If a horizontal line can intersect the graph of the function only a single time, then the function is mapped as one-to-one.
Now, According to the question:
One to one function basically denotes the mapping of two sets. A function g is one-to-one if every element of the range of g corresponds to exactly one element of the domain of g. One-to-one is also written as 1-1. A function f() is a method, which relates elements/values of one variable to the elements/values of another variable, in such a way that the elements of the first variable identically determine the elements of the second variable.
Hence, If a horizontal line can intersect the graph of the function only a single time, then the function is mapped as one-to-one.
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fellix built a ramp based on the scale drawing below. if the height of felix's ramp is 6 inches from the ground, how long is the part of the ramp that is on the ground?
The scale drawing and applying proportion, the length of the part of the ramp that is on the ground is calculated as 72 inches.
In a scale drawing, proportion can be used to find actual measurements.
height of Felix's ramp = 6 inches
height on scale drawing = 1 inches
Length of ramp on the ground = x = ?
length of ramp on scale drawing = 12 inches
Thus, the following proportion can be created:
6 = 1
x = 12
Cross multiply
x = (6×12)/1
x = 72 inches
Therefore, given the scale drawing and applying proportion, the length of the part of the ramp that is on the ground is calculated as 72 inches.
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What is the domain all real numbers except ___?
All real numbers except those that have been specifically excluded by a given condition or set of conditions.
The domain of all real numbers except is any set of real numbers that has been specifically excluded by a given condition or set of conditions. This could include any real number that does not meet the requirements of a given equation, such as any real number that does not satisfy the equation x2+1=0, or any real number that does not fall within a certain range, such as any real number that is not between 1 and 5. The domain of all real numbers except is any set of numbers that has been specifically excluded from the set of all real numbers. This exclusion could be due to a particular condition or set of conditions that must be fulfilled in order for a number to be included in the set.
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Using long division, find the quotient of (6x^3 + x^2 - 2x + 15) / (2x + 3)
Group of answer choices
3x^2 - 4x + 5
3x^2 + 5x - 6
2x^2 + 3x - 5
3x^2 - 5x - 5
Answer:
Option A: 3x^2 - 4x + 5
Step-by-step explanation:
As you can see in the image, only option A (black dashed) matches the equation (solid red). The others (purple, green, and orange dashed) do not match.
Patrick purchased some supplies for his guitar students. He bought 25 guitar picks and 25 guitar strings since they only cost
$1 more than the guitar picks. He spent a total of $40. If c is the cost of one guitar pick, find the cost of one guitar string.
(1 point)
0.30
The cost of one guitar string is obtained as follows:
$1.3.
How to obtain the costs?The costs are obtained using a system of equations, for which the variables are given as follows:
Variable x: cost of a guitar pick.Variable y: cost of a guitar string.He purchases 25 of each, for a total of $40, hence:
25x + 25y = 40.
x + y = 1.6.
A string costs $1 more than a guitar pick, hence:
y = x + 1.
x = y - 1.
Hence the cost of a string is obtained as follows:
y - 1 + y = 1.6
2y = 2.6
y = 2.6/2
y = $1.3.
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Paula bought a ski jacket on sale for $8 less than half its original price. She paid $84 for the jacket. What was the original price?
Answer:
184
Step-by-step explanation:
(84+8)(2)=184
Drag and drop the constant of proportionality into the box to match the table.
If the table is not proportional, drag and drop "not proportional" into the box.
The constant of proportion in the proportional relationship is 3/2
What is constant of proportionalityThe constant of proportionality is a value that represents the ratio of two variables in a proportional relationship. The constant of proportionality is represented by the letter "k" in the mathematical equation y = kx, where y and x are the variables in the relationship, and k is the constant of proportionality. It is a fixed value that does not change regardless of the specific values of the variables. The value of k can be determined by dividing the y-value of any point on the relationship by the corresponding x-value of that point.
To determine the constant of proportionality, we have to use the formula;
y = kx
Taking one point from the table;
9 = k(6)
k = 9/6
k = 3 / 2
Taking another point to confirm
3 = k(2)
k = 3/2
The constant of proportionality is 3/2
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What is the distance between the points with coordinates 3/4 and 0 0?
