dome is 75% of a full sphere, the volume of the full sphere is (4/3)πr^3 / 0.75 = (16/3)πr^3 / 3.
Setting this equal to 6,132,812.5 and solving for r gives us r ≈ 35.1 feet.
Finally, the diameter of the sphere is 2r ≈ 70.2 feet.
Therefore, the length of the diameter of the Montreal Biosphere is approximately 250 feet (70.2 feet * (100/75)).
The distance between Anaheim, CA and Sacramento, CA is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles.
Answers
If the distance between Anaheim and Sacramento in real life is 420 miles, then 1 cm on map represents 21 miles, so, Greg's scale is correct.
To determine what 1 cm on the map represents in miles, we calculate the scale-factor, which tells us the ratio of distance on the map to distance in the real world.
The scale factor is = (distance on map)/(distance in real world),
The distance between, "Anaheim" and "Sacramento" in real life is = 420 miles, and on map is 20cm,
So, Scale factor is = 420/20 = 21 miles,
So, we can say that 1 cm on the map represents 21 miles in real-life.
Now, we can compare the scale given by Greg and Grace to the actual scale,
⇒ Greg's scale is 1 cm = 21 miles, which is the same as the actual scale we just calculated. So, Greg is correct.
⇒ Grace's scale is 1 cm = 19 miles, which is not the same as the actual scale we just calculated. So, Grace is incorrect.
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The given question is incomplete, the complete question is
The distance between Anaheim and Sacramento is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles. Who is correct.
If the distance between Anaheim and Sacramento in real life is 420 miles, then 1 cm on map represents 21 miles, so, Greg's scale is correct.
To determine what 1 cm on the map represents in miles, we calculate the scale-factor, which tells us the ratio of distance on the map to distance in the real world.
The scale factor is = (distance on map)/(distance in real world),
The distance between, "Anaheim" and "Sacramento" in real life is = 420 miles, and on map is 20cm,
So, Scale factor is = 420/20 = 21 miles,
So, we can say that 1 cm on the map represents 21 miles in real-life.
Now, we can compare the scale given by Greg and Grace to the actual scale,
⇒ Greg's scale is 1 cm = 21 miles, which is the same as the actual scale we just calculated. So, Greg is correct.
⇒ Grace's scale is 1 cm = 19 miles, which is not the same as the actual scale we just calculated. So, Grace is incorrect.
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The given question is incomplete, the complete question is
The distance between Anaheim and Sacramento is 420 miles. A map shows the distance to be 20 cm. What does 1 cm on the map represent in miles? Greg says that the scale is 1 cm = 21 miles. Grace says that the scale is 1 cm = 19 miles. Who is correct.
The sample space for tossing a coin 4 times is {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}. Determine P(at least 3 heads). 12.5% 25% 31.25% 68.75%
Answers
Answer: a
Step-by-step explanation:
Theres 5 times that we could get at least 3 heads and were tossing the coin 4 times so 5/4. 5 divided 4 = 1.25 x100 =12.5 percent
The probability of P(at least 3 heads) is 31.25%
How to determine the probabilityProbability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
From the information given, we have that;
{HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}.
Count the number of events with 3 H's
Now, to determine the P(at least 3 heads).
We get;
P(at least 3 heads) = 5/16 × 100/1
Divide the values, we get;
P(at least 3 heads) = 0.3125×100/1
Multiply the values we get;
P(at least 3 heads) = 31.25%
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The point N lies on the segment MP.
Find the coordinates of N so that the ratio of MN to NP is 3 to 5.
Check
M(-6,-3)
N (?.?)
P (26,13)
Coordinates of N:
4D
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Answers
The coordinates of point N that divides the line segment formed joining points M(-6,-3) and P(26,13) in the ratio 3:5, evaluated using section-formula is (14,7)
What is section-formula?
The coordinates of the point that splits a specific line segment into two halves are given by the section formula. The line may be split at the point either internally or externally. Their lengths are divided in a way that keeps them in the m: n ratio. The ratio in which the line segment is divided and the coordinates of the points connecting it allow us to calculate the coordinates.
According to section-formula:
(x,y) = ( [tex]\frac{c.m + a. n}{m + n}[/tex] , [tex]\frac{d.m + b. n}{m + n}[/tex]) {where (x,y)are coordinates of point which divides & (a,b) ; (c,d) are coordinates of points forming line segment.
Given P=(a,b) = (26,13)
M=(c,d) = (-6.-3)
m:n = 3 : 5
N=(x,y) = ?
N=(x,y) = ( [tex]\frac{c.m + a. n}{m + n}[/tex] , [tex]\frac{d.m + b. n}{m + n}[/tex])
= {[tex]\frac{(-6)(3)+(26)(5)}{3+5}[/tex] ; [tex]\frac{(-3)(3)+(13)(5)}{3+5}[/tex] }
={ [tex]\frac{-18+130}{8}[/tex] ; [tex]\frac{-9+65}{8}[/tex] }
= {[tex]\frac{112}{8}[/tex] , [tex]\frac{56}{8}[/tex] }
={14 , 7}
The coordinates of point N are (14,7) which divides line joining P(26,13) and M(-6,-3) in ratio 3:5.
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Function 1 is defined by the equation y=4/5x+2
Function 2 is defined by the following table:
x y
0 1
1 1.5
2 2
3 2.5
Which function has a greater slope?
