There are 100 degrees between the normal freezing and boiling points of water.
On the Celsius temperature scale, the difference between the normal freezing point (0°C) and the normal boiling point (100°C) of water is 100°C - 0°C = 100°C.
Celsius, also called centigrade, scale based on 0° for the freezing point of water and 100° for the boiling point of water.On the Kelvin temperature scale, the equivalent temperatures for the normal freezing and boiling points of water are 273.15 K and 373.15 K, respectively. The difference between these two temperatures on the Kelvin scale is 373.15 K - 273.15 K = 100 K.
So, in both Celsius and Kelvin scales, there are 100 degrees between the normal freezing and boiling points of water.
Therefore, there are 100 degrees between the normal freezing and boiling points of water.
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Charlotte works in a department store selling clothing. She makes a guaranteed salary of $500 per week, but is paid a commission on top of her base salary equal to 30% of her total sales for the week. How much would Charlotte make in a week in which she made $1575 in sales? How much would Charlotte make in a week if she made
x
x dollars in sales?
Answer:
Below
Step-by-step explanation:
Her base salary (500) for the week PLUS her comission (.3 * 1575)
totals 972.50 dollars
a matrix consisting entirely of zeros is called a
A matrix consisting entirely of zeros is called a zero matrix, or an all-zero matrix.
It is denoted with the symbol O and can be written in a matrix form, such as O = [0 0 0 0] where the number of columns and rows depends on the size of the matrix. A zero matrix is a matrix which has all its elements equal to zero. It has a number of special properties that make it useful in linear algebra. For instance, the sum of any two zero matrices is a zero matrix, and any scalar multiple of a zero matrix is a zero matrix. Additionally, the product of two zero matrices is a zero matrix, and the product of a zero matrix and an identity matrix is a zero matrix. These properties make it useful in solving systems of linear equations where all the coefficients are zero. Finally, the inverse of a zero matrix does not exist since its determinant is zero.
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B-1. Suppose a sample of 200 drivers under the age of 18 results in 150 who still use a cell phone while driving. What is the value of the test statistic? (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places. )
The value of the test statistic in this case is 75.00. This suggests that 75% of drivers under the age of 18 still use a cell phone while driving.
The value of the test statistic in this case is the percentage of drivers under the age of 18 who still use a cell phone while driving. The test statistic is calculated using the following formula:
Test Statistic = (Number of Drivers under 18 using Cell Phone)/ (Total Number of Drivers under 18) x 100
For this case, the test statistic is calculated as follows:
Test Statistic = (150/200) x 100 = 75.00
Therefore, the value of the test statistic in this case is 75.00. This suggests that 75% of drivers under the age of 18 still use a cell phone while driving.
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The graph represents a relation where x represents the independent variable and y represents the dependent variable.
What is the domain of the relation?
{−3, −2, −1, 0, 1, 2, 4}
{−3, 0, 1, 4}
{−2, −1, 0, 1, 4}
{−3, −1, 0, 2, 4}
The correct option representing the domain of the relation is given as follows:
{−3, −1, 0, 2, 4}
How to obtain the domain of the relation?The domain of a function is the set that contains all the input values of the function, hence on the graph it is the values of x, representing the number of years.
The values of x are the values of x for which there is a dot, hence they are given as follows:
x = -3.x = -1.x = 0.x = 2.x = 4.Meaning that the fourth option represents the correct option.
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if d1 +d2 = 7.0d3, d1-d2 = 3.0d3 and d3= 1.3i +4.6j ,then what are (a) the x component of d1 (b) the y component of d1 (c) the x component of d2 (d) the y component of d2?
The values of the x component of d1 is 6.5, the y component of d1 is 23 the x component of d2 is 2.6 and the y component of d2 is 9.2
Given that,
d1 +d2 = 7.0d3, (1)
d1-d2 = 3.0d3 (2)
and d3= 1.3i +4.6j (3)
Adding equation 1 and equation 2
d1 +d2 +d1 -d2 = 7 d3 + 3 d3
2d1 = 10 d3
d1 = 5d3
and we also have that d3= 1.3i +4.6j
substitute the given d3 in d1 = 5d3
therefore , d1 = 5(1.3i +4.6j)
d1 = 6.5i + 23 j
here the x component of d1 is 6.5
subtract 2 from 1
d1+d2-d1+d2 = 7d3-3d3
2d2 = 4d3
d2 = 2d3
d2 = 2(1.3i +4.6j)
= 2.6 i + 9.2j
here the x component of d2 = 2.6
the y component of d2 = 9.2
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A wimming pool i being drained. The number of gallon of water in the pool change with time t according to the equation G = -4t 100
The equation that correctly solves the given equation for t is C) t = (100 - G) / 4
To solve for t in the equation G = -4t + 100, we need to isolate t on one side of the equation. To do this, we start by subtracting 100 from both sides:
G - 100 = -4t + 100 - 100
Simplifying the right side:
G - 100 = -4t
Finally, dividing both sides by -4:
t = (100 - G) / -4
So, option C) t = (100 - G) / 4 correctly represents the equation for t in terms of G.