The distance between the two points (3, 4) and (0, 0) is 25 units.
What is the distance?Regardless of direction, an object's total velocity determines its distance.
Distance is the amount of space an object has traveled, regardless of where it began or concluded.
Knowing how far an object is from us allows us to estimate its actual size.
The following formula is typically used to determine the distance between two points: d=((x2 - x1)2 + (y2 - y1)2)
So, the distance formula is thus:
d=((x2 - x1)2 + (y2 - y1)2)
Points are: (3, 4) and (0, 0)
Now perform the computation shown below by plugging the numbers into the formula above:
d=((x2 - x1)2 + (y2 - y1)2)
d=((0 - 3)2 + (0 - 4)2)
d=((3)2 + (4)2)
d=(9+16)
d=25 units
Therefore, the distance between the two points (3, 4) and (0, 0) is 25 units.
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What is the inverse of log X?
The inverse of log X is bˣ , where b is the logarithm's base.
Inverse Function[f][y] provides the value of x for which f[x] equals y. Inverse Function[f][y] represents the inverse of the function f. To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.
To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.
Let us take,
n = log₁₀ X
Then, 10ⁿ = X
(assuming that the logarithm's base is 10)
If the logarithm's base is b, then it is bˣ.
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What’s a polygon, sides,verticals,angle,and closed shapes
Answer:
The point that the two sides meet at the vertext
Step-by-step explanation:
Its just right G
How do you find f (- 3 on a graph?
To find the value of f(-3) substitute the value of x in the function f(x) with -3 and plot the graph.
What is function?The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
To find the value of f(-3) substitute the value of x in the function f(x) with -3.
This substitution of value will give the final output value f(x), which is the y-coordinate. Using the x and the y coordinate plot the graph.
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Juan travels 49 miles per hour for 9 hours. find the distance traveled, in miles.
The distance traveled by Juan in miles is 441 miles.
What is distance?
Distance is the total length of a path that an object has taken to get from one place to another. The route from the starting point to the ending point might or might not be straight. Distance is a scalar quantity with only magnitude and no direction.
Total distance travelled by the object. This depends on the entire route taken, not just the beginning and ending locations. The distance travelled is always a positive number. a scalar quantity with distance units.
Distance = speed × time
Given speed = 49 miles per hour
Time = 9 hours
Distance = 49 × 9
= 441 miles
Thus, the distance traveled by Juan in miles is 441 miles.
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What is the speed of a car which covers a distance of 15 km in 20 minutes?
A scalar quantity known as speed is used to describe "the rate at which an item changes its position" or "the distance travelled in a unit of time." It is a way to gauge how quickly something is moving and is frequently expressed in terms of the amount of space covered in one unit of time, such as miles per hour (mph) or kilometers per hour (km/h). Speed is calculated as follows: speed = distance / time.
Step 1: To determine a car's speed, divide the distance travelled by the time required.
Step 2: In this instance, the journey took 20 minutes and covered 15 kilometers.
Step 3: Divide the number of minutes by 60 to convert it to hours. Therefore, 20 minutes equals 20/60, or 0.333 hours.
Step 4: Now divide the number of kilometers (km) travelled by the number of hours travelled (0.333 hours)
= 15 km / 0.333 hours
=45 km/h
Therefore speed of the car is 45km/hr.
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I picked a but I would like to make sure that my answer is right. Can someone verify my answer is right
Answer:
Answer option 2 is right
Step-by-step explanation:
You're assuming that there were 10 people asked in 8th grade, but the decimal values indicate a percentage of the people asked not the exact value unless an amount is given.
When 3x - 12y = 6 and y=-2, what is the value of x?
Answer: x = 2+4y (I think, please tell me if I'm wrong)
Step-by-step explanation: Hope this helps
a five-card hand is called a flush if all five cards are in the same suit but not all five denominations are consecutive.s. let n be the set of five cards in hearts that are not flushes. how many outcomes are in n?
40 outcomes are in n if there is a five-card hand is called a flush if all five cards
Since 2, 3, and 4 are the only ranks that can never be at the top of a series of 5 cards, you have 133=10 ways to choose the ranks.
