The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) is g(f(x)) is x.
How can you determine a function's inverse?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 determine the inverse of a function.
steps for determining a function's inverse.
In the equation expressing the function, swap out f(x) with y.
Swap out x and y. To put it another way, swap out every x for a y and vice versa.
Solve for y.
Change y to f-1 (x).
The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x.
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One quarter of this pie chart is blue.
15% is orange.
Yellow
Grey
Blue
are some number cards.
Orange
What percentage is blue or orange?
The other two sections are equal in size.
What percentage of the whole chart is yellow?
I
As per the given equation, the percentage of the whole chart that is yellow is 15%.
How to find the percentage of whole chart yellowed?One quarter of the pie chart is blue, which is 25%.
15% of the pie chart is orange.
When we add the percentages of blue and orange sections, we get 25% + 15% = 40%. So, 40% of the pie chart is blue or orange.
As the other two sections, Yellow and Grey, are equal in size, we can assume that they make up half of the remaining 60% of the pie chart. So each of the Yellow and Grey sections make up 30%/2 = 15% of the pie chart.
Therefore, the percentage of the whole chart that is yellow is 15%.
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The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 246.7 and a standard
deviation of 62.5. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below.
a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or
between 59.2 and 434.2?
b. What is the approximate percentage of women with platelet counts between 184.2 and 309.2?
a) The approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 59.2 and 434.2 is of 99.7%.
b) The approximate percentage of women with platelet counts between 184.2 and 309.2 is of 68%.
What is defined by the Empirical Rule?These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:
68% of the measures within one standard deviation of the mean.95% of the measures within two standard deviation of the mean.99.7% of the measures within three standard deviation of the mean.Hence the percentages are given as follows:
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May I have help on this math question please? thank you if you do!
The rate of change of the function is: 2.
The y-intercept/initial value is: 3.
How to Find the Rate of Change and Initial Value of Linear Function?The rate of change is also the slope of a function, which is calculated as, m = change in y / change in x.
Given the points, (0, 3) and (2, 7):
Rate of change/slope (m) = (7 - 3) / (2 - 0)
m = 4/2
m = 2
To find the initial value/y-intercept (b), substitute m = 2 and (x, y) = (0, 3) into y = mx + b:
3 = 2(0) + b
3 = 0 + b
3 = b
b = 3
y-intercept = 3.
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Station A and Station B are 120 miles apart. A train traveling from station A to station B travels exactly 1/3 of the distance when it is held up and stops for 16 minutes. When the train continues its journey,the engineer increases its avarage speed by 15 mph so that the train will arive at station B on schedule. Find the avarage speed of the train before it stopped for minutes
The required average speed of the train is calculated to be 60 mph, when the train travels certain distance and stops.
Distance between station A and station B is given as 120 miles.
A train traveling from station A to station B travels exactly 1/3rd of the distance when it is held up and stops for 16 minutes.
Let, its average speed was x mph.
Then, total time taken if it didn't stop = 120/x h
Now, before stop it took time = ( 1/3 × 120)/x h = (40/x) h
After stop the time it took = 80/(x + 15) h
i.e, 40/x + 16/60 + 80/(x+15) = 120/x
⇒ 80/(x + 15) + 8/30 = 80/x
⇒ 80(1/x - 1/(x + 15)) = 8/30
⇒ 10 × (15/x² + 15x) = 1/30
⇒ x² + 15x = 10 × 15 × 30
⇒ x² +15x - 450 = 0
⇒ x² +75x -60x - 450 = 0
⇒ (x+75)(x-60) = 0
⇒ x = 60 or, x = -75
As speed cannot be negative, the average speed is 60 mph.
The given question is incomplete. The complete question is 'Find the average speed of the train before it stopped for 16 minutes.'
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[tex]\sqrt{45)[/tex]
The required solution to the given radical expression √45 is 3√5.
What are the radical expressions?Any expression that contains a radical symbol is considered a radical expression. To find the square roots, cubic roots, and higher, radical symbols are used. For example, √7, √6, and √11 are in the radial form.
The radical expression is given in the question
√45
As per the given question, the required solution would be as:
√45 = √(3 × 3 × 5)
√45 = 3√5
Thus, the solution to the given expression is 3√5.
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Solve the system.
2(x+y) = 9
1 = − 4(x+y)
Answer:
1 = 18
Step-by-step explanation:
Nora hired a plumber to come to her house. The equation
y = 35x + 50 represents the costs in dollars, y, of hiring the plumber for x hours. Interpret the y-intercept.