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Your question is incomplete but most probably the full question was:
A swimming pool is being drained. The number of gallons of water in the pool changes with time t according to the equation G = -4t + 100.
Which equation correctly solves the given equation for t?
A) t = 4G - 100
B) t = -4G + 100
C) t =
100 - G
4
D) t =
G - 100
4
Two year ago, a car wa valued at $24,000. Thi year, the value of the car i $23,160. What wa the percent decreae in the value of the car?
A car was worth $24,000 two years ago. The automobile is worth $23,160 this year. 3.5% of the value of the car has decreased.
How to calculate percent?The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage. An enormous, red percentage symbol with a black outline. If you multiply two percentages that are fractions of 100 or decimals, you can find the percentage of another percentage. Calculating, for instance, 50% of 40% results in (50/100) x (40/100) = 0.50 x 0.40 = 0.20 = 20/100 = 20%. As we can see, it provides us with the exact same response as the first approach: 2/5 as a percentage equals 40%. A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed.24,000 - 23,160 = 840
840/24,000 = 0.035
Simplifying the above equation, we get,
0.035 = 3.5%
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Triangle RST has coordinates:
R (-2, 1)
Si-8, 2)
T-4,5)
Draw the translation of RST 8 units
right and 4 units down on your
recording sheet.
What are the coordinates of R'?
A. R' (-3, 6)
B. R' (0,-2)
C. R' (6,-3)
D. R' (4,1)
The correct option is option D. That is, R'(4,1). The RST coordinates of the given point is: (4,1).
The midpoint is the spot that is in the center of a line that connects two locations. The two reference points that make up a line's endpoints are where it finds its middle. At the halfway point, the line that links these two locations is evenly divided in half. Additionally, if a line is drawn to split the line that links these two points, the midway point is achieved. The midpoint formula may be used to determine the midpoint between two locations when we know their coordinates. The midpoint formula may be used to determine the coordinates of the other endpoint if we know the midpoint's coordinates as well as those of the other endpoint. RST coordinate is (4,1).
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Kareem make muffin uing a ratio of 3. 5 cup of flour for every 1. 75 cup of ugar. If he ha 3. 5 cup of ugar, how much flour doe he need to make the muffin?
Kareem make muffin using a ratio of 3. 5 cup of flour for every 1. 75 cup of sugar. If he ha 3. 5 cup of sugar, flour doe he need to make the muffin is 7 cups.
The ratio that Kareem uses to make the muffin is 3.5 cups of flour for every 1.75 cups of sugar .
let the number of cups of flour be "y" and
the number of cups of sugar be "x" .
So , y ∝ x ,
y = k*x , where k is the constant of proportionality .
From the given data ,
3.5 = k*1.75
k = 3.5/1.75
k = 2 .
we have to find the cups of flour that Kareem needs , if he has 3.5 cups of sugar .
the equation becomes ,
y = 2*3.5
y = 7
Therefore , Kareem needs 7 cups of flour .
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other.
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Hello! help quick thank you
The expressions for (h - g)(x) and (h . g)(x) are -x - 8 and (x - 5)(2x + 3)
While the function (h + g) (-1) is -5
How to evaluate the functionFrom the question, we have the following parameters that can be used in our computation:
g (x) = 2x+3
h(x) = x - 5
This means that
(h - g)(x) = x - 5 - 2x - 3
Evaluate
(h - g)(x) = -x - 8
Also, we have
(h . g)(x) = (x - 5)(2x + 3)
Lastly, we have
(h + g)(-1) = (x - 5) + (2x + 3)
So, we have the following equation
(h + g)(-1) = ((-1) - 5) + (2(-1) + 3)
Evaluate
(h + g)(-1) = -5
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Which of the following functions are solutions of the differential equation y″−4y′−21y=0? A. y(x)=e7xy(x)=e7x
B. y(x)=0y(x)=0
C. y(x)=exy(x)=ex
D. y(x)=e−3xy(x)=e−3x
E. y(x)=e−xy(x)=e−x
F. y(x)=−3xy(x)=−3x
G. y(x)=7xy(x)=7x
The functions that are solutions of the differential equation y" - 4y' -21y = 0 is -Option E: y(x) = [tex]e^{-3x}[/tex] Option F: y(x) = [tex]e^{7x}[/tex]
Differential equation definitionA differential equation is any equation that has one or more terms and one or more derivatives of the dependent variable with respect to the independent variable.