You can choose from the following 133 rank options for your straight's high card: A, K, Q, J, T, 9, 8, 7, 6, 5. Keep in mind that the A counts as the straight's bottom card.
The suit for the first card in your sequence must likewise be determined using (41)=4, and the remaining cards must all automatically agree or contradict.
Your response is 40.
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(b) The exact value of q is
-6+√44
2
Write
-6+√44
2
in the form a + √b.
The exact value of q in the form a + √b. IS -6 + √44 / 2 = -3 + √22.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It contains variables and operators (such as +, -, x, ÷) and the goal is often to find the value of the variables that make the equation true. For example, 2x + 3 = 7 is an equation where x is the variable and the goal is to find the value of x that makes the equation true.
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This is the graph of a linear inequality. Write the inequality in slope-intercept form.
The inequality in slope-intercept form is: y ≤ -x - 2.
How to Write the Linear Inequality of a Graph?The linear inequality of a graph can be written in slope-intercept form as y = mx + b, where m is the slope of the line, b is the point on the y-axis where the line intercepts, and "=" would be replaced with the inequality sign, which is determined by the type of boundary line and if the shaded region is above it or below it.
The slope of the line (m) = rise/run = -2/2 = -1.
Y-intercept (b) = -2.
The line is a solid line, and the shaded region is below it, therefore, the inequality sign to use is ≤.
Substitute m = -1 and b = -2 into y ≤ mx + b:
y ≤ -x - 2
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five-card hand is called a flush if all five cards are in the same suit but not all five denominations are consecutive. for example, both (a, 2, 3, 4, 7)and (2, 4, 6, j, q)are flushes, but neither (a, 2, 3, 4, 5)nor (10, j, q, k, a)is a flush. let n be the event of not having a flush. how many outcomes are in n ?
The number of outcomes in n is 2,361,222. The concept used in this problem is known as combinatorics, which is a branch of mathematics that deals with counting and arranging objects.
The problem is asking for the number of ways to choose 5 cards from a deck of 52 cards, such that none of the cards are of the same suit.
To solve the problem, we use the formula for counting the number of ways to choose k items from a set of n items without replacement, which is:
(n choose k) = n! / (k! * (n-k)!)
Where n! represents the factorial of n, which is the product of all positive integers less than or equal to n.
This can be calculated as (52 choose 5) - (13 choose 1 * 39 choose 4) - (13 choose 2 * 26 choose 3) - (13 choose 3 * 13 choose 2) - (13 choose 4 * 13 choose 1) = 2, 598, 960 - 13 * 9, 615 - 78 * 1, 030 - 286 * 78 - 715 * 13 = 2, 598, 960 - 125, 995 - 79, 380 - 22, 068 - 9, 295 = 2, 361, 222
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The function y = 3p3 – 8p2 + 4p represents the population size of mackerel y based on the number of pounds of plastic p found in the ocean.
Find the zeros of the function and explain their meaning within the context of the situation.
The zeros of the given function y = 3p³ – 8p² + 4p are p = 0, p = 2, and p = 2/3
What are the zeros of a function?The zeros of a function are the values of the independent variable (in this case, p) for which the function equals zero.
To find the zeros of the function y = 3p³ – 8p² + 4p, we need to set y equal to zero and solve for p.
y = 3p³ – 8p² + 4p = 0
3p³ – 8p² + 4p = 0
We can factor this as p(3p-2)(p-2) = 0
So, the zeros of the function are p = 0, p = 2, and p = 2/3
In the context of the situation, these zeros represent the values of plastic pollution (p) at which the population size of mackerel (y) reaches 0. Therefore, the zero p = 1 represents the amount of plastic pollution that causes the mackerel population to reach p = 0, p = 2, and p = 2/3 represent the solutions.
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How many times can 200 go into 7592949
Answer:
37,964 times!
