We deduce that g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit up in the graph of g(x). The best choice is C.
Describe a graph.A diagram that shows how a variable varies in relation to one or more other variables, such as a collection of points, lines, line segments, curves, or regions.
Right-shift a function
Inside the function's argument, subtract. For instance, is essentially moved b units to the right.
You go to the right while subtracting from the parameter of the function.
Accordingly, f(x) is moved two units to the right in g(x) = f(x - 2).
also to advance a function
Outside of the function, add. For instance, is essentially shifted up units.
G(x) = f(x - 2) + 3 hence says that f(x) is shifted up by 3 units.
Overall, then, using two transformations, we deduce that g(x) = f(x - 2) + 3 denotes a 2-unit right and 3-unit upswing in the graph of g(x).
Therefore, choice C is right.
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I need help on solving these equations linear. Please helpppp
The solution of the first set of equations is x = 15 and y = 5 and the second is x = 14.25 and y = 7.75.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation.
a)
As per the given first system of equation,
2x - 4y = 10
x + 5y = 40 → 2x + 10y = 80
Subtract both
10y + 4y = 80 - 10
14y = 70
y = 5
And, x = 40 - 5(5) = 15
b)
As per the given first system of equation,
3x - 5y = 4 and
-2x + 6y = 18 → -x + 3y = 9 → -3x + 9y = 27
Add both
-5y + 9y = 4 + 27
4y = 31
y = 7.75
x = (4 + 5(7.75))/3 = 14.25
Hence "The solution of the first set of equations is x = 15 and y = 5 and the second is x = 14.25 and y = 7.75".
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
The correct statements are:
- 6x + 15 < 10 - 5x ⇒ 3rd answer
Step-by-step explanation
An open circle is at 5 and a bold line starts at 5 and is pointing to the right ⇒ 4th answer
Step-by-step explanation:
∵ The inequality is -3(2x - 5) < 5(2 - x)
At first simplify each side
∵ -3(2x - 5) = -3(2x) + -3(-5)
Remember (-)(-) = (+)
∴ -3(2x - 5) = - 6x + 15
∵ 5(2 - x) = 5(2) + 5(-x)
Remember (+)(-) = (-)
∴ 5(2 - x) = 10 - 5x
∴ - 6x + 15 < 10 - 5x
Subtract 15 from both sides
∴ - 6x < -5 - 5x
Add 5x to both sides
∴ - x < - 5
Remember the coefficient of x is negative, then when you divide both sides by it you must reverse the sign of inequality
∵ The coefficient of x is -1
∴ Divide both sides by -1
∴ x > 5
Please help, what is the common side of the triangles ABC and DCB?
BC is the common side of both the triangles.
Answer:
BC
Step-by-step explanation:
Common side in both triangles is BC
Sides of ΔABC,
AB ; BC and AC
Sides of ΔDCB,
DC, BC and DB
at a certain high school, the distribution of backpack weight is approximately normal with a mean of 19.7 pounds and a standard deviation of 3.1 pounds. a random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. what is the probability that my next five samples will average 22 pounds?
For all samples of 5, there is a 0.05 probability that the sample mean would be higher than 22 pounds.
The assortment of bags weighs 19.7 pounds on average.
3.1 pounds is the standard deviation.
The sampling distribution theorem and the normal probability density function were both utilized.
The z-score formula is used to address problems involving samples with regularly distributed data.
Mean standard deviation, the z-score of a measure X is given by:
z = (x - μ) ÷ σ
The Z-score computes the number of standard deviations. The metric used is the average.
After calculating the Z-score, we look at the p-value associated with it in the z-score table.
This p-value represents the probability that the measure's value is smaller than X, or the percentage of X.
By taking away 1, we can determine the chance that the measure surpasses X.
If n is at least 30, the Central Limitation Theorem can also be applied to variables that are skewed.
No of the sample size, the sample mean will always be the same.
However, the standard error will change.
P(a > 22) denotes the likelihood that the sample means will be greater than 22.
The likelihood that they give it a chance will weigh more than 22 pounds is around 0.05 for all sampling of size 5.