The given differential equation is y" - 4y' -21 = 0
This can be written as characteristic equation -
m² - 4m - 21 = 0
m² - 7m + 3m - 21 = 0
m(m - 7) + 3(m - 7) = 0
(m + 3)(m - 7) = 0
m = -3 and m = 7
The general solution is given by
[tex]y = (C1 + xC2)e^{-3x}[/tex]
[tex]y = C1 e^{-3x} + C2 xe^{-3x}[/tex]
[tex]y = (C1 + xC2)e^{7x}[/tex]
[tex]y = C1 e^{7x} + C2 xe^{7x}[/tex]
So, now the solutions are y = [tex]e^{-3x}[/tex], [tex]y = xe^{-3x}[/tex], [tex]y = e^{7x}[/tex]and [tex]y = xe^{7x}.[/tex]
Therefore, the solutions are y = [tex]e^{-3x}[/tex] and [tex]y = e^{7x}[/tex]
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For The Following Frequency Distribution, How Many Individuals Had A Score Of X = 5? Х F 2 5 4 4 3 2 3 A)1 B)2 C)3D)4
By looking at the frequency of each value, we can see how many individuals had a score of X = 5, which is 4 individuals.
Frequency distribution is a way of organizing data by counting how many times each value appears in a set of data.
In this specific frequency distribution, the value of X = 5 appears once. The frequency, F, for X = 5 is 4, which means that 4 individuals had a score of 5.
This information can be found by looking at the row where X = 5. The frequency distribution allows us to see a pattern in the data, in this case, the frequency of scores.
By analyzing the frequency distribution, we can see that there are more individuals with scores of 2 and 4 compared to those with scores of 3 and 5.
Therefore option (d) is correct.
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Write an equation for a parabola that has a vertex at (2, 3), focus at (2,5), and directrix at y = 1.
f(x) = (x - 2)² +3
f(x) = 2(x - 5)² + 2
f(x)=(x-3)² + 2
f(x) = 2(x - 3)² + 1
Each new shaded triangle is half the size of the smallest
shaded triangle in the previous step. If the pattern continues,
what percent of the square will be shaded in step 5?
step 1
step 2
step 3
A 96. 9%
B 75. 0%
C 87. 5%
D 92. 7%
Percent of the square will be shaded is 96.9%. Option A -96. 9%
In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used.
Percent is from the Latin adverbial phrase per centum meaning “by the hundred.”
For Complete Question with Diagram, please refer attached image below
step 1 : 50%
step 2 : 50% + 25% = 75%
step 3 : 50% + 25% + 12.5% = 87.5%
step 4 : 50% + 25% + 12.5% + 6.25% = 93.75%
step 5 : 50% + 25% + 12.5% + 6.25% + 3.125% = 96.9%
Thus, percent of the square will be shaded is 96.9%. Option A -96. 9%
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Percent of the square that will be shaded is 96.9%. Option A -96. 9%
In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used.
Percent is from the Latin adverbial phrase per centum meaning “by the hundred.”
For the Complete Question with the Diagram, please refer attached image below
step 1 : 50%
step 2 : 50% + 25% = 75%
step 3 : 50% + 25% + 12.5% = 87.5%
step 4 : 50% + 25% + 12.5% + 6.25% = 93.75%
step 5 : 50% + 25% + 12.5% + 6.25% + 3.125% = 96.9%
Thus, the percentage of the square will be shaded is 96.9%. Option A -96. 9%
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PLEASE HELP!!!
Begin by graphing the absolute value function, . Then use transformations of this graph to graph the given function.
h(x)=lxl+3
What transformations are needed in order to obtain the graph of h(x) from the graph of f(x)? Select all that apply.