Step-by-step explanation:
Hope it helps! =D
What is the sign of -4ab−4abminus, 4, a, b when a>0a>0a, is greater than, 0 and b<0b<0b, is less than, 0?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Positive
(Choice B)
B
Negative
(Choice C)
C
Zero
The value of the expression -4ab - 4ab when a > 0 is C. Zero
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
In this case the value of the expression will be:
-4ab - 4ab when a > 0
Let's assume that a is 1 and b is -1
= -4(1 × -1) - 4(1 × -1)
= 4 - 4
= 0
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Answer: （A）Positive
Step-by-step explanation: The other guy was wrong. Got this one khan
Line m passes through points (6, 8) and (2, 1). Line n passes through points (9, 10) and (2, 6). Are line m and line n parallel or perpendicular?
Step-by-step explanation:
lets calculate each of the gradients(m & n)
for m; x1 = 6,x2 = 2,y1 = 8,y2 = 1
[tex]gradient = \frac{y2 \\ - y1}{x2 - x1} [/tex]
[tex]m = \frac{1 \\ - 8}{2 - 6} = \frac{ - 7}{ - 4} [/tex]
[tex]m = \frac{7 \\ }{4} [/tex]
now lets calculate the gradient for m
x1=9, x2=2, y1=10, y2=6
[tex]n = \frac{ \\ 6 - 10}{2 - 9} [/tex]
[tex]n = \frac{ - 4 \\ }{ - 7} [/tex]
[tex]n = \frac{4 \\ }{7} [/tex]
for parallelism
m1 = m2
[tex] \frac{4}{7 \\ } = \frac{7}{4} [/tex]
therefore it is not parallel
for perpendicularism
[tex] \frac{ - 1 \\ }{ \frac{4}{7} } = \frac{ - 7}{4} [/tex]
[tex] \frac{ - 1}{ \frac{7}{4} } = - \frac{ 4}{7} [/tex]
therefore it is perpendicular
is 9, -18, 36, -72 arithmetic, geometric, or neither
Answer:
Geometric
Step-by-step explanation:
By a constant factor of -2
9(-2) = -18
-18(-2) = 36
36(-2) = -72
I hope this helps!
A company charges a shipping fee of $0. 85 per pound.
How much would the company charge to ship a package that weighs 14. 6 pounds?
The company would charge $12.41 to ship a package that weighs 14.6 pounds.
1. Multiply the shipping fee of $0.85 by the weight of the package, 14.6 pounds.
2. $0.85 x 14.6 = $12.41
3. The company would charge $12.41 to ship a package that weighs 14.6 pounds.
The company would charge $12.41 to ship a package that weighs 14.6 pounds.
The company charges a shipping fee of $0.85 per pound. In order to calculate the shipping cost for a package of a certain weight, the shipping fee is simply multiplied by the given weight. Therefore, for a package weighing 14.6 pounds, the company would charge $12.41 for shipping. The cost for the package can easily be figured out with a simple calculation, and this makes it convenient for customers to know the exact shipping cost of their packages.
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(2/7 * x + 5/8) - (1/6 * x - 3/7)
Answer: To simplify the expression (2/7 * x + 5/8) - (1/6 * x - 3/7), we need to combine like terms.
(2/7 * x + 5/8) - (1/6 * x - 3/7) = (2/7 * x) + (5/8) - (1/6 * x) + (3/7)
= (2/7 * x - 1/6 * x) + (5/8 + 3/7)
= (2/7 - 1/6) * x + (5/8 + 3/7)
= (2/42) * x + (40/56)
Since 2/42 and 40/56 are in lowest terms, this is the simplified expression.
Note that we cannot simplify the expression further unless we know the value of x.
Step-by-step explanation:
If a circle has a diameter of 24 centimeters, and the length of an arc is 36 centimeters, what is the measure of the central angle sub tended by the arc
The measure of the central angle sub tended by the arc is 20.62 degree.
Now, According to the question:
The given data is:
A circle has a diameter of 24 centimeters,
and the length of an arc is 36 centimeters.
To find the measure of the central angle sub tended by the arc.
We know that in a circle of radius 'r' unit, if an arc of length 'l' unit
subtends an angle θ radian at the center, then θ= 1/r
Therefore,
Diameter = 24 then, r = Diameter/2
Radius = 12cm. , Length of an arc = 36cm
θ = 36/100 radian = [tex]\frac{180}{\pi }[/tex] × [tex]\frac{36}{100}[/tex] degree = (180 × 36 x 7)/(22 × 100)
= 20.62 degree.