The meaning of the y-intercept is that Nora paid her plumber an initial fee of $50.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x and y represents the data points.m represents the slope of a line.c represents the y-intercept of a line.What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
In this scenario, the y-intercept of this equation is 50 and it represents the initial fee being charged by the plumber.
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A microscope shows you an image of an object that is 8 times the objects actual size, so the scale factor of the enlargement is 8. An insect has a body length of 7 millimeters. What is the body length of the insect under the microscope?
56 centimeters
56 millimeters
560 millimeters
560 centimeters
The insect's length as seen via a microscope is found to be 56 millimeters.
Define the term scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of such a different size is known as a scale factor (bigger or smaller).It is important to specify how significantly the shape has grown when describing expansion. For instance, a scale factor of 3 shows that the new geometry is three times as large as the original.The shape will just be smaller if the scaling factor is a fraction. Reduction is the term for this. So, a scaling factor of 1/2 shows that the new geometry is equal to half of the old shape.For the stated question:
The scale factor of a enlargement is 8 because a microscope displays a picture of an object which is 8 times larger than the object actually is. A 7 millimetre bug has a body length.Then,
body length (under microscope) = 7*8 millimeters
body length (under microscope) = 56 millimeters
Thus, the insect's length as seen via a microscope is found to be 56 millimeters.
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PLS HELP IF SOMEONE KNOWS THE ANSWER!!!!!!!!!!
Answer:
see below.
Step-by-step explanation:
1. g(x) = 2^(x-5) +3
2. g(x)= 1/3 * 2^x
3. f(x) was vertically stretched by 3. K value is 3. The Y intercept became augmented by 3 folds.
4. k value = 5, the curve basically got "lifted" up by 5 units.
Mrs. Everett, the P.E. teacher, is pairing off students to race against each other. Antonio can run 8 meters per second, and Devin can run 9 meters per second. Mrs. Everett decides to give Antonio a head start of 50 meters since he runs more slowly. Once the students start running, Devin will quickly catch up to Antonio. How long will that take?
Write a system of equations, graph them, and type the solution.
The time it took for Devin to catch Antonio is given as follows:
50 seconds.
How to model the situation?The position functions for each of Antonio and Devin can be modeled by linear functions in slope-intercept format, as follows:
y = mx + b.
In which:
The slope m represents the velocity.The intercept b represents the initial position.Antonio starts 50 meters in front of Devin, hence the functions, considering their velocities, are given as follows:
A(x) = 50 + 8x.D(x) = 9x.(these two equations compose the system of equations).
Devin will catch up to Antonio when:
D(x) = A(x).
Hence:
9x = 50 + 8x
x = 50 seconds.
(which is shown by the point of intersection of the graph).
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What are the explicit equation and domain for an arithmetic sequence with a first term of 9 and a second term of 1?
The explicit equation for this arithmetic sequence is: aₙ = 9 + (n-1)(-8).
What in mathematics is an arithmetic sequence?An arithmetic series is one that has the following formula: a, a + d, a + 2d, a + 3d, a + 4d,... The basic distinction of the sequence is d, and the number an is the first term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
How do you discover the mathematical order?The formula for an arithmetic sequence is given as an=a1+(n1)d, where an a n is a broad term, a1 a 1 is the initial term, and d is the huge distinction. This is done in order to locate the general phrase in the list.
The general form of the explicit equation for an arithmetic sequence is:
an = a1 + (n-1)d
Given that the first term is 9 and the second term is 1,
d = a2 - a1 = 1 - 9 = -8
So the explicit equation for this arithmetic sequence is:
aₙ = 9 + (n-1)(-8)
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Given ; WV is parallel to YZ, X is the midpoint of VY
Prove : Triangle VWX is congruent to Triangle YZX
Statement Given
1. X is the midpoint of VY 1. Given
2. WV ║ YZ 2. Given
3. VX = XY 3. X is midpoint
4. ∠WXY = ∠YXZ 4. Corresponding Angle Theorem
5. ∠WVX = ∠XYZ 5. Vertical Angle Theorem
6. △YXZ = △VWZ 6. AA Similarity
7. WV ≅ YZ 7. Prove
We know that WV ║ YZ, X is the midpoint of VY.
If X is the midpoint of VY. So VX = XY
The corresponding angles in the two regions of intersection are congruent when a line intersects two parallel lines.
From the Corresponding Angle Theorem
∠WXY = ∠YXZ
When two straight lines cross, the Vertical Angle Theorem states that they create two sets of linear pairings with congruent angles.