A. Vertical stretch/shrink
B. Horizontal stretch/shrink
C. Reflection about the x-axis
D. Vertical translation
E. Horizontal translation
F. Reflection about the y-axis
The transformation that is needed in order to obtain the graph of h(x) from the graph of f(x) is D. Vertical translation
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
f(x) = |x|
h(x) = |x| + 3
Using the above as a guide, we have the following:
h(x) = f(x) + 3
This means that the function f(x) is translated 3 units up to get the function h(x)
See attachnent for the graph
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Health and safety guidelines set the highest sound intensity level in the workplace to 90. 0 db. One workshop with 32 similar machines produces a sound intensity level of 92. 0 db. How many of them must be shut down to bring the workshop into compliance with the guidelines?.
The sound intensity level should be decreased by 2 dB to carry the studio into consistency with the rules.
A decrease of 2 dB can be accomplished by one or the other by closing down a portion of the machines (since the sound intensity level declines by 6 dB for each splitting of the sound power) or by introducing sound-sealing materials.
Thus, to carry the studio consistent with the rules, 16 machines would need to be closed down.
It's vital to follow well-being and security rules in the working environment to guarantee the prosperity of representatives and forestall hearing harm. Decreasing the number of machines or introducing soundproofing materials can bring the studio into consistency.
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Find the sum of the interior angles and the measure interior angle for the given regular Polyguns round to the nearest tenif needed A 12-gon 102-gon 90-gon 36-gon
The sum of interior angle in 12-gon is 1800°, in 102-gon is 18000°, in 90-gon is 15840° and 36-gon is 6120° and measure of interior angle in 12-gon is 150°, in 102-gon is 176.5°, in 90-gon is 176° and 36-gon is 170°
What do you mean by polygon?A polygon is a two-dimensional geometric shape consisting of straight lines and having three or more sides. The sides of a polygon are line segments that connect its vertices, or corners, and the vertices are where the sides meet. The most common types of polyggon include triangles, squares, rectangles, and hexagons. There are also many types of irregular polygon, which have sides of different lengths or angles, as well as regular polygon, which have equal sides and equal interior angles.
The sum of the interior angles and the measure of the interior angle of a regular polygon can be found using the formula:
Sum of interior angles = (n-2) * 180°
Measure of interior angle = Sum of interior angles / n
Where n is the number of sides of the polygon.
For a 12-gon:
Sum of interior angles = (12-2) * 180° = 1800°
Measure of interior angle = 1800° / 12 = 150°
For a 102-gon:
Sum of interior angles = (102-2) * 180° = 18000°
Measure of interior angle = 18000° / 102 = 176.5°
For a 90-gon:
Sum of interior angles = (90-2) * 180° = 15840°
Measure of interior angle = 15840° / 90 = 176°
For a 36-gon:
Sum of interior angles = (36-2) * 180° = 6120°
Measure of interior angle = 6120° / 36 = 170°
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what is 20 liters increased by 60%?
Therefore , the solution of the given problem of percentage comes out to be 32 liters after 60% increased.
Define percentage.Any value that may be expressed as a fraction of 100 is referred to as a percentage in mathematics. The acronyms "pct.," "pct," or "pc" are also occasionally used. However, the "%" symbol is typically used to denote it. The proportional amount has no dimensions and is flat. Percentages can be viewed as fractions because their numerator is 100. To indicate that a number is a percent, it needs to be followed by the percent symbol (%).
Here,
Given:
=> 20 liters is the given volume
It is increased by 60% ,
then the final volume is :
=> 20 + 60/100 *20
=> 20 + 0.6*20
=> 20 + 12
=> 32 liters
Therefore , the solution of the given problem of percentage comes out to be 32 liters after 60% increased.
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what is x - 3 equal to evaluate
The equation x - 3 = 2 when evaluated is x = 5
How to evaluate the equationFrom the question, we have the following parameters that can be used in our computation:
x - 3 equal to 2.
Express the equation properly
So, we have the following representation
x - 3 = 2
Add 3 to both sides of the equation
This gives
x - 3 + 3 = 2 + 3
Evaluate the like terms
x = 5
Hence, the solution is x = 5
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Complete question
What is x - 3 equal to 2.
Evaluate
If co A = 1/2 then what i the poitive value of co 1/2 B,in implet radical form with a rational denominator?