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Find g(x), where g(x) is the translation 2
units left of f(x)= -5x + 5.
Answer:
g(x)=(-5x+2)+5
Step-by-step explanation:
tan(x+pie) + sin(x+pie) + sin (x-pie) = 0
Answer:
[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Double Angle Identities}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]
Given equation:
[tex]\tan (x + \pi) + \sin(x + \pi) + \sin(x - \pi)=0[/tex]
Simplify using the double angle identities:
[tex]\implies \dfrac{\tan x + \tan \pi}{1 -\tan x \tan \pi} + \sin x \cos \pi+\cos x \sin \pi + \sin x \cos \pi -\cos x \sin \pi=0[/tex]
[tex]\implies \dfrac{\tan x + 0}{1 -\tan x(0)} + \sin x (-1)+\cos x (0) + \sin x(-1) -\cos x (0)=0[/tex]
[tex]\implies \dfrac{\tan x}{1} -\sin x - \sin x=0[/tex]
[tex]\implies \tan x-2\sin x =0[/tex]
Use the tan identity to rewrite tan(x) in terms of sin(x) and cos(x):
[tex]\implies \dfrac{\sin x}{ \cos x}-2\sin x=0[/tex]
Multiply both sides by cos(x):
[tex]\implies \dfrac{\sin x\cos x}{ \cos x}-2\sin x\cos x=0(\cos x)[/tex]
[tex]\implies \sin x-2\sin x \cos x=0[/tex]
Factor out sin(x) from the left side of the equation:
[tex]\implies \sin x(1-2 \cos x)=0[/tex]
Apply the zero-product property.
Case 1
[tex]\implies \sin x=0[/tex]
[tex]\implies x=\sin^{-1}(0)[/tex]
[tex]\implies x=2\pi n, \; \pi+2\pi n[/tex]
Case 2
[tex]\implies 1-2 \cos x=0[/tex]
[tex]\implies 1=2 \cos x[/tex]
[tex]\implies \cos x=\dfrac{1}{2}[/tex]
[tex]\implies x= \cos ^{-1} \left(\dfrac{1}{2}\right)[/tex]
[tex]\implies x=\dfrac{\pi }{3}+2\pi n, \;\dfrac{5\pi }{3}+2\pi n[/tex]
Solution
[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]
FIND THE SLOPE FROM THE TABLE
a.
b.
c.
d.
Answer:
The answer should be -5/2
Step-by-step explanation:
To find the slope take two plots from the table:
(-2,6) and (0,1)
M= y2-y1 / x2-x1
M= 1-6 / 0--2=-5/2
2.356 in expanded form
Answer: 2 + 0.3 + 0.05 + 0.006
Step-by-step explanation: You just have to technically un add the stuff of you understand it that way.
Hope i helped you
Have a great day Darling
jack paid $99 for 6 pizzas. How much did he pay per pizza?
Answer:
99/6=16.5 per pizza
have u good day
Answer:
16 and a half, ($16.50)
Step-by-step explanation:
99 / 6 = 16.5
The perimeters of the
square and the rectangle
below are the same. Write
and solve an equation to find
the value of x.
3x
x-2
Area =
121 in 2
Answer:
Step-by-step explanation:
A formula is a method that has been proven to work when solving specific types of problems.
Let’s explore some of those familiar formulas by looking at rectangles, squares, area and perimeter.
The perimeter of a figure is the distance around the figure. Perimeter is the sum of all of the sides in a square or rectangle. Since a rectangle has two sets of parallel sides, the formula for determining perimeter of a rectangle is:
and
Let’s look at an example.
[Figure 2]
The rectangle above shows its dimensions. Find the perimeter.
First, substitute the values for the width and the length into the perimeter formula.
Next, complete the multiplication and addition to find the perimeter.
The answer is 42.
The perimeter of the rectangle is 42 inches.
Area is the amount of square units inside the figure. Area is found by multiplying the . The formula for finding the area of a rectangle is:
You can use the dimensions from the rectangle above to find the area of this rectangle.