From the Vertical Angle Theorem
∠WVX = ∠XYZ
According to the AA similarity theorem, two triangles are similar if two of their triangles' triangles are congruent with two of their other triangles' angles.
By AA Similarity
△YXZ = △VWZ
Hence, WV ≅ YZ
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The complete question is given below:
What percent of 102 is 17
Answer:
16.6666666666667%
Step-by-step explanation:
17/102 = x/100
17*100/102 = x
x = 16.66666667
Answer:
The percent is:
16.667%
Step-by-step explanation:
17 / 102 = 0.16667
0.16667 * 100 = 16.667%
Please only give answers
The y-intercept of the linear function 11x - 10y = 2 is given as follows:
y = -1/5.
How to obtain the y-intercept?The function for this problem is defined as follows:
11x - 10y = 2.
The y-intercept of a function is given by the value assumed by y when x assumes a value of 0.
Considering it's concept, the y-intercept of the function in this problem is obtained as follows:
-10y = 2
10y = -2
y = -2/10
y = -1/5.
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Select the correct answer.
If Georgia and Farrah work together, it takes them 8 minutes to clean the espresso machine at their coffee shop. Alone, Farrah takes 12 minutes less than Georgia to clean the machine. If x is the number of minutes it takes Georgia to clean the machine by herself, the situation can be represented by this equation
Georgia takes 24 minutes to clean the espresso machine by herself.
The correct answer is an option D.
The equation for the situation is:
[tex]\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8}[/tex]
here, x is the number of minutes it takes Georgia to clean the machine by herself.
We need to find the value of x.
Consider the equation,
[tex]\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8} \\\\\frac{(x -12)+x}{x(x-12)}=\frac{1}{8}\\\\\frac{x -12+x}{x^2-12x}=\frac{1}{8}[/tex]
(2x - 12) × 8 = x² - 12x
16x - 96 = x² - 12x
x² - 12x -16x + 96 = 0
x² - 28x + 96 = 0
x²-24x-4x+96 = 0
(x - 24)(x - 4) = 0
x = 24 or x = 4
If x = 4, then x - 12 would be negative which is not possible.
Thus, it takes 24 minutes for Georgia.
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Find the complete question below.
The image of (3, -5) after a dilation with respect to the origin is (15, -25). What is the scale
factor of the dilation?
04
05
06
O 12
The scale factor of the dilation is equal to: B. 5.
What is scale factor?In Geometry, a scale factor simply refers to the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge or reduce a function representing their size.
Generally speaking, the transformation rule for the dilation of a geometric object based on a specific scale factor with respect to the origin is given by this mathematical expression:
(x, y) → (SFx, SFy)
Where:
x and y represents the data points.SF represents the scale factor.Scale factor = 15/3 = -25/-5
Scale factor = 5.
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How do I find the perpendicular line of y = -3x + 2. The perpendicular line passes through the point 6, 8 (please break down into steps)
Answer:
y = [tex]\frac{1}{3}[/tex]x + 6
Step-by-step explanation:
The equation we currently have right now is y = -3x+2. Since we know that the line equation is y = mx + b, let's take out m to find the slope of a perpendicular line. M will be -3.
To convert a regular slope to a perpendicular one, we have to:
- reciprocal/flip it (this means that if m = 3, the perpendicular will be [tex]\frac{1}{3}[/tex])
- swap the signs (this will mean that if a number is positive, then it will become negative)
Therefore, if m = -3, the perpendicular slope will be [tex]\frac{1}{3}[/tex] (we flipped and changed signs)
Now, we are also given that this line passes through the point (6,8), so we can use this formula: [tex]y - y1 = m(x-x1)[/tex]
What do we know right now?
- y1 = 8 (from (6,8))
- x1 = 6 (from (6,8))
- m = [tex]\frac{1}{3}[/tex]
Let's plug in what we know:
y - 8 = [tex]\frac{1}{3}[/tex](x - 6)
y = [tex]\frac{1}{3}[/tex](x-6) + 8
y = [tex]\frac{1}{3}[/tex]x - 2 + 8
y = [tex]\frac{1}{3}[/tex]x + 6
The graph shown here is the graph of which of the following rational
functions?
-10
10
FOO
10
O A. F(X) = (2+1)(²-3)
B. F(x) = (z+1)(x-2)(z-3)
D-2
O C. F(x) = (2-1)(x+3)
According to the graph the rational function represented in the graph is [tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex], and option A is correct answer.