The answer is cos(B/2) = 2√5 / 5
Half angle formula of cosine: cos B/2 = ±√[(1 + cos B) / 2]
Given: The positive value of cos 1/2 B in the simplest radical form with a rational denominator, if cos B = 3/5:
Regarding applying the cosine half-angle formula:
cos²(B/2) = (1 + cos B) / 2
put value of cos B =3/5 (given)
cos²(B/2) = (1 + 3/5) / 2
on simplifying
cos²(B/2) = (8/5) / 2
cos²(B/2) = 4/5
on taking under root we get
cos(B/2) = 2/√5
use a rational denominator and the simplest radical form hence, cos(B/2) = 2√5 / 5
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By what percent is the population increasing/decreasing?
three point charges are located at the corners of an equilateral triangle
At the four corners of an equilateral triangle are three point charges.
Due to the fact that three charges do not cancel one another out with Colombian force, the system can never reach equilibrium.
A subatomic particle's electric charge causes it to experience a force when it is in an electric and magnetic field.
What does the phrase "charge" actually mean?Electric charge is the property of matter that causes it to experience a force when subjected to an electromagnetic field. Protons and electrons most typically carry positive and negative charges, which are the two forms of electric charges. Energy is created by charge movement.
The most frequent charge carriers for positive and negative electric charges, respectively, are protons and electrons. The coulomb (C) is the standard unit of electric charge used by the International System of Units (ISO) (SI).
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Complete question -
Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic force are acting
Joshua invested $750 in an account paying an interest rate of 3 % compounded
quarterly. Josiah invested $750 in an account paying an interest rate of 25 %
compounded annually. After 18 years, how much more money would Joshua have in
his account than Josiah, to the nearest dollar
Rounding to the nearest dollar, Joshua would have $4,129 more in his account than Josiah after 18 years.
To find the amount of money in the account after 18 years,
We can use the formula:
A = P * (1 + r/n)^(nt),
where A is the amount of money in the account,
P is the principal amount ($750),
r is the interest rate (3% or 25%),
n is the number of times the interest is compounded per year (4 or 1), and t is the number of years (18).
For Joshua's account:
A = 750 * (1 + 0.03/4)^(4 * 18)
= 750 * (1.0075)^72
= $1417.15
For Josiah's account:
A = 750 * (1 + 0.25)^18 = 750 * (1.25)^18
= $5547.01
The difference in the amount of money in the two accounts will be
=$5547.01 - $1417.15 = $4129.86.
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M is located at ( -7 , -6 ) on coordinate plane . point p is located 5 units from m . point P has the same x coordinate as point m.
The possible locations of point P are (-7, -1) and (-7, -11)
How to determine the location of point P?From the question, we have the following parameters that can be used in our computation:
M = (-7, -6)
Also, we have"
P = 5 units from M
And
P = same x coordinate as point m.
This means that
P = (-7, y)
5 units from (-7, -6) is calculated as
(-7, -6 + 5) and (-7, -6 - 5)
Evaluate
(-7, -1) and (-7, -11)
Hence, the possible location is (-7, -1) and (-7, -11)
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Let Q(t) = t^2. find a formula for the slope of the secant line over the interval [3,t]. (express numbers in exact form. use symbolic notation and fractions where needed.)
The slope of the secant line over the interval [3, t] for the curve Q(t) = t² is given by the formula m = (t² - 9) / (t - 3).
The slope of a line is a measure of how steep the line is. It tells us how much the line is rising or falling as we move from left to right.
The secant line is a line that passes through two points on a curve. In this case, the curve is Q(t) = t².
To find the slope of the secant line over the interval [3, t], we need to find the slope of the line that passes through the points (3, 9) and (t, t²).
The slope of the line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
So, using this formula, we can find the slope of the secant line over the interval [3, t]:
m = (t² - 9) / (t - 3)
This formula gives us the exact slope of the secant line over the interval [3, t]. We can simplify it if needed, but the answer will always be in exact form.
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The function g(x) = x2 is transformed to obtain function h: h(x) = g(x) + 1. Which statement describes how the graph of h is different from the graph of g? A. The graph of h is the graph of g vertically shifted up 1 unit. B. The graph of h is the graph of g horizontally shifted left 1 unit. C. The graph of h is the graph of g vertically shifted down 1 unit. D. The graph of h is the graph of g horizontally shifted right 1 unit. Reset Next
A statement which best describes how the graph of h is different from the graph of g include the following: A. The graph of h is the graph of g vertically shifted up 1 unit.
What is a translation?In Mathematics, the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.
In Mathematics, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.In this scenario, the function g(x) = x² is translated upward by 1 units to produce h(x) = g(x) + 1.