First, fill the values for and into the formula for area.
Next, solve for the area by multiplying.
The answer is 108.
The area of the rectangle is .
Notice that the unit of measurement for area is squared. That is because you multiplied a unit measure times itself: . Area is always written in square units.
You can also find the perimeter and area of a square. Remember that a square has four equal sides given the symbol . You can use the following formula for finding the perimeter of a square:
Let’s look at an example.
A rectangle has a length of 12 feet and a perimeter of 72 feet. Write and solve an equation to determine the width of the rectangle.
First, substitute the values for the perimeter and the length into the perimeter formula.
Next, complete the multiplication.
Then, subtract 24 from both sides to get your variable alone on the right side.
Then, multiply both sides by the reciprocal of 2 to isolate your variable.
The answer is 24.
The width of the rectangle is 24 feet.
Examples
Example 1
Earlier, you were given a problem about Raj and his garden fence.
He knows that the area of the land is 240 square feet, the length of one side is 15 feet, and needs to know the width of the land.
First, substitute the values for the area and the side length into the area formula.
Next, multiply both sides by the reciprocal of 15 in order to isolate the variable .
The answer is 16.
The width of Raj’s garden is 16 ft. Therefore the dimensions of the garden are 16 ft by 15 ft.
Example 2
A square has a perimeter of 196 inches. Determine the length of one side of the square.
First, substitute the value for the perimeter into the perimeter formula.
Next, multiply both sides by the reciprocal of 4 to isolate your variable.
The answer is 49.
Example 3
Find the perimeter of the following square if the side length is 4.5 inches.
First, substitute the value for the side length into the perimeter formula.
Next, multiply by 4 to solve for the perimeter.
The answer is 18.
Example 4
Can you find the area of the square in Example 1?
First, substitute the value for the side length into the area formula.
Next, multiply to solve for the area.
The answer is 20.25.
The area of the square is .
Example 5
A square has an area of 144 sq. meters. What is the side length?
First, substitute the value for the area into the area formula.
Next, take the square root of the area to isolate . Remember that the opposite of square is square root.
The answer is 12.
Which statement is true?
O There is a x-intercept at (0, -2).
There is a y-intercept at (0, -2).
O There are no y-intercepts.
O There are no x-intercepts.
CH
The correct option is A) There is a x-intercept at (0, -2).
What is x-intercept and y-intercept ?
The graph's intercept is the location where the line or curve crosses the axis. The term "x-intercept" refers to a point that crosses the x-axis. The y-intercept is the location where a point crosses the y-axis. The x- or y-axis intersection point is what is meant by an intercept for a line. Typically, the y-axis is taken into account if the axis is not stated. It is typically represented by the letter "b."
The y-axis will always be crossed by that line, even if it is far from the top or bottom of the chart, because it is precisely vertical.
The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.
Here in the given graph x axis crossed the line at (-2,0) and y axis crossed the line at ( 0 ,-3) .
Hence the correct option is A) There is a x-intercept at (0, -2).
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help!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
5/6 is closest to 1 and 2/5 is closest to 1/2 so the difference is closest to 1/2.
i need solving this problem
The percentage statement 28 is 35% of 80 is written in the form
a/b = p/100 as 28/80 = 35/100.
Explain the term percentages?A ratio or value that can be stated as a fraction over 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its total and then multiply it by 100.The proportion usually applies to a component per hundred. Per 100 refers to what the word percent means.For the given question.
The statement defining the percentage is ;
28 is 35% of 80.
This can be written as;
35% of 80 = 28
Solve percentage.
35×80/100 = 28
35/100 = 28/80
Or,
28/80 = 35/100
This is the form
a/b = p/100
a = 28
b = 80
p = 35
Thus, the percentage statement 28 is 35% of 80 is written in the form
a/b = p/100 as 28/80 = 35/100.