What is vertical asymptote?At the margins of the coordinate plane, the curve approaches lines known as asymptotes. When the denominator of such a rational function gets close to zero, vertical asymptotes happen. Since it would divide by zero, a rational function never traverse a vertical asymptote. A graph's vertical asymptote is a vertical line with the equation x=a, where the graph tends to positive or negative infinity as the inputs go closer to a.
For the given graph we can see that the vertical asymptotes are -1 and 3, and there is no horizontal asymptote.
In option A:
[tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex]
The horizontal asymptote is none.
The vertical asymptote is -1 and 3.
Hence, this is the correct option.
Option B:
[tex]F(x) = \frac{1}{(x-2)(x+1 )(x-3)}[/tex]
The horizontal asymptote is 0.
The vertical asymptote is 2, -1 , and 3.
Hence, option B is incorrect.
Option C:
[tex]F(x) = \frac{x-2}{(x-1 )(x+3)}[/tex]
The horizontal asymptote is none.
The vertical asymptote is 1 and -3.
Hence, option C is incorrect.
Hence, according to the graph the rational function represented in the graph is [tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex], and option A is correct answer.
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a) if a leaf completes the color transformation, what is the probability that it will complete the textural transformation?
the probability that it will complete the textural transformation
is 0.90334.
Let A be the event that a leaf completes the color transformation and B be the event that a leaf completes the textural transformation.
n(A) = 243 + 26 = 269
n(B) = 243 + 13 = 256
n (A∩ B) = 243
n(S) = 243 +26+13+18 = 300
Finding the Probability of the event that the leaf completes the color transformation by using the Probability of an event formula
P(A)= 269 / 300
= 0.89667
p(A∩ B) = 243/300
= 0.81
By using the conditional probability of a leaf completing textural transformation given a leaf completing color transformation
P(B/A) = p(A∩ B) / P(A)
= 0.81/0.89667
= 0.90334
The conditional probability of a leaf completing textural transformation given a leaf completing color transformation is 0.90334
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The complete question is :
The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by type of transformation completed:
(a) ) If a leaf completes the color transformation, what is the probability that it will complete the textural transformation?
Find the indicated real nth root(s) of a. n=2, a= -49
As, a = -49 is a negative number, so there is no real root for the integer.
What is square root?
A number's square root is a value that, when multiplied by itself, yields the original number. The other way to square an integer is to find its square root.
The expression is given as - a = -49
The value for n is n = 2
Find the nth root value for the expression a.
Since a = -49 is a negative number there is no real square root for the number.
If it would have been a = 49, then there would have been one real square root.
n=2 which generates √49.
This gives the value as 7.
Therefore, there are no roots for -49.
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Jeffrey wants to make jam. He needs a combination of raspberries and blackberries totaling six pounds. Blueberries cost $1.00 per pound, and raspberries cost $2.00 per pound. If Jeffrey can afford $11.60, how many pounds of each berry should he buy?
The amount for each berry are 5.60 and 1.60 respectively.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =
Given that, Jeffrey wants to make jam. He needs a combination of raspberries and blackberries totaling six pounds. Blueberries cost $1.00 per pound, and raspberries cost $2.00 per pound. If Jeffrey can afford $11.60,
We will set a system of linear equations, to solve this,
Establishing the equation,
Let the amount of raspberries be x and that of blueberries be y,
x + y = 6
y = 6-x...(i)
2x + y = 11.60
y = 11.60 - 2x...(ii)
Equating eq(i) and eq(ii)
6-x = 11.60 -2x
x = 5.60
Put x = 5.60 in eq(i)
y = 6-5.60
y = 1.60
Hence, the amount for each berry are 5.60 and 1.60 respectively.
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Please helppp please now ASAP
Answer:
Step-by-step explanation:
ok so with triangle sum theorem the equation we use for this is n-2•180 (n equals number of sides, for 3*180 is 540, 540-all non variable numbers leave us with 165, divide 165 by 13 and that’s your answer, if anything round. Please lmk if this is wrong
Solve the equation ax + b = c for x.
x =
Answer:
X = C - B
--------
A
Step-by-step explanation:
Solving for X is pretty much getting X alone on one side of the equal sign. That's when we would do the "opposite" of what the original equation is showing. And we do that to both sides.
For example, we see +b. The opposite of addition is subtraction, so we do just that. We do -b on BOTH sides of the equal sign. b -b = 0. It cancels it out. c-b is just as it says. So now we have ax = c-b.
Now we see ax are right next to each other with no symbol, which means they are being multiplied. The opposite of multiplication is division. So we'll do that exactly. We will divide A on both sides. ax/a gets rid of that a and leaves the x alone. Dividing c-b/a gives you just that, making the answer X = C-B/A
Solve the equation
A = 1/2bh for b.