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the accurate scale drawing shows a car and a lamp post
the car is a real width of 1.5 metres
find an estimate for the real height, in meters of the lamp post
An estimate of the real height of the lamp post is 9m.
What is the estimate of the real height?The first step is to determine the scale of the drawing. The scale can be determined by dividing the height of the lamp post by the height of the car. The height of the lamp post when measured with a ruler is 10.8 cm and the height of the car is 1.8cm
here, we have,
Scale = length of the lamp post / height of the car
10.8 / 1.8 = 6
Now, multiply the scale by the width of the car.
The real height of the lamp post = 6 x 1.5 = 9m
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Evaluate {( 6
7
)
3
}
2 X {( 6
7
)
2 }
2 ÷
36
49
and expre it a a power of 2
Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²
We can start by evaluating each bracketed expression first:
{(67)3} = 67 * 67 * 67 = 42,949,769
{(67)2} = 67 * 67 = 4489
Next, we evaluate the first part of the expression:
(67)3 * 2 = 42,949,769 * 2 = 85,899,538
Next, we evaluate the second part of the expression:
(67)2 * (67)2 = 4489 * 4489 = 20,067,961
Finally, we divide the result of the first part by the result of the second part:
85,899,538 / 20,067,961 = 4.286766
To express this result as a power of 2, we find the nearest power of 2 and write it in exponential form:
2² = 4
Thus, Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²
To learn more about exponentials,
Visit; brainly.com/question/28596571
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Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²
We can start by evaluating each bracketed expression first:
{(67)³} = 67 * 67 * 67 = 42,949,769
{(67)²} = 67 * 67 = 4489
Next, we evaluate the first part of the expression:
(67)³ * 2 = 42,949,769 * 2 = 85,899,538
Next, we evaluate the second part of the expression:
(67)² * (67)² = 4489 * 4489 = 20,067,961
Finally, we divide the result of the first part by the result of the second part:
85,899,538 / 20,067,961 = 4.286766
To express this result as a power of 2, we find the nearest power of 2 and write it in exponential form:
2² = 4
Thus, Since 4.286766 is closer to 4 than it is to 8, we can write the final result as: 4.286766 ≈ 2²
To learn more about exponentials :
brainly.com/question/28596571
#SPJ4
let a = r − {1} and define f : a → a by f (x) = x x − 1 for all x ∈ a. (a) prove that f is bijective. (b) determine f −1. (c) determine f ◦ f ◦ f
(b) The value of f^(-1) is g.
(c) The value of f ◦ f ◦ f = f ◦ (f ◦ f) is f((f ◦ f)(x)) = f((x * (x-1))*((x * (x-1)) - 1)).
According to the question
(a) To prove that f is bijective, we need to show that it is both injective (one-to-one) and surjective (onto).
Injectivity: Let x, y ∈ a such that f(x) = f(y). Then, x * (x-1) = y * (y-1). Multiplying both sides by x-1, we get x = y, meaning that f is injective.
Surjectivity: Let z ∈ a. Then, z = z * (z-1) / (z-1), which means that there exists an x ∈ a such that f(x) = z. This shows that f is surjective.
Therefore, f is bijective.
(b) To find the inverse of f, we need to find a function g: a → a such that f(g(x)) = x and g(f(x)) = x for all x ∈ a.
Consider the function g: a → a defined by g(x) = x / (x-1) for all x ∈ a.
Let x ∈ a. Then, f(g(x)) = f(x / (x-1)) = (x / (x-1)) * ((x / (x-1)) - 1) = x. Similarly, g(f(x)) = g(x * (x-1)) = x * (x-1) / (x * (x-1) - 1) = x. This shows that f and g are inverses.
Therefore, f^(-1) = g.
(c) To find f ◦ f ◦ f, we first evaluate f ◦ f and then evaluate f of the result.
Let x ∈ a. Then, (f ◦ f)(x) = f(f(x)) = f(x * (x-1)) = (x * (x-1)) * ((x * (x-1)) - 1). Hence, f ◦ f ◦ f = f ◦ (f ◦ f) = f((f ◦ f)(x)) = f((x * (x-1)) * ((x * (x-1)) - 1)).
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27.3=3/4y
y=?
Can you please help me?
Answer: 36.4
Step-by-step explanation:
27.3= (3/4)y
divide both sides by 3/4 to isolate the y
27.3/(3/4)= 36.4
To double-check, plug in 36.4 to y; should get you 27.3