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Given that D( x ) = 2 x , select all of the following that are true statements. D( x ) is a direct variation. D( x ) is a function. D( x ) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). x is the dependent variable. D(6) = 3 1 Attempts Remain
The true statements are:
D(x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4).D(x) is a direct variation.x is the dependent variable.D(x) is a function.How to determine the true statements?The function is given as D(x) = 2x
The function D(x) is a linear function, and it is also a proportional function
Proportional functions represent direct variation
This means that (b) and (e) are true
Also set x = 5, 6 and -2
So, we have the following equations
D(5) = 2 x 5 = 10
D(6) = 2 x 6 = 12
D(-2) = 2 x -2 = -4
This means that (a) is true
Lastly, the function D(x) is dependent on x for its value
This means that x is the dependent variable.
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Can anyone write the equation of this graph?
The equation of the graph in the figure is f(x) = |x - 3| + 5
How to find the equation of the graph line?Given that the graph is an absolute value graph
We start by calculating the vertex of the graph
In this case, the graph has it minimum point located at the coordinate (3, 5)
This coordinate can then be interpreted as
(h, k) = (3, 5)
As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k
Substitute the known values in the above equation
So, we have the following equation
f(x) = |x - 3| + 5
Hence, the equation of the graph is f(x) = |x - 3| + 5
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Wyatt made a scale drawing of a picnic area near the river. The picnic area, which is 84 yards long in real life, is 231 inches long in the drawing. What scale did Wyatt use?
The scale that Wyatt has made use of based on the figures in the question is 1 inch to 0.36 yards.
What is a scale in mathematics?Building construction would be extremely challenging without a blueprint. You'd be lost without a map! Large objects, such as roads and buildings, can be easily visualized on paper using scale drawings. Scale drawings are even used by a GPS
The scale that Wyatt has used for this drawing is given as:
84 / 231 = 0.36
We would say that for every 1 inch, Wyatt made use of 0.36yards.
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Which equation represents a line which is perpendicular to the line y=7/6x-8
The equation of a line that is perpendicular to y = 7 / 6 x - 8 is y = -6 / 7 x + 8.
How to find the equation of a line?The equation of a line can be represented in different form such as standard form, general form, slope intercept form and point slope form.
The lines that are perpendicular to each other will have the products of their slopes as negative 1.
Therefore, let express the equation in slope intercept form.
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = 7 / 6 x - 8
The slope of the equation is 7 / 6.
Therefore, let's find the equation of the line that is perpendicular to y = 7 / 6 x - 8.
m₁m₂ = -1
7 / 6 m₂ = -1
cross multiply
7m₂ = -6
m₂ = - 6 / 7
Hence, the equation of the line perpendicular to y = 7/6x - 8 should have the slope as - 6 / 7.
Hence, the equation can be y = -6 / 7 x + 8.
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26% of all college students major in stem (science, technology, engineering, and math). if 36 college students are randomly selected, find the probability that a. exactly 7 of them major in stem. b. at most 10 of them major in stem. c. at least 7 of them major in stem. d. between 9 and 15 (including 9 and 15) of them major in stem.
The probabilities will be 0.1081 , 0.676, 0.863, 0.605 respectively.
let us consider, the chances of getting stem be a success(S) and not getting it be a failure(F) , and the total probability be 1 .
as per the statement 26% students are major in stem
total students selected randomly are 36.
∴ P(S) = 0.26
P( F) = 1 - 0.26 = 0.74
Now the binomial probability of success is given by
[tex]P(x) = C^{n} _{x} S^{x} F^{n-x}[/tex]
where C is for the combination formula
S is changes of success
F is chances of failure
x = no. of times success
n = total times the experiment done
From the provided information we can solve each case as follows :
A) exactly 7 of them major in stem
P(7) = [tex]C^{36} _{7} (0.26)^{7} (0.74)^{29}[/tex]
= 0.1081
B)at most 10 of them major in stem
it means P(0,1,2...10)
∴ P = P(0) + P(1) +......+P(10)
P = 0.676
C) at least 7 of them major in stem.
it means P(7,8,9...36)
∴ P = P(7) + P(8) + ...+ P(36)
P = 0.863
D) between 9 and 15 (including 9 and 15) of them major in stem.