Answer:
[tex]\frac{2A}{h}[/tex] = b
Step-by-step explanation:
A = [tex]\frac{1}{2}[/tex] bh Multiply both sides by [tex]\frac{2}{h}[/tex]
[tex]\frac{2}{h}[/tex] x [tex]\frac{A}{1}[/tex] = [tex]\frac{2}{h}[/tex] x [tex]\frac{h}{2}[/tex] x b
[tex]\frac{2A}{h}[/tex] = b
The width of a rectangular garden is 4 meters less than 2 times the length. The area of the garden is 6 square meters. Which is the function to find the dimensions of the the garden?
a) 2l^2−4l−6=0
b) 2w^2+4w+6=0
c) 2w^2+4w−6=0
d) 2l^2−4l+6=0
The dimensions of the the garden are 8 x 12
What is Quadratic Equation?
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f. (x).
A = l x w
l = 2w-4
A = w (2w-4)
A = 2w² -4w
96m² = 2w² - 4w
0 = 2w² - 4w - 96 divide both sides by 2
0 = w² - 2w -48
(w-8) ( w +6) = 0
w = 8 since it can't equal -6
length therefore = 2w-4 = 16-4 = 12
Hence, the dimensions of the garden are 8 x 12
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Full question:
A rectangular garden has a length that is 4 meters less than twice its width. Can you set up a quadratic equation to find the dimensions of the garden if its area is 96m^2?
Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. What is the balance after 5 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
The amount of money in Lucia's account after 5 years will be $1,105.5.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. Then the amount of money after 5 years will be given as,
A = $600 × (1 + 0.13)⁵
A = $600 × (1.13)⁵
A = $600 × 1.84
A = $1,105.5
The amount of money in Lucia's account after 5 years will be $1,105.5.
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Explain how rectangles are related to squares.
Enter rectangles or squares in the answer boxes. Words may be used more than once.
Answer:
Rectangles
Squares
A square is a special type of rectangle. All squares are rectangles, but not all rectangles are squares. In a square, all four sides are equal in length (congruent), making it a special case of a rectangle where all angles are right angles and all four sides have the same length. In contrast, a rectangle can have sides of different lengths.
What Is The Estimated Weight Of Three Containers Weighing 1. 656 kg each? (Math 5 Quarter 2, Week 5) I Need A Nice And Clear Answer
The estimated weight of three containers weighing 1. 656 kg each = 5 kg
Let w represents the weight of each contaoner.
Here, each container weighs 1.656 kg
⇒ w = 1.656 kg
Here, the weight of all containers are the same.
To determine the estimated weight of three containers we us the Unitary method.
We simply multiply the given weight by the number of containers.
Let W be the estimated weight of three containers.
Using Unitary method,
W = 3 × w
W = 3 × 1.656
W = 4.968
W ≈ 5 kg
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Jasmine gets paid $96 for 3 hours, how many dimes is she making an hour? How many nickels is she making an hour? how many quarters is she making an hour? how many pennies is she making an hour? use the problem.
[tex]x = [/tex]
Answer:
Step-by-step explanation:
I DON'T KNOW
In a quadrilateral ABCD,if m(<A)=80,m(<B)=100° and m(<D)=110°,find m(<C).
In quadrilateral ABCD, m∠C = 70°.
What is quadrilateral?A quadrilateral in geometry is a four-sided polygon with four edges and four corners.
Given:
ABCD is a quadrilateral.
m∠A =80°, m∠B = 100° and m∠D = 110°.
The sum of all the interior angles is 360°.
m∠A + m∠B + m∠C + m∠D = 360°.
80 + 100 + 110 + m∠C = 360
m∠C = 360 - 290
m∠C = 70°
Therefore, m∠C = 70°
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Step-by-step explanation:
In a quadrilateral, the sum of the measures of the angles is 360 degrees. Therefore, if we know the measures of three of the angles in a quadrilateral, we can use this information to find the measure of the fourth angle.
In this case, we know that:
m(<A) = 80 degrees
m(<B) = 100 degrees
m(<D) = 110 degrees
So, to find m(<C), we can use the equation:
m(<A) + m(<B) + m(<C) + m(<D) = 360
Substituting in the known values, we get:
80 + 100 + m(<C) + 110 = 360
Solving for m(<C), we get:
m(<C) = 360 - (80 + 100 + 110) = 360 - 290 = 70 degrees
So the measure of angle C is 70 degrees.