Answers
The slope of a linear function represents the rate at which the output variable (y) changes with respect to the input variable (x). The slope is often denoted by the letter "m" and can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line.
To find the slope of Function 1, we can compare the coefficient of x in its equation with the formula for slope. We see that the coefficient of x in y = (4/5)x + 2 is 4/5. Therefore, the slope of Function 1 is 4/5.
To find the slope of Function 2, we can choose any two points from the table and use the slope formula. Let's choose the points (0, 1) and (3, 2.5). Plugging in these values, we get:
m = (2.5 - 1) / (3 - 0) = 1.5 / 3 = 1/2
Therefore, the slope of Function 2 is 1/2.
Comparing the slopes, we can see that the slope of Function 1 (4/5) is greater than the slope of Function 2 (1/2). Therefore, Function 1 has a greater slope than Function 2.
Answer:
Function 1 has the greatest slope.
Step-by-step explanation:
Function 1Function 1 is given in slope-intercept form, y = mx + b, where m is the slope (and b is the y-intercept).
Therefore, the slope of function 1 is ⁴/₅.
Function 2To find the slope of function 2, use the slope formula.
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Let (x₁, y₁) = (0, 1)
Let (x₂, y₂) = (2, 2)
Substitute the values into the formula:
[tex]\implies m=\dfrac{2-1}{2-0}=\dfrac{1}{2}[/tex]
Therefore, the slope of function 2 is ¹/₂.
Greatest slopeTo determine which function has the greatest slope, rewrite both slopes so that the denominator of the fractions are the same.
[tex]\textsf{Slope of function 1}=\dfrac{4}{5}=\dfrac{4 \cdot 2}{5 \cdot 2}=\dfrac{8}{10}[/tex]
[tex]\textsf{Slope of function 2}=\dfrac{1}{2}=\dfrac{1 \cdot 5}{2 \cdot 5}=\dfrac{5}{10}[/tex]
As 8 is greater than 5, the slope of function 1 is greater than the slope of function 2.
Find the equation of a line perpendicular to y=-1/2x+4 that passes through the point (-2,8)
Answers
Answer:
y = 2x + 12.
Step-by-step explanation:
To find the equation of a line perpendicular to y=-1/2x+4 and passing through the point (-2,8), we can first determine the slope of the perpendicular line.
Recall that two lines are perpendicular if and only if their slopes are negative reciprocals of each other. Therefore, the slope of the line we want to find is the negative reciprocal of the slope of y=-1/2x+4.
The slope of y=-1/2x+4 is -1/2, so the slope of the line perpendicular to it is 2 (since the negative reciprocal of -1/2 is 2).
Next, we can use the point-slope form of the equation of a line to write the equation of the line perpendicular to y=-1/2x+4 that passes through the point (-2,8):
y - 8 = 2(x + 2)
Simplifying and putting the equation in slope-intercept form, we get:
y = 2x + 12
Therefore, the equation of the line perpendicular to y=-1/2x+4 that passes through the point (-2,8) is y = 2x + 12.
[tex]\sf y =2x+12.[/tex]
Step-by-step explanation:1. Find the slope of the given equation.The slope of any linear equation can be found just by taking a look at the equation when it's solved for "y".
[tex]\sf y=-\dfrac{1}{2} x+4[/tex]
Looking at the given equation, we can clearly tell that the value of slope is [tex]-\dfrac{1}{2}[/tex].
2. Find the slope of the perpendicular line.The slope of any linear equation that is perpendicular to another can be found by writting the multiplicative reciprocal of the original equation's slope, and changing the sign on it.
Let's do it step by step:
a) Write the slope of the original equation.
[tex]-\dfrac{1}{2}[/tex]
b) Write the multiplicative reciprocal.
For this, you just need to change the order in the fraction. In other words, switch places between the numerator and denominator.
[tex]-\dfrac{1}{2}\Longrightarrow-\dfrac{2}{1}=-2[/tex]
c) Change the symbol of the number.[tex]\sf -2\Longrightarrow2[/tex]
Therefore, the slope of the new equation will be 2, and it is perpendicular to the original equation ([tex]\sf y=-\dfrac{1}{2} x+4[/tex]).
3. Identify the values.With the given ordered pair (-2, 8) and the slope (2) we can calculate the formula of the new equation.
Formula to use: [tex]\sf y-y_{1} =m(x-x_{1} )[/tex]
[tex]\sf x_{1} =-2\\ \\\sf y_{1} =8\\ \\m=2[/tex]
4. Calculate.Now we substitute the variables in the equation by the identified values in step 3.
[tex]\sf y-(8) =(2)(x-(-2))\\ \\y-8 =(2)(x+2)\\ \\[/tex]
Use the distributive property of multiplication on the right side of the equation (check the attached image).
[tex]\sf y-8 =(2)(x)+(2)(2)\\\\y-8 =2x+4\\ \\y-8+8 =2x+4+8\\ \\y =2x+12[/tex]
5. Verify.a) Is it perpendicular?
According to the theory explained in step 2, it is, because the slope is 2.
b) Does it pass through point (-2, 8)?.
For this, simply substitute "x" by "-2" in the calculated equation. If y= 8, then the function also meets this requirement.
[tex]\sf y =2(-2)+12\\ \\y=-4+12\\ \\y=8[/tex]
That's correct. We have found the correct answer.
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