In this case we subtract P(0,1,2...8) from P(0,1,2,...15)
and get P(9,10,11,...15)
∴ P(9,10,11,...15) = P(0,1,2,...15) - P(0,1,2...8)
= 0.987 - 0.382
= 0.605
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Solve:
2000(2000^2000)
(A) 2000^2001
(B) 4000^2000
(C) 2000^4000
(D) 4,000,000^2000
(E) 2000^4,000,000
PLEASE ANSWER ASAP!!!
Answer:
They all come out to be infinity
2 times 221 divide 4 ?
If the taxi company only has $10.50 to spend, what value does this represent?
The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.
Amount to spend by the taxi driver ≤ 10.50.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
The taxi company only has $10.50 to spend.
This means that,
The maximum amount to spend is $10.50.
We can also represent as:
Amount to spend by the taxi driver ≤ 10.50.
Thus,
The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.
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solve
14+3h = 5h
h= .....
Answer:
h=2
h= -7/5
hope this helped :)
The distance (D) that a spring is stretched by a hanging object varies directly as the
weight (W) of the object. If a 6-kg object stretches a spring 29 cm, how far will a 25- kg weight stretch the spring?
Pls help asap! Tysm if u do!
The 25 Kg weight will stretch the spring 120.84 cm .
In the question ,
it is given that
the distance(D) that spring stretches by hanging objects vary directly to the weight(W) of the object .
which means
D ∝ W
to remove the proportionality sign , we write the constant k
So, D = k × W ,
where k is the constant of proportionality
given that 6 Kg weight stretches the spring 29 cm
So,
29 = k * 6
k = 29/6
to find the stretch for 25 Kg weight
D = (29/6)*25
D = 120.84 cm
Therefore ,The 25 Kg weight will stretch the spring 120.84 cm .
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What is 9 4/5+7 2/3 = ? as a mixed number
Answer:
42/4/5 first you divide 72➗ 3 then you get 24 then see the picture is you
Answer:
17 7/15
Step-by-step explanation:
Rewrite:
9 + 4/5 + 7 + 2/3
Add whole numbers:
9 + 7 = 16
Add fractions:
4/5 + 2/3 --> 12/15 + 10/15 = 22/15
Simplify:
22/15 --> 1 7/15
Add all components:
16 + 1 7/15 = 17 7/15
Range and domain
Help pls
The domain and the range of the function are the sets X = {- 9, - 7, - 5, - 3, - 1, 1, 3} and Y = {- 5, - 3, - 1, 1, 3, 5, 7}.
How to derive the domain and the range of a function
Herein we need to determine the domain and the range of a function, functions are relations such that every element of the domain is related only to one element of the range.
Graphically speaking, the domain of a function are represented by the set of x-coordinates and the range by a set of y-coordinates. The picture shows a discrete function, that is, a function with a finite set of points. Then, the domain and range are listed by the following sets:
Domain
X = {- 9, - 7, - 5, - 3, - 1, 1, 3}
Range
Y = {- 5, - 3, - 1, 1, 3, 5, 7}
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pasagot po nito
(A) 4, 9, 14, 19, 24, …
Give the next two terms:
Give an expression for the nth term:
Find the 30th term:
(B) 8, 10, 12, 14, 16, …
Give the next two terms:
Give an expression for the nth term:
Find the 30th term:
(C) 1, 8, 15, 22, 29, …
Give the next two terms:
Give an expression for the nth term:
Find the 20th term:
For each of the arithmetic sequences, we have that:
a)
The next two terms are 29 and 34.The expression for the nth term is of: [tex]a_n = 4 + 5(n - 1)[/tex].The 30th term is: 149.b)
The next two terms are 18 and 20.The expression for the nth term is of: [tex]a_n = 8 + 2(n - 1)[/tex].The 30th term is: 66.c)
The next two terms are 36 and 43.The expression for the nth term is of: [tex]a_n = 1 + 7(n - 1)[/tex].The 20th term is: 134.What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the following rule:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
For the sequences in this problem, we have that:
The first terms are, respectively, 4, 8 and 1.The common ratios are, respectively, 5, 2 and 7.Then the general rule is applied to find the nth term of the sequence, while the next two terms are found adding the common ratio.