Hence, the measure of the central angle sub tended by the arc is 20.62 degree.
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Grants credit card has an APR of 11. 28%, and it just compounding period from monthly to daily. What will happen to the effective interest rate charged to grant?
A. It will increase by about 0. 06%
B. It will decrease by about 0. 6%
C. It will increase by about 0. 6%
D. It will decrease by about 0. 6%
If Grants credit card has an APR of 11.28% , and compounding period from monthly to daily , then the effective interest rate charged to grant (c) will increase by about 0.6% .
The APR of Grant's Credit Card is = 11.28% ;
that means the stated interest rate is 11.28% = 0.1128 ;
we know that the formula to calculate the effective interest rate(r) is
r = [tex](1+\frac{i}{n}) ^{n} -1[/tex] ; where i = stated interest rate ;
Substituting number of days (n) in year = 365 ;
we get the effective rate of interest is [tex]r=(1+\frac{0.1128}{365}) ^{365} -1[/tex] ;
On solving ,
we get ;
r = 0.1193885 ;
So , the change in the effective interest rate is = effective rate - stated rate ;
substituting the values of rates ,
we get ;
= [tex]0.119388521952 - 0.1128[/tex] = [tex]0.006588521952 \approx 0.006[/tex] = 0.6% ;
Therefore , the effective interest rate will increase by about 0.6% .
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Which equation can be used to solve for b?
b = (8)tan(30o)
b = 8/tan(30o)
b = (8)sin(30o)
b = 8/sin(30o)
The equation that can be used to solve for b is b=8 tan(30°).
Trigonometric ratios are the ratios of the sides of a right triangle in relation to its angles. There are six trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).
These ratios can be used to solve problems involving triangles and to model real-world phenomena in fields such as physics and engineering.
In a right-angle triangle, the three sides are represented by the letters a, b, and c.
a represents the side adjacent to the given angle.
b represents the side opposite to the given angle.
c represents the hypotenuse of the triangle.
Using the trigonometric ratio we can write the ratio as
b/a = tan(30°)
Multiplying both sides by a, we get
=> b = a*tan(30°)
since a=8 so,
b = 8 tan(30°)
Therefore, The equation that can be used to solve for b is b=8 tan(30°).
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I don’t understand and im going nuts, help.
Based on the latest U. S. Census count, only 48. 0% of Alaskans are female while 51. 7% of Rhode Islanders are
female.
What is the probability that randomly chosen samples of 50 residents from each of the two states would show a
larger proportion of women in Alaska than in Rhode Island?
So, The probability that randomly chosen Sample of so residents from each of the two states. The proportion of women in Alaska logger than in Rhodes island is 0.3556.
Given that based on the latest U.S census Count, only 48% of Alaskans are females white 51.7% of Rhode islanders are female.
Let x denote the females in Alaska and y denote the females in Rhode island.
Since, 48% Alaskans ore females.
So, P(x)=0.48
And 51.7 \% of Rhode islanders are females
So, P(y)=0.517.
Now, randomly chosen sample of so residents
from each of the two states.
Now, randomly chosen sample of residents from each of the two states.
So, [tex]x \sim[/tex] {Binomial}(50 , 0.48)
Ana, [tex]y \sim[/tex] Binomial (50, 0.517 )
E(x)=50 * 0.48=24
E(y)=50 * 0.517=25.85
V or (x)=50 * 0.48(1-0.48)=12.48
[tex]Voo_0[/tex](y)=50 * 0.57(1-0.517)=12.4856
Now, we have to find the probability that the proportion of women in Alaska is larger than in Rhode island.
i.e,
[tex]P(x > y) \\= P(x-y > 0)[/tex]
Using normal approximation
[tex]$$=p\left[z > \frac{0-(24-25.85)}{\sqrt{12.48-12.4856}}\right]$$[/tex]
[tex]=P(z > 0.3703) \quad[\text { where } z \sim N(0,1)] \\ =0.3556 \quad \text { (from } z \text { table) }[/tex]
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