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Calculus Ladder Sliding Down
Answer:
[tex]\left.\dfrac{\text{d}x}{\text{d}t}\right|_{h=2}\approx0.184\; \sf m/s[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Given variables:
a = length of the ladder.h = height of the ladder's top at time t.x = distance of the ladder from the wall at time t.Given a = 8.9, use Pythagoras Theorem to create an equation for x² in terms of h²:
[tex]\implies x^2+h^2=a^2[/tex]
[tex]\implies x^2+h^2=8.9^2[/tex]
[tex]\implies x^2+h^2=79.21[/tex]
[tex]\implies x^2=79.21-h^2[/tex]
Differentiate with respect to h:
[tex]\implies 2x\dfrac{\text{d}x}{\text{d}h}=0-2h[/tex]
[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{2h}{2x}[/tex]
[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{h}{x}[/tex]
Given:
[tex]\dfrac{\text{d}h}{\text{d}t}=-0.8\; \sf m/s[/tex]
Therefore:
[tex]\begin{aligned} \dfrac{\text{d}x}{\text{d}t}&=\dfrac{\text{d}x}{\text{d}h}\times \dfrac{\text{d}h}{\text{d}t}}\\\\ \implies &=-\dfrac{h}{x} \times -0.8\\\\ &=\dfrac{0.8h}{x} \end{aligned}[/tex]
Calculate x when h = 2:
[tex]\implies x^2=79.21-2^2[/tex]
[tex]\implies x^2=79.21-4[/tex]
[tex]\implies x^2=75.21[/tex]
[tex]\implies x=\sqrt{75.21}[/tex]
Substitute the values of h and x into the equation for dx/dt:
[tex]\implies \dfrac{\text{d}x}{\text{d}t}=\dfrac{0.8 \times 2}{\sqrt{75.21}}=0.1844939751[/tex]
Therefore, the rate of the ladder's distance from the wall is 0.184 m/s (3 d.p.)
jim and craig, working together, can mow the lawn in 5 hours. working alone, craig takes five times as long as jim. how long does it take jim to mow the lawn alone?
In linear equation ,Shirley takes 1.66 hours to paint the deck alone.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Let Shirley's time = x
Let Craig's time = 5x
(5x + x)/2 = 5
We split up the hours by 2 because we want to find out how much time individually.
6x/2 = 5
6x = 10
x = 1.66
Shirley takes 1.66 hours to paint the deck alone.
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What’s the value of x?
By using the property of similar triangles, it can be obtained that
Value of x is 7.2
What are similar triangles?
Two triangles are said to be similar if the corrosponding angles are equal and the corrosponding sides are similar.
The different axioms of similarity are-
SAS axiom, AA axiom, SSS axiom
By the property of similar triangles,
[tex]\frac{9}{9 + 6} = \frac{x}{12}\\x = \frac{9}{15} \times 12\\x = 7.2[/tex]
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having driven a hybrid car for 4.5 years, a driver believes the car gets more than 33 miles per gallon (mpg). the driver kept records of all car fill-ups and taking a sample of 15 found a sample average of 32.84 mpg and sample standard deviation of 1.86 mpg. assuming that the underlying distribution is normal, what can be concluded at the 0.05 level of significance?
By probability, There is insufficient evidence to conclude that the gas mileage is greater than 33 mpg.
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.p value is calculated using online p value calculator (you will find it by searching online).
p value interpretation: if the null hypothesis is true then the probability that the sample average is greater than 33 mpg is 0.373143.
[ the p value associated with a test is the probability that we obtain the observed value of the test statistic or a value that is more extreme in the direction given by the alternative hypothesis, when H0 is true ].
decision: accept H0 at 5% level of significance as p value >0.05
[level of significance is chosen as 5 %= 0.05]
conclusion : there is insufficient evidence to conclude that the gas mileage is greater than 33 mpg.
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